TSTP Solution File: LCL524+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL524+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 14:37:30 EDT 2022
% Result : Theorem 32.85s 33.06s
% Output : Refutation 38.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 50
% Syntax : Number of clauses : 216 ( 153 unt; 0 nHn; 216 RR)
% Number of literals : 284 ( 0 equ; 71 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 27 ( 26 usr; 25 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
op_or,
file('LCL524+1.p',unknown),
[] ).
cnf(2,axiom,
op_implies_and,
file('LCL524+1.p',unknown),
[] ).
cnf(3,axiom,
op_equiv,
file('LCL524+1.p',unknown),
[] ).
cnf(4,axiom,
modus_ponens,
file('LCL524+1.p',unknown),
[] ).
cnf(5,axiom,
modus_tollens,
file('LCL524+1.p',unknown),
[] ).
cnf(6,axiom,
implies_1,
file('LCL524+1.p',unknown),
[] ).
cnf(7,axiom,
implies_2,
file('LCL524+1.p',unknown),
[] ).
cnf(8,axiom,
implies_3,
file('LCL524+1.p',unknown),
[] ).
cnf(9,axiom,
and_1,
file('LCL524+1.p',unknown),
[] ).
cnf(10,axiom,
and_2,
file('LCL524+1.p',unknown),
[] ).
cnf(11,axiom,
and_3,
file('LCL524+1.p',unknown),
[] ).
cnf(12,axiom,
or_1,
file('LCL524+1.p',unknown),
[] ).
cnf(14,axiom,
or_3,
file('LCL524+1.p',unknown),
[] ).
cnf(16,axiom,
equivalence_2,
file('LCL524+1.p',unknown),
[] ).
cnf(17,axiom,
equivalence_3,
file('LCL524+1.p',unknown),
[] ).
cnf(18,axiom,
substitution_of_equivalents,
file('LCL524+1.p',unknown),
[] ).
cnf(19,axiom,
op_possibly,
file('LCL524+1.p',unknown),
[] ).
cnf(20,axiom,
necessitation,
file('LCL524+1.p',unknown),
[] ).
cnf(21,axiom,
axiom_K,
file('LCL524+1.p',unknown),
[] ).
cnf(22,axiom,
axiom_M,
file('LCL524+1.p',unknown),
[] ).
cnf(23,axiom,
axiom_5,
file('LCL524+1.p',unknown),
[] ).
cnf(24,axiom,
~ axiom_B,
file('LCL524+1.p',unknown),
[] ).
cnf(25,axiom,
is_a_theorem(skc95),
file('LCL524+1.p',unknown),
[] ).
cnf(31,axiom,
is_a_theorem(implies__dfg(skc95,skc94)),
file('LCL524+1.p',unknown),
[] ).
cnf(40,axiom,
( ~ axiom_M
| is_a_theorem(implies__dfg(necessarily(u),u)) ),
file('LCL524+1.p',unknown),
[] ).
cnf(44,axiom,
( ~ implies_1
| is_a_theorem(implies__dfg(u,implies__dfg(v,u))) ),
file('LCL524+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ and_1
| is_a_theorem(implies__dfg(and__dfg(u,v),u)) ),
file('LCL524+1.p',unknown),
[] ).
cnf(48,axiom,
( ~ and_2
| is_a_theorem(implies__dfg(and__dfg(u,v),v)) ),
file('LCL524+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ or_1
| is_a_theorem(implies__dfg(u,or__dfg(u,v))) ),
file('LCL524+1.p',unknown),
[] ).
cnf(58,axiom,
( ~ r1
| is_a_theorem(implies__dfg(or__dfg(u,u),u)) ),
file('LCL524+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ is_a_theorem(implies__dfg(or__dfg(skc138,skc138),skc138))
| r1 ),
file('LCL524+1.p',unknown),
[] ).
cnf(62,axiom,
( ~ is_a_theorem(u)
| ~ necessitation
| is_a_theorem(necessarily(u)) ),
file('LCL524+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ is_a_theorem(implies__dfg(skc160,necessarily(possibly(skc160))))
| axiom_B ),
file('LCL524+1.p',unknown),
[] ).
cnf(75,axiom,
( ~ axiom_5
| is_a_theorem(implies__dfg(possibly(u),necessarily(possibly(u)))) ),
file('LCL524+1.p',unknown),
[] ).
cnf(85,axiom,
( ~ op_possibly
| equal(not__dfg(necessarily(not__dfg(u))),possibly(u)) ),
file('LCL524+1.p',unknown),
[] ).
cnf(87,axiom,
( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv__dfg(u,v))
| equal(u,v) ),
file('LCL524+1.p',unknown),
[] ).
cnf(88,axiom,
( ~ and_3
| is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))) ),
file('LCL524+1.p',unknown),
[] ).
cnf(92,axiom,
( ~ equivalence_2
| is_a_theorem(implies__dfg(equiv__dfg(u,v),implies__dfg(v,u))) ),
file('LCL524+1.p',unknown),
[] ).
cnf(94,axiom,
( ~ r3
| is_a_theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))) ),
file('LCL524+1.p',unknown),
[] ).
cnf(95,axiom,
( ~ is_a_theorem(implies__dfg(or__dfg(skc142,skc141),or__dfg(skc141,skc142)))
| r3 ),
file('LCL524+1.p',unknown),
[] ).
cnf(101,axiom,
( ~ op_implies_and
| equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)) ),
file('LCL524+1.p',unknown),
[] ).
cnf(102,axiom,
( ~ is_a_theorem(u)
| ~ modus_ponens
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL524+1.p',unknown),
[] ).
cnf(103,axiom,
( ~ modus_tollens
| is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),not__dfg(v)),implies__dfg(v,u))) ),
file('LCL524+1.p',unknown),
[] ).
cnf(105,axiom,
( ~ implies_2
| is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))) ),
file('LCL524+1.p',unknown),
[] ).
cnf(107,axiom,
( ~ op_or
| equal(not__dfg(and__dfg(not__dfg(u),not__dfg(v))),or__dfg(u,v)) ),
file('LCL524+1.p',unknown),
[] ).
cnf(113,axiom,
( ~ op_equiv
| equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)) ),
file('LCL524+1.p',unknown),
[] ).
cnf(114,axiom,
( ~ axiom_K
| is_a_theorem(implies__dfg(necessarily(implies__dfg(u,v)),implies__dfg(necessarily(u),necessarily(v)))) ),
file('LCL524+1.p',unknown),
[] ).
cnf(119,axiom,
( ~ implies_3
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))) ),
file('LCL524+1.p',unknown),
[] ).
cnf(121,axiom,
( ~ equivalence_3
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,u),equiv__dfg(u,v)))) ),
file('LCL524+1.p',unknown),
[] ).
cnf(135,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('LCL524+1.p',unknown),
[] ).
cnf(141,plain,
is_a_theorem(implies__dfg(necessarily(u),u)),
inference(mrr,[status(thm)],[40,22]),
[iquote('0:MRR:40.0,22.0')] ).
cnf(142,plain,
~ is_a_theorem(implies__dfg(skc160,necessarily(possibly(skc160)))),
inference(mrr,[status(thm)],[64,24]),
[iquote('0:MRR:64.1,24.0')] ).
cnf(143,plain,
( ~ is_a_theorem(u)
| is_a_theorem(necessarily(u)) ),
inference(mrr,[status(thm)],[62,20]),
[iquote('0:MRR:62.1,20.0')] ).
cnf(146,plain,
is_a_theorem(implies__dfg(u,or__dfg(u,v))),
inference(mrr,[status(thm)],[50,12]),
[iquote('0:MRR:50.0,12.0')] ).
cnf(147,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),v)),
inference(mrr,[status(thm)],[48,10]),
[iquote('0:MRR:48.0,10.0')] ).
cnf(148,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),u)),
inference(mrr,[status(thm)],[46,9]),
[iquote('0:MRR:46.0,9.0')] ).
cnf(150,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
inference(mrr,[status(thm)],[44,6]),
[iquote('0:MRR:44.0,6.0')] ).
cnf(151,plain,
equal(not__dfg(necessarily(not__dfg(u))),possibly(u)),
inference(mrr,[status(thm)],[85,19]),
[iquote('0:MRR:85.0,19.0')] ).
cnf(152,plain,
is_a_theorem(implies__dfg(possibly(u),necessarily(possibly(u)))),
inference(mrr,[status(thm)],[75,23]),
[iquote('0:MRR:75.0,23.0')] ).
cnf(153,plain,
is_a_theorem(implies__dfg(equiv__dfg(u,v),implies__dfg(v,u))),
inference(mrr,[status(thm)],[92,16]),
[iquote('0:MRR:92.0,16.0')] ).
cnf(155,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))),
inference(mrr,[status(thm)],[88,11]),
[iquote('0:MRR:88.0,11.0')] ).
cnf(156,plain,
( ~ is_a_theorem(equiv__dfg(u,v))
| equal(u,v) ),
inference(mrr,[status(thm)],[87,18]),
[iquote('0:MRR:87.0,18.0')] ).
cnf(157,plain,
equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)),
inference(mrr,[status(thm)],[101,2]),
[iquote('0:MRR:101.0,2.0')] ).
cnf(158,plain,
( ~ op_or
| equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)) ),
inference(rew,[status(thm),theory(equality)],[157,107]),
[iquote('0:Rew:157.0,107.1')] ).
cnf(159,plain,
equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)),
inference(mrr,[status(thm)],[158,1]),
[iquote('0:MRR:158.0,1.0')] ).
cnf(165,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))),
inference(mrr,[status(thm)],[105,7]),
[iquote('0:MRR:105.0,7.0')] ).
cnf(166,plain,
( ~ modus_tollens
| is_a_theorem(implies__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,u))) ),
inference(rew,[status(thm),theory(equality)],[159,103]),
[iquote('0:Rew:159.0,103.1')] ).
cnf(167,plain,
is_a_theorem(implies__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,u))),
inference(mrr,[status(thm)],[166,5]),
[iquote('0:MRR:166.0,5.0')] ).
cnf(168,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(mrr,[status(thm)],[102,4]),
[iquote('0:MRR:102.1,4.0')] ).
cnf(169,plain,
is_a_theorem(implies__dfg(necessarily(implies__dfg(u,v)),implies__dfg(necessarily(u),necessarily(v)))),
inference(mrr,[status(thm)],[114,21]),
[iquote('0:MRR:114.0,21.0')] ).
cnf(170,plain,
equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)),
inference(mrr,[status(thm)],[113,3]),
[iquote('0:MRR:113.0,3.0')] ).
cnf(171,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,u),equiv__dfg(u,v)))),
inference(mrr,[status(thm)],[121,17]),
[iquote('0:MRR:121.0,17.0')] ).
cnf(172,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))),
inference(mrr,[status(thm)],[119,8]),
[iquote('0:MRR:119.0,8.0')] ).
cnf(176,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)],[135,14]),
[iquote('0:MRR:135.0,14.0')] ).
cnf(181,plain,
equal(not__dfg(necessarily(possibly(u))),possibly(necessarily(not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[151]),
[iquote('0:SpR:151.0,151.0')] ).
cnf(198,plain,
equal(or__dfg(necessarily(not__dfg(u)),v),implies__dfg(possibly(u),v)),
inference(spr,[status(thm),theory(equality)],[151,159]),
[iquote('0:SpR:151.0,159.0')] ).
cnf(227,plain,
equal(implies__dfg(possibly(necessarily(not__dfg(u))),v),or__dfg(necessarily(possibly(u)),v)),
inference(spr,[status(thm),theory(equality)],[181,159]),
[iquote('0:SpR:181.0,159.0')] ).
cnf(237,plain,
equal(not__dfg(necessarily(implies__dfg(u,v))),possibly(and__dfg(u,not__dfg(v)))),
inference(spr,[status(thm),theory(equality)],[157,151]),
[iquote('0:SpR:157.0,151.0')] ).
cnf(238,plain,
equal(or__dfg(and__dfg(u,not__dfg(v)),w),implies__dfg(implies__dfg(u,v),w)),
inference(spr,[status(thm),theory(equality)],[157,159]),
[iquote('0:SpR:157.0,159.0')] ).
cnf(245,plain,
equal(not__dfg(and__dfg(u,possibly(v))),implies__dfg(u,necessarily(not__dfg(v)))),
inference(spr,[status(thm),theory(equality)],[151,157]),
[iquote('0:SpR:151.0,157.0')] ).
cnf(253,plain,
is_a_theorem(implies__dfg(or__dfg(u,not__dfg(not__dfg(v))),or__dfg(v,u))),
inference(spr,[status(thm),theory(equality)],[159,167]),
[iquote('0:SpR:159.0,167.0')] ).
cnf(359,plain,
( ~ is_a_theorem(skc95)
| is_a_theorem(skc94) ),
inference(res,[status(thm),theory(equality)],[31,168]),
[iquote('0:Res:31.0,168.1')] ).
cnf(360,plain,
( ~ is_a_theorem(necessarily(u))
| is_a_theorem(u) ),
inference(res,[status(thm),theory(equality)],[141,168]),
[iquote('0:Res:141.0,168.1')] ).
cnf(367,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[150,168]),
[iquote('0:Res:150.0,168.1')] ).
cnf(368,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,and__dfg(u,v))) ),
inference(res,[status(thm),theory(equality)],[155,168]),
[iquote('0:Res:155.0,168.1')] ).
cnf(381,plain,
is_a_theorem(skc94),
inference(ssi,[status(thm)],[359,25]),
[iquote('0:SSi:359.0,25.0')] ).
cnf(386,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(u,v)))
| is_a_theorem(implies__dfg(u,v)) ),
inference(res,[status(thm),theory(equality)],[165,168]),
[iquote('0:Res:165.0,168.1')] ).
cnf(404,plain,
( ~ is_a_theorem(necessarily(implies__dfg(u,v)))
| is_a_theorem(implies__dfg(necessarily(u),necessarily(v))) ),
inference(res,[status(thm),theory(equality)],[169,168]),
[iquote('0:Res:169.0,168.1')] ).
cnf(481,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)],[170,368]),
[iquote('0:SpR:170.0,368.1')] ).
cnf(604,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)],[172,168]),
[iquote('0:Res:172.0,168.1')] ).
cnf(1034,plain,
equal(possibly(and__dfg(not__dfg(u),not__dfg(v))),not__dfg(necessarily(or__dfg(u,v)))),
inference(spr,[status(thm),theory(equality)],[159,237]),
[iquote('0:SpR:159.0,237.0')] ).
cnf(1415,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(u,u),v))),
inference(sor,[status(thm)],[386,176]),
[iquote('0:SoR:386.0,176.0')] ).
cnf(1420,plain,
is_a_theorem(implies__dfg(u,and__dfg(u,u))),
inference(sor,[status(thm)],[386,155]),
[iquote('0:SoR:386.0,155.0')] ).
cnf(1421,plain,
is_a_theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[386,150]),
[iquote('0:SoR:386.0,150.0')] ).
cnf(2306,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(necessarily(u),necessarily(v))) ),
inference(sor,[status(thm)],[404,143]),
[iquote('0:SoR:404.0,143.1')] ).
cnf(4935,plain,
is_a_theorem(implies__dfg(necessarily(u),necessarily(and__dfg(u,u)))),
inference(sor,[status(thm)],[2306,1420]),
[iquote('0:SoR:2306.0,1420.0')] ).
cnf(4940,plain,
is_a_theorem(implies__dfg(necessarily(u),necessarily(implies__dfg(v,u)))),
inference(sor,[status(thm)],[2306,150]),
[iquote('0:SoR:2306.0,150.0')] ).
cnf(5028,plain,
( ~ is_a_theorem(necessarily(u))
| is_a_theorem(necessarily(and__dfg(u,u))) ),
inference(res,[status(thm),theory(equality)],[4935,168]),
[iquote('0:Res:4935.0,168.1')] ).
cnf(5037,plain,
( ~ is_a_theorem(necessarily(u))
| is_a_theorem(necessarily(implies__dfg(v,u))) ),
inference(res,[status(thm),theory(equality)],[4940,168]),
[iquote('0:Res:4940.0,168.1')] ).
cnf(5217,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),implies__dfg(skc95,u))),
inference(sor,[status(thm)],[604,31]),
[iquote('0:SoR:604.0,31.0')] ).
cnf(5232,plain,
( ~ is_a_theorem(implies__dfg(skc94,u))
| is_a_theorem(implies__dfg(skc95,u)) ),
inference(res,[status(thm),theory(equality)],[5217,168]),
[iquote('0:Res:5217.0,168.1')] ).
cnf(5257,plain,
is_a_theorem(implies__dfg(skc95,and__dfg(skc94,skc94))),
inference(sor,[status(thm)],[5232,1420]),
[iquote('0:SoR:5232.0,1420.0')] ).
cnf(5261,plain,
is_a_theorem(implies__dfg(skc95,implies__dfg(u,and__dfg(skc94,u)))),
inference(sor,[status(thm)],[5232,155]),
[iquote('0:SoR:5232.0,155.0')] ).
cnf(5262,plain,
is_a_theorem(implies__dfg(skc95,implies__dfg(u,skc94))),
inference(sor,[status(thm)],[5232,150]),
[iquote('0:SoR:5232.0,150.0')] ).
cnf(5472,plain,
is_a_theorem(implies__dfg(necessarily(skc95),necessarily(and__dfg(skc94,skc94)))),
inference(sor,[status(thm)],[2306,5257]),
[iquote('0:SoR:2306.0,5257.0')] ).
cnf(5480,plain,
is_a_theorem(implies__dfg(necessarily(skc95),necessarily(implies__dfg(u,skc94)))),
inference(sor,[status(thm)],[2306,5262]),
[iquote('0:SoR:2306.0,5262.0')] ).
cnf(5486,plain,
( ~ is_a_theorem(skc95)
| is_a_theorem(implies__dfg(u,skc94)) ),
inference(res,[status(thm),theory(equality)],[5262,168]),
[iquote('0:Res:5262.0,168.1')] ).
cnf(5487,plain,
is_a_theorem(implies__dfg(u,skc94)),
inference(ssi,[status(thm)],[5486,25]),
[iquote('0:SSi:5486.0,25.0')] ).
cnf(5489,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),implies__dfg(v,u))),
inference(sor,[status(thm)],[604,5487]),
[iquote('0:SoR:604.0,5487.0')] ).
cnf(6151,plain,
( ~ is_a_theorem(necessarily(skc95))
| is_a_theorem(necessarily(and__dfg(skc94,skc94))) ),
inference(res,[status(thm),theory(equality)],[5472,168]),
[iquote('0:Res:5472.0,168.1')] ).
cnf(6152,plain,
is_a_theorem(necessarily(and__dfg(skc94,skc94))),
inference(ssi,[status(thm)],[6151,143,25]),
[iquote('0:SSi:6151.0,143.0,25.1')] ).
cnf(6363,plain,
( ~ is_a_theorem(necessarily(skc95))
| is_a_theorem(necessarily(implies__dfg(u,skc94))) ),
inference(res,[status(thm),theory(equality)],[5480,168]),
[iquote('0:Res:5480.0,168.1')] ).
cnf(6364,plain,
is_a_theorem(necessarily(implies__dfg(u,skc94))),
inference(ssi,[status(thm)],[6363,143,25]),
[iquote('0:SSi:6363.0,143.0,25.1')] ).
cnf(6610,plain,
( ~ is_a_theorem(skc95)
| is_a_theorem(implies__dfg(u,and__dfg(skc94,u))) ),
inference(res,[status(thm),theory(equality)],[5261,168]),
[iquote('0:Res:5261.0,168.1')] ).
cnf(6611,plain,
is_a_theorem(implies__dfg(u,and__dfg(skc94,u))),
inference(ssi,[status(thm)],[6610,25]),
[iquote('0:SSi:6610.0,25.0')] ).
cnf(6758,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),u)),
inference(sor,[status(thm)],[386,5489]),
[iquote('0:SoR:386.0,5489.0')] ).
cnf(10743,plain,
( ~ is_a_theorem(u)
| is_a_theorem(necessarily(and__dfg(u,u))) ),
inference(sor,[status(thm)],[5028,143]),
[iquote('0:SoR:5028.0,143.1')] ).
cnf(11031,plain,
( ~ is_a_theorem(implies__dfg(u,u))
| is_a_theorem(necessarily(equiv__dfg(u,u))) ),
inference(spr,[status(thm),theory(equality)],[170,10743]),
[iquote('0:SpR:170.0,10743.1')] ).
cnf(11033,plain,
is_a_theorem(necessarily(equiv__dfg(u,u))),
inference(ssi,[status(thm)],[11031,1421]),
[iquote('0:SSi:11031.0,1421.0')] ).
cnf(11570,plain,
is_a_theorem(necessarily(implies__dfg(u,equiv__dfg(v,v)))),
inference(sor,[status(thm)],[5037,11033]),
[iquote('0:SoR:5037.0,11033.0')] ).
cnf(11603,plain,
is_a_theorem(necessarily(implies__dfg(u,and__dfg(skc94,skc94)))),
inference(sor,[status(thm)],[5037,6152]),
[iquote('0:SoR:5037.0,6152.0')] ).
cnf(11608,plain,
is_a_theorem(necessarily(implies__dfg(u,implies__dfg(v,skc94)))),
inference(sor,[status(thm)],[5037,6364]),
[iquote('0:SoR:5037.0,6364.0')] ).
cnf(11689,plain,
is_a_theorem(implies__dfg(u,and__dfg(skc94,skc94))),
inference(sor,[status(thm)],[360,11603]),
[iquote('0:SoR:360.0,11603.0')] ).
cnf(11913,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,skc94))),
inference(sor,[status(thm)],[360,11608]),
[iquote('0:SoR:360.0,11608.0')] ).
cnf(12048,plain,
is_a_theorem(implies__dfg(u,equiv__dfg(v,v))),
inference(sor,[status(thm)],[360,11570]),
[iquote('0:SoR:360.0,11570.0')] ).
cnf(24921,plain,
( ~ r3
| is_a_theorem(implies__dfg(implies__dfg(or__dfg(u,v),or__dfg(v,u)),equiv__dfg(or__dfg(v,u),or__dfg(u,v)))) ),
inference(sor,[status(thm)],[481,94]),
[iquote('0:SoR:481.0,94.1')] ).
cnf(24923,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)],[481,58]),
[iquote('0:SoR:481.0,58.1')] ).
cnf(24962,plain,
is_a_theorem(implies__dfg(implies__dfg(necessarily(possibly(u)),possibly(u)),equiv__dfg(possibly(u),necessarily(possibly(u))))),
inference(sor,[status(thm)],[481,152]),
[iquote('0:SoR:481.0,152.0')] ).
cnf(24964,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),equiv__dfg(u,skc94))),
inference(sor,[status(thm)],[481,5487]),
[iquote('0:SoR:481.0,5487.0')] ).
cnf(24975,plain,
is_a_theorem(implies__dfg(implies__dfg(and__dfg(u,u),u),equiv__dfg(u,and__dfg(u,u)))),
inference(sor,[status(thm)],[481,1420]),
[iquote('0:SoR:481.0,1420.0')] ).
cnf(25049,plain,
( ~ is_a_theorem(implies__dfg(skc94,u))
| is_a_theorem(equiv__dfg(u,skc94)) ),
inference(res,[status(thm),theory(equality)],[24964,168]),
[iquote('0:Res:24964.0,168.1')] ).
cnf(25071,plain,
is_a_theorem(equiv__dfg(implies__dfg(u,skc94),skc94)),
inference(sor,[status(thm)],[25049,11913]),
[iquote('0:SoR:25049.0,11913.0')] ).
cnf(25084,plain,
is_a_theorem(equiv__dfg(and__dfg(skc94,skc94),skc94)),
inference(sor,[status(thm)],[25049,11689]),
[iquote('0:SoR:25049.0,11689.0')] ).
cnf(25090,plain,
is_a_theorem(equiv__dfg(equiv__dfg(u,u),skc94)),
inference(sor,[status(thm)],[25049,12048]),
[iquote('0:SoR:25049.0,12048.0')] ).
cnf(25133,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equiv__dfg(u,skc94)) ),
inference(sor,[status(thm)],[25049,367]),
[iquote('0:SoR:25049.0,367.1')] ).
cnf(26411,plain,
equal(and__dfg(skc94,skc94),skc94),
inference(res,[status(thm),theory(equality)],[25084,156]),
[iquote('0:Res:25084.0,156.0')] ).
cnf(27082,plain,
equal(implies__dfg(u,skc94),skc94),
inference(res,[status(thm),theory(equality)],[25071,156]),
[iquote('0:Res:25071.0,156.0')] ).
cnf(27467,plain,
equal(and__dfg(implies__dfg(skc94,u),skc94),equiv__dfg(skc94,u)),
inference(spr,[status(thm),theory(equality)],[27082,170]),
[iquote('0:SpR:27082.0,170.0')] ).
cnf(27468,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),implies__dfg(skc94,equiv__dfg(skc94,u)))),
inference(spr,[status(thm),theory(equality)],[27082,171]),
[iquote('0:SpR:27082.0,171.0')] ).
cnf(27510,plain,
equal(and__dfg(skc94,implies__dfg(skc94,u)),equiv__dfg(u,skc94)),
inference(spr,[status(thm),theory(equality)],[27082,170]),
[iquote('0:SpR:27082.0,170.0')] ).
cnf(29645,plain,
equal(equiv__dfg(u,u),skc94),
inference(res,[status(thm),theory(equality)],[25090,156]),
[iquote('0:Res:25090.0,156.0')] ).
cnf(30140,plain,
is_a_theorem(implies__dfg(skc94,implies__dfg(u,u))),
inference(spr,[status(thm),theory(equality)],[29645,153]),
[iquote('0:SpR:29645.0,153.0')] ).
cnf(30179,plain,
is_a_theorem(equiv__dfg(implies__dfg(u,u),skc94)),
inference(sor,[status(thm)],[25049,30140]),
[iquote('0:SoR:25049.0,30140.0')] ).
cnf(30237,plain,
equal(implies__dfg(u,u),skc94),
inference(res,[status(thm),theory(equality)],[30179,156]),
[iquote('0:Res:30179.0,156.0')] ).
cnf(30402,plain,
is_a_theorem(implies__dfg(skc94,implies__dfg(or__dfg(u,u),u))),
inference(spr,[status(thm),theory(equality)],[30237,1415]),
[iquote('0:SpR:30237.0,1415.0')] ).
cnf(32362,plain,
( ~ is_a_theorem(u)
| equal(u,skc94) ),
inference(res,[status(thm),theory(equality)],[25133,156]),
[iquote('0:Res:25133.1,156.0')] ).
cnf(32759,plain,
equal(implies__dfg(implies__dfg(skc94,u),u),skc94),
inference(ems,[status(thm)],[32362,6758]),
[iquote('0:EmS:32362.0,6758.0')] ).
cnf(32851,plain,
equal(implies__dfg(u,and__dfg(skc94,u)),skc94),
inference(ems,[status(thm)],[32362,6611]),
[iquote('0:EmS:32362.0,6611.0')] ).
cnf(32866,plain,
equal(implies__dfg(or__dfg(u,not__dfg(not__dfg(v))),or__dfg(v,u)),skc94),
inference(ems,[status(thm)],[32362,253]),
[iquote('0:EmS:32362.0,253.0')] ).
cnf(32867,plain,
( ~ r3
| equal(implies__dfg(or__dfg(u,v),or__dfg(v,u)),skc94) ),
inference(ems,[status(thm)],[32362,94]),
[iquote('0:EmS:32362.0,94.1')] ).
cnf(32906,plain,
equal(implies__dfg(u,implies__dfg(v,u)),skc94),
inference(ems,[status(thm)],[32362,150]),
[iquote('0:EmS:32362.0,150.0')] ).
cnf(32910,plain,
equal(implies__dfg(u,or__dfg(u,v)),skc94),
inference(ems,[status(thm)],[32362,146]),
[iquote('0:EmS:32362.0,146.0')] ).
cnf(32916,plain,
equal(implies__dfg(and__dfg(u,v),u),skc94),
inference(ems,[status(thm)],[32362,148]),
[iquote('0:EmS:32362.0,148.0')] ).
cnf(32917,plain,
equal(implies__dfg(and__dfg(u,v),v),skc94),
inference(ems,[status(thm)],[32362,147]),
[iquote('0:EmS:32362.0,147.0')] ).
cnf(32919,plain,
equal(implies__dfg(necessarily(u),u),skc94),
inference(ems,[status(thm)],[32362,141]),
[iquote('0:EmS:32362.0,141.0')] ).
cnf(32939,plain,
is_a_theorem(implies__dfg(skc94,equiv__dfg(possibly(u),necessarily(possibly(u))))),
inference(rew,[status(thm),theory(equality)],[32919,24962]),
[iquote('0:Rew:32919.0,24962.0')] ).
cnf(33271,plain,
( ~ r1
| is_a_theorem(implies__dfg(skc94,equiv__dfg(or__dfg(u,u),u))) ),
inference(rew,[status(thm),theory(equality)],[32910,24923]),
[iquote('0:Rew:32910.0,24923.1')] ).
cnf(33280,plain,
is_a_theorem(implies__dfg(skc94,equiv__dfg(u,and__dfg(u,u)))),
inference(rew,[status(thm),theory(equality)],[32916,24975]),
[iquote('0:Rew:32916.0,24975.0')] ).
cnf(34158,plain,
( ~ r3
| is_a_theorem(implies__dfg(skc94,equiv__dfg(or__dfg(u,v),or__dfg(v,u)))) ),
inference(rew,[status(thm),theory(equality)],[32867,24921]),
[iquote('0:Rew:32867.1,24921.1')] ).
cnf(35238,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)],[32759,170]),
[iquote('0:SpR:32759.0,170.0')] ).
cnf(35262,plain,
equal(equiv__dfg(u,implies__dfg(skc94,u)),and__dfg(skc94,skc94)),
inference(rew,[status(thm),theory(equality)],[32906,35238]),
[iquote('0:Rew:32906.0,35238.0')] ).
cnf(35263,plain,
equal(equiv__dfg(u,implies__dfg(skc94,u)),skc94),
inference(rew,[status(thm),theory(equality)],[26411,35262]),
[iquote('0:Rew:26411.0,35262.0')] ).
cnf(35374,plain,
equal(and__dfg(implies__dfg(and__dfg(skc94,u),u),skc94),equiv__dfg(and__dfg(skc94,u),u)),
inference(spr,[status(thm),theory(equality)],[32851,170]),
[iquote('0:SpR:32851.0,170.0')] ).
cnf(35440,plain,
equal(equiv__dfg(and__dfg(skc94,u),u),and__dfg(skc94,skc94)),
inference(rew,[status(thm),theory(equality)],[32917,35374]),
[iquote('0:Rew:32917.0,35374.0')] ).
cnf(35441,plain,
equal(equiv__dfg(and__dfg(skc94,u),u),skc94),
inference(rew,[status(thm),theory(equality)],[26411,35440]),
[iquote('0:Rew:26411.0,35440.0')] ).
cnf(35511,plain,
( ~ is_a_theorem(skc94)
| equal(implies__dfg(skc94,u),u) ),
inference(spl,[status(thm),theory(equality)],[35263,156]),
[iquote('0:SpL:35263.0,156.0')] ).
cnf(35512,plain,
equal(implies__dfg(skc94,u),u),
inference(mrr,[status(thm)],[35511,381]),
[iquote('0:MRR:35511.0,381.0')] ).
cnf(35552,plain,
is_a_theorem(implies__dfg(or__dfg(u,u),u)),
inference(rew,[status(thm),theory(equality)],[35512,30402]),
[iquote('0:Rew:35512.0,30402.0')] ).
cnf(35564,plain,
( ~ r3
| is_a_theorem(equiv__dfg(or__dfg(u,v),or__dfg(v,u))) ),
inference(rew,[status(thm),theory(equality)],[35512,34158]),
[iquote('0:Rew:35512.0,34158.1')] ).
cnf(35594,plain,
is_a_theorem(equiv__dfg(possibly(u),necessarily(possibly(u)))),
inference(rew,[status(thm),theory(equality)],[35512,32939]),
[iquote('0:Rew:35512.0,32939.0')] ).
cnf(35595,plain,
( ~ r1
| is_a_theorem(equiv__dfg(or__dfg(u,u),u)) ),
inference(rew,[status(thm),theory(equality)],[35512,33271]),
[iquote('0:Rew:35512.0,33271.1')] ).
cnf(35599,plain,
is_a_theorem(equiv__dfg(u,and__dfg(u,u))),
inference(rew,[status(thm),theory(equality)],[35512,33280]),
[iquote('0:Rew:35512.0,33280.0')] ).
cnf(35606,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),equiv__dfg(skc94,u))),
inference(rew,[status(thm),theory(equality)],[35512,27468]),
[iquote('0:Rew:35512.0,27468.0')] ).
cnf(35688,plain,
equal(and__dfg(u,skc94),equiv__dfg(skc94,u)),
inference(rew,[status(thm),theory(equality)],[35512,27467]),
[iquote('0:Rew:35512.0,27467.0')] ).
cnf(35689,plain,
equal(and__dfg(skc94,u),equiv__dfg(u,skc94)),
inference(rew,[status(thm),theory(equality)],[35512,27510]),
[iquote('0:Rew:35512.0,27510.0')] ).
cnf(35708,plain,
r1,
inference(mrr,[status(thm)],[59,35552]),
[iquote('0:MRR:59.0,35552.0')] ).
cnf(36055,plain,
equal(equiv__dfg(equiv__dfg(u,skc94),u),skc94),
inference(rew,[status(thm),theory(equality)],[35689,35441]),
[iquote('0:Rew:35689.0,35441.0')] ).
cnf(36062,plain,
is_a_theorem(equiv__dfg(or__dfg(u,u),u)),
inference(mrr,[status(thm)],[35595,35708]),
[iquote('0:MRR:35595.0,35708.0')] ).
cnf(36063,plain,
is_a_theorem(implies__dfg(u,equiv__dfg(skc94,u))),
inference(rew,[status(thm),theory(equality)],[35512,35606]),
[iquote('0:Rew:35512.0,35606.0')] ).
cnf(36532,plain,
equal(implies__dfg(u,equiv__dfg(skc94,u)),skc94),
inference(ems,[status(thm)],[32362,36063]),
[iquote('0:EmS:32362.0,36063.0')] ).
cnf(36571,plain,
equal(and__dfg(u,u),u),
inference(res,[status(thm),theory(equality)],[35599,156]),
[iquote('0:Res:35599.0,156.0')] ).
cnf(36741,plain,
equal(implies__dfg(not__dfg(u),u),not__dfg(not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[36571,157]),
[iquote('0:SpR:36571.0,157.0')] ).
cnf(36743,plain,
equal(implies__dfg(implies__dfg(not__dfg(u),u),v),or__dfg(not__dfg(u),v)),
inference(spr,[status(thm),theory(equality)],[36571,238]),
[iquote('0:SpR:36571.0,238.0')] ).
cnf(36745,plain,
equal(implies__dfg(possibly(u),necessarily(not__dfg(u))),not__dfg(possibly(u))),
inference(spr,[status(thm),theory(equality)],[36571,245]),
[iquote('0:SpR:36571.0,245.0')] ).
cnf(36749,plain,
equal(not__dfg(necessarily(or__dfg(u,u))),possibly(not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[36571,1034]),
[iquote('0:SpR:36571.0,1034.0')] ).
cnf(36755,plain,
equal(or__dfg(u,u),not__dfg(not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[159,36741]),
[iquote('0:Rew:159.0,36741.0')] ).
cnf(36794,plain,
equal(implies__dfg(or__dfg(u,u),v),or__dfg(not__dfg(u),v)),
inference(rew,[status(thm),theory(equality)],[159,36743]),
[iquote('0:Rew:159.0,36743.0')] ).
cnf(36916,plain,
equal(or__dfg(u,u),u),
inference(res,[status(thm),theory(equality)],[36062,156]),
[iquote('0:Res:36062.0,156.0')] ).
cnf(36925,plain,
equal(not__dfg(necessarily(u)),possibly(not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[36916,36749]),
[iquote('0:Rew:36916.0,36749.0')] ).
cnf(36929,plain,
equal(not__dfg(not__dfg(u)),u),
inference(rew,[status(thm),theory(equality)],[36916,36755]),
[iquote('0:Rew:36916.0,36755.0')] ).
cnf(36930,plain,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[36916,36794]),
[iquote('0:Rew:36916.0,36794.0')] ).
cnf(37693,plain,
equal(implies__dfg(or__dfg(u,v),or__dfg(v,u)),skc94),
inference(rew,[status(thm),theory(equality)],[36929,32866]),
[iquote('0:Rew:36929.0,32866.0')] ).
cnf(38955,plain,
( ~ is_a_theorem(skc94)
| r3 ),
inference(rew,[status(thm),theory(equality)],[37693,95]),
[iquote('0:Rew:37693.0,95.0')] ).
cnf(38966,plain,
r3,
inference(mrr,[status(thm)],[38955,381]),
[iquote('0:MRR:38955.0,381.0')] ).
cnf(39409,plain,
is_a_theorem(equiv__dfg(or__dfg(u,v),or__dfg(v,u))),
inference(mrr,[status(thm)],[35564,38966]),
[iquote('0:MRR:35564.0,38966.0')] ).
cnf(42389,plain,
equal(implies__dfg(possibly(u),necessarily(not__dfg(u))),necessarily(not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[36916,198]),
[iquote('0:SpR:36916.0,198.0')] ).
cnf(42395,plain,
equal(not__dfg(possibly(u)),necessarily(not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[36745,42389]),
[iquote('0:Rew:36745.0,42389.0')] ).
cnf(42850,plain,
equal(necessarily(possibly(u)),possibly(u)),
inference(res,[status(thm),theory(equality)],[35594,156]),
[iquote('0:Res:35594.0,156.0')] ).
cnf(42852,plain,
equal(implies__dfg(possibly(necessarily(not__dfg(u))),v),or__dfg(possibly(u),v)),
inference(rew,[status(thm),theory(equality)],[42850,227]),
[iquote('0:Rew:42850.0,227.0')] ).
cnf(42854,plain,
~ is_a_theorem(implies__dfg(skc160,possibly(skc160))),
inference(rew,[status(thm),theory(equality)],[42850,142]),
[iquote('0:Rew:42850.0,142.0')] ).
cnf(44914,plain,
( ~ is_a_theorem(skc94)
| equal(equiv__dfg(u,skc94),u) ),
inference(spl,[status(thm),theory(equality)],[36055,156]),
[iquote('0:SpL:36055.0,156.0')] ).
cnf(44915,plain,
equal(equiv__dfg(u,skc94),u),
inference(mrr,[status(thm)],[44914,381]),
[iquote('0:MRR:44914.0,381.0')] ).
cnf(44917,plain,
equal(and__dfg(skc94,u),u),
inference(rew,[status(thm),theory(equality)],[44915,35689]),
[iquote('0:Rew:44915.0,35689.0')] ).
cnf(45370,plain,
equal(and__dfg(skc94,implies__dfg(equiv__dfg(skc94,u),u)),equiv__dfg(u,equiv__dfg(skc94,u))),
inference(spr,[status(thm),theory(equality)],[36532,170]),
[iquote('0:SpR:36532.0,170.0')] ).
cnf(45384,plain,
equal(equiv__dfg(u,equiv__dfg(skc94,u)),implies__dfg(equiv__dfg(skc94,u),u)),
inference(rew,[status(thm),theory(equality)],[44917,45370]),
[iquote('0:Rew:44917.0,45370.0')] ).
cnf(45423,plain,
equal(possibly(not__dfg(possibly(u))),not__dfg(possibly(u))),
inference(spr,[status(thm),theory(equality)],[42850,36925]),
[iquote('0:SpR:42850.0,36925.0')] ).
cnf(45431,plain,
equal(possibly(necessarily(not__dfg(u))),necessarily(not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[42395,45423]),
[iquote('0:Rew:42395.0,45423.0')] ).
cnf(45543,plain,
equal(implies__dfg(necessarily(not__dfg(u)),v),or__dfg(possibly(u),v)),
inference(rew,[status(thm),theory(equality)],[45431,42852]),
[iquote('0:Rew:45431.0,42852.0')] ).
cnf(45985,plain,
equal(or__dfg(possibly(u),not__dfg(u)),skc94),
inference(spr,[status(thm),theory(equality)],[45543,32919]),
[iquote('0:SpR:45543.0,32919.0')] ).
cnf(46899,plain,
equal(implies__dfg(equiv__dfg(skc94,u),u),skc94),
inference(spr,[status(thm),theory(equality)],[35688,32916]),
[iquote('0:SpR:35688.0,32916.0')] ).
cnf(46909,plain,
equal(equiv__dfg(u,equiv__dfg(skc94,u)),skc94),
inference(rew,[status(thm),theory(equality)],[46899,45384]),
[iquote('0:Rew:46899.0,45384.0')] ).
cnf(46955,plain,
( ~ is_a_theorem(skc94)
| equal(equiv__dfg(skc94,u),u) ),
inference(spl,[status(thm),theory(equality)],[46909,156]),
[iquote('0:SpL:46909.0,156.0')] ).
cnf(46956,plain,
equal(equiv__dfg(skc94,u),u),
inference(mrr,[status(thm)],[46955,381]),
[iquote('0:MRR:46955.0,381.0')] ).
cnf(51154,plain,
is_a_theorem(equiv__dfg(skc94,or__dfg(not__dfg(u),possibly(u)))),
inference(spr,[status(thm),theory(equality)],[45985,39409]),
[iquote('0:SpR:45985.0,39409.0')] ).
cnf(51455,plain,
is_a_theorem(implies__dfg(u,possibly(u))),
inference(rew,[status(thm),theory(equality)],[46956,51154,36930]),
[iquote('0:Rew:46956.0,51154.0,36930.0,51154.0')] ).
cnf(51456,plain,
$false,
inference(unc,[status(thm)],[51455,42854]),
[iquote('0:UnC:51455.0,42854.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : LCL524+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jul 3 03:45:15 EDT 2022
% 0.13/0.35 % CPUTime :
% 32.85/33.06
% 32.85/33.06 SPASS V 3.9
% 32.85/33.06 SPASS beiseite: Proof found.
% 32.85/33.06 % SZS status Theorem
% 32.85/33.06 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 32.85/33.06 SPASS derived 36555 clauses, backtracked 0 clauses, performed 2 splits and kept 16398 clauses.
% 32.85/33.06 SPASS allocated 152360 KBytes.
% 32.85/33.06 SPASS spent 0:0:32.65 on the problem.
% 32.85/33.06 0:00:00.04 for the input.
% 32.85/33.06 0:00:00.06 for the FLOTTER CNF translation.
% 32.85/33.06 0:00:00.47 for inferences.
% 32.85/33.06 0:00:00.09 for the backtracking.
% 32.85/33.06 0:0:31.58 for the reduction.
% 32.85/33.06
% 32.85/33.06
% 32.85/33.06 Here is a proof with depth 14, length 216 :
% 32.85/33.06 % SZS output start Refutation
% See solution above
% 38.94/39.13 Formulae used in the proof : hilbert_op_or hilbert_op_implies_and hilbert_op_equiv hilbert_modus_ponens hilbert_modus_tollens hilbert_implies_1 hilbert_implies_2 hilbert_implies_3 hilbert_and_1 hilbert_and_2 hilbert_and_3 hilbert_or_1 hilbert_or_3 hilbert_equivalence_2 hilbert_equivalence_3 substitution_of_equivalents km5_op_possibly km5_necessitation km5_axiom_K km5_axiom_M km5_axiom_5 km4b_axiom_B modus_ponens axiom_M and_3 implies_1 and_1 and_2 or_1 r1 necessitation axiom_B axiom_5 op_possibly equivalence_2 r3 op_implies_and modus_tollens implies_2 op_or op_equiv axiom_K implies_3 equivalence_3 or_3
% 38.94/39.13
%------------------------------------------------------------------------------