TSTP Solution File: GRP624+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GRP624+1 : TPTP v5.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.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 10:14:59 EST 2010
% Result : Theorem 3.63s
% Output : CNFRefutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 11
% Syntax : Number of formulae : 132 ( 16 unt; 0 def)
% Number of atoms : 801 ( 53 equ)
% Maximal formula atoms : 42 ( 6 avg)
% Number of connectives : 1075 ( 406 ~; 509 |; 121 &)
% ( 5 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-6 aty)
% Number of variables : 216 ( 2 sgn 135 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(4,axiom,
! [X1,X2,X3,X4,X5,X6] :
( ( ~ v1_xboole_0(X1)
& ~ v1_xboole_0(X2)
& v1_funct_1(X4)
& v1_funct_2(X4,k2_zfmisc_1(X1,X2),X3)
& m1_relset_1(X4,k2_zfmisc_1(X1,X2),X3)
& m1_subset_1(X5,X1)
& m1_subset_1(X6,X2) )
=> k2_binop_1(X1,X2,X3,X4,X5,X6) = k1_binop_1(X4,X5,X6) ),
file('/tmp/tmpsDcBWj/sel_GRP624+1.p_1',redefinition_k2_binop_1) ).
fof(8,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
<=> m1_relset_1(X3,X1,X2) ),
file('/tmp/tmpsDcBWj/sel_GRP624+1.p_1',redefinition_m2_relset_1) ).
fof(24,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
file('/tmp/tmpsDcBWj/sel_GRP624+1.p_1',fc1_struct_0) ).
fof(26,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> ! [X3] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> k1_binop_1(k2_autgroup(X1),X2,X3) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X3,X2) ) ) ),
file('/tmp/tmpsDcBWj/sel_GRP624+1.p_1',t15_autgroup) ).
fof(38,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
& m2_relset_1(X2,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1)) )
=> ( X2 = k2_autgroup(X1)
<=> ! [X3] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> ! [X4] :
( m2_fraenkel(X4,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> k2_binop_1(k1_autgroup(X1),k1_autgroup(X1),k1_autgroup(X1),X2,X3,X4) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X4,X3) ) ) ) ) ),
file('/tmp/tmpsDcBWj/sel_GRP624+1.p_1',d2_autgroup) ).
fof(39,axiom,
! [X1,X2,X3] :
( m1_fraenkel(X3,X1,X2)
=> ( ~ v1_xboole_0(X3)
& v1_fraenkel(X3) ) ),
file('/tmp/tmpsDcBWj/sel_GRP624+1.p_1',dt_m1_fraenkel) ).
fof(46,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> m1_fraenkel(k1_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
file('/tmp/tmpsDcBWj/sel_GRP624+1.p_1',dt_k1_autgroup) ).
fof(61,axiom,
! [X1] :
( l1_group_1(X1)
=> l1_struct_0(X1) ),
file('/tmp/tmpsDcBWj/sel_GRP624+1.p_1',dt_l1_group_1) ).
fof(67,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ) ),
file('/tmp/tmpsDcBWj/sel_GRP624+1.p_1',t13_autgroup) ).
fof(72,axiom,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X2)
& m1_fraenkel(X3,X1,X2) )
=> ! [X4] :
( m2_fraenkel(X4,X1,X2,X3)
<=> m1_subset_1(X4,X3) ) ),
file('/tmp/tmpsDcBWj/sel_GRP624+1.p_1',redefinition_m2_fraenkel) ).
fof(73,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ( v1_funct_1(k2_autgroup(X1))
& v1_funct_2(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
& m2_relset_1(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1)) ) ),
file('/tmp/tmpsDcBWj/sel_GRP624+1.p_1',dt_k2_autgroup) ).
fof(80,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> ! [X3] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> k1_binop_1(k2_autgroup(X1),X2,X3) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X3,X2) ) ) ),
inference(assume_negation,[status(cth)],[26]) ).
fof(81,plain,
! [X1,X2,X3,X4,X5,X6] :
( ( ~ v1_xboole_0(X1)
& ~ v1_xboole_0(X2)
& v1_funct_1(X4)
& v1_funct_2(X4,k2_zfmisc_1(X1,X2),X3)
& m1_relset_1(X4,k2_zfmisc_1(X1,X2),X3)
& m1_subset_1(X5,X1)
& m1_subset_1(X6,X2) )
=> k2_binop_1(X1,X2,X3,X4,X5,X6) = k1_binop_1(X4,X5,X6) ),
inference(fof_simplification,[status(thm)],[4,theory(equality)]) ).
fof(89,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[24,theory(equality)]) ).
fof(90,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> ! [X3] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> k1_binop_1(k2_autgroup(X1),X2,X3) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X3,X2) ) ) ),
inference(fof_simplification,[status(thm)],[80,theory(equality)]) ).
fof(94,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
& m2_relset_1(X2,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1)) )
=> ( X2 = k2_autgroup(X1)
<=> ! [X3] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> ! [X4] :
( m2_fraenkel(X4,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> k2_binop_1(k1_autgroup(X1),k1_autgroup(X1),k1_autgroup(X1),X2,X3,X4) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X4,X3) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[38,theory(equality)]) ).
fof(95,plain,
! [X1,X2,X3] :
( m1_fraenkel(X3,X1,X2)
=> ( ~ v1_xboole_0(X3)
& v1_fraenkel(X3) ) ),
inference(fof_simplification,[status(thm)],[39,theory(equality)]) ).
fof(97,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> m1_fraenkel(k1_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[46,theory(equality)]) ).
fof(101,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ) ),
inference(fof_simplification,[status(thm)],[67,theory(equality)]) ).
fof(103,plain,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X2)
& m1_fraenkel(X3,X1,X2) )
=> ! [X4] :
( m2_fraenkel(X4,X1,X2,X3)
<=> m1_subset_1(X4,X3) ) ),
inference(fof_simplification,[status(thm)],[72,theory(equality)]) ).
fof(104,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ( v1_funct_1(k2_autgroup(X1))
& v1_funct_2(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
& m2_relset_1(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1)) ) ),
inference(fof_simplification,[status(thm)],[73,theory(equality)]) ).
fof(117,plain,
! [X1,X2,X3,X4,X5,X6] :
( v1_xboole_0(X1)
| v1_xboole_0(X2)
| ~ v1_funct_1(X4)
| ~ v1_funct_2(X4,k2_zfmisc_1(X1,X2),X3)
| ~ m1_relset_1(X4,k2_zfmisc_1(X1,X2),X3)
| ~ m1_subset_1(X5,X1)
| ~ m1_subset_1(X6,X2)
| k2_binop_1(X1,X2,X3,X4,X5,X6) = k1_binop_1(X4,X5,X6) ),
inference(fof_nnf,[status(thm)],[81]) ).
fof(118,plain,
! [X7,X8,X9,X10,X11,X12] :
( v1_xboole_0(X7)
| v1_xboole_0(X8)
| ~ v1_funct_1(X10)
| ~ v1_funct_2(X10,k2_zfmisc_1(X7,X8),X9)
| ~ m1_relset_1(X10,k2_zfmisc_1(X7,X8),X9)
| ~ m1_subset_1(X11,X7)
| ~ m1_subset_1(X12,X8)
| k2_binop_1(X7,X8,X9,X10,X11,X12) = k1_binop_1(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[117]) ).
cnf(119,plain,
( k2_binop_1(X1,X2,X3,X4,X5,X6) = k1_binop_1(X4,X5,X6)
| v1_xboole_0(X2)
| v1_xboole_0(X1)
| ~ m1_subset_1(X6,X2)
| ~ m1_subset_1(X5,X1)
| ~ m1_relset_1(X4,k2_zfmisc_1(X1,X2),X3)
| ~ v1_funct_2(X4,k2_zfmisc_1(X1,X2),X3)
| ~ v1_funct_1(X4) ),
inference(split_conjunct,[status(thm)],[118]) ).
fof(131,plain,
! [X1,X2,X3] :
( ( ~ m2_relset_1(X3,X1,X2)
| m1_relset_1(X3,X1,X2) )
& ( ~ m1_relset_1(X3,X1,X2)
| m2_relset_1(X3,X1,X2) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(132,plain,
! [X4,X5,X6] :
( ( ~ m2_relset_1(X6,X4,X5)
| m1_relset_1(X6,X4,X5) )
& ( ~ m1_relset_1(X6,X4,X5)
| m2_relset_1(X6,X4,X5) ) ),
inference(variable_rename,[status(thm)],[131]) ).
cnf(133,plain,
( m2_relset_1(X1,X2,X3)
| ~ m1_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[132]) ).
cnf(134,plain,
( m1_relset_1(X1,X2,X3)
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[132]) ).
fof(193,plain,
! [X1] :
( v3_struct_0(X1)
| ~ l1_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(fof_nnf,[status(thm)],[89]) ).
fof(194,plain,
! [X2] :
( v3_struct_0(X2)
| ~ l1_struct_0(X2)
| ~ v1_xboole_0(u1_struct_0(X2)) ),
inference(variable_rename,[status(thm)],[193]) ).
cnf(195,plain,
( v3_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1))
| ~ l1_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[194]) ).
fof(202,negated_conjecture,
? [X1] :
( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1)
& ? [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
& ? [X3] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
& k1_binop_1(k2_autgroup(X1),X2,X3) != k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X3,X2) ) ) ),
inference(fof_nnf,[status(thm)],[90]) ).
fof(203,negated_conjecture,
? [X4] :
( ~ v3_struct_0(X4)
& v1_group_1(X4)
& v3_group_1(X4)
& v4_group_1(X4)
& l1_group_1(X4)
& ? [X5] :
( m2_fraenkel(X5,u1_struct_0(X4),u1_struct_0(X4),k4_autgroup(X4))
& ? [X6] :
( m2_fraenkel(X6,u1_struct_0(X4),u1_struct_0(X4),k4_autgroup(X4))
& k1_binop_1(k2_autgroup(X4),X5,X6) != k7_funct_2(u1_struct_0(X4),u1_struct_0(X4),u1_struct_0(X4),X6,X5) ) ) ),
inference(variable_rename,[status(thm)],[202]) ).
fof(204,negated_conjecture,
( ~ v3_struct_0(esk8_0)
& v1_group_1(esk8_0)
& v3_group_1(esk8_0)
& v4_group_1(esk8_0)
& l1_group_1(esk8_0)
& m2_fraenkel(esk9_0,u1_struct_0(esk8_0),u1_struct_0(esk8_0),k4_autgroup(esk8_0))
& m2_fraenkel(esk10_0,u1_struct_0(esk8_0),u1_struct_0(esk8_0),k4_autgroup(esk8_0))
& k1_binop_1(k2_autgroup(esk8_0),esk9_0,esk10_0) != k7_funct_2(u1_struct_0(esk8_0),u1_struct_0(esk8_0),u1_struct_0(esk8_0),esk10_0,esk9_0) ),
inference(skolemize,[status(esa)],[203]) ).
cnf(205,negated_conjecture,
k1_binop_1(k2_autgroup(esk8_0),esk9_0,esk10_0) != k7_funct_2(u1_struct_0(esk8_0),u1_struct_0(esk8_0),u1_struct_0(esk8_0),esk10_0,esk9_0),
inference(split_conjunct,[status(thm)],[204]) ).
cnf(206,negated_conjecture,
m2_fraenkel(esk10_0,u1_struct_0(esk8_0),u1_struct_0(esk8_0),k4_autgroup(esk8_0)),
inference(split_conjunct,[status(thm)],[204]) ).
cnf(207,negated_conjecture,
m2_fraenkel(esk9_0,u1_struct_0(esk8_0),u1_struct_0(esk8_0),k4_autgroup(esk8_0)),
inference(split_conjunct,[status(thm)],[204]) ).
cnf(208,negated_conjecture,
l1_group_1(esk8_0),
inference(split_conjunct,[status(thm)],[204]) ).
cnf(209,negated_conjecture,
v4_group_1(esk8_0),
inference(split_conjunct,[status(thm)],[204]) ).
cnf(210,negated_conjecture,
v3_group_1(esk8_0),
inference(split_conjunct,[status(thm)],[204]) ).
cnf(211,negated_conjecture,
v1_group_1(esk8_0),
inference(split_conjunct,[status(thm)],[204]) ).
cnf(212,negated_conjecture,
~ v3_struct_0(esk8_0),
inference(split_conjunct,[status(thm)],[204]) ).
fof(260,plain,
! [X1] :
( v3_struct_0(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ! [X2] :
( ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
| ~ m2_relset_1(X2,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
| ( ( X2 != k2_autgroup(X1)
| ! [X3] :
( ~ m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ! [X4] :
( ~ m2_fraenkel(X4,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| k2_binop_1(k1_autgroup(X1),k1_autgroup(X1),k1_autgroup(X1),X2,X3,X4) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X4,X3) ) ) )
& ( ? [X3] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
& ? [X4] :
( m2_fraenkel(X4,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
& k2_binop_1(k1_autgroup(X1),k1_autgroup(X1),k1_autgroup(X1),X2,X3,X4) != k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X4,X3) ) )
| X2 = k2_autgroup(X1) ) ) ) ),
inference(fof_nnf,[status(thm)],[94]) ).
fof(261,plain,
! [X5] :
( v3_struct_0(X5)
| ~ v1_group_1(X5)
| ~ v3_group_1(X5)
| ~ v4_group_1(X5)
| ~ l1_group_1(X5)
| ! [X6] :
( ~ v1_funct_1(X6)
| ~ v1_funct_2(X6,k2_zfmisc_1(k1_autgroup(X5),k1_autgroup(X5)),k1_autgroup(X5))
| ~ m2_relset_1(X6,k2_zfmisc_1(k1_autgroup(X5),k1_autgroup(X5)),k1_autgroup(X5))
| ( ( X6 != k2_autgroup(X5)
| ! [X7] :
( ~ m2_fraenkel(X7,u1_struct_0(X5),u1_struct_0(X5),k1_autgroup(X5))
| ! [X8] :
( ~ m2_fraenkel(X8,u1_struct_0(X5),u1_struct_0(X5),k1_autgroup(X5))
| k2_binop_1(k1_autgroup(X5),k1_autgroup(X5),k1_autgroup(X5),X6,X7,X8) = k7_funct_2(u1_struct_0(X5),u1_struct_0(X5),u1_struct_0(X5),X8,X7) ) ) )
& ( ? [X9] :
( m2_fraenkel(X9,u1_struct_0(X5),u1_struct_0(X5),k1_autgroup(X5))
& ? [X10] :
( m2_fraenkel(X10,u1_struct_0(X5),u1_struct_0(X5),k1_autgroup(X5))
& k2_binop_1(k1_autgroup(X5),k1_autgroup(X5),k1_autgroup(X5),X6,X9,X10) != k7_funct_2(u1_struct_0(X5),u1_struct_0(X5),u1_struct_0(X5),X10,X9) ) )
| X6 = k2_autgroup(X5) ) ) ) ),
inference(variable_rename,[status(thm)],[260]) ).
fof(262,plain,
! [X5] :
( v3_struct_0(X5)
| ~ v1_group_1(X5)
| ~ v3_group_1(X5)
| ~ v4_group_1(X5)
| ~ l1_group_1(X5)
| ! [X6] :
( ~ v1_funct_1(X6)
| ~ v1_funct_2(X6,k2_zfmisc_1(k1_autgroup(X5),k1_autgroup(X5)),k1_autgroup(X5))
| ~ m2_relset_1(X6,k2_zfmisc_1(k1_autgroup(X5),k1_autgroup(X5)),k1_autgroup(X5))
| ( ( X6 != k2_autgroup(X5)
| ! [X7] :
( ~ m2_fraenkel(X7,u1_struct_0(X5),u1_struct_0(X5),k1_autgroup(X5))
| ! [X8] :
( ~ m2_fraenkel(X8,u1_struct_0(X5),u1_struct_0(X5),k1_autgroup(X5))
| k2_binop_1(k1_autgroup(X5),k1_autgroup(X5),k1_autgroup(X5),X6,X7,X8) = k7_funct_2(u1_struct_0(X5),u1_struct_0(X5),u1_struct_0(X5),X8,X7) ) ) )
& ( ( m2_fraenkel(esk15_2(X5,X6),u1_struct_0(X5),u1_struct_0(X5),k1_autgroup(X5))
& m2_fraenkel(esk16_2(X5,X6),u1_struct_0(X5),u1_struct_0(X5),k1_autgroup(X5))
& k2_binop_1(k1_autgroup(X5),k1_autgroup(X5),k1_autgroup(X5),X6,esk15_2(X5,X6),esk16_2(X5,X6)) != k7_funct_2(u1_struct_0(X5),u1_struct_0(X5),u1_struct_0(X5),esk16_2(X5,X6),esk15_2(X5,X6)) )
| X6 = k2_autgroup(X5) ) ) ) ),
inference(skolemize,[status(esa)],[261]) ).
fof(263,plain,
! [X5,X6,X7,X8] :
( ( ( ~ m2_fraenkel(X8,u1_struct_0(X5),u1_struct_0(X5),k1_autgroup(X5))
| k2_binop_1(k1_autgroup(X5),k1_autgroup(X5),k1_autgroup(X5),X6,X7,X8) = k7_funct_2(u1_struct_0(X5),u1_struct_0(X5),u1_struct_0(X5),X8,X7)
| ~ m2_fraenkel(X7,u1_struct_0(X5),u1_struct_0(X5),k1_autgroup(X5))
| X6 != k2_autgroup(X5) )
& ( ( m2_fraenkel(esk15_2(X5,X6),u1_struct_0(X5),u1_struct_0(X5),k1_autgroup(X5))
& m2_fraenkel(esk16_2(X5,X6),u1_struct_0(X5),u1_struct_0(X5),k1_autgroup(X5))
& k2_binop_1(k1_autgroup(X5),k1_autgroup(X5),k1_autgroup(X5),X6,esk15_2(X5,X6),esk16_2(X5,X6)) != k7_funct_2(u1_struct_0(X5),u1_struct_0(X5),u1_struct_0(X5),esk16_2(X5,X6),esk15_2(X5,X6)) )
| X6 = k2_autgroup(X5) ) )
| ~ v1_funct_1(X6)
| ~ v1_funct_2(X6,k2_zfmisc_1(k1_autgroup(X5),k1_autgroup(X5)),k1_autgroup(X5))
| ~ m2_relset_1(X6,k2_zfmisc_1(k1_autgroup(X5),k1_autgroup(X5)),k1_autgroup(X5))
| v3_struct_0(X5)
| ~ v1_group_1(X5)
| ~ v3_group_1(X5)
| ~ v4_group_1(X5)
| ~ l1_group_1(X5) ),
inference(shift_quantors,[status(thm)],[262]) ).
fof(264,plain,
! [X5,X6,X7,X8] :
( ( ~ m2_fraenkel(X8,u1_struct_0(X5),u1_struct_0(X5),k1_autgroup(X5))
| k2_binop_1(k1_autgroup(X5),k1_autgroup(X5),k1_autgroup(X5),X6,X7,X8) = k7_funct_2(u1_struct_0(X5),u1_struct_0(X5),u1_struct_0(X5),X8,X7)
| ~ m2_fraenkel(X7,u1_struct_0(X5),u1_struct_0(X5),k1_autgroup(X5))
| X6 != k2_autgroup(X5)
| ~ v1_funct_1(X6)
| ~ v1_funct_2(X6,k2_zfmisc_1(k1_autgroup(X5),k1_autgroup(X5)),k1_autgroup(X5))
| ~ m2_relset_1(X6,k2_zfmisc_1(k1_autgroup(X5),k1_autgroup(X5)),k1_autgroup(X5))
| v3_struct_0(X5)
| ~ v1_group_1(X5)
| ~ v3_group_1(X5)
| ~ v4_group_1(X5)
| ~ l1_group_1(X5) )
& ( m2_fraenkel(esk15_2(X5,X6),u1_struct_0(X5),u1_struct_0(X5),k1_autgroup(X5))
| X6 = k2_autgroup(X5)
| ~ v1_funct_1(X6)
| ~ v1_funct_2(X6,k2_zfmisc_1(k1_autgroup(X5),k1_autgroup(X5)),k1_autgroup(X5))
| ~ m2_relset_1(X6,k2_zfmisc_1(k1_autgroup(X5),k1_autgroup(X5)),k1_autgroup(X5))
| v3_struct_0(X5)
| ~ v1_group_1(X5)
| ~ v3_group_1(X5)
| ~ v4_group_1(X5)
| ~ l1_group_1(X5) )
& ( m2_fraenkel(esk16_2(X5,X6),u1_struct_0(X5),u1_struct_0(X5),k1_autgroup(X5))
| X6 = k2_autgroup(X5)
| ~ v1_funct_1(X6)
| ~ v1_funct_2(X6,k2_zfmisc_1(k1_autgroup(X5),k1_autgroup(X5)),k1_autgroup(X5))
| ~ m2_relset_1(X6,k2_zfmisc_1(k1_autgroup(X5),k1_autgroup(X5)),k1_autgroup(X5))
| v3_struct_0(X5)
| ~ v1_group_1(X5)
| ~ v3_group_1(X5)
| ~ v4_group_1(X5)
| ~ l1_group_1(X5) )
& ( k2_binop_1(k1_autgroup(X5),k1_autgroup(X5),k1_autgroup(X5),X6,esk15_2(X5,X6),esk16_2(X5,X6)) != k7_funct_2(u1_struct_0(X5),u1_struct_0(X5),u1_struct_0(X5),esk16_2(X5,X6),esk15_2(X5,X6))
| X6 = k2_autgroup(X5)
| ~ v1_funct_1(X6)
| ~ v1_funct_2(X6,k2_zfmisc_1(k1_autgroup(X5),k1_autgroup(X5)),k1_autgroup(X5))
| ~ m2_relset_1(X6,k2_zfmisc_1(k1_autgroup(X5),k1_autgroup(X5)),k1_autgroup(X5))
| v3_struct_0(X5)
| ~ v1_group_1(X5)
| ~ v3_group_1(X5)
| ~ v4_group_1(X5)
| ~ l1_group_1(X5) ) ),
inference(distribute,[status(thm)],[263]) ).
cnf(268,plain,
( v3_struct_0(X1)
| k2_binop_1(k1_autgroup(X1),k1_autgroup(X1),k1_autgroup(X1),X2,X3,X4) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X4,X3)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m2_relset_1(X2,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
| ~ v1_funct_2(X2,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
| ~ v1_funct_1(X2)
| X2 != k2_autgroup(X1)
| ~ m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ m2_fraenkel(X4,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ),
inference(split_conjunct,[status(thm)],[264]) ).
fof(269,plain,
! [X1,X2,X3] :
( ~ m1_fraenkel(X3,X1,X2)
| ( ~ v1_xboole_0(X3)
& v1_fraenkel(X3) ) ),
inference(fof_nnf,[status(thm)],[95]) ).
fof(270,plain,
! [X4,X5,X6] :
( ~ m1_fraenkel(X6,X4,X5)
| ( ~ v1_xboole_0(X6)
& v1_fraenkel(X6) ) ),
inference(variable_rename,[status(thm)],[269]) ).
fof(271,plain,
! [X4,X5,X6] :
( ( ~ v1_xboole_0(X6)
| ~ m1_fraenkel(X6,X4,X5) )
& ( v1_fraenkel(X6)
| ~ m1_fraenkel(X6,X4,X5) ) ),
inference(distribute,[status(thm)],[270]) ).
cnf(273,plain,
( ~ m1_fraenkel(X1,X2,X3)
| ~ v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[271]) ).
fof(296,plain,
! [X1] :
( v3_struct_0(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| m1_fraenkel(k1_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
inference(fof_nnf,[status(thm)],[97]) ).
fof(297,plain,
! [X2] :
( v3_struct_0(X2)
| ~ v1_group_1(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2)
| m1_fraenkel(k1_autgroup(X2),u1_struct_0(X2),u1_struct_0(X2)) ),
inference(variable_rename,[status(thm)],[296]) ).
cnf(298,plain,
( m1_fraenkel(k1_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1))
| v3_struct_0(X1)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[297]) ).
fof(340,plain,
! [X1] :
( ~ l1_group_1(X1)
| l1_struct_0(X1) ),
inference(fof_nnf,[status(thm)],[61]) ).
fof(341,plain,
! [X2] :
( ~ l1_group_1(X2)
| l1_struct_0(X2) ),
inference(variable_rename,[status(thm)],[340]) ).
cnf(342,plain,
( l1_struct_0(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[341]) ).
fof(352,plain,
! [X1] :
( v3_struct_0(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ! [X2] :
( ~ m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
| m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ) ),
inference(fof_nnf,[status(thm)],[101]) ).
fof(353,plain,
! [X3] :
( v3_struct_0(X3)
| ~ v1_group_1(X3)
| ~ v3_group_1(X3)
| ~ v4_group_1(X3)
| ~ l1_group_1(X3)
| ! [X4] :
( ~ m2_fraenkel(X4,u1_struct_0(X3),u1_struct_0(X3),k4_autgroup(X3))
| m2_fraenkel(X4,u1_struct_0(X3),u1_struct_0(X3),k1_autgroup(X3)) ) ),
inference(variable_rename,[status(thm)],[352]) ).
fof(354,plain,
! [X3,X4] :
( ~ m2_fraenkel(X4,u1_struct_0(X3),u1_struct_0(X3),k4_autgroup(X3))
| m2_fraenkel(X4,u1_struct_0(X3),u1_struct_0(X3),k1_autgroup(X3))
| v3_struct_0(X3)
| ~ v1_group_1(X3)
| ~ v3_group_1(X3)
| ~ v4_group_1(X3)
| ~ l1_group_1(X3) ),
inference(shift_quantors,[status(thm)],[353]) ).
cnf(355,plain,
( v3_struct_0(X1)
| m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1)) ),
inference(split_conjunct,[status(thm)],[354]) ).
fof(367,plain,
! [X1,X2,X3] :
( v1_xboole_0(X2)
| ~ m1_fraenkel(X3,X1,X2)
| ! [X4] :
( ( ~ m2_fraenkel(X4,X1,X2,X3)
| m1_subset_1(X4,X3) )
& ( ~ m1_subset_1(X4,X3)
| m2_fraenkel(X4,X1,X2,X3) ) ) ),
inference(fof_nnf,[status(thm)],[103]) ).
fof(368,plain,
! [X5,X6,X7] :
( v1_xboole_0(X6)
| ~ m1_fraenkel(X7,X5,X6)
| ! [X8] :
( ( ~ m2_fraenkel(X8,X5,X6,X7)
| m1_subset_1(X8,X7) )
& ( ~ m1_subset_1(X8,X7)
| m2_fraenkel(X8,X5,X6,X7) ) ) ),
inference(variable_rename,[status(thm)],[367]) ).
fof(369,plain,
! [X5,X6,X7,X8] :
( ( ( ~ m2_fraenkel(X8,X5,X6,X7)
| m1_subset_1(X8,X7) )
& ( ~ m1_subset_1(X8,X7)
| m2_fraenkel(X8,X5,X6,X7) ) )
| v1_xboole_0(X6)
| ~ m1_fraenkel(X7,X5,X6) ),
inference(shift_quantors,[status(thm)],[368]) ).
fof(370,plain,
! [X5,X6,X7,X8] :
( ( ~ m2_fraenkel(X8,X5,X6,X7)
| m1_subset_1(X8,X7)
| v1_xboole_0(X6)
| ~ m1_fraenkel(X7,X5,X6) )
& ( ~ m1_subset_1(X8,X7)
| m2_fraenkel(X8,X5,X6,X7)
| v1_xboole_0(X6)
| ~ m1_fraenkel(X7,X5,X6) ) ),
inference(distribute,[status(thm)],[369]) ).
cnf(371,plain,
( v1_xboole_0(X3)
| m2_fraenkel(X4,X2,X3,X1)
| ~ m1_fraenkel(X1,X2,X3)
| ~ m1_subset_1(X4,X1) ),
inference(split_conjunct,[status(thm)],[370]) ).
cnf(372,plain,
( v1_xboole_0(X3)
| m1_subset_1(X4,X1)
| ~ m1_fraenkel(X1,X2,X3)
| ~ m2_fraenkel(X4,X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[370]) ).
fof(373,plain,
! [X1] :
( v3_struct_0(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ( v1_funct_1(k2_autgroup(X1))
& v1_funct_2(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
& m2_relset_1(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1)) ) ),
inference(fof_nnf,[status(thm)],[104]) ).
fof(374,plain,
! [X2] :
( v3_struct_0(X2)
| ~ v1_group_1(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2)
| ( v1_funct_1(k2_autgroup(X2))
& v1_funct_2(k2_autgroup(X2),k2_zfmisc_1(k1_autgroup(X2),k1_autgroup(X2)),k1_autgroup(X2))
& m2_relset_1(k2_autgroup(X2),k2_zfmisc_1(k1_autgroup(X2),k1_autgroup(X2)),k1_autgroup(X2)) ) ),
inference(variable_rename,[status(thm)],[373]) ).
fof(375,plain,
! [X2] :
( ( v1_funct_1(k2_autgroup(X2))
| v3_struct_0(X2)
| ~ v1_group_1(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2) )
& ( v1_funct_2(k2_autgroup(X2),k2_zfmisc_1(k1_autgroup(X2),k1_autgroup(X2)),k1_autgroup(X2))
| v3_struct_0(X2)
| ~ v1_group_1(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2) )
& ( m2_relset_1(k2_autgroup(X2),k2_zfmisc_1(k1_autgroup(X2),k1_autgroup(X2)),k1_autgroup(X2))
| v3_struct_0(X2)
| ~ v1_group_1(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2) ) ),
inference(distribute,[status(thm)],[374]) ).
cnf(376,plain,
( v3_struct_0(X1)
| m2_relset_1(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[375]) ).
cnf(377,plain,
( v3_struct_0(X1)
| v1_funct_2(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[375]) ).
cnf(378,plain,
( v3_struct_0(X1)
| v1_funct_1(k2_autgroup(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[375]) ).
cnf(422,plain,
( v3_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1))
| ~ l1_group_1(X1) ),
inference(spm,[status(thm)],[195,342,theory(equality)]) ).
cnf(459,plain,
( v3_struct_0(X1)
| ~ v1_xboole_0(k1_autgroup(X1))
| ~ v4_group_1(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ l1_group_1(X1) ),
inference(spm,[status(thm)],[273,298,theory(equality)]) ).
cnf(467,plain,
( m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),k1_autgroup(X2))
| v1_xboole_0(u1_struct_0(X2))
| v3_struct_0(X2)
| ~ m1_subset_1(X1,k1_autgroup(X2))
| ~ v4_group_1(X2)
| ~ v1_group_1(X2)
| ~ v3_group_1(X2)
| ~ l1_group_1(X2) ),
inference(spm,[status(thm)],[371,298,theory(equality)]) ).
cnf(477,negated_conjecture,
( m2_fraenkel(esk9_0,u1_struct_0(esk8_0),u1_struct_0(esk8_0),k1_autgroup(esk8_0))
| v3_struct_0(esk8_0)
| ~ v4_group_1(esk8_0)
| ~ v1_group_1(esk8_0)
| ~ v3_group_1(esk8_0)
| ~ l1_group_1(esk8_0) ),
inference(spm,[status(thm)],[355,207,theory(equality)]) ).
cnf(478,negated_conjecture,
( m2_fraenkel(esk10_0,u1_struct_0(esk8_0),u1_struct_0(esk8_0),k1_autgroup(esk8_0))
| v3_struct_0(esk8_0)
| ~ v4_group_1(esk8_0)
| ~ v1_group_1(esk8_0)
| ~ v3_group_1(esk8_0)
| ~ l1_group_1(esk8_0) ),
inference(spm,[status(thm)],[355,206,theory(equality)]) ).
cnf(480,negated_conjecture,
( m2_fraenkel(esk9_0,u1_struct_0(esk8_0),u1_struct_0(esk8_0),k1_autgroup(esk8_0))
| v3_struct_0(esk8_0)
| $false
| ~ v1_group_1(esk8_0)
| ~ v3_group_1(esk8_0)
| ~ l1_group_1(esk8_0) ),
inference(rw,[status(thm)],[477,209,theory(equality)]) ).
cnf(481,negated_conjecture,
( m2_fraenkel(esk9_0,u1_struct_0(esk8_0),u1_struct_0(esk8_0),k1_autgroup(esk8_0))
| v3_struct_0(esk8_0)
| $false
| $false
| ~ v3_group_1(esk8_0)
| ~ l1_group_1(esk8_0) ),
inference(rw,[status(thm)],[480,211,theory(equality)]) ).
cnf(482,negated_conjecture,
( m2_fraenkel(esk9_0,u1_struct_0(esk8_0),u1_struct_0(esk8_0),k1_autgroup(esk8_0))
| v3_struct_0(esk8_0)
| $false
| $false
| $false
| ~ l1_group_1(esk8_0) ),
inference(rw,[status(thm)],[481,210,theory(equality)]) ).
cnf(483,negated_conjecture,
( m2_fraenkel(esk9_0,u1_struct_0(esk8_0),u1_struct_0(esk8_0),k1_autgroup(esk8_0))
| v3_struct_0(esk8_0)
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[482,208,theory(equality)]) ).
cnf(484,negated_conjecture,
( m2_fraenkel(esk9_0,u1_struct_0(esk8_0),u1_struct_0(esk8_0),k1_autgroup(esk8_0))
| v3_struct_0(esk8_0) ),
inference(cn,[status(thm)],[483,theory(equality)]) ).
cnf(485,negated_conjecture,
m2_fraenkel(esk9_0,u1_struct_0(esk8_0),u1_struct_0(esk8_0),k1_autgroup(esk8_0)),
inference(sr,[status(thm)],[484,212,theory(equality)]) ).
cnf(486,negated_conjecture,
( m2_fraenkel(esk10_0,u1_struct_0(esk8_0),u1_struct_0(esk8_0),k1_autgroup(esk8_0))
| v3_struct_0(esk8_0)
| $false
| ~ v1_group_1(esk8_0)
| ~ v3_group_1(esk8_0)
| ~ l1_group_1(esk8_0) ),
inference(rw,[status(thm)],[478,209,theory(equality)]) ).
cnf(487,negated_conjecture,
( m2_fraenkel(esk10_0,u1_struct_0(esk8_0),u1_struct_0(esk8_0),k1_autgroup(esk8_0))
| v3_struct_0(esk8_0)
| $false
| $false
| ~ v3_group_1(esk8_0)
| ~ l1_group_1(esk8_0) ),
inference(rw,[status(thm)],[486,211,theory(equality)]) ).
cnf(488,negated_conjecture,
( m2_fraenkel(esk10_0,u1_struct_0(esk8_0),u1_struct_0(esk8_0),k1_autgroup(esk8_0))
| v3_struct_0(esk8_0)
| $false
| $false
| $false
| ~ l1_group_1(esk8_0) ),
inference(rw,[status(thm)],[487,210,theory(equality)]) ).
cnf(489,negated_conjecture,
( m2_fraenkel(esk10_0,u1_struct_0(esk8_0),u1_struct_0(esk8_0),k1_autgroup(esk8_0))
| v3_struct_0(esk8_0)
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[488,208,theory(equality)]) ).
cnf(490,negated_conjecture,
( m2_fraenkel(esk10_0,u1_struct_0(esk8_0),u1_struct_0(esk8_0),k1_autgroup(esk8_0))
| v3_struct_0(esk8_0) ),
inference(cn,[status(thm)],[489,theory(equality)]) ).
cnf(491,negated_conjecture,
m2_fraenkel(esk10_0,u1_struct_0(esk8_0),u1_struct_0(esk8_0),k1_autgroup(esk8_0)),
inference(sr,[status(thm)],[490,212,theory(equality)]) ).
cnf(498,plain,
( m1_relset_1(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
| v3_struct_0(X1)
| ~ v4_group_1(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ l1_group_1(X1) ),
inference(spm,[status(thm)],[134,376,theory(equality)]) ).
cnf(570,plain,
( k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X4,X3) = k1_binop_1(X2,X3,X4)
| v1_xboole_0(k1_autgroup(X1))
| v3_struct_0(X1)
| ~ m1_relset_1(X2,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
| ~ v1_funct_2(X2,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
| ~ v1_funct_1(X2)
| ~ m1_subset_1(X4,k1_autgroup(X1))
| ~ m1_subset_1(X3,k1_autgroup(X1))
| k2_autgroup(X1) != X2
| ~ m2_fraenkel(X4,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ v4_group_1(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ l1_group_1(X1)
| ~ m2_relset_1(X2,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1)) ),
inference(spm,[status(thm)],[119,268,theory(equality)]) ).
cnf(577,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk8_0))
| m1_subset_1(esk9_0,k1_autgroup(esk8_0))
| ~ m1_fraenkel(k1_autgroup(esk8_0),u1_struct_0(esk8_0),u1_struct_0(esk8_0)) ),
inference(spm,[status(thm)],[372,485,theory(equality)]) ).
cnf(581,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk8_0))
| m1_subset_1(esk10_0,k1_autgroup(esk8_0))
| ~ m1_fraenkel(k1_autgroup(esk8_0),u1_struct_0(esk8_0),u1_struct_0(esk8_0)) ),
inference(spm,[status(thm)],[372,491,theory(equality)]) ).
cnf(617,negated_conjecture,
( ~ l1_group_1(esk8_0)
| ~ v1_xboole_0(u1_struct_0(esk8_0)) ),
inference(spm,[status(thm)],[212,422,theory(equality)]) ).
cnf(621,negated_conjecture,
( $false
| ~ v1_xboole_0(u1_struct_0(esk8_0)) ),
inference(rw,[status(thm)],[617,208,theory(equality)]) ).
cnf(622,negated_conjecture,
~ v1_xboole_0(u1_struct_0(esk8_0)),
inference(cn,[status(thm)],[621,theory(equality)]) ).
cnf(1009,plain,
( m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),k1_autgroup(X2))
| v3_struct_0(X2)
| ~ v4_group_1(X2)
| ~ v1_group_1(X2)
| ~ v3_group_1(X2)
| ~ l1_group_1(X2)
| ~ m1_subset_1(X1,k1_autgroup(X2)) ),
inference(csr,[status(thm)],[467,422]) ).
cnf(1048,negated_conjecture,
( m1_subset_1(esk9_0,k1_autgroup(esk8_0))
| ~ m1_fraenkel(k1_autgroup(esk8_0),u1_struct_0(esk8_0),u1_struct_0(esk8_0)) ),
inference(sr,[status(thm)],[577,622,theory(equality)]) ).
cnf(1049,negated_conjecture,
( m1_subset_1(esk9_0,k1_autgroup(esk8_0))
| v3_struct_0(esk8_0)
| ~ v4_group_1(esk8_0)
| ~ v1_group_1(esk8_0)
| ~ v3_group_1(esk8_0)
| ~ l1_group_1(esk8_0) ),
inference(spm,[status(thm)],[1048,298,theory(equality)]) ).
cnf(1050,negated_conjecture,
( m1_subset_1(esk9_0,k1_autgroup(esk8_0))
| v3_struct_0(esk8_0)
| $false
| ~ v1_group_1(esk8_0)
| ~ v3_group_1(esk8_0)
| ~ l1_group_1(esk8_0) ),
inference(rw,[status(thm)],[1049,209,theory(equality)]) ).
cnf(1051,negated_conjecture,
( m1_subset_1(esk9_0,k1_autgroup(esk8_0))
| v3_struct_0(esk8_0)
| $false
| $false
| ~ v3_group_1(esk8_0)
| ~ l1_group_1(esk8_0) ),
inference(rw,[status(thm)],[1050,211,theory(equality)]) ).
cnf(1052,negated_conjecture,
( m1_subset_1(esk9_0,k1_autgroup(esk8_0))
| v3_struct_0(esk8_0)
| $false
| $false
| $false
| ~ l1_group_1(esk8_0) ),
inference(rw,[status(thm)],[1051,210,theory(equality)]) ).
cnf(1053,negated_conjecture,
( m1_subset_1(esk9_0,k1_autgroup(esk8_0))
| v3_struct_0(esk8_0)
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[1052,208,theory(equality)]) ).
cnf(1054,negated_conjecture,
( m1_subset_1(esk9_0,k1_autgroup(esk8_0))
| v3_struct_0(esk8_0) ),
inference(cn,[status(thm)],[1053,theory(equality)]) ).
cnf(1055,negated_conjecture,
m1_subset_1(esk9_0,k1_autgroup(esk8_0)),
inference(sr,[status(thm)],[1054,212,theory(equality)]) ).
cnf(1076,negated_conjecture,
( m1_subset_1(esk10_0,k1_autgroup(esk8_0))
| ~ m1_fraenkel(k1_autgroup(esk8_0),u1_struct_0(esk8_0),u1_struct_0(esk8_0)) ),
inference(sr,[status(thm)],[581,622,theory(equality)]) ).
cnf(1077,negated_conjecture,
( m1_subset_1(esk10_0,k1_autgroup(esk8_0))
| v3_struct_0(esk8_0)
| ~ v4_group_1(esk8_0)
| ~ v1_group_1(esk8_0)
| ~ v3_group_1(esk8_0)
| ~ l1_group_1(esk8_0) ),
inference(spm,[status(thm)],[1076,298,theory(equality)]) ).
cnf(1078,negated_conjecture,
( m1_subset_1(esk10_0,k1_autgroup(esk8_0))
| v3_struct_0(esk8_0)
| $false
| ~ v1_group_1(esk8_0)
| ~ v3_group_1(esk8_0)
| ~ l1_group_1(esk8_0) ),
inference(rw,[status(thm)],[1077,209,theory(equality)]) ).
cnf(1079,negated_conjecture,
( m1_subset_1(esk10_0,k1_autgroup(esk8_0))
| v3_struct_0(esk8_0)
| $false
| $false
| ~ v3_group_1(esk8_0)
| ~ l1_group_1(esk8_0) ),
inference(rw,[status(thm)],[1078,211,theory(equality)]) ).
cnf(1080,negated_conjecture,
( m1_subset_1(esk10_0,k1_autgroup(esk8_0))
| v3_struct_0(esk8_0)
| $false
| $false
| $false
| ~ l1_group_1(esk8_0) ),
inference(rw,[status(thm)],[1079,210,theory(equality)]) ).
cnf(1081,negated_conjecture,
( m1_subset_1(esk10_0,k1_autgroup(esk8_0))
| v3_struct_0(esk8_0)
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[1080,208,theory(equality)]) ).
cnf(1082,negated_conjecture,
( m1_subset_1(esk10_0,k1_autgroup(esk8_0))
| v3_struct_0(esk8_0) ),
inference(cn,[status(thm)],[1081,theory(equality)]) ).
cnf(1083,negated_conjecture,
m1_subset_1(esk10_0,k1_autgroup(esk8_0)),
inference(sr,[status(thm)],[1082,212,theory(equality)]) ).
cnf(3085,plain,
( k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X4,X3) = k1_binop_1(X2,X3,X4)
| v3_struct_0(X1)
| v1_xboole_0(k1_autgroup(X1))
| k2_autgroup(X1) != X2
| ~ m2_fraenkel(X4,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ v4_group_1(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_relset_1(X2,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
| ~ v1_funct_2(X2,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
| ~ v1_funct_1(X2)
| ~ m1_subset_1(X4,k1_autgroup(X1))
| ~ m1_subset_1(X3,k1_autgroup(X1)) ),
inference(csr,[status(thm)],[570,133]) ).
cnf(3086,plain,
( k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X4,X3) = k1_binop_1(X2,X3,X4)
| v3_struct_0(X1)
| v1_xboole_0(k1_autgroup(X1))
| k2_autgroup(X1) != X2
| ~ m2_fraenkel(X4,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ v4_group_1(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_relset_1(X2,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
| ~ v1_funct_2(X2,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
| ~ v1_funct_1(X2)
| ~ m1_subset_1(X4,k1_autgroup(X1))
| ~ m1_subset_1(X3,k1_autgroup(X1)) ),
inference(csr,[status(thm)],[3085,1009]) ).
cnf(3087,plain,
( k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X4,X3) = k1_binop_1(X2,X3,X4)
| v3_struct_0(X1)
| v1_xboole_0(k1_autgroup(X1))
| k2_autgroup(X1) != X2
| ~ v4_group_1(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_relset_1(X2,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
| ~ v1_funct_2(X2,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
| ~ v1_funct_1(X2)
| ~ m1_subset_1(X4,k1_autgroup(X1))
| ~ m1_subset_1(X3,k1_autgroup(X1)) ),
inference(csr,[status(thm)],[3086,1009]) ).
cnf(3088,plain,
( k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X4,X3) = k1_binop_1(X2,X3,X4)
| v3_struct_0(X1)
| k2_autgroup(X1) != X2
| ~ v4_group_1(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_relset_1(X2,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
| ~ v1_funct_2(X2,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
| ~ v1_funct_1(X2)
| ~ m1_subset_1(X4,k1_autgroup(X1))
| ~ m1_subset_1(X3,k1_autgroup(X1)) ),
inference(csr,[status(thm)],[3087,459]) ).
cnf(3096,plain,
( k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X2,X3) = k1_binop_1(k2_autgroup(X1),X3,X2)
| v3_struct_0(X1)
| ~ v4_group_1(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ l1_group_1(X1)
| ~ v1_funct_2(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
| ~ v1_funct_1(k2_autgroup(X1))
| ~ m1_subset_1(X2,k1_autgroup(X1))
| ~ m1_subset_1(X3,k1_autgroup(X1)) ),
inference(spm,[status(thm)],[3088,498,theory(equality)]) ).
cnf(27667,plain,
( k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X2,X3) = k1_binop_1(k2_autgroup(X1),X3,X2)
| v3_struct_0(X1)
| ~ v4_group_1(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ l1_group_1(X1)
| ~ v1_funct_2(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
| ~ m1_subset_1(X2,k1_autgroup(X1))
| ~ m1_subset_1(X3,k1_autgroup(X1)) ),
inference(csr,[status(thm)],[3096,378]) ).
cnf(27668,plain,
( k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X2,X3) = k1_binop_1(k2_autgroup(X1),X3,X2)
| v3_struct_0(X1)
| ~ v4_group_1(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_subset_1(X2,k1_autgroup(X1))
| ~ m1_subset_1(X3,k1_autgroup(X1)) ),
inference(csr,[status(thm)],[27667,377]) ).
cnf(27670,negated_conjecture,
( v3_struct_0(esk8_0)
| ~ v4_group_1(esk8_0)
| ~ v1_group_1(esk8_0)
| ~ v3_group_1(esk8_0)
| ~ l1_group_1(esk8_0)
| ~ m1_subset_1(esk10_0,k1_autgroup(esk8_0))
| ~ m1_subset_1(esk9_0,k1_autgroup(esk8_0)) ),
inference(spm,[status(thm)],[205,27668,theory(equality)]) ).
cnf(27698,negated_conjecture,
( v3_struct_0(esk8_0)
| $false
| ~ v1_group_1(esk8_0)
| ~ v3_group_1(esk8_0)
| ~ l1_group_1(esk8_0)
| ~ m1_subset_1(esk10_0,k1_autgroup(esk8_0))
| ~ m1_subset_1(esk9_0,k1_autgroup(esk8_0)) ),
inference(rw,[status(thm)],[27670,209,theory(equality)]) ).
cnf(27699,negated_conjecture,
( v3_struct_0(esk8_0)
| $false
| $false
| ~ v3_group_1(esk8_0)
| ~ l1_group_1(esk8_0)
| ~ m1_subset_1(esk10_0,k1_autgroup(esk8_0))
| ~ m1_subset_1(esk9_0,k1_autgroup(esk8_0)) ),
inference(rw,[status(thm)],[27698,211,theory(equality)]) ).
cnf(27700,negated_conjecture,
( v3_struct_0(esk8_0)
| $false
| $false
| $false
| ~ l1_group_1(esk8_0)
| ~ m1_subset_1(esk10_0,k1_autgroup(esk8_0))
| ~ m1_subset_1(esk9_0,k1_autgroup(esk8_0)) ),
inference(rw,[status(thm)],[27699,210,theory(equality)]) ).
cnf(27701,negated_conjecture,
( v3_struct_0(esk8_0)
| $false
| $false
| $false
| $false
| ~ m1_subset_1(esk10_0,k1_autgroup(esk8_0))
| ~ m1_subset_1(esk9_0,k1_autgroup(esk8_0)) ),
inference(rw,[status(thm)],[27700,208,theory(equality)]) ).
cnf(27702,negated_conjecture,
( v3_struct_0(esk8_0)
| $false
| $false
| $false
| $false
| $false
| ~ m1_subset_1(esk9_0,k1_autgroup(esk8_0)) ),
inference(rw,[status(thm)],[27701,1083,theory(equality)]) ).
cnf(27703,negated_conjecture,
( v3_struct_0(esk8_0)
| $false
| $false
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[27702,1055,theory(equality)]) ).
cnf(27704,negated_conjecture,
v3_struct_0(esk8_0),
inference(cn,[status(thm)],[27703,theory(equality)]) ).
cnf(27705,negated_conjecture,
$false,
inference(sr,[status(thm)],[27704,212,theory(equality)]) ).
cnf(27706,negated_conjecture,
$false,
27705,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRP/GRP624+1.p
% --creating new selector for []
% -running prover on /tmp/tmpsDcBWj/sel_GRP624+1.p_1 with time limit 29
% -prover status Theorem
% Problem GRP624+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRP/GRP624+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRP/GRP624+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
%
%------------------------------------------------------------------------------