TSTP Solution File: LCL500+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL500+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 14:37:23 EDT 2022
% Result : Theorem 5.08s 5.27s
% Output : Refutation 5.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 36
% Syntax : Number of clauses : 252 ( 183 unt; 0 nHn; 252 RR)
% Number of literals : 326 ( 0 equ; 82 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('LCL500+1.p',unknown),
[] ).
cnf(2,axiom,
op_implies_and,
file('LCL500+1.p',unknown),
[] ).
cnf(4,axiom,
op_implies_or,
file('LCL500+1.p',unknown),
[] ).
cnf(5,axiom,
op_and,
file('LCL500+1.p',unknown),
[] ).
cnf(6,axiom,
op_equiv,
file('LCL500+1.p',unknown),
[] ).
cnf(7,axiom,
modus_ponens,
file('LCL500+1.p',unknown),
[] ).
cnf(8,axiom,
r1,
file('LCL500+1.p',unknown),
[] ).
cnf(9,axiom,
r2,
file('LCL500+1.p',unknown),
[] ).
cnf(10,axiom,
r3,
file('LCL500+1.p',unknown),
[] ).
cnf(11,axiom,
r4,
file('LCL500+1.p',unknown),
[] ).
cnf(12,axiom,
r5,
file('LCL500+1.p',unknown),
[] ).
cnf(13,axiom,
substitution_of_equivalents,
file('LCL500+1.p',unknown),
[] ).
cnf(14,axiom,
~ kn2,
file('LCL500+1.p',unknown),
[] ).
cnf(15,axiom,
is_a_theorem(skc56),
file('LCL500+1.p',unknown),
[] ).
cnf(16,axiom,
is_a_theorem(implies__dfg(skc56,skc55)),
file('LCL500+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ and_1
| is_a_theorem(implies__dfg(and__dfg(u,v),u)) ),
file('LCL500+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ is_a_theorem(implies__dfg(and__dfg(skc69,skc68),skc69))
| and_1 ),
file('LCL500+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ or_1
| is_a_theorem(implies__dfg(u,or__dfg(u,v))) ),
file('LCL500+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ is_a_theorem(implies__dfg(skc75,or__dfg(skc75,skc74)))
| or_1 ),
file('LCL500+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ kn1
| is_a_theorem(implies__dfg(u,and__dfg(u,u))) ),
file('LCL500+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ is_a_theorem(implies__dfg(skc87,and__dfg(skc87,skc87)))
| kn1 ),
file('LCL500+1.p',unknown),
[] ).
cnf(33,axiom,
( ~ is_a_theorem(implies__dfg(and__dfg(skc89,skc88),skc89))
| kn2 ),
file('LCL500+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ r1
| is_a_theorem(implies__dfg(or__dfg(u,u),u)) ),
file('LCL500+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ r2
| is_a_theorem(implies__dfg(u,or__dfg(v,u))) ),
file('LCL500+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ cn2
| is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(u),v))) ),
file('LCL500+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ is_a_theorem(implies__dfg(skc97,implies__dfg(not__dfg(skc97),skc96)))
| cn2 ),
file('LCL500+1.p',unknown),
[] ).
cnf(42,axiom,
( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv__dfg(u,v))
| equal(u,v) ),
file('LCL500+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ r3
| is_a_theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))) ),
file('LCL500+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ op_implies_or
| equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)) ),
file('LCL500+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ op_implies_and
| equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)) ),
file('LCL500+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ is_a_theorem(u)
| ~ modus_ponens
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL500+1.p',unknown),
[] ).
cnf(58,axiom,
( ~ op_or
| equal(not__dfg(and__dfg(not__dfg(u),not__dfg(v))),or__dfg(u,v)) ),
file('LCL500+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ op_and
| equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and__dfg(u,v)) ),
file('LCL500+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ op_equiv
| equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)) ),
file('LCL500+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('LCL500+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('LCL500+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(77,plain,
~ is_a_theorem(implies__dfg(and__dfg(skc89,skc88),skc89)),
inference(mrr,[status(thm)],[33,14]),
[iquote('0:MRR:33.1,14.0')] ).
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(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(100,plain,
~ and_1,
inference(res,[status(thm),theory(equality)],[22,77]),
[iquote('0:Res:22.1,77.0')] ).
cnf(102,plain,
~ is_a_theorem(implies__dfg(and__dfg(skc69,skc68),skc69)),
inference(mrr,[status(thm)],[23,100]),
[iquote('0:MRR:23.1,100.0')] ).
cnf(107,plain,
( ~ cn2
| or_1 ),
inference(res,[status(thm),theory(equality)],[87,27]),
[iquote('0:Res:87.1,27.0')] ).
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(114,plain,
( ~ or_1
| is_a_theorem(implies__dfg(not__dfg(u),implies__dfg(u,v))) ),
inference(spr,[status(thm),theory(equality)],[79,26]),
[iquote('0:SpR:79.0,26.1')] ).
cnf(118,plain,
( ~ or_1
| is_a_theorem(or__dfg(u,implies__dfg(u,v))) ),
inference(rew,[status(thm),theory(equality)],[86,114]),
[iquote('0:Rew:86.0,114.1')] ).
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(127,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(134,plain,
is_a_theorem(implies__dfg(u,or__dfg(v,not__dfg(not__dfg(u))))),
inference(spr,[status(thm),theory(equality)],[79,122]),
[iquote('0:SpR:79.0,122.0')] ).
cnf(143,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(144,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(150,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(152,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(158,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(170,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(172,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(180,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(183,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(184,plain,
is_a_theorem(or__dfg(and__dfg(u,u),not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[170,111]),
[iquote('0:Rew:170.0,111.0')] ).
cnf(252,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(253,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(254,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(256,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(257,plain,
( ~ is_a_theorem(u)
| is_a_theorem(or__dfg(v,not__dfg(not__dfg(u)))) ),
inference(res,[status(thm),theory(equality)],[134,94]),
[iquote('0:Res:134.0,94.1')] ).
cnf(260,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(261,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(or__dfg(v,not__dfg(u))) ),
inference(res,[status(thm),theory(equality)],[144,94]),
[iquote('0:Res:144.0,94.1')] ).
cnf(265,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(269,plain,
( ~ is_a_theorem(or__dfg(u,not__dfg(v)))
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[143,94]),
[iquote('0:Res:143.0,94.1')] ).
cnf(272,plain,
is_a_theorem(skc55),
inference(ssi,[status(thm)],[253,15]),
[iquote('0:SSi:253.0,15.0')] ).
cnf(273,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(281,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(307,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(308,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(311,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(312,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)],[79,307]),
[iquote('0:Rew:79.0,307.0')] ).
cnf(313,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)],[79,308]),
[iquote('0:Rew:79.0,308.0')] ).
cnf(320,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(321,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(325,plain,
( ~ is_a_theorem(u)
| is_a_theorem(not__dfg(not__dfg(u))) ),
inference(sor,[status(thm)],[254,257]),
[iquote('0:SoR:254.0,257.1')] ).
cnf(331,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)],[84,325]),
[iquote('0:SpR:84.0,325.1')] ).
cnf(350,plain,
( ~ is_a_theorem(u)
| is_a_theorem(or__dfg(u,v)) ),
inference(sor,[status(thm)],[260,256]),
[iquote('0:SoR:260.0,256.1')] ).
cnf(353,plain,
is_a_theorem(or__dfg(not__dfg(u),and__dfg(u,u))),
inference(sor,[status(thm)],[260,184]),
[iquote('0:SoR:260.0,184.0')] ).
cnf(360,plain,
is_a_theorem(or__dfg(implies__dfg(u,not__dfg(v)),v)),
inference(sor,[status(thm)],[260,127]),
[iquote('0:SoR:260.0,127.0')] ).
cnf(362,plain,
( ~ or_1
| is_a_theorem(or__dfg(implies__dfg(u,v),u)) ),
inference(sor,[status(thm)],[260,118]),
[iquote('0:SoR:260.0,118.1')] ).
cnf(363,plain,
is_a_theorem(implies__dfg(u,and__dfg(u,u))),
inference(rew,[status(thm),theory(equality)],[79,353]),
[iquote('0:Rew:79.0,353.0')] ).
cnf(364,plain,
kn1,
inference(mrr,[status(thm)],[31,363]),
[iquote('0:MRR:31.0,363.0')] ).
cnf(368,plain,
is_a_theorem(implies__dfg(implies__dfg(u,u),equiv__dfg(u,u))),
inference(mrr,[status(thm)],[273,364]),
[iquote('0:MRR:273.0,364.0')] ).
cnf(370,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),v)),
inference(rew,[status(thm),theory(equality)],[172,360]),
[iquote('0:Rew:172.0,360.0')] ).
cnf(392,plain,
( ~ is_a_theorem(not__dfg(u))
| is_a_theorem(implies__dfg(u,v)) ),
inference(spr,[status(thm),theory(equality)],[79,350]),
[iquote('0:SpR:79.0,350.1')] ).
cnf(528,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)],[183,86]),
[iquote('0:SpR:183.0,86.0')] ).
cnf(558,plain,
equal(not__dfg(implies__dfg(u,not__dfg(v))),and__dfg(not__dfg(not__dfg(u)),v)),
inference(spr,[status(thm),theory(equality)],[79,183]),
[iquote('0:SpR:79.0,183.0')] ).
cnf(559,plain,
equal(and__dfg(not__dfg(not__dfg(u)),v),and__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[84,558]),
[iquote('0:Rew:84.0,558.0')] ).
cnf(624,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)],[82,559]),
[iquote('0:SpR:82.0,559.0')] ).
cnf(1142,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),not__dfg(not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[152,184]),
[iquote('0:SpR:152.0,184.0')] ).
cnf(1146,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)],[152,143]),
[iquote('0:SpR:152.0,143.0')] ).
cnf(1162,plain,
is_a_theorem(implies__dfg(or__dfg(u,u),not__dfg(not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[86,1142]),
[iquote('0:Rew:86.0,1142.0')] ).
cnf(1177,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)],[170,1146]),
[iquote('0:Rew:170.0,1146.0')] ).
cnf(1225,plain,
( ~ is_a_theorem(or__dfg(u,u))
| is_a_theorem(not__dfg(not__dfg(u))) ),
inference(res,[status(thm),theory(equality)],[1162,94]),
[iquote('0:Res:1162.0,94.1')] ).
cnf(1448,plain,
( ~ or_1
| is_a_theorem(implies__dfg(and__dfg(u,v),u)) ),
inference(spr,[status(thm),theory(equality)],[172,362]),
[iquote('0:SpR:172.0,362.1')] ).
cnf(1564,plain,
~ or_1,
inference(res,[status(thm),theory(equality)],[1448,102]),
[iquote('0:Res:1448.1,102.0')] ).
cnf(1568,plain,
~ cn2,
inference(mrr,[status(thm)],[107,1564]),
[iquote('0:MRR:107.1,1564.0')] ).
cnf(1572,plain,
~ is_a_theorem(implies__dfg(skc97,or__dfg(skc97,skc96))),
inference(mrr,[status(thm)],[88,1568]),
[iquote('0:MRR:88.1,1568.0')] ).
cnf(1622,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)],[312,94]),
[iquote('0:Res:312.0,94.1')] ).
cnf(1687,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)],[313,94]),
[iquote('0:Res:313.0,94.1')] ).
cnf(1932,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)],[95,158]),
[iquote('0:SpR:95.0,158.0')] ).
cnf(2615,plain,
( ~ is_a_theorem(not__dfg(u))
| is_a_theorem(not__dfg(and__dfg(v,u))) ),
inference(sor,[status(thm)],[331,265]),
[iquote('0:SoR:331.0,265.1')] ).
cnf(2854,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)],[79,281]),
[iquote('0:SpR:79.0,281.0')] ).
cnf(2937,plain,
( ~ is_a_theorem(or__dfg(u,v))
| is_a_theorem(or__dfg(u,or__dfg(w,v))) ),
inference(sor,[status(thm)],[311,256]),
[iquote('0:SoR:311.0,256.1')] ).
cnf(2941,plain,
is_a_theorem(or__dfg(u,or__dfg(v,not__dfg(v)))),
inference(sor,[status(thm)],[311,122]),
[iquote('0:SoR:311.0,122.0')] ).
cnf(2945,plain,
is_a_theorem(or__dfg(u,not__dfg(u))),
inference(sor,[status(thm)],[254,2941]),
[iquote('0:SoR:254.0,2941.0')] ).
cnf(2946,plain,
is_a_theorem(or__dfg(or__dfg(u,not__dfg(u)),v)),
inference(sor,[status(thm)],[260,2941]),
[iquote('0:SoR:260.0,2941.0')] ).
cnf(2961,plain,
is_a_theorem(implies__dfg(and__dfg(not__dfg(u),u),v)),
inference(rew,[status(thm),theory(equality)],[528,2946]),
[iquote('0:Rew:528.0,2946.0')] ).
cnf(2969,plain,
is_a_theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[269,2945]),
[iquote('0:SoR:269.0,2945.0')] ).
cnf(3118,plain,
is_a_theorem(implies__dfg(and__dfg(u,not__dfg(u)),v)),
inference(spr,[status(thm),theory(equality)],[559,2961]),
[iquote('0:SpR:559.0,2961.0')] ).
cnf(3121,plain,
is_a_theorem(or__dfg(implies__dfg(u,u),v)),
inference(rew,[status(thm),theory(equality)],[150,3118]),
[iquote('0:Rew:150.0,3118.0')] ).
cnf(3131,plain,
is_a_theorem(implies__dfg(or__dfg(u,implies__dfg(v,v)),or__dfg(u,equiv__dfg(v,v)))),
inference(sor,[status(thm)],[321,368]),
[iquote('0:SoR:321.0,368.0')] ).
cnf(3185,plain,
is_a_theorem(implies__dfg(or__dfg(u,skc56),or__dfg(u,skc55))),
inference(sor,[status(thm)],[321,16]),
[iquote('0:SoR:321.0,16.0')] ).
cnf(3190,plain,
is_a_theorem(or__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[260,3121]),
[iquote('0:SoR:260.0,3121.0')] ).
cnf(3372,plain,
( ~ is_a_theorem(or__dfg(u,skc56))
| is_a_theorem(or__dfg(u,skc55)) ),
inference(res,[status(thm),theory(equality)],[3185,94]),
[iquote('0:Res:3185.0,94.1')] ).
cnf(3375,plain,
is_a_theorem(or__dfg(u,skc55)),
inference(ssi,[status(thm)],[3372,256,15]),
[iquote('0:SSi:3372.0,256.0,15.1')] ).
cnf(3381,plain,
is_a_theorem(not__dfg(not__dfg(skc55))),
inference(sor,[status(thm)],[1225,3375]),
[iquote('0:SoR:1225.0,3375.0')] ).
cnf(3383,plain,
is_a_theorem(or__dfg(skc55,u)),
inference(sor,[status(thm)],[260,3375]),
[iquote('0:SoR:260.0,3375.0')] ).
cnf(3391,plain,
( ~ is_a_theorem(or__dfg(not__dfg(skc55),u))
| is_a_theorem(u) ),
inference(sor,[status(thm)],[252,3381]),
[iquote('0:SoR:252.0,3381.0')] ).
cnf(3396,plain,
( ~ is_a_theorem(implies__dfg(skc55,u))
| is_a_theorem(u) ),
inference(rew,[status(thm),theory(equality)],[79,3391]),
[iquote('0:Rew:79.0,3391.0')] ).
cnf(3423,plain,
is_a_theorem(or__dfg(u,or__dfg(skc55,v))),
inference(sor,[status(thm)],[311,3383]),
[iquote('0:SoR:311.0,3383.0')] ).
cnf(3497,plain,
is_a_theorem(not__dfg(not__dfg(or__dfg(skc55,u)))),
inference(sor,[status(thm)],[1225,3423]),
[iquote('0:SoR:1225.0,3423.0')] ).
cnf(3507,plain,
( ~ is_a_theorem(or__dfg(not__dfg(or__dfg(skc55,u)),v))
| is_a_theorem(v) ),
inference(sor,[status(thm)],[252,3497]),
[iquote('0:SoR:252.0,3497.0')] ).
cnf(3512,plain,
( ~ is_a_theorem(implies__dfg(or__dfg(skc55,u),v))
| is_a_theorem(v) ),
inference(rew,[status(thm),theory(equality)],[79,3507]),
[iquote('0:Rew:79.0,3507.0')] ).
cnf(5193,plain,
is_a_theorem(implies__dfg(or__dfg(u,not__dfg(skc55)),or__dfg(u,v))),
inference(res,[status(thm),theory(equality)],[320,3512]),
[iquote('0:Res:320.0,3512.0')] ).
cnf(5475,plain,
is_a_theorem(implies__dfg(or__dfg(not__dfg(u),not__dfg(skc55)),implies__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[79,5193]),
[iquote('0:SpR:79.0,5193.0')] ).
cnf(5484,plain,
is_a_theorem(or__dfg(and__dfg(u,skc55),implies__dfg(u,v))),
inference(rew,[status(thm),theory(equality)],[170,5475,79]),
[iquote('0:Rew:170.0,5475.0,79.0,5475.0')] ).
cnf(5970,plain,
is_a_theorem(or__dfg(u,or__dfg(v,skc55))),
inference(sor,[status(thm)],[2937,3375]),
[iquote('0:SoR:2937.0,3375.0')] ).
cnf(5991,plain,
is_a_theorem(not__dfg(not__dfg(or__dfg(u,skc55)))),
inference(sor,[status(thm)],[1225,5970]),
[iquote('0:SoR:1225.0,5970.0')] ).
cnf(5994,plain,
is_a_theorem(or__dfg(or__dfg(u,skc55),v)),
inference(sor,[status(thm)],[260,5970]),
[iquote('0:SoR:260.0,5970.0')] ).
cnf(6006,plain,
( ~ is_a_theorem(or__dfg(not__dfg(or__dfg(u,skc55)),v))
| is_a_theorem(v) ),
inference(sor,[status(thm)],[252,5991]),
[iquote('0:SoR:252.0,5991.0')] ).
cnf(6008,plain,
is_a_theorem(not__dfg(not__dfg(implies__dfg(u,skc55)))),
inference(spr,[status(thm),theory(equality)],[79,5991]),
[iquote('0:SpR:79.0,5991.0')] ).
cnf(6013,plain,
( ~ is_a_theorem(implies__dfg(or__dfg(u,skc55),v))
| is_a_theorem(v) ),
inference(rew,[status(thm),theory(equality)],[79,6006]),
[iquote('0:Rew:79.0,6006.0')] ).
cnf(6026,plain,
is_a_theorem(not__dfg(and__dfg(u,not__dfg(implies__dfg(v,skc55))))),
inference(sor,[status(thm)],[2615,6008]),
[iquote('0:SoR:2615.0,6008.0')] ).
cnf(6034,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(6087,plain,
is_a_theorem(or__dfg(u,or__dfg(or__dfg(v,skc55),w))),
inference(sor,[status(thm)],[311,5994]),
[iquote('0:SoR:311.0,5994.0')] ).
cnf(6820,plain,
is_a_theorem(not__dfg(not__dfg(or__dfg(or__dfg(u,skc55),v)))),
inference(sor,[status(thm)],[1225,6087]),
[iquote('0:SoR:1225.0,6087.0')] ).
cnf(6854,plain,
is_a_theorem(not__dfg(not__dfg(or__dfg(implies__dfg(u,skc55),v)))),
inference(spr,[status(thm),theory(equality)],[79,6820]),
[iquote('0:SpR:79.0,6820.0')] ).
cnf(6880,plain,
is_a_theorem(not__dfg(and__dfg(not__dfg(implies__dfg(u,skc55)),v))),
inference(spr,[status(thm),theory(equality)],[183,6854]),
[iquote('0:SpR:183.0,6854.0')] ).
cnf(6881,plain,
is_a_theorem(not__dfg(and__dfg(and__dfg(u,not__dfg(skc55)),v))),
inference(rew,[status(thm),theory(equality)],[624,6880]),
[iquote('0:Rew:624.0,6880.0')] ).
cnf(6952,plain,
is_a_theorem(implies__dfg(and__dfg(and__dfg(u,not__dfg(skc55)),v),w)),
inference(sor,[status(thm)],[392,6881]),
[iquote('0:SoR:392.0,6881.0')] ).
cnf(7168,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)],[3131,94]),
[iquote('0:Res:3131.0,94.1')] ).
cnf(7171,plain,
is_a_theorem(or__dfg(u,equiv__dfg(v,v))),
inference(ssi,[status(thm)],[7168,3190]),
[iquote('0:SSi:7168.0,3190.0')] ).
cnf(7177,plain,
is_a_theorem(not__dfg(not__dfg(equiv__dfg(u,u)))),
inference(sor,[status(thm)],[1225,7171]),
[iquote('0:SoR:1225.0,7171.0')] ).
cnf(9488,plain,
is_a_theorem(or__dfg(u,implies__dfg(or__dfg(u,v),v))),
inference(sor,[status(thm)],[1622,2969]),
[iquote('0:SoR:1622.0,2969.0')] ).
cnf(9519,plain,
is_a_theorem(or__dfg(u,implies__dfg(or__dfg(u,not__dfg(skc55)),v))),
inference(sor,[status(thm)],[1622,5193]),
[iquote('0:SoR:1622.0,5193.0')] ).
cnf(9541,plain,
is_a_theorem(or__dfg(not__dfg(u),implies__dfg(implies__dfg(u,v),v))),
inference(spr,[status(thm),theory(equality)],[79,9488]),
[iquote('0:SpR:79.0,9488.0')] ).
cnf(9551,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),v))),
inference(rew,[status(thm),theory(equality)],[79,9541]),
[iquote('0:Rew:79.0,9541.0')] ).
cnf(9600,plain,
is_a_theorem(implies__dfg(implies__dfg(or__dfg(u,skc55),v),v)),
inference(res,[status(thm),theory(equality)],[9551,6013]),
[iquote('0:Res:9551.0,6013.0')] ).
cnf(9602,plain,
is_a_theorem(implies__dfg(implies__dfg(skc55,u),u)),
inference(res,[status(thm),theory(equality)],[9551,3396]),
[iquote('0:Res:9551.0,3396.0')] ).
cnf(9636,plain,
is_a_theorem(implies__dfg(u,or__dfg(and__dfg(u,skc55),v))),
inference(sor,[status(thm)],[1687,5484]),
[iquote('0:SoR:1687.0,5484.0')] ).
cnf(9664,plain,
is_a_theorem(or__dfg(u,not__dfg(implies__dfg(skc55,u)))),
inference(sor,[status(thm)],[261,9602]),
[iquote('0:SoR:261.0,9602.0')] ).
cnf(9668,plain,
( ~ is_a_theorem(implies__dfg(skc55,u))
| is_a_theorem(u) ),
inference(res,[status(thm),theory(equality)],[9602,94]),
[iquote('0:Res:9602.0,94.1')] ).
cnf(9673,plain,
is_a_theorem(or__dfg(not__dfg(u),and__dfg(skc55,u))),
inference(spr,[status(thm),theory(equality)],[84,9664]),
[iquote('0:SpR:84.0,9664.0')] ).
cnf(9682,plain,
is_a_theorem(implies__dfg(u,and__dfg(skc55,u))),
inference(rew,[status(thm),theory(equality)],[79,9673]),
[iquote('0:Rew:79.0,9673.0')] ).
cnf(10088,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,skc55),v),v)),
inference(spr,[status(thm),theory(equality)],[79,9600]),
[iquote('0:SpR:79.0,9600.0')] ).
cnf(10105,plain,
is_a_theorem(or__dfg(and__dfg(skc55,skc55),u)),
inference(sor,[status(thm)],[9668,9636]),
[iquote('0:SoR:9668.0,9636.0')] ).
cnf(10173,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)],[1932,180]),
[iquote('0:SpR:1932.0,180.0')] ).
cnf(10233,plain,
equal(not__dfg(not__dfg(equiv__dfg(u,v))),equiv__dfg(not__dfg(not__dfg(u)),v)),
inference(rew,[status(thm),theory(equality)],[2854,10173]),
[iquote('0:Rew:2854.0,10173.0')] ).
cnf(10236,plain,
is_a_theorem(equiv__dfg(not__dfg(not__dfg(u)),u)),
inference(rew,[status(thm),theory(equality)],[10233,7177]),
[iquote('0:Rew:10233.0,7177.0')] ).
cnf(10328,plain,
is_a_theorem(implies__dfg(u,and__dfg(skc55,skc55))),
inference(sor,[status(thm)],[269,10105]),
[iquote('0:SoR:269.0,10105.0')] ).
cnf(10445,plain,
equal(not__dfg(not__dfg(u)),u),
inference(res,[status(thm),theory(equality)],[10236,81]),
[iquote('0:Res:10236.0,81.0')] ).
cnf(12603,plain,
is_a_theorem(implies__dfg(not__dfg(equiv__dfg(u,skc55)),and__dfg(skc55,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[1932,10088]),
[iquote('0:SpR:1932.0,10088.0')] ).
cnf(12607,plain,
is_a_theorem(or__dfg(equiv__dfg(u,skc55),and__dfg(skc55,not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[86,12603]),
[iquote('0:Rew:86.0,12603.0')] ).
cnf(13310,plain,
is_a_theorem(or__dfg(and__dfg(skc55,not__dfg(u)),equiv__dfg(u,skc55))),
inference(sor,[status(thm)],[260,12607]),
[iquote('0:SoR:260.0,12607.0')] ).
cnf(13313,plain,
is_a_theorem(implies__dfg(implies__dfg(skc55,u),equiv__dfg(u,skc55))),
inference(rew,[status(thm),theory(equality)],[152,13310]),
[iquote('0:Rew:152.0,13310.0')] ).
cnf(13323,plain,
( ~ is_a_theorem(implies__dfg(skc55,u))
| is_a_theorem(equiv__dfg(u,skc55)) ),
inference(res,[status(thm),theory(equality)],[13313,94]),
[iquote('0:Res:13313.0,94.1')] ).
cnf(14003,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equiv__dfg(u,skc55)) ),
inference(sor,[status(thm)],[13323,265]),
[iquote('0:SoR:13323.0,265.1')] ).
cnf(14015,plain,
is_a_theorem(equiv__dfg(implies__dfg(u,skc55),skc55)),
inference(sor,[status(thm)],[13323,6034]),
[iquote('0:SoR:13323.0,6034.0')] ).
cnf(14039,plain,
is_a_theorem(equiv__dfg(and__dfg(skc55,skc55),skc55)),
inference(sor,[status(thm)],[13323,10328]),
[iquote('0:SoR:13323.0,10328.0')] ).
cnf(14093,plain,
equal(and__dfg(skc55,skc55),skc55),
inference(res,[status(thm),theory(equality)],[14039,81]),
[iquote('0:Res:14039.0,81.0')] ).
cnf(14287,plain,
equal(implies__dfg(u,skc55),skc55),
inference(res,[status(thm),theory(equality)],[14015,81]),
[iquote('0:Res:14015.0,81.0')] ).
cnf(14446,plain,
equal(and__dfg(implies__dfg(skc55,u),skc55),equiv__dfg(skc55,u)),
inference(spr,[status(thm),theory(equality)],[14287,95]),
[iquote('0:SpR:14287.0,95.0')] ).
cnf(14470,plain,
equal(and__dfg(skc55,implies__dfg(skc55,u)),equiv__dfg(u,skc55)),
inference(spr,[status(thm),theory(equality)],[14287,95]),
[iquote('0:SpR:14287.0,95.0')] ).
cnf(14494,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)],[14287,1177]),
[iquote('0:SpR:14287.0,1177.0')] ).
cnf(16974,plain,
( ~ is_a_theorem(u)
| equal(u,skc55) ),
inference(res,[status(thm),theory(equality)],[14003,81]),
[iquote('0:Res:14003.1,81.0')] ).
cnf(17081,plain,
equal(implies__dfg(implies__dfg(skc55,u),u),skc55),
inference(ems,[status(thm)],[16974,9602]),
[iquote('0:EmS:16974.0,9602.0')] ).
cnf(17087,plain,
equal(implies__dfg(u,or__dfg(and__dfg(u,skc55),v)),skc55),
inference(ems,[status(thm)],[16974,9636]),
[iquote('0:EmS:16974.0,9636.0')] ).
cnf(17089,plain,
equal(implies__dfg(u,and__dfg(skc55,u)),skc55),
inference(ems,[status(thm)],[16974,9682]),
[iquote('0:EmS:16974.0,9682.0')] ).
cnf(17121,plain,
equal(implies__dfg(u,implies__dfg(v,u)),skc55),
inference(ems,[status(thm)],[16974,112]),
[iquote('0:EmS:16974.0,112.0')] ).
cnf(17127,plain,
equal(implies__dfg(and__dfg(u,v),v),skc55),
inference(ems,[status(thm)],[16974,370]),
[iquote('0:EmS:16974.0,370.0')] ).
cnf(17157,plain,
equal(implies__dfg(u,or__dfg(v,u)),skc55),
inference(ems,[status(thm)],[16974,75]),
[iquote('0:EmS:16974.0,75.0')] ).
cnf(17158,plain,
equal(implies__dfg(or__dfg(u,u),u),skc55),
inference(ems,[status(thm)],[16974,76]),
[iquote('0:EmS:16974.0,76.0')] ).
cnf(17555,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)],[17081,95]),
[iquote('0:SpR:17081.0,95.0')] ).
cnf(17573,plain,
equal(equiv__dfg(u,implies__dfg(skc55,u)),and__dfg(skc55,skc55)),
inference(rew,[status(thm),theory(equality)],[17121,17555]),
[iquote('0:Rew:17121.0,17555.0')] ).
cnf(17574,plain,
equal(equiv__dfg(u,implies__dfg(skc55,u)),skc55),
inference(rew,[status(thm),theory(equality)],[14093,17573]),
[iquote('0:Rew:14093.0,17573.0')] ).
cnf(17585,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)],[17089,95]),
[iquote('0:SpR:17089.0,95.0')] ).
cnf(17600,plain,
equal(equiv__dfg(and__dfg(skc55,u),u),and__dfg(skc55,skc55)),
inference(rew,[status(thm),theory(equality)],[17127,17585]),
[iquote('0:Rew:17127.0,17585.0')] ).
cnf(17601,plain,
equal(equiv__dfg(and__dfg(skc55,u),u),skc55),
inference(rew,[status(thm),theory(equality)],[14093,17600]),
[iquote('0:Rew:14093.0,17600.0')] ).
cnf(17680,plain,
( ~ is_a_theorem(skc55)
| equal(implies__dfg(skc55,u),u) ),
inference(spl,[status(thm),theory(equality)],[17574,81]),
[iquote('0:SpL:17574.0,81.0')] ).
cnf(17681,plain,
equal(implies__dfg(skc55,u),u),
inference(mrr,[status(thm)],[17680,272]),
[iquote('0:MRR:17680.0,272.0')] ).
cnf(17779,plain,
equal(and__dfg(u,skc55),equiv__dfg(skc55,u)),
inference(rew,[status(thm),theory(equality)],[17681,14446]),
[iquote('0:Rew:17681.0,14446.0')] ).
cnf(17780,plain,
equal(and__dfg(skc55,u),equiv__dfg(u,skc55)),
inference(rew,[status(thm),theory(equality)],[17681,14470]),
[iquote('0:Rew:17681.0,14470.0')] ).
cnf(17845,plain,
equal(implies__dfg(u,or__dfg(equiv__dfg(skc55,u),v)),skc55),
inference(rew,[status(thm),theory(equality)],[17779,17087]),
[iquote('0:Rew:17779.0,17087.0')] ).
cnf(17882,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)],[17780,14494]),
[iquote('0:Rew:17780.0,14494.0')] ).
cnf(17888,plain,
equal(equiv__dfg(equiv__dfg(u,skc55),u),skc55),
inference(rew,[status(thm),theory(equality)],[17780,17601]),
[iquote('0:Rew:17780.0,17601.0')] ).
cnf(17995,plain,
equal(or__dfg(and__dfg(skc55,u),v),implies__dfg(not__dfg(u),v)),
inference(spr,[status(thm),theory(equality)],[17681,170]),
[iquote('0:SpR:17681.0,170.0')] ).
cnf(18001,plain,
equal(or__dfg(and__dfg(skc55,u),v),or__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[86,17995]),
[iquote('0:Rew:86.0,17995.0')] ).
cnf(18002,plain,
equal(or__dfg(equiv__dfg(u,skc55),v),or__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[17780,18001]),
[iquote('0:Rew:17780.0,18001.0')] ).
cnf(18013,plain,
is_a_theorem(or__dfg(u,implies__dfg(u,and__dfg(v,not__dfg(skc55))))),
inference(rew,[status(thm),theory(equality)],[18002,17882]),
[iquote('0:Rew:18002.0,17882.0')] ).
cnf(18167,plain,
( ~ is_a_theorem(skc55)
| equal(equiv__dfg(u,skc55),u) ),
inference(spl,[status(thm),theory(equality)],[17888,81]),
[iquote('0:SpL:17888.0,81.0')] ).
cnf(18168,plain,
equal(equiv__dfg(u,skc55),u),
inference(mrr,[status(thm)],[18167,272]),
[iquote('0:MRR:18167.0,272.0')] ).
cnf(18170,plain,
equal(and__dfg(skc55,u),u),
inference(rew,[status(thm),theory(equality)],[18168,17780]),
[iquote('0:Rew:18168.0,17780.0')] ).
cnf(18490,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)],[17158,95]),
[iquote('0:SpR:17158.0,95.0')] ).
cnf(18509,plain,
equal(equiv__dfg(or__dfg(u,u),u),skc55),
inference(rew,[status(thm),theory(equality)],[18170,18490,17157]),
[iquote('0:Rew:18170.0,18490.0,17157.0,18490.0')] ).
cnf(19007,plain,
( ~ is_a_theorem(skc55)
| equal(or__dfg(u,u),u) ),
inference(spl,[status(thm),theory(equality)],[18509,81]),
[iquote('0:SpL:18509.0,81.0')] ).
cnf(19008,plain,
equal(or__dfg(u,u),u),
inference(mrr,[status(thm)],[19007,272]),
[iquote('0:MRR:19007.0,272.0')] ).
cnf(19058,plain,
equal(implies__dfg(u,not__dfg(u)),not__dfg(u)),
inference(spr,[status(thm),theory(equality)],[19008,79]),
[iquote('0:SpR:19008.0,79.0')] ).
cnf(20535,plain,
is_a_theorem(implies__dfg(equiv__dfg(skc55,and__dfg(u,not__dfg(skc55))),v)),
inference(spr,[status(thm),theory(equality)],[17779,6952]),
[iquote('0:SpR:17779.0,6952.0')] ).
cnf(20592,plain,
is_a_theorem(not__dfg(equiv__dfg(skc55,and__dfg(u,not__dfg(skc55))))),
inference(spr,[status(thm),theory(equality)],[19058,20535]),
[iquote('0:SpR:19058.0,20535.0')] ).
cnf(20613,plain,
equal(not__dfg(equiv__dfg(skc55,and__dfg(u,not__dfg(skc55)))),skc55),
inference(ems,[status(thm)],[16974,20592]),
[iquote('0:EmS:16974.0,20592.0')] ).
cnf(20636,plain,
equal(equiv__dfg(skc55,and__dfg(u,not__dfg(skc55))),not__dfg(skc55)),
inference(spr,[status(thm),theory(equality)],[20613,10445]),
[iquote('0:SpR:20613.0,10445.0')] ).
cnf(21105,plain,
is_a_theorem(or__dfg(u,not__dfg(or__dfg(u,not__dfg(skc55))))),
inference(spr,[status(thm),theory(equality)],[19058,9519]),
[iquote('0:SpR:19058.0,9519.0')] ).
cnf(21129,plain,
is_a_theorem(or__dfg(u,equiv__dfg(skc55,not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[17779,21105,183]),
[iquote('0:Rew:17779.0,21105.0,183.0,21105.0')] ).
cnf(21158,plain,
is_a_theorem(or__dfg(not__dfg(u),equiv__dfg(skc55,u))),
inference(spr,[status(thm),theory(equality)],[10445,21129]),
[iquote('0:SpR:10445.0,21129.0')] ).
cnf(21175,plain,
is_a_theorem(implies__dfg(u,equiv__dfg(skc55,u))),
inference(rew,[status(thm),theory(equality)],[79,21158]),
[iquote('0:Rew:79.0,21158.0')] ).
cnf(21188,plain,
equal(implies__dfg(u,equiv__dfg(skc55,u)),skc55),
inference(ems,[status(thm)],[16974,21175]),
[iquote('0:EmS:16974.0,21175.0')] ).
cnf(21196,plain,
is_a_theorem(or__dfg(equiv__dfg(skc55,u),not__dfg(u))),
inference(sor,[status(thm)],[261,21175]),
[iquote('0:SoR:261.0,21175.0')] ).
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)],[21188,95]),
[iquote('0:SpR:21188.0,95.0')] ).
cnf(21428,plain,
equal(equiv__dfg(u,equiv__dfg(skc55,u)),implies__dfg(equiv__dfg(skc55,u),u)),
inference(rew,[status(thm),theory(equality)],[18170,21410]),
[iquote('0:Rew:18170.0,21410.0')] ).
cnf(21431,plain,
equal(or__dfg(equiv__dfg(skc55,u),not__dfg(u)),skc55),
inference(ems,[status(thm)],[16974,21196]),
[iquote('0:EmS:16974.0,21196.0')] ).
cnf(21677,plain,
equal(and__dfg(not__dfg(equiv__dfg(skc55,u)),u),not__dfg(skc55)),
inference(spr,[status(thm),theory(equality)],[21431,183]),
[iquote('0:SpR:21431.0,183.0')] ).
cnf(22081,plain,
equal(and__dfg(not__dfg(not__dfg(skc55)),and__dfg(u,not__dfg(skc55))),not__dfg(skc55)),
inference(spr,[status(thm),theory(equality)],[20636,21677]),
[iquote('0:SpR:20636.0,21677.0')] ).
cnf(22084,plain,
equal(and__dfg(u,not__dfg(skc55)),not__dfg(skc55)),
inference(rew,[status(thm),theory(equality)],[18170,22081,10445]),
[iquote('0:Rew:18170.0,22081.0,10445.0,22081.0')] ).
cnf(22090,plain,
is_a_theorem(or__dfg(u,implies__dfg(u,not__dfg(skc55)))),
inference(rew,[status(thm),theory(equality)],[22084,18013]),
[iquote('0:Rew:22084.0,18013.0')] ).
cnf(22208,plain,
is_a_theorem(or__dfg(implies__dfg(u,not__dfg(skc55)),u)),
inference(sor,[status(thm)],[260,22090]),
[iquote('0:SoR:260.0,22090.0')] ).
cnf(22232,plain,
is_a_theorem(implies__dfg(equiv__dfg(skc55,u),u)),
inference(rew,[status(thm),theory(equality)],[17779,22208,172]),
[iquote('0:Rew:17779.0,22208.0,172.0,22208.0')] ).
cnf(22338,plain,
equal(implies__dfg(equiv__dfg(skc55,u),u),skc55),
inference(ems,[status(thm)],[16974,22232]),
[iquote('0:EmS:16974.0,22232.0')] ).
cnf(22360,plain,
equal(equiv__dfg(u,equiv__dfg(skc55,u)),skc55),
inference(rew,[status(thm),theory(equality)],[22338,21428]),
[iquote('0:Rew:22338.0,21428.0')] ).
cnf(22403,plain,
( ~ is_a_theorem(skc55)
| equal(equiv__dfg(skc55,u),u) ),
inference(spl,[status(thm),theory(equality)],[22360,81]),
[iquote('0:SpL:22360.0,81.0')] ).
cnf(22404,plain,
equal(equiv__dfg(skc55,u),u),
inference(mrr,[status(thm)],[22403,272]),
[iquote('0:MRR:22403.0,272.0')] ).
cnf(22485,plain,
equal(implies__dfg(u,or__dfg(u,v)),skc55),
inference(rew,[status(thm),theory(equality)],[22404,17845]),
[iquote('0:Rew:22404.0,17845.0')] ).
cnf(22512,plain,
~ is_a_theorem(skc55),
inference(rew,[status(thm),theory(equality)],[22485,1572]),
[iquote('0:Rew:22485.0,1572.0')] ).
cnf(22517,plain,
$false,
inference(mrr,[status(thm)],[22512,272]),
[iquote('0:MRR:22512.0,272.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL500+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 4 06:20:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 5.08/5.27
% 5.08/5.27 SPASS V 3.9
% 5.08/5.27 SPASS beiseite: Proof found.
% 5.08/5.27 % SZS status Theorem
% 5.08/5.27 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.08/5.27 SPASS derived 15555 clauses, backtracked 0 clauses, performed 0 splits and kept 5283 clauses.
% 5.08/5.27 SPASS allocated 119951 KBytes.
% 5.08/5.27 SPASS spent 0:00:04.92 on the problem.
% 5.08/5.27 0:00:00.04 for the input.
% 5.08/5.27 0:00:00.04 for the FLOTTER CNF translation.
% 5.08/5.27 0:00:00.17 for inferences.
% 5.08/5.27 0:00:00.00 for the backtracking.
% 5.08/5.27 0:00:04.59 for the reduction.
% 5.08/5.27
% 5.08/5.27
% 5.08/5.27 Here is a proof with depth 23, length 252 :
% 5.08/5.27 % SZS output start Refutation
% See solution above
% 5.30/5.51 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_kn2 modus_ponens r2 and_1 or_1 kn1 kn2 r1 cn2 r3 op_implies_or op_implies_and op_or op_and op_equiv r4 r5
% 5.30/5.51
%------------------------------------------------------------------------------