TSTP Solution File: SET681+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET681+3 : TPTP v5.0.0. Released v2.2.0.
% 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 : Sun Dec 26 03:10:49 EST 2010
% Result : Theorem 0.22s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 11
% Syntax : Number of formulae : 139 ( 13 unt; 0 def)
% Number of atoms : 657 ( 8 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 862 ( 344 ~; 368 |; 98 &)
% ( 9 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-3 aty)
% Number of variables : 290 ( 22 sgn 150 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X1))
=> ! [X4] :
( ilf_type(X4,member_type(X1))
=> ( member(X4,range(X2,X1,X3))
<=> ? [X5] :
( ilf_type(X5,member_type(X2))
& member(ordered_pair(X5,X4),X3) ) ) ) ) ) ),
file('/tmp/tmpF7hMHH/sel_SET681+3.p_1',prove_relset_1_48) ).
fof(5,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> relation_like(X3) ) ) ),
file('/tmp/tmpF7hMHH/sel_SET681+3.p_1',p26) ).
fof(10,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> range(X1,X2,X3) = range_of(X3) ) ) ),
file('/tmp/tmpF7hMHH/sel_SET681+3.p_1',p29) ).
fof(12,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/tmp/tmpF7hMHH/sel_SET681+3.p_1',p10) ).
fof(19,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,binary_relation_type)
<=> ( relation_like(X1)
& ilf_type(X1,set_type) ) ) ),
file('/tmp/tmpF7hMHH/sel_SET681+3.p_1',p17) ).
fof(23,axiom,
! [X1] : ilf_type(X1,set_type),
file('/tmp/tmpF7hMHH/sel_SET681+3.p_1',p31) ).
fof(24,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,binary_relation_type)
=> ( member(ordered_pair(X1,X2),X3)
=> ( member(X1,domain_of(X3))
& member(X2,range_of(X3)) ) ) ) ) ),
file('/tmp/tmpF7hMHH/sel_SET681+3.p_1',p2) ).
fof(25,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,set_type)
=> ! [X5] :
( ilf_type(X5,relation_type(X1,X2))
=> ( member(ordered_pair(X3,X4),X5)
=> ( member(X3,X1)
& member(X4,X2) ) ) ) ) ) ) ),
file('/tmp/tmpF7hMHH/sel_SET681+3.p_1',p3) ).
fof(26,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( member(X1,range_of(X2))
<=> ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X3,X1),X2) ) ) ) ),
file('/tmp/tmpF7hMHH/sel_SET681+3.p_1',p1) ).
fof(27,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> ilf_type(X3,relation_type(X1,X2)) )
& ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ilf_type(X4,subset_type(cross_product(X1,X2))) ) ) ) ),
file('/tmp/tmpF7hMHH/sel_SET681+3.p_1',p6) ).
fof(31,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
file('/tmp/tmpF7hMHH/sel_SET681+3.p_1',p8) ).
fof(33,negated_conjecture,
~ ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X1))
=> ! [X4] :
( ilf_type(X4,member_type(X1))
=> ( member(X4,range(X2,X1,X3))
<=> ? [X5] :
( ilf_type(X5,member_type(X2))
& member(ordered_pair(X5,X4),X3) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[1]) ).
fof(34,negated_conjecture,
~ ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X1))
=> ! [X4] :
( ilf_type(X4,member_type(X1))
=> ( member(X4,range(X2,X1,X3))
<=> ? [X5] :
( ilf_type(X5,member_type(X2))
& member(ordered_pair(X5,X4),X3) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[33,theory(equality)]) ).
fof(36,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[12,theory(equality)]) ).
fof(37,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[31,theory(equality)]) ).
fof(39,negated_conjecture,
? [X1] :
( ~ empty(X1)
& ilf_type(X1,set_type)
& ? [X2] :
( ~ empty(X2)
& ilf_type(X2,set_type)
& ? [X3] :
( ilf_type(X3,relation_type(X2,X1))
& ? [X4] :
( ilf_type(X4,member_type(X1))
& ( ~ member(X4,range(X2,X1,X3))
| ! [X5] :
( ~ ilf_type(X5,member_type(X2))
| ~ member(ordered_pair(X5,X4),X3) ) )
& ( member(X4,range(X2,X1,X3))
| ? [X5] :
( ilf_type(X5,member_type(X2))
& member(ordered_pair(X5,X4),X3) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[34]) ).
fof(40,negated_conjecture,
? [X6] :
( ~ empty(X6)
& ilf_type(X6,set_type)
& ? [X7] :
( ~ empty(X7)
& ilf_type(X7,set_type)
& ? [X8] :
( ilf_type(X8,relation_type(X7,X6))
& ? [X9] :
( ilf_type(X9,member_type(X6))
& ( ~ member(X9,range(X7,X6,X8))
| ! [X10] :
( ~ ilf_type(X10,member_type(X7))
| ~ member(ordered_pair(X10,X9),X8) ) )
& ( member(X9,range(X7,X6,X8))
| ? [X11] :
( ilf_type(X11,member_type(X7))
& member(ordered_pair(X11,X9),X8) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[39]) ).
fof(41,negated_conjecture,
( ~ empty(esk1_0)
& ilf_type(esk1_0,set_type)
& ~ empty(esk2_0)
& ilf_type(esk2_0,set_type)
& ilf_type(esk3_0,relation_type(esk2_0,esk1_0))
& ilf_type(esk4_0,member_type(esk1_0))
& ( ~ member(esk4_0,range(esk2_0,esk1_0,esk3_0))
| ! [X10] :
( ~ ilf_type(X10,member_type(esk2_0))
| ~ member(ordered_pair(X10,esk4_0),esk3_0) ) )
& ( member(esk4_0,range(esk2_0,esk1_0,esk3_0))
| ( ilf_type(esk5_0,member_type(esk2_0))
& member(ordered_pair(esk5_0,esk4_0),esk3_0) ) ) ),
inference(skolemize,[status(esa)],[40]) ).
fof(42,negated_conjecture,
! [X10] :
( ( ~ ilf_type(X10,member_type(esk2_0))
| ~ member(ordered_pair(X10,esk4_0),esk3_0)
| ~ member(esk4_0,range(esk2_0,esk1_0,esk3_0)) )
& ( member(esk4_0,range(esk2_0,esk1_0,esk3_0))
| ( ilf_type(esk5_0,member_type(esk2_0))
& member(ordered_pair(esk5_0,esk4_0),esk3_0) ) )
& ilf_type(esk4_0,member_type(esk1_0))
& ilf_type(esk3_0,relation_type(esk2_0,esk1_0))
& ~ empty(esk2_0)
& ilf_type(esk2_0,set_type)
& ~ empty(esk1_0)
& ilf_type(esk1_0,set_type) ),
inference(shift_quantors,[status(thm)],[41]) ).
fof(43,negated_conjecture,
! [X10] :
( ( ~ ilf_type(X10,member_type(esk2_0))
| ~ member(ordered_pair(X10,esk4_0),esk3_0)
| ~ member(esk4_0,range(esk2_0,esk1_0,esk3_0)) )
& ( ilf_type(esk5_0,member_type(esk2_0))
| member(esk4_0,range(esk2_0,esk1_0,esk3_0)) )
& ( member(ordered_pair(esk5_0,esk4_0),esk3_0)
| member(esk4_0,range(esk2_0,esk1_0,esk3_0)) )
& ilf_type(esk4_0,member_type(esk1_0))
& ilf_type(esk3_0,relation_type(esk2_0,esk1_0))
& ~ empty(esk2_0)
& ilf_type(esk2_0,set_type)
& ~ empty(esk1_0)
& ilf_type(esk1_0,set_type) ),
inference(distribute,[status(thm)],[42]) ).
cnf(48,negated_conjecture,
ilf_type(esk3_0,relation_type(esk2_0,esk1_0)),
inference(split_conjunct,[status(thm)],[43]) ).
cnf(50,negated_conjecture,
( member(esk4_0,range(esk2_0,esk1_0,esk3_0))
| member(ordered_pair(esk5_0,esk4_0),esk3_0) ),
inference(split_conjunct,[status(thm)],[43]) ).
cnf(51,negated_conjecture,
( member(esk4_0,range(esk2_0,esk1_0,esk3_0))
| ilf_type(esk5_0,member_type(esk2_0)) ),
inference(split_conjunct,[status(thm)],[43]) ).
cnf(52,negated_conjecture,
( ~ member(esk4_0,range(esk2_0,esk1_0,esk3_0))
| ~ member(ordered_pair(X1,esk4_0),esk3_0)
| ~ ilf_type(X1,member_type(esk2_0)) ),
inference(split_conjunct,[status(thm)],[43]) ).
fof(71,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,subset_type(cross_product(X1,X2)))
| relation_like(X3) ) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(72,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,subset_type(cross_product(X4,X5)))
| relation_like(X6) ) ) ),
inference(variable_rename,[status(thm)],[71]) ).
fof(73,plain,
! [X4,X5,X6] :
( ~ ilf_type(X6,subset_type(cross_product(X4,X5)))
| relation_like(X6)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[72]) ).
cnf(74,plain,
( relation_like(X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(split_conjunct,[status(thm)],[73]) ).
fof(103,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,relation_type(X1,X2))
| range(X1,X2,X3) = range_of(X3) ) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(104,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,relation_type(X4,X5))
| range(X4,X5,X6) = range_of(X6) ) ) ),
inference(variable_rename,[status(thm)],[103]) ).
fof(105,plain,
! [X4,X5,X6] :
( ~ ilf_type(X6,relation_type(X4,X5))
| range(X4,X5,X6) = range_of(X6)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[104]) ).
cnf(106,plain,
( range(X1,X2,X3) = range_of(X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[105]) ).
fof(111,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ empty(X1)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X1) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& member(X2,X1) )
| empty(X1) ) ) ),
inference(fof_nnf,[status(thm)],[36]) ).
fof(112,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ( ( ~ empty(X3)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(X4,X3) ) )
& ( ? [X5] :
( ilf_type(X5,set_type)
& member(X5,X3) )
| empty(X3) ) ) ),
inference(variable_rename,[status(thm)],[111]) ).
fof(113,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ( ( ~ empty(X3)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(X4,X3) ) )
& ( ( ilf_type(esk12_1(X3),set_type)
& member(esk12_1(X3),X3) )
| empty(X3) ) ) ),
inference(skolemize,[status(esa)],[112]) ).
fof(114,plain,
! [X3,X4] :
( ( ( ~ ilf_type(X4,set_type)
| ~ member(X4,X3)
| ~ empty(X3) )
& ( ( ilf_type(esk12_1(X3),set_type)
& member(esk12_1(X3),X3) )
| empty(X3) ) )
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[113]) ).
fof(115,plain,
! [X3,X4] :
( ( ~ ilf_type(X4,set_type)
| ~ member(X4,X3)
| ~ empty(X3)
| ~ ilf_type(X3,set_type) )
& ( ilf_type(esk12_1(X3),set_type)
| empty(X3)
| ~ ilf_type(X3,set_type) )
& ( member(esk12_1(X3),X3)
| empty(X3)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[114]) ).
cnf(118,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(X1)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[115]) ).
fof(140,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ ilf_type(X1,binary_relation_type)
| ( relation_like(X1)
& ilf_type(X1,set_type) ) )
& ( ~ relation_like(X1)
| ~ ilf_type(X1,set_type)
| ilf_type(X1,binary_relation_type) ) ) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(141,plain,
! [X2] :
( ~ ilf_type(X2,set_type)
| ( ( ~ ilf_type(X2,binary_relation_type)
| ( relation_like(X2)
& ilf_type(X2,set_type) ) )
& ( ~ relation_like(X2)
| ~ ilf_type(X2,set_type)
| ilf_type(X2,binary_relation_type) ) ) ),
inference(variable_rename,[status(thm)],[140]) ).
fof(142,plain,
! [X2] :
( ( relation_like(X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X2,set_type) )
& ( ilf_type(X2,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X2,set_type) )
& ( ~ relation_like(X2)
| ~ ilf_type(X2,set_type)
| ilf_type(X2,binary_relation_type)
| ~ ilf_type(X2,set_type) ) ),
inference(distribute,[status(thm)],[141]) ).
cnf(143,plain,
( ilf_type(X1,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,set_type)
| ~ relation_like(X1) ),
inference(split_conjunct,[status(thm)],[142]) ).
fof(159,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[23]) ).
cnf(160,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[159]) ).
fof(161,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,binary_relation_type)
| ~ member(ordered_pair(X1,X2),X3)
| ( member(X1,domain_of(X3))
& member(X2,range_of(X3)) ) ) ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(162,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,binary_relation_type)
| ~ member(ordered_pair(X4,X5),X6)
| ( member(X4,domain_of(X6))
& member(X5,range_of(X6)) ) ) ) ),
inference(variable_rename,[status(thm)],[161]) ).
fof(163,plain,
! [X4,X5,X6] :
( ~ ilf_type(X6,binary_relation_type)
| ~ member(ordered_pair(X4,X5),X6)
| ( member(X4,domain_of(X6))
& member(X5,range_of(X6)) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[162]) ).
fof(164,plain,
! [X4,X5,X6] :
( ( member(X4,domain_of(X6))
| ~ member(ordered_pair(X4,X5),X6)
| ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(X5,range_of(X6))
| ~ member(ordered_pair(X4,X5),X6)
| ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[163]) ).
cnf(165,plain,
( member(X2,range_of(X3))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(ordered_pair(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[164]) ).
fof(167,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,relation_type(X1,X2))
| ~ member(ordered_pair(X3,X4),X5)
| ( member(X3,X1)
& member(X4,X2) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(168,plain,
! [X6] :
( ~ ilf_type(X6,set_type)
| ! [X7] :
( ~ ilf_type(X7,set_type)
| ! [X8] :
( ~ ilf_type(X8,set_type)
| ! [X9] :
( ~ ilf_type(X9,set_type)
| ! [X10] :
( ~ ilf_type(X10,relation_type(X6,X7))
| ~ member(ordered_pair(X8,X9),X10)
| ( member(X8,X6)
& member(X9,X7) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[167]) ).
fof(169,plain,
! [X6,X7,X8,X9,X10] :
( ~ ilf_type(X10,relation_type(X6,X7))
| ~ member(ordered_pair(X8,X9),X10)
| ( member(X8,X6)
& member(X9,X7) )
| ~ ilf_type(X9,set_type)
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type) ),
inference(shift_quantors,[status(thm)],[168]) ).
fof(170,plain,
! [X6,X7,X8,X9,X10] :
( ( member(X8,X6)
| ~ member(ordered_pair(X8,X9),X10)
| ~ ilf_type(X10,relation_type(X6,X7))
| ~ ilf_type(X9,set_type)
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type) )
& ( member(X9,X7)
| ~ member(ordered_pair(X8,X9),X10)
| ~ ilf_type(X10,relation_type(X6,X7))
| ~ ilf_type(X9,set_type)
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type) ) ),
inference(distribute,[status(thm)],[169]) ).
cnf(172,plain,
( member(X3,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X5,relation_type(X1,X2))
| ~ member(ordered_pair(X3,X4),X5) ),
inference(split_conjunct,[status(thm)],[170]) ).
fof(173,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,binary_relation_type)
| ( ( ~ member(X1,range_of(X2))
| ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X3,X1),X2) ) )
& ( ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X3,X1),X2) )
| member(X1,range_of(X2)) ) ) ) ),
inference(fof_nnf,[status(thm)],[26]) ).
fof(174,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,binary_relation_type)
| ( ( ~ member(X4,range_of(X5))
| ? [X6] :
( ilf_type(X6,set_type)
& member(ordered_pair(X6,X4),X5) ) )
& ( ! [X7] :
( ~ ilf_type(X7,set_type)
| ~ member(ordered_pair(X7,X4),X5) )
| member(X4,range_of(X5)) ) ) ) ),
inference(variable_rename,[status(thm)],[173]) ).
fof(175,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,binary_relation_type)
| ( ( ~ member(X4,range_of(X5))
| ( ilf_type(esk14_2(X4,X5),set_type)
& member(ordered_pair(esk14_2(X4,X5),X4),X5) ) )
& ( ! [X7] :
( ~ ilf_type(X7,set_type)
| ~ member(ordered_pair(X7,X4),X5) )
| member(X4,range_of(X5)) ) ) ) ),
inference(skolemize,[status(esa)],[174]) ).
fof(176,plain,
! [X4,X5,X7] :
( ( ( ~ ilf_type(X7,set_type)
| ~ member(ordered_pair(X7,X4),X5)
| member(X4,range_of(X5)) )
& ( ~ member(X4,range_of(X5))
| ( ilf_type(esk14_2(X4,X5),set_type)
& member(ordered_pair(esk14_2(X4,X5),X4),X5) ) ) )
| ~ ilf_type(X5,binary_relation_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[175]) ).
fof(177,plain,
! [X4,X5,X7] :
( ( ~ ilf_type(X7,set_type)
| ~ member(ordered_pair(X7,X4),X5)
| member(X4,range_of(X5))
| ~ ilf_type(X5,binary_relation_type)
| ~ ilf_type(X4,set_type) )
& ( ilf_type(esk14_2(X4,X5),set_type)
| ~ member(X4,range_of(X5))
| ~ ilf_type(X5,binary_relation_type)
| ~ ilf_type(X4,set_type) )
& ( member(ordered_pair(esk14_2(X4,X5),X4),X5)
| ~ member(X4,range_of(X5))
| ~ ilf_type(X5,binary_relation_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[176]) ).
cnf(178,plain,
( member(ordered_pair(esk14_2(X1,X2),X1),X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(X1,range_of(X2)) ),
inference(split_conjunct,[status(thm)],[177]) ).
fof(181,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ( ! [X3] :
( ~ ilf_type(X3,subset_type(cross_product(X1,X2)))
| ilf_type(X3,relation_type(X1,X2)) )
& ! [X4] :
( ~ ilf_type(X4,relation_type(X1,X2))
| ilf_type(X4,subset_type(cross_product(X1,X2))) ) ) ) ),
inference(fof_nnf,[status(thm)],[27]) ).
fof(182,plain,
! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ( ! [X7] :
( ~ ilf_type(X7,subset_type(cross_product(X5,X6)))
| ilf_type(X7,relation_type(X5,X6)) )
& ! [X8] :
( ~ ilf_type(X8,relation_type(X5,X6))
| ilf_type(X8,subset_type(cross_product(X5,X6))) ) ) ) ),
inference(variable_rename,[status(thm)],[181]) ).
fof(183,plain,
! [X5,X6,X7,X8] :
( ( ( ~ ilf_type(X8,relation_type(X5,X6))
| ilf_type(X8,subset_type(cross_product(X5,X6))) )
& ( ~ ilf_type(X7,subset_type(cross_product(X5,X6)))
| ilf_type(X7,relation_type(X5,X6)) ) )
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ),
inference(shift_quantors,[status(thm)],[182]) ).
fof(184,plain,
! [X5,X6,X7,X8] :
( ( ~ ilf_type(X8,relation_type(X5,X6))
| ilf_type(X8,subset_type(cross_product(X5,X6)))
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( ~ ilf_type(X7,subset_type(cross_product(X5,X6)))
| ilf_type(X7,relation_type(X5,X6))
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ) ),
inference(distribute,[status(thm)],[183]) ).
cnf(186,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[184]) ).
fof(202,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( empty(X2)
| ~ ilf_type(X2,set_type)
| ( ( ~ ilf_type(X1,member_type(X2))
| member(X1,X2) )
& ( ~ member(X1,X2)
| ilf_type(X1,member_type(X2)) ) ) ) ),
inference(fof_nnf,[status(thm)],[37]) ).
fof(203,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ! [X4] :
( empty(X4)
| ~ ilf_type(X4,set_type)
| ( ( ~ ilf_type(X3,member_type(X4))
| member(X3,X4) )
& ( ~ member(X3,X4)
| ilf_type(X3,member_type(X4)) ) ) ) ),
inference(variable_rename,[status(thm)],[202]) ).
fof(204,plain,
! [X3,X4] :
( empty(X4)
| ~ ilf_type(X4,set_type)
| ( ( ~ ilf_type(X3,member_type(X4))
| member(X3,X4) )
& ( ~ member(X3,X4)
| ilf_type(X3,member_type(X4)) ) )
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[203]) ).
fof(205,plain,
! [X3,X4] :
( ( ~ ilf_type(X3,member_type(X4))
| member(X3,X4)
| empty(X4)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) )
& ( ~ member(X3,X4)
| ilf_type(X3,member_type(X4))
| empty(X4)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[204]) ).
cnf(206,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[205]) ).
cnf(224,negated_conjecture,
( ilf_type(esk5_0,member_type(esk2_0))
| ~ member(ordered_pair(X1,esk4_0),esk3_0)
| ~ ilf_type(X1,member_type(esk2_0)) ),
inference(spm,[status(thm)],[52,51,theory(equality)]) ).
cnf(225,negated_conjecture,
( member(ordered_pair(esk5_0,esk4_0),esk3_0)
| ~ member(ordered_pair(X1,esk4_0),esk3_0)
| ~ ilf_type(X1,member_type(esk2_0)) ),
inference(spm,[status(thm)],[52,50,theory(equality)]) ).
cnf(228,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[118,160,theory(equality)]) ).
cnf(229,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| $false ),
inference(rw,[status(thm)],[228,160,theory(equality)]) ).
cnf(230,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[229,theory(equality)]) ).
cnf(242,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| $false ),
inference(rw,[status(thm)],[143,160,theory(equality)]) ).
cnf(243,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[242,theory(equality)]) ).
cnf(273,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[206,160,theory(equality)]) ).
cnf(274,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2)
| $false
| $false ),
inference(rw,[status(thm)],[273,160,theory(equality)]) ).
cnf(275,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(cn,[status(thm)],[274,theory(equality)]) ).
cnf(276,plain,
( ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[275,230]) ).
cnf(297,plain,
( relation_like(X3)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[74,160,theory(equality)]) ).
cnf(298,plain,
( relation_like(X3)
| $false
| $false
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[297,160,theory(equality)]) ).
cnf(299,plain,
( relation_like(X3)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(cn,[status(thm)],[298,theory(equality)]) ).
cnf(343,plain,
( member(X2,range_of(X3))
| ~ ilf_type(X3,binary_relation_type)
| $false
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X1,X2),X3) ),
inference(rw,[status(thm)],[165,160,theory(equality)]) ).
cnf(344,plain,
( member(X2,range_of(X3))
| ~ ilf_type(X3,binary_relation_type)
| $false
| $false
| ~ member(ordered_pair(X1,X2),X3) ),
inference(rw,[status(thm)],[343,160,theory(equality)]) ).
cnf(345,plain,
( member(X2,range_of(X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ member(ordered_pair(X1,X2),X3) ),
inference(cn,[status(thm)],[344,theory(equality)]) ).
cnf(352,plain,
( range(X1,X2,X3) = range_of(X3)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[106,160,theory(equality)]) ).
cnf(353,plain,
( range(X1,X2,X3) = range_of(X3)
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[352,160,theory(equality)]) ).
cnf(354,plain,
( range(X1,X2,X3) = range_of(X3)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[353,theory(equality)]) ).
cnf(355,negated_conjecture,
( member(esk4_0,range_of(esk3_0))
| ilf_type(esk5_0,member_type(esk2_0))
| ~ ilf_type(esk3_0,relation_type(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[51,354,theory(equality)]) ).
cnf(356,negated_conjecture,
( member(esk4_0,range_of(esk3_0))
| member(ordered_pair(esk5_0,esk4_0),esk3_0)
| ~ ilf_type(esk3_0,relation_type(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[50,354,theory(equality)]) ).
cnf(357,negated_conjecture,
( ~ member(esk4_0,range_of(esk3_0))
| ~ member(ordered_pair(X1,esk4_0),esk3_0)
| ~ ilf_type(X1,member_type(esk2_0))
| ~ ilf_type(esk3_0,relation_type(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[52,354,theory(equality)]) ).
cnf(358,negated_conjecture,
( member(esk4_0,range_of(esk3_0))
| ilf_type(esk5_0,member_type(esk2_0))
| $false ),
inference(rw,[status(thm)],[355,48,theory(equality)]) ).
cnf(359,negated_conjecture,
( member(esk4_0,range_of(esk3_0))
| ilf_type(esk5_0,member_type(esk2_0)) ),
inference(cn,[status(thm)],[358,theory(equality)]) ).
cnf(360,negated_conjecture,
( member(esk4_0,range_of(esk3_0))
| member(ordered_pair(esk5_0,esk4_0),esk3_0)
| $false ),
inference(rw,[status(thm)],[356,48,theory(equality)]) ).
cnf(361,negated_conjecture,
( member(esk4_0,range_of(esk3_0))
| member(ordered_pair(esk5_0,esk4_0),esk3_0) ),
inference(cn,[status(thm)],[360,theory(equality)]) ).
cnf(362,negated_conjecture,
( ~ member(esk4_0,range_of(esk3_0))
| ~ member(ordered_pair(X1,esk4_0),esk3_0)
| ~ ilf_type(X1,member_type(esk2_0))
| $false ),
inference(rw,[status(thm)],[357,48,theory(equality)]) ).
cnf(363,negated_conjecture,
( ~ member(esk4_0,range_of(esk3_0))
| ~ member(ordered_pair(X1,esk4_0),esk3_0)
| ~ ilf_type(X1,member_type(esk2_0)) ),
inference(cn,[status(thm)],[362,theory(equality)]) ).
cnf(364,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[186,160,theory(equality)]) ).
cnf(365,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[364,160,theory(equality)]) ).
cnf(366,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[365,theory(equality)]) ).
cnf(367,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[299,366,theory(equality)]) ).
cnf(378,plain,
( member(ordered_pair(esk14_2(X1,X2),X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| $false
| ~ member(X1,range_of(X2)) ),
inference(rw,[status(thm)],[178,160,theory(equality)]) ).
cnf(379,plain,
( member(ordered_pair(esk14_2(X1,X2),X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(X1,range_of(X2)) ),
inference(cn,[status(thm)],[378,theory(equality)]) ).
cnf(410,plain,
( member(X3,X1)
| $false
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X5,relation_type(X1,X2))
| ~ member(ordered_pair(X3,X4),X5) ),
inference(rw,[status(thm)],[172,160,theory(equality)]) ).
cnf(411,plain,
( member(X3,X1)
| $false
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X5,relation_type(X1,X2))
| ~ member(ordered_pair(X3,X4),X5) ),
inference(rw,[status(thm)],[410,160,theory(equality)]) ).
cnf(412,plain,
( member(X3,X1)
| $false
| $false
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X5,relation_type(X1,X2))
| ~ member(ordered_pair(X3,X4),X5) ),
inference(rw,[status(thm)],[411,160,theory(equality)]) ).
cnf(413,plain,
( member(X3,X1)
| $false
| $false
| $false
| $false
| ~ ilf_type(X5,relation_type(X1,X2))
| ~ member(ordered_pair(X3,X4),X5) ),
inference(rw,[status(thm)],[412,160,theory(equality)]) ).
cnf(414,plain,
( member(X3,X1)
| ~ ilf_type(X5,relation_type(X1,X2))
| ~ member(ordered_pair(X3,X4),X5) ),
inference(cn,[status(thm)],[413,theory(equality)]) ).
cnf(415,negated_conjecture,
( member(X1,esk2_0)
| ~ member(ordered_pair(X1,X2),esk3_0) ),
inference(spm,[status(thm)],[414,48,theory(equality)]) ).
cnf(452,negated_conjecture,
( ilf_type(esk5_0,member_type(esk2_0))
| ~ ilf_type(esk14_2(esk4_0,esk3_0),member_type(esk2_0))
| ~ member(esk4_0,range_of(esk3_0))
| ~ ilf_type(esk3_0,binary_relation_type) ),
inference(spm,[status(thm)],[224,379,theory(equality)]) ).
cnf(458,negated_conjecture,
( member(ordered_pair(esk5_0,esk4_0),esk3_0)
| ~ ilf_type(esk14_2(esk4_0,esk3_0),member_type(esk2_0))
| ~ member(esk4_0,range_of(esk3_0))
| ~ ilf_type(esk3_0,binary_relation_type) ),
inference(spm,[status(thm)],[225,379,theory(equality)]) ).
cnf(461,negated_conjecture,
( member(esk14_2(X1,esk3_0),esk2_0)
| ~ member(X1,range_of(esk3_0))
| ~ ilf_type(esk3_0,binary_relation_type) ),
inference(spm,[status(thm)],[415,379,theory(equality)]) ).
cnf(481,negated_conjecture,
( ilf_type(esk5_0,member_type(esk2_0))
| ~ ilf_type(esk14_2(esk4_0,esk3_0),member_type(esk2_0))
| ~ ilf_type(esk3_0,binary_relation_type) ),
inference(csr,[status(thm)],[452,359]) ).
cnf(482,negated_conjecture,
( ilf_type(esk5_0,member_type(esk2_0))
| ~ ilf_type(esk3_0,binary_relation_type)
| ~ member(esk14_2(esk4_0,esk3_0),esk2_0) ),
inference(spm,[status(thm)],[481,276,theory(equality)]) ).
cnf(483,negated_conjecture,
( member(ordered_pair(esk5_0,esk4_0),esk3_0)
| ~ ilf_type(esk14_2(esk4_0,esk3_0),member_type(esk2_0))
| ~ ilf_type(esk3_0,binary_relation_type) ),
inference(csr,[status(thm)],[458,361]) ).
cnf(484,negated_conjecture,
( member(ordered_pair(esk5_0,esk4_0),esk3_0)
| ~ ilf_type(esk3_0,binary_relation_type)
| ~ member(esk14_2(esk4_0,esk3_0),esk2_0) ),
inference(spm,[status(thm)],[483,276,theory(equality)]) ).
cnf(497,negated_conjecture,
relation_like(esk3_0),
inference(spm,[status(thm)],[367,48,theory(equality)]) ).
cnf(510,negated_conjecture,
ilf_type(esk3_0,binary_relation_type),
inference(spm,[status(thm)],[243,497,theory(equality)]) ).
cnf(513,negated_conjecture,
( member(ordered_pair(esk5_0,esk4_0),esk3_0)
| ~ member(esk14_2(esk4_0,esk3_0),esk2_0)
| $false ),
inference(rw,[status(thm)],[484,510,theory(equality)]) ).
cnf(514,negated_conjecture,
( member(ordered_pair(esk5_0,esk4_0),esk3_0)
| ~ member(esk14_2(esk4_0,esk3_0),esk2_0) ),
inference(cn,[status(thm)],[513,theory(equality)]) ).
cnf(517,negated_conjecture,
( ilf_type(esk5_0,member_type(esk2_0))
| ~ member(esk14_2(esk4_0,esk3_0),esk2_0)
| $false ),
inference(rw,[status(thm)],[482,510,theory(equality)]) ).
cnf(518,negated_conjecture,
( ilf_type(esk5_0,member_type(esk2_0))
| ~ member(esk14_2(esk4_0,esk3_0),esk2_0) ),
inference(cn,[status(thm)],[517,theory(equality)]) ).
cnf(592,negated_conjecture,
( member(esk14_2(X1,esk3_0),esk2_0)
| ~ member(X1,range_of(esk3_0))
| $false ),
inference(rw,[status(thm)],[461,510,theory(equality)]) ).
cnf(593,negated_conjecture,
( member(esk14_2(X1,esk3_0),esk2_0)
| ~ member(X1,range_of(esk3_0)) ),
inference(cn,[status(thm)],[592,theory(equality)]) ).
cnf(595,negated_conjecture,
( ilf_type(esk5_0,member_type(esk2_0))
| ~ member(esk4_0,range_of(esk3_0)) ),
inference(spm,[status(thm)],[518,593,theory(equality)]) ).
cnf(596,negated_conjecture,
( member(ordered_pair(esk5_0,esk4_0),esk3_0)
| ~ member(esk4_0,range_of(esk3_0)) ),
inference(spm,[status(thm)],[514,593,theory(equality)]) ).
cnf(597,negated_conjecture,
ilf_type(esk5_0,member_type(esk2_0)),
inference(csr,[status(thm)],[595,359]) ).
cnf(610,negated_conjecture,
member(ordered_pair(esk5_0,esk4_0),esk3_0),
inference(csr,[status(thm)],[596,361]) ).
cnf(612,negated_conjecture,
( member(esk4_0,range_of(esk3_0))
| ~ ilf_type(esk3_0,binary_relation_type) ),
inference(spm,[status(thm)],[345,610,theory(equality)]) ).
cnf(623,negated_conjecture,
( member(esk4_0,range_of(esk3_0))
| $false ),
inference(rw,[status(thm)],[612,510,theory(equality)]) ).
cnf(624,negated_conjecture,
member(esk4_0,range_of(esk3_0)),
inference(cn,[status(thm)],[623,theory(equality)]) ).
cnf(632,negated_conjecture,
( ~ member(ordered_pair(X1,esk4_0),esk3_0)
| $false
| ~ ilf_type(X1,member_type(esk2_0)) ),
inference(rw,[status(thm)],[363,624,theory(equality)]) ).
cnf(633,negated_conjecture,
( ~ member(ordered_pair(X1,esk4_0),esk3_0)
| ~ ilf_type(X1,member_type(esk2_0)) ),
inference(cn,[status(thm)],[632,theory(equality)]) ).
cnf(647,negated_conjecture,
~ ilf_type(esk5_0,member_type(esk2_0)),
inference(spm,[status(thm)],[633,610,theory(equality)]) ).
cnf(649,negated_conjecture,
$false,
inference(rw,[status(thm)],[647,597,theory(equality)]) ).
cnf(650,negated_conjecture,
$false,
inference(cn,[status(thm)],[649,theory(equality)]) ).
cnf(651,negated_conjecture,
$false,
650,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET681+3.p
% --creating new selector for []
% -running prover on /tmp/tmpF7hMHH/sel_SET681+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET681+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET681+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET681+3.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
%
%------------------------------------------------------------------------------