TSTP Solution File: SET708+4 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET708+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 03:14:45 EST 2010
% Result : Theorem 0.41s
% Output : CNFRefutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 4
% Syntax : Number of formulae : 67 ( 8 unt; 0 def)
% Number of atoms : 591 ( 37 equ)
% Maximal formula atoms : 55 ( 8 avg)
% Number of connectives : 846 ( 322 ~; 358 |; 154 &)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-6 aty)
% Number of functors : 19 ( 19 usr; 7 con; 0-8 aty)
% Number of variables : 370 ( 0 sgn 161 !; 40 ?)
% 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/tmp8E9p7g/sel_SET708+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/tmp8E9p7g/sel_SET708+4.p_1',maps) ).
fof(3,axiom,
! [X9,X2,X1,X3,X4,X10] :
( compose_predicate(X9,X2,X1,X3,X4,X10)
<=> ! [X5,X11] :
( ( member(X5,X3)
& member(X11,X10) )
=> ( apply(X9,X5,X11)
<=> ? [X8] :
( member(X8,X4)
& apply(X1,X5,X8)
& apply(X2,X8,X11) ) ) ) ),
file('/tmp/tmp8E9p7g/sel_SET708+4.p_1',compose_predicate) ).
fof(4,conjecture,
! [X1,X2,X12,X13,X3,X4,X10] :
( ( maps(X1,X3,X4)
& maps(X2,X4,X10)
& compose_predicate(X12,X2,X1,X3,X4,X10)
& compose_predicate(X13,X2,X1,X3,X4,X10) )
=> equal_maps(X12,X13,X3,X10) ),
file('/tmp/tmp8E9p7g/sel_SET708+4.p_1',thII01a) ).
fof(5,negated_conjecture,
~ ! [X1,X2,X12,X13,X3,X4,X10] :
( ( maps(X1,X3,X4)
& maps(X2,X4,X10)
& compose_predicate(X12,X2,X1,X3,X4,X10)
& compose_predicate(X13,X2,X1,X3,X4,X10) )
=> equal_maps(X12,X13,X3,X10) ),
inference(assume_negation,[status(cth)],[4]) ).
fof(6,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(7,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)],[6]) ).
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 ) )
& ( ( 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)],[7]) ).
fof(9,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)],[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)
| 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)],[9]) ).
cnf(11,plain,
( equal_maps(X1,X2,X3,X4)
| esk2_4(X1,X2,X3,X4) != esk3_4(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[10]) ).
cnf(12,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)],[10]) ).
cnf(13,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)],[10]) ).
cnf(14,plain,
( equal_maps(X1,X2,X3,X4)
| member(esk3_4(X1,X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[10]) ).
cnf(15,plain,
( equal_maps(X1,X2,X3,X4)
| member(esk2_4(X1,X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[10]) ).
cnf(16,plain,
( equal_maps(X1,X2,X3,X4)
| member(esk1_4(X1,X2,X3,X4),X3) ),
inference(split_conjunct,[status(thm)],[10]) ).
fof(18,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(19,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)],[18]) ).
fof(20,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)],[19]) ).
fof(21,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)],[20]) ).
fof(22,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)],[21]) ).
cnf(23,plain,
( apply(X1,X4,esk4_4(X1,X2,X3,X4))
| ~ maps(X1,X2,X3)
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(24,plain,
( member(esk4_4(X1,X2,X3,X4),X3)
| ~ maps(X1,X2,X3)
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(25,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)],[22]) ).
fof(38,plain,
! [X9,X2,X1,X3,X4,X10] :
( ( ~ compose_predicate(X9,X2,X1,X3,X4,X10)
| ! [X5,X11] :
( ~ member(X5,X3)
| ~ member(X11,X10)
| ( ( ~ apply(X9,X5,X11)
| ? [X8] :
( member(X8,X4)
& apply(X1,X5,X8)
& apply(X2,X8,X11) ) )
& ( ! [X8] :
( ~ member(X8,X4)
| ~ apply(X1,X5,X8)
| ~ apply(X2,X8,X11) )
| apply(X9,X5,X11) ) ) ) )
& ( ? [X5,X11] :
( member(X5,X3)
& member(X11,X10)
& ( ~ apply(X9,X5,X11)
| ! [X8] :
( ~ member(X8,X4)
| ~ apply(X1,X5,X8)
| ~ apply(X2,X8,X11) ) )
& ( apply(X9,X5,X11)
| ? [X8] :
( member(X8,X4)
& apply(X1,X5,X8)
& apply(X2,X8,X11) ) ) )
| compose_predicate(X9,X2,X1,X3,X4,X10) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(39,plain,
! [X12,X13,X14,X15,X16,X17] :
( ( ~ compose_predicate(X12,X13,X14,X15,X16,X17)
| ! [X18,X19] :
( ~ member(X18,X15)
| ~ member(X19,X17)
| ( ( ~ apply(X12,X18,X19)
| ? [X20] :
( member(X20,X16)
& apply(X14,X18,X20)
& apply(X13,X20,X19) ) )
& ( ! [X21] :
( ~ member(X21,X16)
| ~ apply(X14,X18,X21)
| ~ apply(X13,X21,X19) )
| apply(X12,X18,X19) ) ) ) )
& ( ? [X22,X23] :
( member(X22,X15)
& member(X23,X17)
& ( ~ apply(X12,X22,X23)
| ! [X24] :
( ~ member(X24,X16)
| ~ apply(X14,X22,X24)
| ~ apply(X13,X24,X23) ) )
& ( apply(X12,X22,X23)
| ? [X25] :
( member(X25,X16)
& apply(X14,X22,X25)
& apply(X13,X25,X23) ) ) )
| compose_predicate(X12,X13,X14,X15,X16,X17) ) ),
inference(variable_rename,[status(thm)],[38]) ).
fof(40,plain,
! [X12,X13,X14,X15,X16,X17] :
( ( ~ compose_predicate(X12,X13,X14,X15,X16,X17)
| ! [X18,X19] :
( ~ member(X18,X15)
| ~ member(X19,X17)
| ( ( ~ apply(X12,X18,X19)
| ( member(esk9_8(X12,X13,X14,X15,X16,X17,X18,X19),X16)
& apply(X14,X18,esk9_8(X12,X13,X14,X15,X16,X17,X18,X19))
& apply(X13,esk9_8(X12,X13,X14,X15,X16,X17,X18,X19),X19) ) )
& ( ! [X21] :
( ~ member(X21,X16)
| ~ apply(X14,X18,X21)
| ~ apply(X13,X21,X19) )
| apply(X12,X18,X19) ) ) ) )
& ( ( member(esk10_6(X12,X13,X14,X15,X16,X17),X15)
& member(esk11_6(X12,X13,X14,X15,X16,X17),X17)
& ( ~ apply(X12,esk10_6(X12,X13,X14,X15,X16,X17),esk11_6(X12,X13,X14,X15,X16,X17))
| ! [X24] :
( ~ member(X24,X16)
| ~ apply(X14,esk10_6(X12,X13,X14,X15,X16,X17),X24)
| ~ apply(X13,X24,esk11_6(X12,X13,X14,X15,X16,X17)) ) )
& ( apply(X12,esk10_6(X12,X13,X14,X15,X16,X17),esk11_6(X12,X13,X14,X15,X16,X17))
| ( member(esk12_6(X12,X13,X14,X15,X16,X17),X16)
& apply(X14,esk10_6(X12,X13,X14,X15,X16,X17),esk12_6(X12,X13,X14,X15,X16,X17))
& apply(X13,esk12_6(X12,X13,X14,X15,X16,X17),esk11_6(X12,X13,X14,X15,X16,X17)) ) ) )
| compose_predicate(X12,X13,X14,X15,X16,X17) ) ),
inference(skolemize,[status(esa)],[39]) ).
fof(41,plain,
! [X12,X13,X14,X15,X16,X17,X18,X19,X21,X24] :
( ( ( ( ~ member(X24,X16)
| ~ apply(X14,esk10_6(X12,X13,X14,X15,X16,X17),X24)
| ~ apply(X13,X24,esk11_6(X12,X13,X14,X15,X16,X17))
| ~ apply(X12,esk10_6(X12,X13,X14,X15,X16,X17),esk11_6(X12,X13,X14,X15,X16,X17)) )
& ( apply(X12,esk10_6(X12,X13,X14,X15,X16,X17),esk11_6(X12,X13,X14,X15,X16,X17))
| ( member(esk12_6(X12,X13,X14,X15,X16,X17),X16)
& apply(X14,esk10_6(X12,X13,X14,X15,X16,X17),esk12_6(X12,X13,X14,X15,X16,X17))
& apply(X13,esk12_6(X12,X13,X14,X15,X16,X17),esk11_6(X12,X13,X14,X15,X16,X17)) ) )
& member(esk10_6(X12,X13,X14,X15,X16,X17),X15)
& member(esk11_6(X12,X13,X14,X15,X16,X17),X17) )
| compose_predicate(X12,X13,X14,X15,X16,X17) )
& ( ( ( ~ member(X21,X16)
| ~ apply(X14,X18,X21)
| ~ apply(X13,X21,X19)
| apply(X12,X18,X19) )
& ( ~ apply(X12,X18,X19)
| ( member(esk9_8(X12,X13,X14,X15,X16,X17,X18,X19),X16)
& apply(X14,X18,esk9_8(X12,X13,X14,X15,X16,X17,X18,X19))
& apply(X13,esk9_8(X12,X13,X14,X15,X16,X17,X18,X19),X19) ) ) )
| ~ member(X18,X15)
| ~ member(X19,X17)
| ~ compose_predicate(X12,X13,X14,X15,X16,X17) ) ),
inference(shift_quantors,[status(thm)],[40]) ).
fof(42,plain,
! [X12,X13,X14,X15,X16,X17,X18,X19,X21,X24] :
( ( ~ member(X24,X16)
| ~ apply(X14,esk10_6(X12,X13,X14,X15,X16,X17),X24)
| ~ apply(X13,X24,esk11_6(X12,X13,X14,X15,X16,X17))
| ~ apply(X12,esk10_6(X12,X13,X14,X15,X16,X17),esk11_6(X12,X13,X14,X15,X16,X17))
| compose_predicate(X12,X13,X14,X15,X16,X17) )
& ( member(esk12_6(X12,X13,X14,X15,X16,X17),X16)
| apply(X12,esk10_6(X12,X13,X14,X15,X16,X17),esk11_6(X12,X13,X14,X15,X16,X17))
| compose_predicate(X12,X13,X14,X15,X16,X17) )
& ( apply(X14,esk10_6(X12,X13,X14,X15,X16,X17),esk12_6(X12,X13,X14,X15,X16,X17))
| apply(X12,esk10_6(X12,X13,X14,X15,X16,X17),esk11_6(X12,X13,X14,X15,X16,X17))
| compose_predicate(X12,X13,X14,X15,X16,X17) )
& ( apply(X13,esk12_6(X12,X13,X14,X15,X16,X17),esk11_6(X12,X13,X14,X15,X16,X17))
| apply(X12,esk10_6(X12,X13,X14,X15,X16,X17),esk11_6(X12,X13,X14,X15,X16,X17))
| compose_predicate(X12,X13,X14,X15,X16,X17) )
& ( member(esk10_6(X12,X13,X14,X15,X16,X17),X15)
| compose_predicate(X12,X13,X14,X15,X16,X17) )
& ( member(esk11_6(X12,X13,X14,X15,X16,X17),X17)
| compose_predicate(X12,X13,X14,X15,X16,X17) )
& ( ~ member(X21,X16)
| ~ apply(X14,X18,X21)
| ~ apply(X13,X21,X19)
| apply(X12,X18,X19)
| ~ member(X18,X15)
| ~ member(X19,X17)
| ~ compose_predicate(X12,X13,X14,X15,X16,X17) )
& ( member(esk9_8(X12,X13,X14,X15,X16,X17,X18,X19),X16)
| ~ apply(X12,X18,X19)
| ~ member(X18,X15)
| ~ member(X19,X17)
| ~ compose_predicate(X12,X13,X14,X15,X16,X17) )
& ( apply(X14,X18,esk9_8(X12,X13,X14,X15,X16,X17,X18,X19))
| ~ apply(X12,X18,X19)
| ~ member(X18,X15)
| ~ member(X19,X17)
| ~ compose_predicate(X12,X13,X14,X15,X16,X17) )
& ( apply(X13,esk9_8(X12,X13,X14,X15,X16,X17,X18,X19),X19)
| ~ apply(X12,X18,X19)
| ~ member(X18,X15)
| ~ member(X19,X17)
| ~ compose_predicate(X12,X13,X14,X15,X16,X17) ) ),
inference(distribute,[status(thm)],[41]) ).
cnf(43,plain,
( apply(X2,esk9_8(X1,X2,X3,X4,X5,X6,X8,X7),X7)
| ~ compose_predicate(X1,X2,X3,X4,X5,X6)
| ~ member(X7,X6)
| ~ member(X8,X4)
| ~ apply(X1,X8,X7) ),
inference(split_conjunct,[status(thm)],[42]) ).
cnf(44,plain,
( apply(X3,X8,esk9_8(X1,X2,X3,X4,X5,X6,X8,X7))
| ~ compose_predicate(X1,X2,X3,X4,X5,X6)
| ~ member(X7,X6)
| ~ member(X8,X4)
| ~ apply(X1,X8,X7) ),
inference(split_conjunct,[status(thm)],[42]) ).
cnf(45,plain,
( member(esk9_8(X1,X2,X3,X4,X5,X6,X8,X7),X5)
| ~ compose_predicate(X1,X2,X3,X4,X5,X6)
| ~ member(X7,X6)
| ~ member(X8,X4)
| ~ apply(X1,X8,X7) ),
inference(split_conjunct,[status(thm)],[42]) ).
cnf(46,plain,
( apply(X1,X8,X7)
| ~ compose_predicate(X1,X2,X3,X4,X5,X6)
| ~ member(X7,X6)
| ~ member(X8,X4)
| ~ apply(X2,X9,X7)
| ~ apply(X3,X8,X9)
| ~ member(X9,X5) ),
inference(split_conjunct,[status(thm)],[42]) ).
fof(53,negated_conjecture,
? [X1,X2,X12,X13,X3,X4,X10] :
( maps(X1,X3,X4)
& maps(X2,X4,X10)
& compose_predicate(X12,X2,X1,X3,X4,X10)
& compose_predicate(X13,X2,X1,X3,X4,X10)
& ~ equal_maps(X12,X13,X3,X10) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(54,negated_conjecture,
? [X14,X15,X16,X17,X18,X19,X20] :
( maps(X14,X18,X19)
& maps(X15,X19,X20)
& compose_predicate(X16,X15,X14,X18,X19,X20)
& compose_predicate(X17,X15,X14,X18,X19,X20)
& ~ equal_maps(X16,X17,X18,X20) ),
inference(variable_rename,[status(thm)],[53]) ).
fof(55,negated_conjecture,
( maps(esk13_0,esk17_0,esk18_0)
& maps(esk14_0,esk18_0,esk19_0)
& compose_predicate(esk15_0,esk14_0,esk13_0,esk17_0,esk18_0,esk19_0)
& compose_predicate(esk16_0,esk14_0,esk13_0,esk17_0,esk18_0,esk19_0)
& ~ equal_maps(esk15_0,esk16_0,esk17_0,esk19_0) ),
inference(skolemize,[status(esa)],[54]) ).
cnf(56,negated_conjecture,
~ equal_maps(esk15_0,esk16_0,esk17_0,esk19_0),
inference(split_conjunct,[status(thm)],[55]) ).
cnf(57,negated_conjecture,
compose_predicate(esk16_0,esk14_0,esk13_0,esk17_0,esk18_0,esk19_0),
inference(split_conjunct,[status(thm)],[55]) ).
cnf(58,negated_conjecture,
compose_predicate(esk15_0,esk14_0,esk13_0,esk17_0,esk18_0,esk19_0),
inference(split_conjunct,[status(thm)],[55]) ).
cnf(59,negated_conjecture,
maps(esk14_0,esk18_0,esk19_0),
inference(split_conjunct,[status(thm)],[55]) ).
cnf(60,negated_conjecture,
maps(esk13_0,esk17_0,esk18_0),
inference(split_conjunct,[status(thm)],[55]) ).
cnf(65,negated_conjecture,
( X1 = X2
| ~ apply(esk13_0,X3,X2)
| ~ apply(esk13_0,X3,X1)
| ~ member(X3,esk17_0)
| ~ member(X2,esk18_0)
| ~ member(X1,esk18_0) ),
inference(spm,[status(thm)],[25,60,theory(equality)]) ).
cnf(66,negated_conjecture,
( X1 = X2
| ~ apply(esk14_0,X3,X2)
| ~ apply(esk14_0,X3,X1)
| ~ member(X3,esk18_0)
| ~ member(X2,esk19_0)
| ~ member(X1,esk19_0) ),
inference(spm,[status(thm)],[25,59,theory(equality)]) ).
cnf(75,negated_conjecture,
( apply(esk15_0,X1,X2)
| ~ apply(esk13_0,X1,X3)
| ~ apply(esk14_0,X3,X2)
| ~ member(X3,esk18_0)
| ~ member(X1,esk17_0)
| ~ member(X2,esk19_0) ),
inference(spm,[status(thm)],[46,58,theory(equality)]) ).
cnf(85,negated_conjecture,
( X1 = esk9_8(X2,X3,esk13_0,X4,X5,X6,X7,X8)
| ~ apply(esk13_0,X7,X1)
| ~ member(X7,esk17_0)
| ~ member(esk9_8(X2,X3,esk13_0,X4,X5,X6,X7,X8),esk18_0)
| ~ member(X1,esk18_0)
| ~ compose_predicate(X2,X3,esk13_0,X4,X5,X6)
| ~ apply(X2,X7,X8)
| ~ member(X7,X4)
| ~ member(X8,X6) ),
inference(spm,[status(thm)],[65,44,theory(equality)]) ).
cnf(105,negated_conjecture,
( apply(esk15_0,X1,X2)
| ~ apply(esk14_0,esk9_8(X3,X4,esk13_0,X5,X6,X7,X1,X8),X2)
| ~ member(esk9_8(X3,X4,esk13_0,X5,X6,X7,X1,X8),esk18_0)
| ~ member(X1,esk17_0)
| ~ member(X2,esk19_0)
| ~ compose_predicate(X3,X4,esk13_0,X5,X6,X7)
| ~ apply(X3,X1,X8)
| ~ member(X1,X5)
| ~ member(X8,X7) ),
inference(spm,[status(thm)],[75,44,theory(equality)]) ).
cnf(459,negated_conjecture,
( X1 = esk9_8(X2,X3,esk13_0,X4,esk18_0,X5,X6,X7)
| ~ compose_predicate(X2,X3,esk13_0,X4,esk18_0,X5)
| ~ apply(esk13_0,X6,X1)
| ~ apply(X2,X6,X7)
| ~ member(X6,esk17_0)
| ~ member(X1,esk18_0)
| ~ member(X6,X4)
| ~ member(X7,X5) ),
inference(spm,[status(thm)],[85,45,theory(equality)]) ).
cnf(460,negated_conjecture,
( esk4_4(esk13_0,X1,X2,X3) = esk9_8(X4,X5,esk13_0,X6,esk18_0,X7,X3,X8)
| ~ compose_predicate(X4,X5,esk13_0,X6,esk18_0,X7)
| ~ apply(X4,X3,X8)
| ~ member(X3,esk17_0)
| ~ member(esk4_4(esk13_0,X1,X2,X3),esk18_0)
| ~ member(X3,X6)
| ~ member(X8,X7)
| ~ maps(esk13_0,X1,X2)
| ~ member(X3,X1) ),
inference(spm,[status(thm)],[459,23,theory(equality)]) ).
cnf(724,negated_conjecture,
( apply(esk15_0,X1,X2)
| ~ compose_predicate(X3,esk14_0,esk13_0,X4,X5,X6)
| ~ apply(X3,X1,X2)
| ~ member(esk9_8(X3,esk14_0,esk13_0,X4,X5,X6,X1,X2),esk18_0)
| ~ member(X1,esk17_0)
| ~ member(X2,esk19_0)
| ~ member(X1,X4)
| ~ member(X2,X6) ),
inference(spm,[status(thm)],[105,43,theory(equality)]) ).
cnf(728,negated_conjecture,
( apply(esk15_0,X1,X2)
| ~ compose_predicate(X3,esk14_0,esk13_0,X4,esk18_0,X5)
| ~ apply(X3,X1,X2)
| ~ member(X1,esk17_0)
| ~ member(X2,esk19_0)
| ~ member(X1,X4)
| ~ member(X2,X5) ),
inference(spm,[status(thm)],[724,45,theory(equality)]) ).
cnf(730,negated_conjecture,
( apply(esk15_0,X1,X2)
| ~ apply(esk16_0,X1,X2)
| ~ member(X1,esk17_0)
| ~ member(X2,esk19_0) ),
inference(spm,[status(thm)],[728,57,theory(equality)]) ).
cnf(732,negated_conjecture,
( apply(esk15_0,esk1_4(X1,esk16_0,X2,X3),esk3_4(X1,esk16_0,X2,X3))
| equal_maps(X1,esk16_0,X2,X3)
| ~ member(esk1_4(X1,esk16_0,X2,X3),esk17_0)
| ~ member(esk3_4(X1,esk16_0,X2,X3),esk19_0) ),
inference(spm,[status(thm)],[730,12,theory(equality)]) ).
cnf(963,negated_conjecture,
( esk4_4(esk13_0,X1,esk18_0,X2) = esk9_8(X3,X4,esk13_0,X5,esk18_0,X6,X2,X7)
| ~ compose_predicate(X3,X4,esk13_0,X5,esk18_0,X6)
| ~ maps(esk13_0,X1,esk18_0)
| ~ apply(X3,X2,X7)
| ~ member(X2,esk17_0)
| ~ member(X2,X5)
| ~ member(X7,X6)
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[460,24,theory(equality)]) ).
cnf(974,negated_conjecture,
( apply(X1,esk4_4(esk13_0,X7,esk18_0,X5),X6)
| ~ compose_predicate(X2,X1,esk13_0,X3,esk18_0,X4)
| ~ apply(X2,X5,X6)
| ~ member(X5,X3)
| ~ member(X6,X4)
| ~ maps(esk13_0,X7,esk18_0)
| ~ member(X5,esk17_0)
| ~ member(X5,X7) ),
inference(spm,[status(thm)],[43,963,theory(equality)]) ).
cnf(1036,negated_conjecture,
( apply(esk14_0,esk4_4(esk13_0,X1,esk18_0,X2),X3)
| ~ maps(esk13_0,X1,esk18_0)
| ~ apply(esk15_0,X2,X3)
| ~ member(X2,esk17_0)
| ~ member(X3,esk19_0)
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[974,58,theory(equality)]) ).
cnf(1038,negated_conjecture,
( X1 = X2
| ~ apply(esk14_0,esk4_4(esk13_0,X3,esk18_0,X4),X1)
| ~ member(esk4_4(esk13_0,X3,esk18_0,X4),esk18_0)
| ~ member(X2,esk19_0)
| ~ member(X1,esk19_0)
| ~ maps(esk13_0,X3,esk18_0)
| ~ apply(esk15_0,X4,X2)
| ~ member(X4,esk17_0)
| ~ member(X4,X3) ),
inference(spm,[status(thm)],[66,1036,theory(equality)]) ).
cnf(1123,negated_conjecture,
( X1 = X2
| ~ maps(esk13_0,X3,esk18_0)
| ~ apply(esk14_0,esk4_4(esk13_0,X3,esk18_0,X4),X1)
| ~ apply(esk15_0,X4,X2)
| ~ member(X2,esk19_0)
| ~ member(X1,esk19_0)
| ~ member(X4,esk17_0)
| ~ member(X4,X3) ),
inference(csr,[status(thm)],[1038,24]) ).
cnf(1133,negated_conjecture,
( X1 = X2
| ~ maps(esk13_0,X3,esk18_0)
| ~ apply(esk15_0,X4,X2)
| ~ member(X2,esk19_0)
| ~ member(X1,esk19_0)
| ~ member(X4,esk17_0)
| ~ member(X4,X3)
| ~ apply(esk15_0,X4,X1) ),
inference(spm,[status(thm)],[1123,1036,theory(equality)]) ).
cnf(1135,negated_conjecture,
( X1 = X2
| ~ apply(esk15_0,X3,X2)
| ~ apply(esk15_0,X3,X1)
| ~ member(X2,esk19_0)
| ~ member(X1,esk19_0)
| ~ member(X3,esk17_0) ),
inference(spm,[status(thm)],[1133,60,theory(equality)]) ).
cnf(1138,negated_conjecture,
( X1 = esk2_4(esk15_0,X2,X3,X4)
| equal_maps(esk15_0,X2,X3,X4)
| ~ apply(esk15_0,esk1_4(esk15_0,X2,X3,X4),X1)
| ~ member(esk2_4(esk15_0,X2,X3,X4),esk19_0)
| ~ member(X1,esk19_0)
| ~ member(esk1_4(esk15_0,X2,X3,X4),esk17_0) ),
inference(spm,[status(thm)],[1135,13,theory(equality)]) ).
cnf(1384,negated_conjecture,
( esk3_4(esk15_0,esk16_0,X1,X2) = esk2_4(esk15_0,esk16_0,X1,X2)
| equal_maps(esk15_0,esk16_0,X1,X2)
| ~ member(esk2_4(esk15_0,esk16_0,X1,X2),esk19_0)
| ~ member(esk1_4(esk15_0,esk16_0,X1,X2),esk17_0)
| ~ member(esk3_4(esk15_0,esk16_0,X1,X2),esk19_0) ),
inference(spm,[status(thm)],[1138,732,theory(equality)]) ).
cnf(1389,negated_conjecture,
( equal_maps(esk15_0,esk16_0,X1,X2)
| ~ member(esk2_4(esk15_0,esk16_0,X1,X2),esk19_0)
| ~ member(esk1_4(esk15_0,esk16_0,X1,X2),esk17_0)
| ~ member(esk3_4(esk15_0,esk16_0,X1,X2),esk19_0) ),
inference(csr,[status(thm)],[1384,11]) ).
cnf(1390,negated_conjecture,
( equal_maps(esk15_0,esk16_0,X1,esk19_0)
| ~ member(esk2_4(esk15_0,esk16_0,X1,esk19_0),esk19_0)
| ~ member(esk1_4(esk15_0,esk16_0,X1,esk19_0),esk17_0) ),
inference(spm,[status(thm)],[1389,14,theory(equality)]) ).
cnf(1391,negated_conjecture,
( equal_maps(esk15_0,esk16_0,X1,esk19_0)
| ~ member(esk1_4(esk15_0,esk16_0,X1,esk19_0),esk17_0) ),
inference(csr,[status(thm)],[1390,15]) ).
cnf(1392,negated_conjecture,
equal_maps(esk15_0,esk16_0,esk17_0,esk19_0),
inference(spm,[status(thm)],[1391,16,theory(equality)]) ).
cnf(1393,negated_conjecture,
$false,
inference(sr,[status(thm)],[1392,56,theory(equality)]) ).
cnf(1394,negated_conjecture,
$false,
1393,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET708+4.p
% --creating new selector for [SET006+0.ax, SET006+1.ax]
% -running prover on /tmp/tmp8E9p7g/sel_SET708+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET708+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET708+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET708+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
%
%------------------------------------------------------------------------------