TSTP Solution File: NUM535+2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM535+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 : Mon Jul 18 12:27:31 EDT 2022
% Result : Theorem 1.32s 1.51s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 23
% Syntax : Number of formulae : 133 ( 40 unt; 3 def)
% Number of atoms : 620 ( 159 equ)
% Maximal formula atoms : 54 ( 4 avg)
% Number of connectives : 798 ( 311 ~; 294 |; 124 &)
% ( 45 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 151 ( 1 sgn 91 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEOfElem,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ) ).
fof(mDefCons,definition,
! [W0,W1] :
( ( aSet0(W0)
& aElement0(W1) )
=> ! [W2] :
( W2 = sdtpldt0(W0,W1)
<=> ( aSet0(W2)
& ! [W3] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& ( aElementOf0(W3,W0)
| W3 = W1 ) ) ) ) ) ) ).
fof(mDefDiff,definition,
! [W0,W1] :
( ( aSet0(W0)
& aElement0(W1) )
=> ! [W2] :
( W2 = sdtmndt0(W0,W1)
<=> ( aSet0(W2)
& ! [W3] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& W3 != W1 ) ) ) ) ) ).
fof(m__617,hypothesis,
aSet0(xS) ).
fof(m__617_02,hypothesis,
aElementOf0(xx,xS) ).
fof(m__,conjecture,
( ( ( aSet0(sdtmndt0(xS,xx))
& ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( aElement0(W0)
& aElementOf0(W0,xS)
& W0 != xx ) ) )
=> ( ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( aElement0(W0)
& ( aElementOf0(W0,sdtmndt0(xS,xx))
| W0 = xx ) ) ) )
=> ( ! [W0] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) )
& ( ( aSet0(sdtmndt0(xS,xx))
& ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( aElement0(W0)
& aElementOf0(W0,xS)
& W0 != xx ) ) )
=> ( ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( aElement0(W0)
& ( aElementOf0(W0,sdtmndt0(xS,xx))
| W0 = xx ) ) ) )
=> ( ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
=> aElementOf0(W0,xS) )
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) ) ) ) ) ).
fof(definition_0,definition,
! [W0] :
( definitionFOFtoCNF_0(W0)
<=> ( ~ aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| W0 = xx ) ) ) ).
fof(subgoal_0,plain,
( ( aSet0(sdtmndt0(xS,xx))
& ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( aElement0(W0)
& aElementOf0(W0,xS)
& W0 != xx ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( aElement0(W0)
& ( aElementOf0(W0,sdtmndt0(xS,xx))
| W0 = xx ) ) )
& ~ ! [W0] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
=> aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(strip,[],[m__]) ).
fof(subgoal_1,plain,
( ( ( ( aSet0(sdtmndt0(xS,xx))
& ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( aElement0(W0)
& aElementOf0(W0,xS)
& W0 != xx ) ) )
=> ( ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( aElement0(W0)
& ( aElementOf0(W0,sdtmndt0(xS,xx))
| W0 = xx ) ) ) )
=> ( ! [W0] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) )
& aSet0(sdtmndt0(xS,xx))
& ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( aElement0(W0)
& aElementOf0(W0,xS)
& W0 != xx ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( aElement0(W0)
& ( aElementOf0(W0,sdtmndt0(xS,xx))
| W0 = xx ) ) )
& ~ ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
=> aElementOf0(W0,xS) ) )
=> aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ( ( aSet0(sdtmndt0(xS,xx))
& ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( aElement0(W0)
& aElementOf0(W0,xS)
& W0 != xx ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( aElement0(W0)
& ( aElementOf0(W0,sdtmndt0(xS,xx))
| W0 = xx ) ) )
& ~ ! [W0] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
=> aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& aSet0(sdtmndt0(xS,xx))
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ? [W0] :
( ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(W0,xS) )
& ! [W0] :
( ~ aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| W0 = xx ) )
& ! [W0] :
( ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ~ aElement0(W0)
| ( W0 != xx
& ~ aElementOf0(W0,sdtmndt0(xS,xx)) ) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
? [W0] :
( ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(W0,xS) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ aElementOf0(skolemFOFtoCNF_W0,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(skolemFOFtoCNF_W0,xS) ),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ aElementOf0(skolemFOFtoCNF_W0,sdtpldt0(sdtmndt0(xS,xx),xx)),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [W0] :
( ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ~ aElement0(W0)
| ( W0 != xx
& ~ aElementOf0(W0,sdtmndt0(xS,xx)) ) ) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_5,plain,
! [W0] :
( ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ~ aElement0(W0)
| ( W0 != xx
& ~ aElementOf0(W0,sdtmndt0(xS,xx)) ) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [W0] :
( ( ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(W0) )
& ( W0 != xx
| ~ aElement0(W0)
| aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( ~ aElement0(W0)
| ~ aElementOf0(W0,sdtmndt0(xS,xx))
| aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
| W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [W0] :
( ~ aElement0(W0)
| ~ aElementOf0(W0,sdtmndt0(xS,xx))
| aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
aElementOf0(skolemFOFtoCNF_W0,xS),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_9,plain,
! [W0] :
( ~ aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| W0 = xx ) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_10,plain,
! [W0] :
( ~ aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| W0 = xx ) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [W0] :
( ( W0 != xx
| ~ aElementOf0(W0,sdtmndt0(xS,xx)) )
& ( ~ aElementOf0(W0,sdtmndt0(xS,xx))
| aElement0(W0) )
& ( ~ aElementOf0(W0,sdtmndt0(xS,xx))
| aElementOf0(W0,xS) )
& ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) ) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [W0] :
( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [W0] :
( ~ aSet0(W0)
| ! [W1] :
( ~ aElementOf0(W1,W0)
| aElement0(W1) ) ),
inference(canonicalize,[],[mEOfElem]) ).
fof(normalize_0_14,plain,
! [W0] :
( ~ aSet0(W0)
| ! [W1] :
( ~ aElementOf0(W1,W0)
| aElement0(W1) ) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [W0,W1] :
( ~ aElementOf0(W1,W0)
| ~ aSet0(W0)
| aElement0(W1) ),
inference(clausify,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
aSet0(xS),
inference(canonicalize,[],[m__617]) ).
fof(normalize_0_17,plain,
! [W0,W1] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2] :
( W2 != sdtmndt0(W0,W1)
<=> ( ~ aSet0(W2)
| ? [W3] :
( ~ aElementOf0(W3,W2)
<=> ( W3 != W1
& aElement0(W3)
& aElementOf0(W3,W0) ) ) ) ) ),
inference(canonicalize,[],[mDefDiff]) ).
fof(normalize_0_18,plain,
! [W0,W1] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2] :
( W2 != sdtmndt0(W0,W1)
<=> ( ~ aSet0(W2)
| ? [W3] :
( ~ aElementOf0(W3,W2)
<=> ( W3 != W1
& aElement0(W3)
& aElementOf0(W3,W0) ) ) ) ) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [W0,W1,W2,W3] :
( ( W2 != sdtmndt0(W0,W1)
| ~ aElement0(W1)
| ~ aSet0(W0)
| aSet0(W2) )
& ( W2 != sdtmndt0(W0,W1)
| W3 != W1
| ~ aElement0(W1)
| ~ aElementOf0(W3,W2)
| ~ aSet0(W0) )
& ( W2 != sdtmndt0(W0,W1)
| ~ aElement0(W1)
| ~ aElementOf0(W3,W2)
| ~ aSet0(W0)
| aElement0(W3) )
& ( W2 != sdtmndt0(W0,W1)
| ~ aElement0(W1)
| ~ aElementOf0(W3,W2)
| ~ aSet0(W0)
| aElementOf0(W3,W0) )
& ( skolemFOFtoCNF_W3_1(W0,W1,W2) != W1
| ~ aElement0(W1)
| ~ aSet0(W0)
| ~ aSet0(W2)
| W2 = sdtmndt0(W0,W1)
| aElementOf0(skolemFOFtoCNF_W3_1(W0,W1,W2),W2) )
& ( ~ aElement0(W1)
| ~ aSet0(W0)
| ~ aSet0(W2)
| W2 = sdtmndt0(W0,W1)
| aElement0(skolemFOFtoCNF_W3_1(W0,W1,W2))
| aElementOf0(skolemFOFtoCNF_W3_1(W0,W1,W2),W2) )
& ( ~ aElement0(W1)
| ~ aSet0(W0)
| ~ aSet0(W2)
| W2 = sdtmndt0(W0,W1)
| aElementOf0(skolemFOFtoCNF_W3_1(W0,W1,W2),W0)
| aElementOf0(skolemFOFtoCNF_W3_1(W0,W1,W2),W2) )
& ( W2 != sdtmndt0(W0,W1)
| ~ aElement0(W1)
| ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ~ aSet0(W0)
| W3 = W1
| aElementOf0(W3,W2) )
& ( ~ aElement0(W1)
| ~ aElement0(skolemFOFtoCNF_W3_1(W0,W1,W2))
| ~ aElementOf0(skolemFOFtoCNF_W3_1(W0,W1,W2),W0)
| ~ aElementOf0(skolemFOFtoCNF_W3_1(W0,W1,W2),W2)
| ~ aSet0(W0)
| ~ aSet0(W2)
| W2 = sdtmndt0(W0,W1)
| skolemFOFtoCNF_W3_1(W0,W1,W2) = W1 ) ),
inference(clausify,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [W0,W1,W2] :
( W2 != sdtmndt0(W0,W1)
| ~ aElement0(W1)
| ~ aSet0(W0)
| aSet0(W2) ),
inference(conjunct,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [W0,W1] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2] :
( W2 != sdtpldt0(W0,W1)
<=> ( ~ aSet0(W2)
| ? [W3] :
( ~ aElementOf0(W3,W2)
<=> ( aElement0(W3)
& ( W3 = W1
| aElementOf0(W3,W0) ) ) ) ) ) ),
inference(canonicalize,[],[mDefCons]) ).
fof(normalize_0_22,plain,
! [W0,W1] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2] :
( W2 != sdtpldt0(W0,W1)
<=> ( ~ aSet0(W2)
| ? [W3] :
( ~ aElementOf0(W3,W2)
<=> ( aElement0(W3)
& ( W3 = W1
| aElementOf0(W3,W0) ) ) ) ) ) ),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [W0,W1,W2,W3] :
( ( W2 != sdtpldt0(W0,W1)
| ~ aElement0(W1)
| ~ aSet0(W0)
| aSet0(W2) )
& ( W2 != sdtpldt0(W0,W1)
| ~ aElement0(W1)
| ~ aElementOf0(W3,W2)
| ~ aSet0(W0)
| aElement0(W3) )
& ( W2 != sdtpldt0(W0,W1)
| W3 != W1
| ~ aElement0(W1)
| ~ aElement0(W3)
| ~ aSet0(W0)
| aElementOf0(W3,W2) )
& ( W2 != sdtpldt0(W0,W1)
| ~ aElement0(W1)
| ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ~ aSet0(W0)
| aElementOf0(W3,W2) )
& ( W2 != sdtpldt0(W0,W1)
| ~ aElement0(W1)
| ~ aElementOf0(W3,W2)
| ~ aSet0(W0)
| W3 = W1
| aElementOf0(W3,W0) )
& ( ~ aElement0(W1)
| ~ aSet0(W0)
| ~ aSet0(W2)
| W2 = sdtpldt0(W0,W1)
| aElement0(skolemFOFtoCNF_W3(W0,W1,W2))
| aElementOf0(skolemFOFtoCNF_W3(W0,W1,W2),W2) )
& ( skolemFOFtoCNF_W3(W0,W1,W2) != W1
| ~ aElement0(W1)
| ~ aElement0(skolemFOFtoCNF_W3(W0,W1,W2))
| ~ aElementOf0(skolemFOFtoCNF_W3(W0,W1,W2),W2)
| ~ aSet0(W0)
| ~ aSet0(W2)
| W2 = sdtpldt0(W0,W1) )
& ( ~ aElement0(W1)
| ~ aElement0(skolemFOFtoCNF_W3(W0,W1,W2))
| ~ aElementOf0(skolemFOFtoCNF_W3(W0,W1,W2),W0)
| ~ aElementOf0(skolemFOFtoCNF_W3(W0,W1,W2),W2)
| ~ aSet0(W0)
| ~ aSet0(W2)
| W2 = sdtpldt0(W0,W1) )
& ( ~ aElement0(W1)
| ~ aSet0(W0)
| ~ aSet0(W2)
| W2 = sdtpldt0(W0,W1)
| skolemFOFtoCNF_W3(W0,W1,W2) = W1
| aElementOf0(skolemFOFtoCNF_W3(W0,W1,W2),W0)
| aElementOf0(skolemFOFtoCNF_W3(W0,W1,W2),W2) ) ),
inference(clausify,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [W0,W1,W2,W3] :
( W2 != sdtpldt0(W0,W1)
| W3 != W1
| ~ aElement0(W1)
| ~ aElement0(W3)
| ~ aSet0(W0)
| aElementOf0(W3,W2) ),
inference(conjunct,[],[normalize_0_23]) ).
cnf(refute_0_0,plain,
~ aElementOf0(skolemFOFtoCNF_W0,sdtpldt0(sdtmndt0(xS,xx),xx)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ aElement0(W0)
| ~ aElementOf0(W0,sdtmndt0(xS,xx))
| aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_2,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| ~ aElementOf0(skolemFOFtoCNF_W0,sdtmndt0(xS,xx))
| aElementOf0(skolemFOFtoCNF_W0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(subst,[],[refute_0_1:[bind(W0,$fot(skolemFOFtoCNF_W0))]]) ).
cnf(refute_0_3,plain,
aElementOf0(skolemFOFtoCNF_W0,xS),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_4,plain,
( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_5,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| ~ aElementOf0(skolemFOFtoCNF_W0,xS)
| skolemFOFtoCNF_W0 = xx
| aElementOf0(skolemFOFtoCNF_W0,sdtmndt0(xS,xx)) ),
inference(subst,[],[refute_0_4:[bind(W0,$fot(skolemFOFtoCNF_W0))]]) ).
cnf(refute_0_6,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| skolemFOFtoCNF_W0 = xx
| aElementOf0(skolemFOFtoCNF_W0,sdtmndt0(xS,xx)) ),
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W0,xS) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ aElementOf0(W1,W0)
| ~ aSet0(W0)
| aElement0(W1) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_8,plain,
( ~ aElementOf0(skolemFOFtoCNF_W0,xS)
| ~ aSet0(xS)
| aElement0(skolemFOFtoCNF_W0) ),
inference(subst,[],[refute_0_7:[bind(W0,$fot(xS)),bind(W1,$fot(skolemFOFtoCNF_W0))]]) ).
cnf(refute_0_9,plain,
( ~ aSet0(xS)
| aElement0(skolemFOFtoCNF_W0) ),
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W0,xS) )],[refute_0_3,refute_0_8]) ).
cnf(refute_0_10,plain,
aSet0(xS),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_11,plain,
aElement0(skolemFOFtoCNF_W0),
inference(resolve,[$cnf( aSet0(xS) )],[refute_0_10,refute_0_9]) ).
cnf(refute_0_12,plain,
( skolemFOFtoCNF_W0 = xx
| aElementOf0(skolemFOFtoCNF_W0,sdtmndt0(xS,xx)) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W0) )],[refute_0_11,refute_0_6]) ).
cnf(refute_0_13,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| skolemFOFtoCNF_W0 = xx
| aElementOf0(skolemFOFtoCNF_W0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W0,sdtmndt0(xS,xx)) )],[refute_0_12,refute_0_2]) ).
cnf(refute_0_14,plain,
( skolemFOFtoCNF_W0 = xx
| aElementOf0(skolemFOFtoCNF_W0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W0) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
skolemFOFtoCNF_W0 = xx,
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )],[refute_0_14,refute_0_0]) ).
cnf(refute_0_16,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_17,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_18,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( skolemFOFtoCNF_W0 != xx
| xx = skolemFOFtoCNF_W0 ),
inference(subst,[],[refute_0_18:[bind(X,$fot(skolemFOFtoCNF_W0)),bind(Y,$fot(xx))]]) ).
cnf(refute_0_20,plain,
xx = skolemFOFtoCNF_W0,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W0,xx) )],[refute_0_15,refute_0_19]) ).
cnf(refute_0_21,plain,
sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),xx) = sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),xx),
introduced(tautology,[refl,[$fot(sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),xx))]]) ).
cnf(refute_0_22,plain,
( sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),xx) != sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),xx)
| xx != skolemFOFtoCNF_W0
| sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),xx) = sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0) ),
introduced(tautology,[equality,[$cnf( $equal(sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),xx),sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),xx)) ),[1,1],$fot(skolemFOFtoCNF_W0)]]) ).
cnf(refute_0_23,plain,
( xx != skolemFOFtoCNF_W0
| sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),xx) = sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0) ),
inference(resolve,[$cnf( $equal(sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),xx),sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),xx)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),xx) = sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0),
inference(resolve,[$cnf( $equal(xx,skolemFOFtoCNF_W0) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
sdtmndt0(xS,xx) = sdtmndt0(xS,xx),
introduced(tautology,[refl,[$fot(sdtmndt0(xS,xx))]]) ).
cnf(refute_0_26,plain,
( sdtmndt0(xS,xx) != sdtmndt0(xS,xx)
| xx != skolemFOFtoCNF_W0
| sdtmndt0(xS,xx) = sdtmndt0(xS,skolemFOFtoCNF_W0) ),
introduced(tautology,[equality,[$cnf( $equal(sdtmndt0(xS,xx),sdtmndt0(xS,xx)) ),[1,1],$fot(skolemFOFtoCNF_W0)]]) ).
cnf(refute_0_27,plain,
( xx != skolemFOFtoCNF_W0
| sdtmndt0(xS,xx) = sdtmndt0(xS,skolemFOFtoCNF_W0) ),
inference(resolve,[$cnf( $equal(sdtmndt0(xS,xx),sdtmndt0(xS,xx)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
sdtmndt0(xS,xx) = sdtmndt0(xS,skolemFOFtoCNF_W0),
inference(resolve,[$cnf( $equal(xx,skolemFOFtoCNF_W0) )],[refute_0_20,refute_0_27]) ).
cnf(refute_0_29,plain,
sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(sdtmndt0(xS,xx),xx),
introduced(tautology,[refl,[$fot(sdtpldt0(sdtmndt0(xS,xx),xx))]]) ).
cnf(refute_0_30,plain,
( sdtmndt0(xS,xx) != sdtmndt0(xS,skolemFOFtoCNF_W0)
| sdtpldt0(sdtmndt0(xS,xx),xx) != sdtpldt0(sdtmndt0(xS,xx),xx)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),xx) ),
introduced(tautology,[equality,[$cnf( $equal(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtmndt0(xS,xx),xx)) ),[1,0],$fot(sdtmndt0(xS,skolemFOFtoCNF_W0))]]) ).
cnf(refute_0_31,plain,
( sdtmndt0(xS,xx) != sdtmndt0(xS,skolemFOFtoCNF_W0)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),xx) ),
inference(resolve,[$cnf( $equal(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtmndt0(xS,xx),xx)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),xx),
inference(resolve,[$cnf( $equal(sdtmndt0(xS,xx),sdtmndt0(xS,skolemFOFtoCNF_W0)) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_34,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_18,refute_0_33]) ).
cnf(refute_0_35,plain,
( sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),xx) != sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0)
| sdtpldt0(sdtmndt0(xS,xx),xx) != sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),xx)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0) ),
inference(subst,[],[refute_0_34:[bind(X,$fot(sdtpldt0(sdtmndt0(xS,xx),xx))),bind(Y,$fot(sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),xx))),bind(Z,$fot(sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0)))]]) ).
cnf(refute_0_36,plain,
( sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),xx) != sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0) ),
inference(resolve,[$cnf( $equal(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),xx)) )],[refute_0_32,refute_0_35]) ).
cnf(refute_0_37,plain,
sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0),
inference(resolve,[$cnf( $equal(sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),xx),sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0)) )],[refute_0_24,refute_0_36]) ).
cnf(refute_0_38,plain,
( sdtpldt0(sdtmndt0(xS,xx),xx) != sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0)
| ~ aElementOf0(skolemFOFtoCNF_W0,sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0))
| aElementOf0(skolemFOFtoCNF_W0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
introduced(tautology,[equality,[$cnf( ~ aElementOf0(skolemFOFtoCNF_W0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),[1],$fot(sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0))]]) ).
cnf(refute_0_39,plain,
( ~ aElementOf0(skolemFOFtoCNF_W0,sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0))
| aElementOf0(skolemFOFtoCNF_W0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolve,[$cnf( $equal(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
~ aElementOf0(skolemFOFtoCNF_W0,sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0)),
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )],[refute_0_39,refute_0_0]) ).
cnf(refute_0_41,plain,
( W2 != sdtmndt0(W0,W1)
| ~ aElement0(W1)
| ~ aSet0(W0)
| aSet0(W2) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_42,plain,
( sdtmndt0(W0,W1) != sdtmndt0(W0,W1)
| ~ aElement0(W1)
| ~ aSet0(W0)
| aSet0(sdtmndt0(W0,W1)) ),
inference(subst,[],[refute_0_41:[bind(W2,$fot(sdtmndt0(W0,W1)))]]) ).
cnf(refute_0_43,plain,
sdtmndt0(W0,W1) = sdtmndt0(W0,W1),
introduced(tautology,[refl,[$fot(sdtmndt0(W0,W1))]]) ).
cnf(refute_0_44,plain,
( ~ aElement0(W1)
| ~ aSet0(W0)
| aSet0(sdtmndt0(W0,W1)) ),
inference(resolve,[$cnf( $equal(sdtmndt0(W0,W1),sdtmndt0(W0,W1)) )],[refute_0_43,refute_0_42]) ).
cnf(refute_0_45,plain,
( ~ aElement0(X_22)
| ~ aSet0(xS)
| aSet0(sdtmndt0(xS,X_22)) ),
inference(subst,[],[refute_0_44:[bind(W0,$fot(xS)),bind(W1,$fot(X_22))]]) ).
cnf(refute_0_46,plain,
( ~ aElement0(X_22)
| aSet0(sdtmndt0(xS,X_22)) ),
inference(resolve,[$cnf( aSet0(xS) )],[refute_0_10,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| aSet0(sdtmndt0(xS,skolemFOFtoCNF_W0)) ),
inference(subst,[],[refute_0_46:[bind(X_22,$fot(skolemFOFtoCNF_W0))]]) ).
cnf(refute_0_48,plain,
aSet0(sdtmndt0(xS,skolemFOFtoCNF_W0)),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W0) )],[refute_0_11,refute_0_47]) ).
cnf(refute_0_49,plain,
( W2 != sdtpldt0(W0,W1)
| W3 != W1
| ~ aElement0(W1)
| ~ aElement0(W3)
| ~ aSet0(W0)
| aElementOf0(W3,W2) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_50,plain,
( W1 != W1
| sdtpldt0(W0,W1) != sdtpldt0(W0,W1)
| ~ aElement0(W1)
| ~ aSet0(W0)
| aElementOf0(W1,sdtpldt0(W0,W1)) ),
inference(subst,[],[refute_0_49:[bind(W2,$fot(sdtpldt0(W0,W1))),bind(W3,$fot(W1))]]) ).
cnf(refute_0_51,plain,
W1 = W1,
introduced(tautology,[refl,[$fot(W1)]]) ).
cnf(refute_0_52,plain,
( sdtpldt0(W0,W1) != sdtpldt0(W0,W1)
| ~ aElement0(W1)
| ~ aSet0(W0)
| aElementOf0(W1,sdtpldt0(W0,W1)) ),
inference(resolve,[$cnf( $equal(W1,W1) )],[refute_0_51,refute_0_50]) ).
cnf(refute_0_53,plain,
sdtpldt0(W0,W1) = sdtpldt0(W0,W1),
introduced(tautology,[refl,[$fot(sdtpldt0(W0,W1))]]) ).
cnf(refute_0_54,plain,
( ~ aElement0(W1)
| ~ aSet0(W0)
| aElementOf0(W1,sdtpldt0(W0,W1)) ),
inference(resolve,[$cnf( $equal(sdtpldt0(W0,W1),sdtpldt0(W0,W1)) )],[refute_0_53,refute_0_52]) ).
cnf(refute_0_55,plain,
( ~ aElement0(X_48)
| ~ aSet0(sdtmndt0(xS,skolemFOFtoCNF_W0))
| aElementOf0(X_48,sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),X_48)) ),
inference(subst,[],[refute_0_54:[bind(W0,$fot(sdtmndt0(xS,skolemFOFtoCNF_W0))),bind(W1,$fot(X_48))]]) ).
cnf(refute_0_56,plain,
( ~ aElement0(X_48)
| aElementOf0(X_48,sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),X_48)) ),
inference(resolve,[$cnf( aSet0(sdtmndt0(xS,skolemFOFtoCNF_W0)) )],[refute_0_48,refute_0_55]) ).
cnf(refute_0_57,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| aElementOf0(skolemFOFtoCNF_W0,sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0)) ),
inference(subst,[],[refute_0_56:[bind(X_48,$fot(skolemFOFtoCNF_W0))]]) ).
cnf(refute_0_58,plain,
aElementOf0(skolemFOFtoCNF_W0,sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0)),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W0) )],[refute_0_11,refute_0_57]) ).
cnf(refute_0_59,plain,
$false,
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W0,sdtpldt0(sdtmndt0(xS,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0)) )],[refute_0_58,refute_0_40]) ).
fof(negate_1_0,plain,
~ ( ( ( ( aSet0(sdtmndt0(xS,xx))
& ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( aElement0(W0)
& aElementOf0(W0,xS)
& W0 != xx ) ) )
=> ( ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( aElement0(W0)
& ( aElementOf0(W0,sdtmndt0(xS,xx))
| W0 = xx ) ) ) )
=> ( ! [W0] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) )
& aSet0(sdtmndt0(xS,xx))
& ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( aElement0(W0)
& aElementOf0(W0,xS)
& W0 != xx ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( aElement0(W0)
& ( aElementOf0(W0,sdtmndt0(xS,xx))
| W0 = xx ) ) )
& ~ ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
=> aElementOf0(W0,xS) ) )
=> aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
aElementOf0(xx,xS),
inference(canonicalize,[],[m__617_02]) ).
fof(normalize_1_1,plain,
! [W0] :
( ~ aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( ~ definitionFOFtoCNF_0(W0)
<=> ( W0 != xx
& aElement0(W0)
& aElementOf0(W0,xS) ) ) ),
inference(canonicalize,[],[definition_0]) ).
fof(normalize_1_2,plain,
! [W0] :
( ( W0 != xx
| ~ aElementOf0(W0,sdtmndt0(xS,xx))
| ~ definitionFOFtoCNF_0(W0) )
& ( W0 != xx
| aElementOf0(W0,sdtmndt0(xS,xx))
| definitionFOFtoCNF_0(W0) )
& ( ~ aElementOf0(W0,sdtmndt0(xS,xx))
| ~ definitionFOFtoCNF_0(W0)
| aElement0(W0) )
& ( ~ aElementOf0(W0,sdtmndt0(xS,xx))
| ~ definitionFOFtoCNF_0(W0)
| aElementOf0(W0,xS) )
& ( aElement0(W0)
| aElementOf0(W0,sdtmndt0(xS,xx))
| definitionFOFtoCNF_0(W0) )
& ( aElementOf0(W0,sdtmndt0(xS,xx))
| aElementOf0(W0,xS)
| definitionFOFtoCNF_0(W0) )
& ( ~ aElement0(W0)
| ~ aElementOf0(W0,sdtmndt0(xS,xx))
| ~ aElementOf0(W0,xS)
| W0 = xx
| definitionFOFtoCNF_0(W0) )
& ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| ~ definitionFOFtoCNF_0(W0)
| W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) ) ),
inference(clausify,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [W0] :
( ~ aElementOf0(W0,sdtmndt0(xS,xx))
| ~ definitionFOFtoCNF_0(W0)
| aElementOf0(W0,xS) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
( ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& aSet0(sdtmndt0(xS,xx))
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ( ~ aSet0(sdtmndt0(xS,xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ? [W0] :
( ~ aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( W0 != xx
& aElement0(W0)
& aElementOf0(W0,xS) ) )
| ? [W0] :
( ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( aElement0(W0)
& ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) ) ) )
| ! [W0] :
( ~ aElementOf0(W0,xS)
| aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
& ? [W0] :
( ~ aElementOf0(W0,xS)
& aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ! [W0] :
( ~ aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| W0 = xx ) )
& ! [W0] :
( ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ~ aElement0(W0)
| ( W0 != xx
& ~ aElementOf0(W0,sdtmndt0(xS,xx)) ) ) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_5,plain,
! [W0] :
( ~ aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| W0 = xx ) ),
inference(conjunct,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [W0] : definitionFOFtoCNF_0(W0),
inference(simplify,[],[normalize_1_5,normalize_1_1]) ).
fof(normalize_1_7,plain,
! [W0] : definitionFOFtoCNF_0(W0),
inference(specialize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
? [W0] :
( ~ aElementOf0(W0,xS)
& aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(conjunct,[],[normalize_1_4]) ).
fof(normalize_1_9,plain,
( ~ aElementOf0(skolemFOFtoCNF_W0_3,xS)
& aElementOf0(skolemFOFtoCNF_W0_3,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(skolemize,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
aElementOf0(skolemFOFtoCNF_W0_3,sdtpldt0(sdtmndt0(xS,xx),xx)),
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [W0] :
( ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ~ aElement0(W0)
| ( W0 != xx
& ~ aElementOf0(W0,sdtmndt0(xS,xx)) ) ) ),
inference(conjunct,[],[normalize_1_4]) ).
fof(normalize_1_12,plain,
! [W0] :
( ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ~ aElement0(W0)
| ( W0 != xx
& ~ aElementOf0(W0,sdtmndt0(xS,xx)) ) ) ),
inference(specialize,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
! [W0] :
( ( ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(W0) )
& ( W0 != xx
| ~ aElement0(W0)
| aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( ~ aElement0(W0)
| ~ aElementOf0(W0,sdtmndt0(xS,xx))
| aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
| W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) ) ),
inference(clausify,[],[normalize_1_12]) ).
fof(normalize_1_14,plain,
! [W0] :
( ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
| W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) ),
inference(conjunct,[],[normalize_1_13]) ).
fof(normalize_1_15,plain,
~ aElementOf0(skolemFOFtoCNF_W0_3,xS),
inference(conjunct,[],[normalize_1_9]) ).
cnf(refute_1_0,plain,
aElementOf0(xx,xS),
inference(canonicalize,[],[normalize_1_0]) ).
cnf(refute_1_1,plain,
( ~ aElementOf0(W0,sdtmndt0(xS,xx))
| ~ definitionFOFtoCNF_0(W0)
| aElementOf0(W0,xS) ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_2,plain,
definitionFOFtoCNF_0(W0),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_3,plain,
( ~ aElementOf0(W0,sdtmndt0(xS,xx))
| aElementOf0(W0,xS) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(W0) )],[refute_1_2,refute_1_1]) ).
cnf(refute_1_4,plain,
( ~ aElementOf0(skolemFOFtoCNF_W0_3,sdtmndt0(xS,xx))
| aElementOf0(skolemFOFtoCNF_W0_3,xS) ),
inference(subst,[],[refute_1_3:[bind(W0,$fot(skolemFOFtoCNF_W0_3))]]) ).
cnf(refute_1_5,plain,
aElementOf0(skolemFOFtoCNF_W0_3,sdtpldt0(sdtmndt0(xS,xx),xx)),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_6,plain,
( ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
| W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) ),
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_7,plain,
( ~ aElementOf0(skolemFOFtoCNF_W0_3,sdtpldt0(sdtmndt0(xS,xx),xx))
| skolemFOFtoCNF_W0_3 = xx
| aElementOf0(skolemFOFtoCNF_W0_3,sdtmndt0(xS,xx)) ),
inference(subst,[],[refute_1_6:[bind(W0,$fot(skolemFOFtoCNF_W0_3))]]) ).
cnf(refute_1_8,plain,
( skolemFOFtoCNF_W0_3 = xx
| aElementOf0(skolemFOFtoCNF_W0_3,sdtmndt0(xS,xx)) ),
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W0_3,sdtpldt0(sdtmndt0(xS,xx),xx)) )],[refute_1_5,refute_1_7]) ).
cnf(refute_1_9,plain,
( skolemFOFtoCNF_W0_3 = xx
| aElementOf0(skolemFOFtoCNF_W0_3,xS) ),
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W0_3,sdtmndt0(xS,xx)) )],[refute_1_8,refute_1_4]) ).
cnf(refute_1_10,plain,
~ aElementOf0(skolemFOFtoCNF_W0_3,xS),
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_11,plain,
skolemFOFtoCNF_W0_3 = xx,
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W0_3,xS) )],[refute_1_9,refute_1_10]) ).
cnf(refute_1_12,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_13,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_14,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_12,refute_1_13]) ).
cnf(refute_1_15,plain,
( skolemFOFtoCNF_W0_3 != xx
| xx = skolemFOFtoCNF_W0_3 ),
inference(subst,[],[refute_1_14:[bind(X,$fot(skolemFOFtoCNF_W0_3)),bind(Y,$fot(xx))]]) ).
cnf(refute_1_16,plain,
xx = skolemFOFtoCNF_W0_3,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W0_3,xx) )],[refute_1_11,refute_1_15]) ).
cnf(refute_1_17,plain,
( xx != skolemFOFtoCNF_W0_3
| ~ aElementOf0(xx,xS)
| aElementOf0(skolemFOFtoCNF_W0_3,xS) ),
introduced(tautology,[equality,[$cnf( aElementOf0(xx,xS) ),[0],$fot(skolemFOFtoCNF_W0_3)]]) ).
cnf(refute_1_18,plain,
( ~ aElementOf0(xx,xS)
| aElementOf0(skolemFOFtoCNF_W0_3,xS) ),
inference(resolve,[$cnf( $equal(xx,skolemFOFtoCNF_W0_3) )],[refute_1_16,refute_1_17]) ).
cnf(refute_1_19,plain,
aElementOf0(skolemFOFtoCNF_W0_3,xS),
inference(resolve,[$cnf( aElementOf0(xx,xS) )],[refute_1_0,refute_1_18]) ).
cnf(refute_1_20,plain,
$false,
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W0_3,xS) )],[refute_1_19,refute_1_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : NUM535+2 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Wed Jul 6 19:29:29 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.32/1.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.32/1.51
% 1.32/1.51 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.32/1.52
%------------------------------------------------------------------------------