%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COM016+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 01:32:32 EDT 2022
% Result : Theorem 0.18s 0.41s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 9 unt; 0 def)
% Number of atoms : 141 ( 10 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 166 ( 60 ~; 60 |; 46 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 21 ( 0 sgn 8 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__731,hypothesis,
( aElement0(xa)
& aElement0(xb)
& aElement0(xc) ) ).
fof(m__731_02,hypothesis,
( ( aReductOfIn0(xb,xa,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtplgtdt0(W0,xR,xb) ) )
& sdtmndtplgtdt0(xa,xR,xb)
& ( aReductOfIn0(xc,xa,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtplgtdt0(W0,xR,xc) ) )
& sdtmndtplgtdt0(xa,xR,xc) ) ).
fof(m__,conjecture,
? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& ( W0 = xb
| aReductOfIn0(xb,W0,xR)
| ? [W1] :
( aElement0(W1)
& aReductOfIn0(W1,W0,xR)
& sdtmndtplgtdt0(W1,xR,xb) )
| sdtmndtplgtdt0(W0,xR,xb)
| sdtmndtasgtdt0(W0,xR,xb) ) ) ).
fof(subgoal_0,plain,
? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& ( W0 = xb
| aReductOfIn0(xb,W0,xR)
| ? [W1] :
( aElement0(W1)
& aReductOfIn0(W1,W0,xR)
& sdtmndtplgtdt0(W1,xR,xb) )
| sdtmndtplgtdt0(W0,xR,xb)
| sdtmndtasgtdt0(W0,xR,xb) ) ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& ( W0 = xb
| aReductOfIn0(xb,W0,xR)
| ? [W1] :
( aElement0(W1)
& aReductOfIn0(W1,W0,xR)
& sdtmndtplgtdt0(W1,xR,xb) )
| sdtmndtplgtdt0(W0,xR,xb)
| sdtmndtasgtdt0(W0,xR,xb) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( sdtmndtplgtdt0(xa,xR,xb)
& sdtmndtplgtdt0(xa,xR,xc)
& ( aReductOfIn0(xb,xa,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtplgtdt0(W0,xR,xb) ) )
& ( aReductOfIn0(xc,xa,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtplgtdt0(W0,xR,xc) ) ) ),
inference(canonicalize,[],[m__731_02]) ).
fof(normalize_0_1,plain,
( aReductOfIn0(xb,xa,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtplgtdt0(W0,xR,xb) ) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ( aElement0(skolemFOFtoCNF_W0)
| aReductOfIn0(xb,xa,xR) )
& ( aReductOfIn0(skolemFOFtoCNF_W0,xa,xR)
| aReductOfIn0(xb,xa,xR) )
& ( aReductOfIn0(xb,xa,xR)
| sdtmndtplgtdt0(skolemFOFtoCNF_W0,xR,xb) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( aReductOfIn0(xb,xa,xR)
| sdtmndtplgtdt0(skolemFOFtoCNF_W0,xR,xb) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [W0] :
( ~ aElement0(W0)
| ~ aReductOfIn0(W0,xa,xR)
| ( W0 != xb
& ~ aReductOfIn0(xb,W0,xR)
& ~ sdtmndtasgtdt0(W0,xR,xb)
& ~ sdtmndtplgtdt0(W0,xR,xb)
& ! [W1] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,W0,xR)
| ~ sdtmndtplgtdt0(W1,xR,xb) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
! [W0] :
( ~ aElement0(W0)
| ~ aReductOfIn0(W0,xa,xR)
| ( W0 != xb
& ~ aReductOfIn0(xb,W0,xR)
& ~ sdtmndtasgtdt0(W0,xR,xb)
& ~ sdtmndtplgtdt0(W0,xR,xb)
& ! [W1] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,W0,xR)
| ~ sdtmndtplgtdt0(W1,xR,xb) ) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [W0,W1] :
( ( W0 != xb
| ~ aElement0(W0)
| ~ aReductOfIn0(W0,xa,xR) )
& ( ~ aElement0(W0)
| ~ aReductOfIn0(W0,xa,xR)
| ~ aReductOfIn0(xb,W0,xR) )
& ( ~ aElement0(W0)
| ~ aReductOfIn0(W0,xa,xR)
| ~ sdtmndtasgtdt0(W0,xR,xb) )
& ( ~ aElement0(W0)
| ~ aReductOfIn0(W0,xa,xR)
| ~ sdtmndtplgtdt0(W0,xR,xb) )
& ( ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aReductOfIn0(W0,xa,xR)
| ~ aReductOfIn0(W1,W0,xR)
| ~ sdtmndtplgtdt0(W1,xR,xb) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [W0] :
( W0 != xb
| ~ aElement0(W0)
| ~ aReductOfIn0(W0,xa,xR) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
( aElement0(xa)
& aElement0(xb)
& aElement0(xc) ),
inference(canonicalize,[],[m__731]) ).
fof(normalize_0_9,plain,
aElement0(xb),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [W0] :
( ~ aElement0(W0)
| ~ aReductOfIn0(W0,xa,xR)
| ~ sdtmndtplgtdt0(W0,xR,xb) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_11,plain,
( aElement0(skolemFOFtoCNF_W0)
| aReductOfIn0(xb,xa,xR) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_12,plain,
( aReductOfIn0(skolemFOFtoCNF_W0,xa,xR)
| aReductOfIn0(xb,xa,xR) ),
inference(conjunct,[],[normalize_0_2]) ).
cnf(refute_0_0,plain,
( aReductOfIn0(xb,xa,xR)
| sdtmndtplgtdt0(skolemFOFtoCNF_W0,xR,xb) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( W0 != xb
| ~ aElement0(W0)
| ~ aReductOfIn0(W0,xa,xR) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_2,plain,
( xb != xb
| ~ aElement0(xb)
| ~ aReductOfIn0(xb,xa,xR) ),
inference(subst,[],[refute_0_1:[bind(W0,$fot(xb))]]) ).
cnf(refute_0_3,plain,
xb = xb,
introduced(tautology,[refl,[$fot(xb)]]) ).
cnf(refute_0_4,plain,
( ~ aElement0(xb)
| ~ aReductOfIn0(xb,xa,xR) ),
inference(resolve,[$cnf( $equal(xb,xb) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
aElement0(xb),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_6,plain,
~ aReductOfIn0(xb,xa,xR),
inference(resolve,[$cnf( aElement0(xb) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
sdtmndtplgtdt0(skolemFOFtoCNF_W0,xR,xb),
inference(resolve,[$cnf( aReductOfIn0(xb,xa,xR) )],[refute_0_0,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ aElement0(W0)
| ~ aReductOfIn0(W0,xa,xR)
| ~ sdtmndtplgtdt0(W0,xR,xb) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| ~ aReductOfIn0(skolemFOFtoCNF_W0,xa,xR)
| ~ sdtmndtplgtdt0(skolemFOFtoCNF_W0,xR,xb) ),
inference(subst,[],[refute_0_8:[bind(W0,$fot(skolemFOFtoCNF_W0))]]) ).
cnf(refute_0_10,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| ~ aReductOfIn0(skolemFOFtoCNF_W0,xa,xR) ),
inference(resolve,[$cnf( sdtmndtplgtdt0(skolemFOFtoCNF_W0,xR,xb) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
( aElement0(skolemFOFtoCNF_W0)
| aReductOfIn0(xb,xa,xR) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_12,plain,
aElement0(skolemFOFtoCNF_W0),
inference(resolve,[$cnf( aReductOfIn0(xb,xa,xR) )],[refute_0_11,refute_0_6]) ).
cnf(refute_0_13,plain,
~ aReductOfIn0(skolemFOFtoCNF_W0,xa,xR),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W0) )],[refute_0_12,refute_0_10]) ).
cnf(refute_0_14,plain,
( aReductOfIn0(skolemFOFtoCNF_W0,xa,xR)
| aReductOfIn0(xb,xa,xR) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_15,plain,
aReductOfIn0(skolemFOFtoCNF_W0,xa,xR),
inference(resolve,[$cnf( aReductOfIn0(xb,xa,xR) )],[refute_0_14,refute_0_6]) ).
cnf(refute_0_16,plain,
$false,
inference(resolve,[$cnf( aReductOfIn0(skolemFOFtoCNF_W0,xa,xR) )],[refute_0_15,refute_0_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COM016+4 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 16 17:32:19 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.41
% 0.18/0.41 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.18/0.41
%------------------------------------------------------------------------------