TSTP Solution File: SET728+4 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET728+4 : TPTP v5.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art02.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 03:20:54 EST 2010
% Result : Theorem 0.82s
% Output : CNFRefutation 0.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 5
% Syntax : Number of formulae : 89 ( 9 unt; 0 def)
% Number of atoms : 619 ( 45 equ)
% Maximal formula atoms : 55 ( 6 avg)
% Number of connectives : 879 ( 349 ~; 378 |; 139 &)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-7 aty)
% Number of variables : 390 ( 0 sgn 164 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3,X4] :
( equal_maps(X1,X2,X3,X4)
<=> ! [X5,X6,X7] :
( ( member(X5,X3)
& member(X6,X4)
& member(X7,X4) )
=> ( ( apply(X1,X5,X6)
& apply(X2,X5,X7) )
=> X6 = X7 ) ) ),
file('/tmp/tmpFNV_4P/sel_SET728+4.p_1',equal_maps) ).
fof(2,axiom,
! [X1,X3,X4] :
( maps(X1,X3,X4)
<=> ( ! [X5] :
( member(X5,X3)
=> ? [X8] :
( member(X8,X4)
& apply(X1,X5,X8) ) )
& ! [X5,X6,X7] :
( ( member(X5,X3)
& member(X6,X4)
& member(X7,X4) )
=> ( ( apply(X1,X5,X6)
& apply(X1,X5,X7) )
=> X6 = X7 ) ) ) ),
file('/tmp/tmpFNV_4P/sel_SET728+4.p_1',maps) ).
fof(3,axiom,
! [X1,X3] :
( identity(X1,X3)
<=> ! [X5] :
( member(X5,X3)
=> apply(X1,X5,X5) ) ),
file('/tmp/tmpFNV_4P/sel_SET728+4.p_1',identity) ).
fof(4,axiom,
! [X2,X1,X3,X4,X9,X5,X10] :
( ( member(X5,X3)
& member(X10,X9) )
=> ( apply(compose_function(X2,X1,X3,X4,X9),X5,X10)
<=> ? [X8] :
( member(X8,X4)
& apply(X1,X5,X8)
& apply(X2,X8,X10) ) ) ),
file('/tmp/tmpFNV_4P/sel_SET728+4.p_1',compose_function) ).
fof(5,conjecture,
! [X1,X2,X11,X3,X4] :
( ( maps(X1,X3,X4)
& maps(X2,X4,X3)
& maps(X11,X4,X3)
& identity(compose_function(X2,X1,X3,X4,X3),X3)
& identity(compose_function(X1,X11,X4,X3,X4),X4) )
=> equal_maps(X2,X11,X4,X3) ),
file('/tmp/tmpFNV_4P/sel_SET728+4.p_1',thII19) ).
fof(6,negated_conjecture,
~ ! [X1,X2,X11,X3,X4] :
( ( maps(X1,X3,X4)
& maps(X2,X4,X3)
& maps(X11,X4,X3)
& identity(compose_function(X2,X1,X3,X4,X3),X3)
& identity(compose_function(X1,X11,X4,X3,X4),X4) )
=> equal_maps(X2,X11,X4,X3) ),
inference(assume_negation,[status(cth)],[5]) ).
fof(7,plain,
! [X1,X2,X3,X4] :
( ( ~ equal_maps(X1,X2,X3,X4)
| ! [X5,X6,X7] :
( ~ member(X5,X3)
| ~ member(X6,X4)
| ~ member(X7,X4)
| ~ apply(X1,X5,X6)
| ~ apply(X2,X5,X7)
| X6 = X7 ) )
& ( ? [X5,X6,X7] :
( member(X5,X3)
& member(X6,X4)
& member(X7,X4)
& apply(X1,X5,X6)
& apply(X2,X5,X7)
& X6 != X7 )
| equal_maps(X1,X2,X3,X4) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(8,plain,
! [X8,X9,X10,X11] :
( ( ~ equal_maps(X8,X9,X10,X11)
| ! [X12,X13,X14] :
( ~ member(X12,X10)
| ~ member(X13,X11)
| ~ member(X14,X11)
| ~ apply(X8,X12,X13)
| ~ apply(X9,X12,X14)
| X13 = X14 ) )
& ( ? [X15,X16,X17] :
( member(X15,X10)
& member(X16,X11)
& member(X17,X11)
& apply(X8,X15,X16)
& apply(X9,X15,X17)
& X16 != X17 )
| equal_maps(X8,X9,X10,X11) ) ),
inference(variable_rename,[status(thm)],[7]) ).
fof(9,plain,
! [X8,X9,X10,X11] :
( ( ~ equal_maps(X8,X9,X10,X11)
| ! [X12,X13,X14] :
( ~ member(X12,X10)
| ~ member(X13,X11)
| ~ member(X14,X11)
| ~ apply(X8,X12,X13)
| ~ apply(X9,X12,X14)
| X13 = X14 ) )
& ( ( member(esk1_4(X8,X9,X10,X11),X10)
& member(esk2_4(X8,X9,X10,X11),X11)
& member(esk3_4(X8,X9,X10,X11),X11)
& apply(X8,esk1_4(X8,X9,X10,X11),esk2_4(X8,X9,X10,X11))
& apply(X9,esk1_4(X8,X9,X10,X11),esk3_4(X8,X9,X10,X11))
& esk2_4(X8,X9,X10,X11) != esk3_4(X8,X9,X10,X11) )
| equal_maps(X8,X9,X10,X11) ) ),
inference(skolemize,[status(esa)],[8]) ).
fof(10,plain,
! [X8,X9,X10,X11,X12,X13,X14] :
( ( ~ member(X12,X10)
| ~ member(X13,X11)
| ~ member(X14,X11)
| ~ apply(X8,X12,X13)
| ~ apply(X9,X12,X14)
| X13 = X14
| ~ equal_maps(X8,X9,X10,X11) )
& ( ( member(esk1_4(X8,X9,X10,X11),X10)
& member(esk2_4(X8,X9,X10,X11),X11)
& member(esk3_4(X8,X9,X10,X11),X11)
& apply(X8,esk1_4(X8,X9,X10,X11),esk2_4(X8,X9,X10,X11))
& apply(X9,esk1_4(X8,X9,X10,X11),esk3_4(X8,X9,X10,X11))
& esk2_4(X8,X9,X10,X11) != esk3_4(X8,X9,X10,X11) )
| equal_maps(X8,X9,X10,X11) ) ),
inference(shift_quantors,[status(thm)],[9]) ).
fof(11,plain,
! [X8,X9,X10,X11,X12,X13,X14] :
( ( ~ member(X12,X10)
| ~ member(X13,X11)
| ~ member(X14,X11)
| ~ apply(X8,X12,X13)
| ~ apply(X9,X12,X14)
| X13 = X14
| ~ equal_maps(X8,X9,X10,X11) )
& ( member(esk1_4(X8,X9,X10,X11),X10)
| equal_maps(X8,X9,X10,X11) )
& ( member(esk2_4(X8,X9,X10,X11),X11)
| equal_maps(X8,X9,X10,X11) )
& ( member(esk3_4(X8,X9,X10,X11),X11)
| equal_maps(X8,X9,X10,X11) )
& ( apply(X8,esk1_4(X8,X9,X10,X11),esk2_4(X8,X9,X10,X11))
| equal_maps(X8,X9,X10,X11) )
& ( apply(X9,esk1_4(X8,X9,X10,X11),esk3_4(X8,X9,X10,X11))
| equal_maps(X8,X9,X10,X11) )
& ( esk2_4(X8,X9,X10,X11) != esk3_4(X8,X9,X10,X11)
| equal_maps(X8,X9,X10,X11) ) ),
inference(distribute,[status(thm)],[10]) ).
cnf(12,plain,
( equal_maps(X1,X2,X3,X4)
| esk2_4(X1,X2,X3,X4) != esk3_4(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[11]) ).
cnf(13,plain,
( equal_maps(X1,X2,X3,X4)
| apply(X2,esk1_4(X1,X2,X3,X4),esk3_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[11]) ).
cnf(14,plain,
( equal_maps(X1,X2,X3,X4)
| apply(X1,esk1_4(X1,X2,X3,X4),esk2_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[11]) ).
cnf(15,plain,
( equal_maps(X1,X2,X3,X4)
| member(esk3_4(X1,X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[11]) ).
cnf(16,plain,
( equal_maps(X1,X2,X3,X4)
| member(esk2_4(X1,X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[11]) ).
cnf(17,plain,
( equal_maps(X1,X2,X3,X4)
| member(esk1_4(X1,X2,X3,X4),X3) ),
inference(split_conjunct,[status(thm)],[11]) ).
fof(19,plain,
! [X1,X3,X4] :
( ( ~ maps(X1,X3,X4)
| ( ! [X5] :
( ~ member(X5,X3)
| ? [X8] :
( member(X8,X4)
& apply(X1,X5,X8) ) )
& ! [X5,X6,X7] :
( ~ member(X5,X3)
| ~ member(X6,X4)
| ~ member(X7,X4)
| ~ apply(X1,X5,X6)
| ~ apply(X1,X5,X7)
| X6 = X7 ) ) )
& ( ? [X5] :
( member(X5,X3)
& ! [X8] :
( ~ member(X8,X4)
| ~ apply(X1,X5,X8) ) )
| ? [X5,X6,X7] :
( member(X5,X3)
& member(X6,X4)
& member(X7,X4)
& apply(X1,X5,X6)
& apply(X1,X5,X7)
& X6 != X7 )
| maps(X1,X3,X4) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(20,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)],[19]) ).
fof(21,plain,
! [X9,X10,X11] :
( ( ~ maps(X9,X10,X11)
| ( ! [X12] :
( ~ member(X12,X10)
| ( member(esk4_4(X9,X10,X11,X12),X11)
& apply(X9,X12,esk4_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(esk5_3(X9,X10,X11),X10)
& ! [X18] :
( ~ member(X18,X11)
| ~ apply(X9,esk5_3(X9,X10,X11),X18) ) )
| ( member(esk6_3(X9,X10,X11),X10)
& member(esk7_3(X9,X10,X11),X11)
& member(esk8_3(X9,X10,X11),X11)
& apply(X9,esk6_3(X9,X10,X11),esk7_3(X9,X10,X11))
& apply(X9,esk6_3(X9,X10,X11),esk8_3(X9,X10,X11))
& esk7_3(X9,X10,X11) != esk8_3(X9,X10,X11) )
| maps(X9,X10,X11) ) ),
inference(skolemize,[status(esa)],[20]) ).
fof(22,plain,
! [X9,X10,X11,X12,X14,X15,X16,X18] :
( ( ( ( ~ member(X18,X11)
| ~ apply(X9,esk5_3(X9,X10,X11),X18) )
& member(esk5_3(X9,X10,X11),X10) )
| ( member(esk6_3(X9,X10,X11),X10)
& member(esk7_3(X9,X10,X11),X11)
& member(esk8_3(X9,X10,X11),X11)
& apply(X9,esk6_3(X9,X10,X11),esk7_3(X9,X10,X11))
& apply(X9,esk6_3(X9,X10,X11),esk8_3(X9,X10,X11))
& esk7_3(X9,X10,X11) != esk8_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(esk4_4(X9,X10,X11,X12),X11)
& apply(X9,X12,esk4_4(X9,X10,X11,X12)) ) ) )
| ~ maps(X9,X10,X11) ) ),
inference(shift_quantors,[status(thm)],[21]) ).
fof(23,plain,
! [X9,X10,X11,X12,X14,X15,X16,X18] :
( ( member(esk6_3(X9,X10,X11),X10)
| ~ member(X18,X11)
| ~ apply(X9,esk5_3(X9,X10,X11),X18)
| maps(X9,X10,X11) )
& ( member(esk7_3(X9,X10,X11),X11)
| ~ member(X18,X11)
| ~ apply(X9,esk5_3(X9,X10,X11),X18)
| maps(X9,X10,X11) )
& ( member(esk8_3(X9,X10,X11),X11)
| ~ member(X18,X11)
| ~ apply(X9,esk5_3(X9,X10,X11),X18)
| maps(X9,X10,X11) )
& ( apply(X9,esk6_3(X9,X10,X11),esk7_3(X9,X10,X11))
| ~ member(X18,X11)
| ~ apply(X9,esk5_3(X9,X10,X11),X18)
| maps(X9,X10,X11) )
& ( apply(X9,esk6_3(X9,X10,X11),esk8_3(X9,X10,X11))
| ~ member(X18,X11)
| ~ apply(X9,esk5_3(X9,X10,X11),X18)
| maps(X9,X10,X11) )
& ( esk7_3(X9,X10,X11) != esk8_3(X9,X10,X11)
| ~ member(X18,X11)
| ~ apply(X9,esk5_3(X9,X10,X11),X18)
| maps(X9,X10,X11) )
& ( member(esk6_3(X9,X10,X11),X10)
| member(esk5_3(X9,X10,X11),X10)
| maps(X9,X10,X11) )
& ( member(esk7_3(X9,X10,X11),X11)
| member(esk5_3(X9,X10,X11),X10)
| maps(X9,X10,X11) )
& ( member(esk8_3(X9,X10,X11),X11)
| member(esk5_3(X9,X10,X11),X10)
| maps(X9,X10,X11) )
& ( apply(X9,esk6_3(X9,X10,X11),esk7_3(X9,X10,X11))
| member(esk5_3(X9,X10,X11),X10)
| maps(X9,X10,X11) )
& ( apply(X9,esk6_3(X9,X10,X11),esk8_3(X9,X10,X11))
| member(esk5_3(X9,X10,X11),X10)
| maps(X9,X10,X11) )
& ( esk7_3(X9,X10,X11) != esk8_3(X9,X10,X11)
| member(esk5_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(esk4_4(X9,X10,X11,X12),X11)
| ~ member(X12,X10)
| ~ maps(X9,X10,X11) )
& ( apply(X9,X12,esk4_4(X9,X10,X11,X12))
| ~ member(X12,X10)
| ~ maps(X9,X10,X11) ) ),
inference(distribute,[status(thm)],[22]) ).
cnf(24,plain,
( apply(X1,X4,esk4_4(X1,X2,X3,X4))
| ~ maps(X1,X2,X3)
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[23]) ).
cnf(25,plain,
( member(esk4_4(X1,X2,X3,X4),X3)
| ~ maps(X1,X2,X3)
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[23]) ).
cnf(26,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)],[23]) ).
fof(39,plain,
! [X1,X3] :
( ( ~ identity(X1,X3)
| ! [X5] :
( ~ member(X5,X3)
| apply(X1,X5,X5) ) )
& ( ? [X5] :
( member(X5,X3)
& ~ apply(X1,X5,X5) )
| identity(X1,X3) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(40,plain,
! [X6,X7] :
( ( ~ identity(X6,X7)
| ! [X8] :
( ~ member(X8,X7)
| apply(X6,X8,X8) ) )
& ( ? [X9] :
( member(X9,X7)
& ~ apply(X6,X9,X9) )
| identity(X6,X7) ) ),
inference(variable_rename,[status(thm)],[39]) ).
fof(41,plain,
! [X6,X7] :
( ( ~ identity(X6,X7)
| ! [X8] :
( ~ member(X8,X7)
| apply(X6,X8,X8) ) )
& ( ( member(esk9_2(X6,X7),X7)
& ~ apply(X6,esk9_2(X6,X7),esk9_2(X6,X7)) )
| identity(X6,X7) ) ),
inference(skolemize,[status(esa)],[40]) ).
fof(42,plain,
! [X6,X7,X8] :
( ( ~ member(X8,X7)
| apply(X6,X8,X8)
| ~ identity(X6,X7) )
& ( ( member(esk9_2(X6,X7),X7)
& ~ apply(X6,esk9_2(X6,X7),esk9_2(X6,X7)) )
| identity(X6,X7) ) ),
inference(shift_quantors,[status(thm)],[41]) ).
fof(43,plain,
! [X6,X7,X8] :
( ( ~ member(X8,X7)
| apply(X6,X8,X8)
| ~ identity(X6,X7) )
& ( member(esk9_2(X6,X7),X7)
| identity(X6,X7) )
& ( ~ apply(X6,esk9_2(X6,X7),esk9_2(X6,X7))
| identity(X6,X7) ) ),
inference(distribute,[status(thm)],[42]) ).
cnf(46,plain,
( apply(X1,X3,X3)
| ~ identity(X1,X2)
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[43]) ).
fof(47,plain,
! [X2,X1,X3,X4,X9,X5,X10] :
( ~ member(X5,X3)
| ~ member(X10,X9)
| ( ( ~ apply(compose_function(X2,X1,X3,X4,X9),X5,X10)
| ? [X8] :
( member(X8,X4)
& apply(X1,X5,X8)
& apply(X2,X8,X10) ) )
& ( ! [X8] :
( ~ member(X8,X4)
| ~ apply(X1,X5,X8)
| ~ apply(X2,X8,X10) )
| apply(compose_function(X2,X1,X3,X4,X9),X5,X10) ) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(48,plain,
! [X11,X12,X13,X14,X15,X16,X17] :
( ~ member(X16,X13)
| ~ member(X17,X15)
| ( ( ~ apply(compose_function(X11,X12,X13,X14,X15),X16,X17)
| ? [X18] :
( member(X18,X14)
& apply(X12,X16,X18)
& apply(X11,X18,X17) ) )
& ( ! [X19] :
( ~ member(X19,X14)
| ~ apply(X12,X16,X19)
| ~ apply(X11,X19,X17) )
| apply(compose_function(X11,X12,X13,X14,X15),X16,X17) ) ) ),
inference(variable_rename,[status(thm)],[47]) ).
fof(49,plain,
! [X11,X12,X13,X14,X15,X16,X17] :
( ~ member(X16,X13)
| ~ member(X17,X15)
| ( ( ~ apply(compose_function(X11,X12,X13,X14,X15),X16,X17)
| ( member(esk10_7(X11,X12,X13,X14,X15,X16,X17),X14)
& apply(X12,X16,esk10_7(X11,X12,X13,X14,X15,X16,X17))
& apply(X11,esk10_7(X11,X12,X13,X14,X15,X16,X17),X17) ) )
& ( ! [X19] :
( ~ member(X19,X14)
| ~ apply(X12,X16,X19)
| ~ apply(X11,X19,X17) )
| apply(compose_function(X11,X12,X13,X14,X15),X16,X17) ) ) ),
inference(skolemize,[status(esa)],[48]) ).
fof(50,plain,
! [X11,X12,X13,X14,X15,X16,X17,X19] :
( ( ( ~ member(X19,X14)
| ~ apply(X12,X16,X19)
| ~ apply(X11,X19,X17)
| apply(compose_function(X11,X12,X13,X14,X15),X16,X17) )
& ( ~ apply(compose_function(X11,X12,X13,X14,X15),X16,X17)
| ( member(esk10_7(X11,X12,X13,X14,X15,X16,X17),X14)
& apply(X12,X16,esk10_7(X11,X12,X13,X14,X15,X16,X17))
& apply(X11,esk10_7(X11,X12,X13,X14,X15,X16,X17),X17) ) ) )
| ~ member(X16,X13)
| ~ member(X17,X15) ),
inference(shift_quantors,[status(thm)],[49]) ).
fof(51,plain,
! [X11,X12,X13,X14,X15,X16,X17,X19] :
( ( ~ member(X19,X14)
| ~ apply(X12,X16,X19)
| ~ apply(X11,X19,X17)
| apply(compose_function(X11,X12,X13,X14,X15),X16,X17)
| ~ member(X16,X13)
| ~ member(X17,X15) )
& ( member(esk10_7(X11,X12,X13,X14,X15,X16,X17),X14)
| ~ apply(compose_function(X11,X12,X13,X14,X15),X16,X17)
| ~ member(X16,X13)
| ~ member(X17,X15) )
& ( apply(X12,X16,esk10_7(X11,X12,X13,X14,X15,X16,X17))
| ~ apply(compose_function(X11,X12,X13,X14,X15),X16,X17)
| ~ member(X16,X13)
| ~ member(X17,X15) )
& ( apply(X11,esk10_7(X11,X12,X13,X14,X15,X16,X17),X17)
| ~ apply(compose_function(X11,X12,X13,X14,X15),X16,X17)
| ~ member(X16,X13)
| ~ member(X17,X15) ) ),
inference(distribute,[status(thm)],[50]) ).
cnf(52,plain,
( apply(X5,esk10_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)],[51]) ).
cnf(53,plain,
( apply(X6,X3,esk10_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)],[51]) ).
cnf(54,plain,
( member(esk10_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)],[51]) ).
fof(56,negated_conjecture,
? [X1,X2,X11,X3,X4] :
( maps(X1,X3,X4)
& maps(X2,X4,X3)
& maps(X11,X4,X3)
& identity(compose_function(X2,X1,X3,X4,X3),X3)
& identity(compose_function(X1,X11,X4,X3,X4),X4)
& ~ equal_maps(X2,X11,X4,X3) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(57,negated_conjecture,
? [X12,X13,X14,X15,X16] :
( maps(X12,X15,X16)
& maps(X13,X16,X15)
& maps(X14,X16,X15)
& identity(compose_function(X13,X12,X15,X16,X15),X15)
& identity(compose_function(X12,X14,X16,X15,X16),X16)
& ~ equal_maps(X13,X14,X16,X15) ),
inference(variable_rename,[status(thm)],[56]) ).
fof(58,negated_conjecture,
( maps(esk11_0,esk14_0,esk15_0)
& maps(esk12_0,esk15_0,esk14_0)
& maps(esk13_0,esk15_0,esk14_0)
& identity(compose_function(esk12_0,esk11_0,esk14_0,esk15_0,esk14_0),esk14_0)
& identity(compose_function(esk11_0,esk13_0,esk15_0,esk14_0,esk15_0),esk15_0)
& ~ equal_maps(esk12_0,esk13_0,esk15_0,esk14_0) ),
inference(skolemize,[status(esa)],[57]) ).
cnf(59,negated_conjecture,
~ equal_maps(esk12_0,esk13_0,esk15_0,esk14_0),
inference(split_conjunct,[status(thm)],[58]) ).
cnf(60,negated_conjecture,
identity(compose_function(esk11_0,esk13_0,esk15_0,esk14_0,esk15_0),esk15_0),
inference(split_conjunct,[status(thm)],[58]) ).
cnf(61,negated_conjecture,
identity(compose_function(esk12_0,esk11_0,esk14_0,esk15_0,esk14_0),esk14_0),
inference(split_conjunct,[status(thm)],[58]) ).
cnf(62,negated_conjecture,
maps(esk13_0,esk15_0,esk14_0),
inference(split_conjunct,[status(thm)],[58]) ).
cnf(63,negated_conjecture,
maps(esk12_0,esk15_0,esk14_0),
inference(split_conjunct,[status(thm)],[58]) ).
cnf(64,negated_conjecture,
maps(esk11_0,esk14_0,esk15_0),
inference(split_conjunct,[status(thm)],[58]) ).
cnf(65,negated_conjecture,
( apply(compose_function(esk11_0,esk13_0,esk15_0,esk14_0,esk15_0),X1,X1)
| ~ member(X1,esk15_0) ),
inference(spm,[status(thm)],[46,60,theory(equality)]) ).
cnf(66,negated_conjecture,
( apply(compose_function(esk12_0,esk11_0,esk14_0,esk15_0,esk14_0),X1,X1)
| ~ member(X1,esk14_0) ),
inference(spm,[status(thm)],[46,61,theory(equality)]) ).
cnf(70,negated_conjecture,
( X1 = X2
| ~ apply(esk11_0,X3,X2)
| ~ apply(esk11_0,X3,X1)
| ~ member(X3,esk14_0)
| ~ member(X2,esk15_0)
| ~ member(X1,esk15_0) ),
inference(spm,[status(thm)],[26,64,theory(equality)]) ).
cnf(71,negated_conjecture,
( X1 = X2
| ~ apply(esk12_0,X3,X2)
| ~ apply(esk12_0,X3,X1)
| ~ member(X3,esk15_0)
| ~ member(X2,esk14_0)
| ~ member(X1,esk14_0) ),
inference(spm,[status(thm)],[26,63,theory(equality)]) ).
cnf(72,negated_conjecture,
( X1 = X2
| ~ apply(esk13_0,X3,X2)
| ~ apply(esk13_0,X3,X1)
| ~ member(X3,esk15_0)
| ~ member(X2,esk14_0)
| ~ member(X1,esk14_0) ),
inference(spm,[status(thm)],[26,62,theory(equality)]) ).
cnf(109,negated_conjecture,
( X1 = esk4_4(esk11_0,X2,X3,X4)
| ~ apply(esk11_0,X4,X1)
| ~ member(X4,esk14_0)
| ~ member(esk4_4(esk11_0,X2,X3,X4),esk15_0)
| ~ member(X1,esk15_0)
| ~ maps(esk11_0,X2,X3)
| ~ member(X4,X2) ),
inference(spm,[status(thm)],[70,24,theory(equality)]) ).
cnf(114,negated_conjecture,
( X1 = esk10_7(X2,esk11_0,X3,X4,X5,X6,X7)
| ~ apply(esk11_0,X6,X1)
| ~ member(X6,esk14_0)
| ~ member(esk10_7(X2,esk11_0,X3,X4,X5,X6,X7),esk15_0)
| ~ member(X1,esk15_0)
| ~ apply(compose_function(X2,esk11_0,X3,X4,X5),X6,X7)
| ~ member(X6,X3)
| ~ member(X7,X5) ),
inference(spm,[status(thm)],[70,53,theory(equality)]) ).
cnf(118,negated_conjecture,
( X1 = esk2_4(esk12_0,X2,X3,X4)
| equal_maps(esk12_0,X2,X3,X4)
| ~ apply(esk12_0,esk1_4(esk12_0,X2,X3,X4),X1)
| ~ member(esk1_4(esk12_0,X2,X3,X4),esk15_0)
| ~ member(esk2_4(esk12_0,X2,X3,X4),esk14_0)
| ~ member(X1,esk14_0) ),
inference(spm,[status(thm)],[71,14,theory(equality)]) ).
cnf(123,negated_conjecture,
( X1 = esk4_4(esk13_0,X2,X3,X4)
| ~ apply(esk13_0,X4,X1)
| ~ member(X4,esk15_0)
| ~ member(esk4_4(esk13_0,X2,X3,X4),esk14_0)
| ~ member(X1,esk14_0)
| ~ maps(esk13_0,X2,X3)
| ~ member(X4,X2) ),
inference(spm,[status(thm)],[72,24,theory(equality)]) ).
cnf(128,negated_conjecture,
( X1 = esk10_7(X2,esk13_0,X3,X4,X5,X6,X7)
| ~ apply(esk13_0,X6,X1)
| ~ member(X6,esk15_0)
| ~ member(esk10_7(X2,esk13_0,X3,X4,X5,X6,X7),esk14_0)
| ~ member(X1,esk14_0)
| ~ apply(compose_function(X2,esk13_0,X3,X4,X5),X6,X7)
| ~ member(X6,X3)
| ~ member(X7,X5) ),
inference(spm,[status(thm)],[72,53,theory(equality)]) ).
cnf(155,negated_conjecture,
( X1 = esk4_4(esk11_0,X2,esk15_0,X3)
| ~ maps(esk11_0,X2,esk15_0)
| ~ apply(esk11_0,X3,X1)
| ~ member(X3,esk14_0)
| ~ member(X1,esk15_0)
| ~ member(X3,X2) ),
inference(spm,[status(thm)],[109,25,theory(equality)]) ).
cnf(174,negated_conjecture,
( X1 = esk4_4(esk13_0,X2,esk14_0,X3)
| ~ maps(esk13_0,X2,esk14_0)
| ~ apply(esk13_0,X3,X1)
| ~ member(X3,esk15_0)
| ~ member(X1,esk14_0)
| ~ member(X3,X2) ),
inference(spm,[status(thm)],[123,25,theory(equality)]) ).
cnf(176,negated_conjecture,
( esk3_4(X1,esk13_0,X2,X3) = esk4_4(esk13_0,X4,esk14_0,esk1_4(X1,esk13_0,X2,X3))
| equal_maps(X1,esk13_0,X2,X3)
| ~ maps(esk13_0,X4,esk14_0)
| ~ member(esk1_4(X1,esk13_0,X2,X3),esk15_0)
| ~ member(esk3_4(X1,esk13_0,X2,X3),esk14_0)
| ~ member(esk1_4(X1,esk13_0,X2,X3),X4) ),
inference(spm,[status(thm)],[174,13,theory(equality)]) ).
cnf(758,negated_conjecture,
( X1 = esk10_7(X2,esk11_0,X3,esk15_0,X4,X5,X6)
| ~ apply(compose_function(X2,esk11_0,X3,esk15_0,X4),X5,X6)
| ~ apply(esk11_0,X5,X1)
| ~ member(X5,esk14_0)
| ~ member(X1,esk15_0)
| ~ member(X5,X3)
| ~ member(X6,X4) ),
inference(spm,[status(thm)],[114,54,theory(equality)]) ).
cnf(759,negated_conjecture,
( esk4_4(esk11_0,X1,X2,X3) = esk10_7(X4,esk11_0,X5,esk15_0,X6,X3,X7)
| ~ apply(compose_function(X4,esk11_0,X5,esk15_0,X6),X3,X7)
| ~ member(X3,esk14_0)
| ~ member(esk4_4(esk11_0,X1,X2,X3),esk15_0)
| ~ member(X3,X5)
| ~ member(X7,X6)
| ~ maps(esk11_0,X1,X2)
| ~ member(X3,X1) ),
inference(spm,[status(thm)],[758,24,theory(equality)]) ).
cnf(811,negated_conjecture,
( X1 = esk10_7(X2,esk13_0,X3,esk14_0,X4,X5,X6)
| ~ apply(compose_function(X2,esk13_0,X3,esk14_0,X4),X5,X6)
| ~ apply(esk13_0,X5,X1)
| ~ member(X5,esk15_0)
| ~ member(X1,esk14_0)
| ~ member(X5,X3)
| ~ member(X6,X4) ),
inference(spm,[status(thm)],[128,54,theory(equality)]) ).
cnf(812,negated_conjecture,
( esk4_4(esk13_0,X1,X2,X3) = esk10_7(X4,esk13_0,X5,esk14_0,X6,X3,X7)
| ~ apply(compose_function(X4,esk13_0,X5,esk14_0,X6),X3,X7)
| ~ member(X3,esk15_0)
| ~ member(esk4_4(esk13_0,X1,X2,X3),esk14_0)
| ~ member(X3,X5)
| ~ member(X7,X6)
| ~ maps(esk13_0,X1,X2)
| ~ member(X3,X1) ),
inference(spm,[status(thm)],[811,24,theory(equality)]) ).
cnf(1128,negated_conjecture,
( esk4_4(esk11_0,X1,esk15_0,X2) = esk10_7(X3,esk11_0,X4,esk15_0,X5,X2,X6)
| ~ maps(esk11_0,X1,esk15_0)
| ~ apply(compose_function(X3,esk11_0,X4,esk15_0,X5),X2,X6)
| ~ member(X2,esk14_0)
| ~ member(X2,X4)
| ~ member(X6,X5)
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[759,25,theory(equality)]) ).
cnf(1139,negated_conjecture,
( apply(X1,esk4_4(esk11_0,X6,esk15_0,X4),X5)
| ~ apply(compose_function(X1,esk11_0,X2,esk15_0,X3),X4,X5)
| ~ member(X4,X2)
| ~ member(X5,X3)
| ~ maps(esk11_0,X6,esk15_0)
| ~ member(X4,esk14_0)
| ~ member(X4,X6) ),
inference(spm,[status(thm)],[52,1128,theory(equality)]) ).
cnf(1187,negated_conjecture,
( apply(esk12_0,esk4_4(esk11_0,X1,esk15_0,X2),X2)
| ~ maps(esk11_0,X1,esk15_0)
| ~ member(X2,esk14_0)
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[1139,66,theory(equality)]) ).
cnf(1688,negated_conjecture,
( esk4_4(esk13_0,X1,esk14_0,X2) = esk10_7(X3,esk13_0,X4,esk14_0,X5,X2,X6)
| ~ maps(esk13_0,X1,esk14_0)
| ~ apply(compose_function(X3,esk13_0,X4,esk14_0,X5),X2,X6)
| ~ member(X2,esk15_0)
| ~ member(X2,X4)
| ~ member(X6,X5)
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[812,25,theory(equality)]) ).
cnf(1699,negated_conjecture,
( apply(X1,esk4_4(esk13_0,X6,esk14_0,X4),X5)
| ~ apply(compose_function(X1,esk13_0,X2,esk14_0,X3),X4,X5)
| ~ member(X4,X2)
| ~ member(X5,X3)
| ~ maps(esk13_0,X6,esk14_0)
| ~ member(X4,esk15_0)
| ~ member(X4,X6) ),
inference(spm,[status(thm)],[52,1688,theory(equality)]) ).
cnf(1747,negated_conjecture,
( apply(esk11_0,esk4_4(esk13_0,X1,esk14_0,X2),X2)
| ~ maps(esk13_0,X1,esk14_0)
| ~ member(X2,esk15_0)
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[1699,65,theory(equality)]) ).
cnf(1758,negated_conjecture,
( X1 = esk4_4(esk11_0,X2,esk15_0,esk4_4(esk13_0,X3,esk14_0,X1))
| ~ maps(esk11_0,X2,esk15_0)
| ~ member(esk4_4(esk13_0,X3,esk14_0,X1),esk14_0)
| ~ member(X1,esk15_0)
| ~ member(esk4_4(esk13_0,X3,esk14_0,X1),X2)
| ~ maps(esk13_0,X3,esk14_0)
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[155,1747,theory(equality)]) ).
cnf(1802,negated_conjecture,
( esk4_4(esk11_0,X2,esk15_0,esk4_4(esk13_0,X3,esk14_0,X1)) = X1
| ~ maps(esk13_0,X3,esk14_0)
| ~ maps(esk11_0,X2,esk15_0)
| ~ member(esk4_4(esk13_0,X3,esk14_0,X1),X2)
| ~ member(X1,esk15_0)
| ~ member(X1,X3) ),
inference(csr,[status(thm)],[1758,25]) ).
cnf(1818,negated_conjecture,
( apply(esk12_0,X3,esk4_4(esk13_0,X2,esk14_0,X3))
| ~ maps(esk11_0,X1,esk15_0)
| ~ member(esk4_4(esk13_0,X2,esk14_0,X3),esk14_0)
| ~ member(esk4_4(esk13_0,X2,esk14_0,X3),X1)
| ~ maps(esk13_0,X2,esk14_0)
| ~ member(X3,esk15_0)
| ~ member(X3,X2) ),
inference(spm,[status(thm)],[1187,1802,theory(equality)]) ).
cnf(1846,negated_conjecture,
( apply(esk12_0,X3,esk4_4(esk13_0,X2,esk14_0,X3))
| ~ maps(esk13_0,X2,esk14_0)
| ~ maps(esk11_0,X1,esk15_0)
| ~ member(esk4_4(esk13_0,X2,esk14_0,X3),X1)
| ~ member(X3,esk15_0)
| ~ member(X3,X2) ),
inference(csr,[status(thm)],[1818,25]) ).
cnf(1847,negated_conjecture,
( apply(esk12_0,X1,esk4_4(esk13_0,X2,esk14_0,X1))
| ~ maps(esk11_0,esk14_0,esk15_0)
| ~ maps(esk13_0,X2,esk14_0)
| ~ member(X1,esk15_0)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[1846,25,theory(equality)]) ).
cnf(1855,negated_conjecture,
( apply(esk12_0,X1,esk4_4(esk13_0,X2,esk14_0,X1))
| $false
| ~ maps(esk13_0,X2,esk14_0)
| ~ member(X1,esk15_0)
| ~ member(X1,X2) ),
inference(rw,[status(thm)],[1847,64,theory(equality)]) ).
cnf(1856,negated_conjecture,
( apply(esk12_0,X1,esk4_4(esk13_0,X2,esk14_0,X1))
| ~ maps(esk13_0,X2,esk14_0)
| ~ member(X1,esk15_0)
| ~ member(X1,X2) ),
inference(cn,[status(thm)],[1855,theory(equality)]) ).
cnf(1876,negated_conjecture,
( apply(esk12_0,esk1_4(X1,esk13_0,X2,X3),esk3_4(X1,esk13_0,X2,X3))
| equal_maps(X1,esk13_0,X2,X3)
| ~ maps(esk13_0,X4,esk14_0)
| ~ member(esk1_4(X1,esk13_0,X2,X3),esk15_0)
| ~ member(esk1_4(X1,esk13_0,X2,X3),X4)
| ~ member(esk3_4(X1,esk13_0,X2,X3),esk14_0) ),
inference(spm,[status(thm)],[1856,176,theory(equality)]) ).
cnf(4663,negated_conjecture,
( apply(esk12_0,esk1_4(X1,esk13_0,X2,X3),esk3_4(X1,esk13_0,X2,X3))
| equal_maps(X1,esk13_0,X2,X3)
| ~ maps(esk13_0,X2,esk14_0)
| ~ member(esk1_4(X1,esk13_0,X2,X3),esk15_0)
| ~ member(esk3_4(X1,esk13_0,X2,X3),esk14_0) ),
inference(spm,[status(thm)],[1876,17,theory(equality)]) ).
cnf(4667,negated_conjecture,
( esk3_4(esk12_0,esk13_0,X1,X2) = esk2_4(esk12_0,esk13_0,X1,X2)
| equal_maps(esk12_0,esk13_0,X1,X2)
| ~ member(esk1_4(esk12_0,esk13_0,X1,X2),esk15_0)
| ~ member(esk2_4(esk12_0,esk13_0,X1,X2),esk14_0)
| ~ member(esk3_4(esk12_0,esk13_0,X1,X2),esk14_0)
| ~ maps(esk13_0,X1,esk14_0) ),
inference(spm,[status(thm)],[118,4663,theory(equality)]) ).
cnf(4672,negated_conjecture,
( equal_maps(esk12_0,esk13_0,X1,X2)
| ~ maps(esk13_0,X1,esk14_0)
| ~ member(esk1_4(esk12_0,esk13_0,X1,X2),esk15_0)
| ~ member(esk2_4(esk12_0,esk13_0,X1,X2),esk14_0)
| ~ member(esk3_4(esk12_0,esk13_0,X1,X2),esk14_0) ),
inference(csr,[status(thm)],[4667,12]) ).
cnf(4673,negated_conjecture,
( equal_maps(esk12_0,esk13_0,X1,esk14_0)
| ~ maps(esk13_0,X1,esk14_0)
| ~ member(esk1_4(esk12_0,esk13_0,X1,esk14_0),esk15_0)
| ~ member(esk2_4(esk12_0,esk13_0,X1,esk14_0),esk14_0) ),
inference(spm,[status(thm)],[4672,15,theory(equality)]) ).
cnf(4674,negated_conjecture,
( equal_maps(esk12_0,esk13_0,X1,esk14_0)
| ~ maps(esk13_0,X1,esk14_0)
| ~ member(esk1_4(esk12_0,esk13_0,X1,esk14_0),esk15_0) ),
inference(csr,[status(thm)],[4673,16]) ).
cnf(4675,negated_conjecture,
( equal_maps(esk12_0,esk13_0,esk15_0,esk14_0)
| ~ maps(esk13_0,esk15_0,esk14_0) ),
inference(spm,[status(thm)],[4674,17,theory(equality)]) ).
cnf(4676,negated_conjecture,
( equal_maps(esk12_0,esk13_0,esk15_0,esk14_0)
| $false ),
inference(rw,[status(thm)],[4675,62,theory(equality)]) ).
cnf(4677,negated_conjecture,
equal_maps(esk12_0,esk13_0,esk15_0,esk14_0),
inference(cn,[status(thm)],[4676,theory(equality)]) ).
cnf(4678,negated_conjecture,
$false,
inference(sr,[status(thm)],[4677,59,theory(equality)]) ).
cnf(4679,negated_conjecture,
$false,
4678,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET728+4.p
% --creating new selector for [SET006+0.ax, SET006+1.ax]
% -running prover on /tmp/tmpFNV_4P/sel_SET728+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET728+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET728+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET728+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
%
%------------------------------------------------------------------------------