TSTP Solution File: LCL490+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL490+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 14:37:20 EDT 2022
% Result : Theorem 5.27s 5.46s
% Output : Refutation 5.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 30
% Syntax : Number of clauses : 234 ( 178 unt; 0 nHn; 234 RR)
% Number of literals : 295 ( 0 equ; 64 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 17 ( 16 usr; 15 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
op_or,
file('LCL490+1.p',unknown),
[] ).
cnf(2,axiom,
op_implies_and,
file('LCL490+1.p',unknown),
[] ).
cnf(4,axiom,
op_implies_or,
file('LCL490+1.p',unknown),
[] ).
cnf(5,axiom,
op_and,
file('LCL490+1.p',unknown),
[] ).
cnf(6,axiom,
op_equiv,
file('LCL490+1.p',unknown),
[] ).
cnf(7,axiom,
modus_ponens,
file('LCL490+1.p',unknown),
[] ).
cnf(8,axiom,
r1,
file('LCL490+1.p',unknown),
[] ).
cnf(9,axiom,
r2,
file('LCL490+1.p',unknown),
[] ).
cnf(10,axiom,
r3,
file('LCL490+1.p',unknown),
[] ).
cnf(11,axiom,
r4,
file('LCL490+1.p',unknown),
[] ).
cnf(12,axiom,
r5,
file('LCL490+1.p',unknown),
[] ).
cnf(13,axiom,
substitution_of_equivalents,
file('LCL490+1.p',unknown),
[] ).
cnf(14,axiom,
~ or_1,
file('LCL490+1.p',unknown),
[] ).
cnf(15,axiom,
is_a_theorem(skc56),
file('LCL490+1.p',unknown),
[] ).
cnf(16,axiom,
is_a_theorem(implies__dfg(skc56,skc55)),
file('LCL490+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ is_a_theorem(implies__dfg(skc75,or__dfg(skc75,skc74)))
| or_1 ),
file('LCL490+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ kn1
| is_a_theorem(implies__dfg(u,and__dfg(u,u))) ),
file('LCL490+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ is_a_theorem(implies__dfg(skc87,and__dfg(skc87,skc87)))
| kn1 ),
file('LCL490+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ r1
| is_a_theorem(implies__dfg(or__dfg(u,u),u)) ),
file('LCL490+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ r2
| is_a_theorem(implies__dfg(u,or__dfg(v,u))) ),
file('LCL490+1.p',unknown),
[] ).
cnf(42,axiom,
( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv__dfg(u,v))
| equal(u,v) ),
file('LCL490+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ r3
| is_a_theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))) ),
file('LCL490+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ op_implies_or
| equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)) ),
file('LCL490+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ op_implies_and
| equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)) ),
file('LCL490+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ is_a_theorem(u)
| ~ modus_ponens
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL490+1.p',unknown),
[] ).
cnf(58,axiom,
( ~ op_or
| equal(not__dfg(and__dfg(not__dfg(u),not__dfg(v))),or__dfg(u,v)) ),
file('LCL490+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ op_and
| equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and__dfg(u,v)) ),
file('LCL490+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ op_equiv
| equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)) ),
file('LCL490+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('LCL490+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('LCL490+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,
~ is_a_theorem(implies__dfg(skc75,or__dfg(skc75,skc74))),
inference(mrr,[status(thm)],[27,14]),
[iquote('0:MRR:27.1,14.0')] ).
cnf(79,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(80,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(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)],[79,59]),
[iquote('0:Rew:79.0,59.1')] ).
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(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(111,plain,
is_a_theorem(implies__dfg(implies__dfg(u,not__dfg(u)),not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[79,76]),
[iquote('0:SpR:79.0,76.0')] ).
cnf(112,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
inference(spr,[status(thm),theory(equality)],[79,75]),
[iquote('0:SpR:79.0,75.0')] ).
cnf(116,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(118,plain,
is_a_theorem(or__dfg(u,implies__dfg(v,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[86,112]),
[iquote('0:SpR:86.0,112.0')] ).
cnf(121,plain,
is_a_theorem(implies__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,u))),
inference(spr,[status(thm),theory(equality)],[79,80]),
[iquote('0:SpR:79.0,80.0')] ).
cnf(122,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),or__dfg(v,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[79,80]),
[iquote('0:SpR:79.0,80.0')] ).
cnf(125,plain,
is_a_theorem(implies__dfg(u,or__dfg(v,not__dfg(not__dfg(u))))),
inference(spr,[status(thm),theory(equality)],[79,116]),
[iquote('0:SpR:79.0,116.0')] ).
cnf(136,plain,
equal(implies__dfg(and__dfg(u,not__dfg(v)),w),or__dfg(implies__dfg(u,v),w)),
inference(spr,[status(thm),theory(equality)],[82,79]),
[iquote('0:SpR:82.0,79.0')] ).
cnf(138,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(145,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(154,plain,
equal(implies__dfg(implies__dfg(u,not__dfg(v)),w),or__dfg(and__dfg(u,v),w)),
inference(spr,[status(thm),theory(equality)],[84,79]),
[iquote('0:SpR:84.0,79.0')] ).
cnf(156,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(164,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(167,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(168,plain,
is_a_theorem(or__dfg(and__dfg(u,u),not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[154,111]),
[iquote('0:Rew:154.0,111.0')] ).
cnf(236,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(237,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(238,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(240,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(241,plain,
( ~ is_a_theorem(or__dfg(u,v))
| is_a_theorem(or__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[80,94]),
[iquote('0:Res:80.0,94.1')] ).
cnf(242,plain,
( ~ is_a_theorem(u)
| is_a_theorem(or__dfg(v,not__dfg(not__dfg(u)))) ),
inference(res,[status(thm),theory(equality)],[125,94]),
[iquote('0:Res:125.0,94.1')] ).
cnf(244,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(or__dfg(v,not__dfg(u))) ),
inference(res,[status(thm),theory(equality)],[122,94]),
[iquote('0:Res:122.0,94.1')] ).
cnf(249,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[112,94]),
[iquote('0:Res:112.0,94.1')] ).
cnf(253,plain,
( ~ is_a_theorem(or__dfg(u,not__dfg(v)))
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[121,94]),
[iquote('0:Res:121.0,94.1')] ).
cnf(256,plain,
is_a_theorem(skc55),
inference(ssi,[status(thm)],[237,15]),
[iquote('0:SSi:237.0,15.0')] ).
cnf(259,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(269,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(294,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)],[79,97]),
[iquote('0:SpR:79.0,97.0')] ).
cnf(295,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)],[79,97]),
[iquote('0:SpR:79.0,97.0')] ).
cnf(298,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(299,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)],[79,294]),
[iquote('0:Rew:79.0,294.0')] ).
cnf(300,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)],[79,295]),
[iquote('0:Rew:79.0,295.0')] ).
cnf(307,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(308,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(311,plain,
( ~ is_a_theorem(u)
| is_a_theorem(not__dfg(not__dfg(u))) ),
inference(sor,[status(thm)],[238,242]),
[iquote('0:SoR:238.0,242.1')] ).
cnf(316,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)],[84,311]),
[iquote('0:SpR:84.0,311.1')] ).
cnf(330,plain,
( ~ is_a_theorem(u)
| is_a_theorem(or__dfg(u,v)) ),
inference(sor,[status(thm)],[241,240]),
[iquote('0:SoR:241.0,240.1')] ).
cnf(333,plain,
is_a_theorem(or__dfg(not__dfg(u),and__dfg(u,u))),
inference(sor,[status(thm)],[241,168]),
[iquote('0:SoR:241.0,168.0')] ).
cnf(336,plain,
is_a_theorem(or__dfg(implies__dfg(u,not__dfg(v)),v)),
inference(sor,[status(thm)],[241,118]),
[iquote('0:SoR:241.0,118.0')] ).
cnf(339,plain,
is_a_theorem(implies__dfg(u,and__dfg(u,u))),
inference(rew,[status(thm),theory(equality)],[79,333]),
[iquote('0:Rew:79.0,333.0')] ).
cnf(340,plain,
kn1,
inference(mrr,[status(thm)],[31,339]),
[iquote('0:MRR:31.0,339.0')] ).
cnf(344,plain,
is_a_theorem(implies__dfg(implies__dfg(u,u),equiv__dfg(u,u))),
inference(mrr,[status(thm)],[259,340]),
[iquote('0:MRR:259.0,340.0')] ).
cnf(346,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),v)),
inference(rew,[status(thm),theory(equality)],[156,336]),
[iquote('0:Rew:156.0,336.0')] ).
cnf(369,plain,
( ~ is_a_theorem(not__dfg(u))
| is_a_theorem(implies__dfg(u,v)) ),
inference(spr,[status(thm),theory(equality)],[79,330]),
[iquote('0:SpR:79.0,330.1')] ).
cnf(489,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)],[167,86]),
[iquote('0:SpR:167.0,86.0')] ).
cnf(517,plain,
equal(not__dfg(implies__dfg(u,not__dfg(v))),and__dfg(not__dfg(not__dfg(u)),v)),
inference(spr,[status(thm),theory(equality)],[79,167]),
[iquote('0:SpR:79.0,167.0')] ).
cnf(518,plain,
equal(and__dfg(not__dfg(not__dfg(u)),v),and__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[84,517]),
[iquote('0:Rew:84.0,517.0')] ).
cnf(576,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)],[82,518]),
[iquote('0:SpR:82.0,518.0')] ).
cnf(1111,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),not__dfg(not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[138,168]),
[iquote('0:SpR:138.0,168.0')] ).
cnf(1123,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)],[138,121]),
[iquote('0:SpR:138.0,121.0')] ).
cnf(1144,plain,
is_a_theorem(implies__dfg(or__dfg(u,u),not__dfg(not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[86,1111]),
[iquote('0:Rew:86.0,1111.0')] ).
cnf(1153,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)],[154,1123]),
[iquote('0:Rew:154.0,1123.0')] ).
cnf(1202,plain,
( ~ is_a_theorem(or__dfg(u,u))
| is_a_theorem(not__dfg(not__dfg(u))) ),
inference(res,[status(thm),theory(equality)],[1144,94]),
[iquote('0:Res:1144.0,94.1')] ).
cnf(1560,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)],[299,94]),
[iquote('0:Res:299.0,94.1')] ).
cnf(1626,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)],[300,94]),
[iquote('0:Res:300.0,94.1')] ).
cnf(1856,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)],[95,145]),
[iquote('0:SpR:95.0,145.0')] ).
cnf(2392,plain,
( ~ is_a_theorem(not__dfg(u))
| is_a_theorem(not__dfg(and__dfg(v,u))) ),
inference(sor,[status(thm)],[316,249]),
[iquote('0:SoR:316.0,249.1')] ).
cnf(2818,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)],[79,269]),
[iquote('0:SpR:79.0,269.0')] ).
cnf(2889,plain,
( ~ is_a_theorem(or__dfg(u,v))
| is_a_theorem(or__dfg(u,or__dfg(w,v))) ),
inference(sor,[status(thm)],[298,240]),
[iquote('0:SoR:298.0,240.1')] ).
cnf(2893,plain,
is_a_theorem(or__dfg(u,or__dfg(v,not__dfg(v)))),
inference(sor,[status(thm)],[298,116]),
[iquote('0:SoR:298.0,116.0')] ).
cnf(2897,plain,
is_a_theorem(or__dfg(u,not__dfg(u))),
inference(sor,[status(thm)],[238,2893]),
[iquote('0:SoR:238.0,2893.0')] ).
cnf(2898,plain,
is_a_theorem(or__dfg(or__dfg(u,not__dfg(u)),v)),
inference(sor,[status(thm)],[241,2893]),
[iquote('0:SoR:241.0,2893.0')] ).
cnf(2913,plain,
is_a_theorem(implies__dfg(and__dfg(not__dfg(u),u),v)),
inference(rew,[status(thm),theory(equality)],[489,2898]),
[iquote('0:Rew:489.0,2898.0')] ).
cnf(2921,plain,
is_a_theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[253,2897]),
[iquote('0:SoR:253.0,2897.0')] ).
cnf(3070,plain,
is_a_theorem(implies__dfg(and__dfg(u,not__dfg(u)),v)),
inference(spr,[status(thm),theory(equality)],[518,2913]),
[iquote('0:SpR:518.0,2913.0')] ).
cnf(3073,plain,
is_a_theorem(or__dfg(implies__dfg(u,u),v)),
inference(rew,[status(thm),theory(equality)],[136,3070]),
[iquote('0:Rew:136.0,3070.0')] ).
cnf(3083,plain,
is_a_theorem(implies__dfg(or__dfg(u,implies__dfg(v,v)),or__dfg(u,equiv__dfg(v,v)))),
inference(sor,[status(thm)],[308,344]),
[iquote('0:SoR:308.0,344.0')] ).
cnf(3138,plain,
is_a_theorem(implies__dfg(or__dfg(u,skc56),or__dfg(u,skc55))),
inference(sor,[status(thm)],[308,16]),
[iquote('0:SoR:308.0,16.0')] ).
cnf(3143,plain,
is_a_theorem(or__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[241,3073]),
[iquote('0:SoR:241.0,3073.0')] ).
cnf(3326,plain,
( ~ is_a_theorem(or__dfg(u,skc56))
| is_a_theorem(or__dfg(u,skc55)) ),
inference(res,[status(thm),theory(equality)],[3138,94]),
[iquote('0:Res:3138.0,94.1')] ).
cnf(3329,plain,
is_a_theorem(or__dfg(u,skc55)),
inference(ssi,[status(thm)],[3326,240,15]),
[iquote('0:SSi:3326.0,240.0,15.1')] ).
cnf(3335,plain,
is_a_theorem(not__dfg(not__dfg(skc55))),
inference(sor,[status(thm)],[1202,3329]),
[iquote('0:SoR:1202.0,3329.0')] ).
cnf(3337,plain,
is_a_theorem(or__dfg(skc55,u)),
inference(sor,[status(thm)],[241,3329]),
[iquote('0:SoR:241.0,3329.0')] ).
cnf(3345,plain,
( ~ is_a_theorem(or__dfg(not__dfg(skc55),u))
| is_a_theorem(u) ),
inference(sor,[status(thm)],[236,3335]),
[iquote('0:SoR:236.0,3335.0')] ).
cnf(3350,plain,
( ~ is_a_theorem(implies__dfg(skc55,u))
| is_a_theorem(u) ),
inference(rew,[status(thm),theory(equality)],[79,3345]),
[iquote('0:Rew:79.0,3345.0')] ).
cnf(3377,plain,
is_a_theorem(or__dfg(u,or__dfg(skc55,v))),
inference(sor,[status(thm)],[298,3337]),
[iquote('0:SoR:298.0,3337.0')] ).
cnf(3453,plain,
is_a_theorem(not__dfg(not__dfg(or__dfg(skc55,u)))),
inference(sor,[status(thm)],[1202,3377]),
[iquote('0:SoR:1202.0,3377.0')] ).
cnf(3463,plain,
( ~ is_a_theorem(or__dfg(not__dfg(or__dfg(skc55,u)),v))
| is_a_theorem(v) ),
inference(sor,[status(thm)],[236,3453]),
[iquote('0:SoR:236.0,3453.0')] ).
cnf(3468,plain,
( ~ is_a_theorem(implies__dfg(or__dfg(skc55,u),v))
| is_a_theorem(v) ),
inference(rew,[status(thm),theory(equality)],[79,3463]),
[iquote('0:Rew:79.0,3463.0')] ).
cnf(5142,plain,
is_a_theorem(implies__dfg(or__dfg(u,not__dfg(skc55)),or__dfg(u,v))),
inference(res,[status(thm),theory(equality)],[307,3468]),
[iquote('0:Res:307.0,3468.0')] ).
cnf(5377,plain,
is_a_theorem(implies__dfg(or__dfg(not__dfg(u),not__dfg(skc55)),implies__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[79,5142]),
[iquote('0:SpR:79.0,5142.0')] ).
cnf(5386,plain,
is_a_theorem(or__dfg(and__dfg(u,skc55),implies__dfg(u,v))),
inference(rew,[status(thm),theory(equality)],[154,5377,79]),
[iquote('0:Rew:154.0,5377.0,79.0,5377.0')] ).
cnf(5968,plain,
is_a_theorem(or__dfg(u,or__dfg(v,skc55))),
inference(sor,[status(thm)],[2889,3329]),
[iquote('0:SoR:2889.0,3329.0')] ).
cnf(5988,plain,
is_a_theorem(not__dfg(not__dfg(or__dfg(u,skc55)))),
inference(sor,[status(thm)],[1202,5968]),
[iquote('0:SoR:1202.0,5968.0')] ).
cnf(5991,plain,
is_a_theorem(or__dfg(or__dfg(u,skc55),v)),
inference(sor,[status(thm)],[241,5968]),
[iquote('0:SoR:241.0,5968.0')] ).
cnf(6004,plain,
( ~ is_a_theorem(or__dfg(not__dfg(or__dfg(u,skc55)),v))
| is_a_theorem(v) ),
inference(sor,[status(thm)],[236,5988]),
[iquote('0:SoR:236.0,5988.0')] ).
cnf(6006,plain,
is_a_theorem(not__dfg(not__dfg(implies__dfg(u,skc55)))),
inference(spr,[status(thm),theory(equality)],[79,5988]),
[iquote('0:SpR:79.0,5988.0')] ).
cnf(6012,plain,
( ~ is_a_theorem(implies__dfg(or__dfg(u,skc55),v))
| is_a_theorem(v) ),
inference(rew,[status(thm),theory(equality)],[79,6004]),
[iquote('0:Rew:79.0,6004.0')] ).
cnf(6026,plain,
is_a_theorem(not__dfg(and__dfg(u,not__dfg(implies__dfg(v,skc55))))),
inference(sor,[status(thm)],[2392,6006]),
[iquote('0:SoR:2392.0,6006.0')] ).
cnf(6035,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,skc55))),
inference(rew,[status(thm),theory(equality)],[82,6026]),
[iquote('0:Rew:82.0,6026.0')] ).
cnf(6088,plain,
is_a_theorem(or__dfg(u,or__dfg(or__dfg(v,skc55),w))),
inference(sor,[status(thm)],[298,5991]),
[iquote('0:SoR:298.0,5991.0')] ).
cnf(6975,plain,
is_a_theorem(not__dfg(not__dfg(or__dfg(or__dfg(u,skc55),v)))),
inference(sor,[status(thm)],[1202,6088]),
[iquote('0:SoR:1202.0,6088.0')] ).
cnf(6993,plain,
is_a_theorem(not__dfg(not__dfg(or__dfg(implies__dfg(u,skc55),v)))),
inference(spr,[status(thm),theory(equality)],[79,6975]),
[iquote('0:SpR:79.0,6975.0')] ).
cnf(7055,plain,
is_a_theorem(not__dfg(and__dfg(not__dfg(implies__dfg(u,skc55)),v))),
inference(spr,[status(thm),theory(equality)],[167,6993]),
[iquote('0:SpR:167.0,6993.0')] ).
cnf(7056,plain,
is_a_theorem(not__dfg(and__dfg(and__dfg(u,not__dfg(skc55)),v))),
inference(rew,[status(thm),theory(equality)],[576,7055]),
[iquote('0:Rew:576.0,7055.0')] ).
cnf(7134,plain,
is_a_theorem(implies__dfg(and__dfg(and__dfg(u,not__dfg(skc55)),v),w)),
inference(sor,[status(thm)],[369,7056]),
[iquote('0:SoR:369.0,7056.0')] ).
cnf(7199,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)],[3083,94]),
[iquote('0:Res:3083.0,94.1')] ).
cnf(7202,plain,
is_a_theorem(or__dfg(u,equiv__dfg(v,v))),
inference(ssi,[status(thm)],[7199,3143]),
[iquote('0:SSi:7199.0,3143.0')] ).
cnf(7208,plain,
is_a_theorem(not__dfg(not__dfg(equiv__dfg(u,u)))),
inference(sor,[status(thm)],[1202,7202]),
[iquote('0:SoR:1202.0,7202.0')] ).
cnf(9413,plain,
is_a_theorem(or__dfg(u,implies__dfg(or__dfg(u,v),v))),
inference(sor,[status(thm)],[1560,2921]),
[iquote('0:SoR:1560.0,2921.0')] ).
cnf(9444,plain,
is_a_theorem(or__dfg(u,implies__dfg(or__dfg(u,not__dfg(skc55)),v))),
inference(sor,[status(thm)],[1560,5142]),
[iquote('0:SoR:1560.0,5142.0')] ).
cnf(9466,plain,
is_a_theorem(or__dfg(not__dfg(u),implies__dfg(implies__dfg(u,v),v))),
inference(spr,[status(thm),theory(equality)],[79,9413]),
[iquote('0:SpR:79.0,9413.0')] ).
cnf(9476,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),v))),
inference(rew,[status(thm),theory(equality)],[79,9466]),
[iquote('0:Rew:79.0,9466.0')] ).
cnf(9526,plain,
is_a_theorem(implies__dfg(implies__dfg(skc55,u),u)),
inference(res,[status(thm),theory(equality)],[9476,3350]),
[iquote('0:Res:9476.0,3350.0')] ).
cnf(9560,plain,
is_a_theorem(implies__dfg(u,or__dfg(and__dfg(u,skc55),v))),
inference(sor,[status(thm)],[1626,5386]),
[iquote('0:SoR:1626.0,5386.0')] ).
cnf(9588,plain,
is_a_theorem(or__dfg(u,not__dfg(implies__dfg(skc55,u)))),
inference(sor,[status(thm)],[244,9526]),
[iquote('0:SoR:244.0,9526.0')] ).
cnf(9592,plain,
( ~ is_a_theorem(implies__dfg(skc55,u))
| is_a_theorem(u) ),
inference(res,[status(thm),theory(equality)],[9526,94]),
[iquote('0:Res:9526.0,94.1')] ).
cnf(9597,plain,
is_a_theorem(or__dfg(not__dfg(u),and__dfg(skc55,u))),
inference(spr,[status(thm),theory(equality)],[84,9588]),
[iquote('0:SpR:84.0,9588.0')] ).
cnf(9606,plain,
is_a_theorem(implies__dfg(u,and__dfg(skc55,u))),
inference(rew,[status(thm),theory(equality)],[79,9597]),
[iquote('0:Rew:79.0,9597.0')] ).
cnf(10009,plain,
is_a_theorem(or__dfg(and__dfg(skc55,skc55),u)),
inference(sor,[status(thm)],[9592,9560]),
[iquote('0:SoR:9592.0,9560.0')] ).
cnf(10031,plain,
is_a_theorem(implies__dfg(u,and__dfg(skc55,skc55))),
inference(sor,[status(thm)],[253,10009]),
[iquote('0:SoR:253.0,10009.0')] ).
cnf(10089,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)],[1856,164]),
[iquote('0:SpR:1856.0,164.0')] ).
cnf(10150,plain,
equal(not__dfg(not__dfg(equiv__dfg(u,v))),equiv__dfg(not__dfg(not__dfg(u)),v)),
inference(rew,[status(thm),theory(equality)],[2818,10089]),
[iquote('0:Rew:2818.0,10089.0')] ).
cnf(10153,plain,
is_a_theorem(equiv__dfg(not__dfg(not__dfg(u)),u)),
inference(rew,[status(thm),theory(equality)],[10150,7208]),
[iquote('0:Rew:10150.0,7208.0')] ).
cnf(10349,plain,
equal(not__dfg(not__dfg(u)),u),
inference(res,[status(thm),theory(equality)],[10153,81]),
[iquote('0:Res:10153.0,81.0')] ).
cnf(13825,plain,
is_a_theorem(implies__dfg(implies__dfg(or__dfg(u,skc55),v),v)),
inference(res,[status(thm),theory(equality)],[9476,6012]),
[iquote('0:Res:9476.0,6012.0')] ).
cnf(14101,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,skc55),v),v)),
inference(spr,[status(thm),theory(equality)],[79,13825]),
[iquote('0:SpR:79.0,13825.0')] ).
cnf(14124,plain,
is_a_theorem(implies__dfg(not__dfg(equiv__dfg(u,skc55)),and__dfg(skc55,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[1856,14101]),
[iquote('0:SpR:1856.0,14101.0')] ).
cnf(14128,plain,
is_a_theorem(or__dfg(equiv__dfg(u,skc55),and__dfg(skc55,not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[86,14124]),
[iquote('0:Rew:86.0,14124.0')] ).
cnf(14192,plain,
is_a_theorem(or__dfg(and__dfg(skc55,not__dfg(u)),equiv__dfg(u,skc55))),
inference(sor,[status(thm)],[241,14128]),
[iquote('0:SoR:241.0,14128.0')] ).
cnf(14195,plain,
is_a_theorem(implies__dfg(implies__dfg(skc55,u),equiv__dfg(u,skc55))),
inference(rew,[status(thm),theory(equality)],[138,14192]),
[iquote('0:Rew:138.0,14192.0')] ).
cnf(14239,plain,
( ~ is_a_theorem(implies__dfg(skc55,u))
| is_a_theorem(equiv__dfg(u,skc55)) ),
inference(res,[status(thm),theory(equality)],[14195,94]),
[iquote('0:Res:14195.0,94.1')] ).
cnf(14254,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equiv__dfg(u,skc55)) ),
inference(sor,[status(thm)],[14239,249]),
[iquote('0:SoR:14239.0,249.1')] ).
cnf(14266,plain,
is_a_theorem(equiv__dfg(implies__dfg(u,skc55),skc55)),
inference(sor,[status(thm)],[14239,6035]),
[iquote('0:SoR:14239.0,6035.0')] ).
cnf(14292,plain,
is_a_theorem(equiv__dfg(and__dfg(skc55,skc55),skc55)),
inference(sor,[status(thm)],[14239,10031]),
[iquote('0:SoR:14239.0,10031.0')] ).
cnf(14302,plain,
equal(and__dfg(skc55,skc55),skc55),
inference(res,[status(thm),theory(equality)],[14292,81]),
[iquote('0:Res:14292.0,81.0')] ).
cnf(14531,plain,
equal(implies__dfg(u,skc55),skc55),
inference(res,[status(thm),theory(equality)],[14266,81]),
[iquote('0:Res:14266.0,81.0')] ).
cnf(14692,plain,
equal(and__dfg(implies__dfg(skc55,u),skc55),equiv__dfg(skc55,u)),
inference(spr,[status(thm),theory(equality)],[14531,95]),
[iquote('0:SpR:14531.0,95.0')] ).
cnf(14720,plain,
equal(and__dfg(skc55,implies__dfg(skc55,u)),equiv__dfg(u,skc55)),
inference(spr,[status(thm),theory(equality)],[14531,95]),
[iquote('0:SpR:14531.0,95.0')] ).
cnf(14745,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)],[14531,1153]),
[iquote('0:SpR:14531.0,1153.0')] ).
cnf(17346,plain,
( ~ is_a_theorem(u)
| equal(u,skc55) ),
inference(res,[status(thm),theory(equality)],[14254,81]),
[iquote('0:Res:14254.1,81.0')] ).
cnf(17414,plain,
equal(implies__dfg(implies__dfg(skc55,u),u),skc55),
inference(ems,[status(thm)],[17346,9526]),
[iquote('0:EmS:17346.0,9526.0')] ).
cnf(17424,plain,
equal(implies__dfg(u,or__dfg(and__dfg(u,skc55),v)),skc55),
inference(ems,[status(thm)],[17346,9560]),
[iquote('0:EmS:17346.0,9560.0')] ).
cnf(17426,plain,
equal(implies__dfg(u,and__dfg(skc55,u)),skc55),
inference(ems,[status(thm)],[17346,9606]),
[iquote('0:EmS:17346.0,9606.0')] ).
cnf(17458,plain,
equal(implies__dfg(u,implies__dfg(v,u)),skc55),
inference(ems,[status(thm)],[17346,112]),
[iquote('0:EmS:17346.0,112.0')] ).
cnf(17464,plain,
equal(implies__dfg(and__dfg(u,v),v),skc55),
inference(ems,[status(thm)],[17346,346]),
[iquote('0:EmS:17346.0,346.0')] ).
cnf(17494,plain,
equal(implies__dfg(u,or__dfg(v,u)),skc55),
inference(ems,[status(thm)],[17346,75]),
[iquote('0:EmS:17346.0,75.0')] ).
cnf(17495,plain,
equal(implies__dfg(or__dfg(u,u),u),skc55),
inference(ems,[status(thm)],[17346,76]),
[iquote('0:EmS:17346.0,76.0')] ).
cnf(18031,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)],[17414,95]),
[iquote('0:SpR:17414.0,95.0')] ).
cnf(18049,plain,
equal(equiv__dfg(u,implies__dfg(skc55,u)),and__dfg(skc55,skc55)),
inference(rew,[status(thm),theory(equality)],[17458,18031]),
[iquote('0:Rew:17458.0,18031.0')] ).
cnf(18050,plain,
equal(equiv__dfg(u,implies__dfg(skc55,u)),skc55),
inference(rew,[status(thm),theory(equality)],[14302,18049]),
[iquote('0:Rew:14302.0,18049.0')] ).
cnf(18061,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)],[17426,95]),
[iquote('0:SpR:17426.0,95.0')] ).
cnf(18076,plain,
equal(equiv__dfg(and__dfg(skc55,u),u),and__dfg(skc55,skc55)),
inference(rew,[status(thm),theory(equality)],[17464,18061]),
[iquote('0:Rew:17464.0,18061.0')] ).
cnf(18077,plain,
equal(equiv__dfg(and__dfg(skc55,u),u),skc55),
inference(rew,[status(thm),theory(equality)],[14302,18076]),
[iquote('0:Rew:14302.0,18076.0')] ).
cnf(18111,plain,
( ~ is_a_theorem(skc55)
| equal(implies__dfg(skc55,u),u) ),
inference(spl,[status(thm),theory(equality)],[18050,81]),
[iquote('0:SpL:18050.0,81.0')] ).
cnf(18112,plain,
equal(implies__dfg(skc55,u),u),
inference(mrr,[status(thm)],[18111,256]),
[iquote('0:MRR:18111.0,256.0')] ).
cnf(18223,plain,
equal(and__dfg(u,skc55),equiv__dfg(skc55,u)),
inference(rew,[status(thm),theory(equality)],[18112,14692]),
[iquote('0:Rew:18112.0,14692.0')] ).
cnf(18224,plain,
equal(and__dfg(skc55,u),equiv__dfg(u,skc55)),
inference(rew,[status(thm),theory(equality)],[18112,14720]),
[iquote('0:Rew:18112.0,14720.0')] ).
cnf(18295,plain,
equal(implies__dfg(u,or__dfg(equiv__dfg(skc55,u),v)),skc55),
inference(rew,[status(thm),theory(equality)],[18223,17424]),
[iquote('0:Rew:18223.0,17424.0')] ).
cnf(18345,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)],[18224,14745]),
[iquote('0:Rew:18224.0,14745.0')] ).
cnf(18351,plain,
equal(equiv__dfg(equiv__dfg(u,skc55),u),skc55),
inference(rew,[status(thm),theory(equality)],[18224,18077]),
[iquote('0:Rew:18224.0,18077.0')] ).
cnf(18546,plain,
equal(or__dfg(and__dfg(skc55,u),v),implies__dfg(not__dfg(u),v)),
inference(spr,[status(thm),theory(equality)],[18112,154]),
[iquote('0:SpR:18112.0,154.0')] ).
cnf(18552,plain,
equal(or__dfg(and__dfg(skc55,u),v),or__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[86,18546]),
[iquote('0:Rew:86.0,18546.0')] ).
cnf(18553,plain,
equal(or__dfg(equiv__dfg(u,skc55),v),or__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[18224,18552]),
[iquote('0:Rew:18224.0,18552.0')] ).
cnf(18571,plain,
is_a_theorem(or__dfg(u,implies__dfg(u,and__dfg(v,not__dfg(skc55))))),
inference(rew,[status(thm),theory(equality)],[18553,18345]),
[iquote('0:Rew:18553.0,18345.0')] ).
cnf(18698,plain,
( ~ is_a_theorem(skc55)
| equal(equiv__dfg(u,skc55),u) ),
inference(spl,[status(thm),theory(equality)],[18351,81]),
[iquote('0:SpL:18351.0,81.0')] ).
cnf(18699,plain,
equal(equiv__dfg(u,skc55),u),
inference(mrr,[status(thm)],[18698,256]),
[iquote('0:MRR:18698.0,256.0')] ).
cnf(18701,plain,
equal(and__dfg(skc55,u),u),
inference(rew,[status(thm),theory(equality)],[18699,18224]),
[iquote('0:Rew:18699.0,18224.0')] ).
cnf(19090,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)],[17495,95]),
[iquote('0:SpR:17495.0,95.0')] ).
cnf(19109,plain,
equal(equiv__dfg(or__dfg(u,u),u),skc55),
inference(rew,[status(thm),theory(equality)],[18701,19090,17494]),
[iquote('0:Rew:18701.0,19090.0,17494.0,19090.0')] ).
cnf(19524,plain,
( ~ is_a_theorem(skc55)
| equal(or__dfg(u,u),u) ),
inference(spl,[status(thm),theory(equality)],[19109,81]),
[iquote('0:SpL:19109.0,81.0')] ).
cnf(19525,plain,
equal(or__dfg(u,u),u),
inference(mrr,[status(thm)],[19524,256]),
[iquote('0:MRR:19524.0,256.0')] ).
cnf(19638,plain,
equal(implies__dfg(u,not__dfg(u)),not__dfg(u)),
inference(spr,[status(thm),theory(equality)],[19525,79]),
[iquote('0:SpR:19525.0,79.0')] ).
cnf(21004,plain,
is_a_theorem(implies__dfg(equiv__dfg(skc55,and__dfg(u,not__dfg(skc55))),v)),
inference(spr,[status(thm),theory(equality)],[18223,7134]),
[iquote('0:SpR:18223.0,7134.0')] ).
cnf(21144,plain,
is_a_theorem(not__dfg(equiv__dfg(skc55,and__dfg(u,not__dfg(skc55))))),
inference(spr,[status(thm),theory(equality)],[19638,21004]),
[iquote('0:SpR:19638.0,21004.0')] ).
cnf(21165,plain,
equal(not__dfg(equiv__dfg(skc55,and__dfg(u,not__dfg(skc55)))),skc55),
inference(ems,[status(thm)],[17346,21144]),
[iquote('0:EmS:17346.0,21144.0')] ).
cnf(21188,plain,
equal(equiv__dfg(skc55,and__dfg(u,not__dfg(skc55))),not__dfg(skc55)),
inference(spr,[status(thm),theory(equality)],[21165,10349]),
[iquote('0:SpR:21165.0,10349.0')] ).
cnf(21606,plain,
is_a_theorem(or__dfg(u,not__dfg(or__dfg(u,not__dfg(skc55))))),
inference(spr,[status(thm),theory(equality)],[19638,9444]),
[iquote('0:SpR:19638.0,9444.0')] ).
cnf(21630,plain,
is_a_theorem(or__dfg(u,equiv__dfg(skc55,not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[18223,21606,167]),
[iquote('0:Rew:18223.0,21606.0,167.0,21606.0')] ).
cnf(21768,plain,
is_a_theorem(or__dfg(not__dfg(u),equiv__dfg(skc55,u))),
inference(spr,[status(thm),theory(equality)],[10349,21630]),
[iquote('0:SpR:10349.0,21630.0')] ).
cnf(21785,plain,
is_a_theorem(implies__dfg(u,equiv__dfg(skc55,u))),
inference(rew,[status(thm),theory(equality)],[79,21768]),
[iquote('0:Rew:79.0,21768.0')] ).
cnf(21798,plain,
equal(implies__dfg(u,equiv__dfg(skc55,u)),skc55),
inference(ems,[status(thm)],[17346,21785]),
[iquote('0:EmS:17346.0,21785.0')] ).
cnf(21806,plain,
is_a_theorem(or__dfg(equiv__dfg(skc55,u),not__dfg(u))),
inference(sor,[status(thm)],[244,21785]),
[iquote('0:SoR:244.0,21785.0')] ).
cnf(21892,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)],[21798,95]),
[iquote('0:SpR:21798.0,95.0')] ).
cnf(21910,plain,
equal(equiv__dfg(u,equiv__dfg(skc55,u)),implies__dfg(equiv__dfg(skc55,u),u)),
inference(rew,[status(thm),theory(equality)],[18701,21892]),
[iquote('0:Rew:18701.0,21892.0')] ).
cnf(22021,plain,
equal(or__dfg(equiv__dfg(skc55,u),not__dfg(u)),skc55),
inference(ems,[status(thm)],[17346,21806]),
[iquote('0:EmS:17346.0,21806.0')] ).
cnf(22183,plain,
equal(and__dfg(not__dfg(equiv__dfg(skc55,u)),u),not__dfg(skc55)),
inference(spr,[status(thm),theory(equality)],[22021,167]),
[iquote('0:SpR:22021.0,167.0')] ).
cnf(22697,plain,
equal(and__dfg(not__dfg(not__dfg(skc55)),and__dfg(u,not__dfg(skc55))),not__dfg(skc55)),
inference(spr,[status(thm),theory(equality)],[21188,22183]),
[iquote('0:SpR:21188.0,22183.0')] ).
cnf(22700,plain,
equal(and__dfg(u,not__dfg(skc55)),not__dfg(skc55)),
inference(rew,[status(thm),theory(equality)],[18701,22697,10349]),
[iquote('0:Rew:18701.0,22697.0,10349.0,22697.0')] ).
cnf(22706,plain,
is_a_theorem(or__dfg(u,implies__dfg(u,not__dfg(skc55)))),
inference(rew,[status(thm),theory(equality)],[22700,18571]),
[iquote('0:Rew:22700.0,18571.0')] ).
cnf(22973,plain,
is_a_theorem(or__dfg(implies__dfg(u,not__dfg(skc55)),u)),
inference(sor,[status(thm)],[241,22706]),
[iquote('0:SoR:241.0,22706.0')] ).
cnf(22998,plain,
is_a_theorem(implies__dfg(equiv__dfg(skc55,u),u)),
inference(rew,[status(thm),theory(equality)],[18223,22973,156]),
[iquote('0:Rew:18223.0,22973.0,156.0,22973.0')] ).
cnf(23021,plain,
equal(implies__dfg(equiv__dfg(skc55,u),u),skc55),
inference(ems,[status(thm)],[17346,22998]),
[iquote('0:EmS:17346.0,22998.0')] ).
cnf(23044,plain,
equal(equiv__dfg(u,equiv__dfg(skc55,u)),skc55),
inference(rew,[status(thm),theory(equality)],[23021,21910]),
[iquote('0:Rew:23021.0,21910.0')] ).
cnf(23086,plain,
( ~ is_a_theorem(skc55)
| equal(equiv__dfg(skc55,u),u) ),
inference(spl,[status(thm),theory(equality)],[23044,81]),
[iquote('0:SpL:23044.0,81.0')] ).
cnf(23087,plain,
equal(equiv__dfg(skc55,u),u),
inference(mrr,[status(thm)],[23086,256]),
[iquote('0:MRR:23086.0,256.0')] ).
cnf(23155,plain,
equal(implies__dfg(u,or__dfg(u,v)),skc55),
inference(rew,[status(thm),theory(equality)],[23087,18295]),
[iquote('0:Rew:23087.0,18295.0')] ).
cnf(23191,plain,
~ is_a_theorem(skc55),
inference(rew,[status(thm),theory(equality)],[23155,78]),
[iquote('0:Rew:23155.0,78.0')] ).
cnf(23196,plain,
$false,
inference(mrr,[status(thm)],[23191,256]),
[iquote('0:MRR:23191.0,256.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LCL490+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 4 03:43:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 5.27/5.46
% 5.27/5.46 SPASS V 3.9
% 5.27/5.46 SPASS beiseite: Proof found.
% 5.27/5.46 % SZS status Theorem
% 5.27/5.46 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.27/5.46 SPASS derived 16050 clauses, backtracked 0 clauses, performed 0 splits and kept 5505 clauses.
% 5.27/5.46 SPASS allocated 120702 KBytes.
% 5.27/5.46 SPASS spent 0:00:05.10 on the problem.
% 5.27/5.46 0:00:00.03 for the input.
% 5.27/5.46 0:00:00.04 for the FLOTTER CNF translation.
% 5.27/5.46 0:00:00.16 for inferences.
% 5.27/5.46 0:00:00.00 for the backtracking.
% 5.27/5.46 0:00:04.78 for the reduction.
% 5.27/5.46
% 5.27/5.46
% 5.27/5.46 Here is a proof with depth 23, length 234 :
% 5.27/5.46 % SZS output start Refutation
% See solution above
% 5.53/5.71 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_or_1 modus_ponens r2 or_1 kn1 r1 r3 op_implies_or op_implies_and op_or op_and op_equiv r4 r5
% 5.53/5.71
%------------------------------------------------------------------------------