TSTP Solution File: GRP623+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GRP623+1 : TPTP v5.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 10:14:20 EST 2010
% Result : Theorem 1.24s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 15
% Syntax : Number of formulae : 123 ( 11 unt; 0 def)
% Number of atoms : 532 ( 4 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 665 ( 256 ~; 284 |; 95 &)
% ( 4 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 187 ( 2 sgn 123 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(7,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
<=> m1_relset_1(X3,X1,X2) ),
file('/tmp/tmpEO4pNe/sel_GRP623+1.p_1',redefinition_m2_relset_1) ).
fof(12,axiom,
! [X1,X2] :
( r2_hidden(X1,X2)
=> m1_subset_1(X1,X2) ),
file('/tmp/tmpEO4pNe/sel_GRP623+1.p_1',t1_subset) ).
fof(13,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> m1_fraenkel(k4_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
file('/tmp/tmpEO4pNe/sel_GRP623+1.p_1',dt_k4_autgroup) ).
fof(14,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> r1_tarski(k4_autgroup(X1),k1_autgroup(X1)) ),
file('/tmp/tmpEO4pNe/sel_GRP623+1.p_1',t14_autgroup) ).
fof(21,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
file('/tmp/tmpEO4pNe/sel_GRP623+1.p_1',fc1_struct_0) ).
fof(34,axiom,
! [X1,X2,X3] :
( m1_fraenkel(X3,X1,X2)
=> ( ~ v1_xboole_0(X3)
& v1_fraenkel(X3) ) ),
file('/tmp/tmpEO4pNe/sel_GRP623+1.p_1',dt_m1_fraenkel) ).
fof(40,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/tmpEO4pNe/sel_GRP623+1.p_1',dt_k1_autgroup) ).
fof(43,axiom,
! [X1,X2] :
( m1_subset_1(X1,X2)
=> ( v1_xboole_0(X2)
| r2_hidden(X1,X2) ) ),
file('/tmp/tmpEO4pNe/sel_GRP623+1.p_1',t2_subset) ).
fof(47,axiom,
! [X1,X2] :
( ( ~ v1_xboole_0(X1)
& v1_funct_1(X2)
& v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
& m1_relset_1(X2,k2_zfmisc_1(X1,X1),X1) )
=> ( ~ v3_struct_0(g1_group_1(X1,X2))
& v1_group_1(g1_group_1(X1,X2)) ) ),
file('/tmp/tmpEO4pNe/sel_GRP623+1.p_1',fc1_group_1) ).
fof(48,axiom,
! [X1] :
( l1_group_1(X1)
=> l1_struct_0(X1) ),
file('/tmp/tmpEO4pNe/sel_GRP623+1.p_1',dt_l1_group_1) ).
fof(53,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/tmpEO4pNe/sel_GRP623+1.p_1',t13_autgroup) ).
fof(55,axiom,
! [X1] :
( l1_group_1(X1)
=> ( v1_group_1(X1)
=> X1 = g1_group_1(u1_struct_0(X1),u1_group_1(X1)) ) ),
file('/tmp/tmpEO4pNe/sel_GRP623+1.p_1',abstractness_v1_group_1) ).
fof(58,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/tmpEO4pNe/sel_GRP623+1.p_1',redefinition_m2_fraenkel) ).
fof(60,axiom,
! [X1] :
( l1_group_1(X1)
=> ( v1_funct_1(u1_group_1(X1))
& v1_funct_2(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
& m2_relset_1(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1)) ) ),
file('/tmp/tmpEO4pNe/sel_GRP623+1.p_1',dt_u1_group_1) ).
fof(62,axiom,
! [X1,X2] :
( r1_tarski(X1,X2)
<=> ! [X3] :
( r2_hidden(X3,X1)
=> r2_hidden(X3,X2) ) ),
file('/tmp/tmpEO4pNe/sel_GRP623+1.p_1',d3_tarski) ).
fof(65,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> r1_tarski(k4_autgroup(X1),k1_autgroup(X1)) ),
inference(assume_negation,[status(cth)],[14]) ).
fof(67,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> m1_fraenkel(k4_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[13,theory(equality)]) ).
fof(68,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> r1_tarski(k4_autgroup(X1),k1_autgroup(X1)) ),
inference(fof_simplification,[status(thm)],[65,theory(equality)]) ).
fof(71,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[21,theory(equality)]) ).
fof(75,plain,
! [X1,X2,X3] :
( m1_fraenkel(X3,X1,X2)
=> ( ~ v1_xboole_0(X3)
& v1_fraenkel(X3) ) ),
inference(fof_simplification,[status(thm)],[34,theory(equality)]) ).
fof(77,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)],[40,theory(equality)]) ).
fof(80,plain,
! [X1,X2] :
( ( ~ v1_xboole_0(X1)
& v1_funct_1(X2)
& v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
& m1_relset_1(X2,k2_zfmisc_1(X1,X1),X1) )
=> ( ~ v3_struct_0(g1_group_1(X1,X2))
& v1_group_1(g1_group_1(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[47,theory(equality)]) ).
fof(81,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)],[53,theory(equality)]) ).
fof(83,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)],[58,theory(equality)]) ).
fof(107,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)],[7]) ).
fof(108,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)],[107]) ).
cnf(110,plain,
( m1_relset_1(X1,X2,X3)
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[108]) ).
fof(128,plain,
! [X1,X2] :
( ~ r2_hidden(X1,X2)
| m1_subset_1(X1,X2) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(129,plain,
! [X3,X4] :
( ~ r2_hidden(X3,X4)
| m1_subset_1(X3,X4) ),
inference(variable_rename,[status(thm)],[128]) ).
cnf(130,plain,
( m1_subset_1(X1,X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[129]) ).
fof(131,plain,
! [X1] :
( v3_struct_0(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| m1_fraenkel(k4_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
inference(fof_nnf,[status(thm)],[67]) ).
fof(132,plain,
! [X2] :
( v3_struct_0(X2)
| ~ v1_group_1(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2)
| m1_fraenkel(k4_autgroup(X2),u1_struct_0(X2),u1_struct_0(X2)) ),
inference(variable_rename,[status(thm)],[131]) ).
cnf(133,plain,
( m1_fraenkel(k4_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)],[132]) ).
fof(134,negated_conjecture,
? [X1] :
( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1)
& ~ r1_tarski(k4_autgroup(X1),k1_autgroup(X1)) ),
inference(fof_nnf,[status(thm)],[68]) ).
fof(135,negated_conjecture,
? [X2] :
( ~ v3_struct_0(X2)
& v1_group_1(X2)
& v3_group_1(X2)
& v4_group_1(X2)
& l1_group_1(X2)
& ~ r1_tarski(k4_autgroup(X2),k1_autgroup(X2)) ),
inference(variable_rename,[status(thm)],[134]) ).
fof(136,negated_conjecture,
( ~ v3_struct_0(esk5_0)
& v1_group_1(esk5_0)
& v3_group_1(esk5_0)
& v4_group_1(esk5_0)
& l1_group_1(esk5_0)
& ~ r1_tarski(k4_autgroup(esk5_0),k1_autgroup(esk5_0)) ),
inference(skolemize,[status(esa)],[135]) ).
cnf(137,negated_conjecture,
~ r1_tarski(k4_autgroup(esk5_0),k1_autgroup(esk5_0)),
inference(split_conjunct,[status(thm)],[136]) ).
cnf(138,negated_conjecture,
l1_group_1(esk5_0),
inference(split_conjunct,[status(thm)],[136]) ).
cnf(139,negated_conjecture,
v4_group_1(esk5_0),
inference(split_conjunct,[status(thm)],[136]) ).
cnf(140,negated_conjecture,
v3_group_1(esk5_0),
inference(split_conjunct,[status(thm)],[136]) ).
cnf(141,negated_conjecture,
v1_group_1(esk5_0),
inference(split_conjunct,[status(thm)],[136]) ).
cnf(142,negated_conjecture,
~ v3_struct_0(esk5_0),
inference(split_conjunct,[status(thm)],[136]) ).
fof(166,plain,
! [X1] :
( v3_struct_0(X1)
| ~ l1_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(fof_nnf,[status(thm)],[71]) ).
fof(167,plain,
! [X2] :
( v3_struct_0(X2)
| ~ l1_struct_0(X2)
| ~ v1_xboole_0(u1_struct_0(X2)) ),
inference(variable_rename,[status(thm)],[166]) ).
cnf(168,plain,
( v3_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1))
| ~ l1_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[167]) ).
fof(221,plain,
! [X1,X2,X3] :
( ~ m1_fraenkel(X3,X1,X2)
| ( ~ v1_xboole_0(X3)
& v1_fraenkel(X3) ) ),
inference(fof_nnf,[status(thm)],[75]) ).
fof(222,plain,
! [X4,X5,X6] :
( ~ m1_fraenkel(X6,X4,X5)
| ( ~ v1_xboole_0(X6)
& v1_fraenkel(X6) ) ),
inference(variable_rename,[status(thm)],[221]) ).
fof(223,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)],[222]) ).
cnf(225,plain,
( ~ m1_fraenkel(X1,X2,X3)
| ~ v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[223]) ).
fof(245,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)],[77]) ).
fof(246,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)],[245]) ).
cnf(247,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)],[246]) ).
fof(252,plain,
! [X1,X2] :
( ~ m1_subset_1(X1,X2)
| v1_xboole_0(X2)
| r2_hidden(X1,X2) ),
inference(fof_nnf,[status(thm)],[43]) ).
fof(253,plain,
! [X3,X4] :
( ~ m1_subset_1(X3,X4)
| v1_xboole_0(X4)
| r2_hidden(X3,X4) ),
inference(variable_rename,[status(thm)],[252]) ).
cnf(254,plain,
( r2_hidden(X1,X2)
| v1_xboole_0(X2)
| ~ m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[253]) ).
fof(268,plain,
! [X1,X2] :
( v1_xboole_0(X1)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
| ~ m1_relset_1(X2,k2_zfmisc_1(X1,X1),X1)
| ( ~ v3_struct_0(g1_group_1(X1,X2))
& v1_group_1(g1_group_1(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[80]) ).
fof(269,plain,
! [X3,X4] :
( v1_xboole_0(X3)
| ~ v1_funct_1(X4)
| ~ v1_funct_2(X4,k2_zfmisc_1(X3,X3),X3)
| ~ m1_relset_1(X4,k2_zfmisc_1(X3,X3),X3)
| ( ~ v3_struct_0(g1_group_1(X3,X4))
& v1_group_1(g1_group_1(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[268]) ).
fof(270,plain,
! [X3,X4] :
( ( ~ v3_struct_0(g1_group_1(X3,X4))
| v1_xboole_0(X3)
| ~ v1_funct_1(X4)
| ~ v1_funct_2(X4,k2_zfmisc_1(X3,X3),X3)
| ~ m1_relset_1(X4,k2_zfmisc_1(X3,X3),X3) )
& ( v1_group_1(g1_group_1(X3,X4))
| v1_xboole_0(X3)
| ~ v1_funct_1(X4)
| ~ v1_funct_2(X4,k2_zfmisc_1(X3,X3),X3)
| ~ m1_relset_1(X4,k2_zfmisc_1(X3,X3),X3) ) ),
inference(distribute,[status(thm)],[269]) ).
cnf(272,plain,
( v1_xboole_0(X2)
| ~ m1_relset_1(X1,k2_zfmisc_1(X2,X2),X2)
| ~ v1_funct_2(X1,k2_zfmisc_1(X2,X2),X2)
| ~ v1_funct_1(X1)
| ~ v3_struct_0(g1_group_1(X2,X1)) ),
inference(split_conjunct,[status(thm)],[270]) ).
fof(273,plain,
! [X1] :
( ~ l1_group_1(X1)
| l1_struct_0(X1) ),
inference(fof_nnf,[status(thm)],[48]) ).
fof(274,plain,
! [X2] :
( ~ l1_group_1(X2)
| l1_struct_0(X2) ),
inference(variable_rename,[status(thm)],[273]) ).
cnf(275,plain,
( l1_struct_0(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[274]) ).
fof(286,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)],[81]) ).
fof(287,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)],[286]) ).
fof(288,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)],[287]) ).
cnf(289,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)],[288]) ).
fof(294,plain,
! [X1] :
( ~ l1_group_1(X1)
| ~ v1_group_1(X1)
| X1 = g1_group_1(u1_struct_0(X1),u1_group_1(X1)) ),
inference(fof_nnf,[status(thm)],[55]) ).
fof(295,plain,
! [X2] :
( ~ l1_group_1(X2)
| ~ v1_group_1(X2)
| X2 = g1_group_1(u1_struct_0(X2),u1_group_1(X2)) ),
inference(variable_rename,[status(thm)],[294]) ).
cnf(296,plain,
( X1 = g1_group_1(u1_struct_0(X1),u1_group_1(X1))
| ~ v1_group_1(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[295]) ).
fof(299,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)],[83]) ).
fof(300,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)],[299]) ).
fof(301,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)],[300]) ).
fof(302,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)],[301]) ).
cnf(303,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)],[302]) ).
cnf(304,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)],[302]) ).
fof(311,plain,
! [X1] :
( ~ l1_group_1(X1)
| ( v1_funct_1(u1_group_1(X1))
& v1_funct_2(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
& m2_relset_1(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1)) ) ),
inference(fof_nnf,[status(thm)],[60]) ).
fof(312,plain,
! [X2] :
( ~ l1_group_1(X2)
| ( v1_funct_1(u1_group_1(X2))
& v1_funct_2(u1_group_1(X2),k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(X2)),u1_struct_0(X2))
& m2_relset_1(u1_group_1(X2),k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(X2)),u1_struct_0(X2)) ) ),
inference(variable_rename,[status(thm)],[311]) ).
fof(313,plain,
! [X2] :
( ( v1_funct_1(u1_group_1(X2))
| ~ l1_group_1(X2) )
& ( v1_funct_2(u1_group_1(X2),k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(X2)),u1_struct_0(X2))
| ~ l1_group_1(X2) )
& ( m2_relset_1(u1_group_1(X2),k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(X2)),u1_struct_0(X2))
| ~ l1_group_1(X2) ) ),
inference(distribute,[status(thm)],[312]) ).
cnf(314,plain,
( m2_relset_1(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[313]) ).
cnf(315,plain,
( v1_funct_2(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[313]) ).
cnf(316,plain,
( v1_funct_1(u1_group_1(X1))
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[313]) ).
fof(320,plain,
! [X1,X2] :
( ( ~ r1_tarski(X1,X2)
| ! [X3] :
( ~ r2_hidden(X3,X1)
| r2_hidden(X3,X2) ) )
& ( ? [X3] :
( r2_hidden(X3,X1)
& ~ r2_hidden(X3,X2) )
| r1_tarski(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[62]) ).
fof(321,plain,
! [X4,X5] :
( ( ~ r1_tarski(X4,X5)
| ! [X6] :
( ~ r2_hidden(X6,X4)
| r2_hidden(X6,X5) ) )
& ( ? [X7] :
( r2_hidden(X7,X4)
& ~ r2_hidden(X7,X5) )
| r1_tarski(X4,X5) ) ),
inference(variable_rename,[status(thm)],[320]) ).
fof(322,plain,
! [X4,X5] :
( ( ~ r1_tarski(X4,X5)
| ! [X6] :
( ~ r2_hidden(X6,X4)
| r2_hidden(X6,X5) ) )
& ( ( r2_hidden(esk22_2(X4,X5),X4)
& ~ r2_hidden(esk22_2(X4,X5),X5) )
| r1_tarski(X4,X5) ) ),
inference(skolemize,[status(esa)],[321]) ).
fof(323,plain,
! [X4,X5,X6] :
( ( ~ r2_hidden(X6,X4)
| r2_hidden(X6,X5)
| ~ r1_tarski(X4,X5) )
& ( ( r2_hidden(esk22_2(X4,X5),X4)
& ~ r2_hidden(esk22_2(X4,X5),X5) )
| r1_tarski(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[322]) ).
fof(324,plain,
! [X4,X5,X6] :
( ( ~ r2_hidden(X6,X4)
| r2_hidden(X6,X5)
| ~ r1_tarski(X4,X5) )
& ( r2_hidden(esk22_2(X4,X5),X4)
| r1_tarski(X4,X5) )
& ( ~ r2_hidden(esk22_2(X4,X5),X5)
| r1_tarski(X4,X5) ) ),
inference(distribute,[status(thm)],[323]) ).
cnf(325,plain,
( r1_tarski(X1,X2)
| ~ r2_hidden(esk22_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[324]) ).
cnf(326,plain,
( r1_tarski(X1,X2)
| r2_hidden(esk22_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[324]) ).
cnf(351,plain,
( v3_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1))
| ~ l1_group_1(X1) ),
inference(spm,[status(thm)],[168,275,theory(equality)]) ).
cnf(357,plain,
( m1_subset_1(esk22_2(X1,X2),X1)
| r1_tarski(X1,X2) ),
inference(spm,[status(thm)],[130,326,theory(equality)]) ).
cnf(371,plain,
( r1_tarski(X1,X2)
| v1_xboole_0(X2)
| ~ m1_subset_1(esk22_2(X1,X2),X2) ),
inference(spm,[status(thm)],[325,254,theory(equality)]) ).
cnf(392,plain,
( v3_struct_0(X1)
| ~ v1_xboole_0(k1_autgroup(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1) ),
inference(spm,[status(thm)],[225,247,theory(equality)]) ).
cnf(393,plain,
( m1_relset_1(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ l1_group_1(X1) ),
inference(spm,[status(thm)],[110,314,theory(equality)]) ).
cnf(421,plain,
( v1_xboole_0(u1_struct_0(X1))
| ~ v3_struct_0(g1_group_1(u1_struct_0(X1),u1_group_1(X1)))
| ~ m1_relset_1(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ v1_funct_1(u1_group_1(X1))
| ~ l1_group_1(X1) ),
inference(spm,[status(thm)],[272,315,theory(equality)]) ).
cnf(431,plain,
( v1_xboole_0(u1_struct_0(X1))
| m1_subset_1(X2,k1_autgroup(X1))
| v3_struct_0(X1)
| ~ m1_fraenkel(k1_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1))
| ~ m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1) ),
inference(spm,[status(thm)],[304,289,theory(equality)]) ).
cnf(468,negated_conjecture,
( ~ l1_group_1(esk5_0)
| ~ v1_xboole_0(u1_struct_0(esk5_0)) ),
inference(spm,[status(thm)],[142,351,theory(equality)]) ).
cnf(472,negated_conjecture,
( $false
| ~ v1_xboole_0(u1_struct_0(esk5_0)) ),
inference(rw,[status(thm)],[468,138,theory(equality)]) ).
cnf(473,negated_conjecture,
~ v1_xboole_0(u1_struct_0(esk5_0)),
inference(cn,[status(thm)],[472,theory(equality)]) ).
cnf(1014,plain,
( v1_xboole_0(u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v3_struct_0(g1_group_1(u1_struct_0(X1),u1_group_1(X1)))
| ~ m1_relset_1(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1)) ),
inference(csr,[status(thm)],[421,316]) ).
cnf(1015,plain,
( v1_xboole_0(u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v3_struct_0(g1_group_1(u1_struct_0(X1),u1_group_1(X1))) ),
inference(csr,[status(thm)],[1014,393]) ).
cnf(1016,plain,
( v1_xboole_0(u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v3_struct_0(X1)
| ~ v1_group_1(X1) ),
inference(spm,[status(thm)],[1015,296,theory(equality)]) ).
cnf(1127,plain,
( v3_struct_0(X1)
| v1_xboole_0(u1_struct_0(X1))
| m1_subset_1(X2,k1_autgroup(X1))
| ~ m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1) ),
inference(csr,[status(thm)],[431,247]) ).
cnf(1128,plain,
( v1_xboole_0(u1_struct_0(X1))
| m1_subset_1(X2,k1_autgroup(X1))
| ~ m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1) ),
inference(csr,[status(thm)],[1127,1016]) ).
cnf(1130,plain,
( v1_xboole_0(u1_struct_0(X1))
| m1_subset_1(X2,k1_autgroup(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m1_fraenkel(k4_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1))
| ~ m1_subset_1(X2,k4_autgroup(X1)) ),
inference(spm,[status(thm)],[1128,303,theory(equality)]) ).
cnf(8863,plain,
( v1_xboole_0(u1_struct_0(X1))
| m1_subset_1(X2,k1_autgroup(X1))
| v3_struct_0(X1)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m1_subset_1(X2,k4_autgroup(X1)) ),
inference(spm,[status(thm)],[1130,133,theory(equality)]) ).
cnf(8871,plain,
( v1_xboole_0(u1_struct_0(X1))
| m1_subset_1(X2,k1_autgroup(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m1_subset_1(X2,k4_autgroup(X1)) ),
inference(csr,[status(thm)],[8863,1016]) ).
cnf(8875,plain,
( r1_tarski(X1,k1_autgroup(X2))
| v1_xboole_0(k1_autgroup(X2))
| v1_xboole_0(u1_struct_0(X2))
| ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2)
| ~ m1_subset_1(esk22_2(X1,k1_autgroup(X2)),k4_autgroup(X2)) ),
inference(spm,[status(thm)],[371,8871,theory(equality)]) ).
cnf(16122,plain,
( r1_tarski(k4_autgroup(X1),k1_autgroup(X1))
| v1_xboole_0(u1_struct_0(X1))
| v1_xboole_0(k1_autgroup(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1) ),
inference(spm,[status(thm)],[8875,357,theory(equality)]) ).
cnf(16138,negated_conjecture,
( v1_xboole_0(k1_autgroup(esk5_0))
| v1_xboole_0(u1_struct_0(esk5_0))
| ~ l1_group_1(esk5_0)
| ~ v4_group_1(esk5_0)
| ~ v3_group_1(esk5_0)
| ~ v1_group_1(esk5_0) ),
inference(spm,[status(thm)],[137,16122,theory(equality)]) ).
cnf(16142,negated_conjecture,
( v1_xboole_0(k1_autgroup(esk5_0))
| v1_xboole_0(u1_struct_0(esk5_0))
| $false
| ~ v4_group_1(esk5_0)
| ~ v3_group_1(esk5_0)
| ~ v1_group_1(esk5_0) ),
inference(rw,[status(thm)],[16138,138,theory(equality)]) ).
cnf(16143,negated_conjecture,
( v1_xboole_0(k1_autgroup(esk5_0))
| v1_xboole_0(u1_struct_0(esk5_0))
| $false
| $false
| ~ v3_group_1(esk5_0)
| ~ v1_group_1(esk5_0) ),
inference(rw,[status(thm)],[16142,139,theory(equality)]) ).
cnf(16144,negated_conjecture,
( v1_xboole_0(k1_autgroup(esk5_0))
| v1_xboole_0(u1_struct_0(esk5_0))
| $false
| $false
| $false
| ~ v1_group_1(esk5_0) ),
inference(rw,[status(thm)],[16143,140,theory(equality)]) ).
cnf(16145,negated_conjecture,
( v1_xboole_0(k1_autgroup(esk5_0))
| v1_xboole_0(u1_struct_0(esk5_0))
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[16144,141,theory(equality)]) ).
cnf(16146,negated_conjecture,
( v1_xboole_0(k1_autgroup(esk5_0))
| v1_xboole_0(u1_struct_0(esk5_0)) ),
inference(cn,[status(thm)],[16145,theory(equality)]) ).
cnf(16147,negated_conjecture,
v1_xboole_0(k1_autgroup(esk5_0)),
inference(sr,[status(thm)],[16146,473,theory(equality)]) ).
cnf(16150,negated_conjecture,
( v3_struct_0(esk5_0)
| ~ l1_group_1(esk5_0)
| ~ v4_group_1(esk5_0)
| ~ v3_group_1(esk5_0)
| ~ v1_group_1(esk5_0) ),
inference(spm,[status(thm)],[392,16147,theory(equality)]) ).
cnf(16167,negated_conjecture,
( v3_struct_0(esk5_0)
| $false
| ~ v4_group_1(esk5_0)
| ~ v3_group_1(esk5_0)
| ~ v1_group_1(esk5_0) ),
inference(rw,[status(thm)],[16150,138,theory(equality)]) ).
cnf(16168,negated_conjecture,
( v3_struct_0(esk5_0)
| $false
| $false
| ~ v3_group_1(esk5_0)
| ~ v1_group_1(esk5_0) ),
inference(rw,[status(thm)],[16167,139,theory(equality)]) ).
cnf(16169,negated_conjecture,
( v3_struct_0(esk5_0)
| $false
| $false
| $false
| ~ v1_group_1(esk5_0) ),
inference(rw,[status(thm)],[16168,140,theory(equality)]) ).
cnf(16170,negated_conjecture,
( v3_struct_0(esk5_0)
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[16169,141,theory(equality)]) ).
cnf(16171,negated_conjecture,
v3_struct_0(esk5_0),
inference(cn,[status(thm)],[16170,theory(equality)]) ).
cnf(16172,negated_conjecture,
$false,
inference(sr,[status(thm)],[16171,142,theory(equality)]) ).
cnf(16173,negated_conjecture,
$false,
16172,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRP/GRP623+1.p
% --creating new selector for []
% -running prover on /tmp/tmpEO4pNe/sel_GRP623+1.p_1 with time limit 29
% -prover status Theorem
% Problem GRP623+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRP/GRP623+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRP/GRP623+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
%
%------------------------------------------------------------------------------