TSTP Solution File: NUM618+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM618+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n005.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 12:28:16 EDT 2022
% Result : Theorem 0.41s 0.59s
% Output : CNFRefutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 7 unt; 0 def)
% Number of atoms : 62 ( 22 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 59 ( 26 ~; 19 |; 13 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn 8 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__4982,hypothesis,
! [W0] :
( aElementOf0(W0,xO)
=> ? [W1] :
( aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,W1) = W0 ) ) ).
fof(m__5365,hypothesis,
( aElementOf0(xx,szNzAzT0)
& aElementOf0(xx,xO) ) ).
fof(m__,conjecture,
? [W0] :
( aElementOf0(W0,szNzAzT0)
& xx = sdtlpdtrp0(xe,W0) ) ).
fof(subgoal_0,plain,
? [W0] :
( aElementOf0(W0,szNzAzT0)
& xx = sdtlpdtrp0(xe,W0) ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ? [W0] :
( aElementOf0(W0,szNzAzT0)
& xx = sdtlpdtrp0(xe,W0) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [W0] :
( xx != sdtlpdtrp0(xe,W0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [W0] :
( xx != sdtlpdtrp0(xe,W0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( aElementOf0(xx,szNzAzT0)
& aElementOf0(xx,xO) ),
inference(canonicalize,[],[m__5365]) ).
fof(normalize_0_3,plain,
aElementOf0(xx,xO),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [W0] :
( ~ aElementOf0(W0,xO)
| ? [W1] :
( sdtlpdtrp0(xe,W1) = W0
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(W1,szNzAzT0) ) ),
inference(canonicalize,[],[m__4982]) ).
fof(normalize_0_5,plain,
! [W0] :
( ~ aElementOf0(W0,xO)
| ? [W1] :
( sdtlpdtrp0(xe,W1) = W0
& aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(W1,szNzAzT0) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [W0] :
( ( ~ aElementOf0(W0,xO)
| sdtlpdtrp0(xe,skolemFOFtoCNF_W1_5(W0)) = W0 )
& ( ~ aElementOf0(W0,xO)
| aElementOf0(skolemFOFtoCNF_W1_5(W0),sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& ( ~ aElementOf0(W0,xO)
| aElementOf0(skolemFOFtoCNF_W1_5(W0),szNzAzT0) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [W0] :
( ~ aElementOf0(W0,xO)
| sdtlpdtrp0(xe,skolemFOFtoCNF_W1_5(W0)) = W0 ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [W0] :
( ~ aElementOf0(W0,xO)
| aElementOf0(skolemFOFtoCNF_W1_5(W0),szNzAzT0) ),
inference(conjunct,[],[normalize_0_6]) ).
cnf(refute_0_0,plain,
( xx != sdtlpdtrp0(xe,W0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( xx != sdtlpdtrp0(xe,skolemFOFtoCNF_W1_5(xx))
| ~ aElementOf0(skolemFOFtoCNF_W1_5(xx),szNzAzT0) ),
inference(subst,[],[refute_0_0:[bind(W0,$fot(skolemFOFtoCNF_W1_5(xx)))]]) ).
cnf(refute_0_2,plain,
aElementOf0(xx,xO),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
( ~ aElementOf0(W0,xO)
| sdtlpdtrp0(xe,skolemFOFtoCNF_W1_5(W0)) = W0 ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_4,plain,
( ~ aElementOf0(xx,xO)
| sdtlpdtrp0(xe,skolemFOFtoCNF_W1_5(xx)) = xx ),
inference(subst,[],[refute_0_3:[bind(W0,$fot(xx))]]) ).
cnf(refute_0_5,plain,
sdtlpdtrp0(xe,skolemFOFtoCNF_W1_5(xx)) = xx,
inference(resolve,[$cnf( aElementOf0(xx,xO) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( sdtlpdtrp0(xe,skolemFOFtoCNF_W1_5(xx)) != xx
| xx != xx
| xx = sdtlpdtrp0(xe,skolemFOFtoCNF_W1_5(xx)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(xx,sdtlpdtrp0(xe,skolemFOFtoCNF_W1_5(xx))) ),[1],$fot(xx)]]) ).
cnf(refute_0_7,plain,
( xx != xx
| xx = sdtlpdtrp0(xe,skolemFOFtoCNF_W1_5(xx)) ),
inference(resolve,[$cnf( $equal(sdtlpdtrp0(xe,skolemFOFtoCNF_W1_5(xx)),xx) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( xx != xx
| ~ aElementOf0(skolemFOFtoCNF_W1_5(xx),szNzAzT0) ),
inference(resolve,[$cnf( $equal(xx,sdtlpdtrp0(xe,skolemFOFtoCNF_W1_5(xx))) )],[refute_0_7,refute_0_1]) ).
cnf(refute_0_9,plain,
xx = xx,
introduced(tautology,[refl,[$fot(xx)]]) ).
cnf(refute_0_10,plain,
~ aElementOf0(skolemFOFtoCNF_W1_5(xx),szNzAzT0),
inference(resolve,[$cnf( $equal(xx,xx) )],[refute_0_9,refute_0_8]) ).
cnf(refute_0_11,plain,
( ~ aElementOf0(W0,xO)
| aElementOf0(skolemFOFtoCNF_W1_5(W0),szNzAzT0) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_12,plain,
( ~ aElementOf0(xx,xO)
| aElementOf0(skolemFOFtoCNF_W1_5(xx),szNzAzT0) ),
inference(subst,[],[refute_0_11:[bind(W0,$fot(xx))]]) ).
cnf(refute_0_13,plain,
aElementOf0(skolemFOFtoCNF_W1_5(xx),szNzAzT0),
inference(resolve,[$cnf( aElementOf0(xx,xO) )],[refute_0_2,refute_0_12]) ).
cnf(refute_0_14,plain,
$false,
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W1_5(xx),szNzAzT0) )],[refute_0_13,refute_0_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM618+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Wed Jul 6 14:13:07 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.41/0.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.41/0.59
% 0.41/0.59 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.41/0.59
%------------------------------------------------------------------------------