TSTP Solution File: COM021+4 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COM021+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 : Fri Jul 15 01:32:35 EDT 2022
% Result : Theorem 0.19s 0.46s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 13 unt; 0 def)
% Number of atoms : 126 ( 28 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 126 ( 31 ~; 33 |; 60 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 21 ( 1 sgn 4 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__818,hypothesis,
( aElement0(xd)
& ( xw = xd
| ( ( aReductOfIn0(xd,xw,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xw,xR)
& sdtmndtplgtdt0(W0,xR,xd) ) )
& sdtmndtplgtdt0(xw,xR,xd) ) )
& sdtmndtasgtdt0(xw,xR,xd)
& ~ ? [W0] : aReductOfIn0(W0,xd,xR)
& aNormalFormOfIn0(xd,xw,xR) ) ).
fof(m__850,hypothesis,
( aElement0(xx)
& ( xb = xx
| ( ( aReductOfIn0(xx,xb,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xb,xR)
& sdtmndtplgtdt0(W0,xR,xx) ) )
& sdtmndtplgtdt0(xb,xR,xx) ) )
& sdtmndtasgtdt0(xb,xR,xx)
& ( xd = xx
| ( ( aReductOfIn0(xx,xd,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xd,xR)
& sdtmndtplgtdt0(W0,xR,xx) ) )
& sdtmndtplgtdt0(xd,xR,xx) ) )
& sdtmndtasgtdt0(xd,xR,xx) ) ).
fof(m__,conjecture,
( xb = xd
| aReductOfIn0(xd,xb,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xb,xR)
& sdtmndtplgtdt0(W0,xR,xd) )
| sdtmndtplgtdt0(xb,xR,xd)
| sdtmndtasgtdt0(xb,xR,xd) ) ).
fof(subgoal_0,plain,
( ( xb != xd
& ~ aReductOfIn0(xd,xb,xR)
& ~ ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xb,xR)
& sdtmndtplgtdt0(W0,xR,xd) )
& ~ sdtmndtplgtdt0(xb,xR,xd) )
=> sdtmndtasgtdt0(xb,xR,xd) ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ( ( xb != xd
& ~ aReductOfIn0(xd,xb,xR)
& ~ ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xb,xR)
& sdtmndtplgtdt0(W0,xR,xd) )
& ~ sdtmndtplgtdt0(xb,xR,xd) )
=> sdtmndtasgtdt0(xb,xR,xd) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( aElement0(xx)
& sdtmndtasgtdt0(xb,xR,xx)
& sdtmndtasgtdt0(xd,xR,xx)
& ( xb = xx
| ( sdtmndtplgtdt0(xb,xR,xx)
& ( aReductOfIn0(xx,xb,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xb,xR)
& sdtmndtplgtdt0(W0,xR,xx) ) ) ) )
& ( xd = xx
| ( sdtmndtplgtdt0(xd,xR,xx)
& ( aReductOfIn0(xx,xd,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xd,xR)
& sdtmndtplgtdt0(W0,xR,xx) ) ) ) ) ),
inference(canonicalize,[],[m__850]) ).
fof(normalize_0_1,plain,
( aElement0(xd)
& aNormalFormOfIn0(xd,xw,xR)
& sdtmndtasgtdt0(xw,xR,xd)
& ( xw = xd
| ( sdtmndtplgtdt0(xw,xR,xd)
& ( aReductOfIn0(xd,xw,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xw,xR)
& sdtmndtplgtdt0(W0,xR,xd) ) ) ) )
& ! [W0] : ~ aReductOfIn0(W0,xd,xR) ),
inference(canonicalize,[],[m__818]) ).
fof(normalize_0_2,plain,
! [W0] : ~ aReductOfIn0(W0,xd,xR),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [W0] : ~ aReductOfIn0(W0,xd,xR),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
( aElement0(xx)
& sdtmndtasgtdt0(xb,xR,xx)
& sdtmndtasgtdt0(xd,xR,xx)
& ( xb = xx
| ( sdtmndtplgtdt0(xb,xR,xx)
& ( aReductOfIn0(xx,xb,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xb,xR)
& sdtmndtplgtdt0(W0,xR,xx) ) ) ) )
& ( xd = xx
| ( aReductOfIn0(xx,xd,xR)
& sdtmndtplgtdt0(xd,xR,xx) ) ) ),
inference(simplify,[],[normalize_0_0,normalize_0_3]) ).
fof(normalize_0_5,plain,
sdtmndtasgtdt0(xb,xR,xx),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
( xd = xx
| ( aReductOfIn0(xx,xd,xR)
& sdtmndtplgtdt0(xd,xR,xx) ) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_7,plain,
( ( xd = xx
| aReductOfIn0(xx,xd,xR) )
& ( xd = xx
| sdtmndtplgtdt0(xd,xR,xx) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
( xd = xx
| aReductOfIn0(xx,xd,xR) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
( xb != xd
& ~ aReductOfIn0(xd,xb,xR)
& ~ sdtmndtasgtdt0(xb,xR,xd)
& ~ sdtmndtplgtdt0(xb,xR,xd)
& ! [W0] :
( ~ aElement0(W0)
| ~ aReductOfIn0(W0,xb,xR)
| ~ sdtmndtplgtdt0(W0,xR,xd) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_10,plain,
~ sdtmndtasgtdt0(xb,xR,xd),
inference(conjunct,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
sdtmndtasgtdt0(xb,xR,xx),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_1,plain,
( xd = xx
| aReductOfIn0(xx,xd,xR) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_2,plain,
~ aReductOfIn0(W0,xd,xR),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
~ aReductOfIn0(xx,xd,xR),
inference(subst,[],[refute_0_2:[bind(W0,$fot(xx))]]) ).
cnf(refute_0_4,plain,
xd = xx,
inference(resolve,[$cnf( aReductOfIn0(xx,xd,xR) )],[refute_0_1,refute_0_3]) ).
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( $equal(X,X) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( xd != xx
| xx = xd ),
inference(subst,[],[refute_0_7:[bind(X,$fot(xd)),bind(Y,$fot(xx))]]) ).
cnf(refute_0_9,plain,
xx = xd,
inference(resolve,[$cnf( $equal(xd,xx) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( xx != xd
| ~ sdtmndtasgtdt0(xb,xR,xx)
| sdtmndtasgtdt0(xb,xR,xd) ),
introduced(tautology,[equality,[$cnf( sdtmndtasgtdt0(xb,xR,xx) ),[2],$fot(xd)]]) ).
cnf(refute_0_11,plain,
( ~ sdtmndtasgtdt0(xb,xR,xx)
| sdtmndtasgtdt0(xb,xR,xd) ),
inference(resolve,[$cnf( $equal(xx,xd) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
sdtmndtasgtdt0(xb,xR,xd),
inference(resolve,[$cnf( sdtmndtasgtdt0(xb,xR,xx) )],[refute_0_0,refute_0_11]) ).
cnf(refute_0_13,plain,
~ sdtmndtasgtdt0(xb,xR,xd),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_14,plain,
$false,
inference(resolve,[$cnf( sdtmndtasgtdt0(xb,xR,xd) )],[refute_0_12,refute_0_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : COM021+4 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n018.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 Jun 16 16:58:31 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46
% 0.19/0.46 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.47
%------------------------------------------------------------------------------