TSTP Solution File: LCL501+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL501+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 14:37:24 EDT 2022
% Result : Theorem 117.42s 117.67s
% Output : Refutation 129.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 65
% Number of leaves : 34
% Syntax : Number of clauses : 302 ( 225 unt; 0 nHn; 302 RR)
% Number of literals : 385 ( 0 equ; 94 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 19 ( 18 usr; 17 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 13 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
op_or,
file('LCL501+1.p',unknown),
[] ).
cnf(2,axiom,
op_implies_and,
file('LCL501+1.p',unknown),
[] ).
cnf(4,axiom,
op_implies_or,
file('LCL501+1.p',unknown),
[] ).
cnf(5,axiom,
op_and,
file('LCL501+1.p',unknown),
[] ).
cnf(6,axiom,
op_equiv,
file('LCL501+1.p',unknown),
[] ).
cnf(7,axiom,
modus_ponens,
file('LCL501+1.p',unknown),
[] ).
cnf(8,axiom,
r1,
file('LCL501+1.p',unknown),
[] ).
cnf(9,axiom,
r2,
file('LCL501+1.p',unknown),
[] ).
cnf(10,axiom,
r3,
file('LCL501+1.p',unknown),
[] ).
cnf(11,axiom,
r4,
file('LCL501+1.p',unknown),
[] ).
cnf(12,axiom,
r5,
file('LCL501+1.p',unknown),
[] ).
cnf(13,axiom,
substitution_of_equivalents,
file('LCL501+1.p',unknown),
[] ).
cnf(14,axiom,
~ kn3,
file('LCL501+1.p',unknown),
[] ).
cnf(15,axiom,
is_a_theorem(skc56),
file('LCL501+1.p',unknown),
[] ).
cnf(16,axiom,
is_a_theorem(implies__dfg(skc56,skc55)),
file('LCL501+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ kn1
| is_a_theorem(implies__dfg(u,and__dfg(u,u))) ),
file('LCL501+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ is_a_theorem(implies__dfg(skc87,and__dfg(skc87,skc87)))
| kn1 ),
file('LCL501+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ r1
| is_a_theorem(implies__dfg(or__dfg(u,u),u)) ),
file('LCL501+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ r2
| is_a_theorem(implies__dfg(u,or__dfg(v,u))) ),
file('LCL501+1.p',unknown),
[] ).
cnf(42,axiom,
( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv__dfg(u,v))
| equal(u,v) ),
file('LCL501+1.p',unknown),
[] ).
cnf(43,axiom,
( ~ and_3
| is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))) ),
file('LCL501+1.p',unknown),
[] ).
cnf(44,axiom,
( ~ is_a_theorem(implies__dfg(skc73,implies__dfg(skc72,and__dfg(skc73,skc72))))
| and_3 ),
file('LCL501+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ r3
| is_a_theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))) ),
file('LCL501+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ op_implies_or
| equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)) ),
file('LCL501+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ op_implies_and
| equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)) ),
file('LCL501+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ is_a_theorem(u)
| ~ modus_ponens
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL501+1.p',unknown),
[] ).
cnf(58,axiom,
( ~ op_or
| equal(not__dfg(and__dfg(not__dfg(u),not__dfg(v))),or__dfg(u,v)) ),
file('LCL501+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ op_and
| equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and__dfg(u,v)) ),
file('LCL501+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ op_equiv
| equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)) ),
file('LCL501+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ equivalence_3
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,u),equiv__dfg(u,v)))) ),
file('LCL501+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ is_a_theorem(implies__dfg(implies__dfg(skc86,skc85),implies__dfg(implies__dfg(skc85,skc86),equiv__dfg(skc86,skc85))))
| equivalence_3 ),
file('LCL501+1.p',unknown),
[] ).
cnf(67,axiom,
( ~ r4
| is_a_theorem(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))) ),
file('LCL501+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ r5
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))) ),
file('LCL501+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ is_a_theorem(implies__dfg(implies__dfg(skc92,skc91),implies__dfg(not__dfg(and__dfg(skc91,skc90)),not__dfg(and__dfg(skc90,skc92)))))
| kn3 ),
file('LCL501+1.p',unknown),
[] ).
cnf(75,plain,
is_a_theorem(implies__dfg(u,or__dfg(v,u))),
inference(mrr,[status(thm)],[36,9]),
[iquote('0:MRR:36.0,9.0')] ).
cnf(76,plain,
is_a_theorem(implies__dfg(or__dfg(u,u),u)),
inference(mrr,[status(thm)],[34,8]),
[iquote('0:MRR:34.0,8.0')] ).
cnf(78,plain,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
inference(mrr,[status(thm)],[51,4]),
[iquote('0:MRR:51.0,4.0')] ).
cnf(79,plain,
is_a_theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
inference(mrr,[status(thm)],[49,10]),
[iquote('0:MRR:49.0,10.0')] ).
cnf(80,plain,
( ~ is_a_theorem(equiv__dfg(u,v))
| equal(u,v) ),
inference(mrr,[status(thm)],[42,13]),
[iquote('0:MRR:42.0,13.0')] ).
cnf(81,plain,
equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)),
inference(mrr,[status(thm)],[52,2]),
[iquote('0:MRR:52.0,2.0')] ).
cnf(82,plain,
( ~ op_and
| equal(not__dfg(implies__dfg(u,not__dfg(v))),and__dfg(u,v)) ),
inference(rew,[status(thm),theory(equality)],[78,59]),
[iquote('0:Rew:78.0,59.1')] ).
cnf(83,plain,
equal(not__dfg(implies__dfg(u,not__dfg(v))),and__dfg(u,v)),
inference(mrr,[status(thm)],[82,5]),
[iquote('0:MRR:82.0,5.0')] ).
cnf(84,plain,
( ~ op_or
| equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)) ),
inference(rew,[status(thm),theory(equality)],[81,58]),
[iquote('0:Rew:81.0,58.1')] ).
cnf(85,plain,
equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)),
inference(mrr,[status(thm)],[84,1]),
[iquote('0:MRR:84.0,1.0')] ).
cnf(93,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(mrr,[status(thm)],[53,7]),
[iquote('0:MRR:53.1,7.0')] ).
cnf(94,plain,
equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)),
inference(mrr,[status(thm)],[60,6]),
[iquote('0:MRR:60.0,6.0')] ).
cnf(95,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),
inference(mrr,[status(thm)],[69,12]),
[iquote('0:MRR:69.0,12.0')] ).
cnf(96,plain,
is_a_theorem(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
inference(mrr,[status(thm)],[67,11]),
[iquote('0:MRR:67.0,11.0')] ).
cnf(97,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(skc92,skc91),or__dfg(and__dfg(skc91,skc90),not__dfg(and__dfg(skc90,skc92)))))
| kn3 ),
inference(rew,[status(thm),theory(equality)],[85,74]),
[iquote('0:Rew:85.0,74.0')] ).
cnf(98,plain,
~ is_a_theorem(implies__dfg(implies__dfg(skc92,skc91),or__dfg(and__dfg(skc91,skc90),not__dfg(and__dfg(skc90,skc92))))),
inference(mrr,[status(thm)],[97,14]),
[iquote('0:MRR:97.1,14.0')] ).
cnf(113,plain,
is_a_theorem(implies__dfg(implies__dfg(u,not__dfg(u)),not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[78,76]),
[iquote('0:SpR:78.0,76.0')] ).
cnf(114,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
inference(spr,[status(thm),theory(equality)],[78,75]),
[iquote('0:SpR:78.0,75.0')] ).
cnf(121,plain,
is_a_theorem(or__dfg(u,or__dfg(v,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[85,75]),
[iquote('0:SpR:85.0,75.0')] ).
cnf(129,plain,
is_a_theorem(or__dfg(u,implies__dfg(v,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[85,114]),
[iquote('0:SpR:85.0,114.0')] ).
cnf(135,plain,
is_a_theorem(implies__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,u))),
inference(spr,[status(thm),theory(equality)],[78,79]),
[iquote('0:SpR:78.0,79.0')] ).
cnf(136,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),or__dfg(v,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[78,79]),
[iquote('0:SpR:78.0,79.0')] ).
cnf(154,plain,
equal(implies__dfg(and__dfg(u,not__dfg(v)),w),or__dfg(implies__dfg(u,v),w)),
inference(spr,[status(thm),theory(equality)],[81,78]),
[iquote('0:SpR:81.0,78.0')] ).
cnf(155,plain,
equal(or__dfg(and__dfg(u,not__dfg(v)),w),implies__dfg(implies__dfg(u,v),w)),
inference(spr,[status(thm),theory(equality)],[81,85]),
[iquote('0:SpR:81.0,85.0')] ).
cnf(163,plain,
equal(not__dfg(and__dfg(u,implies__dfg(v,w))),implies__dfg(u,and__dfg(v,not__dfg(w)))),
inference(spr,[status(thm),theory(equality)],[81]),
[iquote('0:SpR:81.0,81.0')] ).
cnf(172,plain,
equal(implies__dfg(implies__dfg(u,not__dfg(v)),w),or__dfg(and__dfg(u,v),w)),
inference(spr,[status(thm),theory(equality)],[83,78]),
[iquote('0:SpR:83.0,78.0')] ).
cnf(173,plain,
equal(or__dfg(implies__dfg(u,not__dfg(v)),w),implies__dfg(and__dfg(u,v),w)),
inference(spr,[status(thm),theory(equality)],[83,85]),
[iquote('0:SpR:83.0,85.0')] ).
cnf(182,plain,
equal(not__dfg(implies__dfg(u,and__dfg(v,w))),and__dfg(u,implies__dfg(v,not__dfg(w)))),
inference(spr,[status(thm),theory(equality)],[83]),
[iquote('0:SpR:83.0,83.0')] ).
cnf(185,plain,
equal(not__dfg(or__dfg(u,not__dfg(v))),and__dfg(not__dfg(u),v)),
inference(spr,[status(thm),theory(equality)],[85,83]),
[iquote('0:SpR:85.0,83.0')] ).
cnf(186,plain,
is_a_theorem(or__dfg(and__dfg(u,u),not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[172,113]),
[iquote('0:Rew:172.0,113.0')] ).
cnf(199,plain,
is_a_theorem(implies__dfg(implies__dfg(u,not__dfg(v)),implies__dfg(v,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[78,135]),
[iquote('0:SpR:78.0,135.0')] ).
cnf(200,plain,
is_a_theorem(or__dfg(and__dfg(u,v),implies__dfg(v,not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[172,199]),
[iquote('0:Rew:172.0,199.0')] ).
cnf(251,plain,
( ~ and_3
| is_a_theorem(implies__dfg(u,or__dfg(v,and__dfg(u,not__dfg(v))))) ),
inference(spr,[status(thm),theory(equality)],[85,43]),
[iquote('0:SpR:85.0,43.1')] ).
cnf(254,plain,
( ~ is_a_theorem(not__dfg(u))
| ~ is_a_theorem(or__dfg(u,v))
| is_a_theorem(v) ),
inference(spl,[status(thm),theory(equality)],[85,93]),
[iquote('0:SpL:85.0,93.1')] ).
cnf(255,plain,
( ~ is_a_theorem(skc56)
| is_a_theorem(skc55) ),
inference(res,[status(thm),theory(equality)],[16,93]),
[iquote('0:Res:16.0,93.1')] ).
cnf(258,plain,
( ~ is_a_theorem(u)
| is_a_theorem(or__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[75,93]),
[iquote('0:Res:75.0,93.1')] ).
cnf(262,plain,
( ~ is_a_theorem(or__dfg(u,v))
| is_a_theorem(or__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[79,93]),
[iquote('0:Res:79.0,93.1')] ).
cnf(263,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(or__dfg(v,not__dfg(u))) ),
inference(res,[status(thm),theory(equality)],[136,93]),
[iquote('0:Res:136.0,93.1')] ).
cnf(269,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[114,93]),
[iquote('0:Res:114.0,93.1')] ).
cnf(273,plain,
( ~ is_a_theorem(or__dfg(u,not__dfg(v)))
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[135,93]),
[iquote('0:Res:135.0,93.1')] ).
cnf(276,plain,
is_a_theorem(skc55),
inference(ssi,[status(thm)],[255,15]),
[iquote('0:SSi:255.0,15.0')] ).
cnf(279,plain,
( ~ kn1
| is_a_theorem(implies__dfg(implies__dfg(u,u),equiv__dfg(u,u))) ),
inference(spr,[status(thm),theory(equality)],[94,30]),
[iquote('0:SpR:94.0,30.1')] ).
cnf(286,plain,
( ~ and_3
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,u),equiv__dfg(u,v)))) ),
inference(spr,[status(thm),theory(equality)],[94,43]),
[iquote('0:SpR:94.0,43.1')] ).
cnf(289,plain,
equal(and__dfg(or__dfg(u,v),implies__dfg(v,not__dfg(u))),equiv__dfg(not__dfg(u),v)),
inference(spr,[status(thm),theory(equality)],[85,94]),
[iquote('0:SpR:85.0,94.0')] ).
cnf(314,plain,
is_a_theorem(implies__dfg(or__dfg(not__dfg(u),or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
inference(spr,[status(thm),theory(equality)],[78,96]),
[iquote('0:SpR:78.0,96.0')] ).
cnf(315,plain,
is_a_theorem(implies__dfg(or__dfg(u,or__dfg(not__dfg(v),w)),implies__dfg(v,or__dfg(u,w)))),
inference(spr,[status(thm),theory(equality)],[78,96]),
[iquote('0:SpR:78.0,96.0')] ).
cnf(318,plain,
( ~ is_a_theorem(or__dfg(u,or__dfg(v,w)))
| is_a_theorem(or__dfg(v,or__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[96,93]),
[iquote('0:Res:96.0,93.1')] ).
cnf(319,plain,
is_a_theorem(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[78,314]),
[iquote('0:Rew:78.0,314.0')] ).
cnf(320,plain,
is_a_theorem(implies__dfg(or__dfg(u,implies__dfg(v,w)),implies__dfg(v,or__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[78,315]),
[iquote('0:Rew:78.0,315.0')] ).
cnf(327,plain,
is_a_theorem(implies__dfg(or__dfg(u,v),implies__dfg(or__dfg(w,not__dfg(u)),or__dfg(w,v)))),
inference(spr,[status(thm),theory(equality)],[85,95]),
[iquote('0:SpR:85.0,95.0')] ).
cnf(328,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(or__dfg(w,u),or__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[95,93]),
[iquote('0:Res:95.0,93.1')] ).
cnf(359,plain,
is_a_theorem(or__dfg(implies__dfg(u,not__dfg(v)),and__dfg(v,u))),
inference(sor,[status(thm)],[262,200]),
[iquote('0:SoR:262.0,200.0')] ).
cnf(361,plain,
is_a_theorem(or__dfg(not__dfg(u),and__dfg(u,u))),
inference(sor,[status(thm)],[262,186]),
[iquote('0:SoR:262.0,186.0')] ).
cnf(368,plain,
is_a_theorem(or__dfg(implies__dfg(u,not__dfg(v)),v)),
inference(sor,[status(thm)],[262,129]),
[iquote('0:SoR:262.0,129.0')] ).
cnf(371,plain,
is_a_theorem(implies__dfg(u,and__dfg(u,u))),
inference(rew,[status(thm),theory(equality)],[78,361]),
[iquote('0:Rew:78.0,361.0')] ).
cnf(372,plain,
kn1,
inference(mrr,[status(thm)],[31,371]),
[iquote('0:MRR:31.0,371.0')] ).
cnf(376,plain,
is_a_theorem(implies__dfg(implies__dfg(u,u),equiv__dfg(u,u))),
inference(mrr,[status(thm)],[279,372]),
[iquote('0:MRR:279.0,372.0')] ).
cnf(378,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),v)),
inference(rew,[status(thm),theory(equality)],[173,368]),
[iquote('0:Rew:173.0,368.0')] ).
cnf(386,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),and__dfg(v,u))),
inference(rew,[status(thm),theory(equality)],[173,359]),
[iquote('0:Rew:173.0,359.0')] ).
cnf(431,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| ~ equivalence_3
| is_a_theorem(implies__dfg(implies__dfg(v,u),equiv__dfg(u,v))) ),
inference(res,[status(thm),theory(equality)],[63,93]),
[iquote('0:Res:63.1,93.1')] ).
cnf(527,plain,
equal(or__dfg(or__dfg(u,not__dfg(v)),w),implies__dfg(and__dfg(not__dfg(u),v),w)),
inference(spr,[status(thm),theory(equality)],[185,85]),
[iquote('0:SpR:185.0,85.0')] ).
cnf(555,plain,
equal(and__dfg(not__dfg(u),and__dfg(v,not__dfg(w))),not__dfg(or__dfg(u,implies__dfg(v,w)))),
inference(spr,[status(thm),theory(equality)],[81,185]),
[iquote('0:SpR:81.0,185.0')] ).
cnf(557,plain,
equal(not__dfg(implies__dfg(u,not__dfg(v))),and__dfg(not__dfg(not__dfg(u)),v)),
inference(spr,[status(thm),theory(equality)],[78,185]),
[iquote('0:SpR:78.0,185.0')] ).
cnf(558,plain,
equal(and__dfg(not__dfg(not__dfg(u)),v),and__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[83,557]),
[iquote('0:Rew:83.0,557.0')] ).
cnf(1042,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),or__dfg(w,and__dfg(u,not__dfg(v))))),
inference(spr,[status(thm),theory(equality)],[155,79]),
[iquote('0:SpR:155.0,79.0')] ).
cnf(1059,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),not__dfg(not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[155,186]),
[iquote('0:SpR:155.0,186.0')] ).
cnf(1094,plain,
is_a_theorem(implies__dfg(or__dfg(u,u),not__dfg(not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[85,1059]),
[iquote('0:Rew:85.0,1059.0')] ).
cnf(1158,plain,
( ~ is_a_theorem(or__dfg(u,u))
| is_a_theorem(not__dfg(not__dfg(u))) ),
inference(res,[status(thm),theory(equality)],[1094,93]),
[iquote('0:Res:1094.0,93.1')] ).
cnf(1492,plain,
is_a_theorem(implies__dfg(implies__dfg(u,or__dfg(not__dfg(v),w)),implies__dfg(v,implies__dfg(u,w)))),
inference(spr,[status(thm),theory(equality)],[78,319]),
[iquote('0:SpR:78.0,319.0')] ).
cnf(1501,plain,
( ~ is_a_theorem(implies__dfg(u,or__dfg(v,w)))
| is_a_theorem(or__dfg(v,implies__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[319,93]),
[iquote('0:Res:319.0,93.1')] ).
cnf(1503,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(v,implies__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[78,1492]),
[iquote('0:Rew:78.0,1492.0')] ).
cnf(1551,plain,
( ~ is_a_theorem(or__dfg(u,implies__dfg(v,w)))
| is_a_theorem(implies__dfg(v,or__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[320,93]),
[iquote('0:Res:320.0,93.1')] ).
cnf(1761,plain,
equal(implies__dfg(implies__dfg(u,v),and__dfg(v,not__dfg(u))),not__dfg(equiv__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[94,163]),
[iquote('0:SpR:94.0,163.0')] ).
cnf(2696,plain,
equal(and__dfg(implies__dfg(u,v),implies__dfg(v,not__dfg(not__dfg(u)))),equiv__dfg(not__dfg(not__dfg(u)),v)),
inference(spr,[status(thm),theory(equality)],[78,289]),
[iquote('0:SpR:78.0,289.0')] ).
cnf(2777,plain,
( ~ is_a_theorem(or__dfg(u,v))
| is_a_theorem(or__dfg(u,or__dfg(w,v))) ),
inference(sor,[status(thm)],[318,258]),
[iquote('0:SoR:318.0,258.1')] ).
cnf(2780,plain,
is_a_theorem(or__dfg(u,or__dfg(v,not__dfg(v)))),
inference(sor,[status(thm)],[318,121]),
[iquote('0:SoR:318.0,121.0')] ).
cnf(2787,plain,
is_a_theorem(or__dfg(or__dfg(u,not__dfg(u)),v)),
inference(sor,[status(thm)],[262,2780]),
[iquote('0:SoR:262.0,2780.0')] ).
cnf(2802,plain,
is_a_theorem(implies__dfg(and__dfg(not__dfg(u),u),v)),
inference(rew,[status(thm),theory(equality)],[527,2787]),
[iquote('0:Rew:527.0,2787.0')] ).
cnf(2941,plain,
is_a_theorem(implies__dfg(or__dfg(u,implies__dfg(v,v)),or__dfg(u,equiv__dfg(v,v)))),
inference(sor,[status(thm)],[328,376]),
[iquote('0:SoR:328.0,376.0')] ).
cnf(2951,plain,
( ~ and_3
| is_a_theorem(implies__dfg(or__dfg(u,v),or__dfg(u,or__dfg(w,and__dfg(v,not__dfg(w)))))) ),
inference(sor,[status(thm)],[328,251]),
[iquote('0:SoR:328.0,251.1')] ).
cnf(3012,plain,
is_a_theorem(implies__dfg(or__dfg(u,skc56),or__dfg(u,skc55))),
inference(sor,[status(thm)],[328,16]),
[iquote('0:SoR:328.0,16.0')] ).
cnf(3023,plain,
is_a_theorem(implies__dfg(and__dfg(u,not__dfg(u)),v)),
inference(spr,[status(thm),theory(equality)],[558,2802]),
[iquote('0:SpR:558.0,2802.0')] ).
cnf(3026,plain,
is_a_theorem(or__dfg(implies__dfg(u,u),v)),
inference(rew,[status(thm),theory(equality)],[154,3023]),
[iquote('0:Rew:154.0,3023.0')] ).
cnf(3031,plain,
is_a_theorem(not__dfg(not__dfg(implies__dfg(u,u)))),
inference(sor,[status(thm)],[1158,3026]),
[iquote('0:SoR:1158.0,3026.0')] ).
cnf(3033,plain,
is_a_theorem(or__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[262,3026]),
[iquote('0:SoR:262.0,3026.0')] ).
cnf(3034,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[273,3026]),
[iquote('0:SoR:273.0,3026.0')] ).
cnf(3040,plain,
( ~ is_a_theorem(or__dfg(not__dfg(implies__dfg(u,u)),v))
| is_a_theorem(v) ),
inference(sor,[status(thm)],[254,3031]),
[iquote('0:SoR:254.0,3031.0')] ).
cnf(3050,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,u),v))
| is_a_theorem(v) ),
inference(rew,[status(thm),theory(equality)],[78,3040]),
[iquote('0:Rew:78.0,3040.0')] ).
cnf(3073,plain,
( ~ and_3
| equivalence_3 ),
inference(res,[status(thm),theory(equality)],[286,64]),
[iquote('0:Res:286.1,64.0')] ).
cnf(3164,plain,
( ~ is_a_theorem(or__dfg(u,skc56))
| is_a_theorem(or__dfg(u,skc55)) ),
inference(res,[status(thm),theory(equality)],[3012,93]),
[iquote('0:Res:3012.0,93.1')] ).
cnf(3167,plain,
is_a_theorem(or__dfg(u,skc55)),
inference(ssi,[status(thm)],[3164,258,15]),
[iquote('0:SSi:3164.0,258.0,15.1')] ).
cnf(3172,plain,
is_a_theorem(not__dfg(not__dfg(skc55))),
inference(sor,[status(thm)],[1158,3167]),
[iquote('0:SoR:1158.0,3167.0')] ).
cnf(3174,plain,
is_a_theorem(or__dfg(skc55,u)),
inference(sor,[status(thm)],[262,3167]),
[iquote('0:SoR:262.0,3167.0')] ).
cnf(3178,plain,
( ~ is_a_theorem(or__dfg(not__dfg(skc55),u))
| is_a_theorem(u) ),
inference(sor,[status(thm)],[254,3172]),
[iquote('0:SoR:254.0,3172.0')] ).
cnf(3181,plain,
( ~ is_a_theorem(implies__dfg(skc55,u))
| is_a_theorem(u) ),
inference(rew,[status(thm),theory(equality)],[78,3178]),
[iquote('0:Rew:78.0,3178.0')] ).
cnf(3182,plain,
is_a_theorem(or__dfg(u,or__dfg(skc55,v))),
inference(sor,[status(thm)],[318,3174]),
[iquote('0:SoR:318.0,3174.0')] ).
cnf(3216,plain,
is_a_theorem(not__dfg(not__dfg(or__dfg(skc55,u)))),
inference(sor,[status(thm)],[1158,3182]),
[iquote('0:SoR:1158.0,3182.0')] ).
cnf(3222,plain,
( ~ is_a_theorem(or__dfg(not__dfg(or__dfg(skc55,u)),v))
| is_a_theorem(v) ),
inference(sor,[status(thm)],[254,3216]),
[iquote('0:SoR:254.0,3216.0')] ).
cnf(3226,plain,
( ~ is_a_theorem(implies__dfg(or__dfg(skc55,u),v))
| is_a_theorem(v) ),
inference(rew,[status(thm),theory(equality)],[78,3222]),
[iquote('0:Rew:78.0,3222.0')] ).
cnf(3377,plain,
( ~ equivalence_3
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(or__dfg(u,not__dfg(v)),or__dfg(u,w)),or__dfg(v,w)),equiv__dfg(or__dfg(v,w),implies__dfg(or__dfg(u,not__dfg(v)),or__dfg(u,w))))) ),
inference(sor,[status(thm)],[431,327]),
[iquote('0:SoR:431.0,327.0')] ).
cnf(3393,plain,
( ~ equivalence_3
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w))),equiv__dfg(or__dfg(v,implies__dfg(u,w)),implies__dfg(u,or__dfg(v,w))))) ),
inference(sor,[status(thm)],[431,320]),
[iquote('0:SoR:431.0,320.0')] ).
cnf(3394,plain,
( ~ equivalence_3
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),or__dfg(v,not__dfg(u))),equiv__dfg(or__dfg(v,not__dfg(u)),implies__dfg(u,v)))) ),
inference(sor,[status(thm)],[431,135]),
[iquote('0:SoR:431.0,135.0')] ).
cnf(4682,plain,
is_a_theorem(implies__dfg(or__dfg(u,not__dfg(skc55)),or__dfg(u,v))),
inference(res,[status(thm),theory(equality)],[327,3226]),
[iquote('0:Res:327.0,3226.0')] ).
cnf(5007,plain,
is_a_theorem(implies__dfg(or__dfg(not__dfg(u),not__dfg(skc55)),implies__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[78,4682]),
[iquote('0:SpR:78.0,4682.0')] ).
cnf(5016,plain,
is_a_theorem(or__dfg(and__dfg(u,skc55),implies__dfg(u,v))),
inference(rew,[status(thm),theory(equality)],[172,5007,78]),
[iquote('0:Rew:172.0,5007.0,78.0,5007.0')] ).
cnf(5596,plain,
is_a_theorem(or__dfg(u,or__dfg(v,skc55))),
inference(sor,[status(thm)],[2777,3167]),
[iquote('0:SoR:2777.0,3167.0')] ).
cnf(5609,plain,
is_a_theorem(or__dfg(u,or__dfg(v,implies__dfg(w,not__dfg(u))))),
inference(sor,[status(thm)],[2777,129]),
[iquote('0:SoR:2777.0,129.0')] ).
cnf(5618,plain,
is_a_theorem(not__dfg(not__dfg(or__dfg(u,skc55)))),
inference(sor,[status(thm)],[1158,5596]),
[iquote('0:SoR:1158.0,5596.0')] ).
cnf(5622,plain,
is_a_theorem(or__dfg(u,implies__dfg(v,skc55))),
inference(spr,[status(thm),theory(equality)],[78,5596]),
[iquote('0:SpR:78.0,5596.0')] ).
cnf(5631,plain,
is_a_theorem(not__dfg(not__dfg(implies__dfg(u,skc55)))),
inference(spr,[status(thm),theory(equality)],[78,5618]),
[iquote('0:SpR:78.0,5618.0')] ).
cnf(5648,plain,
( ~ is_a_theorem(or__dfg(not__dfg(implies__dfg(u,skc55)),v))
| is_a_theorem(v) ),
inference(sor,[status(thm)],[254,5631]),
[iquote('0:SoR:254.0,5631.0')] ).
cnf(5654,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,skc55),v))
| is_a_theorem(v) ),
inference(rew,[status(thm),theory(equality)],[78,5648]),
[iquote('0:Rew:78.0,5648.0')] ).
cnf(5730,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,skc55))),
inference(spr,[status(thm),theory(equality)],[78,5622]),
[iquote('0:SpR:78.0,5622.0')] ).
cnf(7024,plain,
( ~ is_a_theorem(or__dfg(u,implies__dfg(v,v)))
| is_a_theorem(or__dfg(u,equiv__dfg(v,v))) ),
inference(res,[status(thm),theory(equality)],[2941,93]),
[iquote('0:Res:2941.0,93.1')] ).
cnf(7027,plain,
is_a_theorem(or__dfg(u,equiv__dfg(v,v))),
inference(ssi,[status(thm)],[7024,3033]),
[iquote('0:SSi:7024.0,3033.0')] ).
cnf(7032,plain,
is_a_theorem(not__dfg(not__dfg(equiv__dfg(u,u)))),
inference(sor,[status(thm)],[1158,7027]),
[iquote('0:SoR:1158.0,7027.0')] ).
cnf(9207,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),v))),
inference(res,[status(thm),theory(equality)],[1503,3050]),
[iquote('0:Res:1503.0,3050.0')] ).
cnf(9361,plain,
is_a_theorem(or__dfg(u,implies__dfg(or__dfg(u,not__dfg(skc55)),v))),
inference(sor,[status(thm)],[1501,4682]),
[iquote('0:SoR:1501.0,4682.0')] ).
cnf(9453,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,skc55),v),v)),
inference(res,[status(thm),theory(equality)],[9207,5654]),
[iquote('0:Res:9207.0,5654.0')] ).
cnf(9455,plain,
is_a_theorem(implies__dfg(implies__dfg(skc55,u),u)),
inference(res,[status(thm),theory(equality)],[9207,3181]),
[iquote('0:Res:9207.0,3181.0')] ).
cnf(9467,plain,
is_a_theorem(or__dfg(u,not__dfg(implies__dfg(skc55,u)))),
inference(sor,[status(thm)],[263,9455]),
[iquote('0:SoR:263.0,9455.0')] ).
cnf(9470,plain,
( ~ is_a_theorem(implies__dfg(skc55,u))
| is_a_theorem(u) ),
inference(res,[status(thm),theory(equality)],[9455,93]),
[iquote('0:Res:9455.0,93.1')] ).
cnf(9503,plain,
is_a_theorem(implies__dfg(u,or__dfg(and__dfg(u,skc55),v))),
inference(sor,[status(thm)],[1551,5016]),
[iquote('0:SoR:1551.0,5016.0')] ).
cnf(9508,plain,
is_a_theorem(implies__dfg(u,or__dfg(and__dfg(v,u),not__dfg(v)))),
inference(sor,[status(thm)],[1551,200]),
[iquote('0:SoR:1551.0,200.0')] ).
cnf(9531,plain,
is_a_theorem(or__dfg(not__dfg(u),and__dfg(skc55,u))),
inference(spr,[status(thm),theory(equality)],[83,9467]),
[iquote('0:SpR:83.0,9467.0')] ).
cnf(9540,plain,
is_a_theorem(implies__dfg(u,and__dfg(skc55,u))),
inference(rew,[status(thm),theory(equality)],[78,9531]),
[iquote('0:Rew:78.0,9531.0')] ).
cnf(9997,plain,
equal(and__dfg(implies__dfg(u,v),implies__dfg(v,not__dfg(not__dfg(u)))),not__dfg(not__dfg(equiv__dfg(u,v)))),
inference(spr,[status(thm),theory(equality)],[1761,182]),
[iquote('0:SpR:1761.0,182.0')] ).
cnf(10108,plain,
equal(not__dfg(not__dfg(equiv__dfg(u,v))),equiv__dfg(not__dfg(not__dfg(u)),v)),
inference(rew,[status(thm),theory(equality)],[2696,9997]),
[iquote('0:Rew:2696.0,9997.0')] ).
cnf(10109,plain,
is_a_theorem(equiv__dfg(not__dfg(not__dfg(u)),u)),
inference(rew,[status(thm),theory(equality)],[10108,7032]),
[iquote('0:Rew:10108.0,7032.0')] ).
cnf(10187,plain,
equal(not__dfg(not__dfg(u)),u),
inference(res,[status(thm),theory(equality)],[10109,80]),
[iquote('0:Res:10109.0,80.0')] ).
cnf(11059,plain,
equal(not__dfg(and__dfg(u,v)),implies__dfg(u,not__dfg(v))),
inference(spr,[status(thm),theory(equality)],[10187,81]),
[iquote('0:SpR:10187.0,81.0')] ).
cnf(11069,plain,
equal(not__dfg(implies__dfg(u,v)),and__dfg(u,not__dfg(v))),
inference(spr,[status(thm),theory(equality)],[10187,83]),
[iquote('0:SpR:10187.0,83.0')] ).
cnf(11160,plain,
~ is_a_theorem(implies__dfg(implies__dfg(skc92,skc91),or__dfg(and__dfg(skc91,skc90),implies__dfg(skc90,not__dfg(skc92))))),
inference(rew,[status(thm),theory(equality)],[11059,98]),
[iquote('0:Rew:11059.0,98.0')] ).
cnf(11736,plain,
is_a_theorem(implies__dfg(not__dfg(equiv__dfg(u,skc55)),and__dfg(skc55,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[1761,9453]),
[iquote('0:SpR:1761.0,9453.0')] ).
cnf(11742,plain,
is_a_theorem(or__dfg(equiv__dfg(u,skc55),and__dfg(skc55,not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[85,11736]),
[iquote('0:Rew:85.0,11736.0')] ).
cnf(11751,plain,
is_a_theorem(or__dfg(and__dfg(skc55,skc55),u)),
inference(sor,[status(thm)],[9470,9503]),
[iquote('0:SoR:9470.0,9503.0')] ).
cnf(11772,plain,
is_a_theorem(implies__dfg(u,and__dfg(skc55,skc55))),
inference(sor,[status(thm)],[273,11751]),
[iquote('0:SoR:273.0,11751.0')] ).
cnf(12762,plain,
is_a_theorem(or__dfg(and__dfg(skc55,not__dfg(u)),equiv__dfg(u,skc55))),
inference(sor,[status(thm)],[262,11742]),
[iquote('0:SoR:262.0,11742.0')] ).
cnf(12765,plain,
is_a_theorem(implies__dfg(implies__dfg(skc55,u),equiv__dfg(u,skc55))),
inference(rew,[status(thm),theory(equality)],[155,12762]),
[iquote('0:Rew:155.0,12762.0')] ).
cnf(12774,plain,
( ~ is_a_theorem(implies__dfg(skc55,u))
| is_a_theorem(equiv__dfg(u,skc55)) ),
inference(res,[status(thm),theory(equality)],[12765,93]),
[iquote('0:Res:12765.0,93.1')] ).
cnf(13033,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equiv__dfg(u,skc55)) ),
inference(sor,[status(thm)],[12774,269]),
[iquote('0:SoR:12774.0,269.1')] ).
cnf(13045,plain,
is_a_theorem(equiv__dfg(implies__dfg(u,skc55),skc55)),
inference(sor,[status(thm)],[12774,5730]),
[iquote('0:SoR:12774.0,5730.0')] ).
cnf(13047,plain,
is_a_theorem(equiv__dfg(implies__dfg(u,u),skc55)),
inference(sor,[status(thm)],[12774,3034]),
[iquote('0:SoR:12774.0,3034.0')] ).
cnf(13069,plain,
is_a_theorem(equiv__dfg(and__dfg(skc55,skc55),skc55)),
inference(sor,[status(thm)],[12774,11772]),
[iquote('0:SoR:12774.0,11772.0')] ).
cnf(13084,plain,
equal(and__dfg(skc55,skc55),skc55),
inference(res,[status(thm),theory(equality)],[13069,80]),
[iquote('0:Res:13069.0,80.0')] ).
cnf(13198,plain,
equal(implies__dfg(u,skc55),skc55),
inference(res,[status(thm),theory(equality)],[13045,80]),
[iquote('0:Res:13045.0,80.0')] ).
cnf(13391,plain,
equal(and__dfg(implies__dfg(skc55,u),skc55),equiv__dfg(skc55,u)),
inference(spr,[status(thm),theory(equality)],[13198,94]),
[iquote('0:SpR:13198.0,94.0')] ).
cnf(13429,plain,
equal(and__dfg(skc55,implies__dfg(skc55,u)),equiv__dfg(u,skc55)),
inference(spr,[status(thm),theory(equality)],[13198,94]),
[iquote('0:SpR:13198.0,94.0')] ).
cnf(13444,plain,
is_a_theorem(implies__dfg(implies__dfg(skc55,u),or__dfg(u,and__dfg(v,not__dfg(skc55))))),
inference(spr,[status(thm),theory(equality)],[13198,1042]),
[iquote('0:SpR:13198.0,1042.0')] ).
cnf(14819,plain,
equal(implies__dfg(u,u),skc55),
inference(res,[status(thm),theory(equality)],[13047,80]),
[iquote('0:Res:13047.0,80.0')] ).
cnf(15056,plain,
equal(or__dfg(u,not__dfg(u)),skc55),
inference(spr,[status(thm),theory(equality)],[14819,85]),
[iquote('0:SpR:14819.0,85.0')] ).
cnf(15603,plain,
equal(and__dfg(not__dfg(u),u),not__dfg(skc55)),
inference(spr,[status(thm),theory(equality)],[15056,185]),
[iquote('0:SpR:15056.0,185.0')] ).
cnf(16241,plain,
( ~ is_a_theorem(u)
| equal(u,skc55) ),
inference(res,[status(thm),theory(equality)],[13033,80]),
[iquote('0:Res:13033.1,80.0')] ).
cnf(16287,plain,
equal(or__dfg(and__dfg(u,skc55),implies__dfg(u,v)),skc55),
inference(ems,[status(thm)],[16241,5016]),
[iquote('0:EmS:16241.0,5016.0')] ).
cnf(16308,plain,
equal(implies__dfg(implies__dfg(skc55,u),u),skc55),
inference(ems,[status(thm)],[16241,9455]),
[iquote('0:EmS:16241.0,9455.0')] ).
cnf(16325,plain,
equal(implies__dfg(u,and__dfg(skc55,u)),skc55),
inference(ems,[status(thm)],[16241,9540]),
[iquote('0:EmS:16241.0,9540.0')] ).
cnf(16360,plain,
equal(implies__dfg(u,implies__dfg(v,u)),skc55),
inference(ems,[status(thm)],[16241,114]),
[iquote('0:EmS:16241.0,114.0')] ).
cnf(16366,plain,
equal(implies__dfg(and__dfg(u,v),and__dfg(v,u)),skc55),
inference(ems,[status(thm)],[16241,386]),
[iquote('0:EmS:16241.0,386.0')] ).
cnf(16367,plain,
equal(implies__dfg(and__dfg(u,v),v),skc55),
inference(ems,[status(thm)],[16241,378]),
[iquote('0:EmS:16241.0,378.0')] ).
cnf(16395,plain,
equal(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w))),skc55),
inference(ems,[status(thm)],[16241,319]),
[iquote('0:EmS:16241.0,319.0')] ).
cnf(16397,plain,
equal(implies__dfg(implies__dfg(u,v),or__dfg(v,not__dfg(u))),skc55),
inference(ems,[status(thm)],[16241,136]),
[iquote('0:EmS:16241.0,136.0')] ).
cnf(16399,plain,
equal(implies__dfg(or__dfg(u,v),or__dfg(v,u)),skc55),
inference(ems,[status(thm)],[16241,79]),
[iquote('0:EmS:16241.0,79.0')] ).
cnf(16404,plain,
equal(implies__dfg(u,or__dfg(v,u)),skc55),
inference(ems,[status(thm)],[16241,75]),
[iquote('0:EmS:16241.0,75.0')] ).
cnf(16405,plain,
equal(implies__dfg(or__dfg(u,u),u),skc55),
inference(ems,[status(thm)],[16241,76]),
[iquote('0:EmS:16241.0,76.0')] ).
cnf(16595,plain,
( ~ equivalence_3
| is_a_theorem(implies__dfg(skc55,equiv__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,u)))) ),
inference(rew,[status(thm),theory(equality)],[16397,3394]),
[iquote('0:Rew:16397.0,3394.1')] ).
cnf(16650,plain,
( ~ equivalence_3
| is_a_theorem(implies__dfg(skc55,equiv__dfg(or__dfg(u,implies__dfg(v,w)),implies__dfg(v,or__dfg(u,w))))) ),
inference(rew,[status(thm),theory(equality)],[16395,3393]),
[iquote('0:Rew:16395.0,3393.1')] ).
cnf(16708,plain,
equal(and__dfg(u,not__dfg(u)),not__dfg(skc55)),
inference(spr,[status(thm),theory(equality)],[10187,15603]),
[iquote('0:SpR:10187.0,15603.0')] ).
cnf(16806,plain,
equal(and__dfg(implies__dfg(u,implies__dfg(skc55,u)),skc55),equiv__dfg(u,implies__dfg(skc55,u))),
inference(spr,[status(thm),theory(equality)],[16308,94]),
[iquote('0:SpR:16308.0,94.0')] ).
cnf(16823,plain,
equal(equiv__dfg(u,implies__dfg(skc55,u)),and__dfg(skc55,skc55)),
inference(rew,[status(thm),theory(equality)],[16360,16806]),
[iquote('0:Rew:16360.0,16806.0')] ).
cnf(16824,plain,
equal(equiv__dfg(u,implies__dfg(skc55,u)),skc55),
inference(rew,[status(thm),theory(equality)],[13084,16823]),
[iquote('0:Rew:13084.0,16823.0')] ).
cnf(16835,plain,
equal(and__dfg(implies__dfg(and__dfg(skc55,u),u),skc55),equiv__dfg(and__dfg(skc55,u),u)),
inference(spr,[status(thm),theory(equality)],[16325,94]),
[iquote('0:SpR:16325.0,94.0')] ).
cnf(16850,plain,
equal(equiv__dfg(and__dfg(skc55,u),u),and__dfg(skc55,skc55)),
inference(rew,[status(thm),theory(equality)],[16367,16835]),
[iquote('0:Rew:16367.0,16835.0')] ).
cnf(16851,plain,
equal(equiv__dfg(and__dfg(skc55,u),u),skc55),
inference(rew,[status(thm),theory(equality)],[13084,16850]),
[iquote('0:Rew:13084.0,16850.0')] ).
cnf(16929,plain,
( ~ is_a_theorem(skc55)
| equal(implies__dfg(skc55,u),u) ),
inference(spl,[status(thm),theory(equality)],[16824,80]),
[iquote('0:SpL:16824.0,80.0')] ).
cnf(16930,plain,
equal(implies__dfg(skc55,u),u),
inference(mrr,[status(thm)],[16929,276]),
[iquote('0:MRR:16929.0,276.0')] ).
cnf(16959,plain,
( ~ equivalence_3
| is_a_theorem(equiv__dfg(or__dfg(u,implies__dfg(v,w)),implies__dfg(v,or__dfg(u,w)))) ),
inference(rew,[status(thm),theory(equality)],[16930,16650]),
[iquote('0:Rew:16930.0,16650.1')] ).
cnf(16960,plain,
( ~ equivalence_3
| is_a_theorem(equiv__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,u))) ),
inference(rew,[status(thm),theory(equality)],[16930,16595]),
[iquote('0:Rew:16930.0,16595.1')] ).
cnf(17019,plain,
equal(and__dfg(u,skc55),equiv__dfg(skc55,u)),
inference(rew,[status(thm),theory(equality)],[16930,13391]),
[iquote('0:Rew:16930.0,13391.0')] ).
cnf(17020,plain,
equal(and__dfg(skc55,u),equiv__dfg(u,skc55)),
inference(rew,[status(thm),theory(equality)],[16930,13429]),
[iquote('0:Rew:16930.0,13429.0')] ).
cnf(17021,plain,
is_a_theorem(implies__dfg(u,or__dfg(u,and__dfg(v,not__dfg(skc55))))),
inference(rew,[status(thm),theory(equality)],[16930,13444]),
[iquote('0:Rew:16930.0,13444.0')] ).
cnf(17094,plain,
equal(or__dfg(equiv__dfg(skc55,u),implies__dfg(u,v)),skc55),
inference(rew,[status(thm),theory(equality)],[17019,16287]),
[iquote('0:Rew:17019.0,16287.0')] ).
cnf(17115,plain,
equal(equiv__dfg(equiv__dfg(u,skc55),u),skc55),
inference(rew,[status(thm),theory(equality)],[17020,16851]),
[iquote('0:Rew:17020.0,16851.0')] ).
cnf(17297,plain,
( ~ equivalence_3
| equal(or__dfg(u,not__dfg(v)),implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[16960,80]),
[iquote('0:Res:16960.1,80.0')] ).
cnf(17317,plain,
( ~ equivalence_3
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),or__dfg(v,w)),or__dfg(u,w)),equiv__dfg(or__dfg(u,w),implies__dfg(implies__dfg(u,v),or__dfg(v,w))))) ),
inference(rew,[status(thm),theory(equality)],[17297,3377]),
[iquote('0:Rew:17297.1,3377.1')] ).
cnf(17395,plain,
( ~ is_a_theorem(skc55)
| equal(equiv__dfg(u,skc55),u) ),
inference(spl,[status(thm),theory(equality)],[17115,80]),
[iquote('0:SpL:17115.0,80.0')] ).
cnf(17396,plain,
equal(equiv__dfg(u,skc55),u),
inference(mrr,[status(thm)],[17395,276]),
[iquote('0:MRR:17395.0,276.0')] ).
cnf(17398,plain,
equal(and__dfg(skc55,u),u),
inference(rew,[status(thm),theory(equality)],[17396,17020]),
[iquote('0:Rew:17396.0,17020.0')] ).
cnf(17723,plain,
equal(and__dfg(skc55,implies__dfg(u,or__dfg(u,u))),equiv__dfg(or__dfg(u,u),u)),
inference(spr,[status(thm),theory(equality)],[16405,94]),
[iquote('0:SpR:16405.0,94.0')] ).
cnf(17742,plain,
equal(equiv__dfg(or__dfg(u,u),u),skc55),
inference(rew,[status(thm),theory(equality)],[17398,17723,16404]),
[iquote('0:Rew:17398.0,17723.0,16404.0,17723.0')] ).
cnf(18158,plain,
( ~ is_a_theorem(skc55)
| equal(or__dfg(u,u),u) ),
inference(spl,[status(thm),theory(equality)],[17742,80]),
[iquote('0:SpL:17742.0,80.0')] ).
cnf(18159,plain,
equal(or__dfg(u,u),u),
inference(mrr,[status(thm)],[18158,276]),
[iquote('0:MRR:18158.0,276.0')] ).
cnf(18192,plain,
equal(implies__dfg(u,not__dfg(u)),not__dfg(u)),
inference(spr,[status(thm),theory(equality)],[18159,78]),
[iquote('0:SpR:18159.0,78.0')] ).
cnf(19483,plain,
is_a_theorem(or__dfg(u,not__dfg(or__dfg(u,not__dfg(skc55))))),
inference(spr,[status(thm),theory(equality)],[18192,9361]),
[iquote('0:SpR:18192.0,9361.0')] ).
cnf(19506,plain,
is_a_theorem(or__dfg(u,equiv__dfg(skc55,not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[17019,19483,185]),
[iquote('0:Rew:17019.0,19483.0,185.0,19483.0')] ).
cnf(19634,plain,
is_a_theorem(or__dfg(not__dfg(u),equiv__dfg(skc55,u))),
inference(spr,[status(thm),theory(equality)],[10187,19506]),
[iquote('0:SpR:10187.0,19506.0')] ).
cnf(19649,plain,
is_a_theorem(implies__dfg(u,equiv__dfg(skc55,u))),
inference(rew,[status(thm),theory(equality)],[78,19634]),
[iquote('0:Rew:78.0,19634.0')] ).
cnf(19661,plain,
equal(implies__dfg(u,equiv__dfg(skc55,u)),skc55),
inference(ems,[status(thm)],[16241,19649]),
[iquote('0:EmS:16241.0,19649.0')] ).
cnf(19740,plain,
equal(and__dfg(skc55,implies__dfg(equiv__dfg(skc55,u),u)),equiv__dfg(u,equiv__dfg(skc55,u))),
inference(spr,[status(thm),theory(equality)],[19661,94]),
[iquote('0:SpR:19661.0,94.0')] ).
cnf(19757,plain,
equal(equiv__dfg(u,equiv__dfg(skc55,u)),implies__dfg(equiv__dfg(skc55,u),u)),
inference(rew,[status(thm),theory(equality)],[17398,19740]),
[iquote('0:Rew:17398.0,19740.0')] ).
cnf(20454,plain,
( ~ equivalence_3
| equal(or__dfg(u,implies__dfg(v,w)),implies__dfg(v,or__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[16959,80]),
[iquote('0:Res:16959.1,80.0')] ).
cnf(22897,plain,
is_a_theorem(implies__dfg(u,or__dfg(u,not__dfg(skc55)))),
inference(spr,[status(thm),theory(equality)],[16708,17021]),
[iquote('0:SpR:16708.0,17021.0')] ).
cnf(22958,plain,
is_a_theorem(or__dfg(u,implies__dfg(u,not__dfg(skc55)))),
inference(sor,[status(thm)],[1501,22897]),
[iquote('0:SoR:1501.0,22897.0')] ).
cnf(23026,plain,
is_a_theorem(or__dfg(implies__dfg(u,not__dfg(skc55)),u)),
inference(sor,[status(thm)],[262,22958]),
[iquote('0:SoR:262.0,22958.0')] ).
cnf(23060,plain,
is_a_theorem(implies__dfg(equiv__dfg(skc55,u),u)),
inference(rew,[status(thm),theory(equality)],[17019,23026,173]),
[iquote('0:Rew:17019.0,23026.0,173.0,23026.0')] ).
cnf(23085,plain,
equal(implies__dfg(equiv__dfg(skc55,u),u),skc55),
inference(ems,[status(thm)],[16241,23060]),
[iquote('0:EmS:16241.0,23060.0')] ).
cnf(23118,plain,
equal(equiv__dfg(u,equiv__dfg(skc55,u)),skc55),
inference(rew,[status(thm),theory(equality)],[23085,19757]),
[iquote('0:Rew:23085.0,19757.0')] ).
cnf(23353,plain,
( ~ is_a_theorem(skc55)
| equal(equiv__dfg(skc55,u),u) ),
inference(spl,[status(thm),theory(equality)],[23118,80]),
[iquote('0:SpL:23118.0,80.0')] ).
cnf(23354,plain,
equal(equiv__dfg(skc55,u),u),
inference(mrr,[status(thm)],[23353,276]),
[iquote('0:MRR:23353.0,276.0')] ).
cnf(23468,plain,
equal(or__dfg(u,implies__dfg(u,v)),skc55),
inference(rew,[status(thm),theory(equality)],[23354,17094]),
[iquote('0:Rew:23354.0,17094.0')] ).
cnf(25412,plain,
( ~ and_3
| is_a_theorem(implies__dfg(skc55,or__dfg(u,or__dfg(v,and__dfg(implies__dfg(u,w),not__dfg(v)))))) ),
inference(spr,[status(thm),theory(equality)],[23468,2951]),
[iquote('0:SpR:23468.0,2951.1')] ).
cnf(25446,plain,
( ~ and_3
| is_a_theorem(or__dfg(u,or__dfg(v,and__dfg(implies__dfg(u,w),not__dfg(v))))) ),
inference(rew,[status(thm),theory(equality)],[16930,25412]),
[iquote('0:Rew:16930.0,25412.1')] ).
cnf(31909,plain,
is_a_theorem(or__dfg(not__dfg(u),or__dfg(v,implies__dfg(w,u)))),
inference(spr,[status(thm),theory(equality)],[10187,5609]),
[iquote('0:SpR:10187.0,5609.0')] ).
cnf(31966,plain,
is_a_theorem(implies__dfg(u,or__dfg(v,implies__dfg(w,u)))),
inference(rew,[status(thm),theory(equality)],[78,31909]),
[iquote('0:Rew:78.0,31909.0')] ).
cnf(32026,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,u)))),
inference(spr,[status(thm),theory(equality)],[78,31966]),
[iquote('0:SpR:78.0,31966.0')] ).
cnf(32326,plain,
equal(implies__dfg(u,implies__dfg(v,implies__dfg(w,u))),skc55),
inference(ems,[status(thm)],[16241,32026]),
[iquote('0:EmS:16241.0,32026.0')] ).
cnf(33448,plain,
equal(implies__dfg(u,or__dfg(and__dfg(v,u),not__dfg(v))),skc55),
inference(ems,[status(thm)],[16241,9508]),
[iquote('0:EmS:16241.0,9508.0')] ).
cnf(35947,plain,
equal(and__dfg(implies__dfg(and__dfg(u,v),and__dfg(v,u)),skc55),equiv__dfg(and__dfg(u,v),and__dfg(v,u))),
inference(spr,[status(thm),theory(equality)],[16366,94]),
[iquote('0:SpR:16366.0,94.0')] ).
cnf(36075,plain,
equal(equiv__dfg(and__dfg(u,v),and__dfg(v,u)),skc55),
inference(rew,[status(thm),theory(equality)],[17398,35947,16366]),
[iquote('0:Rew:17398.0,35947.0,16366.0,35947.0')] ).
cnf(36082,plain,
equal(and__dfg(implies__dfg(or__dfg(u,v),or__dfg(v,u)),skc55),equiv__dfg(or__dfg(u,v),or__dfg(v,u))),
inference(spr,[status(thm),theory(equality)],[16399,94]),
[iquote('0:SpR:16399.0,94.0')] ).
cnf(36180,plain,
equal(equiv__dfg(or__dfg(u,v),or__dfg(v,u)),skc55),
inference(rew,[status(thm),theory(equality)],[17398,36082,16399]),
[iquote('0:Rew:17398.0,36082.0,16399.0,36082.0')] ).
cnf(46279,plain,
( ~ is_a_theorem(skc55)
| equal(and__dfg(u,v),and__dfg(v,u)) ),
inference(spl,[status(thm),theory(equality)],[36075,80]),
[iquote('0:SpL:36075.0,80.0')] ).
cnf(46298,plain,
equal(and__dfg(u,v),and__dfg(v,u)),
inference(mrr,[status(thm)],[46279,276]),
[iquote('0:MRR:46279.0,276.0')] ).
cnf(46307,plain,
~ is_a_theorem(implies__dfg(implies__dfg(skc92,skc91),or__dfg(and__dfg(skc90,skc91),implies__dfg(skc90,not__dfg(skc92))))),
inference(rew,[status(thm),theory(equality)],[46298,11160]),
[iquote('0:Rew:46298.0,11160.0')] ).
cnf(46310,plain,
( ~ is_a_theorem(implies__dfg(skc73,implies__dfg(skc72,and__dfg(skc72,skc73))))
| and_3 ),
inference(rew,[status(thm),theory(equality)],[46298,44]),
[iquote('0:Rew:46298.0,44.0')] ).
cnf(47718,plain,
( ~ is_a_theorem(skc55)
| equal(or__dfg(u,v),or__dfg(v,u)) ),
inference(spl,[status(thm),theory(equality)],[36180,80]),
[iquote('0:SpL:36180.0,80.0')] ).
cnf(47754,plain,
equal(or__dfg(u,v),or__dfg(v,u)),
inference(mrr,[status(thm)],[47718,276]),
[iquote('0:MRR:47718.0,276.0')] ).
cnf(48060,plain,
equal(implies__dfg(u,or__dfg(not__dfg(v),and__dfg(v,u))),skc55),
inference(rew,[status(thm),theory(equality)],[47754,33448]),
[iquote('0:Rew:47754.0,33448.0')] ).
cnf(48104,plain,
equal(implies__dfg(u,implies__dfg(v,and__dfg(v,u))),skc55),
inference(rew,[status(thm),theory(equality)],[78,48060]),
[iquote('0:Rew:78.0,48060.0')] ).
cnf(48105,plain,
( ~ is_a_theorem(skc55)
| and_3 ),
inference(rew,[status(thm),theory(equality)],[48104,46310]),
[iquote('0:Rew:48104.0,46310.0')] ).
cnf(48109,plain,
and_3,
inference(mrr,[status(thm)],[48105,276]),
[iquote('0:MRR:48105.0,276.0')] ).
cnf(48110,plain,
equivalence_3,
inference(mrr,[status(thm)],[3073,48109]),
[iquote('0:MRR:3073.0,48109.0')] ).
cnf(48215,plain,
is_a_theorem(or__dfg(u,or__dfg(v,and__dfg(implies__dfg(u,w),not__dfg(v))))),
inference(mrr,[status(thm)],[25446,48109]),
[iquote('0:MRR:25446.0,48109.0')] ).
cnf(48396,plain,
equal(or__dfg(u,not__dfg(v)),implies__dfg(v,u)),
inference(mrr,[status(thm)],[17297,48110]),
[iquote('0:MRR:17297.0,48110.0')] ).
cnf(48404,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),or__dfg(v,w)),or__dfg(u,w)),equiv__dfg(or__dfg(u,w),implies__dfg(implies__dfg(u,v),or__dfg(v,w))))),
inference(mrr,[status(thm)],[17317,48110]),
[iquote('0:MRR:17317.0,48110.0')] ).
cnf(48415,plain,
equal(or__dfg(u,implies__dfg(v,w)),implies__dfg(v,or__dfg(u,w))),
inference(mrr,[status(thm)],[20454,48110]),
[iquote('0:MRR:20454.0,48110.0')] ).
cnf(48859,plain,
~ is_a_theorem(implies__dfg(implies__dfg(skc92,skc91),implies__dfg(skc90,or__dfg(and__dfg(skc90,skc91),not__dfg(skc92))))),
inference(rew,[status(thm),theory(equality)],[48415,46307]),
[iquote('0:Rew:48415.0,46307.0')] ).
cnf(48866,plain,
equal(and__dfg(not__dfg(u),and__dfg(v,not__dfg(w))),not__dfg(implies__dfg(v,or__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[48415,555]),
[iquote('0:Rew:48415.0,555.0')] ).
cnf(49930,plain,
~ is_a_theorem(implies__dfg(implies__dfg(skc92,skc91),implies__dfg(skc90,or__dfg(not__dfg(skc92),and__dfg(skc90,skc91))))),
inference(rew,[status(thm),theory(equality)],[47754,48859]),
[iquote('0:Rew:47754.0,48859.0')] ).
cnf(49931,plain,
~ is_a_theorem(implies__dfg(implies__dfg(skc92,skc91),implies__dfg(skc90,implies__dfg(skc92,and__dfg(skc90,skc91))))),
inference(rew,[status(thm),theory(equality)],[78,49930]),
[iquote('0:Rew:78.0,49930.0')] ).
cnf(49932,plain,
equal(and__dfg(not__dfg(u),and__dfg(v,not__dfg(w))),and__dfg(v,not__dfg(or__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[11069,48866]),
[iquote('0:Rew:11069.0,48866.0')] ).
cnf(50982,plain,
equal(or__dfg(u,implies__dfg(v,not__dfg(w))),implies__dfg(and__dfg(v,w),u)),
inference(spr,[status(thm),theory(equality)],[47754,173]),
[iquote('0:SpR:47754.0,173.0')] ).
cnf(50984,plain,
equal(or__dfg(u,and__dfg(v,not__dfg(w))),implies__dfg(implies__dfg(v,w),u)),
inference(spr,[status(thm),theory(equality)],[47754,155]),
[iquote('0:SpR:47754.0,155.0')] ).
cnf(51036,plain,
equal(implies__dfg(and__dfg(u,v),w),implies__dfg(u,implies__dfg(v,w))),
inference(rew,[status(thm),theory(equality)],[48396,50982,48415]),
[iquote('0:Rew:48396.0,50982.0,48415.0,50982.0')] ).
cnf(51042,plain,
equal(implies__dfg(u,implies__dfg(not__dfg(v),w)),or__dfg(implies__dfg(u,v),w)),
inference(rew,[status(thm),theory(equality)],[51036,154]),
[iquote('0:Rew:51036.0,154.0')] ).
cnf(51376,plain,
is_a_theorem(or__dfg(u,implies__dfg(implies__dfg(implies__dfg(u,v),w),w))),
inference(rew,[status(thm),theory(equality)],[50984,48215]),
[iquote('0:Rew:50984.0,48215.0')] ).
cnf(51439,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),or__dfg(u,w))),
inference(rew,[status(thm),theory(equality)],[48415,51376]),
[iquote('0:Rew:48415.0,51376.0')] ).
cnf(51442,plain,
equal(or__dfg(implies__dfg(u,v),w),implies__dfg(u,or__dfg(v,w))),
inference(rew,[status(thm),theory(equality)],[85,51042]),
[iquote('0:Rew:85.0,51042.0')] ).
cnf(52877,plain,
equal(implies__dfg(u,or__dfg(v,not__dfg(w))),implies__dfg(w,implies__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[48396,51442]),
[iquote('0:SpR:48396.0,51442.0')] ).
cnf(52910,plain,
equal(implies__dfg(u,implies__dfg(v,w)),implies__dfg(v,implies__dfg(u,w))),
inference(rew,[status(thm),theory(equality)],[48396,52877]),
[iquote('0:Rew:48396.0,52877.0')] ).
cnf(52913,plain,
~ is_a_theorem(implies__dfg(skc90,implies__dfg(implies__dfg(skc92,skc91),implies__dfg(skc92,and__dfg(skc90,skc91))))),
inference(rew,[status(thm),theory(equality)],[52910,49931]),
[iquote('0:Rew:52910.0,49931.0')] ).
cnf(53279,plain,
~ is_a_theorem(implies__dfg(skc90,implies__dfg(skc92,implies__dfg(implies__dfg(skc92,skc91),and__dfg(skc90,skc91))))),
inference(rew,[status(thm),theory(equality)],[52910,52913]),
[iquote('0:Rew:52910.0,52913.0')] ).
cnf(70895,plain,
equal(implies__dfg(implies__dfg(implies__dfg(u,v),w),or__dfg(u,w)),skc55),
inference(ems,[status(thm)],[16241,51439]),
[iquote('0:EmS:16241.0,51439.0')] ).
cnf(109933,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),v),or__dfg(u,v)),equiv__dfg(or__dfg(u,v),implies__dfg(implies__dfg(u,v),v)))),
inference(spr,[status(thm),theory(equality)],[18159,48404]),
[iquote('0:SpR:18159.0,48404.0')] ).
cnf(110059,plain,
is_a_theorem(implies__dfg(skc55,equiv__dfg(or__dfg(u,v),implies__dfg(implies__dfg(u,v),v)))),
inference(rew,[status(thm),theory(equality)],[70895,109933]),
[iquote('0:Rew:70895.0,109933.0')] ).
cnf(110060,plain,
is_a_theorem(equiv__dfg(or__dfg(u,v),implies__dfg(implies__dfg(u,v),v))),
inference(rew,[status(thm),theory(equality)],[16930,110059]),
[iquote('0:Rew:16930.0,110059.0')] ).
cnf(110547,plain,
equal(implies__dfg(implies__dfg(u,v),v),or__dfg(u,v)),
inference(res,[status(thm),theory(equality)],[110060,80]),
[iquote('0:Res:110060.0,80.0')] ).
cnf(115497,plain,
equal(or__dfg(and__dfg(u,v),not__dfg(v)),or__dfg(u,not__dfg(v))),
inference(spr,[status(thm),theory(equality)],[110547,172]),
[iquote('0:SpR:110547.0,172.0')] ).
cnf(115530,plain,
equal(implies__dfg(or__dfg(u,v),v),or__dfg(not__dfg(u),v)),
inference(spr,[status(thm),theory(equality)],[85,110547]),
[iquote('0:SpR:85.0,110547.0')] ).
cnf(115591,plain,
equal(implies__dfg(or__dfg(u,v),v),implies__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[78,115530]),
[iquote('0:Rew:78.0,115530.0')] ).
cnf(115772,plain,
equal(implies__dfg(u,and__dfg(v,u)),implies__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[48396,115497]),
[iquote('0:Rew:48396.0,115497.0,48396.0,115497.0')] ).
cnf(123157,plain,
equal(implies__dfg(implies__dfg(u,or__dfg(v,w)),w),implies__dfg(implies__dfg(u,v),w)),
inference(spr,[status(thm),theory(equality)],[51442,115591]),
[iquote('0:SpR:51442.0,115591.0')] ).
cnf(125340,plain,
equal(implies__dfg(and__dfg(u,not__dfg(v)),and__dfg(u,not__dfg(or__dfg(w,v)))),implies__dfg(and__dfg(u,not__dfg(v)),not__dfg(w))),
inference(spr,[status(thm),theory(equality)],[49932,115772]),
[iquote('0:SpR:49932.0,115772.0')] ).
cnf(125653,plain,
equal(implies__dfg(u,implies__dfg(not__dfg(v),and__dfg(u,not__dfg(or__dfg(w,v))))),implies__dfg(u,implies__dfg(not__dfg(v),not__dfg(w)))),
inference(rew,[status(thm),theory(equality)],[51036,125340]),
[iquote('0:Rew:51036.0,125340.0,51036.0,125340.0')] ).
cnf(125654,plain,
equal(implies__dfg(u,or__dfg(v,and__dfg(u,not__dfg(or__dfg(w,v))))),implies__dfg(u,implies__dfg(w,v))),
inference(rew,[status(thm),theory(equality)],[85,125653,48396]),
[iquote('0:Rew:85.0,125653.0,48396.0,125653.0,85.0,125653.0')] ).
cnf(125655,plain,
equal(implies__dfg(u,implies__dfg(implies__dfg(u,v),w)),implies__dfg(u,implies__dfg(v,w))),
inference(rew,[status(thm),theory(equality)],[123157,125654,50984]),
[iquote('0:Rew:123157.0,125654.0,50984.0,125654.0')] ).
cnf(125657,plain,
~ is_a_theorem(implies__dfg(skc90,implies__dfg(skc92,implies__dfg(skc91,and__dfg(skc90,skc91))))),
inference(rew,[status(thm),theory(equality)],[125655,53279]),
[iquote('0:Rew:125655.0,53279.0')] ).
cnf(126168,plain,
~ is_a_theorem(skc55),
inference(rew,[status(thm),theory(equality)],[32326,125657,115772]),
[iquote('0:Rew:32326.0,125657.0,115772.0,125657.0')] ).
cnf(126169,plain,
$false,
inference(mrr,[status(thm)],[126168,276]),
[iquote('0:MRR:126168.0,276.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL501+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n011.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
% 0.13/0.34 % DateTime : Sun Jul 3 07:22:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 117.42/117.67
% 117.42/117.67 SPASS V 3.9
% 117.42/117.67 SPASS beiseite: Proof found.
% 117.42/117.67 % SZS status Theorem
% 117.42/117.67 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 117.42/117.67 SPASS derived 71367 clauses, backtracked 0 clauses, performed 0 splits and kept 18634 clauses.
% 117.42/117.67 SPASS allocated 226997 KBytes.
% 117.42/117.67 SPASS spent 0:1:57.18 on the problem.
% 117.42/117.67 0:00:00.03 for the input.
% 117.42/117.67 0:00:00.04 for the FLOTTER CNF translation.
% 117.42/117.67 0:00:00.56 for inferences.
% 117.42/117.67 0:00:00.00 for the backtracking.
% 117.42/117.67 0:1:56.32 for the reduction.
% 117.42/117.67
% 117.42/117.67
% 117.42/117.67 Here is a proof with depth 22, length 302 :
% 117.42/117.67 % SZS output start Refutation
% See solution above
% 129.72/129.93 Formulae used in the proof : rosser_op_or rosser_op_implies_and principia_op_implies_or principia_op_and principia_op_equiv principia_modus_ponens principia_r1 principia_r2 principia_r3 principia_r4 principia_r5 substitution_of_equivalents rosser_kn3 modus_ponens r2 kn1 r1 and_3 r3 op_implies_or op_implies_and op_or op_and op_equiv equivalence_3 r4 r5 kn3
% 129.72/129.93
%------------------------------------------------------------------------------