%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN377+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 09:01:54 EDT 2022
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 58 ( 34 unt; 0 def)
% Number of atoms : 112 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 93 ( 39 ~; 10 |; 14 &)
% ( 18 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 89 ( 12 sgn 51 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(x2128,conjecture,
( ! [X] :
( big_p(X)
<=> ! [Y] : big_p(Y) )
<=> ( ? [X] : big_p(X)
<=> ! [Y] : big_p(Y) ) ) ).
fof(subgoal_0,plain,
( ( ! [X] :
( big_p(X)
<=> ! [Y] : big_p(Y) )
& ? [X] : big_p(X) )
=> ! [Y] : big_p(Y) ),
inference(strip,[],[x2128]) ).
fof(subgoal_1,plain,
( ( ! [X] :
( big_p(X)
<=> ! [Y] : big_p(Y) )
& ! [Y] : big_p(Y) )
=> ? [X] : big_p(X) ),
inference(strip,[],[x2128]) ).
fof(subgoal_2,plain,
( ( ? [X] : big_p(X)
<=> ! [Y] : big_p(Y) )
=> ! [X] :
( big_p(X)
=> ! [Y] : big_p(Y) ) ),
inference(strip,[],[x2128]) ).
fof(subgoal_3,plain,
( ( ? [X] : big_p(X)
<=> ! [Y] : big_p(Y) )
=> ! [X] :
( ! [Y] : big_p(Y)
=> big_p(X) ) ),
inference(strip,[],[x2128]) ).
fof(negate_0_0,plain,
~ ( ( ! [X] :
( big_p(X)
<=> ! [Y] : big_p(Y) )
& ? [X] : big_p(X) )
=> ! [Y] : big_p(Y) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ? [X] : big_p(X)
& ? [Y] : ~ big_p(Y)
& ! [X] :
( ~ big_p(X)
<=> ? [Y] : ~ big_p(Y) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
? [Y] : ~ big_p(Y),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ big_p(skolemFOFtoCNF_Y),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
? [X] : big_p(X),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_4,plain,
big_p(skolemFOFtoCNF_X),
inference(skolemize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X] :
( ~ big_p(X)
<=> ? [Y] : ~ big_p(Y) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_6,plain,
! [X] :
( ~ big_p(X)
<=> ? [Y] : ~ big_p(Y) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ( ~ big_p(X)
| big_p(Y) )
& ( ~ big_p(skolemFOFtoCNF_Y_1)
| big_p(X) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ~ big_p(X)
| big_p(Y) ),
inference(conjunct,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
~ big_p(skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
big_p(skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ big_p(X)
| big_p(Y) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_3,plain,
( ~ big_p(skolemFOFtoCNF_X)
| big_p(X_1) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(X_1))]]) ).
cnf(refute_0_4,plain,
big_p(X_1),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
big_p(skolemFOFtoCNF_Y),
inference(subst,[],[refute_0_4:[bind(X_1,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_6,plain,
$false,
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_Y) )],[refute_0_5,refute_0_0]) ).
fof(negate_1_0,plain,
~ ( ( ! [X] :
( big_p(X)
<=> ! [Y] : big_p(Y) )
& ! [Y] : big_p(Y) )
=> ? [X] : big_p(X) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
( ! [X] : ~ big_p(X)
& ! [X] :
( ~ big_p(X)
<=> ? [Y] : ~ big_p(Y) )
& ! [Y] : big_p(Y) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
! [Y] : big_p(Y),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [Y] : big_p(Y),
inference(specialize,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [X] : ~ big_p(X),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_4,plain,
! [X] : ~ big_p(X),
inference(specialize,[],[normalize_1_3]) ).
cnf(refute_1_0,plain,
big_p(Y),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
~ big_p(X),
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_2,plain,
~ big_p(Y),
inference(subst,[],[refute_1_1:[bind(X,$fot(Y))]]) ).
cnf(refute_1_3,plain,
$false,
inference(resolve,[$cnf( big_p(Y) )],[refute_1_0,refute_1_2]) ).
fof(negate_2_0,plain,
~ ( ( ? [X] : big_p(X)
<=> ! [Y] : big_p(Y) )
=> ! [X] :
( big_p(X)
=> ! [Y] : big_p(Y) ) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
( ( ? [X] : big_p(X)
<=> ! [Y] : big_p(Y) )
& ? [X] : big_p(X)
& ? [Y] : ~ big_p(Y) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_1,plain,
? [Y] : ~ big_p(Y),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_2,plain,
~ big_p(skolemFOFtoCNF_Y_4),
inference(skolemize,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
? [X] : big_p(X),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_4,plain,
big_p(skolemFOFtoCNF_X_2),
inference(skolemize,[],[normalize_2_3]) ).
fof(normalize_2_5,plain,
( ? [X] : big_p(X)
<=> ! [Y] : big_p(Y) ),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_6,plain,
! [X,Y] :
( ( ~ big_p(X)
| big_p(Y) )
& ( ~ big_p(skolemFOFtoCNF_Y_3)
| big_p(skolemFOFtoCNF_X_1) ) ),
inference(clausify,[],[normalize_2_5]) ).
fof(normalize_2_7,plain,
! [X,Y] :
( ~ big_p(X)
| big_p(Y) ),
inference(conjunct,[],[normalize_2_6]) ).
cnf(refute_2_0,plain,
~ big_p(skolemFOFtoCNF_Y_4),
inference(canonicalize,[],[normalize_2_2]) ).
cnf(refute_2_1,plain,
big_p(skolemFOFtoCNF_X_2),
inference(canonicalize,[],[normalize_2_4]) ).
cnf(refute_2_2,plain,
( ~ big_p(X)
| big_p(Y) ),
inference(canonicalize,[],[normalize_2_7]) ).
cnf(refute_2_3,plain,
( ~ big_p(skolemFOFtoCNF_X_2)
| big_p(X_4) ),
inference(subst,[],[refute_2_2:[bind(X,$fot(skolemFOFtoCNF_X_2)),bind(Y,$fot(X_4))]]) ).
cnf(refute_2_4,plain,
big_p(X_4),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X_2) )],[refute_2_1,refute_2_3]) ).
cnf(refute_2_5,plain,
big_p(skolemFOFtoCNF_Y_4),
inference(subst,[],[refute_2_4:[bind(X_4,$fot(skolemFOFtoCNF_Y_4))]]) ).
cnf(refute_2_6,plain,
$false,
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_Y_4) )],[refute_2_5,refute_2_0]) ).
fof(negate_3_0,plain,
~ ( ( ? [X] : big_p(X)
<=> ! [Y] : big_p(Y) )
=> ! [X] :
( ! [Y] : big_p(Y)
=> big_p(X) ) ),
inference(negate,[],[subgoal_3]) ).
fof(normalize_3_0,plain,
( ( ? [X] : big_p(X)
<=> ! [Y] : big_p(Y) )
& ? [X] : ~ big_p(X)
& ! [Y] : big_p(Y) ),
inference(canonicalize,[],[negate_3_0]) ).
fof(normalize_3_1,plain,
? [X] : ~ big_p(X),
inference(conjunct,[],[normalize_3_0]) ).
fof(normalize_3_2,plain,
~ big_p(skolemFOFtoCNF_X_4),
inference(skolemize,[],[normalize_3_1]) ).
fof(normalize_3_3,plain,
! [Y] : big_p(Y),
inference(conjunct,[],[normalize_3_0]) ).
fof(normalize_3_4,plain,
! [Y] : big_p(Y),
inference(specialize,[],[normalize_3_3]) ).
cnf(refute_3_0,plain,
~ big_p(skolemFOFtoCNF_X_4),
inference(canonicalize,[],[normalize_3_2]) ).
cnf(refute_3_1,plain,
big_p(Y),
inference(canonicalize,[],[normalize_3_4]) ).
cnf(refute_3_2,plain,
big_p(skolemFOFtoCNF_X_4),
inference(subst,[],[refute_3_1:[bind(Y,$fot(skolemFOFtoCNF_X_4))]]) ).
cnf(refute_3_3,plain,
$false,
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X_4) )],[refute_3_2,refute_3_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN377+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n020.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 : Tue Jul 12 06:04:57 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35
% 0.13/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35
%------------------------------------------------------------------------------