TSTP Solution File: GRP641+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GRP641+1 : TPTP v5.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art09.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sat Dec 25 10:54:04 EST 2010
% Result : Theorem 0.83s
% Output : CNFRefutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 12
% Syntax : Number of formulae : 117 ( 28 unt; 0 def)
% Number of atoms : 551 ( 58 equ)
% Maximal formula atoms : 38 ( 4 avg)
% Number of connectives : 691 ( 257 ~; 304 |; 99 &)
% ( 2 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn 74 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> k2_group_1(X2) = k2_group_1(X1) ) ),
file('/tmp/tmp7-P27a/sel_GRP641+1.p_1',t53_group_2) ).
fof(3,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
& m2_relset_1(X2,k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1))) )
=> ( X2 = k1_latsubgr(X1)
<=> ! [X3] :
( ( v1_group_1(X3)
& m1_group_2(X3,X1) )
=> k1_funct_1(X2,X3) = u1_struct_0(X3) ) ) ) ),
file('/tmp/tmp7-P27a/sel_GRP641+1.p_1',d1_latsubgr) ).
fof(15,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
file('/tmp/tmp7-P27a/sel_GRP641+1.p_1',fc1_struct_0) ).
fof(16,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( ( v1_group_1(X2)
& m1_group_2(X2,X1) )
=> r2_hidden(k2_group_1(X1),k1_funct_1(k1_latsubgr(X1),X2)) ) ),
file('/tmp/tmp7-P27a/sel_GRP641+1.p_1',t19_latsubgr) ).
fof(26,axiom,
v1_xboole_0(k1_xboole_0),
file('/tmp/tmp7-P27a/sel_GRP641+1.p_1',fc1_xboole_0) ).
fof(27,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_group_1(X1) )
=> m1_subset_1(k2_group_1(X1),u1_struct_0(X1)) ),
file('/tmp/tmp7-P27a/sel_GRP641+1.p_1',dt_k2_group_1) ).
fof(34,axiom,
! [X1,X2] :
( m1_subset_1(X1,X2)
=> ( v1_xboole_0(X2)
| r2_hidden(X1,X2) ) ),
file('/tmp/tmp7-P27a/sel_GRP641+1.p_1',t2_subset) ).
fof(36,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ( v1_funct_1(k1_latsubgr(X1))
& v1_funct_2(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
& m2_relset_1(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1))) ) ),
file('/tmp/tmp7-P27a/sel_GRP641+1.p_1',dt_k1_latsubgr) ).
fof(41,axiom,
! [X1] :
( l1_group_1(X1)
=> l1_struct_0(X1) ),
file('/tmp/tmp7-P27a/sel_GRP641+1.p_1',dt_l1_group_1) ).
fof(45,axiom,
! [X1] :
( v1_xboole_0(X1)
=> X1 = k1_xboole_0 ),
file('/tmp/tmp7-P27a/sel_GRP641+1.p_1',t6_boole) ).
fof(52,axiom,
? [X1] : v1_xboole_0(X1),
file('/tmp/tmp7-P27a/sel_GRP641+1.p_1',rc1_xboole_0) ).
fof(53,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> ( ~ v3_struct_0(X2)
& v3_group_1(X2)
& l1_group_1(X2) ) ) ),
file('/tmp/tmp7-P27a/sel_GRP641+1.p_1',dt_m1_group_2) ).
fof(56,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( ( v1_group_1(X2)
& m1_group_2(X2,X1) )
=> r2_hidden(k2_group_1(X1),k1_funct_1(k1_latsubgr(X1),X2)) ) ),
inference(assume_negation,[status(cth)],[16]) ).
fof(57,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> k2_group_1(X2) = k2_group_1(X1) ) ),
inference(fof_simplification,[status(thm)],[2,theory(equality)]) ).
fof(58,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
& m2_relset_1(X2,k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1))) )
=> ( X2 = k1_latsubgr(X1)
<=> ! [X3] :
( ( v1_group_1(X3)
& m1_group_2(X3,X1) )
=> k1_funct_1(X2,X3) = u1_struct_0(X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[3,theory(equality)]) ).
fof(62,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[15,theory(equality)]) ).
fof(63,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( ( v1_group_1(X2)
& m1_group_2(X2,X1) )
=> r2_hidden(k2_group_1(X1),k1_funct_1(k1_latsubgr(X1),X2)) ) ),
inference(fof_simplification,[status(thm)],[56,theory(equality)]) ).
fof(66,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_group_1(X1) )
=> m1_subset_1(k2_group_1(X1),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[27,theory(equality)]) ).
fof(68,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ( v1_funct_1(k1_latsubgr(X1))
& v1_funct_2(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
& m2_relset_1(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1))) ) ),
inference(fof_simplification,[status(thm)],[36,theory(equality)]) ).
fof(72,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> ( ~ v3_struct_0(X2)
& v3_group_1(X2)
& l1_group_1(X2) ) ) ),
inference(fof_simplification,[status(thm)],[53,theory(equality)]) ).
fof(76,plain,
! [X1] :
( v3_struct_0(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ! [X2] :
( ~ m1_group_2(X2,X1)
| k2_group_1(X2) = k2_group_1(X1) ) ),
inference(fof_nnf,[status(thm)],[57]) ).
fof(77,plain,
! [X3] :
( v3_struct_0(X3)
| ~ v3_group_1(X3)
| ~ v4_group_1(X3)
| ~ l1_group_1(X3)
| ! [X4] :
( ~ m1_group_2(X4,X3)
| k2_group_1(X4) = k2_group_1(X3) ) ),
inference(variable_rename,[status(thm)],[76]) ).
fof(78,plain,
! [X3,X4] :
( ~ m1_group_2(X4,X3)
| k2_group_1(X4) = k2_group_1(X3)
| v3_struct_0(X3)
| ~ v3_group_1(X3)
| ~ v4_group_1(X3)
| ~ l1_group_1(X3) ),
inference(shift_quantors,[status(thm)],[77]) ).
cnf(79,plain,
( v3_struct_0(X1)
| k2_group_1(X2) = k2_group_1(X1)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ m1_group_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[78]) ).
fof(80,plain,
! [X1] :
( v3_struct_0(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ! [X2] :
( ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
| ~ m2_relset_1(X2,k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
| ( ( X2 != k1_latsubgr(X1)
| ! [X3] :
( ~ v1_group_1(X3)
| ~ m1_group_2(X3,X1)
| k1_funct_1(X2,X3) = u1_struct_0(X3) ) )
& ( ? [X3] :
( v1_group_1(X3)
& m1_group_2(X3,X1)
& k1_funct_1(X2,X3) != u1_struct_0(X3) )
| X2 = k1_latsubgr(X1) ) ) ) ),
inference(fof_nnf,[status(thm)],[58]) ).
fof(81,plain,
! [X4] :
( v3_struct_0(X4)
| ~ v3_group_1(X4)
| ~ v4_group_1(X4)
| ~ l1_group_1(X4)
| ! [X5] :
( ~ v1_funct_1(X5)
| ~ v1_funct_2(X5,k1_group_3(X4),k1_zfmisc_1(u1_struct_0(X4)))
| ~ m2_relset_1(X5,k1_group_3(X4),k1_zfmisc_1(u1_struct_0(X4)))
| ( ( X5 != k1_latsubgr(X4)
| ! [X6] :
( ~ v1_group_1(X6)
| ~ m1_group_2(X6,X4)
| k1_funct_1(X5,X6) = u1_struct_0(X6) ) )
& ( ? [X7] :
( v1_group_1(X7)
& m1_group_2(X7,X4)
& k1_funct_1(X5,X7) != u1_struct_0(X7) )
| X5 = k1_latsubgr(X4) ) ) ) ),
inference(variable_rename,[status(thm)],[80]) ).
fof(82,plain,
! [X4] :
( v3_struct_0(X4)
| ~ v3_group_1(X4)
| ~ v4_group_1(X4)
| ~ l1_group_1(X4)
| ! [X5] :
( ~ v1_funct_1(X5)
| ~ v1_funct_2(X5,k1_group_3(X4),k1_zfmisc_1(u1_struct_0(X4)))
| ~ m2_relset_1(X5,k1_group_3(X4),k1_zfmisc_1(u1_struct_0(X4)))
| ( ( X5 != k1_latsubgr(X4)
| ! [X6] :
( ~ v1_group_1(X6)
| ~ m1_group_2(X6,X4)
| k1_funct_1(X5,X6) = u1_struct_0(X6) ) )
& ( ( v1_group_1(esk1_2(X4,X5))
& m1_group_2(esk1_2(X4,X5),X4)
& k1_funct_1(X5,esk1_2(X4,X5)) != u1_struct_0(esk1_2(X4,X5)) )
| X5 = k1_latsubgr(X4) ) ) ) ),
inference(skolemize,[status(esa)],[81]) ).
fof(83,plain,
! [X4,X5,X6] :
( ( ( ~ v1_group_1(X6)
| ~ m1_group_2(X6,X4)
| k1_funct_1(X5,X6) = u1_struct_0(X6)
| X5 != k1_latsubgr(X4) )
& ( ( v1_group_1(esk1_2(X4,X5))
& m1_group_2(esk1_2(X4,X5),X4)
& k1_funct_1(X5,esk1_2(X4,X5)) != u1_struct_0(esk1_2(X4,X5)) )
| X5 = k1_latsubgr(X4) ) )
| ~ v1_funct_1(X5)
| ~ v1_funct_2(X5,k1_group_3(X4),k1_zfmisc_1(u1_struct_0(X4)))
| ~ m2_relset_1(X5,k1_group_3(X4),k1_zfmisc_1(u1_struct_0(X4)))
| v3_struct_0(X4)
| ~ v3_group_1(X4)
| ~ v4_group_1(X4)
| ~ l1_group_1(X4) ),
inference(shift_quantors,[status(thm)],[82]) ).
fof(84,plain,
! [X4,X5,X6] :
( ( ~ v1_group_1(X6)
| ~ m1_group_2(X6,X4)
| k1_funct_1(X5,X6) = u1_struct_0(X6)
| X5 != k1_latsubgr(X4)
| ~ v1_funct_1(X5)
| ~ v1_funct_2(X5,k1_group_3(X4),k1_zfmisc_1(u1_struct_0(X4)))
| ~ m2_relset_1(X5,k1_group_3(X4),k1_zfmisc_1(u1_struct_0(X4)))
| v3_struct_0(X4)
| ~ v3_group_1(X4)
| ~ v4_group_1(X4)
| ~ l1_group_1(X4) )
& ( v1_group_1(esk1_2(X4,X5))
| X5 = k1_latsubgr(X4)
| ~ v1_funct_1(X5)
| ~ v1_funct_2(X5,k1_group_3(X4),k1_zfmisc_1(u1_struct_0(X4)))
| ~ m2_relset_1(X5,k1_group_3(X4),k1_zfmisc_1(u1_struct_0(X4)))
| v3_struct_0(X4)
| ~ v3_group_1(X4)
| ~ v4_group_1(X4)
| ~ l1_group_1(X4) )
& ( m1_group_2(esk1_2(X4,X5),X4)
| X5 = k1_latsubgr(X4)
| ~ v1_funct_1(X5)
| ~ v1_funct_2(X5,k1_group_3(X4),k1_zfmisc_1(u1_struct_0(X4)))
| ~ m2_relset_1(X5,k1_group_3(X4),k1_zfmisc_1(u1_struct_0(X4)))
| v3_struct_0(X4)
| ~ v3_group_1(X4)
| ~ v4_group_1(X4)
| ~ l1_group_1(X4) )
& ( k1_funct_1(X5,esk1_2(X4,X5)) != u1_struct_0(esk1_2(X4,X5))
| X5 = k1_latsubgr(X4)
| ~ v1_funct_1(X5)
| ~ v1_funct_2(X5,k1_group_3(X4),k1_zfmisc_1(u1_struct_0(X4)))
| ~ m2_relset_1(X5,k1_group_3(X4),k1_zfmisc_1(u1_struct_0(X4)))
| v3_struct_0(X4)
| ~ v3_group_1(X4)
| ~ v4_group_1(X4)
| ~ l1_group_1(X4) ) ),
inference(distribute,[status(thm)],[83]) ).
cnf(88,plain,
( v3_struct_0(X1)
| k1_funct_1(X2,X3) = u1_struct_0(X3)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ m2_relset_1(X2,k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
| ~ v1_funct_2(X2,k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
| ~ v1_funct_1(X2)
| X2 != k1_latsubgr(X1)
| ~ m1_group_2(X3,X1)
| ~ v1_group_1(X3) ),
inference(split_conjunct,[status(thm)],[84]) ).
fof(130,plain,
! [X1] :
( v3_struct_0(X1)
| ~ l1_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(fof_nnf,[status(thm)],[62]) ).
fof(131,plain,
! [X2] :
( v3_struct_0(X2)
| ~ l1_struct_0(X2)
| ~ v1_xboole_0(u1_struct_0(X2)) ),
inference(variable_rename,[status(thm)],[130]) ).
cnf(132,plain,
( v3_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1))
| ~ l1_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[131]) ).
fof(133,negated_conjecture,
? [X1] :
( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1)
& ? [X2] :
( v1_group_1(X2)
& m1_group_2(X2,X1)
& ~ r2_hidden(k2_group_1(X1),k1_funct_1(k1_latsubgr(X1),X2)) ) ),
inference(fof_nnf,[status(thm)],[63]) ).
fof(134,negated_conjecture,
? [X3] :
( ~ v3_struct_0(X3)
& v3_group_1(X3)
& v4_group_1(X3)
& l1_group_1(X3)
& ? [X4] :
( v1_group_1(X4)
& m1_group_2(X4,X3)
& ~ r2_hidden(k2_group_1(X3),k1_funct_1(k1_latsubgr(X3),X4)) ) ),
inference(variable_rename,[status(thm)],[133]) ).
fof(135,negated_conjecture,
( ~ v3_struct_0(esk6_0)
& v3_group_1(esk6_0)
& v4_group_1(esk6_0)
& l1_group_1(esk6_0)
& v1_group_1(esk7_0)
& m1_group_2(esk7_0,esk6_0)
& ~ r2_hidden(k2_group_1(esk6_0),k1_funct_1(k1_latsubgr(esk6_0),esk7_0)) ),
inference(skolemize,[status(esa)],[134]) ).
cnf(136,negated_conjecture,
~ r2_hidden(k2_group_1(esk6_0),k1_funct_1(k1_latsubgr(esk6_0),esk7_0)),
inference(split_conjunct,[status(thm)],[135]) ).
cnf(137,negated_conjecture,
m1_group_2(esk7_0,esk6_0),
inference(split_conjunct,[status(thm)],[135]) ).
cnf(138,negated_conjecture,
v1_group_1(esk7_0),
inference(split_conjunct,[status(thm)],[135]) ).
cnf(139,negated_conjecture,
l1_group_1(esk6_0),
inference(split_conjunct,[status(thm)],[135]) ).
cnf(140,negated_conjecture,
v4_group_1(esk6_0),
inference(split_conjunct,[status(thm)],[135]) ).
cnf(141,negated_conjecture,
v3_group_1(esk6_0),
inference(split_conjunct,[status(thm)],[135]) ).
cnf(142,negated_conjecture,
~ v3_struct_0(esk6_0),
inference(split_conjunct,[status(thm)],[135]) ).
cnf(173,plain,
v1_xboole_0(k1_xboole_0),
inference(split_conjunct,[status(thm)],[26]) ).
fof(174,plain,
! [X1] :
( v3_struct_0(X1)
| ~ l1_group_1(X1)
| m1_subset_1(k2_group_1(X1),u1_struct_0(X1)) ),
inference(fof_nnf,[status(thm)],[66]) ).
fof(175,plain,
! [X2] :
( v3_struct_0(X2)
| ~ l1_group_1(X2)
| m1_subset_1(k2_group_1(X2),u1_struct_0(X2)) ),
inference(variable_rename,[status(thm)],[174]) ).
cnf(176,plain,
( m1_subset_1(k2_group_1(X1),u1_struct_0(X1))
| v3_struct_0(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[175]) ).
fof(195,plain,
! [X1,X2] :
( ~ m1_subset_1(X1,X2)
| v1_xboole_0(X2)
| r2_hidden(X1,X2) ),
inference(fof_nnf,[status(thm)],[34]) ).
fof(196,plain,
! [X3,X4] :
( ~ m1_subset_1(X3,X4)
| v1_xboole_0(X4)
| r2_hidden(X3,X4) ),
inference(variable_rename,[status(thm)],[195]) ).
cnf(197,plain,
( r2_hidden(X1,X2)
| v1_xboole_0(X2)
| ~ m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[196]) ).
fof(199,plain,
! [X1] :
( v3_struct_0(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ( v1_funct_1(k1_latsubgr(X1))
& v1_funct_2(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
& m2_relset_1(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1))) ) ),
inference(fof_nnf,[status(thm)],[68]) ).
fof(200,plain,
! [X2] :
( v3_struct_0(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2)
| ( v1_funct_1(k1_latsubgr(X2))
& v1_funct_2(k1_latsubgr(X2),k1_group_3(X2),k1_zfmisc_1(u1_struct_0(X2)))
& m2_relset_1(k1_latsubgr(X2),k1_group_3(X2),k1_zfmisc_1(u1_struct_0(X2))) ) ),
inference(variable_rename,[status(thm)],[199]) ).
fof(201,plain,
! [X2] :
( ( v1_funct_1(k1_latsubgr(X2))
| v3_struct_0(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2) )
& ( v1_funct_2(k1_latsubgr(X2),k1_group_3(X2),k1_zfmisc_1(u1_struct_0(X2)))
| v3_struct_0(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2) )
& ( m2_relset_1(k1_latsubgr(X2),k1_group_3(X2),k1_zfmisc_1(u1_struct_0(X2)))
| v3_struct_0(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2) ) ),
inference(distribute,[status(thm)],[200]) ).
cnf(202,plain,
( v3_struct_0(X1)
| m2_relset_1(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1) ),
inference(split_conjunct,[status(thm)],[201]) ).
cnf(203,plain,
( v3_struct_0(X1)
| v1_funct_2(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1) ),
inference(split_conjunct,[status(thm)],[201]) ).
cnf(204,plain,
( v3_struct_0(X1)
| v1_funct_1(k1_latsubgr(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1) ),
inference(split_conjunct,[status(thm)],[201]) ).
fof(218,plain,
! [X1] :
( ~ l1_group_1(X1)
| l1_struct_0(X1) ),
inference(fof_nnf,[status(thm)],[41]) ).
fof(219,plain,
! [X2] :
( ~ l1_group_1(X2)
| l1_struct_0(X2) ),
inference(variable_rename,[status(thm)],[218]) ).
cnf(220,plain,
( l1_struct_0(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[219]) ).
fof(226,plain,
! [X1] :
( ~ v1_xboole_0(X1)
| X1 = k1_xboole_0 ),
inference(fof_nnf,[status(thm)],[45]) ).
fof(227,plain,
! [X2] :
( ~ v1_xboole_0(X2)
| X2 = k1_xboole_0 ),
inference(variable_rename,[status(thm)],[226]) ).
cnf(228,plain,
( X1 = k1_xboole_0
| ~ v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[227]) ).
fof(253,plain,
? [X2] : v1_xboole_0(X2),
inference(variable_rename,[status(thm)],[52]) ).
fof(254,plain,
v1_xboole_0(esk16_0),
inference(skolemize,[status(esa)],[253]) ).
cnf(255,plain,
v1_xboole_0(esk16_0),
inference(split_conjunct,[status(thm)],[254]) ).
fof(256,plain,
! [X1] :
( v3_struct_0(X1)
| ~ v3_group_1(X1)
| ~ l1_group_1(X1)
| ! [X2] :
( ~ m1_group_2(X2,X1)
| ( ~ v3_struct_0(X2)
& v3_group_1(X2)
& l1_group_1(X2) ) ) ),
inference(fof_nnf,[status(thm)],[72]) ).
fof(257,plain,
! [X3] :
( v3_struct_0(X3)
| ~ v3_group_1(X3)
| ~ l1_group_1(X3)
| ! [X4] :
( ~ m1_group_2(X4,X3)
| ( ~ v3_struct_0(X4)
& v3_group_1(X4)
& l1_group_1(X4) ) ) ),
inference(variable_rename,[status(thm)],[256]) ).
fof(258,plain,
! [X3,X4] :
( ~ m1_group_2(X4,X3)
| ( ~ v3_struct_0(X4)
& v3_group_1(X4)
& l1_group_1(X4) )
| v3_struct_0(X3)
| ~ v3_group_1(X3)
| ~ l1_group_1(X3) ),
inference(shift_quantors,[status(thm)],[257]) ).
fof(259,plain,
! [X3,X4] :
( ( ~ v3_struct_0(X4)
| ~ m1_group_2(X4,X3)
| v3_struct_0(X3)
| ~ v3_group_1(X3)
| ~ l1_group_1(X3) )
& ( v3_group_1(X4)
| ~ m1_group_2(X4,X3)
| v3_struct_0(X3)
| ~ v3_group_1(X3)
| ~ l1_group_1(X3) )
& ( l1_group_1(X4)
| ~ m1_group_2(X4,X3)
| v3_struct_0(X3)
| ~ v3_group_1(X3)
| ~ l1_group_1(X3) ) ),
inference(distribute,[status(thm)],[258]) ).
cnf(260,plain,
( v3_struct_0(X1)
| l1_group_1(X2)
| ~ l1_group_1(X1)
| ~ v3_group_1(X1)
| ~ m1_group_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[259]) ).
cnf(262,plain,
( v3_struct_0(X1)
| ~ l1_group_1(X1)
| ~ v3_group_1(X1)
| ~ m1_group_2(X2,X1)
| ~ v3_struct_0(X2) ),
inference(split_conjunct,[status(thm)],[259]) ).
cnf(274,plain,
k1_xboole_0 = esk16_0,
inference(spm,[status(thm)],[228,255,theory(equality)]) ).
cnf(359,plain,
( r2_hidden(k2_group_1(X1),u1_struct_0(X1))
| v1_xboole_0(u1_struct_0(X1))
| v3_struct_0(X1)
| ~ l1_group_1(X1) ),
inference(spm,[status(thm)],[197,176,theory(equality)]) ).
cnf(389,negated_conjecture,
( l1_group_1(esk7_0)
| v3_struct_0(esk6_0)
| ~ l1_group_1(esk6_0)
| ~ v3_group_1(esk6_0) ),
inference(spm,[status(thm)],[260,137,theory(equality)]) ).
cnf(391,negated_conjecture,
( l1_group_1(esk7_0)
| v3_struct_0(esk6_0)
| $false
| ~ v3_group_1(esk6_0) ),
inference(rw,[status(thm)],[389,139,theory(equality)]) ).
cnf(392,negated_conjecture,
( l1_group_1(esk7_0)
| v3_struct_0(esk6_0)
| $false
| $false ),
inference(rw,[status(thm)],[391,141,theory(equality)]) ).
cnf(393,negated_conjecture,
( l1_group_1(esk7_0)
| v3_struct_0(esk6_0) ),
inference(cn,[status(thm)],[392,theory(equality)]) ).
cnf(394,negated_conjecture,
l1_group_1(esk7_0),
inference(sr,[status(thm)],[393,142,theory(equality)]) ).
cnf(412,negated_conjecture,
( v3_struct_0(esk6_0)
| ~ l1_group_1(esk6_0)
| ~ v3_group_1(esk6_0)
| ~ v3_struct_0(esk7_0) ),
inference(spm,[status(thm)],[262,137,theory(equality)]) ).
cnf(414,negated_conjecture,
( v3_struct_0(esk6_0)
| $false
| ~ v3_group_1(esk6_0)
| ~ v3_struct_0(esk7_0) ),
inference(rw,[status(thm)],[412,139,theory(equality)]) ).
cnf(415,negated_conjecture,
( v3_struct_0(esk6_0)
| $false
| $false
| ~ v3_struct_0(esk7_0) ),
inference(rw,[status(thm)],[414,141,theory(equality)]) ).
cnf(416,negated_conjecture,
( v3_struct_0(esk6_0)
| ~ v3_struct_0(esk7_0) ),
inference(cn,[status(thm)],[415,theory(equality)]) ).
cnf(417,negated_conjecture,
~ v3_struct_0(esk7_0),
inference(sr,[status(thm)],[416,142,theory(equality)]) ).
cnf(449,negated_conjecture,
( k2_group_1(esk6_0) = k2_group_1(esk7_0)
| v3_struct_0(esk6_0)
| ~ l1_group_1(esk6_0)
| ~ v4_group_1(esk6_0)
| ~ v3_group_1(esk6_0) ),
inference(spm,[status(thm)],[79,137,theory(equality)]) ).
cnf(451,negated_conjecture,
( k2_group_1(esk6_0) = k2_group_1(esk7_0)
| v3_struct_0(esk6_0)
| $false
| ~ v4_group_1(esk6_0)
| ~ v3_group_1(esk6_0) ),
inference(rw,[status(thm)],[449,139,theory(equality)]) ).
cnf(452,negated_conjecture,
( k2_group_1(esk6_0) = k2_group_1(esk7_0)
| v3_struct_0(esk6_0)
| $false
| $false
| ~ v3_group_1(esk6_0) ),
inference(rw,[status(thm)],[451,140,theory(equality)]) ).
cnf(453,negated_conjecture,
( k2_group_1(esk6_0) = k2_group_1(esk7_0)
| v3_struct_0(esk6_0)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[452,141,theory(equality)]) ).
cnf(454,negated_conjecture,
( k2_group_1(esk6_0) = k2_group_1(esk7_0)
| v3_struct_0(esk6_0) ),
inference(cn,[status(thm)],[453,theory(equality)]) ).
cnf(455,negated_conjecture,
k2_group_1(esk6_0) = k2_group_1(esk7_0),
inference(sr,[status(thm)],[454,142,theory(equality)]) ).
cnf(546,plain,
( k1_funct_1(k1_latsubgr(X1),X2) = u1_struct_0(X2)
| v3_struct_0(X1)
| ~ v1_group_1(X2)
| ~ m2_relset_1(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
| ~ v1_funct_2(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
| ~ v1_funct_1(k1_latsubgr(X1))
| ~ m1_group_2(X2,X1)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1) ),
inference(er,[status(thm)],[88,theory(equality)]) ).
cnf(551,plain,
v1_xboole_0(esk16_0),
inference(rw,[status(thm)],[173,274,theory(equality)]) ).
cnf(552,plain,
( esk16_0 = X1
| ~ v1_xboole_0(X1) ),
inference(rw,[status(thm)],[228,274,theory(equality)]) ).
cnf(554,negated_conjecture,
~ r2_hidden(k2_group_1(esk7_0),k1_funct_1(k1_latsubgr(esk6_0),esk7_0)),
inference(rw,[status(thm)],[136,455,theory(equality)]) ).
cnf(14174,plain,
( k1_funct_1(k1_latsubgr(X1),X2) = u1_struct_0(X2)
| v3_struct_0(X1)
| ~ v1_group_1(X2)
| ~ m2_relset_1(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
| ~ v1_funct_2(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
| ~ m1_group_2(X2,X1)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1) ),
inference(csr,[status(thm)],[546,204]) ).
cnf(14175,plain,
( k1_funct_1(k1_latsubgr(X1),X2) = u1_struct_0(X2)
| v3_struct_0(X1)
| ~ v1_group_1(X2)
| ~ m2_relset_1(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
| ~ m1_group_2(X2,X1)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1) ),
inference(csr,[status(thm)],[14174,203]) ).
cnf(14176,plain,
( k1_funct_1(k1_latsubgr(X1),X2) = u1_struct_0(X2)
| v3_struct_0(X1)
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X1)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1) ),
inference(csr,[status(thm)],[14175,202]) ).
cnf(14177,negated_conjecture,
( k1_funct_1(k1_latsubgr(esk6_0),esk7_0) = u1_struct_0(esk7_0)
| v3_struct_0(esk6_0)
| ~ v1_group_1(esk7_0)
| ~ l1_group_1(esk6_0)
| ~ v4_group_1(esk6_0)
| ~ v3_group_1(esk6_0) ),
inference(spm,[status(thm)],[14176,137,theory(equality)]) ).
cnf(14179,negated_conjecture,
( k1_funct_1(k1_latsubgr(esk6_0),esk7_0) = u1_struct_0(esk7_0)
| v3_struct_0(esk6_0)
| $false
| ~ l1_group_1(esk6_0)
| ~ v4_group_1(esk6_0)
| ~ v3_group_1(esk6_0) ),
inference(rw,[status(thm)],[14177,138,theory(equality)]) ).
cnf(14180,negated_conjecture,
( k1_funct_1(k1_latsubgr(esk6_0),esk7_0) = u1_struct_0(esk7_0)
| v3_struct_0(esk6_0)
| $false
| $false
| ~ v4_group_1(esk6_0)
| ~ v3_group_1(esk6_0) ),
inference(rw,[status(thm)],[14179,139,theory(equality)]) ).
cnf(14181,negated_conjecture,
( k1_funct_1(k1_latsubgr(esk6_0),esk7_0) = u1_struct_0(esk7_0)
| v3_struct_0(esk6_0)
| $false
| $false
| $false
| ~ v3_group_1(esk6_0) ),
inference(rw,[status(thm)],[14180,140,theory(equality)]) ).
cnf(14182,negated_conjecture,
( k1_funct_1(k1_latsubgr(esk6_0),esk7_0) = u1_struct_0(esk7_0)
| v3_struct_0(esk6_0)
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[14181,141,theory(equality)]) ).
cnf(14183,negated_conjecture,
( k1_funct_1(k1_latsubgr(esk6_0),esk7_0) = u1_struct_0(esk7_0)
| v3_struct_0(esk6_0) ),
inference(cn,[status(thm)],[14182,theory(equality)]) ).
cnf(14184,negated_conjecture,
k1_funct_1(k1_latsubgr(esk6_0),esk7_0) = u1_struct_0(esk7_0),
inference(sr,[status(thm)],[14183,142,theory(equality)]) ).
cnf(14187,negated_conjecture,
~ r2_hidden(k2_group_1(esk7_0),u1_struct_0(esk7_0)),
inference(rw,[status(thm)],[554,14184,theory(equality)]) ).
cnf(14193,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk7_0))
| v3_struct_0(esk7_0)
| ~ l1_group_1(esk7_0) ),
inference(spm,[status(thm)],[14187,359,theory(equality)]) ).
cnf(14194,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk7_0))
| v3_struct_0(esk7_0)
| $false ),
inference(rw,[status(thm)],[14193,394,theory(equality)]) ).
cnf(14195,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk7_0))
| v3_struct_0(esk7_0) ),
inference(cn,[status(thm)],[14194,theory(equality)]) ).
cnf(14196,negated_conjecture,
v1_xboole_0(u1_struct_0(esk7_0)),
inference(sr,[status(thm)],[14195,417,theory(equality)]) ).
cnf(14202,negated_conjecture,
esk16_0 = u1_struct_0(esk7_0),
inference(spm,[status(thm)],[552,14196,theory(equality)]) ).
cnf(14247,negated_conjecture,
( v3_struct_0(esk7_0)
| ~ l1_struct_0(esk7_0)
| ~ v1_xboole_0(esk16_0) ),
inference(spm,[status(thm)],[132,14202,theory(equality)]) ).
cnf(14284,negated_conjecture,
( v3_struct_0(esk7_0)
| ~ l1_struct_0(esk7_0)
| $false ),
inference(rw,[status(thm)],[14247,551,theory(equality)]) ).
cnf(14285,negated_conjecture,
( v3_struct_0(esk7_0)
| ~ l1_struct_0(esk7_0) ),
inference(cn,[status(thm)],[14284,theory(equality)]) ).
cnf(14286,negated_conjecture,
~ l1_struct_0(esk7_0),
inference(sr,[status(thm)],[14285,417,theory(equality)]) ).
cnf(14437,negated_conjecture,
~ l1_group_1(esk7_0),
inference(spm,[status(thm)],[14286,220,theory(equality)]) ).
cnf(14438,negated_conjecture,
$false,
inference(rw,[status(thm)],[14437,394,theory(equality)]) ).
cnf(14439,negated_conjecture,
$false,
inference(cn,[status(thm)],[14438,theory(equality)]) ).
cnf(14440,negated_conjecture,
$false,
14439,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRP/GRP641+1.p
% --creating new selector for []
% -running prover on /tmp/tmp7-P27a/sel_GRP641+1.p_1 with time limit 29
% -prover status Theorem
% Problem GRP641+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRP/GRP641+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRP/GRP641+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
%
%------------------------------------------------------------------------------