%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP620+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 : Sat Jul 16 11:48:20 EDT 2022
% Result : Theorem 0.68s 0.91s
% Output : Refutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 35
% Syntax : Number of clauses : 109 ( 38 unt; 51 nHn; 109 RR)
% Number of literals : 415 ( 0 equ; 257 neg)
% Maximal clause size : 18 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 24 ( 23 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
v1_group_1(skc15),
file('GRP620+1.p',unknown),
[] ).
cnf(2,axiom,
v3_group_1(skc15),
file('GRP620+1.p',unknown),
[] ).
cnf(3,axiom,
v4_group_1(skc15),
file('GRP620+1.p',unknown),
[] ).
cnf(4,axiom,
l1_group_1(skc15),
file('GRP620+1.p',unknown),
[] ).
cnf(32,axiom,
~ v3_struct_0(skc15),
file('GRP620+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ l1_group_1(u)
| l1_struct_0(u) ),
file('GRP620+1.p',unknown),
[] ).
cnf(56,axiom,
( ~ m1_fraenkel(u,v,w)
| v1_fraenkel(u) ),
file('GRP620+1.p',unknown),
[] ).
cnf(57,axiom,
( ~ r2_hidden(u,v)
| m1_subset_1(u,v) ),
file('GRP620+1.p',unknown),
[] ).
cnf(59,axiom,
m2_fraenkel(skc16,u1_struct_0(skc15),u1_struct_0(skc15),k1_autgroup(skc15)),
file('GRP620+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ v1_xboole_0(u)
| ~ m1_fraenkel(u,v,w) ),
file('GRP620+1.p',unknown),
[] ).
cnf(65,axiom,
( ~ v1_fraenkel(u)
| ~ m1_subset_1(v,u)
| v1_relat_1(v) ),
file('GRP620+1.p',unknown),
[] ).
cnf(68,axiom,
( ~ v1_funct_1(u)
| ~ v1_relat_1(u)
| v1_relat_1(k2_funct_1(u)) ),
file('GRP620+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ v1_funct_1(u)
| ~ v1_relat_1(u)
| v1_funct_1(k2_funct_1(u)) ),
file('GRP620+1.p',unknown),
[] ).
cnf(70,axiom,
( ~ l1_struct_0(u)
| ~ v1_xboole_0(u1_struct_0(u))
| v3_struct_0(u) ),
file('GRP620+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ m1_subset_1(u,v)
| v1_xboole_0(v)
| r2_hidden(u,v) ),
file('GRP620+1.p',unknown),
[] ).
cnf(76,axiom,
~ m2_fraenkel(k2_funct_1(skc16),u1_struct_0(skc15),u1_struct_0(skc15),k1_autgroup(skc15)),
file('GRP620+1.p',unknown),
[] ).
cnf(77,axiom,
( ~ v3_group_1(u)
| ~ l1_group_1(u)
| v3_struct_0(u)
| v2_group_1(u) ),
file('GRP620+1.p',unknown),
[] ).
cnf(80,axiom,
( skP0(u,v)
| m2_fraenkel(skf12(v,u),u1_struct_0(v),u1_struct_0(v),u) ),
file('GRP620+1.p',unknown),
[] ).
cnf(87,axiom,
( ~ m1_fraenkel(u,v,w)
| ~ m2_fraenkel(x,v,w,u)
| v1_xboole_0(w)
| v1_funct_1(x) ),
file('GRP620+1.p',unknown),
[] ).
cnf(89,axiom,
( ~ skP0(u,v)
| ~ m2_fraenkel(w,u1_struct_0(v),u1_struct_0(v),u)
| v1_group_6(w,v,v) ),
file('GRP620+1.p',unknown),
[] ).
cnf(90,axiom,
( ~ m1_fraenkel(u,v,w)
| ~ m2_fraenkel(x,v,w,u)
| v1_xboole_0(w)
| m1_subset_1(x,u) ),
file('GRP620+1.p',unknown),
[] ).
cnf(91,axiom,
( ~ m1_subset_1(u,v)
| ~ m1_fraenkel(v,w,x)
| v1_xboole_0(x)
| m2_fraenkel(u,w,x,v) ),
file('GRP620+1.p',unknown),
[] ).
cnf(93,axiom,
( ~ m1_fraenkel(u,v,w)
| ~ m2_fraenkel(x,v,w,u)
| v1_xboole_0(w)
| v1_funct_2(x,v,w) ),
file('GRP620+1.p',unknown),
[] ).
cnf(94,axiom,
( ~ m1_fraenkel(u,v,w)
| ~ m2_fraenkel(x,v,w,u)
| v1_xboole_0(w)
| m2_relset_1(x,v,w) ),
file('GRP620+1.p',unknown),
[] ).
cnf(99,axiom,
( ~ l1_group_1(u)
| ~ v4_group_1(u)
| ~ v3_group_1(u)
| ~ v1_group_1(u)
| v3_struct_0(u)
| m1_fraenkel(k1_autgroup(u),u1_struct_0(u),u1_struct_0(u)) ),
file('GRP620+1.p',unknown),
[] ).
cnf(105,axiom,
( ~ l1_group_1(u)
| ~ v4_group_1(u)
| ~ v3_group_1(u)
| ~ v1_group_1(u)
| ~ m2_fraenkel(v,u1_struct_0(u),u1_struct_0(u),k1_autgroup(u))
| v3_struct_0(u)
| v1_funct_1(k2_funct_1(v)) ),
file('GRP620+1.p',unknown),
[] ).
cnf(109,axiom,
( ~ l1_group_1(u)
| ~ v4_group_1(u)
| ~ v3_group_1(u)
| ~ v1_group_1(u)
| ~ m2_fraenkel(v,u1_struct_0(u),u1_struct_0(u),k1_autgroup(u))
| v3_struct_0(u)
| v1_group_6(k2_funct_1(v),u,u) ),
file('GRP620+1.p',unknown),
[] ).
cnf(113,axiom,
( ~ l1_group_1(u)
| ~ v4_group_1(u)
| ~ v3_group_1(u)
| ~ v1_group_1(u)
| ~ equal(v,k1_autgroup(u))
| ~ m1_fraenkel(v,u1_struct_0(u),u1_struct_0(u))
| v3_struct_0(u)
| skP0(v,u) ),
file('GRP620+1.p',unknown),
[] ).
cnf(114,axiom,
( ~ l1_group_1(u)
| ~ v4_group_1(u)
| ~ v3_group_1(u)
| ~ v1_group_1(u)
| ~ m2_fraenkel(v,u1_struct_0(u),u1_struct_0(u),k1_autgroup(u))
| v3_struct_0(u)
| m2_relset_1(k2_funct_1(v),u1_struct_0(u),u1_struct_0(u)) ),
file('GRP620+1.p',unknown),
[] ).
cnf(115,axiom,
( ~ l1_group_1(u)
| ~ v4_group_1(u)
| ~ v3_group_1(u)
| ~ v1_group_1(u)
| ~ m2_fraenkel(v,u1_struct_0(u),u1_struct_0(u),k1_autgroup(u))
| v3_struct_0(u)
| v1_funct_2(k2_funct_1(v),u1_struct_0(u),u1_struct_0(u)) ),
file('GRP620+1.p',unknown),
[] ).
cnf(124,axiom,
( ~ v1_funct_1(u)
| ~ l1_group_1(v)
| ~ v4_group_1(v)
| ~ v3_group_1(v)
| ~ v1_group_1(v)
| ~ v1_group_6(u,v,v)
| ~ v4_group_6(u,v,v)
| ~ m2_relset_1(u,u1_struct_0(v),u1_struct_0(v))
| ~ v1_funct_2(u,u1_struct_0(v),u1_struct_0(v))
| v3_struct_0(v)
| r2_hidden(u,k1_autgroup(v)) ),
file('GRP620+1.p',unknown),
[] ).
cnf(125,axiom,
( ~ v1_funct_1(u)
| ~ l1_group_1(v)
| ~ v4_group_1(v)
| ~ v3_group_1(v)
| ~ v1_group_1(v)
| ~ r2_hidden(u,k1_autgroup(v))
| ~ v1_group_6(u,v,v)
| ~ m2_relset_1(u,u1_struct_0(v),u1_struct_0(v))
| ~ v1_funct_2(u,u1_struct_0(v),u1_struct_0(v))
| v3_struct_0(v)
| v4_group_6(u,v,v) ),
file('GRP620+1.p',unknown),
[] ).
cnf(128,axiom,
( ~ v1_funct_1(u)
| ~ l1_group_1(v)
| ~ v4_group_1(v)
| ~ v3_group_1(v)
| ~ l1_group_1(w)
| ~ v4_group_1(w)
| ~ v3_group_1(w)
| ~ v1_group_6(u,w,v)
| ~ v2_group_6(u,w,v)
| ~ m2_relset_1(u,u1_struct_0(w),u1_struct_0(v))
| ~ v1_funct_2(u,u1_struct_0(w),u1_struct_0(v))
| v3_struct_0(v)
| v3_struct_0(w)
| v2_funct_1(u) ),
file('GRP620+1.p',unknown),
[] ).
cnf(129,axiom,
( ~ v1_funct_1(u)
| ~ l1_group_1(v)
| ~ v4_group_1(v)
| ~ v3_group_1(v)
| ~ l1_group_1(w)
| ~ v4_group_1(w)
| ~ v3_group_1(w)
| ~ v1_group_6(u,w,v)
| ~ v4_group_6(u,w,v)
| ~ m2_relset_1(u,u1_struct_0(w),u1_struct_0(v))
| ~ v1_funct_2(u,u1_struct_0(w),u1_struct_0(v))
| v3_struct_0(v)
| v3_struct_0(w)
| v2_group_6(u,w,v) ),
file('GRP620+1.p',unknown),
[] ).
cnf(135,axiom,
( ~ v1_funct_1(u)
| ~ l1_group_1(v)
| ~ v4_group_1(v)
| ~ v3_group_1(v)
| ~ l1_group_1(w)
| ~ v4_group_1(w)
| ~ v3_group_1(w)
| ~ v1_funct_1(k2_funct_1(u))
| ~ v4_group_6(u,v,w)
| ~ v1_group_6(u,v,w)
| ~ m2_relset_1(u,u1_struct_0(v),u1_struct_0(w))
| ~ v1_funct_2(u,u1_struct_0(v),u1_struct_0(w))
| ~ v1_group_6(k2_funct_1(u),w,v)
| ~ m2_relset_1(k2_funct_1(u),u1_struct_0(w),u1_struct_0(v))
| ~ v1_funct_2(k2_funct_1(u),u1_struct_0(w),u1_struct_0(v))
| v3_struct_0(v)
| v3_struct_0(w)
| v4_group_6(k2_funct_1(u),w,v) ),
file('GRP620+1.p',unknown),
[] ).
cnf(162,plain,
( ~ v1_group_1(skc15)
| ~ v3_group_1(skc15)
| ~ v4_group_1(skc15)
| v3_struct_0(skc15)
| m1_fraenkel(k1_autgroup(skc15),u1_struct_0(skc15),u1_struct_0(skc15)) ),
inference(res,[status(thm),theory(equality)],[4,99]),
[iquote('0:Res:4.0,99.3')] ).
cnf(166,plain,
( ~ v3_group_1(skc15)
| v2_group_1(skc15)
| v3_struct_0(skc15) ),
inference(res,[status(thm),theory(equality)],[4,77]),
[iquote('0:Res:4.0,77.0')] ).
cnf(168,plain,
l1_struct_0(skc15),
inference(res,[status(thm),theory(equality)],[4,46]),
[iquote('0:Res:4.0,46.0')] ).
cnf(278,plain,
( ~ v3_group_1(skc15)
| ~ v4_group_1(skc15)
| ~ l1_group_1(skc15)
| ~ equal(u,k1_autgroup(skc15))
| ~ m1_fraenkel(u,u1_struct_0(skc15),u1_struct_0(skc15))
| skP0(u,skc15)
| v3_struct_0(skc15) ),
inference(res,[status(thm),theory(equality)],[1,113]),
[iquote('0:Res:1.0,113.0')] ).
cnf(279,plain,
( ~ v3_group_1(skc15)
| ~ v4_group_1(skc15)
| ~ l1_group_1(skc15)
| ~ m2_fraenkel(u,u1_struct_0(skc15),u1_struct_0(skc15),k1_autgroup(skc15))
| v1_group_6(k2_funct_1(u),skc15,skc15)
| v3_struct_0(skc15) ),
inference(res,[status(thm),theory(equality)],[1,109]),
[iquote('0:Res:1.0,109.0')] ).
cnf(280,plain,
( ~ v3_group_1(skc15)
| ~ v4_group_1(skc15)
| ~ l1_group_1(skc15)
| ~ m2_fraenkel(u,u1_struct_0(skc15),u1_struct_0(skc15),k1_autgroup(skc15))
| v1_funct_1(k2_funct_1(u))
| v3_struct_0(skc15) ),
inference(res,[status(thm),theory(equality)],[1,105]),
[iquote('0:Res:1.0,105.0')] ).
cnf(286,plain,
v2_group_1(skc15),
inference(mrr,[status(thm)],[166,2,32]),
[iquote('0:MRR:166.0,166.2,2.0,32.0')] ).
cnf(288,plain,
m1_fraenkel(k1_autgroup(skc15),u1_struct_0(skc15),u1_struct_0(skc15)),
inference(mrr,[status(thm)],[162,1,2,3,32]),
[iquote('0:MRR:162.0,162.1,162.2,162.3,1.0,2.0,3.0,32.0')] ).
cnf(289,plain,
( ~ m2_fraenkel(u,u1_struct_0(skc15),u1_struct_0(skc15),k1_autgroup(skc15))
| v1_funct_1(k2_funct_1(u)) ),
inference(mrr,[status(thm)],[280,2,3,4,32]),
[iquote('0:MRR:280.0,280.1,280.2,280.5,2.0,3.0,4.0,32.0')] ).
cnf(296,plain,
( ~ m2_fraenkel(u,u1_struct_0(skc15),u1_struct_0(skc15),k1_autgroup(skc15))
| v1_group_6(k2_funct_1(u),skc15,skc15) ),
inference(mrr,[status(thm)],[279,2,3,4,32]),
[iquote('0:MRR:279.0,279.1,279.2,279.5,2.0,3.0,4.0,32.0')] ).
cnf(299,plain,
( ~ equal(u,k1_autgroup(skc15))
| ~ m1_fraenkel(u,u1_struct_0(skc15),u1_struct_0(skc15))
| skP0(u,skc15) ),
inference(mrr,[status(thm)],[278,2,3,4,32]),
[iquote('0:MRR:278.0,278.1,278.2,278.6,2.0,3.0,4.0,32.0')] ).
cnf(346,plain,
v1_fraenkel(k1_autgroup(skc15)),
inference(res,[status(thm),theory(equality)],[288,56]),
[iquote('0:Res:288.0,56.0')] ).
cnf(352,plain,
~ v1_xboole_0(k1_autgroup(skc15)),
inference(res,[status(thm),theory(equality)],[288,61]),
[iquote('0:Res:288.0,61.1')] ).
cnf(477,plain,
( ~ m1_fraenkel(k1_autgroup(skc15),u1_struct_0(skc15),u1_struct_0(skc15))
| v1_xboole_0(u1_struct_0(skc15))
| v1_funct_1(skc16) ),
inference(res,[status(thm),theory(equality)],[59,87]),
[iquote('0:Res:59.0,87.1')] ).
cnf(479,plain,
( v1_xboole_0(u1_struct_0(skc15))
| v1_funct_1(skc16) ),
inference(mrr,[status(thm)],[477,288]),
[iquote('0:MRR:477.0,288.0')] ).
cnf(485,plain,
( ~ l1_struct_0(skc15)
| v1_funct_1(skc16)
| v3_struct_0(skc15) ),
inference(res,[status(thm),theory(equality)],[479,70]),
[iquote('0:Res:479.0,70.1')] ).
cnf(487,plain,
( v1_funct_1(skc16)
| v3_struct_0(skc15) ),
inference(ssi,[status(thm)],[485,1,3,2,4,286,168]),
[iquote('0:SSi:485.0,1.0,3.0,2.0,4.0,286.0,168.0')] ).
cnf(488,plain,
v1_funct_1(skc16),
inference(mrr,[status(thm)],[487,32]),
[iquote('0:MRR:487.1,32.0')] ).
cnf(504,plain,
v1_funct_1(k2_funct_1(skc16)),
inference(res,[status(thm),theory(equality)],[59,289]),
[iquote('0:Res:59.0,289.0')] ).
cnf(508,plain,
( ~ skP0(k1_autgroup(skc15),skc15)
| v1_group_6(skc16,skc15,skc15) ),
inference(res,[status(thm),theory(equality)],[59,89]),
[iquote('0:Res:59.0,89.1')] ).
cnf(520,plain,
( ~ m1_subset_1(k2_funct_1(skc16),k1_autgroup(skc15))
| ~ m1_fraenkel(k1_autgroup(skc15),u1_struct_0(skc15),u1_struct_0(skc15))
| v1_xboole_0(u1_struct_0(skc15)) ),
inference(res,[status(thm),theory(equality)],[91,76]),
[iquote('0:Res:91.3,76.0')] ).
cnf(525,plain,
( ~ m1_subset_1(k2_funct_1(skc16),k1_autgroup(skc15))
| v1_xboole_0(u1_struct_0(skc15)) ),
inference(mrr,[status(thm)],[520,288]),
[iquote('0:MRR:520.1,288.0')] ).
cnf(528,plain,
( ~ r2_hidden(k2_funct_1(skc16),k1_autgroup(skc15))
| v1_xboole_0(u1_struct_0(skc15)) ),
inference(res,[status(thm),theory(equality)],[57,525]),
[iquote('0:Res:57.1,525.0')] ).
cnf(533,plain,
( ~ m1_fraenkel(k1_autgroup(skc15),u1_struct_0(skc15),u1_struct_0(skc15))
| v1_xboole_0(u1_struct_0(skc15))
| m1_subset_1(skc16,k1_autgroup(skc15)) ),
inference(res,[status(thm),theory(equality)],[59,90]),
[iquote('0:Res:59.0,90.1')] ).
cnf(537,plain,
( v1_xboole_0(u1_struct_0(skc15))
| m1_subset_1(skc16,k1_autgroup(skc15)) ),
inference(mrr,[status(thm)],[533,288]),
[iquote('0:MRR:533.0,288.0')] ).
cnf(539,plain,
v1_xboole_0(u1_struct_0(skc15)),
inference(spt,[spt(split,[position(s1)])],[537]),
[iquote('1:Spt:537.0')] ).
cnf(545,plain,
( ~ l1_struct_0(skc15)
| v3_struct_0(skc15) ),
inference(res,[status(thm),theory(equality)],[539,70]),
[iquote('1:Res:539.0,70.1')] ).
cnf(586,plain,
v3_struct_0(skc15),
inference(ssi,[status(thm)],[545,1,3,2,4,286,168]),
[iquote('1:SSi:545.0,1.0,3.0,2.0,4.0,286.0,168.0')] ).
cnf(587,plain,
$false,
inference(mrr,[status(thm)],[586,32]),
[iquote('1:MRR:586.0,32.0')] ).
cnf(611,plain,
~ v1_xboole_0(u1_struct_0(skc15)),
inference(spt,[spt(split,[position(sa)])],[587,539]),
[iquote('1:Spt:587.0,537.0,539.0')] ).
cnf(612,plain,
m1_subset_1(skc16,k1_autgroup(skc15)),
inference(spt,[spt(split,[position(s2)])],[537]),
[iquote('1:Spt:587.0,537.1')] ).
cnf(614,plain,
~ r2_hidden(k2_funct_1(skc16),k1_autgroup(skc15)),
inference(mrr,[status(thm)],[528,611]),
[iquote('1:MRR:528.1,611.0')] ).
cnf(617,plain,
( ~ v1_fraenkel(k1_autgroup(skc15))
| v1_relat_1(skc16) ),
inference(res,[status(thm),theory(equality)],[612,65]),
[iquote('1:Res:612.0,65.1')] ).
cnf(618,plain,
( v1_xboole_0(k1_autgroup(skc15))
| r2_hidden(skc16,k1_autgroup(skc15)) ),
inference(res,[status(thm),theory(equality)],[612,74]),
[iquote('1:Res:612.0,74.0')] ).
cnf(620,plain,
v1_relat_1(skc16),
inference(ssi,[status(thm)],[617,346]),
[iquote('1:SSi:617.0,346.0')] ).
cnf(621,plain,
r2_hidden(skc16,k1_autgroup(skc15)),
inference(mrr,[status(thm)],[618,352]),
[iquote('1:MRR:618.0,352.0')] ).
cnf(674,plain,
( ~ m1_fraenkel(k1_autgroup(skc15),u1_struct_0(skc15),u1_struct_0(skc15))
| v1_xboole_0(u1_struct_0(skc15))
| m2_relset_1(skc16,u1_struct_0(skc15),u1_struct_0(skc15)) ),
inference(res,[status(thm),theory(equality)],[59,94]),
[iquote('0:Res:59.0,94.1')] ).
cnf(677,plain,
m2_relset_1(skc16,u1_struct_0(skc15),u1_struct_0(skc15)),
inference(mrr,[status(thm)],[674,288,611]),
[iquote('1:MRR:674.0,674.1,288.0,611.0')] ).
cnf(690,plain,
( ~ m1_fraenkel(k1_autgroup(skc15),u1_struct_0(skc15),u1_struct_0(skc15))
| v1_xboole_0(u1_struct_0(skc15))
| v1_funct_2(skc16,u1_struct_0(skc15),u1_struct_0(skc15)) ),
inference(res,[status(thm),theory(equality)],[59,93]),
[iquote('0:Res:59.0,93.1')] ).
cnf(693,plain,
v1_funct_2(skc16,u1_struct_0(skc15),u1_struct_0(skc15)),
inference(mrr,[status(thm)],[690,288,611]),
[iquote('1:MRR:690.0,690.1,288.0,611.0')] ).
cnf(780,plain,
( skP0(k1_autgroup(skc15),skc15)
| v1_group_6(k2_funct_1(skf12(skc15,k1_autgroup(skc15))),skc15,skc15) ),
inference(res,[status(thm),theory(equality)],[80,296]),
[iquote('0:Res:80.1,296.0')] ).
cnf(781,plain,
v1_group_6(k2_funct_1(skc16),skc15,skc15),
inference(res,[status(thm),theory(equality)],[59,296]),
[iquote('0:Res:59.0,296.0')] ).
cnf(808,plain,
skP0(k1_autgroup(skc15),skc15),
inference(spt,[spt(split,[position(s2s1)])],[780]),
[iquote('2:Spt:780.0')] ).
cnf(809,plain,
v1_group_6(skc16,skc15,skc15),
inference(mrr,[status(thm)],[508,808]),
[iquote('2:MRR:508.0,808.0')] ).
cnf(1021,plain,
( ~ equal(k1_autgroup(skc15),k1_autgroup(skc15))
| skP0(k1_autgroup(skc15),skc15) ),
inference(res,[status(thm),theory(equality)],[288,299]),
[iquote('0:Res:288.0,299.1')] ).
cnf(1023,plain,
skP0(k1_autgroup(skc15),skc15),
inference(obv,[status(thm),theory(equality)],[1021]),
[iquote('0:Obv:1021.0')] ).
cnf(1285,plain,
( ~ l1_group_1(skc15)
| ~ v4_group_1(skc15)
| ~ v3_group_1(skc15)
| ~ v1_group_1(skc15)
| v3_struct_0(skc15)
| m2_relset_1(k2_funct_1(skc16),u1_struct_0(skc15),u1_struct_0(skc15)) ),
inference(res,[status(thm),theory(equality)],[59,114]),
[iquote('0:Res:59.0,114.4')] ).
cnf(1288,plain,
( v3_struct_0(skc15)
| m2_relset_1(k2_funct_1(skc16),u1_struct_0(skc15),u1_struct_0(skc15)) ),
inference(ssi,[status(thm)],[1285,1,3,2,4,286,168]),
[iquote('0:SSi:1285.3,1285.2,1285.1,1285.0,1.0,3.0,2.0,4.0,286.0,168.0,1.0,3.0,2.0,4.0,286.0,168.0,1.0,3.0,2.0,4.0,286.0,168.0,1.0,3.0,2.0,4.0,286.0,168.0')] ).
cnf(1289,plain,
m2_relset_1(k2_funct_1(skc16),u1_struct_0(skc15),u1_struct_0(skc15)),
inference(mrr,[status(thm)],[1288,32]),
[iquote('0:MRR:1288.0,32.0')] ).
cnf(1336,plain,
( ~ l1_group_1(skc15)
| ~ v4_group_1(skc15)
| ~ v3_group_1(skc15)
| ~ v1_group_1(skc15)
| v3_struct_0(skc15)
| v1_funct_2(k2_funct_1(skc16),u1_struct_0(skc15),u1_struct_0(skc15)) ),
inference(res,[status(thm),theory(equality)],[59,115]),
[iquote('0:Res:59.0,115.4')] ).
cnf(1339,plain,
( v3_struct_0(skc15)
| v1_funct_2(k2_funct_1(skc16),u1_struct_0(skc15),u1_struct_0(skc15)) ),
inference(ssi,[status(thm)],[1336,1,3,2,4,286,168]),
[iquote('0:SSi:1336.3,1336.2,1336.1,1336.0,1.0,3.0,2.0,4.0,286.0,168.0,1.0,3.0,2.0,4.0,286.0,168.0,1.0,3.0,2.0,4.0,286.0,168.0,1.0,3.0,2.0,4.0,286.0,168.0')] ).
cnf(1340,plain,
v1_funct_2(k2_funct_1(skc16),u1_struct_0(skc15),u1_struct_0(skc15)),
inference(mrr,[status(thm)],[1339,32]),
[iquote('0:MRR:1339.0,32.0')] ).
cnf(1561,plain,
( ~ v1_funct_1(skc16)
| ~ l1_group_1(skc15)
| ~ v4_group_1(skc15)
| ~ v3_group_1(skc15)
| ~ v1_group_1(skc15)
| ~ r2_hidden(skc16,k1_autgroup(skc15))
| ~ v1_group_6(skc16,skc15,skc15)
| ~ v1_funct_2(skc16,u1_struct_0(skc15),u1_struct_0(skc15))
| v3_struct_0(skc15)
| v4_group_6(skc16,skc15,skc15) ),
inference(res,[status(thm),theory(equality)],[677,125]),
[iquote('1:Res:677.0,125.7')] ).
cnf(1565,plain,
( ~ r2_hidden(skc16,k1_autgroup(skc15))
| ~ v1_group_6(skc16,skc15,skc15)
| ~ v1_funct_2(skc16,u1_struct_0(skc15),u1_struct_0(skc15))
| v3_struct_0(skc15)
| v4_group_6(skc16,skc15,skc15) ),
inference(ssi,[status(thm)],[1561,1,3,2,4,286,168,488,620]),
[iquote('1:SSi:1561.4,1561.3,1561.2,1561.1,1561.0,1.0,3.0,2.0,4.0,286.0,168.0,1.0,3.0,2.0,4.0,286.0,168.0,1.0,3.0,2.0,4.0,286.0,168.0,1.0,3.0,2.0,4.0,286.0,168.0,488.0,620.0')] ).
cnf(1566,plain,
v4_group_6(skc16,skc15,skc15),
inference(mrr,[status(thm)],[1565,621,809,693,32]),
[iquote('2:MRR:1565.0,1565.1,1565.2,1565.3,621.0,809.0,693.0,32.0')] ).
cnf(1610,plain,
( ~ v1_funct_1(k2_funct_1(skc16))
| ~ l1_group_1(skc15)
| ~ v4_group_1(skc15)
| ~ v3_group_1(skc15)
| ~ v1_group_1(skc15)
| ~ v1_group_6(k2_funct_1(skc16),skc15,skc15)
| ~ v4_group_6(k2_funct_1(skc16),skc15,skc15)
| ~ v1_funct_2(k2_funct_1(skc16),u1_struct_0(skc15),u1_struct_0(skc15))
| v3_struct_0(skc15)
| r2_hidden(k2_funct_1(skc16),k1_autgroup(skc15)) ),
inference(res,[status(thm),theory(equality)],[1289,124]),
[iquote('0:Res:1289.0,124.7')] ).
cnf(1612,plain,
( ~ v1_group_6(k2_funct_1(skc16),skc15,skc15)
| ~ v4_group_6(k2_funct_1(skc16),skc15,skc15)
| ~ v1_funct_2(k2_funct_1(skc16),u1_struct_0(skc15),u1_struct_0(skc15))
| v3_struct_0(skc15)
| r2_hidden(k2_funct_1(skc16),k1_autgroup(skc15)) ),
inference(ssi,[status(thm)],[1610,1,3,2,4,286,168,68,488,620,69]),
[iquote('1:SSi:1610.4,1610.3,1610.2,1610.1,1610.0,1.0,3.0,2.2,4.0,286.0,168.2,1.0,3.0,2.0,4.0,286.0,168.0,1.0,3.0,2.0,4.0,286.0,168.0,1.0,3.0,2.0,4.0,286.0,168.0,68.0,488.0,620.0,69.0,488.0,620.0')] ).
cnf(1613,plain,
~ v4_group_6(k2_funct_1(skc16),skc15,skc15),
inference(mrr,[status(thm)],[1612,781,1340,32,614]),
[iquote('1:MRR:1612.0,1612.2,1612.3,1612.4,781.0,1340.0,32.0,614.0')] ).
cnf(1732,plain,
( ~ v1_funct_1(skc16)
| ~ l1_group_1(skc15)
| ~ v4_group_1(skc15)
| ~ v3_group_1(skc15)
| ~ l1_group_1(skc15)
| ~ v4_group_1(skc15)
| ~ v3_group_1(skc15)
| ~ v1_group_6(skc16,skc15,skc15)
| ~ v2_group_6(skc16,skc15,skc15)
| ~ v1_funct_2(skc16,u1_struct_0(skc15),u1_struct_0(skc15))
| v3_struct_0(skc15)
| v3_struct_0(skc15)
| v2_funct_1(skc16) ),
inference(res,[status(thm),theory(equality)],[677,128]),
[iquote('1:Res:677.0,128.9')] ).
cnf(1736,plain,
( ~ v1_funct_1(skc16)
| ~ l1_group_1(skc15)
| ~ v4_group_1(skc15)
| ~ v3_group_1(skc15)
| ~ v1_group_6(skc16,skc15,skc15)
| ~ v2_group_6(skc16,skc15,skc15)
| ~ v1_funct_2(skc16,u1_struct_0(skc15),u1_struct_0(skc15))
| v3_struct_0(skc15)
| v2_funct_1(skc16) ),
inference(obv,[status(thm),theory(equality)],[1732]),
[iquote('1:Obv:1732.10')] ).
cnf(1737,plain,
( ~ v1_group_6(skc16,skc15,skc15)
| ~ v2_group_6(skc16,skc15,skc15)
| ~ v1_funct_2(skc16,u1_struct_0(skc15),u1_struct_0(skc15))
| v3_struct_0(skc15)
| v2_funct_1(skc16) ),
inference(ssi,[status(thm)],[1736,1,3,2,4,286,168,488,620]),
[iquote('1:SSi:1736.3,1736.2,1736.1,1736.0,1.0,3.0,2.0,4.0,286.0,168.0,1.0,3.0,2.0,4.0,286.0,168.0,1.0,3.0,2.0,4.0,286.0,168.0,488.0,620.0')] ).
cnf(1738,plain,
( ~ v2_group_6(skc16,skc15,skc15)
| v2_funct_1(skc16) ),
inference(mrr,[status(thm)],[1737,809,693,32]),
[iquote('2:MRR:1737.0,1737.2,1737.3,809.0,693.0,32.0')] ).
cnf(1773,plain,
( ~ v1_funct_1(skc16)
| ~ l1_group_1(skc15)
| ~ v4_group_1(skc15)
| ~ v3_group_1(skc15)
| ~ l1_group_1(skc15)
| ~ v4_group_1(skc15)
| ~ v3_group_1(skc15)
| ~ v1_group_6(skc16,skc15,skc15)
| ~ v4_group_6(skc16,skc15,skc15)
| ~ v1_funct_2(skc16,u1_struct_0(skc15),u1_struct_0(skc15))
| v3_struct_0(skc15)
| v3_struct_0(skc15)
| v2_group_6(skc16,skc15,skc15) ),
inference(res,[status(thm),theory(equality)],[677,129]),
[iquote('1:Res:677.0,129.9')] ).
cnf(1777,plain,
( ~ v1_funct_1(skc16)
| ~ l1_group_1(skc15)
| ~ v4_group_1(skc15)
| ~ v3_group_1(skc15)
| ~ v1_group_6(skc16,skc15,skc15)
| ~ v4_group_6(skc16,skc15,skc15)
| ~ v1_funct_2(skc16,u1_struct_0(skc15),u1_struct_0(skc15))
| v3_struct_0(skc15)
| v2_group_6(skc16,skc15,skc15) ),
inference(obv,[status(thm),theory(equality)],[1773]),
[iquote('1:Obv:1773.10')] ).
cnf(1778,plain,
( ~ v1_group_6(skc16,skc15,skc15)
| ~ v4_group_6(skc16,skc15,skc15)
| ~ v1_funct_2(skc16,u1_struct_0(skc15),u1_struct_0(skc15))
| v3_struct_0(skc15)
| v2_group_6(skc16,skc15,skc15) ),
inference(ssi,[status(thm)],[1777,1,3,2,4,286,168,488,620]),
[iquote('1:SSi:1777.3,1777.2,1777.1,1777.0,1.0,3.0,2.0,4.0,286.0,168.0,1.0,3.0,2.0,4.0,286.0,168.0,1.0,3.0,2.0,4.0,286.0,168.0,488.0,620.0')] ).
cnf(1779,plain,
v2_group_6(skc16,skc15,skc15),
inference(mrr,[status(thm)],[1778,809,1566,693,32]),
[iquote('2:MRR:1778.0,1778.1,1778.2,1778.3,809.0,1566.0,693.0,32.0')] ).
cnf(1780,plain,
v2_funct_1(skc16),
inference(mrr,[status(thm)],[1738,1779]),
[iquote('2:MRR:1738.0,1779.0')] ).
cnf(2087,plain,
( ~ v1_funct_1(skc16)
| ~ l1_group_1(skc15)
| ~ v4_group_1(skc15)
| ~ v3_group_1(skc15)
| ~ l1_group_1(skc15)
| ~ v4_group_1(skc15)
| ~ v3_group_1(skc15)
| ~ v1_funct_1(k2_funct_1(skc16))
| ~ v4_group_6(skc16,skc15,skc15)
| ~ v1_group_6(skc16,skc15,skc15)
| ~ m2_relset_1(skc16,u1_struct_0(skc15),u1_struct_0(skc15))
| ~ v1_funct_2(skc16,u1_struct_0(skc15),u1_struct_0(skc15))
| ~ v1_group_6(k2_funct_1(skc16),skc15,skc15)
| ~ v1_funct_2(k2_funct_1(skc16),u1_struct_0(skc15),u1_struct_0(skc15))
| v3_struct_0(skc15)
| v3_struct_0(skc15)
| v4_group_6(k2_funct_1(skc16),skc15,skc15) ),
inference(res,[status(thm),theory(equality)],[1289,135]),
[iquote('0:Res:1289.0,135.13')] ).
cnf(2089,plain,
( ~ v1_funct_1(skc16)
| ~ l1_group_1(skc15)
| ~ v4_group_1(skc15)
| ~ v3_group_1(skc15)
| ~ v1_funct_1(k2_funct_1(skc16))
| ~ v4_group_6(skc16,skc15,skc15)
| ~ v1_group_6(skc16,skc15,skc15)
| ~ m2_relset_1(skc16,u1_struct_0(skc15),u1_struct_0(skc15))
| ~ v1_funct_2(skc16,u1_struct_0(skc15),u1_struct_0(skc15))
| ~ v1_group_6(k2_funct_1(skc16),skc15,skc15)
| ~ v1_funct_2(k2_funct_1(skc16),u1_struct_0(skc15),u1_struct_0(skc15))
| v3_struct_0(skc15)
| v4_group_6(k2_funct_1(skc16),skc15,skc15) ),
inference(obv,[status(thm),theory(equality)],[2087]),
[iquote('0:Obv:2087.14')] ).
cnf(2090,plain,
( ~ v1_funct_1(k2_funct_1(skc16))
| ~ v4_group_6(skc16,skc15,skc15)
| ~ v1_group_6(skc16,skc15,skc15)
| ~ m2_relset_1(skc16,u1_struct_0(skc15),u1_struct_0(skc15))
| ~ v1_funct_2(skc16,u1_struct_0(skc15),u1_struct_0(skc15))
| ~ v1_group_6(k2_funct_1(skc16),skc15,skc15)
| ~ v1_funct_2(k2_funct_1(skc16),u1_struct_0(skc15),u1_struct_0(skc15))
| v3_struct_0(skc15)
| v4_group_6(k2_funct_1(skc16),skc15,skc15) ),
inference(ssi,[status(thm)],[2089,1,3,2,4,286,168,488,620,1780]),
[iquote('2:SSi:2089.3,2089.2,2089.1,2089.0,1.0,3.0,2.0,4.0,286.0,168.0,1.0,3.0,2.0,4.0,286.0,168.0,1.0,3.0,2.0,4.0,286.0,168.0,488.0,620.0,1780.0')] ).
cnf(2091,plain,
$false,
inference(mrr,[status(thm)],[2090,504,1566,809,677,693,781,1340,32,1613]),
[iquote('2:MRR:2090.0,2090.1,2090.2,2090.3,2090.4,2090.5,2090.6,2090.7,2090.8,504.0,1566.0,809.0,677.0,693.0,781.0,1340.0,32.0,1613.0')] ).
cnf(2106,plain,
~ skP0(k1_autgroup(skc15),skc15),
inference(spt,[spt(split,[position(s2sa)])],[2091,808]),
[iquote('2:Spt:2091.0,780.0,808.0')] ).
cnf(2107,plain,
v1_group_6(k2_funct_1(skf12(skc15,k1_autgroup(skc15))),skc15,skc15),
inference(spt,[spt(split,[position(s2s2)])],[780]),
[iquote('2:Spt:2091.0,780.1')] ).
cnf(2108,plain,
$false,
inference(mrr,[status(thm)],[2106,1023]),
[iquote('2:MRR:2106.0,1023.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP620+1 : TPTP v8.1.0. Released v3.4.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n020.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 : Mon Jun 13 15:48:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.68/0.91
% 0.68/0.91 SPASS V 3.9
% 0.68/0.91 SPASS beiseite: Proof found.
% 0.68/0.91 % SZS status Theorem
% 0.68/0.91 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.68/0.91 SPASS derived 1347 clauses, backtracked 78 clauses, performed 4 splits and kept 848 clauses.
% 0.68/0.91 SPASS allocated 100379 KBytes.
% 0.68/0.91 SPASS spent 0:00:00.55 on the problem.
% 0.68/0.91 0:00:00.04 for the input.
% 0.68/0.91 0:00:00.06 for the FLOTTER CNF translation.
% 0.68/0.91 0:00:00.03 for inferences.
% 0.68/0.91 0:00:00.01 for the backtracking.
% 0.68/0.91 0:00:00.35 for the reduction.
% 0.68/0.91
% 0.68/0.91
% 0.68/0.91 Here is a proof with depth 3, length 109 :
% 0.68/0.91 % SZS output start Refutation
% See solution above
% 0.68/0.91 Formulae used in the proof : t7_autgroup dt_l1_group_1 dt_m1_fraenkel t1_subset cc1_fraenkel dt_k2_funct_1 fc1_struct_0 t2_subset cc1_group_1 d1_autgroup rc3_funct_1 dt_m2_fraenkel redefinition_m2_fraenkel dt_k1_autgroup t6_autgroup t5_autgroup d12_group_6 d14_group_6 t73_group_6
% 0.76/0.93
%------------------------------------------------------------------------------