TSTP Solution File: LCL548+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL548+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 14:37:37 EDT 2022
% Result : Theorem 10.35s 10.51s
% Output : Refutation 11.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 43
% Syntax : Number of clauses : 164 ( 117 unt; 1 nHn; 164 RR)
% Number of literals : 217 ( 0 equ; 58 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 23 ( 22 usr; 21 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
op_strict_implies,
file('LCL548+1.p',unknown),
[] ).
cnf(6,axiom,
op_strict_equiv,
file('LCL548+1.p',unknown),
[] ).
cnf(8,axiom,
op_implies_and,
file('LCL548+1.p',unknown),
[] ).
cnf(9,axiom,
op_equiv,
file('LCL548+1.p',unknown),
[] ).
cnf(10,axiom,
modus_ponens,
file('LCL548+1.p',unknown),
[] ).
cnf(12,axiom,
implies_1,
file('LCL548+1.p',unknown),
[] ).
cnf(13,axiom,
implies_2,
file('LCL548+1.p',unknown),
[] ).
cnf(14,axiom,
implies_3,
file('LCL548+1.p',unknown),
[] ).
cnf(15,axiom,
and_1,
file('LCL548+1.p',unknown),
[] ).
cnf(16,axiom,
and_2,
file('LCL548+1.p',unknown),
[] ).
cnf(17,axiom,
and_3,
file('LCL548+1.p',unknown),
[] ).
cnf(23,axiom,
equivalence_3,
file('LCL548+1.p',unknown),
[] ).
cnf(24,axiom,
substitution_of_equivalents,
file('LCL548+1.p',unknown),
[] ).
cnf(25,axiom,
op_possibly,
file('LCL548+1.p',unknown),
[] ).
cnf(26,axiom,
necessitation,
file('LCL548+1.p',unknown),
[] ).
cnf(27,axiom,
axiom_K,
file('LCL548+1.p',unknown),
[] ).
cnf(28,axiom,
axiom_M,
file('LCL548+1.p',unknown),
[] ).
cnf(29,axiom,
axiom_4,
file('LCL548+1.p',unknown),
[] ).
cnf(31,axiom,
~ axiom_m9,
file('LCL548+1.p',unknown),
[] ).
cnf(32,axiom,
is_a_theorem(skc95),
file('LCL548+1.p',unknown),
[] ).
cnf(38,axiom,
is_a_theorem(implies__dfg(skc95,skc94)),
file('LCL548+1.p',unknown),
[] ).
cnf(44,axiom,
( substitution_strict_equiv
| is_a_theorem(strict_equiv(skc155,skc154)) ),
file('LCL548+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ equal(skc155,skc154)
| substitution_strict_equiv ),
file('LCL548+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ axiom_M
| is_a_theorem(implies__dfg(necessarily(u),u)) ),
file('LCL548+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ implies_1
| is_a_theorem(implies__dfg(u,implies__dfg(v,u))) ),
file('LCL548+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ and_1
| is_a_theorem(implies__dfg(and__dfg(u,v),u)) ),
file('LCL548+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ and_2
| is_a_theorem(implies__dfg(and__dfg(u,v),v)) ),
file('LCL548+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ is_a_theorem(u)
| ~ necessitation
| is_a_theorem(necessarily(u)) ),
file('LCL548+1.p',unknown),
[] ).
cnf(80,axiom,
( ~ axiom_4
| is_a_theorem(implies__dfg(necessarily(u),necessarily(necessarily(u)))) ),
file('LCL548+1.p',unknown),
[] ).
cnf(89,axiom,
( ~ is_a_theorem(strict_implies(possibly(possibly(skc186)),possibly(skc186)))
| axiom_m9 ),
file('LCL548+1.p',unknown),
[] ).
cnf(92,axiom,
( ~ op_possibly
| equal(not__dfg(necessarily(not__dfg(u))),possibly(u)) ),
file('LCL548+1.p',unknown),
[] ).
cnf(94,axiom,
( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv__dfg(u,v))
| equal(u,v) ),
file('LCL548+1.p',unknown),
[] ).
cnf(95,axiom,
( ~ and_3
| is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))) ),
file('LCL548+1.p',unknown),
[] ).
cnf(104,axiom,
( ~ substitution_strict_equiv
| ~ is_a_theorem(strict_equiv(u,v))
| equal(u,v) ),
file('LCL548+1.p',unknown),
[] ).
cnf(107,axiom,
( ~ op_strict_implies
| equal(necessarily(implies__dfg(u,v)),strict_implies(u,v)) ),
file('LCL548+1.p',unknown),
[] ).
cnf(108,axiom,
( ~ op_implies_and
| equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)) ),
file('LCL548+1.p',unknown),
[] ).
cnf(109,axiom,
( ~ is_a_theorem(u)
| ~ modus_ponens
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL548+1.p',unknown),
[] ).
cnf(112,axiom,
( ~ implies_2
| is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))) ),
file('LCL548+1.p',unknown),
[] ).
cnf(120,axiom,
( ~ op_equiv
| equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)) ),
file('LCL548+1.p',unknown),
[] ).
cnf(121,axiom,
( ~ axiom_K
| is_a_theorem(implies__dfg(necessarily(implies__dfg(u,v)),implies__dfg(necessarily(u),necessarily(v)))) ),
file('LCL548+1.p',unknown),
[] ).
cnf(125,axiom,
( ~ op_strict_equiv
| equal(and__dfg(strict_implies(u,v),strict_implies(v,u)),strict_equiv(u,v)) ),
file('LCL548+1.p',unknown),
[] ).
cnf(126,axiom,
( ~ implies_3
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))) ),
file('LCL548+1.p',unknown),
[] ).
cnf(128,axiom,
( ~ equivalence_3
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,u),equiv__dfg(u,v)))) ),
file('LCL548+1.p',unknown),
[] ).
cnf(148,plain,
is_a_theorem(implies__dfg(necessarily(u),u)),
inference(mrr,[status(thm)],[47,28]),
[iquote('0:MRR:47.0,28.0')] ).
cnf(150,plain,
( ~ is_a_theorem(u)
| is_a_theorem(necessarily(u)) ),
inference(mrr,[status(thm)],[69,26]),
[iquote('0:MRR:69.1,26.0')] ).
cnf(154,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),v)),
inference(mrr,[status(thm)],[55,16]),
[iquote('0:MRR:55.0,16.0')] ).
cnf(155,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),u)),
inference(mrr,[status(thm)],[53,15]),
[iquote('0:MRR:53.0,15.0')] ).
cnf(157,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
inference(mrr,[status(thm)],[51,12]),
[iquote('0:MRR:51.0,12.0')] ).
cnf(158,plain,
equal(not__dfg(necessarily(not__dfg(u))),possibly(u)),
inference(mrr,[status(thm)],[92,25]),
[iquote('0:MRR:92.0,25.0')] ).
cnf(159,plain,
~ is_a_theorem(strict_implies(possibly(possibly(skc186)),possibly(skc186))),
inference(mrr,[status(thm)],[89,31]),
[iquote('0:MRR:89.1,31.0')] ).
cnf(160,plain,
is_a_theorem(implies__dfg(necessarily(u),necessarily(necessarily(u)))),
inference(mrr,[status(thm)],[80,29]),
[iquote('0:MRR:80.0,29.0')] ).
cnf(161,plain,
equal(necessarily(implies__dfg(u,v)),strict_implies(u,v)),
inference(mrr,[status(thm)],[107,4]),
[iquote('0:MRR:107.0,4.0')] ).
cnf(164,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))),
inference(mrr,[status(thm)],[95,17]),
[iquote('0:MRR:95.0,17.0')] ).
cnf(165,plain,
( ~ is_a_theorem(equiv__dfg(u,v))
| equal(u,v) ),
inference(mrr,[status(thm)],[94,24]),
[iquote('0:MRR:94.0,24.0')] ).
cnf(166,plain,
equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)),
inference(mrr,[status(thm)],[108,8]),
[iquote('0:MRR:108.0,8.0')] ).
cnf(174,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))),
inference(mrr,[status(thm)],[112,13]),
[iquote('0:MRR:112.0,13.0')] ).
cnf(177,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(mrr,[status(thm)],[109,10]),
[iquote('0:MRR:109.1,10.0')] ).
cnf(178,plain,
equal(and__dfg(strict_implies(u,v),strict_implies(v,u)),strict_equiv(u,v)),
inference(mrr,[status(thm)],[125,6]),
[iquote('0:MRR:125.0,6.0')] ).
cnf(179,plain,
( ~ axiom_K
| is_a_theorem(implies__dfg(strict_implies(u,v),implies__dfg(necessarily(u),necessarily(v)))) ),
inference(rew,[status(thm),theory(equality)],[161,121]),
[iquote('0:Rew:161.0,121.1')] ).
cnf(180,plain,
is_a_theorem(implies__dfg(strict_implies(u,v),implies__dfg(necessarily(u),necessarily(v)))),
inference(mrr,[status(thm)],[179,27]),
[iquote('0:MRR:179.0,27.0')] ).
cnf(181,plain,
equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)),
inference(mrr,[status(thm)],[120,9]),
[iquote('0:MRR:120.0,9.0')] ).
cnf(182,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,u),equiv__dfg(u,v)))),
inference(mrr,[status(thm)],[128,23]),
[iquote('0:MRR:128.0,23.0')] ).
cnf(183,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))),
inference(mrr,[status(thm)],[126,14]),
[iquote('0:MRR:126.0,14.0')] ).
cnf(192,plain,
substitution_strict_equiv,
inference(spt,[spt(split,[position(s1)])],[44]),
[iquote('1:Spt:44.0')] ).
cnf(193,plain,
( ~ is_a_theorem(strict_equiv(u,v))
| equal(u,v) ),
inference(mrr,[status(thm)],[104,192]),
[iquote('1:MRR:104.0,192.0')] ).
cnf(215,plain,
is_a_theorem(implies__dfg(strict_implies(u,v),implies__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[161,148]),
[iquote('0:SpR:161.0,148.0')] ).
cnf(216,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(strict_implies(u,v)) ),
inference(spr,[status(thm),theory(equality)],[161,150]),
[iquote('0:SpR:161.0,150.1')] ).
cnf(263,plain,
equal(not__dfg(necessarily(implies__dfg(u,v))),possibly(and__dfg(u,not__dfg(v)))),
inference(spr,[status(thm),theory(equality)],[166,158]),
[iquote('0:SpR:166.0,158.0')] ).
cnf(275,plain,
equal(possibly(and__dfg(u,not__dfg(v))),not__dfg(strict_implies(u,v))),
inference(rew,[status(thm),theory(equality)],[161,263]),
[iquote('0:Rew:161.0,263.0')] ).
cnf(295,plain,
is_a_theorem(strict_implies(and__dfg(u,v),v)),
inference(sor,[status(thm)],[216,154]),
[iquote('0:SoR:216.0,154.0')] ).
cnf(298,plain,
is_a_theorem(strict_implies(u,implies__dfg(v,u))),
inference(sor,[status(thm)],[216,157]),
[iquote('0:SoR:216.0,157.0')] ).
cnf(304,plain,
is_a_theorem(strict_implies(skc95,skc94)),
inference(sor,[status(thm)],[216,38]),
[iquote('0:SoR:216.0,38.0')] ).
cnf(383,plain,
( ~ is_a_theorem(skc95)
| is_a_theorem(skc94) ),
inference(res,[status(thm),theory(equality)],[38,177]),
[iquote('0:Res:38.0,177.1')] ).
cnf(389,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[157,177]),
[iquote('0:Res:157.0,177.1')] ).
cnf(399,plain,
( ~ is_a_theorem(strict_implies(u,v))
| is_a_theorem(implies__dfg(u,v)) ),
inference(res,[status(thm),theory(equality)],[215,177]),
[iquote('0:Res:215.0,177.1')] ).
cnf(400,plain,
( ~ is_a_theorem(strict_implies(u,v))
| is_a_theorem(implies__dfg(necessarily(u),necessarily(v))) ),
inference(res,[status(thm),theory(equality)],[180,177]),
[iquote('0:Res:180.0,177.1')] ).
cnf(405,plain,
is_a_theorem(skc94),
inference(ssi,[status(thm)],[383,32]),
[iquote('0:SSi:383.0,32.0')] ).
cnf(412,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(u,v)))
| is_a_theorem(implies__dfg(u,v)) ),
inference(res,[status(thm),theory(equality)],[174,177]),
[iquote('0:Res:174.0,177.1')] ).
cnf(426,plain,
is_a_theorem(implies__dfg(strict_equiv(u,v),strict_implies(v,u))),
inference(spr,[status(thm),theory(equality)],[178,154]),
[iquote('0:SpR:178.0,154.0')] ).
cnf(427,plain,
is_a_theorem(implies__dfg(strict_equiv(u,v),strict_implies(u,v))),
inference(spr,[status(thm),theory(equality)],[178,155]),
[iquote('0:SpR:178.0,155.0')] ).
cnf(554,plain,
( ~ is_a_theorem(strict_equiv(u,v))
| is_a_theorem(strict_implies(v,u)) ),
inference(res,[status(thm),theory(equality)],[426,177]),
[iquote('0:Res:426.0,177.1')] ).
cnf(556,plain,
( ~ is_a_theorem(strict_equiv(u,v))
| is_a_theorem(strict_implies(u,v)) ),
inference(res,[status(thm),theory(equality)],[427,177]),
[iquote('0:Res:427.0,177.1')] ).
cnf(560,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(v,u),equiv__dfg(u,v))) ),
inference(res,[status(thm),theory(equality)],[182,177]),
[iquote('0:Res:182.0,177.1')] ).
cnf(573,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)],[183,177]),
[iquote('0:Res:183.0,177.1')] ).
cnf(2011,plain,
is_a_theorem(implies__dfg(necessarily(skc95),necessarily(skc94))),
inference(sor,[status(thm)],[400,304]),
[iquote('0:SoR:400.0,304.0')] ).
cnf(2015,plain,
is_a_theorem(implies__dfg(necessarily(u),necessarily(implies__dfg(v,u)))),
inference(sor,[status(thm)],[400,298]),
[iquote('0:SoR:400.0,298.0')] ).
cnf(2029,plain,
is_a_theorem(implies__dfg(necessarily(u),strict_implies(v,u))),
inference(rew,[status(thm),theory(equality)],[161,2015]),
[iquote('0:Rew:161.0,2015.0')] ).
cnf(2054,plain,
( ~ is_a_theorem(necessarily(skc95))
| is_a_theorem(necessarily(skc94)) ),
inference(res,[status(thm),theory(equality)],[2011,177]),
[iquote('0:Res:2011.0,177.1')] ).
cnf(2055,plain,
is_a_theorem(necessarily(skc94)),
inference(ssi,[status(thm)],[2054,150,32]),
[iquote('0:SSi:2054.0,150.0,32.1')] ).
cnf(2063,plain,
( ~ is_a_theorem(necessarily(u))
| is_a_theorem(strict_implies(v,u)) ),
inference(res,[status(thm),theory(equality)],[2029,177]),
[iquote('0:Res:2029.0,177.1')] ).
cnf(2128,plain,
is_a_theorem(strict_implies(u,skc94)),
inference(sor,[status(thm)],[2063,2055]),
[iquote('0:SoR:2063.0,2055.0')] ).
cnf(2133,plain,
is_a_theorem(implies__dfg(u,skc94)),
inference(sor,[status(thm)],[399,2128]),
[iquote('0:SoR:399.0,2128.0')] ).
cnf(2145,plain,
is_a_theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[412,157]),
[iquote('0:SoR:412.0,157.0')] ).
cnf(2197,plain,
is_a_theorem(strict_implies(u,u)),
inference(sor,[status(thm)],[216,2145]),
[iquote('0:SoR:216.0,2145.0')] ).
cnf(4144,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),equiv__dfg(u,skc94))),
inference(sor,[status(thm)],[560,2133]),
[iquote('0:SoR:560.0,2133.0')] ).
cnf(4156,plain,
is_a_theorem(implies__dfg(implies__dfg(necessarily(necessarily(u)),necessarily(u)),equiv__dfg(necessarily(u),necessarily(necessarily(u))))),
inference(sor,[status(thm)],[560,160]),
[iquote('0:SoR:560.0,160.0')] ).
cnf(4321,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),implies__dfg(v,u))),
inference(sor,[status(thm)],[573,2133]),
[iquote('0:SoR:573.0,2133.0')] ).
cnf(5805,plain,
( ~ is_a_theorem(implies__dfg(skc94,u))
| is_a_theorem(equiv__dfg(u,skc94)) ),
inference(res,[status(thm),theory(equality)],[4144,177]),
[iquote('0:Res:4144.0,177.1')] ).
cnf(5815,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),u)),
inference(sor,[status(thm)],[412,4321]),
[iquote('0:SoR:412.0,4321.0')] ).
cnf(5823,plain,
is_a_theorem(strict_implies(implies__dfg(skc94,u),u)),
inference(sor,[status(thm)],[216,5815]),
[iquote('0:SoR:216.0,5815.0')] ).
cnf(5824,plain,
( ~ is_a_theorem(implies__dfg(skc94,u))
| is_a_theorem(u) ),
inference(res,[status(thm),theory(equality)],[5815,177]),
[iquote('0:Res:5815.0,177.1')] ).
cnf(5829,plain,
is_a_theorem(implies__dfg(necessarily(implies__dfg(skc94,u)),necessarily(u))),
inference(sor,[status(thm)],[400,5823]),
[iquote('0:SoR:400.0,5823.0')] ).
cnf(5832,plain,
is_a_theorem(implies__dfg(strict_implies(skc94,u),necessarily(u))),
inference(rew,[status(thm),theory(equality)],[161,5829]),
[iquote('0:Rew:161.0,5829.0')] ).
cnf(5865,plain,
is_a_theorem(implies__dfg(u,and__dfg(skc94,u))),
inference(sor,[status(thm)],[5824,164]),
[iquote('0:SoR:5824.0,164.0')] ).
cnf(5905,plain,
is_a_theorem(strict_implies(u,and__dfg(skc94,u))),
inference(sor,[status(thm)],[216,5865]),
[iquote('0:SoR:216.0,5865.0')] ).
cnf(5958,plain,
( ~ is_a_theorem(strict_implies(skc94,u))
| is_a_theorem(necessarily(u)) ),
inference(res,[status(thm),theory(equality)],[5832,177]),
[iquote('0:Res:5832.0,177.1')] ).
cnf(6524,plain,
is_a_theorem(necessarily(and__dfg(skc94,skc94))),
inference(sor,[status(thm)],[5958,5905]),
[iquote('0:SoR:5958.0,5905.0')] ).
cnf(6543,plain,
is_a_theorem(strict_implies(u,and__dfg(skc94,skc94))),
inference(sor,[status(thm)],[2063,6524]),
[iquote('0:SoR:2063.0,6524.0')] ).
cnf(6548,plain,
is_a_theorem(implies__dfg(u,and__dfg(skc94,skc94))),
inference(sor,[status(thm)],[399,6543]),
[iquote('0:SoR:399.0,6543.0')] ).
cnf(11279,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equiv__dfg(u,skc94)) ),
inference(sor,[status(thm)],[5805,389]),
[iquote('0:SoR:5805.0,389.1')] ).
cnf(11302,plain,
is_a_theorem(equiv__dfg(and__dfg(skc94,skc94),skc94)),
inference(sor,[status(thm)],[5805,6548]),
[iquote('0:SoR:5805.0,6548.0')] ).
cnf(11336,plain,
is_a_theorem(equiv__dfg(implies__dfg(u,skc94),skc94)),
inference(sor,[status(thm)],[5805,157]),
[iquote('0:SoR:5805.0,157.0')] ).
cnf(12885,plain,
equal(and__dfg(skc94,skc94),skc94),
inference(res,[status(thm),theory(equality)],[11302,165]),
[iquote('0:Res:11302.0,165.0')] ).
cnf(13238,plain,
equal(implies__dfg(u,skc94),skc94),
inference(res,[status(thm),theory(equality)],[11336,165]),
[iquote('0:Res:11336.0,165.0')] ).
cnf(13290,plain,
equal(and__dfg(skc94,implies__dfg(skc94,u)),equiv__dfg(u,skc94)),
inference(spr,[status(thm),theory(equality)],[13238,181]),
[iquote('0:SpR:13238.0,181.0')] ).
cnf(14604,plain,
( ~ is_a_theorem(u)
| equal(u,skc94) ),
inference(res,[status(thm),theory(equality)],[11279,165]),
[iquote('0:Res:11279.1,165.0')] ).
cnf(14768,plain,
equal(strict_implies(and__dfg(u,v),v),skc94),
inference(ems,[status(thm)],[14604,295]),
[iquote('0:EmS:14604.0,295.0')] ).
cnf(14771,plain,
equal(strict_implies(implies__dfg(skc94,u),u),skc94),
inference(ems,[status(thm)],[14604,5823]),
[iquote('0:EmS:14604.0,5823.0')] ).
cnf(14772,plain,
equal(strict_implies(u,u),skc94),
inference(ems,[status(thm)],[14604,2197]),
[iquote('0:EmS:14604.0,2197.0')] ).
cnf(14787,plain,
equal(strict_implies(u,and__dfg(skc94,u)),skc94),
inference(ems,[status(thm)],[14604,5905]),
[iquote('0:EmS:14604.0,5905.0')] ).
cnf(14791,plain,
equal(strict_implies(u,implies__dfg(v,u)),skc94),
inference(ems,[status(thm)],[14604,298]),
[iquote('0:EmS:14604.0,298.0')] ).
cnf(14936,plain,
equal(implies__dfg(necessarily(u),u),skc94),
inference(ems,[status(thm)],[14604,148]),
[iquote('0:EmS:14604.0,148.0')] ).
cnf(15039,plain,
is_a_theorem(implies__dfg(skc94,equiv__dfg(necessarily(u),necessarily(necessarily(u))))),
inference(rew,[status(thm),theory(equality)],[14936,4156]),
[iquote('0:Rew:14936.0,4156.0')] ).
cnf(15732,plain,
is_a_theorem(equiv__dfg(necessarily(u),necessarily(necessarily(u)))),
inference(sor,[status(thm)],[5824,15039]),
[iquote('0:SoR:5824.0,15039.0')] ).
cnf(16448,plain,
equal(and__dfg(skc94,strict_implies(u,implies__dfg(skc94,u))),strict_equiv(implies__dfg(skc94,u),u)),
inference(spr,[status(thm),theory(equality)],[14771,178]),
[iquote('0:SpR:14771.0,178.0')] ).
cnf(16456,plain,
equal(strict_equiv(implies__dfg(skc94,u),u),and__dfg(skc94,skc94)),
inference(rew,[status(thm),theory(equality)],[14791,16448]),
[iquote('0:Rew:14791.0,16448.0')] ).
cnf(16457,plain,
equal(strict_equiv(implies__dfg(skc94,u),u),skc94),
inference(rew,[status(thm),theory(equality)],[12885,16456]),
[iquote('0:Rew:12885.0,16456.0')] ).
cnf(16461,plain,
equal(and__dfg(skc94,strict_implies(and__dfg(skc94,u),u)),strict_equiv(u,and__dfg(skc94,u))),
inference(spr,[status(thm),theory(equality)],[14787,178]),
[iquote('0:SpR:14787.0,178.0')] ).
cnf(16470,plain,
equal(strict_equiv(u,and__dfg(skc94,u)),and__dfg(skc94,skc94)),
inference(rew,[status(thm),theory(equality)],[14768,16461]),
[iquote('0:Rew:14768.0,16461.0')] ).
cnf(16471,plain,
equal(strict_equiv(u,and__dfg(skc94,u)),skc94),
inference(rew,[status(thm),theory(equality)],[12885,16470]),
[iquote('0:Rew:12885.0,16470.0')] ).
cnf(16609,plain,
equal(necessarily(necessarily(u)),necessarily(u)),
inference(res,[status(thm),theory(equality)],[15732,165]),
[iquote('0:Res:15732.0,165.0')] ).
cnf(17465,plain,
( ~ is_a_theorem(skc94)
| equal(implies__dfg(skc94,u),u) ),
inference(spl,[status(thm),theory(equality)],[16457,193]),
[iquote('1:SpL:16457.0,193.0')] ).
cnf(17467,plain,
equal(implies__dfg(skc94,u),u),
inference(mrr,[status(thm)],[17465,405]),
[iquote('1:MRR:17465.0,405.0')] ).
cnf(17593,plain,
equal(and__dfg(skc94,u),equiv__dfg(u,skc94)),
inference(rew,[status(thm),theory(equality)],[17467,13290]),
[iquote('1:Rew:17467.0,13290.0')] ).
cnf(17734,plain,
equal(strict_equiv(u,equiv__dfg(u,skc94)),skc94),
inference(rew,[status(thm),theory(equality)],[17593,16471]),
[iquote('1:Rew:17593.0,16471.0')] ).
cnf(17817,plain,
equal(strict_implies(skc94,u),necessarily(u)),
inference(spr,[status(thm),theory(equality)],[17467,161]),
[iquote('1:SpR:17467.0,161.0')] ).
cnf(18781,plain,
equal(not__dfg(equiv__dfg(not__dfg(u),skc94)),implies__dfg(skc94,u)),
inference(spr,[status(thm),theory(equality)],[17593,166]),
[iquote('1:SpR:17593.0,166.0')] ).
cnf(18782,plain,
equal(possibly(equiv__dfg(not__dfg(u),skc94)),not__dfg(strict_implies(skc94,u))),
inference(spr,[status(thm),theory(equality)],[17593,275]),
[iquote('1:SpR:17593.0,275.0')] ).
cnf(18792,plain,
equal(not__dfg(equiv__dfg(not__dfg(u),skc94)),u),
inference(rew,[status(thm),theory(equality)],[17467,18781]),
[iquote('1:Rew:17467.0,18781.0')] ).
cnf(18793,plain,
equal(possibly(equiv__dfg(not__dfg(u),skc94)),not__dfg(necessarily(u))),
inference(rew,[status(thm),theory(equality)],[17817,18782]),
[iquote('1:Rew:17817.0,18782.0')] ).
cnf(18850,plain,
( ~ is_a_theorem(skc94)
| equal(equiv__dfg(u,skc94),u) ),
inference(spl,[status(thm),theory(equality)],[17734,193]),
[iquote('1:SpL:17734.0,193.0')] ).
cnf(18851,plain,
equal(equiv__dfg(u,skc94),u),
inference(mrr,[status(thm)],[18850,405]),
[iquote('1:MRR:18850.0,405.0')] ).
cnf(18934,plain,
equal(not__dfg(not__dfg(u)),u),
inference(rew,[status(thm),theory(equality)],[18851,18792]),
[iquote('1:Rew:18851.0,18792.0')] ).
cnf(18935,plain,
equal(not__dfg(necessarily(u)),possibly(not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[18851,18793]),
[iquote('1:Rew:18851.0,18793.0')] ).
cnf(22809,plain,
equal(possibly(not__dfg(necessarily(u))),not__dfg(necessarily(u))),
inference(spr,[status(thm),theory(equality)],[16609,18935]),
[iquote('1:SpR:16609.0,18935.0')] ).
cnf(22813,plain,
equal(possibly(possibly(not__dfg(u))),possibly(not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[18935,22809]),
[iquote('1:Rew:18935.0,22809.0')] ).
cnf(24705,plain,
equal(possibly(possibly(u)),possibly(u)),
inference(spr,[status(thm),theory(equality)],[18934,22813]),
[iquote('1:SpR:18934.0,22813.0')] ).
cnf(24711,plain,
~ is_a_theorem(strict_implies(possibly(skc186),possibly(skc186))),
inference(rew,[status(thm),theory(equality)],[24705,159]),
[iquote('1:Rew:24705.0,159.0')] ).
cnf(24754,plain,
~ is_a_theorem(skc94),
inference(rew,[status(thm),theory(equality)],[14772,24711]),
[iquote('1:Rew:14772.0,24711.0')] ).
cnf(24755,plain,
$false,
inference(mrr,[status(thm)],[24754,405]),
[iquote('1:MRR:24754.0,405.0')] ).
cnf(24768,plain,
~ substitution_strict_equiv,
inference(spt,[spt(split,[position(sa)])],[24755,192]),
[iquote('1:Spt:24755.0,44.0,192.0')] ).
cnf(24769,plain,
is_a_theorem(strict_equiv(skc155,skc154)),
inference(spt,[spt(split,[position(s2)])],[44]),
[iquote('1:Spt:24755.0,44.1')] ).
cnf(24772,plain,
~ equal(skc155,skc154),
inference(mrr,[status(thm)],[45,24768]),
[iquote('1:MRR:45.1,24768.0')] ).
cnf(24792,plain,
is_a_theorem(strict_implies(skc155,skc154)),
inference(sor,[status(thm)],[556,24769]),
[iquote('1:SoR:556.0,24769.0')] ).
cnf(24793,plain,
is_a_theorem(strict_implies(skc154,skc155)),
inference(sor,[status(thm)],[554,24769]),
[iquote('1:SoR:554.0,24769.0')] ).
cnf(24802,plain,
is_a_theorem(implies__dfg(skc155,skc154)),
inference(sor,[status(thm)],[399,24792]),
[iquote('1:SoR:399.0,24792.0')] ).
cnf(24824,plain,
is_a_theorem(implies__dfg(skc154,skc155)),
inference(sor,[status(thm)],[399,24793]),
[iquote('1:SoR:399.0,24793.0')] ).
cnf(24826,plain,
equal(implies__dfg(skc155,skc154),skc94),
inference(ems,[status(thm)],[14604,24802]),
[iquote('1:EmS:14604.0,24802.0')] ).
cnf(24833,plain,
equal(implies__dfg(skc154,skc155),skc94),
inference(ems,[status(thm)],[14604,24824]),
[iquote('1:EmS:14604.0,24824.0')] ).
cnf(24860,plain,
equal(and__dfg(implies__dfg(skc154,skc155),skc94),equiv__dfg(skc154,skc155)),
inference(spr,[status(thm),theory(equality)],[24826,181]),
[iquote('1:SpR:24826.0,181.0')] ).
cnf(24868,plain,
equal(and__dfg(skc94,skc94),equiv__dfg(skc154,skc155)),
inference(rew,[status(thm),theory(equality)],[24833,24860]),
[iquote('1:Rew:24833.0,24860.0')] ).
cnf(24869,plain,
equal(equiv__dfg(skc154,skc155),skc94),
inference(rew,[status(thm),theory(equality)],[12885,24868]),
[iquote('1:Rew:12885.0,24868.0')] ).
cnf(24891,plain,
( ~ is_a_theorem(skc94)
| equal(skc155,skc154) ),
inference(spl,[status(thm),theory(equality)],[24869,165]),
[iquote('1:SpL:24869.0,165.0')] ).
cnf(24892,plain,
$false,
inference(mrr,[status(thm)],[24891,405,24772]),
[iquote('1:MRR:24891.0,24891.1,405.0,24772.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL548+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jul 4 09:10:53 EDT 2022
% 0.13/0.33 % CPUTime :
% 10.35/10.51
% 10.35/10.51 SPASS V 3.9
% 10.35/10.51 SPASS beiseite: Proof found.
% 10.35/10.51 % SZS status Theorem
% 10.35/10.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.35/10.51 SPASS derived 16862 clauses, backtracked 2598 clauses, performed 3 splits and kept 10907 clauses.
% 10.35/10.51 SPASS allocated 127155 KBytes.
% 10.35/10.51 SPASS spent 0:0:10.15 on the problem.
% 10.35/10.51 0:00:00.04 for the input.
% 10.35/10.51 0:00:00.06 for the FLOTTER CNF translation.
% 10.35/10.51 0:00:00.18 for inferences.
% 10.35/10.51 0:00:00.25 for the backtracking.
% 10.35/10.51 0:00:09.49 for the reduction.
% 10.35/10.51
% 10.35/10.51
% 10.35/10.51 Here is a proof with depth 16, length 164 :
% 10.35/10.51 % SZS output start Refutation
% See solution above
% 11.49/11.70 Formulae used in the proof : s1_0_op_strict_implies s1_0_op_strict_equiv hilbert_op_implies_and hilbert_op_equiv hilbert_modus_ponens hilbert_implies_1 hilbert_implies_2 hilbert_implies_3 hilbert_and_1 hilbert_and_2 hilbert_and_3 hilbert_equivalence_3 substitution_of_equivalents km4b_op_possibly km4b_necessitation km4b_axiom_K km4b_axiom_M km4b_axiom_4 s1_0_m6s3m9b_axiom_m9 modus_ponens axiom_M and_3 substitution_strict_equiv implies_1 and_1 and_2 necessitation axiom_4 axiom_m9 op_possibly op_strict_implies op_implies_and implies_2 op_equiv axiom_K op_strict_equiv implies_3 equivalence_3
% 11.49/11.70
%------------------------------------------------------------------------------