TSTP Solution File: SET715+4 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET715+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 03:16:36 EST 2010
% Result : Theorem 16.85s
% Output : CNFRefutation 16.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 8
% Syntax : Number of formulae : 155 ( 10 unt; 0 def)
% Number of atoms : 1026 ( 51 equ)
% Maximal formula atoms : 55 ( 6 avg)
% Number of connectives : 1552 ( 681 ~; 702 |; 151 &)
% ( 7 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 3 con; 0-7 aty)
% Number of variables : 732 ( 22 sgn 215 !; 33 ?)
% 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/tmpcr7spg/sel_SET715+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/tmpcr7spg/sel_SET715+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/tmpcr7spg/sel_SET715+4.p_1',maps) ).
fof(4,axiom,
! [X1,X2] :
( identity(X1,X2)
<=> ! [X6] :
( member(X6,X2)
=> apply(X1,X6,X6) ) ),
file('/tmp/tmpcr7spg/sel_SET715+4.p_1',identity) ).
fof(5,axiom,
! [X9,X1,X2,X3,X10,X6,X11] :
( ( member(X6,X2)
& member(X11,X10) )
=> ( apply(compose_function(X9,X1,X2,X3,X10),X6,X11)
<=> ? [X4] :
( member(X4,X3)
& apply(X1,X6,X4)
& apply(X9,X4,X11) ) ) ),
file('/tmp/tmpcr7spg/sel_SET715+4.p_1',compose_function) ).
fof(6,axiom,
! [X1,X2,X3] :
( injective(X1,X2,X3)
<=> ! [X12,X13,X4] :
( ( member(X12,X2)
& member(X13,X2)
& member(X4,X3) )
=> ( ( apply(X1,X12,X4)
& apply(X1,X13,X4) )
=> X12 = X13 ) ) ),
file('/tmp/tmpcr7spg/sel_SET715+4.p_1',injective) ).
fof(7,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/tmpcr7spg/sel_SET715+4.p_1',inverse_function) ).
fof(8,conjecture,
! [X1,X2,X3] :
( ( maps(X1,X2,X3)
& one_to_one(X1,X2,X3) )
=> identity(compose_function(X1,inverse_function(X1,X2,X3),X3,X2,X3),X3) ),
file('/tmp/tmpcr7spg/sel_SET715+4.p_1',thII06) ).
fof(9,negated_conjecture,
~ ! [X1,X2,X3] :
( ( maps(X1,X2,X3)
& one_to_one(X1,X2,X3) )
=> identity(compose_function(X1,inverse_function(X1,X2,X3),X3,X2,X3),X3) ),
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(15,plain,
( apply(X1,esk1_4(X1,X2,X3,X4),X4)
| ~ surjective(X1,X2,X3)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[14]) ).
cnf(16,plain,
( member(esk1_4(X1,X2,X3,X4),X2)
| ~ surjective(X1,X2,X3)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[14]) ).
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(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]) ).
fof(53,plain,
! [X9,X1,X2,X3,X10,X6,X11] :
( ~ member(X6,X2)
| ~ member(X11,X10)
| ( ( ~ apply(compose_function(X9,X1,X2,X3,X10),X6,X11)
| ? [X4] :
( member(X4,X3)
& apply(X1,X6,X4)
& apply(X9,X4,X11) ) )
& ( ! [X4] :
( ~ member(X4,X3)
| ~ apply(X1,X6,X4)
| ~ apply(X9,X4,X11) )
| apply(compose_function(X9,X1,X2,X3,X10),X6,X11) ) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(54,plain,
! [X12,X13,X14,X15,X16,X17,X18] :
( ~ member(X17,X14)
| ~ member(X18,X16)
| ( ( ~ apply(compose_function(X12,X13,X14,X15,X16),X17,X18)
| ? [X19] :
( member(X19,X15)
& apply(X13,X17,X19)
& apply(X12,X19,X18) ) )
& ( ! [X20] :
( ~ member(X20,X15)
| ~ apply(X13,X17,X20)
| ~ apply(X12,X20,X18) )
| apply(compose_function(X12,X13,X14,X15,X16),X17,X18) ) ) ),
inference(variable_rename,[status(thm)],[53]) ).
fof(55,plain,
! [X12,X13,X14,X15,X16,X17,X18] :
( ~ member(X17,X14)
| ~ member(X18,X16)
| ( ( ~ apply(compose_function(X12,X13,X14,X15,X16),X17,X18)
| ( member(esk9_7(X12,X13,X14,X15,X16,X17,X18),X15)
& apply(X13,X17,esk9_7(X12,X13,X14,X15,X16,X17,X18))
& apply(X12,esk9_7(X12,X13,X14,X15,X16,X17,X18),X18) ) )
& ( ! [X20] :
( ~ member(X20,X15)
| ~ apply(X13,X17,X20)
| ~ apply(X12,X20,X18) )
| apply(compose_function(X12,X13,X14,X15,X16),X17,X18) ) ) ),
inference(skolemize,[status(esa)],[54]) ).
fof(56,plain,
! [X12,X13,X14,X15,X16,X17,X18,X20] :
( ( ( ~ member(X20,X15)
| ~ apply(X13,X17,X20)
| ~ apply(X12,X20,X18)
| apply(compose_function(X12,X13,X14,X15,X16),X17,X18) )
& ( ~ apply(compose_function(X12,X13,X14,X15,X16),X17,X18)
| ( member(esk9_7(X12,X13,X14,X15,X16,X17,X18),X15)
& apply(X13,X17,esk9_7(X12,X13,X14,X15,X16,X17,X18))
& apply(X12,esk9_7(X12,X13,X14,X15,X16,X17,X18),X18) ) ) )
| ~ member(X17,X14)
| ~ member(X18,X16) ),
inference(shift_quantors,[status(thm)],[55]) ).
fof(57,plain,
! [X12,X13,X14,X15,X16,X17,X18,X20] :
( ( ~ member(X20,X15)
| ~ apply(X13,X17,X20)
| ~ apply(X12,X20,X18)
| apply(compose_function(X12,X13,X14,X15,X16),X17,X18)
| ~ member(X17,X14)
| ~ member(X18,X16) )
& ( member(esk9_7(X12,X13,X14,X15,X16,X17,X18),X15)
| ~ apply(compose_function(X12,X13,X14,X15,X16),X17,X18)
| ~ member(X17,X14)
| ~ member(X18,X16) )
& ( apply(X13,X17,esk9_7(X12,X13,X14,X15,X16,X17,X18))
| ~ apply(compose_function(X12,X13,X14,X15,X16),X17,X18)
| ~ member(X17,X14)
| ~ member(X18,X16) )
& ( apply(X12,esk9_7(X12,X13,X14,X15,X16,X17,X18),X18)
| ~ apply(compose_function(X12,X13,X14,X15,X16),X17,X18)
| ~ member(X17,X14)
| ~ member(X18,X16) ) ),
inference(distribute,[status(thm)],[56]) ).
cnf(58,plain,
( apply(X5,esk9_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)],[57]) ).
cnf(59,plain,
( apply(X6,X3,esk9_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)],[57]) ).
cnf(60,plain,
( member(esk9_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)],[57]) ).
cnf(61,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)],[57]) ).
fof(62,plain,
! [X1,X2,X3] :
( ( ~ injective(X1,X2,X3)
| ! [X12,X13,X4] :
( ~ member(X12,X2)
| ~ member(X13,X2)
| ~ member(X4,X3)
| ~ apply(X1,X12,X4)
| ~ apply(X1,X13,X4)
| X12 = X13 ) )
& ( ? [X12,X13,X4] :
( member(X12,X2)
& member(X13,X2)
& member(X4,X3)
& apply(X1,X12,X4)
& apply(X1,X13,X4)
& X12 != X13 )
| injective(X1,X2,X3) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(63,plain,
! [X14,X15,X16] :
( ( ~ injective(X14,X15,X16)
| ! [X17,X18,X19] :
( ~ member(X17,X15)
| ~ member(X18,X15)
| ~ member(X19,X16)
| ~ apply(X14,X17,X19)
| ~ apply(X14,X18,X19)
| X17 = X18 ) )
& ( ? [X20,X21,X22] :
( member(X20,X15)
& member(X21,X15)
& member(X22,X16)
& apply(X14,X20,X22)
& apply(X14,X21,X22)
& X20 != X21 )
| injective(X14,X15,X16) ) ),
inference(variable_rename,[status(thm)],[62]) ).
fof(64,plain,
! [X14,X15,X16] :
( ( ~ injective(X14,X15,X16)
| ! [X17,X18,X19] :
( ~ member(X17,X15)
| ~ member(X18,X15)
| ~ member(X19,X16)
| ~ apply(X14,X17,X19)
| ~ apply(X14,X18,X19)
| X17 = X18 ) )
& ( ( member(esk10_3(X14,X15,X16),X15)
& member(esk11_3(X14,X15,X16),X15)
& member(esk12_3(X14,X15,X16),X16)
& apply(X14,esk10_3(X14,X15,X16),esk12_3(X14,X15,X16))
& apply(X14,esk11_3(X14,X15,X16),esk12_3(X14,X15,X16))
& esk10_3(X14,X15,X16) != esk11_3(X14,X15,X16) )
| injective(X14,X15,X16) ) ),
inference(skolemize,[status(esa)],[63]) ).
fof(65,plain,
! [X14,X15,X16,X17,X18,X19] :
( ( ~ member(X17,X15)
| ~ member(X18,X15)
| ~ member(X19,X16)
| ~ apply(X14,X17,X19)
| ~ apply(X14,X18,X19)
| X17 = X18
| ~ injective(X14,X15,X16) )
& ( ( member(esk10_3(X14,X15,X16),X15)
& member(esk11_3(X14,X15,X16),X15)
& member(esk12_3(X14,X15,X16),X16)
& apply(X14,esk10_3(X14,X15,X16),esk12_3(X14,X15,X16))
& apply(X14,esk11_3(X14,X15,X16),esk12_3(X14,X15,X16))
& esk10_3(X14,X15,X16) != esk11_3(X14,X15,X16) )
| injective(X14,X15,X16) ) ),
inference(shift_quantors,[status(thm)],[64]) ).
fof(66,plain,
! [X14,X15,X16,X17,X18,X19] :
( ( ~ member(X17,X15)
| ~ member(X18,X15)
| ~ member(X19,X16)
| ~ apply(X14,X17,X19)
| ~ apply(X14,X18,X19)
| X17 = X18
| ~ injective(X14,X15,X16) )
& ( member(esk10_3(X14,X15,X16),X15)
| injective(X14,X15,X16) )
& ( member(esk11_3(X14,X15,X16),X15)
| injective(X14,X15,X16) )
& ( member(esk12_3(X14,X15,X16),X16)
| injective(X14,X15,X16) )
& ( apply(X14,esk10_3(X14,X15,X16),esk12_3(X14,X15,X16))
| injective(X14,X15,X16) )
& ( apply(X14,esk11_3(X14,X15,X16),esk12_3(X14,X15,X16))
| injective(X14,X15,X16) )
& ( esk10_3(X14,X15,X16) != esk11_3(X14,X15,X16)
| injective(X14,X15,X16) ) ),
inference(distribute,[status(thm)],[65]) ).
cnf(73,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)],[66]) ).
fof(74,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)],[7]) ).
fof(75,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)],[74]) ).
fof(76,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)],[75]) ).
cnf(77,plain,
( apply(X5,X3,X1)
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ apply(inverse_function(X5,X4,X2),X1,X3) ),
inference(split_conjunct,[status(thm)],[76]) ).
cnf(78,plain,
( apply(inverse_function(X5,X4,X2),X1,X3)
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ apply(X5,X3,X1) ),
inference(split_conjunct,[status(thm)],[76]) ).
fof(79,negated_conjecture,
? [X1,X2,X3] :
( maps(X1,X2,X3)
& one_to_one(X1,X2,X3)
& ~ identity(compose_function(X1,inverse_function(X1,X2,X3),X3,X2,X3),X3) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(80,negated_conjecture,
? [X4,X5,X6] :
( maps(X4,X5,X6)
& one_to_one(X4,X5,X6)
& ~ identity(compose_function(X4,inverse_function(X4,X5,X6),X6,X5,X6),X6) ),
inference(variable_rename,[status(thm)],[79]) ).
fof(81,negated_conjecture,
( maps(esk13_0,esk14_0,esk15_0)
& one_to_one(esk13_0,esk14_0,esk15_0)
& ~ identity(compose_function(esk13_0,inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,esk14_0,esk15_0),esk15_0) ),
inference(skolemize,[status(esa)],[80]) ).
cnf(82,negated_conjecture,
~ identity(compose_function(esk13_0,inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,esk14_0,esk15_0),esk15_0),
inference(split_conjunct,[status(thm)],[81]) ).
cnf(83,negated_conjecture,
one_to_one(esk13_0,esk14_0,esk15_0),
inference(split_conjunct,[status(thm)],[81]) ).
cnf(84,negated_conjecture,
maps(esk13_0,esk14_0,esk15_0),
inference(split_conjunct,[status(thm)],[81]) ).
cnf(85,negated_conjecture,
surjective(esk13_0,esk14_0,esk15_0),
inference(spm,[status(thm)],[23,83,theory(equality)]) ).
cnf(86,negated_conjecture,
injective(esk13_0,esk14_0,esk15_0),
inference(spm,[status(thm)],[24,83,theory(equality)]) ).
cnf(96,plain,
( apply(X1,X2,esk1_4(inverse_function(X1,X3,X4),X5,X6,X2))
| ~ member(X2,X3)
| ~ member(esk1_4(inverse_function(X1,X3,X4),X5,X6,X2),X4)
| ~ member(X2,X6)
| ~ surjective(inverse_function(X1,X3,X4),X5,X6) ),
inference(spm,[status(thm)],[77,15,theory(equality)]) ).
cnf(107,negated_conjecture,
( X1 = X2
| ~ apply(esk13_0,X3,X2)
| ~ apply(esk13_0,X3,X1)
| ~ member(X3,esk14_0)
| ~ member(X2,esk15_0)
| ~ member(X1,esk15_0) ),
inference(spm,[status(thm)],[32,84,theory(equality)]) ).
cnf(119,plain,
( surjective(X1,X2,X3)
| ~ member(esk9_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)],[18,58,theory(equality)]) ).
cnf(120,plain,
( apply(X1,X2,esk9_7(inverse_function(X1,X3,X4),X5,X6,X7,X8,X9,X2))
| ~ member(X2,X3)
| ~ member(esk9_7(inverse_function(X1,X3,X4),X5,X6,X7,X8,X9,X2),X4)
| ~ apply(compose_function(inverse_function(X1,X3,X4),X5,X6,X7,X8),X9,X2)
| ~ member(X9,X6)
| ~ member(X2,X8) ),
inference(spm,[status(thm)],[77,58,theory(equality)]) ).
cnf(121,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)],[61,30,theory(equality)]) ).
cnf(123,plain,
( apply(compose_function(X1,inverse_function(X2,X3,X4),X5,X6,X7),X8,X9)
| ~ apply(X1,X10,X9)
| ~ member(X10,X6)
| ~ member(X8,X5)
| ~ member(X9,X7)
| ~ apply(X2,X10,X8)
| ~ member(X10,X3)
| ~ member(X8,X4) ),
inference(spm,[status(thm)],[61,78,theory(equality)]) ).
cnf(130,negated_conjecture,
( X1 = X2
| ~ apply(esk13_0,X2,X3)
| ~ apply(esk13_0,X1,X3)
| ~ member(X3,esk15_0)
| ~ member(X2,esk14_0)
| ~ member(X1,esk14_0) ),
inference(spm,[status(thm)],[73,86,theory(equality)]) ).
cnf(131,negated_conjecture,
( X1 = esk3_4(esk13_0,X2,X3,X4)
| ~ apply(esk13_0,X4,X1)
| ~ member(X4,esk14_0)
| ~ member(esk3_4(esk13_0,X2,X3,X4),esk15_0)
| ~ member(X1,esk15_0)
| ~ maps(esk13_0,X2,X3)
| ~ member(X4,X2) ),
inference(spm,[status(thm)],[107,30,theory(equality)]) ).
cnf(134,negated_conjecture,
( X1 = X2
| ~ apply(esk13_0,esk1_4(esk13_0,X3,X4,X2),X1)
| ~ member(esk1_4(esk13_0,X3,X4,X2),esk14_0)
| ~ member(X2,esk15_0)
| ~ member(X1,esk15_0)
| ~ member(X2,X4)
| ~ surjective(esk13_0,X3,X4) ),
inference(spm,[status(thm)],[107,15,theory(equality)]) ).
cnf(143,negated_conjecture,
( X1 = esk1_4(esk13_0,X2,X3,X4)
| ~ apply(esk13_0,X1,X4)
| ~ member(X4,esk15_0)
| ~ member(esk1_4(esk13_0,X2,X3,X4),esk14_0)
| ~ member(X1,esk14_0)
| ~ member(X4,X3)
| ~ surjective(esk13_0,X2,X3) ),
inference(spm,[status(thm)],[130,15,theory(equality)]) ).
cnf(147,negated_conjecture,
( X1 = esk9_7(esk13_0,X2,X3,X4,X5,X6,X7)
| ~ apply(esk13_0,X1,X7)
| ~ member(X7,esk15_0)
| ~ member(esk9_7(esk13_0,X2,X3,X4,X5,X6,X7),esk14_0)
| ~ member(X1,esk14_0)
| ~ apply(compose_function(esk13_0,X2,X3,X4,X5),X6,X7)
| ~ member(X6,X3)
| ~ member(X7,X5) ),
inference(spm,[status(thm)],[130,58,theory(equality)]) ).
cnf(193,negated_conjecture,
( X1 = esk3_4(esk13_0,X2,esk15_0,X3)
| ~ maps(esk13_0,X2,esk15_0)
| ~ apply(esk13_0,X3,X1)
| ~ member(X3,esk14_0)
| ~ member(X1,esk15_0)
| ~ member(X3,X2) ),
inference(spm,[status(thm)],[131,31,theory(equality)]) ).
cnf(194,negated_conjecture,
( esk3_4(esk13_0,X1,X2,X3) = esk3_4(esk13_0,X4,esk15_0,X3)
| ~ maps(esk13_0,X4,esk15_0)
| ~ member(X3,esk14_0)
| ~ member(esk3_4(esk13_0,X1,X2,X3),esk15_0)
| ~ member(X3,X4)
| ~ maps(esk13_0,X1,X2)
| ~ member(X3,X1) ),
inference(spm,[status(thm)],[193,30,theory(equality)]) ).
cnf(203,negated_conjecture,
( X1 = esk1_4(esk13_0,esk14_0,X2,X3)
| ~ apply(esk13_0,X1,X3)
| ~ member(X3,esk15_0)
| ~ member(X1,esk14_0)
| ~ member(X3,X2)
| ~ surjective(esk13_0,esk14_0,X2) ),
inference(spm,[status(thm)],[143,16,theory(equality)]) ).
cnf(212,negated_conjecture,
( esk1_4(esk13_0,X1,X2,X3) = esk1_4(esk13_0,esk14_0,X4,X3)
| ~ member(X3,esk15_0)
| ~ member(esk1_4(esk13_0,X1,X2,X3),esk14_0)
| ~ member(X3,X4)
| ~ surjective(esk13_0,esk14_0,X4)
| ~ member(X3,X2)
| ~ surjective(esk13_0,X1,X2) ),
inference(spm,[status(thm)],[203,15,theory(equality)]) ).
cnf(219,negated_conjecture,
( esk3_4(esk13_0,X1,esk15_0,X2) = esk3_4(esk13_0,X3,esk15_0,X2)
| ~ maps(esk13_0,X3,esk15_0)
| ~ maps(esk13_0,X1,esk15_0)
| ~ member(X2,esk14_0)
| ~ member(X2,X3)
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[194,31,theory(equality)]) ).
cnf(254,plain,
( apply(X1,X2,esk1_4(inverse_function(X1,X3,X4),X4,X5,X2))
| ~ member(X2,X3)
| ~ member(X2,X5)
| ~ surjective(inverse_function(X1,X3,X4),X4,X5) ),
inference(spm,[status(thm)],[96,16,theory(equality)]) ).
cnf(261,plain,
( apply(X1,esk1_4(inverse_function(inverse_function(X1,X2,X3),X4,X5),X5,X6,X7),X7)
| ~ member(esk1_4(inverse_function(inverse_function(X1,X2,X3),X4,X5),X5,X6,X7),X2)
| ~ member(X7,X3)
| ~ member(X7,X4)
| ~ member(X7,X6)
| ~ surjective(inverse_function(inverse_function(X1,X2,X3),X4,X5),X5,X6) ),
inference(spm,[status(thm)],[77,254,theory(equality)]) ).
cnf(268,plain,
( apply(compose_function(X1,X2,X3,X4,X5),X6,X7)
| ~ apply(X1,esk1_4(inverse_function(X2,X8,X9),X9,X10,X6),X7)
| ~ member(esk1_4(inverse_function(X2,X8,X9),X9,X10,X6),X4)
| ~ member(X6,X3)
| ~ member(X7,X5)
| ~ member(X6,X8)
| ~ member(X6,X10)
| ~ surjective(inverse_function(X2,X8,X9),X9,X10) ),
inference(spm,[status(thm)],[61,254,theory(equality)]) ).
cnf(269,negated_conjecture,
( X1 = esk1_4(inverse_function(esk13_0,X2,X3),X3,X4,X5)
| ~ apply(esk13_0,X5,X1)
| ~ member(X5,esk14_0)
| ~ member(esk1_4(inverse_function(esk13_0,X2,X3),X3,X4,X5),esk15_0)
| ~ member(X1,esk15_0)
| ~ member(X5,X2)
| ~ member(X5,X4)
| ~ surjective(inverse_function(esk13_0,X2,X3),X3,X4) ),
inference(spm,[status(thm)],[107,254,theory(equality)]) ).
cnf(355,negated_conjecture,
( esk1_4(esk13_0,esk14_0,X1,X2) = esk1_4(esk13_0,esk14_0,X3,X2)
| ~ member(X2,esk15_0)
| ~ member(X2,X3)
| ~ member(X2,X1)
| ~ surjective(esk13_0,esk14_0,X3)
| ~ surjective(esk13_0,esk14_0,X1) ),
inference(spm,[status(thm)],[212,16,theory(equality)]) ).
cnf(363,negated_conjecture,
( X1 = X2
| ~ apply(esk13_0,esk1_4(esk13_0,esk14_0,X4,X2),X1)
| ~ member(esk1_4(esk13_0,esk14_0,X4,X2),esk14_0)
| ~ member(X2,esk15_0)
| ~ member(X1,esk15_0)
| ~ member(X2,X3)
| ~ surjective(esk13_0,esk14_0,X3)
| ~ member(X2,X4)
| ~ surjective(esk13_0,esk14_0,X4) ),
inference(spm,[status(thm)],[134,355,theory(equality)]) ).
cnf(420,plain,
( apply(compose_function(X1,inverse_function(X2,X3,X4),X5,X6,X7),X8,X9)
| ~ apply(X2,esk1_4(X1,X10,X11,X9),X8)
| ~ member(esk1_4(X1,X10,X11,X9),X6)
| ~ member(X8,X5)
| ~ member(X9,X7)
| ~ member(esk1_4(X1,X10,X11,X9),X3)
| ~ member(X8,X4)
| ~ member(X9,X11)
| ~ surjective(X1,X10,X11) ),
inference(spm,[status(thm)],[123,15,theory(equality)]) ).
cnf(484,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)],[119,60,theory(equality)]) ).
cnf(524,negated_conjecture,
( X1 = X2
| ~ apply(esk13_0,esk1_4(esk13_0,esk14_0,X4,X2),X1)
| ~ member(esk1_4(esk13_0,esk14_0,X4,X2),esk14_0)
| ~ member(X2,esk15_0)
| ~ member(X1,esk15_0)
| ~ member(X2,X4)
| ~ member(X2,X3)
| ~ surjective(esk13_0,esk14_0,X4) ),
inference(csr,[status(thm)],[363,134]) ).
cnf(525,negated_conjecture,
( X1 = X2
| ~ apply(esk13_0,esk1_4(esk13_0,esk14_0,X4,X2),X1)
| ~ member(esk1_4(esk13_0,esk14_0,X4,X2),esk14_0)
| ~ member(X2,esk15_0)
| ~ member(X1,esk15_0)
| ~ member(X2,X4)
| ~ surjective(esk13_0,esk14_0,X4) ),
inference(csr,[status(thm)],[524,134]) ).
cnf(526,negated_conjecture,
( X1 = X2
| ~ apply(esk13_0,esk1_4(esk13_0,esk14_0,X4,X2),X1)
| ~ member(X2,esk15_0)
| ~ member(X1,esk15_0)
| ~ member(X2,X4)
| ~ surjective(esk13_0,esk14_0,X4) ),
inference(csr,[status(thm)],[525,16]) ).
cnf(527,negated_conjecture,
( esk3_4(esk13_0,X1,X2,esk1_4(esk13_0,esk14_0,X3,X4)) = X4
| ~ member(X4,esk15_0)
| ~ member(esk3_4(esk13_0,X1,X2,esk1_4(esk13_0,esk14_0,X3,X4)),esk15_0)
| ~ member(X4,X3)
| ~ surjective(esk13_0,esk14_0,X3)
| ~ maps(esk13_0,X1,X2)
| ~ member(esk1_4(esk13_0,esk14_0,X3,X4),X1) ),
inference(spm,[status(thm)],[526,30,theory(equality)]) ).
cnf(564,negated_conjecture,
( esk3_4(esk13_0,X1,esk15_0,esk1_4(esk13_0,esk14_0,X2,X3)) = X3
| ~ maps(esk13_0,X1,esk15_0)
| ~ member(esk1_4(esk13_0,esk14_0,X2,X3),X1)
| ~ member(X3,esk15_0)
| ~ member(X3,X2)
| ~ surjective(esk13_0,esk14_0,X2) ),
inference(spm,[status(thm)],[527,31,theory(equality)]) ).
cnf(836,plain,
( apply(X1,X2,esk9_7(inverse_function(X1,X3,X4),X5,X6,X4,X7,X8,X2))
| ~ apply(compose_function(inverse_function(X1,X3,X4),X5,X6,X4,X7),X8,X2)
| ~ member(X2,X3)
| ~ member(X8,X6)
| ~ member(X2,X7) ),
inference(spm,[status(thm)],[120,60,theory(equality)]) ).
cnf(857,negated_conjecture,
( esk9_7(inverse_function(esk13_0,X1,X2),X3,X4,X2,X5,X6,esk1_4(esk13_0,esk14_0,X7,X8)) = X8
| ~ member(X8,esk15_0)
| ~ member(esk9_7(inverse_function(esk13_0,X1,X2),X3,X4,X2,X5,X6,esk1_4(esk13_0,esk14_0,X7,X8)),esk15_0)
| ~ member(X8,X7)
| ~ surjective(esk13_0,esk14_0,X7)
| ~ apply(compose_function(inverse_function(esk13_0,X1,X2),X3,X4,X2,X5),X6,esk1_4(esk13_0,esk14_0,X7,X8))
| ~ member(esk1_4(esk13_0,esk14_0,X7,X8),X1)
| ~ member(X6,X4)
| ~ member(esk1_4(esk13_0,esk14_0,X7,X8),X5) ),
inference(spm,[status(thm)],[526,836,theory(equality)]) ).
cnf(1150,negated_conjecture,
( X1 = esk1_4(inverse_function(esk13_0,X2,esk15_0),esk15_0,X3,X4)
| ~ apply(esk13_0,X4,X1)
| ~ member(X4,esk14_0)
| ~ member(X1,esk15_0)
| ~ member(X4,X2)
| ~ member(X4,X3)
| ~ surjective(inverse_function(esk13_0,X2,esk15_0),esk15_0,X3) ),
inference(spm,[status(thm)],[269,16,theory(equality)]) ).
cnf(1151,negated_conjecture,
( esk3_4(esk13_0,X1,X2,X3) = esk1_4(inverse_function(esk13_0,X4,esk15_0),esk15_0,X5,X3)
| ~ member(X3,esk14_0)
| ~ member(esk3_4(esk13_0,X1,X2,X3),esk15_0)
| ~ member(X3,X4)
| ~ member(X3,X5)
| ~ surjective(inverse_function(esk13_0,X4,esk15_0),esk15_0,X5)
| ~ maps(esk13_0,X1,X2)
| ~ member(X3,X1) ),
inference(spm,[status(thm)],[1150,30,theory(equality)]) ).
cnf(1167,negated_conjecture,
( esk3_4(esk13_0,X1,esk15_0,X2) = esk1_4(inverse_function(esk13_0,X3,esk15_0),esk15_0,X4,X2)
| ~ maps(esk13_0,X1,esk15_0)
| ~ member(X2,esk14_0)
| ~ member(X2,X3)
| ~ member(X2,X4)
| ~ member(X2,X1)
| ~ surjective(inverse_function(esk13_0,X3,esk15_0),esk15_0,X4) ),
inference(spm,[status(thm)],[1151,31,theory(equality)]) ).
cnf(1179,negated_conjecture,
( apply(inverse_function(esk13_0,X1,esk15_0),esk3_4(esk13_0,X4,esk15_0,X3),X3)
| ~ member(X3,X2)
| ~ surjective(inverse_function(esk13_0,X1,esk15_0),esk15_0,X2)
| ~ maps(esk13_0,X4,esk15_0)
| ~ member(X3,esk14_0)
| ~ member(X3,X1)
| ~ member(X3,X4) ),
inference(spm,[status(thm)],[15,1167,theory(equality)]) ).
cnf(1231,negated_conjecture,
( X1 = esk9_7(esk13_0,X2,X3,esk14_0,X4,X5,X6)
| ~ apply(compose_function(esk13_0,X2,X3,esk14_0,X4),X5,X6)
| ~ apply(esk13_0,X1,X6)
| ~ member(X6,esk15_0)
| ~ member(X1,esk14_0)
| ~ member(X5,X3)
| ~ member(X6,X4) ),
inference(spm,[status(thm)],[147,60,theory(equality)]) ).
cnf(1232,negated_conjecture,
( X1 = esk9_7(esk13_0,X2,X3,esk14_0,X4,X5,esk3_4(esk13_0,X6,X7,X1))
| ~ apply(compose_function(esk13_0,X2,X3,esk14_0,X4),X5,esk3_4(esk13_0,X6,X7,X1))
| ~ member(esk3_4(esk13_0,X6,X7,X1),esk15_0)
| ~ member(X1,esk14_0)
| ~ member(X5,X3)
| ~ member(esk3_4(esk13_0,X6,X7,X1),X4)
| ~ maps(esk13_0,X6,X7)
| ~ member(X1,X6) ),
inference(spm,[status(thm)],[1231,30,theory(equality)]) ).
cnf(2790,plain,
( apply(X1,esk1_4(inverse_function(inverse_function(X1,X2,X3),X4,X2),X2,X5,X6),X6)
| ~ member(X6,X3)
| ~ member(X6,X4)
| ~ member(X6,X5)
| ~ surjective(inverse_function(inverse_function(X1,X2,X3),X4,X2),X2,X5) ),
inference(spm,[status(thm)],[261,16,theory(equality)]) ).
cnf(2916,negated_conjecture,
( apply(X1,X2,X7)
| ~ apply(compose_function(esk13_0,X1,X3,esk14_0,X4),X2,esk3_4(esk13_0,X5,X6,X7))
| ~ member(X2,X3)
| ~ member(esk3_4(esk13_0,X5,X6,X7),X4)
| ~ maps(esk13_0,X5,X6)
| ~ member(esk3_4(esk13_0,X5,X6,X7),esk15_0)
| ~ member(X7,esk14_0)
| ~ member(X7,X5) ),
inference(spm,[status(thm)],[59,1232,theory(equality)]) ).
cnf(3250,plain,
( apply(compose_function(X1,inverse_function(X1,X2,X3),X4,X5,X6),X7,X7)
| ~ member(esk1_4(inverse_function(inverse_function(X1,X2,X3),X8,X2),X2,X9,X7),X5)
| ~ member(X7,X4)
| ~ member(X7,X6)
| ~ member(X7,X8)
| ~ member(X7,X9)
| ~ surjective(inverse_function(inverse_function(X1,X2,X3),X8,X2),X2,X9)
| ~ member(X7,X3) ),
inference(spm,[status(thm)],[268,2790,theory(equality)]) ).
cnf(4775,plain,
( apply(compose_function(X1,inverse_function(X1,X2,X3),X4,X2,X5),X6,X6)
| ~ member(X6,X4)
| ~ member(X6,X5)
| ~ member(X6,X7)
| ~ member(X6,X8)
| ~ member(X6,X3)
| ~ surjective(inverse_function(inverse_function(X1,X2,X3),X7,X2),X2,X8) ),
inference(spm,[status(thm)],[3250,16,theory(equality)]) ).
cnf(5199,plain,
( apply(compose_function(X1,inverse_function(X1,X2,X3),X4,X5,X6),X7,X7)
| ~ member(esk1_4(X1,X8,X9,X7),X5)
| ~ member(esk1_4(X1,X8,X9,X7),X2)
| ~ member(X7,X4)
| ~ member(X7,X6)
| ~ member(X7,X3)
| ~ member(X7,X9)
| ~ surjective(X1,X8,X9) ),
inference(spm,[status(thm)],[420,15,theory(equality)]) ).
cnf(5237,plain,
( apply(compose_function(X1,inverse_function(X1,X2,X3),X4,X5,X6),X7,X7)
| ~ member(esk1_4(X1,X5,X8,X7),X2)
| ~ member(X7,X4)
| ~ member(X7,X6)
| ~ member(X7,X3)
| ~ member(X7,X8)
| ~ surjective(X1,X5,X8) ),
inference(spm,[status(thm)],[5199,16,theory(equality)]) ).
cnf(5258,plain,
( apply(compose_function(X1,inverse_function(X1,X2,X3),X4,X2,X5),X6,X6)
| ~ member(X6,X4)
| ~ member(X6,X5)
| ~ member(X6,X3)
| ~ member(X6,X7)
| ~ surjective(X1,X2,X7) ),
inference(spm,[status(thm)],[5237,16,theory(equality)]) ).
cnf(5279,negated_conjecture,
( apply(compose_function(esk13_0,inverse_function(esk13_0,esk14_0,X1),X2,esk14_0,X3),X4,X4)
| ~ member(X4,X2)
| ~ member(X4,X3)
| ~ member(X4,X1)
| ~ member(X4,esk15_0) ),
inference(spm,[status(thm)],[5258,85,theory(equality)]) ).
cnf(5316,negated_conjecture,
( apply(inverse_function(esk13_0,esk14_0,X1),esk3_4(esk13_0,X2,X3,X4),X4)
| ~ maps(esk13_0,X2,X3)
| ~ member(esk3_4(esk13_0,X2,X3,X4),esk15_0)
| ~ member(esk3_4(esk13_0,X2,X3,X4),X6)
| ~ member(X4,esk14_0)
| ~ member(esk3_4(esk13_0,X2,X3,X4),X5)
| ~ member(X4,X2)
| ~ member(esk3_4(esk13_0,X2,X3,X4),X1) ),
inference(spm,[status(thm)],[2916,5279,theory(equality)]) ).
cnf(6804,negated_conjecture,
( apply(inverse_function(esk13_0,esk14_0,X1),esk3_4(esk13_0,X2,X3,X4),X4)
| ~ maps(esk13_0,X2,X3)
| ~ member(esk3_4(esk13_0,X2,X3,X4),esk15_0)
| ~ member(esk3_4(esk13_0,X2,X3,X4),X5)
| ~ member(esk3_4(esk13_0,X2,X3,X4),X1)
| ~ member(X4,esk14_0)
| ~ member(X4,X2) ),
inference(spm,[status(thm)],[5316,31,theory(equality)]) ).
cnf(6819,negated_conjecture,
( apply(inverse_function(esk13_0,esk14_0,X1),esk3_4(esk13_0,X2,X3,X4),X4)
| ~ maps(esk13_0,X2,X3)
| ~ member(esk3_4(esk13_0,X2,X3,X4),esk15_0)
| ~ member(esk3_4(esk13_0,X2,X3,X4),X1)
| ~ member(X4,esk14_0)
| ~ member(X4,X2) ),
inference(spm,[status(thm)],[6804,31,theory(equality)]) ).
cnf(6837,negated_conjecture,
( apply(inverse_function(esk13_0,esk14_0,X1),esk3_4(esk13_0,X4,esk15_0,X3),X3)
| ~ maps(esk13_0,X2,esk15_0)
| ~ member(esk3_4(esk13_0,X4,esk15_0,X3),esk15_0)
| ~ member(esk3_4(esk13_0,X4,esk15_0,X3),X1)
| ~ member(X3,esk14_0)
| ~ member(X3,X2)
| ~ maps(esk13_0,X4,esk15_0)
| ~ member(X3,X4) ),
inference(spm,[status(thm)],[6819,219,theory(equality)]) ).
cnf(6872,negated_conjecture,
( apply(inverse_function(esk13_0,esk14_0,X1),esk3_4(esk13_0,X4,esk15_0,X3),X3)
| ~ maps(esk13_0,X4,esk15_0)
| ~ maps(esk13_0,X2,esk15_0)
| ~ member(esk3_4(esk13_0,X4,esk15_0,X3),esk15_0)
| ~ member(esk3_4(esk13_0,X4,esk15_0,X3),X1)
| ~ member(X3,esk14_0)
| ~ member(X3,X4) ),
inference(csr,[status(thm)],[6837,6819]) ).
cnf(6873,negated_conjecture,
( apply(inverse_function(esk13_0,esk14_0,X1),esk3_4(esk13_0,X4,esk15_0,X3),X3)
| ~ maps(esk13_0,X4,esk15_0)
| ~ maps(esk13_0,X2,esk15_0)
| ~ member(esk3_4(esk13_0,X4,esk15_0,X3),X1)
| ~ member(X3,esk14_0)
| ~ member(X3,X4) ),
inference(csr,[status(thm)],[6872,31]) ).
cnf(6874,negated_conjecture,
( apply(inverse_function(esk13_0,esk14_0,X1),esk3_4(esk13_0,X2,esk15_0,X3),X3)
| ~ maps(esk13_0,X2,esk15_0)
| ~ member(esk3_4(esk13_0,X2,esk15_0,X3),X1)
| ~ member(X3,esk14_0)
| ~ member(X3,X2) ),
inference(spm,[status(thm)],[6873,84,theory(equality)]) ).
cnf(6895,negated_conjecture,
( apply(compose_function(inverse_function(esk13_0,esk14_0,X1),esk13_0,X2,X3,X4),X5,X5)
| ~ maps(esk13_0,X6,esk15_0)
| ~ member(esk3_4(esk13_0,X6,esk15_0,X5),X3)
| ~ member(X5,X2)
| ~ member(X5,X4)
| ~ member(X5,X6)
| ~ member(esk3_4(esk13_0,X6,esk15_0,X5),X1)
| ~ member(X5,esk14_0) ),
inference(spm,[status(thm)],[121,6874,theory(equality)]) ).
cnf(7230,negated_conjecture,
( apply(compose_function(inverse_function(esk13_0,esk14_0,X1),esk13_0,X2,esk15_0,X3),X4,X4)
| ~ maps(esk13_0,X5,esk15_0)
| ~ member(esk3_4(esk13_0,X5,esk15_0,X4),X1)
| ~ member(X4,esk14_0)
| ~ member(X4,X2)
| ~ member(X4,X3)
| ~ member(X4,X5) ),
inference(spm,[status(thm)],[6895,31,theory(equality)]) ).
cnf(7250,negated_conjecture,
( apply(compose_function(inverse_function(esk13_0,esk14_0,esk15_0),esk13_0,X1,esk15_0,X2),X3,X3)
| ~ maps(esk13_0,X4,esk15_0)
| ~ member(X3,esk14_0)
| ~ member(X3,X1)
| ~ member(X3,X2)
| ~ member(X3,X4) ),
inference(spm,[status(thm)],[7230,31,theory(equality)]) ).
cnf(7265,negated_conjecture,
( apply(compose_function(inverse_function(esk13_0,esk14_0,esk15_0),esk13_0,X1,esk15_0,X2),X3,X3)
| ~ member(X3,esk14_0)
| ~ member(X3,X1)
| ~ member(X3,X2) ),
inference(spm,[status(thm)],[7250,84,theory(equality)]) ).
cnf(7281,negated_conjecture,
( surjective(inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,X1)
| ~ member(esk2_3(inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,X1),X3)
| ~ member(esk2_3(inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,X1),X2)
| ~ member(esk2_3(inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,X1),esk14_0) ),
inference(spm,[status(thm)],[484,7265,theory(equality)]) ).
cnf(7434,negated_conjecture,
( surjective(inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,esk14_0)
| ~ member(esk2_3(inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,esk14_0),X1)
| ~ member(esk2_3(inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,esk14_0),X2) ),
inference(spm,[status(thm)],[7281,17,theory(equality)]) ).
cnf(7435,negated_conjecture,
( surjective(inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,esk14_0)
| ~ member(esk2_3(inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,esk14_0),X1) ),
inference(spm,[status(thm)],[7434,17,theory(equality)]) ).
cnf(7436,negated_conjecture,
surjective(inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,esk14_0),
inference(spm,[status(thm)],[7435,17,theory(equality)]) ).
cnf(7441,negated_conjecture,
( apply(inverse_function(esk13_0,esk14_0,esk15_0),esk3_4(esk13_0,X1,esk15_0,X2),X2)
| ~ maps(esk13_0,X1,esk15_0)
| ~ member(X2,esk14_0)
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[1179,7436,theory(equality)]) ).
cnf(7446,negated_conjecture,
( apply(compose_function(inverse_function(esk13_0,esk14_0,esk15_0),inverse_function(inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,X1),X2,esk15_0,X3),X4,X4)
| ~ member(X4,X2)
| ~ member(X4,X3)
| ~ member(X4,X1)
| ~ member(X4,esk14_0) ),
inference(spm,[status(thm)],[5258,7436,theory(equality)]) ).
cnf(7521,negated_conjecture,
( apply(inverse_function(esk13_0,esk14_0,esk15_0),X3,esk1_4(esk13_0,esk14_0,X2,X3))
| ~ maps(esk13_0,X1,esk15_0)
| ~ member(esk1_4(esk13_0,esk14_0,X2,X3),esk14_0)
| ~ member(esk1_4(esk13_0,esk14_0,X2,X3),X1)
| ~ member(X3,esk15_0)
| ~ member(X3,X2)
| ~ surjective(esk13_0,esk14_0,X2) ),
inference(spm,[status(thm)],[7441,564,theory(equality)]) ).
cnf(7847,negated_conjecture,
( apply(inverse_function(esk13_0,esk14_0,esk15_0),X3,esk1_4(esk13_0,esk14_0,X2,X3))
| ~ maps(esk13_0,X1,esk15_0)
| ~ member(esk1_4(esk13_0,esk14_0,X2,X3),X1)
| ~ member(X3,esk15_0)
| ~ member(X3,X2)
| ~ surjective(esk13_0,esk14_0,X2) ),
inference(csr,[status(thm)],[7521,16]) ).
cnf(7848,negated_conjecture,
( apply(inverse_function(esk13_0,esk14_0,esk15_0),X1,esk1_4(esk13_0,esk14_0,X2,X1))
| ~ maps(esk13_0,esk14_0,esk15_0)
| ~ member(X1,esk15_0)
| ~ member(X1,X2)
| ~ surjective(esk13_0,esk14_0,X2) ),
inference(spm,[status(thm)],[7847,16,theory(equality)]) ).
cnf(7863,negated_conjecture,
( apply(inverse_function(esk13_0,esk14_0,esk15_0),X1,esk1_4(esk13_0,esk14_0,X2,X1))
| $false
| ~ member(X1,esk15_0)
| ~ member(X1,X2)
| ~ surjective(esk13_0,esk14_0,X2) ),
inference(rw,[status(thm)],[7848,84,theory(equality)]) ).
cnf(7864,negated_conjecture,
( apply(inverse_function(esk13_0,esk14_0,esk15_0),X1,esk1_4(esk13_0,esk14_0,X2,X1))
| ~ member(X1,esk15_0)
| ~ member(X1,X2)
| ~ surjective(esk13_0,esk14_0,X2) ),
inference(cn,[status(thm)],[7863,theory(equality)]) ).
cnf(7872,negated_conjecture,
( apply(compose_function(X1,inverse_function(esk13_0,esk14_0,esk15_0),X2,X3,X4),X5,X6)
| ~ apply(X1,esk1_4(esk13_0,esk14_0,X7,X5),X6)
| ~ member(esk1_4(esk13_0,esk14_0,X7,X5),X3)
| ~ member(X5,X2)
| ~ member(X6,X4)
| ~ member(X5,esk15_0)
| ~ member(X5,X7)
| ~ surjective(esk13_0,esk14_0,X7) ),
inference(spm,[status(thm)],[61,7864,theory(equality)]) ).
cnf(23418,negated_conjecture,
( esk9_7(inverse_function(esk13_0,X1,esk15_0),X2,X3,esk15_0,X4,X5,esk1_4(esk13_0,esk14_0,X6,X7)) = X7
| ~ apply(compose_function(inverse_function(esk13_0,X1,esk15_0),X2,X3,esk15_0,X4),X5,esk1_4(esk13_0,esk14_0,X6,X7))
| ~ member(esk1_4(esk13_0,esk14_0,X6,X7),X1)
| ~ member(esk1_4(esk13_0,esk14_0,X6,X7),X4)
| ~ member(X7,esk15_0)
| ~ member(X7,X6)
| ~ member(X5,X3)
| ~ surjective(esk13_0,esk14_0,X6) ),
inference(spm,[status(thm)],[857,60,theory(equality)]) ).
cnf(44535,negated_conjecture,
( apply(X1,X2,X7)
| ~ apply(compose_function(inverse_function(esk13_0,X3,esk15_0),X1,X4,esk15_0,X5),X2,esk1_4(esk13_0,esk14_0,X6,X7))
| ~ member(X2,X4)
| ~ member(esk1_4(esk13_0,esk14_0,X6,X7),X5)
| ~ member(esk1_4(esk13_0,esk14_0,X6,X7),X3)
| ~ member(X7,esk15_0)
| ~ member(X7,X6)
| ~ surjective(esk13_0,esk14_0,X6) ),
inference(spm,[status(thm)],[59,23418,theory(equality)]) ).
cnf(44712,negated_conjecture,
( apply(inverse_function(inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,X1),esk1_4(esk13_0,esk14_0,X2,X3),X3)
| ~ member(esk1_4(esk13_0,esk14_0,X2,X3),X5)
| ~ member(esk1_4(esk13_0,esk14_0,X2,X3),esk14_0)
| ~ member(X3,esk15_0)
| ~ member(esk1_4(esk13_0,esk14_0,X2,X3),X4)
| ~ member(X3,X2)
| ~ surjective(esk13_0,esk14_0,X2)
| ~ member(esk1_4(esk13_0,esk14_0,X2,X3),X1) ),
inference(spm,[status(thm)],[44535,7446,theory(equality)]) ).
cnf(70199,negated_conjecture,
( apply(inverse_function(inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,X1),esk1_4(esk13_0,esk14_0,X2,X3),X3)
| ~ member(esk1_4(esk13_0,esk14_0,X2,X3),X4)
| ~ member(esk1_4(esk13_0,esk14_0,X2,X3),X1)
| ~ member(esk1_4(esk13_0,esk14_0,X2,X3),X5)
| ~ member(X3,esk15_0)
| ~ member(X3,X2)
| ~ surjective(esk13_0,esk14_0,X2) ),
inference(csr,[status(thm)],[44712,16]) ).
cnf(70200,negated_conjecture,
( apply(inverse_function(inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,X1),esk1_4(esk13_0,esk14_0,X2,X3),X3)
| ~ member(esk1_4(esk13_0,esk14_0,X2,X3),X4)
| ~ member(esk1_4(esk13_0,esk14_0,X2,X3),X1)
| ~ member(X3,esk15_0)
| ~ member(X3,X2)
| ~ surjective(esk13_0,esk14_0,X2) ),
inference(spm,[status(thm)],[70199,16,theory(equality)]) ).
cnf(70219,negated_conjecture,
( apply(inverse_function(inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,X1),esk1_4(esk13_0,esk14_0,X2,X3),X3)
| ~ member(esk1_4(esk13_0,esk14_0,X2,X3),X1)
| ~ member(X3,esk15_0)
| ~ member(X3,X2)
| ~ surjective(esk13_0,esk14_0,X2) ),
inference(spm,[status(thm)],[70200,16,theory(equality)]) ).
cnf(70274,negated_conjecture,
( apply(compose_function(inverse_function(inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,X1),inverse_function(esk13_0,esk14_0,esk15_0),X2,X3,X4),X5,X5)
| ~ member(esk1_4(esk13_0,esk14_0,X6,X5),X3)
| ~ member(X5,esk15_0)
| ~ member(X5,X2)
| ~ member(X5,X4)
| ~ member(X5,X6)
| ~ surjective(esk13_0,esk14_0,X6)
| ~ member(esk1_4(esk13_0,esk14_0,X6,X5),X1) ),
inference(spm,[status(thm)],[7872,70219,theory(equality)]) ).
cnf(72032,negated_conjecture,
( apply(compose_function(inverse_function(inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,X1),inverse_function(esk13_0,esk14_0,esk15_0),X2,esk14_0,X3),X4,X4)
| ~ member(esk1_4(esk13_0,esk14_0,X5,X4),X1)
| ~ member(X4,esk15_0)
| ~ member(X4,X2)
| ~ member(X4,X3)
| ~ member(X4,X5)
| ~ surjective(esk13_0,esk14_0,X5) ),
inference(spm,[status(thm)],[70274,16,theory(equality)]) ).
cnf(72053,negated_conjecture,
( apply(compose_function(inverse_function(inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,esk14_0),inverse_function(esk13_0,esk14_0,esk15_0),X1,esk14_0,X2),X3,X3)
| ~ member(X3,esk15_0)
| ~ member(X3,X1)
| ~ member(X3,X2)
| ~ member(X3,X4)
| ~ surjective(esk13_0,esk14_0,X4) ),
inference(spm,[status(thm)],[72032,16,theory(equality)]) ).
cnf(72072,negated_conjecture,
( apply(compose_function(inverse_function(inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,esk14_0),inverse_function(esk13_0,esk14_0,esk15_0),X1,esk14_0,X2),X3,X3)
| ~ member(X3,esk15_0)
| ~ member(X3,X1)
| ~ member(X3,X2) ),
inference(spm,[status(thm)],[72053,85,theory(equality)]) ).
cnf(72088,negated_conjecture,
( surjective(inverse_function(inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,esk14_0),esk14_0,X1)
| ~ member(esk2_3(inverse_function(inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,esk14_0),esk14_0,X1),X3)
| ~ member(esk2_3(inverse_function(inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,esk14_0),esk14_0,X1),X2)
| ~ member(esk2_3(inverse_function(inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,esk14_0),esk14_0,X1),esk15_0) ),
inference(spm,[status(thm)],[484,72072,theory(equality)]) ).
cnf(73581,negated_conjecture,
( surjective(inverse_function(inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,esk14_0),esk14_0,esk15_0)
| ~ member(esk2_3(inverse_function(inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,esk14_0),esk14_0,esk15_0),X1)
| ~ member(esk2_3(inverse_function(inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,esk14_0),esk14_0,esk15_0),X2) ),
inference(spm,[status(thm)],[72088,17,theory(equality)]) ).
cnf(73582,negated_conjecture,
( surjective(inverse_function(inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,esk14_0),esk14_0,esk15_0)
| ~ member(esk2_3(inverse_function(inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,esk14_0),esk14_0,esk15_0),X1) ),
inference(spm,[status(thm)],[73581,17,theory(equality)]) ).
cnf(73583,negated_conjecture,
surjective(inverse_function(inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,esk14_0),esk14_0,esk15_0),
inference(spm,[status(thm)],[73582,17,theory(equality)]) ).
cnf(73592,negated_conjecture,
( apply(compose_function(esk13_0,inverse_function(esk13_0,esk14_0,esk15_0),X1,esk14_0,X2),X3,X3)
| ~ member(X3,X1)
| ~ member(X3,X2)
| ~ member(X3,esk15_0) ),
inference(spm,[status(thm)],[4775,73583,theory(equality)]) ).
cnf(73618,negated_conjecture,
( identity(compose_function(esk13_0,inverse_function(esk13_0,esk14_0,esk15_0),X1,esk14_0,X2),X3)
| ~ member(esk8_2(compose_function(esk13_0,inverse_function(esk13_0,esk14_0,esk15_0),X1,esk14_0,X2),X3),esk15_0)
| ~ member(esk8_2(compose_function(esk13_0,inverse_function(esk13_0,esk14_0,esk15_0),X1,esk14_0,X2),X3),X1)
| ~ member(esk8_2(compose_function(esk13_0,inverse_function(esk13_0,esk14_0,esk15_0),X1,esk14_0,X2),X3),X2) ),
inference(spm,[status(thm)],[50,73592,theory(equality)]) ).
cnf(76988,negated_conjecture,
( identity(compose_function(esk13_0,inverse_function(esk13_0,esk14_0,esk15_0),X1,esk14_0,X2),esk15_0)
| ~ member(esk8_2(compose_function(esk13_0,inverse_function(esk13_0,esk14_0,esk15_0),X1,esk14_0,X2),esk15_0),X1)
| ~ member(esk8_2(compose_function(esk13_0,inverse_function(esk13_0,esk14_0,esk15_0),X1,esk14_0,X2),esk15_0),X2) ),
inference(spm,[status(thm)],[73618,51,theory(equality)]) ).
cnf(76989,negated_conjecture,
( identity(compose_function(esk13_0,inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,esk14_0,X1),esk15_0)
| ~ member(esk8_2(compose_function(esk13_0,inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,esk14_0,X1),esk15_0),X1) ),
inference(spm,[status(thm)],[76988,51,theory(equality)]) ).
cnf(76990,negated_conjecture,
identity(compose_function(esk13_0,inverse_function(esk13_0,esk14_0,esk15_0),esk15_0,esk14_0,esk15_0),esk15_0),
inference(spm,[status(thm)],[76989,51,theory(equality)]) ).
cnf(76991,negated_conjecture,
$false,
inference(sr,[status(thm)],[76990,82,theory(equality)]) ).
cnf(76992,negated_conjecture,
$false,
76991,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET715+4.p
% --creating new selector for [SET006+0.ax, SET006+1.ax]
% -running prover on /tmp/tmpcr7spg/sel_SET715+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET715+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET715+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET715+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
%
%------------------------------------------------------------------------------