TSTP Solution File: LAT386+4 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : LAT386+4 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art09.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 17:22:31 EST 2010
% Result : Theorem 4.16s
% Output : CNFRefutation 4.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 72
% Number of leaves : 11
% Syntax : Number of formulae : 192 ( 25 unt; 0 def)
% Number of atoms : 940 ( 41 equ)
% Maximal formula atoms : 37 ( 4 avg)
% Number of connectives : 1156 ( 408 ~; 426 |; 267 &)
% ( 0 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 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 : 215 ( 0 sgn 116 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/tmp/tmp_5ue2K/sel_LAT386+4.p_1',mEOfElem) ).
fof(4,axiom,
! [X1] :
( aFunction0(X1)
=> ! [X2] :
( aElementOf0(X2,szDzozmdt0(X1))
=> aElementOf0(sdtlpdtrp0(X1,X2),szRzazndt0(X1)) ) ),
file('/tmp/tmp_5ue2K/sel_LAT386+4.p_1',mImgSort) ).
fof(10,axiom,
! [X1] :
( aElement0(X1)
=> sdtlseqdt0(X1,X1) ),
file('/tmp/tmp_5ue2K/sel_LAT386+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/tmp_5ue2K/sel_LAT386+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/tmp_5ue2K/sel_LAT386+4.p_1',m__1244) ).
fof(21,axiom,
( aSet0(xT)
& ! [X1] :
( aElementOf0(X1,xT)
=> aElementOf0(X1,xS) )
& aSubsetOf0(xT,xS) ),
file('/tmp/tmp_5ue2K/sel_LAT386+4.p_1',m__1173) ).
fof(25,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/tmp_5ue2K/sel_LAT386+4.p_1',m__1144) ).
fof(26,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/tmp_5ue2K/sel_LAT386+4.p_1',m__1123) ).
fof(28,conjecture,
( ( ! [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/tmp_5ue2K/sel_LAT386+4.p_1',m__) ).
fof(29,axiom,
! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aElement0(X3) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X3) )
=> sdtlseqdt0(X1,X3) ) ),
file('/tmp/tmp_5ue2K/sel_LAT386+4.p_1',mTrans) ).
fof(30,negated_conjecture,
~ ( ( ! [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(assume_negation,[status(cth)],[28]) ).
fof(31,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(32,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)],[26,theory(equality)]) ).
fof(33,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(34,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)],[32,33,theory(equality)]) ).
fof(38,plain,
! [X1] :
( ~ aSet0(X1)
| ! [X2] :
( ~ aElementOf0(X2,X1)
| aElement0(X2) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(39,plain,
! [X3] :
( ~ aSet0(X3)
| ! [X4] :
( ~ aElementOf0(X4,X3)
| aElement0(X4) ) ),
inference(variable_rename,[status(thm)],[38]) ).
fof(40,plain,
! [X3,X4] :
( ~ aElementOf0(X4,X3)
| aElement0(X4)
| ~ aSet0(X3) ),
inference(shift_quantors,[status(thm)],[39]) ).
cnf(41,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[40]) ).
fof(52,plain,
! [X1] :
( ~ aFunction0(X1)
| ! [X2] :
( ~ aElementOf0(X2,szDzozmdt0(X1))
| aElementOf0(sdtlpdtrp0(X1,X2),szRzazndt0(X1)) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(53,plain,
! [X3] :
( ~ aFunction0(X3)
| ! [X4] :
( ~ aElementOf0(X4,szDzozmdt0(X3))
| aElementOf0(sdtlpdtrp0(X3,X4),szRzazndt0(X3)) ) ),
inference(variable_rename,[status(thm)],[52]) ).
fof(54,plain,
! [X3,X4] :
( ~ aElementOf0(X4,szDzozmdt0(X3))
| aElementOf0(sdtlpdtrp0(X3,X4),szRzazndt0(X3))
| ~ aFunction0(X3) ),
inference(shift_quantors,[status(thm)],[53]) ).
cnf(55,plain,
( aElementOf0(sdtlpdtrp0(X1,X2),szRzazndt0(X1))
| ~ aFunction0(X1)
| ~ aElementOf0(X2,szDzozmdt0(X1)) ),
inference(split_conjunct,[status(thm)],[54]) ).
fof(87,plain,
! [X1] :
( ~ aElement0(X1)
| sdtlseqdt0(X1,X1) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(88,plain,
! [X2] :
( ~ aElement0(X2)
| sdtlseqdt0(X2,X2) ),
inference(variable_rename,[status(thm)],[87]) ).
cnf(89,plain,
( sdtlseqdt0(X1,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[88]) ).
fof(118,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)],[31]) ).
fof(119,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)],[118]) ).
fof(120,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)],[119]) ).
fof(121,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)],[120]) ).
fof(122,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)],[121]) ).
cnf(124,plain,
aLowerBoundOfIn0(xp,xP,xU),
inference(split_conjunct,[status(thm)],[122]) ).
cnf(125,plain,
aElementOf0(xp,xU),
inference(split_conjunct,[status(thm)],[122]) ).
cnf(126,plain,
( sdtlseqdt0(xp,X1)
| ~ aElementOf0(X1,xP) ),
inference(split_conjunct,[status(thm)],[122]) ).
cnf(127,plain,
( sdtlseqdt0(X1,xp)
| ~ aLowerBoundOfIn0(X1,xP,xU) ),
inference(split_conjunct,[status(thm)],[122]) ).
cnf(128,plain,
( sdtlseqdt0(X1,xp)
| ~ aElementOf0(X1,xU)
| ~ sdtlseqdt0(X1,esk6_1(X1)) ),
inference(split_conjunct,[status(thm)],[122]) ).
cnf(129,plain,
( sdtlseqdt0(X1,xp)
| aElementOf0(esk6_1(X1),xP)
| ~ aElementOf0(X1,xU) ),
inference(split_conjunct,[status(thm)],[122]) ).
fof(140,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(141,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)],[140]) ).
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)
| ( 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)],[141]) ).
fof(143,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)],[142]) ).
fof(144,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)],[143]) ).
cnf(146,plain,
aSet0(xP),
inference(split_conjunct,[status(thm)],[144]) ).
cnf(148,plain,
( aElementOf0(X1,xP)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X1),X1)
| ~ aElementOf0(X1,xU)
| ~ sdtlseqdt0(esk8_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[144]) ).
cnf(149,plain,
( aElementOf0(X1,xP)
| aElementOf0(esk8_1(X1),xT)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X1),X1)
| ~ aElementOf0(X1,xU) ),
inference(split_conjunct,[status(thm)],[144]) ).
cnf(151,plain,
( sdtlseqdt0(sdtlpdtrp0(xf,X1),X1)
| ~ aElementOf0(X1,xP) ),
inference(split_conjunct,[status(thm)],[144]) ).
cnf(152,plain,
( aElementOf0(X1,xU)
| ~ aElementOf0(X1,xP) ),
inference(split_conjunct,[status(thm)],[144]) ).
cnf(153,plain,
( sdtlseqdt0(X2,X1)
| ~ aElementOf0(X1,xP)
| ~ aElementOf0(X2,xT) ),
inference(split_conjunct,[status(thm)],[144]) ).
fof(161,plain,
( aSet0(xT)
& ! [X1] :
( ~ aElementOf0(X1,xT)
| aElementOf0(X1,xS) )
& aSubsetOf0(xT,xS) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(162,plain,
( aSet0(xT)
& ! [X2] :
( ~ aElementOf0(X2,xT)
| aElementOf0(X2,xS) )
& aSubsetOf0(xT,xS) ),
inference(variable_rename,[status(thm)],[161]) ).
fof(163,plain,
! [X2] :
( ( ~ aElementOf0(X2,xT)
| aElementOf0(X2,xS) )
& aSet0(xT)
& aSubsetOf0(xT,xS) ),
inference(shift_quantors,[status(thm)],[162]) ).
cnf(165,plain,
aSet0(xT),
inference(split_conjunct,[status(thm)],[163]) ).
cnf(166,plain,
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,xT) ),
inference(split_conjunct,[status(thm)],[163]) ).
fof(184,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)],[25]) ).
fof(185,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)],[184]) ).
fof(186,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)],[185]) ).
fof(187,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)],[186]) ).
cnf(189,plain,
aSet0(xS),
inference(split_conjunct,[status(thm)],[187]) ).
cnf(193,plain,
( sdtlpdtrp0(xf,X1) = X1
| ~ aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[187]) ).
cnf(194,plain,
( aElementOf0(X1,szDzozmdt0(xf))
| ~ aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[187]) ).
fof(195,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)],[34]) ).
fof(196,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)],[195]) ).
fof(197,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)],[196]) ).
fof(198,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)],[197]) ).
fof(199,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)],[198]) ).
cnf(201,plain,
szRzazndt0(xf) = xU,
inference(split_conjunct,[status(thm)],[199]) ).
cnf(202,plain,
szDzozmdt0(xf) = szRzazndt0(xf),
inference(split_conjunct,[status(thm)],[199]) ).
cnf(204,plain,
aFunction0(xf),
inference(split_conjunct,[status(thm)],[199]) ).
cnf(206,plain,
aSet0(xU),
inference(split_conjunct,[status(thm)],[199]) ).
cnf(210,plain,
( sdtlseqdt0(sdtlpdtrp0(xf,X1),sdtlpdtrp0(xf,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,szDzozmdt0(xf))
| ~ aElementOf0(X1,szDzozmdt0(xf)) ),
inference(split_conjunct,[status(thm)],[199]) ).
fof(221,negated_conjecture,
( ( ? [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)],[30]) ).
fof(222,negated_conjecture,
( ( ? [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)],[221]) ).
fof(223,negated_conjecture,
( ( aElementOf0(esk15_0,xP)
& ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),esk15_0)
& ~ aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU) )
| ( aElementOf0(esk16_0,xT)
& ~ sdtlseqdt0(esk16_0,sdtlpdtrp0(xf,xp))
& ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU) ) ),
inference(skolemize,[status(esa)],[222]) ).
fof(224,negated_conjecture,
( ( aElementOf0(esk16_0,xT)
| aElementOf0(esk15_0,xP) )
& ( ~ sdtlseqdt0(esk16_0,sdtlpdtrp0(xf,xp))
| aElementOf0(esk15_0,xP) )
& ( ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
| aElementOf0(esk15_0,xP) )
& ( aElementOf0(esk16_0,xT)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),esk15_0) )
& ( ~ sdtlseqdt0(esk16_0,sdtlpdtrp0(xf,xp))
| ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),esk15_0) )
& ( ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),esk15_0) )
& ( aElementOf0(esk16_0,xT)
| ~ aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU) )
& ( ~ sdtlseqdt0(esk16_0,sdtlpdtrp0(xf,xp))
| ~ aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU) )
& ( ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
| ~ aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU) ) ),
inference(distribute,[status(thm)],[223]) ).
cnf(229,negated_conjecture,
( ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),esk15_0)
| ~ sdtlseqdt0(esk16_0,sdtlpdtrp0(xf,xp)) ),
inference(split_conjunct,[status(thm)],[224]) ).
cnf(230,negated_conjecture,
( aElementOf0(esk16_0,xT)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),esk15_0) ),
inference(split_conjunct,[status(thm)],[224]) ).
cnf(232,negated_conjecture,
( aElementOf0(esk15_0,xP)
| ~ sdtlseqdt0(esk16_0,sdtlpdtrp0(xf,xp)) ),
inference(split_conjunct,[status(thm)],[224]) ).
cnf(233,negated_conjecture,
( aElementOf0(esk15_0,xP)
| aElementOf0(esk16_0,xT) ),
inference(split_conjunct,[status(thm)],[224]) ).
fof(234,plain,
! [X1,X2,X3] :
( ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3)
| sdtlseqdt0(X1,X3) ),
inference(fof_nnf,[status(thm)],[29]) ).
fof(235,plain,
! [X4,X5,X6] :
( ~ aElement0(X4)
| ~ aElement0(X5)
| ~ aElement0(X6)
| ~ sdtlseqdt0(X4,X5)
| ~ sdtlseqdt0(X5,X6)
| sdtlseqdt0(X4,X6) ),
inference(variable_rename,[status(thm)],[234]) ).
cnf(236,plain,
( sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X3,X2)
| ~ sdtlseqdt0(X1,X3)
| ~ aElement0(X2)
| ~ aElement0(X3)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[235]) ).
cnf(256,plain,
xU = szDzozmdt0(xf),
inference(rw,[status(thm)],[202,201,theory(equality)]) ).
cnf(259,plain,
sdtlseqdt0(xp,xp),
inference(spm,[status(thm)],[127,124,theory(equality)]) ).
cnf(279,plain,
( aElementOf0(X1,xU)
| ~ aElementOf0(X1,xS) ),
inference(rw,[status(thm)],[194,256,theory(equality)]) ).
cnf(280,plain,
( aElementOf0(X1,xU)
| ~ aElementOf0(X1,xT) ),
inference(spm,[status(thm)],[279,166,theory(equality)]) ).
cnf(308,plain,
( sdtlseqdt0(X1,xp)
| ~ aElementOf0(X1,xU)
| ~ aElementOf0(X1,xT)
| ~ aElementOf0(esk6_1(X1),xP) ),
inference(spm,[status(thm)],[128,153,theory(equality)]) ).
cnf(319,plain,
( aElement0(xp)
| ~ aSet0(xU) ),
inference(spm,[status(thm)],[41,125,theory(equality)]) ).
cnf(321,plain,
( aElement0(X1)
| ~ aSet0(xS)
| ~ aElementOf0(X1,xT) ),
inference(spm,[status(thm)],[41,166,theory(equality)]) ).
cnf(325,plain,
( aElement0(xp)
| $false ),
inference(rw,[status(thm)],[319,206,theory(equality)]) ).
cnf(326,plain,
aElement0(xp),
inference(cn,[status(thm)],[325,theory(equality)]) ).
cnf(329,plain,
( aElement0(X1)
| $false
| ~ aElementOf0(X1,xT) ),
inference(rw,[status(thm)],[321,189,theory(equality)]) ).
cnf(330,plain,
( aElement0(X1)
| ~ aElementOf0(X1,xT) ),
inference(cn,[status(thm)],[329,theory(equality)]) ).
cnf(398,plain,
( sdtlseqdt0(sdtlpdtrp0(xf,X1),sdtlpdtrp0(xf,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,xU)
| ~ aElementOf0(X1,szDzozmdt0(xf)) ),
inference(rw,[status(thm)],[210,256,theory(equality)]) ).
cnf(399,plain,
( sdtlseqdt0(sdtlpdtrp0(xf,X1),sdtlpdtrp0(xf,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,xU)
| ~ aElementOf0(X1,xU) ),
inference(rw,[status(thm)],[398,256,theory(equality)]) ).
cnf(400,plain,
( sdtlseqdt0(X1,sdtlpdtrp0(xf,X2))
| ~ aElementOf0(X2,xU)
| ~ aElementOf0(X1,xU)
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X1,xS) ),
inference(spm,[status(thm)],[399,193,theory(equality)]) ).
cnf(403,plain,
( aElementOf0(esk8_1(sdtlpdtrp0(xf,X1)),xT)
| aElementOf0(sdtlpdtrp0(xf,X1),xP)
| ~ aElementOf0(sdtlpdtrp0(xf,X1),xU)
| ~ aElementOf0(X1,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X1),X1) ),
inference(spm,[status(thm)],[149,399,theory(equality)]) ).
cnf(439,plain,
( aElementOf0(sdtlpdtrp0(xf,X1),xU)
| ~ aFunction0(xf)
| ~ aElementOf0(X1,szDzozmdt0(xf)) ),
inference(spm,[status(thm)],[55,201,theory(equality)]) ).
cnf(443,plain,
( aElementOf0(sdtlpdtrp0(xf,X1),xU)
| $false
| ~ aElementOf0(X1,szDzozmdt0(xf)) ),
inference(rw,[status(thm)],[439,204,theory(equality)]) ).
cnf(444,plain,
( aElementOf0(sdtlpdtrp0(xf,X1),xU)
| $false
| ~ aElementOf0(X1,xU) ),
inference(rw,[status(thm)],[443,256,theory(equality)]) ).
cnf(445,plain,
( aElementOf0(sdtlpdtrp0(xf,X1),xU)
| ~ aElementOf0(X1,xU) ),
inference(cn,[status(thm)],[444,theory(equality)]) ).
cnf(505,plain,
( sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X1,xp)
| ~ aElement0(xp)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElementOf0(X2,xP) ),
inference(spm,[status(thm)],[236,126,theory(equality)]) ).
cnf(506,plain,
( sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X1,sdtlpdtrp0(xf,X2))
| ~ aElement0(sdtlpdtrp0(xf,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElementOf0(X2,xP) ),
inference(spm,[status(thm)],[236,151,theory(equality)]) ).
cnf(756,plain,
( aElement0(sdtlpdtrp0(xf,X1))
| ~ aSet0(xU)
| ~ aElementOf0(X1,xU) ),
inference(spm,[status(thm)],[41,445,theory(equality)]) ).
cnf(759,plain,
( aElement0(sdtlpdtrp0(xf,X1))
| $false
| ~ aElementOf0(X1,xU) ),
inference(rw,[status(thm)],[756,206,theory(equality)]) ).
cnf(760,plain,
( aElement0(sdtlpdtrp0(xf,X1))
| ~ aElementOf0(X1,xU) ),
inference(cn,[status(thm)],[759,theory(equality)]) ).
cnf(764,plain,
( sdtlseqdt0(X1,xp)
| ~ aElementOf0(X1,xU)
| ~ aElementOf0(X1,xT) ),
inference(csr,[status(thm)],[308,129]) ).
cnf(765,plain,
( sdtlseqdt0(X1,xp)
| ~ aElementOf0(X1,xT) ),
inference(csr,[status(thm)],[764,280]) ).
cnf(771,plain,
( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,X2)
| ~ aElement0(X2)
| ~ aElement0(xp)
| ~ aElement0(X1)
| ~ aElementOf0(X2,xT) ),
inference(spm,[status(thm)],[236,765,theory(equality)]) ).
cnf(786,plain,
( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,X2)
| ~ aElement0(X2)
| $false
| ~ aElement0(X1)
| ~ aElementOf0(X2,xT) ),
inference(rw,[status(thm)],[771,326,theory(equality)]) ).
cnf(787,plain,
( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,X2)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElementOf0(X2,xT) ),
inference(cn,[status(thm)],[786,theory(equality)]) ).
cnf(1788,plain,
( sdtlseqdt0(X1,sdtlpdtrp0(xf,X2))
| ~ aElementOf0(X1,xS)
| ~ aElementOf0(X2,xU)
| ~ sdtlseqdt0(X1,X2) ),
inference(csr,[status(thm)],[400,279]) ).
cnf(1789,plain,
( aElementOf0(esk15_0,xP)
| ~ aElementOf0(xp,xU)
| ~ aElementOf0(esk16_0,xS)
| ~ sdtlseqdt0(esk16_0,xp) ),
inference(spm,[status(thm)],[232,1788,theory(equality)]) ).
cnf(1792,plain,
( aElementOf0(sdtlpdtrp0(xf,X1),xP)
| ~ aElementOf0(sdtlpdtrp0(xf,X1),xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,X1)),sdtlpdtrp0(xf,X1))
| ~ aElementOf0(X1,xU)
| ~ aElementOf0(esk8_1(sdtlpdtrp0(xf,X1)),xS)
| ~ sdtlseqdt0(esk8_1(sdtlpdtrp0(xf,X1)),X1) ),
inference(spm,[status(thm)],[148,1788,theory(equality)]) ).
cnf(1803,plain,
( aElementOf0(esk15_0,xP)
| $false
| ~ aElementOf0(esk16_0,xS)
| ~ sdtlseqdt0(esk16_0,xp) ),
inference(rw,[status(thm)],[1789,125,theory(equality)]) ).
cnf(1804,plain,
( aElementOf0(esk15_0,xP)
| ~ aElementOf0(esk16_0,xS)
| ~ sdtlseqdt0(esk16_0,xp) ),
inference(cn,[status(thm)],[1803,theory(equality)]) ).
cnf(1812,plain,
( aElementOf0(esk15_0,xP)
| ~ aElementOf0(esk16_0,xS)
| ~ aElementOf0(esk16_0,xT) ),
inference(spm,[status(thm)],[1804,765,theory(equality)]) ).
cnf(1815,plain,
( aElementOf0(esk15_0,xP)
| ~ aElementOf0(esk16_0,xS) ),
inference(csr,[status(thm)],[1812,233]) ).
cnf(1816,plain,
( aElementOf0(esk15_0,xP)
| ~ aElementOf0(esk16_0,xT) ),
inference(spm,[status(thm)],[1815,166,theory(equality)]) ).
cnf(1817,plain,
aElementOf0(esk15_0,xP),
inference(csr,[status(thm)],[1816,233]) ).
cnf(1818,plain,
aElementOf0(esk15_0,xU),
inference(spm,[status(thm)],[152,1817,theory(equality)]) ).
cnf(1820,plain,
( aElement0(esk15_0)
| ~ aSet0(xP) ),
inference(spm,[status(thm)],[41,1817,theory(equality)]) ).
cnf(1834,plain,
( aElement0(esk15_0)
| $false ),
inference(rw,[status(thm)],[1820,146,theory(equality)]) ).
cnf(1835,plain,
aElement0(esk15_0),
inference(cn,[status(thm)],[1834,theory(equality)]) ).
cnf(1921,plain,
( aElementOf0(esk8_1(sdtlpdtrp0(xf,X1)),xT)
| aElementOf0(sdtlpdtrp0(xf,X1),xP)
| ~ aElementOf0(X1,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X1),X1) ),
inference(csr,[status(thm)],[403,445]) ).
cnf(1922,plain,
( aElementOf0(esk8_1(sdtlpdtrp0(xf,X1)),xT)
| aElementOf0(sdtlpdtrp0(xf,X1),xP)
| ~ aElementOf0(X1,xU)
| ~ aElementOf0(X1,xP) ),
inference(spm,[status(thm)],[1921,151,theory(equality)]) ).
cnf(2551,plain,
( aElementOf0(esk8_1(sdtlpdtrp0(xf,X1)),xT)
| aElementOf0(sdtlpdtrp0(xf,X1),xP)
| ~ aElementOf0(X1,xP) ),
inference(csr,[status(thm)],[1922,152]) ).
cnf(3263,plain,
( sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X1,xp)
| $false
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElementOf0(X2,xP) ),
inference(rw,[status(thm)],[505,326,theory(equality)]) ).
cnf(3264,plain,
( sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X1,xp)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElementOf0(X2,xP) ),
inference(cn,[status(thm)],[3263,theory(equality)]) ).
cnf(3266,plain,
( sdtlseqdt0(X1,esk15_0)
| ~ aElementOf0(esk15_0,xP)
| ~ sdtlseqdt0(X1,xp)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[3264,1835,theory(equality)]) ).
cnf(3297,plain,
( sdtlseqdt0(X1,esk15_0)
| $false
| ~ sdtlseqdt0(X1,xp)
| ~ aElement0(X1) ),
inference(rw,[status(thm)],[3266,1817,theory(equality)]) ).
cnf(3298,plain,
( sdtlseqdt0(X1,esk15_0)
| ~ sdtlseqdt0(X1,xp)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[3297,theory(equality)]) ).
cnf(3299,plain,
( sdtlseqdt0(xp,esk15_0)
| ~ sdtlseqdt0(xp,xp) ),
inference(spm,[status(thm)],[3298,326,theory(equality)]) ).
cnf(3305,plain,
( sdtlseqdt0(X1,esk15_0)
| ~ sdtlseqdt0(X1,xp)
| ~ aElementOf0(X1,xT) ),
inference(spm,[status(thm)],[3298,330,theory(equality)]) ).
cnf(3331,plain,
( sdtlseqdt0(xp,esk15_0)
| $false ),
inference(rw,[status(thm)],[3299,259,theory(equality)]) ).
cnf(3332,plain,
sdtlseqdt0(xp,esk15_0),
inference(cn,[status(thm)],[3331,theory(equality)]) ).
cnf(3368,plain,
( sdtlseqdt0(X1,esk15_0)
| ~ aElementOf0(X1,xT) ),
inference(csr,[status(thm)],[3305,765]) ).
cnf(3412,plain,
( sdtlseqdt0(sdtlpdtrp0(xf,X1),X2)
| ~ aElementOf0(X2,xP)
| ~ aElement0(sdtlpdtrp0(xf,X2))
| ~ aElement0(X2)
| ~ aElement0(sdtlpdtrp0(xf,X1))
| ~ aElementOf0(X2,xU)
| ~ aElementOf0(X1,xU)
| ~ sdtlseqdt0(X1,X2) ),
inference(spm,[status(thm)],[506,399,theory(equality)]) ).
cnf(8029,plain,
( sdtlseqdt0(X1,xp)
| ~ aElementOf0(X2,xT)
| ~ sdtlseqdt0(X1,X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[787,330]) ).
cnf(14457,plain,
( aElementOf0(sdtlpdtrp0(xf,X1),xP)
| ~ aElementOf0(esk8_1(sdtlpdtrp0(xf,X1)),xS)
| ~ aElementOf0(X1,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,X1)),sdtlpdtrp0(xf,X1))
| ~ sdtlseqdt0(esk8_1(sdtlpdtrp0(xf,X1)),X1) ),
inference(csr,[status(thm)],[1792,445]) ).
cnf(14466,plain,
( aElementOf0(sdtlpdtrp0(xf,esk15_0),xP)
| ~ aElementOf0(esk8_1(sdtlpdtrp0(xf,esk15_0)),xS)
| ~ aElementOf0(esk15_0,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,esk15_0)),sdtlpdtrp0(xf,esk15_0))
| ~ aElementOf0(esk8_1(sdtlpdtrp0(xf,esk15_0)),xT) ),
inference(spm,[status(thm)],[14457,3368,theory(equality)]) ).
cnf(14482,plain,
( aElementOf0(sdtlpdtrp0(xf,esk15_0),xP)
| ~ aElementOf0(esk8_1(sdtlpdtrp0(xf,esk15_0)),xS)
| $false
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,esk15_0)),sdtlpdtrp0(xf,esk15_0))
| ~ aElementOf0(esk8_1(sdtlpdtrp0(xf,esk15_0)),xT) ),
inference(rw,[status(thm)],[14466,1818,theory(equality)]) ).
cnf(14483,plain,
( aElementOf0(sdtlpdtrp0(xf,esk15_0),xP)
| ~ aElementOf0(esk8_1(sdtlpdtrp0(xf,esk15_0)),xS)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,esk15_0)),sdtlpdtrp0(xf,esk15_0))
| ~ aElementOf0(esk8_1(sdtlpdtrp0(xf,esk15_0)),xT) ),
inference(cn,[status(thm)],[14482,theory(equality)]) ).
cnf(14836,plain,
( aElementOf0(sdtlpdtrp0(xf,esk15_0),xP)
| ~ aElementOf0(esk8_1(sdtlpdtrp0(xf,esk15_0)),xT)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,esk15_0)),sdtlpdtrp0(xf,esk15_0)) ),
inference(csr,[status(thm)],[14483,166]) ).
cnf(14839,plain,
( aElementOf0(sdtlpdtrp0(xf,esk15_0),xP)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,esk15_0)),sdtlpdtrp0(xf,esk15_0))
| ~ aElementOf0(esk15_0,xP) ),
inference(spm,[status(thm)],[14836,2551,theory(equality)]) ).
cnf(14845,plain,
( aElementOf0(sdtlpdtrp0(xf,esk15_0),xP)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,esk15_0)),sdtlpdtrp0(xf,esk15_0))
| $false ),
inference(rw,[status(thm)],[14839,1817,theory(equality)]) ).
cnf(14846,plain,
( aElementOf0(sdtlpdtrp0(xf,esk15_0),xP)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,esk15_0)),sdtlpdtrp0(xf,esk15_0)) ),
inference(cn,[status(thm)],[14845,theory(equality)]) ).
cnf(14851,plain,
( aElementOf0(sdtlpdtrp0(xf,esk15_0),xP)
| ~ aElementOf0(esk15_0,xU)
| ~ aElementOf0(sdtlpdtrp0(xf,esk15_0),xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,esk15_0),esk15_0) ),
inference(spm,[status(thm)],[14846,399,theory(equality)]) ).
cnf(14855,plain,
( aElementOf0(sdtlpdtrp0(xf,esk15_0),xP)
| $false
| ~ aElementOf0(sdtlpdtrp0(xf,esk15_0),xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,esk15_0),esk15_0) ),
inference(rw,[status(thm)],[14851,1818,theory(equality)]) ).
cnf(14856,plain,
( aElementOf0(sdtlpdtrp0(xf,esk15_0),xP)
| ~ aElementOf0(sdtlpdtrp0(xf,esk15_0),xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,esk15_0),esk15_0) ),
inference(cn,[status(thm)],[14855,theory(equality)]) ).
cnf(14859,plain,
( aElementOf0(sdtlpdtrp0(xf,esk15_0),xP)
| ~ aElementOf0(sdtlpdtrp0(xf,esk15_0),xU)
| ~ aElementOf0(esk15_0,xP) ),
inference(spm,[status(thm)],[14856,151,theory(equality)]) ).
cnf(14866,plain,
( aElementOf0(sdtlpdtrp0(xf,esk15_0),xP)
| ~ aElementOf0(sdtlpdtrp0(xf,esk15_0),xU)
| $false ),
inference(rw,[status(thm)],[14859,1817,theory(equality)]) ).
cnf(14867,plain,
( aElementOf0(sdtlpdtrp0(xf,esk15_0),xP)
| ~ aElementOf0(sdtlpdtrp0(xf,esk15_0),xU) ),
inference(cn,[status(thm)],[14866,theory(equality)]) ).
cnf(14882,plain,
( aElement0(sdtlpdtrp0(xf,esk15_0))
| ~ aSet0(xP)
| ~ aElementOf0(sdtlpdtrp0(xf,esk15_0),xU) ),
inference(spm,[status(thm)],[41,14867,theory(equality)]) ).
cnf(14892,plain,
( aElement0(sdtlpdtrp0(xf,esk15_0))
| $false
| ~ aElementOf0(sdtlpdtrp0(xf,esk15_0),xU) ),
inference(rw,[status(thm)],[14882,146,theory(equality)]) ).
cnf(14893,plain,
( aElement0(sdtlpdtrp0(xf,esk15_0))
| ~ aElementOf0(sdtlpdtrp0(xf,esk15_0),xU) ),
inference(cn,[status(thm)],[14892,theory(equality)]) ).
cnf(39619,plain,
( sdtlseqdt0(sdtlpdtrp0(xf,X1),X2)
| ~ aElementOf0(X1,xU)
| ~ aElementOf0(X2,xP)
| ~ sdtlseqdt0(X1,X2)
| ~ aElement0(sdtlpdtrp0(xf,X2))
| ~ aElement0(sdtlpdtrp0(xf,X1))
| ~ aElement0(X2) ),
inference(csr,[status(thm)],[3412,152]) ).
cnf(39620,plain,
( sdtlseqdt0(sdtlpdtrp0(xf,X1),X2)
| ~ aElementOf0(X1,xU)
| ~ aElementOf0(X2,xP)
| ~ sdtlseqdt0(X1,X2)
| ~ aElement0(sdtlpdtrp0(xf,X2))
| ~ aElement0(X2) ),
inference(csr,[status(thm)],[39619,760]) ).
cnf(39626,plain,
( sdtlseqdt0(sdtlpdtrp0(xf,X1),esk15_0)
| ~ aElementOf0(esk15_0,xP)
| ~ aElementOf0(X1,xU)
| ~ sdtlseqdt0(X1,esk15_0)
| ~ aElement0(esk15_0)
| ~ aElementOf0(sdtlpdtrp0(xf,esk15_0),xU) ),
inference(spm,[status(thm)],[39620,14893,theory(equality)]) ).
cnf(39667,plain,
( sdtlseqdt0(sdtlpdtrp0(xf,X1),esk15_0)
| $false
| ~ aElementOf0(X1,xU)
| ~ sdtlseqdt0(X1,esk15_0)
| ~ aElement0(esk15_0)
| ~ aElementOf0(sdtlpdtrp0(xf,esk15_0),xU) ),
inference(rw,[status(thm)],[39626,1817,theory(equality)]) ).
cnf(39668,plain,
( sdtlseqdt0(sdtlpdtrp0(xf,X1),esk15_0)
| $false
| ~ aElementOf0(X1,xU)
| ~ sdtlseqdt0(X1,esk15_0)
| $false
| ~ aElementOf0(sdtlpdtrp0(xf,esk15_0),xU) ),
inference(rw,[status(thm)],[39667,1835,theory(equality)]) ).
cnf(39669,plain,
( sdtlseqdt0(sdtlpdtrp0(xf,X1),esk15_0)
| ~ aElementOf0(X1,xU)
| ~ sdtlseqdt0(X1,esk15_0)
| ~ aElementOf0(sdtlpdtrp0(xf,esk15_0),xU) ),
inference(cn,[status(thm)],[39668,theory(equality)]) ).
cnf(41358,plain,
( aElementOf0(esk16_0,xT)
| ~ aElementOf0(sdtlpdtrp0(xf,esk15_0),xU)
| ~ aElementOf0(xp,xU)
| ~ sdtlseqdt0(xp,esk15_0) ),
inference(spm,[status(thm)],[230,39669,theory(equality)]) ).
cnf(41359,plain,
( ~ sdtlseqdt0(esk16_0,sdtlpdtrp0(xf,xp))
| ~ aElementOf0(sdtlpdtrp0(xf,esk15_0),xU)
| ~ aElementOf0(xp,xU)
| ~ sdtlseqdt0(xp,esk15_0) ),
inference(spm,[status(thm)],[229,39669,theory(equality)]) ).
cnf(41404,plain,
( aElementOf0(esk16_0,xT)
| ~ aElementOf0(sdtlpdtrp0(xf,esk15_0),xU)
| $false
| ~ sdtlseqdt0(xp,esk15_0) ),
inference(rw,[status(thm)],[41358,125,theory(equality)]) ).
cnf(41405,plain,
( aElementOf0(esk16_0,xT)
| ~ aElementOf0(sdtlpdtrp0(xf,esk15_0),xU)
| $false
| $false ),
inference(rw,[status(thm)],[41404,3332,theory(equality)]) ).
cnf(41406,plain,
( aElementOf0(esk16_0,xT)
| ~ aElementOf0(sdtlpdtrp0(xf,esk15_0),xU) ),
inference(cn,[status(thm)],[41405,theory(equality)]) ).
cnf(41407,plain,
( ~ sdtlseqdt0(esk16_0,sdtlpdtrp0(xf,xp))
| ~ aElementOf0(sdtlpdtrp0(xf,esk15_0),xU)
| $false
| ~ sdtlseqdt0(xp,esk15_0) ),
inference(rw,[status(thm)],[41359,125,theory(equality)]) ).
cnf(41408,plain,
( ~ sdtlseqdt0(esk16_0,sdtlpdtrp0(xf,xp))
| ~ aElementOf0(sdtlpdtrp0(xf,esk15_0),xU)
| $false
| $false ),
inference(rw,[status(thm)],[41407,3332,theory(equality)]) ).
cnf(41409,plain,
( ~ sdtlseqdt0(esk16_0,sdtlpdtrp0(xf,xp))
| ~ aElementOf0(sdtlpdtrp0(xf,esk15_0),xU) ),
inference(cn,[status(thm)],[41408,theory(equality)]) ).
cnf(41468,plain,
( aElementOf0(esk16_0,xT)
| ~ aElementOf0(esk15_0,xU) ),
inference(spm,[status(thm)],[41406,445,theory(equality)]) ).
cnf(41472,plain,
( aElementOf0(esk16_0,xT)
| $false ),
inference(rw,[status(thm)],[41468,1818,theory(equality)]) ).
cnf(41473,plain,
aElementOf0(esk16_0,xT),
inference(cn,[status(thm)],[41472,theory(equality)]) ).
cnf(41486,plain,
( aElement0(esk16_0)
| ~ aSet0(xT) ),
inference(spm,[status(thm)],[41,41473,theory(equality)]) ).
cnf(41506,plain,
( aElement0(esk16_0)
| $false ),
inference(rw,[status(thm)],[41486,165,theory(equality)]) ).
cnf(41507,plain,
aElement0(esk16_0),
inference(cn,[status(thm)],[41506,theory(equality)]) ).
cnf(41528,plain,
( ~ aElementOf0(sdtlpdtrp0(xf,esk15_0),xU)
| ~ aElementOf0(xp,xU)
| ~ aElementOf0(esk16_0,xS)
| ~ sdtlseqdt0(esk16_0,xp) ),
inference(spm,[status(thm)],[41409,1788,theory(equality)]) ).
cnf(41531,plain,
( ~ aElementOf0(sdtlpdtrp0(xf,esk15_0),xU)
| $false
| ~ aElementOf0(esk16_0,xS)
| ~ sdtlseqdt0(esk16_0,xp) ),
inference(rw,[status(thm)],[41528,125,theory(equality)]) ).
cnf(41532,plain,
( ~ aElementOf0(sdtlpdtrp0(xf,esk15_0),xU)
| ~ aElementOf0(esk16_0,xS)
| ~ sdtlseqdt0(esk16_0,xp) ),
inference(cn,[status(thm)],[41531,theory(equality)]) ).
cnf(41546,plain,
sdtlseqdt0(esk16_0,esk16_0),
inference(spm,[status(thm)],[89,41507,theory(equality)]) ).
cnf(41587,plain,
( sdtlseqdt0(esk16_0,xp)
| ~ aElementOf0(esk16_0,xT)
| ~ aElement0(esk16_0) ),
inference(spm,[status(thm)],[8029,41546,theory(equality)]) ).
cnf(41598,plain,
( sdtlseqdt0(esk16_0,xp)
| $false
| ~ aElement0(esk16_0) ),
inference(rw,[status(thm)],[41587,41473,theory(equality)]) ).
cnf(41599,plain,
( sdtlseqdt0(esk16_0,xp)
| $false
| $false ),
inference(rw,[status(thm)],[41598,41507,theory(equality)]) ).
cnf(41600,plain,
sdtlseqdt0(esk16_0,xp),
inference(cn,[status(thm)],[41599,theory(equality)]) ).
cnf(46365,plain,
( ~ aElementOf0(sdtlpdtrp0(xf,esk15_0),xU)
| ~ aElementOf0(esk16_0,xS)
| $false ),
inference(rw,[status(thm)],[41532,41600,theory(equality)]) ).
cnf(46366,plain,
( ~ aElementOf0(sdtlpdtrp0(xf,esk15_0),xU)
| ~ aElementOf0(esk16_0,xS) ),
inference(cn,[status(thm)],[46365,theory(equality)]) ).
cnf(46368,plain,
( ~ aElementOf0(esk16_0,xS)
| ~ aElementOf0(esk15_0,xU) ),
inference(spm,[status(thm)],[46366,445,theory(equality)]) ).
cnf(46373,plain,
( ~ aElementOf0(esk16_0,xS)
| $false ),
inference(rw,[status(thm)],[46368,1818,theory(equality)]) ).
cnf(46374,plain,
~ aElementOf0(esk16_0,xS),
inference(cn,[status(thm)],[46373,theory(equality)]) ).
cnf(46377,plain,
~ aElementOf0(esk16_0,xT),
inference(spm,[status(thm)],[46374,166,theory(equality)]) ).
cnf(46378,plain,
$false,
inference(rw,[status(thm)],[46377,41473,theory(equality)]) ).
cnf(46379,plain,
$false,
inference(cn,[status(thm)],[46378,theory(equality)]) ).
cnf(46380,plain,
$false,
46379,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/LAT/LAT386+4.p
% --creating new selector for []
% -running prover on /tmp/tmp_5ue2K/sel_LAT386+4.p_1 with time limit 29
% -prover status Theorem
% Problem LAT386+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/LAT/LAT386+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/LAT/LAT386+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
%
%------------------------------------------------------------------------------