TSTP Solution File: SYN078+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN078+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n009.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 08:59:22 EDT 2022
% Result : Theorem 0.13s 0.34s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 47 ( 18 unt; 0 def)
% Number of atoms : 106 ( 29 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 97 ( 38 ~; 26 |; 18 &)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 45 ( 0 sgn 21 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel56,conjecture,
( ! [X] :
( ? [Y] :
( big_p(Y)
& X = f(Y) )
=> big_p(X) )
<=> ! [U] :
( big_p(U)
=> big_p(f(U)) ) ) ).
fof(subgoal_0,plain,
( ! [X] :
( ? [Y] :
( big_p(Y)
& X = f(Y) )
=> big_p(X) )
=> ! [U] :
( big_p(U)
=> big_p(f(U)) ) ),
inference(strip,[],[pel56]) ).
fof(subgoal_1,plain,
( ! [U] :
( big_p(U)
=> big_p(f(U)) )
=> ! [X] :
( ? [Y] :
( big_p(Y)
& X = f(Y) )
=> big_p(X) ) ),
inference(strip,[],[pel56]) ).
fof(negate_0_0,plain,
~ ( ! [X] :
( ? [Y] :
( big_p(Y)
& X = f(Y) )
=> big_p(X) )
=> ! [U] :
( big_p(U)
=> big_p(f(U)) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ? [U] :
( ~ big_p(f(U))
& big_p(U) )
& ! [X] :
( big_p(X)
| ! [Y] :
( X != f(Y)
| ~ big_p(Y) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
? [U] :
( ~ big_p(f(U))
& big_p(U) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ big_p(f(skolemFOFtoCNF_U))
& big_p(skolemFOFtoCNF_U) ),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
big_p(skolemFOFtoCNF_U),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X] :
( big_p(X)
| ! [Y] :
( X != f(Y)
| ~ big_p(Y) ) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_5,plain,
! [X] :
( big_p(X)
| ! [Y] :
( X != f(Y)
| ~ big_p(Y) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( X != f(Y)
| ~ big_p(Y)
| big_p(X) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
~ big_p(f(skolemFOFtoCNF_U)),
inference(conjunct,[],[normalize_0_2]) ).
cnf(refute_0_0,plain,
big_p(skolemFOFtoCNF_U),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( X != f(Y)
| ~ big_p(Y)
| big_p(X) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( f(Y) != f(Y)
| ~ big_p(Y)
| big_p(f(Y)) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(f(Y)))]]) ).
cnf(refute_0_3,plain,
f(Y) = f(Y),
introduced(tautology,[refl,[$fot(f(Y))]]) ).
cnf(refute_0_4,plain,
( ~ big_p(Y)
| big_p(f(Y)) ),
inference(resolve,[$cnf( $equal(f(Y),f(Y)) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
( ~ big_p(skolemFOFtoCNF_U)
| big_p(f(skolemFOFtoCNF_U)) ),
inference(subst,[],[refute_0_4:[bind(Y,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_6,plain,
big_p(f(skolemFOFtoCNF_U)),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_U) )],[refute_0_0,refute_0_5]) ).
cnf(refute_0_7,plain,
~ big_p(f(skolemFOFtoCNF_U)),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_8,plain,
$false,
inference(resolve,[$cnf( big_p(f(skolemFOFtoCNF_U)) )],[refute_0_6,refute_0_7]) ).
fof(negate_1_0,plain,
~ ( ! [U] :
( big_p(U)
=> big_p(f(U)) )
=> ! [X] :
( ? [Y] :
( big_p(Y)
& X = f(Y) )
=> big_p(X) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
( ? [X] :
( ~ big_p(X)
& ? [Y] :
( X = f(Y)
& big_p(Y) ) )
& ! [U] :
( ~ big_p(U)
| big_p(f(U)) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
? [X] :
( ~ big_p(X)
& ? [Y] :
( X = f(Y)
& big_p(Y) ) ),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
( ~ big_p(skolemFOFtoCNF_X)
& ? [Y] :
( skolemFOFtoCNF_X = f(Y)
& big_p(Y) ) ),
inference(skolemize,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
? [Y] :
( skolemFOFtoCNF_X = f(Y)
& big_p(Y) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
( skolemFOFtoCNF_X = f(skolemFOFtoCNF_Y)
& big_p(skolemFOFtoCNF_Y) ),
inference(skolemize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
big_p(skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [U] :
( ~ big_p(U)
| big_p(f(U)) ),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_7,plain,
! [U] :
( ~ big_p(U)
| big_p(f(U)) ),
inference(specialize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
skolemFOFtoCNF_X = f(skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_1_4]) ).
fof(normalize_1_9,plain,
~ big_p(skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_1_2]) ).
cnf(refute_1_0,plain,
big_p(skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_1_5]) ).
cnf(refute_1_1,plain,
( ~ big_p(U)
| big_p(f(U)) ),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_2,plain,
( ~ big_p(skolemFOFtoCNF_Y)
| big_p(f(skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_1_1:[bind(U,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_1_3,plain,
big_p(f(skolemFOFtoCNF_Y)),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_Y) )],[refute_1_0,refute_1_2]) ).
cnf(refute_1_4,plain,
skolemFOFtoCNF_X = f(skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_5,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_1_6,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_1_7,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_1_5,refute_1_6]) ).
cnf(refute_1_8,plain,
( skolemFOFtoCNF_X != f(skolemFOFtoCNF_Y)
| f(skolemFOFtoCNF_Y) = skolemFOFtoCNF_X ),
inference(subst,[],[refute_1_7:[bind(X0,$fot(skolemFOFtoCNF_X)),bind(Y0,$fot(f(skolemFOFtoCNF_Y)))]]) ).
cnf(refute_1_9,plain,
f(skolemFOFtoCNF_Y) = skolemFOFtoCNF_X,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y)) )],[refute_1_4,refute_1_8]) ).
cnf(refute_1_10,plain,
( f(skolemFOFtoCNF_Y) != skolemFOFtoCNF_X
| ~ big_p(f(skolemFOFtoCNF_Y))
| big_p(skolemFOFtoCNF_X) ),
introduced(tautology,[equality,[$cnf( big_p(f(skolemFOFtoCNF_Y)) ),[0],$fot(skolemFOFtoCNF_X)]]) ).
cnf(refute_1_11,plain,
( ~ big_p(f(skolemFOFtoCNF_Y))
| big_p(skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_Y),skolemFOFtoCNF_X) )],[refute_1_9,refute_1_10]) ).
cnf(refute_1_12,plain,
big_p(skolemFOFtoCNF_X),
inference(resolve,[$cnf( big_p(f(skolemFOFtoCNF_Y)) )],[refute_1_3,refute_1_11]) ).
cnf(refute_1_13,plain,
~ big_p(skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_14,plain,
$false,
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X) )],[refute_1_12,refute_1_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN078+1 : TPTP v8.1.0. Released v2.0.0.
% 0.04/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jul 11 12:11:07 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34
% 0.13/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.34
%------------------------------------------------------------------------------