TSTP Solution File: GRP622+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GRP622+1 : TPTP v5.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.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 10:12:27 EST 2010
% Result : Theorem 5.09s
% Output : CNFRefutation 5.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 14
% Syntax : Number of formulae : 118 ( 11 unt; 0 def)
% Number of atoms : 496 ( 9 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 619 ( 241 ~; 260 |; 90 &)
% ( 4 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 209 ( 1 sgn 126 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(7,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
<=> m1_relset_1(X3,X1,X2) ),
file('/tmp/tmp-YGLCg/sel_GRP622+1.p_1',redefinition_m2_relset_1) ).
fof(12,axiom,
! [X1,X2] :
( r2_hidden(X1,X2)
=> m1_subset_1(X1,X2) ),
file('/tmp/tmp-YGLCg/sel_GRP622+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/tmp-YGLCg/sel_GRP622+1.p_1',dt_k4_autgroup) ).
fof(20,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
file('/tmp/tmp-YGLCg/sel_GRP622+1.p_1',fc1_struct_0) ).
fof(41,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_fraenkel(u1_struct_0(X1),u1_struct_0(X1))) ),
file('/tmp/tmp-YGLCg/sel_GRP622+1.p_1',t12_autgroup) ).
fof(44,axiom,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X2)
& m1_fraenkel(X3,X1,X2) )
=> ! [X4] :
( m2_fraenkel(X4,X1,X2,X3)
=> ( v1_funct_1(X4)
& v1_funct_2(X4,X1,X2)
& m2_relset_1(X4,X1,X2) ) ) ),
file('/tmp/tmp-YGLCg/sel_GRP622+1.p_1',dt_m2_fraenkel) ).
fof(50,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/tmp-YGLCg/sel_GRP622+1.p_1',fc1_group_1) ).
fof(51,axiom,
! [X1,X2] :
( ~ v1_xboole_0(X2)
=> k1_fraenkel(X1,X2) = k1_funct_2(X1,X2) ),
file('/tmp/tmp-YGLCg/sel_GRP622+1.p_1',redefinition_k1_fraenkel) ).
fof(52,axiom,
! [X1] :
( l1_group_1(X1)
=> l1_struct_0(X1) ),
file('/tmp/tmp-YGLCg/sel_GRP622+1.p_1',dt_l1_group_1) ).
fof(58,axiom,
! [X1] :
( l1_group_1(X1)
=> ( v1_group_1(X1)
=> X1 = g1_group_1(u1_struct_0(X1),u1_group_1(X1)) ) ),
file('/tmp/tmp-YGLCg/sel_GRP622+1.p_1',abstractness_v1_group_1) ).
fof(61,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/tmp-YGLCg/sel_GRP622+1.p_1',redefinition_m2_fraenkel) ).
fof(62,axiom,
! [X1,X2] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,X1,X1)
& m2_relset_1(X2,X1,X1) )
=> r2_hidden(X2,k1_funct_2(X1,X1)) ),
file('/tmp/tmp-YGLCg/sel_GRP622+1.p_1',t12_funct_2) ).
fof(64,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/tmp-YGLCg/sel_GRP622+1.p_1',dt_u1_group_1) ).
fof(66,axiom,
! [X1,X2] :
( r1_tarski(X1,X2)
<=> ! [X3] :
( r2_hidden(X3,X1)
=> r2_hidden(X3,X2) ) ),
file('/tmp/tmp-YGLCg/sel_GRP622+1.p_1',d3_tarski) ).
fof(70,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_fraenkel(u1_struct_0(X1),u1_struct_0(X1))) ),
inference(assume_negation,[status(cth)],[41]) ).
fof(73,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(76,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[20,theory(equality)]) ).
fof(83,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_fraenkel(u1_struct_0(X1),u1_struct_0(X1))) ),
inference(fof_simplification,[status(thm)],[70,theory(equality)]) ).
fof(84,plain,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X2)
& m1_fraenkel(X3,X1,X2) )
=> ! [X4] :
( m2_fraenkel(X4,X1,X2,X3)
=> ( v1_funct_1(X4)
& v1_funct_2(X4,X1,X2)
& m2_relset_1(X4,X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[44,theory(equality)]) ).
fof(87,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)],[50,theory(equality)]) ).
fof(88,plain,
! [X1,X2] :
( ~ v1_xboole_0(X2)
=> k1_fraenkel(X1,X2) = k1_funct_2(X1,X2) ),
inference(fof_simplification,[status(thm)],[51,theory(equality)]) ).
fof(90,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)],[61,theory(equality)]) ).
fof(114,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(115,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)],[114]) ).
cnf(117,plain,
( m1_relset_1(X1,X2,X3)
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[115]) ).
fof(131,plain,
! [X1,X2] :
( ~ r2_hidden(X1,X2)
| m1_subset_1(X1,X2) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(132,plain,
! [X3,X4] :
( ~ r2_hidden(X3,X4)
| m1_subset_1(X3,X4) ),
inference(variable_rename,[status(thm)],[131]) ).
cnf(133,plain,
( m1_subset_1(X1,X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[132]) ).
fof(134,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)],[73]) ).
fof(135,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)],[134]) ).
cnf(136,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)],[135]) ).
fof(160,plain,
! [X1] :
( v3_struct_0(X1)
| ~ l1_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(fof_nnf,[status(thm)],[76]) ).
fof(161,plain,
! [X2] :
( v3_struct_0(X2)
| ~ l1_struct_0(X2)
| ~ v1_xboole_0(u1_struct_0(X2)) ),
inference(variable_rename,[status(thm)],[160]) ).
cnf(162,plain,
( v3_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1))
| ~ l1_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[161]) ).
fof(243,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_fraenkel(u1_struct_0(X1),u1_struct_0(X1))) ),
inference(fof_nnf,[status(thm)],[83]) ).
fof(244,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_fraenkel(u1_struct_0(X2),u1_struct_0(X2))) ),
inference(variable_rename,[status(thm)],[243]) ).
fof(245,negated_conjecture,
( ~ v3_struct_0(esk15_0)
& v1_group_1(esk15_0)
& v3_group_1(esk15_0)
& v4_group_1(esk15_0)
& l1_group_1(esk15_0)
& ~ r1_tarski(k4_autgroup(esk15_0),k1_fraenkel(u1_struct_0(esk15_0),u1_struct_0(esk15_0))) ),
inference(skolemize,[status(esa)],[244]) ).
cnf(246,negated_conjecture,
~ r1_tarski(k4_autgroup(esk15_0),k1_fraenkel(u1_struct_0(esk15_0),u1_struct_0(esk15_0))),
inference(split_conjunct,[status(thm)],[245]) ).
cnf(247,negated_conjecture,
l1_group_1(esk15_0),
inference(split_conjunct,[status(thm)],[245]) ).
cnf(248,negated_conjecture,
v4_group_1(esk15_0),
inference(split_conjunct,[status(thm)],[245]) ).
cnf(249,negated_conjecture,
v3_group_1(esk15_0),
inference(split_conjunct,[status(thm)],[245]) ).
cnf(250,negated_conjecture,
v1_group_1(esk15_0),
inference(split_conjunct,[status(thm)],[245]) ).
cnf(251,negated_conjecture,
~ v3_struct_0(esk15_0),
inference(split_conjunct,[status(thm)],[245]) ).
fof(258,plain,
! [X1,X2,X3] :
( v1_xboole_0(X2)
| ~ m1_fraenkel(X3,X1,X2)
| ! [X4] :
( ~ m2_fraenkel(X4,X1,X2,X3)
| ( v1_funct_1(X4)
& v1_funct_2(X4,X1,X2)
& m2_relset_1(X4,X1,X2) ) ) ),
inference(fof_nnf,[status(thm)],[84]) ).
fof(259,plain,
! [X5,X6,X7] :
( v1_xboole_0(X6)
| ~ m1_fraenkel(X7,X5,X6)
| ! [X8] :
( ~ m2_fraenkel(X8,X5,X6,X7)
| ( v1_funct_1(X8)
& v1_funct_2(X8,X5,X6)
& m2_relset_1(X8,X5,X6) ) ) ),
inference(variable_rename,[status(thm)],[258]) ).
fof(260,plain,
! [X5,X6,X7,X8] :
( ~ m2_fraenkel(X8,X5,X6,X7)
| ( v1_funct_1(X8)
& v1_funct_2(X8,X5,X6)
& m2_relset_1(X8,X5,X6) )
| v1_xboole_0(X6)
| ~ m1_fraenkel(X7,X5,X6) ),
inference(shift_quantors,[status(thm)],[259]) ).
fof(261,plain,
! [X5,X6,X7,X8] :
( ( v1_funct_1(X8)
| ~ m2_fraenkel(X8,X5,X6,X7)
| v1_xboole_0(X6)
| ~ m1_fraenkel(X7,X5,X6) )
& ( v1_funct_2(X8,X5,X6)
| ~ m2_fraenkel(X8,X5,X6,X7)
| v1_xboole_0(X6)
| ~ m1_fraenkel(X7,X5,X6) )
& ( m2_relset_1(X8,X5,X6)
| ~ m2_fraenkel(X8,X5,X6,X7)
| v1_xboole_0(X6)
| ~ m1_fraenkel(X7,X5,X6) ) ),
inference(distribute,[status(thm)],[260]) ).
cnf(262,plain,
( v1_xboole_0(X3)
| m2_relset_1(X4,X2,X3)
| ~ m1_fraenkel(X1,X2,X3)
| ~ m2_fraenkel(X4,X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[261]) ).
cnf(263,plain,
( v1_xboole_0(X3)
| v1_funct_2(X4,X2,X3)
| ~ m1_fraenkel(X1,X2,X3)
| ~ m2_fraenkel(X4,X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[261]) ).
cnf(264,plain,
( v1_xboole_0(X3)
| v1_funct_1(X4)
| ~ m1_fraenkel(X1,X2,X3)
| ~ m2_fraenkel(X4,X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[261]) ).
fof(280,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)],[87]) ).
fof(281,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)],[280]) ).
fof(282,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)],[281]) ).
cnf(284,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)],[282]) ).
fof(285,plain,
! [X1,X2] :
( v1_xboole_0(X2)
| k1_fraenkel(X1,X2) = k1_funct_2(X1,X2) ),
inference(fof_nnf,[status(thm)],[88]) ).
fof(286,plain,
! [X3,X4] :
( v1_xboole_0(X4)
| k1_fraenkel(X3,X4) = k1_funct_2(X3,X4) ),
inference(variable_rename,[status(thm)],[285]) ).
cnf(287,plain,
( k1_fraenkel(X1,X2) = k1_funct_2(X1,X2)
| v1_xboole_0(X2) ),
inference(split_conjunct,[status(thm)],[286]) ).
fof(288,plain,
! [X1] :
( ~ l1_group_1(X1)
| l1_struct_0(X1) ),
inference(fof_nnf,[status(thm)],[52]) ).
fof(289,plain,
! [X2] :
( ~ l1_group_1(X2)
| l1_struct_0(X2) ),
inference(variable_rename,[status(thm)],[288]) ).
cnf(290,plain,
( l1_struct_0(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[289]) ).
fof(303,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)],[58]) ).
fof(304,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)],[303]) ).
cnf(305,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)],[304]) ).
fof(308,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)],[90]) ).
fof(309,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)],[308]) ).
fof(310,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)],[309]) ).
fof(311,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)],[310]) ).
cnf(312,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)],[311]) ).
fof(314,plain,
! [X1,X2] :
( ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X1,X1)
| ~ m2_relset_1(X2,X1,X1)
| r2_hidden(X2,k1_funct_2(X1,X1)) ),
inference(fof_nnf,[status(thm)],[62]) ).
fof(315,plain,
! [X3,X4] :
( ~ v1_funct_1(X4)
| ~ v1_funct_2(X4,X3,X3)
| ~ m2_relset_1(X4,X3,X3)
| r2_hidden(X4,k1_funct_2(X3,X3)) ),
inference(variable_rename,[status(thm)],[314]) ).
cnf(316,plain,
( r2_hidden(X1,k1_funct_2(X2,X2))
| ~ m2_relset_1(X1,X2,X2)
| ~ v1_funct_2(X1,X2,X2)
| ~ v1_funct_1(X1) ),
inference(split_conjunct,[status(thm)],[315]) ).
fof(323,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)],[64]) ).
fof(324,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)],[323]) ).
fof(325,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)],[324]) ).
cnf(326,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)],[325]) ).
cnf(327,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)],[325]) ).
cnf(328,plain,
( v1_funct_1(u1_group_1(X1))
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[325]) ).
fof(331,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)],[66]) ).
fof(332,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)],[331]) ).
fof(333,plain,
! [X4,X5] :
( ( ~ r1_tarski(X4,X5)
| ! [X6] :
( ~ r2_hidden(X6,X4)
| r2_hidden(X6,X5) ) )
& ( ( r2_hidden(esk21_2(X4,X5),X4)
& ~ r2_hidden(esk21_2(X4,X5),X5) )
| r1_tarski(X4,X5) ) ),
inference(skolemize,[status(esa)],[332]) ).
fof(334,plain,
! [X4,X5,X6] :
( ( ~ r2_hidden(X6,X4)
| r2_hidden(X6,X5)
| ~ r1_tarski(X4,X5) )
& ( ( r2_hidden(esk21_2(X4,X5),X4)
& ~ r2_hidden(esk21_2(X4,X5),X5) )
| r1_tarski(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[333]) ).
fof(335,plain,
! [X4,X5,X6] :
( ( ~ r2_hidden(X6,X4)
| r2_hidden(X6,X5)
| ~ r1_tarski(X4,X5) )
& ( r2_hidden(esk21_2(X4,X5),X4)
| r1_tarski(X4,X5) )
& ( ~ r2_hidden(esk21_2(X4,X5),X5)
| r1_tarski(X4,X5) ) ),
inference(distribute,[status(thm)],[334]) ).
cnf(336,plain,
( r1_tarski(X1,X2)
| ~ r2_hidden(esk21_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[335]) ).
cnf(337,plain,
( r1_tarski(X1,X2)
| r2_hidden(esk21_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[335]) ).
cnf(366,plain,
( v3_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1))
| ~ l1_group_1(X1) ),
inference(spm,[status(thm)],[162,290,theory(equality)]) ).
cnf(374,plain,
( m1_subset_1(esk21_2(X1,X2),X1)
| r1_tarski(X1,X2) ),
inference(spm,[status(thm)],[133,337,theory(equality)]) ).
cnf(378,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk15_0))
| ~ r1_tarski(k4_autgroup(esk15_0),k1_funct_2(u1_struct_0(esk15_0),u1_struct_0(esk15_0))) ),
inference(spm,[status(thm)],[246,287,theory(equality)]) ).
cnf(412,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)],[117,326,theory(equality)]) ).
cnf(419,plain,
( v1_xboole_0(X1)
| v1_funct_1(X2)
| ~ m1_fraenkel(X4,X3,X1)
| ~ m1_subset_1(X2,X4) ),
inference(spm,[status(thm)],[264,312,theory(equality)]) ).
cnf(423,plain,
( m2_relset_1(X1,X2,X3)
| v1_xboole_0(X3)
| ~ m1_fraenkel(X4,X2,X3)
| ~ m1_subset_1(X1,X4) ),
inference(spm,[status(thm)],[262,312,theory(equality)]) ).
cnf(425,plain,
( v1_funct_2(X1,X2,X3)
| v1_xboole_0(X3)
| ~ m1_fraenkel(X4,X2,X3)
| ~ m1_subset_1(X1,X4) ),
inference(spm,[status(thm)],[263,312,theory(equality)]) ).
cnf(429,plain,
( r1_tarski(X1,k1_funct_2(X2,X2))
| ~ v1_funct_2(esk21_2(X1,k1_funct_2(X2,X2)),X2,X2)
| ~ m2_relset_1(esk21_2(X1,k1_funct_2(X2,X2)),X2,X2)
| ~ v1_funct_1(esk21_2(X1,k1_funct_2(X2,X2))) ),
inference(spm,[status(thm)],[336,316,theory(equality)]) ).
cnf(444,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)],[284,327,theory(equality)]) ).
cnf(486,negated_conjecture,
( ~ l1_group_1(esk15_0)
| ~ v1_xboole_0(u1_struct_0(esk15_0)) ),
inference(spm,[status(thm)],[251,366,theory(equality)]) ).
cnf(490,negated_conjecture,
( $false
| ~ v1_xboole_0(u1_struct_0(esk15_0)) ),
inference(rw,[status(thm)],[486,247,theory(equality)]) ).
cnf(491,negated_conjecture,
~ v1_xboole_0(u1_struct_0(esk15_0)),
inference(cn,[status(thm)],[490,theory(equality)]) ).
cnf(517,negated_conjecture,
~ r1_tarski(k4_autgroup(esk15_0),k1_funct_2(u1_struct_0(esk15_0),u1_struct_0(esk15_0))),
inference(sr,[status(thm)],[378,491,theory(equality)]) ).
cnf(753,plain,
( v1_xboole_0(u1_struct_0(X1))
| v1_funct_1(X2)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,k4_autgroup(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1) ),
inference(spm,[status(thm)],[419,136,theory(equality)]) ).
cnf(831,plain,
( m2_relset_1(X1,u1_struct_0(X2),u1_struct_0(X2))
| v1_xboole_0(u1_struct_0(X2))
| v3_struct_0(X2)
| ~ m1_subset_1(X1,k4_autgroup(X2))
| ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2) ),
inference(spm,[status(thm)],[423,136,theory(equality)]) ).
cnf(885,plain,
( v1_funct_2(X1,u1_struct_0(X2),u1_struct_0(X2))
| v1_xboole_0(u1_struct_0(X2))
| v3_struct_0(X2)
| ~ m1_subset_1(X1,k4_autgroup(X2))
| ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2) ),
inference(spm,[status(thm)],[425,136,theory(equality)]) ).
cnf(1156,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)],[444,328]) ).
cnf(1157,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)],[1156,412]) ).
cnf(1158,plain,
( v1_xboole_0(u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v3_struct_0(X1)
| ~ v1_group_1(X1) ),
inference(spm,[status(thm)],[1157,305,theory(equality)]) ).
cnf(1499,plain,
( v1_xboole_0(u1_struct_0(X1))
| v1_funct_1(X2)
| ~ 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)],[753,1158]) ).
cnf(3416,plain,
( m2_relset_1(X1,u1_struct_0(X2),u1_struct_0(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(X1,k4_autgroup(X2)) ),
inference(csr,[status(thm)],[831,1158]) ).
cnf(3422,plain,
( r1_tarski(X1,k1_funct_2(u1_struct_0(X2),u1_struct_0(X2)))
| v1_xboole_0(u1_struct_0(X2))
| ~ v1_funct_2(esk21_2(X1,k1_funct_2(u1_struct_0(X2),u1_struct_0(X2))),u1_struct_0(X2),u1_struct_0(X2))
| ~ v1_funct_1(esk21_2(X1,k1_funct_2(u1_struct_0(X2),u1_struct_0(X2))))
| ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2)
| ~ m1_subset_1(esk21_2(X1,k1_funct_2(u1_struct_0(X2),u1_struct_0(X2))),k4_autgroup(X2)) ),
inference(spm,[status(thm)],[429,3416,theory(equality)]) ).
cnf(5793,plain,
( v1_funct_2(X1,u1_struct_0(X2),u1_struct_0(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(X1,k4_autgroup(X2)) ),
inference(csr,[status(thm)],[885,1158]) ).
cnf(72071,plain,
( r1_tarski(X1,k1_funct_2(u1_struct_0(X2),u1_struct_0(X2)))
| v1_xboole_0(u1_struct_0(X2))
| ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2)
| ~ v1_funct_2(esk21_2(X1,k1_funct_2(u1_struct_0(X2),u1_struct_0(X2))),u1_struct_0(X2),u1_struct_0(X2))
| ~ m1_subset_1(esk21_2(X1,k1_funct_2(u1_struct_0(X2),u1_struct_0(X2))),k4_autgroup(X2)) ),
inference(csr,[status(thm)],[3422,1499]) ).
cnf(72072,plain,
( r1_tarski(X1,k1_funct_2(u1_struct_0(X2),u1_struct_0(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(esk21_2(X1,k1_funct_2(u1_struct_0(X2),u1_struct_0(X2))),k4_autgroup(X2)) ),
inference(csr,[status(thm)],[72071,5793]) ).
cnf(72074,plain,
( r1_tarski(k4_autgroup(X1),k1_funct_2(u1_struct_0(X1),u1_struct_0(X1)))
| v1_xboole_0(u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1) ),
inference(spm,[status(thm)],[72072,374,theory(equality)]) ).
cnf(72174,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk15_0))
| ~ l1_group_1(esk15_0)
| ~ v4_group_1(esk15_0)
| ~ v3_group_1(esk15_0)
| ~ v1_group_1(esk15_0) ),
inference(spm,[status(thm)],[517,72074,theory(equality)]) ).
cnf(72187,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk15_0))
| $false
| ~ v4_group_1(esk15_0)
| ~ v3_group_1(esk15_0)
| ~ v1_group_1(esk15_0) ),
inference(rw,[status(thm)],[72174,247,theory(equality)]) ).
cnf(72188,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk15_0))
| $false
| $false
| ~ v3_group_1(esk15_0)
| ~ v1_group_1(esk15_0) ),
inference(rw,[status(thm)],[72187,248,theory(equality)]) ).
cnf(72189,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk15_0))
| $false
| $false
| $false
| ~ v1_group_1(esk15_0) ),
inference(rw,[status(thm)],[72188,249,theory(equality)]) ).
cnf(72190,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk15_0))
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[72189,250,theory(equality)]) ).
cnf(72191,negated_conjecture,
v1_xboole_0(u1_struct_0(esk15_0)),
inference(cn,[status(thm)],[72190,theory(equality)]) ).
cnf(72192,negated_conjecture,
$false,
inference(sr,[status(thm)],[72191,491,theory(equality)]) ).
cnf(72193,negated_conjecture,
$false,
72192,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRP/GRP622+1.p
% --creating new selector for []
% -running prover on /tmp/tmp-YGLCg/sel_GRP622+1.p_1 with time limit 29
% -prover status Theorem
% Problem GRP622+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRP/GRP622+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRP/GRP622+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
%
%------------------------------------------------------------------------------