TSTP Solution File: SET675+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET675+3 : TPTP v5.0.0. Released v2.2.0.
% 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 : Sun Dec 26 03:10:11 EST 2010
% Result : Theorem 11.19s
% Output : CNFRefutation 11.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 12
% Syntax : Number of formulae : 117 ( 11 unt; 0 def)
% Number of atoms : 427 ( 107 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 541 ( 231 ~; 248 |; 28 &)
% ( 1 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-4 aty)
% Number of variables : 260 ( 8 sgn 121 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> domain(X1,X2,X3) = domain_of(X3) ) ) ),
file('/tmp/tmpdauUZ0/sel_SET675+3.p_1',p27) ).
fof(7,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/tmpdauUZ0/sel_SET675+3.p_1',p23) ).
fof(9,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/tmpdauUZ0/sel_SET675+3.p_1',p29) ).
fof(11,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ! [X4] :
( ilf_type(X4,set_type)
=> inverse4(X1,X2,X3,X4) = inverse2(X3,X4) ) ) ) ),
file('/tmp/tmpdauUZ0/sel_SET675+3.p_1',p33) ).
fof(12,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X1))
=> ( image4(X2,X1,X3,inverse4(X2,X1,X3,X1)) = range(X2,X1,X3)
& inverse4(X2,X1,X3,image4(X2,X1,X3,X2)) = domain(X2,X1,X3) ) ) ) ),
file('/tmp/tmpdauUZ0/sel_SET675+3.p_1',prove_relset_1_39) ).
fof(16,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,binary_relation_type)
<=> ( relation_like(X1)
& ilf_type(X1,set_type) ) ) ),
file('/tmp/tmpdauUZ0/sel_SET675+3.p_1',p12) ).
fof(25,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ! [X4] :
( ilf_type(X4,set_type)
=> image4(X1,X2,X3,X4) = image(X3,X4) ) ) ) ),
file('/tmp/tmpdauUZ0/sel_SET675+3.p_1',p31) ).
fof(27,axiom,
! [X1] : ilf_type(X1,set_type),
file('/tmp/tmpdauUZ0/sel_SET675+3.p_1',p35) ).
fof(28,axiom,
! [X1] :
( ilf_type(X1,binary_relation_type)
=> inverse2(X1,range_of(X1)) = domain_of(X1) ),
file('/tmp/tmpdauUZ0/sel_SET675+3.p_1',p2) ).
fof(29,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( image4(X1,X2,X3,X1) = range(X1,X2,X3)
& inverse4(X1,X2,X3,X2) = domain(X1,X2,X3) ) ) ) ),
file('/tmp/tmpdauUZ0/sel_SET675+3.p_1',p3) ).
fof(30,axiom,
! [X1] :
( ilf_type(X1,binary_relation_type)
=> image(X1,domain_of(X1)) = range_of(X1) ),
file('/tmp/tmpdauUZ0/sel_SET675+3.p_1',p1) ).
fof(33,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/tmpdauUZ0/sel_SET675+3.p_1',p4) ).
fof(37,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X1))
=> ( image4(X2,X1,X3,inverse4(X2,X1,X3,X1)) = range(X2,X1,X3)
& inverse4(X2,X1,X3,image4(X2,X1,X3,X2)) = domain(X2,X1,X3) ) ) ) ),
inference(assume_negation,[status(cth)],[12]) ).
fof(54,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,relation_type(X1,X2))
| domain(X1,X2,X3) = domain_of(X3) ) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(55,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,relation_type(X4,X5))
| domain(X4,X5,X6) = domain_of(X6) ) ) ),
inference(variable_rename,[status(thm)],[54]) ).
fof(56,plain,
! [X4,X5,X6] :
( ~ ilf_type(X6,relation_type(X4,X5))
| domain(X4,X5,X6) = domain_of(X6)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[55]) ).
cnf(57,plain,
( domain(X1,X2,X3) = domain_of(X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[56]) ).
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)],[7]) ).
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(86,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)],[9]) ).
fof(87,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)],[86]) ).
fof(88,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)],[87]) ).
cnf(89,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)],[88]) ).
fof(94,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,relation_type(X1,X2))
| ! [X4] :
( ~ ilf_type(X4,set_type)
| inverse4(X1,X2,X3,X4) = inverse2(X3,X4) ) ) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(95,plain,
! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ! [X7] :
( ~ ilf_type(X7,relation_type(X5,X6))
| ! [X8] :
( ~ ilf_type(X8,set_type)
| inverse4(X5,X6,X7,X8) = inverse2(X7,X8) ) ) ) ),
inference(variable_rename,[status(thm)],[94]) ).
fof(96,plain,
! [X5,X6,X7,X8] :
( ~ ilf_type(X8,set_type)
| inverse4(X5,X6,X7,X8) = inverse2(X7,X8)
| ~ ilf_type(X7,relation_type(X5,X6))
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ),
inference(shift_quantors,[status(thm)],[95]) ).
cnf(97,plain,
( inverse4(X1,X2,X3,X4) = inverse2(X3,X4)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X4,set_type) ),
inference(split_conjunct,[status(thm)],[96]) ).
fof(98,negated_conjecture,
? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ilf_type(X3,relation_type(X2,X1))
& ( image4(X2,X1,X3,inverse4(X2,X1,X3,X1)) != range(X2,X1,X3)
| inverse4(X2,X1,X3,image4(X2,X1,X3,X2)) != domain(X2,X1,X3) ) ) ) ),
inference(fof_nnf,[status(thm)],[37]) ).
fof(99,negated_conjecture,
? [X4] :
( ilf_type(X4,set_type)
& ? [X5] :
( ilf_type(X5,set_type)
& ? [X6] :
( ilf_type(X6,relation_type(X5,X4))
& ( image4(X5,X4,X6,inverse4(X5,X4,X6,X4)) != range(X5,X4,X6)
| inverse4(X5,X4,X6,image4(X5,X4,X6,X5)) != domain(X5,X4,X6) ) ) ) ),
inference(variable_rename,[status(thm)],[98]) ).
fof(100,negated_conjecture,
( ilf_type(esk6_0,set_type)
& ilf_type(esk7_0,set_type)
& ilf_type(esk8_0,relation_type(esk7_0,esk6_0))
& ( image4(esk7_0,esk6_0,esk8_0,inverse4(esk7_0,esk6_0,esk8_0,esk6_0)) != range(esk7_0,esk6_0,esk8_0)
| inverse4(esk7_0,esk6_0,esk8_0,image4(esk7_0,esk6_0,esk8_0,esk7_0)) != domain(esk7_0,esk6_0,esk8_0) ) ),
inference(skolemize,[status(esa)],[99]) ).
cnf(101,negated_conjecture,
( inverse4(esk7_0,esk6_0,esk8_0,image4(esk7_0,esk6_0,esk8_0,esk7_0)) != domain(esk7_0,esk6_0,esk8_0)
| image4(esk7_0,esk6_0,esk8_0,inverse4(esk7_0,esk6_0,esk8_0,esk6_0)) != range(esk7_0,esk6_0,esk8_0) ),
inference(split_conjunct,[status(thm)],[100]) ).
cnf(102,negated_conjecture,
ilf_type(esk8_0,relation_type(esk7_0,esk6_0)),
inference(split_conjunct,[status(thm)],[100]) ).
fof(116,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)],[16]) ).
fof(117,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)],[116]) ).
fof(118,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)],[117]) ).
cnf(119,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)],[118]) ).
fof(165,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,relation_type(X1,X2))
| ! [X4] :
( ~ ilf_type(X4,set_type)
| image4(X1,X2,X3,X4) = image(X3,X4) ) ) ) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(166,plain,
! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ! [X7] :
( ~ ilf_type(X7,relation_type(X5,X6))
| ! [X8] :
( ~ ilf_type(X8,set_type)
| image4(X5,X6,X7,X8) = image(X7,X8) ) ) ) ),
inference(variable_rename,[status(thm)],[165]) ).
fof(167,plain,
! [X5,X6,X7,X8] :
( ~ ilf_type(X8,set_type)
| image4(X5,X6,X7,X8) = image(X7,X8)
| ~ ilf_type(X7,relation_type(X5,X6))
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ),
inference(shift_quantors,[status(thm)],[166]) ).
cnf(168,plain,
( image4(X1,X2,X3,X4) = image(X3,X4)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X4,set_type) ),
inference(split_conjunct,[status(thm)],[167]) ).
fof(173,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[27]) ).
cnf(174,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[173]) ).
fof(175,plain,
! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| inverse2(X1,range_of(X1)) = domain_of(X1) ),
inference(fof_nnf,[status(thm)],[28]) ).
fof(176,plain,
! [X2] :
( ~ ilf_type(X2,binary_relation_type)
| inverse2(X2,range_of(X2)) = domain_of(X2) ),
inference(variable_rename,[status(thm)],[175]) ).
cnf(177,plain,
( inverse2(X1,range_of(X1)) = domain_of(X1)
| ~ ilf_type(X1,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[176]) ).
fof(178,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,relation_type(X1,X2))
| ( image4(X1,X2,X3,X1) = range(X1,X2,X3)
& inverse4(X1,X2,X3,X2) = domain(X1,X2,X3) ) ) ) ),
inference(fof_nnf,[status(thm)],[29]) ).
fof(179,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,relation_type(X4,X5))
| ( image4(X4,X5,X6,X4) = range(X4,X5,X6)
& inverse4(X4,X5,X6,X5) = domain(X4,X5,X6) ) ) ) ),
inference(variable_rename,[status(thm)],[178]) ).
fof(180,plain,
! [X4,X5,X6] :
( ~ ilf_type(X6,relation_type(X4,X5))
| ( image4(X4,X5,X6,X4) = range(X4,X5,X6)
& inverse4(X4,X5,X6,X5) = domain(X4,X5,X6) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[179]) ).
fof(181,plain,
! [X4,X5,X6] :
( ( image4(X4,X5,X6,X4) = range(X4,X5,X6)
| ~ ilf_type(X6,relation_type(X4,X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( inverse4(X4,X5,X6,X5) = domain(X4,X5,X6)
| ~ ilf_type(X6,relation_type(X4,X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[180]) ).
cnf(182,plain,
( inverse4(X1,X2,X3,X2) = domain(X1,X2,X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[181]) ).
cnf(183,plain,
( image4(X1,X2,X3,X1) = range(X1,X2,X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[181]) ).
fof(184,plain,
! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| image(X1,domain_of(X1)) = range_of(X1) ),
inference(fof_nnf,[status(thm)],[30]) ).
fof(185,plain,
! [X2] :
( ~ ilf_type(X2,binary_relation_type)
| image(X2,domain_of(X2)) = range_of(X2) ),
inference(variable_rename,[status(thm)],[184]) ).
cnf(186,plain,
( image(X1,domain_of(X1)) = range_of(X1)
| ~ ilf_type(X1,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[185]) ).
fof(198,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)],[33]) ).
fof(199,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)],[198]) ).
fof(200,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)],[199]) ).
fof(201,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)],[200]) ).
cnf(203,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)],[201]) ).
cnf(231,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| $false ),
inference(rw,[status(thm)],[119,174,theory(equality)]) ).
cnf(232,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[231,theory(equality)]) ).
cnf(287,plain,
( domain(X1,X2,X3) = domain_of(X3)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[57,174,theory(equality)]) ).
cnf(288,plain,
( domain(X1,X2,X3) = domain_of(X3)
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[287,174,theory(equality)]) ).
cnf(289,plain,
( domain(X1,X2,X3) = domain_of(X3)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[288,theory(equality)]) ).
cnf(290,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)],[89,174,theory(equality)]) ).
cnf(291,plain,
( range(X1,X2,X3) = range_of(X3)
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[290,174,theory(equality)]) ).
cnf(292,plain,
( range(X1,X2,X3) = range_of(X3)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[291,theory(equality)]) ).
cnf(293,plain,
( relation_like(X3)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[74,174,theory(equality)]) ).
cnf(294,plain,
( relation_like(X3)
| $false
| $false
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[293,174,theory(equality)]) ).
cnf(295,plain,
( relation_like(X3)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(cn,[status(thm)],[294,theory(equality)]) ).
cnf(334,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)],[203,174,theory(equality)]) ).
cnf(335,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[334,174,theory(equality)]) ).
cnf(336,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[335,theory(equality)]) ).
cnf(337,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[295,336,theory(equality)]) ).
cnf(368,plain,
( inverse4(X1,X2,X3,X2) = domain(X1,X2,X3)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[182,174,theory(equality)]) ).
cnf(369,plain,
( inverse4(X1,X2,X3,X2) = domain(X1,X2,X3)
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[368,174,theory(equality)]) ).
cnf(370,plain,
( inverse4(X1,X2,X3,X2) = domain(X1,X2,X3)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[369,theory(equality)]) ).
cnf(371,plain,
( inverse4(X1,X2,X3,X2) = domain_of(X3)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(spm,[status(thm)],[289,370,theory(equality)]) ).
cnf(373,plain,
( image4(X1,X2,X3,X1) = range(X1,X2,X3)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[183,174,theory(equality)]) ).
cnf(374,plain,
( image4(X1,X2,X3,X1) = range(X1,X2,X3)
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[373,174,theory(equality)]) ).
cnf(375,plain,
( image4(X1,X2,X3,X1) = range(X1,X2,X3)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[374,theory(equality)]) ).
cnf(376,plain,
( image4(X1,X2,X3,X1) = range_of(X3)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(spm,[status(thm)],[292,375,theory(equality)]) ).
cnf(401,plain,
( inverse4(X1,X2,X3,X4) = inverse2(X3,X4)
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[97,174,theory(equality)]) ).
cnf(402,plain,
( inverse4(X1,X2,X3,X4) = inverse2(X3,X4)
| $false
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[401,174,theory(equality)]) ).
cnf(403,plain,
( inverse4(X1,X2,X3,X4) = inverse2(X3,X4)
| $false
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[402,174,theory(equality)]) ).
cnf(404,plain,
( inverse4(X1,X2,X3,X4) = inverse2(X3,X4)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[403,theory(equality)]) ).
cnf(405,plain,
( inverse4(X2,X3,X1,range_of(X1)) = domain_of(X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[177,404,theory(equality)]) ).
cnf(409,plain,
( image4(X1,X2,X3,X4) = image(X3,X4)
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[168,174,theory(equality)]) ).
cnf(410,plain,
( image4(X1,X2,X3,X4) = image(X3,X4)
| $false
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[409,174,theory(equality)]) ).
cnf(411,plain,
( image4(X1,X2,X3,X4) = image(X3,X4)
| $false
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[410,174,theory(equality)]) ).
cnf(412,plain,
( image4(X1,X2,X3,X4) = image(X3,X4)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[411,theory(equality)]) ).
cnf(413,plain,
( image4(X2,X3,X1,domain_of(X1)) = range_of(X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[186,412,theory(equality)]) ).
cnf(436,negated_conjecture,
relation_like(esk8_0),
inference(spm,[status(thm)],[337,102,theory(equality)]) ).
cnf(438,negated_conjecture,
ilf_type(esk8_0,binary_relation_type),
inference(spm,[status(thm)],[232,436,theory(equality)]) ).
cnf(570,negated_conjecture,
( inverse4(esk7_0,esk6_0,esk8_0,image4(esk7_0,esk6_0,esk8_0,esk7_0)) != domain(esk7_0,esk6_0,esk8_0)
| image4(esk7_0,esk6_0,esk8_0,domain_of(esk8_0)) != range(esk7_0,esk6_0,esk8_0)
| ~ ilf_type(esk8_0,relation_type(esk7_0,esk6_0)) ),
inference(spm,[status(thm)],[101,371,theory(equality)]) ).
cnf(571,negated_conjecture,
( inverse4(esk7_0,esk6_0,esk8_0,image4(esk7_0,esk6_0,esk8_0,esk7_0)) != domain(esk7_0,esk6_0,esk8_0)
| image4(esk7_0,esk6_0,esk8_0,domain_of(esk8_0)) != range(esk7_0,esk6_0,esk8_0)
| $false ),
inference(rw,[status(thm)],[570,102,theory(equality)]) ).
cnf(572,negated_conjecture,
( inverse4(esk7_0,esk6_0,esk8_0,image4(esk7_0,esk6_0,esk8_0,esk7_0)) != domain(esk7_0,esk6_0,esk8_0)
| image4(esk7_0,esk6_0,esk8_0,domain_of(esk8_0)) != range(esk7_0,esk6_0,esk8_0) ),
inference(cn,[status(thm)],[571,theory(equality)]) ).
cnf(2624,negated_conjecture,
( inverse4(esk7_0,esk6_0,esk8_0,range_of(esk8_0)) != domain(esk7_0,esk6_0,esk8_0)
| image4(esk7_0,esk6_0,esk8_0,domain_of(esk8_0)) != range(esk7_0,esk6_0,esk8_0)
| ~ ilf_type(esk8_0,relation_type(esk7_0,esk6_0)) ),
inference(spm,[status(thm)],[572,376,theory(equality)]) ).
cnf(2630,negated_conjecture,
( inverse4(esk7_0,esk6_0,esk8_0,range_of(esk8_0)) != domain(esk7_0,esk6_0,esk8_0)
| image4(esk7_0,esk6_0,esk8_0,domain_of(esk8_0)) != range(esk7_0,esk6_0,esk8_0)
| $false ),
inference(rw,[status(thm)],[2624,102,theory(equality)]) ).
cnf(2631,negated_conjecture,
( inverse4(esk7_0,esk6_0,esk8_0,range_of(esk8_0)) != domain(esk7_0,esk6_0,esk8_0)
| image4(esk7_0,esk6_0,esk8_0,domain_of(esk8_0)) != range(esk7_0,esk6_0,esk8_0) ),
inference(cn,[status(thm)],[2630,theory(equality)]) ).
cnf(78717,negated_conjecture,
( inverse4(esk7_0,esk6_0,esk8_0,range_of(esk8_0)) != domain(esk7_0,esk6_0,esk8_0)
| range_of(esk8_0) != range(esk7_0,esk6_0,esk8_0)
| ~ ilf_type(esk8_0,relation_type(esk7_0,esk6_0))
| ~ ilf_type(esk8_0,binary_relation_type) ),
inference(spm,[status(thm)],[2631,413,theory(equality)]) ).
cnf(78724,negated_conjecture,
( inverse4(esk7_0,esk6_0,esk8_0,range_of(esk8_0)) != domain(esk7_0,esk6_0,esk8_0)
| range_of(esk8_0) != range(esk7_0,esk6_0,esk8_0)
| $false
| ~ ilf_type(esk8_0,binary_relation_type) ),
inference(rw,[status(thm)],[78717,102,theory(equality)]) ).
cnf(78725,negated_conjecture,
( inverse4(esk7_0,esk6_0,esk8_0,range_of(esk8_0)) != domain(esk7_0,esk6_0,esk8_0)
| range_of(esk8_0) != range(esk7_0,esk6_0,esk8_0)
| $false
| $false ),
inference(rw,[status(thm)],[78724,438,theory(equality)]) ).
cnf(78726,negated_conjecture,
( inverse4(esk7_0,esk6_0,esk8_0,range_of(esk8_0)) != domain(esk7_0,esk6_0,esk8_0)
| range_of(esk8_0) != range(esk7_0,esk6_0,esk8_0) ),
inference(cn,[status(thm)],[78725,theory(equality)]) ).
cnf(123514,negated_conjecture,
( domain_of(esk8_0) != domain(esk7_0,esk6_0,esk8_0)
| range(esk7_0,esk6_0,esk8_0) != range_of(esk8_0)
| ~ ilf_type(esk8_0,relation_type(esk7_0,esk6_0))
| ~ ilf_type(esk8_0,binary_relation_type) ),
inference(spm,[status(thm)],[78726,405,theory(equality)]) ).
cnf(123521,negated_conjecture,
( domain_of(esk8_0) != domain(esk7_0,esk6_0,esk8_0)
| range(esk7_0,esk6_0,esk8_0) != range_of(esk8_0)
| $false
| ~ ilf_type(esk8_0,binary_relation_type) ),
inference(rw,[status(thm)],[123514,102,theory(equality)]) ).
cnf(123522,negated_conjecture,
( domain_of(esk8_0) != domain(esk7_0,esk6_0,esk8_0)
| range(esk7_0,esk6_0,esk8_0) != range_of(esk8_0)
| $false
| $false ),
inference(rw,[status(thm)],[123521,438,theory(equality)]) ).
cnf(123523,negated_conjecture,
( domain_of(esk8_0) != domain(esk7_0,esk6_0,esk8_0)
| range(esk7_0,esk6_0,esk8_0) != range_of(esk8_0) ),
inference(cn,[status(thm)],[123522,theory(equality)]) ).
cnf(123536,negated_conjecture,
( domain(esk7_0,esk6_0,esk8_0) != domain_of(esk8_0)
| ~ ilf_type(esk8_0,relation_type(esk7_0,esk6_0)) ),
inference(spm,[status(thm)],[123523,292,theory(equality)]) ).
cnf(123544,negated_conjecture,
( domain(esk7_0,esk6_0,esk8_0) != domain_of(esk8_0)
| $false ),
inference(rw,[status(thm)],[123536,102,theory(equality)]) ).
cnf(123545,negated_conjecture,
domain(esk7_0,esk6_0,esk8_0) != domain_of(esk8_0),
inference(cn,[status(thm)],[123544,theory(equality)]) ).
cnf(123560,negated_conjecture,
~ ilf_type(esk8_0,relation_type(esk7_0,esk6_0)),
inference(spm,[status(thm)],[123545,289,theory(equality)]) ).
cnf(123568,negated_conjecture,
$false,
inference(rw,[status(thm)],[123560,102,theory(equality)]) ).
cnf(123569,negated_conjecture,
$false,
inference(cn,[status(thm)],[123568,theory(equality)]) ).
cnf(123570,negated_conjecture,
$false,
123569,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET675+3.p
% --creating new selector for []
% -running prover on /tmp/tmpdauUZ0/sel_SET675+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET675+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET675+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET675+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
%
%------------------------------------------------------------------------------