TSTP Solution File: LCL527+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL527+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n005.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 : Sun Jul 17 12:52:56 EDT 2022
% Result : Theorem 2.38s 2.58s
% Output : CNFRefutation 2.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 20 unt; 0 def)
% Number of atoms : 105 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 99 ( 40 ~; 38 |; 13 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 4 prp; 0-1 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 16 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(Y) ) ) ).
fof(and_3,axiom,
( and_3
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) ) ).
fof(hilbert_modus_ponens,axiom,
modus_ponens ).
fof(hilbert_and_3,axiom,
and_3 ).
fof(adjunction,axiom,
( adjunction
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(Y) )
=> is_a_theorem(and(X,Y)) ) ) ).
fof(s1_0_adjunction,conjecture,
adjunction ).
fof(subgoal_0,plain,
adjunction,
inference(strip,[],[s1_0_adjunction]) ).
fof(negate_0_0,plain,
~ adjunction,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ adjunction
<=> ? [X,Y] :
( ~ is_a_theorem(and(X,Y))
& is_a_theorem(X)
& is_a_theorem(Y) ) ),
inference(canonicalize,[],[adjunction]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ( ~ is_a_theorem(and(skolemFOFtoCNF_X_17,skolemFOFtoCNF_Y_16))
| adjunction )
& ( adjunction
| is_a_theorem(skolemFOFtoCNF_X_17) )
& ( adjunction
| is_a_theorem(skolemFOFtoCNF_Y_16) )
& ( ~ adjunction
| ~ is_a_theorem(X)
| ~ is_a_theorem(Y)
| is_a_theorem(and(X,Y)) ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( adjunction
| is_a_theorem(skolemFOFtoCNF_Y_16) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ adjunction,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_4,plain,
( ~ modus_ponens
<=> ? [X,Y] :
( ~ is_a_theorem(Y)
& is_a_theorem(X)
& is_a_theorem(implies(X,Y)) ) ),
inference(canonicalize,[],[modus_ponens]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ( ~ is_a_theorem(skolemFOFtoCNF_Y)
| modus_ponens )
& ( is_a_theorem(implies(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| modus_ponens )
& ( is_a_theorem(skolemFOFtoCNF_X)
| modus_ponens )
& ( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
modus_ponens,
inference(canonicalize,[],[hilbert_modus_ponens]) ).
fof(normalize_0_8,plain,
( adjunction
| is_a_theorem(skolemFOFtoCNF_X_17) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_9,plain,
( ~ and_3
<=> ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(canonicalize,[],[and_3]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ( ~ and_3
| is_a_theorem(implies(X,implies(Y,and(X,Y)))) )
& ( ~ is_a_theorem(implies(skolemFOFtoCNF_X_8,implies(skolemFOFtoCNF_Y_8,and(skolemFOFtoCNF_X_8,skolemFOFtoCNF_Y_8))))
| and_3 ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( ~ and_3
| is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
and_3,
inference(canonicalize,[],[hilbert_and_3]) ).
fof(normalize_0_13,plain,
( ~ is_a_theorem(and(skolemFOFtoCNF_X_17,skolemFOFtoCNF_Y_16))
| adjunction ),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
( adjunction
| is_a_theorem(skolemFOFtoCNF_Y_16) ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ adjunction,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
is_a_theorem(skolemFOFtoCNF_Y_16),
inference(resolve,[$cnf( adjunction )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
modus_ponens,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) ),
inference(resolve,[$cnf( modus_ponens )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(X_2083)
| ~ is_a_theorem(implies(X_2083,and(skolemFOFtoCNF_X_17,X_2083)))
| is_a_theorem(and(skolemFOFtoCNF_X_17,X_2083)) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_2083)),bind(Y,$fot(and(skolemFOFtoCNF_X_17,X_2083)))]]) ).
cnf(refute_0_7,plain,
( adjunction
| is_a_theorem(skolemFOFtoCNF_X_17) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_8,plain,
is_a_theorem(skolemFOFtoCNF_X_17),
inference(resolve,[$cnf( adjunction )],[refute_0_7,refute_0_1]) ).
cnf(refute_0_9,plain,
( ~ and_3
| is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_10,plain,
and_3,
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_11,plain,
is_a_theorem(implies(X,implies(Y,and(X,Y)))),
inference(resolve,[$cnf( and_3 )],[refute_0_10,refute_0_9]) ).
cnf(refute_0_12,plain,
is_a_theorem(implies(X_624,implies(Y,and(X_624,Y)))),
inference(subst,[],[refute_0_11:[bind(X,$fot(X_624))]]) ).
cnf(refute_0_13,plain,
( ~ is_a_theorem(X_624)
| ~ is_a_theorem(implies(X_624,implies(Y,and(X_624,Y))))
| is_a_theorem(implies(Y,and(X_624,Y))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_624)),bind(Y,$fot(implies(Y,and(X_624,Y))))]]) ).
cnf(refute_0_14,plain,
( ~ is_a_theorem(X_624)
| is_a_theorem(implies(Y,and(X_624,Y))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_624,implies(Y,and(X_624,Y)))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ is_a_theorem(skolemFOFtoCNF_X_17)
| is_a_theorem(implies(X_2081,and(skolemFOFtoCNF_X_17,X_2081))) ),
inference(subst,[],[refute_0_14:[bind(Y,$fot(X_2081)),bind(X_624,$fot(skolemFOFtoCNF_X_17))]]) ).
cnf(refute_0_16,plain,
is_a_theorem(implies(X_2081,and(skolemFOFtoCNF_X_17,X_2081))),
inference(resolve,[$cnf( is_a_theorem(skolemFOFtoCNF_X_17) )],[refute_0_8,refute_0_15]) ).
cnf(refute_0_17,plain,
is_a_theorem(implies(X_2083,and(skolemFOFtoCNF_X_17,X_2083))),
inference(subst,[],[refute_0_16:[bind(X_2081,$fot(X_2083))]]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(X_2083)
| is_a_theorem(and(skolemFOFtoCNF_X_17,X_2083)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_2083,and(skolemFOFtoCNF_X_17,X_2083))) )],[refute_0_17,refute_0_6]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(skolemFOFtoCNF_Y_16)
| is_a_theorem(and(skolemFOFtoCNF_X_17,skolemFOFtoCNF_Y_16)) ),
inference(subst,[],[refute_0_18:[bind(X_2083,$fot(skolemFOFtoCNF_Y_16))]]) ).
cnf(refute_0_20,plain,
is_a_theorem(and(skolemFOFtoCNF_X_17,skolemFOFtoCNF_Y_16)),
inference(resolve,[$cnf( is_a_theorem(skolemFOFtoCNF_Y_16) )],[refute_0_2,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ is_a_theorem(and(skolemFOFtoCNF_X_17,skolemFOFtoCNF_Y_16))
| adjunction ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_22,plain,
~ is_a_theorem(and(skolemFOFtoCNF_X_17,skolemFOFtoCNF_Y_16)),
inference(resolve,[$cnf( adjunction )],[refute_0_21,refute_0_1]) ).
cnf(refute_0_23,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(and(skolemFOFtoCNF_X_17,skolemFOFtoCNF_Y_16)) )],[refute_0_20,refute_0_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL527+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 3 14:24:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.38/2.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.38/2.58
% 2.38/2.58 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.38/2.58
%------------------------------------------------------------------------------