TSTP Solution File: RNG050+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : RNG050+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 20:35:52 EDT 2022
% Result : Theorem 1.83s 2.05s
% Output : CNFRefutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 38 ( 15 unt; 0 def)
% Number of atoms : 84 ( 39 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 86 ( 40 ~; 34 |; 3 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSZeroSc,axiom,
aScalar0(sz0z00) ).
fof(mLERef,axiom,
! [W0] :
( aScalar0(W0)
=> sdtlseqdt0(W0,W0) ) ).
fof(mDefSPZ,axiom,
! [W0,W1] :
( ( aVector0(W0)
& aVector0(W1) )
=> ( ( aDimensionOf0(W0) = aDimensionOf0(W1)
& aDimensionOf0(W1) = sz00 )
=> sdtasasdt0(W0,W1) = sz0z00 ) ) ).
fof(m__1542,hypothesis,
aVector0(xs) ).
fof(m__,conjecture,
( ( aDimensionOf0(xs) != sz00
=> sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) )
=> sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ) ).
fof(subgoal_0,plain,
( ( aDimensionOf0(xs) != sz00
=> sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) )
=> sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ( ( aDimensionOf0(xs) != sz00
=> sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) )
=> sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
& ( aDimensionOf0(xs) = sz00
| sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
aVector0(xs),
inference(canonicalize,[],[m__1542]) ).
fof(normalize_0_3,plain,
! [W0,W1] :
( aDimensionOf0(W0) != aDimensionOf0(W1)
| aDimensionOf0(W1) != sz00
| ~ aVector0(W0)
| ~ aVector0(W1)
| sdtasasdt0(W0,W1) = sz0z00 ),
inference(canonicalize,[],[mDefSPZ]) ).
fof(normalize_0_4,plain,
! [W0,W1] :
( aDimensionOf0(W0) != aDimensionOf0(W1)
| aDimensionOf0(W1) != sz00
| ~ aVector0(W0)
| ~ aVector0(W1)
| sdtasasdt0(W0,W1) = sz0z00 ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
( aDimensionOf0(xs) = sz00
| sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_6,plain,
aDimensionOf0(xs) = sz00,
inference(simplify,[],[normalize_0_5,normalize_0_1]) ).
fof(normalize_0_7,plain,
aScalar0(sz0z00),
inference(canonicalize,[],[mSZeroSc]) ).
fof(normalize_0_8,plain,
! [W0] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ),
inference(canonicalize,[],[mLERef]) ).
fof(normalize_0_9,plain,
! [W0] :
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ),
inference(specialize,[],[normalize_0_8]) ).
cnf(refute_0_0,plain,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
aVector0(xs),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_2,plain,
( aDimensionOf0(W0) != aDimensionOf0(W1)
| aDimensionOf0(W1) != sz00
| ~ aVector0(W0)
| ~ aVector0(W1)
| sdtasasdt0(W0,W1) = sz0z00 ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( aDimensionOf0(W0) != sz00
| aDimensionOf0(W1) != sz00
| aDimensionOf0(W0) = aDimensionOf0(W1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(aDimensionOf0(W0),aDimensionOf0(W1)) ),[1],$fot(sz00)]]) ).
cnf(refute_0_4,plain,
( aDimensionOf0(W0) != sz00
| aDimensionOf0(W1) != sz00
| ~ aVector0(W0)
| ~ aVector0(W1)
| sdtasasdt0(W0,W1) = sz0z00 ),
inference(resolve,[$cnf( $equal(aDimensionOf0(W0),aDimensionOf0(W1)) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
( aDimensionOf0(xs) != sz00
| ~ aVector0(xs)
| sdtasasdt0(xs,xs) = sz0z00 ),
inference(subst,[],[refute_0_4:[bind(W0,$fot(xs)),bind(W1,$fot(xs))]]) ).
cnf(refute_0_6,plain,
( aDimensionOf0(xs) != sz00
| sdtasasdt0(xs,xs) = sz0z00 ),
inference(resolve,[$cnf( aVector0(xs) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
aDimensionOf0(xs) = sz00,
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_8,plain,
( aDimensionOf0(xs) != sz00
| sz00 != sz00
| aDimensionOf0(xs) = sz00 ),
introduced(tautology,[equality,[$cnf( ~ $equal(aDimensionOf0(xs),sz00) ),[0],$fot(sz00)]]) ).
cnf(refute_0_9,plain,
( sz00 != sz00
| aDimensionOf0(xs) = sz00 ),
inference(resolve,[$cnf( $equal(aDimensionOf0(xs),sz00) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( sz00 != sz00
| sdtasasdt0(xs,xs) = sz0z00 ),
inference(resolve,[$cnf( $equal(aDimensionOf0(xs),sz00) )],[refute_0_9,refute_0_6]) ).
cnf(refute_0_11,plain,
sz00 = sz00,
introduced(tautology,[refl,[$fot(sz00)]]) ).
cnf(refute_0_12,plain,
sdtasasdt0(xs,xs) = sz0z00,
inference(resolve,[$cnf( $equal(sz00,sz00) )],[refute_0_11,refute_0_10]) ).
cnf(refute_0_13,plain,
( sdtasasdt0(xs,xs) != sz0z00
| ~ sdtlseqdt0(sz0z00,sz0z00)
| sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
introduced(tautology,[equality,[$cnf( ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),[1],$fot(sz0z00)]]) ).
cnf(refute_0_14,plain,
( ~ sdtlseqdt0(sz0z00,sz0z00)
| sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
inference(resolve,[$cnf( $equal(sdtasasdt0(xs,xs),sz0z00) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
~ sdtlseqdt0(sz0z00,sz0z00),
inference(resolve,[$cnf( sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) )],[refute_0_14,refute_0_0]) ).
cnf(refute_0_16,plain,
aScalar0(sz0z00),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_17,plain,
( ~ aScalar0(W0)
| sdtlseqdt0(W0,W0) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_18,plain,
( ~ aScalar0(sz0z00)
| sdtlseqdt0(sz0z00,sz0z00) ),
inference(subst,[],[refute_0_17:[bind(W0,$fot(sz0z00))]]) ).
cnf(refute_0_19,plain,
sdtlseqdt0(sz0z00,sz0z00),
inference(resolve,[$cnf( aScalar0(sz0z00) )],[refute_0_16,refute_0_18]) ).
cnf(refute_0_20,plain,
$false,
inference(resolve,[$cnf( sdtlseqdt0(sz0z00,sz0z00) )],[refute_0_19,refute_0_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG050+1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n022.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 : Mon May 30 15:38:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.83/2.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.83/2.05
% 1.83/2.05 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.83/2.05
%------------------------------------------------------------------------------