%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET732+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 03:21:42 EST 2010
% Result : Theorem 0.57s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of formulae : 84 ( 10 unt; 0 def)
% Number of atoms : 432 ( 25 equ)
% Maximal formula atoms : 19 ( 5 avg)
% Number of connectives : 556 ( 208 ~; 216 |; 117 &)
% ( 7 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-4 aty)
% Number of variables : 261 ( 0 sgn 142 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpb45g5Z/sel_SET732+4.p_1',subset) ).
fof(2,axiom,
! [X4,X1,X2] :
( surjective(X4,X1,X2)
<=> ! [X5] :
( member(X5,X2)
=> ? [X6] :
( member(X6,X1)
& apply(X4,X6,X5) ) ) ),
file('/tmp/tmpb45g5Z/sel_SET732+4.p_1',surjective) ).
fof(3,axiom,
! [X4,X1,X2] :
( one_to_one(X4,X1,X2)
<=> ( injective(X4,X1,X2)
& surjective(X4,X1,X2) ) ),
file('/tmp/tmpb45g5Z/sel_SET732+4.p_1',one_to_one) ).
fof(5,axiom,
! [X4,X1,X5] :
( member(X5,image2(X4,X1))
<=> ? [X3] :
( member(X3,X1)
& apply(X4,X3,X5) ) ),
file('/tmp/tmpb45g5Z/sel_SET732+4.p_1',image2) ).
fof(6,axiom,
! [X4,X1,X2] :
( injective(X4,X1,X2)
<=> ! [X9,X10,X5] :
( ( member(X9,X1)
& member(X10,X1)
& member(X5,X2) )
=> ( ( apply(X4,X9,X5)
& apply(X4,X10,X5) )
=> X9 = X10 ) ) ),
file('/tmp/tmpb45g5Z/sel_SET732+4.p_1',injective) ).
fof(7,conjecture,
! [X4,X11,X1,X2,X12] :
( ( maps(X4,X1,X2)
& subset(X12,X2)
& image2(X4,X1) = X12
& ! [X3,X5] :
( ( member(X3,X1)
& member(X5,X12) )
=> ( apply(X11,X3,X5)
<=> apply(X4,X3,X5) ) )
& injective(X4,X1,X2) )
=> one_to_one(X11,X1,X12) ),
file('/tmp/tmpb45g5Z/sel_SET732+4.p_1',thII23) ).
fof(8,negated_conjecture,
~ ! [X4,X11,X1,X2,X12] :
( ( maps(X4,X1,X2)
& subset(X12,X2)
& image2(X4,X1) = X12
& ! [X3,X5] :
( ( member(X3,X1)
& member(X5,X12) )
=> ( apply(X11,X3,X5)
<=> apply(X4,X3,X5) ) )
& injective(X4,X1,X2) )
=> one_to_one(X11,X1,X12) ),
inference(assume_negation,[status(cth)],[7]) ).
fof(9,plain,
! [X1,X2] :
( ( ~ subset(X1,X2)
| ! [X3] :
( ~ member(X3,X1)
| member(X3,X2) ) )
& ( ? [X3] :
( member(X3,X1)
& ~ member(X3,X2) )
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(10,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ? [X7] :
( member(X7,X4)
& ~ member(X7,X5) )
| subset(X4,X5) ) ),
inference(variable_rename,[status(thm)],[9]) ).
fof(11,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ( member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[10]) ).
fof(12,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( ( member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[11]) ).
fof(13,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( member(esk1_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ member(esk1_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[12]) ).
cnf(16,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[13]) ).
fof(17,plain,
! [X4,X1,X2] :
( ( ~ surjective(X4,X1,X2)
| ! [X5] :
( ~ member(X5,X2)
| ? [X6] :
( member(X6,X1)
& apply(X4,X6,X5) ) ) )
& ( ? [X5] :
( member(X5,X2)
& ! [X6] :
( ~ member(X6,X1)
| ~ apply(X4,X6,X5) ) )
| surjective(X4,X1,X2) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(18,plain,
! [X7,X8,X9] :
( ( ~ surjective(X7,X8,X9)
| ! [X10] :
( ~ member(X10,X9)
| ? [X11] :
( member(X11,X8)
& apply(X7,X11,X10) ) ) )
& ( ? [X12] :
( member(X12,X9)
& ! [X13] :
( ~ member(X13,X8)
| ~ apply(X7,X13,X12) ) )
| surjective(X7,X8,X9) ) ),
inference(variable_rename,[status(thm)],[17]) ).
fof(19,plain,
! [X7,X8,X9] :
( ( ~ surjective(X7,X8,X9)
| ! [X10] :
( ~ member(X10,X9)
| ( member(esk2_4(X7,X8,X9,X10),X8)
& apply(X7,esk2_4(X7,X8,X9,X10),X10) ) ) )
& ( ( member(esk3_3(X7,X8,X9),X9)
& ! [X13] :
( ~ member(X13,X8)
| ~ apply(X7,X13,esk3_3(X7,X8,X9)) ) )
| surjective(X7,X8,X9) ) ),
inference(skolemize,[status(esa)],[18]) ).
fof(20,plain,
! [X7,X8,X9,X10,X13] :
( ( ( ( ~ member(X13,X8)
| ~ apply(X7,X13,esk3_3(X7,X8,X9)) )
& member(esk3_3(X7,X8,X9),X9) )
| surjective(X7,X8,X9) )
& ( ~ member(X10,X9)
| ( member(esk2_4(X7,X8,X9,X10),X8)
& apply(X7,esk2_4(X7,X8,X9,X10),X10) )
| ~ surjective(X7,X8,X9) ) ),
inference(shift_quantors,[status(thm)],[19]) ).
fof(21,plain,
! [X7,X8,X9,X10,X13] :
( ( ~ member(X13,X8)
| ~ apply(X7,X13,esk3_3(X7,X8,X9))
| surjective(X7,X8,X9) )
& ( member(esk3_3(X7,X8,X9),X9)
| surjective(X7,X8,X9) )
& ( member(esk2_4(X7,X8,X9,X10),X8)
| ~ member(X10,X9)
| ~ surjective(X7,X8,X9) )
& ( apply(X7,esk2_4(X7,X8,X9,X10),X10)
| ~ member(X10,X9)
| ~ surjective(X7,X8,X9) ) ),
inference(distribute,[status(thm)],[20]) ).
cnf(24,plain,
( surjective(X1,X2,X3)
| member(esk3_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[21]) ).
cnf(25,plain,
( surjective(X1,X2,X3)
| ~ apply(X1,X4,esk3_3(X1,X2,X3))
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[21]) ).
fof(26,plain,
! [X4,X1,X2] :
( ( ~ one_to_one(X4,X1,X2)
| ( injective(X4,X1,X2)
& surjective(X4,X1,X2) ) )
& ( ~ injective(X4,X1,X2)
| ~ surjective(X4,X1,X2)
| one_to_one(X4,X1,X2) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(27,plain,
! [X5,X6,X7] :
( ( ~ one_to_one(X5,X6,X7)
| ( injective(X5,X6,X7)
& surjective(X5,X6,X7) ) )
& ( ~ injective(X5,X6,X7)
| ~ surjective(X5,X6,X7)
| one_to_one(X5,X6,X7) ) ),
inference(variable_rename,[status(thm)],[26]) ).
fof(28,plain,
! [X5,X6,X7] :
( ( injective(X5,X6,X7)
| ~ one_to_one(X5,X6,X7) )
& ( surjective(X5,X6,X7)
| ~ one_to_one(X5,X6,X7) )
& ( ~ injective(X5,X6,X7)
| ~ surjective(X5,X6,X7)
| one_to_one(X5,X6,X7) ) ),
inference(distribute,[status(thm)],[27]) ).
cnf(29,plain,
( one_to_one(X1,X2,X3)
| ~ surjective(X1,X2,X3)
| ~ injective(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[28]) ).
fof(52,plain,
! [X4,X1,X5] :
( ( ~ member(X5,image2(X4,X1))
| ? [X3] :
( member(X3,X1)
& apply(X4,X3,X5) ) )
& ( ! [X3] :
( ~ member(X3,X1)
| ~ apply(X4,X3,X5) )
| member(X5,image2(X4,X1)) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(53,plain,
! [X6,X7,X8] :
( ( ~ member(X8,image2(X6,X7))
| ? [X9] :
( member(X9,X7)
& apply(X6,X9,X8) ) )
& ( ! [X10] :
( ~ member(X10,X7)
| ~ apply(X6,X10,X8) )
| member(X8,image2(X6,X7)) ) ),
inference(variable_rename,[status(thm)],[52]) ).
fof(54,plain,
! [X6,X7,X8] :
( ( ~ member(X8,image2(X6,X7))
| ( member(esk9_3(X6,X7,X8),X7)
& apply(X6,esk9_3(X6,X7,X8),X8) ) )
& ( ! [X10] :
( ~ member(X10,X7)
| ~ apply(X6,X10,X8) )
| member(X8,image2(X6,X7)) ) ),
inference(skolemize,[status(esa)],[53]) ).
fof(55,plain,
! [X6,X7,X8,X10] :
( ( ~ member(X10,X7)
| ~ apply(X6,X10,X8)
| member(X8,image2(X6,X7)) )
& ( ~ member(X8,image2(X6,X7))
| ( member(esk9_3(X6,X7,X8),X7)
& apply(X6,esk9_3(X6,X7,X8),X8) ) ) ),
inference(shift_quantors,[status(thm)],[54]) ).
fof(56,plain,
! [X6,X7,X8,X10] :
( ( ~ member(X10,X7)
| ~ apply(X6,X10,X8)
| member(X8,image2(X6,X7)) )
& ( member(esk9_3(X6,X7,X8),X7)
| ~ member(X8,image2(X6,X7)) )
& ( apply(X6,esk9_3(X6,X7,X8),X8)
| ~ member(X8,image2(X6,X7)) ) ),
inference(distribute,[status(thm)],[55]) ).
cnf(57,plain,
( apply(X2,esk9_3(X2,X3,X1),X1)
| ~ member(X1,image2(X2,X3)) ),
inference(split_conjunct,[status(thm)],[56]) ).
cnf(58,plain,
( member(esk9_3(X2,X3,X1),X3)
| ~ member(X1,image2(X2,X3)) ),
inference(split_conjunct,[status(thm)],[56]) ).
cnf(59,plain,
( member(X1,image2(X2,X3))
| ~ apply(X2,X4,X1)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[56]) ).
fof(60,plain,
! [X4,X1,X2] :
( ( ~ injective(X4,X1,X2)
| ! [X9,X10,X5] :
( ~ member(X9,X1)
| ~ member(X10,X1)
| ~ member(X5,X2)
| ~ apply(X4,X9,X5)
| ~ apply(X4,X10,X5)
| X9 = X10 ) )
& ( ? [X9,X10,X5] :
( member(X9,X1)
& member(X10,X1)
& member(X5,X2)
& apply(X4,X9,X5)
& apply(X4,X10,X5)
& X9 != X10 )
| injective(X4,X1,X2) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(61,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)],[60]) ).
fof(62,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(esk10_3(X11,X12,X13),X12)
& member(esk11_3(X11,X12,X13),X12)
& member(esk12_3(X11,X12,X13),X13)
& apply(X11,esk10_3(X11,X12,X13),esk12_3(X11,X12,X13))
& apply(X11,esk11_3(X11,X12,X13),esk12_3(X11,X12,X13))
& esk10_3(X11,X12,X13) != esk11_3(X11,X12,X13) )
| injective(X11,X12,X13) ) ),
inference(skolemize,[status(esa)],[61]) ).
fof(63,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(esk10_3(X11,X12,X13),X12)
& member(esk11_3(X11,X12,X13),X12)
& member(esk12_3(X11,X12,X13),X13)
& apply(X11,esk10_3(X11,X12,X13),esk12_3(X11,X12,X13))
& apply(X11,esk11_3(X11,X12,X13),esk12_3(X11,X12,X13))
& esk10_3(X11,X12,X13) != esk11_3(X11,X12,X13) )
| injective(X11,X12,X13) ) ),
inference(shift_quantors,[status(thm)],[62]) ).
fof(64,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(esk10_3(X11,X12,X13),X12)
| injective(X11,X12,X13) )
& ( member(esk11_3(X11,X12,X13),X12)
| injective(X11,X12,X13) )
& ( member(esk12_3(X11,X12,X13),X13)
| injective(X11,X12,X13) )
& ( apply(X11,esk10_3(X11,X12,X13),esk12_3(X11,X12,X13))
| injective(X11,X12,X13) )
& ( apply(X11,esk11_3(X11,X12,X13),esk12_3(X11,X12,X13))
| injective(X11,X12,X13) )
& ( esk10_3(X11,X12,X13) != esk11_3(X11,X12,X13)
| injective(X11,X12,X13) ) ),
inference(distribute,[status(thm)],[63]) ).
cnf(65,plain,
( injective(X1,X2,X3)
| esk10_3(X1,X2,X3) != esk11_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[64]) ).
cnf(66,plain,
( injective(X1,X2,X3)
| apply(X1,esk11_3(X1,X2,X3),esk12_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[64]) ).
cnf(67,plain,
( injective(X1,X2,X3)
| apply(X1,esk10_3(X1,X2,X3),esk12_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[64]) ).
cnf(68,plain,
( injective(X1,X2,X3)
| member(esk12_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[64]) ).
cnf(69,plain,
( injective(X1,X2,X3)
| member(esk11_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[64]) ).
cnf(70,plain,
( injective(X1,X2,X3)
| member(esk10_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[64]) ).
cnf(71,plain,
( X4 = X5
| ~ injective(X1,X2,X3)
| ~ apply(X1,X5,X6)
| ~ apply(X1,X4,X6)
| ~ member(X6,X3)
| ~ member(X5,X2)
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[64]) ).
fof(72,negated_conjecture,
? [X4,X11,X1,X2,X12] :
( maps(X4,X1,X2)
& subset(X12,X2)
& image2(X4,X1) = X12
& ! [X3,X5] :
( ~ member(X3,X1)
| ~ member(X5,X12)
| ( ( ~ apply(X11,X3,X5)
| apply(X4,X3,X5) )
& ( ~ apply(X4,X3,X5)
| apply(X11,X3,X5) ) ) )
& injective(X4,X1,X2)
& ~ one_to_one(X11,X1,X12) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(73,negated_conjecture,
? [X13,X14,X15,X16,X17] :
( maps(X13,X15,X16)
& subset(X17,X16)
& image2(X13,X15) = X17
& ! [X18,X19] :
( ~ member(X18,X15)
| ~ member(X19,X17)
| ( ( ~ apply(X14,X18,X19)
| apply(X13,X18,X19) )
& ( ~ apply(X13,X18,X19)
| apply(X14,X18,X19) ) ) )
& injective(X13,X15,X16)
& ~ one_to_one(X14,X15,X17) ),
inference(variable_rename,[status(thm)],[72]) ).
fof(74,negated_conjecture,
( maps(esk13_0,esk15_0,esk16_0)
& subset(esk17_0,esk16_0)
& image2(esk13_0,esk15_0) = esk17_0
& ! [X18,X19] :
( ~ member(X18,esk15_0)
| ~ member(X19,esk17_0)
| ( ( ~ apply(esk14_0,X18,X19)
| apply(esk13_0,X18,X19) )
& ( ~ apply(esk13_0,X18,X19)
| apply(esk14_0,X18,X19) ) ) )
& injective(esk13_0,esk15_0,esk16_0)
& ~ one_to_one(esk14_0,esk15_0,esk17_0) ),
inference(skolemize,[status(esa)],[73]) ).
fof(75,negated_conjecture,
! [X18,X19] :
( ( ~ member(X18,esk15_0)
| ~ member(X19,esk17_0)
| ( ( ~ apply(esk14_0,X18,X19)
| apply(esk13_0,X18,X19) )
& ( ~ apply(esk13_0,X18,X19)
| apply(esk14_0,X18,X19) ) ) )
& maps(esk13_0,esk15_0,esk16_0)
& subset(esk17_0,esk16_0)
& image2(esk13_0,esk15_0) = esk17_0
& injective(esk13_0,esk15_0,esk16_0)
& ~ one_to_one(esk14_0,esk15_0,esk17_0) ),
inference(shift_quantors,[status(thm)],[74]) ).
fof(76,negated_conjecture,
! [X18,X19] :
( ( ~ apply(esk14_0,X18,X19)
| apply(esk13_0,X18,X19)
| ~ member(X18,esk15_0)
| ~ member(X19,esk17_0) )
& ( ~ apply(esk13_0,X18,X19)
| apply(esk14_0,X18,X19)
| ~ member(X18,esk15_0)
| ~ member(X19,esk17_0) )
& maps(esk13_0,esk15_0,esk16_0)
& subset(esk17_0,esk16_0)
& image2(esk13_0,esk15_0) = esk17_0
& injective(esk13_0,esk15_0,esk16_0)
& ~ one_to_one(esk14_0,esk15_0,esk17_0) ),
inference(distribute,[status(thm)],[75]) ).
cnf(77,negated_conjecture,
~ one_to_one(esk14_0,esk15_0,esk17_0),
inference(split_conjunct,[status(thm)],[76]) ).
cnf(78,negated_conjecture,
injective(esk13_0,esk15_0,esk16_0),
inference(split_conjunct,[status(thm)],[76]) ).
cnf(79,negated_conjecture,
image2(esk13_0,esk15_0) = esk17_0,
inference(split_conjunct,[status(thm)],[76]) ).
cnf(80,negated_conjecture,
subset(esk17_0,esk16_0),
inference(split_conjunct,[status(thm)],[76]) ).
cnf(82,negated_conjecture,
( apply(esk14_0,X2,X1)
| ~ member(X1,esk17_0)
| ~ member(X2,esk15_0)
| ~ apply(esk13_0,X2,X1) ),
inference(split_conjunct,[status(thm)],[76]) ).
cnf(83,negated_conjecture,
( apply(esk13_0,X2,X1)
| ~ member(X1,esk17_0)
| ~ member(X2,esk15_0)
| ~ apply(esk14_0,X2,X1) ),
inference(split_conjunct,[status(thm)],[76]) ).
cnf(84,negated_conjecture,
( member(X1,esk16_0)
| ~ member(X1,esk17_0) ),
inference(spm,[status(thm)],[16,80,theory(equality)]) ).
cnf(87,negated_conjecture,
( member(X1,image2(esk14_0,X2))
| ~ member(X3,X2)
| ~ apply(esk13_0,X3,X1)
| ~ member(X3,esk15_0)
| ~ member(X1,esk17_0) ),
inference(spm,[status(thm)],[59,82,theory(equality)]) ).
cnf(90,negated_conjecture,
( ~ injective(esk14_0,esk15_0,esk17_0)
| ~ surjective(esk14_0,esk15_0,esk17_0) ),
inference(spm,[status(thm)],[77,29,theory(equality)]) ).
cnf(95,negated_conjecture,
( apply(esk13_0,esk10_3(esk14_0,X1,X2),esk12_3(esk14_0,X1,X2))
| injective(esk14_0,X1,X2)
| ~ member(esk10_3(esk14_0,X1,X2),esk15_0)
| ~ member(esk12_3(esk14_0,X1,X2),esk17_0) ),
inference(spm,[status(thm)],[83,67,theory(equality)]) ).
cnf(97,negated_conjecture,
( apply(esk13_0,esk11_3(esk14_0,X1,X2),esk12_3(esk14_0,X1,X2))
| injective(esk14_0,X1,X2)
| ~ member(esk11_3(esk14_0,X1,X2),esk15_0)
| ~ member(esk12_3(esk14_0,X1,X2),esk17_0) ),
inference(spm,[status(thm)],[83,66,theory(equality)]) ).
cnf(100,plain,
( surjective(X1,X2,X3)
| ~ member(esk9_3(X1,X4,esk3_3(X1,X2,X3)),X2)
| ~ member(esk3_3(X1,X2,X3),image2(X1,X4)) ),
inference(spm,[status(thm)],[25,57,theory(equality)]) ).
cnf(104,negated_conjecture,
( X1 = X2
| ~ apply(esk13_0,X2,X3)
| ~ apply(esk13_0,X1,X3)
| ~ member(X3,esk16_0)
| ~ member(X2,esk15_0)
| ~ member(X1,esk15_0) ),
inference(spm,[status(thm)],[71,78,theory(equality)]) ).
cnf(124,negated_conjecture,
( member(X1,image2(esk14_0,X2))
| ~ member(esk9_3(esk13_0,X3,X1),esk15_0)
| ~ member(X1,esk17_0)
| ~ member(esk9_3(esk13_0,X3,X1),X2)
| ~ member(X1,image2(esk13_0,X3)) ),
inference(spm,[status(thm)],[87,57,theory(equality)]) ).
cnf(184,negated_conjecture,
( X1 = esk10_3(esk14_0,X2,X3)
| injective(esk14_0,X2,X3)
| ~ apply(esk13_0,X1,esk12_3(esk14_0,X2,X3))
| ~ member(esk12_3(esk14_0,X2,X3),esk16_0)
| ~ member(esk10_3(esk14_0,X2,X3),esk15_0)
| ~ member(X1,esk15_0)
| ~ member(esk12_3(esk14_0,X2,X3),esk17_0) ),
inference(spm,[status(thm)],[104,95,theory(equality)]) ).
cnf(196,plain,
( surjective(X1,X2,X3)
| ~ member(esk3_3(X1,X2,X3),image2(X1,X2)) ),
inference(spm,[status(thm)],[100,58,theory(equality)]) ).
cnf(228,negated_conjecture,
( member(X1,image2(esk14_0,X2))
| ~ member(esk9_3(esk13_0,esk15_0,X1),X2)
| ~ member(X1,image2(esk13_0,esk15_0))
| ~ member(X1,esk17_0) ),
inference(spm,[status(thm)],[124,58,theory(equality)]) ).
cnf(229,negated_conjecture,
( member(X1,image2(esk14_0,X2))
| ~ member(esk9_3(esk13_0,esk15_0,X1),X2)
| ~ member(X1,esk17_0)
| ~ member(X1,esk17_0) ),
inference(rw,[status(thm)],[228,79,theory(equality)]) ).
cnf(230,negated_conjecture,
( member(X1,image2(esk14_0,X2))
| ~ member(esk9_3(esk13_0,esk15_0,X1),X2)
| ~ member(X1,esk17_0) ),
inference(cn,[status(thm)],[229,theory(equality)]) ).
cnf(231,negated_conjecture,
( member(X1,image2(esk14_0,esk15_0))
| ~ member(X1,esk17_0)
| ~ member(X1,image2(esk13_0,esk15_0)) ),
inference(spm,[status(thm)],[230,58,theory(equality)]) ).
cnf(236,negated_conjecture,
( member(X1,image2(esk14_0,esk15_0))
| ~ member(X1,esk17_0)
| ~ member(X1,esk17_0) ),
inference(rw,[status(thm)],[231,79,theory(equality)]) ).
cnf(237,negated_conjecture,
( member(X1,image2(esk14_0,esk15_0))
| ~ member(X1,esk17_0) ),
inference(cn,[status(thm)],[236,theory(equality)]) ).
cnf(242,negated_conjecture,
( surjective(esk14_0,esk15_0,X1)
| ~ member(esk3_3(esk14_0,esk15_0,X1),esk17_0) ),
inference(spm,[status(thm)],[196,237,theory(equality)]) ).
cnf(244,negated_conjecture,
surjective(esk14_0,esk15_0,esk17_0),
inference(spm,[status(thm)],[242,24,theory(equality)]) ).
cnf(252,negated_conjecture,
( ~ injective(esk14_0,esk15_0,esk17_0)
| $false ),
inference(rw,[status(thm)],[90,244,theory(equality)]) ).
cnf(253,negated_conjecture,
~ injective(esk14_0,esk15_0,esk17_0),
inference(cn,[status(thm)],[252,theory(equality)]) ).
cnf(2731,negated_conjecture,
( X1 = esk10_3(esk14_0,X2,X3)
| injective(esk14_0,X2,X3)
| ~ apply(esk13_0,X1,esk12_3(esk14_0,X2,X3))
| ~ member(esk10_3(esk14_0,X2,X3),esk15_0)
| ~ member(esk12_3(esk14_0,X2,X3),esk17_0)
| ~ member(X1,esk15_0) ),
inference(csr,[status(thm)],[184,84]) ).
cnf(2735,negated_conjecture,
( esk11_3(esk14_0,X1,X2) = esk10_3(esk14_0,X1,X2)
| injective(esk14_0,X1,X2)
| ~ member(esk10_3(esk14_0,X1,X2),esk15_0)
| ~ member(esk12_3(esk14_0,X1,X2),esk17_0)
| ~ member(esk11_3(esk14_0,X1,X2),esk15_0) ),
inference(spm,[status(thm)],[2731,97,theory(equality)]) ).
cnf(4055,negated_conjecture,
( injective(esk14_0,X1,X2)
| ~ member(esk10_3(esk14_0,X1,X2),esk15_0)
| ~ member(esk12_3(esk14_0,X1,X2),esk17_0)
| ~ member(esk11_3(esk14_0,X1,X2),esk15_0) ),
inference(csr,[status(thm)],[2735,65]) ).
cnf(4056,negated_conjecture,
( injective(esk14_0,X1,esk17_0)
| ~ member(esk10_3(esk14_0,X1,esk17_0),esk15_0)
| ~ member(esk11_3(esk14_0,X1,esk17_0),esk15_0) ),
inference(spm,[status(thm)],[4055,68,theory(equality)]) ).
cnf(4057,negated_conjecture,
( injective(esk14_0,esk15_0,esk17_0)
| ~ member(esk10_3(esk14_0,esk15_0,esk17_0),esk15_0) ),
inference(spm,[status(thm)],[4056,69,theory(equality)]) ).
cnf(4058,negated_conjecture,
~ member(esk10_3(esk14_0,esk15_0,esk17_0),esk15_0),
inference(sr,[status(thm)],[4057,253,theory(equality)]) ).
cnf(4059,negated_conjecture,
injective(esk14_0,esk15_0,esk17_0),
inference(spm,[status(thm)],[4058,70,theory(equality)]) ).
cnf(4060,negated_conjecture,
$false,
inference(sr,[status(thm)],[4059,253,theory(equality)]) ).
cnf(4061,negated_conjecture,
$false,
4060,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET732+4.p
% --creating new selector for [SET006+0.ax, SET006+1.ax]
% -running prover on /tmp/tmpb45g5Z/sel_SET732+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET732+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET732+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET732+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
%
%------------------------------------------------------------------------------