TSTP Solution File: SET729+4 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET729+4 : TPTP v5.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art03.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 03:21:06 EST 2010
% Result : Theorem 3.97s
% Output : CNFRefutation 3.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 8
% Syntax : Number of formulae : 167 ( 8 unt; 0 def)
% Number of atoms : 993 ( 70 equ)
% Maximal formula atoms : 55 ( 5 avg)
% Number of connectives : 1324 ( 498 ~; 626 |; 179 &)
% ( 10 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 17 ( 17 usr; 2 con; 0-7 aty)
% Number of variables : 526 ( 3 sgn 229 !; 35 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] :
( surjective(X1,X2,X3)
<=> ! [X4] :
( member(X4,X3)
=> ? [X5] :
( member(X5,X2)
& apply(X1,X5,X4) ) ) ),
file('/tmp/tmpnBawlf/sel_SET729+4.p_1',surjective) ).
fof(2,axiom,
! [X1,X2,X3] :
( one_to_one(X1,X2,X3)
<=> ( injective(X1,X2,X3)
& surjective(X1,X2,X3) ) ),
file('/tmp/tmpnBawlf/sel_SET729+4.p_1',one_to_one) ).
fof(3,axiom,
! [X1,X2,X3] :
( maps(X1,X2,X3)
<=> ( ! [X6] :
( member(X6,X2)
=> ? [X4] :
( member(X4,X3)
& apply(X1,X6,X4) ) )
& ! [X6,X7,X8] :
( ( member(X6,X2)
& member(X7,X3)
& member(X8,X3) )
=> ( ( apply(X1,X6,X7)
& apply(X1,X6,X8) )
=> X7 = X8 ) ) ) ),
file('/tmp/tmpnBawlf/sel_SET729+4.p_1',maps) ).
fof(4,axiom,
! [X1,X2] :
( identity(X1,X2)
<=> ! [X6] :
( member(X6,X2)
=> apply(X1,X6,X6) ) ),
file('/tmp/tmpnBawlf/sel_SET729+4.p_1',identity) ).
fof(5,axiom,
! [X9,X1,X2,X3] :
( inverse_predicate(X9,X1,X2,X3)
<=> ! [X6,X4] :
( ( member(X6,X2)
& member(X4,X3) )
=> ( apply(X1,X6,X4)
<=> apply(X9,X4,X6) ) ) ),
file('/tmp/tmpnBawlf/sel_SET729+4.p_1',inverse_predicate) ).
fof(6,axiom,
! [X1,X2,X3] :
( injective(X1,X2,X3)
<=> ! [X10,X11,X4] :
( ( member(X10,X2)
& member(X11,X2)
& member(X4,X3) )
=> ( ( apply(X1,X10,X4)
& apply(X1,X11,X4) )
=> X10 = X11 ) ) ),
file('/tmp/tmpnBawlf/sel_SET729+4.p_1',injective) ).
fof(7,axiom,
! [X9,X1,X2,X3,X12,X6,X13] :
( ( member(X6,X2)
& member(X13,X12) )
=> ( apply(compose_function(X9,X1,X2,X3,X12),X6,X13)
<=> ? [X4] :
( member(X4,X3)
& apply(X1,X6,X4)
& apply(X9,X4,X13) ) ) ),
file('/tmp/tmpnBawlf/sel_SET729+4.p_1',compose_function) ).
fof(8,conjecture,
! [X1,X2] :
( maps(X1,X2,X2)
=> ( ( one_to_one(X1,X2,X2)
& inverse_predicate(X1,X1,X2,X2) )
<=> identity(compose_function(X1,X1,X2,X2,X2),X2) ) ),
file('/tmp/tmpnBawlf/sel_SET729+4.p_1',thII20) ).
fof(9,negated_conjecture,
~ ! [X1,X2] :
( maps(X1,X2,X2)
=> ( ( one_to_one(X1,X2,X2)
& inverse_predicate(X1,X1,X2,X2) )
<=> identity(compose_function(X1,X1,X2,X2,X2),X2) ) ),
inference(assume_negation,[status(cth)],[8]) ).
fof(10,plain,
! [X1,X2,X3] :
( ( ~ surjective(X1,X2,X3)
| ! [X4] :
( ~ member(X4,X3)
| ? [X5] :
( member(X5,X2)
& apply(X1,X5,X4) ) ) )
& ( ? [X4] :
( member(X4,X3)
& ! [X5] :
( ~ member(X5,X2)
| ~ apply(X1,X5,X4) ) )
| surjective(X1,X2,X3) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(11,plain,
! [X6,X7,X8] :
( ( ~ surjective(X6,X7,X8)
| ! [X9] :
( ~ member(X9,X8)
| ? [X10] :
( member(X10,X7)
& apply(X6,X10,X9) ) ) )
& ( ? [X11] :
( member(X11,X8)
& ! [X12] :
( ~ member(X12,X7)
| ~ apply(X6,X12,X11) ) )
| surjective(X6,X7,X8) ) ),
inference(variable_rename,[status(thm)],[10]) ).
fof(12,plain,
! [X6,X7,X8] :
( ( ~ surjective(X6,X7,X8)
| ! [X9] :
( ~ member(X9,X8)
| ( member(esk1_4(X6,X7,X8,X9),X7)
& apply(X6,esk1_4(X6,X7,X8,X9),X9) ) ) )
& ( ( member(esk2_3(X6,X7,X8),X8)
& ! [X12] :
( ~ member(X12,X7)
| ~ apply(X6,X12,esk2_3(X6,X7,X8)) ) )
| surjective(X6,X7,X8) ) ),
inference(skolemize,[status(esa)],[11]) ).
fof(13,plain,
! [X6,X7,X8,X9,X12] :
( ( ( ( ~ member(X12,X7)
| ~ apply(X6,X12,esk2_3(X6,X7,X8)) )
& member(esk2_3(X6,X7,X8),X8) )
| surjective(X6,X7,X8) )
& ( ~ member(X9,X8)
| ( member(esk1_4(X6,X7,X8,X9),X7)
& apply(X6,esk1_4(X6,X7,X8,X9),X9) )
| ~ surjective(X6,X7,X8) ) ),
inference(shift_quantors,[status(thm)],[12]) ).
fof(14,plain,
! [X6,X7,X8,X9,X12] :
( ( ~ member(X12,X7)
| ~ apply(X6,X12,esk2_3(X6,X7,X8))
| surjective(X6,X7,X8) )
& ( member(esk2_3(X6,X7,X8),X8)
| surjective(X6,X7,X8) )
& ( member(esk1_4(X6,X7,X8,X9),X7)
| ~ member(X9,X8)
| ~ surjective(X6,X7,X8) )
& ( apply(X6,esk1_4(X6,X7,X8,X9),X9)
| ~ member(X9,X8)
| ~ surjective(X6,X7,X8) ) ),
inference(distribute,[status(thm)],[13]) ).
cnf(17,plain,
( surjective(X1,X2,X3)
| member(esk2_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[14]) ).
cnf(18,plain,
( surjective(X1,X2,X3)
| ~ apply(X1,X4,esk2_3(X1,X2,X3))
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[14]) ).
fof(19,plain,
! [X1,X2,X3] :
( ( ~ one_to_one(X1,X2,X3)
| ( injective(X1,X2,X3)
& surjective(X1,X2,X3) ) )
& ( ~ injective(X1,X2,X3)
| ~ surjective(X1,X2,X3)
| one_to_one(X1,X2,X3) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(20,plain,
! [X4,X5,X6] :
( ( ~ one_to_one(X4,X5,X6)
| ( injective(X4,X5,X6)
& surjective(X4,X5,X6) ) )
& ( ~ injective(X4,X5,X6)
| ~ surjective(X4,X5,X6)
| one_to_one(X4,X5,X6) ) ),
inference(variable_rename,[status(thm)],[19]) ).
fof(21,plain,
! [X4,X5,X6] :
( ( injective(X4,X5,X6)
| ~ one_to_one(X4,X5,X6) )
& ( surjective(X4,X5,X6)
| ~ one_to_one(X4,X5,X6) )
& ( ~ injective(X4,X5,X6)
| ~ surjective(X4,X5,X6)
| one_to_one(X4,X5,X6) ) ),
inference(distribute,[status(thm)],[20]) ).
cnf(22,plain,
( one_to_one(X1,X2,X3)
| ~ surjective(X1,X2,X3)
| ~ injective(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[21]) ).
cnf(23,plain,
( surjective(X1,X2,X3)
| ~ one_to_one(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[21]) ).
cnf(24,plain,
( injective(X1,X2,X3)
| ~ one_to_one(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[21]) ).
fof(25,plain,
! [X1,X2,X3] :
( ( ~ maps(X1,X2,X3)
| ( ! [X6] :
( ~ member(X6,X2)
| ? [X4] :
( member(X4,X3)
& apply(X1,X6,X4) ) )
& ! [X6,X7,X8] :
( ~ member(X6,X2)
| ~ member(X7,X3)
| ~ member(X8,X3)
| ~ apply(X1,X6,X7)
| ~ apply(X1,X6,X8)
| X7 = X8 ) ) )
& ( ? [X6] :
( member(X6,X2)
& ! [X4] :
( ~ member(X4,X3)
| ~ apply(X1,X6,X4) ) )
| ? [X6,X7,X8] :
( member(X6,X2)
& member(X7,X3)
& member(X8,X3)
& apply(X1,X6,X7)
& apply(X1,X6,X8)
& X7 != X8 )
| maps(X1,X2,X3) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(26,plain,
! [X9,X10,X11] :
( ( ~ maps(X9,X10,X11)
| ( ! [X12] :
( ~ member(X12,X10)
| ? [X13] :
( member(X13,X11)
& apply(X9,X12,X13) ) )
& ! [X14,X15,X16] :
( ~ member(X14,X10)
| ~ member(X15,X11)
| ~ member(X16,X11)
| ~ apply(X9,X14,X15)
| ~ apply(X9,X14,X16)
| X15 = X16 ) ) )
& ( ? [X17] :
( member(X17,X10)
& ! [X18] :
( ~ member(X18,X11)
| ~ apply(X9,X17,X18) ) )
| ? [X19,X20,X21] :
( member(X19,X10)
& member(X20,X11)
& member(X21,X11)
& apply(X9,X19,X20)
& apply(X9,X19,X21)
& X20 != X21 )
| maps(X9,X10,X11) ) ),
inference(variable_rename,[status(thm)],[25]) ).
fof(27,plain,
! [X9,X10,X11] :
( ( ~ maps(X9,X10,X11)
| ( ! [X12] :
( ~ member(X12,X10)
| ( member(esk3_4(X9,X10,X11,X12),X11)
& apply(X9,X12,esk3_4(X9,X10,X11,X12)) ) )
& ! [X14,X15,X16] :
( ~ member(X14,X10)
| ~ member(X15,X11)
| ~ member(X16,X11)
| ~ apply(X9,X14,X15)
| ~ apply(X9,X14,X16)
| X15 = X16 ) ) )
& ( ( member(esk4_3(X9,X10,X11),X10)
& ! [X18] :
( ~ member(X18,X11)
| ~ apply(X9,esk4_3(X9,X10,X11),X18) ) )
| ( member(esk5_3(X9,X10,X11),X10)
& member(esk6_3(X9,X10,X11),X11)
& member(esk7_3(X9,X10,X11),X11)
& apply(X9,esk5_3(X9,X10,X11),esk6_3(X9,X10,X11))
& apply(X9,esk5_3(X9,X10,X11),esk7_3(X9,X10,X11))
& esk6_3(X9,X10,X11) != esk7_3(X9,X10,X11) )
| maps(X9,X10,X11) ) ),
inference(skolemize,[status(esa)],[26]) ).
fof(28,plain,
! [X9,X10,X11,X12,X14,X15,X16,X18] :
( ( ( ( ~ member(X18,X11)
| ~ apply(X9,esk4_3(X9,X10,X11),X18) )
& member(esk4_3(X9,X10,X11),X10) )
| ( member(esk5_3(X9,X10,X11),X10)
& member(esk6_3(X9,X10,X11),X11)
& member(esk7_3(X9,X10,X11),X11)
& apply(X9,esk5_3(X9,X10,X11),esk6_3(X9,X10,X11))
& apply(X9,esk5_3(X9,X10,X11),esk7_3(X9,X10,X11))
& esk6_3(X9,X10,X11) != esk7_3(X9,X10,X11) )
| maps(X9,X10,X11) )
& ( ( ( ~ member(X14,X10)
| ~ member(X15,X11)
| ~ member(X16,X11)
| ~ apply(X9,X14,X15)
| ~ apply(X9,X14,X16)
| X15 = X16 )
& ( ~ member(X12,X10)
| ( member(esk3_4(X9,X10,X11,X12),X11)
& apply(X9,X12,esk3_4(X9,X10,X11,X12)) ) ) )
| ~ maps(X9,X10,X11) ) ),
inference(shift_quantors,[status(thm)],[27]) ).
fof(29,plain,
! [X9,X10,X11,X12,X14,X15,X16,X18] :
( ( member(esk5_3(X9,X10,X11),X10)
| ~ member(X18,X11)
| ~ apply(X9,esk4_3(X9,X10,X11),X18)
| maps(X9,X10,X11) )
& ( member(esk6_3(X9,X10,X11),X11)
| ~ member(X18,X11)
| ~ apply(X9,esk4_3(X9,X10,X11),X18)
| maps(X9,X10,X11) )
& ( member(esk7_3(X9,X10,X11),X11)
| ~ member(X18,X11)
| ~ apply(X9,esk4_3(X9,X10,X11),X18)
| maps(X9,X10,X11) )
& ( apply(X9,esk5_3(X9,X10,X11),esk6_3(X9,X10,X11))
| ~ member(X18,X11)
| ~ apply(X9,esk4_3(X9,X10,X11),X18)
| maps(X9,X10,X11) )
& ( apply(X9,esk5_3(X9,X10,X11),esk7_3(X9,X10,X11))
| ~ member(X18,X11)
| ~ apply(X9,esk4_3(X9,X10,X11),X18)
| maps(X9,X10,X11) )
& ( esk6_3(X9,X10,X11) != esk7_3(X9,X10,X11)
| ~ member(X18,X11)
| ~ apply(X9,esk4_3(X9,X10,X11),X18)
| maps(X9,X10,X11) )
& ( member(esk5_3(X9,X10,X11),X10)
| member(esk4_3(X9,X10,X11),X10)
| maps(X9,X10,X11) )
& ( member(esk6_3(X9,X10,X11),X11)
| member(esk4_3(X9,X10,X11),X10)
| maps(X9,X10,X11) )
& ( member(esk7_3(X9,X10,X11),X11)
| member(esk4_3(X9,X10,X11),X10)
| maps(X9,X10,X11) )
& ( apply(X9,esk5_3(X9,X10,X11),esk6_3(X9,X10,X11))
| member(esk4_3(X9,X10,X11),X10)
| maps(X9,X10,X11) )
& ( apply(X9,esk5_3(X9,X10,X11),esk7_3(X9,X10,X11))
| member(esk4_3(X9,X10,X11),X10)
| maps(X9,X10,X11) )
& ( esk6_3(X9,X10,X11) != esk7_3(X9,X10,X11)
| member(esk4_3(X9,X10,X11),X10)
| maps(X9,X10,X11) )
& ( ~ member(X14,X10)
| ~ member(X15,X11)
| ~ member(X16,X11)
| ~ apply(X9,X14,X15)
| ~ apply(X9,X14,X16)
| X15 = X16
| ~ maps(X9,X10,X11) )
& ( member(esk3_4(X9,X10,X11,X12),X11)
| ~ member(X12,X10)
| ~ maps(X9,X10,X11) )
& ( apply(X9,X12,esk3_4(X9,X10,X11,X12))
| ~ member(X12,X10)
| ~ maps(X9,X10,X11) ) ),
inference(distribute,[status(thm)],[28]) ).
cnf(30,plain,
( apply(X1,X4,esk3_4(X1,X2,X3,X4))
| ~ maps(X1,X2,X3)
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[29]) ).
cnf(31,plain,
( member(esk3_4(X1,X2,X3,X4),X3)
| ~ maps(X1,X2,X3)
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[29]) ).
cnf(32,plain,
( X4 = X5
| ~ maps(X1,X2,X3)
| ~ apply(X1,X6,X5)
| ~ apply(X1,X6,X4)
| ~ member(X5,X3)
| ~ member(X4,X3)
| ~ member(X6,X2) ),
inference(split_conjunct,[status(thm)],[29]) ).
fof(45,plain,
! [X1,X2] :
( ( ~ identity(X1,X2)
| ! [X6] :
( ~ member(X6,X2)
| apply(X1,X6,X6) ) )
& ( ? [X6] :
( member(X6,X2)
& ~ apply(X1,X6,X6) )
| identity(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(46,plain,
! [X7,X8] :
( ( ~ identity(X7,X8)
| ! [X9] :
( ~ member(X9,X8)
| apply(X7,X9,X9) ) )
& ( ? [X10] :
( member(X10,X8)
& ~ apply(X7,X10,X10) )
| identity(X7,X8) ) ),
inference(variable_rename,[status(thm)],[45]) ).
fof(47,plain,
! [X7,X8] :
( ( ~ identity(X7,X8)
| ! [X9] :
( ~ member(X9,X8)
| apply(X7,X9,X9) ) )
& ( ( member(esk8_2(X7,X8),X8)
& ~ apply(X7,esk8_2(X7,X8),esk8_2(X7,X8)) )
| identity(X7,X8) ) ),
inference(skolemize,[status(esa)],[46]) ).
fof(48,plain,
! [X7,X8,X9] :
( ( ~ member(X9,X8)
| apply(X7,X9,X9)
| ~ identity(X7,X8) )
& ( ( member(esk8_2(X7,X8),X8)
& ~ apply(X7,esk8_2(X7,X8),esk8_2(X7,X8)) )
| identity(X7,X8) ) ),
inference(shift_quantors,[status(thm)],[47]) ).
fof(49,plain,
! [X7,X8,X9] :
( ( ~ member(X9,X8)
| apply(X7,X9,X9)
| ~ identity(X7,X8) )
& ( member(esk8_2(X7,X8),X8)
| identity(X7,X8) )
& ( ~ apply(X7,esk8_2(X7,X8),esk8_2(X7,X8))
| identity(X7,X8) ) ),
inference(distribute,[status(thm)],[48]) ).
cnf(50,plain,
( identity(X1,X2)
| ~ apply(X1,esk8_2(X1,X2),esk8_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[49]) ).
cnf(51,plain,
( identity(X1,X2)
| member(esk8_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[49]) ).
cnf(52,plain,
( apply(X1,X3,X3)
| ~ identity(X1,X2)
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[49]) ).
fof(53,plain,
! [X9,X1,X2,X3] :
( ( ~ inverse_predicate(X9,X1,X2,X3)
| ! [X6,X4] :
( ~ member(X6,X2)
| ~ member(X4,X3)
| ( ( ~ apply(X1,X6,X4)
| apply(X9,X4,X6) )
& ( ~ apply(X9,X4,X6)
| apply(X1,X6,X4) ) ) ) )
& ( ? [X6,X4] :
( member(X6,X2)
& member(X4,X3)
& ( ~ apply(X1,X6,X4)
| ~ apply(X9,X4,X6) )
& ( apply(X1,X6,X4)
| apply(X9,X4,X6) ) )
| inverse_predicate(X9,X1,X2,X3) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(54,plain,
! [X10,X11,X12,X13] :
( ( ~ inverse_predicate(X10,X11,X12,X13)
| ! [X14,X15] :
( ~ member(X14,X12)
| ~ member(X15,X13)
| ( ( ~ apply(X11,X14,X15)
| apply(X10,X15,X14) )
& ( ~ apply(X10,X15,X14)
| apply(X11,X14,X15) ) ) ) )
& ( ? [X16,X17] :
( member(X16,X12)
& member(X17,X13)
& ( ~ apply(X11,X16,X17)
| ~ apply(X10,X17,X16) )
& ( apply(X11,X16,X17)
| apply(X10,X17,X16) ) )
| inverse_predicate(X10,X11,X12,X13) ) ),
inference(variable_rename,[status(thm)],[53]) ).
fof(55,plain,
! [X10,X11,X12,X13] :
( ( ~ inverse_predicate(X10,X11,X12,X13)
| ! [X14,X15] :
( ~ member(X14,X12)
| ~ member(X15,X13)
| ( ( ~ apply(X11,X14,X15)
| apply(X10,X15,X14) )
& ( ~ apply(X10,X15,X14)
| apply(X11,X14,X15) ) ) ) )
& ( ( member(esk9_4(X10,X11,X12,X13),X12)
& member(esk10_4(X10,X11,X12,X13),X13)
& ( ~ apply(X11,esk9_4(X10,X11,X12,X13),esk10_4(X10,X11,X12,X13))
| ~ apply(X10,esk10_4(X10,X11,X12,X13),esk9_4(X10,X11,X12,X13)) )
& ( apply(X11,esk9_4(X10,X11,X12,X13),esk10_4(X10,X11,X12,X13))
| apply(X10,esk10_4(X10,X11,X12,X13),esk9_4(X10,X11,X12,X13)) ) )
| inverse_predicate(X10,X11,X12,X13) ) ),
inference(skolemize,[status(esa)],[54]) ).
fof(56,plain,
! [X10,X11,X12,X13,X14,X15] :
( ( ~ member(X14,X12)
| ~ member(X15,X13)
| ( ( ~ apply(X11,X14,X15)
| apply(X10,X15,X14) )
& ( ~ apply(X10,X15,X14)
| apply(X11,X14,X15) ) )
| ~ inverse_predicate(X10,X11,X12,X13) )
& ( ( member(esk9_4(X10,X11,X12,X13),X12)
& member(esk10_4(X10,X11,X12,X13),X13)
& ( ~ apply(X11,esk9_4(X10,X11,X12,X13),esk10_4(X10,X11,X12,X13))
| ~ apply(X10,esk10_4(X10,X11,X12,X13),esk9_4(X10,X11,X12,X13)) )
& ( apply(X11,esk9_4(X10,X11,X12,X13),esk10_4(X10,X11,X12,X13))
| apply(X10,esk10_4(X10,X11,X12,X13),esk9_4(X10,X11,X12,X13)) ) )
| inverse_predicate(X10,X11,X12,X13) ) ),
inference(shift_quantors,[status(thm)],[55]) ).
fof(57,plain,
! [X10,X11,X12,X13,X14,X15] :
( ( ~ apply(X11,X14,X15)
| apply(X10,X15,X14)
| ~ member(X14,X12)
| ~ member(X15,X13)
| ~ inverse_predicate(X10,X11,X12,X13) )
& ( ~ apply(X10,X15,X14)
| apply(X11,X14,X15)
| ~ member(X14,X12)
| ~ member(X15,X13)
| ~ inverse_predicate(X10,X11,X12,X13) )
& ( member(esk9_4(X10,X11,X12,X13),X12)
| inverse_predicate(X10,X11,X12,X13) )
& ( member(esk10_4(X10,X11,X12,X13),X13)
| inverse_predicate(X10,X11,X12,X13) )
& ( ~ apply(X11,esk9_4(X10,X11,X12,X13),esk10_4(X10,X11,X12,X13))
| ~ apply(X10,esk10_4(X10,X11,X12,X13),esk9_4(X10,X11,X12,X13))
| inverse_predicate(X10,X11,X12,X13) )
& ( apply(X11,esk9_4(X10,X11,X12,X13),esk10_4(X10,X11,X12,X13))
| apply(X10,esk10_4(X10,X11,X12,X13),esk9_4(X10,X11,X12,X13))
| inverse_predicate(X10,X11,X12,X13) ) ),
inference(distribute,[status(thm)],[56]) ).
cnf(58,plain,
( inverse_predicate(X1,X2,X3,X4)
| apply(X1,esk10_4(X1,X2,X3,X4),esk9_4(X1,X2,X3,X4))
| apply(X2,esk9_4(X1,X2,X3,X4),esk10_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[57]) ).
cnf(59,plain,
( inverse_predicate(X1,X2,X3,X4)
| ~ apply(X1,esk10_4(X1,X2,X3,X4),esk9_4(X1,X2,X3,X4))
| ~ apply(X2,esk9_4(X1,X2,X3,X4),esk10_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[57]) ).
cnf(60,plain,
( inverse_predicate(X1,X2,X3,X4)
| member(esk10_4(X1,X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[57]) ).
cnf(61,plain,
( inverse_predicate(X1,X2,X3,X4)
| member(esk9_4(X1,X2,X3,X4),X3) ),
inference(split_conjunct,[status(thm)],[57]) ).
cnf(62,plain,
( apply(X2,X6,X5)
| ~ inverse_predicate(X1,X2,X3,X4)
| ~ member(X5,X4)
| ~ member(X6,X3)
| ~ apply(X1,X5,X6) ),
inference(split_conjunct,[status(thm)],[57]) ).
fof(64,plain,
! [X1,X2,X3] :
( ( ~ injective(X1,X2,X3)
| ! [X10,X11,X4] :
( ~ member(X10,X2)
| ~ member(X11,X2)
| ~ member(X4,X3)
| ~ apply(X1,X10,X4)
| ~ apply(X1,X11,X4)
| X10 = X11 ) )
& ( ? [X10,X11,X4] :
( member(X10,X2)
& member(X11,X2)
& member(X4,X3)
& apply(X1,X10,X4)
& apply(X1,X11,X4)
& X10 != X11 )
| injective(X1,X2,X3) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(65,plain,
! [X12,X13,X14] :
( ( ~ injective(X12,X13,X14)
| ! [X15,X16,X17] :
( ~ member(X15,X13)
| ~ member(X16,X13)
| ~ member(X17,X14)
| ~ apply(X12,X15,X17)
| ~ apply(X12,X16,X17)
| X15 = X16 ) )
& ( ? [X18,X19,X20] :
( member(X18,X13)
& member(X19,X13)
& member(X20,X14)
& apply(X12,X18,X20)
& apply(X12,X19,X20)
& X18 != X19 )
| injective(X12,X13,X14) ) ),
inference(variable_rename,[status(thm)],[64]) ).
fof(66,plain,
! [X12,X13,X14] :
( ( ~ injective(X12,X13,X14)
| ! [X15,X16,X17] :
( ~ member(X15,X13)
| ~ member(X16,X13)
| ~ member(X17,X14)
| ~ apply(X12,X15,X17)
| ~ apply(X12,X16,X17)
| X15 = X16 ) )
& ( ( member(esk11_3(X12,X13,X14),X13)
& member(esk12_3(X12,X13,X14),X13)
& member(esk13_3(X12,X13,X14),X14)
& apply(X12,esk11_3(X12,X13,X14),esk13_3(X12,X13,X14))
& apply(X12,esk12_3(X12,X13,X14),esk13_3(X12,X13,X14))
& esk11_3(X12,X13,X14) != esk12_3(X12,X13,X14) )
| injective(X12,X13,X14) ) ),
inference(skolemize,[status(esa)],[65]) ).
fof(67,plain,
! [X12,X13,X14,X15,X16,X17] :
( ( ~ member(X15,X13)
| ~ member(X16,X13)
| ~ member(X17,X14)
| ~ apply(X12,X15,X17)
| ~ apply(X12,X16,X17)
| X15 = X16
| ~ injective(X12,X13,X14) )
& ( ( member(esk11_3(X12,X13,X14),X13)
& member(esk12_3(X12,X13,X14),X13)
& member(esk13_3(X12,X13,X14),X14)
& apply(X12,esk11_3(X12,X13,X14),esk13_3(X12,X13,X14))
& apply(X12,esk12_3(X12,X13,X14),esk13_3(X12,X13,X14))
& esk11_3(X12,X13,X14) != esk12_3(X12,X13,X14) )
| injective(X12,X13,X14) ) ),
inference(shift_quantors,[status(thm)],[66]) ).
fof(68,plain,
! [X12,X13,X14,X15,X16,X17] :
( ( ~ member(X15,X13)
| ~ member(X16,X13)
| ~ member(X17,X14)
| ~ apply(X12,X15,X17)
| ~ apply(X12,X16,X17)
| X15 = X16
| ~ injective(X12,X13,X14) )
& ( member(esk11_3(X12,X13,X14),X13)
| injective(X12,X13,X14) )
& ( member(esk12_3(X12,X13,X14),X13)
| injective(X12,X13,X14) )
& ( member(esk13_3(X12,X13,X14),X14)
| injective(X12,X13,X14) )
& ( apply(X12,esk11_3(X12,X13,X14),esk13_3(X12,X13,X14))
| injective(X12,X13,X14) )
& ( apply(X12,esk12_3(X12,X13,X14),esk13_3(X12,X13,X14))
| injective(X12,X13,X14) )
& ( esk11_3(X12,X13,X14) != esk12_3(X12,X13,X14)
| injective(X12,X13,X14) ) ),
inference(distribute,[status(thm)],[67]) ).
cnf(69,plain,
( injective(X1,X2,X3)
| esk11_3(X1,X2,X3) != esk12_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[68]) ).
cnf(70,plain,
( injective(X1,X2,X3)
| apply(X1,esk12_3(X1,X2,X3),esk13_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[68]) ).
cnf(71,plain,
( injective(X1,X2,X3)
| apply(X1,esk11_3(X1,X2,X3),esk13_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[68]) ).
cnf(72,plain,
( injective(X1,X2,X3)
| member(esk13_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[68]) ).
cnf(73,plain,
( injective(X1,X2,X3)
| member(esk12_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[68]) ).
cnf(74,plain,
( injective(X1,X2,X3)
| member(esk11_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[68]) ).
fof(76,plain,
! [X9,X1,X2,X3,X12,X6,X13] :
( ~ member(X6,X2)
| ~ member(X13,X12)
| ( ( ~ apply(compose_function(X9,X1,X2,X3,X12),X6,X13)
| ? [X4] :
( member(X4,X3)
& apply(X1,X6,X4)
& apply(X9,X4,X13) ) )
& ( ! [X4] :
( ~ member(X4,X3)
| ~ apply(X1,X6,X4)
| ~ apply(X9,X4,X13) )
| apply(compose_function(X9,X1,X2,X3,X12),X6,X13) ) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(77,plain,
! [X14,X15,X16,X17,X18,X19,X20] :
( ~ member(X19,X16)
| ~ member(X20,X18)
| ( ( ~ apply(compose_function(X14,X15,X16,X17,X18),X19,X20)
| ? [X21] :
( member(X21,X17)
& apply(X15,X19,X21)
& apply(X14,X21,X20) ) )
& ( ! [X22] :
( ~ member(X22,X17)
| ~ apply(X15,X19,X22)
| ~ apply(X14,X22,X20) )
| apply(compose_function(X14,X15,X16,X17,X18),X19,X20) ) ) ),
inference(variable_rename,[status(thm)],[76]) ).
fof(78,plain,
! [X14,X15,X16,X17,X18,X19,X20] :
( ~ member(X19,X16)
| ~ member(X20,X18)
| ( ( ~ apply(compose_function(X14,X15,X16,X17,X18),X19,X20)
| ( member(esk14_7(X14,X15,X16,X17,X18,X19,X20),X17)
& apply(X15,X19,esk14_7(X14,X15,X16,X17,X18,X19,X20))
& apply(X14,esk14_7(X14,X15,X16,X17,X18,X19,X20),X20) ) )
& ( ! [X22] :
( ~ member(X22,X17)
| ~ apply(X15,X19,X22)
| ~ apply(X14,X22,X20) )
| apply(compose_function(X14,X15,X16,X17,X18),X19,X20) ) ) ),
inference(skolemize,[status(esa)],[77]) ).
fof(79,plain,
! [X14,X15,X16,X17,X18,X19,X20,X22] :
( ( ( ~ member(X22,X17)
| ~ apply(X15,X19,X22)
| ~ apply(X14,X22,X20)
| apply(compose_function(X14,X15,X16,X17,X18),X19,X20) )
& ( ~ apply(compose_function(X14,X15,X16,X17,X18),X19,X20)
| ( member(esk14_7(X14,X15,X16,X17,X18,X19,X20),X17)
& apply(X15,X19,esk14_7(X14,X15,X16,X17,X18,X19,X20))
& apply(X14,esk14_7(X14,X15,X16,X17,X18,X19,X20),X20) ) ) )
| ~ member(X19,X16)
| ~ member(X20,X18) ),
inference(shift_quantors,[status(thm)],[78]) ).
fof(80,plain,
! [X14,X15,X16,X17,X18,X19,X20,X22] :
( ( ~ member(X22,X17)
| ~ apply(X15,X19,X22)
| ~ apply(X14,X22,X20)
| apply(compose_function(X14,X15,X16,X17,X18),X19,X20)
| ~ member(X19,X16)
| ~ member(X20,X18) )
& ( member(esk14_7(X14,X15,X16,X17,X18,X19,X20),X17)
| ~ apply(compose_function(X14,X15,X16,X17,X18),X19,X20)
| ~ member(X19,X16)
| ~ member(X20,X18) )
& ( apply(X15,X19,esk14_7(X14,X15,X16,X17,X18,X19,X20))
| ~ apply(compose_function(X14,X15,X16,X17,X18),X19,X20)
| ~ member(X19,X16)
| ~ member(X20,X18) )
& ( apply(X14,esk14_7(X14,X15,X16,X17,X18,X19,X20),X20)
| ~ apply(compose_function(X14,X15,X16,X17,X18),X19,X20)
| ~ member(X19,X16)
| ~ member(X20,X18) ) ),
inference(distribute,[status(thm)],[79]) ).
cnf(81,plain,
( apply(X5,esk14_7(X5,X6,X4,X7,X2,X3,X1),X1)
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ apply(compose_function(X5,X6,X4,X7,X2),X3,X1) ),
inference(split_conjunct,[status(thm)],[80]) ).
cnf(82,plain,
( apply(X6,X3,esk14_7(X5,X6,X4,X7,X2,X3,X1))
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ apply(compose_function(X5,X6,X4,X7,X2),X3,X1) ),
inference(split_conjunct,[status(thm)],[80]) ).
cnf(83,plain,
( member(esk14_7(X5,X6,X4,X7,X2,X3,X1),X7)
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ apply(compose_function(X5,X6,X4,X7,X2),X3,X1) ),
inference(split_conjunct,[status(thm)],[80]) ).
cnf(84,plain,
( apply(compose_function(X5,X6,X4,X7,X2),X3,X1)
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ apply(X5,X8,X1)
| ~ apply(X6,X3,X8)
| ~ member(X8,X7) ),
inference(split_conjunct,[status(thm)],[80]) ).
fof(85,negated_conjecture,
? [X1,X2] :
( maps(X1,X2,X2)
& ( ~ one_to_one(X1,X2,X2)
| ~ inverse_predicate(X1,X1,X2,X2)
| ~ identity(compose_function(X1,X1,X2,X2,X2),X2) )
& ( ( one_to_one(X1,X2,X2)
& inverse_predicate(X1,X1,X2,X2) )
| identity(compose_function(X1,X1,X2,X2,X2),X2) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(86,negated_conjecture,
? [X3,X4] :
( maps(X3,X4,X4)
& ( ~ one_to_one(X3,X4,X4)
| ~ inverse_predicate(X3,X3,X4,X4)
| ~ identity(compose_function(X3,X3,X4,X4,X4),X4) )
& ( ( one_to_one(X3,X4,X4)
& inverse_predicate(X3,X3,X4,X4) )
| identity(compose_function(X3,X3,X4,X4,X4),X4) ) ),
inference(variable_rename,[status(thm)],[85]) ).
fof(87,negated_conjecture,
( maps(esk15_0,esk16_0,esk16_0)
& ( ~ one_to_one(esk15_0,esk16_0,esk16_0)
| ~ inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| ~ identity(compose_function(esk15_0,esk15_0,esk16_0,esk16_0,esk16_0),esk16_0) )
& ( ( one_to_one(esk15_0,esk16_0,esk16_0)
& inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0) )
| identity(compose_function(esk15_0,esk15_0,esk16_0,esk16_0,esk16_0),esk16_0) ) ),
inference(skolemize,[status(esa)],[86]) ).
fof(88,negated_conjecture,
( maps(esk15_0,esk16_0,esk16_0)
& ( ~ one_to_one(esk15_0,esk16_0,esk16_0)
| ~ inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| ~ identity(compose_function(esk15_0,esk15_0,esk16_0,esk16_0,esk16_0),esk16_0) )
& ( one_to_one(esk15_0,esk16_0,esk16_0)
| identity(compose_function(esk15_0,esk15_0,esk16_0,esk16_0,esk16_0),esk16_0) )
& ( inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| identity(compose_function(esk15_0,esk15_0,esk16_0,esk16_0,esk16_0),esk16_0) ) ),
inference(distribute,[status(thm)],[87]) ).
cnf(89,negated_conjecture,
( identity(compose_function(esk15_0,esk15_0,esk16_0,esk16_0,esk16_0),esk16_0)
| inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0) ),
inference(split_conjunct,[status(thm)],[88]) ).
cnf(90,negated_conjecture,
( identity(compose_function(esk15_0,esk15_0,esk16_0,esk16_0,esk16_0),esk16_0)
| one_to_one(esk15_0,esk16_0,esk16_0) ),
inference(split_conjunct,[status(thm)],[88]) ).
cnf(91,negated_conjecture,
( ~ identity(compose_function(esk15_0,esk15_0,esk16_0,esk16_0,esk16_0),esk16_0)
| ~ inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| ~ one_to_one(esk15_0,esk16_0,esk16_0) ),
inference(split_conjunct,[status(thm)],[88]) ).
cnf(92,negated_conjecture,
maps(esk15_0,esk16_0,esk16_0),
inference(split_conjunct,[status(thm)],[88]) ).
cnf(93,negated_conjecture,
( apply(compose_function(esk15_0,esk15_0,esk16_0,esk16_0,esk16_0),X1,X1)
| one_to_one(esk15_0,esk16_0,esk16_0)
| ~ member(X1,esk16_0) ),
inference(spm,[status(thm)],[52,90,theory(equality)]) ).
cnf(94,negated_conjecture,
( apply(compose_function(esk15_0,esk15_0,esk16_0,esk16_0,esk16_0),X1,X1)
| inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| ~ member(X1,esk16_0) ),
inference(spm,[status(thm)],[52,89,theory(equality)]) ).
cnf(104,negated_conjecture,
( X1 = X2
| ~ apply(esk15_0,X3,X2)
| ~ apply(esk15_0,X3,X1)
| ~ member(X3,esk16_0)
| ~ member(X2,esk16_0)
| ~ member(X1,esk16_0) ),
inference(spm,[status(thm)],[32,92,theory(equality)]) ).
cnf(113,plain,
( surjective(X1,X2,X3)
| ~ member(esk14_7(X1,X4,X5,X6,X7,X8,esk2_3(X1,X2,X3)),X2)
| ~ apply(compose_function(X1,X4,X5,X6,X7),X8,esk2_3(X1,X2,X3))
| ~ member(X8,X5)
| ~ member(esk2_3(X1,X2,X3),X7) ),
inference(spm,[status(thm)],[18,81,theory(equality)]) ).
cnf(115,plain,
( apply(compose_function(X1,X2,X3,X4,X5),X6,X7)
| ~ apply(X1,esk3_4(X2,X8,X9,X6),X7)
| ~ member(esk3_4(X2,X8,X9,X6),X4)
| ~ member(X6,X3)
| ~ member(X7,X5)
| ~ maps(X2,X8,X9)
| ~ member(X6,X8) ),
inference(spm,[status(thm)],[84,30,theory(equality)]) ).
cnf(146,negated_conjecture,
( X1 = esk3_4(esk15_0,X2,X3,X4)
| ~ apply(esk15_0,X4,X1)
| ~ member(X4,esk16_0)
| ~ member(esk3_4(esk15_0,X2,X3,X4),esk16_0)
| ~ member(X1,esk16_0)
| ~ maps(esk15_0,X2,X3)
| ~ member(X4,X2) ),
inference(spm,[status(thm)],[104,30,theory(equality)]) ).
cnf(151,negated_conjecture,
( X1 = esk14_7(X2,esk15_0,X3,X4,X5,X6,X7)
| ~ apply(esk15_0,X6,X1)
| ~ member(X6,esk16_0)
| ~ member(esk14_7(X2,esk15_0,X3,X4,X5,X6,X7),esk16_0)
| ~ member(X1,esk16_0)
| ~ apply(compose_function(X2,esk15_0,X3,X4,X5),X6,X7)
| ~ member(X6,X3)
| ~ member(X7,X5) ),
inference(spm,[status(thm)],[104,82,theory(equality)]) ).
cnf(175,negated_conjecture,
( X1 = esk3_4(esk15_0,X2,esk16_0,X3)
| ~ maps(esk15_0,X2,esk16_0)
| ~ apply(esk15_0,X3,X1)
| ~ member(X3,esk16_0)
| ~ member(X1,esk16_0)
| ~ member(X3,X2) ),
inference(spm,[status(thm)],[146,31,theory(equality)]) ).
cnf(177,negated_conjecture,
( esk13_3(esk15_0,X1,X2) = esk3_4(esk15_0,X3,esk16_0,esk11_3(esk15_0,X1,X2))
| injective(esk15_0,X1,X2)
| ~ maps(esk15_0,X3,esk16_0)
| ~ member(esk11_3(esk15_0,X1,X2),esk16_0)
| ~ member(esk13_3(esk15_0,X1,X2),esk16_0)
| ~ member(esk11_3(esk15_0,X1,X2),X3) ),
inference(spm,[status(thm)],[175,71,theory(equality)]) ).
cnf(178,negated_conjecture,
( esk3_4(esk15_0,X1,X2,X3) = esk3_4(esk15_0,X4,esk16_0,X3)
| ~ maps(esk15_0,X4,esk16_0)
| ~ member(X3,esk16_0)
| ~ member(esk3_4(esk15_0,X1,X2,X3),esk16_0)
| ~ member(X3,X4)
| ~ maps(esk15_0,X1,X2)
| ~ member(X3,X1) ),
inference(spm,[status(thm)],[175,30,theory(equality)]) ).
cnf(179,negated_conjecture,
( esk13_3(esk15_0,X1,X2) = esk3_4(esk15_0,X3,esk16_0,esk12_3(esk15_0,X1,X2))
| injective(esk15_0,X1,X2)
| ~ maps(esk15_0,X3,esk16_0)
| ~ member(esk12_3(esk15_0,X1,X2),esk16_0)
| ~ member(esk13_3(esk15_0,X1,X2),esk16_0)
| ~ member(esk12_3(esk15_0,X1,X2),X3) ),
inference(spm,[status(thm)],[175,70,theory(equality)]) ).
cnf(185,negated_conjecture,
( esk9_4(esk15_0,X1,X2,X3) = esk3_4(esk15_0,X4,esk16_0,esk10_4(esk15_0,X1,X2,X3))
| inverse_predicate(esk15_0,X1,X2,X3)
| apply(X1,esk9_4(esk15_0,X1,X2,X3),esk10_4(esk15_0,X1,X2,X3))
| ~ maps(esk15_0,X4,esk16_0)
| ~ member(esk10_4(esk15_0,X1,X2,X3),esk16_0)
| ~ member(esk9_4(esk15_0,X1,X2,X3),esk16_0)
| ~ member(esk10_4(esk15_0,X1,X2,X3),X4) ),
inference(spm,[status(thm)],[175,58,theory(equality)]) ).
cnf(223,negated_conjecture,
( esk3_4(esk15_0,X1,esk16_0,X2) = esk3_4(esk15_0,X3,esk16_0,X2)
| ~ maps(esk15_0,X3,esk16_0)
| ~ maps(esk15_0,X1,esk16_0)
| ~ member(X2,esk16_0)
| ~ member(X2,X3)
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[178,31,theory(equality)]) ).
cnf(385,plain,
( surjective(X1,X2,X3)
| ~ apply(compose_function(X1,X4,X5,X2,X6),X7,esk2_3(X1,X2,X3))
| ~ member(esk2_3(X1,X2,X3),X6)
| ~ member(X7,X5) ),
inference(spm,[status(thm)],[113,83,theory(equality)]) ).
cnf(400,negated_conjecture,
( surjective(esk15_0,esk16_0,X1)
| one_to_one(esk15_0,esk16_0,esk16_0)
| ~ member(esk2_3(esk15_0,esk16_0,X1),esk16_0) ),
inference(spm,[status(thm)],[385,93,theory(equality)]) ).
cnf(405,negated_conjecture,
( one_to_one(esk15_0,esk16_0,esk16_0)
| surjective(esk15_0,esk16_0,esk16_0) ),
inference(spm,[status(thm)],[400,17,theory(equality)]) ).
cnf(406,negated_conjecture,
surjective(esk15_0,esk16_0,esk16_0),
inference(csr,[status(thm)],[405,23]) ).
cnf(532,negated_conjecture,
( X1 = esk14_7(X2,esk15_0,X3,esk16_0,X4,X5,X6)
| ~ apply(compose_function(X2,esk15_0,X3,esk16_0,X4),X5,X6)
| ~ apply(esk15_0,X5,X1)
| ~ member(X5,esk16_0)
| ~ member(X1,esk16_0)
| ~ member(X5,X3)
| ~ member(X6,X4) ),
inference(spm,[status(thm)],[151,83,theory(equality)]) ).
cnf(541,negated_conjecture,
( esk3_4(esk15_0,X1,X2,X3) = esk14_7(X4,esk15_0,X5,esk16_0,X6,X3,X7)
| ~ apply(compose_function(X4,esk15_0,X5,esk16_0,X6),X3,X7)
| ~ member(X3,esk16_0)
| ~ member(esk3_4(esk15_0,X1,X2,X3),esk16_0)
| ~ member(X3,X5)
| ~ member(X7,X6)
| ~ maps(esk15_0,X1,X2)
| ~ member(X3,X1) ),
inference(spm,[status(thm)],[532,30,theory(equality)]) ).
cnf(857,negated_conjecture,
( esk3_4(esk15_0,X1,esk16_0,X2) = esk14_7(X3,esk15_0,X4,esk16_0,X5,X2,X6)
| ~ maps(esk15_0,X1,esk16_0)
| ~ apply(compose_function(X3,esk15_0,X4,esk16_0,X5),X2,X6)
| ~ member(X2,esk16_0)
| ~ member(X2,X4)
| ~ member(X6,X5)
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[541,31,theory(equality)]) ).
cnf(869,negated_conjecture,
( apply(X1,esk3_4(esk15_0,X6,esk16_0,X4),X5)
| ~ apply(compose_function(X1,esk15_0,X2,esk16_0,X3),X4,X5)
| ~ member(X4,X2)
| ~ member(X5,X3)
| ~ maps(esk15_0,X6,esk16_0)
| ~ member(X4,esk16_0)
| ~ member(X4,X6) ),
inference(spm,[status(thm)],[81,857,theory(equality)]) ).
cnf(922,negated_conjecture,
( apply(esk15_0,esk3_4(esk15_0,X1,esk16_0,X2),X2)
| one_to_one(esk15_0,esk16_0,esk16_0)
| ~ maps(esk15_0,X1,esk16_0)
| ~ member(X2,esk16_0)
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[869,93,theory(equality)]) ).
cnf(923,negated_conjecture,
( apply(esk15_0,esk3_4(esk15_0,X1,esk16_0,X2),X2)
| inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| ~ maps(esk15_0,X1,esk16_0)
| ~ member(X2,esk16_0)
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[869,94,theory(equality)]) ).
cnf(948,negated_conjecture,
( one_to_one(esk15_0,esk16_0,esk16_0)
| apply(esk15_0,esk13_3(esk15_0,X2,X3),esk11_3(esk15_0,X2,X3))
| injective(esk15_0,X2,X3)
| ~ maps(esk15_0,X1,esk16_0)
| ~ member(esk11_3(esk15_0,X2,X3),esk16_0)
| ~ member(esk11_3(esk15_0,X2,X3),X1)
| ~ member(esk13_3(esk15_0,X2,X3),esk16_0) ),
inference(spm,[status(thm)],[922,177,theory(equality)]) ).
cnf(949,negated_conjecture,
( one_to_one(esk15_0,esk16_0,esk16_0)
| apply(esk15_0,esk13_3(esk15_0,X2,X3),esk12_3(esk15_0,X2,X3))
| injective(esk15_0,X2,X3)
| ~ maps(esk15_0,X1,esk16_0)
| ~ member(esk12_3(esk15_0,X2,X3),esk16_0)
| ~ member(esk12_3(esk15_0,X2,X3),X1)
| ~ member(esk13_3(esk15_0,X2,X3),esk16_0) ),
inference(spm,[status(thm)],[922,179,theory(equality)]) ).
cnf(1231,negated_conjecture,
( esk3_4(esk15_0,X1,esk16_0,esk10_4(esk15_0,X2,X3,esk16_0)) = esk9_4(esk15_0,X2,X3,esk16_0)
| inverse_predicate(esk15_0,X2,X3,esk16_0)
| apply(X2,esk9_4(esk15_0,X2,X3,esk16_0),esk10_4(esk15_0,X2,X3,esk16_0))
| ~ maps(esk15_0,X1,esk16_0)
| ~ member(esk9_4(esk15_0,X2,X3,esk16_0),esk16_0)
| ~ member(esk10_4(esk15_0,X2,X3,esk16_0),X1) ),
inference(spm,[status(thm)],[185,60,theory(equality)]) ).
cnf(1720,negated_conjecture,
( injective(esk15_0,X1,X2)
| one_to_one(esk15_0,esk16_0,esk16_0)
| apply(esk15_0,esk13_3(esk15_0,X1,X2),esk11_3(esk15_0,X1,X2))
| ~ maps(esk15_0,X1,esk16_0)
| ~ member(esk11_3(esk15_0,X1,X2),esk16_0)
| ~ member(esk13_3(esk15_0,X1,X2),esk16_0) ),
inference(spm,[status(thm)],[948,74,theory(equality)]) ).
cnf(1734,negated_conjecture,
( X1 = esk11_3(esk15_0,X2,X3)
| injective(esk15_0,X2,X3)
| one_to_one(esk15_0,esk16_0,esk16_0)
| ~ apply(esk15_0,esk13_3(esk15_0,X2,X3),X1)
| ~ member(esk13_3(esk15_0,X2,X3),esk16_0)
| ~ member(esk11_3(esk15_0,X2,X3),esk16_0)
| ~ member(X1,esk16_0)
| ~ maps(esk15_0,X2,esk16_0) ),
inference(spm,[status(thm)],[104,1720,theory(equality)]) ).
cnf(1817,negated_conjecture,
( injective(esk15_0,X1,X2)
| one_to_one(esk15_0,esk16_0,esk16_0)
| apply(esk15_0,esk13_3(esk15_0,X1,X2),esk12_3(esk15_0,X1,X2))
| ~ maps(esk15_0,X1,esk16_0)
| ~ member(esk12_3(esk15_0,X1,X2),esk16_0)
| ~ member(esk13_3(esk15_0,X1,X2),esk16_0) ),
inference(spm,[status(thm)],[949,73,theory(equality)]) ).
cnf(1836,negated_conjecture,
( esk12_3(esk15_0,X1,X2) = esk11_3(esk15_0,X1,X2)
| injective(esk15_0,X1,X2)
| one_to_one(esk15_0,esk16_0,esk16_0)
| ~ maps(esk15_0,X1,esk16_0)
| ~ member(esk13_3(esk15_0,X1,X2),esk16_0)
| ~ member(esk11_3(esk15_0,X1,X2),esk16_0)
| ~ member(esk12_3(esk15_0,X1,X2),esk16_0) ),
inference(spm,[status(thm)],[1734,1817,theory(equality)]) ).
cnf(1837,negated_conjecture,
( injective(esk15_0,X1,X2)
| one_to_one(esk15_0,esk16_0,esk16_0)
| ~ maps(esk15_0,X1,esk16_0)
| ~ member(esk13_3(esk15_0,X1,X2),esk16_0)
| ~ member(esk11_3(esk15_0,X1,X2),esk16_0)
| ~ member(esk12_3(esk15_0,X1,X2),esk16_0) ),
inference(csr,[status(thm)],[1836,69]) ).
cnf(1838,negated_conjecture,
( injective(esk15_0,X1,esk16_0)
| one_to_one(esk15_0,esk16_0,esk16_0)
| ~ maps(esk15_0,X1,esk16_0)
| ~ member(esk11_3(esk15_0,X1,esk16_0),esk16_0)
| ~ member(esk12_3(esk15_0,X1,esk16_0),esk16_0) ),
inference(spm,[status(thm)],[1837,72,theory(equality)]) ).
cnf(1839,negated_conjecture,
( injective(esk15_0,esk16_0,esk16_0)
| one_to_one(esk15_0,esk16_0,esk16_0)
| ~ maps(esk15_0,esk16_0,esk16_0)
| ~ member(esk11_3(esk15_0,esk16_0,esk16_0),esk16_0) ),
inference(spm,[status(thm)],[1838,73,theory(equality)]) ).
cnf(1840,negated_conjecture,
( injective(esk15_0,esk16_0,esk16_0)
| one_to_one(esk15_0,esk16_0,esk16_0)
| $false
| ~ member(esk11_3(esk15_0,esk16_0,esk16_0),esk16_0) ),
inference(rw,[status(thm)],[1839,92,theory(equality)]) ).
cnf(1841,negated_conjecture,
( injective(esk15_0,esk16_0,esk16_0)
| one_to_one(esk15_0,esk16_0,esk16_0)
| ~ member(esk11_3(esk15_0,esk16_0,esk16_0),esk16_0) ),
inference(cn,[status(thm)],[1840,theory(equality)]) ).
cnf(1842,negated_conjecture,
( injective(esk15_0,esk16_0,esk16_0)
| one_to_one(esk15_0,esk16_0,esk16_0) ),
inference(csr,[status(thm)],[1841,74]) ).
cnf(1843,negated_conjecture,
injective(esk15_0,esk16_0,esk16_0),
inference(csr,[status(thm)],[1842,24]) ).
cnf(23878,negated_conjecture,
( esk3_4(esk15_0,X1,esk16_0,esk10_4(esk15_0,X2,esk16_0,esk16_0)) = esk9_4(esk15_0,X2,esk16_0,esk16_0)
| inverse_predicate(esk15_0,X2,esk16_0,esk16_0)
| apply(X2,esk9_4(esk15_0,X2,esk16_0,esk16_0),esk10_4(esk15_0,X2,esk16_0,esk16_0))
| ~ maps(esk15_0,X1,esk16_0)
| ~ member(esk10_4(esk15_0,X2,esk16_0,esk16_0),X1) ),
inference(spm,[status(thm)],[1231,61,theory(equality)]) ).
cnf(23879,negated_conjecture,
( esk3_4(esk15_0,esk16_0,esk16_0,esk10_4(esk15_0,X1,esk16_0,esk16_0)) = esk9_4(esk15_0,X1,esk16_0,esk16_0)
| inverse_predicate(esk15_0,X1,esk16_0,esk16_0)
| apply(X1,esk9_4(esk15_0,X1,esk16_0,esk16_0),esk10_4(esk15_0,X1,esk16_0,esk16_0))
| ~ maps(esk15_0,esk16_0,esk16_0) ),
inference(spm,[status(thm)],[23878,60,theory(equality)]) ).
cnf(23880,negated_conjecture,
( esk3_4(esk15_0,esk16_0,esk16_0,esk10_4(esk15_0,X1,esk16_0,esk16_0)) = esk9_4(esk15_0,X1,esk16_0,esk16_0)
| inverse_predicate(esk15_0,X1,esk16_0,esk16_0)
| apply(X1,esk9_4(esk15_0,X1,esk16_0,esk16_0),esk10_4(esk15_0,X1,esk16_0,esk16_0))
| $false ),
inference(rw,[status(thm)],[23879,92,theory(equality)]) ).
cnf(23881,negated_conjecture,
( esk3_4(esk15_0,esk16_0,esk16_0,esk10_4(esk15_0,X1,esk16_0,esk16_0)) = esk9_4(esk15_0,X1,esk16_0,esk16_0)
| inverse_predicate(esk15_0,X1,esk16_0,esk16_0)
| apply(X1,esk9_4(esk15_0,X1,esk16_0,esk16_0),esk10_4(esk15_0,X1,esk16_0,esk16_0)) ),
inference(cn,[status(thm)],[23880,theory(equality)]) ).
cnf(23884,negated_conjecture,
( X1 = esk10_4(esk15_0,esk15_0,esk16_0,esk16_0)
| esk3_4(esk15_0,esk16_0,esk16_0,esk10_4(esk15_0,esk15_0,esk16_0,esk16_0)) = esk9_4(esk15_0,esk15_0,esk16_0,esk16_0)
| inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| ~ apply(esk15_0,esk9_4(esk15_0,esk15_0,esk16_0,esk16_0),X1)
| ~ member(esk9_4(esk15_0,esk15_0,esk16_0,esk16_0),esk16_0)
| ~ member(esk10_4(esk15_0,esk15_0,esk16_0,esk16_0),esk16_0)
| ~ member(X1,esk16_0) ),
inference(spm,[status(thm)],[104,23881,theory(equality)]) ).
cnf(24013,negated_conjecture,
( esk3_4(esk15_0,esk16_0,esk16_0,esk10_4(esk15_0,esk15_0,esk16_0,esk16_0)) = esk9_4(esk15_0,esk15_0,esk16_0,esk16_0)
| X1 = esk10_4(esk15_0,esk15_0,esk16_0,esk16_0)
| inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| ~ apply(esk15_0,esk9_4(esk15_0,esk15_0,esk16_0,esk16_0),X1)
| ~ member(esk9_4(esk15_0,esk15_0,esk16_0,esk16_0),esk16_0)
| ~ member(X1,esk16_0) ),
inference(csr,[status(thm)],[23884,60]) ).
cnf(24014,negated_conjecture,
( esk3_4(esk15_0,esk16_0,esk16_0,esk10_4(esk15_0,esk15_0,esk16_0,esk16_0)) = esk9_4(esk15_0,esk15_0,esk16_0,esk16_0)
| X1 = esk10_4(esk15_0,esk15_0,esk16_0,esk16_0)
| inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| ~ apply(esk15_0,esk9_4(esk15_0,esk15_0,esk16_0,esk16_0),X1)
| ~ member(X1,esk16_0) ),
inference(csr,[status(thm)],[24013,61]) ).
cnf(24015,negated_conjecture,
( esk3_4(esk15_0,esk16_0,esk16_0,esk10_4(esk15_0,esk15_0,esk16_0,esk16_0)) = esk9_4(esk15_0,esk15_0,esk16_0,esk16_0)
| esk3_4(esk15_0,X1,X2,esk9_4(esk15_0,esk15_0,esk16_0,esk16_0)) = esk10_4(esk15_0,esk15_0,esk16_0,esk16_0)
| inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| ~ member(esk3_4(esk15_0,X1,X2,esk9_4(esk15_0,esk15_0,esk16_0,esk16_0)),esk16_0)
| ~ maps(esk15_0,X1,X2)
| ~ member(esk9_4(esk15_0,esk15_0,esk16_0,esk16_0),X1) ),
inference(spm,[status(thm)],[24014,30,theory(equality)]) ).
cnf(24023,negated_conjecture,
( esk3_4(esk15_0,esk16_0,esk16_0,esk10_4(esk15_0,esk15_0,esk16_0,esk16_0)) = esk9_4(esk15_0,esk15_0,esk16_0,esk16_0)
| esk3_4(esk15_0,X1,esk16_0,esk9_4(esk15_0,esk15_0,esk16_0,esk16_0)) = esk10_4(esk15_0,esk15_0,esk16_0,esk16_0)
| inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| ~ maps(esk15_0,X1,esk16_0)
| ~ member(esk9_4(esk15_0,esk15_0,esk16_0,esk16_0),X1) ),
inference(spm,[status(thm)],[24015,31,theory(equality)]) ).
cnf(24031,negated_conjecture,
( esk3_4(esk15_0,esk16_0,esk16_0,esk10_4(esk15_0,esk15_0,esk16_0,esk16_0)) = esk9_4(esk15_0,esk15_0,esk16_0,esk16_0)
| esk3_4(esk15_0,esk16_0,esk16_0,esk9_4(esk15_0,esk15_0,esk16_0,esk16_0)) = esk10_4(esk15_0,esk15_0,esk16_0,esk16_0)
| inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| ~ maps(esk15_0,esk16_0,esk16_0) ),
inference(spm,[status(thm)],[24023,61,theory(equality)]) ).
cnf(24032,negated_conjecture,
( esk3_4(esk15_0,esk16_0,esk16_0,esk10_4(esk15_0,esk15_0,esk16_0,esk16_0)) = esk9_4(esk15_0,esk15_0,esk16_0,esk16_0)
| esk3_4(esk15_0,esk16_0,esk16_0,esk9_4(esk15_0,esk15_0,esk16_0,esk16_0)) = esk10_4(esk15_0,esk15_0,esk16_0,esk16_0)
| inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| $false ),
inference(rw,[status(thm)],[24031,92,theory(equality)]) ).
cnf(24033,negated_conjecture,
( esk3_4(esk15_0,esk16_0,esk16_0,esk10_4(esk15_0,esk15_0,esk16_0,esk16_0)) = esk9_4(esk15_0,esk15_0,esk16_0,esk16_0)
| esk3_4(esk15_0,esk16_0,esk16_0,esk9_4(esk15_0,esk15_0,esk16_0,esk16_0)) = esk10_4(esk15_0,esk15_0,esk16_0,esk16_0)
| inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0) ),
inference(cn,[status(thm)],[24032,theory(equality)]) ).
cnf(24035,negated_conjecture,
( apply(esk15_0,esk10_4(esk15_0,esk15_0,esk16_0,esk16_0),esk9_4(esk15_0,esk15_0,esk16_0,esk16_0))
| esk3_4(esk15_0,esk16_0,esk16_0,esk9_4(esk15_0,esk15_0,esk16_0,esk16_0)) = esk10_4(esk15_0,esk15_0,esk16_0,esk16_0)
| inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| ~ maps(esk15_0,esk16_0,esk16_0)
| ~ member(esk10_4(esk15_0,esk15_0,esk16_0,esk16_0),esk16_0) ),
inference(spm,[status(thm)],[30,24033,theory(equality)]) ).
cnf(24043,negated_conjecture,
( inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| apply(esk15_0,esk9_4(esk15_0,esk15_0,esk16_0,esk16_0),esk10_4(esk15_0,esk15_0,esk16_0,esk16_0))
| esk3_4(esk15_0,esk16_0,esk16_0,esk9_4(esk15_0,esk15_0,esk16_0,esk16_0)) = esk10_4(esk15_0,esk15_0,esk16_0,esk16_0)
| ~ maps(esk15_0,esk16_0,esk16_0)
| ~ member(esk10_4(esk15_0,esk15_0,esk16_0,esk16_0),esk16_0) ),
inference(spm,[status(thm)],[923,24033,theory(equality)]) ).
cnf(24100,negated_conjecture,
( apply(esk15_0,esk10_4(esk15_0,esk15_0,esk16_0,esk16_0),esk9_4(esk15_0,esk15_0,esk16_0,esk16_0))
| esk3_4(esk15_0,esk16_0,esk16_0,esk9_4(esk15_0,esk15_0,esk16_0,esk16_0)) = esk10_4(esk15_0,esk15_0,esk16_0,esk16_0)
| inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| $false
| ~ member(esk10_4(esk15_0,esk15_0,esk16_0,esk16_0),esk16_0) ),
inference(rw,[status(thm)],[24035,92,theory(equality)]) ).
cnf(24101,negated_conjecture,
( apply(esk15_0,esk10_4(esk15_0,esk15_0,esk16_0,esk16_0),esk9_4(esk15_0,esk15_0,esk16_0,esk16_0))
| esk3_4(esk15_0,esk16_0,esk16_0,esk9_4(esk15_0,esk15_0,esk16_0,esk16_0)) = esk10_4(esk15_0,esk15_0,esk16_0,esk16_0)
| inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| ~ member(esk10_4(esk15_0,esk15_0,esk16_0,esk16_0),esk16_0) ),
inference(cn,[status(thm)],[24100,theory(equality)]) ).
cnf(24116,negated_conjecture,
( inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| apply(esk15_0,esk9_4(esk15_0,esk15_0,esk16_0,esk16_0),esk10_4(esk15_0,esk15_0,esk16_0,esk16_0))
| esk3_4(esk15_0,esk16_0,esk16_0,esk9_4(esk15_0,esk15_0,esk16_0,esk16_0)) = esk10_4(esk15_0,esk15_0,esk16_0,esk16_0)
| $false
| ~ member(esk10_4(esk15_0,esk15_0,esk16_0,esk16_0),esk16_0) ),
inference(rw,[status(thm)],[24043,92,theory(equality)]) ).
cnf(24117,negated_conjecture,
( inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| apply(esk15_0,esk9_4(esk15_0,esk15_0,esk16_0,esk16_0),esk10_4(esk15_0,esk15_0,esk16_0,esk16_0))
| esk3_4(esk15_0,esk16_0,esk16_0,esk9_4(esk15_0,esk15_0,esk16_0,esk16_0)) = esk10_4(esk15_0,esk15_0,esk16_0,esk16_0)
| ~ member(esk10_4(esk15_0,esk15_0,esk16_0,esk16_0),esk16_0) ),
inference(cn,[status(thm)],[24116,theory(equality)]) ).
cnf(24240,negated_conjecture,
( esk3_4(esk15_0,esk16_0,esk16_0,esk9_4(esk15_0,esk15_0,esk16_0,esk16_0)) = esk10_4(esk15_0,esk15_0,esk16_0,esk16_0)
| inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| apply(esk15_0,esk10_4(esk15_0,esk15_0,esk16_0,esk16_0),esk9_4(esk15_0,esk15_0,esk16_0,esk16_0)) ),
inference(csr,[status(thm)],[24101,60]) ).
cnf(24263,negated_conjecture,
( esk3_4(esk15_0,esk16_0,esk16_0,esk9_4(esk15_0,esk15_0,esk16_0,esk16_0)) = esk10_4(esk15_0,esk15_0,esk16_0,esk16_0)
| inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| apply(esk15_0,esk9_4(esk15_0,esk15_0,esk16_0,esk16_0),esk10_4(esk15_0,esk15_0,esk16_0,esk16_0)) ),
inference(csr,[status(thm)],[24117,60]) ).
cnf(24265,negated_conjecture,
( inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| esk3_4(esk15_0,esk16_0,esk16_0,esk9_4(esk15_0,esk15_0,esk16_0,esk16_0)) = esk10_4(esk15_0,esk15_0,esk16_0,esk16_0)
| ~ apply(esk15_0,esk10_4(esk15_0,esk15_0,esk16_0,esk16_0),esk9_4(esk15_0,esk15_0,esk16_0,esk16_0)) ),
inference(spm,[status(thm)],[59,24263,theory(equality)]) ).
cnf(24286,negated_conjecture,
( esk3_4(esk15_0,esk16_0,esk16_0,esk9_4(esk15_0,esk15_0,esk16_0,esk16_0)) = esk10_4(esk15_0,esk15_0,esk16_0,esk16_0)
| inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0) ),
inference(csr,[status(thm)],[24265,24240]) ).
cnf(24288,negated_conjecture,
( apply(esk15_0,esk9_4(esk15_0,esk15_0,esk16_0,esk16_0),esk10_4(esk15_0,esk15_0,esk16_0,esk16_0))
| inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| ~ maps(esk15_0,esk16_0,esk16_0)
| ~ member(esk9_4(esk15_0,esk15_0,esk16_0,esk16_0),esk16_0) ),
inference(spm,[status(thm)],[30,24286,theory(equality)]) ).
cnf(24296,negated_conjecture,
( inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| apply(esk15_0,esk10_4(esk15_0,esk15_0,esk16_0,esk16_0),esk9_4(esk15_0,esk15_0,esk16_0,esk16_0))
| ~ maps(esk15_0,esk16_0,esk16_0)
| ~ member(esk9_4(esk15_0,esk15_0,esk16_0,esk16_0),esk16_0) ),
inference(spm,[status(thm)],[923,24286,theory(equality)]) ).
cnf(24353,negated_conjecture,
( apply(esk15_0,esk9_4(esk15_0,esk15_0,esk16_0,esk16_0),esk10_4(esk15_0,esk15_0,esk16_0,esk16_0))
| inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| $false
| ~ member(esk9_4(esk15_0,esk15_0,esk16_0,esk16_0),esk16_0) ),
inference(rw,[status(thm)],[24288,92,theory(equality)]) ).
cnf(24354,negated_conjecture,
( apply(esk15_0,esk9_4(esk15_0,esk15_0,esk16_0,esk16_0),esk10_4(esk15_0,esk15_0,esk16_0,esk16_0))
| inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| ~ member(esk9_4(esk15_0,esk15_0,esk16_0,esk16_0),esk16_0) ),
inference(cn,[status(thm)],[24353,theory(equality)]) ).
cnf(24369,negated_conjecture,
( inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| apply(esk15_0,esk10_4(esk15_0,esk15_0,esk16_0,esk16_0),esk9_4(esk15_0,esk15_0,esk16_0,esk16_0))
| $false
| ~ member(esk9_4(esk15_0,esk15_0,esk16_0,esk16_0),esk16_0) ),
inference(rw,[status(thm)],[24296,92,theory(equality)]) ).
cnf(24370,negated_conjecture,
( inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| apply(esk15_0,esk10_4(esk15_0,esk15_0,esk16_0,esk16_0),esk9_4(esk15_0,esk15_0,esk16_0,esk16_0))
| ~ member(esk9_4(esk15_0,esk15_0,esk16_0,esk16_0),esk16_0) ),
inference(cn,[status(thm)],[24369,theory(equality)]) ).
cnf(24483,negated_conjecture,
( inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| apply(esk15_0,esk9_4(esk15_0,esk15_0,esk16_0,esk16_0),esk10_4(esk15_0,esk15_0,esk16_0,esk16_0)) ),
inference(csr,[status(thm)],[24354,61]) ).
cnf(24485,negated_conjecture,
( inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| ~ apply(esk15_0,esk10_4(esk15_0,esk15_0,esk16_0,esk16_0),esk9_4(esk15_0,esk15_0,esk16_0,esk16_0)) ),
inference(spm,[status(thm)],[59,24483,theory(equality)]) ).
cnf(24594,negated_conjecture,
( inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0)
| apply(esk15_0,esk10_4(esk15_0,esk15_0,esk16_0,esk16_0),esk9_4(esk15_0,esk15_0,esk16_0,esk16_0)) ),
inference(csr,[status(thm)],[24370,61]) ).
cnf(24595,negated_conjecture,
inverse_predicate(esk15_0,esk15_0,esk16_0,esk16_0),
inference(csr,[status(thm)],[24594,24485]) ).
cnf(24596,negated_conjecture,
( apply(esk15_0,X1,X2)
| ~ apply(esk15_0,X2,X1)
| ~ member(X1,esk16_0)
| ~ member(X2,esk16_0) ),
inference(spm,[status(thm)],[62,24595,theory(equality)]) ).
cnf(24805,negated_conjecture,
( $false
| ~ identity(compose_function(esk15_0,esk15_0,esk16_0,esk16_0,esk16_0),esk16_0)
| ~ one_to_one(esk15_0,esk16_0,esk16_0) ),
inference(rw,[status(thm)],[91,24595,theory(equality)]) ).
cnf(24806,negated_conjecture,
( ~ identity(compose_function(esk15_0,esk15_0,esk16_0,esk16_0,esk16_0),esk16_0)
| ~ one_to_one(esk15_0,esk16_0,esk16_0) ),
inference(cn,[status(thm)],[24805,theory(equality)]) ).
cnf(24810,negated_conjecture,
( apply(esk15_0,esk3_4(esk15_0,X1,X2,X3),X3)
| ~ member(esk3_4(esk15_0,X1,X2,X3),esk16_0)
| ~ member(X3,esk16_0)
| ~ maps(esk15_0,X1,X2)
| ~ member(X3,X1) ),
inference(spm,[status(thm)],[24596,30,theory(equality)]) ).
cnf(24850,negated_conjecture,
( apply(esk15_0,esk3_4(esk15_0,X3,esk16_0,X2),X2)
| ~ maps(esk15_0,X1,esk16_0)
| ~ member(esk3_4(esk15_0,X3,esk16_0,X2),esk16_0)
| ~ member(X2,esk16_0)
| ~ member(X2,X1)
| ~ maps(esk15_0,X3,esk16_0)
| ~ member(X2,X3) ),
inference(spm,[status(thm)],[24810,223,theory(equality)]) ).
cnf(25200,negated_conjecture,
( apply(esk15_0,esk3_4(esk15_0,X3,esk16_0,X2),X2)
| ~ maps(esk15_0,X3,esk16_0)
| ~ maps(esk15_0,X1,esk16_0)
| ~ member(esk3_4(esk15_0,X3,esk16_0,X2),esk16_0)
| ~ member(X2,esk16_0)
| ~ member(X2,X3) ),
inference(csr,[status(thm)],[24850,24810]) ).
cnf(25201,negated_conjecture,
( apply(esk15_0,esk3_4(esk15_0,X3,esk16_0,X2),X2)
| ~ maps(esk15_0,X3,esk16_0)
| ~ maps(esk15_0,X1,esk16_0)
| ~ member(X2,esk16_0)
| ~ member(X2,X3) ),
inference(csr,[status(thm)],[25200,31]) ).
cnf(25202,negated_conjecture,
( apply(esk15_0,esk3_4(esk15_0,X1,esk16_0,X2),X2)
| ~ maps(esk15_0,X1,esk16_0)
| ~ member(X2,esk16_0)
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[25201,92,theory(equality)]) ).
cnf(25209,negated_conjecture,
( apply(compose_function(esk15_0,esk15_0,X1,X2,X3),X4,X4)
| ~ maps(esk15_0,X5,esk16_0)
| ~ member(esk3_4(esk15_0,X5,esk16_0,X4),X2)
| ~ member(X4,X1)
| ~ member(X4,X3)
| ~ member(X4,X5)
| ~ member(X4,esk16_0) ),
inference(spm,[status(thm)],[115,25202,theory(equality)]) ).
cnf(25457,negated_conjecture,
( apply(compose_function(esk15_0,esk15_0,X1,esk16_0,X2),X3,X3)
| ~ maps(esk15_0,X4,esk16_0)
| ~ member(X3,esk16_0)
| ~ member(X3,X1)
| ~ member(X3,X2)
| ~ member(X3,X4) ),
inference(spm,[status(thm)],[25209,31,theory(equality)]) ).
cnf(25476,negated_conjecture,
( apply(compose_function(esk15_0,esk15_0,X1,esk16_0,X2),X3,X3)
| ~ member(X3,esk16_0)
| ~ member(X3,X1)
| ~ member(X3,X2) ),
inference(spm,[status(thm)],[25457,92,theory(equality)]) ).
cnf(25477,negated_conjecture,
( identity(compose_function(esk15_0,esk15_0,X1,esk16_0,X2),X3)
| ~ member(esk8_2(compose_function(esk15_0,esk15_0,X1,esk16_0,X2),X3),esk16_0)
| ~ member(esk8_2(compose_function(esk15_0,esk15_0,X1,esk16_0,X2),X3),X1)
| ~ member(esk8_2(compose_function(esk15_0,esk15_0,X1,esk16_0,X2),X3),X2) ),
inference(spm,[status(thm)],[50,25476,theory(equality)]) ).
cnf(27958,negated_conjecture,
( identity(compose_function(esk15_0,esk15_0,X1,esk16_0,X2),esk16_0)
| ~ member(esk8_2(compose_function(esk15_0,esk15_0,X1,esk16_0,X2),esk16_0),X1)
| ~ member(esk8_2(compose_function(esk15_0,esk15_0,X1,esk16_0,X2),esk16_0),X2) ),
inference(spm,[status(thm)],[25477,51,theory(equality)]) ).
cnf(27959,negated_conjecture,
( identity(compose_function(esk15_0,esk15_0,esk16_0,esk16_0,X1),esk16_0)
| ~ member(esk8_2(compose_function(esk15_0,esk15_0,esk16_0,esk16_0,X1),esk16_0),X1) ),
inference(spm,[status(thm)],[27958,51,theory(equality)]) ).
cnf(27960,negated_conjecture,
identity(compose_function(esk15_0,esk15_0,esk16_0,esk16_0,esk16_0),esk16_0),
inference(spm,[status(thm)],[27959,51,theory(equality)]) ).
cnf(27969,negated_conjecture,
( $false
| ~ one_to_one(esk15_0,esk16_0,esk16_0) ),
inference(rw,[status(thm)],[24806,27960,theory(equality)]) ).
cnf(27970,negated_conjecture,
~ one_to_one(esk15_0,esk16_0,esk16_0),
inference(cn,[status(thm)],[27969,theory(equality)]) ).
cnf(27972,negated_conjecture,
( ~ injective(esk15_0,esk16_0,esk16_0)
| ~ surjective(esk15_0,esk16_0,esk16_0) ),
inference(spm,[status(thm)],[27970,22,theory(equality)]) ).
cnf(27974,negated_conjecture,
( $false
| ~ surjective(esk15_0,esk16_0,esk16_0) ),
inference(rw,[status(thm)],[27972,1843,theory(equality)]) ).
cnf(27975,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[27974,406,theory(equality)]) ).
cnf(27976,negated_conjecture,
$false,
inference(cn,[status(thm)],[27975,theory(equality)]) ).
cnf(27977,negated_conjecture,
$false,
27976,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET729+4.p
% --creating new selector for [SET006+0.ax, SET006+1.ax]
% -running prover on /tmp/tmpnBawlf/sel_SET729+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET729+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET729+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET729+4.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
%
%------------------------------------------------------------------------------