TSTP Solution File: SET712+4 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET712+4 : TPTP v5.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 03:16:00 EST 2010
% Result : Theorem 6.58s
% Output : CNFRefutation 6.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 63
% Number of leaves : 6
% Syntax : Number of formulae : 200 ( 19 unt; 0 def)
% Number of atoms : 1043 ( 66 equ)
% Maximal formula atoms : 55 ( 5 avg)
% Number of connectives : 1426 ( 583 ~; 706 |; 123 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-4 aty)
% Number of variables : 609 ( 0 sgn 150 !; 28 ?)
% 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/tmprVy2GO/sel_SET712+4.p_1',surjective) ).
fof(2,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/tmprVy2GO/sel_SET712+4.p_1',maps) ).
fof(3,axiom,
! [X1,X2,X3,X6,X4] :
( ( member(X6,X2)
& member(X4,X3) )
=> ( apply(X1,X6,X4)
<=> apply(inverse_function(X1,X2,X3),X4,X6) ) ),
file('/tmp/tmprVy2GO/sel_SET712+4.p_1',inverse_function) ).
fof(4,axiom,
! [X1,X2,X3] :
( injective(X1,X2,X3)
<=> ! [X9,X10,X4] :
( ( member(X9,X2)
& member(X10,X2)
& member(X4,X3) )
=> ( ( apply(X1,X9,X4)
& apply(X1,X10,X4) )
=> X9 = X10 ) ) ),
file('/tmp/tmprVy2GO/sel_SET712+4.p_1',injective) ).
fof(5,axiom,
! [X1,X2,X3] :
( one_to_one(X1,X2,X3)
<=> ( injective(X1,X2,X3)
& surjective(X1,X2,X3) ) ),
file('/tmp/tmprVy2GO/sel_SET712+4.p_1',one_to_one) ).
fof(6,conjecture,
! [X1,X2,X3] :
( ( maps(X1,X2,X3)
& one_to_one(X1,X2,X3) )
=> maps(inverse_function(X1,X2,X3),X3,X2) ),
file('/tmp/tmprVy2GO/sel_SET712+4.p_1',thII03) ).
fof(7,negated_conjecture,
~ ! [X1,X2,X3] :
( ( maps(X1,X2,X3)
& one_to_one(X1,X2,X3) )
=> maps(inverse_function(X1,X2,X3),X3,X2) ),
inference(assume_negation,[status(cth)],[6]) ).
fof(8,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(9,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)],[8]) ).
fof(10,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)],[9]) ).
fof(11,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)],[10]) ).
fof(12,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)],[11]) ).
cnf(13,plain,
( apply(X1,esk1_4(X1,X2,X3,X4),X4)
| ~ surjective(X1,X2,X3)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[12]) ).
cnf(14,plain,
( member(esk1_4(X1,X2,X3,X4),X2)
| ~ surjective(X1,X2,X3)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[12]) ).
cnf(15,plain,
( surjective(X1,X2,X3)
| member(esk2_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[12]) ).
cnf(16,plain,
( surjective(X1,X2,X3)
| ~ apply(X1,X4,esk2_3(X1,X2,X3))
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[12]) ).
fof(17,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)],[2]) ).
fof(18,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)],[17]) ).
fof(19,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)],[18]) ).
fof(20,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)],[19]) ).
fof(21,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)],[20]) ).
cnf(22,plain,
( apply(X1,X4,esk3_4(X1,X2,X3,X4))
| ~ maps(X1,X2,X3)
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[21]) ).
cnf(23,plain,
( member(esk3_4(X1,X2,X3,X4),X3)
| ~ maps(X1,X2,X3)
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[21]) ).
cnf(24,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)],[21]) ).
cnf(25,plain,
( maps(X1,X2,X3)
| member(esk4_3(X1,X2,X3),X2)
| esk6_3(X1,X2,X3) != esk7_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[21]) ).
cnf(26,plain,
( maps(X1,X2,X3)
| member(esk4_3(X1,X2,X3),X2)
| apply(X1,esk5_3(X1,X2,X3),esk7_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[21]) ).
cnf(27,plain,
( maps(X1,X2,X3)
| member(esk4_3(X1,X2,X3),X2)
| apply(X1,esk5_3(X1,X2,X3),esk6_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[21]) ).
cnf(28,plain,
( maps(X1,X2,X3)
| member(esk4_3(X1,X2,X3),X2)
| member(esk7_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[21]) ).
cnf(29,plain,
( maps(X1,X2,X3)
| member(esk4_3(X1,X2,X3),X2)
| member(esk6_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[21]) ).
cnf(30,plain,
( maps(X1,X2,X3)
| member(esk4_3(X1,X2,X3),X2)
| member(esk5_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[21]) ).
cnf(31,plain,
( maps(X1,X2,X3)
| ~ apply(X1,esk4_3(X1,X2,X3),X4)
| ~ member(X4,X3)
| esk6_3(X1,X2,X3) != esk7_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[21]) ).
cnf(32,plain,
( maps(X1,X2,X3)
| apply(X1,esk5_3(X1,X2,X3),esk7_3(X1,X2,X3))
| ~ apply(X1,esk4_3(X1,X2,X3),X4)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[21]) ).
cnf(33,plain,
( maps(X1,X2,X3)
| apply(X1,esk5_3(X1,X2,X3),esk6_3(X1,X2,X3))
| ~ apply(X1,esk4_3(X1,X2,X3),X4)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[21]) ).
cnf(34,plain,
( maps(X1,X2,X3)
| member(esk7_3(X1,X2,X3),X3)
| ~ apply(X1,esk4_3(X1,X2,X3),X4)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[21]) ).
cnf(35,plain,
( maps(X1,X2,X3)
| member(esk6_3(X1,X2,X3),X3)
| ~ apply(X1,esk4_3(X1,X2,X3),X4)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[21]) ).
cnf(36,plain,
( maps(X1,X2,X3)
| member(esk5_3(X1,X2,X3),X2)
| ~ apply(X1,esk4_3(X1,X2,X3),X4)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[21]) ).
fof(37,plain,
! [X1,X2,X3,X6,X4] :
( ~ member(X6,X2)
| ~ member(X4,X3)
| ( ( ~ apply(X1,X6,X4)
| apply(inverse_function(X1,X2,X3),X4,X6) )
& ( ~ apply(inverse_function(X1,X2,X3),X4,X6)
| apply(X1,X6,X4) ) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(38,plain,
! [X7,X8,X9,X10,X11] :
( ~ member(X10,X8)
| ~ member(X11,X9)
| ( ( ~ apply(X7,X10,X11)
| apply(inverse_function(X7,X8,X9),X11,X10) )
& ( ~ apply(inverse_function(X7,X8,X9),X11,X10)
| apply(X7,X10,X11) ) ) ),
inference(variable_rename,[status(thm)],[37]) ).
fof(39,plain,
! [X7,X8,X9,X10,X11] :
( ( ~ apply(X7,X10,X11)
| apply(inverse_function(X7,X8,X9),X11,X10)
| ~ member(X10,X8)
| ~ member(X11,X9) )
& ( ~ apply(inverse_function(X7,X8,X9),X11,X10)
| apply(X7,X10,X11)
| ~ member(X10,X8)
| ~ member(X11,X9) ) ),
inference(distribute,[status(thm)],[38]) ).
cnf(40,plain,
( apply(X5,X3,X1)
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ apply(inverse_function(X5,X4,X2),X1,X3) ),
inference(split_conjunct,[status(thm)],[39]) ).
cnf(41,plain,
( apply(inverse_function(X5,X4,X2),X1,X3)
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ apply(X5,X3,X1) ),
inference(split_conjunct,[status(thm)],[39]) ).
fof(42,plain,
! [X1,X2,X3] :
( ( ~ injective(X1,X2,X3)
| ! [X9,X10,X4] :
( ~ member(X9,X2)
| ~ member(X10,X2)
| ~ member(X4,X3)
| ~ apply(X1,X9,X4)
| ~ apply(X1,X10,X4)
| X9 = X10 ) )
& ( ? [X9,X10,X4] :
( member(X9,X2)
& member(X10,X2)
& member(X4,X3)
& apply(X1,X9,X4)
& apply(X1,X10,X4)
& X9 != X10 )
| injective(X1,X2,X3) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(43,plain,
! [X11,X12,X13] :
( ( ~ injective(X11,X12,X13)
| ! [X14,X15,X16] :
( ~ member(X14,X12)
| ~ member(X15,X12)
| ~ member(X16,X13)
| ~ apply(X11,X14,X16)
| ~ apply(X11,X15,X16)
| X14 = X15 ) )
& ( ? [X17,X18,X19] :
( member(X17,X12)
& member(X18,X12)
& member(X19,X13)
& apply(X11,X17,X19)
& apply(X11,X18,X19)
& X17 != X18 )
| injective(X11,X12,X13) ) ),
inference(variable_rename,[status(thm)],[42]) ).
fof(44,plain,
! [X11,X12,X13] :
( ( ~ injective(X11,X12,X13)
| ! [X14,X15,X16] :
( ~ member(X14,X12)
| ~ member(X15,X12)
| ~ member(X16,X13)
| ~ apply(X11,X14,X16)
| ~ apply(X11,X15,X16)
| X14 = X15 ) )
& ( ( member(esk8_3(X11,X12,X13),X12)
& member(esk9_3(X11,X12,X13),X12)
& member(esk10_3(X11,X12,X13),X13)
& apply(X11,esk8_3(X11,X12,X13),esk10_3(X11,X12,X13))
& apply(X11,esk9_3(X11,X12,X13),esk10_3(X11,X12,X13))
& esk8_3(X11,X12,X13) != esk9_3(X11,X12,X13) )
| injective(X11,X12,X13) ) ),
inference(skolemize,[status(esa)],[43]) ).
fof(45,plain,
! [X11,X12,X13,X14,X15,X16] :
( ( ~ member(X14,X12)
| ~ member(X15,X12)
| ~ member(X16,X13)
| ~ apply(X11,X14,X16)
| ~ apply(X11,X15,X16)
| X14 = X15
| ~ injective(X11,X12,X13) )
& ( ( member(esk8_3(X11,X12,X13),X12)
& member(esk9_3(X11,X12,X13),X12)
& member(esk10_3(X11,X12,X13),X13)
& apply(X11,esk8_3(X11,X12,X13),esk10_3(X11,X12,X13))
& apply(X11,esk9_3(X11,X12,X13),esk10_3(X11,X12,X13))
& esk8_3(X11,X12,X13) != esk9_3(X11,X12,X13) )
| injective(X11,X12,X13) ) ),
inference(shift_quantors,[status(thm)],[44]) ).
fof(46,plain,
! [X11,X12,X13,X14,X15,X16] :
( ( ~ member(X14,X12)
| ~ member(X15,X12)
| ~ member(X16,X13)
| ~ apply(X11,X14,X16)
| ~ apply(X11,X15,X16)
| X14 = X15
| ~ injective(X11,X12,X13) )
& ( member(esk8_3(X11,X12,X13),X12)
| injective(X11,X12,X13) )
& ( member(esk9_3(X11,X12,X13),X12)
| injective(X11,X12,X13) )
& ( member(esk10_3(X11,X12,X13),X13)
| injective(X11,X12,X13) )
& ( apply(X11,esk8_3(X11,X12,X13),esk10_3(X11,X12,X13))
| injective(X11,X12,X13) )
& ( apply(X11,esk9_3(X11,X12,X13),esk10_3(X11,X12,X13))
| injective(X11,X12,X13) )
& ( esk8_3(X11,X12,X13) != esk9_3(X11,X12,X13)
| injective(X11,X12,X13) ) ),
inference(distribute,[status(thm)],[45]) ).
cnf(47,plain,
( injective(X1,X2,X3)
| esk8_3(X1,X2,X3) != esk9_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[46]) ).
cnf(48,plain,
( injective(X1,X2,X3)
| apply(X1,esk9_3(X1,X2,X3),esk10_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[46]) ).
cnf(49,plain,
( injective(X1,X2,X3)
| apply(X1,esk8_3(X1,X2,X3),esk10_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[46]) ).
cnf(50,plain,
( injective(X1,X2,X3)
| member(esk10_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[46]) ).
cnf(51,plain,
( injective(X1,X2,X3)
| member(esk9_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[46]) ).
cnf(52,plain,
( injective(X1,X2,X3)
| member(esk8_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[46]) ).
cnf(53,plain,
( X4 = X5
| ~ injective(X1,X2,X3)
| ~ apply(X1,X5,X6)
| ~ apply(X1,X4,X6)
| ~ member(X6,X3)
| ~ member(X5,X2)
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[46]) ).
fof(54,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)],[5]) ).
fof(55,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)],[54]) ).
fof(56,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)],[55]) ).
cnf(58,plain,
( surjective(X1,X2,X3)
| ~ one_to_one(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[56]) ).
cnf(59,plain,
( injective(X1,X2,X3)
| ~ one_to_one(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[56]) ).
fof(60,negated_conjecture,
? [X1,X2,X3] :
( maps(X1,X2,X3)
& one_to_one(X1,X2,X3)
& ~ maps(inverse_function(X1,X2,X3),X3,X2) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(61,negated_conjecture,
? [X4,X5,X6] :
( maps(X4,X5,X6)
& one_to_one(X4,X5,X6)
& ~ maps(inverse_function(X4,X5,X6),X6,X5) ),
inference(variable_rename,[status(thm)],[60]) ).
fof(62,negated_conjecture,
( maps(esk11_0,esk12_0,esk13_0)
& one_to_one(esk11_0,esk12_0,esk13_0)
& ~ maps(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0) ),
inference(skolemize,[status(esa)],[61]) ).
cnf(63,negated_conjecture,
~ maps(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),
inference(split_conjunct,[status(thm)],[62]) ).
cnf(64,negated_conjecture,
one_to_one(esk11_0,esk12_0,esk13_0),
inference(split_conjunct,[status(thm)],[62]) ).
cnf(65,negated_conjecture,
maps(esk11_0,esk12_0,esk13_0),
inference(split_conjunct,[status(thm)],[62]) ).
cnf(66,negated_conjecture,
surjective(esk11_0,esk12_0,esk13_0),
inference(spm,[status(thm)],[58,64,theory(equality)]) ).
cnf(67,negated_conjecture,
injective(esk11_0,esk12_0,esk13_0),
inference(spm,[status(thm)],[59,64,theory(equality)]) ).
cnf(70,plain,
( surjective(inverse_function(X1,X2,X3),X4,X5)
| ~ member(X6,X4)
| ~ apply(X1,esk2_3(inverse_function(X1,X2,X3),X4,X5),X6)
| ~ member(esk2_3(inverse_function(X1,X2,X3),X4,X5),X2)
| ~ member(X6,X3) ),
inference(spm,[status(thm)],[16,41,theory(equality)]) ).
cnf(73,plain,
( apply(X1,esk10_3(inverse_function(X1,X2,X3),X4,X5),esk8_3(inverse_function(X1,X2,X3),X4,X5))
| injective(inverse_function(X1,X2,X3),X4,X5)
| ~ member(esk10_3(inverse_function(X1,X2,X3),X4,X5),X2)
| ~ member(esk8_3(inverse_function(X1,X2,X3),X4,X5),X3) ),
inference(spm,[status(thm)],[40,49,theory(equality)]) ).
cnf(74,plain,
( apply(X1,esk10_3(inverse_function(X1,X2,X3),X4,X5),esk9_3(inverse_function(X1,X2,X3),X4,X5))
| injective(inverse_function(X1,X2,X3),X4,X5)
| ~ member(esk10_3(inverse_function(X1,X2,X3),X4,X5),X2)
| ~ member(esk9_3(inverse_function(X1,X2,X3),X4,X5),X3) ),
inference(spm,[status(thm)],[40,48,theory(equality)]) ).
cnf(77,plain,
( apply(X1,esk6_3(inverse_function(X1,X2,X3),X4,X5),esk5_3(inverse_function(X1,X2,X3),X4,X5))
| maps(inverse_function(X1,X2,X3),X4,X5)
| member(esk4_3(inverse_function(X1,X2,X3),X4,X5),X4)
| ~ member(esk6_3(inverse_function(X1,X2,X3),X4,X5),X2)
| ~ member(esk5_3(inverse_function(X1,X2,X3),X4,X5),X3) ),
inference(spm,[status(thm)],[40,27,theory(equality)]) ).
cnf(78,plain,
( apply(X1,esk7_3(inverse_function(X1,X2,X3),X4,X5),esk5_3(inverse_function(X1,X2,X3),X4,X5))
| maps(inverse_function(X1,X2,X3),X4,X5)
| member(esk4_3(inverse_function(X1,X2,X3),X4,X5),X4)
| ~ member(esk7_3(inverse_function(X1,X2,X3),X4,X5),X2)
| ~ member(esk5_3(inverse_function(X1,X2,X3),X4,X5),X3) ),
inference(spm,[status(thm)],[40,26,theory(equality)]) ).
cnf(80,plain,
( maps(inverse_function(X1,X2,X3),X4,X5)
| member(esk5_3(inverse_function(X1,X2,X3),X4,X5),X4)
| ~ member(X6,X5)
| ~ apply(X1,X6,esk4_3(inverse_function(X1,X2,X3),X4,X5))
| ~ member(X6,X2)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X4,X5),X3) ),
inference(spm,[status(thm)],[36,41,theory(equality)]) ).
cnf(82,plain,
( maps(inverse_function(X1,X2,X3),X4,X5)
| member(esk6_3(inverse_function(X1,X2,X3),X4,X5),X5)
| ~ member(X6,X5)
| ~ apply(X1,X6,esk4_3(inverse_function(X1,X2,X3),X4,X5))
| ~ member(X6,X2)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X4,X5),X3) ),
inference(spm,[status(thm)],[35,41,theory(equality)]) ).
cnf(84,plain,
( maps(inverse_function(X1,X2,X3),X4,X5)
| member(esk7_3(inverse_function(X1,X2,X3),X4,X5),X5)
| ~ member(X6,X5)
| ~ apply(X1,X6,esk4_3(inverse_function(X1,X2,X3),X4,X5))
| ~ member(X6,X2)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X4,X5),X3) ),
inference(spm,[status(thm)],[34,41,theory(equality)]) ).
cnf(86,plain,
( maps(inverse_function(X1,X2,X3),X4,X5)
| esk7_3(inverse_function(X1,X2,X3),X4,X5) != esk6_3(inverse_function(X1,X2,X3),X4,X5)
| ~ member(X6,X5)
| ~ apply(X1,X6,esk4_3(inverse_function(X1,X2,X3),X4,X5))
| ~ member(X6,X2)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X4,X5),X3) ),
inference(spm,[status(thm)],[31,41,theory(equality)]) ).
cnf(87,negated_conjecture,
( X1 = X2
| ~ apply(esk11_0,X3,X2)
| ~ apply(esk11_0,X3,X1)
| ~ member(X3,esk12_0)
| ~ member(X2,esk13_0)
| ~ member(X1,esk13_0) ),
inference(spm,[status(thm)],[24,65,theory(equality)]) ).
cnf(92,negated_conjecture,
( X1 = X2
| ~ apply(esk11_0,X2,X3)
| ~ apply(esk11_0,X1,X3)
| ~ member(X3,esk13_0)
| ~ member(X2,esk12_0)
| ~ member(X1,esk12_0) ),
inference(spm,[status(thm)],[53,67,theory(equality)]) ).
cnf(93,negated_conjecture,
( X1 = esk3_4(esk11_0,X2,X3,X4)
| ~ apply(esk11_0,X4,X1)
| ~ member(X4,esk12_0)
| ~ member(esk3_4(esk11_0,X2,X3,X4),esk13_0)
| ~ member(X1,esk13_0)
| ~ maps(esk11_0,X2,X3)
| ~ member(X4,X2) ),
inference(spm,[status(thm)],[87,22,theory(equality)]) ).
cnf(102,negated_conjecture,
( X1 = esk1_4(esk11_0,X2,X3,X4)
| ~ apply(esk11_0,X1,X4)
| ~ member(X4,esk13_0)
| ~ member(esk1_4(esk11_0,X2,X3,X4),esk12_0)
| ~ member(X1,esk12_0)
| ~ member(X4,X3)
| ~ surjective(esk11_0,X2,X3) ),
inference(spm,[status(thm)],[92,13,theory(equality)]) ).
cnf(111,plain,
( surjective(inverse_function(X1,X2,X3),X4,X5)
| ~ member(esk2_3(inverse_function(X1,X2,X3),X4,X5),X2)
| ~ member(esk3_4(X1,X6,X7,esk2_3(inverse_function(X1,X2,X3),X4,X5)),X4)
| ~ member(esk3_4(X1,X6,X7,esk2_3(inverse_function(X1,X2,X3),X4,X5)),X3)
| ~ maps(X1,X6,X7)
| ~ member(esk2_3(inverse_function(X1,X2,X3),X4,X5),X6) ),
inference(spm,[status(thm)],[70,22,theory(equality)]) ).
cnf(124,negated_conjecture,
( X1 = esk3_4(esk11_0,X2,esk13_0,X3)
| ~ maps(esk11_0,X2,esk13_0)
| ~ apply(esk11_0,X3,X1)
| ~ member(X3,esk12_0)
| ~ member(X1,esk13_0)
| ~ member(X3,X2) ),
inference(spm,[status(thm)],[93,23,theory(equality)]) ).
cnf(129,negated_conjecture,
( X1 = esk3_4(esk11_0,X2,esk13_0,esk1_4(esk11_0,X3,X4,X1))
| ~ maps(esk11_0,X2,esk13_0)
| ~ member(esk1_4(esk11_0,X3,X4,X1),esk12_0)
| ~ member(X1,esk13_0)
| ~ member(esk1_4(esk11_0,X3,X4,X1),X2)
| ~ member(X1,X4)
| ~ surjective(esk11_0,X3,X4) ),
inference(spm,[status(thm)],[124,13,theory(equality)]) ).
cnf(153,negated_conjecture,
( esk8_3(inverse_function(esk11_0,X1,X2),X3,X4) = esk3_4(esk11_0,X5,esk13_0,esk10_3(inverse_function(esk11_0,X1,X2),X3,X4))
| injective(inverse_function(esk11_0,X1,X2),X3,X4)
| ~ maps(esk11_0,X5,esk13_0)
| ~ member(esk10_3(inverse_function(esk11_0,X1,X2),X3,X4),esk12_0)
| ~ member(esk8_3(inverse_function(esk11_0,X1,X2),X3,X4),esk13_0)
| ~ member(esk10_3(inverse_function(esk11_0,X1,X2),X3,X4),X5)
| ~ member(esk10_3(inverse_function(esk11_0,X1,X2),X3,X4),X1)
| ~ member(esk8_3(inverse_function(esk11_0,X1,X2),X3,X4),X2) ),
inference(spm,[status(thm)],[124,73,theory(equality)]) ).
cnf(154,negated_conjecture,
( X1 = esk1_4(esk11_0,esk12_0,X2,X3)
| ~ apply(esk11_0,X1,X3)
| ~ member(X3,esk13_0)
| ~ member(X1,esk12_0)
| ~ member(X3,X2)
| ~ surjective(esk11_0,esk12_0,X2) ),
inference(spm,[status(thm)],[102,14,theory(equality)]) ).
cnf(158,negated_conjecture,
( esk1_4(esk11_0,X1,X2,X3) = esk1_4(esk11_0,esk12_0,X4,X3)
| ~ member(X3,esk13_0)
| ~ member(esk1_4(esk11_0,X1,X2,X3),esk12_0)
| ~ member(X3,X4)
| ~ surjective(esk11_0,esk12_0,X4)
| ~ member(X3,X2)
| ~ surjective(esk11_0,X1,X2) ),
inference(spm,[status(thm)],[154,13,theory(equality)]) ).
cnf(201,negated_conjecture,
( esk9_3(inverse_function(esk11_0,X1,X2),X3,X4) = esk3_4(esk11_0,X5,esk13_0,esk10_3(inverse_function(esk11_0,X1,X2),X3,X4))
| injective(inverse_function(esk11_0,X1,X2),X3,X4)
| ~ maps(esk11_0,X5,esk13_0)
| ~ member(esk10_3(inverse_function(esk11_0,X1,X2),X3,X4),esk12_0)
| ~ member(esk9_3(inverse_function(esk11_0,X1,X2),X3,X4),esk13_0)
| ~ member(esk10_3(inverse_function(esk11_0,X1,X2),X3,X4),X5)
| ~ member(esk10_3(inverse_function(esk11_0,X1,X2),X3,X4),X1)
| ~ member(esk9_3(inverse_function(esk11_0,X1,X2),X3,X4),X2) ),
inference(spm,[status(thm)],[124,74,theory(equality)]) ).
cnf(224,negated_conjecture,
( X1 = esk6_3(inverse_function(esk11_0,X2,X3),X4,X5)
| maps(inverse_function(esk11_0,X2,X3),X4,X5)
| member(esk4_3(inverse_function(esk11_0,X2,X3),X4,X5),X4)
| ~ apply(esk11_0,X1,esk5_3(inverse_function(esk11_0,X2,X3),X4,X5))
| ~ member(esk5_3(inverse_function(esk11_0,X2,X3),X4,X5),esk13_0)
| ~ member(esk6_3(inverse_function(esk11_0,X2,X3),X4,X5),esk12_0)
| ~ member(X1,esk12_0)
| ~ member(esk6_3(inverse_function(esk11_0,X2,X3),X4,X5),X2)
| ~ member(esk5_3(inverse_function(esk11_0,X2,X3),X4,X5),X3) ),
inference(spm,[status(thm)],[92,77,theory(equality)]) ).
cnf(305,negated_conjecture,
( esk1_4(esk11_0,esk12_0,X1,X2) = esk1_4(esk11_0,esk12_0,X3,X2)
| ~ member(X2,esk13_0)
| ~ member(X2,X3)
| ~ member(X2,X1)
| ~ surjective(esk11_0,esk12_0,X3)
| ~ surjective(esk11_0,esk12_0,X1) ),
inference(spm,[status(thm)],[158,14,theory(equality)]) ).
cnf(334,plain,
( maps(inverse_function(X1,X2,X3),X4,X5)
| member(esk5_3(inverse_function(X1,X2,X3),X4,X5),X4)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X4,X5),X3)
| ~ member(esk1_4(X1,X6,X7,esk4_3(inverse_function(X1,X2,X3),X4,X5)),X5)
| ~ member(esk1_4(X1,X6,X7,esk4_3(inverse_function(X1,X2,X3),X4,X5)),X2)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X4,X5),X7)
| ~ surjective(X1,X6,X7) ),
inference(spm,[status(thm)],[80,13,theory(equality)]) ).
cnf(357,plain,
( maps(inverse_function(X1,X2,X3),X4,X5)
| member(esk6_3(inverse_function(X1,X2,X3),X4,X5),X5)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X4,X5),X3)
| ~ member(esk1_4(X1,X6,X7,esk4_3(inverse_function(X1,X2,X3),X4,X5)),X5)
| ~ member(esk1_4(X1,X6,X7,esk4_3(inverse_function(X1,X2,X3),X4,X5)),X2)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X4,X5),X7)
| ~ surjective(X1,X6,X7) ),
inference(spm,[status(thm)],[82,13,theory(equality)]) ).
cnf(384,plain,
( maps(inverse_function(X1,X2,X3),X4,X5)
| member(esk7_3(inverse_function(X1,X2,X3),X4,X5),X5)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X4,X5),X3)
| ~ member(esk1_4(X1,X6,X7,esk4_3(inverse_function(X1,X2,X3),X4,X5)),X5)
| ~ member(esk1_4(X1,X6,X7,esk4_3(inverse_function(X1,X2,X3),X4,X5)),X2)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X4,X5),X7)
| ~ surjective(X1,X6,X7) ),
inference(spm,[status(thm)],[84,13,theory(equality)]) ).
cnf(415,plain,
( maps(inverse_function(X1,X2,X3),X4,X5)
| esk7_3(inverse_function(X1,X2,X3),X4,X5) != esk6_3(inverse_function(X1,X2,X3),X4,X5)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X4,X5),X3)
| ~ member(esk1_4(X1,X6,X7,esk4_3(inverse_function(X1,X2,X3),X4,X5)),X5)
| ~ member(esk1_4(X1,X6,X7,esk4_3(inverse_function(X1,X2,X3),X4,X5)),X2)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X4,X5),X7)
| ~ surjective(X1,X6,X7) ),
inference(spm,[status(thm)],[86,13,theory(equality)]) ).
cnf(598,plain,
( surjective(inverse_function(X1,X2,X3),X4,X5)
| ~ maps(X1,X6,X4)
| ~ member(esk3_4(X1,X6,X4,esk2_3(inverse_function(X1,X2,X3),X4,X5)),X3)
| ~ member(esk2_3(inverse_function(X1,X2,X3),X4,X5),X2)
| ~ member(esk2_3(inverse_function(X1,X2,X3),X4,X5),X6) ),
inference(spm,[status(thm)],[111,23,theory(equality)]) ).
cnf(656,plain,
( surjective(inverse_function(X1,X2,X3),X3,X4)
| ~ maps(X1,X5,X3)
| ~ member(esk2_3(inverse_function(X1,X2,X3),X3,X4),X2)
| ~ member(esk2_3(inverse_function(X1,X2,X3),X3,X4),X5) ),
inference(spm,[status(thm)],[598,23,theory(equality)]) ).
cnf(659,plain,
( surjective(inverse_function(X1,X2,X3),X3,X2)
| ~ maps(X1,X4,X3)
| ~ member(esk2_3(inverse_function(X1,X2,X3),X3,X2),X4) ),
inference(spm,[status(thm)],[656,15,theory(equality)]) ).
cnf(660,plain,
( surjective(inverse_function(X1,X2,X3),X3,X2)
| ~ maps(X1,X2,X3) ),
inference(spm,[status(thm)],[659,15,theory(equality)]) ).
cnf(1096,negated_conjecture,
( esk3_4(esk11_0,X1,esk13_0,esk10_3(inverse_function(esk11_0,X2,X3),X4,X2)) = esk8_3(inverse_function(esk11_0,X2,X3),X4,X2)
| injective(inverse_function(esk11_0,X2,X3),X4,X2)
| ~ maps(esk11_0,X1,esk13_0)
| ~ member(esk10_3(inverse_function(esk11_0,X2,X3),X4,X2),esk12_0)
| ~ member(esk8_3(inverse_function(esk11_0,X2,X3),X4,X2),esk13_0)
| ~ member(esk10_3(inverse_function(esk11_0,X2,X3),X4,X2),X1)
| ~ member(esk8_3(inverse_function(esk11_0,X2,X3),X4,X2),X3) ),
inference(spm,[status(thm)],[153,50,theory(equality)]) ).
cnf(1355,negated_conjecture,
( esk3_4(esk11_0,X1,esk13_0,esk10_3(inverse_function(esk11_0,X2,X3),X4,X2)) = esk9_3(inverse_function(esk11_0,X2,X3),X4,X2)
| injective(inverse_function(esk11_0,X2,X3),X4,X2)
| ~ maps(esk11_0,X1,esk13_0)
| ~ member(esk10_3(inverse_function(esk11_0,X2,X3),X4,X2),esk12_0)
| ~ member(esk9_3(inverse_function(esk11_0,X2,X3),X4,X2),esk13_0)
| ~ member(esk10_3(inverse_function(esk11_0,X2,X3),X4,X2),X1)
| ~ member(esk9_3(inverse_function(esk11_0,X2,X3),X4,X2),X3) ),
inference(spm,[status(thm)],[201,50,theory(equality)]) ).
cnf(1547,negated_conjecture,
( esk7_3(inverse_function(esk11_0,X1,X2),X3,X4) = esk6_3(inverse_function(esk11_0,X1,X2),X3,X4)
| maps(inverse_function(esk11_0,X1,X2),X3,X4)
| member(esk4_3(inverse_function(esk11_0,X1,X2),X3,X4),X3)
| ~ member(esk5_3(inverse_function(esk11_0,X1,X2),X3,X4),esk13_0)
| ~ member(esk6_3(inverse_function(esk11_0,X1,X2),X3,X4),esk12_0)
| ~ member(esk6_3(inverse_function(esk11_0,X1,X2),X3,X4),X1)
| ~ member(esk5_3(inverse_function(esk11_0,X1,X2),X3,X4),X2)
| ~ member(esk7_3(inverse_function(esk11_0,X1,X2),X3,X4),esk12_0)
| ~ member(esk7_3(inverse_function(esk11_0,X1,X2),X3,X4),X1) ),
inference(spm,[status(thm)],[224,78,theory(equality)]) ).
cnf(2256,plain,
( maps(inverse_function(X1,X2,X3),X4,X5)
| member(esk5_3(inverse_function(X1,X2,X3),X4,X5),X4)
| ~ member(esk1_4(X1,X5,X6,esk4_3(inverse_function(X1,X2,X3),X4,X5)),X2)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X4,X5),X3)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X4,X5),X6)
| ~ surjective(X1,X5,X6) ),
inference(spm,[status(thm)],[334,14,theory(equality)]) ).
cnf(2391,plain,
( maps(inverse_function(X1,X2,X3),X4,X5)
| member(esk6_3(inverse_function(X1,X2,X3),X4,X5),X5)
| ~ member(esk1_4(X1,X5,X6,esk4_3(inverse_function(X1,X2,X3),X4,X5)),X2)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X4,X5),X3)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X4,X5),X6)
| ~ surjective(X1,X5,X6) ),
inference(spm,[status(thm)],[357,14,theory(equality)]) ).
cnf(2400,plain,
( maps(inverse_function(X1,X2,X3),X4,X2)
| member(esk6_3(inverse_function(X1,X2,X3),X4,X2),X2)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X4,X2),X3)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X4,X2),X5)
| ~ surjective(X1,X2,X5) ),
inference(spm,[status(thm)],[2391,14,theory(equality)]) ).
cnf(2407,plain,
( maps(inverse_function(X1,X2,X3),X3,X2)
| member(esk6_3(inverse_function(X1,X2,X3),X3,X2),X2)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X3,X2),X4)
| ~ surjective(X1,X2,X4) ),
inference(spm,[status(thm)],[2400,29,theory(equality)]) ).
cnf(2536,plain,
( maps(inverse_function(X1,X2,X3),X4,X5)
| member(esk7_3(inverse_function(X1,X2,X3),X4,X5),X5)
| ~ member(esk1_4(X1,X5,X6,esk4_3(inverse_function(X1,X2,X3),X4,X5)),X2)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X4,X5),X3)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X4,X5),X6)
| ~ surjective(X1,X5,X6) ),
inference(spm,[status(thm)],[384,14,theory(equality)]) ).
cnf(2543,plain,
( maps(inverse_function(X1,X2,X3),X4,X2)
| member(esk7_3(inverse_function(X1,X2,X3),X4,X2),X2)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X4,X2),X3)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X4,X2),X5)
| ~ surjective(X1,X2,X5) ),
inference(spm,[status(thm)],[2536,14,theory(equality)]) ).
cnf(2551,plain,
( maps(inverse_function(X1,X2,X3),X3,X2)
| member(esk7_3(inverse_function(X1,X2,X3),X3,X2),X2)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X3,X2),X4)
| ~ surjective(X1,X2,X4) ),
inference(spm,[status(thm)],[2543,28,theory(equality)]) ).
cnf(2553,plain,
( maps(inverse_function(X1,X2,X3),X3,X2)
| member(esk7_3(inverse_function(X1,X2,X3),X3,X2),X2)
| ~ surjective(X1,X2,X3) ),
inference(spm,[status(thm)],[2551,28,theory(equality)]) ).
cnf(2935,plain,
( maps(inverse_function(X1,X2,X3),X4,X5)
| esk7_3(inverse_function(X1,X2,X3),X4,X5) != esk6_3(inverse_function(X1,X2,X3),X4,X5)
| ~ member(esk1_4(X1,X5,X6,esk4_3(inverse_function(X1,X2,X3),X4,X5)),X2)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X4,X5),X3)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X4,X5),X6)
| ~ surjective(X1,X5,X6) ),
inference(spm,[status(thm)],[415,14,theory(equality)]) ).
cnf(2942,plain,
( maps(inverse_function(X1,X2,X3),X4,X2)
| esk7_3(inverse_function(X1,X2,X3),X4,X2) != esk6_3(inverse_function(X1,X2,X3),X4,X2)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X4,X2),X3)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X4,X2),X5)
| ~ surjective(X1,X2,X5) ),
inference(spm,[status(thm)],[2935,14,theory(equality)]) ).
cnf(2972,plain,
( maps(inverse_function(X1,X2,X3),X4,X2)
| member(esk5_3(inverse_function(X1,X2,X3),X4,X2),X4)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X4,X2),X3)
| ~ member(esk4_3(inverse_function(X1,X2,X3),X4,X2),X5)
| ~ surjective(X1,X2,X5) ),
inference(spm,[status(thm)],[2256,14,theory(equality)]) ).
cnf(6396,negated_conjecture,
( esk3_4(esk11_0,X1,esk13_0,esk10_3(inverse_function(esk11_0,X2,X3),X3,X2)) = esk8_3(inverse_function(esk11_0,X2,X3),X3,X2)
| injective(inverse_function(esk11_0,X2,X3),X3,X2)
| ~ maps(esk11_0,X1,esk13_0)
| ~ member(esk10_3(inverse_function(esk11_0,X2,X3),X3,X2),esk12_0)
| ~ member(esk8_3(inverse_function(esk11_0,X2,X3),X3,X2),esk13_0)
| ~ member(esk10_3(inverse_function(esk11_0,X2,X3),X3,X2),X1) ),
inference(spm,[status(thm)],[1096,52,theory(equality)]) ).
cnf(6398,negated_conjecture,
( apply(esk11_0,esk10_3(inverse_function(esk11_0,X1,X2),X2,X1),esk8_3(inverse_function(esk11_0,X1,X2),X2,X1))
| injective(inverse_function(esk11_0,X1,X2),X2,X1)
| ~ maps(esk11_0,X3,esk13_0)
| ~ member(esk10_3(inverse_function(esk11_0,X1,X2),X2,X1),X3)
| ~ member(esk10_3(inverse_function(esk11_0,X1,X2),X2,X1),esk12_0)
| ~ member(esk8_3(inverse_function(esk11_0,X1,X2),X2,X1),esk13_0) ),
inference(spm,[status(thm)],[22,6396,theory(equality)]) ).
cnf(6434,negated_conjecture,
( injective(inverse_function(esk11_0,X1,X2),X2,X1)
| apply(esk11_0,esk10_3(inverse_function(esk11_0,X1,X2),X2,X1),esk8_3(inverse_function(esk11_0,X1,X2),X2,X1))
| ~ maps(esk11_0,X1,esk13_0)
| ~ member(esk10_3(inverse_function(esk11_0,X1,X2),X2,X1),esk12_0)
| ~ member(esk8_3(inverse_function(esk11_0,X1,X2),X2,X1),esk13_0) ),
inference(spm,[status(thm)],[6398,50,theory(equality)]) ).
cnf(6435,negated_conjecture,
( X1 = esk8_3(inverse_function(esk11_0,X2,X3),X3,X2)
| injective(inverse_function(esk11_0,X2,X3),X3,X2)
| ~ apply(esk11_0,esk10_3(inverse_function(esk11_0,X2,X3),X3,X2),X1)
| ~ member(esk10_3(inverse_function(esk11_0,X2,X3),X3,X2),esk12_0)
| ~ member(esk8_3(inverse_function(esk11_0,X2,X3),X3,X2),esk13_0)
| ~ member(X1,esk13_0)
| ~ maps(esk11_0,X2,esk13_0) ),
inference(spm,[status(thm)],[87,6434,theory(equality)]) ).
cnf(6520,negated_conjecture,
( esk3_4(esk11_0,X1,esk13_0,esk10_3(inverse_function(esk11_0,X2,X3),X3,X2)) = esk9_3(inverse_function(esk11_0,X2,X3),X3,X2)
| injective(inverse_function(esk11_0,X2,X3),X3,X2)
| ~ maps(esk11_0,X1,esk13_0)
| ~ member(esk10_3(inverse_function(esk11_0,X2,X3),X3,X2),esk12_0)
| ~ member(esk9_3(inverse_function(esk11_0,X2,X3),X3,X2),esk13_0)
| ~ member(esk10_3(inverse_function(esk11_0,X2,X3),X3,X2),X1) ),
inference(spm,[status(thm)],[1355,51,theory(equality)]) ).
cnf(6522,negated_conjecture,
( apply(esk11_0,esk10_3(inverse_function(esk11_0,X1,X2),X2,X1),esk9_3(inverse_function(esk11_0,X1,X2),X2,X1))
| injective(inverse_function(esk11_0,X1,X2),X2,X1)
| ~ maps(esk11_0,X3,esk13_0)
| ~ member(esk10_3(inverse_function(esk11_0,X1,X2),X2,X1),X3)
| ~ member(esk10_3(inverse_function(esk11_0,X1,X2),X2,X1),esk12_0)
| ~ member(esk9_3(inverse_function(esk11_0,X1,X2),X2,X1),esk13_0) ),
inference(spm,[status(thm)],[22,6520,theory(equality)]) ).
cnf(6559,negated_conjecture,
( injective(inverse_function(esk11_0,X1,X2),X2,X1)
| apply(esk11_0,esk10_3(inverse_function(esk11_0,X1,X2),X2,X1),esk9_3(inverse_function(esk11_0,X1,X2),X2,X1))
| ~ maps(esk11_0,X1,esk13_0)
| ~ member(esk10_3(inverse_function(esk11_0,X1,X2),X2,X1),esk12_0)
| ~ member(esk9_3(inverse_function(esk11_0,X1,X2),X2,X1),esk13_0) ),
inference(spm,[status(thm)],[6522,50,theory(equality)]) ).
cnf(6569,negated_conjecture,
( esk9_3(inverse_function(esk11_0,X1,X2),X2,X1) = esk8_3(inverse_function(esk11_0,X1,X2),X2,X1)
| injective(inverse_function(esk11_0,X1,X2),X2,X1)
| ~ maps(esk11_0,X1,esk13_0)
| ~ member(esk10_3(inverse_function(esk11_0,X1,X2),X2,X1),esk12_0)
| ~ member(esk8_3(inverse_function(esk11_0,X1,X2),X2,X1),esk13_0)
| ~ member(esk9_3(inverse_function(esk11_0,X1,X2),X2,X1),esk13_0) ),
inference(spm,[status(thm)],[6435,6559,theory(equality)]) ).
cnf(6581,negated_conjecture,
( injective(inverse_function(esk11_0,X1,X2),X2,X1)
| ~ maps(esk11_0,X1,esk13_0)
| ~ member(esk10_3(inverse_function(esk11_0,X1,X2),X2,X1),esk12_0)
| ~ member(esk8_3(inverse_function(esk11_0,X1,X2),X2,X1),esk13_0)
| ~ member(esk9_3(inverse_function(esk11_0,X1,X2),X2,X1),esk13_0) ),
inference(csr,[status(thm)],[6569,47]) ).
cnf(6582,negated_conjecture,
( injective(inverse_function(esk11_0,esk12_0,X1),X1,esk12_0)
| ~ maps(esk11_0,esk12_0,esk13_0)
| ~ member(esk8_3(inverse_function(esk11_0,esk12_0,X1),X1,esk12_0),esk13_0)
| ~ member(esk9_3(inverse_function(esk11_0,esk12_0,X1),X1,esk12_0),esk13_0) ),
inference(spm,[status(thm)],[6581,50,theory(equality)]) ).
cnf(6583,negated_conjecture,
( injective(inverse_function(esk11_0,esk12_0,X1),X1,esk12_0)
| $false
| ~ member(esk8_3(inverse_function(esk11_0,esk12_0,X1),X1,esk12_0),esk13_0)
| ~ member(esk9_3(inverse_function(esk11_0,esk12_0,X1),X1,esk12_0),esk13_0) ),
inference(rw,[status(thm)],[6582,65,theory(equality)]) ).
cnf(6584,negated_conjecture,
( injective(inverse_function(esk11_0,esk12_0,X1),X1,esk12_0)
| ~ member(esk8_3(inverse_function(esk11_0,esk12_0,X1),X1,esk12_0),esk13_0)
| ~ member(esk9_3(inverse_function(esk11_0,esk12_0,X1),X1,esk12_0),esk13_0) ),
inference(cn,[status(thm)],[6583,theory(equality)]) ).
cnf(6585,negated_conjecture,
( injective(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)
| ~ member(esk8_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk13_0) ),
inference(spm,[status(thm)],[6584,51,theory(equality)]) ).
cnf(6586,negated_conjecture,
injective(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),
inference(csr,[status(thm)],[6585,52]) ).
cnf(6587,negated_conjecture,
( X1 = X2
| ~ apply(inverse_function(esk11_0,esk12_0,esk13_0),X2,X3)
| ~ apply(inverse_function(esk11_0,esk12_0,esk13_0),X1,X3)
| ~ member(X3,esk12_0)
| ~ member(X2,esk13_0)
| ~ member(X1,esk13_0) ),
inference(spm,[status(thm)],[53,6586,theory(equality)]) ).
cnf(6591,negated_conjecture,
( X1 = X2
| ~ apply(inverse_function(esk11_0,esk12_0,esk13_0),X1,X3)
| ~ member(X3,esk12_0)
| ~ member(X2,esk13_0)
| ~ member(X1,esk13_0)
| ~ apply(esk11_0,X3,X2) ),
inference(spm,[status(thm)],[6587,41,theory(equality)]) ).
cnf(6667,negated_conjecture,
( esk1_4(inverse_function(esk11_0,esk12_0,esk13_0),X1,X2,X3) = X4
| ~ apply(esk11_0,X3,X4)
| ~ member(X3,esk12_0)
| ~ member(X4,esk13_0)
| ~ member(esk1_4(inverse_function(esk11_0,esk12_0,esk13_0),X1,X2,X3),esk13_0)
| ~ member(X3,X2)
| ~ surjective(inverse_function(esk11_0,esk12_0,esk13_0),X1,X2) ),
inference(spm,[status(thm)],[6591,13,theory(equality)]) ).
cnf(7185,negated_conjecture,
( esk1_4(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,X1,X2) = X3
| ~ apply(esk11_0,X2,X3)
| ~ member(X2,esk12_0)
| ~ member(X3,esk13_0)
| ~ member(X2,X1)
| ~ surjective(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,X1) ),
inference(spm,[status(thm)],[6667,14,theory(equality)]) ).
cnf(7216,negated_conjecture,
( esk1_4(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,X1,X2) = esk3_4(esk11_0,X3,X4,X2)
| ~ member(X2,esk12_0)
| ~ member(esk3_4(esk11_0,X3,X4,X2),esk13_0)
| ~ member(X2,X1)
| ~ surjective(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,X1)
| ~ maps(esk11_0,X3,X4)
| ~ member(X2,X3) ),
inference(spm,[status(thm)],[7185,22,theory(equality)]) ).
cnf(7291,negated_conjecture,
( esk1_4(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,X1,X2) = esk3_4(esk11_0,X3,esk13_0,X2)
| ~ maps(esk11_0,X3,esk13_0)
| ~ member(X2,esk12_0)
| ~ member(X2,X1)
| ~ member(X2,X3)
| ~ surjective(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,X1) ),
inference(spm,[status(thm)],[7216,23,theory(equality)]) ).
cnf(7311,negated_conjecture,
( apply(inverse_function(esk11_0,esk12_0,esk13_0),esk3_4(esk11_0,X3,esk13_0,X2),X2)
| ~ member(X2,X1)
| ~ surjective(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,X1)
| ~ maps(esk11_0,X3,esk13_0)
| ~ member(X2,esk12_0)
| ~ member(X2,X3) ),
inference(spm,[status(thm)],[13,7291,theory(equality)]) ).
cnf(7460,negated_conjecture,
( apply(inverse_function(esk11_0,esk12_0,esk13_0),esk3_4(esk11_0,X1,esk13_0,X2),X2)
| ~ maps(esk11_0,X1,esk13_0)
| ~ member(X2,esk12_0)
| ~ member(X2,X1)
| ~ maps(esk11_0,esk12_0,esk13_0) ),
inference(spm,[status(thm)],[7311,660,theory(equality)]) ).
cnf(7461,negated_conjecture,
( apply(inverse_function(esk11_0,esk12_0,esk13_0),esk3_4(esk11_0,X1,esk13_0,X2),X2)
| ~ maps(esk11_0,X1,esk13_0)
| ~ member(X2,esk12_0)
| ~ member(X2,X1)
| $false ),
inference(rw,[status(thm)],[7460,65,theory(equality)]) ).
cnf(7462,negated_conjecture,
( apply(inverse_function(esk11_0,esk12_0,esk13_0),esk3_4(esk11_0,X1,esk13_0,X2),X2)
| ~ maps(esk11_0,X1,esk13_0)
| ~ member(X2,esk12_0)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[7461,theory(equality)]) ).
cnf(7510,negated_conjecture,
( apply(inverse_function(esk11_0,esk12_0,esk13_0),X4,esk1_4(esk11_0,X2,X3,X4))
| ~ maps(esk11_0,X1,esk13_0)
| ~ member(esk1_4(esk11_0,X2,X3,X4),esk12_0)
| ~ member(esk1_4(esk11_0,X2,X3,X4),X1)
| ~ member(X4,esk13_0)
| ~ member(X4,X3)
| ~ surjective(esk11_0,X2,X3) ),
inference(spm,[status(thm)],[7462,129,theory(equality)]) ).
cnf(7643,negated_conjecture,
( apply(inverse_function(esk11_0,esk12_0,esk13_0),X1,esk1_4(esk11_0,X2,X3,X1))
| ~ maps(esk11_0,X2,esk13_0)
| ~ member(esk1_4(esk11_0,X2,X3,X1),esk12_0)
| ~ member(X1,esk13_0)
| ~ member(X1,X3)
| ~ surjective(esk11_0,X2,X3) ),
inference(spm,[status(thm)],[7510,14,theory(equality)]) ).
cnf(7672,negated_conjecture,
( apply(inverse_function(esk11_0,esk12_0,esk13_0),X1,esk1_4(esk11_0,esk12_0,X3,X1))
| ~ maps(esk11_0,esk12_0,esk13_0)
| ~ member(esk1_4(esk11_0,esk12_0,X3,X1),esk12_0)
| ~ member(X1,esk13_0)
| ~ member(X1,X2)
| ~ surjective(esk11_0,esk12_0,X2)
| ~ member(X1,X3)
| ~ surjective(esk11_0,esk12_0,X3) ),
inference(spm,[status(thm)],[7643,305,theory(equality)]) ).
cnf(7701,negated_conjecture,
( apply(inverse_function(esk11_0,esk12_0,esk13_0),X1,esk1_4(esk11_0,esk12_0,X3,X1))
| $false
| ~ member(esk1_4(esk11_0,esk12_0,X3,X1),esk12_0)
| ~ member(X1,esk13_0)
| ~ member(X1,X2)
| ~ surjective(esk11_0,esk12_0,X2)
| ~ member(X1,X3)
| ~ surjective(esk11_0,esk12_0,X3) ),
inference(rw,[status(thm)],[7672,65,theory(equality)]) ).
cnf(7702,negated_conjecture,
( apply(inverse_function(esk11_0,esk12_0,esk13_0),X1,esk1_4(esk11_0,esk12_0,X3,X1))
| ~ member(esk1_4(esk11_0,esk12_0,X3,X1),esk12_0)
| ~ member(X1,esk13_0)
| ~ member(X1,X2)
| ~ surjective(esk11_0,esk12_0,X2)
| ~ member(X1,X3)
| ~ surjective(esk11_0,esk12_0,X3) ),
inference(cn,[status(thm)],[7701,theory(equality)]) ).
cnf(7730,negated_conjecture,
( apply(inverse_function(esk11_0,esk12_0,esk13_0),X1,esk1_4(esk11_0,esk12_0,X3,X1))
| ~ member(X1,esk13_0)
| ~ member(X1,X2)
| ~ member(X1,X3)
| ~ surjective(esk11_0,esk12_0,X2)
| ~ surjective(esk11_0,esk12_0,X3) ),
inference(csr,[status(thm)],[7702,14]) ).
cnf(7731,negated_conjecture,
( apply(inverse_function(esk11_0,esk12_0,esk13_0),X1,esk1_4(esk11_0,esk12_0,X2,X1))
| ~ member(X1,esk13_0)
| ~ member(X1,X2)
| ~ surjective(esk11_0,esk12_0,X2) ),
inference(spm,[status(thm)],[7730,66,theory(equality)]) ).
cnf(7737,negated_conjecture,
( maps(inverse_function(esk11_0,esk12_0,esk13_0),X1,X2)
| apply(inverse_function(esk11_0,esk12_0,esk13_0),esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),X1,X2),esk6_3(inverse_function(esk11_0,esk12_0,esk13_0),X1,X2))
| ~ member(esk1_4(esk11_0,esk12_0,X3,esk4_3(inverse_function(esk11_0,esk12_0,esk13_0),X1,X2)),X2)
| ~ member(esk4_3(inverse_function(esk11_0,esk12_0,esk13_0),X1,X2),esk13_0)
| ~ member(esk4_3(inverse_function(esk11_0,esk12_0,esk13_0),X1,X2),X3)
| ~ surjective(esk11_0,esk12_0,X3) ),
inference(spm,[status(thm)],[33,7731,theory(equality)]) ).
cnf(7738,negated_conjecture,
( maps(inverse_function(esk11_0,esk12_0,esk13_0),X1,X2)
| apply(inverse_function(esk11_0,esk12_0,esk13_0),esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),X1,X2),esk7_3(inverse_function(esk11_0,esk12_0,esk13_0),X1,X2))
| ~ member(esk1_4(esk11_0,esk12_0,X3,esk4_3(inverse_function(esk11_0,esk12_0,esk13_0),X1,X2)),X2)
| ~ member(esk4_3(inverse_function(esk11_0,esk12_0,esk13_0),X1,X2),esk13_0)
| ~ member(esk4_3(inverse_function(esk11_0,esk12_0,esk13_0),X1,X2),X3)
| ~ surjective(esk11_0,esk12_0,X3) ),
inference(spm,[status(thm)],[32,7731,theory(equality)]) ).
cnf(14668,negated_conjecture,
( maps(inverse_function(esk11_0,X1,X2),X3,X4)
| member(esk4_3(inverse_function(esk11_0,X1,X2),X3,X4),X3)
| ~ member(esk5_3(inverse_function(esk11_0,X1,X2),X3,X4),esk13_0)
| ~ member(esk6_3(inverse_function(esk11_0,X1,X2),X3,X4),esk12_0)
| ~ member(esk7_3(inverse_function(esk11_0,X1,X2),X3,X4),esk12_0)
| ~ member(esk6_3(inverse_function(esk11_0,X1,X2),X3,X4),X1)
| ~ member(esk5_3(inverse_function(esk11_0,X1,X2),X3,X4),X2)
| ~ member(esk7_3(inverse_function(esk11_0,X1,X2),X3,X4),X1) ),
inference(csr,[status(thm)],[1547,25]) ).
cnf(14670,negated_conjecture,
( maps(inverse_function(esk11_0,esk12_0,X1),X1,esk12_0)
| member(esk4_3(inverse_function(esk11_0,esk12_0,X1),X1,esk12_0),X1)
| ~ member(esk5_3(inverse_function(esk11_0,esk12_0,X1),X1,esk12_0),esk13_0)
| ~ member(esk6_3(inverse_function(esk11_0,esk12_0,X1),X1,esk12_0),esk12_0)
| ~ member(esk5_3(inverse_function(esk11_0,esk12_0,X1),X1,esk12_0),X1)
| ~ member(esk7_3(inverse_function(esk11_0,esk12_0,X1),X1,esk12_0),esk12_0)
| ~ surjective(esk11_0,esk12_0,X1) ),
inference(spm,[status(thm)],[14668,2553,theory(equality)]) ).
cnf(14671,negated_conjecture,
( maps(inverse_function(esk11_0,esk12_0,X1),X1,esk12_0)
| member(esk4_3(inverse_function(esk11_0,esk12_0,X1),X1,esk12_0),X1)
| ~ member(esk5_3(inverse_function(esk11_0,esk12_0,X1),X1,esk12_0),esk13_0)
| ~ member(esk6_3(inverse_function(esk11_0,esk12_0,X1),X1,esk12_0),esk12_0)
| ~ member(esk5_3(inverse_function(esk11_0,esk12_0,X1),X1,esk12_0),X1)
| ~ surjective(esk11_0,esk12_0,X1) ),
inference(csr,[status(thm)],[14670,28]) ).
cnf(14672,negated_conjecture,
( maps(inverse_function(esk11_0,esk12_0,X1),X1,esk12_0)
| member(esk4_3(inverse_function(esk11_0,esk12_0,X1),X1,esk12_0),X1)
| ~ member(esk5_3(inverse_function(esk11_0,esk12_0,X1),X1,esk12_0),esk13_0)
| ~ member(esk6_3(inverse_function(esk11_0,esk12_0,X1),X1,esk12_0),esk12_0)
| ~ surjective(esk11_0,esk12_0,X1) ),
inference(csr,[status(thm)],[14671,30]) ).
cnf(14673,negated_conjecture,
( maps(inverse_function(esk11_0,esk12_0,X1),X1,esk12_0)
| member(esk4_3(inverse_function(esk11_0,esk12_0,X1),X1,esk12_0),X1)
| ~ member(esk5_3(inverse_function(esk11_0,esk12_0,X1),X1,esk12_0),esk13_0)
| ~ surjective(esk11_0,esk12_0,X1) ),
inference(csr,[status(thm)],[14672,29]) ).
cnf(14674,negated_conjecture,
( maps(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)
| member(esk4_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk13_0)
| ~ surjective(esk11_0,esk12_0,esk13_0) ),
inference(spm,[status(thm)],[14673,30,theory(equality)]) ).
cnf(14675,negated_conjecture,
( maps(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)
| member(esk4_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk13_0)
| $false ),
inference(rw,[status(thm)],[14674,66,theory(equality)]) ).
cnf(14676,negated_conjecture,
( maps(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)
| member(esk4_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk13_0) ),
inference(cn,[status(thm)],[14675,theory(equality)]) ).
cnf(14677,negated_conjecture,
member(esk4_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk13_0),
inference(sr,[status(thm)],[14676,63,theory(equality)]) ).
cnf(14685,negated_conjecture,
( maps(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)
| member(esk6_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk12_0)
| ~ surjective(esk11_0,esk12_0,esk13_0) ),
inference(spm,[status(thm)],[2407,14677,theory(equality)]) ).
cnf(14687,negated_conjecture,
( maps(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)
| member(esk7_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk12_0)
| ~ surjective(esk11_0,esk12_0,esk13_0) ),
inference(spm,[status(thm)],[2551,14677,theory(equality)]) ).
cnf(14688,negated_conjecture,
( maps(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)
| esk7_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0) != esk6_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)
| ~ member(esk4_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),X1)
| ~ surjective(esk11_0,esk12_0,X1) ),
inference(spm,[status(thm)],[2942,14677,theory(equality)]) ).
cnf(14689,negated_conjecture,
( maps(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)
| member(esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk13_0)
| ~ member(esk4_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),X1)
| ~ surjective(esk11_0,esk12_0,X1) ),
inference(spm,[status(thm)],[2972,14677,theory(equality)]) ).
cnf(14691,negated_conjecture,
( maps(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)
| member(esk6_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk12_0)
| $false ),
inference(rw,[status(thm)],[14685,66,theory(equality)]) ).
cnf(14692,negated_conjecture,
( maps(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)
| member(esk6_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk12_0) ),
inference(cn,[status(thm)],[14691,theory(equality)]) ).
cnf(14693,negated_conjecture,
member(esk6_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk12_0),
inference(sr,[status(thm)],[14692,63,theory(equality)]) ).
cnf(14695,negated_conjecture,
( maps(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)
| member(esk7_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk12_0)
| $false ),
inference(rw,[status(thm)],[14687,66,theory(equality)]) ).
cnf(14696,negated_conjecture,
( maps(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)
| member(esk7_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk12_0) ),
inference(cn,[status(thm)],[14695,theory(equality)]) ).
cnf(14697,negated_conjecture,
member(esk7_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk12_0),
inference(sr,[status(thm)],[14696,63,theory(equality)]) ).
cnf(14698,negated_conjecture,
( esk7_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0) != esk6_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)
| ~ member(esk4_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),X1)
| ~ surjective(esk11_0,esk12_0,X1) ),
inference(sr,[status(thm)],[14688,63,theory(equality)]) ).
cnf(14699,negated_conjecture,
( member(esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk13_0)
| ~ member(esk4_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),X1)
| ~ surjective(esk11_0,esk12_0,X1) ),
inference(sr,[status(thm)],[14689,63,theory(equality)]) ).
cnf(14739,negated_conjecture,
( member(esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk13_0)
| ~ surjective(esk11_0,esk12_0,esk13_0) ),
inference(spm,[status(thm)],[14699,14677,theory(equality)]) ).
cnf(14740,negated_conjecture,
( member(esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk13_0)
| $false ),
inference(rw,[status(thm)],[14739,66,theory(equality)]) ).
cnf(14741,negated_conjecture,
member(esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk13_0),
inference(cn,[status(thm)],[14740,theory(equality)]) ).
cnf(28775,negated_conjecture,
( maps(inverse_function(esk11_0,esk12_0,esk13_0),X1,esk12_0)
| apply(inverse_function(esk11_0,esk12_0,esk13_0),esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),X1,esk12_0),esk6_3(inverse_function(esk11_0,esk12_0,esk13_0),X1,esk12_0))
| ~ member(esk4_3(inverse_function(esk11_0,esk12_0,esk13_0),X1,esk12_0),esk13_0)
| ~ member(esk4_3(inverse_function(esk11_0,esk12_0,esk13_0),X1,esk12_0),X2)
| ~ surjective(esk11_0,esk12_0,X2) ),
inference(spm,[status(thm)],[7737,14,theory(equality)]) ).
cnf(28781,negated_conjecture,
( maps(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)
| apply(inverse_function(esk11_0,esk12_0,esk13_0),esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk6_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0))
| ~ member(esk4_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk13_0)
| ~ surjective(esk11_0,esk12_0,esk13_0) ),
inference(spm,[status(thm)],[28775,14677,theory(equality)]) ).
cnf(28784,negated_conjecture,
( maps(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)
| apply(inverse_function(esk11_0,esk12_0,esk13_0),esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk6_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0))
| $false
| ~ surjective(esk11_0,esk12_0,esk13_0) ),
inference(rw,[status(thm)],[28781,14677,theory(equality)]) ).
cnf(28785,negated_conjecture,
( maps(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)
| apply(inverse_function(esk11_0,esk12_0,esk13_0),esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk6_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0))
| $false
| $false ),
inference(rw,[status(thm)],[28784,66,theory(equality)]) ).
cnf(28786,negated_conjecture,
( maps(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)
| apply(inverse_function(esk11_0,esk12_0,esk13_0),esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk6_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)) ),
inference(cn,[status(thm)],[28785,theory(equality)]) ).
cnf(28787,negated_conjecture,
apply(inverse_function(esk11_0,esk12_0,esk13_0),esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk6_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)),
inference(sr,[status(thm)],[28786,63,theory(equality)]) ).
cnf(28788,negated_conjecture,
( apply(esk11_0,esk6_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0))
| ~ member(esk6_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk12_0)
| ~ member(esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk13_0) ),
inference(spm,[status(thm)],[40,28787,theory(equality)]) ).
cnf(28798,negated_conjecture,
( apply(esk11_0,esk6_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0))
| $false
| ~ member(esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk13_0) ),
inference(rw,[status(thm)],[28788,14693,theory(equality)]) ).
cnf(28799,negated_conjecture,
( apply(esk11_0,esk6_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0))
| $false
| $false ),
inference(rw,[status(thm)],[28798,14741,theory(equality)]) ).
cnf(28800,negated_conjecture,
apply(esk11_0,esk6_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)),
inference(cn,[status(thm)],[28799,theory(equality)]) ).
cnf(28842,negated_conjecture,
( X1 = esk6_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)
| ~ apply(esk11_0,X1,esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0))
| ~ member(esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk13_0)
| ~ member(esk6_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk12_0)
| ~ member(X1,esk12_0) ),
inference(spm,[status(thm)],[92,28800,theory(equality)]) ).
cnf(28856,negated_conjecture,
( X1 = esk6_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)
| ~ apply(esk11_0,X1,esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0))
| $false
| ~ member(esk6_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk12_0)
| ~ member(X1,esk12_0) ),
inference(rw,[status(thm)],[28842,14741,theory(equality)]) ).
cnf(28857,negated_conjecture,
( X1 = esk6_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)
| ~ apply(esk11_0,X1,esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0))
| $false
| $false
| ~ member(X1,esk12_0) ),
inference(rw,[status(thm)],[28856,14693,theory(equality)]) ).
cnf(28858,negated_conjecture,
( X1 = esk6_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)
| ~ apply(esk11_0,X1,esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0))
| ~ member(X1,esk12_0) ),
inference(cn,[status(thm)],[28857,theory(equality)]) ).
cnf(33709,negated_conjecture,
( maps(inverse_function(esk11_0,esk12_0,esk13_0),X1,esk12_0)
| apply(inverse_function(esk11_0,esk12_0,esk13_0),esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),X1,esk12_0),esk7_3(inverse_function(esk11_0,esk12_0,esk13_0),X1,esk12_0))
| ~ member(esk4_3(inverse_function(esk11_0,esk12_0,esk13_0),X1,esk12_0),esk13_0)
| ~ member(esk4_3(inverse_function(esk11_0,esk12_0,esk13_0),X1,esk12_0),X2)
| ~ surjective(esk11_0,esk12_0,X2) ),
inference(spm,[status(thm)],[7738,14,theory(equality)]) ).
cnf(33715,negated_conjecture,
( maps(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)
| apply(inverse_function(esk11_0,esk12_0,esk13_0),esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk7_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0))
| ~ member(esk4_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk13_0)
| ~ surjective(esk11_0,esk12_0,esk13_0) ),
inference(spm,[status(thm)],[33709,14677,theory(equality)]) ).
cnf(33718,negated_conjecture,
( maps(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)
| apply(inverse_function(esk11_0,esk12_0,esk13_0),esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk7_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0))
| $false
| ~ surjective(esk11_0,esk12_0,esk13_0) ),
inference(rw,[status(thm)],[33715,14677,theory(equality)]) ).
cnf(33719,negated_conjecture,
( maps(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)
| apply(inverse_function(esk11_0,esk12_0,esk13_0),esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk7_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0))
| $false
| $false ),
inference(rw,[status(thm)],[33718,66,theory(equality)]) ).
cnf(33720,negated_conjecture,
( maps(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)
| apply(inverse_function(esk11_0,esk12_0,esk13_0),esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk7_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)) ),
inference(cn,[status(thm)],[33719,theory(equality)]) ).
cnf(33721,negated_conjecture,
apply(inverse_function(esk11_0,esk12_0,esk13_0),esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk7_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)),
inference(sr,[status(thm)],[33720,63,theory(equality)]) ).
cnf(33722,negated_conjecture,
( apply(esk11_0,esk7_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0))
| ~ member(esk7_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk12_0)
| ~ member(esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk13_0) ),
inference(spm,[status(thm)],[40,33721,theory(equality)]) ).
cnf(33732,negated_conjecture,
( apply(esk11_0,esk7_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0))
| $false
| ~ member(esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk13_0) ),
inference(rw,[status(thm)],[33722,14697,theory(equality)]) ).
cnf(33733,negated_conjecture,
( apply(esk11_0,esk7_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0))
| $false
| $false ),
inference(rw,[status(thm)],[33732,14741,theory(equality)]) ).
cnf(33734,negated_conjecture,
apply(esk11_0,esk7_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk5_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)),
inference(cn,[status(thm)],[33733,theory(equality)]) ).
cnf(33814,negated_conjecture,
( esk7_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0) = esk6_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)
| ~ member(esk7_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),esk12_0) ),
inference(spm,[status(thm)],[28858,33734,theory(equality)]) ).
cnf(33858,negated_conjecture,
( esk7_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0) = esk6_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0)
| $false ),
inference(rw,[status(thm)],[33814,14697,theory(equality)]) ).
cnf(33859,negated_conjecture,
esk7_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0) = esk6_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),
inference(cn,[status(thm)],[33858,theory(equality)]) ).
cnf(33906,negated_conjecture,
( $false
| ~ member(esk4_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),X1)
| ~ surjective(esk11_0,esk12_0,X1) ),
inference(rw,[status(thm)],[14698,33859,theory(equality)]) ).
cnf(33907,negated_conjecture,
( ~ member(esk4_3(inverse_function(esk11_0,esk12_0,esk13_0),esk13_0,esk12_0),X1)
| ~ surjective(esk11_0,esk12_0,X1) ),
inference(cn,[status(thm)],[33906,theory(equality)]) ).
cnf(34022,negated_conjecture,
~ surjective(esk11_0,esk12_0,esk13_0),
inference(spm,[status(thm)],[33907,14677,theory(equality)]) ).
cnf(34023,negated_conjecture,
$false,
inference(rw,[status(thm)],[34022,66,theory(equality)]) ).
cnf(34024,negated_conjecture,
$false,
inference(cn,[status(thm)],[34023,theory(equality)]) ).
cnf(34025,negated_conjecture,
$false,
34024,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET712+4.p
% --creating new selector for [SET006+0.ax, SET006+1.ax]
% -running prover on /tmp/tmprVy2GO/sel_SET712+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET712+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET712+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET712+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
%
%------------------------------------------------------------------------------