TSTP Solution File: LCL541+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL541+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 14:37:35 EDT 2022
% Result : Theorem 81.95s 82.19s
% Output : Refutation 99.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 45
% Syntax : Number of clauses : 193 ( 135 unt; 1 nHn; 193 RR)
% Number of literals : 257 ( 0 equ; 69 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('LCL541+1.p',unknown),
[] ).
cnf(6,axiom,
op_strict_equiv,
file('LCL541+1.p',unknown),
[] ).
cnf(7,axiom,
op_or,
file('LCL541+1.p',unknown),
[] ).
cnf(8,axiom,
op_implies_and,
file('LCL541+1.p',unknown),
[] ).
cnf(9,axiom,
op_equiv,
file('LCL541+1.p',unknown),
[] ).
cnf(10,axiom,
modus_ponens,
file('LCL541+1.p',unknown),
[] ).
cnf(11,axiom,
modus_tollens,
file('LCL541+1.p',unknown),
[] ).
cnf(12,axiom,
implies_1,
file('LCL541+1.p',unknown),
[] ).
cnf(13,axiom,
implies_2,
file('LCL541+1.p',unknown),
[] ).
cnf(14,axiom,
implies_3,
file('LCL541+1.p',unknown),
[] ).
cnf(15,axiom,
and_1,
file('LCL541+1.p',unknown),
[] ).
cnf(16,axiom,
and_2,
file('LCL541+1.p',unknown),
[] ).
cnf(17,axiom,
and_3,
file('LCL541+1.p',unknown),
[] ).
cnf(23,axiom,
equivalence_3,
file('LCL541+1.p',unknown),
[] ).
cnf(24,axiom,
substitution_of_equivalents,
file('LCL541+1.p',unknown),
[] ).
cnf(26,axiom,
necessitation,
file('LCL541+1.p',unknown),
[] ).
cnf(27,axiom,
axiom_K,
file('LCL541+1.p',unknown),
[] ).
cnf(28,axiom,
axiom_M,
file('LCL541+1.p',unknown),
[] ).
cnf(31,axiom,
~ axiom_m1,
file('LCL541+1.p',unknown),
[] ).
cnf(32,axiom,
is_a_theorem(skc95),
file('LCL541+1.p',unknown),
[] ).
cnf(38,axiom,
is_a_theorem(implies__dfg(skc95,skc94)),
file('LCL541+1.p',unknown),
[] ).
cnf(44,axiom,
( substitution_strict_equiv
| is_a_theorem(strict_equiv(skc155,skc154)) ),
file('LCL541+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ equal(skc155,skc154)
| substitution_strict_equiv ),
file('LCL541+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ axiom_M
| is_a_theorem(implies__dfg(necessarily(u),u)) ),
file('LCL541+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ implies_1
| is_a_theorem(implies__dfg(u,implies__dfg(v,u))) ),
file('LCL541+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ and_1
| is_a_theorem(implies__dfg(and__dfg(u,v),u)) ),
file('LCL541+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ and_2
| is_a_theorem(implies__dfg(and__dfg(u,v),v)) ),
file('LCL541+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ is_a_theorem(u)
| ~ necessitation
| is_a_theorem(necessarily(u)) ),
file('LCL541+1.p',unknown),
[] ).
cnf(94,axiom,
( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv__dfg(u,v))
| equal(u,v) ),
file('LCL541+1.p',unknown),
[] ).
cnf(95,axiom,
( ~ and_3
| is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))) ),
file('LCL541+1.p',unknown),
[] ).
cnf(101,axiom,
( ~ r3
| is_a_theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))) ),
file('LCL541+1.p',unknown),
[] ).
cnf(102,axiom,
( ~ is_a_theorem(implies__dfg(or__dfg(skc142,skc141),or__dfg(skc141,skc142)))
| r3 ),
file('LCL541+1.p',unknown),
[] ).
cnf(104,axiom,
( ~ substitution_strict_equiv
| ~ is_a_theorem(strict_equiv(u,v))
| equal(u,v) ),
file('LCL541+1.p',unknown),
[] ).
cnf(106,axiom,
( ~ is_a_theorem(strict_implies(and__dfg(skc171,skc170),and__dfg(skc170,skc171)))
| axiom_m1 ),
file('LCL541+1.p',unknown),
[] ).
cnf(107,axiom,
( ~ op_strict_implies
| equal(necessarily(implies__dfg(u,v)),strict_implies(u,v)) ),
file('LCL541+1.p',unknown),
[] ).
cnf(108,axiom,
( ~ op_implies_and
| equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)) ),
file('LCL541+1.p',unknown),
[] ).
cnf(109,axiom,
( ~ is_a_theorem(u)
| ~ modus_ponens
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL541+1.p',unknown),
[] ).
cnf(110,axiom,
( ~ modus_tollens
| is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),not__dfg(v)),implies__dfg(v,u))) ),
file('LCL541+1.p',unknown),
[] ).
cnf(112,axiom,
( ~ implies_2
| is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))) ),
file('LCL541+1.p',unknown),
[] ).
cnf(114,axiom,
( ~ op_or
| equal(not__dfg(and__dfg(not__dfg(u),not__dfg(v))),or__dfg(u,v)) ),
file('LCL541+1.p',unknown),
[] ).
cnf(120,axiom,
( ~ op_equiv
| equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)) ),
file('LCL541+1.p',unknown),
[] ).
cnf(121,axiom,
( ~ axiom_K
| is_a_theorem(implies__dfg(necessarily(implies__dfg(u,v)),implies__dfg(necessarily(u),necessarily(v)))) ),
file('LCL541+1.p',unknown),
[] ).
cnf(125,axiom,
( ~ op_strict_equiv
| equal(and__dfg(strict_implies(u,v),strict_implies(v,u)),strict_equiv(u,v)) ),
file('LCL541+1.p',unknown),
[] ).
cnf(126,axiom,
( ~ implies_3
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))) ),
file('LCL541+1.p',unknown),
[] ).
cnf(128,axiom,
( ~ equivalence_3
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,u),equiv__dfg(u,v)))) ),
file('LCL541+1.p',unknown),
[] ).
cnf(148,plain,
is_a_theorem(implies__dfg(necessarily(u),u)),
inference(mrr,[status(thm)],[47,28]),
[iquote('0:MRR:47.0,28.0')] ).
cnf(150,plain,
( ~ is_a_theorem(u)
| is_a_theorem(necessarily(u)) ),
inference(mrr,[status(thm)],[69,26]),
[iquote('0:MRR:69.1,26.0')] ).
cnf(154,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),v)),
inference(mrr,[status(thm)],[55,16]),
[iquote('0:MRR:55.0,16.0')] ).
cnf(155,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),u)),
inference(mrr,[status(thm)],[53,15]),
[iquote('0:MRR:53.0,15.0')] ).
cnf(157,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
inference(mrr,[status(thm)],[51,12]),
[iquote('0:MRR:51.0,12.0')] ).
cnf(160,plain,
equal(necessarily(implies__dfg(u,v)),strict_implies(u,v)),
inference(mrr,[status(thm)],[107,4]),
[iquote('0:MRR:107.0,4.0')] ).
cnf(161,plain,
~ is_a_theorem(strict_implies(and__dfg(skc171,skc170),and__dfg(skc170,skc171))),
inference(mrr,[status(thm)],[106,31]),
[iquote('0:MRR:106.1,31.0')] ).
cnf(164,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))),
inference(mrr,[status(thm)],[95,17]),
[iquote('0:MRR:95.0,17.0')] ).
cnf(165,plain,
( ~ is_a_theorem(equiv__dfg(u,v))
| equal(u,v) ),
inference(mrr,[status(thm)],[94,24]),
[iquote('0:MRR:94.0,24.0')] ).
cnf(166,plain,
equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)),
inference(mrr,[status(thm)],[108,8]),
[iquote('0:MRR:108.0,8.0')] ).
cnf(167,plain,
( ~ op_or
| equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)) ),
inference(rew,[status(thm),theory(equality)],[166,114]),
[iquote('0:Rew:166.0,114.1')] ).
cnf(168,plain,
equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)),
inference(mrr,[status(thm)],[167,7]),
[iquote('0:MRR:167.0,7.0')] ).
cnf(174,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))),
inference(mrr,[status(thm)],[112,13]),
[iquote('0:MRR:112.0,13.0')] ).
cnf(175,plain,
( ~ modus_tollens
| is_a_theorem(implies__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,u))) ),
inference(rew,[status(thm),theory(equality)],[168,110]),
[iquote('0:Rew:168.0,110.1')] ).
cnf(176,plain,
is_a_theorem(implies__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,u))),
inference(mrr,[status(thm)],[175,11]),
[iquote('0:MRR:175.0,11.0')] ).
cnf(177,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(mrr,[status(thm)],[109,10]),
[iquote('0:MRR:109.1,10.0')] ).
cnf(178,plain,
equal(and__dfg(strict_implies(u,v),strict_implies(v,u)),strict_equiv(u,v)),
inference(mrr,[status(thm)],[125,6]),
[iquote('0:MRR:125.0,6.0')] ).
cnf(179,plain,
( ~ axiom_K
| is_a_theorem(implies__dfg(strict_implies(u,v),implies__dfg(necessarily(u),necessarily(v)))) ),
inference(rew,[status(thm),theory(equality)],[160,121]),
[iquote('0:Rew:160.0,121.1')] ).
cnf(180,plain,
is_a_theorem(implies__dfg(strict_implies(u,v),implies__dfg(necessarily(u),necessarily(v)))),
inference(mrr,[status(thm)],[179,27]),
[iquote('0:MRR:179.0,27.0')] ).
cnf(181,plain,
equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)),
inference(mrr,[status(thm)],[120,9]),
[iquote('0:MRR:120.0,9.0')] ).
cnf(182,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,u),equiv__dfg(u,v)))),
inference(mrr,[status(thm)],[128,23]),
[iquote('0:MRR:128.0,23.0')] ).
cnf(183,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))),
inference(mrr,[status(thm)],[126,14]),
[iquote('0:MRR:126.0,14.0')] ).
cnf(192,plain,
substitution_strict_equiv,
inference(spt,[spt(split,[position(s1)])],[44]),
[iquote('1:Spt:44.0')] ).
cnf(193,plain,
( ~ is_a_theorem(strict_equiv(u,v))
| equal(u,v) ),
inference(mrr,[status(thm)],[104,192]),
[iquote('1:MRR:104.0,192.0')] ).
cnf(217,plain,
is_a_theorem(implies__dfg(strict_implies(u,v),implies__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[160,148]),
[iquote('0:SpR:160.0,148.0')] ).
cnf(218,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(strict_implies(u,v)) ),
inference(spr,[status(thm),theory(equality)],[160,150]),
[iquote('0:SpR:160.0,150.1')] ).
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)],[166,168]),
[iquote('0:SpR:166.0,168.0')] ).
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)],[166]),
[iquote('0:SpR:166.0,166.0')] ).
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)],[168,176]),
[iquote('0:SpR:168.0,176.0')] ).
cnf(296,plain,
is_a_theorem(strict_implies(and__dfg(u,v),v)),
inference(sor,[status(thm)],[218,154]),
[iquote('0:SoR:218.0,154.0')] ).
cnf(299,plain,
is_a_theorem(strict_implies(u,implies__dfg(v,u))),
inference(sor,[status(thm)],[218,157]),
[iquote('0:SoR:218.0,157.0')] ).
cnf(305,plain,
is_a_theorem(strict_implies(skc95,skc94)),
inference(sor,[status(thm)],[218,38]),
[iquote('0:SoR:218.0,38.0')] ).
cnf(354,plain,
( ~ is_a_theorem(skc95)
| is_a_theorem(skc94) ),
inference(res,[status(thm),theory(equality)],[38,177]),
[iquote('0:Res:38.0,177.1')] ).
cnf(360,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[157,177]),
[iquote('0:Res:157.0,177.1')] ).
cnf(370,plain,
( ~ is_a_theorem(strict_implies(u,v))
| is_a_theorem(implies__dfg(u,v)) ),
inference(res,[status(thm),theory(equality)],[217,177]),
[iquote('0:Res:217.0,177.1')] ).
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)],[180,177]),
[iquote('0:Res:180.0,177.1')] ).
cnf(374,plain,
is_a_theorem(skc94),
inference(ssi,[status(thm)],[354,32]),
[iquote('0:SSi:354.0,32.0')] ).
cnf(381,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(u,v)))
| is_a_theorem(implies__dfg(u,v)) ),
inference(res,[status(thm),theory(equality)],[174,177]),
[iquote('0:Res:174.0,177.1')] ).
cnf(395,plain,
is_a_theorem(implies__dfg(strict_equiv(u,v),strict_implies(v,u))),
inference(spr,[status(thm),theory(equality)],[178,154]),
[iquote('0:SpR:178.0,154.0')] ).
cnf(396,plain,
is_a_theorem(implies__dfg(strict_equiv(u,v),strict_implies(u,v))),
inference(spr,[status(thm),theory(equality)],[178,155]),
[iquote('0:SpR:178.0,155.0')] ).
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)],[182,177]),
[iquote('0:Res:182.0,177.1')] ).
cnf(522,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)],[183,177]),
[iquote('0:Res:183.0,177.1')] ).
cnf(1890,plain,
is_a_theorem(implies__dfg(necessarily(skc95),necessarily(skc94))),
inference(sor,[status(thm)],[371,305]),
[iquote('0:SoR:371.0,305.0')] ).
cnf(1894,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(1908,plain,
is_a_theorem(implies__dfg(necessarily(u),strict_implies(v,u))),
inference(rew,[status(thm),theory(equality)],[160,1894]),
[iquote('0:Rew:160.0,1894.0')] ).
cnf(1933,plain,
( ~ is_a_theorem(necessarily(skc95))
| is_a_theorem(necessarily(skc94)) ),
inference(res,[status(thm),theory(equality)],[1890,177]),
[iquote('0:Res:1890.0,177.1')] ).
cnf(1934,plain,
is_a_theorem(necessarily(skc94)),
inference(ssi,[status(thm)],[1933,150,32]),
[iquote('0:SSi:1933.0,150.0,32.1')] ).
cnf(1942,plain,
( ~ is_a_theorem(necessarily(u))
| is_a_theorem(strict_implies(v,u)) ),
inference(res,[status(thm),theory(equality)],[1908,177]),
[iquote('0:Res:1908.0,177.1')] ).
cnf(1994,plain,
is_a_theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[381,157]),
[iquote('0:SoR:381.0,157.0')] ).
cnf(2040,plain,
is_a_theorem(strict_implies(u,u)),
inference(sor,[status(thm)],[218,1994]),
[iquote('0:SoR:218.0,1994.0')] ).
cnf(2271,plain,
is_a_theorem(strict_implies(u,skc94)),
inference(sor,[status(thm)],[1942,1934]),
[iquote('0:SoR:1942.0,1934.0')] ).
cnf(2276,plain,
is_a_theorem(implies__dfg(u,skc94)),
inference(sor,[status(thm)],[370,2271]),
[iquote('0:SoR:370.0,2271.0')] ).
cnf(3925,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)],[511,101]),
[iquote('0:SoR:511.0,101.1')] ).
cnf(3931,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),equiv__dfg(u,skc94))),
inference(sor,[status(thm)],[511,2276]),
[iquote('0:SoR:511.0,2276.0')] ).
cnf(4113,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),implies__dfg(v,u))),
inference(sor,[status(thm)],[522,2276]),
[iquote('0:SoR:522.0,2276.0')] ).
cnf(5599,plain,
( ~ is_a_theorem(implies__dfg(skc94,u))
| is_a_theorem(equiv__dfg(u,skc94)) ),
inference(res,[status(thm),theory(equality)],[3931,177]),
[iquote('0:Res:3931.0,177.1')] ).
cnf(5609,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),u)),
inference(sor,[status(thm)],[381,4113]),
[iquote('0:SoR:381.0,4113.0')] ).
cnf(5617,plain,
is_a_theorem(strict_implies(implies__dfg(skc94,u),u)),
inference(sor,[status(thm)],[218,5609]),
[iquote('0:SoR:218.0,5609.0')] ).
cnf(5618,plain,
( ~ is_a_theorem(implies__dfg(skc94,u))
| is_a_theorem(u) ),
inference(res,[status(thm),theory(equality)],[5609,177]),
[iquote('0:Res:5609.0,177.1')] ).
cnf(5623,plain,
is_a_theorem(implies__dfg(necessarily(implies__dfg(skc94,u)),necessarily(u))),
inference(sor,[status(thm)],[371,5617]),
[iquote('0:SoR:371.0,5617.0')] ).
cnf(5626,plain,
is_a_theorem(implies__dfg(strict_implies(skc94,u),necessarily(u))),
inference(rew,[status(thm),theory(equality)],[160,5623]),
[iquote('0:Rew:160.0,5623.0')] ).
cnf(5659,plain,
is_a_theorem(implies__dfg(u,and__dfg(skc94,u))),
inference(sor,[status(thm)],[5618,164]),
[iquote('0:SoR:5618.0,164.0')] ).
cnf(5713,plain,
is_a_theorem(strict_implies(u,and__dfg(skc94,u))),
inference(sor,[status(thm)],[218,5659]),
[iquote('0:SoR:218.0,5659.0')] ).
cnf(5802,plain,
( ~ is_a_theorem(strict_implies(skc94,u))
| is_a_theorem(necessarily(u)) ),
inference(res,[status(thm),theory(equality)],[5626,177]),
[iquote('0:Res:5626.0,177.1')] ).
cnf(6443,plain,
is_a_theorem(necessarily(and__dfg(skc94,skc94))),
inference(sor,[status(thm)],[5802,5713]),
[iquote('0:SoR:5802.0,5713.0')] ).
cnf(6461,plain,
is_a_theorem(strict_implies(u,and__dfg(skc94,skc94))),
inference(sor,[status(thm)],[1942,6443]),
[iquote('0:SoR:1942.0,6443.0')] ).
cnf(6466,plain,
is_a_theorem(implies__dfg(u,and__dfg(skc94,skc94))),
inference(sor,[status(thm)],[370,6461]),
[iquote('0:SoR:370.0,6461.0')] ).
cnf(11033,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equiv__dfg(u,skc94)) ),
inference(sor,[status(thm)],[5599,360]),
[iquote('0:SoR:5599.0,360.1')] ).
cnf(11056,plain,
is_a_theorem(equiv__dfg(and__dfg(skc94,skc94),skc94)),
inference(sor,[status(thm)],[5599,6466]),
[iquote('0:SoR:5599.0,6466.0')] ).
cnf(11089,plain,
is_a_theorem(equiv__dfg(implies__dfg(u,skc94),skc94)),
inference(sor,[status(thm)],[5599,157]),
[iquote('0:SoR:5599.0,157.0')] ).
cnf(12661,plain,
equal(and__dfg(skc94,skc94),skc94),
inference(res,[status(thm),theory(equality)],[11056,165]),
[iquote('0:Res:11056.0,165.0')] ).
cnf(12986,plain,
equal(implies__dfg(u,skc94),skc94),
inference(res,[status(thm),theory(equality)],[11089,165]),
[iquote('0:Res:11089.0,165.0')] ).
cnf(13036,plain,
equal(and__dfg(skc94,implies__dfg(skc94,u)),equiv__dfg(u,skc94)),
inference(spr,[status(thm),theory(equality)],[12986,181]),
[iquote('0:SpR:12986.0,181.0')] ).
cnf(14172,plain,
( ~ is_a_theorem(u)
| equal(u,skc94) ),
inference(res,[status(thm),theory(equality)],[11033,165]),
[iquote('0:Res:11033.1,165.0')] ).
cnf(14373,plain,
equal(strict_implies(and__dfg(u,v),v),skc94),
inference(ems,[status(thm)],[14172,296]),
[iquote('0:EmS:14172.0,296.0')] ).
cnf(14376,plain,
equal(strict_implies(implies__dfg(skc94,u),u),skc94),
inference(ems,[status(thm)],[14172,5617]),
[iquote('0:EmS:14172.0,5617.0')] ).
cnf(14377,plain,
equal(strict_implies(u,u),skc94),
inference(ems,[status(thm)],[14172,2040]),
[iquote('0:EmS:14172.0,2040.0')] ).
cnf(14392,plain,
equal(strict_implies(u,and__dfg(skc94,u)),skc94),
inference(ems,[status(thm)],[14172,5713]),
[iquote('0:EmS:14172.0,5713.0')] ).
cnf(14396,plain,
equal(strict_implies(u,implies__dfg(v,u)),skc94),
inference(ems,[status(thm)],[14172,299]),
[iquote('0:EmS:14172.0,299.0')] ).
cnf(14453,plain,
equal(implies__dfg(or__dfg(u,not__dfg(not__dfg(v))),or__dfg(v,u)),skc94),
inference(ems,[status(thm)],[14172,283]),
[iquote('0:EmS:14172.0,283.0')] ).
cnf(14466,plain,
equal(implies__dfg(strict_equiv(u,v),strict_implies(u,v)),skc94),
inference(ems,[status(thm)],[14172,396]),
[iquote('0:EmS:14172.0,396.0')] ).
cnf(14467,plain,
equal(implies__dfg(strict_equiv(u,v),strict_implies(v,u)),skc94),
inference(ems,[status(thm)],[14172,395]),
[iquote('0:EmS:14172.0,395.0')] ).
cnf(14510,plain,
equal(implies__dfg(strict_implies(u,v),implies__dfg(u,v)),skc94),
inference(ems,[status(thm)],[14172,217]),
[iquote('0:EmS:14172.0,217.0')] ).
cnf(14513,plain,
( ~ r3
| equal(implies__dfg(or__dfg(u,v),or__dfg(v,u)),skc94) ),
inference(ems,[status(thm)],[14172,101]),
[iquote('0:EmS:14172.0,101.1')] ).
cnf(15163,plain,
( ~ r3
| is_a_theorem(implies__dfg(skc94,equiv__dfg(or__dfg(u,v),or__dfg(v,u)))) ),
inference(rew,[status(thm),theory(equality)],[14513,3925]),
[iquote('0:Rew:14513.1,3925.1')] ).
cnf(16017,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)],[14376,178]),
[iquote('0:SpR:14376.0,178.0')] ).
cnf(16025,plain,
equal(strict_equiv(implies__dfg(skc94,u),u),and__dfg(skc94,skc94)),
inference(rew,[status(thm),theory(equality)],[14396,16017]),
[iquote('0:Rew:14396.0,16017.0')] ).
cnf(16026,plain,
equal(strict_equiv(implies__dfg(skc94,u),u),skc94),
inference(rew,[status(thm),theory(equality)],[12661,16025]),
[iquote('0:Rew:12661.0,16025.0')] ).
cnf(16030,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)],[14392,178]),
[iquote('0:SpR:14392.0,178.0')] ).
cnf(16037,plain,
equal(strict_equiv(u,and__dfg(skc94,u)),and__dfg(skc94,skc94)),
inference(rew,[status(thm),theory(equality)],[14373,16030]),
[iquote('0:Rew:14373.0,16030.0')] ).
cnf(16038,plain,
equal(strict_equiv(u,and__dfg(skc94,u)),skc94),
inference(rew,[status(thm),theory(equality)],[12661,16037]),
[iquote('0:Rew:12661.0,16037.0')] ).
cnf(17085,plain,
( ~ is_a_theorem(skc94)
| equal(implies__dfg(skc94,u),u) ),
inference(spl,[status(thm),theory(equality)],[16026,193]),
[iquote('1:SpL:16026.0,193.0')] ).
cnf(17087,plain,
equal(implies__dfg(skc94,u),u),
inference(mrr,[status(thm)],[17085,374]),
[iquote('1:MRR:17085.0,374.0')] ).
cnf(17117,plain,
( ~ r3
| is_a_theorem(equiv__dfg(or__dfg(u,v),or__dfg(v,u))) ),
inference(rew,[status(thm),theory(equality)],[17087,15163]),
[iquote('1:Rew:17087.0,15163.1')] ).
cnf(17210,plain,
equal(and__dfg(skc94,u),equiv__dfg(u,skc94)),
inference(rew,[status(thm),theory(equality)],[17087,13036]),
[iquote('1:Rew:17087.0,13036.0')] ).
cnf(17306,plain,
equal(strict_equiv(u,equiv__dfg(u,skc94)),skc94),
inference(rew,[status(thm),theory(equality)],[17210,16038]),
[iquote('1:Rew:17210.0,16038.0')] ).
cnf(18373,plain,
equal(not__dfg(equiv__dfg(not__dfg(u),skc94)),implies__dfg(skc94,u)),
inference(spr,[status(thm),theory(equality)],[17210,166]),
[iquote('1:SpR:17210.0,166.0')] ).
cnf(18375,plain,
equal(or__dfg(equiv__dfg(not__dfg(u),skc94),v),implies__dfg(implies__dfg(skc94,u),v)),
inference(spr,[status(thm),theory(equality)],[17210,265]),
[iquote('1:SpR:17210.0,265.0')] ).
cnf(18379,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)],[17210,271]),
[iquote('1:SpR:17210.0,271.0')] ).
cnf(18384,plain,
equal(not__dfg(equiv__dfg(not__dfg(u),skc94)),u),
inference(rew,[status(thm),theory(equality)],[17087,18373]),
[iquote('1:Rew:17087.0,18373.0')] ).
cnf(18388,plain,
equal(or__dfg(equiv__dfg(not__dfg(u),skc94),v),implies__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[17087,18375]),
[iquote('1:Rew:17087.0,18375.0')] ).
cnf(18391,plain,
equal(not__dfg(equiv__dfg(implies__dfg(u,v),skc94)),and__dfg(u,not__dfg(v))),
inference(rew,[status(thm),theory(equality)],[17087,18379]),
[iquote('1:Rew:17087.0,18379.0')] ).
cnf(18441,plain,
( ~ is_a_theorem(skc94)
| equal(equiv__dfg(u,skc94),u) ),
inference(spl,[status(thm),theory(equality)],[17306,193]),
[iquote('1:SpL:17306.0,193.0')] ).
cnf(18442,plain,
equal(equiv__dfg(u,skc94),u),
inference(mrr,[status(thm)],[18441,374]),
[iquote('1:MRR:18441.0,374.0')] ).
cnf(18521,plain,
equal(not__dfg(implies__dfg(u,v)),and__dfg(u,not__dfg(v))),
inference(rew,[status(thm),theory(equality)],[18442,18391]),
[iquote('1:Rew:18442.0,18391.0')] ).
cnf(18532,plain,
equal(not__dfg(not__dfg(u)),u),
inference(rew,[status(thm),theory(equality)],[18442,18384]),
[iquote('1:Rew:18442.0,18384.0')] ).
cnf(18534,plain,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[18442,18388]),
[iquote('1:Rew:18442.0,18388.0')] ).
cnf(18826,plain,
equal(implies__dfg(or__dfg(u,v),or__dfg(v,u)),skc94),
inference(rew,[status(thm),theory(equality)],[18532,14453]),
[iquote('1:Rew:18532.0,14453.0')] ).
cnf(20158,plain,
( ~ is_a_theorem(skc94)
| r3 ),
inference(rew,[status(thm),theory(equality)],[18826,102]),
[iquote('1:Rew:18826.0,102.0')] ).
cnf(20167,plain,
r3,
inference(mrr,[status(thm)],[20158,374]),
[iquote('1:MRR:20158.0,374.0')] ).
cnf(20312,plain,
is_a_theorem(equiv__dfg(or__dfg(u,v),or__dfg(v,u))),
inference(mrr,[status(thm)],[17117,20167]),
[iquote('1:MRR:17117.0,20167.0')] ).
cnf(22670,plain,
equal(or__dfg(u,v),or__dfg(v,u)),
inference(res,[status(thm),theory(equality)],[20312,165]),
[iquote('1:Res:20312.0,165.0')] ).
cnf(27822,plain,
equal(or__dfg(u,not__dfg(v)),implies__dfg(v,u)),
inference(spr,[status(thm),theory(equality)],[18534,22670]),
[iquote('1:SpR:18534.0,22670.0')] ).
cnf(32245,plain,
equal(implies__dfg(u,not__dfg(v)),implies__dfg(v,not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[27822,18534]),
[iquote('1:SpR:27822.0,18534.0')] ).
cnf(122619,plain,
equal(not__dfg(implies__dfg(u,not__dfg(v))),and__dfg(v,not__dfg(not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[32245,18521]),
[iquote('1:SpR:32245.0,18521.0')] ).
cnf(122926,plain,
equal(and__dfg(u,v),and__dfg(v,u)),
inference(rew,[status(thm),theory(equality)],[18532,122619,18521]),
[iquote('1:Rew:18532.0,122619.0,18521.0,122619.0,18532.0,122619.0')] ).
cnf(122961,plain,
~ is_a_theorem(strict_implies(and__dfg(skc170,skc171),and__dfg(skc170,skc171))),
inference(rew,[status(thm),theory(equality)],[122926,161]),
[iquote('1:Rew:122926.0,161.0')] ).
cnf(123400,plain,
~ is_a_theorem(skc94),
inference(rew,[status(thm),theory(equality)],[14377,122961]),
[iquote('1:Rew:14377.0,122961.0')] ).
cnf(123401,plain,
$false,
inference(mrr,[status(thm)],[123400,374]),
[iquote('1:MRR:123400.0,374.0')] ).
cnf(124263,plain,
~ substitution_strict_equiv,
inference(spt,[spt(split,[position(sa)])],[123401,192]),
[iquote('1:Spt:123401.0,44.0,192.0')] ).
cnf(124264,plain,
is_a_theorem(strict_equiv(skc155,skc154)),
inference(spt,[spt(split,[position(s2)])],[44]),
[iquote('1:Spt:123401.0,44.1')] ).
cnf(124267,plain,
~ equal(skc155,skc154),
inference(mrr,[status(thm)],[45,124263]),
[iquote('1:MRR:45.1,124263.0')] ).
cnf(125832,plain,
equal(strict_equiv(skc155,skc154),skc94),
inference(ems,[status(thm)],[14172,124264]),
[iquote('1:EmS:14172.0,124264.0')] ).
cnf(125925,plain,
equal(implies__dfg(skc94,strict_implies(skc155,skc154)),skc94),
inference(spr,[status(thm),theory(equality)],[125832,14466]),
[iquote('1:SpR:125832.0,14466.0')] ).
cnf(125926,plain,
equal(implies__dfg(skc94,strict_implies(skc154,skc155)),skc94),
inference(spr,[status(thm),theory(equality)],[125832,14467]),
[iquote('1:SpR:125832.0,14467.0')] ).
cnf(126384,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)],[125925,181]),
[iquote('1:SpR:125925.0,181.0')] ).
cnf(126400,plain,
equal(equiv__dfg(strict_implies(skc155,skc154),skc94),skc94),
inference(rew,[status(thm),theory(equality)],[12661,126384,12986]),
[iquote('1:Rew:12661.0,126384.0,12986.0,126384.0')] ).
cnf(126404,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)],[125926,181]),
[iquote('1:SpR:125926.0,181.0')] ).
cnf(126420,plain,
equal(equiv__dfg(strict_implies(skc154,skc155),skc94),skc94),
inference(rew,[status(thm),theory(equality)],[12661,126404,12986]),
[iquote('1:Rew:12661.0,126404.0,12986.0,126404.0')] ).
cnf(126472,plain,
( ~ is_a_theorem(skc94)
| equal(strict_implies(skc155,skc154),skc94) ),
inference(spl,[status(thm),theory(equality)],[126400,165]),
[iquote('1:SpL:126400.0,165.0')] ).
cnf(126473,plain,
equal(strict_implies(skc155,skc154),skc94),
inference(mrr,[status(thm)],[126472,374]),
[iquote('1:MRR:126472.0,374.0')] ).
cnf(126487,plain,
equal(implies__dfg(skc94,implies__dfg(skc155,skc154)),skc94),
inference(spr,[status(thm),theory(equality)],[126473,14510]),
[iquote('1:SpR:126473.0,14510.0')] ).
cnf(126597,plain,
( ~ is_a_theorem(skc94)
| equal(strict_implies(skc154,skc155),skc94) ),
inference(spl,[status(thm),theory(equality)],[126420,165]),
[iquote('1:SpL:126420.0,165.0')] ).
cnf(126598,plain,
equal(strict_implies(skc154,skc155),skc94),
inference(mrr,[status(thm)],[126597,374]),
[iquote('1:MRR:126597.0,374.0')] ).
cnf(126615,plain,
equal(implies__dfg(skc94,implies__dfg(skc154,skc155)),skc94),
inference(spr,[status(thm),theory(equality)],[126598,14510]),
[iquote('1:SpR:126598.0,14510.0')] ).
cnf(126721,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)],[126487,181]),
[iquote('1:SpR:126487.0,181.0')] ).
cnf(126737,plain,
equal(equiv__dfg(implies__dfg(skc155,skc154),skc94),skc94),
inference(rew,[status(thm),theory(equality)],[12661,126721,12986]),
[iquote('1:Rew:12661.0,126721.0,12986.0,126721.0')] ).
cnf(126759,plain,
equal(and__dfg(implies__dfg(implies__dfg(skc154,skc155),skc94),skc94),equiv__dfg(implies__dfg(skc154,skc155),skc94)),
inference(spr,[status(thm),theory(equality)],[126615,181]),
[iquote('1:SpR:126615.0,181.0')] ).
cnf(126775,plain,
equal(equiv__dfg(implies__dfg(skc154,skc155),skc94),skc94),
inference(rew,[status(thm),theory(equality)],[12661,126759,12986]),
[iquote('1:Rew:12661.0,126759.0,12986.0,126759.0')] ).
cnf(126810,plain,
( ~ is_a_theorem(skc94)
| equal(implies__dfg(skc155,skc154),skc94) ),
inference(spl,[status(thm),theory(equality)],[126737,165]),
[iquote('1:SpL:126737.0,165.0')] ).
cnf(126811,plain,
equal(implies__dfg(skc155,skc154),skc94),
inference(mrr,[status(thm)],[126810,374]),
[iquote('1:MRR:126810.0,374.0')] ).
cnf(126820,plain,
equal(and__dfg(implies__dfg(skc154,skc155),skc94),equiv__dfg(skc154,skc155)),
inference(spr,[status(thm),theory(equality)],[126811,181]),
[iquote('1:SpR:126811.0,181.0')] ).
cnf(126885,plain,
( ~ is_a_theorem(skc94)
| equal(implies__dfg(skc154,skc155),skc94) ),
inference(spl,[status(thm),theory(equality)],[126775,165]),
[iquote('1:SpL:126775.0,165.0')] ).
cnf(126886,plain,
equal(implies__dfg(skc154,skc155),skc94),
inference(mrr,[status(thm)],[126885,374]),
[iquote('1:MRR:126885.0,374.0')] ).
cnf(126893,plain,
equal(and__dfg(skc94,skc94),equiv__dfg(skc154,skc155)),
inference(rew,[status(thm),theory(equality)],[126886,126820]),
[iquote('1:Rew:126886.0,126820.0')] ).
cnf(126895,plain,
equal(equiv__dfg(skc154,skc155),skc94),
inference(rew,[status(thm),theory(equality)],[12661,126893]),
[iquote('1:Rew:12661.0,126893.0')] ).
cnf(126923,plain,
( ~ is_a_theorem(skc94)
| equal(skc155,skc154) ),
inference(spl,[status(thm),theory(equality)],[126895,165]),
[iquote('1:SpL:126895.0,165.0')] ).
cnf(126924,plain,
$false,
inference(mrr,[status(thm)],[126923,374,124267]),
[iquote('1:MRR:126923.0,126923.1,374.0,124267.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL541+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 2 16:42:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 81.95/82.19
% 81.95/82.19 SPASS V 3.9
% 81.95/82.19 SPASS beiseite: Proof found.
% 81.95/82.19 % SZS status Theorem
% 81.95/82.19 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 81.95/82.19 SPASS derived 76048 clauses, backtracked 5254 clauses, performed 3 splits and kept 23655 clauses.
% 81.95/82.19 SPASS allocated 209198 KBytes.
% 81.95/82.19 SPASS spent 0:1:21.70 on the problem.
% 81.95/82.19 0:00:00.04 for the input.
% 81.95/82.19 0:00:00.06 for the FLOTTER CNF translation.
% 81.95/82.19 0:00:00.65 for inferences.
% 81.95/82.19 0:00:07.34 for the backtracking.
% 81.95/82.19 0:1:13.06 for the reduction.
% 81.95/82.19
% 81.95/82.19
% 81.95/82.19 Here is a proof with depth 19, length 193 :
% 81.95/82.19 % SZS output start Refutation
% See solution above
% 99.46/99.68 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 km4b_necessitation km4b_axiom_K km4b_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
% 99.46/99.68
%------------------------------------------------------------------------------