TSTP Solution File: NUM622+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM622+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 12:28:19 EDT 2022
% Result : Theorem 13.79s 14.04s
% Output : CNFRefutation 13.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 16 unt; 0 def)
% Number of atoms : 107 ( 23 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 102 ( 33 ~; 30 |; 33 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 20 !; 1 ?)
% 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__4730,hypothesis,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( ( aSet0(W1)
& ( ( ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
| aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
& sbrdtbr0(W1) = xk )
| aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
=> sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ) ).
fof(m__5309,hypothesis,
( aElementOf0(xn,szDzozmdt0(xd))
& sdtlpdtrp0(xd,xn) = szDzizrdt0(xd)
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xn,szNzAzT0)
& sdtlpdtrp0(xe,xn) = xp ) ).
fof(m__5461,hypothesis,
( ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xn))
=> aElementOf0(W0,sdtlpdtrp0(xN,xm)) )
& aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)) ) ).
fof(m__,conjecture,
aElementOf0(xp,sdtlpdtrp0(xN,xm)) ).
fof(subgoal_0,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
& ! [W0] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) ) ),
inference(canonicalize,[],[m__5461]) ).
fof(normalize_0_1,plain,
! [W0] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [W0] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( sdtlpdtrp0(xd,xn) = szDzizrdt0(xd)
& sdtlpdtrp0(xe,xn) = xp
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xn,szDzozmdt0(xd))
& aElementOf0(xn,szNzAzT0) ),
inference(canonicalize,[],[m__5309]) ).
fof(normalize_0_4,plain,
aElementOf0(xn,szDzozmdt0(xd)),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
( szDzozmdt0(xd) = szNzAzT0
& aFunction0(xd)
& ! [W0] :
( ~ aElementOf0(W0,szNzAzT0)
| ! [W1] :
( ~ aSet0(W1)
| sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1)
| ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
& ( sbrdtbr0(W1) != xk
| ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ? [W2] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& aElementOf0(W2,W1) ) ) ) ) ) ) ),
inference(canonicalize,[],[m__4730]) ).
fof(normalize_0_6,plain,
szDzozmdt0(xd) = szNzAzT0,
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,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_8,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_7]) ).
fof(normalize_0_9,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_8]) ).
fof(normalize_0_10,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_9]) ).
fof(normalize_0_11,plain,
! [W0] :
( ~ aElementOf0(W0,szNzAzT0)
| aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0)) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
sdtlpdtrp0(xe,xn) = xp,
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_13,plain,
~ aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(canonicalize,[],[negate_0_0]) ).
cnf(refute_0_0,plain,
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ aElementOf0(xp,sdtlpdtrp0(xN,xn))
| aElementOf0(xp,sdtlpdtrp0(xN,xm)) ),
inference(subst,[],[refute_0_0:[bind(W0,$fot(xp))]]) ).
cnf(refute_0_2,plain,
aElementOf0(xn,szDzozmdt0(xd)),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
szDzozmdt0(xd) = szNzAzT0,
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
( szDzozmdt0(xd) != szNzAzT0
| ~ aElementOf0(xn,szDzozmdt0(xd))
| aElementOf0(xn,szNzAzT0) ),
introduced(tautology,[equality,[$cnf( aElementOf0(xn,szDzozmdt0(xd)) ),[1],$fot(szNzAzT0)]]) ).
cnf(refute_0_5,plain,
( ~ aElementOf0(xn,szDzozmdt0(xd))
| aElementOf0(xn,szNzAzT0) ),
inference(resolve,[$cnf( $equal(szDzozmdt0(xd),szNzAzT0) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
aElementOf0(xn,szNzAzT0),
inference(resolve,[$cnf( aElementOf0(xn,szDzozmdt0(xd)) )],[refute_0_2,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ aElementOf0(W0,szNzAzT0)
| aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0)) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_8,plain,
( ~ aElementOf0(xn,szNzAzT0)
| aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn)) ),
inference(subst,[],[refute_0_7:[bind(W0,$fot(xn))]]) ).
cnf(refute_0_9,plain,
aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn)),
inference(resolve,[$cnf( aElementOf0(xn,szNzAzT0) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
sdtlpdtrp0(xe,xn) = xp,
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_11,plain,
( sdtlpdtrp0(xe,xn) != xp
| ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| aElementOf0(xp,sdtlpdtrp0(xN,xn)) ),
introduced(tautology,[equality,[$cnf( aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn)) ),[0],$fot(xp)]]) ).
cnf(refute_0_12,plain,
( ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| aElementOf0(xp,sdtlpdtrp0(xN,xn)) ),
inference(resolve,[$cnf( $equal(sdtlpdtrp0(xe,xn),xp) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xn)),
inference(resolve,[$cnf( aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn)) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(resolve,[$cnf( aElementOf0(xp,sdtlpdtrp0(xN,xn)) )],[refute_0_13,refute_0_1]) ).
cnf(refute_0_15,plain,
~ aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_16,plain,
$false,
inference(resolve,[$cnf( aElementOf0(xp,sdtlpdtrp0(xN,xm)) )],[refute_0_14,refute_0_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM622+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 : n025.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 Jul 5 23:49:42 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 13.79/14.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.79/14.04
% 13.79/14.04 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.79/14.04
%------------------------------------------------------------------------------