TSTP Solution File: GRP631+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP631+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 11:48:26 EDT 2022
% Result : Theorem 0.37s 0.55s
% Output : Refutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 38
% Syntax : Number of clauses : 94 ( 40 unt; 25 nHn; 94 RR)
% Number of literals : 245 ( 0 equ; 134 neg)
% Maximal clause size : 9 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 26 ( 25 usr; 1 prp; 0-4 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-6 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
v1_group_1(skc15),
file('GRP631+1.p',unknown),
[] ).
cnf(2,axiom,
v3_group_1(skc15),
file('GRP631+1.p',unknown),
[] ).
cnf(3,axiom,
v4_group_1(skc15),
file('GRP631+1.p',unknown),
[] ).
cnf(4,axiom,
l1_group_1(skc15),
file('GRP631+1.p',unknown),
[] ).
cnf(32,axiom,
~ v3_struct_0(skc15),
file('GRP631+1.p',unknown),
[] ).
cnf(36,axiom,
v1_relat_1(k6_relat_1(u)),
file('GRP631+1.p',unknown),
[] ).
cnf(37,axiom,
v1_funct_1(k6_relat_1(u)),
file('GRP631+1.p',unknown),
[] ).
cnf(38,axiom,
v1_relat_2(k6_relat_1(u)),
file('GRP631+1.p',unknown),
[] ).
cnf(39,axiom,
v3_relat_2(k6_relat_1(u)),
file('GRP631+1.p',unknown),
[] ).
cnf(40,axiom,
v4_relat_2(k6_relat_1(u)),
file('GRP631+1.p',unknown),
[] ).
cnf(41,axiom,
v8_relat_2(k6_relat_1(u)),
file('GRP631+1.p',unknown),
[] ).
cnf(56,axiom,
m1_subset_1(skc16,u1_struct_0(skc15)),
file('GRP631+1.p',unknown),
[] ).
cnf(63,axiom,
v1_partfun1(k6_partfun1(u),u,u),
file('GRP631+1.p',unknown),
[] ).
cnf(64,axiom,
m2_relset_1(k6_partfun1(u),u,u),
file('GRP631+1.p',unknown),
[] ).
cnf(65,axiom,
( ~ l1_group_1(u)
| l1_struct_0(u) ),
file('GRP631+1.p',unknown),
[] ).
cnf(72,axiom,
equal(k6_partfun1(u),k6_relat_1(u)),
file('GRP631+1.p',unknown),
[] ).
cnf(82,axiom,
( ~ m1_fraenkel(u,v,w)
| v1_fraenkel(u) ),
file('GRP631+1.p',unknown),
[] ).
cnf(84,axiom,
( ~ v1_xboole_0(u)
| ~ r2_hidden(v,u) ),
file('GRP631+1.p',unknown),
[] ).
cnf(89,axiom,
( ~ v1_fraenkel(u)
| ~ m1_subset_1(v,u)
| v1_relat_1(v) ),
file('GRP631+1.p',unknown),
[] ).
cnf(92,axiom,
( ~ l1_struct_0(u)
| ~ v1_xboole_0(u1_struct_0(u))
| v3_struct_0(u) ),
file('GRP631+1.p',unknown),
[] ).
cnf(94,axiom,
( ~ m2_relset_1(u,v,w)
| m1_relset_1(u,v,w) ),
file('GRP631+1.p',unknown),
[] ).
cnf(96,axiom,
( ~ m1_subset_1(u,v)
| v1_xboole_0(v)
| r2_hidden(u,v) ),
file('GRP631+1.p',unknown),
[] ).
cnf(98,axiom,
( ~ v3_group_1(u)
| ~ l1_group_1(u)
| v3_struct_0(u)
| v2_group_1(u) ),
file('GRP631+1.p',unknown),
[] ).
cnf(99,axiom,
( ~ l1_group_1(u)
| v3_struct_0(u)
| m1_subset_1(k2_group_1(u),u1_struct_0(u)) ),
file('GRP631+1.p',unknown),
[] ).
cnf(109,axiom,
( ~ m1_fraenkel(u,v,w)
| ~ m2_fraenkel(x,v,w,u)
| v1_xboole_0(w)
| v1_funct_1(x) ),
file('GRP631+1.p',unknown),
[] ).
cnf(111,axiom,
( ~ m2_relset_1(u,v,w)
| equal(k7_relset_1(v,v,v,w,k6_partfun1(v),u),u) ),
file('GRP631+1.p',unknown),
[] ).
cnf(112,axiom,
( ~ m2_relset_1(u,v,w)
| equal(k7_relset_1(v,w,w,w,u,k6_partfun1(w)),u) ),
file('GRP631+1.p',unknown),
[] ).
cnf(115,axiom,
( ~ m1_fraenkel(u,v,w)
| ~ m2_fraenkel(x,v,w,u)
| v1_xboole_0(w)
| m1_subset_1(x,u) ),
file('GRP631+1.p',unknown),
[] ).
cnf(117,axiom,
( ~ v1_funct_1(u)
| ~ m1_relset_1(u,v,w)
| ~ v1_partfun1(u,v,w)
| v1_funct_2(u,v,w) ),
file('GRP631+1.p',unknown),
[] ).
cnf(118,axiom,
( ~ m1_fraenkel(u,v,w)
| ~ m2_fraenkel(x,v,w,u)
| v1_xboole_0(w)
| v1_funct_2(x,v,w) ),
file('GRP631+1.p',unknown),
[] ).
cnf(119,axiom,
( ~ m1_fraenkel(u,v,w)
| ~ m2_fraenkel(x,v,w,u)
| v1_xboole_0(w)
| m2_relset_1(x,v,w) ),
file('GRP631+1.p',unknown),
[] ).
cnf(124,axiom,
( ~ m1_relset_1(u,v,w)
| ~ m1_relset_1(x,y,z)
| equal(k7_relset_1(y,z,v,w,x,u),k5_relat_1(x,u)) ),
file('GRP631+1.p',unknown),
[] ).
cnf(125,axiom,
( ~ l1_group_1(u)
| ~ v4_group_1(u)
| ~ v3_group_1(u)
| ~ v1_group_1(u)
| v3_struct_0(u)
| m1_fraenkel(k4_autgroup(u),u1_struct_0(u),u1_struct_0(u)) ),
file('GRP631+1.p',unknown),
[] ).
cnf(129,axiom,
( ~ v1_group_1(u)
| ~ v3_group_1(u)
| ~ v4_group_1(u)
| ~ l1_group_1(u)
| v3_struct_0(u)
| equal(k6_autgroup(u,k2_group_1(u)),k6_partfun1(u1_struct_0(u))) ),
file('GRP631+1.p',unknown),
[] ).
cnf(132,axiom,
( ~ v1_relat_2(u)
| ~ v1_funct_1(u)
| ~ v1_funct_2(u,v,v)
| ~ m1_relset_1(u,v,v)
| ~ v1_partfun1(u,v,v)
| v2_funct_1(u) ),
file('GRP631+1.p',unknown),
[] ).
cnf(139,axiom,
( ~ v1_group_1(u)
| ~ v3_group_1(u)
| ~ v4_group_1(u)
| ~ l1_group_1(u)
| ~ m1_subset_1(v,u1_struct_0(u))
| v3_struct_0(u)
| m2_fraenkel(k6_autgroup(u,v),u1_struct_0(u),u1_struct_0(u),k4_autgroup(u)) ),
file('GRP631+1.p',unknown),
[] ).
cnf(143,axiom,
( ~ v1_funct_1(u)
| ~ v1_funct_1(v)
| ~ m1_relset_1(v,w,x)
| ~ v1_funct_2(v,w,x)
| ~ v1_funct_2(u,x,y)
| ~ m1_relset_1(u,x,y)
| v1_xboole_0(x)
| equal(k7_funct_2(w,x,y,v,u),k5_relat_1(v,u)) ),
file('GRP631+1.p',unknown),
[] ).
cnf(144,axiom,
( ~ equal(k7_funct_2(u1_struct_0(skc15),u1_struct_0(skc15),u1_struct_0(skc15),k6_autgroup(skc15,k2_group_1(skc15)),k6_autgroup(skc15,skc16)),k6_autgroup(skc15,skc16))
| ~ equal(k7_funct_2(u1_struct_0(skc15),u1_struct_0(skc15),u1_struct_0(skc15),k6_autgroup(skc15,skc16),k6_autgroup(skc15,k2_group_1(skc15))),k6_autgroup(skc15,skc16)) ),
file('GRP631+1.p',unknown),
[] ).
cnf(145,plain,
m2_relset_1(k6_relat_1(u),u,u),
inference(rew,[status(thm),theory(equality)],[72,64]),
[iquote('0:Rew:72.0,64.0')] ).
cnf(146,plain,
v1_partfun1(k6_relat_1(u),u,u),
inference(rew,[status(thm),theory(equality)],[72,63]),
[iquote('0:Rew:72.0,63.0')] ).
cnf(148,plain,
( ~ m2_relset_1(u,v,w)
| equal(k7_relset_1(v,w,w,w,u,k6_relat_1(w)),u) ),
inference(rew,[status(thm),theory(equality)],[72,112]),
[iquote('0:Rew:72.0,112.1')] ).
cnf(149,plain,
( ~ m2_relset_1(u,v,w)
| equal(k7_relset_1(v,v,v,w,k6_relat_1(v),u),u) ),
inference(rew,[status(thm),theory(equality)],[72,111]),
[iquote('0:Rew:72.0,111.1')] ).
cnf(152,plain,
( ~ l1_group_1(u)
| ~ v4_group_1(u)
| ~ v3_group_1(u)
| ~ v1_group_1(u)
| v3_struct_0(u)
| equal(k6_autgroup(u,k2_group_1(u)),k6_relat_1(u1_struct_0(u))) ),
inference(rew,[status(thm),theory(equality)],[72,129]),
[iquote('0:Rew:72.0,129.5')] ).
cnf(153,plain,
( ~ v1_funct_1(u)
| ~ v1_relat_2(u)
| ~ v1_partfun1(u,v,v)
| ~ m1_relset_1(u,v,v)
| v2_funct_1(u) ),
inference(mrr,[status(thm)],[132,117]),
[iquote('0:MRR:132.2,117.3')] ).
cnf(160,plain,
( ~ v1_group_1(skc15)
| ~ v3_group_1(skc15)
| ~ v4_group_1(skc15)
| v3_struct_0(skc15)
| equal(k6_autgroup(skc15,k2_group_1(skc15)),k6_relat_1(u1_struct_0(skc15))) ),
inference(res,[status(thm),theory(equality)],[4,152]),
[iquote('0:Res:4.0,152.3')] ).
cnf(161,plain,
( ~ v1_group_1(skc15)
| ~ v3_group_1(skc15)
| ~ v4_group_1(skc15)
| v3_struct_0(skc15)
| m1_fraenkel(k4_autgroup(skc15),u1_struct_0(skc15),u1_struct_0(skc15)) ),
inference(res,[status(thm),theory(equality)],[4,125]),
[iquote('0:Res:4.0,125.3')] ).
cnf(165,plain,
( ~ v3_group_1(skc15)
| v2_group_1(skc15)
| v3_struct_0(skc15) ),
inference(res,[status(thm),theory(equality)],[4,98]),
[iquote('0:Res:4.0,98.0')] ).
cnf(166,plain,
( v3_struct_0(skc15)
| m1_subset_1(k2_group_1(skc15),u1_struct_0(skc15)) ),
inference(res,[status(thm),theory(equality)],[4,99]),
[iquote('0:Res:4.0,99.0')] ).
cnf(168,plain,
l1_struct_0(skc15),
inference(res,[status(thm),theory(equality)],[4,65]),
[iquote('0:Res:4.0,65.0')] ).
cnf(185,plain,
( ~ l1_struct_0(skc15)
| ~ v1_xboole_0(u1_struct_0(skc15)) ),
inference(res,[status(thm),theory(equality)],[92,32]),
[iquote('0:Res:92.2,32.0')] ).
cnf(189,plain,
( ~ l1_group_1(skc15)
| ~ v4_group_1(skc15)
| ~ v3_group_1(skc15)
| ~ v1_group_1(skc15)
| m2_fraenkel(k6_autgroup(skc15,skc16),u1_struct_0(skc15),u1_struct_0(skc15),k4_autgroup(skc15))
| v3_struct_0(skc15) ),
inference(res,[status(thm),theory(equality)],[56,139]),
[iquote('0:Res:56.0,139.4')] ).
cnf(191,plain,
( r2_hidden(skc16,u1_struct_0(skc15))
| v1_xboole_0(u1_struct_0(skc15)) ),
inference(res,[status(thm),theory(equality)],[56,96]),
[iquote('0:Res:56.0,96.0')] ).
cnf(192,plain,
v2_group_1(skc15),
inference(mrr,[status(thm)],[165,2,32]),
[iquote('0:MRR:165.0,165.2,2.0,32.0')] ).
cnf(193,plain,
m1_subset_1(k2_group_1(skc15),u1_struct_0(skc15)),
inference(mrr,[status(thm)],[166,32]),
[iquote('0:MRR:166.0,32.0')] ).
cnf(194,plain,
~ v1_xboole_0(u1_struct_0(skc15)),
inference(mrr,[status(thm)],[185,168]),
[iquote('0:MRR:185.0,168.0')] ).
cnf(196,plain,
r2_hidden(skc16,u1_struct_0(skc15)),
inference(mrr,[status(thm)],[191,194]),
[iquote('0:MRR:191.1,194.0')] ).
cnf(198,plain,
m1_fraenkel(k4_autgroup(skc15),u1_struct_0(skc15),u1_struct_0(skc15)),
inference(mrr,[status(thm)],[161,1,2,3,32]),
[iquote('0:MRR:161.0,161.1,161.2,161.3,1.0,2.0,3.0,32.0')] ).
cnf(199,plain,
equal(k6_autgroup(skc15,k2_group_1(skc15)),k6_relat_1(u1_struct_0(skc15))),
inference(mrr,[status(thm)],[160,1,2,3,32]),
[iquote('0:MRR:160.0,160.1,160.2,160.3,1.0,2.0,3.0,32.0')] ).
cnf(200,plain,
( ~ equal(k7_funct_2(u1_struct_0(skc15),u1_struct_0(skc15),u1_struct_0(skc15),k6_relat_1(u1_struct_0(skc15)),k6_autgroup(skc15,skc16)),k6_autgroup(skc15,skc16))
| ~ equal(k7_funct_2(u1_struct_0(skc15),u1_struct_0(skc15),u1_struct_0(skc15),k6_autgroup(skc15,skc16),k6_autgroup(skc15,k2_group_1(skc15))),k6_autgroup(skc15,skc16)) ),
inference(rew,[status(thm),theory(equality)],[199,144]),
[iquote('0:Rew:199.0,144.0')] ).
cnf(201,plain,
m2_fraenkel(k6_autgroup(skc15,skc16),u1_struct_0(skc15),u1_struct_0(skc15),k4_autgroup(skc15)),
inference(mrr,[status(thm)],[189,4,3,2,1,32]),
[iquote('0:MRR:189.0,189.1,189.2,189.3,189.5,4.0,3.0,2.0,1.0,32.0')] ).
cnf(203,plain,
( ~ equal(k7_funct_2(u1_struct_0(skc15),u1_struct_0(skc15),u1_struct_0(skc15),k6_relat_1(u1_struct_0(skc15)),k6_autgroup(skc15,skc16)),k6_autgroup(skc15,skc16))
| ~ equal(k7_funct_2(u1_struct_0(skc15),u1_struct_0(skc15),u1_struct_0(skc15),k6_autgroup(skc15,skc16),k6_relat_1(u1_struct_0(skc15))),k6_autgroup(skc15,skc16)) ),
inference(rew,[status(thm),theory(equality)],[199,200]),
[iquote('0:Rew:199.0,200.1')] ).
cnf(221,plain,
~ v1_xboole_0(u1_struct_0(skc15)),
inference(res,[status(thm),theory(equality)],[196,84]),
[iquote('0:Res:196.0,84.1')] ).
cnf(225,plain,
v1_fraenkel(k4_autgroup(skc15)),
inference(res,[status(thm),theory(equality)],[198,82]),
[iquote('0:Res:198.0,82.0')] ).
cnf(252,plain,
m1_relset_1(k6_relat_1(u),u,u),
inference(res,[status(thm),theory(equality)],[145,94]),
[iquote('0:Res:145.0,94.0')] ).
cnf(322,plain,
( ~ m1_fraenkel(k4_autgroup(skc15),u1_struct_0(skc15),u1_struct_0(skc15))
| v1_xboole_0(u1_struct_0(skc15))
| v1_funct_1(k6_autgroup(skc15,skc16)) ),
inference(res,[status(thm),theory(equality)],[201,109]),
[iquote('0:Res:201.0,109.1')] ).
cnf(323,plain,
v1_funct_1(k6_autgroup(skc15,skc16)),
inference(mrr,[status(thm)],[322,198,221]),
[iquote('0:MRR:322.0,322.1,198.0,221.0')] ).
cnf(393,plain,
( ~ m1_fraenkel(k4_autgroup(skc15),u1_struct_0(skc15),u1_struct_0(skc15))
| v1_xboole_0(u1_struct_0(skc15))
| m1_subset_1(k6_autgroup(skc15,skc16),k4_autgroup(skc15)) ),
inference(res,[status(thm),theory(equality)],[201,115]),
[iquote('0:Res:201.0,115.1')] ).
cnf(396,plain,
m1_subset_1(k6_autgroup(skc15,skc16),k4_autgroup(skc15)),
inference(mrr,[status(thm)],[393,198,221]),
[iquote('0:MRR:393.0,393.1,198.0,221.0')] ).
cnf(399,plain,
( ~ v1_fraenkel(k4_autgroup(skc15))
| v1_relat_1(k6_autgroup(skc15,skc16)) ),
inference(res,[status(thm),theory(equality)],[396,89]),
[iquote('0:Res:396.0,89.1')] ).
cnf(401,plain,
v1_relat_1(k6_autgroup(skc15,skc16)),
inference(ssi,[status(thm)],[399,225]),
[iquote('0:SSi:399.0,225.0')] ).
cnf(448,plain,
( ~ m1_fraenkel(k4_autgroup(skc15),u1_struct_0(skc15),u1_struct_0(skc15))
| v1_xboole_0(u1_struct_0(skc15))
| m2_relset_1(k6_autgroup(skc15,skc16),u1_struct_0(skc15),u1_struct_0(skc15)) ),
inference(res,[status(thm),theory(equality)],[201,119]),
[iquote('0:Res:201.0,119.1')] ).
cnf(451,plain,
m2_relset_1(k6_autgroup(skc15,skc16),u1_struct_0(skc15),u1_struct_0(skc15)),
inference(mrr,[status(thm)],[448,198,221]),
[iquote('0:MRR:448.0,448.1,198.0,221.0')] ).
cnf(456,plain,
m1_relset_1(k6_autgroup(skc15,skc16),u1_struct_0(skc15),u1_struct_0(skc15)),
inference(res,[status(thm),theory(equality)],[451,94]),
[iquote('0:Res:451.0,94.0')] ).
cnf(463,plain,
( ~ m1_fraenkel(k4_autgroup(skc15),u1_struct_0(skc15),u1_struct_0(skc15))
| v1_xboole_0(u1_struct_0(skc15))
| v1_funct_2(k6_autgroup(skc15,skc16),u1_struct_0(skc15),u1_struct_0(skc15)) ),
inference(res,[status(thm),theory(equality)],[201,118]),
[iquote('0:Res:201.0,118.1')] ).
cnf(466,plain,
v1_funct_2(k6_autgroup(skc15,skc16),u1_struct_0(skc15),u1_struct_0(skc15)),
inference(mrr,[status(thm)],[463,198,221]),
[iquote('0:MRR:463.0,463.1,198.0,221.0')] ).
cnf(474,plain,
( ~ v1_funct_1(k6_relat_1(u))
| ~ v1_relat_2(k6_relat_1(u))
| ~ m1_relset_1(k6_relat_1(u),u,u)
| v2_funct_1(k6_relat_1(u)) ),
inference(res,[status(thm),theory(equality)],[146,153]),
[iquote('0:Res:146.0,153.2')] ).
cnf(477,plain,
( ~ m1_relset_1(k6_relat_1(u),u,u)
| v2_funct_1(k6_relat_1(u)) ),
inference(ssi,[status(thm)],[474,40,41,39,38,36,37]),
[iquote('0:SSi:474.1,474.0,40.0,41.0,39.0,38.0,36.0,37.0,40.0,41.0,39.0,38.0,36.0,37.0')] ).
cnf(478,plain,
v2_funct_1(k6_relat_1(u)),
inference(mrr,[status(thm)],[477,252]),
[iquote('0:MRR:477.0,252.0')] ).
cnf(577,plain,
( ~ m1_relset_1(u,v,w)
| ~ m1_relset_1(k6_relat_1(v),v,v)
| ~ m2_relset_1(u,v,w)
| equal(k5_relat_1(k6_relat_1(v),u),u) ),
inference(spr,[status(thm),theory(equality)],[124,149]),
[iquote('0:SpR:124.2,149.1')] ).
cnf(578,plain,
( ~ m1_relset_1(k6_relat_1(u),u,u)
| ~ m1_relset_1(v,w,u)
| ~ m2_relset_1(v,w,u)
| equal(k5_relat_1(v,k6_relat_1(u)),v) ),
inference(spr,[status(thm),theory(equality)],[124,148]),
[iquote('0:SpR:124.2,148.1')] ).
cnf(580,plain,
( ~ m2_relset_1(u,v,w)
| equal(k5_relat_1(u,k6_relat_1(w)),u) ),
inference(mrr,[status(thm)],[578,252,94]),
[iquote('0:MRR:578.0,578.1,252.0,94.1')] ).
cnf(581,plain,
( ~ m2_relset_1(u,v,w)
| equal(k5_relat_1(k6_relat_1(v),u),u) ),
inference(mrr,[status(thm)],[577,94,252]),
[iquote('0:MRR:577.0,577.1,94.1,252.0')] ).
cnf(606,plain,
equal(k5_relat_1(k6_autgroup(skc15,skc16),k6_relat_1(u1_struct_0(skc15))),k6_autgroup(skc15,skc16)),
inference(res,[status(thm),theory(equality)],[451,580]),
[iquote('0:Res:451.0,580.0')] ).
cnf(645,plain,
equal(k5_relat_1(k6_relat_1(u1_struct_0(skc15)),k6_autgroup(skc15,skc16)),k6_autgroup(skc15,skc16)),
inference(res,[status(thm),theory(equality)],[451,581]),
[iquote('0:Res:451.0,581.0')] ).
cnf(760,plain,
( ~ v1_group_1(skc15)
| ~ v3_group_1(skc15)
| ~ v4_group_1(skc15)
| ~ l1_group_1(skc15)
| ~ m1_subset_1(k2_group_1(skc15),u1_struct_0(skc15))
| v3_struct_0(skc15)
| m2_fraenkel(k6_relat_1(u1_struct_0(skc15)),u1_struct_0(skc15),u1_struct_0(skc15),k4_autgroup(skc15)) ),
inference(spr,[status(thm),theory(equality)],[199,139]),
[iquote('0:SpR:199.0,139.6')] ).
cnf(766,plain,
( ~ m1_subset_1(k2_group_1(skc15),u1_struct_0(skc15))
| v3_struct_0(skc15)
| m2_fraenkel(k6_relat_1(u1_struct_0(skc15)),u1_struct_0(skc15),u1_struct_0(skc15),k4_autgroup(skc15)) ),
inference(ssi,[status(thm)],[760,3,2,1,4,192,168]),
[iquote('0:SSi:760.3,760.2,760.1,760.0,3.0,2.0,1.0,4.0,192.0,168.0,3.0,2.0,1.0,4.0,192.0,168.0,3.0,2.0,1.0,4.0,192.0,168.0,3.0,2.0,1.0,4.0,192.0,168.0')] ).
cnf(767,plain,
m2_fraenkel(k6_relat_1(u1_struct_0(skc15)),u1_struct_0(skc15),u1_struct_0(skc15),k4_autgroup(skc15)),
inference(mrr,[status(thm)],[766,193,32]),
[iquote('0:MRR:766.0,766.1,193.0,32.0')] ).
cnf(777,plain,
( ~ m1_fraenkel(k4_autgroup(skc15),u1_struct_0(skc15),u1_struct_0(skc15))
| v1_xboole_0(u1_struct_0(skc15))
| v1_funct_2(k6_relat_1(u1_struct_0(skc15)),u1_struct_0(skc15),u1_struct_0(skc15)) ),
inference(res,[status(thm),theory(equality)],[767,118]),
[iquote('0:Res:767.0,118.1')] ).
cnf(782,plain,
v1_funct_2(k6_relat_1(u1_struct_0(skc15)),u1_struct_0(skc15),u1_struct_0(skc15)),
inference(mrr,[status(thm)],[777,198,221]),
[iquote('0:MRR:777.0,777.1,198.0,221.0')] ).
cnf(892,plain,
( ~ v1_funct_1(k6_relat_1(u1_struct_0(skc15)))
| ~ v1_funct_1(k6_autgroup(skc15,skc16))
| ~ m1_relset_1(k6_autgroup(skc15,skc16),u1_struct_0(skc15),u1_struct_0(skc15))
| ~ v1_funct_2(k6_autgroup(skc15,skc16),u1_struct_0(skc15),u1_struct_0(skc15))
| ~ v1_funct_2(k6_relat_1(u1_struct_0(skc15)),u1_struct_0(skc15),u1_struct_0(skc15))
| ~ m1_relset_1(k6_relat_1(u1_struct_0(skc15)),u1_struct_0(skc15),u1_struct_0(skc15))
| ~ equal(k7_funct_2(u1_struct_0(skc15),u1_struct_0(skc15),u1_struct_0(skc15),k6_relat_1(u1_struct_0(skc15)),k6_autgroup(skc15,skc16)),k6_autgroup(skc15,skc16))
| ~ equal(k5_relat_1(k6_autgroup(skc15,skc16),k6_relat_1(u1_struct_0(skc15))),k6_autgroup(skc15,skc16))
| v1_xboole_0(u1_struct_0(skc15)) ),
inference(spl,[status(thm),theory(equality)],[143,203]),
[iquote('0:SpL:143.7,203.1')] ).
cnf(893,plain,
( ~ v1_funct_1(k6_relat_1(u1_struct_0(skc15)))
| ~ v1_funct_1(k6_autgroup(skc15,skc16))
| ~ m1_relset_1(k6_autgroup(skc15,skc16),u1_struct_0(skc15),u1_struct_0(skc15))
| ~ v1_funct_2(k6_autgroup(skc15,skc16),u1_struct_0(skc15),u1_struct_0(skc15))
| ~ v1_funct_2(k6_relat_1(u1_struct_0(skc15)),u1_struct_0(skc15),u1_struct_0(skc15))
| ~ m1_relset_1(k6_relat_1(u1_struct_0(skc15)),u1_struct_0(skc15),u1_struct_0(skc15))
| ~ equal(k6_autgroup(skc15,skc16),k6_autgroup(skc15,skc16))
| ~ equal(k6_autgroup(skc15,skc16),k6_autgroup(skc15,skc16))
| v1_xboole_0(u1_struct_0(skc15)) ),
inference(rew,[status(thm),theory(equality)],[606,892,645,143]),
[iquote('0:Rew:606.0,892.7,645.0,892.6,143.7,892.6')] ).
cnf(894,plain,
( ~ v1_funct_1(k6_relat_1(u1_struct_0(skc15)))
| ~ v1_funct_1(k6_autgroup(skc15,skc16))
| ~ m1_relset_1(k6_autgroup(skc15,skc16),u1_struct_0(skc15),u1_struct_0(skc15))
| ~ v1_funct_2(k6_autgroup(skc15,skc16),u1_struct_0(skc15),u1_struct_0(skc15))
| ~ v1_funct_2(k6_relat_1(u1_struct_0(skc15)),u1_struct_0(skc15),u1_struct_0(skc15))
| ~ m1_relset_1(k6_relat_1(u1_struct_0(skc15)),u1_struct_0(skc15),u1_struct_0(skc15))
| v1_xboole_0(u1_struct_0(skc15)) ),
inference(obv,[status(thm),theory(equality)],[893]),
[iquote('0:Obv:893.7')] ).
cnf(895,plain,
( ~ m1_relset_1(k6_autgroup(skc15,skc16),u1_struct_0(skc15),u1_struct_0(skc15))
| ~ v1_funct_2(k6_autgroup(skc15,skc16),u1_struct_0(skc15),u1_struct_0(skc15))
| ~ v1_funct_2(k6_relat_1(u1_struct_0(skc15)),u1_struct_0(skc15),u1_struct_0(skc15))
| ~ m1_relset_1(k6_relat_1(u1_struct_0(skc15)),u1_struct_0(skc15),u1_struct_0(skc15))
| v1_xboole_0(u1_struct_0(skc15)) ),
inference(ssi,[status(thm)],[894,323,401,40,41,39,38,36,37,478]),
[iquote('0:SSi:894.1,894.0,323.0,401.0,40.0,41.0,39.0,38.0,36.0,37.0,478.0')] ).
cnf(896,plain,
$false,
inference(mrr,[status(thm)],[895,456,466,782,252,221]),
[iquote('0:MRR:895.0,895.1,895.2,895.3,895.4,456.0,466.0,782.0,252.0,221.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP631+1 : TPTP v8.1.0. Released v3.4.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n006.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 05:13:57 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.37/0.55
% 0.37/0.55 SPASS V 3.9
% 0.37/0.55 SPASS beiseite: Proof found.
% 0.37/0.55 % SZS status Theorem
% 0.37/0.55 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.37/0.55 SPASS derived 603 clauses, backtracked 0 clauses, performed 1 splits and kept 501 clauses.
% 0.37/0.55 SPASS allocated 98634 KBytes.
% 0.37/0.55 SPASS spent 0:00:00.21 on the problem.
% 0.37/0.55 0:00:00.04 for the input.
% 0.37/0.55 0:00:00.04 for the FLOTTER CNF translation.
% 0.37/0.55 0:00:00.01 for inferences.
% 0.37/0.55 0:00:00.00 for the backtracking.
% 0.37/0.55 0:00:00.08 for the reduction.
% 0.37/0.55
% 0.37/0.55
% 0.37/0.55 Here is a proof with depth 3, length 94 :
% 0.37/0.55 % SZS output start Refutation
% See solution above
% 0.37/0.56 Formulae used in the proof : t29_autgroup fc2_partfun1 dt_k6_partfun1 dt_l1_group_1 redefinition_k6_partfun1 dt_m1_fraenkel t7_boole cc1_fraenkel fc1_struct_0 redefinition_m2_relset_1 t2_subset cc1_group_1 dt_k2_group_1 dt_m2_fraenkel t23_funct_2 redefinition_m2_fraenkel cc1_funct_2 redefinition_k7_relset_1 dt_k4_autgroup t24_autgroup cc4_funct_2 dt_k6_autgroup redefinition_k7_funct_2
% 0.37/0.56
%------------------------------------------------------------------------------