%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU411+1 : TPTP v5.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art02.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 : Sun Dec 26 08:37:14 EST 2010
% Result : Theorem 3.76s
% Output : CNFRefutation 3.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 12
% Syntax : Number of formulae : 95 ( 25 unt; 0 def)
% Number of atoms : 521 ( 37 equ)
% Maximal formula atoms : 28 ( 5 avg)
% Number of connectives : 639 ( 213 ~; 237 |; 162 &)
% ( 5 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 183 ( 15 sgn 111 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(8,axiom,
! [X1,X2] :
( r2_hidden(X1,X2)
=> m1_subset_1(X1,X2) ),
file('/tmp/tmpFCikqw/sel_SEU411+1.p_1',t1_subset) ).
fof(9,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v4_orders_2(X1)
& v1_yellow_0(X1)
& l1_orders_2(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> r1_orders_2(X1,k3_yellow_0(X1),X2) ) ),
file('/tmp/tmpFCikqw/sel_SEU411+1.p_1',t44_yellow_0) ).
fof(12,axiom,
! [X1,X2,X3] :
( ( r2_hidden(X1,X2)
& m1_subset_1(X2,k1_zfmisc_1(X3)) )
=> m1_subset_1(X1,X3) ),
file('/tmp/tmpFCikqw/sel_SEU411+1.p_1',t4_subset) ).
fof(17,axiom,
! [X1] :
( l1_orders_2(X1)
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ( v12_waybel_0(X2,X1)
<=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( ( r2_hidden(X3,X2)
& r1_orders_2(X1,X4,X3) )
=> r2_hidden(X4,X2) ) ) ) ) ) ),
file('/tmp/tmpFCikqw/sel_SEU411+1.p_1',d19_waybel_0) ).
fof(19,axiom,
! [X1,X2] :
( m1_subset_1(X1,X2)
=> ( v1_xboole_0(X2)
| r2_hidden(X1,X2) ) ),
file('/tmp/tmpFCikqw/sel_SEU411+1.p_1',t2_subset) ).
fof(21,axiom,
! [X1,X2,X3] :
( X3 = k3_xboole_0(X1,X2)
<=> ! [X4] :
( r2_hidden(X4,X3)
<=> ( r2_hidden(X4,X1)
& r2_hidden(X4,X2) ) ) ),
file('/tmp/tmpFCikqw/sel_SEU411+1.p_1',d3_xboole_0) ).
fof(24,axiom,
! [X1] :
( X1 = k1_xboole_0
<=> ! [X2] : ~ r2_hidden(X2,X1) ),
file('/tmp/tmpFCikqw/sel_SEU411+1.p_1',d1_xboole_0) ).
fof(26,axiom,
! [X1,X2] : k3_xboole_0(X1,X2) = k3_xboole_0(X2,X1),
file('/tmp/tmpFCikqw/sel_SEU411+1.p_1',commutativity_k3_xboole_0) ).
fof(28,axiom,
! [X1,X2] : k3_xboole_0(X1,X1) = X1,
file('/tmp/tmpFCikqw/sel_SEU411+1.p_1',idempotence_k3_xboole_0) ).
fof(29,axiom,
! [X1] :
? [X2] : m1_subset_1(X2,X1),
file('/tmp/tmpFCikqw/sel_SEU411+1.p_1',existence_m1_subset_1) ).
fof(35,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v2_orders_2(X1)
& v3_orders_2(X1)
& v4_orders_2(X1)
& v1_yellow_0(X1)
& v1_lattice3(X1)
& l1_orders_2(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v2_orders_2(X2)
& v3_orders_2(X2)
& v4_orders_2(X2)
& v1_yellow_0(X2)
& v1_lattice3(X2)
& l1_orders_2(X2) )
=> ( ( ~ v1_xboole_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)))
& v1_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),X2)
& v12_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),X2)
& m1_subset_1(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),k1_zfmisc_1(u1_struct_0(X2))) )
=> r2_hidden(k3_yellow_0(X2),u1_struct_0(X1)) ) ) ),
file('/tmp/tmpFCikqw/sel_SEU411+1.p_1',t20_latsum_1) ).
fof(38,axiom,
! [X1] :
( l1_orders_2(X1)
=> m1_subset_1(k3_yellow_0(X1),u1_struct_0(X1)) ),
file('/tmp/tmpFCikqw/sel_SEU411+1.p_1',dt_k3_yellow_0) ).
fof(40,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v2_orders_2(X1)
& v3_orders_2(X1)
& v4_orders_2(X1)
& v1_yellow_0(X1)
& v1_lattice3(X1)
& l1_orders_2(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v2_orders_2(X2)
& v3_orders_2(X2)
& v4_orders_2(X2)
& v1_yellow_0(X2)
& v1_lattice3(X2)
& l1_orders_2(X2) )
=> ( ( ~ v1_xboole_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)))
& v1_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),X2)
& v12_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),X2)
& m1_subset_1(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),k1_zfmisc_1(u1_struct_0(X2))) )
=> r2_hidden(k3_yellow_0(X2),u1_struct_0(X1)) ) ) ),
inference(assume_negation,[status(cth)],[35]) ).
fof(42,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v4_orders_2(X1)
& v1_yellow_0(X1)
& l1_orders_2(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> r1_orders_2(X1,k3_yellow_0(X1),X2) ) ),
inference(fof_simplification,[status(thm)],[9,theory(equality)]) ).
fof(47,plain,
! [X1] :
( X1 = k1_xboole_0
<=> ! [X2] : ~ r2_hidden(X2,X1) ),
inference(fof_simplification,[status(thm)],[24,theory(equality)]) ).
fof(51,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v2_orders_2(X1)
& v3_orders_2(X1)
& v4_orders_2(X1)
& v1_yellow_0(X1)
& v1_lattice3(X1)
& l1_orders_2(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v2_orders_2(X2)
& v3_orders_2(X2)
& v4_orders_2(X2)
& v1_yellow_0(X2)
& v1_lattice3(X2)
& l1_orders_2(X2) )
=> ( ( ~ v1_xboole_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)))
& v1_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),X2)
& v12_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),X2)
& m1_subset_1(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),k1_zfmisc_1(u1_struct_0(X2))) )
=> r2_hidden(k3_yellow_0(X2),u1_struct_0(X1)) ) ) ),
inference(fof_simplification,[status(thm)],[40,theory(equality)]) ).
fof(69,plain,
! [X1,X2] :
( ~ r2_hidden(X1,X2)
| m1_subset_1(X1,X2) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(70,plain,
! [X3,X4] :
( ~ r2_hidden(X3,X4)
| m1_subset_1(X3,X4) ),
inference(variable_rename,[status(thm)],[69]) ).
cnf(71,plain,
( m1_subset_1(X1,X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[70]) ).
fof(72,plain,
! [X1] :
( v3_struct_0(X1)
| ~ v4_orders_2(X1)
| ~ v1_yellow_0(X1)
| ~ l1_orders_2(X1)
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| r1_orders_2(X1,k3_yellow_0(X1),X2) ) ),
inference(fof_nnf,[status(thm)],[42]) ).
fof(73,plain,
! [X3] :
( v3_struct_0(X3)
| ~ v4_orders_2(X3)
| ~ v1_yellow_0(X3)
| ~ l1_orders_2(X3)
| ! [X4] :
( ~ m1_subset_1(X4,u1_struct_0(X3))
| r1_orders_2(X3,k3_yellow_0(X3),X4) ) ),
inference(variable_rename,[status(thm)],[72]) ).
fof(74,plain,
! [X3,X4] :
( ~ m1_subset_1(X4,u1_struct_0(X3))
| r1_orders_2(X3,k3_yellow_0(X3),X4)
| v3_struct_0(X3)
| ~ v4_orders_2(X3)
| ~ v1_yellow_0(X3)
| ~ l1_orders_2(X3) ),
inference(shift_quantors,[status(thm)],[73]) ).
cnf(75,plain,
( v3_struct_0(X1)
| r1_orders_2(X1,k3_yellow_0(X1),X2)
| ~ l1_orders_2(X1)
| ~ v1_yellow_0(X1)
| ~ v4_orders_2(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[74]) ).
fof(83,plain,
! [X1,X2,X3] :
( ~ r2_hidden(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X3))
| m1_subset_1(X1,X3) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(84,plain,
! [X4,X5,X6] :
( ~ r2_hidden(X4,X5)
| ~ m1_subset_1(X5,k1_zfmisc_1(X6))
| m1_subset_1(X4,X6) ),
inference(variable_rename,[status(thm)],[83]) ).
cnf(85,plain,
( m1_subset_1(X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(X2))
| ~ r2_hidden(X1,X3) ),
inference(split_conjunct,[status(thm)],[84]) ).
fof(94,plain,
! [X1] :
( ~ l1_orders_2(X1)
| ! [X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ( ( ~ v12_waybel_0(X2,X1)
| ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X1))
| ! [X4] :
( ~ m1_subset_1(X4,u1_struct_0(X1))
| ~ r2_hidden(X3,X2)
| ~ r1_orders_2(X1,X4,X3)
| r2_hidden(X4,X2) ) ) )
& ( ? [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
& ? [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
& r2_hidden(X3,X2)
& r1_orders_2(X1,X4,X3)
& ~ r2_hidden(X4,X2) ) )
| v12_waybel_0(X2,X1) ) ) ) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(95,plain,
! [X5] :
( ~ l1_orders_2(X5)
| ! [X6] :
( ~ m1_subset_1(X6,k1_zfmisc_1(u1_struct_0(X5)))
| ( ( ~ v12_waybel_0(X6,X5)
| ! [X7] :
( ~ m1_subset_1(X7,u1_struct_0(X5))
| ! [X8] :
( ~ m1_subset_1(X8,u1_struct_0(X5))
| ~ r2_hidden(X7,X6)
| ~ r1_orders_2(X5,X8,X7)
| r2_hidden(X8,X6) ) ) )
& ( ? [X9] :
( m1_subset_1(X9,u1_struct_0(X5))
& ? [X10] :
( m1_subset_1(X10,u1_struct_0(X5))
& r2_hidden(X9,X6)
& r1_orders_2(X5,X10,X9)
& ~ r2_hidden(X10,X6) ) )
| v12_waybel_0(X6,X5) ) ) ) ),
inference(variable_rename,[status(thm)],[94]) ).
fof(96,plain,
! [X5] :
( ~ l1_orders_2(X5)
| ! [X6] :
( ~ m1_subset_1(X6,k1_zfmisc_1(u1_struct_0(X5)))
| ( ( ~ v12_waybel_0(X6,X5)
| ! [X7] :
( ~ m1_subset_1(X7,u1_struct_0(X5))
| ! [X8] :
( ~ m1_subset_1(X8,u1_struct_0(X5))
| ~ r2_hidden(X7,X6)
| ~ r1_orders_2(X5,X8,X7)
| r2_hidden(X8,X6) ) ) )
& ( ( m1_subset_1(esk3_2(X5,X6),u1_struct_0(X5))
& m1_subset_1(esk4_2(X5,X6),u1_struct_0(X5))
& r2_hidden(esk3_2(X5,X6),X6)
& r1_orders_2(X5,esk4_2(X5,X6),esk3_2(X5,X6))
& ~ r2_hidden(esk4_2(X5,X6),X6) )
| v12_waybel_0(X6,X5) ) ) ) ),
inference(skolemize,[status(esa)],[95]) ).
fof(97,plain,
! [X5,X6,X7,X8] :
( ( ( ~ m1_subset_1(X8,u1_struct_0(X5))
| ~ r2_hidden(X7,X6)
| ~ r1_orders_2(X5,X8,X7)
| r2_hidden(X8,X6)
| ~ m1_subset_1(X7,u1_struct_0(X5))
| ~ v12_waybel_0(X6,X5) )
& ( ( m1_subset_1(esk3_2(X5,X6),u1_struct_0(X5))
& m1_subset_1(esk4_2(X5,X6),u1_struct_0(X5))
& r2_hidden(esk3_2(X5,X6),X6)
& r1_orders_2(X5,esk4_2(X5,X6),esk3_2(X5,X6))
& ~ r2_hidden(esk4_2(X5,X6),X6) )
| v12_waybel_0(X6,X5) ) )
| ~ m1_subset_1(X6,k1_zfmisc_1(u1_struct_0(X5)))
| ~ l1_orders_2(X5) ),
inference(shift_quantors,[status(thm)],[96]) ).
fof(98,plain,
! [X5,X6,X7,X8] :
( ( ~ m1_subset_1(X8,u1_struct_0(X5))
| ~ r2_hidden(X7,X6)
| ~ r1_orders_2(X5,X8,X7)
| r2_hidden(X8,X6)
| ~ m1_subset_1(X7,u1_struct_0(X5))
| ~ v12_waybel_0(X6,X5)
| ~ m1_subset_1(X6,k1_zfmisc_1(u1_struct_0(X5)))
| ~ l1_orders_2(X5) )
& ( m1_subset_1(esk3_2(X5,X6),u1_struct_0(X5))
| v12_waybel_0(X6,X5)
| ~ m1_subset_1(X6,k1_zfmisc_1(u1_struct_0(X5)))
| ~ l1_orders_2(X5) )
& ( m1_subset_1(esk4_2(X5,X6),u1_struct_0(X5))
| v12_waybel_0(X6,X5)
| ~ m1_subset_1(X6,k1_zfmisc_1(u1_struct_0(X5)))
| ~ l1_orders_2(X5) )
& ( r2_hidden(esk3_2(X5,X6),X6)
| v12_waybel_0(X6,X5)
| ~ m1_subset_1(X6,k1_zfmisc_1(u1_struct_0(X5)))
| ~ l1_orders_2(X5) )
& ( r1_orders_2(X5,esk4_2(X5,X6),esk3_2(X5,X6))
| v12_waybel_0(X6,X5)
| ~ m1_subset_1(X6,k1_zfmisc_1(u1_struct_0(X5)))
| ~ l1_orders_2(X5) )
& ( ~ r2_hidden(esk4_2(X5,X6),X6)
| v12_waybel_0(X6,X5)
| ~ m1_subset_1(X6,k1_zfmisc_1(u1_struct_0(X5)))
| ~ l1_orders_2(X5) ) ),
inference(distribute,[status(thm)],[97]) ).
cnf(104,plain,
( r2_hidden(X4,X2)
| ~ l1_orders_2(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ v12_waybel_0(X2,X1)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ r1_orders_2(X1,X4,X3)
| ~ r2_hidden(X3,X2)
| ~ m1_subset_1(X4,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[98]) ).
fof(108,plain,
! [X1,X2] :
( ~ m1_subset_1(X1,X2)
| v1_xboole_0(X2)
| r2_hidden(X1,X2) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(109,plain,
! [X3,X4] :
( ~ m1_subset_1(X3,X4)
| v1_xboole_0(X4)
| r2_hidden(X3,X4) ),
inference(variable_rename,[status(thm)],[108]) ).
cnf(110,plain,
( r2_hidden(X1,X2)
| v1_xboole_0(X2)
| ~ m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[109]) ).
fof(112,plain,
! [X1,X2,X3] :
( ( X3 != k3_xboole_0(X1,X2)
| ! [X4] :
( ( ~ r2_hidden(X4,X3)
| ( r2_hidden(X4,X1)
& r2_hidden(X4,X2) ) )
& ( ~ r2_hidden(X4,X1)
| ~ r2_hidden(X4,X2)
| r2_hidden(X4,X3) ) ) )
& ( ? [X4] :
( ( ~ r2_hidden(X4,X3)
| ~ r2_hidden(X4,X1)
| ~ r2_hidden(X4,X2) )
& ( r2_hidden(X4,X3)
| ( r2_hidden(X4,X1)
& r2_hidden(X4,X2) ) ) )
| X3 = k3_xboole_0(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(113,plain,
! [X5,X6,X7] :
( ( X7 != k3_xboole_0(X5,X6)
| ! [X8] :
( ( ~ r2_hidden(X8,X7)
| ( r2_hidden(X8,X5)
& r2_hidden(X8,X6) ) )
& ( ~ r2_hidden(X8,X5)
| ~ r2_hidden(X8,X6)
| r2_hidden(X8,X7) ) ) )
& ( ? [X9] :
( ( ~ r2_hidden(X9,X7)
| ~ r2_hidden(X9,X5)
| ~ r2_hidden(X9,X6) )
& ( r2_hidden(X9,X7)
| ( r2_hidden(X9,X5)
& r2_hidden(X9,X6) ) ) )
| X7 = k3_xboole_0(X5,X6) ) ),
inference(variable_rename,[status(thm)],[112]) ).
fof(114,plain,
! [X5,X6,X7] :
( ( X7 != k3_xboole_0(X5,X6)
| ! [X8] :
( ( ~ r2_hidden(X8,X7)
| ( r2_hidden(X8,X5)
& r2_hidden(X8,X6) ) )
& ( ~ r2_hidden(X8,X5)
| ~ r2_hidden(X8,X6)
| r2_hidden(X8,X7) ) ) )
& ( ( ( ~ r2_hidden(esk5_3(X5,X6,X7),X7)
| ~ r2_hidden(esk5_3(X5,X6,X7),X5)
| ~ r2_hidden(esk5_3(X5,X6,X7),X6) )
& ( r2_hidden(esk5_3(X5,X6,X7),X7)
| ( r2_hidden(esk5_3(X5,X6,X7),X5)
& r2_hidden(esk5_3(X5,X6,X7),X6) ) ) )
| X7 = k3_xboole_0(X5,X6) ) ),
inference(skolemize,[status(esa)],[113]) ).
fof(115,plain,
! [X5,X6,X7,X8] :
( ( ( ( ~ r2_hidden(X8,X7)
| ( r2_hidden(X8,X5)
& r2_hidden(X8,X6) ) )
& ( ~ r2_hidden(X8,X5)
| ~ r2_hidden(X8,X6)
| r2_hidden(X8,X7) ) )
| X7 != k3_xboole_0(X5,X6) )
& ( ( ( ~ r2_hidden(esk5_3(X5,X6,X7),X7)
| ~ r2_hidden(esk5_3(X5,X6,X7),X5)
| ~ r2_hidden(esk5_3(X5,X6,X7),X6) )
& ( r2_hidden(esk5_3(X5,X6,X7),X7)
| ( r2_hidden(esk5_3(X5,X6,X7),X5)
& r2_hidden(esk5_3(X5,X6,X7),X6) ) ) )
| X7 = k3_xboole_0(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[114]) ).
fof(116,plain,
! [X5,X6,X7,X8] :
( ( r2_hidden(X8,X5)
| ~ r2_hidden(X8,X7)
| X7 != k3_xboole_0(X5,X6) )
& ( r2_hidden(X8,X6)
| ~ r2_hidden(X8,X7)
| X7 != k3_xboole_0(X5,X6) )
& ( ~ r2_hidden(X8,X5)
| ~ r2_hidden(X8,X6)
| r2_hidden(X8,X7)
| X7 != k3_xboole_0(X5,X6) )
& ( ~ r2_hidden(esk5_3(X5,X6,X7),X7)
| ~ r2_hidden(esk5_3(X5,X6,X7),X5)
| ~ r2_hidden(esk5_3(X5,X6,X7),X6)
| X7 = k3_xboole_0(X5,X6) )
& ( r2_hidden(esk5_3(X5,X6,X7),X5)
| r2_hidden(esk5_3(X5,X6,X7),X7)
| X7 = k3_xboole_0(X5,X6) )
& ( r2_hidden(esk5_3(X5,X6,X7),X6)
| r2_hidden(esk5_3(X5,X6,X7),X7)
| X7 = k3_xboole_0(X5,X6) ) ),
inference(distribute,[status(thm)],[115]) ).
cnf(121,plain,
( r2_hidden(X4,X3)
| X1 != k3_xboole_0(X2,X3)
| ~ r2_hidden(X4,X1) ),
inference(split_conjunct,[status(thm)],[116]) ).
fof(134,plain,
! [X1] :
( ( X1 != k1_xboole_0
| ! [X2] : ~ r2_hidden(X2,X1) )
& ( ? [X2] : r2_hidden(X2,X1)
| X1 = k1_xboole_0 ) ),
inference(fof_nnf,[status(thm)],[47]) ).
fof(135,plain,
! [X3] :
( ( X3 != k1_xboole_0
| ! [X4] : ~ r2_hidden(X4,X3) )
& ( ? [X5] : r2_hidden(X5,X3)
| X3 = k1_xboole_0 ) ),
inference(variable_rename,[status(thm)],[134]) ).
fof(136,plain,
! [X3] :
( ( X3 != k1_xboole_0
| ! [X4] : ~ r2_hidden(X4,X3) )
& ( r2_hidden(esk8_1(X3),X3)
| X3 = k1_xboole_0 ) ),
inference(skolemize,[status(esa)],[135]) ).
fof(137,plain,
! [X3,X4] :
( ( ~ r2_hidden(X4,X3)
| X3 != k1_xboole_0 )
& ( r2_hidden(esk8_1(X3),X3)
| X3 = k1_xboole_0 ) ),
inference(shift_quantors,[status(thm)],[136]) ).
cnf(138,plain,
( X1 = k1_xboole_0
| r2_hidden(esk8_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(139,plain,
( X1 != k1_xboole_0
| ~ r2_hidden(X2,X1) ),
inference(split_conjunct,[status(thm)],[137]) ).
fof(144,plain,
! [X3,X4] : k3_xboole_0(X3,X4) = k3_xboole_0(X4,X3),
inference(variable_rename,[status(thm)],[26]) ).
cnf(145,plain,
k3_xboole_0(X1,X2) = k3_xboole_0(X2,X1),
inference(split_conjunct,[status(thm)],[144]) ).
fof(150,plain,
! [X3,X4] : k3_xboole_0(X3,X3) = X3,
inference(variable_rename,[status(thm)],[28]) ).
cnf(151,plain,
k3_xboole_0(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[150]) ).
fof(152,plain,
! [X3] :
? [X4] : m1_subset_1(X4,X3),
inference(variable_rename,[status(thm)],[29]) ).
fof(153,plain,
! [X3] : m1_subset_1(esk9_1(X3),X3),
inference(skolemize,[status(esa)],[152]) ).
cnf(154,plain,
m1_subset_1(esk9_1(X1),X1),
inference(split_conjunct,[status(thm)],[153]) ).
fof(167,negated_conjecture,
? [X1] :
( ~ v3_struct_0(X1)
& v2_orders_2(X1)
& v3_orders_2(X1)
& v4_orders_2(X1)
& v1_yellow_0(X1)
& v1_lattice3(X1)
& l1_orders_2(X1)
& ? [X2] :
( ~ v3_struct_0(X2)
& v2_orders_2(X2)
& v3_orders_2(X2)
& v4_orders_2(X2)
& v1_yellow_0(X2)
& v1_lattice3(X2)
& l1_orders_2(X2)
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)))
& v1_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),X2)
& v12_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),X2)
& m1_subset_1(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),k1_zfmisc_1(u1_struct_0(X2)))
& ~ r2_hidden(k3_yellow_0(X2),u1_struct_0(X1)) ) ),
inference(fof_nnf,[status(thm)],[51]) ).
fof(168,negated_conjecture,
? [X3] :
( ~ v3_struct_0(X3)
& v2_orders_2(X3)
& v3_orders_2(X3)
& v4_orders_2(X3)
& v1_yellow_0(X3)
& v1_lattice3(X3)
& l1_orders_2(X3)
& ? [X4] :
( ~ v3_struct_0(X4)
& v2_orders_2(X4)
& v3_orders_2(X4)
& v4_orders_2(X4)
& v1_yellow_0(X4)
& v1_lattice3(X4)
& l1_orders_2(X4)
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(X3),u1_struct_0(X4)))
& v1_waybel_0(k3_xboole_0(u1_struct_0(X3),u1_struct_0(X4)),X4)
& v12_waybel_0(k3_xboole_0(u1_struct_0(X3),u1_struct_0(X4)),X4)
& m1_subset_1(k3_xboole_0(u1_struct_0(X3),u1_struct_0(X4)),k1_zfmisc_1(u1_struct_0(X4)))
& ~ r2_hidden(k3_yellow_0(X4),u1_struct_0(X3)) ) ),
inference(variable_rename,[status(thm)],[167]) ).
fof(169,negated_conjecture,
( ~ v3_struct_0(esk11_0)
& v2_orders_2(esk11_0)
& v3_orders_2(esk11_0)
& v4_orders_2(esk11_0)
& v1_yellow_0(esk11_0)
& v1_lattice3(esk11_0)
& l1_orders_2(esk11_0)
& ~ v3_struct_0(esk12_0)
& v2_orders_2(esk12_0)
& v3_orders_2(esk12_0)
& v4_orders_2(esk12_0)
& v1_yellow_0(esk12_0)
& v1_lattice3(esk12_0)
& l1_orders_2(esk12_0)
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(esk11_0),u1_struct_0(esk12_0)))
& v1_waybel_0(k3_xboole_0(u1_struct_0(esk11_0),u1_struct_0(esk12_0)),esk12_0)
& v12_waybel_0(k3_xboole_0(u1_struct_0(esk11_0),u1_struct_0(esk12_0)),esk12_0)
& m1_subset_1(k3_xboole_0(u1_struct_0(esk11_0),u1_struct_0(esk12_0)),k1_zfmisc_1(u1_struct_0(esk12_0)))
& ~ r2_hidden(k3_yellow_0(esk12_0),u1_struct_0(esk11_0)) ),
inference(skolemize,[status(esa)],[168]) ).
cnf(170,negated_conjecture,
~ r2_hidden(k3_yellow_0(esk12_0),u1_struct_0(esk11_0)),
inference(split_conjunct,[status(thm)],[169]) ).
cnf(171,negated_conjecture,
m1_subset_1(k3_xboole_0(u1_struct_0(esk11_0),u1_struct_0(esk12_0)),k1_zfmisc_1(u1_struct_0(esk12_0))),
inference(split_conjunct,[status(thm)],[169]) ).
cnf(172,negated_conjecture,
v12_waybel_0(k3_xboole_0(u1_struct_0(esk11_0),u1_struct_0(esk12_0)),esk12_0),
inference(split_conjunct,[status(thm)],[169]) ).
cnf(174,negated_conjecture,
~ v1_xboole_0(k3_xboole_0(u1_struct_0(esk11_0),u1_struct_0(esk12_0))),
inference(split_conjunct,[status(thm)],[169]) ).
cnf(175,negated_conjecture,
l1_orders_2(esk12_0),
inference(split_conjunct,[status(thm)],[169]) ).
cnf(177,negated_conjecture,
v1_yellow_0(esk12_0),
inference(split_conjunct,[status(thm)],[169]) ).
cnf(178,negated_conjecture,
v4_orders_2(esk12_0),
inference(split_conjunct,[status(thm)],[169]) ).
cnf(181,negated_conjecture,
~ v3_struct_0(esk12_0),
inference(split_conjunct,[status(thm)],[169]) ).
fof(198,plain,
! [X1] :
( ~ l1_orders_2(X1)
| m1_subset_1(k3_yellow_0(X1),u1_struct_0(X1)) ),
inference(fof_nnf,[status(thm)],[38]) ).
fof(199,plain,
! [X2] :
( ~ l1_orders_2(X2)
| m1_subset_1(k3_yellow_0(X2),u1_struct_0(X2)) ),
inference(variable_rename,[status(thm)],[198]) ).
cnf(200,plain,
( m1_subset_1(k3_yellow_0(X1),u1_struct_0(X1))
| ~ l1_orders_2(X1) ),
inference(split_conjunct,[status(thm)],[199]) ).
cnf(209,plain,
( m1_subset_1(esk8_1(X1),X1)
| k1_xboole_0 = X1 ),
inference(spm,[status(thm)],[71,138,theory(equality)]) ).
cnf(215,negated_conjecture,
m1_subset_1(k3_xboole_0(u1_struct_0(esk12_0),u1_struct_0(esk11_0)),k1_zfmisc_1(u1_struct_0(esk12_0))),
inference(rw,[status(thm)],[171,145,theory(equality)]) ).
cnf(217,negated_conjecture,
v12_waybel_0(k3_xboole_0(u1_struct_0(esk12_0),u1_struct_0(esk11_0)),esk12_0),
inference(rw,[status(thm)],[172,145,theory(equality)]) ).
cnf(218,negated_conjecture,
~ v1_xboole_0(k3_xboole_0(u1_struct_0(esk12_0),u1_struct_0(esk11_0))),
inference(rw,[status(thm)],[174,145,theory(equality)]) ).
cnf(221,plain,
( v1_xboole_0(X1)
| r2_hidden(esk9_1(X1),X1) ),
inference(spm,[status(thm)],[110,154,theory(equality)]) ).
cnf(231,plain,
( r2_hidden(X1,X2)
| ~ r2_hidden(X1,k3_xboole_0(X3,X2)) ),
inference(er,[status(thm)],[121,theory(equality)]) ).
cnf(295,plain,
( r2_hidden(X4,X2)
| ~ v12_waybel_0(X2,X1)
| ~ r1_orders_2(X1,X4,X3)
| ~ l1_orders_2(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ m1_subset_1(X4,u1_struct_0(X1))
| ~ r2_hidden(X3,X2) ),
inference(csr,[status(thm)],[104,85]) ).
cnf(296,plain,
( r2_hidden(k3_yellow_0(X1),X2)
| v3_struct_0(X1)
| ~ v12_waybel_0(X2,X1)
| ~ l1_orders_2(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ m1_subset_1(k3_yellow_0(X1),u1_struct_0(X1))
| ~ r2_hidden(X3,X2)
| ~ v1_yellow_0(X1)
| ~ v4_orders_2(X1)
| ~ m1_subset_1(X3,u1_struct_0(X1)) ),
inference(spm,[status(thm)],[295,75,theory(equality)]) ).
cnf(336,plain,
( v1_xboole_0(X1)
| r2_hidden(esk8_1(X1),X1)
| k1_xboole_0 = X1 ),
inference(spm,[status(thm)],[110,209,theory(equality)]) ).
cnf(362,plain,
( v1_xboole_0(X1)
| k1_xboole_0 != X1 ),
inference(spm,[status(thm)],[139,221,theory(equality)]) ).
cnf(457,plain,
( v1_xboole_0(X1)
| r2_hidden(esk8_1(X1),X1) ),
inference(csr,[status(thm)],[336,362]) ).
cnf(466,plain,
( r2_hidden(esk8_1(k3_xboole_0(X1,X2)),X2)
| v1_xboole_0(k3_xboole_0(X1,X2)) ),
inference(spm,[status(thm)],[231,457,theory(equality)]) ).
cnf(2748,plain,
( v3_struct_0(X1)
| r2_hidden(k3_yellow_0(X1),X2)
| ~ v12_waybel_0(X2,X1)
| ~ l1_orders_2(X1)
| ~ v1_yellow_0(X1)
| ~ v4_orders_2(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ m1_subset_1(k3_yellow_0(X1),u1_struct_0(X1))
| ~ r2_hidden(X3,X2) ),
inference(csr,[status(thm)],[296,85]) ).
cnf(2749,plain,
( v3_struct_0(X1)
| r2_hidden(k3_yellow_0(X1),X2)
| ~ v12_waybel_0(X2,X1)
| ~ l1_orders_2(X1)
| ~ v1_yellow_0(X1)
| ~ v4_orders_2(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ r2_hidden(X3,X2) ),
inference(csr,[status(thm)],[2748,200]) ).
cnf(2767,plain,
( v3_struct_0(X1)
| r2_hidden(k3_yellow_0(X1),X2)
| v1_xboole_0(k3_xboole_0(X3,X2))
| ~ v12_waybel_0(X2,X1)
| ~ l1_orders_2(X1)
| ~ v1_yellow_0(X1)
| ~ v4_orders_2(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(spm,[status(thm)],[2749,466,theory(equality)]) ).
cnf(76347,negated_conjecture,
( v3_struct_0(esk12_0)
| v1_xboole_0(k3_xboole_0(X1,k3_xboole_0(u1_struct_0(esk12_0),u1_struct_0(esk11_0))))
| r2_hidden(k3_yellow_0(esk12_0),k3_xboole_0(u1_struct_0(esk12_0),u1_struct_0(esk11_0)))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(esk12_0),u1_struct_0(esk11_0)),esk12_0)
| ~ l1_orders_2(esk12_0)
| ~ v1_yellow_0(esk12_0)
| ~ v4_orders_2(esk12_0) ),
inference(spm,[status(thm)],[2767,215,theory(equality)]) ).
cnf(76466,negated_conjecture,
( v3_struct_0(esk12_0)
| v1_xboole_0(k3_xboole_0(X1,k3_xboole_0(u1_struct_0(esk12_0),u1_struct_0(esk11_0))))
| r2_hidden(k3_yellow_0(esk12_0),k3_xboole_0(u1_struct_0(esk12_0),u1_struct_0(esk11_0)))
| $false
| ~ l1_orders_2(esk12_0)
| ~ v1_yellow_0(esk12_0)
| ~ v4_orders_2(esk12_0) ),
inference(rw,[status(thm)],[76347,217,theory(equality)]) ).
cnf(76467,negated_conjecture,
( v3_struct_0(esk12_0)
| v1_xboole_0(k3_xboole_0(X1,k3_xboole_0(u1_struct_0(esk12_0),u1_struct_0(esk11_0))))
| r2_hidden(k3_yellow_0(esk12_0),k3_xboole_0(u1_struct_0(esk12_0),u1_struct_0(esk11_0)))
| $false
| $false
| ~ v1_yellow_0(esk12_0)
| ~ v4_orders_2(esk12_0) ),
inference(rw,[status(thm)],[76466,175,theory(equality)]) ).
cnf(76468,negated_conjecture,
( v3_struct_0(esk12_0)
| v1_xboole_0(k3_xboole_0(X1,k3_xboole_0(u1_struct_0(esk12_0),u1_struct_0(esk11_0))))
| r2_hidden(k3_yellow_0(esk12_0),k3_xboole_0(u1_struct_0(esk12_0),u1_struct_0(esk11_0)))
| $false
| $false
| $false
| ~ v4_orders_2(esk12_0) ),
inference(rw,[status(thm)],[76467,177,theory(equality)]) ).
cnf(76469,negated_conjecture,
( v3_struct_0(esk12_0)
| v1_xboole_0(k3_xboole_0(X1,k3_xboole_0(u1_struct_0(esk12_0),u1_struct_0(esk11_0))))
| r2_hidden(k3_yellow_0(esk12_0),k3_xboole_0(u1_struct_0(esk12_0),u1_struct_0(esk11_0)))
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[76468,178,theory(equality)]) ).
cnf(76470,negated_conjecture,
( v3_struct_0(esk12_0)
| v1_xboole_0(k3_xboole_0(X1,k3_xboole_0(u1_struct_0(esk12_0),u1_struct_0(esk11_0))))
| r2_hidden(k3_yellow_0(esk12_0),k3_xboole_0(u1_struct_0(esk12_0),u1_struct_0(esk11_0))) ),
inference(cn,[status(thm)],[76469,theory(equality)]) ).
cnf(76471,negated_conjecture,
( v1_xboole_0(k3_xboole_0(X1,k3_xboole_0(u1_struct_0(esk12_0),u1_struct_0(esk11_0))))
| r2_hidden(k3_yellow_0(esk12_0),k3_xboole_0(u1_struct_0(esk12_0),u1_struct_0(esk11_0))) ),
inference(sr,[status(thm)],[76470,181,theory(equality)]) ).
cnf(76478,negated_conjecture,
( v1_xboole_0(k3_xboole_0(u1_struct_0(esk12_0),u1_struct_0(esk11_0)))
| r2_hidden(k3_yellow_0(esk12_0),k3_xboole_0(u1_struct_0(esk12_0),u1_struct_0(esk11_0))) ),
inference(spm,[status(thm)],[76471,151,theory(equality)]) ).
cnf(76631,negated_conjecture,
r2_hidden(k3_yellow_0(esk12_0),k3_xboole_0(u1_struct_0(esk12_0),u1_struct_0(esk11_0))),
inference(sr,[status(thm)],[76478,218,theory(equality)]) ).
cnf(76685,negated_conjecture,
r2_hidden(k3_yellow_0(esk12_0),u1_struct_0(esk11_0)),
inference(spm,[status(thm)],[231,76631,theory(equality)]) ).
cnf(76711,negated_conjecture,
$false,
inference(sr,[status(thm)],[76685,170,theory(equality)]) ).
cnf(76712,negated_conjecture,
$false,
76711,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU411+1.p
% --creating new selector for []
% -running prover on /tmp/tmpFCikqw/sel_SEU411+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU411+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU411+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU411+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
%
%------------------------------------------------------------------------------