TSTP Solution File: LAT387+4 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : LAT387+4 : TPTP v5.0.0. Released v4.0.0.
% 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 : Sat Dec 25 17:22:54 EST 2010
% Result : Theorem 0.33s
% Output : CNFRefutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 11
% Syntax : Number of formulae : 153 ( 17 unt; 0 def)
% Number of atoms : 913 ( 75 equ)
% Maximal formula atoms : 95 ( 5 avg)
% Number of connectives : 1153 ( 393 ~; 391 |; 311 &)
% ( 0 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-3 aty)
% Number of variables : 178 ( 0 sgn 124 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/tmp/tmp4T6wRo/sel_LAT387+4.p_1',mEOfElem) ).
fof(4,axiom,
! [X1] :
( aFunction0(X1)
=> ! [X2] :
( aElementOf0(X2,szDzozmdt0(X1))
=> aElementOf0(sdtlpdtrp0(X1,X2),szRzazndt0(X1)) ) ),
file('/tmp/tmp4T6wRo/sel_LAT387+4.p_1',mImgSort) ).
fof(10,axiom,
! [X1] :
( aElement0(X1)
=> sdtlseqdt0(X1,X1) ),
file('/tmp/tmp4T6wRo/sel_LAT387+4.p_1',mARefl) ).
fof(16,axiom,
( aElementOf0(xp,xU)
& aElementOf0(xp,xU)
& ! [X1] :
( aElementOf0(X1,xP)
=> sdtlseqdt0(xp,X1) )
& aLowerBoundOfIn0(xp,xP,xU)
& ! [X1] :
( ( ( aElementOf0(X1,xU)
& ! [X2] :
( aElementOf0(X2,xP)
=> sdtlseqdt0(X1,X2) ) )
| aLowerBoundOfIn0(X1,xP,xU) )
=> sdtlseqdt0(X1,xp) )
& aInfimumOfIn0(xp,xP,xU) ),
file('/tmp/tmp4T6wRo/sel_LAT387+4.p_1',m__1261) ).
fof(18,axiom,
( aSet0(xP)
& ! [X1] :
( ( aElementOf0(X1,xP)
=> ( aElementOf0(X1,xU)
& sdtlseqdt0(sdtlpdtrp0(xf,X1),X1)
& ! [X2] :
( aElementOf0(X2,xT)
=> sdtlseqdt0(X2,X1) )
& aUpperBoundOfIn0(X1,xT,xU) ) )
& ( ( aElementOf0(X1,xU)
& sdtlseqdt0(sdtlpdtrp0(xf,X1),X1)
& ( ! [X2] :
( aElementOf0(X2,xT)
=> sdtlseqdt0(X2,X1) )
| aUpperBoundOfIn0(X1,xT,xU) ) )
=> aElementOf0(X1,xP) ) )
& xP = cS1241(xU,xf,xT) ),
file('/tmp/tmp4T6wRo/sel_LAT387+4.p_1',m__1244) ).
fof(20,axiom,
( ! [X1] :
( aElementOf0(X1,xP)
=> sdtlseqdt0(sdtlpdtrp0(xf,xp),X1) )
& aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)
& ! [X1] :
( aElementOf0(X1,xT)
=> sdtlseqdt0(X1,sdtlpdtrp0(xf,xp)) )
& aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU) ),
file('/tmp/tmp4T6wRo/sel_LAT387+4.p_1',m__1299) ).
fof(23,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/tmp/tmp4T6wRo/sel_LAT387+4.p_1',mASymm) ).
fof(26,axiom,
( aSet0(xS)
& ! [X1] :
( ( aElementOf0(X1,xS)
=> ( aElementOf0(X1,szDzozmdt0(xf))
& sdtlpdtrp0(xf,X1) = X1
& aFixedPointOf0(X1,xf) ) )
& ( ( ( aElementOf0(X1,szDzozmdt0(xf))
& sdtlpdtrp0(xf,X1) = X1 )
| aFixedPointOf0(X1,xf) )
=> aElementOf0(X1,xS) ) )
& xS = cS1142(xf) ),
file('/tmp/tmp4T6wRo/sel_LAT387+4.p_1',m__1144) ).
fof(27,axiom,
( aSet0(xU)
& ! [X1] :
( ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xU) ) )
| aSubsetOf0(X1,xU) )
=> ? [X2] :
( aElementOf0(X2,xU)
& aElementOf0(X2,xU)
& ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X2,X3) )
& aLowerBoundOfIn0(X2,X1,xU)
& ! [X3] :
( ( ( aElementOf0(X3,xU)
& ! [X4] :
( aElementOf0(X4,X1)
=> sdtlseqdt0(X3,X4) ) )
| aLowerBoundOfIn0(X3,X1,xU) )
=> sdtlseqdt0(X3,X2) )
& aInfimumOfIn0(X2,X1,xU)
& ? [X3] :
( aElementOf0(X3,xU)
& aElementOf0(X3,xU)
& ! [X4] :
( aElementOf0(X4,X1)
=> sdtlseqdt0(X4,X3) )
& aUpperBoundOfIn0(X3,X1,xU)
& ! [X4] :
( ( ( aElementOf0(X4,xU)
& ! [X5] :
( aElementOf0(X5,X1)
=> sdtlseqdt0(X5,X4) ) )
| aUpperBoundOfIn0(X4,X1,xU) )
=> sdtlseqdt0(X3,X4) )
& aSupremumOfIn0(X3,X1,xU) ) ) )
& aCompleteLattice0(xU)
& aFunction0(xf)
& ! [X1,X2] :
( ( aElementOf0(X1,szDzozmdt0(xf))
& aElementOf0(X2,szDzozmdt0(xf)) )
=> ( sdtlseqdt0(X1,X2)
=> sdtlseqdt0(sdtlpdtrp0(xf,X1),sdtlpdtrp0(xf,X2)) ) )
& isMonotone0(xf)
& szDzozmdt0(xf) = szRzazndt0(xf)
& szRzazndt0(xf) = xU
& isOn0(xf,xU) ),
file('/tmp/tmp4T6wRo/sel_LAT387+4.p_1',m__1123) ).
fof(29,conjecture,
( ( ( aElementOf0(xp,szDzozmdt0(xf))
& sdtlpdtrp0(xf,xp) = xp )
| aFixedPointOf0(xp,xf) )
& ( ( ( ! [X1] :
( aElementOf0(X1,xT)
=> sdtlseqdt0(X1,xp) )
| aUpperBoundOfIn0(xp,xT,xS) )
& ! [X1] :
( ( aElementOf0(X1,xS)
& ! [X2] :
( aElementOf0(X2,xT)
=> sdtlseqdt0(X2,X1) )
& aUpperBoundOfIn0(X1,xT,xS) )
=> sdtlseqdt0(xp,X1) ) )
| aSupremumOfIn0(xp,xT,xS) ) ),
file('/tmp/tmp4T6wRo/sel_LAT387+4.p_1',m__) ).
fof(31,negated_conjecture,
~ ( ( ( aElementOf0(xp,szDzozmdt0(xf))
& sdtlpdtrp0(xf,xp) = xp )
| aFixedPointOf0(xp,xf) )
& ( ( ( ! [X1] :
( aElementOf0(X1,xT)
=> sdtlseqdt0(X1,xp) )
| aUpperBoundOfIn0(xp,xT,xS) )
& ! [X1] :
( ( aElementOf0(X1,xS)
& ! [X2] :
( aElementOf0(X2,xT)
=> sdtlseqdt0(X2,X1) )
& aUpperBoundOfIn0(X1,xT,xS) )
=> sdtlseqdt0(xp,X1) ) )
| aSupremumOfIn0(xp,xT,xS) ) ),
inference(assume_negation,[status(cth)],[29]) ).
fof(32,plain,
( aElementOf0(xp,xU)
& ! [X1] :
( aElementOf0(X1,xP)
=> sdtlseqdt0(xp,X1) )
& aLowerBoundOfIn0(xp,xP,xU)
& ! [X1] :
( ( ( aElementOf0(X1,xU)
& ! [X2] :
( aElementOf0(X2,xP)
=> sdtlseqdt0(X1,X2) ) )
| aLowerBoundOfIn0(X1,xP,xU) )
=> sdtlseqdt0(X1,xp) )
& aInfimumOfIn0(xp,xP,xU) ),
inference(fof_simplification,[status(thm)],[16,theory(equality)]) ).
fof(33,plain,
( aSet0(xU)
& ! [X1] :
( ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xU) ) )
| aSubsetOf0(X1,xU) )
=> ? [X2] :
( aElementOf0(X2,xU)
& ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X2,X3) )
& aLowerBoundOfIn0(X2,X1,xU)
& ! [X3] :
( ( ( aElementOf0(X3,xU)
& ! [X4] :
( aElementOf0(X4,X1)
=> sdtlseqdt0(X3,X4) ) )
| aLowerBoundOfIn0(X3,X1,xU) )
=> sdtlseqdt0(X3,X2) )
& aInfimumOfIn0(X2,X1,xU)
& ? [X3] :
( aElementOf0(X3,xU)
& ! [X4] :
( aElementOf0(X4,X1)
=> sdtlseqdt0(X4,X3) )
& aUpperBoundOfIn0(X3,X1,xU)
& ! [X4] :
( ( ( aElementOf0(X4,xU)
& ! [X5] :
( aElementOf0(X5,X1)
=> sdtlseqdt0(X5,X4) ) )
| aUpperBoundOfIn0(X4,X1,xU) )
=> sdtlseqdt0(X3,X4) )
& aSupremumOfIn0(X3,X1,xU) ) ) )
& aCompleteLattice0(xU)
& aFunction0(xf)
& ! [X1,X2] :
( ( aElementOf0(X1,szDzozmdt0(xf))
& aElementOf0(X2,szDzozmdt0(xf)) )
=> ( sdtlseqdt0(X1,X2)
=> sdtlseqdt0(sdtlpdtrp0(xf,X1),sdtlpdtrp0(xf,X2)) ) )
& isMonotone0(xf)
& szDzozmdt0(xf) = szRzazndt0(xf)
& szRzazndt0(xf) = xU
& isOn0(xf,xU) ),
inference(fof_simplification,[status(thm)],[27,theory(equality)]) ).
fof(34,plain,
! [X1] :
( epred1_1(X1)
=> ? [X2] :
( aElementOf0(X2,xU)
& ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X2,X3) )
& aLowerBoundOfIn0(X2,X1,xU)
& ! [X3] :
( ( ( aElementOf0(X3,xU)
& ! [X4] :
( aElementOf0(X4,X1)
=> sdtlseqdt0(X3,X4) ) )
| aLowerBoundOfIn0(X3,X1,xU) )
=> sdtlseqdt0(X3,X2) )
& aInfimumOfIn0(X2,X1,xU)
& ? [X3] :
( aElementOf0(X3,xU)
& ! [X4] :
( aElementOf0(X4,X1)
=> sdtlseqdt0(X4,X3) )
& aUpperBoundOfIn0(X3,X1,xU)
& ! [X4] :
( ( ( aElementOf0(X4,xU)
& ! [X5] :
( aElementOf0(X5,X1)
=> sdtlseqdt0(X5,X4) ) )
| aUpperBoundOfIn0(X4,X1,xU) )
=> sdtlseqdt0(X3,X4) )
& aSupremumOfIn0(X3,X1,xU) ) ) ),
introduced(definition) ).
fof(35,plain,
( aSet0(xU)
& ! [X1] :
( ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xU) ) )
| aSubsetOf0(X1,xU) )
=> epred1_1(X1) )
& aCompleteLattice0(xU)
& aFunction0(xf)
& ! [X1,X2] :
( ( aElementOf0(X1,szDzozmdt0(xf))
& aElementOf0(X2,szDzozmdt0(xf)) )
=> ( sdtlseqdt0(X1,X2)
=> sdtlseqdt0(sdtlpdtrp0(xf,X1),sdtlpdtrp0(xf,X2)) ) )
& isMonotone0(xf)
& szDzozmdt0(xf) = szRzazndt0(xf)
& szRzazndt0(xf) = xU
& isOn0(xf,xU) ),
inference(apply_def,[status(esa)],[33,34,theory(equality)]) ).
fof(39,plain,
! [X1] :
( ~ aSet0(X1)
| ! [X2] :
( ~ aElementOf0(X2,X1)
| aElement0(X2) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(40,plain,
! [X3] :
( ~ aSet0(X3)
| ! [X4] :
( ~ aElementOf0(X4,X3)
| aElement0(X4) ) ),
inference(variable_rename,[status(thm)],[39]) ).
fof(41,plain,
! [X3,X4] :
( ~ aElementOf0(X4,X3)
| aElement0(X4)
| ~ aSet0(X3) ),
inference(shift_quantors,[status(thm)],[40]) ).
cnf(42,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[41]) ).
fof(53,plain,
! [X1] :
( ~ aFunction0(X1)
| ! [X2] :
( ~ aElementOf0(X2,szDzozmdt0(X1))
| aElementOf0(sdtlpdtrp0(X1,X2),szRzazndt0(X1)) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(54,plain,
! [X3] :
( ~ aFunction0(X3)
| ! [X4] :
( ~ aElementOf0(X4,szDzozmdt0(X3))
| aElementOf0(sdtlpdtrp0(X3,X4),szRzazndt0(X3)) ) ),
inference(variable_rename,[status(thm)],[53]) ).
fof(55,plain,
! [X3,X4] :
( ~ aElementOf0(X4,szDzozmdt0(X3))
| aElementOf0(sdtlpdtrp0(X3,X4),szRzazndt0(X3))
| ~ aFunction0(X3) ),
inference(shift_quantors,[status(thm)],[54]) ).
cnf(56,plain,
( aElementOf0(sdtlpdtrp0(X1,X2),szRzazndt0(X1))
| ~ aFunction0(X1)
| ~ aElementOf0(X2,szDzozmdt0(X1)) ),
inference(split_conjunct,[status(thm)],[55]) ).
fof(88,plain,
! [X1] :
( ~ aElement0(X1)
| sdtlseqdt0(X1,X1) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(89,plain,
! [X2] :
( ~ aElement0(X2)
| sdtlseqdt0(X2,X2) ),
inference(variable_rename,[status(thm)],[88]) ).
cnf(90,plain,
( sdtlseqdt0(X1,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[89]) ).
fof(119,plain,
( aElementOf0(xp,xU)
& ! [X1] :
( ~ aElementOf0(X1,xP)
| sdtlseqdt0(xp,X1) )
& aLowerBoundOfIn0(xp,xP,xU)
& ! [X1] :
( ( ( ~ aElementOf0(X1,xU)
| ? [X2] :
( aElementOf0(X2,xP)
& ~ sdtlseqdt0(X1,X2) ) )
& ~ aLowerBoundOfIn0(X1,xP,xU) )
| sdtlseqdt0(X1,xp) )
& aInfimumOfIn0(xp,xP,xU) ),
inference(fof_nnf,[status(thm)],[32]) ).
fof(120,plain,
( aElementOf0(xp,xU)
& ! [X3] :
( ~ aElementOf0(X3,xP)
| sdtlseqdt0(xp,X3) )
& aLowerBoundOfIn0(xp,xP,xU)
& ! [X4] :
( ( ( ~ aElementOf0(X4,xU)
| ? [X5] :
( aElementOf0(X5,xP)
& ~ sdtlseqdt0(X4,X5) ) )
& ~ aLowerBoundOfIn0(X4,xP,xU) )
| sdtlseqdt0(X4,xp) )
& aInfimumOfIn0(xp,xP,xU) ),
inference(variable_rename,[status(thm)],[119]) ).
fof(121,plain,
( aElementOf0(xp,xU)
& ! [X3] :
( ~ aElementOf0(X3,xP)
| sdtlseqdt0(xp,X3) )
& aLowerBoundOfIn0(xp,xP,xU)
& ! [X4] :
( ( ( ~ aElementOf0(X4,xU)
| ( aElementOf0(esk6_1(X4),xP)
& ~ sdtlseqdt0(X4,esk6_1(X4)) ) )
& ~ aLowerBoundOfIn0(X4,xP,xU) )
| sdtlseqdt0(X4,xp) )
& aInfimumOfIn0(xp,xP,xU) ),
inference(skolemize,[status(esa)],[120]) ).
fof(122,plain,
! [X3,X4] :
( ( ( ( ~ aElementOf0(X4,xU)
| ( aElementOf0(esk6_1(X4),xP)
& ~ sdtlseqdt0(X4,esk6_1(X4)) ) )
& ~ aLowerBoundOfIn0(X4,xP,xU) )
| sdtlseqdt0(X4,xp) )
& ( ~ aElementOf0(X3,xP)
| sdtlseqdt0(xp,X3) )
& aElementOf0(xp,xU)
& aLowerBoundOfIn0(xp,xP,xU)
& aInfimumOfIn0(xp,xP,xU) ),
inference(shift_quantors,[status(thm)],[121]) ).
fof(123,plain,
! [X3,X4] :
( ( aElementOf0(esk6_1(X4),xP)
| ~ aElementOf0(X4,xU)
| sdtlseqdt0(X4,xp) )
& ( ~ sdtlseqdt0(X4,esk6_1(X4))
| ~ aElementOf0(X4,xU)
| sdtlseqdt0(X4,xp) )
& ( ~ aLowerBoundOfIn0(X4,xP,xU)
| sdtlseqdt0(X4,xp) )
& ( ~ aElementOf0(X3,xP)
| sdtlseqdt0(xp,X3) )
& aElementOf0(xp,xU)
& aLowerBoundOfIn0(xp,xP,xU)
& aInfimumOfIn0(xp,xP,xU) ),
inference(distribute,[status(thm)],[122]) ).
cnf(126,plain,
aElementOf0(xp,xU),
inference(split_conjunct,[status(thm)],[123]) ).
cnf(127,plain,
( sdtlseqdt0(xp,X1)
| ~ aElementOf0(X1,xP) ),
inference(split_conjunct,[status(thm)],[123]) ).
cnf(128,plain,
( sdtlseqdt0(X1,xp)
| ~ aLowerBoundOfIn0(X1,xP,xU) ),
inference(split_conjunct,[status(thm)],[123]) ).
fof(141,plain,
( aSet0(xP)
& ! [X1] :
( ( ~ aElementOf0(X1,xP)
| ( aElementOf0(X1,xU)
& sdtlseqdt0(sdtlpdtrp0(xf,X1),X1)
& ! [X2] :
( ~ aElementOf0(X2,xT)
| sdtlseqdt0(X2,X1) )
& aUpperBoundOfIn0(X1,xT,xU) ) )
& ( ~ aElementOf0(X1,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X1),X1)
| ( ? [X2] :
( aElementOf0(X2,xT)
& ~ sdtlseqdt0(X2,X1) )
& ~ aUpperBoundOfIn0(X1,xT,xU) )
| aElementOf0(X1,xP) ) )
& xP = cS1241(xU,xf,xT) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(142,plain,
( aSet0(xP)
& ! [X3] :
( ( ~ aElementOf0(X3,xP)
| ( aElementOf0(X3,xU)
& sdtlseqdt0(sdtlpdtrp0(xf,X3),X3)
& ! [X4] :
( ~ aElementOf0(X4,xT)
| sdtlseqdt0(X4,X3) )
& aUpperBoundOfIn0(X3,xT,xU) ) )
& ( ~ aElementOf0(X3,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X3),X3)
| ( ? [X5] :
( aElementOf0(X5,xT)
& ~ sdtlseqdt0(X5,X3) )
& ~ aUpperBoundOfIn0(X3,xT,xU) )
| aElementOf0(X3,xP) ) )
& xP = cS1241(xU,xf,xT) ),
inference(variable_rename,[status(thm)],[141]) ).
fof(143,plain,
( aSet0(xP)
& ! [X3] :
( ( ~ aElementOf0(X3,xP)
| ( aElementOf0(X3,xU)
& sdtlseqdt0(sdtlpdtrp0(xf,X3),X3)
& ! [X4] :
( ~ aElementOf0(X4,xT)
| sdtlseqdt0(X4,X3) )
& aUpperBoundOfIn0(X3,xT,xU) ) )
& ( ~ aElementOf0(X3,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X3),X3)
| ( aElementOf0(esk8_1(X3),xT)
& ~ sdtlseqdt0(esk8_1(X3),X3)
& ~ aUpperBoundOfIn0(X3,xT,xU) )
| aElementOf0(X3,xP) ) )
& xP = cS1241(xU,xf,xT) ),
inference(skolemize,[status(esa)],[142]) ).
fof(144,plain,
! [X3,X4] :
( ( ( ( ~ aElementOf0(X4,xT)
| sdtlseqdt0(X4,X3) )
& aElementOf0(X3,xU)
& sdtlseqdt0(sdtlpdtrp0(xf,X3),X3)
& aUpperBoundOfIn0(X3,xT,xU) )
| ~ aElementOf0(X3,xP) )
& ( ~ aElementOf0(X3,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X3),X3)
| ( aElementOf0(esk8_1(X3),xT)
& ~ sdtlseqdt0(esk8_1(X3),X3)
& ~ aUpperBoundOfIn0(X3,xT,xU) )
| aElementOf0(X3,xP) )
& aSet0(xP)
& xP = cS1241(xU,xf,xT) ),
inference(shift_quantors,[status(thm)],[143]) ).
fof(145,plain,
! [X3,X4] :
( ( ~ aElementOf0(X4,xT)
| sdtlseqdt0(X4,X3)
| ~ aElementOf0(X3,xP) )
& ( aElementOf0(X3,xU)
| ~ aElementOf0(X3,xP) )
& ( sdtlseqdt0(sdtlpdtrp0(xf,X3),X3)
| ~ aElementOf0(X3,xP) )
& ( aUpperBoundOfIn0(X3,xT,xU)
| ~ aElementOf0(X3,xP) )
& ( aElementOf0(esk8_1(X3),xT)
| ~ aElementOf0(X3,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X3),X3)
| aElementOf0(X3,xP) )
& ( ~ sdtlseqdt0(esk8_1(X3),X3)
| ~ aElementOf0(X3,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X3),X3)
| aElementOf0(X3,xP) )
& ( ~ aUpperBoundOfIn0(X3,xT,xU)
| ~ aElementOf0(X3,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X3),X3)
| aElementOf0(X3,xP) )
& aSet0(xP)
& xP = cS1241(xU,xf,xT) ),
inference(distribute,[status(thm)],[144]) ).
cnf(147,plain,
aSet0(xP),
inference(split_conjunct,[status(thm)],[145]) ).
cnf(148,plain,
( aElementOf0(X1,xP)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X1),X1)
| ~ aElementOf0(X1,xU)
| ~ aUpperBoundOfIn0(X1,xT,xU) ),
inference(split_conjunct,[status(thm)],[145]) ).
cnf(149,plain,
( aElementOf0(X1,xP)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X1),X1)
| ~ aElementOf0(X1,xU)
| ~ sdtlseqdt0(esk8_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[145]) ).
cnf(150,plain,
( aElementOf0(X1,xP)
| aElementOf0(esk8_1(X1),xT)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X1),X1)
| ~ aElementOf0(X1,xU) ),
inference(split_conjunct,[status(thm)],[145]) ).
cnf(154,plain,
( sdtlseqdt0(X2,X1)
| ~ aElementOf0(X1,xP)
| ~ aElementOf0(X2,xT) ),
inference(split_conjunct,[status(thm)],[145]) ).
fof(158,plain,
( ! [X1] :
( ~ aElementOf0(X1,xP)
| sdtlseqdt0(sdtlpdtrp0(xf,xp),X1) )
& aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)
& ! [X1] :
( ~ aElementOf0(X1,xT)
| sdtlseqdt0(X1,sdtlpdtrp0(xf,xp)) )
& aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(159,plain,
( ! [X2] :
( ~ aElementOf0(X2,xP)
| sdtlseqdt0(sdtlpdtrp0(xf,xp),X2) )
& aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)
& ! [X3] :
( ~ aElementOf0(X3,xT)
| sdtlseqdt0(X3,sdtlpdtrp0(xf,xp)) )
& aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU) ),
inference(variable_rename,[status(thm)],[158]) ).
fof(160,plain,
! [X2,X3] :
( ( ~ aElementOf0(X3,xT)
| sdtlseqdt0(X3,sdtlpdtrp0(xf,xp)) )
& ( ~ aElementOf0(X2,xP)
| sdtlseqdt0(sdtlpdtrp0(xf,xp),X2) )
& aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)
& aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU) ),
inference(shift_quantors,[status(thm)],[159]) ).
cnf(161,plain,
aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU),
inference(split_conjunct,[status(thm)],[160]) ).
cnf(162,plain,
aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU),
inference(split_conjunct,[status(thm)],[160]) ).
cnf(164,plain,
( sdtlseqdt0(X1,sdtlpdtrp0(xf,xp))
| ~ aElementOf0(X1,xT) ),
inference(split_conjunct,[status(thm)],[160]) ).
fof(175,plain,
! [X1,X2] :
( ~ aElement0(X1)
| ~ aElement0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1)
| X1 = X2 ),
inference(fof_nnf,[status(thm)],[23]) ).
fof(176,plain,
! [X3,X4] :
( ~ aElement0(X3)
| ~ aElement0(X4)
| ~ sdtlseqdt0(X3,X4)
| ~ sdtlseqdt0(X4,X3)
| X3 = X4 ),
inference(variable_rename,[status(thm)],[175]) ).
cnf(177,plain,
( X1 = X2
| ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[176]) ).
fof(192,plain,
( aSet0(xS)
& ! [X1] :
( ( ~ aElementOf0(X1,xS)
| ( aElementOf0(X1,szDzozmdt0(xf))
& sdtlpdtrp0(xf,X1) = X1
& aFixedPointOf0(X1,xf) ) )
& ( ( ( ~ aElementOf0(X1,szDzozmdt0(xf))
| sdtlpdtrp0(xf,X1) != X1 )
& ~ aFixedPointOf0(X1,xf) )
| aElementOf0(X1,xS) ) )
& xS = cS1142(xf) ),
inference(fof_nnf,[status(thm)],[26]) ).
fof(193,plain,
( aSet0(xS)
& ! [X2] :
( ( ~ aElementOf0(X2,xS)
| ( aElementOf0(X2,szDzozmdt0(xf))
& sdtlpdtrp0(xf,X2) = X2
& aFixedPointOf0(X2,xf) ) )
& ( ( ( ~ aElementOf0(X2,szDzozmdt0(xf))
| sdtlpdtrp0(xf,X2) != X2 )
& ~ aFixedPointOf0(X2,xf) )
| aElementOf0(X2,xS) ) )
& xS = cS1142(xf) ),
inference(variable_rename,[status(thm)],[192]) ).
fof(194,plain,
! [X2] :
( ( ~ aElementOf0(X2,xS)
| ( aElementOf0(X2,szDzozmdt0(xf))
& sdtlpdtrp0(xf,X2) = X2
& aFixedPointOf0(X2,xf) ) )
& ( ( ( ~ aElementOf0(X2,szDzozmdt0(xf))
| sdtlpdtrp0(xf,X2) != X2 )
& ~ aFixedPointOf0(X2,xf) )
| aElementOf0(X2,xS) )
& aSet0(xS)
& xS = cS1142(xf) ),
inference(shift_quantors,[status(thm)],[193]) ).
fof(195,plain,
! [X2] :
( ( aElementOf0(X2,szDzozmdt0(xf))
| ~ aElementOf0(X2,xS) )
& ( sdtlpdtrp0(xf,X2) = X2
| ~ aElementOf0(X2,xS) )
& ( aFixedPointOf0(X2,xf)
| ~ aElementOf0(X2,xS) )
& ( ~ aElementOf0(X2,szDzozmdt0(xf))
| sdtlpdtrp0(xf,X2) != X2
| aElementOf0(X2,xS) )
& ( ~ aFixedPointOf0(X2,xf)
| aElementOf0(X2,xS) )
& aSet0(xS)
& xS = cS1142(xf) ),
inference(distribute,[status(thm)],[194]) ).
cnf(197,plain,
aSet0(xS),
inference(split_conjunct,[status(thm)],[195]) ).
cnf(199,plain,
( aElementOf0(X1,xS)
| sdtlpdtrp0(xf,X1) != X1
| ~ aElementOf0(X1,szDzozmdt0(xf)) ),
inference(split_conjunct,[status(thm)],[195]) ).
cnf(200,plain,
( aFixedPointOf0(X1,xf)
| ~ aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[195]) ).
cnf(201,plain,
( sdtlpdtrp0(xf,X1) = X1
| ~ aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[195]) ).
cnf(202,plain,
( aElementOf0(X1,szDzozmdt0(xf))
| ~ aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[195]) ).
fof(203,plain,
( aSet0(xU)
& ! [X1] :
( ( ( ~ aSet0(X1)
| ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,xU) ) )
& ~ aSubsetOf0(X1,xU) )
| epred1_1(X1) )
& aCompleteLattice0(xU)
& aFunction0(xf)
& ! [X1,X2] :
( ~ aElementOf0(X1,szDzozmdt0(xf))
| ~ aElementOf0(X2,szDzozmdt0(xf))
| ~ sdtlseqdt0(X1,X2)
| sdtlseqdt0(sdtlpdtrp0(xf,X1),sdtlpdtrp0(xf,X2)) )
& isMonotone0(xf)
& szDzozmdt0(xf) = szRzazndt0(xf)
& szRzazndt0(xf) = xU
& isOn0(xf,xU) ),
inference(fof_nnf,[status(thm)],[35]) ).
fof(204,plain,
( aSet0(xU)
& ! [X3] :
( ( ( ~ aSet0(X3)
| ? [X4] :
( aElementOf0(X4,X3)
& ~ aElementOf0(X4,xU) ) )
& ~ aSubsetOf0(X3,xU) )
| epred1_1(X3) )
& aCompleteLattice0(xU)
& aFunction0(xf)
& ! [X5,X6] :
( ~ aElementOf0(X5,szDzozmdt0(xf))
| ~ aElementOf0(X6,szDzozmdt0(xf))
| ~ sdtlseqdt0(X5,X6)
| sdtlseqdt0(sdtlpdtrp0(xf,X5),sdtlpdtrp0(xf,X6)) )
& isMonotone0(xf)
& szDzozmdt0(xf) = szRzazndt0(xf)
& szRzazndt0(xf) = xU
& isOn0(xf,xU) ),
inference(variable_rename,[status(thm)],[203]) ).
fof(205,plain,
( aSet0(xU)
& ! [X3] :
( ( ( ~ aSet0(X3)
| ( aElementOf0(esk12_1(X3),X3)
& ~ aElementOf0(esk12_1(X3),xU) ) )
& ~ aSubsetOf0(X3,xU) )
| epred1_1(X3) )
& aCompleteLattice0(xU)
& aFunction0(xf)
& ! [X5,X6] :
( ~ aElementOf0(X5,szDzozmdt0(xf))
| ~ aElementOf0(X6,szDzozmdt0(xf))
| ~ sdtlseqdt0(X5,X6)
| sdtlseqdt0(sdtlpdtrp0(xf,X5),sdtlpdtrp0(xf,X6)) )
& isMonotone0(xf)
& szDzozmdt0(xf) = szRzazndt0(xf)
& szRzazndt0(xf) = xU
& isOn0(xf,xU) ),
inference(skolemize,[status(esa)],[204]) ).
fof(206,plain,
! [X3,X5,X6] :
( ( ~ aElementOf0(X5,szDzozmdt0(xf))
| ~ aElementOf0(X6,szDzozmdt0(xf))
| ~ sdtlseqdt0(X5,X6)
| sdtlseqdt0(sdtlpdtrp0(xf,X5),sdtlpdtrp0(xf,X6)) )
& ( ( ( ~ aSet0(X3)
| ( aElementOf0(esk12_1(X3),X3)
& ~ aElementOf0(esk12_1(X3),xU) ) )
& ~ aSubsetOf0(X3,xU) )
| epred1_1(X3) )
& aSet0(xU)
& aCompleteLattice0(xU)
& aFunction0(xf)
& isMonotone0(xf)
& szDzozmdt0(xf) = szRzazndt0(xf)
& szRzazndt0(xf) = xU
& isOn0(xf,xU) ),
inference(shift_quantors,[status(thm)],[205]) ).
fof(207,plain,
! [X3,X5,X6] :
( ( ~ aElementOf0(X5,szDzozmdt0(xf))
| ~ aElementOf0(X6,szDzozmdt0(xf))
| ~ sdtlseqdt0(X5,X6)
| sdtlseqdt0(sdtlpdtrp0(xf,X5),sdtlpdtrp0(xf,X6)) )
& ( aElementOf0(esk12_1(X3),X3)
| ~ aSet0(X3)
| epred1_1(X3) )
& ( ~ aElementOf0(esk12_1(X3),xU)
| ~ aSet0(X3)
| epred1_1(X3) )
& ( ~ aSubsetOf0(X3,xU)
| epred1_1(X3) )
& aSet0(xU)
& aCompleteLattice0(xU)
& aFunction0(xf)
& isMonotone0(xf)
& szDzozmdt0(xf) = szRzazndt0(xf)
& szRzazndt0(xf) = xU
& isOn0(xf,xU) ),
inference(distribute,[status(thm)],[206]) ).
cnf(209,plain,
szRzazndt0(xf) = xU,
inference(split_conjunct,[status(thm)],[207]) ).
cnf(210,plain,
szDzozmdt0(xf) = szRzazndt0(xf),
inference(split_conjunct,[status(thm)],[207]) ).
cnf(212,plain,
aFunction0(xf),
inference(split_conjunct,[status(thm)],[207]) ).
cnf(214,plain,
aSet0(xU),
inference(split_conjunct,[status(thm)],[207]) ).
cnf(218,plain,
( sdtlseqdt0(sdtlpdtrp0(xf,X1),sdtlpdtrp0(xf,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,szDzozmdt0(xf))
| ~ aElementOf0(X1,szDzozmdt0(xf)) ),
inference(split_conjunct,[status(thm)],[207]) ).
fof(229,negated_conjecture,
( ( ( ~ aElementOf0(xp,szDzozmdt0(xf))
| sdtlpdtrp0(xf,xp) != xp )
& ~ aFixedPointOf0(xp,xf) )
| ( ( ( ? [X1] :
( aElementOf0(X1,xT)
& ~ sdtlseqdt0(X1,xp) )
& ~ aUpperBoundOfIn0(xp,xT,xS) )
| ? [X1] :
( aElementOf0(X1,xS)
& ! [X2] :
( ~ aElementOf0(X2,xT)
| sdtlseqdt0(X2,X1) )
& aUpperBoundOfIn0(X1,xT,xS)
& ~ sdtlseqdt0(xp,X1) ) )
& ~ aSupremumOfIn0(xp,xT,xS) ) ),
inference(fof_nnf,[status(thm)],[31]) ).
fof(230,negated_conjecture,
( ( ( ~ aElementOf0(xp,szDzozmdt0(xf))
| sdtlpdtrp0(xf,xp) != xp )
& ~ aFixedPointOf0(xp,xf) )
| ( ( ( ? [X3] :
( aElementOf0(X3,xT)
& ~ sdtlseqdt0(X3,xp) )
& ~ aUpperBoundOfIn0(xp,xT,xS) )
| ? [X4] :
( aElementOf0(X4,xS)
& ! [X5] :
( ~ aElementOf0(X5,xT)
| sdtlseqdt0(X5,X4) )
& aUpperBoundOfIn0(X4,xT,xS)
& ~ sdtlseqdt0(xp,X4) ) )
& ~ aSupremumOfIn0(xp,xT,xS) ) ),
inference(variable_rename,[status(thm)],[229]) ).
fof(231,negated_conjecture,
( ( ( ~ aElementOf0(xp,szDzozmdt0(xf))
| sdtlpdtrp0(xf,xp) != xp )
& ~ aFixedPointOf0(xp,xf) )
| ( ( ( aElementOf0(esk15_0,xT)
& ~ sdtlseqdt0(esk15_0,xp)
& ~ aUpperBoundOfIn0(xp,xT,xS) )
| ( aElementOf0(esk16_0,xS)
& ! [X5] :
( ~ aElementOf0(X5,xT)
| sdtlseqdt0(X5,esk16_0) )
& aUpperBoundOfIn0(esk16_0,xT,xS)
& ~ sdtlseqdt0(xp,esk16_0) ) )
& ~ aSupremumOfIn0(xp,xT,xS) ) ),
inference(skolemize,[status(esa)],[230]) ).
fof(232,negated_conjecture,
! [X5] :
( ( ( ( ( ~ aElementOf0(X5,xT)
| sdtlseqdt0(X5,esk16_0) )
& aElementOf0(esk16_0,xS)
& aUpperBoundOfIn0(esk16_0,xT,xS)
& ~ sdtlseqdt0(xp,esk16_0) )
| ( aElementOf0(esk15_0,xT)
& ~ sdtlseqdt0(esk15_0,xp)
& ~ aUpperBoundOfIn0(xp,xT,xS) ) )
& ~ aSupremumOfIn0(xp,xT,xS) )
| ( ( ~ aElementOf0(xp,szDzozmdt0(xf))
| sdtlpdtrp0(xf,xp) != xp )
& ~ aFixedPointOf0(xp,xf) ) ),
inference(shift_quantors,[status(thm)],[231]) ).
fof(233,negated_conjecture,
! [X5] :
( ( ~ aElementOf0(xp,szDzozmdt0(xf))
| sdtlpdtrp0(xf,xp) != xp
| aElementOf0(esk15_0,xT)
| ~ aElementOf0(X5,xT)
| sdtlseqdt0(X5,esk16_0) )
& ( ~ aFixedPointOf0(xp,xf)
| aElementOf0(esk15_0,xT)
| ~ aElementOf0(X5,xT)
| sdtlseqdt0(X5,esk16_0) )
& ( ~ aElementOf0(xp,szDzozmdt0(xf))
| sdtlpdtrp0(xf,xp) != xp
| ~ sdtlseqdt0(esk15_0,xp)
| ~ aElementOf0(X5,xT)
| sdtlseqdt0(X5,esk16_0) )
& ( ~ aFixedPointOf0(xp,xf)
| ~ sdtlseqdt0(esk15_0,xp)
| ~ aElementOf0(X5,xT)
| sdtlseqdt0(X5,esk16_0) )
& ( ~ aElementOf0(xp,szDzozmdt0(xf))
| sdtlpdtrp0(xf,xp) != xp
| ~ aUpperBoundOfIn0(xp,xT,xS)
| ~ aElementOf0(X5,xT)
| sdtlseqdt0(X5,esk16_0) )
& ( ~ aFixedPointOf0(xp,xf)
| ~ aUpperBoundOfIn0(xp,xT,xS)
| ~ aElementOf0(X5,xT)
| sdtlseqdt0(X5,esk16_0) )
& ( ~ aElementOf0(xp,szDzozmdt0(xf))
| sdtlpdtrp0(xf,xp) != xp
| aElementOf0(esk15_0,xT)
| aElementOf0(esk16_0,xS) )
& ( ~ aFixedPointOf0(xp,xf)
| aElementOf0(esk15_0,xT)
| aElementOf0(esk16_0,xS) )
& ( ~ aElementOf0(xp,szDzozmdt0(xf))
| sdtlpdtrp0(xf,xp) != xp
| ~ sdtlseqdt0(esk15_0,xp)
| aElementOf0(esk16_0,xS) )
& ( ~ aFixedPointOf0(xp,xf)
| ~ sdtlseqdt0(esk15_0,xp)
| aElementOf0(esk16_0,xS) )
& ( ~ aElementOf0(xp,szDzozmdt0(xf))
| sdtlpdtrp0(xf,xp) != xp
| ~ aUpperBoundOfIn0(xp,xT,xS)
| aElementOf0(esk16_0,xS) )
& ( ~ aFixedPointOf0(xp,xf)
| ~ aUpperBoundOfIn0(xp,xT,xS)
| aElementOf0(esk16_0,xS) )
& ( ~ aElementOf0(xp,szDzozmdt0(xf))
| sdtlpdtrp0(xf,xp) != xp
| aElementOf0(esk15_0,xT)
| aUpperBoundOfIn0(esk16_0,xT,xS) )
& ( ~ aFixedPointOf0(xp,xf)
| aElementOf0(esk15_0,xT)
| aUpperBoundOfIn0(esk16_0,xT,xS) )
& ( ~ aElementOf0(xp,szDzozmdt0(xf))
| sdtlpdtrp0(xf,xp) != xp
| ~ sdtlseqdt0(esk15_0,xp)
| aUpperBoundOfIn0(esk16_0,xT,xS) )
& ( ~ aFixedPointOf0(xp,xf)
| ~ sdtlseqdt0(esk15_0,xp)
| aUpperBoundOfIn0(esk16_0,xT,xS) )
& ( ~ aElementOf0(xp,szDzozmdt0(xf))
| sdtlpdtrp0(xf,xp) != xp
| ~ aUpperBoundOfIn0(xp,xT,xS)
| aUpperBoundOfIn0(esk16_0,xT,xS) )
& ( ~ aFixedPointOf0(xp,xf)
| ~ aUpperBoundOfIn0(xp,xT,xS)
| aUpperBoundOfIn0(esk16_0,xT,xS) )
& ( ~ aElementOf0(xp,szDzozmdt0(xf))
| sdtlpdtrp0(xf,xp) != xp
| aElementOf0(esk15_0,xT)
| ~ sdtlseqdt0(xp,esk16_0) )
& ( ~ aFixedPointOf0(xp,xf)
| aElementOf0(esk15_0,xT)
| ~ sdtlseqdt0(xp,esk16_0) )
& ( ~ aElementOf0(xp,szDzozmdt0(xf))
| sdtlpdtrp0(xf,xp) != xp
| ~ sdtlseqdt0(esk15_0,xp)
| ~ sdtlseqdt0(xp,esk16_0) )
& ( ~ aFixedPointOf0(xp,xf)
| ~ sdtlseqdt0(esk15_0,xp)
| ~ sdtlseqdt0(xp,esk16_0) )
& ( ~ aElementOf0(xp,szDzozmdt0(xf))
| sdtlpdtrp0(xf,xp) != xp
| ~ aUpperBoundOfIn0(xp,xT,xS)
| ~ sdtlseqdt0(xp,esk16_0) )
& ( ~ aFixedPointOf0(xp,xf)
| ~ aUpperBoundOfIn0(xp,xT,xS)
| ~ sdtlseqdt0(xp,esk16_0) )
& ( ~ aElementOf0(xp,szDzozmdt0(xf))
| sdtlpdtrp0(xf,xp) != xp
| ~ aSupremumOfIn0(xp,xT,xS) )
& ( ~ aFixedPointOf0(xp,xf)
| ~ aSupremumOfIn0(xp,xT,xS) ) ),
inference(distribute,[status(thm)],[232]) ).
cnf(238,negated_conjecture,
( ~ sdtlseqdt0(xp,esk16_0)
| ~ sdtlseqdt0(esk15_0,xp)
| ~ aFixedPointOf0(xp,xf) ),
inference(split_conjunct,[status(thm)],[233]) ).
cnf(240,negated_conjecture,
( aElementOf0(esk15_0,xT)
| ~ sdtlseqdt0(xp,esk16_0)
| ~ aFixedPointOf0(xp,xf) ),
inference(split_conjunct,[status(thm)],[233]) ).
cnf(250,negated_conjecture,
( aElementOf0(esk16_0,xS)
| ~ sdtlseqdt0(esk15_0,xp)
| ~ aFixedPointOf0(xp,xf) ),
inference(split_conjunct,[status(thm)],[233]) ).
cnf(252,negated_conjecture,
( aElementOf0(esk16_0,xS)
| aElementOf0(esk15_0,xT)
| ~ aFixedPointOf0(xp,xf) ),
inference(split_conjunct,[status(thm)],[233]) ).
cnf(256,negated_conjecture,
( sdtlseqdt0(X1,esk16_0)
| ~ aElementOf0(X1,xT)
| ~ sdtlseqdt0(esk15_0,xp)
| ~ aFixedPointOf0(xp,xf) ),
inference(split_conjunct,[status(thm)],[233]) ).
cnf(258,negated_conjecture,
( sdtlseqdt0(X1,esk16_0)
| aElementOf0(esk15_0,xT)
| ~ aElementOf0(X1,xT)
| ~ aFixedPointOf0(xp,xf) ),
inference(split_conjunct,[status(thm)],[233]) ).
cnf(282,plain,
xU = szDzozmdt0(xf),
inference(rw,[status(thm)],[210,209,theory(equality)]) ).
cnf(298,plain,
( ~ sdtlseqdt0(xp,esk16_0)
| ~ sdtlseqdt0(esk15_0,xp)
| ~ aElementOf0(xp,xS) ),
inference(spm,[status(thm)],[238,200,theory(equality)]) ).
cnf(300,plain,
( aElementOf0(esk15_0,xT)
| ~ sdtlseqdt0(xp,esk16_0)
| ~ aElementOf0(xp,xS) ),
inference(spm,[status(thm)],[240,200,theory(equality)]) ).
cnf(301,plain,
( aElementOf0(esk16_0,xS)
| ~ sdtlseqdt0(esk15_0,xp)
| ~ aElementOf0(xp,xS) ),
inference(spm,[status(thm)],[250,200,theory(equality)]) ).
cnf(304,plain,
( aElementOf0(esk16_0,xS)
| aElementOf0(esk15_0,xT)
| ~ aElementOf0(xp,xS) ),
inference(spm,[status(thm)],[252,200,theory(equality)]) ).
cnf(308,plain,
( aElementOf0(X1,xU)
| ~ aElementOf0(X1,xS) ),
inference(rw,[status(thm)],[202,282,theory(equality)]) ).
cnf(312,plain,
( sdtlseqdt0(X1,esk16_0)
| ~ aElementOf0(X1,xT)
| ~ sdtlseqdt0(esk15_0,xp)
| ~ aElementOf0(xp,xS) ),
inference(spm,[status(thm)],[256,200,theory(equality)]) ).
cnf(314,plain,
( aElementOf0(esk15_0,xT)
| sdtlseqdt0(X1,esk16_0)
| ~ aElementOf0(X1,xT)
| ~ aElementOf0(xp,xS) ),
inference(spm,[status(thm)],[258,200,theory(equality)]) ).
cnf(317,plain,
( aUpperBoundOfIn0(xp,xT,xU)
| ~ aElementOf0(xp,xS) ),
inference(spm,[status(thm)],[161,201,theory(equality)]) ).
cnf(319,plain,
( sdtlseqdt0(X1,xp)
| ~ aElementOf0(X1,xT)
| ~ aElementOf0(xp,xS) ),
inference(spm,[status(thm)],[164,201,theory(equality)]) ).
cnf(335,plain,
( aElementOf0(X1,xS)
| sdtlpdtrp0(xf,X1) != X1
| ~ aElementOf0(X1,xU) ),
inference(rw,[status(thm)],[199,282,theory(equality)]) ).
cnf(339,plain,
sdtlseqdt0(sdtlpdtrp0(xf,xp),xp),
inference(spm,[status(thm)],[128,162,theory(equality)]) ).
cnf(352,plain,
( aElement0(xp)
| ~ aSet0(xU) ),
inference(spm,[status(thm)],[42,126,theory(equality)]) ).
cnf(356,plain,
( aElement0(xp)
| $false ),
inference(rw,[status(thm)],[352,214,theory(equality)]) ).
cnf(357,plain,
aElement0(xp),
inference(cn,[status(thm)],[356,theory(equality)]) ).
cnf(385,plain,
( sdtlseqdt0(sdtlpdtrp0(xf,X1),sdtlpdtrp0(xf,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,xU)
| ~ aElementOf0(X1,szDzozmdt0(xf)) ),
inference(rw,[status(thm)],[218,282,theory(equality)]) ).
cnf(386,plain,
( sdtlseqdt0(sdtlpdtrp0(xf,X1),sdtlpdtrp0(xf,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,xU)
| ~ aElementOf0(X1,xU) ),
inference(rw,[status(thm)],[385,282,theory(equality)]) ).
cnf(443,plain,
( aElementOf0(sdtlpdtrp0(xf,X1),xU)
| ~ aFunction0(xf)
| ~ aElementOf0(X1,szDzozmdt0(xf)) ),
inference(spm,[status(thm)],[56,209,theory(equality)]) ).
cnf(447,plain,
( aElementOf0(sdtlpdtrp0(xf,X1),xU)
| $false
| ~ aElementOf0(X1,szDzozmdt0(xf)) ),
inference(rw,[status(thm)],[443,212,theory(equality)]) ).
cnf(448,plain,
( aElementOf0(sdtlpdtrp0(xf,X1),xU)
| $false
| ~ aElementOf0(X1,xU) ),
inference(rw,[status(thm)],[447,282,theory(equality)]) ).
cnf(449,plain,
( aElementOf0(sdtlpdtrp0(xf,X1),xU)
| ~ aElementOf0(X1,xU) ),
inference(cn,[status(thm)],[448,theory(equality)]) ).
cnf(455,plain,
( aElementOf0(sdtlpdtrp0(xf,xp),xP)
| ~ aElementOf0(sdtlpdtrp0(xf,xp),xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,xp)),sdtlpdtrp0(xf,xp))
| ~ aElementOf0(esk8_1(sdtlpdtrp0(xf,xp)),xT) ),
inference(spm,[status(thm)],[149,164,theory(equality)]) ).
cnf(744,plain,
( aElementOf0(xp,xP)
| ~ aUpperBoundOfIn0(xp,xT,xU)
| ~ aElementOf0(xp,xU) ),
inference(spm,[status(thm)],[148,339,theory(equality)]) ).
cnf(746,plain,
( xp = sdtlpdtrp0(xf,xp)
| ~ sdtlseqdt0(xp,sdtlpdtrp0(xf,xp))
| ~ aElement0(sdtlpdtrp0(xf,xp))
| ~ aElement0(xp) ),
inference(spm,[status(thm)],[177,339,theory(equality)]) ).
cnf(749,plain,
( aElementOf0(xp,xP)
| ~ aUpperBoundOfIn0(xp,xT,xU)
| $false ),
inference(rw,[status(thm)],[744,126,theory(equality)]) ).
cnf(750,plain,
( aElementOf0(xp,xP)
| ~ aUpperBoundOfIn0(xp,xT,xU) ),
inference(cn,[status(thm)],[749,theory(equality)]) ).
cnf(756,plain,
( aElementOf0(esk16_0,xS)
| ~ aElementOf0(xp,xS)
| ~ aElementOf0(esk15_0,xT)
| ~ aElementOf0(xp,xP) ),
inference(spm,[status(thm)],[301,154,theory(equality)]) ).
cnf(845,plain,
( aElementOf0(esk16_0,xS)
| ~ aElementOf0(xp,xP)
| ~ aElementOf0(xp,xS) ),
inference(csr,[status(thm)],[756,304]) ).
cnf(848,plain,
( aElement0(esk16_0)
| ~ aSet0(xS)
| ~ aElementOf0(xp,xS)
| ~ aElementOf0(xp,xP) ),
inference(spm,[status(thm)],[42,845,theory(equality)]) ).
cnf(851,plain,
( aElement0(esk16_0)
| $false
| ~ aElementOf0(xp,xS)
| ~ aElementOf0(xp,xP) ),
inference(rw,[status(thm)],[848,197,theory(equality)]) ).
cnf(852,plain,
( aElement0(esk16_0)
| ~ aElementOf0(xp,xS)
| ~ aElementOf0(xp,xP) ),
inference(cn,[status(thm)],[851,theory(equality)]) ).
cnf(857,plain,
( aElementOf0(xp,xP)
| ~ aElementOf0(xp,xS) ),
inference(spm,[status(thm)],[750,317,theory(equality)]) ).
cnf(876,plain,
( aElement0(esk16_0)
| ~ aElementOf0(xp,xS) ),
inference(csr,[status(thm)],[852,857]) ).
cnf(877,plain,
( sdtlseqdt0(esk16_0,esk16_0)
| ~ aElementOf0(xp,xS) ),
inference(spm,[status(thm)],[90,876,theory(equality)]) ).
cnf(879,plain,
( sdtlpdtrp0(xf,xp) = xp
| ~ sdtlseqdt0(xp,sdtlpdtrp0(xf,xp))
| ~ aElement0(sdtlpdtrp0(xf,xp))
| $false ),
inference(rw,[status(thm)],[746,357,theory(equality)]) ).
cnf(880,plain,
( sdtlpdtrp0(xf,xp) = xp
| ~ sdtlseqdt0(xp,sdtlpdtrp0(xf,xp))
| ~ aElement0(sdtlpdtrp0(xf,xp)) ),
inference(cn,[status(thm)],[879,theory(equality)]) ).
cnf(889,plain,
( ~ aElementOf0(xp,xS)
| ~ sdtlseqdt0(xp,esk16_0)
| ~ aElementOf0(esk15_0,xT) ),
inference(spm,[status(thm)],[298,319,theory(equality)]) ).
cnf(890,plain,
( aElementOf0(esk16_0,xS)
| ~ aElementOf0(xp,xS)
| ~ aElementOf0(esk15_0,xT) ),
inference(spm,[status(thm)],[301,319,theory(equality)]) ).
cnf(891,plain,
( sdtlseqdt0(X1,esk16_0)
| ~ aElementOf0(xp,xS)
| ~ aElementOf0(X1,xT)
| ~ aElementOf0(esk15_0,xT) ),
inference(spm,[status(thm)],[312,319,theory(equality)]) ).
cnf(905,plain,
( ~ aElementOf0(xp,xS)
| ~ sdtlseqdt0(xp,esk16_0) ),
inference(csr,[status(thm)],[889,300]) ).
cnf(906,plain,
( ~ aElementOf0(xp,xS)
| ~ aElementOf0(esk16_0,xP) ),
inference(spm,[status(thm)],[905,127,theory(equality)]) ).
cnf(908,plain,
( aElementOf0(esk16_0,xS)
| ~ aElementOf0(xp,xS) ),
inference(csr,[status(thm)],[890,304]) ).
cnf(909,plain,
( aElementOf0(esk16_0,xU)
| ~ aElementOf0(xp,xS) ),
inference(spm,[status(thm)],[308,908,theory(equality)]) ).
cnf(953,plain,
( sdtlseqdt0(X1,esk16_0)
| ~ aElementOf0(xp,xS)
| ~ aElementOf0(X1,xT) ),
inference(csr,[status(thm)],[314,891]) ).
cnf(955,plain,
( aElementOf0(esk16_0,xP)
| ~ aElementOf0(esk16_0,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,esk16_0),esk16_0)
| ~ aElementOf0(xp,xS)
| ~ aElementOf0(esk8_1(esk16_0),xT) ),
inference(spm,[status(thm)],[149,953,theory(equality)]) ).
cnf(1053,plain,
( aElementOf0(esk16_0,xP)
| ~ aElementOf0(esk16_0,xU)
| ~ aElementOf0(xp,xS)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,esk16_0),esk16_0) ),
inference(csr,[status(thm)],[955,150]) ).
cnf(1054,plain,
( aElementOf0(esk16_0,xP)
| ~ aElementOf0(xp,xS)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,esk16_0),esk16_0) ),
inference(csr,[status(thm)],[1053,909]) ).
cnf(1055,plain,
( ~ aElementOf0(xp,xS)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,esk16_0),esk16_0) ),
inference(csr,[status(thm)],[1054,906]) ).
cnf(1056,plain,
( ~ aElementOf0(xp,xS)
| ~ sdtlseqdt0(esk16_0,esk16_0)
| ~ aElementOf0(esk16_0,xS) ),
inference(spm,[status(thm)],[1055,201,theory(equality)]) ).
cnf(1061,plain,
( ~ aElementOf0(xp,xS)
| ~ sdtlseqdt0(esk16_0,esk16_0) ),
inference(csr,[status(thm)],[1056,908]) ).
cnf(1062,plain,
~ aElementOf0(xp,xS),
inference(csr,[status(thm)],[1061,877]) ).
cnf(1179,plain,
( aElementOf0(sdtlpdtrp0(xf,xp),xP)
| ~ aElementOf0(sdtlpdtrp0(xf,xp),xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,xp)),sdtlpdtrp0(xf,xp)) ),
inference(csr,[status(thm)],[455,150]) ).
cnf(1185,plain,
( aElementOf0(sdtlpdtrp0(xf,xp),xP)
| ~ aElementOf0(sdtlpdtrp0(xf,xp),xU)
| ~ aElementOf0(xp,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),xp) ),
inference(spm,[status(thm)],[1179,386,theory(equality)]) ).
cnf(1192,plain,
( aElementOf0(sdtlpdtrp0(xf,xp),xP)
| ~ aElementOf0(sdtlpdtrp0(xf,xp),xU)
| $false
| ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),xp) ),
inference(rw,[status(thm)],[1185,126,theory(equality)]) ).
cnf(1193,plain,
( aElementOf0(sdtlpdtrp0(xf,xp),xP)
| ~ aElementOf0(sdtlpdtrp0(xf,xp),xU)
| $false
| $false ),
inference(rw,[status(thm)],[1192,339,theory(equality)]) ).
cnf(1194,plain,
( aElementOf0(sdtlpdtrp0(xf,xp),xP)
| ~ aElementOf0(sdtlpdtrp0(xf,xp),xU) ),
inference(cn,[status(thm)],[1193,theory(equality)]) ).
cnf(1206,plain,
( aElement0(sdtlpdtrp0(xf,xp))
| ~ aSet0(xP)
| ~ aElementOf0(sdtlpdtrp0(xf,xp),xU) ),
inference(spm,[status(thm)],[42,1194,theory(equality)]) ).
cnf(1212,plain,
( aElement0(sdtlpdtrp0(xf,xp))
| $false
| ~ aElementOf0(sdtlpdtrp0(xf,xp),xU) ),
inference(rw,[status(thm)],[1206,147,theory(equality)]) ).
cnf(1213,plain,
( aElement0(sdtlpdtrp0(xf,xp))
| ~ aElementOf0(sdtlpdtrp0(xf,xp),xU) ),
inference(cn,[status(thm)],[1212,theory(equality)]) ).
cnf(1216,plain,
( sdtlpdtrp0(xf,xp) = xp
| ~ sdtlseqdt0(xp,sdtlpdtrp0(xf,xp))
| ~ aElementOf0(sdtlpdtrp0(xf,xp),xU) ),
inference(spm,[status(thm)],[880,1213,theory(equality)]) ).
cnf(1221,plain,
( sdtlpdtrp0(xf,xp) = xp
| ~ aElementOf0(sdtlpdtrp0(xf,xp),xU)
| ~ aElementOf0(sdtlpdtrp0(xf,xp),xP) ),
inference(spm,[status(thm)],[1216,127,theory(equality)]) ).
cnf(1251,plain,
( sdtlpdtrp0(xf,xp) = xp
| ~ aElementOf0(sdtlpdtrp0(xf,xp),xU) ),
inference(csr,[status(thm)],[1221,1194]) ).
cnf(1287,plain,
( sdtlpdtrp0(xf,xp) = xp
| ~ aElementOf0(xp,xU) ),
inference(spm,[status(thm)],[1251,449,theory(equality)]) ).
cnf(1292,plain,
( sdtlpdtrp0(xf,xp) = xp
| $false ),
inference(rw,[status(thm)],[1287,126,theory(equality)]) ).
cnf(1293,plain,
sdtlpdtrp0(xf,xp) = xp,
inference(cn,[status(thm)],[1292,theory(equality)]) ).
cnf(1294,plain,
( aElementOf0(xp,xS)
| ~ aElementOf0(xp,xU) ),
inference(spm,[status(thm)],[335,1293,theory(equality)]) ).
cnf(1378,plain,
( aElementOf0(xp,xS)
| $false ),
inference(rw,[status(thm)],[1294,126,theory(equality)]) ).
cnf(1379,plain,
aElementOf0(xp,xS),
inference(cn,[status(thm)],[1378,theory(equality)]) ).
cnf(1380,plain,
$false,
inference(sr,[status(thm)],[1379,1062,theory(equality)]) ).
cnf(1381,plain,
$false,
1380,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/LAT/LAT387+4.p
% --creating new selector for []
% -running prover on /tmp/tmp4T6wRo/sel_LAT387+4.p_1 with time limit 29
% -prover status Theorem
% Problem LAT387+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/LAT/LAT387+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/LAT/LAT387+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
%
%------------------------------------------------------------------------------