TSTP Solution File: LAT387+4 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LAT387+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 06:03:41 EDT 2022
% Result : Theorem 7.98s 8.14s
% Output : CNFRefutation 7.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 30
% Syntax : Number of formulae : 255 ( 48 unt; 1 def)
% Number of atoms : 903 ( 111 equ)
% Maximal formula atoms : 37 ( 3 avg)
% Number of connectives : 1034 ( 386 ~; 400 |; 205 &)
% ( 2 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 15 usr; 2 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-3 aty)
% Number of variables : 231 ( 0 sgn 135 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEOfElem,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ) ).
fof(mARefl,axiom,
! [W0] :
( aElement0(W0)
=> sdtlseqdt0(W0,W0) ) ).
fof(mASymm,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> W0 = W1 ) ) ).
fof(mImgSort,axiom,
! [W0] :
( aFunction0(W0)
=> ! [W1] :
( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),szRzazndt0(W0)) ) ) ).
fof(m__1123,hypothesis,
( aSet0(xU)
& ! [W0] :
( ( ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xU) ) )
| aSubsetOf0(W0,xU) )
=> ? [W1] :
( aElementOf0(W1,xU)
& aElementOf0(W1,xU)
& ! [W2] :
( aElementOf0(W2,W0)
=> sdtlseqdt0(W1,W2) )
& aLowerBoundOfIn0(W1,W0,xU)
& ! [W2] :
( ( ( aElementOf0(W2,xU)
& ! [W3] :
( aElementOf0(W3,W0)
=> sdtlseqdt0(W2,W3) ) )
| aLowerBoundOfIn0(W2,W0,xU) )
=> sdtlseqdt0(W2,W1) )
& aInfimumOfIn0(W1,W0,xU)
& ? [W2] :
( aElementOf0(W2,xU)
& aElementOf0(W2,xU)
& ! [W3] :
( aElementOf0(W3,W0)
=> sdtlseqdt0(W3,W2) )
& aUpperBoundOfIn0(W2,W0,xU)
& ! [W3] :
( ( ( aElementOf0(W3,xU)
& ! [W4] :
( aElementOf0(W4,W0)
=> sdtlseqdt0(W4,W3) ) )
| aUpperBoundOfIn0(W3,W0,xU) )
=> sdtlseqdt0(W2,W3) )
& aSupremumOfIn0(W2,W0,xU) ) ) )
& aCompleteLattice0(xU)
& aFunction0(xf)
& ! [W0,W1] :
( ( aElementOf0(W0,szDzozmdt0(xf))
& aElementOf0(W1,szDzozmdt0(xf)) )
=> ( sdtlseqdt0(W0,W1)
=> sdtlseqdt0(sdtlpdtrp0(xf,W0),sdtlpdtrp0(xf,W1)) ) )
& isMonotone0(xf)
& szDzozmdt0(xf) = szRzazndt0(xf)
& szRzazndt0(xf) = xU
& isOn0(xf,xU) ) ).
fof(m__1144,hypothesis,
( aSet0(xS)
& ! [W0] :
( ( aElementOf0(W0,xS)
=> ( aElementOf0(W0,szDzozmdt0(xf))
& sdtlpdtrp0(xf,W0) = W0
& aFixedPointOf0(W0,xf) ) )
& ( ( ( aElementOf0(W0,szDzozmdt0(xf))
& sdtlpdtrp0(xf,W0) = W0 )
| aFixedPointOf0(W0,xf) )
=> aElementOf0(W0,xS) ) )
& xS = cS1142(xf) ) ).
fof(m__1244,hypothesis,
( aSet0(xP)
& ! [W0] :
( ( aElementOf0(W0,xP)
=> ( aElementOf0(W0,xU)
& sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
& ! [W1] :
( aElementOf0(W1,xT)
=> sdtlseqdt0(W1,W0) )
& aUpperBoundOfIn0(W0,xT,xU) ) )
& ( ( aElementOf0(W0,xU)
& sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
& ( ! [W1] :
( aElementOf0(W1,xT)
=> sdtlseqdt0(W1,W0) )
| aUpperBoundOfIn0(W0,xT,xU) ) )
=> aElementOf0(W0,xP) ) )
& xP = cS1241(xU,xf,xT) ) ).
fof(m__1261,hypothesis,
( aElementOf0(xp,xU)
& aElementOf0(xp,xU)
& ! [W0] :
( aElementOf0(W0,xP)
=> sdtlseqdt0(xp,W0) )
& aLowerBoundOfIn0(xp,xP,xU)
& ! [W0] :
( ( ( aElementOf0(W0,xU)
& ! [W1] :
( aElementOf0(W1,xP)
=> sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xP,xU) )
=> sdtlseqdt0(W0,xp) )
& aInfimumOfIn0(xp,xP,xU) ) ).
fof(m__1299,hypothesis,
( ! [W0] :
( aElementOf0(W0,xP)
=> sdtlseqdt0(sdtlpdtrp0(xf,xp),W0) )
& aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)
& ! [W0] :
( aElementOf0(W0,xT)
=> sdtlseqdt0(W0,sdtlpdtrp0(xf,xp)) )
& aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU) ) ).
fof(m__,conjecture,
( ( ( aElementOf0(xp,szDzozmdt0(xf))
& sdtlpdtrp0(xf,xp) = xp )
| aFixedPointOf0(xp,xf) )
& ( ( ( ! [W0] :
( aElementOf0(W0,xT)
=> sdtlseqdt0(W0,xp) )
| aUpperBoundOfIn0(xp,xT,xS) )
& ! [W0] :
( ( aElementOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,xT)
=> sdtlseqdt0(W1,W0) )
& aUpperBoundOfIn0(W0,xT,xS) )
=> sdtlseqdt0(xp,W0) ) )
| aSupremumOfIn0(xp,xT,xS) ) ) ).
fof(definition_0,definition,
( definitionFOFtoCNF_1
<=> ( ~ aUpperBoundOfIn0(xp,xT,xS)
& ? [W0] :
( ~ sdtlseqdt0(W0,xp)
& aElementOf0(W0,xT) ) ) ) ).
fof(subgoal_0,plain,
( ~ ( aElementOf0(xp,szDzozmdt0(xf))
& sdtlpdtrp0(xf,xp) = xp )
=> aFixedPointOf0(xp,xf) ),
inference(strip,[],[m__]) ).
fof(subgoal_1,plain,
( ( ( ( aElementOf0(xp,szDzozmdt0(xf))
& sdtlpdtrp0(xf,xp) = xp )
| aFixedPointOf0(xp,xf) )
& ~ ( ( ! [W0] :
( aElementOf0(W0,xT)
=> sdtlseqdt0(W0,xp) )
| aUpperBoundOfIn0(xp,xT,xS) )
& ! [W0] :
( ( aElementOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,xT)
=> sdtlseqdt0(W1,W0) )
& aUpperBoundOfIn0(W0,xT,xS) )
=> sdtlseqdt0(xp,W0) ) ) )
=> aSupremumOfIn0(xp,xT,xS) ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ( ~ ( aElementOf0(xp,szDzozmdt0(xf))
& sdtlpdtrp0(xf,xp) = xp )
=> aFixedPointOf0(xp,xf) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)
& aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
& ! [W0] :
( ~ aElementOf0(W0,xP)
| sdtlseqdt0(sdtlpdtrp0(xf,xp),W0) )
& ! [W0] :
( ~ aElementOf0(W0,xT)
| sdtlseqdt0(W0,sdtlpdtrp0(xf,xp)) ) ),
inference(canonicalize,[],[m__1299]) ).
fof(normalize_0_1,plain,
aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( aElementOf0(xp,xU)
& aInfimumOfIn0(xp,xP,xU)
& aLowerBoundOfIn0(xp,xP,xU)
& ! [W0] :
( ~ aElementOf0(W0,xP)
| sdtlseqdt0(xp,W0) )
& ! [W0] :
( sdtlseqdt0(W0,xp)
| ( ~ aLowerBoundOfIn0(W0,xP,xU)
& ( ~ aElementOf0(W0,xU)
| ? [W1] :
( ~ sdtlseqdt0(W0,W1)
& aElementOf0(W1,xP) ) ) ) ) ),
inference(canonicalize,[],[m__1261]) ).
fof(normalize_0_3,plain,
! [W0] :
( sdtlseqdt0(W0,xp)
| ( ~ aLowerBoundOfIn0(W0,xP,xU)
& ( ~ aElementOf0(W0,xU)
| ? [W1] :
( ~ sdtlseqdt0(W0,W1)
& aElementOf0(W1,xP) ) ) ) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [W0] :
( sdtlseqdt0(W0,xp)
| ( ~ aLowerBoundOfIn0(W0,xP,xU)
& ( ~ aElementOf0(W0,xU)
| ? [W1] :
( ~ sdtlseqdt0(W0,W1)
& aElementOf0(W1,xP) ) ) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [W0] :
( ( ~ aLowerBoundOfIn0(W0,xP,xU)
| sdtlseqdt0(W0,xp) )
& ( ~ aElementOf0(W0,xU)
| ~ sdtlseqdt0(W0,skolemFOFtoCNF_W1_6(W0))
| sdtlseqdt0(W0,xp) )
& ( ~ aElementOf0(W0,xU)
| aElementOf0(skolemFOFtoCNF_W1_6(W0),xP)
| sdtlseqdt0(W0,xp) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [W0] :
( ~ aLowerBoundOfIn0(W0,xP,xU)
| sdtlseqdt0(W0,xp) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [W0,W1] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| W0 = W1 ),
inference(canonicalize,[],[mASymm]) ).
fof(normalize_0_8,plain,
! [W0,W1] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| W0 = W1 ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [W0] :
( ~ aSet0(W0)
| ! [W1] :
( ~ aElementOf0(W1,W0)
| aElement0(W1) ) ),
inference(canonicalize,[],[mEOfElem]) ).
fof(normalize_0_10,plain,
! [W0] :
( ~ aSet0(W0)
| ! [W1] :
( ~ aElementOf0(W1,W0)
| aElement0(W1) ) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [W0,W1] :
( ~ aElementOf0(W1,W0)
| ~ aSet0(W0)
| aElement0(W1) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
aElementOf0(xp,xU),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_13,plain,
! [W0] :
( ~ aFunction0(W0)
| ! [W1] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),szRzazndt0(W0)) ) ),
inference(canonicalize,[],[mImgSort]) ).
fof(normalize_0_14,plain,
! [W0] :
( ~ aFunction0(W0)
| ! [W1] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),szRzazndt0(W0)) ) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [W0,W1] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| ~ aFunction0(W0)
| aElementOf0(sdtlpdtrp0(W0,W1),szRzazndt0(W0)) ),
inference(clausify,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
( szDzozmdt0(xf) = szRzazndt0(xf)
& szRzazndt0(xf) = xU
& aCompleteLattice0(xU)
& aFunction0(xf)
& aSet0(xU)
& isMonotone0(xf)
& isOn0(xf,xU)
& ! [W0] :
( ( ~ aSubsetOf0(W0,xU)
& ( ~ aSet0(W0)
| ? [W1] :
( ~ aElementOf0(W1,xU)
& aElementOf0(W1,W0) ) ) )
| ? [W1] :
( aElementOf0(W1,xU)
& aInfimumOfIn0(W1,W0,xU)
& aLowerBoundOfIn0(W1,W0,xU)
& ? [W2] :
( aElementOf0(W2,xU)
& aSupremumOfIn0(W2,W0,xU)
& aUpperBoundOfIn0(W2,W0,xU)
& ! [W3] :
( ~ aElementOf0(W3,W0)
| sdtlseqdt0(W3,W2) )
& ! [W3] :
( sdtlseqdt0(W2,W3)
| ( ~ aUpperBoundOfIn0(W3,W0,xU)
& ( ~ aElementOf0(W3,xU)
| ? [W4] :
( ~ sdtlseqdt0(W4,W3)
& aElementOf0(W4,W0) ) ) ) ) )
& ! [W2] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) )
& ! [W2] :
( sdtlseqdt0(W2,W1)
| ( ~ aLowerBoundOfIn0(W2,W0,xU)
& ( ~ aElementOf0(W2,xU)
| ? [W3] :
( ~ sdtlseqdt0(W2,W3)
& aElementOf0(W3,W0) ) ) ) ) ) )
& ! [W0,W1] :
( ~ aElementOf0(W0,szDzozmdt0(xf))
| ~ aElementOf0(W1,szDzozmdt0(xf))
| ~ sdtlseqdt0(W0,W1)
| sdtlseqdt0(sdtlpdtrp0(xf,W0),sdtlpdtrp0(xf,W1)) ) ),
inference(canonicalize,[],[m__1123]) ).
fof(normalize_0_17,plain,
szRzazndt0(xf) = xU,
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
szDzozmdt0(xf) = szRzazndt0(xf),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_19,plain,
aFunction0(xf),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_20,plain,
aSet0(xU),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_21,plain,
! [W0] :
( ~ aElementOf0(W0,xP)
| sdtlseqdt0(xp,W0) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_22,plain,
! [W0] :
( ~ aElementOf0(W0,xP)
| sdtlseqdt0(xp,W0) ),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
( xP = cS1241(xU,xf,xT)
& aSet0(xP)
& ! [W0] :
( ~ aElementOf0(W0,xP)
| ( aElementOf0(W0,xU)
& aUpperBoundOfIn0(W0,xT,xU)
& sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
& ! [W1] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ) ) )
& ! [W0] :
( ~ aElementOf0(W0,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
| aElementOf0(W0,xP)
| ( ~ aUpperBoundOfIn0(W0,xT,xU)
& ? [W1] :
( ~ sdtlseqdt0(W1,W0)
& aElementOf0(W1,xT) ) ) ) ),
inference(canonicalize,[],[m__1244]) ).
fof(normalize_0_24,plain,
! [W0] :
( ~ aElementOf0(W0,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
| aElementOf0(W0,xP)
| ( ~ aUpperBoundOfIn0(W0,xT,xU)
& ? [W1] :
( ~ sdtlseqdt0(W1,W0)
& aElementOf0(W1,xT) ) ) ),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [W0] :
( ~ aElementOf0(W0,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
| aElementOf0(W0,xP)
| ( ~ aUpperBoundOfIn0(W0,xT,xU)
& ? [W1] :
( ~ sdtlseqdt0(W1,W0)
& aElementOf0(W1,xT) ) ) ),
inference(specialize,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [W0] :
( ( ~ aElementOf0(W0,xU)
| ~ aUpperBoundOfIn0(W0,xT,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
| aElementOf0(W0,xP) )
& ( ~ aElementOf0(W0,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
| ~ sdtlseqdt0(skolemFOFtoCNF_W1_5(W0),W0)
| aElementOf0(W0,xP) )
& ( ~ aElementOf0(W0,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
| aElementOf0(W0,xP)
| aElementOf0(skolemFOFtoCNF_W1_5(W0),xT) ) ),
inference(clausify,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
! [W0] :
( ~ aElementOf0(W0,xU)
| ~ aUpperBoundOfIn0(W0,xT,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
| aElementOf0(W0,xP) ),
inference(conjunct,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [W0,W1] :
( ~ aElementOf0(W0,szDzozmdt0(xf))
| ~ aElementOf0(W1,szDzozmdt0(xf))
| ~ sdtlseqdt0(W0,W1)
| sdtlseqdt0(sdtlpdtrp0(xf,W0),sdtlpdtrp0(xf,W1)) ),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_29,plain,
! [W0,W1] :
( ~ aElementOf0(W0,szDzozmdt0(xf))
| ~ aElementOf0(W1,szDzozmdt0(xf))
| ~ sdtlseqdt0(W0,W1)
| sdtlseqdt0(sdtlpdtrp0(xf,W0),sdtlpdtrp0(xf,W1)) ),
inference(specialize,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_31,plain,
( ~ aFixedPointOf0(xp,xf)
& ( sdtlpdtrp0(xf,xp) != xp
| ~ aElementOf0(xp,szDzozmdt0(xf)) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_32,plain,
( sdtlpdtrp0(xf,xp) != xp
| ~ aElementOf0(xp,szDzozmdt0(xf)) ),
inference(conjunct,[],[normalize_0_31]) ).
cnf(refute_0_0,plain,
aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ aLowerBoundOfIn0(W0,xP,xU)
| sdtlseqdt0(W0,xp) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( ~ aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)
| sdtlseqdt0(sdtlpdtrp0(xf,xp),xp) ),
inference(subst,[],[refute_0_1:[bind(W0,$fot(sdtlpdtrp0(xf,xp)))]]) ).
cnf(refute_0_3,plain,
sdtlseqdt0(sdtlpdtrp0(xf,xp),xp),
inference(resolve,[$cnf( aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ aElement0(W0)
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| W0 = W1 ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ aElement0(sdtlpdtrp0(xf,xp))
| ~ aElement0(xp)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),xp)
| ~ sdtlseqdt0(xp,sdtlpdtrp0(xf,xp))
| sdtlpdtrp0(xf,xp) = xp ),
inference(subst,[],[refute_0_4:[bind(W0,$fot(sdtlpdtrp0(xf,xp))),bind(W1,$fot(xp))]]) ).
cnf(refute_0_6,plain,
( ~ aElement0(sdtlpdtrp0(xf,xp))
| ~ aElement0(xp)
| ~ sdtlseqdt0(xp,sdtlpdtrp0(xf,xp))
| sdtlpdtrp0(xf,xp) = xp ),
inference(resolve,[$cnf( sdtlseqdt0(sdtlpdtrp0(xf,xp),xp) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ aElementOf0(W1,W0)
| ~ aSet0(W0)
| aElement0(W1) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_8,plain,
( ~ aElementOf0(sdtlpdtrp0(xf,xp),xU)
| ~ aSet0(xU)
| aElement0(sdtlpdtrp0(xf,xp)) ),
inference(subst,[],[refute_0_7:[bind(W0,$fot(xU)),bind(W1,$fot(sdtlpdtrp0(xf,xp)))]]) ).
cnf(refute_0_9,plain,
aElementOf0(xp,xU),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_10,plain,
( ~ aElementOf0(W1,szDzozmdt0(W0))
| ~ aFunction0(W0)
| aElementOf0(sdtlpdtrp0(W0,W1),szRzazndt0(W0)) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_11,plain,
( ~ aElementOf0(X_79,szDzozmdt0(xf))
| ~ aFunction0(xf)
| aElementOf0(sdtlpdtrp0(xf,X_79),szRzazndt0(xf)) ),
inference(subst,[],[refute_0_10:[bind(W0,$fot(xf)),bind(W1,$fot(X_79))]]) ).
cnf(refute_0_12,plain,
szRzazndt0(xf) = xU,
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_13,plain,
szDzozmdt0(xf) = szRzazndt0(xf),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_14,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_15,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_16,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( szDzozmdt0(xf) != szRzazndt0(xf)
| szRzazndt0(xf) = szDzozmdt0(xf) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(szDzozmdt0(xf))),bind(Y,$fot(szRzazndt0(xf)))]]) ).
cnf(refute_0_18,plain,
szRzazndt0(xf) = szDzozmdt0(xf),
inference(resolve,[$cnf( $equal(szDzozmdt0(xf),szRzazndt0(xf)) )],[refute_0_13,refute_0_17]) ).
cnf(refute_0_19,plain,
( szRzazndt0(xf) != szDzozmdt0(xf)
| szRzazndt0(xf) != xU
| szDzozmdt0(xf) = xU ),
introduced(tautology,[equality,[$cnf( $equal(szRzazndt0(xf),xU) ),[0],$fot(szDzozmdt0(xf))]]) ).
cnf(refute_0_20,plain,
( szRzazndt0(xf) != xU
| szDzozmdt0(xf) = xU ),
inference(resolve,[$cnf( $equal(szRzazndt0(xf),szDzozmdt0(xf)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
szDzozmdt0(xf) = xU,
inference(resolve,[$cnf( $equal(szRzazndt0(xf),xU) )],[refute_0_12,refute_0_20]) ).
cnf(refute_0_22,plain,
( szDzozmdt0(xf) != xU
| ~ aElementOf0(X_79,xU)
| aElementOf0(X_79,szDzozmdt0(xf)) ),
introduced(tautology,[equality,[$cnf( ~ aElementOf0(X_79,szDzozmdt0(xf)) ),[1],$fot(xU)]]) ).
cnf(refute_0_23,plain,
( ~ aElementOf0(X_79,xU)
| aElementOf0(X_79,szDzozmdt0(xf)) ),
inference(resolve,[$cnf( $equal(szDzozmdt0(xf),xU) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ aElementOf0(X_79,xU)
| ~ aFunction0(xf)
| aElementOf0(sdtlpdtrp0(xf,X_79),szRzazndt0(xf)) ),
inference(resolve,[$cnf( aElementOf0(X_79,szDzozmdt0(xf)) )],[refute_0_23,refute_0_11]) ).
cnf(refute_0_25,plain,
( szRzazndt0(xf) != xU
| ~ aElementOf0(sdtlpdtrp0(xf,X_79),szRzazndt0(xf))
| aElementOf0(sdtlpdtrp0(xf,X_79),xU) ),
introduced(tautology,[equality,[$cnf( aElementOf0(sdtlpdtrp0(xf,X_79),szRzazndt0(xf)) ),[1],$fot(xU)]]) ).
cnf(refute_0_26,plain,
( ~ aElementOf0(sdtlpdtrp0(xf,X_79),szRzazndt0(xf))
| aElementOf0(sdtlpdtrp0(xf,X_79),xU) ),
inference(resolve,[$cnf( $equal(szRzazndt0(xf),xU) )],[refute_0_12,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ aElementOf0(X_79,xU)
| ~ aFunction0(xf)
| aElementOf0(sdtlpdtrp0(xf,X_79),xU) ),
inference(resolve,[$cnf( aElementOf0(sdtlpdtrp0(xf,X_79),szRzazndt0(xf)) )],[refute_0_24,refute_0_26]) ).
cnf(refute_0_28,plain,
aFunction0(xf),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_29,plain,
( ~ aElementOf0(X_79,xU)
| aElementOf0(sdtlpdtrp0(xf,X_79),xU) ),
inference(resolve,[$cnf( aFunction0(xf) )],[refute_0_28,refute_0_27]) ).
cnf(refute_0_30,plain,
( ~ aElementOf0(xp,xU)
| aElementOf0(sdtlpdtrp0(xf,xp),xU) ),
inference(subst,[],[refute_0_29:[bind(X_79,$fot(xp))]]) ).
cnf(refute_0_31,plain,
aElementOf0(sdtlpdtrp0(xf,xp),xU),
inference(resolve,[$cnf( aElementOf0(xp,xU) )],[refute_0_9,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ aSet0(xU)
| aElement0(sdtlpdtrp0(xf,xp)) ),
inference(resolve,[$cnf( aElementOf0(sdtlpdtrp0(xf,xp),xU) )],[refute_0_31,refute_0_8]) ).
cnf(refute_0_33,plain,
aSet0(xU),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_34,plain,
aElement0(sdtlpdtrp0(xf,xp)),
inference(resolve,[$cnf( aSet0(xU) )],[refute_0_33,refute_0_32]) ).
cnf(refute_0_35,plain,
( ~ aElement0(xp)
| ~ sdtlseqdt0(xp,sdtlpdtrp0(xf,xp))
| sdtlpdtrp0(xf,xp) = xp ),
inference(resolve,[$cnf( aElement0(sdtlpdtrp0(xf,xp)) )],[refute_0_34,refute_0_6]) ).
cnf(refute_0_36,plain,
( ~ aElementOf0(xp,xU)
| ~ aSet0(xU)
| aElement0(xp) ),
inference(subst,[],[refute_0_7:[bind(W0,$fot(xU)),bind(W1,$fot(xp))]]) ).
cnf(refute_0_37,plain,
( ~ aSet0(xU)
| aElement0(xp) ),
inference(resolve,[$cnf( aElementOf0(xp,xU) )],[refute_0_9,refute_0_36]) ).
cnf(refute_0_38,plain,
aElement0(xp),
inference(resolve,[$cnf( aSet0(xU) )],[refute_0_33,refute_0_37]) ).
cnf(refute_0_39,plain,
( ~ sdtlseqdt0(xp,sdtlpdtrp0(xf,xp))
| sdtlpdtrp0(xf,xp) = xp ),
inference(resolve,[$cnf( aElement0(xp) )],[refute_0_38,refute_0_35]) ).
cnf(refute_0_40,plain,
( ~ aElementOf0(W0,xP)
| sdtlseqdt0(xp,W0) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_41,plain,
( ~ aElementOf0(sdtlpdtrp0(xf,xp),xP)
| sdtlseqdt0(xp,sdtlpdtrp0(xf,xp)) ),
inference(subst,[],[refute_0_40:[bind(W0,$fot(sdtlpdtrp0(xf,xp)))]]) ).
cnf(refute_0_42,plain,
( ~ aElementOf0(W0,xU)
| ~ aUpperBoundOfIn0(W0,xT,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
| aElementOf0(W0,xP) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_43,plain,
( ~ aElementOf0(sdtlpdtrp0(xf,xp),xU)
| ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,xp)),sdtlpdtrp0(xf,xp))
| aElementOf0(sdtlpdtrp0(xf,xp),xP) ),
inference(subst,[],[refute_0_42:[bind(W0,$fot(sdtlpdtrp0(xf,xp)))]]) ).
cnf(refute_0_44,plain,
( ~ aElementOf0(W0,szDzozmdt0(xf))
| ~ aElementOf0(W1,szDzozmdt0(xf))
| ~ sdtlseqdt0(W0,W1)
| sdtlseqdt0(sdtlpdtrp0(xf,W0),sdtlpdtrp0(xf,W1)) ),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_45,plain,
( szDzozmdt0(xf) != xU
| ~ aElementOf0(W0,xU)
| aElementOf0(W0,szDzozmdt0(xf)) ),
introduced(tautology,[equality,[$cnf( ~ aElementOf0(W0,szDzozmdt0(xf)) ),[1],$fot(xU)]]) ).
cnf(refute_0_46,plain,
( ~ aElementOf0(W0,xU)
| aElementOf0(W0,szDzozmdt0(xf)) ),
inference(resolve,[$cnf( $equal(szDzozmdt0(xf),xU) )],[refute_0_21,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ aElementOf0(W0,xU)
| ~ aElementOf0(W1,szDzozmdt0(xf))
| ~ sdtlseqdt0(W0,W1)
| sdtlseqdt0(sdtlpdtrp0(xf,W0),sdtlpdtrp0(xf,W1)) ),
inference(resolve,[$cnf( aElementOf0(W0,szDzozmdt0(xf)) )],[refute_0_46,refute_0_44]) ).
cnf(refute_0_48,plain,
( szDzozmdt0(xf) != xU
| ~ aElementOf0(W1,xU)
| aElementOf0(W1,szDzozmdt0(xf)) ),
introduced(tautology,[equality,[$cnf( ~ aElementOf0(W1,szDzozmdt0(xf)) ),[1],$fot(xU)]]) ).
cnf(refute_0_49,plain,
( ~ aElementOf0(W1,xU)
| aElementOf0(W1,szDzozmdt0(xf)) ),
inference(resolve,[$cnf( $equal(szDzozmdt0(xf),xU) )],[refute_0_21,refute_0_48]) ).
cnf(refute_0_50,plain,
( ~ aElementOf0(W0,xU)
| ~ aElementOf0(W1,xU)
| ~ sdtlseqdt0(W0,W1)
| sdtlseqdt0(sdtlpdtrp0(xf,W0),sdtlpdtrp0(xf,W1)) ),
inference(resolve,[$cnf( aElementOf0(W1,szDzozmdt0(xf)) )],[refute_0_49,refute_0_47]) ).
cnf(refute_0_51,plain,
( ~ aElementOf0(sdtlpdtrp0(xf,xp),xU)
| ~ aElementOf0(xp,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),xp)
| sdtlseqdt0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,xp)),sdtlpdtrp0(xf,xp)) ),
inference(subst,[],[refute_0_50:[bind(W0,$fot(sdtlpdtrp0(xf,xp))),bind(W1,$fot(xp))]]) ).
cnf(refute_0_52,plain,
( ~ aElementOf0(sdtlpdtrp0(xf,xp),xU)
| ~ aElementOf0(xp,xU)
| sdtlseqdt0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,xp)),sdtlpdtrp0(xf,xp)) ),
inference(resolve,[$cnf( sdtlseqdt0(sdtlpdtrp0(xf,xp),xp) )],[refute_0_3,refute_0_51]) ).
cnf(refute_0_53,plain,
( ~ aElementOf0(xp,xU)
| sdtlseqdt0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,xp)),sdtlpdtrp0(xf,xp)) ),
inference(resolve,[$cnf( aElementOf0(sdtlpdtrp0(xf,xp),xU) )],[refute_0_31,refute_0_52]) ).
cnf(refute_0_54,plain,
sdtlseqdt0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,xp)),sdtlpdtrp0(xf,xp)),
inference(resolve,[$cnf( aElementOf0(xp,xU) )],[refute_0_9,refute_0_53]) ).
cnf(refute_0_55,plain,
( ~ aElementOf0(sdtlpdtrp0(xf,xp),xU)
| ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
| aElementOf0(sdtlpdtrp0(xf,xp),xP) ),
inference(resolve,[$cnf( sdtlseqdt0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,xp)),sdtlpdtrp0(xf,xp)) )],[refute_0_54,refute_0_43]) ).
cnf(refute_0_56,plain,
( ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
| aElementOf0(sdtlpdtrp0(xf,xp),xP) ),
inference(resolve,[$cnf( aElementOf0(sdtlpdtrp0(xf,xp),xU) )],[refute_0_31,refute_0_55]) ).
cnf(refute_0_57,plain,
aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_58,plain,
aElementOf0(sdtlpdtrp0(xf,xp),xP),
inference(resolve,[$cnf( aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU) )],[refute_0_57,refute_0_56]) ).
cnf(refute_0_59,plain,
sdtlseqdt0(xp,sdtlpdtrp0(xf,xp)),
inference(resolve,[$cnf( aElementOf0(sdtlpdtrp0(xf,xp),xP) )],[refute_0_58,refute_0_41]) ).
cnf(refute_0_60,plain,
sdtlpdtrp0(xf,xp) = xp,
inference(resolve,[$cnf( sdtlseqdt0(xp,sdtlpdtrp0(xf,xp)) )],[refute_0_59,refute_0_39]) ).
cnf(refute_0_61,plain,
( sdtlpdtrp0(xf,xp) != xp
| ~ aElementOf0(xp,szDzozmdt0(xf)) ),
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_62,plain,
( szDzozmdt0(xf) != xU
| ~ aElementOf0(xp,xU)
| aElementOf0(xp,szDzozmdt0(xf)) ),
introduced(tautology,[equality,[$cnf( ~ aElementOf0(xp,szDzozmdt0(xf)) ),[1],$fot(xU)]]) ).
cnf(refute_0_63,plain,
( ~ aElementOf0(xp,xU)
| aElementOf0(xp,szDzozmdt0(xf)) ),
inference(resolve,[$cnf( $equal(szDzozmdt0(xf),xU) )],[refute_0_21,refute_0_62]) ).
cnf(refute_0_64,plain,
( sdtlpdtrp0(xf,xp) != xp
| ~ aElementOf0(xp,xU) ),
inference(resolve,[$cnf( aElementOf0(xp,szDzozmdt0(xf)) )],[refute_0_63,refute_0_61]) ).
cnf(refute_0_65,plain,
sdtlpdtrp0(xf,xp) != xp,
inference(resolve,[$cnf( aElementOf0(xp,xU) )],[refute_0_9,refute_0_64]) ).
cnf(refute_0_66,plain,
$false,
inference(resolve,[$cnf( $equal(sdtlpdtrp0(xf,xp),xp) )],[refute_0_60,refute_0_65]) ).
fof(negate_1_0,plain,
~ ( ( ( ( aElementOf0(xp,szDzozmdt0(xf))
& sdtlpdtrp0(xf,xp) = xp )
| aFixedPointOf0(xp,xf) )
& ~ ( ( ! [W0] :
( aElementOf0(W0,xT)
=> sdtlseqdt0(W0,xp) )
| aUpperBoundOfIn0(xp,xT,xS) )
& ! [W0] :
( ( aElementOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,xT)
=> sdtlseqdt0(W1,W0) )
& aUpperBoundOfIn0(W0,xT,xS) )
=> sdtlseqdt0(xp,W0) ) ) )
=> aSupremumOfIn0(xp,xT,xS) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
( ~ definitionFOFtoCNF_1
<=> ( aUpperBoundOfIn0(xp,xT,xS)
| ! [W0] :
( ~ aElementOf0(W0,xT)
| sdtlseqdt0(W0,xp) ) ) ),
inference(canonicalize,[],[definition_0]) ).
fof(normalize_1_1,plain,
! [W0] :
( ( ~ aUpperBoundOfIn0(xp,xT,xS)
| ~ definitionFOFtoCNF_1 )
& ( ~ definitionFOFtoCNF_1
| ~ sdtlseqdt0(skolemFOFtoCNF_W0,xp) )
& ( ~ definitionFOFtoCNF_1
| aElementOf0(skolemFOFtoCNF_W0,xT) )
& ( ~ aElementOf0(W0,xT)
| aUpperBoundOfIn0(xp,xT,xS)
| definitionFOFtoCNF_1
| sdtlseqdt0(W0,xp) ) ),
inference(clausify,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
( ~ definitionFOFtoCNF_1
| ~ sdtlseqdt0(skolemFOFtoCNF_W0,xp) ),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
( aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)
& aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
& ! [W0] :
( ~ aElementOf0(W0,xP)
| sdtlseqdt0(sdtlpdtrp0(xf,xp),W0) )
& ! [W0] :
( ~ aElementOf0(W0,xT)
| sdtlseqdt0(W0,sdtlpdtrp0(xf,xp)) ) ),
inference(canonicalize,[],[m__1299]) ).
fof(normalize_1_4,plain,
! [W0] :
( ~ aElementOf0(W0,xT)
| sdtlseqdt0(W0,sdtlpdtrp0(xf,xp)) ),
inference(conjunct,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [W0] :
( ~ aElementOf0(W0,xT)
| sdtlseqdt0(W0,sdtlpdtrp0(xf,xp)) ),
inference(specialize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
( xS = cS1142(xf)
& aSet0(xS)
& ! [W0] :
( ~ aElementOf0(W0,xS)
| ( sdtlpdtrp0(xf,W0) = W0
& aElementOf0(W0,szDzozmdt0(xf))
& aFixedPointOf0(W0,xf) ) )
& ! [W0] :
( aElementOf0(W0,xS)
| ( ~ aFixedPointOf0(W0,xf)
& ( sdtlpdtrp0(xf,W0) != W0
| ~ aElementOf0(W0,szDzozmdt0(xf)) ) ) ) ),
inference(canonicalize,[],[m__1144]) ).
fof(normalize_1_7,plain,
! [W0] :
( ~ aElementOf0(W0,xS)
| ( sdtlpdtrp0(xf,W0) = W0
& aElementOf0(W0,szDzozmdt0(xf))
& aFixedPointOf0(W0,xf) ) ),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
! [W0] :
( ~ aElementOf0(W0,xS)
| ( sdtlpdtrp0(xf,W0) = W0
& aElementOf0(W0,szDzozmdt0(xf))
& aFixedPointOf0(W0,xf) ) ),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [W0] :
( ( ~ aElementOf0(W0,xS)
| sdtlpdtrp0(xf,W0) = W0 )
& ( ~ aElementOf0(W0,xS)
| aElementOf0(W0,szDzozmdt0(xf)) )
& ( ~ aElementOf0(W0,xS)
| aFixedPointOf0(W0,xf) ) ),
inference(clausify,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
! [W0] :
( ~ aElementOf0(W0,xS)
| sdtlpdtrp0(xf,W0) = W0 ),
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [W0] :
( aElementOf0(W0,xS)
| ( ~ aFixedPointOf0(W0,xf)
& ( sdtlpdtrp0(xf,W0) != W0
| ~ aElementOf0(W0,szDzozmdt0(xf)) ) ) ),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_12,plain,
! [W0] :
( aElementOf0(W0,xS)
| ( ~ aFixedPointOf0(W0,xf)
& ( sdtlpdtrp0(xf,W0) != W0
| ~ aElementOf0(W0,szDzozmdt0(xf)) ) ) ),
inference(specialize,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
! [W0] :
( ( ~ aFixedPointOf0(W0,xf)
| aElementOf0(W0,xS) )
& ( sdtlpdtrp0(xf,W0) != W0
| ~ aElementOf0(W0,szDzozmdt0(xf))
| aElementOf0(W0,xS) ) ),
inference(clausify,[],[normalize_1_12]) ).
fof(normalize_1_14,plain,
! [W0] :
( ~ aFixedPointOf0(W0,xf)
| aElementOf0(W0,xS) ),
inference(conjunct,[],[normalize_1_13]) ).
fof(normalize_1_15,plain,
! [W0] :
( sdtlpdtrp0(xf,W0) != W0
| ~ aElementOf0(W0,szDzozmdt0(xf))
| aElementOf0(W0,xS) ),
inference(conjunct,[],[normalize_1_13]) ).
fof(normalize_1_16,plain,
( szDzozmdt0(xf) = szRzazndt0(xf)
& szRzazndt0(xf) = xU
& aCompleteLattice0(xU)
& aFunction0(xf)
& aSet0(xU)
& isMonotone0(xf)
& isOn0(xf,xU)
& ! [W0] :
( ( ~ aSubsetOf0(W0,xU)
& ( ~ aSet0(W0)
| ? [W1] :
( ~ aElementOf0(W1,xU)
& aElementOf0(W1,W0) ) ) )
| ? [W1] :
( aElementOf0(W1,xU)
& aInfimumOfIn0(W1,W0,xU)
& aLowerBoundOfIn0(W1,W0,xU)
& ? [W2] :
( aElementOf0(W2,xU)
& aSupremumOfIn0(W2,W0,xU)
& aUpperBoundOfIn0(W2,W0,xU)
& ! [W3] :
( ~ aElementOf0(W3,W0)
| sdtlseqdt0(W3,W2) )
& ! [W3] :
( sdtlseqdt0(W2,W3)
| ( ~ aUpperBoundOfIn0(W3,W0,xU)
& ( ~ aElementOf0(W3,xU)
| ? [W4] :
( ~ sdtlseqdt0(W4,W3)
& aElementOf0(W4,W0) ) ) ) ) )
& ! [W2] :
( ~ aElementOf0(W2,W0)
| sdtlseqdt0(W1,W2) )
& ! [W2] :
( sdtlseqdt0(W2,W1)
| ( ~ aLowerBoundOfIn0(W2,W0,xU)
& ( ~ aElementOf0(W2,xU)
| ? [W3] :
( ~ sdtlseqdt0(W2,W3)
& aElementOf0(W3,W0) ) ) ) ) ) )
& ! [W0,W1] :
( ~ aElementOf0(W0,szDzozmdt0(xf))
| ~ aElementOf0(W1,szDzozmdt0(xf))
| ~ sdtlseqdt0(W0,W1)
| sdtlseqdt0(sdtlpdtrp0(xf,W0),sdtlpdtrp0(xf,W1)) ) ),
inference(canonicalize,[],[m__1123]) ).
fof(normalize_1_17,plain,
szRzazndt0(xf) = xU,
inference(conjunct,[],[normalize_1_16]) ).
fof(normalize_1_18,plain,
szDzozmdt0(xf) = szRzazndt0(xf),
inference(conjunct,[],[normalize_1_16]) ).
fof(normalize_1_19,plain,
( ~ aSupremumOfIn0(xp,xT,xS)
& ( aFixedPointOf0(xp,xf)
| ( sdtlpdtrp0(xf,xp) = xp
& aElementOf0(xp,szDzozmdt0(xf)) ) )
& ( ( ~ aUpperBoundOfIn0(xp,xT,xS)
& ? [W0] :
( ~ sdtlseqdt0(W0,xp)
& aElementOf0(W0,xT) ) )
| ? [W0] :
( ~ sdtlseqdt0(xp,W0)
& aElementOf0(W0,xS)
& aUpperBoundOfIn0(W0,xT,xS)
& ! [W1] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ) ) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_20,plain,
( aFixedPointOf0(xp,xf)
| ( sdtlpdtrp0(xf,xp) = xp
& aElementOf0(xp,szDzozmdt0(xf)) ) ),
inference(conjunct,[],[normalize_1_19]) ).
fof(normalize_1_21,plain,
( ( sdtlpdtrp0(xf,xp) = xp
| aFixedPointOf0(xp,xf) )
& ( aElementOf0(xp,szDzozmdt0(xf))
| aFixedPointOf0(xp,xf) ) ),
inference(clausify,[],[normalize_1_20]) ).
fof(normalize_1_22,plain,
( sdtlpdtrp0(xf,xp) = xp
| aFixedPointOf0(xp,xf) ),
inference(conjunct,[],[normalize_1_21]) ).
fof(normalize_1_23,plain,
( aElementOf0(xp,xU)
& aInfimumOfIn0(xp,xP,xU)
& aLowerBoundOfIn0(xp,xP,xU)
& ! [W0] :
( ~ aElementOf0(W0,xP)
| sdtlseqdt0(xp,W0) )
& ! [W0] :
( sdtlseqdt0(W0,xp)
| ( ~ aLowerBoundOfIn0(W0,xP,xU)
& ( ~ aElementOf0(W0,xU)
| ? [W1] :
( ~ sdtlseqdt0(W0,W1)
& aElementOf0(W1,xP) ) ) ) ) ),
inference(canonicalize,[],[m__1261]) ).
fof(normalize_1_24,plain,
aElementOf0(xp,xU),
inference(conjunct,[],[normalize_1_23]) ).
fof(normalize_1_25,plain,
( ~ definitionFOFtoCNF_1
| aElementOf0(skolemFOFtoCNF_W0,xT) ),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_26,plain,
( ( ~ aUpperBoundOfIn0(xp,xT,xS)
& ? [W0] :
( ~ sdtlseqdt0(W0,xp)
& aElementOf0(W0,xT) ) )
| ? [W0] :
( ~ sdtlseqdt0(xp,W0)
& aElementOf0(W0,xS)
& aUpperBoundOfIn0(W0,xT,xS)
& ! [W1] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ) ) ),
inference(conjunct,[],[normalize_1_19]) ).
fof(normalize_1_27,plain,
( definitionFOFtoCNF_1
| ? [W0] :
( ~ sdtlseqdt0(xp,W0)
& aElementOf0(W0,xS)
& aUpperBoundOfIn0(W0,xT,xS)
& ! [W1] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ) ) ),
inference(simplify,[],[normalize_1_26,normalize_1_0]) ).
fof(normalize_1_28,plain,
! [W1] :
( ( ~ sdtlseqdt0(xp,skolemFOFtoCNF_W0_1)
| definitionFOFtoCNF_1 )
& ( aElementOf0(skolemFOFtoCNF_W0_1,xS)
| definitionFOFtoCNF_1 )
& ( aUpperBoundOfIn0(skolemFOFtoCNF_W0_1,xT,xS)
| definitionFOFtoCNF_1 )
& ( ~ aElementOf0(W1,xT)
| definitionFOFtoCNF_1
| sdtlseqdt0(W1,skolemFOFtoCNF_W0_1) ) ),
inference(clausify,[],[normalize_1_27]) ).
fof(normalize_1_29,plain,
( ~ sdtlseqdt0(xp,skolemFOFtoCNF_W0_1)
| definitionFOFtoCNF_1 ),
inference(conjunct,[],[normalize_1_28]) ).
fof(normalize_1_30,plain,
! [W0] :
( ~ aElementOf0(W0,xP)
| sdtlseqdt0(xp,W0) ),
inference(conjunct,[],[normalize_1_23]) ).
fof(normalize_1_31,plain,
! [W0] :
( ~ aElementOf0(W0,xP)
| sdtlseqdt0(xp,W0) ),
inference(specialize,[],[normalize_1_30]) ).
fof(normalize_1_32,plain,
( aElementOf0(skolemFOFtoCNF_W0_1,xS)
| definitionFOFtoCNF_1 ),
inference(conjunct,[],[normalize_1_28]) ).
fof(normalize_1_33,plain,
! [W0] :
( ~ aElementOf0(W0,xS)
| aElementOf0(W0,szDzozmdt0(xf)) ),
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_34,plain,
! [W0] :
( ~ aElement0(W0)
| sdtlseqdt0(W0,W0) ),
inference(canonicalize,[],[mARefl]) ).
fof(normalize_1_35,plain,
! [W0] :
( ~ aElement0(W0)
| sdtlseqdt0(W0,W0) ),
inference(specialize,[],[normalize_1_34]) ).
fof(normalize_1_36,plain,
! [W0] :
( ~ aSet0(W0)
| ! [W1] :
( ~ aElementOf0(W1,W0)
| aElement0(W1) ) ),
inference(canonicalize,[],[mEOfElem]) ).
fof(normalize_1_37,plain,
! [W0] :
( ~ aSet0(W0)
| ! [W1] :
( ~ aElementOf0(W1,W0)
| aElement0(W1) ) ),
inference(specialize,[],[normalize_1_36]) ).
fof(normalize_1_38,plain,
! [W0,W1] :
( ~ aElementOf0(W1,W0)
| ~ aSet0(W0)
| aElement0(W1) ),
inference(clausify,[],[normalize_1_37]) ).
fof(normalize_1_39,plain,
! [W0] :
( ~ aFunction0(W0)
| ! [W1] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),szRzazndt0(W0)) ) ),
inference(canonicalize,[],[mImgSort]) ).
fof(normalize_1_40,plain,
! [W0] :
( ~ aFunction0(W0)
| ! [W1] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),szRzazndt0(W0)) ) ),
inference(specialize,[],[normalize_1_39]) ).
fof(normalize_1_41,plain,
! [W0,W1] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| ~ aFunction0(W0)
| aElementOf0(sdtlpdtrp0(W0,W1),szRzazndt0(W0)) ),
inference(clausify,[],[normalize_1_40]) ).
fof(normalize_1_42,plain,
aFunction0(xf),
inference(conjunct,[],[normalize_1_16]) ).
fof(normalize_1_43,plain,
aSet0(xU),
inference(conjunct,[],[normalize_1_16]) ).
fof(normalize_1_44,plain,
( xP = cS1241(xU,xf,xT)
& aSet0(xP)
& ! [W0] :
( ~ aElementOf0(W0,xP)
| ( aElementOf0(W0,xU)
& aUpperBoundOfIn0(W0,xT,xU)
& sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
& ! [W1] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ) ) )
& ! [W0] :
( ~ aElementOf0(W0,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
| aElementOf0(W0,xP)
| ( ~ aUpperBoundOfIn0(W0,xT,xU)
& ? [W1] :
( ~ sdtlseqdt0(W1,W0)
& aElementOf0(W1,xT) ) ) ) ),
inference(canonicalize,[],[m__1244]) ).
fof(normalize_1_45,plain,
! [W0] :
( ~ aElementOf0(W0,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
| aElementOf0(W0,xP)
| ( ~ aUpperBoundOfIn0(W0,xT,xU)
& ? [W1] :
( ~ sdtlseqdt0(W1,W0)
& aElementOf0(W1,xT) ) ) ),
inference(conjunct,[],[normalize_1_44]) ).
fof(normalize_1_46,plain,
! [W0] :
( ~ aElementOf0(W0,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
| aElementOf0(W0,xP)
| ( ~ aUpperBoundOfIn0(W0,xT,xU)
& ? [W1] :
( ~ sdtlseqdt0(W1,W0)
& aElementOf0(W1,xT) ) ) ),
inference(specialize,[],[normalize_1_45]) ).
fof(normalize_1_47,plain,
! [W0] :
( ( ~ aElementOf0(W0,xU)
| ~ aUpperBoundOfIn0(W0,xT,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
| aElementOf0(W0,xP) )
& ( ~ aElementOf0(W0,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
| ~ sdtlseqdt0(skolemFOFtoCNF_W1_5(W0),W0)
| aElementOf0(W0,xP) )
& ( ~ aElementOf0(W0,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
| aElementOf0(W0,xP)
| aElementOf0(skolemFOFtoCNF_W1_5(W0),xT) ) ),
inference(clausify,[],[normalize_1_46]) ).
fof(normalize_1_48,plain,
! [W0] :
( ~ aElementOf0(W0,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
| ~ sdtlseqdt0(skolemFOFtoCNF_W1_5(W0),W0)
| aElementOf0(W0,xP) ),
inference(conjunct,[],[normalize_1_47]) ).
fof(normalize_1_49,plain,
! [W1] :
( ~ aElementOf0(W1,xT)
| definitionFOFtoCNF_1
| sdtlseqdt0(W1,skolemFOFtoCNF_W0_1) ),
inference(conjunct,[],[normalize_1_28]) ).
fof(normalize_1_50,plain,
! [W0] :
( ~ aElementOf0(W0,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
| aElementOf0(W0,xP)
| aElementOf0(skolemFOFtoCNF_W1_5(W0),xT) ),
inference(conjunct,[],[normalize_1_47]) ).
cnf(refute_1_0,plain,
( ~ definitionFOFtoCNF_1
| ~ sdtlseqdt0(skolemFOFtoCNF_W0,xp) ),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
( ~ aElementOf0(W0,xT)
| sdtlseqdt0(W0,sdtlpdtrp0(xf,xp)) ),
inference(canonicalize,[],[normalize_1_5]) ).
cnf(refute_1_2,plain,
( ~ aElementOf0(W0,xS)
| sdtlpdtrp0(xf,W0) = W0 ),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_3,plain,
( ~ aElementOf0(xp,xS)
| sdtlpdtrp0(xf,xp) = xp ),
inference(subst,[],[refute_1_2:[bind(W0,$fot(xp))]]) ).
cnf(refute_1_4,plain,
( ~ aFixedPointOf0(W0,xf)
| aElementOf0(W0,xS) ),
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_5,plain,
( ~ aFixedPointOf0(xp,xf)
| aElementOf0(xp,xS) ),
inference(subst,[],[refute_1_4:[bind(W0,$fot(xp))]]) ).
cnf(refute_1_6,plain,
( sdtlpdtrp0(xf,W0) != W0
| ~ aElementOf0(W0,szDzozmdt0(xf))
| aElementOf0(W0,xS) ),
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_7,plain,
szRzazndt0(xf) = xU,
inference(canonicalize,[],[normalize_1_17]) ).
cnf(refute_1_8,plain,
szDzozmdt0(xf) = szRzazndt0(xf),
inference(canonicalize,[],[normalize_1_18]) ).
cnf(refute_1_9,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_10,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_11,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_9,refute_1_10]) ).
cnf(refute_1_12,plain,
( szDzozmdt0(xf) != szRzazndt0(xf)
| szRzazndt0(xf) = szDzozmdt0(xf) ),
inference(subst,[],[refute_1_11:[bind(X,$fot(szDzozmdt0(xf))),bind(Y,$fot(szRzazndt0(xf)))]]) ).
cnf(refute_1_13,plain,
szRzazndt0(xf) = szDzozmdt0(xf),
inference(resolve,[$cnf( $equal(szDzozmdt0(xf),szRzazndt0(xf)) )],[refute_1_8,refute_1_12]) ).
cnf(refute_1_14,plain,
( szRzazndt0(xf) != szDzozmdt0(xf)
| szRzazndt0(xf) != xU
| szDzozmdt0(xf) = xU ),
introduced(tautology,[equality,[$cnf( $equal(szRzazndt0(xf),xU) ),[0],$fot(szDzozmdt0(xf))]]) ).
cnf(refute_1_15,plain,
( szRzazndt0(xf) != xU
| szDzozmdt0(xf) = xU ),
inference(resolve,[$cnf( $equal(szRzazndt0(xf),szDzozmdt0(xf)) )],[refute_1_13,refute_1_14]) ).
cnf(refute_1_16,plain,
szDzozmdt0(xf) = xU,
inference(resolve,[$cnf( $equal(szRzazndt0(xf),xU) )],[refute_1_7,refute_1_15]) ).
cnf(refute_1_17,plain,
( szDzozmdt0(xf) != xU
| ~ aElementOf0(W0,xU)
| aElementOf0(W0,szDzozmdt0(xf)) ),
introduced(tautology,[equality,[$cnf( ~ aElementOf0(W0,szDzozmdt0(xf)) ),[1],$fot(xU)]]) ).
cnf(refute_1_18,plain,
( ~ aElementOf0(W0,xU)
| aElementOf0(W0,szDzozmdt0(xf)) ),
inference(resolve,[$cnf( $equal(szDzozmdt0(xf),xU) )],[refute_1_16,refute_1_17]) ).
cnf(refute_1_19,plain,
( sdtlpdtrp0(xf,W0) != W0
| ~ aElementOf0(W0,xU)
| aElementOf0(W0,xS) ),
inference(resolve,[$cnf( aElementOf0(W0,szDzozmdt0(xf)) )],[refute_1_18,refute_1_6]) ).
cnf(refute_1_20,plain,
( sdtlpdtrp0(xf,xp) != xp
| ~ aElementOf0(xp,xU)
| aElementOf0(xp,xS) ),
inference(subst,[],[refute_1_19:[bind(W0,$fot(xp))]]) ).
cnf(refute_1_21,plain,
( sdtlpdtrp0(xf,xp) = xp
| aFixedPointOf0(xp,xf) ),
inference(canonicalize,[],[normalize_1_22]) ).
cnf(refute_1_22,plain,
( sdtlpdtrp0(xf,xp) != xp
| xp != xp
| sdtlpdtrp0(xf,xp) = xp ),
introduced(tautology,[equality,[$cnf( ~ $equal(sdtlpdtrp0(xf,xp),xp) ),[0],$fot(xp)]]) ).
cnf(refute_1_23,plain,
( xp != xp
| sdtlpdtrp0(xf,xp) = xp
| aFixedPointOf0(xp,xf) ),
inference(resolve,[$cnf( $equal(sdtlpdtrp0(xf,xp),xp) )],[refute_1_21,refute_1_22]) ).
cnf(refute_1_24,plain,
( xp != xp
| ~ aElementOf0(xp,xU)
| aElementOf0(xp,xS)
| aFixedPointOf0(xp,xf) ),
inference(resolve,[$cnf( $equal(sdtlpdtrp0(xf,xp),xp) )],[refute_1_23,refute_1_20]) ).
cnf(refute_1_25,plain,
xp = xp,
introduced(tautology,[refl,[$fot(xp)]]) ).
cnf(refute_1_26,plain,
( ~ aElementOf0(xp,xU)
| aElementOf0(xp,xS)
| aFixedPointOf0(xp,xf) ),
inference(resolve,[$cnf( $equal(xp,xp) )],[refute_1_25,refute_1_24]) ).
cnf(refute_1_27,plain,
aElementOf0(xp,xU),
inference(canonicalize,[],[normalize_1_24]) ).
cnf(refute_1_28,plain,
( aElementOf0(xp,xS)
| aFixedPointOf0(xp,xf) ),
inference(resolve,[$cnf( aElementOf0(xp,xU) )],[refute_1_27,refute_1_26]) ).
cnf(refute_1_29,plain,
aElementOf0(xp,xS),
inference(resolve,[$cnf( aFixedPointOf0(xp,xf) )],[refute_1_28,refute_1_5]) ).
cnf(refute_1_30,plain,
sdtlpdtrp0(xf,xp) = xp,
inference(resolve,[$cnf( aElementOf0(xp,xS) )],[refute_1_29,refute_1_3]) ).
cnf(refute_1_31,plain,
( sdtlpdtrp0(xf,xp) != xp
| ~ sdtlseqdt0(W0,sdtlpdtrp0(xf,xp))
| sdtlseqdt0(W0,xp) ),
introduced(tautology,[equality,[$cnf( sdtlseqdt0(W0,sdtlpdtrp0(xf,xp)) ),[1],$fot(xp)]]) ).
cnf(refute_1_32,plain,
( ~ sdtlseqdt0(W0,sdtlpdtrp0(xf,xp))
| sdtlseqdt0(W0,xp) ),
inference(resolve,[$cnf( $equal(sdtlpdtrp0(xf,xp),xp) )],[refute_1_30,refute_1_31]) ).
cnf(refute_1_33,plain,
( ~ aElementOf0(W0,xT)
| sdtlseqdt0(W0,xp) ),
inference(resolve,[$cnf( sdtlseqdt0(W0,sdtlpdtrp0(xf,xp)) )],[refute_1_1,refute_1_32]) ).
cnf(refute_1_34,plain,
( ~ aElementOf0(skolemFOFtoCNF_W0,xT)
| sdtlseqdt0(skolemFOFtoCNF_W0,xp) ),
inference(subst,[],[refute_1_33:[bind(W0,$fot(skolemFOFtoCNF_W0))]]) ).
cnf(refute_1_35,plain,
( ~ definitionFOFtoCNF_1
| aElementOf0(skolemFOFtoCNF_W0,xT) ),
inference(canonicalize,[],[normalize_1_25]) ).
cnf(refute_1_36,plain,
( ~ sdtlseqdt0(xp,skolemFOFtoCNF_W0_1)
| definitionFOFtoCNF_1 ),
inference(canonicalize,[],[normalize_1_29]) ).
cnf(refute_1_37,plain,
( ~ aElementOf0(W0,xP)
| sdtlseqdt0(xp,W0) ),
inference(canonicalize,[],[normalize_1_31]) ).
cnf(refute_1_38,plain,
( ~ aElementOf0(skolemFOFtoCNF_W0_1,xP)
| sdtlseqdt0(xp,skolemFOFtoCNF_W0_1) ),
inference(subst,[],[refute_1_37:[bind(W0,$fot(skolemFOFtoCNF_W0_1))]]) ).
cnf(refute_1_39,plain,
( aElementOf0(skolemFOFtoCNF_W0_1,xS)
| definitionFOFtoCNF_1 ),
inference(canonicalize,[],[normalize_1_32]) ).
cnf(refute_1_40,plain,
( ~ aElementOf0(W0,xS)
| aElementOf0(W0,szDzozmdt0(xf)) ),
inference(canonicalize,[],[normalize_1_33]) ).
cnf(refute_1_41,plain,
( szDzozmdt0(xf) != xU
| ~ aElementOf0(W0,szDzozmdt0(xf))
| aElementOf0(W0,xU) ),
introduced(tautology,[equality,[$cnf( aElementOf0(W0,szDzozmdt0(xf)) ),[1],$fot(xU)]]) ).
cnf(refute_1_42,plain,
( ~ aElementOf0(W0,szDzozmdt0(xf))
| aElementOf0(W0,xU) ),
inference(resolve,[$cnf( $equal(szDzozmdt0(xf),xU) )],[refute_1_16,refute_1_41]) ).
cnf(refute_1_43,plain,
( ~ aElementOf0(W0,xS)
| aElementOf0(W0,xU) ),
inference(resolve,[$cnf( aElementOf0(W0,szDzozmdt0(xf)) )],[refute_1_40,refute_1_42]) ).
cnf(refute_1_44,plain,
( ~ aElementOf0(skolemFOFtoCNF_W0_1,xS)
| aElementOf0(skolemFOFtoCNF_W0_1,xU) ),
inference(subst,[],[refute_1_43:[bind(W0,$fot(skolemFOFtoCNF_W0_1))]]) ).
cnf(refute_1_45,plain,
( aElementOf0(skolemFOFtoCNF_W0_1,xU)
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W0_1,xS) )],[refute_1_39,refute_1_44]) ).
cnf(refute_1_46,plain,
( ~ aElement0(W0)
| sdtlseqdt0(W0,W0) ),
inference(canonicalize,[],[normalize_1_35]) ).
cnf(refute_1_47,plain,
( ~ aElement0(sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1))
| sdtlseqdt0(sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1),sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1)) ),
inference(subst,[],[refute_1_46:[bind(W0,$fot(sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1)))]]) ).
cnf(refute_1_48,plain,
( ~ aElementOf0(W1,W0)
| ~ aSet0(W0)
| aElement0(W1) ),
inference(canonicalize,[],[normalize_1_38]) ).
cnf(refute_1_49,plain,
( ~ aElementOf0(sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1),xU)
| ~ aSet0(xU)
| aElement0(sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1)) ),
inference(subst,[],[refute_1_48:[bind(W0,$fot(xU)),bind(W1,$fot(sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1)))]]) ).
cnf(refute_1_50,plain,
( ~ aElementOf0(W1,szDzozmdt0(W0))
| ~ aFunction0(W0)
| aElementOf0(sdtlpdtrp0(W0,W1),szRzazndt0(W0)) ),
inference(canonicalize,[],[normalize_1_41]) ).
cnf(refute_1_51,plain,
( ~ aElementOf0(X_361,szDzozmdt0(xf))
| ~ aFunction0(xf)
| aElementOf0(sdtlpdtrp0(xf,X_361),szRzazndt0(xf)) ),
inference(subst,[],[refute_1_50:[bind(W0,$fot(xf)),bind(W1,$fot(X_361))]]) ).
cnf(refute_1_52,plain,
( szDzozmdt0(xf) != xU
| ~ aElementOf0(X_361,xU)
| aElementOf0(X_361,szDzozmdt0(xf)) ),
introduced(tautology,[equality,[$cnf( ~ aElementOf0(X_361,szDzozmdt0(xf)) ),[1],$fot(xU)]]) ).
cnf(refute_1_53,plain,
( ~ aElementOf0(X_361,xU)
| aElementOf0(X_361,szDzozmdt0(xf)) ),
inference(resolve,[$cnf( $equal(szDzozmdt0(xf),xU) )],[refute_1_16,refute_1_52]) ).
cnf(refute_1_54,plain,
( ~ aElementOf0(X_361,xU)
| ~ aFunction0(xf)
| aElementOf0(sdtlpdtrp0(xf,X_361),szRzazndt0(xf)) ),
inference(resolve,[$cnf( aElementOf0(X_361,szDzozmdt0(xf)) )],[refute_1_53,refute_1_51]) ).
cnf(refute_1_55,plain,
( szRzazndt0(xf) != xU
| ~ aElementOf0(sdtlpdtrp0(xf,X_361),szRzazndt0(xf))
| aElementOf0(sdtlpdtrp0(xf,X_361),xU) ),
introduced(tautology,[equality,[$cnf( aElementOf0(sdtlpdtrp0(xf,X_361),szRzazndt0(xf)) ),[1],$fot(xU)]]) ).
cnf(refute_1_56,plain,
( ~ aElementOf0(sdtlpdtrp0(xf,X_361),szRzazndt0(xf))
| aElementOf0(sdtlpdtrp0(xf,X_361),xU) ),
inference(resolve,[$cnf( $equal(szRzazndt0(xf),xU) )],[refute_1_7,refute_1_55]) ).
cnf(refute_1_57,plain,
( ~ aElementOf0(X_361,xU)
| ~ aFunction0(xf)
| aElementOf0(sdtlpdtrp0(xf,X_361),xU) ),
inference(resolve,[$cnf( aElementOf0(sdtlpdtrp0(xf,X_361),szRzazndt0(xf)) )],[refute_1_54,refute_1_56]) ).
cnf(refute_1_58,plain,
aFunction0(xf),
inference(canonicalize,[],[normalize_1_42]) ).
cnf(refute_1_59,plain,
( ~ aElementOf0(X_361,xU)
| aElementOf0(sdtlpdtrp0(xf,X_361),xU) ),
inference(resolve,[$cnf( aFunction0(xf) )],[refute_1_58,refute_1_57]) ).
cnf(refute_1_60,plain,
( ~ aElementOf0(skolemFOFtoCNF_W0_1,xU)
| aElementOf0(sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1),xU) ),
inference(subst,[],[refute_1_59:[bind(X_361,$fot(skolemFOFtoCNF_W0_1))]]) ).
cnf(refute_1_61,plain,
( aElementOf0(sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1),xU)
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W0_1,xU) )],[refute_1_45,refute_1_60]) ).
cnf(refute_1_62,plain,
( ~ aSet0(xU)
| aElement0(sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1))
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( aElementOf0(sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1),xU) )],[refute_1_61,refute_1_49]) ).
cnf(refute_1_63,plain,
aSet0(xU),
inference(canonicalize,[],[normalize_1_43]) ).
cnf(refute_1_64,plain,
( aElement0(sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1))
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( aSet0(xU) )],[refute_1_63,refute_1_62]) ).
cnf(refute_1_65,plain,
( definitionFOFtoCNF_1
| sdtlseqdt0(sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1),sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1)) ),
inference(resolve,[$cnf( aElement0(sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1)) )],[refute_1_64,refute_1_47]) ).
cnf(refute_1_66,plain,
( ~ aElementOf0(skolemFOFtoCNF_W0_1,xS)
| sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1) = skolemFOFtoCNF_W0_1 ),
inference(subst,[],[refute_1_2:[bind(W0,$fot(skolemFOFtoCNF_W0_1))]]) ).
cnf(refute_1_67,plain,
( sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1) = skolemFOFtoCNF_W0_1
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W0_1,xS) )],[refute_1_39,refute_1_66]) ).
cnf(refute_1_68,plain,
( sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1) != skolemFOFtoCNF_W0_1
| ~ sdtlseqdt0(sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1),sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1))
| sdtlseqdt0(sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1),skolemFOFtoCNF_W0_1) ),
introduced(tautology,[equality,[$cnf( sdtlseqdt0(sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1),sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1)) ),[1],$fot(skolemFOFtoCNF_W0_1)]]) ).
cnf(refute_1_69,plain,
( ~ sdtlseqdt0(sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1),sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1))
| definitionFOFtoCNF_1
| sdtlseqdt0(sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1),skolemFOFtoCNF_W0_1) ),
inference(resolve,[$cnf( $equal(sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1),skolemFOFtoCNF_W0_1) )],[refute_1_67,refute_1_68]) ).
cnf(refute_1_70,plain,
( definitionFOFtoCNF_1
| sdtlseqdt0(sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1),skolemFOFtoCNF_W0_1) ),
inference(resolve,[$cnf( sdtlseqdt0(sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1),sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1)) )],[refute_1_65,refute_1_69]) ).
cnf(refute_1_71,plain,
( ~ aElementOf0(W0,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
| ~ sdtlseqdt0(skolemFOFtoCNF_W1_5(W0),W0)
| aElementOf0(W0,xP) ),
inference(canonicalize,[],[normalize_1_48]) ).
cnf(refute_1_72,plain,
( ~ aElementOf0(skolemFOFtoCNF_W0_1,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1),skolemFOFtoCNF_W0_1)
| ~ sdtlseqdt0(skolemFOFtoCNF_W1_5(skolemFOFtoCNF_W0_1),skolemFOFtoCNF_W0_1)
| aElementOf0(skolemFOFtoCNF_W0_1,xP) ),
inference(subst,[],[refute_1_71:[bind(W0,$fot(skolemFOFtoCNF_W0_1))]]) ).
cnf(refute_1_73,plain,
( ~ aElementOf0(skolemFOFtoCNF_W0_1,xU)
| ~ sdtlseqdt0(skolemFOFtoCNF_W1_5(skolemFOFtoCNF_W0_1),skolemFOFtoCNF_W0_1)
| aElementOf0(skolemFOFtoCNF_W0_1,xP)
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( sdtlseqdt0(sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1),skolemFOFtoCNF_W0_1) )],[refute_1_70,refute_1_72]) ).
cnf(refute_1_74,plain,
( ~ aElementOf0(W1,xT)
| definitionFOFtoCNF_1
| sdtlseqdt0(W1,skolemFOFtoCNF_W0_1) ),
inference(canonicalize,[],[normalize_1_49]) ).
cnf(refute_1_75,plain,
( ~ aElementOf0(skolemFOFtoCNF_W1_5(skolemFOFtoCNF_W0_1),xT)
| definitionFOFtoCNF_1
| sdtlseqdt0(skolemFOFtoCNF_W1_5(skolemFOFtoCNF_W0_1),skolemFOFtoCNF_W0_1) ),
inference(subst,[],[refute_1_74:[bind(W1,$fot(skolemFOFtoCNF_W1_5(skolemFOFtoCNF_W0_1)))]]) ).
cnf(refute_1_76,plain,
( ~ aElementOf0(W0,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
| aElementOf0(W0,xP)
| aElementOf0(skolemFOFtoCNF_W1_5(W0),xT) ),
inference(canonicalize,[],[normalize_1_50]) ).
cnf(refute_1_77,plain,
( ~ aElementOf0(skolemFOFtoCNF_W0_1,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1),skolemFOFtoCNF_W0_1)
| aElementOf0(skolemFOFtoCNF_W0_1,xP)
| aElementOf0(skolemFOFtoCNF_W1_5(skolemFOFtoCNF_W0_1),xT) ),
inference(subst,[],[refute_1_76:[bind(W0,$fot(skolemFOFtoCNF_W0_1))]]) ).
cnf(refute_1_78,plain,
( ~ aElementOf0(skolemFOFtoCNF_W0_1,xU)
| aElementOf0(skolemFOFtoCNF_W0_1,xP)
| aElementOf0(skolemFOFtoCNF_W1_5(skolemFOFtoCNF_W0_1),xT)
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( sdtlseqdt0(sdtlpdtrp0(xf,skolemFOFtoCNF_W0_1),skolemFOFtoCNF_W0_1) )],[refute_1_70,refute_1_77]) ).
cnf(refute_1_79,plain,
( aElementOf0(skolemFOFtoCNF_W0_1,xP)
| aElementOf0(skolemFOFtoCNF_W1_5(skolemFOFtoCNF_W0_1),xT)
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W0_1,xU) )],[refute_1_45,refute_1_78]) ).
cnf(refute_1_80,plain,
( aElementOf0(skolemFOFtoCNF_W0_1,xP)
| definitionFOFtoCNF_1
| sdtlseqdt0(skolemFOFtoCNF_W1_5(skolemFOFtoCNF_W0_1),skolemFOFtoCNF_W0_1) ),
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W1_5(skolemFOFtoCNF_W0_1),xT) )],[refute_1_79,refute_1_75]) ).
cnf(refute_1_81,plain,
( ~ aElementOf0(skolemFOFtoCNF_W0_1,xU)
| aElementOf0(skolemFOFtoCNF_W0_1,xP)
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( sdtlseqdt0(skolemFOFtoCNF_W1_5(skolemFOFtoCNF_W0_1),skolemFOFtoCNF_W0_1) )],[refute_1_80,refute_1_73]) ).
cnf(refute_1_82,plain,
( aElementOf0(skolemFOFtoCNF_W0_1,xP)
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W0_1,xU) )],[refute_1_45,refute_1_81]) ).
cnf(refute_1_83,plain,
( definitionFOFtoCNF_1
| sdtlseqdt0(xp,skolemFOFtoCNF_W0_1) ),
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W0_1,xP) )],[refute_1_82,refute_1_38]) ).
cnf(refute_1_84,plain,
definitionFOFtoCNF_1,
inference(resolve,[$cnf( sdtlseqdt0(xp,skolemFOFtoCNF_W0_1) )],[refute_1_83,refute_1_36]) ).
cnf(refute_1_85,plain,
aElementOf0(skolemFOFtoCNF_W0,xT),
inference(resolve,[$cnf( definitionFOFtoCNF_1 )],[refute_1_84,refute_1_35]) ).
cnf(refute_1_86,plain,
sdtlseqdt0(skolemFOFtoCNF_W0,xp),
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W0,xT) )],[refute_1_85,refute_1_34]) ).
cnf(refute_1_87,plain,
~ definitionFOFtoCNF_1,
inference(resolve,[$cnf( sdtlseqdt0(skolemFOFtoCNF_W0,xp) )],[refute_1_86,refute_1_0]) ).
cnf(refute_1_88,plain,
$false,
inference(resolve,[$cnf( definitionFOFtoCNF_1 )],[refute_1_84,refute_1_87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT387+4 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Wed Jun 29 11:48:14 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 7.98/8.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.98/8.14
% 7.98/8.14 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.98/8.15
%------------------------------------------------------------------------------