TSTP Solution File: LCL528+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL528+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 14:37:31 EDT 2022
% Result : Theorem 51.52s 51.74s
% Output : Refutation 60.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 45
% Syntax : Number of clauses : 193 ( 134 unt; 1 nHn; 193 RR)
% Number of literals : 259 ( 0 equ; 71 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 24 ( 23 usr; 22 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
op_strict_implies,
file('LCL528+1.p',unknown),
[] ).
cnf(6,axiom,
op_strict_equiv,
file('LCL528+1.p',unknown),
[] ).
cnf(7,axiom,
op_or,
file('LCL528+1.p',unknown),
[] ).
cnf(8,axiom,
op_implies_and,
file('LCL528+1.p',unknown),
[] ).
cnf(9,axiom,
op_equiv,
file('LCL528+1.p',unknown),
[] ).
cnf(10,axiom,
modus_ponens,
file('LCL528+1.p',unknown),
[] ).
cnf(11,axiom,
modus_tollens,
file('LCL528+1.p',unknown),
[] ).
cnf(12,axiom,
implies_1,
file('LCL528+1.p',unknown),
[] ).
cnf(13,axiom,
implies_2,
file('LCL528+1.p',unknown),
[] ).
cnf(14,axiom,
implies_3,
file('LCL528+1.p',unknown),
[] ).
cnf(15,axiom,
and_1,
file('LCL528+1.p',unknown),
[] ).
cnf(16,axiom,
and_2,
file('LCL528+1.p',unknown),
[] ).
cnf(17,axiom,
and_3,
file('LCL528+1.p',unknown),
[] ).
cnf(23,axiom,
equivalence_3,
file('LCL528+1.p',unknown),
[] ).
cnf(24,axiom,
substitution_of_equivalents,
file('LCL528+1.p',unknown),
[] ).
cnf(26,axiom,
necessitation,
file('LCL528+1.p',unknown),
[] ).
cnf(27,axiom,
axiom_K,
file('LCL528+1.p',unknown),
[] ).
cnf(28,axiom,
axiom_M,
file('LCL528+1.p',unknown),
[] ).
cnf(30,axiom,
~ axiom_m1,
file('LCL528+1.p',unknown),
[] ).
cnf(31,axiom,
is_a_theorem(skc95),
file('LCL528+1.p',unknown),
[] ).
cnf(37,axiom,
is_a_theorem(implies__dfg(skc95,skc94)),
file('LCL528+1.p',unknown),
[] ).
cnf(43,axiom,
( substitution_strict_equiv
| is_a_theorem(strict_equiv(skc155,skc154)) ),
file('LCL528+1.p',unknown),
[] ).
cnf(44,axiom,
( ~ equal(skc155,skc154)
| substitution_strict_equiv ),
file('LCL528+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ axiom_M
| is_a_theorem(implies__dfg(necessarily(u),u)) ),
file('LCL528+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ implies_1
| is_a_theorem(implies__dfg(u,implies__dfg(v,u))) ),
file('LCL528+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ and_1
| is_a_theorem(implies__dfg(and__dfg(u,v),u)) ),
file('LCL528+1.p',unknown),
[] ).
cnf(54,axiom,
( ~ and_2
| is_a_theorem(implies__dfg(and__dfg(u,v),v)) ),
file('LCL528+1.p',unknown),
[] ).
cnf(68,axiom,
( ~ is_a_theorem(u)
| ~ necessitation
| is_a_theorem(necessarily(u)) ),
file('LCL528+1.p',unknown),
[] ).
cnf(93,axiom,
( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv__dfg(u,v))
| equal(u,v) ),
file('LCL528+1.p',unknown),
[] ).
cnf(94,axiom,
( ~ and_3
| is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))) ),
file('LCL528+1.p',unknown),
[] ).
cnf(100,axiom,
( ~ r3
| is_a_theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))) ),
file('LCL528+1.p',unknown),
[] ).
cnf(101,axiom,
( ~ is_a_theorem(implies__dfg(or__dfg(skc142,skc141),or__dfg(skc141,skc142)))
| r3 ),
file('LCL528+1.p',unknown),
[] ).
cnf(103,axiom,
( ~ substitution_strict_equiv
| ~ is_a_theorem(strict_equiv(u,v))
| equal(u,v) ),
file('LCL528+1.p',unknown),
[] ).
cnf(105,axiom,
( ~ is_a_theorem(strict_implies(and__dfg(skc171,skc170),and__dfg(skc170,skc171)))
| axiom_m1 ),
file('LCL528+1.p',unknown),
[] ).
cnf(106,axiom,
( ~ op_strict_implies
| equal(necessarily(implies__dfg(u,v)),strict_implies(u,v)) ),
file('LCL528+1.p',unknown),
[] ).
cnf(107,axiom,
( ~ op_implies_and
| equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)) ),
file('LCL528+1.p',unknown),
[] ).
cnf(108,axiom,
( ~ is_a_theorem(u)
| ~ modus_ponens
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL528+1.p',unknown),
[] ).
cnf(109,axiom,
( ~ modus_tollens
| is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),not__dfg(v)),implies__dfg(v,u))) ),
file('LCL528+1.p',unknown),
[] ).
cnf(111,axiom,
( ~ implies_2
| is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))) ),
file('LCL528+1.p',unknown),
[] ).
cnf(113,axiom,
( ~ op_or
| equal(not__dfg(and__dfg(not__dfg(u),not__dfg(v))),or__dfg(u,v)) ),
file('LCL528+1.p',unknown),
[] ).
cnf(119,axiom,
( ~ op_equiv
| equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)) ),
file('LCL528+1.p',unknown),
[] ).
cnf(120,axiom,
( ~ axiom_K
| is_a_theorem(implies__dfg(necessarily(implies__dfg(u,v)),implies__dfg(necessarily(u),necessarily(v)))) ),
file('LCL528+1.p',unknown),
[] ).
cnf(124,axiom,
( ~ op_strict_equiv
| equal(and__dfg(strict_implies(u,v),strict_implies(v,u)),strict_equiv(u,v)) ),
file('LCL528+1.p',unknown),
[] ).
cnf(125,axiom,
( ~ implies_3
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))) ),
file('LCL528+1.p',unknown),
[] ).
cnf(127,axiom,
( ~ equivalence_3
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,u),equiv__dfg(u,v)))) ),
file('LCL528+1.p',unknown),
[] ).
cnf(147,plain,
is_a_theorem(implies__dfg(necessarily(u),u)),
inference(mrr,[status(thm)],[46,28]),
[iquote('0:MRR:46.0,28.0')] ).
cnf(148,plain,
( ~ is_a_theorem(u)
| is_a_theorem(necessarily(u)) ),
inference(mrr,[status(thm)],[68,26]),
[iquote('0:MRR:68.1,26.0')] ).
cnf(152,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),v)),
inference(mrr,[status(thm)],[54,16]),
[iquote('0:MRR:54.0,16.0')] ).
cnf(153,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),u)),
inference(mrr,[status(thm)],[52,15]),
[iquote('0:MRR:52.0,15.0')] ).
cnf(155,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
inference(mrr,[status(thm)],[50,12]),
[iquote('0:MRR:50.0,12.0')] ).
cnf(158,plain,
equal(necessarily(implies__dfg(u,v)),strict_implies(u,v)),
inference(mrr,[status(thm)],[106,4]),
[iquote('0:MRR:106.0,4.0')] ).
cnf(159,plain,
~ is_a_theorem(strict_implies(and__dfg(skc171,skc170),and__dfg(skc170,skc171))),
inference(mrr,[status(thm)],[105,30]),
[iquote('0:MRR:105.1,30.0')] ).
cnf(162,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))),
inference(mrr,[status(thm)],[94,17]),
[iquote('0:MRR:94.0,17.0')] ).
cnf(163,plain,
( ~ is_a_theorem(equiv__dfg(u,v))
| equal(u,v) ),
inference(mrr,[status(thm)],[93,24]),
[iquote('0:MRR:93.0,24.0')] ).
cnf(164,plain,
equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)),
inference(mrr,[status(thm)],[107,8]),
[iquote('0:MRR:107.0,8.0')] ).
cnf(165,plain,
( ~ op_or
| equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)) ),
inference(rew,[status(thm),theory(equality)],[164,113]),
[iquote('0:Rew:164.0,113.1')] ).
cnf(166,plain,
equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)),
inference(mrr,[status(thm)],[165,7]),
[iquote('0:MRR:165.0,7.0')] ).
cnf(172,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))),
inference(mrr,[status(thm)],[111,13]),
[iquote('0:MRR:111.0,13.0')] ).
cnf(173,plain,
( ~ modus_tollens
| is_a_theorem(implies__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,u))) ),
inference(rew,[status(thm),theory(equality)],[166,109]),
[iquote('0:Rew:166.0,109.1')] ).
cnf(174,plain,
is_a_theorem(implies__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,u))),
inference(mrr,[status(thm)],[173,11]),
[iquote('0:MRR:173.0,11.0')] ).
cnf(175,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(mrr,[status(thm)],[108,10]),
[iquote('0:MRR:108.1,10.0')] ).
cnf(176,plain,
equal(and__dfg(strict_implies(u,v),strict_implies(v,u)),strict_equiv(u,v)),
inference(mrr,[status(thm)],[124,6]),
[iquote('0:MRR:124.0,6.0')] ).
cnf(177,plain,
( ~ axiom_K
| is_a_theorem(implies__dfg(strict_implies(u,v),implies__dfg(necessarily(u),necessarily(v)))) ),
inference(rew,[status(thm),theory(equality)],[158,120]),
[iquote('0:Rew:158.0,120.1')] ).
cnf(178,plain,
is_a_theorem(implies__dfg(strict_implies(u,v),implies__dfg(necessarily(u),necessarily(v)))),
inference(mrr,[status(thm)],[177,27]),
[iquote('0:MRR:177.0,27.0')] ).
cnf(179,plain,
equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)),
inference(mrr,[status(thm)],[119,9]),
[iquote('0:MRR:119.0,9.0')] ).
cnf(180,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,u),equiv__dfg(u,v)))),
inference(mrr,[status(thm)],[127,23]),
[iquote('0:MRR:127.0,23.0')] ).
cnf(181,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))),
inference(mrr,[status(thm)],[125,14]),
[iquote('0:MRR:125.0,14.0')] ).
cnf(190,plain,
substitution_strict_equiv,
inference(spt,[spt(split,[position(s1)])],[43]),
[iquote('1:Spt:43.0')] ).
cnf(191,plain,
( ~ is_a_theorem(strict_equiv(u,v))
| equal(u,v) ),
inference(mrr,[status(thm)],[103,190]),
[iquote('1:MRR:103.0,190.0')] ).
cnf(216,plain,
is_a_theorem(implies__dfg(strict_implies(u,v),implies__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[158,147]),
[iquote('0:SpR:158.0,147.0')] ).
cnf(217,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(strict_implies(u,v)) ),
inference(spr,[status(thm),theory(equality)],[158,148]),
[iquote('0:SpR:158.0,148.1')] ).
cnf(265,plain,
equal(or__dfg(and__dfg(u,not__dfg(v)),w),implies__dfg(implies__dfg(u,v),w)),
inference(spr,[status(thm),theory(equality)],[164,166]),
[iquote('0:SpR:164.0,166.0')] ).
cnf(271,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)],[164]),
[iquote('0:SpR:164.0,164.0')] ).
cnf(283,plain,
is_a_theorem(implies__dfg(or__dfg(u,not__dfg(not__dfg(v))),or__dfg(v,u))),
inference(spr,[status(thm),theory(equality)],[166,174]),
[iquote('0:SpR:166.0,174.0')] ).
cnf(299,plain,
is_a_theorem(strict_implies(u,implies__dfg(v,u))),
inference(sor,[status(thm)],[217,155]),
[iquote('0:SoR:217.0,155.0')] ).
cnf(303,plain,
is_a_theorem(strict_implies(and__dfg(u,v),v)),
inference(sor,[status(thm)],[217,152]),
[iquote('0:SoR:217.0,152.0')] ).
cnf(305,plain,
is_a_theorem(strict_implies(skc95,skc94)),
inference(sor,[status(thm)],[217,37]),
[iquote('0:SoR:217.0,37.0')] ).
cnf(353,plain,
( ~ is_a_theorem(skc95)
| is_a_theorem(skc94) ),
inference(res,[status(thm),theory(equality)],[37,175]),
[iquote('0:Res:37.0,175.1')] ).
cnf(359,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[155,175]),
[iquote('0:Res:155.0,175.1')] ).
cnf(370,plain,
( ~ is_a_theorem(strict_implies(u,v))
| is_a_theorem(implies__dfg(u,v)) ),
inference(res,[status(thm),theory(equality)],[216,175]),
[iquote('0:Res:216.0,175.1')] ).
cnf(371,plain,
( ~ is_a_theorem(strict_implies(u,v))
| is_a_theorem(implies__dfg(necessarily(u),necessarily(v))) ),
inference(res,[status(thm),theory(equality)],[178,175]),
[iquote('0:Res:178.0,175.1')] ).
cnf(373,plain,
is_a_theorem(skc94),
inference(ssi,[status(thm)],[353,31]),
[iquote('0:SSi:353.0,31.0')] ).
cnf(379,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(u,v)))
| is_a_theorem(implies__dfg(u,v)) ),
inference(res,[status(thm),theory(equality)],[172,175]),
[iquote('0:Res:172.0,175.1')] ).
cnf(394,plain,
is_a_theorem(implies__dfg(strict_equiv(u,v),strict_implies(v,u))),
inference(spr,[status(thm),theory(equality)],[176,152]),
[iquote('0:SpR:176.0,152.0')] ).
cnf(395,plain,
is_a_theorem(implies__dfg(strict_equiv(u,v),strict_implies(u,v))),
inference(spr,[status(thm),theory(equality)],[176,153]),
[iquote('0:SpR:176.0,153.0')] ).
cnf(511,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(v,u),equiv__dfg(u,v))) ),
inference(res,[status(thm),theory(equality)],[180,175]),
[iquote('0:Res:180.0,175.1')] ).
cnf(523,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(v,w),implies__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[181,175]),
[iquote('0:Res:181.0,175.1')] ).
cnf(2010,plain,
is_a_theorem(implies__dfg(necessarily(skc95),necessarily(skc94))),
inference(sor,[status(thm)],[371,305]),
[iquote('0:SoR:371.0,305.0')] ).
cnf(2015,plain,
is_a_theorem(implies__dfg(necessarily(u),necessarily(implies__dfg(v,u)))),
inference(sor,[status(thm)],[371,299]),
[iquote('0:SoR:371.0,299.0')] ).
cnf(2030,plain,
is_a_theorem(implies__dfg(necessarily(u),strict_implies(v,u))),
inference(rew,[status(thm),theory(equality)],[158,2015]),
[iquote('0:Rew:158.0,2015.0')] ).
cnf(2055,plain,
( ~ is_a_theorem(necessarily(skc95))
| is_a_theorem(necessarily(skc94)) ),
inference(res,[status(thm),theory(equality)],[2010,175]),
[iquote('0:Res:2010.0,175.1')] ).
cnf(2056,plain,
is_a_theorem(necessarily(skc94)),
inference(ssi,[status(thm)],[2055,148,31]),
[iquote('0:SSi:2055.0,148.0,31.1')] ).
cnf(2064,plain,
( ~ is_a_theorem(necessarily(u))
| is_a_theorem(strict_implies(v,u)) ),
inference(res,[status(thm),theory(equality)],[2030,175]),
[iquote('0:Res:2030.0,175.1')] ).
cnf(2114,plain,
is_a_theorem(strict_implies(u,skc94)),
inference(sor,[status(thm)],[2064,2056]),
[iquote('0:SoR:2064.0,2056.0')] ).
cnf(2123,plain,
is_a_theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[379,155]),
[iquote('0:SoR:379.0,155.0')] ).
cnf(2171,plain,
is_a_theorem(implies__dfg(u,skc94)),
inference(sor,[status(thm)],[370,2114]),
[iquote('0:SoR:370.0,2114.0')] ).
cnf(2187,plain,
is_a_theorem(strict_implies(u,u)),
inference(sor,[status(thm)],[217,2123]),
[iquote('0:SoR:217.0,2123.0')] ).
cnf(4275,plain,
( ~ r3
| is_a_theorem(implies__dfg(implies__dfg(or__dfg(u,v),or__dfg(v,u)),equiv__dfg(or__dfg(v,u),or__dfg(u,v)))) ),
inference(sor,[status(thm)],[511,100]),
[iquote('0:SoR:511.0,100.1')] ).
cnf(4299,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),equiv__dfg(u,skc94))),
inference(sor,[status(thm)],[511,2171]),
[iquote('0:SoR:511.0,2171.0')] ).
cnf(4388,plain,
( ~ is_a_theorem(implies__dfg(skc94,u))
| is_a_theorem(equiv__dfg(u,skc94)) ),
inference(res,[status(thm),theory(equality)],[4299,175]),
[iquote('0:Res:4299.0,175.1')] ).
cnf(4466,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),implies__dfg(v,u))),
inference(sor,[status(thm)],[523,2171]),
[iquote('0:SoR:523.0,2171.0')] ).
cnf(4497,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),u)),
inference(sor,[status(thm)],[379,4466]),
[iquote('0:SoR:379.0,4466.0')] ).
cnf(4503,plain,
is_a_theorem(strict_implies(implies__dfg(skc94,u),u)),
inference(sor,[status(thm)],[217,4497]),
[iquote('0:SoR:217.0,4497.0')] ).
cnf(4504,plain,
( ~ is_a_theorem(implies__dfg(skc94,u))
| is_a_theorem(u) ),
inference(res,[status(thm),theory(equality)],[4497,175]),
[iquote('0:Res:4497.0,175.1')] ).
cnf(4667,plain,
is_a_theorem(implies__dfg(necessarily(implies__dfg(skc94,u)),necessarily(u))),
inference(sor,[status(thm)],[371,4503]),
[iquote('0:SoR:371.0,4503.0')] ).
cnf(4670,plain,
is_a_theorem(implies__dfg(strict_implies(skc94,u),necessarily(u))),
inference(rew,[status(thm),theory(equality)],[158,4667]),
[iquote('0:Rew:158.0,4667.0')] ).
cnf(4686,plain,
is_a_theorem(implies__dfg(u,and__dfg(skc94,u))),
inference(sor,[status(thm)],[4504,162]),
[iquote('0:SoR:4504.0,162.0')] ).
cnf(5019,plain,
is_a_theorem(strict_implies(u,and__dfg(skc94,u))),
inference(sor,[status(thm)],[217,4686]),
[iquote('0:SoR:217.0,4686.0')] ).
cnf(5227,plain,
( ~ is_a_theorem(strict_implies(skc94,u))
| is_a_theorem(necessarily(u)) ),
inference(res,[status(thm),theory(equality)],[4670,175]),
[iquote('0:Res:4670.0,175.1')] ).
cnf(5630,plain,
is_a_theorem(necessarily(and__dfg(skc94,skc94))),
inference(sor,[status(thm)],[5227,5019]),
[iquote('0:SoR:5227.0,5019.0')] ).
cnf(5649,plain,
is_a_theorem(strict_implies(u,and__dfg(skc94,skc94))),
inference(sor,[status(thm)],[2064,5630]),
[iquote('0:SoR:2064.0,5630.0')] ).
cnf(5681,plain,
is_a_theorem(implies__dfg(u,and__dfg(skc94,skc94))),
inference(sor,[status(thm)],[370,5649]),
[iquote('0:SoR:370.0,5649.0')] ).
cnf(7800,plain,
is_a_theorem(equiv__dfg(and__dfg(skc94,skc94),skc94)),
inference(sor,[status(thm)],[4388,5681]),
[iquote('0:SoR:4388.0,5681.0')] ).
cnf(7813,plain,
is_a_theorem(equiv__dfg(implies__dfg(u,skc94),skc94)),
inference(sor,[status(thm)],[4388,155]),
[iquote('0:SoR:4388.0,155.0')] ).
cnf(7817,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equiv__dfg(u,skc94)) ),
inference(sor,[status(thm)],[4388,359]),
[iquote('0:SoR:4388.0,359.1')] ).
cnf(8008,plain,
equal(and__dfg(skc94,skc94),skc94),
inference(res,[status(thm),theory(equality)],[7800,163]),
[iquote('0:Res:7800.0,163.0')] ).
cnf(8179,plain,
equal(implies__dfg(u,skc94),skc94),
inference(res,[status(thm),theory(equality)],[7813,163]),
[iquote('0:Res:7813.0,163.0')] ).
cnf(8228,plain,
equal(and__dfg(skc94,implies__dfg(skc94,u)),equiv__dfg(u,skc94)),
inference(spr,[status(thm),theory(equality)],[8179,179]),
[iquote('0:SpR:8179.0,179.0')] ).
cnf(10395,plain,
( ~ is_a_theorem(u)
| equal(u,skc94) ),
inference(res,[status(thm),theory(equality)],[7817,163]),
[iquote('0:Res:7817.1,163.0')] ).
cnf(10511,plain,
equal(strict_implies(implies__dfg(skc94,u),u),skc94),
inference(ems,[status(thm)],[10395,4503]),
[iquote('0:EmS:10395.0,4503.0')] ).
cnf(10512,plain,
equal(strict_implies(u,u),skc94),
inference(ems,[status(thm)],[10395,2187]),
[iquote('0:EmS:10395.0,2187.0')] ).
cnf(10518,plain,
equal(strict_implies(and__dfg(u,v),v),skc94),
inference(ems,[status(thm)],[10395,303]),
[iquote('0:EmS:10395.0,303.0')] ).
cnf(10526,plain,
equal(strict_implies(u,and__dfg(skc94,u)),skc94),
inference(ems,[status(thm)],[10395,5019]),
[iquote('0:EmS:10395.0,5019.0')] ).
cnf(10531,plain,
equal(strict_implies(u,implies__dfg(v,u)),skc94),
inference(ems,[status(thm)],[10395,299]),
[iquote('0:EmS:10395.0,299.0')] ).
cnf(10578,plain,
equal(implies__dfg(or__dfg(u,not__dfg(not__dfg(v))),or__dfg(v,u)),skc94),
inference(ems,[status(thm)],[10395,283]),
[iquote('0:EmS:10395.0,283.0')] ).
cnf(10591,plain,
equal(implies__dfg(strict_equiv(u,v),strict_implies(u,v)),skc94),
inference(ems,[status(thm)],[10395,395]),
[iquote('0:EmS:10395.0,395.0')] ).
cnf(10592,plain,
equal(implies__dfg(strict_equiv(u,v),strict_implies(v,u)),skc94),
inference(ems,[status(thm)],[10395,394]),
[iquote('0:EmS:10395.0,394.0')] ).
cnf(10620,plain,
equal(implies__dfg(strict_implies(u,v),implies__dfg(u,v)),skc94),
inference(ems,[status(thm)],[10395,216]),
[iquote('0:EmS:10395.0,216.0')] ).
cnf(10624,plain,
( ~ r3
| equal(implies__dfg(or__dfg(u,v),or__dfg(v,u)),skc94) ),
inference(ems,[status(thm)],[10395,100]),
[iquote('0:EmS:10395.0,100.1')] ).
cnf(11153,plain,
( ~ r3
| is_a_theorem(implies__dfg(skc94,equiv__dfg(or__dfg(u,v),or__dfg(v,u)))) ),
inference(rew,[status(thm),theory(equality)],[10624,4275]),
[iquote('0:Rew:10624.1,4275.1')] ).
cnf(12050,plain,
equal(and__dfg(skc94,strict_implies(u,implies__dfg(skc94,u))),strict_equiv(implies__dfg(skc94,u),u)),
inference(spr,[status(thm),theory(equality)],[10511,176]),
[iquote('0:SpR:10511.0,176.0')] ).
cnf(12058,plain,
equal(strict_equiv(implies__dfg(skc94,u),u),and__dfg(skc94,skc94)),
inference(rew,[status(thm),theory(equality)],[10531,12050]),
[iquote('0:Rew:10531.0,12050.0')] ).
cnf(12059,plain,
equal(strict_equiv(implies__dfg(skc94,u),u),skc94),
inference(rew,[status(thm),theory(equality)],[8008,12058]),
[iquote('0:Rew:8008.0,12058.0')] ).
cnf(12063,plain,
equal(and__dfg(skc94,strict_implies(and__dfg(skc94,u),u)),strict_equiv(u,and__dfg(skc94,u))),
inference(spr,[status(thm),theory(equality)],[10526,176]),
[iquote('0:SpR:10526.0,176.0')] ).
cnf(12070,plain,
equal(strict_equiv(u,and__dfg(skc94,u)),and__dfg(skc94,skc94)),
inference(rew,[status(thm),theory(equality)],[10518,12063]),
[iquote('0:Rew:10518.0,12063.0')] ).
cnf(12071,plain,
equal(strict_equiv(u,and__dfg(skc94,u)),skc94),
inference(rew,[status(thm),theory(equality)],[8008,12070]),
[iquote('0:Rew:8008.0,12070.0')] ).
cnf(12179,plain,
( ~ is_a_theorem(skc94)
| equal(implies__dfg(skc94,u),u) ),
inference(spl,[status(thm),theory(equality)],[12059,191]),
[iquote('1:SpL:12059.0,191.0')] ).
cnf(12180,plain,
equal(implies__dfg(skc94,u),u),
inference(mrr,[status(thm)],[12179,373]),
[iquote('1:MRR:12179.0,373.0')] ).
cnf(12201,plain,
( ~ r3
| is_a_theorem(equiv__dfg(or__dfg(u,v),or__dfg(v,u))) ),
inference(rew,[status(thm),theory(equality)],[12180,11153]),
[iquote('1:Rew:12180.0,11153.1')] ).
cnf(12266,plain,
equal(and__dfg(skc94,u),equiv__dfg(u,skc94)),
inference(rew,[status(thm),theory(equality)],[12180,8228]),
[iquote('1:Rew:12180.0,8228.0')] ).
cnf(12342,plain,
equal(strict_equiv(u,equiv__dfg(u,skc94)),skc94),
inference(rew,[status(thm),theory(equality)],[12266,12071]),
[iquote('1:Rew:12266.0,12071.0')] ).
cnf(13875,plain,
equal(not__dfg(equiv__dfg(not__dfg(u),skc94)),implies__dfg(skc94,u)),
inference(spr,[status(thm),theory(equality)],[12266,164]),
[iquote('1:SpR:12266.0,164.0')] ).
cnf(13877,plain,
equal(or__dfg(equiv__dfg(not__dfg(u),skc94),v),implies__dfg(implies__dfg(skc94,u),v)),
inference(spr,[status(thm),theory(equality)],[12266,265]),
[iquote('1:SpR:12266.0,265.0')] ).
cnf(13881,plain,
equal(not__dfg(equiv__dfg(implies__dfg(u,v),skc94)),implies__dfg(skc94,and__dfg(u,not__dfg(v)))),
inference(spr,[status(thm),theory(equality)],[12266,271]),
[iquote('1:SpR:12266.0,271.0')] ).
cnf(13886,plain,
equal(not__dfg(equiv__dfg(not__dfg(u),skc94)),u),
inference(rew,[status(thm),theory(equality)],[12180,13875]),
[iquote('1:Rew:12180.0,13875.0')] ).
cnf(13892,plain,
equal(or__dfg(equiv__dfg(not__dfg(u),skc94),v),implies__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[12180,13877]),
[iquote('1:Rew:12180.0,13877.0')] ).
cnf(13895,plain,
equal(not__dfg(equiv__dfg(implies__dfg(u,v),skc94)),and__dfg(u,not__dfg(v))),
inference(rew,[status(thm),theory(equality)],[12180,13881]),
[iquote('1:Rew:12180.0,13881.0')] ).
cnf(14265,plain,
( ~ is_a_theorem(skc94)
| equal(equiv__dfg(u,skc94),u) ),
inference(spl,[status(thm),theory(equality)],[12342,191]),
[iquote('1:SpL:12342.0,191.0')] ).
cnf(14266,plain,
equal(equiv__dfg(u,skc94),u),
inference(mrr,[status(thm)],[14265,373]),
[iquote('1:MRR:14265.0,373.0')] ).
cnf(14315,plain,
equal(not__dfg(implies__dfg(u,v)),and__dfg(u,not__dfg(v))),
inference(rew,[status(thm),theory(equality)],[14266,13895]),
[iquote('1:Rew:14266.0,13895.0')] ).
cnf(14324,plain,
equal(not__dfg(not__dfg(u)),u),
inference(rew,[status(thm),theory(equality)],[14266,13886]),
[iquote('1:Rew:14266.0,13886.0')] ).
cnf(14326,plain,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[14266,13892]),
[iquote('1:Rew:14266.0,13892.0')] ).
cnf(14548,plain,
equal(implies__dfg(or__dfg(u,v),or__dfg(v,u)),skc94),
inference(rew,[status(thm),theory(equality)],[14324,10578]),
[iquote('1:Rew:14324.0,10578.0')] ).
cnf(15848,plain,
( ~ is_a_theorem(skc94)
| r3 ),
inference(rew,[status(thm),theory(equality)],[14548,101]),
[iquote('1:Rew:14548.0,101.0')] ).
cnf(15857,plain,
r3,
inference(mrr,[status(thm)],[15848,373]),
[iquote('1:MRR:15848.0,373.0')] ).
cnf(15967,plain,
is_a_theorem(equiv__dfg(or__dfg(u,v),or__dfg(v,u))),
inference(mrr,[status(thm)],[12201,15857]),
[iquote('1:MRR:12201.0,15857.0')] ).
cnf(19778,plain,
equal(or__dfg(u,v),or__dfg(v,u)),
inference(res,[status(thm),theory(equality)],[15967,163]),
[iquote('1:Res:15967.0,163.0')] ).
cnf(28644,plain,
equal(or__dfg(u,not__dfg(v)),implies__dfg(v,u)),
inference(spr,[status(thm),theory(equality)],[14326,19778]),
[iquote('1:SpR:14326.0,19778.0')] ).
cnf(32569,plain,
equal(implies__dfg(u,not__dfg(v)),implies__dfg(v,not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[28644,14326]),
[iquote('1:SpR:28644.0,14326.0')] ).
cnf(100639,plain,
equal(not__dfg(implies__dfg(u,not__dfg(v))),and__dfg(v,not__dfg(not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[32569,14315]),
[iquote('1:SpR:32569.0,14315.0')] ).
cnf(100888,plain,
equal(and__dfg(u,v),and__dfg(v,u)),
inference(rew,[status(thm),theory(equality)],[14324,100639,14315]),
[iquote('1:Rew:14324.0,100639.0,14315.0,100639.0,14324.0,100639.0')] ).
cnf(100915,plain,
~ is_a_theorem(strict_implies(and__dfg(skc170,skc171),and__dfg(skc170,skc171))),
inference(rew,[status(thm),theory(equality)],[100888,159]),
[iquote('1:Rew:100888.0,159.0')] ).
cnf(101156,plain,
~ is_a_theorem(skc94),
inference(rew,[status(thm),theory(equality)],[10512,100915]),
[iquote('1:Rew:10512.0,100915.0')] ).
cnf(101157,plain,
$false,
inference(mrr,[status(thm)],[101156,373]),
[iquote('1:MRR:101156.0,373.0')] ).
cnf(101757,plain,
~ substitution_strict_equiv,
inference(spt,[spt(split,[position(sa)])],[101157,190]),
[iquote('1:Spt:101157.0,43.0,190.0')] ).
cnf(101758,plain,
is_a_theorem(strict_equiv(skc155,skc154)),
inference(spt,[spt(split,[position(s2)])],[43]),
[iquote('1:Spt:101157.0,43.1')] ).
cnf(101761,plain,
~ equal(skc155,skc154),
inference(mrr,[status(thm)],[44,101757]),
[iquote('1:MRR:44.1,101757.0')] ).
cnf(102685,plain,
equal(strict_equiv(skc155,skc154),skc94),
inference(ems,[status(thm)],[10395,101758]),
[iquote('1:EmS:10395.0,101758.0')] ).
cnf(102741,plain,
equal(implies__dfg(skc94,strict_implies(skc155,skc154)),skc94),
inference(spr,[status(thm),theory(equality)],[102685,10591]),
[iquote('1:SpR:102685.0,10591.0')] ).
cnf(102742,plain,
equal(implies__dfg(skc94,strict_implies(skc154,skc155)),skc94),
inference(spr,[status(thm),theory(equality)],[102685,10592]),
[iquote('1:SpR:102685.0,10592.0')] ).
cnf(102962,plain,
equal(and__dfg(implies__dfg(strict_implies(skc155,skc154),skc94),skc94),equiv__dfg(strict_implies(skc155,skc154),skc94)),
inference(spr,[status(thm),theory(equality)],[102741,179]),
[iquote('1:SpR:102741.0,179.0')] ).
cnf(102978,plain,
equal(equiv__dfg(strict_implies(skc155,skc154),skc94),skc94),
inference(rew,[status(thm),theory(equality)],[8008,102962,8179]),
[iquote('1:Rew:8008.0,102962.0,8179.0,102962.0')] ).
cnf(102982,plain,
equal(and__dfg(implies__dfg(strict_implies(skc154,skc155),skc94),skc94),equiv__dfg(strict_implies(skc154,skc155),skc94)),
inference(spr,[status(thm),theory(equality)],[102742,179]),
[iquote('1:SpR:102742.0,179.0')] ).
cnf(102998,plain,
equal(equiv__dfg(strict_implies(skc154,skc155),skc94),skc94),
inference(rew,[status(thm),theory(equality)],[8008,102982,8179]),
[iquote('1:Rew:8008.0,102982.0,8179.0,102982.0')] ).
cnf(103089,plain,
( ~ is_a_theorem(skc94)
| equal(strict_implies(skc155,skc154),skc94) ),
inference(spl,[status(thm),theory(equality)],[102978,163]),
[iquote('1:SpL:102978.0,163.0')] ).
cnf(103090,plain,
equal(strict_implies(skc155,skc154),skc94),
inference(mrr,[status(thm)],[103089,373]),
[iquote('1:MRR:103089.0,373.0')] ).
cnf(103103,plain,
equal(implies__dfg(skc94,implies__dfg(skc155,skc154)),skc94),
inference(spr,[status(thm),theory(equality)],[103090,10620]),
[iquote('1:SpR:103090.0,10620.0')] ).
cnf(103165,plain,
( ~ is_a_theorem(skc94)
| equal(strict_implies(skc154,skc155),skc94) ),
inference(spl,[status(thm),theory(equality)],[102998,163]),
[iquote('1:SpL:102998.0,163.0')] ).
cnf(103166,plain,
equal(strict_implies(skc154,skc155),skc94),
inference(mrr,[status(thm)],[103165,373]),
[iquote('1:MRR:103165.0,373.0')] ).
cnf(103182,plain,
equal(implies__dfg(skc94,implies__dfg(skc154,skc155)),skc94),
inference(spr,[status(thm),theory(equality)],[103166,10620]),
[iquote('1:SpR:103166.0,10620.0')] ).
cnf(103223,plain,
equal(and__dfg(implies__dfg(implies__dfg(skc155,skc154),skc94),skc94),equiv__dfg(implies__dfg(skc155,skc154),skc94)),
inference(spr,[status(thm),theory(equality)],[103103,179]),
[iquote('1:SpR:103103.0,179.0')] ).
cnf(103239,plain,
equal(equiv__dfg(implies__dfg(skc155,skc154),skc94),skc94),
inference(rew,[status(thm),theory(equality)],[8008,103223,8179]),
[iquote('1:Rew:8008.0,103223.0,8179.0,103223.0')] ).
cnf(103327,plain,
( ~ is_a_theorem(skc94)
| equal(implies__dfg(skc155,skc154),skc94) ),
inference(spl,[status(thm),theory(equality)],[103239,163]),
[iquote('1:SpL:103239.0,163.0')] ).
cnf(103328,plain,
equal(implies__dfg(skc155,skc154),skc94),
inference(mrr,[status(thm)],[103327,373]),
[iquote('1:MRR:103327.0,373.0')] ).
cnf(103337,plain,
equal(and__dfg(implies__dfg(skc154,skc155),skc94),equiv__dfg(skc154,skc155)),
inference(spr,[status(thm),theory(equality)],[103328,179]),
[iquote('1:SpR:103328.0,179.0')] ).
cnf(103377,plain,
( ~ is_a_theorem(skc94)
| ~ is_a_theorem(skc94)
| is_a_theorem(implies__dfg(skc154,skc155)) ),
inference(spl,[status(thm),theory(equality)],[103182,175]),
[iquote('1:SpL:103182.0,175.1')] ).
cnf(103392,plain,
( ~ is_a_theorem(skc94)
| is_a_theorem(implies__dfg(skc154,skc155)) ),
inference(obv,[status(thm),theory(equality)],[103377]),
[iquote('1:Obv:103377.0')] ).
cnf(103393,plain,
is_a_theorem(implies__dfg(skc154,skc155)),
inference(mrr,[status(thm)],[103392,373]),
[iquote('1:MRR:103392.0,373.0')] ).
cnf(103395,plain,
equal(implies__dfg(skc154,skc155),skc94),
inference(ems,[status(thm)],[10395,103393]),
[iquote('1:EmS:10395.0,103393.0')] ).
cnf(103407,plain,
equal(and__dfg(skc94,skc94),equiv__dfg(skc154,skc155)),
inference(rew,[status(thm),theory(equality)],[103395,103337]),
[iquote('1:Rew:103395.0,103337.0')] ).
cnf(103409,plain,
equal(equiv__dfg(skc154,skc155),skc94),
inference(rew,[status(thm),theory(equality)],[8008,103407]),
[iquote('1:Rew:8008.0,103407.0')] ).
cnf(103465,plain,
( ~ is_a_theorem(skc94)
| equal(skc155,skc154) ),
inference(spl,[status(thm),theory(equality)],[103409,163]),
[iquote('1:SpL:103409.0,163.0')] ).
cnf(103466,plain,
$false,
inference(mrr,[status(thm)],[103465,373,101761]),
[iquote('1:MRR:103465.0,103465.1,373.0,101761.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL528+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.12 % 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 : Sun Jul 3 03:31:45 EDT 2022
% 0.12/0.34 % CPUTime :
% 51.52/51.74
% 51.52/51.74 SPASS V 3.9
% 51.52/51.74 SPASS beiseite: Proof found.
% 51.52/51.74 % SZS status Theorem
% 51.52/51.74 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 51.52/51.74 SPASS derived 62348 clauses, backtracked 4612 clauses, performed 3 splits and kept 19669 clauses.
% 51.52/51.74 SPASS allocated 188579 KBytes.
% 51.52/51.74 SPASS spent 0:0:51.30 on the problem.
% 51.52/51.74 0:00:00.03 for the input.
% 51.52/51.74 0:00:00.06 for the FLOTTER CNF translation.
% 51.52/51.74 0:00:00.44 for inferences.
% 51.52/51.74 0:00:04.28 for the backtracking.
% 51.52/51.74 0:0:46.15 for the reduction.
% 51.52/51.74
% 51.52/51.74
% 51.52/51.74 Here is a proof with depth 19, length 193 :
% 51.52/51.74 % SZS output start Refutation
% See solution above
% 60.84/61.04 Formulae used in the proof : s1_0_op_strict_implies s1_0_op_strict_equiv hilbert_op_or hilbert_op_implies_and hilbert_op_equiv hilbert_modus_ponens hilbert_modus_tollens hilbert_implies_1 hilbert_implies_2 hilbert_implies_3 hilbert_and_1 hilbert_and_2 hilbert_and_3 hilbert_equivalence_3 substitution_of_equivalents km5_necessitation km5_axiom_K km5_axiom_M s1_0_axiom_m1 modus_ponens axiom_M and_3 substitution_strict_equiv implies_1 and_1 and_2 necessitation r3 axiom_m1 op_strict_implies op_implies_and modus_tollens implies_2 op_or op_equiv axiom_K op_strict_equiv implies_3 equivalence_3
% 60.84/61.04
%------------------------------------------------------------------------------