TSTP Solution File: NUM620+3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM620+3 : 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 12:28:18 EDT 2022
% Result : Theorem 9.66s 9.83s
% Output : CNFRefutation 9.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 12 unt; 0 def)
% Number of atoms : 89 ( 21 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 83 ( 29 ~; 25 |; 21 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__4660,hypothesis,
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ).
fof(m__5389,hypothesis,
( aElementOf0(xm,szNzAzT0)
& xx = sdtlpdtrp0(xe,xm) ) ).
fof(m__,conjecture,
( ( ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xm))
=> aElementOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) )
& aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))) )
=> aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ).
fof(subgoal_0,plain,
( ( ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xm))
=> aElementOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) )
& aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))) )
=> aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ( ( ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xm))
=> aElementOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) )
& aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))) )
=> aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( xx = sdtlpdtrp0(xe,xm)
& aElementOf0(xm,szNzAzT0) ),
inference(canonicalize,[],[m__5389]) ).
fof(normalize_0_1,plain,
aElementOf0(xm,szNzAzT0),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( szDzozmdt0(xe) = szNzAzT0
& aFunction0(xe)
& ! [W0] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ) ),
inference(canonicalize,[],[m__4660]) ).
fof(normalize_0_3,plain,
! [W0] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [W0] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [W0,W1] :
( ( ~ aElementOf0(W0,szNzAzT0)
| sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(W0,szNzAzT0)
| aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(W0,szNzAzT0)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [W0] :
( ~ aElementOf0(W0,szNzAzT0)
| aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
xx = sdtlpdtrp0(xe,xm),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_8,plain,
( ~ aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& ! [W0] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| aElementOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_9,plain,
! [W0] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| aElementOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [W0] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| aElementOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
~ aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(conjunct,[],[normalize_0_8]) ).
cnf(refute_0_0,plain,
aElementOf0(xm,szNzAzT0),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ aElementOf0(W0,szNzAzT0)
| aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( ~ aElementOf0(xm,szNzAzT0)
| aElementOf0(sdtlpdtrp0(xe,xm),sdtlpdtrp0(xN,xm)) ),
inference(subst,[],[refute_0_1:[bind(W0,$fot(xm))]]) ).
cnf(refute_0_3,plain,
aElementOf0(sdtlpdtrp0(xe,xm),sdtlpdtrp0(xN,xm)),
inference(resolve,[$cnf( aElementOf0(xm,szNzAzT0) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
xx = sdtlpdtrp0(xe,xm),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_6,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_7,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( xx != sdtlpdtrp0(xe,xm)
| sdtlpdtrp0(xe,xm) = xx ),
inference(subst,[],[refute_0_7:[bind(X,$fot(xx)),bind(Y,$fot(sdtlpdtrp0(xe,xm)))]]) ).
cnf(refute_0_9,plain,
sdtlpdtrp0(xe,xm) = xx,
inference(resolve,[$cnf( $equal(xx,sdtlpdtrp0(xe,xm)) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( sdtlpdtrp0(xe,xm) != xx
| ~ aElementOf0(sdtlpdtrp0(xe,xm),sdtlpdtrp0(xN,xm))
| aElementOf0(xx,sdtlpdtrp0(xN,xm)) ),
introduced(tautology,[equality,[$cnf( aElementOf0(sdtlpdtrp0(xe,xm),sdtlpdtrp0(xN,xm)) ),[0],$fot(xx)]]) ).
cnf(refute_0_11,plain,
( ~ aElementOf0(sdtlpdtrp0(xe,xm),sdtlpdtrp0(xN,xm))
| aElementOf0(xx,sdtlpdtrp0(xN,xm)) ),
inference(resolve,[$cnf( $equal(sdtlpdtrp0(xe,xm),xx) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
aElementOf0(xx,sdtlpdtrp0(xN,xm)),
inference(resolve,[$cnf( aElementOf0(sdtlpdtrp0(xe,xm),sdtlpdtrp0(xN,xm)) )],[refute_0_3,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| aElementOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_14,plain,
( ~ aElementOf0(xx,sdtlpdtrp0(xN,xm))
| aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(subst,[],[refute_0_13:[bind(W0,$fot(xx))]]) ).
cnf(refute_0_15,plain,
aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(resolve,[$cnf( aElementOf0(xx,sdtlpdtrp0(xN,xm)) )],[refute_0_12,refute_0_14]) ).
cnf(refute_0_16,plain,
~ aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_17,plain,
$false,
inference(resolve,[$cnf( aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) )],[refute_0_15,refute_0_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : NUM620+3 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jul 7 12:47:14 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 9.66/9.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.66/9.83
% 9.66/9.83 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.66/9.83
%------------------------------------------------------------------------------