TSTP Solution File: LCL452+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL452+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : Sun Jul 17 12:52:24 EDT 2022
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 58 ( 29 unt; 0 def)
% Number of atoms : 95 ( 38 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 73 ( 36 ~; 29 |; 2 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 59 ( 2 sgn 22 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(or_1,axiom,
( or_1
<=> ! [X,Y] : is_a_theorem(implies(X,or(X,Y))) ) ).
fof(cn2,axiom,
( cn2
<=> ! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q))) ) ).
fof(op_or,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ) ).
fof(hilbert_op_or,axiom,
op_or ).
fof(hilbert_op_implies_and,axiom,
op_implies_and ).
fof(hilbert_or_1,axiom,
or_1 ).
fof(luka_op_or,axiom,
op_or ).
fof(luka_cn2,conjecture,
cn2 ).
fof(subgoal_0,plain,
cn2,
inference(strip,[],[luka_cn2]) ).
fof(negate_0_0,plain,
~ cn2,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ cn2
<=> ? [P,Q] : ~ is_a_theorem(implies(P,implies(not(P),Q))) ),
inference(canonicalize,[],[cn2]) ).
fof(normalize_0_1,plain,
! [P,Q] :
( ( ~ cn2
| is_a_theorem(implies(P,implies(not(P),Q))) )
& ( ~ is_a_theorem(implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3)))
| cn2 ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ is_a_theorem(implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3)))
| cn2 ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( ~ op_or
| ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[op_or]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
op_or,
inference(canonicalize,[],[luka_op_or]) ).
fof(normalize_0_6,plain,
( ~ op_implies_and
| ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[op_implies_and]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
op_implies_and,
inference(canonicalize,[],[hilbert_op_implies_and]) ).
fof(normalize_0_9,plain,
( ~ or_1
<=> ? [X,Y] : ~ is_a_theorem(implies(X,or(X,Y))) ),
inference(canonicalize,[],[or_1]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ( ~ is_a_theorem(implies(skolemFOFtoCNF_X_9,or(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_9)))
| or_1 )
& ( ~ or_1
| is_a_theorem(implies(X,or(X,Y))) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( ~ or_1
| is_a_theorem(implies(X,or(X,Y))) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
or_1,
inference(canonicalize,[],[hilbert_or_1]) ).
fof(normalize_0_13,plain,
~ cn2,
inference(canonicalize,[],[negate_0_0]) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3)))
| cn2 ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
op_or,
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
or(X,Y) = not(and(not(X),not(Y))),
inference(resolve,[$cnf( op_or )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
op_implies_and,
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_6,plain,
implies(X,Y) = not(and(X,not(Y))),
inference(resolve,[$cnf( op_implies_and )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_8,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_9,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( implies(X,Y) != not(and(X,not(Y)))
| not(and(X,not(Y))) = implies(X,Y) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(not(and(X,not(Y)))))]]) ).
cnf(refute_0_11,plain,
not(and(X,not(Y))) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),not(and(X,not(Y)))) )],[refute_0_6,refute_0_10]) ).
cnf(refute_0_12,plain,
not(and(not(X),not(Y))) = implies(not(X),Y),
inference(subst,[],[refute_0_11:[bind(X,$fot(not(X)))]]) ).
cnf(refute_0_13,plain,
( not(and(not(X),not(Y))) != implies(not(X),Y)
| or(X,Y) != not(and(not(X),not(Y)))
| or(X,Y) = implies(not(X),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,Y),not(and(not(X),not(Y)))) ),[1],$fot(implies(not(X),Y))]]) ).
cnf(refute_0_14,plain,
( or(X,Y) != not(and(not(X),not(Y)))
| or(X,Y) = implies(not(X),Y) ),
inference(resolve,[$cnf( $equal(not(and(not(X),not(Y))),implies(not(X),Y)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
or(X,Y) = implies(not(X),Y),
inference(resolve,[$cnf( $equal(or(X,Y),not(and(not(X),not(Y)))) )],[refute_0_3,refute_0_14]) ).
cnf(refute_0_16,plain,
( or(X,Y) != implies(not(X),Y)
| implies(not(X),Y) = or(X,Y) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(or(X,Y))),bind(Y0,$fot(implies(not(X),Y)))]]) ).
cnf(refute_0_17,plain,
implies(not(X),Y) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),implies(not(X),Y)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3) = or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3),
inference(subst,[],[refute_0_17:[bind(X,$fot(skolemFOFtoCNF_P_4)),bind(Y,$fot(skolemFOFtoCNF_Q_3))]]) ).
cnf(refute_0_19,plain,
implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3)) = implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3)),
introduced(tautology,[refl,[$fot(implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3)))]]) ).
cnf(refute_0_20,plain,
( implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3) != or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3)
| implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3)) != implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3))
| implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3)) = implies(skolemFOFtoCNF_P_4,or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3)),implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3))) ),[1,1],$fot(or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3))]]) ).
cnf(refute_0_21,plain,
( implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3) != or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3)
| implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3)) = implies(skolemFOFtoCNF_P_4,or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3)) ),
inference(resolve,[$cnf( $equal(implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3)),implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3)) = implies(skolemFOFtoCNF_P_4,or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3)),
inference(resolve,[$cnf( $equal(implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3),or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3)) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
( implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3)) != implies(skolemFOFtoCNF_P_4,or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3))
| ~ is_a_theorem(implies(skolemFOFtoCNF_P_4,or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3)))
| is_a_theorem(implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3))) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3))) ),[0],$fot(implies(skolemFOFtoCNF_P_4,or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3)))]]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(implies(skolemFOFtoCNF_P_4,or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3)))
| is_a_theorem(implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3))) ),
inference(resolve,[$cnf( $equal(implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3)),implies(skolemFOFtoCNF_P_4,or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ is_a_theorem(implies(skolemFOFtoCNF_P_4,or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3)))
| cn2 ),
inference(resolve,[$cnf( is_a_theorem(implies(skolemFOFtoCNF_P_4,implies(not(skolemFOFtoCNF_P_4),skolemFOFtoCNF_Q_3))) )],[refute_0_24,refute_0_0]) ).
cnf(refute_0_26,plain,
( ~ or_1
| is_a_theorem(implies(X,or(X,Y))) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_27,plain,
or_1,
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_28,plain,
is_a_theorem(implies(X,or(X,Y))),
inference(resolve,[$cnf( or_1 )],[refute_0_27,refute_0_26]) ).
cnf(refute_0_29,plain,
is_a_theorem(implies(skolemFOFtoCNF_P_4,or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3))),
inference(subst,[],[refute_0_28:[bind(X,$fot(skolemFOFtoCNF_P_4)),bind(Y,$fot(skolemFOFtoCNF_Q_3))]]) ).
cnf(refute_0_30,plain,
cn2,
inference(resolve,[$cnf( is_a_theorem(implies(skolemFOFtoCNF_P_4,or(skolemFOFtoCNF_P_4,skolemFOFtoCNF_Q_3))) )],[refute_0_29,refute_0_25]) ).
cnf(refute_0_31,plain,
~ cn2,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_32,plain,
$false,
inference(resolve,[$cnf( cn2 )],[refute_0_30,refute_0_31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL452+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n008.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 : Mon Jul 4 23:41:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38
% 0.12/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.38
%------------------------------------------------------------------------------