TSTP Solution File: SYN986+1.003 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN986+1.003 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 09:12:40 EDT 2022
% Result : Theorem 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 3
% Syntax : Number of formulae : 50 ( 23 unt; 0 def)
% Number of atoms : 102 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 104 ( 52 ~; 41 |; 9 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 17 ( 3 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 : 88 ( 6 sgn 27 !; 12 ?)
% 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,
? [Z3,Z2,Z1,Z0] :
( r(zero,zero,Z3)
& r(zero,Z3,Z2)
& r(zero,Z2,Z1)
& r(zero,Z1,Z0) ) ).
fof(subgoal_0,plain,
? [Z3,Z2,Z1,Z0] :
( r(zero,zero,Z3)
& r(zero,Z3,Z2)
& r(zero,Z2,Z1)
& r(zero,Z1,Z0) ),
inference(strip,[],[ck]) ).
fof(negate_0_0,plain,
~ ? [Z3,Z2,Z1,Z0] :
( r(zero,zero,Z3)
& r(zero,Z3,Z2)
& r(zero,Z2,Z1)
& r(zero,Z1,Z0) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [Y] : r(Y,zero,succ(Y)),
inference(canonicalize,[],[hyp1]) ).
fof(normalize_0_1,plain,
! [Y] : r(Y,zero,succ(Y)),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y,Z,Z1] :
( ~ r(Y,X,Z)
| ~ r(Z,X,Z1)
| r(Y,succ(X),Z1) ),
inference(canonicalize,[],[hyp2]) ).
fof(normalize_0_3,plain,
! [X,Y,Z,Z1] :
( ~ r(Y,X,Z)
| ~ r(Z,X,Z1)
| r(Y,succ(X),Z1) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [Z1,Z2,Z3] :
( ~ r(zero,Z2,Z1)
| ~ r(zero,Z3,Z2)
| ~ r(zero,zero,Z3)
| ! [Z0] : ~ r(zero,Z1,Z0) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
! [Z1,Z2,Z3] :
( ~ r(zero,Z2,Z1)
| ~ r(zero,Z3,Z2)
| ~ r(zero,zero,Z3)
| ! [Z0] : ~ r(zero,Z1,Z0) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [Z0,Z1,Z2,Z3] :
( ~ r(zero,Z1,Z0)
| ~ r(zero,Z2,Z1)
| ~ r(zero,Z3,Z2)
| ~ r(zero,zero,Z3) ),
inference(clausify,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
r(Y,zero,succ(Y)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
r(succ(X_15),zero,succ(succ(X_15))),
inference(subst,[],[refute_0_0:[bind(Y,$fot(succ(X_15)))]]) ).
cnf(refute_0_2,plain,
r(X_12,zero,succ(X_12)),
inference(subst,[],[refute_0_0:[bind(Y,$fot(X_12))]]) ).
cnf(refute_0_3,plain,
( ~ r(Y,X,Z)
| ~ r(Z,X,Z1)
| r(Y,succ(X),Z1) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_4,plain,
( ~ r(X_12,zero,succ(X_12))
| ~ r(succ(X_12),zero,X_14)
| r(X_12,succ(zero),X_14) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(zero)),bind(Y,$fot(X_12)),bind(Z,$fot(succ(X_12))),bind(Z1,$fot(X_14))]]) ).
cnf(refute_0_5,plain,
( ~ r(succ(X_12),zero,X_14)
| r(X_12,succ(zero),X_14) ),
inference(resolve,[$cnf( r(X_12,zero,succ(X_12)) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ r(succ(X_15),zero,succ(succ(X_15)))
| r(X_15,succ(zero),succ(succ(X_15))) ),
inference(subst,[],[refute_0_5:[bind(X_12,$fot(X_15)),bind(X_14,$fot(succ(succ(X_15))))]]) ).
cnf(refute_0_7,plain,
r(X_15,succ(zero),succ(succ(X_15))),
inference(resolve,[$cnf( r(succ(X_15),zero,succ(succ(X_15))) )],[refute_0_1,refute_0_6]) ).
cnf(refute_0_8,plain,
r(succ(succ(X_21)),succ(zero),succ(succ(succ(succ(X_21))))),
inference(subst,[],[refute_0_7:[bind(X_15,$fot(succ(succ(X_21))))]]) ).
cnf(refute_0_9,plain,
( ~ r(X_17,succ(zero),succ(succ(X_17)))
| ~ r(succ(succ(X_17)),succ(zero),Z1)
| r(X_17,succ(succ(zero)),Z1) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(succ(zero))),bind(Y,$fot(X_17)),bind(Z,$fot(succ(succ(X_17))))]]) ).
cnf(refute_0_10,plain,
r(X_17,succ(zero),succ(succ(X_17))),
inference(subst,[],[refute_0_7:[bind(X_15,$fot(X_17))]]) ).
cnf(refute_0_11,plain,
( ~ r(succ(succ(X_17)),succ(zero),Z1)
| r(X_17,succ(succ(zero)),Z1) ),
inference(resolve,[$cnf( r(X_17,succ(zero),succ(succ(X_17))) )],[refute_0_10,refute_0_9]) ).
cnf(refute_0_12,plain,
( ~ r(succ(succ(X_21)),succ(zero),succ(succ(succ(succ(X_21)))))
| r(X_21,succ(succ(zero)),succ(succ(succ(succ(X_21))))) ),
inference(subst,[],[refute_0_11:[bind(Z1,$fot(succ(succ(succ(succ(X_21)))))),bind(X_17,$fot(X_21))]]) ).
cnf(refute_0_13,plain,
r(X_21,succ(succ(zero)),succ(succ(succ(succ(X_21))))),
inference(resolve,[$cnf( r(succ(succ(X_21)),succ(zero),succ(succ(succ(succ(X_21))))) )],[refute_0_8,refute_0_12]) ).
cnf(refute_0_14,plain,
r(zero,succ(succ(zero)),succ(succ(succ(succ(zero))))),
inference(subst,[],[refute_0_13:[bind(X_21,$fot(zero))]]) ).
cnf(refute_0_15,plain,
r(zero,succ(zero),succ(succ(zero))),
inference(subst,[],[refute_0_7:[bind(X_15,$fot(zero))]]) ).
cnf(refute_0_16,plain,
( ~ r(zero,Z1,Z0)
| ~ r(zero,Z2,Z1)
| ~ r(zero,Z3,Z2)
| ~ r(zero,zero,Z3) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_17,plain,
( ~ r(zero,X_31,X_30)
| ~ r(zero,succ(succ(zero)),X_31)
| ~ r(zero,succ(zero),succ(succ(zero)))
| ~ r(zero,zero,succ(zero)) ),
inference(subst,[],[refute_0_16:[bind(Z0,$fot(X_30)),bind(Z1,$fot(X_31)),bind(Z2,$fot(succ(succ(zero)))),bind(Z3,$fot(succ(zero)))]]) ).
cnf(refute_0_18,plain,
( ~ r(zero,X_31,X_30)
| ~ r(zero,succ(succ(zero)),X_31)
| ~ r(zero,zero,succ(zero)) ),
inference(resolve,[$cnf( r(zero,succ(zero),succ(succ(zero))) )],[refute_0_15,refute_0_17]) ).
cnf(refute_0_19,plain,
r(zero,zero,succ(zero)),
inference(subst,[],[refute_0_0:[bind(Y,$fot(zero))]]) ).
cnf(refute_0_20,plain,
( ~ r(zero,X_31,X_30)
| ~ r(zero,succ(succ(zero)),X_31) ),
inference(resolve,[$cnf( r(zero,zero,succ(zero)) )],[refute_0_19,refute_0_18]) ).
cnf(refute_0_21,plain,
( ~ r(zero,succ(succ(succ(succ(zero)))),X_34)
| ~ r(zero,succ(succ(zero)),succ(succ(succ(succ(zero))))) ),
inference(subst,[],[refute_0_20:[bind(X_30,$fot(X_34)),bind(X_31,$fot(succ(succ(succ(succ(zero))))))]]) ).
cnf(refute_0_22,plain,
~ r(zero,succ(succ(succ(succ(zero)))),X_34),
inference(resolve,[$cnf( r(zero,succ(succ(zero)),succ(succ(succ(succ(zero))))) )],[refute_0_14,refute_0_21]) ).
cnf(refute_0_23,plain,
~ r(zero,succ(succ(succ(succ(zero)))),succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(zero))))))))))))))))),
inference(subst,[],[refute_0_22:[bind(X_34,$fot(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(zero))))))))))))))))))]]) ).
cnf(refute_0_24,plain,
r(X_23,succ(succ(zero)),succ(succ(succ(succ(X_23))))),
inference(subst,[],[refute_0_13:[bind(X_21,$fot(X_23))]]) ).
cnf(refute_0_25,plain,
( ~ r(Y,succ(succ(zero)),X_22)
| ~ r(X_22,succ(succ(zero)),succ(succ(succ(succ(X_22)))))
| r(Y,succ(succ(succ(zero))),succ(succ(succ(succ(X_22))))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(succ(succ(zero)))),bind(Z,$fot(X_22)),bind(Z1,$fot(succ(succ(succ(succ(X_22))))))]]) ).
cnf(refute_0_26,plain,
r(X_22,succ(succ(zero)),succ(succ(succ(succ(X_22))))),
inference(subst,[],[refute_0_13:[bind(X_21,$fot(X_22))]]) ).
cnf(refute_0_27,plain,
( ~ r(Y,succ(succ(zero)),X_22)
| r(Y,succ(succ(succ(zero))),succ(succ(succ(succ(X_22))))) ),
inference(resolve,[$cnf( r(X_22,succ(succ(zero)),succ(succ(succ(succ(X_22))))) )],[refute_0_26,refute_0_25]) ).
cnf(refute_0_28,plain,
( ~ r(X_23,succ(succ(zero)),succ(succ(succ(succ(X_23)))))
| r(X_23,succ(succ(succ(zero))),succ(succ(succ(succ(succ(succ(succ(succ(X_23))))))))) ),
inference(subst,[],[refute_0_27:[bind(Y,$fot(X_23)),bind(X_22,$fot(succ(succ(succ(succ(X_23))))))]]) ).
cnf(refute_0_29,plain,
r(X_23,succ(succ(succ(zero))),succ(succ(succ(succ(succ(succ(succ(succ(X_23))))))))),
inference(resolve,[$cnf( r(X_23,succ(succ(zero)),succ(succ(succ(succ(X_23))))) )],[refute_0_24,refute_0_28]) ).
cnf(refute_0_30,plain,
r(X_46,succ(succ(succ(zero))),succ(succ(succ(succ(succ(succ(succ(succ(X_46))))))))),
inference(subst,[],[refute_0_29:[bind(X_23,$fot(X_46))]]) ).
cnf(refute_0_31,plain,
( ~ r(Y,succ(succ(succ(zero))),X_25)
| ~ r(X_25,succ(succ(succ(zero))),succ(succ(succ(succ(succ(succ(succ(succ(X_25)))))))))
| r(Y,succ(succ(succ(succ(zero)))),succ(succ(succ(succ(succ(succ(succ(succ(X_25))))))))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(succ(succ(succ(zero))))),bind(Z,$fot(X_25)),bind(Z1,$fot(succ(succ(succ(succ(succ(succ(succ(succ(X_25))))))))))]]) ).
cnf(refute_0_32,plain,
r(X_25,succ(succ(succ(zero))),succ(succ(succ(succ(succ(succ(succ(succ(X_25))))))))),
inference(subst,[],[refute_0_29:[bind(X_23,$fot(X_25))]]) ).
cnf(refute_0_33,plain,
( ~ r(Y,succ(succ(succ(zero))),X_25)
| r(Y,succ(succ(succ(succ(zero)))),succ(succ(succ(succ(succ(succ(succ(succ(X_25))))))))) ),
inference(resolve,[$cnf( r(X_25,succ(succ(succ(zero))),succ(succ(succ(succ(succ(succ(succ(succ(X_25))))))))) )],[refute_0_32,refute_0_31]) ).
cnf(refute_0_34,plain,
( ~ r(X_46,succ(succ(succ(zero))),succ(succ(succ(succ(succ(succ(succ(succ(X_46)))))))))
| r(X_46,succ(succ(succ(succ(zero)))),succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X_46))))))))))))))))) ),
inference(subst,[],[refute_0_33:[bind(Y,$fot(X_46)),bind(X_25,$fot(succ(succ(succ(succ(succ(succ(succ(succ(X_46))))))))))]]) ).
cnf(refute_0_35,plain,
r(X_46,succ(succ(succ(succ(zero)))),succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X_46))))))))))))))))),
inference(resolve,[$cnf( r(X_46,succ(succ(succ(zero))),succ(succ(succ(succ(succ(succ(succ(succ(X_46))))))))) )],[refute_0_30,refute_0_34]) ).
cnf(refute_0_36,plain,
r(zero,succ(succ(succ(succ(zero)))),succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(zero))))))))))))))))),
inference(subst,[],[refute_0_35:[bind(X_46,$fot(zero))]]) ).
cnf(refute_0_37,plain,
$false,
inference(resolve,[$cnf( r(zero,succ(succ(succ(succ(zero)))),succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(zero))))))))))))))))) )],[refute_0_36,refute_0_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN986+1.003 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 15:46:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.36
% 0.13/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.37
%------------------------------------------------------------------------------