TSTP Solution File: SET734+4 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET734+4 : TPTP v5.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art03.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 03:22:16 EST 2010
% Result : Theorem 0.21s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 37 ( 5 unt; 0 def)
% Number of atoms : 199 ( 0 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 261 ( 99 ~; 97 |; 57 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-7 aty)
% Number of variables : 161 ( 1 sgn 102 !; 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/tmpBXUeKs/sel_SET734+4.p_1',surjective) ).
fof(5,axiom,
! [X1,X2] :
( identity(X1,X2)
<=> ! [X6] :
( member(X6,X2)
=> apply(X1,X6,X6) ) ),
file('/tmp/tmpBXUeKs/sel_SET734+4.p_1',identity) ).
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/tmpBXUeKs/sel_SET734+4.p_1',compose_function) ).
fof(7,conjecture,
! [X1,X11,X2,X3] :
( ( maps(X11,X2,X3)
& maps(X1,X3,X2)
& identity(compose_function(X11,X1,X3,X2,X3),X3) )
=> surjective(X11,X2,X3) ),
file('/tmp/tmpBXUeKs/sel_SET734+4.p_1',thII25) ).
fof(8,negated_conjecture,
~ ! [X1,X11,X2,X3] :
( ( maps(X11,X2,X3)
& maps(X1,X3,X2)
& identity(compose_function(X11,X1,X3,X2,X3),X3) )
=> surjective(X11,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(56,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)],[5]) ).
fof(57,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)],[56]) ).
fof(58,plain,
! [X7,X8] :
( ( ~ identity(X7,X8)
| ! [X9] :
( ~ member(X9,X8)
| apply(X7,X9,X9) ) )
& ( ( member(esk11_2(X7,X8),X8)
& ~ apply(X7,esk11_2(X7,X8),esk11_2(X7,X8)) )
| identity(X7,X8) ) ),
inference(skolemize,[status(esa)],[57]) ).
fof(59,plain,
! [X7,X8,X9] :
( ( ~ member(X9,X8)
| apply(X7,X9,X9)
| ~ identity(X7,X8) )
& ( ( member(esk11_2(X7,X8),X8)
& ~ apply(X7,esk11_2(X7,X8),esk11_2(X7,X8)) )
| identity(X7,X8) ) ),
inference(shift_quantors,[status(thm)],[58]) ).
fof(60,plain,
! [X7,X8,X9] :
( ( ~ member(X9,X8)
| apply(X7,X9,X9)
| ~ identity(X7,X8) )
& ( member(esk11_2(X7,X8),X8)
| identity(X7,X8) )
& ( ~ apply(X7,esk11_2(X7,X8),esk11_2(X7,X8))
| identity(X7,X8) ) ),
inference(distribute,[status(thm)],[59]) ).
cnf(63,plain,
( apply(X1,X3,X3)
| ~ identity(X1,X2)
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[60]) ).
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(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,X2,X3] :
( maps(X11,X2,X3)
& maps(X1,X3,X2)
& identity(compose_function(X11,X1,X3,X2,X3),X3)
& ~ surjective(X11,X2,X3) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(74,negated_conjecture,
? [X12,X13,X14,X15] :
( maps(X13,X14,X15)
& maps(X12,X15,X14)
& identity(compose_function(X13,X12,X15,X14,X15),X15)
& ~ surjective(X13,X14,X15) ),
inference(variable_rename,[status(thm)],[73]) ).
fof(75,negated_conjecture,
( maps(esk14_0,esk15_0,esk16_0)
& maps(esk13_0,esk16_0,esk15_0)
& identity(compose_function(esk14_0,esk13_0,esk16_0,esk15_0,esk16_0),esk16_0)
& ~ surjective(esk14_0,esk15_0,esk16_0) ),
inference(skolemize,[status(esa)],[74]) ).
cnf(76,negated_conjecture,
~ surjective(esk14_0,esk15_0,esk16_0),
inference(split_conjunct,[status(thm)],[75]) ).
cnf(77,negated_conjecture,
identity(compose_function(esk14_0,esk13_0,esk16_0,esk15_0,esk16_0),esk16_0),
inference(split_conjunct,[status(thm)],[75]) ).
cnf(80,negated_conjecture,
( apply(compose_function(esk14_0,esk13_0,esk16_0,esk15_0,esk16_0),X1,X1)
| ~ member(X1,esk16_0) ),
inference(spm,[status(thm)],[63,77,theory(equality)]) ).
cnf(98,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(352,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)],[98,71,theory(equality)]) ).
cnf(355,negated_conjecture,
( surjective(esk14_0,esk15_0,X1)
| ~ member(esk2_3(esk14_0,esk15_0,X1),esk16_0) ),
inference(spm,[status(thm)],[352,80,theory(equality)]) ).
cnf(358,negated_conjecture,
surjective(esk14_0,esk15_0,esk16_0),
inference(spm,[status(thm)],[355,16,theory(equality)]) ).
cnf(359,negated_conjecture,
$false,
inference(sr,[status(thm)],[358,76,theory(equality)]) ).
cnf(360,negated_conjecture,
$false,
359,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET734+4.p
% --creating new selector for [SET006+0.ax, SET006+1.ax]
% -running prover on /tmp/tmpBXUeKs/sel_SET734+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET734+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET734+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET734+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
%
%------------------------------------------------------------------------------