TSTP Solution File: LCL485+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL485+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 14:37:19 EDT 2022
% Result : Theorem 16.93s 17.18s
% Output : Refutation 18.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 32
% Syntax : Number of clauses : 207 ( 141 unt; 0 nHn; 207 RR)
% Number of literals : 279 ( 0 equ; 74 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 18 ( 17 usr; 16 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
op_or,
file('LCL485+1.p',unknown),
[] ).
cnf(2,axiom,
op_implies_and,
file('LCL485+1.p',unknown),
[] ).
cnf(4,axiom,
op_implies_or,
file('LCL485+1.p',unknown),
[] ).
cnf(5,axiom,
op_and,
file('LCL485+1.p',unknown),
[] ).
cnf(6,axiom,
op_equiv,
file('LCL485+1.p',unknown),
[] ).
cnf(7,axiom,
modus_ponens,
file('LCL485+1.p',unknown),
[] ).
cnf(8,axiom,
r1,
file('LCL485+1.p',unknown),
[] ).
cnf(9,axiom,
r2,
file('LCL485+1.p',unknown),
[] ).
cnf(10,axiom,
r3,
file('LCL485+1.p',unknown),
[] ).
cnf(11,axiom,
r4,
file('LCL485+1.p',unknown),
[] ).
cnf(12,axiom,
r5,
file('LCL485+1.p',unknown),
[] ).
cnf(13,axiom,
substitution_of_equivalents,
file('LCL485+1.p',unknown),
[] ).
cnf(14,axiom,
~ implies_2,
file('LCL485+1.p',unknown),
[] ).
cnf(15,axiom,
is_a_theorem(skc56),
file('LCL485+1.p',unknown),
[] ).
cnf(16,axiom,
is_a_theorem(implies__dfg(skc56,skc55)),
file('LCL485+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ r1
| is_a_theorem(implies__dfg(or__dfg(u,u),u)) ),
file('LCL485+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ r2
| is_a_theorem(implies__dfg(u,or__dfg(v,u))) ),
file('LCL485+1.p',unknown),
[] ).
cnf(42,axiom,
( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv__dfg(u,v))
| equal(u,v) ),
file('LCL485+1.p',unknown),
[] ).
cnf(43,axiom,
( ~ and_3
| is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))) ),
file('LCL485+1.p',unknown),
[] ).
cnf(44,axiom,
( ~ is_a_theorem(implies__dfg(skc73,implies__dfg(skc72,and__dfg(skc73,skc72))))
| and_3 ),
file('LCL485+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ r3
| is_a_theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))) ),
file('LCL485+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ op_implies_or
| equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)) ),
file('LCL485+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ op_implies_and
| equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)) ),
file('LCL485+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ is_a_theorem(u)
| ~ modus_ponens
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL485+1.p',unknown),
[] ).
cnf(57,axiom,
( ~ is_a_theorem(implies__dfg(implies__dfg(skc64,implies__dfg(skc64,skc63)),implies__dfg(skc64,skc63)))
| implies_2 ),
file('LCL485+1.p',unknown),
[] ).
cnf(58,axiom,
( ~ op_or
| equal(not__dfg(and__dfg(not__dfg(u),not__dfg(v))),or__dfg(u,v)) ),
file('LCL485+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ op_and
| equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and__dfg(u,v)) ),
file('LCL485+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ op_equiv
| equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)) ),
file('LCL485+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ equivalence_3
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,u),equiv__dfg(u,v)))) ),
file('LCL485+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('LCL485+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('LCL485+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('LCL485+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(91,plain,
~ is_a_theorem(implies__dfg(implies__dfg(skc64,implies__dfg(skc64,skc63)),implies__dfg(skc64,skc63))),
inference(mrr,[status(thm)],[57,14]),
[iquote('0:MRR:57.1,14.0')] ).
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(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)],[85,94]),
[iquote('0:SpL:85.0,94.1')] ).
cnf(256,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(259,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(263,plain,
( ~ is_a_theorem(or__dfg(u,v))
| is_a_theorem(or__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[79,94]),
[iquote('0:Res:79.0,94.1')] ).
cnf(264,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(or__dfg(v,not__dfg(u))) ),
inference(res,[status(thm),theory(equality)],[137,94]),
[iquote('0:Res:137.0,94.1')] ).
cnf(270,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[115,94]),
[iquote('0:Res:115.0,94.1')] ).
cnf(274,plain,
( ~ is_a_theorem(or__dfg(u,not__dfg(v)))
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[136,94]),
[iquote('0:Res:136.0,94.1')] ).
cnf(277,plain,
is_a_theorem(skc55),
inference(ssi,[status(thm)],[256,15]),
[iquote('0:SSi:256.0,15.0')] ).
cnf(299,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)],[95,43]),
[iquote('0:SpR:95.0,43.1')] ).
cnf(305,plain,
is_a_theorem(implies__dfg(or__dfg(not__dfg(u),or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
inference(spr,[status(thm),theory(equality)],[78,97]),
[iquote('0:SpR:78.0,97.0')] ).
cnf(306,plain,
is_a_theorem(implies__dfg(or__dfg(u,or__dfg(not__dfg(v),w)),implies__dfg(v,or__dfg(u,w)))),
inference(spr,[status(thm),theory(equality)],[78,97]),
[iquote('0:SpR:78.0,97.0')] ).
cnf(309,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(310,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)],[78,305]),
[iquote('0:Rew:78.0,305.0')] ).
cnf(311,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)],[78,306]),
[iquote('0:Rew:78.0,306.0')] ).
cnf(319,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(352,plain,
( ~ is_a_theorem(u)
| is_a_theorem(or__dfg(u,v)) ),
inference(sor,[status(thm)],[263,259]),
[iquote('0:SoR:263.0,259.1')] ).
cnf(353,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(355,plain,
is_a_theorem(or__dfg(not__dfg(u),and__dfg(u,u))),
inference(sor,[status(thm)],[263,187]),
[iquote('0:SoR:263.0,187.0')] ).
cnf(362,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(365,plain,
is_a_theorem(implies__dfg(u,and__dfg(u,u))),
inference(rew,[status(thm),theory(equality)],[78,355]),
[iquote('0:Rew:78.0,355.0')] ).
cnf(372,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),v)),
inference(rew,[status(thm),theory(equality)],[174,362]),
[iquote('0:Rew:174.0,362.0')] ).
cnf(380,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),and__dfg(v,u))),
inference(rew,[status(thm),theory(equality)],[174,353]),
[iquote('0:Rew:174.0,353.0')] ).
cnf(394,plain,
( ~ is_a_theorem(not__dfg(u))
| is_a_theorem(implies__dfg(u,v)) ),
inference(spr,[status(thm),theory(equality)],[78,352]),
[iquote('0:SpR:78.0,352.1')] ).
cnf(398,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| ~ equivalence_3
| is_a_theorem(implies__dfg(implies__dfg(v,u),equiv__dfg(u,v))) ),
inference(res,[status(thm),theory(equality)],[63,94]),
[iquote('0:Res:63.1,94.1')] ).
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)],[186,85]),
[iquote('0:SpR:186.0,85.0')] ).
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)],[78,186]),
[iquote('0:SpR:78.0,186.0')] ).
cnf(559,plain,
equal(and__dfg(not__dfg(not__dfg(u)),v),and__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[83,558]),
[iquote('0:Rew:83.0,558.0')] ).
cnf(1041,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(1076,plain,
is_a_theorem(implies__dfg(or__dfg(u,u),not__dfg(not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[85,1041]),
[iquote('0:Rew:85.0,1041.0')] ).
cnf(1137,plain,
( ~ is_a_theorem(or__dfg(u,u))
| is_a_theorem(not__dfg(not__dfg(u))) ),
inference(res,[status(thm),theory(equality)],[1076,94]),
[iquote('0:Res:1076.0,94.1')] ).
cnf(1525,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)],[311,94]),
[iquote('0:Res:311.0,94.1')] ).
cnf(1682,plain,
equal(implies__dfg(implies__dfg(u,v),and__dfg(v,not__dfg(u))),not__dfg(equiv__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[95,164]),
[iquote('0:SpR:95.0,164.0')] ).
cnf(2665,plain,
( ~ is_a_theorem(or__dfg(u,v))
| is_a_theorem(or__dfg(u,or__dfg(w,v))) ),
inference(sor,[status(thm)],[309,259]),
[iquote('0:SoR:309.0,259.1')] ).
cnf(2668,plain,
is_a_theorem(or__dfg(u,or__dfg(v,not__dfg(v)))),
inference(sor,[status(thm)],[309,122]),
[iquote('0:SoR:309.0,122.0')] ).
cnf(2672,plain,
is_a_theorem(or__dfg(or__dfg(u,not__dfg(u)),v)),
inference(sor,[status(thm)],[263,2668]),
[iquote('0:SoR:263.0,2668.0')] ).
cnf(2687,plain,
is_a_theorem(implies__dfg(and__dfg(not__dfg(u),u),v)),
inference(rew,[status(thm),theory(equality)],[528,2672]),
[iquote('0:Rew:528.0,2672.0')] ).
cnf(2831,plain,
is_a_theorem(implies__dfg(and__dfg(u,not__dfg(u)),v)),
inference(spr,[status(thm),theory(equality)],[559,2687]),
[iquote('0:SpR:559.0,2687.0')] ).
cnf(2834,plain,
is_a_theorem(or__dfg(implies__dfg(u,u),v)),
inference(rew,[status(thm),theory(equality)],[155,2831]),
[iquote('0:Rew:155.0,2831.0')] ).
cnf(2911,plain,
is_a_theorem(implies__dfg(or__dfg(u,skc56),or__dfg(u,skc55))),
inference(sor,[status(thm)],[319,16]),
[iquote('0:SoR:319.0,16.0')] ).
cnf(2913,plain,
is_a_theorem(not__dfg(not__dfg(implies__dfg(u,u)))),
inference(sor,[status(thm)],[1137,2834]),
[iquote('0:SoR:1137.0,2834.0')] ).
cnf(2922,plain,
( ~ is_a_theorem(or__dfg(not__dfg(implies__dfg(u,u)),v))
| is_a_theorem(v) ),
inference(sor,[status(thm)],[255,2913]),
[iquote('0:SoR:255.0,2913.0')] ).
cnf(2932,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,u),v))
| is_a_theorem(v) ),
inference(rew,[status(thm),theory(equality)],[78,2922]),
[iquote('0:Rew:78.0,2922.0')] ).
cnf(2963,plain,
( ~ and_3
| equivalence_3 ),
inference(res,[status(thm),theory(equality)],[299,64]),
[iquote('0:Res:299.1,64.0')] ).
cnf(3025,plain,
( ~ is_a_theorem(or__dfg(u,skc56))
| is_a_theorem(or__dfg(u,skc55)) ),
inference(res,[status(thm),theory(equality)],[2911,94]),
[iquote('0:Res:2911.0,94.1')] ).
cnf(3028,plain,
is_a_theorem(or__dfg(u,skc55)),
inference(ssi,[status(thm)],[3025,259,15]),
[iquote('0:SSi:3025.0,259.0,15.1')] ).
cnf(3052,plain,
is_a_theorem(not__dfg(not__dfg(skc55))),
inference(sor,[status(thm)],[1137,3028]),
[iquote('0:SoR:1137.0,3028.0')] ).
cnf(3058,plain,
( ~ is_a_theorem(or__dfg(not__dfg(skc55),u))
| is_a_theorem(u) ),
inference(sor,[status(thm)],[255,3052]),
[iquote('0:SoR:255.0,3052.0')] ).
cnf(3061,plain,
( ~ is_a_theorem(implies__dfg(skc55,u))
| is_a_theorem(u) ),
inference(rew,[status(thm),theory(equality)],[78,3058]),
[iquote('0:Rew:78.0,3058.0')] ).
cnf(3326,plain,
( ~ equivalence_3
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w))),equiv__dfg(or__dfg(v,implies__dfg(u,w)),implies__dfg(u,or__dfg(v,w))))) ),
inference(sor,[status(thm)],[398,311]),
[iquote('0:SoR:398.0,311.0')] ).
cnf(3327,plain,
( ~ equivalence_3
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),or__dfg(v,not__dfg(u))),equiv__dfg(or__dfg(v,not__dfg(u)),implies__dfg(u,v)))) ),
inference(sor,[status(thm)],[398,136]),
[iquote('0:SoR:398.0,136.0')] ).
cnf(5899,plain,
is_a_theorem(or__dfg(u,implies__dfg(or__dfg(u,v),v))),
inference(res,[status(thm),theory(equality)],[310,2932]),
[iquote('0:Res:310.0,2932.0')] ).
cnf(6094,plain,
is_a_theorem(or__dfg(u,or__dfg(v,skc55))),
inference(sor,[status(thm)],[2665,3028]),
[iquote('0:SoR:2665.0,3028.0')] ).
cnf(6117,plain,
is_a_theorem(not__dfg(not__dfg(or__dfg(u,skc55)))),
inference(sor,[status(thm)],[1137,6094]),
[iquote('0:SoR:1137.0,6094.0')] ).
cnf(6121,plain,
is_a_theorem(or__dfg(u,implies__dfg(v,skc55))),
inference(spr,[status(thm),theory(equality)],[78,6094]),
[iquote('0:SpR:78.0,6094.0')] ).
cnf(6129,plain,
( ~ is_a_theorem(or__dfg(not__dfg(or__dfg(u,skc55)),v))
| is_a_theorem(v) ),
inference(sor,[status(thm)],[255,6117]),
[iquote('0:SoR:255.0,6117.0')] ).
cnf(6135,plain,
( ~ is_a_theorem(implies__dfg(or__dfg(u,skc55),v))
| is_a_theorem(v) ),
inference(rew,[status(thm),theory(equality)],[78,6129]),
[iquote('0:Rew:78.0,6129.0')] ).
cnf(6233,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,skc55))),
inference(spr,[status(thm),theory(equality)],[78,6121]),
[iquote('0:SpR:78.0,6121.0')] ).
cnf(7363,plain,
is_a_theorem(or__dfg(not__dfg(u),implies__dfg(implies__dfg(u,v),v))),
inference(spr,[status(thm),theory(equality)],[78,5899]),
[iquote('0:SpR:78.0,5899.0')] ).
cnf(7369,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),v))),
inference(rew,[status(thm),theory(equality)],[78,7363]),
[iquote('0:Rew:78.0,7363.0')] ).
cnf(7553,plain,
is_a_theorem(implies__dfg(implies__dfg(skc55,u),u)),
inference(res,[status(thm),theory(equality)],[7369,3061]),
[iquote('0:Res:7369.0,3061.0')] ).
cnf(7566,plain,
is_a_theorem(or__dfg(u,not__dfg(implies__dfg(skc55,u)))),
inference(sor,[status(thm)],[264,7553]),
[iquote('0:SoR:264.0,7553.0')] ).
cnf(7567,plain,
is_a_theorem(or__dfg(and__dfg(skc55,u),not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[173,7553]),
[iquote('0:SpR:173.0,7553.0')] ).
cnf(7574,plain,
is_a_theorem(or__dfg(not__dfg(u),and__dfg(skc55,u))),
inference(spr,[status(thm),theory(equality)],[83,7566]),
[iquote('0:SpR:83.0,7566.0')] ).
cnf(7581,plain,
is_a_theorem(implies__dfg(u,and__dfg(skc55,u))),
inference(rew,[status(thm),theory(equality)],[78,7574]),
[iquote('0:Rew:78.0,7574.0')] ).
cnf(7707,plain,
is_a_theorem(implies__dfg(implies__dfg(skc55,u),not__dfg(not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[156,7567]),
[iquote('0:SpR:156.0,7567.0')] ).
cnf(7828,plain,
( ~ is_a_theorem(implies__dfg(skc55,u))
| is_a_theorem(not__dfg(not__dfg(u))) ),
inference(res,[status(thm),theory(equality)],[7707,94]),
[iquote('0:Res:7707.0,94.1')] ).
cnf(9263,plain,
is_a_theorem(not__dfg(not__dfg(and__dfg(skc55,skc55)))),
inference(sor,[status(thm)],[7828,7581]),
[iquote('0:SoR:7828.0,7581.0')] ).
cnf(9329,plain,
is_a_theorem(implies__dfg(not__dfg(and__dfg(skc55,skc55)),u)),
inference(sor,[status(thm)],[394,9263]),
[iquote('0:SoR:394.0,9263.0')] ).
cnf(9330,plain,
is_a_theorem(or__dfg(and__dfg(skc55,skc55),u)),
inference(rew,[status(thm),theory(equality)],[85,9329]),
[iquote('0:Rew:85.0,9329.0')] ).
cnf(9354,plain,
is_a_theorem(implies__dfg(u,and__dfg(skc55,skc55))),
inference(sor,[status(thm)],[274,9330]),
[iquote('0:SoR:274.0,9330.0')] ).
cnf(9910,plain,
is_a_theorem(implies__dfg(u,or__dfg(and__dfg(v,u),not__dfg(v)))),
inference(sor,[status(thm)],[1525,201]),
[iquote('0:SoR:1525.0,201.0')] ).
cnf(13784,plain,
is_a_theorem(implies__dfg(implies__dfg(or__dfg(u,skc55),v),v)),
inference(res,[status(thm),theory(equality)],[7369,6135]),
[iquote('0:Res:7369.0,6135.0')] ).
cnf(14096,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,skc55),v),v)),
inference(spr,[status(thm),theory(equality)],[78,13784]),
[iquote('0:SpR:78.0,13784.0')] ).
cnf(14120,plain,
is_a_theorem(implies__dfg(not__dfg(equiv__dfg(u,skc55)),and__dfg(skc55,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[1682,14096]),
[iquote('0:SpR:1682.0,14096.0')] ).
cnf(14125,plain,
is_a_theorem(or__dfg(equiv__dfg(u,skc55),and__dfg(skc55,not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[85,14120]),
[iquote('0:Rew:85.0,14120.0')] ).
cnf(14209,plain,
is_a_theorem(or__dfg(and__dfg(skc55,not__dfg(u)),equiv__dfg(u,skc55))),
inference(sor,[status(thm)],[263,14125]),
[iquote('0:SoR:263.0,14125.0')] ).
cnf(14212,plain,
is_a_theorem(implies__dfg(implies__dfg(skc55,u),equiv__dfg(u,skc55))),
inference(rew,[status(thm),theory(equality)],[156,14209]),
[iquote('0:Rew:156.0,14209.0')] ).
cnf(14222,plain,
( ~ is_a_theorem(implies__dfg(skc55,u))
| is_a_theorem(equiv__dfg(u,skc55)) ),
inference(res,[status(thm),theory(equality)],[14212,94]),
[iquote('0:Res:14212.0,94.1')] ).
cnf(14278,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equiv__dfg(u,skc55)) ),
inference(sor,[status(thm)],[14222,270]),
[iquote('0:SoR:14222.0,270.1')] ).
cnf(14291,plain,
is_a_theorem(equiv__dfg(implies__dfg(u,skc55),skc55)),
inference(sor,[status(thm)],[14222,6233]),
[iquote('0:SoR:14222.0,6233.0')] ).
cnf(14318,plain,
is_a_theorem(equiv__dfg(and__dfg(skc55,skc55),skc55)),
inference(sor,[status(thm)],[14222,9354]),
[iquote('0:SoR:14222.0,9354.0')] ).
cnf(14334,plain,
equal(and__dfg(skc55,skc55),skc55),
inference(res,[status(thm),theory(equality)],[14318,80]),
[iquote('0:Res:14318.0,80.0')] ).
cnf(14555,plain,
equal(implies__dfg(u,skc55),skc55),
inference(res,[status(thm),theory(equality)],[14291,80]),
[iquote('0:Res:14291.0,80.0')] ).
cnf(14899,plain,
equal(and__dfg(skc55,implies__dfg(skc55,u)),equiv__dfg(u,skc55)),
inference(spr,[status(thm),theory(equality)],[14555,95]),
[iquote('0:SpR:14555.0,95.0')] ).
cnf(17904,plain,
( ~ is_a_theorem(u)
| equal(u,skc55) ),
inference(res,[status(thm),theory(equality)],[14278,80]),
[iquote('0:Res:14278.1,80.0')] ).
cnf(17982,plain,
equal(implies__dfg(implies__dfg(skc55,u),u),skc55),
inference(ems,[status(thm)],[17904,7553]),
[iquote('0:EmS:17904.0,7553.0')] ).
cnf(18009,plain,
equal(implies__dfg(u,and__dfg(skc55,u)),skc55),
inference(ems,[status(thm)],[17904,7581]),
[iquote('0:EmS:17904.0,7581.0')] ).
cnf(18010,plain,
equal(implies__dfg(u,and__dfg(u,u)),skc55),
inference(ems,[status(thm)],[17904,365]),
[iquote('0:EmS:17904.0,365.0')] ).
cnf(18039,plain,
equal(implies__dfg(u,implies__dfg(v,u)),skc55),
inference(ems,[status(thm)],[17904,115]),
[iquote('0:EmS:17904.0,115.0')] ).
cnf(18045,plain,
equal(implies__dfg(and__dfg(u,v),and__dfg(v,u)),skc55),
inference(ems,[status(thm)],[17904,380]),
[iquote('0:EmS:17904.0,380.0')] ).
cnf(18046,plain,
equal(implies__dfg(and__dfg(u,v),v),skc55),
inference(ems,[status(thm)],[17904,372]),
[iquote('0:EmS:17904.0,372.0')] ).
cnf(18074,plain,
equal(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w))),skc55),
inference(ems,[status(thm)],[17904,310]),
[iquote('0:EmS:17904.0,310.0')] ).
cnf(18076,plain,
equal(implies__dfg(implies__dfg(u,v),or__dfg(v,not__dfg(u))),skc55),
inference(ems,[status(thm)],[17904,137]),
[iquote('0:EmS:17904.0,137.0')] ).
cnf(18078,plain,
equal(implies__dfg(or__dfg(u,v),or__dfg(v,u)),skc55),
inference(ems,[status(thm)],[17904,79]),
[iquote('0:EmS:17904.0,79.0')] ).
cnf(18083,plain,
equal(implies__dfg(u,or__dfg(v,u)),skc55),
inference(ems,[status(thm)],[17904,75]),
[iquote('0:EmS:17904.0,75.0')] ).
cnf(18084,plain,
equal(implies__dfg(or__dfg(u,u),u),skc55),
inference(ems,[status(thm)],[17904,76]),
[iquote('0:EmS:17904.0,76.0')] ).
cnf(18359,plain,
( ~ equivalence_3
| is_a_theorem(implies__dfg(skc55,equiv__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,u)))) ),
inference(rew,[status(thm),theory(equality)],[18076,3327]),
[iquote('0:Rew:18076.0,3327.1')] ).
cnf(18426,plain,
( ~ equivalence_3
| is_a_theorem(implies__dfg(skc55,equiv__dfg(or__dfg(u,implies__dfg(v,w)),implies__dfg(v,or__dfg(u,w))))) ),
inference(rew,[status(thm),theory(equality)],[18074,3326]),
[iquote('0:Rew:18074.0,3326.1')] ).
cnf(18607,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)],[17982,95]),
[iquote('0:SpR:17982.0,95.0')] ).
cnf(18625,plain,
equal(equiv__dfg(u,implies__dfg(skc55,u)),and__dfg(skc55,skc55)),
inference(rew,[status(thm),theory(equality)],[18039,18607]),
[iquote('0:Rew:18039.0,18607.0')] ).
cnf(18626,plain,
equal(equiv__dfg(u,implies__dfg(skc55,u)),skc55),
inference(rew,[status(thm),theory(equality)],[14334,18625]),
[iquote('0:Rew:14334.0,18625.0')] ).
cnf(18637,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)],[18009,95]),
[iquote('0:SpR:18009.0,95.0')] ).
cnf(18652,plain,
equal(equiv__dfg(and__dfg(skc55,u),u),and__dfg(skc55,skc55)),
inference(rew,[status(thm),theory(equality)],[18046,18637]),
[iquote('0:Rew:18046.0,18637.0')] ).
cnf(18653,plain,
equal(equiv__dfg(and__dfg(skc55,u),u),skc55),
inference(rew,[status(thm),theory(equality)],[14334,18652]),
[iquote('0:Rew:14334.0,18652.0')] ).
cnf(18732,plain,
( ~ is_a_theorem(skc55)
| equal(implies__dfg(skc55,u),u) ),
inference(spl,[status(thm),theory(equality)],[18626,80]),
[iquote('0:SpL:18626.0,80.0')] ).
cnf(18733,plain,
equal(implies__dfg(skc55,u),u),
inference(mrr,[status(thm)],[18732,277]),
[iquote('0:MRR:18732.0,277.0')] ).
cnf(18760,plain,
( ~ equivalence_3
| is_a_theorem(equiv__dfg(or__dfg(u,implies__dfg(v,w)),implies__dfg(v,or__dfg(u,w)))) ),
inference(rew,[status(thm),theory(equality)],[18733,18426]),
[iquote('0:Rew:18733.0,18426.1')] ).
cnf(18761,plain,
( ~ equivalence_3
| is_a_theorem(equiv__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,u))) ),
inference(rew,[status(thm),theory(equality)],[18733,18359]),
[iquote('0:Rew:18733.0,18359.1')] ).
cnf(18832,plain,
equal(and__dfg(skc55,u),equiv__dfg(u,skc55)),
inference(rew,[status(thm),theory(equality)],[18733,14899]),
[iquote('0:Rew:18733.0,14899.0')] ).
cnf(18949,plain,
equal(equiv__dfg(equiv__dfg(u,skc55),u),skc55),
inference(rew,[status(thm),theory(equality)],[18832,18653]),
[iquote('0:Rew:18832.0,18653.0')] ).
cnf(19135,plain,
( ~ equivalence_3
| equal(or__dfg(u,not__dfg(v)),implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[18761,80]),
[iquote('0:Res:18761.1,80.0')] ).
cnf(19232,plain,
( ~ is_a_theorem(skc55)
| equal(equiv__dfg(u,skc55),u) ),
inference(spl,[status(thm),theory(equality)],[18949,80]),
[iquote('0:SpL:18949.0,80.0')] ).
cnf(19233,plain,
equal(equiv__dfg(u,skc55),u),
inference(mrr,[status(thm)],[19232,277]),
[iquote('0:MRR:19232.0,277.0')] ).
cnf(19235,plain,
equal(and__dfg(skc55,u),u),
inference(rew,[status(thm),theory(equality)],[19233,18832]),
[iquote('0:Rew:19233.0,18832.0')] ).
cnf(19382,plain,
equal(and__dfg(skc55,implies__dfg(and__dfg(u,u),u)),equiv__dfg(u,and__dfg(u,u))),
inference(spr,[status(thm),theory(equality)],[18010,95]),
[iquote('0:SpR:18010.0,95.0')] ).
cnf(19400,plain,
equal(equiv__dfg(u,and__dfg(u,u)),implies__dfg(and__dfg(u,u),u)),
inference(rew,[status(thm),theory(equality)],[19235,19382]),
[iquote('0:Rew:19235.0,19382.0')] ).
cnf(19401,plain,
equal(equiv__dfg(u,and__dfg(u,u)),skc55),
inference(rew,[status(thm),theory(equality)],[18046,19400]),
[iquote('0:Rew:18046.0,19400.0')] ).
cnf(19410,plain,
equal(and__dfg(skc55,implies__dfg(implies__dfg(u,v),v)),equiv__dfg(v,implies__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[18039,95]),
[iquote('0:SpR:18039.0,95.0')] ).
cnf(19429,plain,
equal(equiv__dfg(u,implies__dfg(v,u)),implies__dfg(implies__dfg(v,u),u)),
inference(rew,[status(thm),theory(equality)],[19235,19410]),
[iquote('0:Rew:19235.0,19410.0')] ).
cnf(19564,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)],[18084,95]),
[iquote('0:SpR:18084.0,95.0')] ).
cnf(19583,plain,
equal(equiv__dfg(or__dfg(u,u),u),skc55),
inference(rew,[status(thm),theory(equality)],[19235,19564,18083]),
[iquote('0:Rew:19235.0,19564.0,18083.0,19564.0')] ).
cnf(19608,plain,
( ~ is_a_theorem(skc55)
| equal(and__dfg(u,u),u) ),
inference(spl,[status(thm),theory(equality)],[19401,80]),
[iquote('0:SpL:19401.0,80.0')] ).
cnf(19610,plain,
equal(and__dfg(u,u),u),
inference(mrr,[status(thm)],[19608,277]),
[iquote('0:MRR:19608.0,277.0')] ).
cnf(20025,plain,
( ~ is_a_theorem(skc55)
| equal(or__dfg(u,u),u) ),
inference(spl,[status(thm),theory(equality)],[19583,80]),
[iquote('0:SpL:19583.0,80.0')] ).
cnf(20026,plain,
equal(or__dfg(u,u),u),
inference(mrr,[status(thm)],[20025,277]),
[iquote('0:MRR:20025.0,277.0')] ).
cnf(20075,plain,
equal(implies__dfg(u,not__dfg(u)),not__dfg(u)),
inference(spr,[status(thm),theory(equality)],[20026,78]),
[iquote('0:SpR:20026.0,78.0')] ).
cnf(21933,plain,
( ~ equivalence_3
| is_a_theorem(equiv__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,or__dfg(u,not__dfg(v))))) ),
inference(spr,[status(thm),theory(equality)],[20075,18760]),
[iquote('0:SpR:20075.0,18760.1')] ).
cnf(22010,plain,
( ~ equivalence_3
| is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))) ),
inference(rew,[status(thm),theory(equality)],[19135,21933,19429]),
[iquote('0:Rew:19135.1,21933.1,19429.0,21933.1')] ).
cnf(35231,plain,
equal(implies__dfg(u,or__dfg(and__dfg(v,u),not__dfg(v))),skc55),
inference(ems,[status(thm)],[17904,9910]),
[iquote('0:EmS:17904.0,9910.0')] ).
cnf(37590,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)],[18045,95]),
[iquote('0:SpR:18045.0,95.0')] ).
cnf(37715,plain,
equal(equiv__dfg(and__dfg(u,v),and__dfg(v,u)),skc55),
inference(rew,[status(thm),theory(equality)],[19610,37590,18045]),
[iquote('0:Rew:19610.0,37590.0,18045.0,37590.0')] ).
cnf(37722,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)],[18078,95]),
[iquote('0:SpR:18078.0,95.0')] ).
cnf(37814,plain,
equal(equiv__dfg(or__dfg(u,v),or__dfg(v,u)),skc55),
inference(rew,[status(thm),theory(equality)],[19610,37722,18078]),
[iquote('0:Rew:19610.0,37722.0,18078.0,37722.0')] ).
cnf(47769,plain,
( ~ is_a_theorem(skc55)
| equal(and__dfg(u,v),and__dfg(v,u)) ),
inference(spl,[status(thm),theory(equality)],[37715,80]),
[iquote('0:SpL:37715.0,80.0')] ).
cnf(47788,plain,
equal(and__dfg(u,v),and__dfg(v,u)),
inference(mrr,[status(thm)],[47769,277]),
[iquote('0:MRR:47769.0,277.0')] ).
cnf(47800,plain,
( ~ is_a_theorem(implies__dfg(skc73,implies__dfg(skc72,and__dfg(skc72,skc73))))
| and_3 ),
inference(rew,[status(thm),theory(equality)],[47788,44]),
[iquote('0:Rew:47788.0,44.0')] ).
cnf(49169,plain,
( ~ is_a_theorem(skc55)
| equal(or__dfg(u,v),or__dfg(v,u)) ),
inference(spl,[status(thm),theory(equality)],[37814,80]),
[iquote('0:SpL:37814.0,80.0')] ).
cnf(49205,plain,
equal(or__dfg(u,v),or__dfg(v,u)),
inference(mrr,[status(thm)],[49169,277]),
[iquote('0:MRR:49169.0,277.0')] ).
cnf(49547,plain,
equal(implies__dfg(u,or__dfg(not__dfg(v),and__dfg(v,u))),skc55),
inference(rew,[status(thm),theory(equality)],[49205,35231]),
[iquote('0:Rew:49205.0,35231.0')] ).
cnf(49656,plain,
equal(implies__dfg(u,implies__dfg(v,and__dfg(v,u))),skc55),
inference(rew,[status(thm),theory(equality)],[78,49547]),
[iquote('0:Rew:78.0,49547.0')] ).
cnf(49657,plain,
( ~ is_a_theorem(skc55)
| and_3 ),
inference(rew,[status(thm),theory(equality)],[49656,47800]),
[iquote('0:Rew:49656.0,47800.0')] ).
cnf(49662,plain,
and_3,
inference(mrr,[status(thm)],[49657,277]),
[iquote('0:MRR:49657.0,277.0')] ).
cnf(49663,plain,
equivalence_3,
inference(mrr,[status(thm)],[2963,49662]),
[iquote('0:MRR:2963.0,49662.0')] ).
cnf(49950,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))),
inference(mrr,[status(thm)],[22010,49663]),
[iquote('0:MRR:22010.0,49663.0')] ).
cnf(50303,plain,
$false,
inference(unc,[status(thm)],[49950,91]),
[iquote('0:UnC:49950.0,91.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL485+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n021.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 15:53:00 EDT 2022
% 0.12/0.34 % CPUTime :
% 16.93/17.18
% 16.93/17.18 SPASS V 3.9
% 16.93/17.18 SPASS beiseite: Proof found.
% 16.93/17.18 % SZS status Theorem
% 16.93/17.18 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.93/17.18 SPASS derived 33994 clauses, backtracked 0 clauses, performed 0 splits and kept 10068 clauses.
% 16.93/17.18 SPASS allocated 144928 KBytes.
% 16.93/17.18 SPASS spent 0:0:16.79 on the problem.
% 16.93/17.18 0:00:00.04 for the input.
% 16.93/17.18 0:00:00.04 for the FLOTTER CNF translation.
% 16.93/17.18 0:00:00.28 for inferences.
% 16.93/17.18 0:00:00.00 for the backtracking.
% 16.93/17.18 0:0:16.32 for the reduction.
% 16.93/17.18
% 16.93/17.18
% 16.93/17.18 Here is a proof with depth 20, length 207 :
% 16.93/17.18 % SZS output start Refutation
% See solution above
% 18.49/18.72 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_implies_2 modus_ponens r2 r1 and_3 r3 op_implies_or op_implies_and implies_2 op_or op_and op_equiv equivalence_3 r4 r5
% 18.49/18.72
%------------------------------------------------------------------------------