TSTP Solution File: NUM533+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM533+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.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 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 48 ( 17 unt; 1 def)
% Number of atoms : 132 ( 0 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 146 ( 62 ~; 61 |; 15 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 17 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefSub,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) ) ).
fof(m__522,hypothesis,
( aSet0(xA)
& aSet0(xB)
& aSet0(xC) ) ).
fof(m__,conjecture,
( ( aSubsetOf0(xA,xB)
& aSubsetOf0(xB,xC) )
=> aSubsetOf0(xA,xC) ) ).
fof(subgoal_0,plain,
( ( aSubsetOf0(xA,xB)
& aSubsetOf0(xB,xC) )
=> aSubsetOf0(xA,xC) ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ( ( aSubsetOf0(xA,xB)
& aSubsetOf0(xB,xC) )
=> aSubsetOf0(xA,xC) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [W0] :
( ~ aSet0(W0)
| ! [W1] :
( ~ aSubsetOf0(W1,W0)
<=> ( ~ aSet0(W1)
| ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) ) ) ) ),
inference(canonicalize,[],[mDefSub]) ).
fof(normalize_0_1,plain,
! [W0] :
( ~ aSet0(W0)
| ! [W1] :
( ~ aSubsetOf0(W1,W0)
<=> ( ~ aSet0(W1)
| ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) ) ) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [W0,W1,W2] :
( ( ~ aSet0(W0)
| ~ aSubsetOf0(W1,W0)
| aSet0(W1) )
& ( ~ aElementOf0(W2,W1)
| ~ aSet0(W0)
| ~ aSubsetOf0(W1,W0)
| aElementOf0(W2,W0) )
& ( ~ aElementOf0(skolemFOFtoCNF_W2(W0,W1),W0)
| ~ aSet0(W0)
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ( ~ aSet0(W0)
| ~ aSet0(W1)
| aElementOf0(skolemFOFtoCNF_W2(W0,W1),W1)
| aSubsetOf0(W1,W0) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [W0,W1] :
( ~ aElementOf0(skolemFOFtoCNF_W2(W0,W1),W0)
| ~ aSet0(W0)
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
( aSet0(xA)
& aSet0(xB)
& aSet0(xC) ),
inference(canonicalize,[],[m__522]) ).
fof(normalize_0_5,plain,
aSet0(xA),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
aSet0(xC),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_7,plain,
! [W0,W1] :
( ~ aSet0(W0)
| ~ aSet0(W1)
| aElementOf0(skolemFOFtoCNF_W2(W0,W1),W1)
| aSubsetOf0(W1,W0) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_8,plain,
( ~ aSubsetOf0(xA,xC)
& aSubsetOf0(xA,xB)
& aSubsetOf0(xB,xC) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_9,plain,
~ aSubsetOf0(xA,xC),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
aSubsetOf0(xA,xB),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_11,plain,
! [W0,W1,W2] :
( ~ aElementOf0(W2,W1)
| ~ aSet0(W0)
| ~ aSubsetOf0(W1,W0)
| aElementOf0(W2,W0) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_12,plain,
aSet0(xB),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_13,plain,
aSubsetOf0(xB,xC),
inference(conjunct,[],[normalize_0_8]) ).
cnf(refute_0_0,plain,
( ~ aElementOf0(skolemFOFtoCNF_W2(W0,W1),W0)
| ~ aSet0(W0)
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ aElementOf0(skolemFOFtoCNF_W2(xC,xA),xC)
| ~ aSet0(xA)
| ~ aSet0(xC)
| aSubsetOf0(xA,xC) ),
inference(subst,[],[refute_0_0:[bind(W0,$fot(xC)),bind(W1,$fot(xA))]]) ).
cnf(refute_0_2,plain,
aSet0(xA),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
aSet0(xC),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
( ~ aSet0(W0)
| ~ aSet0(W1)
| aElementOf0(skolemFOFtoCNF_W2(W0,W1),W1)
| aSubsetOf0(W1,W0) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ aSet0(X_13)
| ~ aSet0(xC)
| aElementOf0(skolemFOFtoCNF_W2(xC,X_13),X_13)
| aSubsetOf0(X_13,xC) ),
inference(subst,[],[refute_0_4:[bind(W0,$fot(xC)),bind(W1,$fot(X_13))]]) ).
cnf(refute_0_6,plain,
( ~ aSet0(X_13)
| aElementOf0(skolemFOFtoCNF_W2(xC,X_13),X_13)
| aSubsetOf0(X_13,xC) ),
inference(resolve,[$cnf( aSet0(xC) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ aSet0(xA)
| aElementOf0(skolemFOFtoCNF_W2(xC,xA),xA)
| aSubsetOf0(xA,xC) ),
inference(subst,[],[refute_0_6:[bind(X_13,$fot(xA))]]) ).
cnf(refute_0_8,plain,
( aElementOf0(skolemFOFtoCNF_W2(xC,xA),xA)
| aSubsetOf0(xA,xC) ),
inference(resolve,[$cnf( aSet0(xA) )],[refute_0_2,refute_0_7]) ).
cnf(refute_0_9,plain,
~ aSubsetOf0(xA,xC),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_10,plain,
aElementOf0(skolemFOFtoCNF_W2(xC,xA),xA),
inference(resolve,[$cnf( aSubsetOf0(xA,xC) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
aSubsetOf0(xA,xB),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_12,plain,
( ~ aElementOf0(W2,W1)
| ~ aSet0(W0)
| ~ aSubsetOf0(W1,W0)
| aElementOf0(W2,W0) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_13,plain,
( ~ aElementOf0(X_24,xA)
| ~ aSet0(xB)
| ~ aSubsetOf0(xA,xB)
| aElementOf0(X_24,xB) ),
inference(subst,[],[refute_0_12:[bind(W0,$fot(xB)),bind(W1,$fot(xA)),bind(W2,$fot(X_24))]]) ).
cnf(refute_0_14,plain,
( ~ aElementOf0(X_24,xA)
| ~ aSet0(xB)
| aElementOf0(X_24,xB) ),
inference(resolve,[$cnf( aSubsetOf0(xA,xB) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
aSet0(xB),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_16,plain,
( ~ aElementOf0(X_24,xA)
| aElementOf0(X_24,xB) ),
inference(resolve,[$cnf( aSet0(xB) )],[refute_0_15,refute_0_14]) ).
cnf(refute_0_17,plain,
( ~ aElementOf0(skolemFOFtoCNF_W2(xC,xA),xA)
| aElementOf0(skolemFOFtoCNF_W2(xC,xA),xB) ),
inference(subst,[],[refute_0_16:[bind(X_24,$fot(skolemFOFtoCNF_W2(xC,xA)))]]) ).
cnf(refute_0_18,plain,
aElementOf0(skolemFOFtoCNF_W2(xC,xA),xB),
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W2(xC,xA),xA) )],[refute_0_10,refute_0_17]) ).
cnf(refute_0_19,plain,
aSubsetOf0(xB,xC),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_20,plain,
( ~ aElementOf0(X_24,xB)
| ~ aSet0(xC)
| ~ aSubsetOf0(xB,xC)
| aElementOf0(X_24,xC) ),
inference(subst,[],[refute_0_12:[bind(W0,$fot(xC)),bind(W1,$fot(xB)),bind(W2,$fot(X_24))]]) ).
cnf(refute_0_21,plain,
( ~ aElementOf0(X_24,xB)
| ~ aSet0(xC)
| aElementOf0(X_24,xC) ),
inference(resolve,[$cnf( aSubsetOf0(xB,xC) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ aElementOf0(X_24,xB)
| aElementOf0(X_24,xC) ),
inference(resolve,[$cnf( aSet0(xC) )],[refute_0_3,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ aElementOf0(skolemFOFtoCNF_W2(xC,xA),xB)
| aElementOf0(skolemFOFtoCNF_W2(xC,xA),xC) ),
inference(subst,[],[refute_0_22:[bind(X_24,$fot(skolemFOFtoCNF_W2(xC,xA)))]]) ).
cnf(refute_0_24,plain,
aElementOf0(skolemFOFtoCNF_W2(xC,xA),xC),
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W2(xC,xA),xB) )],[refute_0_18,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ aSet0(xA)
| ~ aSet0(xC)
| aSubsetOf0(xA,xC) ),
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W2(xC,xA),xC) )],[refute_0_24,refute_0_1]) ).
cnf(refute_0_26,plain,
( ~ aSet0(xC)
| aSubsetOf0(xA,xC) ),
inference(resolve,[$cnf( aSet0(xA) )],[refute_0_2,refute_0_25]) ).
cnf(refute_0_27,plain,
aSubsetOf0(xA,xC),
inference(resolve,[$cnf( aSet0(xC) )],[refute_0_3,refute_0_26]) ).
cnf(refute_0_28,plain,
$false,
inference(resolve,[$cnf( aSubsetOf0(xA,xC) )],[refute_0_27,refute_0_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NUM533+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Wed Jul 6 15:24:53 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.38
% 0.14/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.14/0.38
%------------------------------------------------------------------------------