TSTP Solution File: SET725+4 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET725+4 : TPTP v5.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 03:20:30 EST 2010
% Result : Theorem 0.56s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 7
% Syntax : Number of formulae : 96 ( 11 unt; 0 def)
% Number of atoms : 632 ( 37 equ)
% Maximal formula atoms : 55 ( 6 avg)
% Number of connectives : 864 ( 328 ~; 358 |; 162 &)
% ( 6 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-7 aty)
% Number of variables : 391 ( 1 sgn 199 !; 37 ?)
% 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/tmpeMSWQI/sel_SET725+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/tmpeMSWQI/sel_SET725+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/tmpeMSWQI/sel_SET725+4.p_1',maps) ).
fof(4,axiom,
! [X1,X2] :
( identity(X1,X2)
<=> ! [X6] :
( member(X6,X2)
=> apply(X1,X6,X6) ) ),
file('/tmp/tmpeMSWQI/sel_SET725+4.p_1',identity) ).
fof(5,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/tmpeMSWQI/sel_SET725+4.p_1',injective) ).
fof(6,axiom,
! [X11,X1,X2,X3,X12,X6,X13] :
( ( member(X6,X2)
& member(X13,X12) )
=> ( apply(compose_function(X11,X1,X2,X3,X12),X6,X13)
<=> ? [X4] :
( member(X4,X3)
& apply(X1,X6,X4)
& apply(X11,X4,X13) ) ) ),
file('/tmp/tmpeMSWQI/sel_SET725+4.p_1',compose_function) ).
fof(7,conjecture,
! [X1,X11,X14,X2,X3] :
( ( maps(X1,X2,X3)
& maps(X11,X3,X2)
& maps(X14,X3,X2)
& identity(compose_function(X11,X1,X2,X3,X2),X2)
& identity(compose_function(X1,X14,X3,X2,X3),X3) )
=> one_to_one(X1,X2,X3) ),
file('/tmp/tmpeMSWQI/sel_SET725+4.p_1',thII16) ).
fof(8,negated_conjecture,
~ ! [X1,X11,X14,X2,X3] :
( ( maps(X1,X2,X3)
& maps(X11,X3,X2)
& maps(X14,X3,X2)
& identity(compose_function(X11,X1,X2,X3,X2),X2)
& identity(compose_function(X1,X14,X3,X2,X3),X3) )
=> one_to_one(X1,X2,X3) ),
inference(assume_negation,[status(cth)],[7]) ).
fof(9,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(10,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)],[9]) ).
fof(11,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)],[10]) ).
fof(12,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)],[11]) ).
fof(13,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)],[12]) ).
cnf(16,plain,
( surjective(X1,X2,X3)
| member(esk2_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[13]) ).
cnf(17,plain,
( surjective(X1,X2,X3)
| ~ apply(X1,X4,esk2_3(X1,X2,X3))
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[13]) ).
fof(18,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(19,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)],[18]) ).
fof(20,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)],[19]) ).
cnf(21,plain,
( one_to_one(X1,X2,X3)
| ~ surjective(X1,X2,X3)
| ~ injective(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[20]) ).
fof(24,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(25,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)],[24]) ).
fof(26,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)],[25]) ).
fof(27,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)],[26]) ).
fof(28,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)],[27]) ).
cnf(29,plain,
( apply(X1,X4,esk3_4(X1,X2,X3,X4))
| ~ maps(X1,X2,X3)
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[28]) ).
cnf(30,plain,
( member(esk3_4(X1,X2,X3,X4),X3)
| ~ maps(X1,X2,X3)
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[28]) ).
cnf(31,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)],[28]) ).
fof(44,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(45,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)],[44]) ).
fof(46,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)],[45]) ).
fof(47,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)],[46]) ).
fof(48,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)],[47]) ).
cnf(51,plain,
( apply(X1,X3,X3)
| ~ identity(X1,X2)
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[48]) ).
fof(52,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)],[5]) ).
fof(53,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)],[52]) ).
fof(54,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(esk9_3(X11,X12,X13),X12)
& member(esk10_3(X11,X12,X13),X12)
& member(esk11_3(X11,X12,X13),X13)
& apply(X11,esk9_3(X11,X12,X13),esk11_3(X11,X12,X13))
& apply(X11,esk10_3(X11,X12,X13),esk11_3(X11,X12,X13))
& esk9_3(X11,X12,X13) != esk10_3(X11,X12,X13) )
| injective(X11,X12,X13) ) ),
inference(skolemize,[status(esa)],[53]) ).
fof(55,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(esk9_3(X11,X12,X13),X12)
& member(esk10_3(X11,X12,X13),X12)
& member(esk11_3(X11,X12,X13),X13)
& apply(X11,esk9_3(X11,X12,X13),esk11_3(X11,X12,X13))
& apply(X11,esk10_3(X11,X12,X13),esk11_3(X11,X12,X13))
& esk9_3(X11,X12,X13) != esk10_3(X11,X12,X13) )
| injective(X11,X12,X13) ) ),
inference(shift_quantors,[status(thm)],[54]) ).
fof(56,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(esk9_3(X11,X12,X13),X12)
| injective(X11,X12,X13) )
& ( member(esk10_3(X11,X12,X13),X12)
| injective(X11,X12,X13) )
& ( member(esk11_3(X11,X12,X13),X13)
| injective(X11,X12,X13) )
& ( apply(X11,esk9_3(X11,X12,X13),esk11_3(X11,X12,X13))
| injective(X11,X12,X13) )
& ( apply(X11,esk10_3(X11,X12,X13),esk11_3(X11,X12,X13))
| injective(X11,X12,X13) )
& ( esk9_3(X11,X12,X13) != esk10_3(X11,X12,X13)
| injective(X11,X12,X13) ) ),
inference(distribute,[status(thm)],[55]) ).
cnf(57,plain,
( injective(X1,X2,X3)
| esk9_3(X1,X2,X3) != esk10_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[56]) ).
cnf(58,plain,
( injective(X1,X2,X3)
| apply(X1,esk10_3(X1,X2,X3),esk11_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[56]) ).
cnf(59,plain,
( injective(X1,X2,X3)
| apply(X1,esk9_3(X1,X2,X3),esk11_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[56]) ).
cnf(60,plain,
( injective(X1,X2,X3)
| member(esk11_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[56]) ).
cnf(61,plain,
( injective(X1,X2,X3)
| member(esk10_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[56]) ).
cnf(62,plain,
( injective(X1,X2,X3)
| member(esk9_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[56]) ).
fof(64,plain,
! [X11,X1,X2,X3,X12,X6,X13] :
( ~ member(X6,X2)
| ~ member(X13,X12)
| ( ( ~ apply(compose_function(X11,X1,X2,X3,X12),X6,X13)
| ? [X4] :
( member(X4,X3)
& apply(X1,X6,X4)
& apply(X11,X4,X13) ) )
& ( ! [X4] :
( ~ member(X4,X3)
| ~ apply(X1,X6,X4)
| ~ apply(X11,X4,X13) )
| apply(compose_function(X11,X1,X2,X3,X12),X6,X13) ) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(65,plain,
! [X14,X15,X16,X17,X18,X19,X20] :
( ~ member(X19,X16)
| ~ member(X20,X18)
| ( ( ~ apply(compose_function(X14,X15,X16,X17,X18),X19,X20)
| ? [X21] :
( member(X21,X17)
& apply(X15,X19,X21)
& apply(X14,X21,X20) ) )
& ( ! [X22] :
( ~ member(X22,X17)
| ~ apply(X15,X19,X22)
| ~ apply(X14,X22,X20) )
| apply(compose_function(X14,X15,X16,X17,X18),X19,X20) ) ) ),
inference(variable_rename,[status(thm)],[64]) ).
fof(66,plain,
! [X14,X15,X16,X17,X18,X19,X20] :
( ~ member(X19,X16)
| ~ member(X20,X18)
| ( ( ~ apply(compose_function(X14,X15,X16,X17,X18),X19,X20)
| ( member(esk12_7(X14,X15,X16,X17,X18,X19,X20),X17)
& apply(X15,X19,esk12_7(X14,X15,X16,X17,X18,X19,X20))
& apply(X14,esk12_7(X14,X15,X16,X17,X18,X19,X20),X20) ) )
& ( ! [X22] :
( ~ member(X22,X17)
| ~ apply(X15,X19,X22)
| ~ apply(X14,X22,X20) )
| apply(compose_function(X14,X15,X16,X17,X18),X19,X20) ) ) ),
inference(skolemize,[status(esa)],[65]) ).
fof(67,plain,
! [X14,X15,X16,X17,X18,X19,X20,X22] :
( ( ( ~ member(X22,X17)
| ~ apply(X15,X19,X22)
| ~ apply(X14,X22,X20)
| apply(compose_function(X14,X15,X16,X17,X18),X19,X20) )
& ( ~ apply(compose_function(X14,X15,X16,X17,X18),X19,X20)
| ( member(esk12_7(X14,X15,X16,X17,X18,X19,X20),X17)
& apply(X15,X19,esk12_7(X14,X15,X16,X17,X18,X19,X20))
& apply(X14,esk12_7(X14,X15,X16,X17,X18,X19,X20),X20) ) ) )
| ~ member(X19,X16)
| ~ member(X20,X18) ),
inference(shift_quantors,[status(thm)],[66]) ).
fof(68,plain,
! [X14,X15,X16,X17,X18,X19,X20,X22] :
( ( ~ member(X22,X17)
| ~ apply(X15,X19,X22)
| ~ apply(X14,X22,X20)
| apply(compose_function(X14,X15,X16,X17,X18),X19,X20)
| ~ member(X19,X16)
| ~ member(X20,X18) )
& ( member(esk12_7(X14,X15,X16,X17,X18,X19,X20),X17)
| ~ apply(compose_function(X14,X15,X16,X17,X18),X19,X20)
| ~ member(X19,X16)
| ~ member(X20,X18) )
& ( apply(X15,X19,esk12_7(X14,X15,X16,X17,X18,X19,X20))
| ~ apply(compose_function(X14,X15,X16,X17,X18),X19,X20)
| ~ member(X19,X16)
| ~ member(X20,X18) )
& ( apply(X14,esk12_7(X14,X15,X16,X17,X18,X19,X20),X20)
| ~ apply(compose_function(X14,X15,X16,X17,X18),X19,X20)
| ~ member(X19,X16)
| ~ member(X20,X18) ) ),
inference(distribute,[status(thm)],[67]) ).
cnf(69,plain,
( apply(X5,esk12_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)],[68]) ).
cnf(70,plain,
( apply(X6,X3,esk12_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)],[68]) ).
cnf(71,plain,
( member(esk12_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)],[68]) ).
fof(73,negated_conjecture,
? [X1,X11,X14,X2,X3] :
( maps(X1,X2,X3)
& maps(X11,X3,X2)
& maps(X14,X3,X2)
& identity(compose_function(X11,X1,X2,X3,X2),X2)
& identity(compose_function(X1,X14,X3,X2,X3),X3)
& ~ one_to_one(X1,X2,X3) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(74,negated_conjecture,
? [X15,X16,X17,X18,X19] :
( maps(X15,X18,X19)
& maps(X16,X19,X18)
& maps(X17,X19,X18)
& identity(compose_function(X16,X15,X18,X19,X18),X18)
& identity(compose_function(X15,X17,X19,X18,X19),X19)
& ~ one_to_one(X15,X18,X19) ),
inference(variable_rename,[status(thm)],[73]) ).
fof(75,negated_conjecture,
( maps(esk13_0,esk16_0,esk17_0)
& maps(esk14_0,esk17_0,esk16_0)
& maps(esk15_0,esk17_0,esk16_0)
& identity(compose_function(esk14_0,esk13_0,esk16_0,esk17_0,esk16_0),esk16_0)
& identity(compose_function(esk13_0,esk15_0,esk17_0,esk16_0,esk17_0),esk17_0)
& ~ one_to_one(esk13_0,esk16_0,esk17_0) ),
inference(skolemize,[status(esa)],[74]) ).
cnf(76,negated_conjecture,
~ one_to_one(esk13_0,esk16_0,esk17_0),
inference(split_conjunct,[status(thm)],[75]) ).
cnf(77,negated_conjecture,
identity(compose_function(esk13_0,esk15_0,esk17_0,esk16_0,esk17_0),esk17_0),
inference(split_conjunct,[status(thm)],[75]) ).
cnf(78,negated_conjecture,
identity(compose_function(esk14_0,esk13_0,esk16_0,esk17_0,esk16_0),esk16_0),
inference(split_conjunct,[status(thm)],[75]) ).
cnf(80,negated_conjecture,
maps(esk14_0,esk17_0,esk16_0),
inference(split_conjunct,[status(thm)],[75]) ).
cnf(81,negated_conjecture,
maps(esk13_0,esk16_0,esk17_0),
inference(split_conjunct,[status(thm)],[75]) ).
cnf(82,negated_conjecture,
( apply(compose_function(esk13_0,esk15_0,esk17_0,esk16_0,esk17_0),X1,X1)
| ~ member(X1,esk17_0) ),
inference(spm,[status(thm)],[51,77,theory(equality)]) ).
cnf(83,negated_conjecture,
( apply(compose_function(esk14_0,esk13_0,esk16_0,esk17_0,esk16_0),X1,X1)
| ~ member(X1,esk16_0) ),
inference(spm,[status(thm)],[51,78,theory(equality)]) ).
cnf(84,negated_conjecture,
( ~ injective(esk13_0,esk16_0,esk17_0)
| ~ surjective(esk13_0,esk16_0,esk17_0) ),
inference(spm,[status(thm)],[76,21,theory(equality)]) ).
cnf(92,negated_conjecture,
( X1 = X2
| ~ apply(esk13_0,X3,X2)
| ~ apply(esk13_0,X3,X1)
| ~ member(X3,esk16_0)
| ~ member(X2,esk17_0)
| ~ member(X1,esk17_0) ),
inference(spm,[status(thm)],[31,81,theory(equality)]) ).
cnf(93,negated_conjecture,
( X1 = X2
| ~ apply(esk14_0,X3,X2)
| ~ apply(esk14_0,X3,X1)
| ~ member(X3,esk17_0)
| ~ member(X2,esk16_0)
| ~ member(X1,esk16_0) ),
inference(spm,[status(thm)],[31,80,theory(equality)]) ).
cnf(103,plain,
( surjective(X1,X2,X3)
| ~ member(esk12_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)],[17,69,theory(equality)]) ).
cnf(134,negated_conjecture,
( X1 = esk3_4(esk13_0,X2,X3,X4)
| ~ apply(esk13_0,X4,X1)
| ~ member(X4,esk16_0)
| ~ member(esk3_4(esk13_0,X2,X3,X4),esk17_0)
| ~ member(X1,esk17_0)
| ~ maps(esk13_0,X2,X3)
| ~ member(X4,X2) ),
inference(spm,[status(thm)],[92,29,theory(equality)]) ).
cnf(140,negated_conjecture,
( X1 = esk12_7(X2,esk13_0,X3,X4,X5,X6,X7)
| ~ apply(esk13_0,X6,X1)
| ~ member(X6,esk16_0)
| ~ member(esk12_7(X2,esk13_0,X3,X4,X5,X6,X7),esk17_0)
| ~ member(X1,esk17_0)
| ~ apply(compose_function(X2,esk13_0,X3,X4,X5),X6,X7)
| ~ member(X6,X3)
| ~ member(X7,X5) ),
inference(spm,[status(thm)],[92,70,theory(equality)]) ).
cnf(198,negated_conjecture,
( X1 = esk3_4(esk13_0,X2,esk17_0,X3)
| ~ maps(esk13_0,X2,esk17_0)
| ~ apply(esk13_0,X3,X1)
| ~ member(X3,esk16_0)
| ~ member(X1,esk17_0)
| ~ member(X3,X2) ),
inference(spm,[status(thm)],[134,30,theory(equality)]) ).
cnf(201,negated_conjecture,
( esk11_3(esk13_0,X1,X2) = esk3_4(esk13_0,X3,esk17_0,esk9_3(esk13_0,X1,X2))
| injective(esk13_0,X1,X2)
| ~ maps(esk13_0,X3,esk17_0)
| ~ member(esk9_3(esk13_0,X1,X2),esk16_0)
| ~ member(esk11_3(esk13_0,X1,X2),esk17_0)
| ~ member(esk9_3(esk13_0,X1,X2),X3) ),
inference(spm,[status(thm)],[198,59,theory(equality)]) ).
cnf(202,negated_conjecture,
( esk11_3(esk13_0,X1,X2) = esk3_4(esk13_0,X3,esk17_0,esk10_3(esk13_0,X1,X2))
| injective(esk13_0,X1,X2)
| ~ maps(esk13_0,X3,esk17_0)
| ~ member(esk10_3(esk13_0,X1,X2),esk16_0)
| ~ member(esk11_3(esk13_0,X1,X2),esk17_0)
| ~ member(esk10_3(esk13_0,X1,X2),X3) ),
inference(spm,[status(thm)],[198,58,theory(equality)]) ).
cnf(422,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)],[103,71,theory(equality)]) ).
cnf(431,negated_conjecture,
( surjective(esk13_0,esk16_0,X1)
| ~ member(esk2_3(esk13_0,esk16_0,X1),esk17_0) ),
inference(spm,[status(thm)],[422,82,theory(equality)]) ).
cnf(435,negated_conjecture,
surjective(esk13_0,esk16_0,esk17_0),
inference(spm,[status(thm)],[431,16,theory(equality)]) ).
cnf(436,negated_conjecture,
( ~ injective(esk13_0,esk16_0,esk17_0)
| $false ),
inference(rw,[status(thm)],[84,435,theory(equality)]) ).
cnf(437,negated_conjecture,
~ injective(esk13_0,esk16_0,esk17_0),
inference(cn,[status(thm)],[436,theory(equality)]) ).
cnf(897,negated_conjecture,
( X1 = esk12_7(X2,esk13_0,X3,esk17_0,X4,X5,X6)
| ~ apply(compose_function(X2,esk13_0,X3,esk17_0,X4),X5,X6)
| ~ apply(esk13_0,X5,X1)
| ~ member(X5,esk16_0)
| ~ member(X1,esk17_0)
| ~ member(X5,X3)
| ~ member(X6,X4) ),
inference(spm,[status(thm)],[140,71,theory(equality)]) ).
cnf(898,negated_conjecture,
( esk3_4(esk13_0,X1,X2,X3) = esk12_7(X4,esk13_0,X5,esk17_0,X6,X3,X7)
| ~ apply(compose_function(X4,esk13_0,X5,esk17_0,X6),X3,X7)
| ~ member(X3,esk16_0)
| ~ member(esk3_4(esk13_0,X1,X2,X3),esk17_0)
| ~ member(X3,X5)
| ~ member(X7,X6)
| ~ maps(esk13_0,X1,X2)
| ~ member(X3,X1) ),
inference(spm,[status(thm)],[897,29,theory(equality)]) ).
cnf(1286,negated_conjecture,
( esk3_4(esk13_0,X1,esk17_0,X2) = esk12_7(X3,esk13_0,X4,esk17_0,X5,X2,X6)
| ~ maps(esk13_0,X1,esk17_0)
| ~ apply(compose_function(X3,esk13_0,X4,esk17_0,X5),X2,X6)
| ~ member(X2,esk16_0)
| ~ member(X2,X4)
| ~ member(X6,X5)
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[898,30,theory(equality)]) ).
cnf(1298,negated_conjecture,
( apply(X1,esk3_4(esk13_0,X6,esk17_0,X4),X5)
| ~ apply(compose_function(X1,esk13_0,X2,esk17_0,X3),X4,X5)
| ~ member(X4,X2)
| ~ member(X5,X3)
| ~ maps(esk13_0,X6,esk17_0)
| ~ member(X4,esk16_0)
| ~ member(X4,X6) ),
inference(spm,[status(thm)],[69,1286,theory(equality)]) ).
cnf(1354,negated_conjecture,
( apply(esk14_0,esk3_4(esk13_0,X1,esk17_0,X2),X2)
| ~ maps(esk13_0,X1,esk17_0)
| ~ member(X2,esk16_0)
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[1298,83,theory(equality)]) ).
cnf(1370,negated_conjecture,
( apply(esk14_0,esk11_3(esk13_0,X2,X3),esk9_3(esk13_0,X2,X3))
| injective(esk13_0,X2,X3)
| ~ maps(esk13_0,X1,esk17_0)
| ~ member(esk9_3(esk13_0,X2,X3),esk16_0)
| ~ member(esk9_3(esk13_0,X2,X3),X1)
| ~ member(esk11_3(esk13_0,X2,X3),esk17_0) ),
inference(spm,[status(thm)],[1354,201,theory(equality)]) ).
cnf(1372,negated_conjecture,
( apply(esk14_0,esk11_3(esk13_0,X2,X3),esk10_3(esk13_0,X2,X3))
| injective(esk13_0,X2,X3)
| ~ maps(esk13_0,X1,esk17_0)
| ~ member(esk10_3(esk13_0,X2,X3),esk16_0)
| ~ member(esk10_3(esk13_0,X2,X3),X1)
| ~ member(esk11_3(esk13_0,X2,X3),esk17_0) ),
inference(spm,[status(thm)],[1354,202,theory(equality)]) ).
cnf(2276,negated_conjecture,
( injective(esk13_0,X1,X2)
| apply(esk14_0,esk11_3(esk13_0,X1,X2),esk9_3(esk13_0,X1,X2))
| ~ maps(esk13_0,X1,esk17_0)
| ~ member(esk9_3(esk13_0,X1,X2),esk16_0)
| ~ member(esk11_3(esk13_0,X1,X2),esk17_0) ),
inference(spm,[status(thm)],[1370,62,theory(equality)]) ).
cnf(2281,negated_conjecture,
( X1 = esk9_3(esk13_0,X2,X3)
| injective(esk13_0,X2,X3)
| ~ apply(esk14_0,esk11_3(esk13_0,X2,X3),X1)
| ~ member(esk11_3(esk13_0,X2,X3),esk17_0)
| ~ member(esk9_3(esk13_0,X2,X3),esk16_0)
| ~ member(X1,esk16_0)
| ~ maps(esk13_0,X2,esk17_0) ),
inference(spm,[status(thm)],[93,2276,theory(equality)]) ).
cnf(2859,negated_conjecture,
( injective(esk13_0,X1,X2)
| apply(esk14_0,esk11_3(esk13_0,X1,X2),esk10_3(esk13_0,X1,X2))
| ~ maps(esk13_0,X1,esk17_0)
| ~ member(esk10_3(esk13_0,X1,X2),esk16_0)
| ~ member(esk11_3(esk13_0,X1,X2),esk17_0) ),
inference(spm,[status(thm)],[1372,61,theory(equality)]) ).
cnf(2868,negated_conjecture,
( esk10_3(esk13_0,X1,X2) = esk9_3(esk13_0,X1,X2)
| injective(esk13_0,X1,X2)
| ~ maps(esk13_0,X1,esk17_0)
| ~ member(esk11_3(esk13_0,X1,X2),esk17_0)
| ~ member(esk9_3(esk13_0,X1,X2),esk16_0)
| ~ member(esk10_3(esk13_0,X1,X2),esk16_0) ),
inference(spm,[status(thm)],[2281,2859,theory(equality)]) ).
cnf(2869,negated_conjecture,
( injective(esk13_0,X1,X2)
| ~ maps(esk13_0,X1,esk17_0)
| ~ member(esk11_3(esk13_0,X1,X2),esk17_0)
| ~ member(esk9_3(esk13_0,X1,X2),esk16_0)
| ~ member(esk10_3(esk13_0,X1,X2),esk16_0) ),
inference(csr,[status(thm)],[2868,57]) ).
cnf(2870,negated_conjecture,
( injective(esk13_0,X1,esk17_0)
| ~ maps(esk13_0,X1,esk17_0)
| ~ member(esk9_3(esk13_0,X1,esk17_0),esk16_0)
| ~ member(esk10_3(esk13_0,X1,esk17_0),esk16_0) ),
inference(spm,[status(thm)],[2869,60,theory(equality)]) ).
cnf(2871,negated_conjecture,
( injective(esk13_0,esk16_0,esk17_0)
| ~ maps(esk13_0,esk16_0,esk17_0)
| ~ member(esk9_3(esk13_0,esk16_0,esk17_0),esk16_0) ),
inference(spm,[status(thm)],[2870,61,theory(equality)]) ).
cnf(2872,negated_conjecture,
( injective(esk13_0,esk16_0,esk17_0)
| $false
| ~ member(esk9_3(esk13_0,esk16_0,esk17_0),esk16_0) ),
inference(rw,[status(thm)],[2871,81,theory(equality)]) ).
cnf(2873,negated_conjecture,
( injective(esk13_0,esk16_0,esk17_0)
| ~ member(esk9_3(esk13_0,esk16_0,esk17_0),esk16_0) ),
inference(cn,[status(thm)],[2872,theory(equality)]) ).
cnf(2874,negated_conjecture,
~ member(esk9_3(esk13_0,esk16_0,esk17_0),esk16_0),
inference(sr,[status(thm)],[2873,437,theory(equality)]) ).
cnf(2875,negated_conjecture,
injective(esk13_0,esk16_0,esk17_0),
inference(spm,[status(thm)],[2874,62,theory(equality)]) ).
cnf(2876,negated_conjecture,
$false,
inference(sr,[status(thm)],[2875,437,theory(equality)]) ).
cnf(2877,negated_conjecture,
$false,
2876,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET725+4.p
% --creating new selector for [SET006+0.ax, SET006+1.ax]
% -running prover on /tmp/tmpeMSWQI/sel_SET725+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET725+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET725+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET725+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
%
%------------------------------------------------------------------------------