TSTP Solution File: LAT381+3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LAT381+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 06:03:38 EDT 2022
% Result : Theorem 0.19s 0.41s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 58 ( 24 unt; 0 def)
% Number of atoms : 180 ( 23 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 200 ( 78 ~; 72 |; 40 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 49 ( 0 sgn 32 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEOfElem,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ) ).
fof(mASymm,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> W0 = W1 ) ) ).
fof(m__725,hypothesis,
aSet0(xT) ).
fof(m__744,hypothesis,
( aElementOf0(xu,xT)
& aElementOf0(xu,xT)
& ! [W0] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(W0,xu) )
& aUpperBoundOfIn0(xu,xS,xT)
& ! [W0] :
( ( ( aElementOf0(W0,xT)
& ! [W1] :
( aElementOf0(W1,xS)
=> sdtlseqdt0(W1,W0) ) )
| aUpperBoundOfIn0(W0,xS,xT) )
=> sdtlseqdt0(xu,W0) )
& aSupremumOfIn0(xu,xS,xT)
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& ! [W0] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(W0,xv) )
& aUpperBoundOfIn0(xv,xS,xT)
& ! [W0] :
( ( ( aElementOf0(W0,xT)
& ! [W1] :
( aElementOf0(W1,xS)
=> sdtlseqdt0(W1,W0) ) )
| aUpperBoundOfIn0(W0,xS,xT) )
=> sdtlseqdt0(xv,W0) )
& aSupremumOfIn0(xv,xS,xT) ) ).
fof(m__,conjecture,
xu = xv ).
fof(subgoal_0,plain,
xu = xv,
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
xu != xv,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( aElementOf0(xu,xT)
& aElementOf0(xv,xT)
& aSupremumOfIn0(xu,xS,xT)
& aSupremumOfIn0(xv,xS,xT)
& aUpperBoundOfIn0(xu,xS,xT)
& aUpperBoundOfIn0(xv,xS,xT)
& ! [W0] :
( ~ aElementOf0(W0,xS)
| sdtlseqdt0(W0,xu) )
& ! [W0] :
( ~ aElementOf0(W0,xS)
| sdtlseqdt0(W0,xv) )
& ! [W0] :
( sdtlseqdt0(xu,W0)
| ( ~ aUpperBoundOfIn0(W0,xS,xT)
& ( ~ aElementOf0(W0,xT)
| ? [W1] :
( ~ sdtlseqdt0(W1,W0)
& aElementOf0(W1,xS) ) ) ) )
& ! [W0] :
( sdtlseqdt0(xv,W0)
| ( ~ aUpperBoundOfIn0(W0,xS,xT)
& ( ~ aElementOf0(W0,xT)
| ? [W1] :
( ~ sdtlseqdt0(W1,W0)
& aElementOf0(W1,xS) ) ) ) ) ),
inference(canonicalize,[],[m__744]) ).
fof(normalize_0_1,plain,
aUpperBoundOfIn0(xu,xS,xT),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [W0] :
( sdtlseqdt0(xv,W0)
| ( ~ aUpperBoundOfIn0(W0,xS,xT)
& ( ~ aElementOf0(W0,xT)
| ? [W1] :
( ~ sdtlseqdt0(W1,W0)
& aElementOf0(W1,xS) ) ) ) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_3,plain,
! [W0] :
( sdtlseqdt0(xv,W0)
| ( ~ aUpperBoundOfIn0(W0,xS,xT)
& ( ~ aElementOf0(W0,xT)
| ? [W1] :
( ~ sdtlseqdt0(W1,W0)
& aElementOf0(W1,xS) ) ) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [W0] :
( ( ~ aUpperBoundOfIn0(W0,xS,xT)
| sdtlseqdt0(xv,W0) )
& ( ~ aElementOf0(W0,xT)
| ~ sdtlseqdt0(skolemFOFtoCNF_W1_2(W0),W0)
| sdtlseqdt0(xv,W0) )
& ( ~ aElementOf0(W0,xT)
| aElementOf0(skolemFOFtoCNF_W1_2(W0),xS)
| sdtlseqdt0(xv,W0) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [W0] :
( ~ aUpperBoundOfIn0(W0,xS,xT)
| sdtlseqdt0(xv,W0) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [W0,W1] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| W0 = W1 ),
inference(canonicalize,[],[mASymm]) ).
fof(normalize_0_7,plain,
! [W0,W1] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| W0 = W1 ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
aElementOf0(xu,xT),
inference(conjunct,[],[normalize_0_0]) ).
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,
aSet0(xT),
inference(canonicalize,[],[m__725]) ).
fof(normalize_0_13,plain,
aElementOf0(xv,xT),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_14,plain,
aUpperBoundOfIn0(xv,xS,xT),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_15,plain,
! [W0] :
( sdtlseqdt0(xu,W0)
| ( ~ aUpperBoundOfIn0(W0,xS,xT)
& ( ~ aElementOf0(W0,xT)
| ? [W1] :
( ~ sdtlseqdt0(W1,W0)
& aElementOf0(W1,xS) ) ) ) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_16,plain,
! [W0] :
( sdtlseqdt0(xu,W0)
| ( ~ aUpperBoundOfIn0(W0,xS,xT)
& ( ~ aElementOf0(W0,xT)
| ? [W1] :
( ~ sdtlseqdt0(W1,W0)
& aElementOf0(W1,xS) ) ) ) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [W0] :
( ( ~ aUpperBoundOfIn0(W0,xS,xT)
| sdtlseqdt0(xu,W0) )
& ( ~ aElementOf0(W0,xT)
| ~ sdtlseqdt0(skolemFOFtoCNF_W1_1(W0),W0)
| sdtlseqdt0(xu,W0) )
& ( ~ aElementOf0(W0,xT)
| aElementOf0(skolemFOFtoCNF_W1_1(W0),xS)
| sdtlseqdt0(xu,W0) ) ),
inference(clausify,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [W0] :
( ~ aUpperBoundOfIn0(W0,xS,xT)
| sdtlseqdt0(xu,W0) ),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
xu != xv,
inference(canonicalize,[],[negate_0_0]) ).
cnf(refute_0_0,plain,
aUpperBoundOfIn0(xu,xS,xT),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ aUpperBoundOfIn0(W0,xS,xT)
| sdtlseqdt0(xv,W0) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( ~ aUpperBoundOfIn0(xu,xS,xT)
| sdtlseqdt0(xv,xu) ),
inference(subst,[],[refute_0_1:[bind(W0,$fot(xu))]]) ).
cnf(refute_0_3,plain,
sdtlseqdt0(xv,xu),
inference(resolve,[$cnf( aUpperBoundOfIn0(xu,xS,xT) )],[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_7]) ).
cnf(refute_0_5,plain,
( ~ aElement0(xu)
| ~ aElement0(xv)
| ~ sdtlseqdt0(xu,xv)
| ~ sdtlseqdt0(xv,xu)
| xv = xu ),
inference(subst,[],[refute_0_4:[bind(W0,$fot(xv)),bind(W1,$fot(xu))]]) ).
cnf(refute_0_6,plain,
( ~ aElement0(xu)
| ~ aElement0(xv)
| ~ sdtlseqdt0(xu,xv)
| xv = xu ),
inference(resolve,[$cnf( sdtlseqdt0(xv,xu) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
aElementOf0(xu,xT),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_8,plain,
( ~ aElementOf0(W1,W0)
| ~ aSet0(W0)
| aElement0(W1) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_9,plain,
( ~ aElementOf0(xu,xT)
| ~ aSet0(xT)
| aElement0(xu) ),
inference(subst,[],[refute_0_8:[bind(W0,$fot(xT)),bind(W1,$fot(xu))]]) ).
cnf(refute_0_10,plain,
( ~ aSet0(xT)
| aElement0(xu) ),
inference(resolve,[$cnf( aElementOf0(xu,xT) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
aSet0(xT),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_12,plain,
aElement0(xu),
inference(resolve,[$cnf( aSet0(xT) )],[refute_0_11,refute_0_10]) ).
cnf(refute_0_13,plain,
( ~ aElement0(xv)
| ~ sdtlseqdt0(xu,xv)
| xv = xu ),
inference(resolve,[$cnf( aElement0(xu) )],[refute_0_12,refute_0_6]) ).
cnf(refute_0_14,plain,
aElementOf0(xv,xT),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_15,plain,
( ~ aElementOf0(xv,xT)
| ~ aSet0(xT)
| aElement0(xv) ),
inference(subst,[],[refute_0_8:[bind(W0,$fot(xT)),bind(W1,$fot(xv))]]) ).
cnf(refute_0_16,plain,
( ~ aSet0(xT)
| aElement0(xv) ),
inference(resolve,[$cnf( aElementOf0(xv,xT) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
aElement0(xv),
inference(resolve,[$cnf( aSet0(xT) )],[refute_0_11,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ sdtlseqdt0(xu,xv)
| xv = xu ),
inference(resolve,[$cnf( aElement0(xv) )],[refute_0_17,refute_0_13]) ).
cnf(refute_0_19,plain,
aUpperBoundOfIn0(xv,xS,xT),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_20,plain,
( ~ aUpperBoundOfIn0(W0,xS,xT)
| sdtlseqdt0(xu,W0) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_21,plain,
( ~ aUpperBoundOfIn0(xv,xS,xT)
| sdtlseqdt0(xu,xv) ),
inference(subst,[],[refute_0_20:[bind(W0,$fot(xv))]]) ).
cnf(refute_0_22,plain,
sdtlseqdt0(xu,xv),
inference(resolve,[$cnf( aUpperBoundOfIn0(xv,xS,xT) )],[refute_0_19,refute_0_21]) ).
cnf(refute_0_23,plain,
xv = xu,
inference(resolve,[$cnf( sdtlseqdt0(xu,xv) )],[refute_0_22,refute_0_18]) ).
cnf(refute_0_24,plain,
xu != xv,
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_25,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_26,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_27,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( xv != xu
| xu = xv ),
inference(subst,[],[refute_0_27:[bind(X,$fot(xv)),bind(Y,$fot(xu))]]) ).
cnf(refute_0_29,plain,
xv != xu,
inference(resolve,[$cnf( $equal(xu,xv) )],[refute_0_28,refute_0_24]) ).
cnf(refute_0_30,plain,
$false,
inference(resolve,[$cnf( $equal(xv,xu) )],[refute_0_23,refute_0_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT381+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 28 18:20:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.41
% 0.19/0.41 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.42
%------------------------------------------------------------------------------