TSTP Solution File: LCL526+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL526+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 12:52:55 EDT 2022
% Result : Theorem 3.26s 3.50s
% Output : CNFRefutation 3.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 27
% Syntax : Number of formulae : 147 ( 66 unt; 0 def)
% Number of atoms : 279 ( 55 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 241 ( 109 ~; 96 |; 16 &)
% ( 14 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 14 ( 11 usr; 11 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 13 con; 0-2 aty)
% Number of variables : 161 ( 4 sgn 55 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(Y) ) ) ).
fof(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X,Y] :
( is_a_theorem(equiv(X,Y))
=> X = Y ) ) ).
fof(and_1,axiom,
( and_1
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),X)) ) ).
fof(and_2,axiom,
( and_2
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) ) ).
fof(and_3,axiom,
( and_3
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) ) ).
fof(op_equiv,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ) ).
fof(hilbert_op_equiv,axiom,
op_equiv ).
fof(hilbert_modus_ponens,axiom,
modus_ponens ).
fof(hilbert_and_1,axiom,
and_1 ).
fof(hilbert_and_2,axiom,
and_2 ).
fof(hilbert_and_3,axiom,
and_3 ).
fof(substitution_of_equivalents_001,axiom,
substitution_of_equivalents ).
fof(substitution_strict_equiv,axiom,
( substitution_strict_equiv
<=> ! [X,Y] :
( is_a_theorem(strict_equiv(X,Y))
=> X = Y ) ) ).
fof(axiom_M,axiom,
( axiom_M
<=> ! [X] : is_a_theorem(implies(necessarily(X),X)) ) ).
fof(op_strict_implies,axiom,
( op_strict_implies
=> ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) ) ).
fof(op_strict_equiv,axiom,
( op_strict_equiv
=> ! [X,Y] : strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X)) ) ).
fof(km5_axiom_M,axiom,
axiom_M ).
fof(s1_0_op_strict_implies,axiom,
op_strict_implies ).
fof(s1_0_op_equiv,axiom,
op_equiv ).
fof(s1_0_op_strict_equiv,axiom,
op_strict_equiv ).
fof(s1_0_substitution_strict_equiv,conjecture,
substitution_strict_equiv ).
fof(subgoal_0,plain,
substitution_strict_equiv,
inference(strip,[],[s1_0_substitution_strict_equiv]) ).
fof(negate_0_0,plain,
~ substitution_strict_equiv,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ substitution_of_equivalents
<=> ? [X,Y] :
( X != Y
& is_a_theorem(equiv(X,Y)) ) ),
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ( skolemFOFtoCNF_X_1 != skolemFOFtoCNF_Y_1
| substitution_of_equivalents )
& ( is_a_theorem(equiv(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| substitution_of_equivalents )
& ( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
substitution_of_equivalents,
inference(canonicalize,[],[substitution_of_equivalents]) ).
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,
( ~ substitution_strict_equiv
<=> ? [X,Y] :
( X != Y
& is_a_theorem(strict_equiv(X,Y)) ) ),
inference(canonicalize,[],[substitution_strict_equiv]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ( skolemFOFtoCNF_X_18 != skolemFOFtoCNF_Y_17
| substitution_strict_equiv )
& ( is_a_theorem(strict_equiv(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17))
| substitution_strict_equiv )
& ( ~ is_a_theorem(strict_equiv(X,Y))
| ~ substitution_strict_equiv
| X = Y ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
( is_a_theorem(strict_equiv(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17))
| substitution_strict_equiv ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
~ substitution_strict_equiv,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_12,plain,
( ~ and_2
<=> ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),Y)) ),
inference(canonicalize,[],[and_2]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ( ~ and_2
| is_a_theorem(implies(and(X,Y),Y)) )
& ( ~ is_a_theorem(implies(and(skolemFOFtoCNF_X_7,skolemFOFtoCNF_Y_7),skolemFOFtoCNF_Y_7))
| and_2 ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X,Y] :
( ~ and_2
| is_a_theorem(implies(and(X,Y),Y)) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
and_2,
inference(canonicalize,[],[hilbert_and_2]) ).
fof(normalize_0_16,plain,
( ~ op_strict_equiv
| ! [X,Y] : strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X)) ),
inference(canonicalize,[],[op_strict_equiv]) ).
fof(normalize_0_17,plain,
! [X,Y] :
( ~ op_strict_equiv
| strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X)) ),
inference(clausify,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
op_strict_equiv,
inference(canonicalize,[],[s1_0_op_strict_equiv]) ).
fof(normalize_0_19,plain,
( ~ axiom_M
<=> ? [X] : ~ is_a_theorem(implies(necessarily(X),X)) ),
inference(canonicalize,[],[axiom_M]) ).
fof(normalize_0_20,plain,
! [X] :
( ( ~ axiom_M
| is_a_theorem(implies(necessarily(X),X)) )
& ( ~ is_a_theorem(implies(necessarily(skolemFOFtoCNF_X_20),skolemFOFtoCNF_X_20))
| axiom_M ) ),
inference(clausify,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [X] :
( ~ axiom_M
| is_a_theorem(implies(necessarily(X),X)) ),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
axiom_M,
inference(canonicalize,[],[km5_axiom_M]) ).
fof(normalize_0_23,plain,
( ~ op_strict_implies
| ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) ),
inference(canonicalize,[],[op_strict_implies]) ).
fof(normalize_0_24,plain,
! [X,Y] :
( ~ op_strict_implies
| strict_implies(X,Y) = necessarily(implies(X,Y)) ),
inference(clausify,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
op_strict_implies,
inference(canonicalize,[],[s1_0_op_strict_implies]) ).
fof(normalize_0_26,plain,
( ~ and_3
<=> ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(canonicalize,[],[and_3]) ).
fof(normalize_0_27,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_26]) ).
fof(normalize_0_28,plain,
! [X,Y] :
( ~ and_3
| is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(conjunct,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
and_3,
inference(canonicalize,[],[hilbert_and_3]) ).
fof(normalize_0_30,plain,
( ~ op_equiv
| ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[op_equiv]) ).
fof(normalize_0_31,plain,
! [X,Y] :
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(clausify,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
op_equiv,
inference(canonicalize,[],[s1_0_op_equiv]) ).
fof(normalize_0_33,plain,
( ~ and_1
<=> ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),X)) ),
inference(canonicalize,[],[and_1]) ).
fof(normalize_0_34,plain,
! [X,Y] :
( ( ~ and_1
| is_a_theorem(implies(and(X,Y),X)) )
& ( ~ is_a_theorem(implies(and(skolemFOFtoCNF_X_6,skolemFOFtoCNF_Y_6),skolemFOFtoCNF_X_6))
| and_1 ) ),
inference(clausify,[],[normalize_0_33]) ).
fof(normalize_0_35,plain,
! [X,Y] :
( ~ and_1
| is_a_theorem(implies(and(X,Y),X)) ),
inference(conjunct,[],[normalize_0_34]) ).
fof(normalize_0_36,plain,
and_1,
inference(canonicalize,[],[hilbert_and_1]) ).
fof(normalize_0_37,plain,
( skolemFOFtoCNF_X_18 != skolemFOFtoCNF_Y_17
| substitution_strict_equiv ),
inference(conjunct,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
substitution_of_equivalents,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(equiv(X,Y))
| X = Y ),
inference(resolve,[$cnf( substitution_of_equivalents )],[refute_0_1,refute_0_0]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18))
| skolemFOFtoCNF_Y_17 = skolemFOFtoCNF_X_18 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_Y_17)),bind(Y,$fot(skolemFOFtoCNF_X_18))]]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_5,plain,
modus_ponens,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) ),
inference(resolve,[$cnf( modus_ponens )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17),equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)))
| ~ is_a_theorem(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17))
| is_a_theorem(equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17))),bind(Y,$fot(equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)))]]) ).
cnf(refute_0_8,plain,
( is_a_theorem(strict_equiv(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17))
| substitution_strict_equiv ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
~ substitution_strict_equiv,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_10,plain,
is_a_theorem(strict_equiv(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)),
inference(resolve,[$cnf( substitution_strict_equiv )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ and_2
| is_a_theorem(implies(and(X,Y),Y)) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_12,plain,
and_2,
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_13,plain,
is_a_theorem(implies(and(X,Y),Y)),
inference(resolve,[$cnf( and_2 )],[refute_0_12,refute_0_11]) ).
cnf(refute_0_14,plain,
is_a_theorem(implies(and(strict_implies(X,Y),strict_implies(Y,X)),strict_implies(Y,X))),
inference(subst,[],[refute_0_13:[bind(X,$fot(strict_implies(X,Y))),bind(Y,$fot(strict_implies(Y,X)))]]) ).
cnf(refute_0_15,plain,
( ~ op_strict_equiv
| strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X)) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_16,plain,
op_strict_equiv,
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_17,plain,
strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X)),
inference(resolve,[$cnf( op_strict_equiv )],[refute_0_16,refute_0_15]) ).
cnf(refute_0_18,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_19,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_20,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( strict_equiv(X,Y) != and(strict_implies(X,Y),strict_implies(Y,X))
| and(strict_implies(X,Y),strict_implies(Y,X)) = strict_equiv(X,Y) ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(strict_equiv(X,Y))),bind(Y0,$fot(and(strict_implies(X,Y),strict_implies(Y,X))))]]) ).
cnf(refute_0_22,plain,
and(strict_implies(X,Y),strict_implies(Y,X)) = strict_equiv(X,Y),
inference(resolve,[$cnf( $equal(strict_equiv(X,Y),and(strict_implies(X,Y),strict_implies(Y,X))) )],[refute_0_17,refute_0_21]) ).
cnf(refute_0_23,plain,
( and(strict_implies(X,Y),strict_implies(Y,X)) != strict_equiv(X,Y)
| ~ is_a_theorem(implies(and(strict_implies(X,Y),strict_implies(Y,X)),strict_implies(Y,X)))
| is_a_theorem(implies(strict_equiv(X,Y),strict_implies(Y,X))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(and(strict_implies(X,Y),strict_implies(Y,X)),strict_implies(Y,X))) ),[0,0],$fot(strict_equiv(X,Y))]]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(implies(and(strict_implies(X,Y),strict_implies(Y,X)),strict_implies(Y,X)))
| is_a_theorem(implies(strict_equiv(X,Y),strict_implies(Y,X))) ),
inference(resolve,[$cnf( $equal(and(strict_implies(X,Y),strict_implies(Y,X)),strict_equiv(X,Y)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
is_a_theorem(implies(strict_equiv(X,Y),strict_implies(Y,X))),
inference(resolve,[$cnf( is_a_theorem(implies(and(strict_implies(X,Y),strict_implies(Y,X)),strict_implies(Y,X))) )],[refute_0_14,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(implies(strict_equiv(X,Y),strict_implies(Y,X)))
| ~ is_a_theorem(strict_equiv(X,Y))
| is_a_theorem(strict_implies(Y,X)) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(strict_equiv(X,Y))),bind(Y,$fot(strict_implies(Y,X)))]]) ).
cnf(refute_0_27,plain,
( ~ is_a_theorem(strict_equiv(X,Y))
| is_a_theorem(strict_implies(Y,X)) ),
inference(resolve,[$cnf( is_a_theorem(implies(strict_equiv(X,Y),strict_implies(Y,X))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ is_a_theorem(strict_equiv(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17))
| is_a_theorem(strict_implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)) ),
inference(subst,[],[refute_0_27:[bind(X,$fot(skolemFOFtoCNF_X_18)),bind(Y,$fot(skolemFOFtoCNF_Y_17))]]) ).
cnf(refute_0_29,plain,
is_a_theorem(strict_implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)),
inference(resolve,[$cnf( is_a_theorem(strict_equiv(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)) )],[refute_0_10,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ axiom_M
| is_a_theorem(implies(necessarily(X),X)) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_31,plain,
axiom_M,
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_32,plain,
is_a_theorem(implies(necessarily(X),X)),
inference(resolve,[$cnf( axiom_M )],[refute_0_31,refute_0_30]) ).
cnf(refute_0_33,plain,
is_a_theorem(implies(necessarily(implies(X_28,X_29)),implies(X_28,X_29))),
inference(subst,[],[refute_0_32:[bind(X,$fot(implies(X_28,X_29)))]]) ).
cnf(refute_0_34,plain,
( ~ op_strict_implies
| strict_implies(X,Y) = necessarily(implies(X,Y)) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_35,plain,
op_strict_implies,
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_36,plain,
strict_implies(X,Y) = necessarily(implies(X,Y)),
inference(resolve,[$cnf( op_strict_implies )],[refute_0_35,refute_0_34]) ).
cnf(refute_0_37,plain,
strict_implies(X_28,X_29) = necessarily(implies(X_28,X_29)),
inference(subst,[],[refute_0_36:[bind(X,$fot(X_28)),bind(Y,$fot(X_29))]]) ).
cnf(refute_0_38,plain,
( strict_implies(X_28,X_29) != necessarily(implies(X_28,X_29))
| necessarily(implies(X_28,X_29)) = strict_implies(X_28,X_29) ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(strict_implies(X_28,X_29))),bind(Y0,$fot(necessarily(implies(X_28,X_29))))]]) ).
cnf(refute_0_39,plain,
necessarily(implies(X_28,X_29)) = strict_implies(X_28,X_29),
inference(resolve,[$cnf( $equal(strict_implies(X_28,X_29),necessarily(implies(X_28,X_29))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( necessarily(implies(X_28,X_29)) != strict_implies(X_28,X_29)
| ~ is_a_theorem(implies(necessarily(implies(X_28,X_29)),implies(X_28,X_29)))
| is_a_theorem(implies(strict_implies(X_28,X_29),implies(X_28,X_29))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(necessarily(implies(X_28,X_29)),implies(X_28,X_29))) ),[0,0],$fot(strict_implies(X_28,X_29))]]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(implies(necessarily(implies(X_28,X_29)),implies(X_28,X_29)))
| is_a_theorem(implies(strict_implies(X_28,X_29),implies(X_28,X_29))) ),
inference(resolve,[$cnf( $equal(necessarily(implies(X_28,X_29)),strict_implies(X_28,X_29)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
is_a_theorem(implies(strict_implies(X_28,X_29),implies(X_28,X_29))),
inference(resolve,[$cnf( is_a_theorem(implies(necessarily(implies(X_28,X_29)),implies(X_28,X_29))) )],[refute_0_33,refute_0_41]) ).
cnf(refute_0_43,plain,
( ~ is_a_theorem(implies(strict_implies(X_28,X_29),implies(X_28,X_29)))
| ~ is_a_theorem(strict_implies(X_28,X_29))
| is_a_theorem(implies(X_28,X_29)) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(strict_implies(X_28,X_29))),bind(Y,$fot(implies(X_28,X_29)))]]) ).
cnf(refute_0_44,plain,
( ~ is_a_theorem(strict_implies(X_28,X_29))
| is_a_theorem(implies(X_28,X_29)) ),
inference(resolve,[$cnf( is_a_theorem(implies(strict_implies(X_28,X_29),implies(X_28,X_29))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
( ~ is_a_theorem(strict_implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18))
| is_a_theorem(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)) ),
inference(subst,[],[refute_0_44:[bind(X_28,$fot(skolemFOFtoCNF_Y_17)),bind(X_29,$fot(skolemFOFtoCNF_X_18))]]) ).
cnf(refute_0_46,plain,
is_a_theorem(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)),
inference(resolve,[$cnf( is_a_theorem(strict_implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)) )],[refute_0_29,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ and_3
| is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_48,plain,
and_3,
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_49,plain,
is_a_theorem(implies(X,implies(Y,and(X,Y)))),
inference(resolve,[$cnf( and_3 )],[refute_0_48,refute_0_47]) ).
cnf(refute_0_50,plain,
is_a_theorem(implies(X_818,implies(Y,and(X_818,Y)))),
inference(subst,[],[refute_0_49:[bind(X,$fot(X_818))]]) ).
cnf(refute_0_51,plain,
( ~ is_a_theorem(X_818)
| ~ is_a_theorem(implies(X_818,implies(Y,and(X_818,Y))))
| is_a_theorem(implies(Y,and(X_818,Y))) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_818)),bind(Y,$fot(implies(Y,and(X_818,Y))))]]) ).
cnf(refute_0_52,plain,
( ~ is_a_theorem(X_818)
| is_a_theorem(implies(Y,and(X_818,Y))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_818,implies(Y,and(X_818,Y)))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
( ~ is_a_theorem(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18))
| is_a_theorem(implies(X_3123,and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),X_3123))) ),
inference(subst,[],[refute_0_52:[bind(Y,$fot(X_3123)),bind(X_818,$fot(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)))]]) ).
cnf(refute_0_54,plain,
is_a_theorem(implies(X_3123,and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),X_3123))),
inference(resolve,[$cnf( is_a_theorem(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)) )],[refute_0_46,refute_0_53]) ).
cnf(refute_0_55,plain,
is_a_theorem(implies(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)))),
inference(subst,[],[refute_0_54:[bind(X_3123,$fot(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)))]]) ).
cnf(refute_0_56,plain,
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_57,plain,
op_equiv,
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_58,plain,
equiv(X,Y) = and(implies(X,Y),implies(Y,X)),
inference(resolve,[$cnf( op_equiv )],[refute_0_57,refute_0_56]) ).
cnf(refute_0_59,plain,
equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18) = and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)),
inference(subst,[],[refute_0_58:[bind(X,$fot(skolemFOFtoCNF_Y_17)),bind(Y,$fot(skolemFOFtoCNF_X_18))]]) ).
cnf(refute_0_60,plain,
( equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18) != and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17))
| and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)) = equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18) ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18))),bind(Y0,$fot(and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17))))]]) ).
cnf(refute_0_61,plain,
and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)) = equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),
inference(resolve,[$cnf( $equal(equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
( and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)) != equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)
| ~ is_a_theorem(implies(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17))))
| is_a_theorem(implies(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17),equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)))) ),[0,1],$fot(equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18))]]) ).
cnf(refute_0_63,plain,
( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17))))
| is_a_theorem(implies(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17),equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18))) ),
inference(resolve,[$cnf( $equal(and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)),equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
is_a_theorem(implies(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17),equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)))) )],[refute_0_55,refute_0_63]) ).
cnf(refute_0_65,plain,
( ~ is_a_theorem(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17))
| is_a_theorem(equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17),equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18))) )],[refute_0_64,refute_0_7]) ).
cnf(refute_0_66,plain,
( ~ and_1
| is_a_theorem(implies(and(X,Y),X)) ),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_67,plain,
and_1,
inference(canonicalize,[],[normalize_0_36]) ).
cnf(refute_0_68,plain,
is_a_theorem(implies(and(X,Y),X)),
inference(resolve,[$cnf( and_1 )],[refute_0_67,refute_0_66]) ).
cnf(refute_0_69,plain,
is_a_theorem(implies(and(strict_implies(X,Y),strict_implies(Y,X)),strict_implies(X,Y))),
inference(subst,[],[refute_0_68:[bind(X,$fot(strict_implies(X,Y))),bind(Y,$fot(strict_implies(Y,X)))]]) ).
cnf(refute_0_70,plain,
( and(strict_implies(X,Y),strict_implies(Y,X)) != strict_equiv(X,Y)
| ~ is_a_theorem(implies(and(strict_implies(X,Y),strict_implies(Y,X)),strict_implies(X,Y)))
| is_a_theorem(implies(strict_equiv(X,Y),strict_implies(X,Y))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(and(strict_implies(X,Y),strict_implies(Y,X)),strict_implies(X,Y))) ),[0,0],$fot(strict_equiv(X,Y))]]) ).
cnf(refute_0_71,plain,
( ~ is_a_theorem(implies(and(strict_implies(X,Y),strict_implies(Y,X)),strict_implies(X,Y)))
| is_a_theorem(implies(strict_equiv(X,Y),strict_implies(X,Y))) ),
inference(resolve,[$cnf( $equal(and(strict_implies(X,Y),strict_implies(Y,X)),strict_equiv(X,Y)) )],[refute_0_22,refute_0_70]) ).
cnf(refute_0_72,plain,
is_a_theorem(implies(strict_equiv(X,Y),strict_implies(X,Y))),
inference(resolve,[$cnf( is_a_theorem(implies(and(strict_implies(X,Y),strict_implies(Y,X)),strict_implies(X,Y))) )],[refute_0_69,refute_0_71]) ).
cnf(refute_0_73,plain,
( ~ is_a_theorem(implies(strict_equiv(X,Y),strict_implies(X,Y)))
| ~ is_a_theorem(strict_equiv(X,Y))
| is_a_theorem(strict_implies(X,Y)) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(strict_equiv(X,Y))),bind(Y,$fot(strict_implies(X,Y)))]]) ).
cnf(refute_0_74,plain,
( ~ is_a_theorem(strict_equiv(X,Y))
| is_a_theorem(strict_implies(X,Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(strict_equiv(X,Y),strict_implies(X,Y))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
( ~ is_a_theorem(strict_equiv(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17))
| is_a_theorem(strict_implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)) ),
inference(subst,[],[refute_0_74:[bind(X,$fot(skolemFOFtoCNF_X_18)),bind(Y,$fot(skolemFOFtoCNF_Y_17))]]) ).
cnf(refute_0_76,plain,
is_a_theorem(strict_implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)),
inference(resolve,[$cnf( is_a_theorem(strict_equiv(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)) )],[refute_0_10,refute_0_75]) ).
cnf(refute_0_77,plain,
( ~ is_a_theorem(strict_implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17))
| is_a_theorem(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)) ),
inference(subst,[],[refute_0_44:[bind(X_28,$fot(skolemFOFtoCNF_X_18)),bind(X_29,$fot(skolemFOFtoCNF_Y_17))]]) ).
cnf(refute_0_78,plain,
is_a_theorem(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)),
inference(resolve,[$cnf( is_a_theorem(strict_implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
is_a_theorem(equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)),
inference(resolve,[$cnf( is_a_theorem(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)) )],[refute_0_78,refute_0_65]) ).
cnf(refute_0_80,plain,
skolemFOFtoCNF_Y_17 = skolemFOFtoCNF_X_18,
inference(resolve,[$cnf( is_a_theorem(equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)) )],[refute_0_79,refute_0_3]) ).
cnf(refute_0_81,plain,
( skolemFOFtoCNF_X_18 != skolemFOFtoCNF_Y_17
| substitution_strict_equiv ),
inference(canonicalize,[],[normalize_0_37]) ).
cnf(refute_0_82,plain,
skolemFOFtoCNF_X_18 != skolemFOFtoCNF_Y_17,
inference(resolve,[$cnf( substitution_strict_equiv )],[refute_0_81,refute_0_9]) ).
cnf(refute_0_83,plain,
( skolemFOFtoCNF_Y_17 != skolemFOFtoCNF_X_18
| skolemFOFtoCNF_X_18 = skolemFOFtoCNF_Y_17 ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(skolemFOFtoCNF_Y_17)),bind(Y0,$fot(skolemFOFtoCNF_X_18))]]) ).
cnf(refute_0_84,plain,
skolemFOFtoCNF_Y_17 != skolemFOFtoCNF_X_18,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17) )],[refute_0_83,refute_0_82]) ).
cnf(refute_0_85,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18) )],[refute_0_80,refute_0_84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL526+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 3 22:15:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 3.26/3.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.26/3.50
% 3.26/3.50 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.26/3.51
%------------------------------------------------------------------------------