TSTP Solution File: NUM531+2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM531+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 12:27:29 EDT 2022
% Result : Theorem 0.12s 0.34s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 41 ( 15 unt; 1 def)
% Number of atoms : 91 ( 29 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 96 ( 46 ~; 28 |; 15 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 28 ( 0 sgn 13 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefEmp,definition,
! [W0] :
( W0 = slcrc0
<=> ( aSet0(W0)
& ~ ? [W1] : aElementOf0(W1,W0) ) ) ).
fof(mEmpFin,axiom,
isFinite0(slcrc0) ).
fof(mCountNFin,axiom,
! [W0] :
( ( aSet0(W0)
& isCountable0(W0) )
=> ~ isFinite0(W0) ) ).
fof(m__,conjecture,
! [W0] :
( ( aSet0(W0)
& isCountable0(W0) )
=> ~ ( ~ ? [W1] : aElementOf0(W1,W0)
& W0 = slcrc0 ) ) ).
fof(subgoal_0,plain,
! [W0] :
( ( aSet0(W0)
& isCountable0(W0)
& ~ ? [W1] : aElementOf0(W1,W0) )
=> W0 != slcrc0 ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ! [W0] :
( ( aSet0(W0)
& isCountable0(W0)
& ~ ? [W1] : aElementOf0(W1,W0) )
=> W0 != slcrc0 ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
isFinite0(slcrc0),
inference(canonicalize,[],[mEmpFin]) ).
fof(normalize_0_1,plain,
? [W0] :
( W0 = slcrc0
& aSet0(W0)
& isCountable0(W0)
& ! [W1] : ~ aElementOf0(W1,W0) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_2,plain,
! [W0] :
( W0 != slcrc0
<=> ( ~ aSet0(W0)
| ? [W1] : aElementOf0(W1,W0) ) ),
inference(canonicalize,[],[mDefEmp]) ).
fof(normalize_0_3,plain,
! [W0] :
( W0 != slcrc0
<=> ( ~ aSet0(W0)
| ? [W1] : aElementOf0(W1,W0) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [W0] :
( W0 = slcrc0
& isCountable0(W0) ),
inference(simplify,[],[normalize_0_1,normalize_0_3]) ).
fof(normalize_0_5,plain,
( skolemFOFtoCNF_W0 = slcrc0
& isCountable0(skolemFOFtoCNF_W0) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
skolemFOFtoCNF_W0 = slcrc0,
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [W0] :
( ~ aSet0(W0)
| ~ isCountable0(W0)
| ~ isFinite0(W0) ),
inference(canonicalize,[],[mCountNFin]) ).
fof(normalize_0_8,plain,
! [W0] :
( ~ aSet0(W0)
| ~ isCountable0(W0)
| ~ isFinite0(W0) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [W0,W1] :
( ( W0 != slcrc0
| ~ aElementOf0(W1,W0) )
& ( W0 != slcrc0
| aSet0(W0) )
& ( ~ aSet0(W0)
| W0 = slcrc0
| aElementOf0(skolemFOFtoCNF_W1(W0),W0) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_10,plain,
! [W0] :
( W0 != slcrc0
| aSet0(W0) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
isCountable0(skolemFOFtoCNF_W0),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
isFinite0(slcrc0),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
skolemFOFtoCNF_W0 = slcrc0,
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( skolemFOFtoCNF_W0 != slcrc0
| slcrc0 = skolemFOFtoCNF_W0 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_W0)),bind(Y,$fot(slcrc0))]]) ).
cnf(refute_0_6,plain,
slcrc0 = skolemFOFtoCNF_W0,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W0,slcrc0) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( slcrc0 != skolemFOFtoCNF_W0
| ~ isFinite0(slcrc0)
| isFinite0(skolemFOFtoCNF_W0) ),
introduced(tautology,[equality,[$cnf( isFinite0(slcrc0) ),[0],$fot(skolemFOFtoCNF_W0)]]) ).
cnf(refute_0_8,plain,
( ~ isFinite0(slcrc0)
| isFinite0(skolemFOFtoCNF_W0) ),
inference(resolve,[$cnf( $equal(slcrc0,skolemFOFtoCNF_W0) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
isFinite0(skolemFOFtoCNF_W0),
inference(resolve,[$cnf( isFinite0(slcrc0) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ aSet0(W0)
| ~ isCountable0(W0)
| ~ isFinite0(W0) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_11,plain,
( ~ aSet0(skolemFOFtoCNF_W0)
| ~ isCountable0(skolemFOFtoCNF_W0)
| ~ isFinite0(skolemFOFtoCNF_W0) ),
inference(subst,[],[refute_0_10:[bind(W0,$fot(skolemFOFtoCNF_W0))]]) ).
cnf(refute_0_12,plain,
( ~ aSet0(skolemFOFtoCNF_W0)
| ~ isCountable0(skolemFOFtoCNF_W0) ),
inference(resolve,[$cnf( isFinite0(skolemFOFtoCNF_W0) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
( W0 != slcrc0
| aSet0(W0) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_14,plain,
( slcrc0 != slcrc0
| aSet0(slcrc0) ),
inference(subst,[],[refute_0_13:[bind(W0,$fot(slcrc0))]]) ).
cnf(refute_0_15,plain,
slcrc0 = slcrc0,
introduced(tautology,[refl,[$fot(slcrc0)]]) ).
cnf(refute_0_16,plain,
aSet0(slcrc0),
inference(resolve,[$cnf( $equal(slcrc0,slcrc0) )],[refute_0_15,refute_0_14]) ).
cnf(refute_0_17,plain,
( slcrc0 != skolemFOFtoCNF_W0
| ~ aSet0(slcrc0)
| aSet0(skolemFOFtoCNF_W0) ),
introduced(tautology,[equality,[$cnf( aSet0(slcrc0) ),[0],$fot(skolemFOFtoCNF_W0)]]) ).
cnf(refute_0_18,plain,
( ~ aSet0(slcrc0)
| aSet0(skolemFOFtoCNF_W0) ),
inference(resolve,[$cnf( $equal(slcrc0,skolemFOFtoCNF_W0) )],[refute_0_6,refute_0_17]) ).
cnf(refute_0_19,plain,
aSet0(skolemFOFtoCNF_W0),
inference(resolve,[$cnf( aSet0(slcrc0) )],[refute_0_16,refute_0_18]) ).
cnf(refute_0_20,plain,
~ isCountable0(skolemFOFtoCNF_W0),
inference(resolve,[$cnf( aSet0(skolemFOFtoCNF_W0) )],[refute_0_19,refute_0_12]) ).
cnf(refute_0_21,plain,
isCountable0(skolemFOFtoCNF_W0),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_22,plain,
$false,
inference(resolve,[$cnf( isCountable0(skolemFOFtoCNF_W0) )],[refute_0_21,refute_0_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : NUM531+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n026.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 : Thu Jul 7 04:28:24 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34
% 0.12/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35
%------------------------------------------------------------------------------