TSTP Solution File: SET674+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET674+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.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 03:09:56 EST 2010
% Result : Theorem 13.64s
% Output : CNFRefutation 13.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 25
% Syntax : Number of formulae : 383 ( 23 unt; 0 def)
% Number of atoms : 1760 ( 121 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 2338 ( 961 ~;1111 |; 175 &)
% ( 15 <=>; 76 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 5 con; 0-4 aty)
% Number of variables : 862 ( 64 sgn 334 !; 33 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
file('/tmp/tmpC30OCt/sel_SET674+3.p_1',p25) ).
fof(2,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X1,power_set(X2))
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
=> member(X3,X2) ) ) ) ) ),
file('/tmp/tmpC30OCt/sel_SET674+3.p_1',p24) ).
fof(3,axiom,
! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ? [X2] : ilf_type(X2,member_type(X1)) ),
file('/tmp/tmpC30OCt/sel_SET674+3.p_1',p27) ).
fof(4,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/tmpC30OCt/sel_SET674+3.p_1',p26) ).
fof(5,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( X1 = X2
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
<=> member(X3,X2) ) ) ) ) ),
file('/tmp/tmpC30OCt/sel_SET674+3.p_1',p21) ).
fof(6,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ? [X2] : ilf_type(X2,subset_type(X1)) ),
file('/tmp/tmpC30OCt/sel_SET674+3.p_1',p20) ).
fof(8,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( subset(X1,X2)
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
=> member(X3,X2) ) ) ) ) ),
file('/tmp/tmpC30OCt/sel_SET674+3.p_1',p22) ).
fof(9,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/tmpC30OCt/sel_SET674+3.p_1',p29) ).
fof(11,axiom,
! [X1] : ilf_type(X1,set_type),
file('/tmp/tmpC30OCt/sel_SET674+3.p_1',p40) ).
fof(13,conjecture,
! [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/tmpC30OCt/sel_SET674+3.p_1',prove_relset_1_38) ).
fof(14,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/tmpC30OCt/sel_SET674+3.p_1',p32) ).
fof(15,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ) ) ),
file('/tmp/tmpC30OCt/sel_SET674+3.p_1',p10) ).
fof(22,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,binary_relation_type)
<=> ( relation_like(X1)
& ilf_type(X1,set_type) ) ) ),
file('/tmp/tmpC30OCt/sel_SET674+3.p_1',p17) ).
fof(24,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ilf_type(X2,subset_type(X1))
<=> ilf_type(X2,member_type(power_set(X1))) ) ) ),
file('/tmp/tmpC30OCt/sel_SET674+3.p_1',p19) ).
fof(25,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/tmp/tmpC30OCt/sel_SET674+3.p_1',p30) ).
fof(27,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/tmpC30OCt/sel_SET674+3.p_1',p36) ).
fof(29,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/tmpC30OCt/sel_SET674+3.p_1',p34) ).
fof(31,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/tmpC30OCt/sel_SET674+3.p_1',p2) ).
fof(32,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/tmpC30OCt/sel_SET674+3.p_1',p3) ).
fof(33,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( member(X1,domain_of(X2))
<=> ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X1,X3),X2) ) ) ) ),
file('/tmp/tmpC30OCt/sel_SET674+3.p_1',p1) ).
fof(35,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/tmpC30OCt/sel_SET674+3.p_1',p7) ).
fof(36,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,binary_relation_type)
=> ( member(X2,image(X3,X1))
<=> ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X4,X2),X3)
& member(X4,X1) ) ) ) ) ),
file('/tmp/tmpC30OCt/sel_SET674+3.p_1',p4) ).
fof(37,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,binary_relation_type)
=> ( member(X2,inverse2(X3,X1))
<=> ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X2,X4),X3)
& member(X4,X1) ) ) ) ) ),
file('/tmp/tmpC30OCt/sel_SET674+3.p_1',p5) ).
fof(38,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/tmpC30OCt/sel_SET674+3.p_1',p8) ).
fof(40,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/tmpC30OCt/sel_SET674+3.p_1',p38) ).
fof(42,negated_conjecture,
~ ! [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(assume_negation,[status(cth)],[13]) ).
fof(43,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_simplification,[status(thm)],[1,theory(equality)]) ).
fof(44,plain,
! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ? [X2] : ilf_type(X2,member_type(X1)) ),
inference(fof_simplification,[status(thm)],[3,theory(equality)]) ).
fof(45,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)],[4,theory(equality)]) ).
fof(46,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[25,theory(equality)]) ).
fof(47,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_nnf,[status(thm)],[43]) ).
fof(48,plain,
! [X2] :
( ~ ilf_type(X2,set_type)
| ( ~ empty(power_set(X2))
& ilf_type(power_set(X2),set_type) ) ),
inference(variable_rename,[status(thm)],[47]) ).
fof(49,plain,
! [X2] :
( ( ~ empty(power_set(X2))
| ~ ilf_type(X2,set_type) )
& ( ilf_type(power_set(X2),set_type)
| ~ ilf_type(X2,set_type) ) ),
inference(distribute,[status(thm)],[48]) ).
cnf(51,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(power_set(X1)) ),
inference(split_conjunct,[status(thm)],[49]) ).
fof(52,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ( ( ~ member(X1,power_set(X2))
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(X3,X1)
| member(X3,X2) ) )
& ( ? [X3] :
( ilf_type(X3,set_type)
& member(X3,X1)
& ~ member(X3,X2) )
| member(X1,power_set(X2)) ) ) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(53,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ( ( ~ member(X4,power_set(X5))
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5) ) )
& ( ? [X7] :
( ilf_type(X7,set_type)
& member(X7,X4)
& ~ member(X7,X5) )
| member(X4,power_set(X5)) ) ) ) ),
inference(variable_rename,[status(thm)],[52]) ).
fof(54,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ( ( ~ member(X4,power_set(X5))
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5) ) )
& ( ( ilf_type(esk1_2(X4,X5),set_type)
& member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| member(X4,power_set(X5)) ) ) ) ),
inference(skolemize,[status(esa)],[53]) ).
fof(55,plain,
! [X4,X5,X6] :
( ( ( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ member(X4,power_set(X5)) )
& ( ( ilf_type(esk1_2(X4,X5),set_type)
& member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| member(X4,power_set(X5)) ) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[54]) ).
fof(56,plain,
! [X4,X5,X6] :
( ( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ilf_type(esk1_2(X4,X5),set_type)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk1_2(X4,X5),X4)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk1_2(X4,X5),X5)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[55]) ).
cnf(60,plain,
( member(X3,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,power_set(X2))
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type) ),
inference(split_conjunct,[status(thm)],[56]) ).
fof(61,plain,
! [X1] :
( empty(X1)
| ~ ilf_type(X1,set_type)
| ? [X2] : ilf_type(X2,member_type(X1)) ),
inference(fof_nnf,[status(thm)],[44]) ).
fof(62,plain,
! [X3] :
( empty(X3)
| ~ ilf_type(X3,set_type)
| ? [X4] : ilf_type(X4,member_type(X3)) ),
inference(variable_rename,[status(thm)],[61]) ).
fof(63,plain,
! [X3] :
( empty(X3)
| ~ ilf_type(X3,set_type)
| ilf_type(esk2_1(X3),member_type(X3)) ),
inference(skolemize,[status(esa)],[62]) ).
cnf(64,plain,
( ilf_type(esk2_1(X1),member_type(X1))
| empty(X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[63]) ).
fof(65,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)],[45]) ).
fof(66,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)],[65]) ).
fof(67,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)],[66]) ).
fof(68,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)],[67]) ).
cnf(69,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)],[68]) ).
cnf(70,plain,
( empty(X2)
| member(X1,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,member_type(X2)) ),
inference(split_conjunct,[status(thm)],[68]) ).
fof(71,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ( ( X1 != X2
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ( ( ~ member(X3,X1)
| member(X3,X2) )
& ( ~ member(X3,X2)
| member(X3,X1) ) ) ) )
& ( ? [X3] :
( ilf_type(X3,set_type)
& ( ~ member(X3,X1)
| ~ member(X3,X2) )
& ( member(X3,X1)
| member(X3,X2) ) )
| X1 = X2 ) ) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(72,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ( ( X4 != X5
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ( ( ~ member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X5)
| member(X6,X4) ) ) ) )
& ( ? [X7] :
( ilf_type(X7,set_type)
& ( ~ member(X7,X4)
| ~ member(X7,X5) )
& ( member(X7,X4)
| member(X7,X5) ) )
| X4 = X5 ) ) ) ),
inference(variable_rename,[status(thm)],[71]) ).
fof(73,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ( ( X4 != X5
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ( ( ~ member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X5)
| member(X6,X4) ) ) ) )
& ( ( ilf_type(esk3_2(X4,X5),set_type)
& ( ~ member(esk3_2(X4,X5),X4)
| ~ member(esk3_2(X4,X5),X5) )
& ( member(esk3_2(X4,X5),X4)
| member(esk3_2(X4,X5),X5) ) )
| X4 = X5 ) ) ) ),
inference(skolemize,[status(esa)],[72]) ).
fof(74,plain,
! [X4,X5,X6] :
( ( ( ~ ilf_type(X6,set_type)
| ( ( ~ member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X5)
| member(X6,X4) ) )
| X4 != X5 )
& ( ( ilf_type(esk3_2(X4,X5),set_type)
& ( ~ member(esk3_2(X4,X5),X4)
| ~ member(esk3_2(X4,X5),X5) )
& ( member(esk3_2(X4,X5),X4)
| member(esk3_2(X4,X5),X5) ) )
| X4 = X5 ) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[73]) ).
fof(75,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ ilf_type(X6,set_type)
| X4 != X5
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(X6,X5)
| member(X6,X4)
| ~ ilf_type(X6,set_type)
| X4 != X5
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ilf_type(esk3_2(X4,X5),set_type)
| X4 = X5
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk3_2(X4,X5),X4)
| ~ member(esk3_2(X4,X5),X5)
| X4 = X5
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk3_2(X4,X5),X4)
| member(esk3_2(X4,X5),X5)
| X4 = X5
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[74]) ).
cnf(76,plain,
( X1 = X2
| member(esk3_2(X1,X2),X2)
| member(esk3_2(X1,X2),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[75]) ).
fof(81,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ? [X2] : ilf_type(X2,subset_type(X1)) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(82,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ? [X4] : ilf_type(X4,subset_type(X3)) ),
inference(variable_rename,[status(thm)],[81]) ).
fof(83,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ilf_type(esk4_1(X3),subset_type(X3)) ),
inference(skolemize,[status(esa)],[82]) ).
cnf(84,plain,
( ilf_type(esk4_1(X1),subset_type(X1))
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[83]) ).
fof(88,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ( ( ~ subset(X1,X2)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(X3,X1)
| member(X3,X2) ) )
& ( ? [X3] :
( ilf_type(X3,set_type)
& member(X3,X1)
& ~ member(X3,X2) )
| subset(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(89,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ( ( ~ subset(X4,X5)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5) ) )
& ( ? [X7] :
( ilf_type(X7,set_type)
& member(X7,X4)
& ~ member(X7,X5) )
| subset(X4,X5) ) ) ) ),
inference(variable_rename,[status(thm)],[88]) ).
fof(90,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ( ( ~ subset(X4,X5)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5) ) )
& ( ( ilf_type(esk5_2(X4,X5),set_type)
& member(esk5_2(X4,X5),X4)
& ~ member(esk5_2(X4,X5),X5) )
| subset(X4,X5) ) ) ) ),
inference(skolemize,[status(esa)],[89]) ).
fof(91,plain,
! [X4,X5,X6] :
( ( ( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( ( ilf_type(esk5_2(X4,X5),set_type)
& member(esk5_2(X4,X5),X4)
& ~ member(esk5_2(X4,X5),X5) )
| subset(X4,X5) ) )
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[90]) ).
fof(92,plain,
! [X4,X5,X6] :
( ( ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ilf_type(esk5_2(X4,X5),set_type)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk5_2(X4,X5),X4)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk5_2(X4,X5),X5)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[91]) ).
cnf(93,plain,
( subset(X1,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(esk5_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[92]) ).
cnf(94,plain,
( subset(X1,X2)
| member(esk5_2(X1,X2),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[92]) ).
fof(97,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)],[9]) ).
fof(98,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)],[97]) ).
fof(99,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)],[98]) ).
cnf(100,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)],[99]) ).
fof(112,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[11]) ).
cnf(113,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[112]) ).
fof(118,negated_conjecture,
? [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)],[42]) ).
fof(119,negated_conjecture,
? [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)],[118]) ).
fof(120,negated_conjecture,
( ilf_type(esk9_0,set_type)
& ilf_type(esk10_0,set_type)
& ilf_type(esk11_0,relation_type(esk9_0,esk10_0))
& ( image4(esk9_0,esk10_0,esk11_0,esk9_0) != range(esk9_0,esk10_0,esk11_0)
| inverse4(esk9_0,esk10_0,esk11_0,esk10_0) != domain(esk9_0,esk10_0,esk11_0) ) ),
inference(skolemize,[status(esa)],[119]) ).
cnf(121,negated_conjecture,
( inverse4(esk9_0,esk10_0,esk11_0,esk10_0) != domain(esk9_0,esk10_0,esk11_0)
| image4(esk9_0,esk10_0,esk11_0,esk9_0) != range(esk9_0,esk10_0,esk11_0) ),
inference(split_conjunct,[status(thm)],[120]) ).
cnf(122,negated_conjecture,
ilf_type(esk11_0,relation_type(esk9_0,esk10_0)),
inference(split_conjunct,[status(thm)],[120]) ).
fof(125,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)],[14]) ).
fof(126,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)],[125]) ).
fof(127,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)],[126]) ).
cnf(128,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)],[127]) ).
fof(129,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ( ( X1 != X2
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ) ) ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(130,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ( ( X3 != X4
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ) ) ),
inference(variable_rename,[status(thm)],[129]) ).
fof(131,plain,
! [X3,X4] :
( ~ ilf_type(X4,set_type)
| ( ( X3 != X4
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) )
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[130]) ).
fof(132,plain,
! [X3,X4] :
( ( subset(X3,X4)
| X3 != X4
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) )
& ( subset(X4,X3)
| X3 != X4
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[131]) ).
cnf(133,plain,
( X1 = X2
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[132]) ).
fof(158,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)],[22]) ).
fof(159,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)],[158]) ).
fof(160,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)],[159]) ).
cnf(161,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)],[160]) ).
fof(167,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ( ( ~ ilf_type(X2,subset_type(X1))
| ilf_type(X2,member_type(power_set(X1))) )
& ( ~ ilf_type(X2,member_type(power_set(X1)))
| ilf_type(X2,subset_type(X1)) ) ) ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(168,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ( ( ~ ilf_type(X4,subset_type(X3))
| ilf_type(X4,member_type(power_set(X3))) )
& ( ~ ilf_type(X4,member_type(power_set(X3)))
| ilf_type(X4,subset_type(X3)) ) ) ) ),
inference(variable_rename,[status(thm)],[167]) ).
fof(169,plain,
! [X3,X4] :
( ~ ilf_type(X4,set_type)
| ( ( ~ ilf_type(X4,subset_type(X3))
| ilf_type(X4,member_type(power_set(X3))) )
& ( ~ ilf_type(X4,member_type(power_set(X3)))
| ilf_type(X4,subset_type(X3)) ) )
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[168]) ).
fof(170,plain,
! [X3,X4] :
( ( ~ ilf_type(X4,subset_type(X3))
| ilf_type(X4,member_type(power_set(X3)))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) )
& ( ~ ilf_type(X4,member_type(power_set(X3)))
| ilf_type(X4,subset_type(X3))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[169]) ).
cnf(172,plain,
( ilf_type(X2,member_type(power_set(X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X2,subset_type(X1)) ),
inference(split_conjunct,[status(thm)],[170]) ).
fof(173,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)],[46]) ).
fof(174,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)],[173]) ).
fof(175,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ( ( ~ empty(X3)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(X4,X3) ) )
& ( ( ilf_type(esk13_1(X3),set_type)
& member(esk13_1(X3),X3) )
| empty(X3) ) ) ),
inference(skolemize,[status(esa)],[174]) ).
fof(176,plain,
! [X3,X4] :
( ( ( ~ ilf_type(X4,set_type)
| ~ member(X4,X3)
| ~ empty(X3) )
& ( ( ilf_type(esk13_1(X3),set_type)
& member(esk13_1(X3),X3) )
| empty(X3) ) )
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[175]) ).
fof(177,plain,
! [X3,X4] :
( ( ~ ilf_type(X4,set_type)
| ~ member(X4,X3)
| ~ empty(X3)
| ~ ilf_type(X3,set_type) )
& ( ilf_type(esk13_1(X3),set_type)
| empty(X3)
| ~ ilf_type(X3,set_type) )
& ( member(esk13_1(X3),X3)
| empty(X3)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[176]) ).
cnf(178,plain,
( empty(X1)
| member(esk13_1(X1),X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[177]) ).
cnf(180,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(X1)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[177]) ).
fof(184,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)],[27]) ).
fof(185,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)],[184]) ).
fof(186,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)],[185]) ).
cnf(187,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)],[186]) ).
fof(192,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)],[29]) ).
fof(193,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)],[192]) ).
fof(194,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)],[193]) ).
cnf(195,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)],[194]) ).
fof(200,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)],[31]) ).
fof(201,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)],[200]) ).
fof(202,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)],[201]) ).
fof(203,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)],[202]) ).
fof(204,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)],[203]) ).
cnf(205,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)],[204]) ).
fof(208,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)],[32]) ).
fof(209,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)],[208]) ).
fof(210,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)],[209]) ).
fof(211,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)],[210]) ).
cnf(212,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)],[211]) ).
cnf(213,plain,
( member(X1,domain_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)],[211]) ).
fof(214,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,binary_relation_type)
| ( ( ~ member(X1,domain_of(X2))
| ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X1,X3),X2) ) )
& ( ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X1,X3),X2) )
| member(X1,domain_of(X2)) ) ) ) ),
inference(fof_nnf,[status(thm)],[33]) ).
fof(215,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,binary_relation_type)
| ( ( ~ member(X4,domain_of(X5))
| ? [X6] :
( ilf_type(X6,set_type)
& member(ordered_pair(X4,X6),X5) ) )
& ( ! [X7] :
( ~ ilf_type(X7,set_type)
| ~ member(ordered_pair(X4,X7),X5) )
| member(X4,domain_of(X5)) ) ) ) ),
inference(variable_rename,[status(thm)],[214]) ).
fof(216,plain,
! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,binary_relation_type)
| ( ( ~ member(X4,domain_of(X5))
| ( ilf_type(esk15_2(X4,X5),set_type)
& member(ordered_pair(X4,esk15_2(X4,X5)),X5) ) )
& ( ! [X7] :
( ~ ilf_type(X7,set_type)
| ~ member(ordered_pair(X4,X7),X5) )
| member(X4,domain_of(X5)) ) ) ) ),
inference(skolemize,[status(esa)],[215]) ).
fof(217,plain,
! [X4,X5,X7] :
( ( ( ~ ilf_type(X7,set_type)
| ~ member(ordered_pair(X4,X7),X5)
| member(X4,domain_of(X5)) )
& ( ~ member(X4,domain_of(X5))
| ( ilf_type(esk15_2(X4,X5),set_type)
& member(ordered_pair(X4,esk15_2(X4,X5)),X5) ) ) )
| ~ ilf_type(X5,binary_relation_type)
| ~ ilf_type(X4,set_type) ),
inference(shift_quantors,[status(thm)],[216]) ).
fof(218,plain,
! [X4,X5,X7] :
( ( ~ ilf_type(X7,set_type)
| ~ member(ordered_pair(X4,X7),X5)
| member(X4,domain_of(X5))
| ~ ilf_type(X5,binary_relation_type)
| ~ ilf_type(X4,set_type) )
& ( ilf_type(esk15_2(X4,X5),set_type)
| ~ member(X4,domain_of(X5))
| ~ ilf_type(X5,binary_relation_type)
| ~ ilf_type(X4,set_type) )
& ( member(ordered_pair(X4,esk15_2(X4,X5)),X5)
| ~ member(X4,domain_of(X5))
| ~ ilf_type(X5,binary_relation_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[217]) ).
cnf(219,plain,
( member(ordered_pair(X1,esk15_2(X1,X2)),X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(X1,domain_of(X2)) ),
inference(split_conjunct,[status(thm)],[218]) ).
fof(230,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)],[35]) ).
fof(231,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)],[230]) ).
fof(232,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)],[231]) ).
fof(233,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)],[232]) ).
cnf(234,plain,
( member(X4,X2)
| ~ 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)],[233]) ).
cnf(235,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)],[233]) ).
fof(236,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,binary_relation_type)
| ( ( ~ member(X2,image(X3,X1))
| ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X4,X2),X3)
& member(X4,X1) ) )
& ( ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(ordered_pair(X4,X2),X3)
| ~ member(X4,X1) )
| member(X2,image(X3,X1)) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[36]) ).
fof(237,plain,
! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ! [X7] :
( ~ ilf_type(X7,binary_relation_type)
| ( ( ~ member(X6,image(X7,X5))
| ? [X8] :
( ilf_type(X8,set_type)
& member(ordered_pair(X8,X6),X7)
& member(X8,X5) ) )
& ( ! [X9] :
( ~ ilf_type(X9,set_type)
| ~ member(ordered_pair(X9,X6),X7)
| ~ member(X9,X5) )
| member(X6,image(X7,X5)) ) ) ) ) ),
inference(variable_rename,[status(thm)],[236]) ).
fof(238,plain,
! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ! [X7] :
( ~ ilf_type(X7,binary_relation_type)
| ( ( ~ member(X6,image(X7,X5))
| ( ilf_type(esk17_3(X5,X6,X7),set_type)
& member(ordered_pair(esk17_3(X5,X6,X7),X6),X7)
& member(esk17_3(X5,X6,X7),X5) ) )
& ( ! [X9] :
( ~ ilf_type(X9,set_type)
| ~ member(ordered_pair(X9,X6),X7)
| ~ member(X9,X5) )
| member(X6,image(X7,X5)) ) ) ) ) ),
inference(skolemize,[status(esa)],[237]) ).
fof(239,plain,
! [X5,X6,X7,X9] :
( ( ( ~ ilf_type(X9,set_type)
| ~ member(ordered_pair(X9,X6),X7)
| ~ member(X9,X5)
| member(X6,image(X7,X5)) )
& ( ~ member(X6,image(X7,X5))
| ( ilf_type(esk17_3(X5,X6,X7),set_type)
& member(ordered_pair(esk17_3(X5,X6,X7),X6),X7)
& member(esk17_3(X5,X6,X7),X5) ) ) )
| ~ ilf_type(X7,binary_relation_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ),
inference(shift_quantors,[status(thm)],[238]) ).
fof(240,plain,
! [X5,X6,X7,X9] :
( ( ~ ilf_type(X9,set_type)
| ~ member(ordered_pair(X9,X6),X7)
| ~ member(X9,X5)
| member(X6,image(X7,X5))
| ~ ilf_type(X7,binary_relation_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( ilf_type(esk17_3(X5,X6,X7),set_type)
| ~ member(X6,image(X7,X5))
| ~ ilf_type(X7,binary_relation_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( member(ordered_pair(esk17_3(X5,X6,X7),X6),X7)
| ~ member(X6,image(X7,X5))
| ~ ilf_type(X7,binary_relation_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( member(esk17_3(X5,X6,X7),X5)
| ~ member(X6,image(X7,X5))
| ~ ilf_type(X7,binary_relation_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ) ),
inference(distribute,[status(thm)],[239]) ).
cnf(242,plain,
( member(ordered_pair(esk17_3(X1,X2,X3),X2),X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(X2,image(X3,X1)) ),
inference(split_conjunct,[status(thm)],[240]) ).
cnf(244,plain,
( member(X2,image(X3,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(X4,X1)
| ~ member(ordered_pair(X4,X2),X3)
| ~ ilf_type(X4,set_type) ),
inference(split_conjunct,[status(thm)],[240]) ).
fof(245,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,binary_relation_type)
| ( ( ~ member(X2,inverse2(X3,X1))
| ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X2,X4),X3)
& member(X4,X1) ) )
& ( ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(ordered_pair(X2,X4),X3)
| ~ member(X4,X1) )
| member(X2,inverse2(X3,X1)) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[37]) ).
fof(246,plain,
! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ! [X7] :
( ~ ilf_type(X7,binary_relation_type)
| ( ( ~ member(X6,inverse2(X7,X5))
| ? [X8] :
( ilf_type(X8,set_type)
& member(ordered_pair(X6,X8),X7)
& member(X8,X5) ) )
& ( ! [X9] :
( ~ ilf_type(X9,set_type)
| ~ member(ordered_pair(X6,X9),X7)
| ~ member(X9,X5) )
| member(X6,inverse2(X7,X5)) ) ) ) ) ),
inference(variable_rename,[status(thm)],[245]) ).
fof(247,plain,
! [X5] :
( ~ ilf_type(X5,set_type)
| ! [X6] :
( ~ ilf_type(X6,set_type)
| ! [X7] :
( ~ ilf_type(X7,binary_relation_type)
| ( ( ~ member(X6,inverse2(X7,X5))
| ( ilf_type(esk18_3(X5,X6,X7),set_type)
& member(ordered_pair(X6,esk18_3(X5,X6,X7)),X7)
& member(esk18_3(X5,X6,X7),X5) ) )
& ( ! [X9] :
( ~ ilf_type(X9,set_type)
| ~ member(ordered_pair(X6,X9),X7)
| ~ member(X9,X5) )
| member(X6,inverse2(X7,X5)) ) ) ) ) ),
inference(skolemize,[status(esa)],[246]) ).
fof(248,plain,
! [X5,X6,X7,X9] :
( ( ( ~ ilf_type(X9,set_type)
| ~ member(ordered_pair(X6,X9),X7)
| ~ member(X9,X5)
| member(X6,inverse2(X7,X5)) )
& ( ~ member(X6,inverse2(X7,X5))
| ( ilf_type(esk18_3(X5,X6,X7),set_type)
& member(ordered_pair(X6,esk18_3(X5,X6,X7)),X7)
& member(esk18_3(X5,X6,X7),X5) ) ) )
| ~ ilf_type(X7,binary_relation_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ),
inference(shift_quantors,[status(thm)],[247]) ).
fof(249,plain,
! [X5,X6,X7,X9] :
( ( ~ ilf_type(X9,set_type)
| ~ member(ordered_pair(X6,X9),X7)
| ~ member(X9,X5)
| member(X6,inverse2(X7,X5))
| ~ ilf_type(X7,binary_relation_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( ilf_type(esk18_3(X5,X6,X7),set_type)
| ~ member(X6,inverse2(X7,X5))
| ~ ilf_type(X7,binary_relation_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( member(ordered_pair(X6,esk18_3(X5,X6,X7)),X7)
| ~ member(X6,inverse2(X7,X5))
| ~ ilf_type(X7,binary_relation_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( member(esk18_3(X5,X6,X7),X5)
| ~ member(X6,inverse2(X7,X5))
| ~ ilf_type(X7,binary_relation_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ) ),
inference(distribute,[status(thm)],[248]) ).
cnf(251,plain,
( member(ordered_pair(X2,esk18_3(X1,X2,X3)),X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(X2,inverse2(X3,X1)) ),
inference(split_conjunct,[status(thm)],[249]) ).
cnf(253,plain,
( member(X2,inverse2(X3,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(X4,X1)
| ~ member(ordered_pair(X2,X4),X3)
| ~ ilf_type(X4,set_type) ),
inference(split_conjunct,[status(thm)],[249]) ).
fof(254,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)],[38]) ).
fof(255,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)],[254]) ).
fof(256,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)],[255]) ).
fof(257,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)],[256]) ).
cnf(259,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)],[257]) ).
fof(265,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)],[40]) ).
fof(266,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)],[265]) ).
fof(267,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)],[266]) ).
cnf(268,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)],[267]) ).
cnf(277,plain,
( ~ empty(power_set(X1))
| $false ),
inference(rw,[status(thm)],[51,113,theory(equality)]) ).
cnf(278,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[277,theory(equality)]) ).
cnf(286,plain,
( ilf_type(esk4_1(X1),subset_type(X1))
| $false ),
inference(rw,[status(thm)],[84,113,theory(equality)]) ).
cnf(287,plain,
ilf_type(esk4_1(X1),subset_type(X1)),
inference(cn,[status(thm)],[286,theory(equality)]) ).
cnf(288,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| $false ),
inference(rw,[status(thm)],[161,113,theory(equality)]) ).
cnf(289,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[288,theory(equality)]) ).
cnf(299,plain,
( empty(X1)
| member(esk13_1(X1),X1)
| $false ),
inference(rw,[status(thm)],[178,113,theory(equality)]) ).
cnf(300,plain,
( empty(X1)
| member(esk13_1(X1),X1) ),
inference(cn,[status(thm)],[299,theory(equality)]) ).
cnf(303,plain,
( empty(X1)
| ilf_type(esk2_1(X1),member_type(X1))
| $false ),
inference(rw,[status(thm)],[64,113,theory(equality)]) ).
cnf(304,plain,
( empty(X1)
| ilf_type(esk2_1(X1),member_type(X1)) ),
inference(cn,[status(thm)],[303,theory(equality)]) ).
cnf(329,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[180,113,theory(equality)]) ).
cnf(330,plain,
( ~ empty(X1)
| ~ member(X2,X1)
| $false
| $false ),
inference(rw,[status(thm)],[329,113,theory(equality)]) ).
cnf(331,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[330,theory(equality)]) ).
cnf(349,plain,
( relation_like(X3)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[100,113,theory(equality)]) ).
cnf(350,plain,
( relation_like(X3)
| $false
| $false
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(rw,[status(thm)],[349,113,theory(equality)]) ).
cnf(351,plain,
( relation_like(X3)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(cn,[status(thm)],[350,theory(equality)]) ).
cnf(353,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[133,113,theory(equality)]) ).
cnf(354,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2)
| $false
| $false ),
inference(rw,[status(thm)],[353,113,theory(equality)]) ).
cnf(355,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(cn,[status(thm)],[354,theory(equality)]) ).
cnf(356,plain,
( subset(X1,X2)
| member(esk5_2(X1,X2),X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[94,113,theory(equality)]) ).
cnf(357,plain,
( subset(X1,X2)
| member(esk5_2(X1,X2),X1)
| $false
| $false ),
inference(rw,[status(thm)],[356,113,theory(equality)]) ).
cnf(358,plain,
( subset(X1,X2)
| member(esk5_2(X1,X2),X1) ),
inference(cn,[status(thm)],[357,theory(equality)]) ).
cnf(364,plain,
( ilf_type(X2,member_type(power_set(X1)))
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,subset_type(X1)) ),
inference(rw,[status(thm)],[172,113,theory(equality)]) ).
cnf(365,plain,
( ilf_type(X2,member_type(power_set(X1)))
| $false
| $false
| ~ ilf_type(X2,subset_type(X1)) ),
inference(rw,[status(thm)],[364,113,theory(equality)]) ).
cnf(366,plain,
( ilf_type(X2,member_type(power_set(X1)))
| ~ ilf_type(X2,subset_type(X1)) ),
inference(cn,[status(thm)],[365,theory(equality)]) ).
cnf(373,plain,
( subset(X1,X2)
| $false
| ~ ilf_type(X1,set_type)
| ~ member(esk5_2(X1,X2),X2) ),
inference(rw,[status(thm)],[93,113,theory(equality)]) ).
cnf(374,plain,
( subset(X1,X2)
| $false
| $false
| ~ member(esk5_2(X1,X2),X2) ),
inference(rw,[status(thm)],[373,113,theory(equality)]) ).
cnf(375,plain,
( subset(X1,X2)
| ~ member(esk5_2(X1,X2),X2) ),
inference(cn,[status(thm)],[374,theory(equality)]) ).
cnf(384,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[69,113,theory(equality)]) ).
cnf(385,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2)
| $false
| $false ),
inference(rw,[status(thm)],[384,113,theory(equality)]) ).
cnf(386,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(cn,[status(thm)],[385,theory(equality)]) ).
cnf(387,plain,
( ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[386,331]) ).
cnf(391,plain,
( empty(X2)
| member(X1,X2)
| $false
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,member_type(X2)) ),
inference(rw,[status(thm)],[70,113,theory(equality)]) ).
cnf(392,plain,
( empty(X2)
| member(X1,X2)
| $false
| $false
| ~ ilf_type(X1,member_type(X2)) ),
inference(rw,[status(thm)],[391,113,theory(equality)]) ).
cnf(393,plain,
( empty(X2)
| member(X1,X2)
| ~ ilf_type(X1,member_type(X2)) ),
inference(cn,[status(thm)],[392,theory(equality)]) ).
cnf(394,plain,
( member(esk2_1(X1),X1)
| empty(X1) ),
inference(spm,[status(thm)],[393,304,theory(equality)]) ).
cnf(395,plain,
( member(X1,power_set(X2))
| empty(power_set(X2))
| ~ ilf_type(X1,subset_type(X2)) ),
inference(spm,[status(thm)],[393,366,theory(equality)]) ).
cnf(396,plain,
( member(X1,power_set(X2))
| ~ ilf_type(X1,subset_type(X2)) ),
inference(sr,[status(thm)],[395,278,theory(equality)]) ).
cnf(410,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)],[128,113,theory(equality)]) ).
cnf(411,plain,
( domain(X1,X2,X3) = domain_of(X3)
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[410,113,theory(equality)]) ).
cnf(412,plain,
( domain(X1,X2,X3) = domain_of(X3)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[411,theory(equality)]) ).
cnf(413,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)],[195,113,theory(equality)]) ).
cnf(414,plain,
( range(X1,X2,X3) = range_of(X3)
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[413,113,theory(equality)]) ).
cnf(415,plain,
( range(X1,X2,X3) = range_of(X3)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[414,theory(equality)]) ).
cnf(424,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)],[259,113,theory(equality)]) ).
cnf(425,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[424,113,theory(equality)]) ).
cnf(426,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[425,theory(equality)]) ).
cnf(427,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[351,426,theory(equality)]) ).
cnf(433,plain,
( member(ordered_pair(X1,esk15_2(X1,X2)),X2)
| ~ ilf_type(X2,binary_relation_type)
| $false
| ~ member(X1,domain_of(X2)) ),
inference(rw,[status(thm)],[219,113,theory(equality)]) ).
cnf(434,plain,
( member(ordered_pair(X1,esk15_2(X1,X2)),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(X1,domain_of(X2)) ),
inference(cn,[status(thm)],[433,theory(equality)]) ).
cnf(437,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)],[205,113,theory(equality)]) ).
cnf(438,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)],[437,theory(equality)]) ).
cnf(441,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)],[212,113,theory(equality)]) ).
cnf(442,plain,
( member(X2,range_of(X3))
| ~ ilf_type(X3,binary_relation_type)
| $false
| $false
| ~ member(ordered_pair(X1,X2),X3) ),
inference(rw,[status(thm)],[441,113,theory(equality)]) ).
cnf(443,plain,
( member(X2,range_of(X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ member(ordered_pair(X1,X2),X3) ),
inference(cn,[status(thm)],[442,theory(equality)]) ).
cnf(463,plain,
( X1 = X2
| member(esk3_2(X1,X2),X2)
| member(esk3_2(X1,X2),X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[76,113,theory(equality)]) ).
cnf(464,plain,
( X1 = X2
| member(esk3_2(X1,X2),X2)
| member(esk3_2(X1,X2),X1)
| $false
| $false ),
inference(rw,[status(thm)],[463,113,theory(equality)]) ).
cnf(465,plain,
( X1 = X2
| member(esk3_2(X1,X2),X2)
| member(esk3_2(X1,X2),X1) ),
inference(cn,[status(thm)],[464,theory(equality)]) ).
cnf(468,plain,
( X1 = X2
| member(esk3_2(X1,X2),X2)
| ~ empty(X1) ),
inference(spm,[status(thm)],[331,465,theory(equality)]) ).
cnf(481,plain,
( member(X1,domain_of(X3))
| ~ ilf_type(X3,binary_relation_type)
| $false
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X1,X2),X3) ),
inference(rw,[status(thm)],[213,113,theory(equality)]) ).
cnf(482,plain,
( member(X1,domain_of(X3))
| ~ ilf_type(X3,binary_relation_type)
| $false
| $false
| ~ member(ordered_pair(X1,X2),X3) ),
inference(rw,[status(thm)],[481,113,theory(equality)]) ).
cnf(483,plain,
( member(X1,domain_of(X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ member(ordered_pair(X1,X2),X3) ),
inference(cn,[status(thm)],[482,theory(equality)]) ).
cnf(485,plain,
( member(esk14_2(X1,X2),domain_of(X2))
| ~ ilf_type(X2,binary_relation_type)
| ~ member(X1,range_of(X2)) ),
inference(spm,[status(thm)],[483,438,theory(equality)]) ).
cnf(498,plain,
( member(X3,X2)
| ~ member(X3,X1)
| $false
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X1,power_set(X2)) ),
inference(rw,[status(thm)],[60,113,theory(equality)]) ).
cnf(499,plain,
( member(X3,X2)
| ~ member(X3,X1)
| $false
| $false
| ~ ilf_type(X1,set_type)
| ~ member(X1,power_set(X2)) ),
inference(rw,[status(thm)],[498,113,theory(equality)]) ).
cnf(500,plain,
( member(X3,X2)
| ~ member(X3,X1)
| $false
| $false
| $false
| ~ member(X1,power_set(X2)) ),
inference(rw,[status(thm)],[499,113,theory(equality)]) ).
cnf(501,plain,
( member(X3,X2)
| ~ member(X3,X1)
| ~ member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[500,theory(equality)]) ).
cnf(529,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)],[187,113,theory(equality)]) ).
cnf(530,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)],[529,113,theory(equality)]) ).
cnf(531,plain,
( image4(X1,X2,X3,X4) = image(X3,X4)
| $false
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[530,113,theory(equality)]) ).
cnf(532,plain,
( image4(X1,X2,X3,X4) = image(X3,X4)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[531,theory(equality)]) ).
cnf(533,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)],[268,113,theory(equality)]) ).
cnf(534,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)],[533,113,theory(equality)]) ).
cnf(535,plain,
( inverse4(X1,X2,X3,X4) = inverse2(X3,X4)
| $false
| $false
| $false
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(rw,[status(thm)],[534,113,theory(equality)]) ).
cnf(536,plain,
( inverse4(X1,X2,X3,X4) = inverse2(X3,X4)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[535,theory(equality)]) ).
cnf(537,negated_conjecture,
( image4(esk9_0,esk10_0,esk11_0,esk9_0) != range(esk9_0,esk10_0,esk11_0)
| inverse2(esk11_0,esk10_0) != domain(esk9_0,esk10_0,esk11_0)
| ~ ilf_type(esk11_0,relation_type(esk9_0,esk10_0)) ),
inference(spm,[status(thm)],[121,536,theory(equality)]) ).
cnf(538,negated_conjecture,
( image4(esk9_0,esk10_0,esk11_0,esk9_0) != range(esk9_0,esk10_0,esk11_0)
| inverse2(esk11_0,esk10_0) != domain(esk9_0,esk10_0,esk11_0)
| $false ),
inference(rw,[status(thm)],[537,122,theory(equality)]) ).
cnf(539,negated_conjecture,
( image4(esk9_0,esk10_0,esk11_0,esk9_0) != range(esk9_0,esk10_0,esk11_0)
| inverse2(esk11_0,esk10_0) != domain(esk9_0,esk10_0,esk11_0) ),
inference(cn,[status(thm)],[538,theory(equality)]) ).
cnf(566,plain,
( member(ordered_pair(X2,esk18_3(X1,X2,X3)),X3)
| ~ ilf_type(X3,binary_relation_type)
| $false
| ~ ilf_type(X1,set_type)
| ~ member(X2,inverse2(X3,X1)) ),
inference(rw,[status(thm)],[251,113,theory(equality)]) ).
cnf(567,plain,
( member(ordered_pair(X2,esk18_3(X1,X2,X3)),X3)
| ~ ilf_type(X3,binary_relation_type)
| $false
| $false
| ~ member(X2,inverse2(X3,X1)) ),
inference(rw,[status(thm)],[566,113,theory(equality)]) ).
cnf(568,plain,
( member(ordered_pair(X2,esk18_3(X1,X2,X3)),X3)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(X2,inverse2(X3,X1)) ),
inference(cn,[status(thm)],[567,theory(equality)]) ).
cnf(571,plain,
( member(esk18_3(X1,X2,X3),range_of(X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ member(X2,inverse2(X3,X1)) ),
inference(spm,[status(thm)],[443,568,theory(equality)]) ).
cnf(572,plain,
( member(X1,domain_of(X2))
| ~ ilf_type(X2,binary_relation_type)
| ~ member(X1,inverse2(X2,X3)) ),
inference(spm,[status(thm)],[483,568,theory(equality)]) ).
cnf(574,plain,
( member(ordered_pair(esk17_3(X1,X2,X3),X2),X3)
| ~ ilf_type(X3,binary_relation_type)
| $false
| ~ ilf_type(X1,set_type)
| ~ member(X2,image(X3,X1)) ),
inference(rw,[status(thm)],[242,113,theory(equality)]) ).
cnf(575,plain,
( member(ordered_pair(esk17_3(X1,X2,X3),X2),X3)
| ~ ilf_type(X3,binary_relation_type)
| $false
| $false
| ~ member(X2,image(X3,X1)) ),
inference(rw,[status(thm)],[574,113,theory(equality)]) ).
cnf(576,plain,
( member(ordered_pair(esk17_3(X1,X2,X3),X2),X3)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(X2,image(X3,X1)) ),
inference(cn,[status(thm)],[575,theory(equality)]) ).
cnf(579,plain,
( member(X1,range_of(X2))
| ~ ilf_type(X2,binary_relation_type)
| ~ member(X1,image(X2,X3)) ),
inference(spm,[status(thm)],[443,576,theory(equality)]) ).
cnf(582,plain,
( member(X2,inverse2(X3,X1))
| ~ member(X4,X1)
| $false
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X2,X4),X3) ),
inference(rw,[status(thm)],[253,113,theory(equality)]) ).
cnf(583,plain,
( member(X2,inverse2(X3,X1))
| ~ member(X4,X1)
| $false
| ~ ilf_type(X3,binary_relation_type)
| $false
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X2,X4),X3) ),
inference(rw,[status(thm)],[582,113,theory(equality)]) ).
cnf(584,plain,
( member(X2,inverse2(X3,X1))
| ~ member(X4,X1)
| $false
| ~ ilf_type(X3,binary_relation_type)
| $false
| $false
| ~ member(ordered_pair(X2,X4),X3) ),
inference(rw,[status(thm)],[583,113,theory(equality)]) ).
cnf(585,plain,
( member(X2,inverse2(X3,X1))
| ~ member(X4,X1)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(ordered_pair(X2,X4),X3) ),
inference(cn,[status(thm)],[584,theory(equality)]) ).
cnf(586,plain,
( member(X1,inverse2(X2,X3))
| ~ member(esk15_2(X1,X2),X3)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(X1,domain_of(X2)) ),
inference(spm,[status(thm)],[585,434,theory(equality)]) ).
cnf(589,plain,
( member(X1,inverse2(X2,X3))
| ~ member(esk18_3(X4,X1,X2),X3)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(X1,inverse2(X2,X4)) ),
inference(spm,[status(thm)],[585,568,theory(equality)]) ).
cnf(591,plain,
( member(X4,X2)
| $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)],[234,113,theory(equality)]) ).
cnf(592,plain,
( member(X4,X2)
| $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)],[591,113,theory(equality)]) ).
cnf(593,plain,
( member(X4,X2)
| $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)],[592,113,theory(equality)]) ).
cnf(594,plain,
( member(X4,X2)
| $false
| $false
| $false
| $false
| ~ ilf_type(X5,relation_type(X1,X2))
| ~ member(ordered_pair(X3,X4),X5) ),
inference(rw,[status(thm)],[593,113,theory(equality)]) ).
cnf(595,plain,
( member(X4,X2)
| ~ ilf_type(X5,relation_type(X1,X2))
| ~ member(ordered_pair(X3,X4),X5) ),
inference(cn,[status(thm)],[594,theory(equality)]) ).
cnf(596,negated_conjecture,
( member(X1,esk10_0)
| ~ member(ordered_pair(X2,X1),esk11_0) ),
inference(spm,[status(thm)],[595,122,theory(equality)]) ).
cnf(598,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)],[235,113,theory(equality)]) ).
cnf(599,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)],[598,113,theory(equality)]) ).
cnf(600,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)],[599,113,theory(equality)]) ).
cnf(601,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)],[600,113,theory(equality)]) ).
cnf(602,plain,
( member(X3,X1)
| ~ ilf_type(X5,relation_type(X1,X2))
| ~ member(ordered_pair(X3,X4),X5) ),
inference(cn,[status(thm)],[601,theory(equality)]) ).
cnf(603,negated_conjecture,
( member(X1,esk9_0)
| ~ member(ordered_pair(X1,X2),esk11_0) ),
inference(spm,[status(thm)],[602,122,theory(equality)]) ).
cnf(605,plain,
( member(X2,image(X3,X1))
| ~ member(X4,X1)
| $false
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X4,X2),X3) ),
inference(rw,[status(thm)],[244,113,theory(equality)]) ).
cnf(606,plain,
( member(X2,image(X3,X1))
| ~ member(X4,X1)
| $false
| ~ ilf_type(X3,binary_relation_type)
| $false
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X4,X2),X3) ),
inference(rw,[status(thm)],[605,113,theory(equality)]) ).
cnf(607,plain,
( member(X2,image(X3,X1))
| ~ member(X4,X1)
| $false
| ~ ilf_type(X3,binary_relation_type)
| $false
| $false
| ~ member(ordered_pair(X4,X2),X3) ),
inference(rw,[status(thm)],[606,113,theory(equality)]) ).
cnf(608,plain,
( member(X2,image(X3,X1))
| ~ member(X4,X1)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(ordered_pair(X4,X2),X3) ),
inference(cn,[status(thm)],[607,theory(equality)]) ).
cnf(609,plain,
( member(esk15_2(X1,X2),image(X2,X3))
| ~ member(X1,X3)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(X1,domain_of(X2)) ),
inference(spm,[status(thm)],[608,434,theory(equality)]) ).
cnf(610,plain,
( member(X1,image(X2,X3))
| ~ member(esk14_2(X1,X2),X3)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(X1,range_of(X2)) ),
inference(spm,[status(thm)],[608,438,theory(equality)]) ).
cnf(637,negated_conjecture,
( image(esk11_0,esk9_0) != range(esk9_0,esk10_0,esk11_0)
| domain(esk9_0,esk10_0,esk11_0) != inverse2(esk11_0,esk10_0)
| ~ ilf_type(esk11_0,relation_type(esk9_0,esk10_0)) ),
inference(spm,[status(thm)],[539,532,theory(equality)]) ).
cnf(638,negated_conjecture,
( image(esk11_0,esk9_0) != range(esk9_0,esk10_0,esk11_0)
| domain(esk9_0,esk10_0,esk11_0) != inverse2(esk11_0,esk10_0)
| $false ),
inference(rw,[status(thm)],[637,122,theory(equality)]) ).
cnf(639,negated_conjecture,
( image(esk11_0,esk9_0) != range(esk9_0,esk10_0,esk11_0)
| domain(esk9_0,esk10_0,esk11_0) != inverse2(esk11_0,esk10_0) ),
inference(cn,[status(thm)],[638,theory(equality)]) ).
cnf(640,negated_conjecture,
( range_of(esk11_0) != image(esk11_0,esk9_0)
| domain(esk9_0,esk10_0,esk11_0) != inverse2(esk11_0,esk10_0)
| ~ ilf_type(esk11_0,relation_type(esk9_0,esk10_0)) ),
inference(spm,[status(thm)],[639,415,theory(equality)]) ).
cnf(641,negated_conjecture,
( range_of(esk11_0) != image(esk11_0,esk9_0)
| domain(esk9_0,esk10_0,esk11_0) != inverse2(esk11_0,esk10_0)
| $false ),
inference(rw,[status(thm)],[640,122,theory(equality)]) ).
cnf(642,negated_conjecture,
( range_of(esk11_0) != image(esk11_0,esk9_0)
| domain(esk9_0,esk10_0,esk11_0) != inverse2(esk11_0,esk10_0) ),
inference(cn,[status(thm)],[641,theory(equality)]) ).
cnf(653,negated_conjecture,
( domain_of(esk11_0) != inverse2(esk11_0,esk10_0)
| image(esk11_0,esk9_0) != range_of(esk11_0)
| ~ ilf_type(esk11_0,relation_type(esk9_0,esk10_0)) ),
inference(spm,[status(thm)],[642,412,theory(equality)]) ).
cnf(654,negated_conjecture,
( domain_of(esk11_0) != inverse2(esk11_0,esk10_0)
| image(esk11_0,esk9_0) != range_of(esk11_0)
| $false ),
inference(rw,[status(thm)],[653,122,theory(equality)]) ).
cnf(655,negated_conjecture,
( domain_of(esk11_0) != inverse2(esk11_0,esk10_0)
| image(esk11_0,esk9_0) != range_of(esk11_0) ),
inference(cn,[status(thm)],[654,theory(equality)]) ).
cnf(656,negated_conjecture,
relation_like(esk11_0),
inference(spm,[status(thm)],[427,122,theory(equality)]) ).
cnf(664,negated_conjecture,
ilf_type(esk11_0,binary_relation_type),
inference(spm,[status(thm)],[289,656,theory(equality)]) ).
cnf(675,negated_conjecture,
( member(esk15_2(X1,esk11_0),esk10_0)
| ~ member(X1,domain_of(esk11_0))
| ~ ilf_type(esk11_0,binary_relation_type) ),
inference(spm,[status(thm)],[596,434,theory(equality)]) ).
cnf(678,negated_conjecture,
( member(esk18_3(X1,X2,esk11_0),esk10_0)
| ~ member(X2,inverse2(esk11_0,X1))
| ~ ilf_type(esk11_0,binary_relation_type) ),
inference(spm,[status(thm)],[596,568,theory(equality)]) ).
cnf(680,negated_conjecture,
( member(esk15_2(X1,esk11_0),esk10_0)
| ~ member(X1,domain_of(esk11_0))
| $false ),
inference(rw,[status(thm)],[675,664,theory(equality)]) ).
cnf(681,negated_conjecture,
( member(esk15_2(X1,esk11_0),esk10_0)
| ~ member(X1,domain_of(esk11_0)) ),
inference(cn,[status(thm)],[680,theory(equality)]) ).
cnf(684,negated_conjecture,
( member(esk18_3(X1,X2,esk11_0),esk10_0)
| ~ member(X2,inverse2(esk11_0,X1))
| $false ),
inference(rw,[status(thm)],[678,664,theory(equality)]) ).
cnf(685,negated_conjecture,
( member(esk18_3(X1,X2,esk11_0),esk10_0)
| ~ member(X2,inverse2(esk11_0,X1)) ),
inference(cn,[status(thm)],[684,theory(equality)]) ).
cnf(711,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ ilf_type(X3,subset_type(X2)) ),
inference(spm,[status(thm)],[501,396,theory(equality)]) ).
cnf(767,negated_conjecture,
( member(X1,esk9_0)
| ~ member(X1,domain_of(esk11_0))
| ~ ilf_type(esk11_0,binary_relation_type) ),
inference(spm,[status(thm)],[603,434,theory(equality)]) ).
cnf(768,negated_conjecture,
( member(esk14_2(X1,esk11_0),esk9_0)
| ~ member(X1,range_of(esk11_0))
| ~ ilf_type(esk11_0,binary_relation_type) ),
inference(spm,[status(thm)],[603,438,theory(equality)]) ).
cnf(772,negated_conjecture,
( member(X1,esk9_0)
| ~ member(X1,domain_of(esk11_0))
| $false ),
inference(rw,[status(thm)],[767,664,theory(equality)]) ).
cnf(773,negated_conjecture,
( member(X1,esk9_0)
| ~ member(X1,domain_of(esk11_0)) ),
inference(cn,[status(thm)],[772,theory(equality)]) ).
cnf(774,negated_conjecture,
( member(esk14_2(X1,esk11_0),esk9_0)
| ~ member(X1,range_of(esk11_0))
| $false ),
inference(rw,[status(thm)],[768,664,theory(equality)]) ).
cnf(775,negated_conjecture,
( member(esk14_2(X1,esk11_0),esk9_0)
| ~ member(X1,range_of(esk11_0)) ),
inference(cn,[status(thm)],[774,theory(equality)]) ).
cnf(796,negated_conjecture,
( member(esk2_1(domain_of(esk11_0)),esk9_0)
| empty(domain_of(esk11_0)) ),
inference(spm,[status(thm)],[773,394,theory(equality)]) ).
cnf(1004,plain,
( X1 = X2
| ~ empty(X2)
| ~ empty(X1) ),
inference(spm,[status(thm)],[331,468,theory(equality)]) ).
cnf(1226,plain,
( ~ empty(domain_of(X2))
| ~ member(X1,range_of(X2))
| ~ ilf_type(X2,binary_relation_type) ),
inference(spm,[status(thm)],[331,485,theory(equality)]) ).
cnf(2478,plain,
( member(esk13_1(image(X1,X2)),range_of(X1))
| empty(image(X1,X2))
| ~ ilf_type(X1,binary_relation_type) ),
inference(spm,[status(thm)],[579,300,theory(equality)]) ).
cnf(2480,plain,
( member(esk5_2(image(X1,X2),X3),range_of(X1))
| subset(image(X1,X2),X3)
| ~ ilf_type(X1,binary_relation_type) ),
inference(spm,[status(thm)],[579,358,theory(equality)]) ).
cnf(2682,negated_conjecture,
( member(X1,inverse2(esk11_0,esk10_0))
| ~ member(X1,domain_of(esk11_0))
| ~ ilf_type(esk11_0,binary_relation_type) ),
inference(spm,[status(thm)],[586,681,theory(equality)]) ).
cnf(2684,negated_conjecture,
( member(X1,inverse2(esk11_0,esk10_0))
| ~ member(X1,domain_of(esk11_0))
| $false ),
inference(rw,[status(thm)],[2682,664,theory(equality)]) ).
cnf(2685,negated_conjecture,
( member(X1,inverse2(esk11_0,esk10_0))
| ~ member(X1,domain_of(esk11_0)) ),
inference(cn,[status(thm)],[2684,theory(equality)]) ).
cnf(2732,negated_conjecture,
( subset(X1,inverse2(esk11_0,esk10_0))
| ~ member(esk5_2(X1,inverse2(esk11_0,esk10_0)),domain_of(esk11_0)) ),
inference(spm,[status(thm)],[375,2685,theory(equality)]) ).
cnf(2733,negated_conjecture,
( ilf_type(X1,member_type(inverse2(esk11_0,esk10_0)))
| ~ member(X1,domain_of(esk11_0)) ),
inference(spm,[status(thm)],[387,2685,theory(equality)]) ).
cnf(3017,plain,
( ~ empty(image(X2,X3))
| ~ member(X1,domain_of(X2))
| ~ member(X1,X3)
| ~ ilf_type(X2,binary_relation_type) ),
inference(spm,[status(thm)],[331,609,theory(equality)]) ).
cnf(3051,negated_conjecture,
( member(X1,image(esk11_0,esk9_0))
| ~ member(X1,range_of(esk11_0))
| ~ ilf_type(esk11_0,binary_relation_type) ),
inference(spm,[status(thm)],[610,775,theory(equality)]) ).
cnf(3054,negated_conjecture,
( member(X1,image(esk11_0,esk9_0))
| ~ member(X1,range_of(esk11_0))
| $false ),
inference(rw,[status(thm)],[3051,664,theory(equality)]) ).
cnf(3055,negated_conjecture,
( member(X1,image(esk11_0,esk9_0))
| ~ member(X1,range_of(esk11_0)) ),
inference(cn,[status(thm)],[3054,theory(equality)]) ).
cnf(3622,negated_conjecture,
( ~ empty(image(esk11_0,esk9_0))
| ~ member(X1,range_of(esk11_0)) ),
inference(spm,[status(thm)],[331,3055,theory(equality)]) ).
cnf(3623,negated_conjecture,
( subset(X1,image(esk11_0,esk9_0))
| ~ member(esk5_2(X1,image(esk11_0,esk9_0)),range_of(esk11_0)) ),
inference(spm,[status(thm)],[375,3055,theory(equality)]) ).
cnf(3624,negated_conjecture,
( ilf_type(X1,member_type(image(esk11_0,esk9_0)))
| ~ member(X1,range_of(esk11_0)) ),
inference(spm,[status(thm)],[387,3055,theory(equality)]) ).
cnf(3720,negated_conjecture,
( member(X1,inverse2(esk11_0,esk10_0))
| ~ member(X1,inverse2(esk11_0,X2))
| ~ ilf_type(esk11_0,binary_relation_type) ),
inference(spm,[status(thm)],[589,685,theory(equality)]) ).
cnf(3721,negated_conjecture,
( member(X1,inverse2(esk11_0,esk10_0))
| ~ member(X1,inverse2(esk11_0,X2))
| $false ),
inference(rw,[status(thm)],[3720,664,theory(equality)]) ).
cnf(3722,negated_conjecture,
( member(X1,inverse2(esk11_0,esk10_0))
| ~ member(X1,inverse2(esk11_0,X2)) ),
inference(cn,[status(thm)],[3721,theory(equality)]) ).
cnf(4310,plain,
( member(X1,X2)
| ~ member(X1,esk4_1(X2)) ),
inference(spm,[status(thm)],[711,287,theory(equality)]) ).
cnf(4372,plain,
( member(esk13_1(esk4_1(X1)),X1)
| empty(esk4_1(X1)) ),
inference(spm,[status(thm)],[4310,300,theory(equality)]) ).
cnf(4403,plain,
( empty(esk4_1(X1))
| ~ empty(X1) ),
inference(spm,[status(thm)],[331,4372,theory(equality)]) ).
cnf(4457,plain,
( X1 = esk4_1(X2)
| ~ empty(X1)
| ~ empty(X2) ),
inference(spm,[status(thm)],[1004,4403,theory(equality)]) ).
cnf(10095,negated_conjecture,
( ilf_type(esk13_1(domain_of(esk11_0)),member_type(inverse2(esk11_0,esk10_0)))
| empty(domain_of(esk11_0)) ),
inference(spm,[status(thm)],[2733,300,theory(equality)]) ).
cnf(10109,negated_conjecture,
( ilf_type(esk2_1(domain_of(esk11_0)),member_type(inverse2(esk11_0,esk10_0)))
| empty(domain_of(esk11_0)) ),
inference(spm,[status(thm)],[2733,394,theory(equality)]) ).
cnf(10162,negated_conjecture,
( member(esk13_1(domain_of(esk11_0)),inverse2(esk11_0,esk10_0))
| empty(inverse2(esk11_0,esk10_0))
| empty(domain_of(esk11_0)) ),
inference(spm,[status(thm)],[393,10095,theory(equality)]) ).
cnf(42293,negated_conjecture,
( member(esk13_1(inverse2(esk11_0,X1)),inverse2(esk11_0,esk10_0))
| empty(inverse2(esk11_0,X1)) ),
inference(spm,[status(thm)],[3722,300,theory(equality)]) ).
cnf(42295,negated_conjecture,
( member(esk5_2(inverse2(esk11_0,X1),X2),inverse2(esk11_0,esk10_0))
| subset(inverse2(esk11_0,X1),X2) ),
inference(spm,[status(thm)],[3722,358,theory(equality)]) ).
cnf(42357,negated_conjecture,
( member(esk13_1(domain_of(esk11_0)),inverse2(esk11_0,esk10_0))
| empty(inverse2(esk11_0,esk10_0))
| empty(domain_of(esk11_0)) ),
inference(spm,[status(thm)],[3722,10162,theory(equality)]) ).
cnf(42535,negated_conjecture,
( member(esk13_1(inverse2(esk11_0,X1)),domain_of(esk11_0))
| empty(inverse2(esk11_0,X1))
| ~ ilf_type(esk11_0,binary_relation_type) ),
inference(spm,[status(thm)],[572,42293,theory(equality)]) ).
cnf(42547,negated_conjecture,
( member(esk13_1(inverse2(esk11_0,X1)),domain_of(esk11_0))
| empty(inverse2(esk11_0,X1))
| $false ),
inference(rw,[status(thm)],[42535,664,theory(equality)]) ).
cnf(42548,negated_conjecture,
( member(esk13_1(inverse2(esk11_0,X1)),domain_of(esk11_0))
| empty(inverse2(esk11_0,X1)) ),
inference(cn,[status(thm)],[42547,theory(equality)]) ).
cnf(42588,negated_conjecture,
( empty(inverse2(esk11_0,X1))
| ~ empty(domain_of(esk11_0)) ),
inference(spm,[status(thm)],[331,42548,theory(equality)]) ).
cnf(42614,negated_conjecture,
( X1 = inverse2(esk11_0,X2)
| ~ empty(X1)
| ~ empty(domain_of(esk11_0)) ),
inference(spm,[status(thm)],[1004,42588,theory(equality)]) ).
cnf(42624,negated_conjecture,
( inverse2(esk11_0,X1) = esk4_1(X2)
| ~ empty(X2)
| ~ empty(domain_of(esk11_0)) ),
inference(spm,[status(thm)],[4457,42588,theory(equality)]) ).
cnf(46233,negated_conjecture,
( inverse2(esk11_0,X1) = inverse2(esk11_0,X2)
| ~ empty(domain_of(esk11_0)) ),
inference(spm,[status(thm)],[42614,42588,theory(equality)]) ).
cnf(51833,negated_conjecture,
( member(esk13_1(domain_of(esk11_0)),inverse2(esk11_0,esk10_0))
| empty(inverse2(esk11_0,esk10_0)) ),
inference(csr,[status(thm)],[42357,42588]) ).
cnf(55144,negated_conjecture,
( member(esk5_2(inverse2(esk11_0,X1),X2),domain_of(esk11_0))
| subset(inverse2(esk11_0,X1),X2)
| ~ ilf_type(esk11_0,binary_relation_type) ),
inference(spm,[status(thm)],[572,42295,theory(equality)]) ).
cnf(55166,negated_conjecture,
( member(esk5_2(inverse2(esk11_0,X1),X2),domain_of(esk11_0))
| subset(inverse2(esk11_0,X1),X2)
| $false ),
inference(rw,[status(thm)],[55144,664,theory(equality)]) ).
cnf(55167,negated_conjecture,
( member(esk5_2(inverse2(esk11_0,X1),X2),domain_of(esk11_0))
| subset(inverse2(esk11_0,X1),X2) ),
inference(cn,[status(thm)],[55166,theory(equality)]) ).
cnf(55282,negated_conjecture,
subset(inverse2(esk11_0,X1),domain_of(esk11_0)),
inference(spm,[status(thm)],[375,55167,theory(equality)]) ).
cnf(114393,plain,
( empty(image(X1,X2))
| ~ empty(domain_of(X1))
| ~ ilf_type(X1,binary_relation_type) ),
inference(spm,[status(thm)],[1226,2478,theory(equality)]) ).
cnf(114633,negated_conjecture,
( ilf_type(esk5_2(image(esk11_0,X1),X2),member_type(image(esk11_0,esk9_0)))
| subset(image(esk11_0,X1),X2)
| ~ ilf_type(esk11_0,binary_relation_type) ),
inference(spm,[status(thm)],[3624,2480,theory(equality)]) ).
cnf(114673,negated_conjecture,
( ilf_type(esk5_2(image(esk11_0,X1),X2),member_type(image(esk11_0,esk9_0)))
| subset(image(esk11_0,X1),X2)
| $false ),
inference(rw,[status(thm)],[114633,664,theory(equality)]) ).
cnf(114674,negated_conjecture,
( ilf_type(esk5_2(image(esk11_0,X1),X2),member_type(image(esk11_0,esk9_0)))
| subset(image(esk11_0,X1),X2) ),
inference(cn,[status(thm)],[114673,theory(equality)]) ).
cnf(114895,negated_conjecture,
( ~ member(X1,range_of(esk11_0))
| ~ empty(domain_of(esk11_0))
| ~ ilf_type(esk11_0,binary_relation_type) ),
inference(spm,[status(thm)],[3622,114393,theory(equality)]) ).
cnf(114922,negated_conjecture,
( ~ member(X1,range_of(esk11_0))
| ~ empty(domain_of(esk11_0))
| $false ),
inference(rw,[status(thm)],[114895,664,theory(equality)]) ).
cnf(114923,negated_conjecture,
( ~ member(X1,range_of(esk11_0))
| ~ empty(domain_of(esk11_0)) ),
inference(cn,[status(thm)],[114922,theory(equality)]) ).
cnf(114940,negated_conjecture,
( X1 = range_of(esk11_0)
| ~ empty(domain_of(esk11_0))
| ~ empty(X1) ),
inference(spm,[status(thm)],[114923,468,theory(equality)]) ).
cnf(114951,negated_conjecture,
( ~ empty(domain_of(esk11_0))
| ~ member(X2,inverse2(esk11_0,X1))
| ~ ilf_type(esk11_0,binary_relation_type) ),
inference(spm,[status(thm)],[114923,571,theory(equality)]) ).
cnf(115344,negated_conjecture,
( empty(image(esk11_0,X1))
| ~ empty(domain_of(esk11_0))
| ~ ilf_type(esk11_0,binary_relation_type) ),
inference(spm,[status(thm)],[114923,2478,theory(equality)]) ).
cnf(115353,negated_conjecture,
( ~ empty(domain_of(esk11_0))
| ~ member(X2,inverse2(esk11_0,X1))
| $false ),
inference(rw,[status(thm)],[114951,664,theory(equality)]) ).
cnf(115354,negated_conjecture,
( ~ empty(domain_of(esk11_0))
| ~ member(X2,inverse2(esk11_0,X1)) ),
inference(cn,[status(thm)],[115353,theory(equality)]) ).
cnf(115355,negated_conjecture,
( empty(image(esk11_0,X1))
| ~ empty(domain_of(esk11_0))
| $false ),
inference(rw,[status(thm)],[115344,664,theory(equality)]) ).
cnf(115356,negated_conjecture,
( empty(image(esk11_0,X1))
| ~ empty(domain_of(esk11_0)) ),
inference(cn,[status(thm)],[115355,theory(equality)]) ).
cnf(123717,negated_conjecture,
( image(esk11_0,X1) = range_of(esk11_0)
| ~ empty(domain_of(esk11_0)) ),
inference(spm,[status(thm)],[114940,115356,theory(equality)]) ).
cnf(123726,negated_conjecture,
( inverse2(esk11_0,esk10_0) != domain_of(esk11_0)
| ~ empty(domain_of(esk11_0)) ),
inference(spm,[status(thm)],[655,123717,theory(equality)]) ).
cnf(124126,negated_conjecture,
( inverse2(esk11_0,X1) != domain_of(esk11_0)
| ~ empty(domain_of(esk11_0)) ),
inference(spm,[status(thm)],[123726,46233,theory(equality)]) ).
cnf(124151,negated_conjecture,
( esk4_1(X2) != domain_of(esk11_0)
| ~ empty(domain_of(esk11_0))
| ~ empty(X2) ),
inference(spm,[status(thm)],[124126,42624,theory(equality)]) ).
cnf(124230,negated_conjecture,
( ~ empty(domain_of(esk11_0))
| ~ empty(X2) ),
inference(csr,[status(thm)],[124151,4457]) ).
cnf(124522,negated_conjecture,
( empty(inverse2(esk11_0,esk10_0))
| ~ empty(domain_of(esk11_0)) ),
inference(spm,[status(thm)],[115354,51833,theory(equality)]) ).
cnf(124691,negated_conjecture,
~ empty(domain_of(esk11_0)),
inference(csr,[status(thm)],[124522,124230]) ).
cnf(124698,negated_conjecture,
member(esk2_1(domain_of(esk11_0)),esk9_0),
inference(sr,[status(thm)],[796,124691,theory(equality)]) ).
cnf(124702,negated_conjecture,
ilf_type(esk2_1(domain_of(esk11_0)),member_type(inverse2(esk11_0,esk10_0))),
inference(sr,[status(thm)],[10109,124691,theory(equality)]) ).
cnf(131435,negated_conjecture,
subset(domain_of(esk11_0),inverse2(esk11_0,esk10_0)),
inference(spm,[status(thm)],[2732,358,theory(equality)]) ).
cnf(131469,negated_conjecture,
( inverse2(esk11_0,esk10_0) = domain_of(esk11_0)
| ~ subset(inverse2(esk11_0,esk10_0),domain_of(esk11_0)) ),
inference(spm,[status(thm)],[355,131435,theory(equality)]) ).
cnf(131482,negated_conjecture,
( inverse2(esk11_0,esk10_0) = domain_of(esk11_0)
| $false ),
inference(rw,[status(thm)],[131469,55282,theory(equality)]) ).
cnf(131483,negated_conjecture,
inverse2(esk11_0,esk10_0) = domain_of(esk11_0),
inference(cn,[status(thm)],[131482,theory(equality)]) ).
cnf(131899,negated_conjecture,
ilf_type(esk2_1(domain_of(esk11_0)),member_type(domain_of(esk11_0))),
inference(rw,[status(thm)],[124702,131483,theory(equality)]) ).
cnf(131986,negated_conjecture,
( $false
| image(esk11_0,esk9_0) != range_of(esk11_0) ),
inference(rw,[status(thm)],[655,131483,theory(equality)]) ).
cnf(131987,negated_conjecture,
image(esk11_0,esk9_0) != range_of(esk11_0),
inference(cn,[status(thm)],[131986,theory(equality)]) ).
cnf(132191,negated_conjecture,
( member(esk2_1(domain_of(esk11_0)),domain_of(esk11_0))
| empty(domain_of(esk11_0)) ),
inference(spm,[status(thm)],[393,131899,theory(equality)]) ).
cnf(132193,negated_conjecture,
member(esk2_1(domain_of(esk11_0)),domain_of(esk11_0)),
inference(sr,[status(thm)],[132191,124691,theory(equality)]) ).
cnf(140025,negated_conjecture,
( ~ member(esk2_1(domain_of(esk11_0)),X1)
| ~ empty(image(esk11_0,X1))
| ~ ilf_type(esk11_0,binary_relation_type) ),
inference(spm,[status(thm)],[3017,132193,theory(equality)]) ).
cnf(140497,negated_conjecture,
( ~ member(esk2_1(domain_of(esk11_0)),X1)
| ~ empty(image(esk11_0,X1))
| $false ),
inference(rw,[status(thm)],[140025,664,theory(equality)]) ).
cnf(140498,negated_conjecture,
( ~ member(esk2_1(domain_of(esk11_0)),X1)
| ~ empty(image(esk11_0,X1)) ),
inference(cn,[status(thm)],[140497,theory(equality)]) ).
cnf(142509,negated_conjecture,
~ empty(image(esk11_0,esk9_0)),
inference(spm,[status(thm)],[140498,124698,theory(equality)]) ).
cnf(147151,negated_conjecture,
( member(esk5_2(image(esk11_0,X1),X2),image(esk11_0,esk9_0))
| empty(image(esk11_0,esk9_0))
| subset(image(esk11_0,X1),X2) ),
inference(spm,[status(thm)],[393,114674,theory(equality)]) ).
cnf(147166,negated_conjecture,
( member(esk5_2(image(esk11_0,X1),X2),image(esk11_0,esk9_0))
| subset(image(esk11_0,X1),X2) ),
inference(sr,[status(thm)],[147151,142509,theory(equality)]) ).
cnf(147178,negated_conjecture,
( member(esk5_2(image(esk11_0,X1),X2),range_of(esk11_0))
| subset(image(esk11_0,X1),X2)
| ~ ilf_type(esk11_0,binary_relation_type) ),
inference(spm,[status(thm)],[579,147166,theory(equality)]) ).
cnf(147205,negated_conjecture,
( member(esk5_2(image(esk11_0,X1),X2),range_of(esk11_0))
| subset(image(esk11_0,X1),X2)
| $false ),
inference(rw,[status(thm)],[147178,664,theory(equality)]) ).
cnf(147206,negated_conjecture,
( member(esk5_2(image(esk11_0,X1),X2),range_of(esk11_0))
| subset(image(esk11_0,X1),X2) ),
inference(cn,[status(thm)],[147205,theory(equality)]) ).
cnf(147438,negated_conjecture,
subset(image(esk11_0,X1),range_of(esk11_0)),
inference(spm,[status(thm)],[375,147206,theory(equality)]) ).
cnf(178375,negated_conjecture,
subset(range_of(esk11_0),image(esk11_0,esk9_0)),
inference(spm,[status(thm)],[3623,358,theory(equality)]) ).
cnf(178409,negated_conjecture,
( image(esk11_0,esk9_0) = range_of(esk11_0)
| ~ subset(image(esk11_0,esk9_0),range_of(esk11_0)) ),
inference(spm,[status(thm)],[355,178375,theory(equality)]) ).
cnf(178422,negated_conjecture,
( image(esk11_0,esk9_0) = range_of(esk11_0)
| $false ),
inference(rw,[status(thm)],[178409,147438,theory(equality)]) ).
cnf(178423,negated_conjecture,
image(esk11_0,esk9_0) = range_of(esk11_0),
inference(cn,[status(thm)],[178422,theory(equality)]) ).
cnf(178424,negated_conjecture,
$false,
inference(sr,[status(thm)],[178423,131987,theory(equality)]) ).
cnf(178425,negated_conjecture,
$false,
178424,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET674+3.p
% --creating new selector for []
% -running prover on /tmp/tmpC30OCt/sel_SET674+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET674+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET674+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET674+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
%
%------------------------------------------------------------------------------