TSTP Solution File: SYN065+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN065+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.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 0.21s 0.35s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 18 unt; 0 def)
% Number of atoms : 58 ( 0 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 61 ( 30 ~; 22 |; 7 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 45 ( 1 sgn 25 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel36_1,axiom,
! [X] :
? [Y] : big_f(X,Y) ).
fof(pel36_3,axiom,
! [X,Y] :
( ( big_f(X,Y)
| big_g(X,Y) )
=> ! [Z] :
( ( big_f(Y,Z)
| big_g(Y,Z) )
=> big_h(X,Z) ) ) ).
fof(pel36,conjecture,
! [X] :
? [Y] : big_h(X,Y) ).
fof(subgoal_0,plain,
! [X] :
? [Y] : big_h(X,Y),
inference(strip,[],[pel36]) ).
fof(negate_0_0,plain,
~ ! [X] :
? [Y] : big_h(X,Y),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X] :
! [Y] : ~ big_h(X,Y),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [Y] : ~ big_h(skolemFOFtoCNF_X,Y),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [Y] : ~ big_h(skolemFOFtoCNF_X,Y),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X] :
? [Y] : big_f(X,Y),
inference(canonicalize,[],[pel36_1]) ).
fof(normalize_0_4,plain,
! [X] :
? [Y] : big_f(X,Y),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X] : big_f(X,skolemFOFtoCNF_Y(X)),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ( ~ big_f(X,Y)
& ~ big_g(X,Y) )
| ! [Z] :
( big_h(X,Z)
| ( ~ big_f(Y,Z)
& ~ big_g(Y,Z) ) ) ),
inference(canonicalize,[],[pel36_3]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ( ~ big_f(X,Y)
& ~ big_g(X,Y) )
| ! [Z] :
( big_h(X,Z)
| ( ~ big_f(Y,Z)
& ~ big_g(Y,Z) ) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Y,Z] :
( ( ~ big_f(X,Y)
| ~ big_f(Y,Z)
| big_h(X,Z) )
& ( ~ big_f(X,Y)
| ~ big_g(Y,Z)
| big_h(X,Z) )
& ( ~ big_f(Y,Z)
| ~ big_g(X,Y)
| big_h(X,Z) )
& ( ~ big_g(X,Y)
| ~ big_g(Y,Z)
| big_h(X,Z) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X,Y,Z] :
( ~ big_f(X,Y)
| ~ big_f(Y,Z)
| big_h(X,Z) ),
inference(conjunct,[],[normalize_0_8]) ).
cnf(refute_0_0,plain,
~ big_h(skolemFOFtoCNF_X,Y),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ big_h(skolemFOFtoCNF_X,skolemFOFtoCNF_Y(skolemFOFtoCNF_Y(skolemFOFtoCNF_X))),
inference(subst,[],[refute_0_0:[bind(Y,$fot(skolemFOFtoCNF_Y(skolemFOFtoCNF_Y(skolemFOFtoCNF_X))))]]) ).
cnf(refute_0_2,plain,
big_f(X,skolemFOFtoCNF_Y(X)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
big_f(X_8,skolemFOFtoCNF_Y(X_8)),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_8))]]) ).
cnf(refute_0_4,plain,
big_f(X_6,skolemFOFtoCNF_Y(X_6)),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_5,plain,
( ~ big_f(X,Y)
| ~ big_f(Y,Z)
| big_h(X,Z) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_6,plain,
( ~ big_f(X_5,X_6)
| ~ big_f(X_6,skolemFOFtoCNF_Y(X_6))
| big_h(X_5,skolemFOFtoCNF_Y(X_6)) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_5)),bind(Y,$fot(X_6)),bind(Z,$fot(skolemFOFtoCNF_Y(X_6)))]]) ).
cnf(refute_0_7,plain,
( ~ big_f(X_5,X_6)
| big_h(X_5,skolemFOFtoCNF_Y(X_6)) ),
inference(resolve,[$cnf( big_f(X_6,skolemFOFtoCNF_Y(X_6)) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ big_f(X_8,skolemFOFtoCNF_Y(X_8))
| big_h(X_8,skolemFOFtoCNF_Y(skolemFOFtoCNF_Y(X_8))) ),
inference(subst,[],[refute_0_7:[bind(X_5,$fot(X_8)),bind(X_6,$fot(skolemFOFtoCNF_Y(X_8)))]]) ).
cnf(refute_0_9,plain,
big_h(X_8,skolemFOFtoCNF_Y(skolemFOFtoCNF_Y(X_8))),
inference(resolve,[$cnf( big_f(X_8,skolemFOFtoCNF_Y(X_8)) )],[refute_0_3,refute_0_8]) ).
cnf(refute_0_10,plain,
big_h(skolemFOFtoCNF_X,skolemFOFtoCNF_Y(skolemFOFtoCNF_Y(skolemFOFtoCNF_X))),
inference(subst,[],[refute_0_9:[bind(X_8,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_11,plain,
$false,
inference(resolve,[$cnf( big_h(skolemFOFtoCNF_X,skolemFOFtoCNF_Y(skolemFOFtoCNF_Y(skolemFOFtoCNF_X))) )],[refute_0_10,refute_0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : SYN065+1 : TPTP v8.1.0. Released v2.0.0.
% 0.13/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n006.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue Jul 12 09:05:20 EDT 2022
% 0.21/0.34 % CPUTime :
% 0.21/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.35
% 0.21/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.21/0.35
%------------------------------------------------------------------------------