TSTP Solution File: SYN066+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN066+1 : TPTP v8.1.0. Bugfixed v3.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 08:59:12 EDT 2022
% Result : Theorem 0.12s 0.33s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 38 ( 15 unt; 0 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 66 ( 25 ~; 25 |; 12 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 87 ( 13 sgn 37 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel37_1,axiom,
! [Z] :
? [W] :
! [X] :
? [Y] :
( ( big_p(X,Z)
=> big_p(Y,W) )
& big_p(Y,Z)
& ( big_p(Y,W)
=> ? [U] : big_q(U,W) ) ) ).
fof(pel37_2,axiom,
! [X,Z] :
( ~ big_p(X,Z)
=> ? [Y] : big_q(Y,Z) ) ).
fof(pel37_3,axiom,
( ? [X,Y] : big_q(X,Y)
=> ! [Z] : big_r(Z,Z) ) ).
fof(pel37,conjecture,
! [X] :
? [Y] : big_r(X,Y) ).
fof(subgoal_0,plain,
! [X] :
? [Y] : big_r(X,Y),
inference(strip,[],[pel37]) ).
fof(negate_0_0,plain,
~ ! [X] :
? [Y] : big_r(X,Y),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X] :
! [Y] : ~ big_r(X,Y),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [Y] : ~ big_r(skolemFOFtoCNF_X,Y),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [Y] : ~ big_r(skolemFOFtoCNF_X,Y),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( ! [Z] : big_r(Z,Z)
| ! [X,Y] : ~ big_q(X,Y) ),
inference(canonicalize,[],[pel37_3]) ).
fof(normalize_0_4,plain,
! [X,Y,Z] :
( ~ big_q(X,Y)
| big_r(Z,Z) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [Z] :
? [W] :
! [X] :
? [Y] :
( big_p(Y,Z)
& ( ~ big_p(X,Z)
| big_p(Y,W) )
& ( ~ big_p(Y,W)
| ? [U] : big_q(U,W) ) ),
inference(canonicalize,[],[pel37_1]) ).
fof(normalize_0_6,plain,
! [Z] :
? [W] :
! [X] :
? [Y] :
( big_p(Y,Z)
& ( ~ big_p(X,Z)
| big_p(Y,W) )
& ( ~ big_p(Y,W)
| ? [U] : big_q(U,W) ) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [Z,X] :
? [Y] :
( big_p(Y,Z)
& ( ~ big_p(X,Z)
| big_p(Y,skolemFOFtoCNF_W(Z)) )
& ( ~ big_p(Y,skolemFOFtoCNF_W(Z))
| ? [U] : big_q(U,skolemFOFtoCNF_W(Z)) ) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Z] :
? [Y] :
( big_p(Y,Z)
& ( ~ big_p(X,Z)
| big_p(Y,skolemFOFtoCNF_W(Z)) )
& ( ~ big_p(Y,skolemFOFtoCNF_W(Z))
| ? [U] : big_q(U,skolemFOFtoCNF_W(Z)) ) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X,Z] :
( big_p(skolemFOFtoCNF_Y(X,Z),Z)
& ( ~ big_p(X,Z)
| big_p(skolemFOFtoCNF_Y(X,Z),skolemFOFtoCNF_W(Z)) )
& ( ~ big_p(skolemFOFtoCNF_Y(X,Z),skolemFOFtoCNF_W(Z))
| ? [U] : big_q(U,skolemFOFtoCNF_W(Z)) ) ),
inference(skolemize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Z] :
( ~ big_p(skolemFOFtoCNF_Y(X,Z),skolemFOFtoCNF_W(Z))
| ? [U] : big_q(U,skolemFOFtoCNF_W(Z)) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X,Z] :
( ~ big_p(skolemFOFtoCNF_Y(X,Z),skolemFOFtoCNF_W(Z))
| big_q(skolemFOFtoCNF_U(Z),skolemFOFtoCNF_W(Z)) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X,Z] :
( big_p(X,Z)
| ? [Y] : big_q(Y,Z) ),
inference(canonicalize,[],[pel37_2]) ).
fof(normalize_0_13,plain,
! [X,Z] :
( big_p(X,Z)
| ? [Y] : big_q(Y,Z) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X,Z] :
( big_p(X,Z)
| big_q(skolemFOFtoCNF_Y_1(Z),Z) ),
inference(clausify,[],[normalize_0_13]) ).
cnf(refute_0_0,plain,
~ big_r(skolemFOFtoCNF_X,Y),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ big_r(skolemFOFtoCNF_X,skolemFOFtoCNF_X),
inference(subst,[],[refute_0_0:[bind(Y,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_2,plain,
( ~ big_q(X,Y)
| big_r(Z,Z) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( ~ big_q(skolemFOFtoCNF_U(X_13),skolemFOFtoCNF_W(X_13))
| big_r(Z,Z) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_U(X_13))),bind(Y,$fot(skolemFOFtoCNF_W(X_13)))]]) ).
cnf(refute_0_4,plain,
( ~ big_p(skolemFOFtoCNF_Y(X,Z),skolemFOFtoCNF_W(Z))
| big_q(skolemFOFtoCNF_U(Z),skolemFOFtoCNF_W(Z)) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_5,plain,
( big_p(X,Z)
| big_q(skolemFOFtoCNF_Y_1(Z),Z) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_6,plain,
( big_p(X,X_6)
| big_q(skolemFOFtoCNF_Y_1(X_6),X_6) ),
inference(subst,[],[refute_0_5:[bind(Z,$fot(X_6))]]) ).
cnf(refute_0_7,plain,
( ~ big_q(skolemFOFtoCNF_Y_1(X_6),X_6)
| big_r(X_7,X_7) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_Y_1(X_6))),bind(Y,$fot(X_6)),bind(Z,$fot(X_7))]]) ).
cnf(refute_0_8,plain,
( big_p(X,X_6)
| big_r(X_7,X_7) ),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_Y_1(X_6),X_6) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( big_p(X_8,X_9)
| big_r(skolemFOFtoCNF_X,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_8)),bind(X_6,$fot(X_9)),bind(X_7,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_10,plain,
big_p(X_8,X_9),
inference(resolve,[$cnf( big_r(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_9,refute_0_1]) ).
cnf(refute_0_11,plain,
big_p(skolemFOFtoCNF_Y(X,Z),skolemFOFtoCNF_W(Z)),
inference(subst,[],[refute_0_10:[bind(X_8,$fot(skolemFOFtoCNF_Y(X,Z))),bind(X_9,$fot(skolemFOFtoCNF_W(Z)))]]) ).
cnf(refute_0_12,plain,
big_q(skolemFOFtoCNF_U(Z),skolemFOFtoCNF_W(Z)),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_Y(X,Z),skolemFOFtoCNF_W(Z)) )],[refute_0_11,refute_0_4]) ).
cnf(refute_0_13,plain,
big_q(skolemFOFtoCNF_U(X_13),skolemFOFtoCNF_W(X_13)),
inference(subst,[],[refute_0_12:[bind(Z,$fot(X_13))]]) ).
cnf(refute_0_14,plain,
big_r(Z,Z),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_U(X_13),skolemFOFtoCNF_W(X_13)) )],[refute_0_13,refute_0_3]) ).
cnf(refute_0_15,plain,
big_r(skolemFOFtoCNF_X,skolemFOFtoCNF_X),
inference(subst,[],[refute_0_14:[bind(Z,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_16,plain,
$false,
inference(resolve,[$cnf( big_r(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_15,refute_0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYN066+1 : TPTP v8.1.0. Bugfixed v3.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.32 % Computer : n008.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jul 12 09:11:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33
% 0.12/0.33 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.33
%------------------------------------------------------------------------------