TSTP Solution File: GRP624+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP624+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 11:48:22 EDT 2022
% Result : Theorem 2.15s 2.33s
% Output : Refutation 2.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 24
% Syntax : Number of clauses : 60 ( 22 unt; 25 nHn; 60 RR)
% Number of literals : 257 ( 0 equ; 174 neg)
% Maximal clause size : 19 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 17 usr; 1 prp; 0-4 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-6 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
v1_group_1(skc16),
file('GRP624+1.p',unknown),
[] ).
cnf(2,axiom,
v3_group_1(skc16),
file('GRP624+1.p',unknown),
[] ).
cnf(3,axiom,
v4_group_1(skc16),
file('GRP624+1.p',unknown),
[] ).
cnf(4,axiom,
l1_group_1(skc16),
file('GRP624+1.p',unknown),
[] ).
cnf(32,axiom,
~ v3_struct_0(skc16),
file('GRP624+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ l1_group_1(u)
| l1_struct_0(u) ),
file('GRP624+1.p',unknown),
[] ).
cnf(59,axiom,
m2_fraenkel(skc18,u1_struct_0(skc16),u1_struct_0(skc16),k4_autgroup(skc16)),
file('GRP624+1.p',unknown),
[] ).
cnf(60,axiom,
m2_fraenkel(skc17,u1_struct_0(skc16),u1_struct_0(skc16),k4_autgroup(skc16)),
file('GRP624+1.p',unknown),
[] ).
cnf(62,axiom,
( ~ v1_xboole_0(u)
| ~ m1_fraenkel(u,v,w) ),
file('GRP624+1.p',unknown),
[] ).
cnf(67,axiom,
( ~ m1_subset_1(u,k1_zfmisc_1(k2_zfmisc_1(v,w)))
| v1_relat_1(u) ),
file('GRP624+1.p',unknown),
[] ).
cnf(68,axiom,
( ~ l1_struct_0(u)
| ~ v1_xboole_0(u1_struct_0(u))
| v3_struct_0(u) ),
file('GRP624+1.p',unknown),
[] ).
cnf(70,axiom,
( ~ m2_relset_1(u,v,w)
| m1_relset_1(u,v,w) ),
file('GRP624+1.p',unknown),
[] ).
cnf(71,axiom,
( ~ m1_relset_1(u,v,w)
| m2_relset_1(u,v,w) ),
file('GRP624+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ v3_group_1(u)
| ~ l1_group_1(u)
| v3_struct_0(u)
| v2_group_1(u) ),
file('GRP624+1.p',unknown),
[] ).
cnf(78,axiom,
( ~ m2_relset_1(u,v,w)
| m1_subset_1(u,k1_zfmisc_1(k2_zfmisc_1(v,w))) ),
file('GRP624+1.p',unknown),
[] ).
cnf(86,axiom,
~ equal(k7_funct_2(u1_struct_0(skc16),u1_struct_0(skc16),u1_struct_0(skc16),skc18,skc17),k1_binop_1(k2_autgroup(skc16),skc17,skc18)),
file('GRP624+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('GRP624+1.p',unknown),
[] ).
cnf(93,axiom,
( ~ l1_group_1(u)
| ~ v4_group_1(u)
| ~ v3_group_1(u)
| ~ v1_group_1(u)
| v3_struct_0(u)
| v1_funct_1(k2_autgroup(u)) ),
file('GRP624+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('GRP624+1.p',unknown),
[] ).
cnf(105,axiom,
( ~ l1_group_1(u)
| ~ v4_group_1(u)
| ~ v3_group_1(u)
| ~ v1_group_1(u)
| v3_struct_0(u)
| m2_relset_1(k2_autgroup(u),k2_zfmisc_1(k1_autgroup(u),k1_autgroup(u)),k1_autgroup(u)) ),
file('GRP624+1.p',unknown),
[] ).
cnf(106,axiom,
( ~ l1_group_1(u)
| ~ v4_group_1(u)
| ~ v3_group_1(u)
| ~ v1_group_1(u)
| v3_struct_0(u)
| v1_funct_2(k2_autgroup(u),k2_zfmisc_1(k1_autgroup(u),k1_autgroup(u)),k1_autgroup(u)) ),
file('GRP624+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),k4_autgroup(u))
| v3_struct_0(u)
| m2_fraenkel(v,u1_struct_0(u),u1_struct_0(u),k1_autgroup(u)) ),
file('GRP624+1.p',unknown),
[] ).
cnf(115,axiom,
( ~ v1_funct_1(u)
| ~ m1_subset_1(v,w)
| ~ m1_subset_1(x,y)
| ~ v1_funct_2(u,k2_zfmisc_1(w,y),z)
| ~ m1_relset_1(u,k2_zfmisc_1(w,y),z)
| v1_xboole_0(y)
| v1_xboole_0(w)
| equal(k2_binop_1(w,y,z,u,v,x),k1_binop_1(u,v,x)) ),
file('GRP624+1.p',unknown),
[] ).
cnf(119,axiom,
( ~ v1_funct_1(u)
| ~ l1_group_1(v)
| ~ v4_group_1(v)
| ~ v3_group_1(v)
| ~ v1_group_1(v)
| ~ equal(u,k2_autgroup(v))
| ~ m2_relset_1(u,k2_zfmisc_1(k1_autgroup(v),k1_autgroup(v)),k1_autgroup(v))
| ~ v1_funct_2(u,k2_zfmisc_1(k1_autgroup(v),k1_autgroup(v)),k1_autgroup(v))
| ~ m2_fraenkel(w,u1_struct_0(v),u1_struct_0(v),k1_autgroup(v))
| ~ m2_fraenkel(x,u1_struct_0(v),u1_struct_0(v),k1_autgroup(v))
| v3_struct_0(v)
| equal(k2_binop_1(k1_autgroup(v),k1_autgroup(v),k1_autgroup(v),u,w,x),k7_funct_2(u1_struct_0(v),u1_struct_0(v),u1_struct_0(v),x,w)) ),
file('GRP624+1.p',unknown),
[] ).
cnf(134,plain,
( ~ v1_group_1(skc16)
| ~ v3_group_1(skc16)
| ~ v4_group_1(skc16)
| v3_struct_0(skc16)
| m1_fraenkel(k1_autgroup(skc16),u1_struct_0(skc16),u1_struct_0(skc16)) ),
inference(res,[status(thm),theory(equality)],[4,99]),
[iquote('0:Res:4.0,99.3')] ).
cnf(136,plain,
( ~ v1_group_1(skc16)
| ~ v3_group_1(skc16)
| ~ v4_group_1(skc16)
| v1_funct_1(k2_autgroup(skc16))
| v3_struct_0(skc16) ),
inference(res,[status(thm),theory(equality)],[4,93]),
[iquote('0:Res:4.0,93.3')] ).
cnf(140,plain,
( ~ v3_group_1(skc16)
| v2_group_1(skc16)
| v3_struct_0(skc16) ),
inference(res,[status(thm),theory(equality)],[4,74]),
[iquote('0:Res:4.0,74.0')] ).
cnf(142,plain,
l1_struct_0(skc16),
inference(res,[status(thm),theory(equality)],[4,45]),
[iquote('0:Res:4.0,45.0')] ).
cnf(169,plain,
( ~ v3_group_1(skc16)
| ~ v4_group_1(skc16)
| ~ l1_group_1(skc16)
| v1_funct_2(k2_autgroup(skc16),k2_zfmisc_1(k1_autgroup(skc16),k1_autgroup(skc16)),k1_autgroup(skc16))
| v3_struct_0(skc16) ),
inference(res,[status(thm),theory(equality)],[1,106]),
[iquote('0:Res:1.0,106.0')] ).
cnf(170,plain,
( ~ v3_group_1(skc16)
| ~ v4_group_1(skc16)
| ~ l1_group_1(skc16)
| m2_relset_1(k2_autgroup(skc16),k2_zfmisc_1(k1_autgroup(skc16),k1_autgroup(skc16)),k1_autgroup(skc16))
| v3_struct_0(skc16) ),
inference(res,[status(thm),theory(equality)],[1,105]),
[iquote('0:Res:1.0,105.0')] ).
cnf(186,plain,
( ~ l1_struct_0(skc16)
| ~ v1_xboole_0(u1_struct_0(skc16)) ),
inference(res,[status(thm),theory(equality)],[68,32]),
[iquote('0:Res:68.2,32.0')] ).
cnf(188,plain,
( ~ v1_group_1(skc16)
| ~ v3_group_1(skc16)
| ~ v4_group_1(skc16)
| ~ l1_group_1(skc16)
| v3_struct_0(skc16)
| m2_fraenkel(skc17,u1_struct_0(skc16),u1_struct_0(skc16),k1_autgroup(skc16)) ),
inference(res,[status(thm),theory(equality)],[60,109]),
[iquote('0:Res:60.0,109.4')] ).
cnf(193,plain,
( ~ v1_group_1(skc16)
| ~ v3_group_1(skc16)
| ~ v4_group_1(skc16)
| ~ l1_group_1(skc16)
| v3_struct_0(skc16)
| m2_fraenkel(skc18,u1_struct_0(skc16),u1_struct_0(skc16),k1_autgroup(skc16)) ),
inference(res,[status(thm),theory(equality)],[59,109]),
[iquote('0:Res:59.0,109.4')] ).
cnf(204,plain,
v2_group_1(skc16),
inference(mrr,[status(thm)],[140,2,32]),
[iquote('0:MRR:140.0,140.2,2.0,32.0')] ).
cnf(205,plain,
~ v1_xboole_0(u1_struct_0(skc16)),
inference(mrr,[status(thm)],[186,142]),
[iquote('0:MRR:186.0,142.0')] ).
cnf(210,plain,
v1_funct_1(k2_autgroup(skc16)),
inference(mrr,[status(thm)],[136,1,2,3,32]),
[iquote('0:MRR:136.0,136.1,136.2,136.4,1.0,2.0,3.0,32.0')] ).
cnf(217,plain,
m1_fraenkel(k1_autgroup(skc16),u1_struct_0(skc16),u1_struct_0(skc16)),
inference(mrr,[status(thm)],[134,1,2,3,32]),
[iquote('0:MRR:134.0,134.1,134.2,134.3,1.0,2.0,3.0,32.0')] ).
cnf(227,plain,
m2_relset_1(k2_autgroup(skc16),k2_zfmisc_1(k1_autgroup(skc16),k1_autgroup(skc16)),k1_autgroup(skc16)),
inference(mrr,[status(thm)],[170,2,3,4,32]),
[iquote('0:MRR:170.0,170.1,170.2,170.4,2.0,3.0,4.0,32.0')] ).
cnf(228,plain,
v1_funct_2(k2_autgroup(skc16),k2_zfmisc_1(k1_autgroup(skc16),k1_autgroup(skc16)),k1_autgroup(skc16)),
inference(mrr,[status(thm)],[169,2,3,4,32]),
[iquote('0:MRR:169.0,169.1,169.2,169.4,2.0,3.0,4.0,32.0')] ).
cnf(229,plain,
m2_fraenkel(skc18,u1_struct_0(skc16),u1_struct_0(skc16),k1_autgroup(skc16)),
inference(mrr,[status(thm)],[193,1,2,3,4,32]),
[iquote('0:MRR:193.0,193.1,193.2,193.3,193.4,1.0,2.0,3.0,4.0,32.0')] ).
cnf(230,plain,
m2_fraenkel(skc17,u1_struct_0(skc16),u1_struct_0(skc16),k1_autgroup(skc16)),
inference(mrr,[status(thm)],[188,1,2,3,4,32]),
[iquote('0:MRR:188.0,188.1,188.2,188.3,188.4,1.0,2.0,3.0,4.0,32.0')] ).
cnf(318,plain,
m1_relset_1(k2_autgroup(skc16),k2_zfmisc_1(k1_autgroup(skc16),k1_autgroup(skc16)),k1_autgroup(skc16)),
inference(res,[status(thm),theory(equality)],[227,70]),
[iquote('0:Res:227.0,70.0')] ).
cnf(349,plain,
( ~ m2_relset_1(u,v,w)
| v1_relat_1(u) ),
inference(res,[status(thm),theory(equality)],[78,67]),
[iquote('0:Res:78.1,67.0')] ).
cnf(350,plain,
v1_relat_1(k2_autgroup(skc16)),
inference(res,[status(thm),theory(equality)],[227,349]),
[iquote('0:Res:227.0,349.0')] ).
cnf(524,plain,
( ~ m1_fraenkel(k1_autgroup(skc16),u1_struct_0(skc16),u1_struct_0(skc16))
| v1_xboole_0(u1_struct_0(skc16))
| m1_subset_1(skc17,k1_autgroup(skc16)) ),
inference(res,[status(thm),theory(equality)],[230,90]),
[iquote('0:Res:230.0,90.1')] ).
cnf(525,plain,
( ~ m1_fraenkel(k1_autgroup(skc16),u1_struct_0(skc16),u1_struct_0(skc16))
| v1_xboole_0(u1_struct_0(skc16))
| m1_subset_1(skc18,k1_autgroup(skc16)) ),
inference(res,[status(thm),theory(equality)],[229,90]),
[iquote('0:Res:229.0,90.1')] ).
cnf(528,plain,
m1_subset_1(skc17,k1_autgroup(skc16)),
inference(mrr,[status(thm)],[524,217,205]),
[iquote('0:MRR:524.0,524.1,217.0,205.0')] ).
cnf(529,plain,
m1_subset_1(skc18,k1_autgroup(skc16)),
inference(mrr,[status(thm)],[525,217,205]),
[iquote('0:MRR:525.0,525.1,217.0,205.0')] ).
cnf(649,plain,
( ~ l1_group_1(u)
| ~ v4_group_1(u)
| ~ v3_group_1(u)
| ~ v1_group_1(u)
| ~ v1_xboole_0(k1_autgroup(u))
| v3_struct_0(u) ),
inference(res,[status(thm),theory(equality)],[99,62]),
[iquote('0:Res:99.5,62.1')] ).
cnf(1422,plain,
( ~ v1_funct_1(u)
| ~ l1_group_1(v)
| ~ v4_group_1(v)
| ~ v3_group_1(v)
| ~ v1_group_1(v)
| ~ v1_funct_1(u)
| ~ equal(u,k2_autgroup(v))
| ~ m2_relset_1(u,k2_zfmisc_1(k1_autgroup(v),k1_autgroup(v)),k1_autgroup(v))
| ~ v1_funct_2(u,k2_zfmisc_1(k1_autgroup(v),k1_autgroup(v)),k1_autgroup(v))
| ~ m2_fraenkel(w,u1_struct_0(v),u1_struct_0(v),k1_autgroup(v))
| ~ m2_fraenkel(x,u1_struct_0(v),u1_struct_0(v),k1_autgroup(v))
| ~ m1_subset_1(w,k1_autgroup(v))
| ~ m1_subset_1(x,k1_autgroup(v))
| ~ v1_funct_2(u,k2_zfmisc_1(k1_autgroup(v),k1_autgroup(v)),k1_autgroup(v))
| ~ m1_relset_1(u,k2_zfmisc_1(k1_autgroup(v),k1_autgroup(v)),k1_autgroup(v))
| v3_struct_0(v)
| v1_xboole_0(k1_autgroup(v))
| v1_xboole_0(k1_autgroup(v))
| equal(k7_funct_2(u1_struct_0(v),u1_struct_0(v),u1_struct_0(v),x,w),k1_binop_1(u,w,x)) ),
inference(spr,[status(thm),theory(equality)],[119,115]),
[iquote('0:SpR:119.11,115.7')] ).
cnf(1425,plain,
( ~ l1_group_1(u)
| ~ v4_group_1(u)
| ~ v3_group_1(u)
| ~ v1_group_1(u)
| ~ v1_funct_1(v)
| ~ equal(v,k2_autgroup(u))
| ~ m2_relset_1(v,k2_zfmisc_1(k1_autgroup(u),k1_autgroup(u)),k1_autgroup(u))
| ~ m2_fraenkel(w,u1_struct_0(u),u1_struct_0(u),k1_autgroup(u))
| ~ m2_fraenkel(x,u1_struct_0(u),u1_struct_0(u),k1_autgroup(u))
| ~ m1_subset_1(w,k1_autgroup(u))
| ~ m1_subset_1(x,k1_autgroup(u))
| ~ v1_funct_2(v,k2_zfmisc_1(k1_autgroup(u),k1_autgroup(u)),k1_autgroup(u))
| ~ m1_relset_1(v,k2_zfmisc_1(k1_autgroup(u),k1_autgroup(u)),k1_autgroup(u))
| v3_struct_0(u)
| v1_xboole_0(k1_autgroup(u))
| equal(k7_funct_2(u1_struct_0(u),u1_struct_0(u),u1_struct_0(u),x,w),k1_binop_1(v,w,x)) ),
inference(obv,[status(thm),theory(equality)],[1422]),
[iquote('0:Obv:1422.16')] ).
cnf(1426,plain,
( ~ l1_group_1(u)
| ~ v4_group_1(u)
| ~ v3_group_1(u)
| ~ v1_group_1(u)
| ~ v1_funct_1(v)
| ~ equal(v,k2_autgroup(u))
| ~ m2_fraenkel(w,u1_struct_0(u),u1_struct_0(u),k1_autgroup(u))
| ~ m2_fraenkel(x,u1_struct_0(u),u1_struct_0(u),k1_autgroup(u))
| ~ m1_subset_1(w,k1_autgroup(u))
| ~ m1_subset_1(x,k1_autgroup(u))
| ~ v1_funct_2(v,k2_zfmisc_1(k1_autgroup(u),k1_autgroup(u)),k1_autgroup(u))
| ~ m1_relset_1(v,k2_zfmisc_1(k1_autgroup(u),k1_autgroup(u)),k1_autgroup(u))
| v3_struct_0(u)
| v1_xboole_0(k1_autgroup(u))
| equal(k7_funct_2(u1_struct_0(u),u1_struct_0(u),u1_struct_0(u),x,w),k1_binop_1(v,w,x)) ),
inference(mrr,[status(thm)],[1425,71]),
[iquote('0:MRR:1425.6,71.1')] ).
cnf(1427,plain,
( ~ l1_group_1(u)
| ~ v4_group_1(u)
| ~ v3_group_1(u)
| ~ v1_group_1(u)
| ~ v1_funct_1(v)
| ~ equal(v,k2_autgroup(u))
| ~ m2_fraenkel(w,u1_struct_0(u),u1_struct_0(u),k1_autgroup(u))
| ~ m2_fraenkel(x,u1_struct_0(u),u1_struct_0(u),k1_autgroup(u))
| ~ m1_subset_1(w,k1_autgroup(u))
| ~ m1_subset_1(x,k1_autgroup(u))
| ~ v1_funct_2(v,k2_zfmisc_1(k1_autgroup(u),k1_autgroup(u)),k1_autgroup(u))
| ~ m1_relset_1(v,k2_zfmisc_1(k1_autgroup(u),k1_autgroup(u)),k1_autgroup(u))
| v3_struct_0(u)
| equal(k7_funct_2(u1_struct_0(u),u1_struct_0(u),u1_struct_0(u),x,w),k1_binop_1(v,w,x)) ),
inference(mrr,[status(thm)],[1426,649]),
[iquote('0:MRR:1426.13,649.4')] ).
cnf(3764,plain,
( ~ l1_group_1(skc16)
| ~ v4_group_1(skc16)
| ~ v3_group_1(skc16)
| ~ v1_group_1(skc16)
| ~ v1_funct_1(k2_autgroup(skc16))
| ~ equal(k2_autgroup(skc16),k2_autgroup(skc16))
| ~ m2_fraenkel(u,u1_struct_0(skc16),u1_struct_0(skc16),k1_autgroup(skc16))
| ~ m2_fraenkel(v,u1_struct_0(skc16),u1_struct_0(skc16),k1_autgroup(skc16))
| ~ m1_subset_1(u,k1_autgroup(skc16))
| ~ m1_subset_1(v,k1_autgroup(skc16))
| ~ m1_relset_1(k2_autgroup(skc16),k2_zfmisc_1(k1_autgroup(skc16),k1_autgroup(skc16)),k1_autgroup(skc16))
| v3_struct_0(skc16)
| equal(k7_funct_2(u1_struct_0(skc16),u1_struct_0(skc16),u1_struct_0(skc16),v,u),k1_binop_1(k2_autgroup(skc16),u,v)) ),
inference(res,[status(thm),theory(equality)],[228,1427]),
[iquote('0:Res:228.0,1427.10')] ).
cnf(3772,plain,
( ~ l1_group_1(skc16)
| ~ v4_group_1(skc16)
| ~ v3_group_1(skc16)
| ~ v1_group_1(skc16)
| ~ v1_funct_1(k2_autgroup(skc16))
| ~ m2_fraenkel(u,u1_struct_0(skc16),u1_struct_0(skc16),k1_autgroup(skc16))
| ~ m2_fraenkel(v,u1_struct_0(skc16),u1_struct_0(skc16),k1_autgroup(skc16))
| ~ m1_subset_1(u,k1_autgroup(skc16))
| ~ m1_subset_1(v,k1_autgroup(skc16))
| ~ m1_relset_1(k2_autgroup(skc16),k2_zfmisc_1(k1_autgroup(skc16),k1_autgroup(skc16)),k1_autgroup(skc16))
| v3_struct_0(skc16)
| equal(k7_funct_2(u1_struct_0(skc16),u1_struct_0(skc16),u1_struct_0(skc16),v,u),k1_binop_1(k2_autgroup(skc16),u,v)) ),
inference(obv,[status(thm),theory(equality)],[3764]),
[iquote('0:Obv:3764.5')] ).
cnf(3773,plain,
( ~ m2_fraenkel(u,u1_struct_0(skc16),u1_struct_0(skc16),k1_autgroup(skc16))
| ~ m2_fraenkel(v,u1_struct_0(skc16),u1_struct_0(skc16),k1_autgroup(skc16))
| ~ m1_subset_1(u,k1_autgroup(skc16))
| ~ m1_subset_1(v,k1_autgroup(skc16))
| ~ m1_relset_1(k2_autgroup(skc16),k2_zfmisc_1(k1_autgroup(skc16),k1_autgroup(skc16)),k1_autgroup(skc16))
| v3_struct_0(skc16)
| equal(k7_funct_2(u1_struct_0(skc16),u1_struct_0(skc16),u1_struct_0(skc16),v,u),k1_binop_1(k2_autgroup(skc16),u,v)) ),
inference(ssi,[status(thm)],[3772,210,350,3,2,1,4,204,142]),
[iquote('0:SSi:3772.4,3772.3,3772.2,3772.1,3772.0,210.0,350.0,3.0,2.0,1.0,4.0,204.0,142.0,3.0,2.0,1.0,4.0,204.0,142.0,3.0,2.0,1.0,4.0,204.0,142.0,3.0,2.0,1.0,4.0,204.0,142.0')] ).
cnf(3774,plain,
( ~ m2_fraenkel(u,u1_struct_0(skc16),u1_struct_0(skc16),k1_autgroup(skc16))
| ~ m2_fraenkel(v,u1_struct_0(skc16),u1_struct_0(skc16),k1_autgroup(skc16))
| ~ m1_subset_1(u,k1_autgroup(skc16))
| ~ m1_subset_1(v,k1_autgroup(skc16))
| equal(k7_funct_2(u1_struct_0(skc16),u1_struct_0(skc16),u1_struct_0(skc16),v,u),k1_binop_1(k2_autgroup(skc16),u,v)) ),
inference(mrr,[status(thm)],[3773,318,32]),
[iquote('0:MRR:3773.4,3773.5,318.0,32.0')] ).
cnf(9439,plain,
( ~ m2_fraenkel(skc17,u1_struct_0(skc16),u1_struct_0(skc16),k1_autgroup(skc16))
| ~ m2_fraenkel(skc18,u1_struct_0(skc16),u1_struct_0(skc16),k1_autgroup(skc16))
| ~ m1_subset_1(skc17,k1_autgroup(skc16))
| ~ m1_subset_1(skc18,k1_autgroup(skc16))
| ~ equal(k1_binop_1(k2_autgroup(skc16),skc17,skc18),k1_binop_1(k2_autgroup(skc16),skc17,skc18)) ),
inference(spl,[status(thm),theory(equality)],[3774,86]),
[iquote('0:SpL:3774.4,86.0')] ).
cnf(9441,plain,
( ~ m2_fraenkel(skc17,u1_struct_0(skc16),u1_struct_0(skc16),k1_autgroup(skc16))
| ~ m2_fraenkel(skc18,u1_struct_0(skc16),u1_struct_0(skc16),k1_autgroup(skc16))
| ~ m1_subset_1(skc17,k1_autgroup(skc16))
| ~ m1_subset_1(skc18,k1_autgroup(skc16)) ),
inference(obv,[status(thm),theory(equality)],[9439]),
[iquote('0:Obv:9439.4')] ).
cnf(9442,plain,
$false,
inference(mrr,[status(thm)],[9441,230,229,528,529]),
[iquote('0:MRR:9441.0,9441.1,9441.2,9441.3,230.0,229.0,528.0,529.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP624+1 : TPTP v8.1.0. Released v3.4.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 00:19:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.15/2.33
% 2.15/2.33 SPASS V 3.9
% 2.15/2.33 SPASS beiseite: Proof found.
% 2.15/2.33 % SZS status Theorem
% 2.15/2.33 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.15/2.33 SPASS derived 6311 clauses, backtracked 160 clauses, performed 11 splits and kept 2349 clauses.
% 2.15/2.33 SPASS allocated 107269 KBytes.
% 2.15/2.33 SPASS spent 0:00:01.98 on the problem.
% 2.15/2.33 0:00:00.04 for the input.
% 2.15/2.33 0:00:00.06 for the FLOTTER CNF translation.
% 2.15/2.33 0:00:00.15 for inferences.
% 2.15/2.33 0:00:00.02 for the backtracking.
% 2.15/2.33 0:00:01.64 for the reduction.
% 2.15/2.33
% 2.15/2.33
% 2.15/2.33 Here is a proof with depth 3, length 60 :
% 2.15/2.33 % SZS output start Refutation
% See solution above
% 2.31/2.51 Formulae used in the proof : t15_autgroup dt_l1_group_1 dt_m1_fraenkel cc1_relset_1 fc1_struct_0 redefinition_m2_relset_1 cc1_group_1 dt_m2_relset_1 redefinition_m2_fraenkel dt_k2_autgroup dt_k1_autgroup t13_autgroup redefinition_k2_binop_1 d2_autgroup
% 2.31/2.51
%------------------------------------------------------------------------------