TSTP Solution File: LCL493+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL493+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 14:37:21 EDT 2022
% Result : Theorem 4.99s 5.17s
% Output : Refutation 5.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 36
% Syntax : Number of clauses : 253 ( 183 unt; 0 nHn; 253 RR)
% Number of literals : 328 ( 0 equ; 83 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 20 ( 19 usr; 18 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 14 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
op_or,
file('LCL493+1.p',unknown),
[] ).
cnf(2,axiom,
op_implies_and,
file('LCL493+1.p',unknown),
[] ).
cnf(4,axiom,
op_implies_or,
file('LCL493+1.p',unknown),
[] ).
cnf(5,axiom,
op_and,
file('LCL493+1.p',unknown),
[] ).
cnf(6,axiom,
op_equiv,
file('LCL493+1.p',unknown),
[] ).
cnf(7,axiom,
modus_ponens,
file('LCL493+1.p',unknown),
[] ).
cnf(8,axiom,
r1,
file('LCL493+1.p',unknown),
[] ).
cnf(9,axiom,
r2,
file('LCL493+1.p',unknown),
[] ).
cnf(10,axiom,
r3,
file('LCL493+1.p',unknown),
[] ).
cnf(11,axiom,
r4,
file('LCL493+1.p',unknown),
[] ).
cnf(12,axiom,
r5,
file('LCL493+1.p',unknown),
[] ).
cnf(13,axiom,
substitution_of_equivalents,
file('LCL493+1.p',unknown),
[] ).
cnf(14,axiom,
~ equivalence_1,
file('LCL493+1.p',unknown),
[] ).
cnf(15,axiom,
is_a_theorem(skc56),
file('LCL493+1.p',unknown),
[] ).
cnf(16,axiom,
is_a_theorem(implies__dfg(skc56,skc55)),
file('LCL493+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ and_1
| is_a_theorem(implies__dfg(and__dfg(u,v),u)) ),
file('LCL493+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ is_a_theorem(implies__dfg(and__dfg(skc69,skc68),skc69))
| and_1 ),
file('LCL493+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ or_1
| is_a_theorem(implies__dfg(u,or__dfg(u,v))) ),
file('LCL493+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ is_a_theorem(implies__dfg(skc75,or__dfg(skc75,skc74)))
| or_1 ),
file('LCL493+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ kn1
| is_a_theorem(implies__dfg(u,and__dfg(u,u))) ),
file('LCL493+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ is_a_theorem(implies__dfg(skc87,and__dfg(skc87,skc87)))
| kn1 ),
file('LCL493+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ r1
| is_a_theorem(implies__dfg(or__dfg(u,u),u)) ),
file('LCL493+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ r2
| is_a_theorem(implies__dfg(u,or__dfg(v,u))) ),
file('LCL493+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ cn2
| is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(u),v))) ),
file('LCL493+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ is_a_theorem(implies__dfg(skc97,implies__dfg(not__dfg(skc97),skc96)))
| cn2 ),
file('LCL493+1.p',unknown),
[] ).
cnf(42,axiom,
( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv__dfg(u,v))
| equal(u,v) ),
file('LCL493+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ is_a_theorem(implies__dfg(equiv__dfg(skc82,skc81),implies__dfg(skc82,skc81)))
| equivalence_1 ),
file('LCL493+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ r3
| is_a_theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))) ),
file('LCL493+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ op_implies_or
| equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)) ),
file('LCL493+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ op_implies_and
| equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)) ),
file('LCL493+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ is_a_theorem(u)
| ~ modus_ponens
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL493+1.p',unknown),
[] ).
cnf(58,axiom,
( ~ op_or
| equal(not__dfg(and__dfg(not__dfg(u),not__dfg(v))),or__dfg(u,v)) ),
file('LCL493+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ op_and
| equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and__dfg(u,v)) ),
file('LCL493+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ op_equiv
| equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)) ),
file('LCL493+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('LCL493+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('LCL493+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(implies__dfg(equiv__dfg(skc82,skc81),implies__dfg(skc82,skc81))),
inference(mrr,[status(thm)],[46,14]),
[iquote('0:MRR:46.1,14.0')] ).
cnf(81,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(82,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(83,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(84,plain,
equal(not__dfg(implies__dfg(u,not__dfg(v))),and__dfg(u,v)),
inference(mrr,[status(thm)],[83,5]),
[iquote('0:MRR:83.0,5.0')] ).
cnf(85,plain,
( ~ op_or
| equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)) ),
inference(rew,[status(thm),theory(equality)],[82,58]),
[iquote('0:Rew:82.0,58.1')] ).
cnf(86,plain,
equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)),
inference(mrr,[status(thm)],[85,1]),
[iquote('0:MRR:85.0,1.0')] ).
cnf(87,plain,
( ~ cn2
| is_a_theorem(implies__dfg(u,or__dfg(u,v))) ),
inference(rew,[status(thm),theory(equality)],[86,38]),
[iquote('0:Rew:86.0,38.1')] ).
cnf(88,plain,
( ~ is_a_theorem(implies__dfg(skc97,or__dfg(skc97,skc96)))
| cn2 ),
inference(rew,[status(thm),theory(equality)],[86,39]),
[iquote('0:Rew:86.0,39.0')] ).
cnf(94,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(95,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(96,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(97,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(110,plain,
( ~ cn2
| or_1 ),
inference(res,[status(thm),theory(equality)],[87,27]),
[iquote('0:Res:87.1,27.0')] ).
cnf(114,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(115,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(117,plain,
( ~ or_1
| is_a_theorem(implies__dfg(not__dfg(u),implies__dfg(u,v))) ),
inference(spr,[status(thm),theory(equality)],[78,26]),
[iquote('0:SpR:78.0,26.1')] ).
cnf(121,plain,
( ~ or_1
| is_a_theorem(or__dfg(u,implies__dfg(u,v))) ),
inference(rew,[status(thm),theory(equality)],[86,117]),
[iquote('0:Rew:86.0,117.1')] ).
cnf(122,plain,
is_a_theorem(or__dfg(u,or__dfg(v,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[86,75]),
[iquote('0:SpR:86.0,75.0')] ).
cnf(130,plain,
is_a_theorem(or__dfg(u,implies__dfg(v,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[86,115]),
[iquote('0:SpR:86.0,115.0')] ).
cnf(132,plain,
is_a_theorem(implies__dfg(u,or__dfg(v,not__dfg(not__dfg(u))))),
inference(spr,[status(thm),theory(equality)],[78,122]),
[iquote('0:SpR:78.0,122.0')] ).
cnf(136,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(137,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(155,plain,
equal(implies__dfg(and__dfg(u,not__dfg(v)),w),or__dfg(implies__dfg(u,v),w)),
inference(spr,[status(thm),theory(equality)],[82,78]),
[iquote('0:SpR:82.0,78.0')] ).
cnf(156,plain,
equal(or__dfg(and__dfg(u,not__dfg(v)),w),implies__dfg(implies__dfg(u,v),w)),
inference(spr,[status(thm),theory(equality)],[82,86]),
[iquote('0:SpR:82.0,86.0')] ).
cnf(164,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)],[82]),
[iquote('0:SpR:82.0,82.0')] ).
cnf(173,plain,
equal(implies__dfg(implies__dfg(u,not__dfg(v)),w),or__dfg(and__dfg(u,v),w)),
inference(spr,[status(thm),theory(equality)],[84,78]),
[iquote('0:SpR:84.0,78.0')] ).
cnf(174,plain,
equal(or__dfg(implies__dfg(u,not__dfg(v)),w),implies__dfg(and__dfg(u,v),w)),
inference(spr,[status(thm),theory(equality)],[84,86]),
[iquote('0:SpR:84.0,86.0')] ).
cnf(183,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)],[84]),
[iquote('0:SpR:84.0,84.0')] ).
cnf(186,plain,
equal(not__dfg(or__dfg(u,not__dfg(v))),and__dfg(not__dfg(u),v)),
inference(spr,[status(thm),theory(equality)],[86,84]),
[iquote('0:SpR:86.0,84.0')] ).
cnf(187,plain,
is_a_theorem(or__dfg(and__dfg(u,u),not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[173,114]),
[iquote('0:Rew:173.0,114.0')] ).
cnf(253,plain,
( ~ is_a_theorem(not__dfg(u))
| ~ is_a_theorem(or__dfg(u,v))
| is_a_theorem(v) ),
inference(spl,[status(thm),theory(equality)],[86,94]),
[iquote('0:SpL:86.0,94.1')] ).
cnf(254,plain,
( ~ is_a_theorem(skc56)
| is_a_theorem(skc55) ),
inference(res,[status(thm),theory(equality)],[16,94]),
[iquote('0:Res:16.0,94.1')] ).
cnf(255,plain,
( ~ is_a_theorem(or__dfg(u,u))
| is_a_theorem(u) ),
inference(res,[status(thm),theory(equality)],[76,94]),
[iquote('0:Res:76.0,94.1')] ).
cnf(257,plain,
( ~ is_a_theorem(u)
| is_a_theorem(or__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[75,94]),
[iquote('0:Res:75.0,94.1')] ).
cnf(258,plain,
( ~ is_a_theorem(u)
| is_a_theorem(or__dfg(v,not__dfg(not__dfg(u)))) ),
inference(res,[status(thm),theory(equality)],[132,94]),
[iquote('0:Res:132.0,94.1')] ).
cnf(261,plain,
( ~ is_a_theorem(or__dfg(u,v))
| is_a_theorem(or__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[79,94]),
[iquote('0:Res:79.0,94.1')] ).
cnf(262,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(or__dfg(v,not__dfg(u))) ),
inference(res,[status(thm),theory(equality)],[137,94]),
[iquote('0:Res:137.0,94.1')] ).
cnf(268,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[115,94]),
[iquote('0:Res:115.0,94.1')] ).
cnf(272,plain,
( ~ is_a_theorem(or__dfg(u,not__dfg(v)))
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[136,94]),
[iquote('0:Res:136.0,94.1')] ).
cnf(274,plain,
is_a_theorem(skc55),
inference(ssi,[status(thm)],[254,15]),
[iquote('0:SSi:254.0,15.0')] ).
cnf(288,plain,
( ~ kn1
| is_a_theorem(implies__dfg(implies__dfg(u,u),equiv__dfg(u,u))) ),
inference(spr,[status(thm),theory(equality)],[95,30]),
[iquote('0:SpR:95.0,30.1')] ).
cnf(291,plain,
( ~ and_1
| is_a_theorem(implies__dfg(equiv__dfg(u,v),implies__dfg(u,v))) ),
inference(spr,[status(thm),theory(equality)],[95,22]),
[iquote('0:SpR:95.0,22.1')] ).
cnf(298,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)],[86,95]),
[iquote('0:SpR:86.0,95.0')] ).
cnf(312,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)],[78,97]),
[iquote('0:SpR:78.0,97.0')] ).
cnf(313,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)],[78,97]),
[iquote('0:SpR:78.0,97.0')] ).
cnf(316,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)],[97,94]),
[iquote('0:Res:97.0,94.1')] ).
cnf(317,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)],[78,312]),
[iquote('0:Rew:78.0,312.0')] ).
cnf(318,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)],[78,313]),
[iquote('0:Rew:78.0,313.0')] ).
cnf(325,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)],[86,96]),
[iquote('0:SpR:86.0,96.0')] ).
cnf(326,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)],[96,94]),
[iquote('0:Res:96.0,94.1')] ).
cnf(329,plain,
( ~ is_a_theorem(u)
| is_a_theorem(not__dfg(not__dfg(u))) ),
inference(sor,[status(thm)],[255,258]),
[iquote('0:SoR:255.0,258.1')] ).
cnf(334,plain,
( ~ is_a_theorem(implies__dfg(u,not__dfg(v)))
| is_a_theorem(not__dfg(and__dfg(u,v))) ),
inference(spr,[status(thm),theory(equality)],[84,329]),
[iquote('0:SpR:84.0,329.1')] ).
cnf(356,plain,
( ~ is_a_theorem(u)
| is_a_theorem(or__dfg(u,v)) ),
inference(sor,[status(thm)],[261,257]),
[iquote('0:SoR:261.0,257.1')] ).
cnf(359,plain,
is_a_theorem(or__dfg(not__dfg(u),and__dfg(u,u))),
inference(sor,[status(thm)],[261,187]),
[iquote('0:SoR:261.0,187.0')] ).
cnf(364,plain,
( ~ or_1
| is_a_theorem(or__dfg(implies__dfg(u,v),u)) ),
inference(sor,[status(thm)],[261,121]),
[iquote('0:SoR:261.0,121.1')] ).
cnf(366,plain,
is_a_theorem(or__dfg(implies__dfg(u,not__dfg(v)),v)),
inference(sor,[status(thm)],[261,130]),
[iquote('0:SoR:261.0,130.0')] ).
cnf(369,plain,
is_a_theorem(implies__dfg(u,and__dfg(u,u))),
inference(rew,[status(thm),theory(equality)],[78,359]),
[iquote('0:Rew:78.0,359.0')] ).
cnf(370,plain,
kn1,
inference(mrr,[status(thm)],[31,369]),
[iquote('0:MRR:31.0,369.0')] ).
cnf(374,plain,
is_a_theorem(implies__dfg(implies__dfg(u,u),equiv__dfg(u,u))),
inference(mrr,[status(thm)],[288,370]),
[iquote('0:MRR:288.0,370.0')] ).
cnf(376,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),v)),
inference(rew,[status(thm),theory(equality)],[174,366]),
[iquote('0:Rew:174.0,366.0')] ).
cnf(398,plain,
( ~ is_a_theorem(not__dfg(u))
| is_a_theorem(implies__dfg(u,v)) ),
inference(spr,[status(thm),theory(equality)],[78,356]),
[iquote('0:SpR:78.0,356.1')] ).
cnf(537,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)],[186,86]),
[iquote('0:SpR:186.0,86.0')] ).
cnf(567,plain,
equal(not__dfg(implies__dfg(u,not__dfg(v))),and__dfg(not__dfg(not__dfg(u)),v)),
inference(spr,[status(thm),theory(equality)],[78,186]),
[iquote('0:SpR:78.0,186.0')] ).
cnf(568,plain,
equal(and__dfg(not__dfg(not__dfg(u)),v),and__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[84,567]),
[iquote('0:Rew:84.0,567.0')] ).
cnf(628,plain,
equal(and__dfg(not__dfg(implies__dfg(u,v)),w),and__dfg(and__dfg(u,not__dfg(v)),w)),
inference(spr,[status(thm),theory(equality)],[82,568]),
[iquote('0:SpR:82.0,568.0')] ).
cnf(644,plain,
~ and_1,
inference(res,[status(thm),theory(equality)],[291,80]),
[iquote('0:Res:291.1,80.0')] ).
cnf(646,plain,
~ is_a_theorem(implies__dfg(and__dfg(skc69,skc68),skc69)),
inference(mrr,[status(thm)],[23,644]),
[iquote('0:MRR:23.1,644.0')] ).
cnf(1102,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),not__dfg(not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[156,187]),
[iquote('0:SpR:156.0,187.0')] ).
cnf(1115,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),not__dfg(w)),implies__dfg(w,and__dfg(u,not__dfg(v))))),
inference(spr,[status(thm),theory(equality)],[156,136]),
[iquote('0:SpR:156.0,136.0')] ).
cnf(1135,plain,
is_a_theorem(implies__dfg(or__dfg(u,u),not__dfg(not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[86,1102]),
[iquote('0:Rew:86.0,1102.0')] ).
cnf(1150,plain,
is_a_theorem(or__dfg(and__dfg(implies__dfg(u,v),w),implies__dfg(w,and__dfg(u,not__dfg(v))))),
inference(rew,[status(thm),theory(equality)],[173,1115]),
[iquote('0:Rew:173.0,1115.0')] ).
cnf(1194,plain,
( ~ is_a_theorem(or__dfg(u,u))
| is_a_theorem(not__dfg(not__dfg(u))) ),
inference(res,[status(thm),theory(equality)],[1135,94]),
[iquote('0:Res:1135.0,94.1')] ).
cnf(1412,plain,
( ~ or_1
| is_a_theorem(implies__dfg(and__dfg(u,v),u)) ),
inference(spr,[status(thm),theory(equality)],[174,364]),
[iquote('0:SpR:174.0,364.1')] ).
cnf(1521,plain,
~ or_1,
inference(res,[status(thm),theory(equality)],[1412,646]),
[iquote('0:Res:1412.1,646.0')] ).
cnf(1525,plain,
~ cn2,
inference(mrr,[status(thm)],[110,1521]),
[iquote('0:MRR:110.1,1521.0')] ).
cnf(1529,plain,
~ is_a_theorem(implies__dfg(skc97,or__dfg(skc97,skc96))),
inference(mrr,[status(thm)],[88,1525]),
[iquote('0:MRR:88.1,1525.0')] ).
cnf(1577,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)],[317,94]),
[iquote('0:Res:317.0,94.1')] ).
cnf(1637,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)],[318,94]),
[iquote('0:Res:318.0,94.1')] ).
cnf(1879,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)],[95,164]),
[iquote('0:SpR:95.0,164.0')] ).
cnf(2651,plain,
( ~ is_a_theorem(not__dfg(u))
| is_a_theorem(not__dfg(and__dfg(v,u))) ),
inference(sor,[status(thm)],[334,268]),
[iquote('0:SoR:334.0,268.1')] ).
cnf(2739,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)],[78,298]),
[iquote('0:SpR:78.0,298.0')] ).
cnf(2865,plain,
( ~ is_a_theorem(or__dfg(u,v))
| is_a_theorem(or__dfg(u,or__dfg(w,v))) ),
inference(sor,[status(thm)],[316,257]),
[iquote('0:SoR:316.0,257.1')] ).
cnf(2869,plain,
is_a_theorem(or__dfg(u,or__dfg(v,not__dfg(v)))),
inference(sor,[status(thm)],[316,122]),
[iquote('0:SoR:316.0,122.0')] ).
cnf(2873,plain,
is_a_theorem(or__dfg(u,not__dfg(u))),
inference(sor,[status(thm)],[255,2869]),
[iquote('0:SoR:255.0,2869.0')] ).
cnf(2874,plain,
is_a_theorem(or__dfg(or__dfg(u,not__dfg(u)),v)),
inference(sor,[status(thm)],[261,2869]),
[iquote('0:SoR:261.0,2869.0')] ).
cnf(2889,plain,
is_a_theorem(implies__dfg(and__dfg(not__dfg(u),u),v)),
inference(rew,[status(thm),theory(equality)],[537,2874]),
[iquote('0:Rew:537.0,2874.0')] ).
cnf(2897,plain,
is_a_theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[272,2873]),
[iquote('0:SoR:272.0,2873.0')] ).
cnf(3045,plain,
is_a_theorem(implies__dfg(and__dfg(u,not__dfg(u)),v)),
inference(spr,[status(thm),theory(equality)],[568,2889]),
[iquote('0:SpR:568.0,2889.0')] ).
cnf(3048,plain,
is_a_theorem(or__dfg(implies__dfg(u,u),v)),
inference(rew,[status(thm),theory(equality)],[155,3045]),
[iquote('0:Rew:155.0,3045.0')] ).
cnf(3058,plain,
is_a_theorem(implies__dfg(or__dfg(u,implies__dfg(v,v)),or__dfg(u,equiv__dfg(v,v)))),
inference(sor,[status(thm)],[326,374]),
[iquote('0:SoR:326.0,374.0')] ).
cnf(3110,plain,
is_a_theorem(implies__dfg(or__dfg(u,skc56),or__dfg(u,skc55))),
inference(sor,[status(thm)],[326,16]),
[iquote('0:SoR:326.0,16.0')] ).
cnf(3115,plain,
is_a_theorem(or__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[261,3048]),
[iquote('0:SoR:261.0,3048.0')] ).
cnf(3297,plain,
( ~ is_a_theorem(or__dfg(u,skc56))
| is_a_theorem(or__dfg(u,skc55)) ),
inference(res,[status(thm),theory(equality)],[3110,94]),
[iquote('0:Res:3110.0,94.1')] ).
cnf(3300,plain,
is_a_theorem(or__dfg(u,skc55)),
inference(ssi,[status(thm)],[3297,257,15]),
[iquote('0:SSi:3297.0,257.0,15.1')] ).
cnf(3306,plain,
is_a_theorem(not__dfg(not__dfg(skc55))),
inference(sor,[status(thm)],[1194,3300]),
[iquote('0:SoR:1194.0,3300.0')] ).
cnf(3308,plain,
is_a_theorem(or__dfg(skc55,u)),
inference(sor,[status(thm)],[261,3300]),
[iquote('0:SoR:261.0,3300.0')] ).
cnf(3316,plain,
( ~ is_a_theorem(or__dfg(not__dfg(skc55),u))
| is_a_theorem(u) ),
inference(sor,[status(thm)],[253,3306]),
[iquote('0:SoR:253.0,3306.0')] ).
cnf(3321,plain,
( ~ is_a_theorem(implies__dfg(skc55,u))
| is_a_theorem(u) ),
inference(rew,[status(thm),theory(equality)],[78,3316]),
[iquote('0:Rew:78.0,3316.0')] ).
cnf(3348,plain,
is_a_theorem(or__dfg(u,or__dfg(skc55,v))),
inference(sor,[status(thm)],[316,3308]),
[iquote('0:SoR:316.0,3308.0')] ).
cnf(3422,plain,
is_a_theorem(not__dfg(not__dfg(or__dfg(skc55,u)))),
inference(sor,[status(thm)],[1194,3348]),
[iquote('0:SoR:1194.0,3348.0')] ).
cnf(3432,plain,
( ~ is_a_theorem(or__dfg(not__dfg(or__dfg(skc55,u)),v))
| is_a_theorem(v) ),
inference(sor,[status(thm)],[253,3422]),
[iquote('0:SoR:253.0,3422.0')] ).
cnf(3437,plain,
( ~ is_a_theorem(implies__dfg(or__dfg(skc55,u),v))
| is_a_theorem(v) ),
inference(rew,[status(thm),theory(equality)],[78,3432]),
[iquote('0:Rew:78.0,3432.0')] ).
cnf(5108,plain,
is_a_theorem(implies__dfg(or__dfg(u,not__dfg(skc55)),or__dfg(u,v))),
inference(res,[status(thm),theory(equality)],[325,3437]),
[iquote('0:Res:325.0,3437.0')] ).
cnf(5390,plain,
is_a_theorem(implies__dfg(or__dfg(not__dfg(u),not__dfg(skc55)),implies__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[78,5108]),
[iquote('0:SpR:78.0,5108.0')] ).
cnf(5399,plain,
is_a_theorem(or__dfg(and__dfg(u,skc55),implies__dfg(u,v))),
inference(rew,[status(thm),theory(equality)],[173,5390,78]),
[iquote('0:Rew:173.0,5390.0,78.0,5390.0')] ).
cnf(5885,plain,
is_a_theorem(or__dfg(u,or__dfg(v,skc55))),
inference(sor,[status(thm)],[2865,3300]),
[iquote('0:SoR:2865.0,3300.0')] ).
cnf(5906,plain,
is_a_theorem(not__dfg(not__dfg(or__dfg(u,skc55)))),
inference(sor,[status(thm)],[1194,5885]),
[iquote('0:SoR:1194.0,5885.0')] ).
cnf(5909,plain,
is_a_theorem(or__dfg(or__dfg(u,skc55),v)),
inference(sor,[status(thm)],[261,5885]),
[iquote('0:SoR:261.0,5885.0')] ).
cnf(5921,plain,
( ~ is_a_theorem(or__dfg(not__dfg(or__dfg(u,skc55)),v))
| is_a_theorem(v) ),
inference(sor,[status(thm)],[253,5906]),
[iquote('0:SoR:253.0,5906.0')] ).
cnf(5923,plain,
is_a_theorem(not__dfg(not__dfg(implies__dfg(u,skc55)))),
inference(spr,[status(thm),theory(equality)],[78,5906]),
[iquote('0:SpR:78.0,5906.0')] ).
cnf(5928,plain,
( ~ is_a_theorem(implies__dfg(or__dfg(u,skc55),v))
| is_a_theorem(v) ),
inference(rew,[status(thm),theory(equality)],[78,5921]),
[iquote('0:Rew:78.0,5921.0')] ).
cnf(5941,plain,
is_a_theorem(not__dfg(and__dfg(u,not__dfg(implies__dfg(v,skc55))))),
inference(sor,[status(thm)],[2651,5923]),
[iquote('0:SoR:2651.0,5923.0')] ).
cnf(5949,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,skc55))),
inference(rew,[status(thm),theory(equality)],[82,5941]),
[iquote('0:Rew:82.0,5941.0')] ).
cnf(6022,plain,
is_a_theorem(or__dfg(u,or__dfg(or__dfg(v,skc55),w))),
inference(sor,[status(thm)],[316,5909]),
[iquote('0:SoR:316.0,5909.0')] ).
cnf(6752,plain,
is_a_theorem(not__dfg(not__dfg(or__dfg(or__dfg(u,skc55),v)))),
inference(sor,[status(thm)],[1194,6022]),
[iquote('0:SoR:1194.0,6022.0')] ).
cnf(6803,plain,
is_a_theorem(not__dfg(not__dfg(or__dfg(implies__dfg(u,skc55),v)))),
inference(spr,[status(thm),theory(equality)],[78,6752]),
[iquote('0:SpR:78.0,6752.0')] ).
cnf(6829,plain,
is_a_theorem(not__dfg(and__dfg(not__dfg(implies__dfg(u,skc55)),v))),
inference(spr,[status(thm),theory(equality)],[186,6803]),
[iquote('0:SpR:186.0,6803.0')] ).
cnf(6830,plain,
is_a_theorem(not__dfg(and__dfg(and__dfg(u,not__dfg(skc55)),v))),
inference(rew,[status(thm),theory(equality)],[628,6829]),
[iquote('0:Rew:628.0,6829.0')] ).
cnf(6904,plain,
is_a_theorem(implies__dfg(and__dfg(and__dfg(u,not__dfg(skc55)),v),w)),
inference(sor,[status(thm)],[398,6830]),
[iquote('0:SoR:398.0,6830.0')] ).
cnf(6941,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)],[3058,94]),
[iquote('0:Res:3058.0,94.1')] ).
cnf(6944,plain,
is_a_theorem(or__dfg(u,equiv__dfg(v,v))),
inference(ssi,[status(thm)],[6941,3115]),
[iquote('0:SSi:6941.0,3115.0')] ).
cnf(6950,plain,
is_a_theorem(not__dfg(not__dfg(equiv__dfg(u,u)))),
inference(sor,[status(thm)],[1194,6944]),
[iquote('0:SoR:1194.0,6944.0')] ).
cnf(9178,plain,
is_a_theorem(or__dfg(u,implies__dfg(or__dfg(u,v),v))),
inference(sor,[status(thm)],[1577,2897]),
[iquote('0:SoR:1577.0,2897.0')] ).
cnf(9210,plain,
is_a_theorem(or__dfg(u,implies__dfg(or__dfg(u,not__dfg(skc55)),v))),
inference(sor,[status(thm)],[1577,5108]),
[iquote('0:SoR:1577.0,5108.0')] ).
cnf(9230,plain,
is_a_theorem(or__dfg(not__dfg(u),implies__dfg(implies__dfg(u,v),v))),
inference(spr,[status(thm),theory(equality)],[78,9178]),
[iquote('0:SpR:78.0,9178.0')] ).
cnf(9240,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),v))),
inference(rew,[status(thm),theory(equality)],[78,9230]),
[iquote('0:Rew:78.0,9230.0')] ).
cnf(9290,plain,
is_a_theorem(implies__dfg(implies__dfg(skc55,u),u)),
inference(res,[status(thm),theory(equality)],[9240,3321]),
[iquote('0:Res:9240.0,3321.0')] ).
cnf(9324,plain,
is_a_theorem(implies__dfg(u,or__dfg(and__dfg(u,skc55),v))),
inference(sor,[status(thm)],[1637,5399]),
[iquote('0:SoR:1637.0,5399.0')] ).
cnf(9351,plain,
is_a_theorem(or__dfg(u,not__dfg(implies__dfg(skc55,u)))),
inference(sor,[status(thm)],[262,9290]),
[iquote('0:SoR:262.0,9290.0')] ).
cnf(9355,plain,
( ~ is_a_theorem(implies__dfg(skc55,u))
| is_a_theorem(u) ),
inference(res,[status(thm),theory(equality)],[9290,94]),
[iquote('0:Res:9290.0,94.1')] ).
cnf(9360,plain,
is_a_theorem(or__dfg(not__dfg(u),and__dfg(skc55,u))),
inference(spr,[status(thm),theory(equality)],[84,9351]),
[iquote('0:SpR:84.0,9351.0')] ).
cnf(9369,plain,
is_a_theorem(implies__dfg(u,and__dfg(skc55,u))),
inference(rew,[status(thm),theory(equality)],[78,9360]),
[iquote('0:Rew:78.0,9360.0')] ).
cnf(9767,plain,
is_a_theorem(or__dfg(and__dfg(skc55,skc55),u)),
inference(sor,[status(thm)],[9355,9324]),
[iquote('0:SoR:9355.0,9324.0')] ).
cnf(9789,plain,
is_a_theorem(implies__dfg(u,and__dfg(skc55,skc55))),
inference(sor,[status(thm)],[272,9767]),
[iquote('0:SoR:272.0,9767.0')] ).
cnf(9811,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)],[1879,183]),
[iquote('0:SpR:1879.0,183.0')] ).
cnf(9900,plain,
equal(not__dfg(not__dfg(equiv__dfg(u,v))),equiv__dfg(not__dfg(not__dfg(u)),v)),
inference(rew,[status(thm),theory(equality)],[2739,9811]),
[iquote('0:Rew:2739.0,9811.0')] ).
cnf(9903,plain,
is_a_theorem(equiv__dfg(not__dfg(not__dfg(u)),u)),
inference(rew,[status(thm),theory(equality)],[9900,6950]),
[iquote('0:Rew:9900.0,6950.0')] ).
cnf(10101,plain,
equal(not__dfg(not__dfg(u)),u),
inference(res,[status(thm),theory(equality)],[9903,81]),
[iquote('0:Res:9903.0,81.0')] ).
cnf(13522,plain,
is_a_theorem(implies__dfg(implies__dfg(or__dfg(u,skc55),v),v)),
inference(res,[status(thm),theory(equality)],[9240,5928]),
[iquote('0:Res:9240.0,5928.0')] ).
cnf(13787,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,skc55),v),v)),
inference(spr,[status(thm),theory(equality)],[78,13522]),
[iquote('0:SpR:78.0,13522.0')] ).
cnf(13844,plain,
is_a_theorem(implies__dfg(not__dfg(equiv__dfg(u,skc55)),and__dfg(skc55,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[1879,13787]),
[iquote('0:SpR:1879.0,13787.0')] ).
cnf(13848,plain,
is_a_theorem(or__dfg(equiv__dfg(u,skc55),and__dfg(skc55,not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[86,13844]),
[iquote('0:Rew:86.0,13844.0')] ).
cnf(13916,plain,
is_a_theorem(or__dfg(and__dfg(skc55,not__dfg(u)),equiv__dfg(u,skc55))),
inference(sor,[status(thm)],[261,13848]),
[iquote('0:SoR:261.0,13848.0')] ).
cnf(13919,plain,
is_a_theorem(implies__dfg(implies__dfg(skc55,u),equiv__dfg(u,skc55))),
inference(rew,[status(thm),theory(equality)],[156,13916]),
[iquote('0:Rew:156.0,13916.0')] ).
cnf(13929,plain,
( ~ is_a_theorem(implies__dfg(skc55,u))
| is_a_theorem(equiv__dfg(u,skc55)) ),
inference(res,[status(thm),theory(equality)],[13919,94]),
[iquote('0:Res:13919.0,94.1')] ).
cnf(13944,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equiv__dfg(u,skc55)) ),
inference(sor,[status(thm)],[13929,268]),
[iquote('0:SoR:13929.0,268.1')] ).
cnf(13956,plain,
is_a_theorem(equiv__dfg(implies__dfg(u,skc55),skc55)),
inference(sor,[status(thm)],[13929,5949]),
[iquote('0:SoR:13929.0,5949.0')] ).
cnf(13982,plain,
is_a_theorem(equiv__dfg(and__dfg(skc55,skc55),skc55)),
inference(sor,[status(thm)],[13929,9789]),
[iquote('0:SoR:13929.0,9789.0')] ).
cnf(14014,plain,
equal(and__dfg(skc55,skc55),skc55),
inference(res,[status(thm),theory(equality)],[13982,81]),
[iquote('0:Res:13982.0,81.0')] ).
cnf(14210,plain,
equal(implies__dfg(u,skc55),skc55),
inference(res,[status(thm),theory(equality)],[13956,81]),
[iquote('0:Res:13956.0,81.0')] ).
cnf(14369,plain,
equal(and__dfg(implies__dfg(skc55,u),skc55),equiv__dfg(skc55,u)),
inference(spr,[status(thm),theory(equality)],[14210,95]),
[iquote('0:SpR:14210.0,95.0')] ).
cnf(14397,plain,
equal(and__dfg(skc55,implies__dfg(skc55,u)),equiv__dfg(u,skc55)),
inference(spr,[status(thm),theory(equality)],[14210,95]),
[iquote('0:SpR:14210.0,95.0')] ).
cnf(14421,plain,
is_a_theorem(or__dfg(and__dfg(skc55,u),implies__dfg(u,and__dfg(v,not__dfg(skc55))))),
inference(spr,[status(thm),theory(equality)],[14210,1150]),
[iquote('0:SpR:14210.0,1150.0')] ).
cnf(16975,plain,
( ~ is_a_theorem(u)
| equal(u,skc55) ),
inference(res,[status(thm),theory(equality)],[13944,81]),
[iquote('0:Res:13944.1,81.0')] ).
cnf(17076,plain,
equal(implies__dfg(implies__dfg(skc55,u),u),skc55),
inference(ems,[status(thm)],[16975,9290]),
[iquote('0:EmS:16975.0,9290.0')] ).
cnf(17086,plain,
equal(implies__dfg(u,or__dfg(and__dfg(u,skc55),v)),skc55),
inference(ems,[status(thm)],[16975,9324]),
[iquote('0:EmS:16975.0,9324.0')] ).
cnf(17088,plain,
equal(implies__dfg(u,and__dfg(skc55,u)),skc55),
inference(ems,[status(thm)],[16975,9369]),
[iquote('0:EmS:16975.0,9369.0')] ).
cnf(17121,plain,
equal(implies__dfg(u,implies__dfg(v,u)),skc55),
inference(ems,[status(thm)],[16975,115]),
[iquote('0:EmS:16975.0,115.0')] ).
cnf(17127,plain,
equal(implies__dfg(and__dfg(u,v),v),skc55),
inference(ems,[status(thm)],[16975,376]),
[iquote('0:EmS:16975.0,376.0')] ).
cnf(17155,plain,
equal(implies__dfg(u,or__dfg(v,u)),skc55),
inference(ems,[status(thm)],[16975,75]),
[iquote('0:EmS:16975.0,75.0')] ).
cnf(17156,plain,
equal(implies__dfg(or__dfg(u,u),u),skc55),
inference(ems,[status(thm)],[16975,76]),
[iquote('0:EmS:16975.0,76.0')] ).
cnf(17636,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)],[17076,95]),
[iquote('0:SpR:17076.0,95.0')] ).
cnf(17654,plain,
equal(equiv__dfg(u,implies__dfg(skc55,u)),and__dfg(skc55,skc55)),
inference(rew,[status(thm),theory(equality)],[17121,17636]),
[iquote('0:Rew:17121.0,17636.0')] ).
cnf(17655,plain,
equal(equiv__dfg(u,implies__dfg(skc55,u)),skc55),
inference(rew,[status(thm),theory(equality)],[14014,17654]),
[iquote('0:Rew:14014.0,17654.0')] ).
cnf(17666,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)],[17088,95]),
[iquote('0:SpR:17088.0,95.0')] ).
cnf(17681,plain,
equal(equiv__dfg(and__dfg(skc55,u),u),and__dfg(skc55,skc55)),
inference(rew,[status(thm),theory(equality)],[17127,17666]),
[iquote('0:Rew:17127.0,17666.0')] ).
cnf(17682,plain,
equal(equiv__dfg(and__dfg(skc55,u),u),skc55),
inference(rew,[status(thm),theory(equality)],[14014,17681]),
[iquote('0:Rew:14014.0,17681.0')] ).
cnf(17747,plain,
( ~ is_a_theorem(skc55)
| equal(implies__dfg(skc55,u),u) ),
inference(spl,[status(thm),theory(equality)],[17655,81]),
[iquote('0:SpL:17655.0,81.0')] ).
cnf(17748,plain,
equal(implies__dfg(skc55,u),u),
inference(mrr,[status(thm)],[17747,274]),
[iquote('0:MRR:17747.0,274.0')] ).
cnf(17861,plain,
equal(and__dfg(u,skc55),equiv__dfg(skc55,u)),
inference(rew,[status(thm),theory(equality)],[17748,14369]),
[iquote('0:Rew:17748.0,14369.0')] ).
cnf(17862,plain,
equal(and__dfg(skc55,u),equiv__dfg(u,skc55)),
inference(rew,[status(thm),theory(equality)],[17748,14397]),
[iquote('0:Rew:17748.0,14397.0')] ).
cnf(17923,plain,
equal(implies__dfg(u,or__dfg(equiv__dfg(skc55,u),v)),skc55),
inference(rew,[status(thm),theory(equality)],[17861,17086]),
[iquote('0:Rew:17861.0,17086.0')] ).
cnf(17961,plain,
is_a_theorem(or__dfg(equiv__dfg(u,skc55),implies__dfg(u,and__dfg(v,not__dfg(skc55))))),
inference(rew,[status(thm),theory(equality)],[17862,14421]),
[iquote('0:Rew:17862.0,14421.0')] ).
cnf(17967,plain,
equal(equiv__dfg(equiv__dfg(u,skc55),u),skc55),
inference(rew,[status(thm),theory(equality)],[17862,17682]),
[iquote('0:Rew:17862.0,17682.0')] ).
cnf(18082,plain,
equal(or__dfg(and__dfg(skc55,u),v),implies__dfg(not__dfg(u),v)),
inference(spr,[status(thm),theory(equality)],[17748,173]),
[iquote('0:SpR:17748.0,173.0')] ).
cnf(18090,plain,
equal(or__dfg(and__dfg(skc55,u),v),or__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[86,18082]),
[iquote('0:Rew:86.0,18082.0')] ).
cnf(18091,plain,
equal(or__dfg(equiv__dfg(u,skc55),v),or__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[17862,18090]),
[iquote('0:Rew:17862.0,18090.0')] ).
cnf(18104,plain,
is_a_theorem(or__dfg(u,implies__dfg(u,and__dfg(v,not__dfg(skc55))))),
inference(rew,[status(thm),theory(equality)],[18091,17961]),
[iquote('0:Rew:18091.0,17961.0')] ).
cnf(18254,plain,
( ~ is_a_theorem(skc55)
| equal(equiv__dfg(u,skc55),u) ),
inference(spl,[status(thm),theory(equality)],[17967,81]),
[iquote('0:SpL:17967.0,81.0')] ).
cnf(18255,plain,
equal(equiv__dfg(u,skc55),u),
inference(mrr,[status(thm)],[18254,274]),
[iquote('0:MRR:18254.0,274.0')] ).
cnf(18257,plain,
equal(and__dfg(skc55,u),u),
inference(rew,[status(thm),theory(equality)],[18255,17862]),
[iquote('0:Rew:18255.0,17862.0')] ).
cnf(18620,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)],[17156,95]),
[iquote('0:SpR:17156.0,95.0')] ).
cnf(18639,plain,
equal(equiv__dfg(or__dfg(u,u),u),skc55),
inference(rew,[status(thm),theory(equality)],[18257,18620,17155]),
[iquote('0:Rew:18257.0,18620.0,17155.0,18620.0')] ).
cnf(19109,plain,
( ~ is_a_theorem(skc55)
| equal(or__dfg(u,u),u) ),
inference(spl,[status(thm),theory(equality)],[18639,81]),
[iquote('0:SpL:18639.0,81.0')] ).
cnf(19110,plain,
equal(or__dfg(u,u),u),
inference(mrr,[status(thm)],[19109,274]),
[iquote('0:MRR:19109.0,274.0')] ).
cnf(19160,plain,
equal(implies__dfg(u,not__dfg(u)),not__dfg(u)),
inference(spr,[status(thm),theory(equality)],[19110,78]),
[iquote('0:SpR:19110.0,78.0')] ).
cnf(20547,plain,
is_a_theorem(implies__dfg(equiv__dfg(skc55,and__dfg(u,not__dfg(skc55))),v)),
inference(spr,[status(thm),theory(equality)],[17861,6904]),
[iquote('0:SpR:17861.0,6904.0')] ).
cnf(20604,plain,
is_a_theorem(not__dfg(equiv__dfg(skc55,and__dfg(u,not__dfg(skc55))))),
inference(spr,[status(thm),theory(equality)],[19160,20547]),
[iquote('0:SpR:19160.0,20547.0')] ).
cnf(20625,plain,
equal(not__dfg(equiv__dfg(skc55,and__dfg(u,not__dfg(skc55)))),skc55),
inference(ems,[status(thm)],[16975,20604]),
[iquote('0:EmS:16975.0,20604.0')] ).
cnf(20648,plain,
equal(equiv__dfg(skc55,and__dfg(u,not__dfg(skc55))),not__dfg(skc55)),
inference(spr,[status(thm),theory(equality)],[20625,10101]),
[iquote('0:SpR:20625.0,10101.0')] ).
cnf(21118,plain,
is_a_theorem(or__dfg(u,not__dfg(or__dfg(u,not__dfg(skc55))))),
inference(spr,[status(thm),theory(equality)],[19160,9210]),
[iquote('0:SpR:19160.0,9210.0')] ).
cnf(21142,plain,
is_a_theorem(or__dfg(u,equiv__dfg(skc55,not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[17861,21118,186]),
[iquote('0:Rew:17861.0,21118.0,186.0,21118.0')] ).
cnf(21171,plain,
is_a_theorem(or__dfg(not__dfg(u),equiv__dfg(skc55,u))),
inference(spr,[status(thm),theory(equality)],[10101,21142]),
[iquote('0:SpR:10101.0,21142.0')] ).
cnf(21188,plain,
is_a_theorem(implies__dfg(u,equiv__dfg(skc55,u))),
inference(rew,[status(thm),theory(equality)],[78,21171]),
[iquote('0:Rew:78.0,21171.0')] ).
cnf(21201,plain,
equal(implies__dfg(u,equiv__dfg(skc55,u)),skc55),
inference(ems,[status(thm)],[16975,21188]),
[iquote('0:EmS:16975.0,21188.0')] ).
cnf(21209,plain,
is_a_theorem(or__dfg(equiv__dfg(skc55,u),not__dfg(u))),
inference(sor,[status(thm)],[262,21188]),
[iquote('0:SoR:262.0,21188.0')] ).
cnf(21410,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)],[21201,95]),
[iquote('0:SpR:21201.0,95.0')] ).
cnf(21429,plain,
equal(equiv__dfg(u,equiv__dfg(skc55,u)),implies__dfg(equiv__dfg(skc55,u),u)),
inference(rew,[status(thm),theory(equality)],[18257,21410]),
[iquote('0:Rew:18257.0,21410.0')] ).
cnf(21432,plain,
equal(or__dfg(equiv__dfg(skc55,u),not__dfg(u)),skc55),
inference(ems,[status(thm)],[16975,21209]),
[iquote('0:EmS:16975.0,21209.0')] ).
cnf(21695,plain,
equal(and__dfg(not__dfg(equiv__dfg(skc55,u)),u),not__dfg(skc55)),
inference(spr,[status(thm),theory(equality)],[21432,186]),
[iquote('0:SpR:21432.0,186.0')] ).
cnf(22101,plain,
equal(and__dfg(not__dfg(not__dfg(skc55)),and__dfg(u,not__dfg(skc55))),not__dfg(skc55)),
inference(spr,[status(thm),theory(equality)],[20648,21695]),
[iquote('0:SpR:20648.0,21695.0')] ).
cnf(22104,plain,
equal(and__dfg(u,not__dfg(skc55)),not__dfg(skc55)),
inference(rew,[status(thm),theory(equality)],[18257,22101,10101]),
[iquote('0:Rew:18257.0,22101.0,10101.0,22101.0')] ).
cnf(22109,plain,
is_a_theorem(or__dfg(u,implies__dfg(u,not__dfg(skc55)))),
inference(rew,[status(thm),theory(equality)],[22104,18104]),
[iquote('0:Rew:22104.0,18104.0')] ).
cnf(22228,plain,
is_a_theorem(or__dfg(implies__dfg(u,not__dfg(skc55)),u)),
inference(sor,[status(thm)],[261,22109]),
[iquote('0:SoR:261.0,22109.0')] ).
cnf(22252,plain,
is_a_theorem(implies__dfg(equiv__dfg(skc55,u),u)),
inference(rew,[status(thm),theory(equality)],[17861,22228,174]),
[iquote('0:Rew:17861.0,22228.0,174.0,22228.0')] ).
cnf(22275,plain,
equal(implies__dfg(equiv__dfg(skc55,u),u),skc55),
inference(ems,[status(thm)],[16975,22252]),
[iquote('0:EmS:16975.0,22252.0')] ).
cnf(22297,plain,
equal(equiv__dfg(u,equiv__dfg(skc55,u)),skc55),
inference(rew,[status(thm),theory(equality)],[22275,21429]),
[iquote('0:Rew:22275.0,21429.0')] ).
cnf(22477,plain,
( ~ is_a_theorem(skc55)
| equal(equiv__dfg(skc55,u),u) ),
inference(spl,[status(thm),theory(equality)],[22297,81]),
[iquote('0:SpL:22297.0,81.0')] ).
cnf(22478,plain,
equal(equiv__dfg(skc55,u),u),
inference(mrr,[status(thm)],[22477,274]),
[iquote('0:MRR:22477.0,274.0')] ).
cnf(22541,plain,
equal(implies__dfg(u,or__dfg(u,v)),skc55),
inference(rew,[status(thm),theory(equality)],[22478,17923]),
[iquote('0:Rew:22478.0,17923.0')] ).
cnf(22578,plain,
~ is_a_theorem(skc55),
inference(rew,[status(thm),theory(equality)],[22541,1529]),
[iquote('0:Rew:22541.0,1529.0')] ).
cnf(22582,plain,
$false,
inference(mrr,[status(thm)],[22578,274]),
[iquote('0:MRR:22578.0,274.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL493+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.11/0.33 % Computer : n024.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sat Jul 2 15:20:30 EDT 2022
% 0.11/0.33 % CPUTime :
% 4.99/5.17
% 4.99/5.17 SPASS V 3.9
% 4.99/5.17 SPASS beiseite: Proof found.
% 4.99/5.17 % SZS status Theorem
% 4.99/5.17 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.99/5.17 SPASS derived 15513 clauses, backtracked 0 clauses, performed 0 splits and kept 5216 clauses.
% 4.99/5.17 SPASS allocated 119952 KBytes.
% 4.99/5.17 SPASS spent 0:00:04.82 on the problem.
% 4.99/5.17 0:00:00.04 for the input.
% 4.99/5.17 0:00:00.04 for the FLOTTER CNF translation.
% 4.99/5.17 0:00:00.16 for inferences.
% 4.99/5.17 0:00:00.00 for the backtracking.
% 4.99/5.17 0:00:04.49 for the reduction.
% 4.99/5.17
% 4.99/5.17
% 4.99/5.17 Here is a proof with depth 23, length 253 :
% 4.99/5.17 % SZS output start Refutation
% See solution above
% 5.23/5.41 Formulae used in the proof : hilbert_op_or hilbert_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 hilbert_equivalence_1 modus_ponens r2 and_1 or_1 kn1 r1 cn2 equivalence_1 r3 op_implies_or op_implies_and op_or op_and op_equiv r4 r5
% 5.23/5.41
%------------------------------------------------------------------------------