TSTP Solution File: SET722+4 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET722+4 : TPTP v5.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 03:19:54 EST 2010
% Result : Theorem 0.29s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 33 ( 5 unt; 0 def)
% Number of atoms : 175 ( 0 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 234 ( 92 ~; 89 |; 47 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-7 aty)
% Number of variables : 164 ( 2 sgn 86 !; 18 ?)
% 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/tmpr4V4T-/sel_SET722+4.p_1',surjective) ).
fof(3,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/tmpr4V4T-/sel_SET722+4.p_1',compose_function) ).
fof(6,conjecture,
! [X1,X9,X2,X3,X10] :
( ( maps(X1,X2,X3)
& maps(X9,X3,X10)
& surjective(compose_function(X9,X1,X2,X3,X10),X2,X10) )
=> surjective(X9,X3,X10) ),
file('/tmp/tmpr4V4T-/sel_SET722+4.p_1',thII13) ).
fof(7,negated_conjecture,
~ ! [X1,X9,X2,X3,X10] :
( ( maps(X1,X2,X3)
& maps(X9,X3,X10)
& surjective(compose_function(X9,X1,X2,X3,X10),X2,X10) )
=> surjective(X9,X3,X10) ),
inference(assume_negation,[status(cth)],[6]) ).
fof(8,plain,
! [X1,X2,X3] :
( ( ~ surjective(X1,X2,X3)
| ! [X4] :
( ~ member(X4,X3)
| ? [X5] :
( member(X5,X2)
& apply(X1,X5,X4) ) ) )
& ( ? [X4] :
( member(X4,X3)
& ! [X5] :
( ~ member(X5,X2)
| ~ apply(X1,X5,X4) ) )
| surjective(X1,X2,X3) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(9,plain,
! [X6,X7,X8] :
( ( ~ surjective(X6,X7,X8)
| ! [X9] :
( ~ member(X9,X8)
| ? [X10] :
( member(X10,X7)
& apply(X6,X10,X9) ) ) )
& ( ? [X11] :
( member(X11,X8)
& ! [X12] :
( ~ member(X12,X7)
| ~ apply(X6,X12,X11) ) )
| surjective(X6,X7,X8) ) ),
inference(variable_rename,[status(thm)],[8]) ).
fof(10,plain,
! [X6,X7,X8] :
( ( ~ surjective(X6,X7,X8)
| ! [X9] :
( ~ member(X9,X8)
| ( member(esk1_4(X6,X7,X8,X9),X7)
& apply(X6,esk1_4(X6,X7,X8,X9),X9) ) ) )
& ( ( member(esk2_3(X6,X7,X8),X8)
& ! [X12] :
( ~ member(X12,X7)
| ~ apply(X6,X12,esk2_3(X6,X7,X8)) ) )
| surjective(X6,X7,X8) ) ),
inference(skolemize,[status(esa)],[9]) ).
fof(11,plain,
! [X6,X7,X8,X9,X12] :
( ( ( ( ~ member(X12,X7)
| ~ apply(X6,X12,esk2_3(X6,X7,X8)) )
& member(esk2_3(X6,X7,X8),X8) )
| surjective(X6,X7,X8) )
& ( ~ member(X9,X8)
| ( member(esk1_4(X6,X7,X8,X9),X7)
& apply(X6,esk1_4(X6,X7,X8,X9),X9) )
| ~ surjective(X6,X7,X8) ) ),
inference(shift_quantors,[status(thm)],[10]) ).
fof(12,plain,
! [X6,X7,X8,X9,X12] :
( ( ~ member(X12,X7)
| ~ apply(X6,X12,esk2_3(X6,X7,X8))
| surjective(X6,X7,X8) )
& ( member(esk2_3(X6,X7,X8),X8)
| surjective(X6,X7,X8) )
& ( member(esk1_4(X6,X7,X8,X9),X7)
| ~ member(X9,X8)
| ~ surjective(X6,X7,X8) )
& ( apply(X6,esk1_4(X6,X7,X8,X9),X9)
| ~ member(X9,X8)
| ~ surjective(X6,X7,X8) ) ),
inference(distribute,[status(thm)],[11]) ).
cnf(13,plain,
( apply(X1,esk1_4(X1,X2,X3,X4),X4)
| ~ surjective(X1,X2,X3)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[12]) ).
cnf(14,plain,
( member(esk1_4(X1,X2,X3,X4),X2)
| ~ surjective(X1,X2,X3)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[12]) ).
cnf(15,plain,
( surjective(X1,X2,X3)
| member(esk2_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[12]) ).
cnf(16,plain,
( surjective(X1,X2,X3)
| ~ apply(X1,X4,esk2_3(X1,X2,X3))
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[12]) ).
fof(37,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)],[3]) ).
fof(38,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)],[37]) ).
fof(39,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(esk8_7(X12,X13,X14,X15,X16,X17,X18),X15)
& apply(X13,X17,esk8_7(X12,X13,X14,X15,X16,X17,X18))
& apply(X12,esk8_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)],[38]) ).
fof(40,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(esk8_7(X12,X13,X14,X15,X16,X17,X18),X15)
& apply(X13,X17,esk8_7(X12,X13,X14,X15,X16,X17,X18))
& apply(X12,esk8_7(X12,X13,X14,X15,X16,X17,X18),X18) ) ) )
| ~ member(X17,X14)
| ~ member(X18,X16) ),
inference(shift_quantors,[status(thm)],[39]) ).
fof(41,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(esk8_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,esk8_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,esk8_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)],[40]) ).
cnf(42,plain,
( apply(X5,esk8_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)],[41]) ).
cnf(44,plain,
( member(esk8_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)],[41]) ).
fof(64,negated_conjecture,
? [X1,X9,X2,X3,X10] :
( maps(X1,X2,X3)
& maps(X9,X3,X10)
& surjective(compose_function(X9,X1,X2,X3,X10),X2,X10)
& ~ surjective(X9,X3,X10) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(65,negated_conjecture,
? [X11,X12,X13,X14,X15] :
( maps(X11,X13,X14)
& maps(X12,X14,X15)
& surjective(compose_function(X12,X11,X13,X14,X15),X13,X15)
& ~ surjective(X12,X14,X15) ),
inference(variable_rename,[status(thm)],[64]) ).
fof(66,negated_conjecture,
( maps(esk12_0,esk14_0,esk15_0)
& maps(esk13_0,esk15_0,esk16_0)
& surjective(compose_function(esk13_0,esk12_0,esk14_0,esk15_0,esk16_0),esk14_0,esk16_0)
& ~ surjective(esk13_0,esk15_0,esk16_0) ),
inference(skolemize,[status(esa)],[65]) ).
cnf(67,negated_conjecture,
~ surjective(esk13_0,esk15_0,esk16_0),
inference(split_conjunct,[status(thm)],[66]) ).
cnf(68,negated_conjecture,
surjective(compose_function(esk13_0,esk12_0,esk14_0,esk15_0,esk16_0),esk14_0,esk16_0),
inference(split_conjunct,[status(thm)],[66]) ).
cnf(95,plain,
( surjective(X1,X2,X3)
| ~ member(esk8_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)],[16,42,theory(equality)]) ).
cnf(327,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)],[95,44,theory(equality)]) ).
cnf(328,plain,
( surjective(X1,X2,X3)
| ~ member(esk2_3(X1,X2,X3),X6)
| ~ member(esk1_4(compose_function(X1,X4,X5,X2,X6),X7,X8,esk2_3(X1,X2,X3)),X5)
| ~ member(esk2_3(X1,X2,X3),X8)
| ~ surjective(compose_function(X1,X4,X5,X2,X6),X7,X8) ),
inference(spm,[status(thm)],[327,13,theory(equality)]) ).
cnf(337,plain,
( surjective(X1,X2,X3)
| ~ member(esk2_3(X1,X2,X3),X6)
| ~ member(esk2_3(X1,X2,X3),X7)
| ~ surjective(compose_function(X1,X4,X5,X2,X6),X5,X7) ),
inference(spm,[status(thm)],[328,14,theory(equality)]) ).
cnf(338,negated_conjecture,
( surjective(esk13_0,esk15_0,X1)
| ~ member(esk2_3(esk13_0,esk15_0,X1),esk16_0) ),
inference(spm,[status(thm)],[337,68,theory(equality)]) ).
cnf(339,negated_conjecture,
surjective(esk13_0,esk15_0,esk16_0),
inference(spm,[status(thm)],[338,15,theory(equality)]) ).
cnf(340,negated_conjecture,
$false,
inference(sr,[status(thm)],[339,67,theory(equality)]) ).
cnf(341,negated_conjecture,
$false,
340,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET722+4.p
% --creating new selector for [SET006+0.ax, SET006+1.ax]
% -running prover on /tmp/tmpr4V4T-/sel_SET722+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET722+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET722+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET722+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
%
%------------------------------------------------------------------------------