TSTP Solution File: LCL512+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL512+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 12:52:50 EDT 2022
% Result : Theorem 0.21s 0.41s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 41 ( 22 unt; 0 def)
% Number of atoms : 66 ( 16 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 51 ( 26 ~; 18 |; 2 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 47 ( 2 sgn 16 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(equivalence_1,axiom,
( equivalence_1
<=> ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(X,Y))) ) ).
fof(kn2,axiom,
( kn2
<=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ) ).
fof(op_equiv,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ) ).
fof(rosser_op_equiv,axiom,
op_equiv ).
fof(rosser_kn2,axiom,
kn2 ).
fof(hilbert_op_equiv,axiom,
op_equiv ).
fof(hilbert_equivalence_1,conjecture,
equivalence_1 ).
fof(subgoal_0,plain,
equivalence_1,
inference(strip,[],[hilbert_equivalence_1]) ).
fof(negate_0_0,plain,
~ equivalence_1,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ equivalence_1
<=> ? [X,Y] : ~ is_a_theorem(implies(equiv(X,Y),implies(X,Y))) ),
inference(canonicalize,[],[equivalence_1]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ( ~ equivalence_1
| is_a_theorem(implies(equiv(X,Y),implies(X,Y))) )
& ( ~ is_a_theorem(implies(equiv(skolemFOFtoCNF_X_12,skolemFOFtoCNF_Y_12),implies(skolemFOFtoCNF_X_12,skolemFOFtoCNF_Y_12)))
| equivalence_1 ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ is_a_theorem(implies(equiv(skolemFOFtoCNF_X_12,skolemFOFtoCNF_Y_12),implies(skolemFOFtoCNF_X_12,skolemFOFtoCNF_Y_12)))
| equivalence_1 ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ equivalence_1,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_4,plain,
( ~ kn2
<=> ? [P,Q] : ~ is_a_theorem(implies(and(P,Q),P)) ),
inference(canonicalize,[],[kn2]) ).
fof(normalize_0_5,plain,
! [P,Q] :
( ( ~ is_a_theorem(implies(and(skolemFOFtoCNF_P_1,skolemFOFtoCNF_Q),skolemFOFtoCNF_P_1))
| kn2 )
& ( ~ kn2
| is_a_theorem(implies(and(P,Q),P)) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [P,Q] :
( ~ kn2
| is_a_theorem(implies(and(P,Q),P)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
kn2,
inference(canonicalize,[],[rosser_kn2]) ).
fof(normalize_0_8,plain,
( ~ op_equiv
| ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[op_equiv]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
op_equiv,
inference(canonicalize,[],[hilbert_op_equiv]) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(equiv(skolemFOFtoCNF_X_12,skolemFOFtoCNF_Y_12),implies(skolemFOFtoCNF_X_12,skolemFOFtoCNF_Y_12)))
| equivalence_1 ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ equivalence_1,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
~ is_a_theorem(implies(equiv(skolemFOFtoCNF_X_12,skolemFOFtoCNF_Y_12),implies(skolemFOFtoCNF_X_12,skolemFOFtoCNF_Y_12))),
inference(resolve,[$cnf( equivalence_1 )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ kn2
| is_a_theorem(implies(and(P,Q),P)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
kn2,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(and(P,Q),P)),
inference(resolve,[$cnf( kn2 )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(and(implies(X_5,X_6),implies(X_6,X_5)),implies(X_5,X_6))),
inference(subst,[],[refute_0_5:[bind(P,$fot(implies(X_5,X_6))),bind(Q,$fot(implies(X_6,X_5)))]]) ).
cnf(refute_0_7,plain,
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_8,plain,
op_equiv,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
equiv(X,Y) = and(implies(X,Y),implies(Y,X)),
inference(resolve,[$cnf( op_equiv )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
equiv(X_5,X_6) = and(implies(X_5,X_6),implies(X_6,X_5)),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_5)),bind(Y,$fot(X_6))]]) ).
cnf(refute_0_11,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_12,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_13,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( equiv(X_5,X_6) != and(implies(X_5,X_6),implies(X_6,X_5))
| and(implies(X_5,X_6),implies(X_6,X_5)) = equiv(X_5,X_6) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(equiv(X_5,X_6))),bind(Y0,$fot(and(implies(X_5,X_6),implies(X_6,X_5))))]]) ).
cnf(refute_0_15,plain,
and(implies(X_5,X_6),implies(X_6,X_5)) = equiv(X_5,X_6),
inference(resolve,[$cnf( $equal(equiv(X_5,X_6),and(implies(X_5,X_6),implies(X_6,X_5))) )],[refute_0_10,refute_0_14]) ).
cnf(refute_0_16,plain,
( and(implies(X_5,X_6),implies(X_6,X_5)) != equiv(X_5,X_6)
| ~ is_a_theorem(implies(and(implies(X_5,X_6),implies(X_6,X_5)),implies(X_5,X_6)))
| is_a_theorem(implies(equiv(X_5,X_6),implies(X_5,X_6))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(and(implies(X_5,X_6),implies(X_6,X_5)),implies(X_5,X_6))) ),[0,0],$fot(equiv(X_5,X_6))]]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(implies(and(implies(X_5,X_6),implies(X_6,X_5)),implies(X_5,X_6)))
| is_a_theorem(implies(equiv(X_5,X_6),implies(X_5,X_6))) ),
inference(resolve,[$cnf( $equal(and(implies(X_5,X_6),implies(X_6,X_5)),equiv(X_5,X_6)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
is_a_theorem(implies(equiv(X_5,X_6),implies(X_5,X_6))),
inference(resolve,[$cnf( is_a_theorem(implies(and(implies(X_5,X_6),implies(X_6,X_5)),implies(X_5,X_6))) )],[refute_0_6,refute_0_17]) ).
cnf(refute_0_19,plain,
is_a_theorem(implies(equiv(skolemFOFtoCNF_X_12,skolemFOFtoCNF_Y_12),implies(skolemFOFtoCNF_X_12,skolemFOFtoCNF_Y_12))),
inference(subst,[],[refute_0_18:[bind(X_5,$fot(skolemFOFtoCNF_X_12)),bind(X_6,$fot(skolemFOFtoCNF_Y_12))]]) ).
cnf(refute_0_20,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(equiv(skolemFOFtoCNF_X_12,skolemFOFtoCNF_Y_12),implies(skolemFOFtoCNF_X_12,skolemFOFtoCNF_Y_12))) )],[refute_0_19,refute_0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : LCL512+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jul 4 09:20:44 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.41
% 0.21/0.41 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.21/0.42
%------------------------------------------------------------------------------