TSTP Solution File: SYN986+1.001 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN986+1.001 : 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 : Thu Jul 21 09:12:39 EDT 2022
% Result : Theorem 0.12s 0.34s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 11 unt; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 42 ( 22 ~; 15 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 42 ( 1 sgn 21 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(hyp1,axiom,
! [Y] : r(Y,zero,succ(Y)) ).
fof(hyp2,axiom,
! [Y,X,Z,Z1] :
( r(Y,X,Z)
=> ( r(Z,X,Z1)
=> r(Y,succ(X),Z1) ) ) ).
fof(ck,conjecture,
? [Z1,Z0] :
( r(zero,zero,Z1)
& r(zero,Z1,Z0) ) ).
fof(subgoal_0,plain,
? [Z1,Z0] :
( r(zero,zero,Z1)
& r(zero,Z1,Z0) ),
inference(strip,[],[ck]) ).
fof(negate_0_0,plain,
~ ? [Z1,Z0] :
( r(zero,zero,Z1)
& r(zero,Z1,Z0) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [Z1] :
( ~ r(zero,zero,Z1)
| ! [Z0] : ~ r(zero,Z1,Z0) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [Z1] :
( ~ r(zero,zero,Z1)
| ! [Z0] : ~ r(zero,Z1,Z0) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [Z0,Z1] :
( ~ r(zero,Z1,Z0)
| ~ r(zero,zero,Z1) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [Y] : r(Y,zero,succ(Y)),
inference(canonicalize,[],[hyp1]) ).
fof(normalize_0_4,plain,
! [Y] : r(Y,zero,succ(Y)),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X,Y,Z,Z1] :
( ~ r(Y,X,Z)
| ~ r(Z,X,Z1)
| r(Y,succ(X),Z1) ),
inference(canonicalize,[],[hyp2]) ).
fof(normalize_0_6,plain,
! [X,Y,Z,Z1] :
( ~ r(Y,X,Z)
| ~ r(Z,X,Z1)
| r(Y,succ(X),Z1) ),
inference(specialize,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
( ~ r(zero,Z1,Z0)
| ~ r(zero,zero,Z1) ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ r(zero,succ(zero),succ(succ(zero)))
| ~ r(zero,zero,succ(zero)) ),
inference(subst,[],[refute_0_0:[bind(Z0,$fot(succ(succ(zero)))),bind(Z1,$fot(succ(zero)))]]) ).
cnf(refute_0_2,plain,
r(Y,zero,succ(Y)),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
r(succ(X_9),zero,succ(succ(X_9))),
inference(subst,[],[refute_0_2:[bind(Y,$fot(succ(X_9)))]]) ).
cnf(refute_0_4,plain,
r(X_6,zero,succ(X_6)),
inference(subst,[],[refute_0_2:[bind(Y,$fot(X_6))]]) ).
cnf(refute_0_5,plain,
( ~ r(Y,X,Z)
| ~ r(Z,X,Z1)
| r(Y,succ(X),Z1) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_6,plain,
( ~ r(X_6,zero,succ(X_6))
| ~ r(succ(X_6),zero,X_8)
| r(X_6,succ(zero),X_8) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(zero)),bind(Y,$fot(X_6)),bind(Z,$fot(succ(X_6))),bind(Z1,$fot(X_8))]]) ).
cnf(refute_0_7,plain,
( ~ r(succ(X_6),zero,X_8)
| r(X_6,succ(zero),X_8) ),
inference(resolve,[$cnf( r(X_6,zero,succ(X_6)) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ r(succ(X_9),zero,succ(succ(X_9)))
| r(X_9,succ(zero),succ(succ(X_9))) ),
inference(subst,[],[refute_0_7:[bind(X_6,$fot(X_9)),bind(X_8,$fot(succ(succ(X_9))))]]) ).
cnf(refute_0_9,plain,
r(X_9,succ(zero),succ(succ(X_9))),
inference(resolve,[$cnf( r(succ(X_9),zero,succ(succ(X_9))) )],[refute_0_3,refute_0_8]) ).
cnf(refute_0_10,plain,
r(zero,succ(zero),succ(succ(zero))),
inference(subst,[],[refute_0_9:[bind(X_9,$fot(zero))]]) ).
cnf(refute_0_11,plain,
~ r(zero,zero,succ(zero)),
inference(resolve,[$cnf( r(zero,succ(zero),succ(succ(zero))) )],[refute_0_10,refute_0_1]) ).
cnf(refute_0_12,plain,
r(zero,zero,succ(zero)),
inference(subst,[],[refute_0_2:[bind(Y,$fot(zero))]]) ).
cnf(refute_0_13,plain,
$false,
inference(resolve,[$cnf( r(zero,zero,succ(zero)) )],[refute_0_12,refute_0_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYN986+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % 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 : Mon Jul 11 23:29:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34
% 0.12/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.34
%------------------------------------------------------------------------------