TSTP Solution File: ALG218+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG218+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 : Thu Jul 14 18:03:02 EDT 2022
% Result : Theorem 0.71s 0.88s
% Output : Refutation 0.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 56
% Syntax : Number of clauses : 149 ( 66 unt; 28 nHn; 149 RR)
% Number of literals : 344 ( 0 equ; 183 neg)
% Maximal clause size : 23 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 29 ( 28 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
v3_rlvect_1(skc14),
file('ALG218+1.p',unknown),
[] ).
cnf(2,axiom,
v4_rlvect_1(skc14),
file('ALG218+1.p',unknown),
[] ).
cnf(3,axiom,
v5_rlvect_1(skc14),
file('ALG218+1.p',unknown),
[] ).
cnf(4,axiom,
v6_rlvect_1(skc14),
file('ALG218+1.p',unknown),
[] ).
cnf(5,axiom,
v4_group_1(skc14),
file('ALG218+1.p',unknown),
[] ).
cnf(6,axiom,
v7_group_1(skc14),
file('ALG218+1.p',unknown),
[] ).
cnf(7,axiom,
v6_vectsp_1(skc14),
file('ALG218+1.p',unknown),
[] ).
cnf(8,axiom,
v7_vectsp_1(skc14),
file('ALG218+1.p',unknown),
[] ).
cnf(9,axiom,
v8_vectsp_1(skc14),
file('ALG218+1.p',unknown),
[] ).
cnf(10,axiom,
v2_vectsp_2(skc14),
file('ALG218+1.p',unknown),
[] ).
cnf(11,axiom,
l3_vectsp_1(skc14),
file('ALG218+1.p',unknown),
[] ).
cnf(12,axiom,
v3_rlvect_1(skc15),
file('ALG218+1.p',unknown),
[] ).
cnf(13,axiom,
v4_rlvect_1(skc15),
file('ALG218+1.p',unknown),
[] ).
cnf(14,axiom,
v5_rlvect_1(skc15),
file('ALG218+1.p',unknown),
[] ).
cnf(15,axiom,
v6_rlvect_1(skc15),
file('ALG218+1.p',unknown),
[] ).
cnf(23,axiom,
v1_xboole_0(k1_xboole_0),
file('ALG218+1.p',unknown),
[] ).
cnf(27,axiom,
~ v3_struct_0(skc15),
file('ALG218+1.p',unknown),
[] ).
cnf(28,axiom,
~ v3_struct_0(skc14),
file('ALG218+1.p',unknown),
[] ).
cnf(29,axiom,
~ v10_vectsp_1(skc14),
file('ALG218+1.p',unknown),
[] ).
cnf(30,axiom,
v5_vectsp_2(skc15,skc14),
file('ALG218+1.p',unknown),
[] ).
cnf(31,axiom,
l1_vectsp_2(skc15,skc14),
file('ALG218+1.p',unknown),
[] ).
cnf(32,axiom,
v1_xboole_0(skf28(u)),
file('ALG218+1.p',unknown),
[] ).
cnf(37,axiom,
~ equal(skc16,k1_xboole_0),
file('ALG218+1.p',unknown),
[] ).
cnf(38,axiom,
m1_subset_1(skf21(u),u),
file('ALG218+1.p',unknown),
[] ).
cnf(39,axiom,
~ v1_xboole_0(k1_zfmisc_1(u)),
file('ALG218+1.p',unknown),
[] ).
cnf(44,axiom,
m1_subset_1(skc16,k1_zfmisc_1(u1_struct_0(skc15))),
file('ALG218+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ l1_rlvect_1(u)
| l2_struct_0(u) ),
file('ALG218+1.p',unknown),
[] ).
cnf(48,axiom,
( ~ l2_struct_0(u)
| l1_struct_0(u) ),
file('ALG218+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ l2_vectsp_1(u)
| l1_vectsp_1(u) ),
file('ALG218+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ l2_vectsp_1(u)
| l2_struct_0(u) ),
file('ALG218+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ l3_vectsp_1(u)
| l2_vectsp_1(u) ),
file('ALG218+1.p',unknown),
[] ).
cnf(54,axiom,
m1_subset_1(skf26(u),k1_zfmisc_1(u)),
file('ALG218+1.p',unknown),
[] ).
cnf(55,axiom,
m1_subset_1(skf28(u),k1_zfmisc_1(u)),
file('ALG218+1.p',unknown),
[] ).
cnf(56,axiom,
~ r2_hidden(skf17(u,v),u),
file('ALG218+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ v1_xboole_0(u)
| equal(u,k1_xboole_0) ),
file('ALG218+1.p',unknown),
[] ).
cnf(64,axiom,
~ equal(k7_rlvect_2(skc15,k1_rlvect_1(skc15)),skc16),
file('ALG218+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ equal(u,v)
| r1_tarski(v,u) ),
file('ALG218+1.p',unknown),
[] ).
cnf(71,axiom,
( ~ r2_hidden(u,v)
| m1_subset_1(u,v) ),
file('ALG218+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ v1_xboole_0(u)
| ~ r2_hidden(v,u) ),
file('ALG218+1.p',unknown),
[] ).
cnf(73,axiom,
equal(k1_rmod_5(skc14,skc15,skc16),k1_rmod_2(skc14,skc15)),
file('ALG218+1.p',unknown),
[] ).
cnf(75,axiom,
( r1_tarski(u,v)
| r2_hidden(skf17(v,u),u) ),
file('ALG218+1.p',unknown),
[] ).
cnf(79,axiom,
( ~ m1_subset_1(u,k1_zfmisc_1(v))
| r1_tarski(u,v) ),
file('ALG218+1.p',unknown),
[] ).
cnf(80,axiom,
( ~ r1_tarski(u,v)
| m1_subset_1(u,k1_zfmisc_1(v)) ),
file('ALG218+1.p',unknown),
[] ).
cnf(81,axiom,
( ~ m1_subset_1(u,k1_zfmisc_1(k2_zfmisc_1(v,w)))
| v1_relat_1(u) ),
file('ALG218+1.p',unknown),
[] ).
cnf(82,axiom,
( ~ l1_struct_0(u)
| ~ l1_vectsp_2(v,u)
| l1_rlvect_1(v) ),
file('ALG218+1.p',unknown),
[] ).
cnf(89,axiom,
( ~ m1_subset_1(u,v)
| v1_xboole_0(v)
| r2_hidden(u,v) ),
file('ALG218+1.p',unknown),
[] ).
cnf(91,axiom,
( ~ r1_tarski(u,v)
| ~ r1_tarski(v,u)
| equal(v,u) ),
file('ALG218+1.p',unknown),
[] ).
cnf(92,axiom,
( ~ r2_hidden(u,v)
| ~ r1_tarski(v,w)
| r2_hidden(u,w) ),
file('ALG218+1.p',unknown),
[] ).
cnf(96,axiom,
( ~ r2_hidden(u,v)
| ~ equal(v,k1_tarski(w))
| equal(u,w) ),
file('ALG218+1.p',unknown),
[] ).
cnf(97,axiom,
( ~ equal(u,v)
| ~ equal(w,k1_tarski(v))
| r2_hidden(u,w) ),
file('ALG218+1.p',unknown),
[] ).
cnf(98,axiom,
( ~ r2_hidden(u,v)
| ~ m1_subset_1(v,k1_zfmisc_1(w))
| m1_subset_1(u,w) ),
file('ALG218+1.p',unknown),
[] ).
cnf(99,axiom,
( ~ v1_xboole_0(u)
| ~ r2_hidden(v,w)
| ~ m1_subset_1(w,k1_zfmisc_1(u)) ),
file('ALG218+1.p',unknown),
[] ).
cnf(102,axiom,
( ~ v6_vectsp_1(u)
| ~ v7_group_1(u)
| ~ l1_vectsp_1(u)
| v3_struct_0(u)
| v2_group_1(u) ),
file('ALG218+1.p',unknown),
[] ).
cnf(108,axiom,
( ~ l1_struct_0(u)
| ~ m1_subset_1(v,u1_struct_0(u))
| v3_struct_0(u)
| equal(k7_rlvect_2(u,v),k1_tarski(v)) ),
file('ALG218+1.p',unknown),
[] ).
cnf(153,axiom,
( ~ v3_rlvect_1(u)
| ~ v4_rlvect_1(u)
| ~ v5_rlvect_1(u)
| ~ v6_rlvect_1(u)
| ~ v4_group_1(u)
| ~ v6_vectsp_1(u)
| ~ v7_vectsp_1(u)
| ~ v8_vectsp_1(u)
| ~ l3_vectsp_1(u)
| ~ v3_rlvect_1(v)
| ~ v4_rlvect_1(v)
| ~ v5_rlvect_1(v)
| ~ v6_rlvect_1(v)
| ~ v5_vectsp_2(v,u)
| ~ l1_vectsp_2(v,u)
| ~ r1_rlvect_1(k1_rmod_2(u,v),w)
| v3_struct_0(u)
| v3_struct_0(v)
| equal(w,k1_rlvect_1(v)) ),
file('ALG218+1.p',unknown),
[] ).
cnf(156,axiom,
( ~ v3_rlvect_1(u)
| ~ v4_rlvect_1(u)
| ~ v5_rlvect_1(u)
| ~ v6_rlvect_1(u)
| ~ v4_group_1(u)
| ~ v7_group_1(u)
| ~ v6_vectsp_1(u)
| ~ v7_vectsp_1(u)
| ~ v8_vectsp_1(u)
| ~ v2_vectsp_2(u)
| ~ l3_vectsp_1(u)
| ~ v3_rlvect_1(v)
| ~ v4_rlvect_1(v)
| ~ v5_rlvect_1(v)
| ~ v6_rlvect_1(v)
| ~ l1_vectsp_2(v,u)
| ~ r2_hidden(w,x)
| ~ v5_vectsp_2(v,u)
| ~ m1_subset_1(x,k1_zfmisc_1(u1_struct_0(v)))
| v3_struct_0(u)
| v10_vectsp_1(u)
| v3_struct_0(v)
| r1_rlvect_1(k1_rmod_5(u,v,x),w) ),
file('ALG218+1.p',unknown),
[] ).
cnf(387,plain,
equal(skf28(u),k1_xboole_0),
inference(ems,[status(thm)],[63,32]),
[iquote('0:EmS:63.0,32.0')] ).
cnf(392,plain,
m1_subset_1(k1_xboole_0,k1_zfmisc_1(u)),
inference(rew,[status(thm),theory(equality)],[387,55]),
[iquote('0:Rew:387.0,55.0')] ).
cnf(401,plain,
r1_tarski(k1_xboole_0,u),
inference(res,[status(thm),theory(equality)],[392,79]),
[iquote('0:Res:392.0,79.0')] ).
cnf(406,plain,
( r1_tarski(u,v)
| m1_subset_1(skf17(v,u),u) ),
inference(res,[status(thm),theory(equality)],[75,71]),
[iquote('0:Res:75.1,71.0')] ).
cnf(407,plain,
( r1_tarski(k1_zfmisc_1(u),v)
| r1_tarski(skf17(v,k1_zfmisc_1(u)),u) ),
inference(res,[status(thm),theory(equality)],[406,79]),
[iquote('0:Res:406.1,79.0')] ).
cnf(409,plain,
( ~ l1_struct_0(skc14)
| l1_rlvect_1(skc15) ),
inference(res,[status(thm),theory(equality)],[31,82]),
[iquote('0:Res:31.0,82.1')] ).
cnf(413,plain,
l1_rlvect_1(skc15),
inference(ssi,[status(thm)],[409,52,50,48,10,6,8,5,11,9,7,4,3,2,1]),
[iquote('0:SSi:409.0,52.0,50.0,48.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.1,2.1,1.1')] ).
cnf(420,plain,
v1_relat_1(k1_xboole_0),
inference(res,[status(thm),theory(equality)],[392,81]),
[iquote('0:Res:392.0,81.0')] ).
cnf(422,plain,
( ~ m1_subset_1(skf17(u,v),u)
| v1_xboole_0(u) ),
inference(res,[status(thm),theory(equality)],[89,56]),
[iquote('0:Res:89.2,56.0')] ).
cnf(433,plain,
( ~ r1_tarski(skf17(k1_zfmisc_1(u),v),u)
| v1_xboole_0(k1_zfmisc_1(u)) ),
inference(res,[status(thm),theory(equality)],[80,422]),
[iquote('0:Res:80.1,422.0')] ).
cnf(434,plain,
~ r1_tarski(skf17(k1_zfmisc_1(u),v),u),
inference(mrr,[status(thm)],[433,39]),
[iquote('0:MRR:433.1,39.0')] ).
cnf(435,plain,
~ equal(skf17(k1_zfmisc_1(u),v),u),
inference(res,[status(thm),theory(equality)],[66,434]),
[iquote('0:Res:66.1,434.0')] ).
cnf(447,plain,
( ~ r1_tarski(u,k1_xboole_0)
| equal(u,k1_xboole_0) ),
inference(res,[status(thm),theory(equality)],[401,91]),
[iquote('0:Res:401.0,91.0')] ).
cnf(460,plain,
( r1_tarski(k1_zfmisc_1(k1_xboole_0),u)
| equal(skf17(u,k1_zfmisc_1(k1_xboole_0)),k1_xboole_0) ),
inference(res,[status(thm),theory(equality)],[407,447]),
[iquote('0:Res:407.1,447.0')] ).
cnf(488,plain,
( ~ v1_xboole_0(u1_struct_0(skc15))
| ~ r2_hidden(u,skc16) ),
inference(res,[status(thm),theory(equality)],[44,99]),
[iquote('0:Res:44.0,99.2')] ).
cnf(531,plain,
( ~ equal(u,v)
| r2_hidden(u,k1_tarski(v)) ),
inference(eqr,[status(thm),theory(equality)],[97]),
[iquote('0:EqR:97.1')] ).
cnf(532,plain,
~ equal(skf17(k1_tarski(u),v),u),
inference(res,[status(thm),theory(equality)],[531,56]),
[iquote('0:Res:531.1,56.0')] ).
cnf(534,plain,
( ~ v1_xboole_0(k1_tarski(u))
| ~ equal(v,u) ),
inference(res,[status(thm),theory(equality)],[531,72]),
[iquote('0:Res:531.1,72.1')] ).
cnf(539,plain,
~ v1_xboole_0(k1_tarski(u)),
inference(aed,[status(thm),theory(equality)],[37,534]),
[iquote('0:AED:37.0,534.1')] ).
cnf(541,plain,
( ~ r2_hidden(u,k1_tarski(v))
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[96]),
[iquote('0:EqR:96.1')] ).
cnf(542,plain,
( r1_tarski(k1_tarski(u),v)
| equal(skf17(v,k1_tarski(u)),u) ),
inference(res,[status(thm),theory(equality)],[75,541]),
[iquote('0:Res:75.1,541.0')] ).
cnf(543,plain,
( ~ m1_subset_1(u,k1_tarski(v))
| v1_xboole_0(k1_tarski(v))
| equal(u,v) ),
inference(res,[status(thm),theory(equality)],[89,541]),
[iquote('0:Res:89.2,541.0')] ).
cnf(545,plain,
( ~ m1_subset_1(u,k1_tarski(v))
| equal(u,v) ),
inference(mrr,[status(thm)],[543,539]),
[iquote('0:MRR:543.1,539.0')] ).
cnf(546,plain,
equal(skf21(k1_tarski(u)),u),
inference(res,[status(thm),theory(equality)],[38,545]),
[iquote('0:Res:38.0,545.0')] ).
cnf(549,plain,
m1_subset_1(u,k1_tarski(u)),
inference(spr,[status(thm),theory(equality)],[546,38]),
[iquote('0:SpR:546.0,38.0')] ).
cnf(554,plain,
( ~ r2_hidden(u,skc16)
| m1_subset_1(u,u1_struct_0(skc15)) ),
inference(res,[status(thm),theory(equality)],[44,98]),
[iquote('0:Res:44.0,98.1')] ).
cnf(557,plain,
( ~ r2_hidden(u,skf26(v))
| m1_subset_1(u,v) ),
inference(res,[status(thm),theory(equality)],[54,98]),
[iquote('0:Res:54.0,98.1')] ).
cnf(562,plain,
( ~ r2_hidden(skf17(u1_struct_0(skc15),u),skc16)
| v1_xboole_0(u1_struct_0(skc15)) ),
inference(res,[status(thm),theory(equality)],[554,422]),
[iquote('0:Res:554.1,422.0')] ).
cnf(563,plain,
~ r2_hidden(skf17(u1_struct_0(skc15),u),skc16),
inference(mrr,[status(thm)],[562,488]),
[iquote('0:MRR:562.1,488.0')] ).
cnf(565,plain,
( ~ m1_subset_1(skf17(u1_struct_0(skc15),u),skc16)
| v1_xboole_0(skc16) ),
inference(res,[status(thm),theory(equality)],[89,563]),
[iquote('0:Res:89.2,563.0')] ).
cnf(568,plain,
( r1_tarski(skf26(u),v)
| m1_subset_1(skf17(v,skf26(u)),u) ),
inference(res,[status(thm),theory(equality)],[75,557]),
[iquote('0:Res:75.1,557.0')] ).
cnf(583,plain,
( r1_tarski(k1_zfmisc_1(k1_xboole_0),u)
| r1_tarski(k1_zfmisc_1(k1_xboole_0),u)
| r2_hidden(k1_xboole_0,k1_zfmisc_1(k1_xboole_0)) ),
inference(spr,[status(thm),theory(equality)],[460,75]),
[iquote('0:SpR:460.1,75.1')] ).
cnf(591,plain,
( ~ equal(k1_xboole_0,u)
| r1_tarski(k1_zfmisc_1(k1_xboole_0),k1_tarski(u)) ),
inference(spl,[status(thm),theory(equality)],[460,532]),
[iquote('0:SpL:460.1,532.0')] ).
cnf(597,plain,
( r1_tarski(k1_zfmisc_1(k1_xboole_0),u)
| r2_hidden(k1_xboole_0,k1_zfmisc_1(k1_xboole_0)) ),
inference(obv,[status(thm),theory(equality)],[583]),
[iquote('0:Obv:583.0')] ).
cnf(602,plain,
( ~ v6_vectsp_1(skc14)
| ~ v7_group_1(skc14)
| ~ l1_vectsp_1(skc14)
| v2_group_1(skc14) ),
inference(res,[status(thm),theory(equality)],[102,28]),
[iquote('0:Res:102.3,28.0')] ).
cnf(608,plain,
v2_group_1(skc14),
inference(ssi,[status(thm)],[602,52,49,10,6,8,5,11,9,7,4,3,2,1]),
[iquote('0:SSi:602.2,602.1,602.0,52.0,49.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.1,1.1')] ).
cnf(610,plain,
r1_tarski(k1_zfmisc_1(k1_xboole_0),u),
inference(spt,[spt(split,[position(s1)])],[597]),
[iquote('1:Spt:597.0')] ).
cnf(613,plain,
equal(k1_zfmisc_1(k1_xboole_0),k1_xboole_0),
inference(res,[status(thm),theory(equality)],[610,447]),
[iquote('1:Res:610.0,447.0')] ).
cnf(630,plain,
~ v1_xboole_0(k1_xboole_0),
inference(spl,[status(thm),theory(equality)],[613,39]),
[iquote('1:SpL:613.0,39.0')] ).
cnf(637,plain,
$false,
inference(mrr,[status(thm)],[630,23]),
[iquote('1:MRR:630.0,23.0')] ).
cnf(643,plain,
r2_hidden(k1_xboole_0,k1_zfmisc_1(k1_xboole_0)),
inference(spt,[spt(split,[position(s2)])],[597]),
[iquote('1:Spt:637.0,597.1')] ).
cnf(746,plain,
( ~ equal(k1_xboole_0,u)
| ~ r1_tarski(k1_tarski(u),k1_zfmisc_1(k1_xboole_0))
| equal(k1_tarski(u),k1_zfmisc_1(k1_xboole_0)) ),
inference(res,[status(thm),theory(equality)],[591,91]),
[iquote('0:Res:591.1,91.0')] ).
cnf(782,plain,
( ~ l1_struct_0(skc15)
| ~ r2_hidden(u,skc16)
| v3_struct_0(skc15)
| equal(k7_rlvect_2(skc15,u),k1_tarski(u)) ),
inference(res,[status(thm),theory(equality)],[554,108]),
[iquote('0:Res:554.1,108.1')] ).
cnf(785,plain,
( ~ r2_hidden(u,skc16)
| v3_struct_0(skc15)
| equal(k7_rlvect_2(skc15,u),k1_tarski(u)) ),
inference(ssi,[status(thm)],[782,46,48,15,14,13,12,413]),
[iquote('0:SSi:782.0,46.0,48.0,15.0,14.0,13.0,12.1,413.1')] ).
cnf(786,plain,
( ~ r2_hidden(u,skc16)
| equal(k7_rlvect_2(skc15,u),k1_tarski(u)) ),
inference(mrr,[status(thm)],[785,27]),
[iquote('0:MRR:785.1,27.0')] ).
cnf(804,plain,
( ~ r2_hidden(k1_rlvect_1(skc15),skc16)
| ~ equal(k1_tarski(k1_rlvect_1(skc15)),skc16) ),
inference(spl,[status(thm),theory(equality)],[786,64]),
[iquote('0:SpL:786.1,64.0')] ).
cnf(828,plain,
( r1_tarski(k1_tarski(u),v)
| r1_tarski(k1_tarski(u),v)
| r2_hidden(u,k1_tarski(u)) ),
inference(spr,[status(thm),theory(equality)],[542,75]),
[iquote('0:SpR:542.1,75.1')] ).
cnf(831,plain,
( ~ r2_hidden(u,v)
| r1_tarski(k1_tarski(u),v) ),
inference(spl,[status(thm),theory(equality)],[542,56]),
[iquote('0:SpL:542.1,56.0')] ).
cnf(834,plain,
( ~ equal(u,v)
| r1_tarski(k1_tarski(u),k1_zfmisc_1(v)) ),
inference(spl,[status(thm),theory(equality)],[542,435]),
[iquote('0:SpL:542.1,435.0')] ).
cnf(835,plain,
( ~ equal(u,v)
| r1_tarski(k1_tarski(u),k1_tarski(v)) ),
inference(spl,[status(thm),theory(equality)],[542,532]),
[iquote('0:SpL:542.1,532.0')] ).
cnf(840,plain,
( ~ equal(k1_xboole_0,u)
| equal(k1_tarski(u),k1_zfmisc_1(k1_xboole_0)) ),
inference(mrr,[status(thm)],[746,834]),
[iquote('0:MRR:746.1,834.1')] ).
cnf(843,plain,
( r1_tarski(k1_tarski(u),v)
| r2_hidden(u,k1_tarski(u)) ),
inference(obv,[status(thm),theory(equality)],[828]),
[iquote('0:Obv:828.0')] ).
cnf(854,plain,
( r2_hidden(u,k1_tarski(u))
| equal(k1_tarski(u),k1_xboole_0) ),
inference(res,[status(thm),theory(equality)],[843,447]),
[iquote('0:Res:843.0,447.0')] ).
cnf(871,plain,
( ~ r1_tarski(k1_tarski(u),v)
| equal(k1_tarski(u),k1_xboole_0)
| r2_hidden(u,v) ),
inference(res,[status(thm),theory(equality)],[854,92]),
[iquote('0:Res:854.0,92.0')] ).
cnf(881,plain,
( ~ equal(k1_xboole_0,u)
| m1_subset_1(u,k1_zfmisc_1(k1_xboole_0)) ),
inference(spr,[status(thm),theory(equality)],[840,549]),
[iquote('0:SpR:840.1,549.0')] ).
cnf(912,plain,
( ~ v1_xboole_0(k1_xboole_0)
| ~ equal(k1_xboole_0,u)
| ~ r2_hidden(v,u) ),
inference(res,[status(thm),theory(equality)],[881,99]),
[iquote('0:Res:881.1,99.2')] ).
cnf(915,plain,
( ~ equal(k1_xboole_0,u)
| ~ r2_hidden(v,u) ),
inference(ssi,[status(thm)],[912,23,420]),
[iquote('0:SSi:912.0,23.0,420.0')] ).
cnf(928,plain,
( ~ equal(u,v)
| ~ equal(k1_tarski(v),k1_xboole_0) ),
inference(res,[status(thm),theory(equality)],[531,915]),
[iquote('0:Res:531.1,915.1')] ).
cnf(933,plain,
~ equal(k1_tarski(u),k1_xboole_0),
inference(aed,[status(thm),theory(equality)],[37,928]),
[iquote('0:AED:37.0,928.0')] ).
cnf(935,plain,
r2_hidden(u,k1_tarski(u)),
inference(mrr,[status(thm)],[854,933]),
[iquote('0:MRR:854.1,933.0')] ).
cnf(938,plain,
( ~ r1_tarski(k1_tarski(u),v)
| r2_hidden(u,v) ),
inference(mrr,[status(thm)],[871,933]),
[iquote('0:MRR:871.1,933.0')] ).
cnf(1022,plain,
( ~ equal(u,k1_tarski(v))
| r2_hidden(v,u) ),
inference(res,[status(thm),theory(equality)],[66,938]),
[iquote('0:Res:66.1,938.0')] ).
cnf(1027,plain,
~ equal(k1_tarski(k1_rlvect_1(skc15)),skc16),
inference(mrr,[status(thm)],[804,1022]),
[iquote('0:MRR:804.0,1022.1')] ).
cnf(1172,plain,
( ~ equal(u,v)
| ~ r1_tarski(k1_tarski(v),k1_tarski(u))
| equal(k1_tarski(v),k1_tarski(u)) ),
inference(res,[status(thm),theory(equality)],[835,91]),
[iquote('0:Res:835.1,91.0')] ).
cnf(1174,plain,
( ~ equal(u,v)
| equal(k1_tarski(v),k1_tarski(u)) ),
inference(mrr,[status(thm)],[1172,835]),
[iquote('0:MRR:1172.1,835.1')] ).
cnf(1310,plain,
( ~ equal(u,k1_rlvect_1(skc15))
| ~ equal(k1_tarski(u),skc16) ),
inference(spl,[status(thm),theory(equality)],[1174,1027]),
[iquote('0:SpL:1174.1,1027.0')] ).
cnf(1759,plain,
( r1_tarski(skf26(skc16),u1_struct_0(skc15))
| v1_xboole_0(skc16) ),
inference(res,[status(thm),theory(equality)],[568,565]),
[iquote('0:Res:568.1,565.0')] ).
cnf(1763,plain,
v1_xboole_0(skc16),
inference(spt,[spt(split,[position(s2s1)])],[1759]),
[iquote('2:Spt:1759.1')] ).
cnf(1766,plain,
equal(skc16,k1_xboole_0),
inference(ems,[status(thm)],[63,1763]),
[iquote('2:EmS:63.0,1763.0')] ).
cnf(1768,plain,
$false,
inference(mrr,[status(thm)],[1766,37]),
[iquote('2:MRR:1766.0,37.0')] ).
cnf(1776,plain,
~ v1_xboole_0(skc16),
inference(spt,[spt(split,[position(s2sa)])],[1768,1763]),
[iquote('2:Spt:1768.0,1759.1,1763.0')] ).
cnf(1777,plain,
r1_tarski(skf26(skc16),u1_struct_0(skc15)),
inference(spt,[spt(split,[position(s2s2)])],[1759]),
[iquote('2:Spt:1768.0,1759.0')] ).
cnf(1993,plain,
( ~ v3_rlvect_1(skc14)
| ~ v4_rlvect_1(skc14)
| ~ v5_rlvect_1(skc14)
| ~ v6_rlvect_1(skc14)
| ~ v4_group_1(skc14)
| ~ v7_group_1(skc14)
| ~ v6_vectsp_1(skc14)
| ~ v7_vectsp_1(skc14)
| ~ v8_vectsp_1(skc14)
| ~ v2_vectsp_2(skc14)
| ~ l3_vectsp_1(skc14)
| ~ v3_rlvect_1(skc15)
| ~ v4_rlvect_1(skc15)
| ~ v5_rlvect_1(skc15)
| ~ v6_rlvect_1(skc15)
| ~ l1_vectsp_2(skc15,skc14)
| ~ r2_hidden(u,skc16)
| ~ v5_vectsp_2(skc15,skc14)
| ~ m1_subset_1(skc16,k1_zfmisc_1(u1_struct_0(skc15)))
| v3_struct_0(skc14)
| v10_vectsp_1(skc14)
| v3_struct_0(skc15)
| r1_rlvect_1(k1_rmod_2(skc14,skc15),u) ),
inference(spr,[status(thm),theory(equality)],[73,156]),
[iquote('0:SpR:73.0,156.22')] ).
cnf(1994,plain,
( ~ l1_vectsp_2(skc15,skc14)
| ~ r2_hidden(u,skc16)
| ~ v5_vectsp_2(skc15,skc14)
| ~ m1_subset_1(skc16,k1_zfmisc_1(u1_struct_0(skc15)))
| v3_struct_0(skc14)
| v10_vectsp_1(skc14)
| v3_struct_0(skc15)
| r1_rlvect_1(k1_rmod_2(skc14,skc15),u) ),
inference(ssi,[status(thm)],[1993,15,14,13,12,413,10,6,8,5,11,9,7,4,3,2,1,608]),
[iquote('0:SSi:1993.14,1993.13,1993.12,1993.11,1993.10,1993.9,1993.8,1993.7,1993.6,1993.5,1993.4,1993.3,1993.2,1993.1,1993.0,15.0,14.0,13.0,12.0,413.0,15.0,14.0,13.0,12.0,413.0,15.0,14.0,13.0,12.0,413.0,15.0,14.0,13.0,12.0,413.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,608.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,608.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,608.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,608.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,608.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,608.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,608.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,608.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,608.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,608.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,608.0')] ).
cnf(1995,plain,
( ~ r2_hidden(u,skc16)
| r1_rlvect_1(k1_rmod_2(skc14,skc15),u) ),
inference(mrr,[status(thm)],[1994,31,30,44,28,29,27]),
[iquote('0:MRR:1994.0,1994.2,1994.3,1994.4,1994.5,1994.6,31.0,30.0,44.0,28.0,29.0,27.0')] ).
cnf(1996,plain,
( ~ v3_rlvect_1(skc14)
| ~ v4_rlvect_1(skc14)
| ~ v5_rlvect_1(skc14)
| ~ v6_rlvect_1(skc14)
| ~ v4_group_1(skc14)
| ~ v6_vectsp_1(skc14)
| ~ v7_vectsp_1(skc14)
| ~ v8_vectsp_1(skc14)
| ~ l3_vectsp_1(skc14)
| ~ v3_rlvect_1(skc15)
| ~ v4_rlvect_1(skc15)
| ~ v5_rlvect_1(skc15)
| ~ v6_rlvect_1(skc15)
| ~ r2_hidden(u,skc16)
| ~ v5_vectsp_2(skc15,skc14)
| ~ l1_vectsp_2(skc15,skc14)
| v3_struct_0(skc14)
| v3_struct_0(skc15)
| equal(u,k1_rlvect_1(skc15)) ),
inference(res,[status(thm),theory(equality)],[1995,153]),
[iquote('0:Res:1995.1,153.15')] ).
cnf(1997,plain,
( ~ r2_hidden(u,skc16)
| ~ v5_vectsp_2(skc15,skc14)
| ~ l1_vectsp_2(skc15,skc14)
| v3_struct_0(skc14)
| v3_struct_0(skc15)
| equal(u,k1_rlvect_1(skc15)) ),
inference(ssi,[status(thm)],[1996,15,14,13,12,413,10,6,8,5,11,9,7,4,3,2,1,608]),
[iquote('0:SSi:1996.12,1996.11,1996.10,1996.9,1996.8,1996.7,1996.6,1996.5,1996.4,1996.3,1996.2,1996.1,1996.0,15.0,14.0,13.0,12.0,413.0,15.0,14.0,13.0,12.0,413.0,15.0,14.0,13.0,12.0,413.0,15.0,14.0,13.0,12.0,413.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,608.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,608.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,608.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,608.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,608.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,608.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,608.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,608.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,608.0')] ).
cnf(1998,plain,
( ~ r2_hidden(u,skc16)
| equal(u,k1_rlvect_1(skc15)) ),
inference(mrr,[status(thm)],[1997,30,31,28,27]),
[iquote('0:MRR:1997.1,1997.2,1997.3,1997.4,30.0,31.0,28.0,27.0')] ).
cnf(2000,plain,
( r1_tarski(skc16,u)
| equal(skf17(u,skc16),k1_rlvect_1(skc15)) ),
inference(res,[status(thm),theory(equality)],[75,1998]),
[iquote('0:Res:75.1,1998.0')] ).
cnf(2001,plain,
( ~ equal(k1_tarski(u),skc16)
| equal(u,k1_rlvect_1(skc15)) ),
inference(res,[status(thm),theory(equality)],[1022,1998]),
[iquote('0:Res:1022.1,1998.0')] ).
cnf(2004,plain,
~ equal(k1_tarski(u),skc16),
inference(mrr,[status(thm)],[2001,1310]),
[iquote('0:MRR:2001.1,1310.0')] ).
cnf(2037,plain,
( r1_tarski(skc16,u)
| r1_tarski(skc16,u)
| r2_hidden(k1_rlvect_1(skc15),skc16) ),
inference(spr,[status(thm),theory(equality)],[2000,75]),
[iquote('0:SpR:2000.1,75.1')] ).
cnf(2040,plain,
( ~ r2_hidden(k1_rlvect_1(skc15),u)
| r1_tarski(skc16,u) ),
inference(spl,[status(thm),theory(equality)],[2000,56]),
[iquote('0:SpL:2000.1,56.0')] ).
cnf(2053,plain,
( r1_tarski(skc16,u)
| r2_hidden(k1_rlvect_1(skc15),skc16) ),
inference(obv,[status(thm),theory(equality)],[2037]),
[iquote('0:Obv:2037.0')] ).
cnf(2056,plain,
r1_tarski(skc16,u),
inference(spt,[spt(split,[position(s2s2s1)])],[2053]),
[iquote('3:Spt:2053.0')] ).
cnf(2060,plain,
equal(skc16,k1_xboole_0),
inference(res,[status(thm),theory(equality)],[2056,447]),
[iquote('3:Res:2056.0,447.0')] ).
cnf(2062,plain,
$false,
inference(mrr,[status(thm)],[2060,37]),
[iquote('3:MRR:2060.0,37.0')] ).
cnf(2086,plain,
r2_hidden(k1_rlvect_1(skc15),skc16),
inference(spt,[spt(split,[position(s2s2s2)])],[2053]),
[iquote('3:Spt:2062.0,2053.1')] ).
cnf(2128,plain,
r1_tarski(skc16,k1_tarski(k1_rlvect_1(skc15))),
inference(res,[status(thm),theory(equality)],[935,2040]),
[iquote('0:Res:935.0,2040.0')] ).
cnf(2138,plain,
( ~ r1_tarski(k1_tarski(k1_rlvect_1(skc15)),skc16)
| equal(k1_tarski(k1_rlvect_1(skc15)),skc16) ),
inference(res,[status(thm),theory(equality)],[2128,91]),
[iquote('0:Res:2128.0,91.0')] ).
cnf(2139,plain,
~ r1_tarski(k1_tarski(k1_rlvect_1(skc15)),skc16),
inference(mrr,[status(thm)],[2138,2004]),
[iquote('0:MRR:2138.1,2004.0')] ).
cnf(2147,plain,
~ r2_hidden(k1_rlvect_1(skc15),skc16),
inference(res,[status(thm),theory(equality)],[831,2139]),
[iquote('0:Res:831.1,2139.0')] ).
cnf(2148,plain,
$false,
inference(mrr,[status(thm)],[2147,2086]),
[iquote('3:MRR:2147.0,2086.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG218+1 : TPTP v8.1.0. Released v3.4.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Wed Jun 8 16:57:06 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.71/0.88
% 0.71/0.88 SPASS V 3.9
% 0.71/0.88 SPASS beiseite: Proof found.
% 0.71/0.88 % SZS status Theorem
% 0.71/0.88 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.71/0.88 SPASS derived 1711 clauses, backtracked 74 clauses, performed 3 splits and kept 999 clauses.
% 0.71/0.88 SPASS allocated 99815 KBytes.
% 0.71/0.88 SPASS spent 0:00:00.52 on the problem.
% 0.71/0.88 0:00:00.04 for the input.
% 0.71/0.88 0:00:00.12 for the FLOTTER CNF translation.
% 0.71/0.88 0:00:00.03 for inferences.
% 0.71/0.88 0:00:00.00 for the backtracking.
% 0.71/0.88 0:00:00.24 for the reduction.
% 0.71/0.88
% 0.71/0.88
% 0.71/0.88 Here is a proof with depth 8, length 149 :
% 0.71/0.88 % SZS output start Refutation
% See solution above
% 0.71/0.89 Formulae used in the proof : t12_rmod_5 fc1_xboole_0 rc2_subset_1 existence_m1_subset_1 fc1_subset_1 dt_l1_rlvect_1 dt_l2_struct_0 dt_l2_vectsp_1 dt_l3_vectsp_1 rc1_subset_1 d3_tarski antisymmetry_r2_hidden t6_boole d10_xboole_0 t1_subset t7_boole t3_subset cc1_relset_1 dt_l1_vectsp_2 t2_subset d1_tarski t4_subset t5_subset cc3_vectsp_2 redefinition_k7_rlvect_2 t46_rmod_2 t10_rmod_5
% 0.71/0.89
%------------------------------------------------------------------------------