TSTP Solution File: LCL495+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL495+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 14:37:22 EDT 2022
% Result : Theorem 15.96s 16.17s
% Output : Refutation 15.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 30
% Syntax : Number of clauses : 178 ( 129 unt; 0 nHn; 178 RR)
% Number of literals : 232 ( 0 equ; 60 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 : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
op_or,
file('LCL495+1.p',unknown),
[] ).
cnf(2,axiom,
op_implies_and,
file('LCL495+1.p',unknown),
[] ).
cnf(4,axiom,
op_implies_or,
file('LCL495+1.p',unknown),
[] ).
cnf(5,axiom,
op_and,
file('LCL495+1.p',unknown),
[] ).
cnf(6,axiom,
op_equiv,
file('LCL495+1.p',unknown),
[] ).
cnf(7,axiom,
modus_ponens,
file('LCL495+1.p',unknown),
[] ).
cnf(8,axiom,
r1,
file('LCL495+1.p',unknown),
[] ).
cnf(9,axiom,
r2,
file('LCL495+1.p',unknown),
[] ).
cnf(10,axiom,
r3,
file('LCL495+1.p',unknown),
[] ).
cnf(11,axiom,
r4,
file('LCL495+1.p',unknown),
[] ).
cnf(12,axiom,
r5,
file('LCL495+1.p',unknown),
[] ).
cnf(13,axiom,
substitution_of_equivalents,
file('LCL495+1.p',unknown),
[] ).
cnf(14,axiom,
~ equivalence_3,
file('LCL495+1.p',unknown),
[] ).
cnf(15,axiom,
is_a_theorem(skc56),
file('LCL495+1.p',unknown),
[] ).
cnf(16,axiom,
is_a_theorem(implies__dfg(skc56,skc55)),
file('LCL495+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ r1
| is_a_theorem(implies__dfg(or__dfg(u,u),u)) ),
file('LCL495+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ r2
| is_a_theorem(implies__dfg(u,or__dfg(v,u))) ),
file('LCL495+1.p',unknown),
[] ).
cnf(42,axiom,
( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv__dfg(u,v))
| equal(u,v) ),
file('LCL495+1.p',unknown),
[] ).
cnf(43,axiom,
( ~ and_3
| is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))) ),
file('LCL495+1.p',unknown),
[] ).
cnf(44,axiom,
( ~ is_a_theorem(implies__dfg(skc73,implies__dfg(skc72,and__dfg(skc73,skc72))))
| and_3 ),
file('LCL495+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ r3
| is_a_theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))) ),
file('LCL495+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ op_implies_or
| equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)) ),
file('LCL495+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ op_implies_and
| equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)) ),
file('LCL495+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ is_a_theorem(u)
| ~ modus_ponens
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL495+1.p',unknown),
[] ).
cnf(58,axiom,
( ~ op_or
| equal(not__dfg(and__dfg(not__dfg(u),not__dfg(v))),or__dfg(u,v)) ),
file('LCL495+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ op_and
| equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and__dfg(u,v)) ),
file('LCL495+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ op_equiv
| equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)) ),
file('LCL495+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ is_a_theorem(implies__dfg(implies__dfg(skc86,skc85),implies__dfg(implies__dfg(skc85,skc86),equiv__dfg(skc86,skc85))))
| equivalence_3 ),
file('LCL495+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('LCL495+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('LCL495+1.p',unknown),
[] ).
cnf(75,plain,
is_a_theorem(implies__dfg(u,or__dfg(v,u))),
inference(mrr,[status(thm)],[36,9]),
[iquote('0:MRR:36.0,9.0')] ).
cnf(76,plain,
is_a_theorem(implies__dfg(or__dfg(u,u),u)),
inference(mrr,[status(thm)],[34,8]),
[iquote('0:MRR:34.0,8.0')] ).
cnf(78,plain,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
inference(mrr,[status(thm)],[51,4]),
[iquote('0:MRR:51.0,4.0')] ).
cnf(79,plain,
is_a_theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
inference(mrr,[status(thm)],[49,10]),
[iquote('0:MRR:49.0,10.0')] ).
cnf(80,plain,
( ~ is_a_theorem(equiv__dfg(u,v))
| equal(u,v) ),
inference(mrr,[status(thm)],[42,13]),
[iquote('0:MRR:42.0,13.0')] ).
cnf(81,plain,
equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)),
inference(mrr,[status(thm)],[52,2]),
[iquote('0:MRR:52.0,2.0')] ).
cnf(82,plain,
( ~ op_and
| equal(not__dfg(implies__dfg(u,not__dfg(v))),and__dfg(u,v)) ),
inference(rew,[status(thm),theory(equality)],[78,59]),
[iquote('0:Rew:78.0,59.1')] ).
cnf(83,plain,
equal(not__dfg(implies__dfg(u,not__dfg(v))),and__dfg(u,v)),
inference(mrr,[status(thm)],[82,5]),
[iquote('0:MRR:82.0,5.0')] ).
cnf(84,plain,
( ~ op_or
| equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)) ),
inference(rew,[status(thm),theory(equality)],[81,58]),
[iquote('0:Rew:81.0,58.1')] ).
cnf(85,plain,
equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)),
inference(mrr,[status(thm)],[84,1]),
[iquote('0:MRR:84.0,1.0')] ).
cnf(93,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(mrr,[status(thm)],[53,7]),
[iquote('0:MRR:53.1,7.0')] ).
cnf(94,plain,
equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)),
inference(mrr,[status(thm)],[60,6]),
[iquote('0:MRR:60.0,6.0')] ).
cnf(95,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),
inference(mrr,[status(thm)],[69,12]),
[iquote('0:MRR:69.0,12.0')] ).
cnf(96,plain,
is_a_theorem(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
inference(mrr,[status(thm)],[67,11]),
[iquote('0:MRR:67.0,11.0')] ).
cnf(97,plain,
~ is_a_theorem(implies__dfg(implies__dfg(skc86,skc85),implies__dfg(implies__dfg(skc85,skc86),equiv__dfg(skc86,skc85)))),
inference(mrr,[status(thm)],[64,14]),
[iquote('0:MRR:64.1,14.0')] ).
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(122,plain,
is_a_theorem(or__dfg(u,or__dfg(v,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[85,75]),
[iquote('0:SpR:85.0,75.0')] ).
cnf(130,plain,
is_a_theorem(or__dfg(u,implies__dfg(v,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[85,115]),
[iquote('0:SpR:85.0,115.0')] ).
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)],[81,78]),
[iquote('0:SpR:81.0,78.0')] ).
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)],[81,85]),
[iquote('0:SpR:81.0,85.0')] ).
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)],[81]),
[iquote('0:SpR:81.0,81.0')] ).
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)],[83,78]),
[iquote('0:SpR:83.0,78.0')] ).
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)],[83,85]),
[iquote('0:SpR:83.0,85.0')] ).
cnf(186,plain,
equal(not__dfg(or__dfg(u,not__dfg(v))),and__dfg(not__dfg(u),v)),
inference(spr,[status(thm),theory(equality)],[85,83]),
[iquote('0:SpR:85.0,83.0')] ).
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(200,plain,
is_a_theorem(implies__dfg(implies__dfg(u,not__dfg(v)),implies__dfg(v,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[78,136]),
[iquote('0:SpR:78.0,136.0')] ).
cnf(201,plain,
is_a_theorem(or__dfg(and__dfg(u,v),implies__dfg(v,not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[173,200]),
[iquote('0:Rew:173.0,200.0')] ).
cnf(255,plain,
( ~ is_a_theorem(not__dfg(u))
| ~ is_a_theorem(or__dfg(u,v))
| is_a_theorem(v) ),
inference(spl,[status(thm),theory(equality)],[85,93]),
[iquote('0:SpL:85.0,93.1')] ).
cnf(256,plain,
( ~ is_a_theorem(skc56)
| is_a_theorem(skc55) ),
inference(res,[status(thm),theory(equality)],[16,93]),
[iquote('0:Res:16.0,93.1')] ).
cnf(259,plain,
( ~ is_a_theorem(u)
| is_a_theorem(or__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[75,93]),
[iquote('0:Res:75.0,93.1')] ).
cnf(263,plain,
( ~ is_a_theorem(or__dfg(u,v))
| is_a_theorem(or__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[79,93]),
[iquote('0:Res:79.0,93.1')] ).
cnf(264,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(or__dfg(v,not__dfg(u))) ),
inference(res,[status(thm),theory(equality)],[137,93]),
[iquote('0:Res:137.0,93.1')] ).
cnf(270,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[115,93]),
[iquote('0:Res:115.0,93.1')] ).
cnf(274,plain,
( ~ is_a_theorem(or__dfg(u,not__dfg(v)))
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[136,93]),
[iquote('0:Res:136.0,93.1')] ).
cnf(277,plain,
is_a_theorem(skc55),
inference(ssi,[status(thm)],[256,15]),
[iquote('0:SSi:256.0,15.0')] ).
cnf(287,plain,
( ~ and_3
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,u),equiv__dfg(u,v)))) ),
inference(spr,[status(thm),theory(equality)],[94,43]),
[iquote('0:SpR:94.0,43.1')] ).
cnf(315,plain,
is_a_theorem(implies__dfg(or__dfg(not__dfg(u),or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
inference(spr,[status(thm),theory(equality)],[78,96]),
[iquote('0:SpR:78.0,96.0')] ).
cnf(316,plain,
is_a_theorem(implies__dfg(or__dfg(u,or__dfg(not__dfg(v),w)),implies__dfg(v,or__dfg(u,w)))),
inference(spr,[status(thm),theory(equality)],[78,96]),
[iquote('0:SpR:78.0,96.0')] ).
cnf(319,plain,
( ~ is_a_theorem(or__dfg(u,or__dfg(v,w)))
| is_a_theorem(or__dfg(v,or__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[96,93]),
[iquote('0:Res:96.0,93.1')] ).
cnf(320,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)],[78,315]),
[iquote('0:Rew:78.0,315.0')] ).
cnf(321,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)],[78,316]),
[iquote('0:Rew:78.0,316.0')] ).
cnf(328,plain,
is_a_theorem(implies__dfg(or__dfg(u,v),implies__dfg(or__dfg(w,not__dfg(u)),or__dfg(w,v)))),
inference(spr,[status(thm),theory(equality)],[85,95]),
[iquote('0:SpR:85.0,95.0')] ).
cnf(329,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(or__dfg(w,u),or__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[95,93]),
[iquote('0:Res:95.0,93.1')] ).
cnf(362,plain,
is_a_theorem(or__dfg(implies__dfg(u,not__dfg(v)),and__dfg(v,u))),
inference(sor,[status(thm)],[263,201]),
[iquote('0:SoR:263.0,201.0')] ).
cnf(371,plain,
is_a_theorem(or__dfg(implies__dfg(u,not__dfg(v)),v)),
inference(sor,[status(thm)],[263,130]),
[iquote('0:SoR:263.0,130.0')] ).
cnf(381,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),v)),
inference(rew,[status(thm),theory(equality)],[174,371]),
[iquote('0:Rew:174.0,371.0')] ).
cnf(389,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),and__dfg(v,u))),
inference(rew,[status(thm),theory(equality)],[174,362]),
[iquote('0:Rew:174.0,362.0')] ).
cnf(526,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)],[186,85]),
[iquote('0:SpR:186.0,85.0')] ).
cnf(556,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(557,plain,
equal(and__dfg(not__dfg(not__dfg(u)),v),and__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[83,556]),
[iquote('0:Rew:83.0,556.0')] ).
cnf(1081,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(1117,plain,
is_a_theorem(implies__dfg(or__dfg(u,u),not__dfg(not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[85,1081]),
[iquote('0:Rew:85.0,1081.0')] ).
cnf(1180,plain,
( ~ is_a_theorem(or__dfg(u,u))
| is_a_theorem(not__dfg(not__dfg(u))) ),
inference(res,[status(thm),theory(equality)],[1117,93]),
[iquote('0:Res:1117.0,93.1')] ).
cnf(1547,plain,
is_a_theorem(implies__dfg(implies__dfg(u,or__dfg(not__dfg(v),w)),implies__dfg(v,implies__dfg(u,w)))),
inference(spr,[status(thm),theory(equality)],[78,320]),
[iquote('0:SpR:78.0,320.0')] ).
cnf(1558,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(v,implies__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[78,1547]),
[iquote('0:Rew:78.0,1547.0')] ).
cnf(1606,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)],[321,93]),
[iquote('0:Res:321.0,93.1')] ).
cnf(1817,plain,
equal(implies__dfg(implies__dfg(u,v),and__dfg(v,not__dfg(u))),not__dfg(equiv__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[94,164]),
[iquote('0:SpR:94.0,164.0')] ).
cnf(2825,plain,
( ~ is_a_theorem(or__dfg(u,v))
| is_a_theorem(or__dfg(u,or__dfg(w,v))) ),
inference(sor,[status(thm)],[319,259]),
[iquote('0:SoR:319.0,259.1')] ).
cnf(2828,plain,
is_a_theorem(or__dfg(u,or__dfg(v,not__dfg(v)))),
inference(sor,[status(thm)],[319,122]),
[iquote('0:SoR:319.0,122.0')] ).
cnf(2832,plain,
is_a_theorem(or__dfg(or__dfg(u,not__dfg(u)),v)),
inference(sor,[status(thm)],[263,2828]),
[iquote('0:SoR:263.0,2828.0')] ).
cnf(2847,plain,
is_a_theorem(implies__dfg(and__dfg(not__dfg(u),u),v)),
inference(rew,[status(thm),theory(equality)],[526,2832]),
[iquote('0:Rew:526.0,2832.0')] ).
cnf(2993,plain,
is_a_theorem(implies__dfg(and__dfg(u,not__dfg(u)),v)),
inference(spr,[status(thm),theory(equality)],[557,2847]),
[iquote('0:SpR:557.0,2847.0')] ).
cnf(2996,plain,
is_a_theorem(or__dfg(implies__dfg(u,u),v)),
inference(rew,[status(thm),theory(equality)],[155,2993]),
[iquote('0:Rew:155.0,2993.0')] ).
cnf(3076,plain,
is_a_theorem(implies__dfg(or__dfg(u,skc56),or__dfg(u,skc55))),
inference(sor,[status(thm)],[329,16]),
[iquote('0:SoR:329.0,16.0')] ).
cnf(3078,plain,
is_a_theorem(not__dfg(not__dfg(implies__dfg(u,u)))),
inference(sor,[status(thm)],[1180,2996]),
[iquote('0:SoR:1180.0,2996.0')] ).
cnf(3087,plain,
( ~ is_a_theorem(or__dfg(not__dfg(implies__dfg(u,u)),v))
| is_a_theorem(v) ),
inference(sor,[status(thm)],[255,3078]),
[iquote('0:SoR:255.0,3078.0')] ).
cnf(3097,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,u),v))
| is_a_theorem(v) ),
inference(rew,[status(thm),theory(equality)],[78,3087]),
[iquote('0:Rew:78.0,3087.0')] ).
cnf(3130,plain,
~ and_3,
inference(res,[status(thm),theory(equality)],[287,97]),
[iquote('0:Res:287.1,97.0')] ).
cnf(3132,plain,
~ is_a_theorem(implies__dfg(skc73,implies__dfg(skc72,and__dfg(skc73,skc72)))),
inference(mrr,[status(thm)],[44,3130]),
[iquote('0:MRR:44.1,3130.0')] ).
cnf(3189,plain,
( ~ is_a_theorem(or__dfg(u,skc56))
| is_a_theorem(or__dfg(u,skc55)) ),
inference(res,[status(thm),theory(equality)],[3076,93]),
[iquote('0:Res:3076.0,93.1')] ).
cnf(3192,plain,
is_a_theorem(or__dfg(u,skc55)),
inference(ssi,[status(thm)],[3189,259,15]),
[iquote('0:SSi:3189.0,259.0,15.1')] ).
cnf(3197,plain,
is_a_theorem(not__dfg(not__dfg(skc55))),
inference(sor,[status(thm)],[1180,3192]),
[iquote('0:SoR:1180.0,3192.0')] ).
cnf(3199,plain,
is_a_theorem(or__dfg(skc55,u)),
inference(sor,[status(thm)],[263,3192]),
[iquote('0:SoR:263.0,3192.0')] ).
cnf(3203,plain,
( ~ is_a_theorem(or__dfg(not__dfg(skc55),u))
| is_a_theorem(u) ),
inference(sor,[status(thm)],[255,3197]),
[iquote('0:SoR:255.0,3197.0')] ).
cnf(3206,plain,
( ~ is_a_theorem(implies__dfg(skc55,u))
| is_a_theorem(u) ),
inference(rew,[status(thm),theory(equality)],[78,3203]),
[iquote('0:Rew:78.0,3203.0')] ).
cnf(3226,plain,
is_a_theorem(or__dfg(u,or__dfg(skc55,v))),
inference(sor,[status(thm)],[319,3199]),
[iquote('0:SoR:319.0,3199.0')] ).
cnf(3238,plain,
is_a_theorem(not__dfg(not__dfg(or__dfg(skc55,u)))),
inference(sor,[status(thm)],[1180,3226]),
[iquote('0:SoR:1180.0,3226.0')] ).
cnf(3244,plain,
( ~ is_a_theorem(or__dfg(not__dfg(or__dfg(skc55,u)),v))
| is_a_theorem(v) ),
inference(sor,[status(thm)],[255,3238]),
[iquote('0:SoR:255.0,3238.0')] ).
cnf(3248,plain,
( ~ is_a_theorem(implies__dfg(or__dfg(skc55,u),v))
| is_a_theorem(v) ),
inference(rew,[status(thm),theory(equality)],[78,3244]),
[iquote('0:Rew:78.0,3244.0')] ).
cnf(4553,plain,
is_a_theorem(implies__dfg(or__dfg(u,not__dfg(skc55)),or__dfg(u,v))),
inference(res,[status(thm),theory(equality)],[328,3248]),
[iquote('0:Res:328.0,3248.0')] ).
cnf(4872,plain,
is_a_theorem(implies__dfg(or__dfg(not__dfg(u),not__dfg(skc55)),implies__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[78,4553]),
[iquote('0:SpR:78.0,4553.0')] ).
cnf(4881,plain,
is_a_theorem(or__dfg(and__dfg(u,skc55),implies__dfg(u,v))),
inference(rew,[status(thm),theory(equality)],[173,4872,78]),
[iquote('0:Rew:173.0,4872.0,78.0,4872.0')] ).
cnf(5734,plain,
is_a_theorem(or__dfg(u,or__dfg(v,skc55))),
inference(sor,[status(thm)],[2825,3192]),
[iquote('0:SoR:2825.0,3192.0')] ).
cnf(5755,plain,
is_a_theorem(not__dfg(not__dfg(or__dfg(u,skc55)))),
inference(sor,[status(thm)],[1180,5734]),
[iquote('0:SoR:1180.0,5734.0')] ).
cnf(5762,plain,
is_a_theorem(implies__dfg(u,or__dfg(v,skc55))),
inference(spr,[status(thm),theory(equality)],[78,5734]),
[iquote('0:SpR:78.0,5734.0')] ).
cnf(5769,plain,
is_a_theorem(not__dfg(not__dfg(implies__dfg(u,skc55)))),
inference(spr,[status(thm),theory(equality)],[78,5755]),
[iquote('0:SpR:78.0,5755.0')] ).
cnf(5787,plain,
( ~ is_a_theorem(or__dfg(not__dfg(implies__dfg(u,skc55)),v))
| is_a_theorem(v) ),
inference(sor,[status(thm)],[255,5769]),
[iquote('0:SoR:255.0,5769.0')] ).
cnf(5794,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,skc55),v))
| is_a_theorem(v) ),
inference(rew,[status(thm),theory(equality)],[78,5787]),
[iquote('0:Rew:78.0,5787.0')] ).
cnf(8914,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),v))),
inference(res,[status(thm),theory(equality)],[1558,3097]),
[iquote('0:Res:1558.0,3097.0')] ).
cnf(9167,plain,
is_a_theorem(implies__dfg(implies__dfg(skc55,u),u)),
inference(res,[status(thm),theory(equality)],[8914,3206]),
[iquote('0:Res:8914.0,3206.0')] ).
cnf(9168,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,skc55),v),v)),
inference(res,[status(thm),theory(equality)],[8914,5794]),
[iquote('0:Res:8914.0,5794.0')] ).
cnf(9181,plain,
is_a_theorem(or__dfg(u,not__dfg(implies__dfg(skc55,u)))),
inference(sor,[status(thm)],[264,9167]),
[iquote('0:SoR:264.0,9167.0')] ).
cnf(9183,plain,
( ~ is_a_theorem(implies__dfg(skc55,u))
| is_a_theorem(u) ),
inference(res,[status(thm),theory(equality)],[9167,93]),
[iquote('0:Res:9167.0,93.1')] ).
cnf(9190,plain,
is_a_theorem(or__dfg(not__dfg(u),and__dfg(skc55,u))),
inference(spr,[status(thm),theory(equality)],[83,9181]),
[iquote('0:SpR:83.0,9181.0')] ).
cnf(9199,plain,
is_a_theorem(implies__dfg(u,and__dfg(skc55,u))),
inference(rew,[status(thm),theory(equality)],[78,9190]),
[iquote('0:Rew:78.0,9190.0')] ).
cnf(9544,plain,
is_a_theorem(implies__dfg(u,or__dfg(and__dfg(u,skc55),v))),
inference(sor,[status(thm)],[1606,4881]),
[iquote('0:SoR:1606.0,4881.0')] ).
cnf(9548,plain,
is_a_theorem(implies__dfg(u,or__dfg(and__dfg(v,u),not__dfg(v)))),
inference(sor,[status(thm)],[1606,201]),
[iquote('0:SoR:1606.0,201.0')] ).
cnf(9724,plain,
is_a_theorem(or__dfg(and__dfg(skc55,skc55),u)),
inference(sor,[status(thm)],[9183,9544]),
[iquote('0:SoR:9183.0,9544.0')] ).
cnf(9748,plain,
is_a_theorem(implies__dfg(u,and__dfg(skc55,skc55))),
inference(sor,[status(thm)],[274,9724]),
[iquote('0:SoR:274.0,9724.0')] ).
cnf(10008,plain,
is_a_theorem(implies__dfg(not__dfg(equiv__dfg(u,skc55)),and__dfg(skc55,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[1817,9168]),
[iquote('0:SpR:1817.0,9168.0')] ).
cnf(10049,plain,
is_a_theorem(or__dfg(equiv__dfg(u,skc55),and__dfg(skc55,not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[85,10008]),
[iquote('0:Rew:85.0,10008.0')] ).
cnf(12964,plain,
is_a_theorem(or__dfg(and__dfg(skc55,not__dfg(u)),equiv__dfg(u,skc55))),
inference(sor,[status(thm)],[263,10049]),
[iquote('0:SoR:263.0,10049.0')] ).
cnf(12967,plain,
is_a_theorem(implies__dfg(implies__dfg(skc55,u),equiv__dfg(u,skc55))),
inference(rew,[status(thm),theory(equality)],[156,12964]),
[iquote('0:Rew:156.0,12964.0')] ).
cnf(12976,plain,
( ~ is_a_theorem(implies__dfg(skc55,u))
| is_a_theorem(equiv__dfg(u,skc55)) ),
inference(res,[status(thm),theory(equality)],[12967,93]),
[iquote('0:Res:12967.0,93.1')] ).
cnf(13506,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equiv__dfg(u,skc55)) ),
inference(sor,[status(thm)],[12976,270]),
[iquote('0:SoR:12976.0,270.1')] ).
cnf(13524,plain,
is_a_theorem(equiv__dfg(or__dfg(u,skc55),skc55)),
inference(sor,[status(thm)],[12976,5762]),
[iquote('0:SoR:12976.0,5762.0')] ).
cnf(13542,plain,
is_a_theorem(equiv__dfg(and__dfg(skc55,skc55),skc55)),
inference(sor,[status(thm)],[12976,9748]),
[iquote('0:SoR:12976.0,9748.0')] ).
cnf(13557,plain,
equal(and__dfg(skc55,skc55),skc55),
inference(res,[status(thm),theory(equality)],[13542,80]),
[iquote('0:Res:13542.0,80.0')] ).
cnf(14287,plain,
equal(or__dfg(u,skc55),skc55),
inference(res,[status(thm),theory(equality)],[13524,80]),
[iquote('0:Res:13524.0,80.0')] ).
cnf(14592,plain,
equal(implies__dfg(u,skc55),skc55),
inference(spr,[status(thm),theory(equality)],[14287,78]),
[iquote('0:SpR:14287.0,78.0')] ).
cnf(14945,plain,
equal(and__dfg(skc55,implies__dfg(skc55,u)),equiv__dfg(u,skc55)),
inference(spr,[status(thm),theory(equality)],[14592,94]),
[iquote('0:SpR:14592.0,94.0')] ).
cnf(16622,plain,
( ~ is_a_theorem(u)
| equal(u,skc55) ),
inference(res,[status(thm),theory(equality)],[13506,80]),
[iquote('0:Res:13506.1,80.0')] ).
cnf(16697,plain,
equal(implies__dfg(implies__dfg(skc55,u),u),skc55),
inference(ems,[status(thm)],[16622,9167]),
[iquote('0:EmS:16622.0,9167.0')] ).
cnf(16703,plain,
equal(implies__dfg(u,and__dfg(skc55,u)),skc55),
inference(ems,[status(thm)],[16622,9199]),
[iquote('0:EmS:16622.0,9199.0')] ).
cnf(16735,plain,
equal(implies__dfg(u,implies__dfg(v,u)),skc55),
inference(ems,[status(thm)],[16622,115]),
[iquote('0:EmS:16622.0,115.0')] ).
cnf(16740,plain,
equal(implies__dfg(and__dfg(u,v),and__dfg(v,u)),skc55),
inference(ems,[status(thm)],[16622,389]),
[iquote('0:EmS:16622.0,389.0')] ).
cnf(16741,plain,
equal(implies__dfg(and__dfg(u,v),v),skc55),
inference(ems,[status(thm)],[16622,381]),
[iquote('0:EmS:16622.0,381.0')] ).
cnf(16775,plain,
equal(implies__dfg(or__dfg(u,v),or__dfg(v,u)),skc55),
inference(ems,[status(thm)],[16622,79]),
[iquote('0:EmS:16622.0,79.0')] ).
cnf(17173,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)],[16697,94]),
[iquote('0:SpR:16697.0,94.0')] ).
cnf(17190,plain,
equal(equiv__dfg(u,implies__dfg(skc55,u)),and__dfg(skc55,skc55)),
inference(rew,[status(thm),theory(equality)],[16735,17173]),
[iquote('0:Rew:16735.0,17173.0')] ).
cnf(17191,plain,
equal(equiv__dfg(u,implies__dfg(skc55,u)),skc55),
inference(rew,[status(thm),theory(equality)],[13557,17190]),
[iquote('0:Rew:13557.0,17190.0')] ).
cnf(17198,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)],[16703,94]),
[iquote('0:SpR:16703.0,94.0')] ).
cnf(17213,plain,
equal(equiv__dfg(and__dfg(skc55,u),u),and__dfg(skc55,skc55)),
inference(rew,[status(thm),theory(equality)],[16741,17198]),
[iquote('0:Rew:16741.0,17198.0')] ).
cnf(17214,plain,
equal(equiv__dfg(and__dfg(skc55,u),u),skc55),
inference(rew,[status(thm),theory(equality)],[13557,17213]),
[iquote('0:Rew:13557.0,17213.0')] ).
cnf(17244,plain,
( ~ is_a_theorem(skc55)
| equal(implies__dfg(skc55,u),u) ),
inference(spl,[status(thm),theory(equality)],[17191,80]),
[iquote('0:SpL:17191.0,80.0')] ).
cnf(17245,plain,
equal(implies__dfg(skc55,u),u),
inference(mrr,[status(thm)],[17244,277]),
[iquote('0:MRR:17244.0,277.0')] ).
cnf(17293,plain,
equal(and__dfg(skc55,u),equiv__dfg(u,skc55)),
inference(rew,[status(thm),theory(equality)],[17245,14945]),
[iquote('0:Rew:17245.0,14945.0')] ).
cnf(17407,plain,
equal(equiv__dfg(equiv__dfg(u,skc55),u),skc55),
inference(rew,[status(thm),theory(equality)],[17293,17214]),
[iquote('0:Rew:17293.0,17214.0')] ).
cnf(17620,plain,
( ~ is_a_theorem(skc55)
| equal(equiv__dfg(u,skc55),u) ),
inference(spl,[status(thm),theory(equality)],[17407,80]),
[iquote('0:SpL:17407.0,80.0')] ).
cnf(17621,plain,
equal(equiv__dfg(u,skc55),u),
inference(mrr,[status(thm)],[17620,277]),
[iquote('0:MRR:17620.0,277.0')] ).
cnf(17623,plain,
equal(and__dfg(skc55,u),u),
inference(rew,[status(thm),theory(equality)],[17621,17293]),
[iquote('0:Rew:17621.0,17293.0')] ).
cnf(35574,plain,
equal(implies__dfg(u,or__dfg(and__dfg(v,u),not__dfg(v))),skc55),
inference(ems,[status(thm)],[16622,9548]),
[iquote('0:EmS:16622.0,9548.0')] ).
cnf(38569,plain,
equal(and__dfg(implies__dfg(and__dfg(u,v),and__dfg(v,u)),skc55),equiv__dfg(and__dfg(u,v),and__dfg(v,u))),
inference(spr,[status(thm),theory(equality)],[16740,94]),
[iquote('0:SpR:16740.0,94.0')] ).
cnf(38698,plain,
equal(equiv__dfg(and__dfg(u,v),and__dfg(v,u)),skc55),
inference(rew,[status(thm),theory(equality)],[17623,38569,16740]),
[iquote('0:Rew:17623.0,38569.0,16740.0,38569.0')] ).
cnf(38704,plain,
equal(and__dfg(implies__dfg(or__dfg(u,v),or__dfg(v,u)),skc55),equiv__dfg(or__dfg(u,v),or__dfg(v,u))),
inference(spr,[status(thm),theory(equality)],[16775,94]),
[iquote('0:SpR:16775.0,94.0')] ).
cnf(38812,plain,
equal(equiv__dfg(or__dfg(u,v),or__dfg(v,u)),skc55),
inference(rew,[status(thm),theory(equality)],[17623,38704,16775]),
[iquote('0:Rew:17623.0,38704.0,16775.0,38704.0')] ).
cnf(49470,plain,
( ~ is_a_theorem(skc55)
| equal(and__dfg(u,v),and__dfg(v,u)) ),
inference(spl,[status(thm),theory(equality)],[38698,80]),
[iquote('0:SpL:38698.0,80.0')] ).
cnf(49489,plain,
equal(and__dfg(u,v),and__dfg(v,u)),
inference(mrr,[status(thm)],[49470,277]),
[iquote('0:MRR:49470.0,277.0')] ).
cnf(49498,plain,
~ is_a_theorem(implies__dfg(skc73,implies__dfg(skc72,and__dfg(skc72,skc73)))),
inference(rew,[status(thm),theory(equality)],[49489,3132]),
[iquote('0:Rew:49489.0,3132.0')] ).
cnf(51298,plain,
( ~ is_a_theorem(skc55)
| equal(or__dfg(u,v),or__dfg(v,u)) ),
inference(spl,[status(thm),theory(equality)],[38812,80]),
[iquote('0:SpL:38812.0,80.0')] ).
cnf(51334,plain,
equal(or__dfg(u,v),or__dfg(v,u)),
inference(mrr,[status(thm)],[51298,277]),
[iquote('0:MRR:51298.0,277.0')] ).
cnf(51671,plain,
equal(implies__dfg(u,or__dfg(not__dfg(v),and__dfg(v,u))),skc55),
inference(rew,[status(thm),theory(equality)],[51334,35574]),
[iquote('0:Rew:51334.0,35574.0')] ).
cnf(51804,plain,
equal(implies__dfg(u,implies__dfg(v,and__dfg(v,u))),skc55),
inference(rew,[status(thm),theory(equality)],[78,51671]),
[iquote('0:Rew:78.0,51671.0')] ).
cnf(51805,plain,
~ is_a_theorem(skc55),
inference(rew,[status(thm),theory(equality)],[51804,49498]),
[iquote('0:Rew:51804.0,49498.0')] ).
cnf(51809,plain,
$false,
inference(mrr,[status(thm)],[51805,277]),
[iquote('0:MRR:51805.0,277.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL495+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 : Sat Jul 2 16:33:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 15.96/16.17
% 15.96/16.17 SPASS V 3.9
% 15.96/16.17 SPASS beiseite: Proof found.
% 15.96/16.17 % SZS status Theorem
% 15.96/16.17 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.96/16.17 SPASS derived 33775 clauses, backtracked 0 clauses, performed 0 splits and kept 9097 clauses.
% 15.96/16.17 SPASS allocated 145376 KBytes.
% 15.96/16.17 SPASS spent 0:0:15.79 on the problem.
% 15.96/16.17 0:00:00.04 for the input.
% 15.96/16.17 0:00:00.04 for the FLOTTER CNF translation.
% 15.96/16.17 0:00:00.27 for inferences.
% 15.96/16.17 0:00:00.00 for the backtracking.
% 15.96/16.17 0:0:15.32 for the reduction.
% 15.96/16.17
% 15.96/16.17
% 15.96/16.17 Here is a proof with depth 16, length 178 :
% 15.96/16.17 % SZS output start Refutation
% See solution above
% 15.96/16.17 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_3 modus_ponens r2 r1 and_3 r3 op_implies_or op_implies_and op_or op_and op_equiv equivalence_3 r4 r5
% 17.23/17.44
%------------------------------------------------------------------------------