TSTP Solution File: SYN359+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN359+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 : Thu Jul 21 09:01:45 EDT 2022
% Result : Theorem 0.13s 0.34s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 25 ( 7 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 62 ( 24 ~; 17 |; 12 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 49 ( 2 sgn 27 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(x2110,conjecture,
( ( ? [X] : big_r(X)
& ! [Y] :
( big_r(Y)
=> ? [Z] : big_q(Y,Z) )
& ! [X,Y] :
( big_q(X,Y)
=> big_q(X,X) ) )
=> ? [X,Y] :
( big_q(X,Y)
& big_r(Y) ) ) ).
fof(subgoal_0,plain,
( ( ? [X] : big_r(X)
& ! [Y] :
( big_r(Y)
=> ? [Z] : big_q(Y,Z) )
& ! [X,Y] :
( big_q(X,Y)
=> big_q(X,X) ) )
=> ? [X,Y] :
( big_q(X,Y)
& big_r(Y) ) ),
inference(strip,[],[x2110]) ).
fof(negate_0_0,plain,
~ ( ( ? [X] : big_r(X)
& ! [Y] :
( big_r(Y)
=> ? [Z] : big_q(Y,Z) )
& ! [X,Y] :
( big_q(X,Y)
=> big_q(X,X) ) )
=> ? [X,Y] :
( big_q(X,Y)
& big_r(Y) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ? [X] : big_r(X)
& ! [X] :
( big_q(X,X)
| ! [Y] : ~ big_q(X,Y) )
& ! [Y] :
( ~ big_r(Y)
| ? [Z] : big_q(Y,Z) )
& ! [X,Y] :
( ~ big_q(X,Y)
| ~ big_r(Y) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ~ big_q(X,Y)
| ~ big_r(Y) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ~ big_q(X,Y)
| ~ big_r(Y) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
? [X] : big_r(X),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_4,plain,
big_r(skolemFOFtoCNF_X),
inference(skolemize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [Y] :
( ~ big_r(Y)
| ? [Z] : big_q(Y,Z) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_6,plain,
! [Y] :
( ~ big_r(Y)
| ? [Z] : big_q(Y,Z) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [Y] :
( ~ big_r(Y)
| big_q(Y,skolemFOFtoCNF_Z(Y)) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X] :
( big_q(X,X)
| ! [Y] : ~ big_q(X,Y) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_9,plain,
! [X] :
( big_q(X,X)
| ! [Y] : ~ big_q(X,Y) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ~ big_q(X,Y)
| big_q(X,X) ),
inference(clausify,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
( ~ big_q(X,Y)
| ~ big_r(Y) ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ big_q(skolemFOFtoCNF_X,skolemFOFtoCNF_X)
| ~ big_r(skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_2,plain,
big_r(skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( ~ big_r(Y)
| big_q(Y,skolemFOFtoCNF_Z(Y)) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_4,plain,
( ~ big_r(skolemFOFtoCNF_X)
| big_q(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_0_3:[bind(Y,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_5,plain,
big_q(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(skolemFOFtoCNF_X)),
inference(resolve,[$cnf( big_r(skolemFOFtoCNF_X) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ big_q(X,Y)
| big_q(X,X) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_7,plain,
( ~ big_q(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(skolemFOFtoCNF_X))
| big_q(skolemFOFtoCNF_X,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Z(skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_8,plain,
big_q(skolemFOFtoCNF_X,skolemFOFtoCNF_X),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(skolemFOFtoCNF_X)) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
~ big_r(skolemFOFtoCNF_X),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_8,refute_0_1]) ).
cnf(refute_0_10,plain,
$false,
inference(resolve,[$cnf( big_r(skolemFOFtoCNF_X) )],[refute_0_2,refute_0_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN359+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n015.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jul 11 15:28:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34
% 0.13/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.34
%------------------------------------------------------------------------------