TSTP Solution File: LCL539+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL539+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 12:53:00 EDT 2022
% Result : Theorem 45.75s 45.94s
% Output : CNFRefutation 45.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 45
% Syntax : Number of formulae : 244 ( 106 unt; 0 def)
% Number of atoms : 473 ( 121 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 412 ( 183 ~; 176 |; 25 &)
% ( 18 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 18 ( 15 usr; 15 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 16 con; 0-2 aty)
% Number of variables : 296 ( 4 sgn 76 !; 16 ?)
% 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_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(op_equiv,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ) ).
fof(hilbert_op_or,axiom,
op_or ).
fof(hilbert_op_implies_and,axiom,
op_implies_and ).
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(necessitation,axiom,
( necessitation
<=> ! [X] :
( is_a_theorem(X)
=> is_a_theorem(necessarily(X)) ) ) ).
fof(modus_ponens_strict_implies,axiom,
( modus_ponens_strict_implies
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(strict_implies(X,Y)) )
=> is_a_theorem(Y) ) ) ).
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(km4b_necessitation,axiom,
necessitation ).
fof(km4b_axiom_M,axiom,
axiom_M ).
fof(s1_0_op_or,axiom,
op_or ).
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_strict_implies
<=> ? [X,Y] :
( ~ is_a_theorem(Y)
& is_a_theorem(X)
& is_a_theorem(strict_implies(X,Y)) ) ),
inference(canonicalize,[],[modus_ponens_strict_implies]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ( ~ is_a_theorem(skolemFOFtoCNF_Y_15)
| modus_ponens_strict_implies )
& ( is_a_theorem(skolemFOFtoCNF_X_16)
| modus_ponens_strict_implies )
& ( is_a_theorem(strict_implies(skolemFOFtoCNF_X_16,skolemFOFtoCNF_Y_15))
| modus_ponens_strict_implies )
& ( ~ is_a_theorem(X)
| ~ is_a_theorem(strict_implies(X,Y))
| ~ modus_ponens_strict_implies
| is_a_theorem(Y) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(strict_implies(X,Y))
| ~ modus_ponens_strict_implies
| is_a_theorem(Y) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
( ~ axiom_M
<=> ? [X] : ~ is_a_theorem(implies(necessarily(X),X)) ),
inference(canonicalize,[],[axiom_M]) ).
fof(normalize_0_8,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_7]) ).
fof(normalize_0_9,plain,
! [X] :
( ~ axiom_M
| is_a_theorem(implies(necessarily(X),X)) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
axiom_M,
inference(canonicalize,[],[km4b_axiom_M]) ).
fof(normalize_0_11,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_12,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_11]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
modus_ponens,
inference(canonicalize,[],[hilbert_modus_ponens]) ).
fof(normalize_0_15,plain,
( ~ necessitation
<=> ? [X] :
( ~ is_a_theorem(necessarily(X))
& is_a_theorem(X) ) ),
inference(canonicalize,[],[necessitation]) ).
fof(normalize_0_16,plain,
! [X] :
( ( ~ is_a_theorem(necessarily(skolemFOFtoCNF_X_15))
| necessitation )
& ( is_a_theorem(skolemFOFtoCNF_X_15)
| necessitation )
& ( ~ is_a_theorem(X)
| ~ necessitation
| is_a_theorem(necessarily(X)) ) ),
inference(clausify,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [X] :
( ~ is_a_theorem(X)
| ~ necessitation
| is_a_theorem(necessarily(X)) ),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
necessitation,
inference(canonicalize,[],[km4b_necessitation]) ).
fof(normalize_0_19,plain,
( ~ and_3
<=> ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(canonicalize,[],[and_3]) ).
fof(normalize_0_20,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_19]) ).
fof(normalize_0_21,plain,
! [X,Y] :
( ~ and_3
| is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
and_3,
inference(canonicalize,[],[hilbert_and_3]) ).
fof(normalize_0_23,plain,
( ~ op_or
| ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[op_or]) ).
fof(normalize_0_24,plain,
! [X,Y] :
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
op_or,
inference(canonicalize,[],[s1_0_op_or]) ).
fof(normalize_0_26,plain,
( ~ op_implies_and
| ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[op_implies_and]) ).
fof(normalize_0_27,plain,
! [X,Y] :
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(clausify,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
op_implies_and,
inference(canonicalize,[],[hilbert_op_implies_and]) ).
fof(normalize_0_29,plain,
( ~ substitution_strict_equiv
<=> ? [X,Y] :
( X != Y
& is_a_theorem(strict_equiv(X,Y)) ) ),
inference(canonicalize,[],[substitution_strict_equiv]) ).
fof(normalize_0_30,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_29]) ).
fof(normalize_0_31,plain,
( is_a_theorem(strict_equiv(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17))
| substitution_strict_equiv ),
inference(conjunct,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
~ substitution_strict_equiv,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_33,plain,
( ~ and_2
<=> ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),Y)) ),
inference(canonicalize,[],[and_2]) ).
fof(normalize_0_34,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_33]) ).
fof(normalize_0_35,plain,
! [X,Y] :
( ~ and_2
| is_a_theorem(implies(and(X,Y),Y)) ),
inference(conjunct,[],[normalize_0_34]) ).
fof(normalize_0_36,plain,
and_2,
inference(canonicalize,[],[hilbert_and_2]) ).
fof(normalize_0_37,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_38,plain,
! [X,Y] :
( ~ op_strict_equiv
| strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X)) ),
inference(clausify,[],[normalize_0_37]) ).
fof(normalize_0_39,plain,
op_strict_equiv,
inference(canonicalize,[],[s1_0_op_strict_equiv]) ).
fof(normalize_0_40,plain,
( ~ op_strict_implies
| ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) ),
inference(canonicalize,[],[op_strict_implies]) ).
fof(normalize_0_41,plain,
! [X,Y] :
( ~ op_strict_implies
| strict_implies(X,Y) = necessarily(implies(X,Y)) ),
inference(clausify,[],[normalize_0_40]) ).
fof(normalize_0_42,plain,
op_strict_implies,
inference(canonicalize,[],[s1_0_op_strict_implies]) ).
fof(normalize_0_43,plain,
( ~ op_equiv
| ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[op_equiv]) ).
fof(normalize_0_44,plain,
! [X,Y] :
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(clausify,[],[normalize_0_43]) ).
fof(normalize_0_45,plain,
op_equiv,
inference(canonicalize,[],[s1_0_op_equiv]) ).
fof(normalize_0_46,plain,
( ~ and_1
<=> ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),X)) ),
inference(canonicalize,[],[and_1]) ).
fof(normalize_0_47,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_46]) ).
fof(normalize_0_48,plain,
! [X,Y] :
( ~ and_1
| is_a_theorem(implies(and(X,Y),X)) ),
inference(conjunct,[],[normalize_0_47]) ).
fof(normalize_0_49,plain,
and_1,
inference(canonicalize,[],[hilbert_and_1]) ).
fof(normalize_0_50,plain,
( ~ is_a_theorem(skolemFOFtoCNF_Y_15)
| modus_ponens_strict_implies ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_51,plain,
( is_a_theorem(skolemFOFtoCNF_X_16)
| modus_ponens_strict_implies ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_52,plain,
( is_a_theorem(strict_implies(skolemFOFtoCNF_X_16,skolemFOFtoCNF_Y_15))
| modus_ponens_strict_implies ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_53,plain,
( skolemFOFtoCNF_X_18 != skolemFOFtoCNF_Y_17
| substitution_strict_equiv ),
inference(conjunct,[],[normalize_0_30]) ).
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,$fot(skolemFOFtoCNF_X_18))]]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(strict_implies(X,Y))
| ~ modus_ponens_strict_implies
| is_a_theorem(Y) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17))
| ~ is_a_theorem(strict_implies(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17),equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)))
| ~ modus_ponens_strict_implies
| is_a_theorem(equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17))),bind(Y,$fot(equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)))]]) ).
cnf(refute_0_6,plain,
( ~ axiom_M
| is_a_theorem(implies(necessarily(X),X)) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_7,plain,
axiom_M,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
is_a_theorem(implies(necessarily(X),X)),
inference(resolve,[$cnf( axiom_M )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
is_a_theorem(implies(necessarily(X_455),X_455)),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_455))]]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_11,plain,
modus_ponens,
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) ),
inference(resolve,[$cnf( modus_ponens )],[refute_0_11,refute_0_10]) ).
cnf(refute_0_13,plain,
( ~ is_a_theorem(implies(necessarily(X_455),X_455))
| ~ is_a_theorem(necessarily(X_455))
| is_a_theorem(X_455) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(necessarily(X_455))),bind(Y,$fot(X_455))]]) ).
cnf(refute_0_14,plain,
( ~ is_a_theorem(necessarily(X_455))
| is_a_theorem(X_455) ),
inference(resolve,[$cnf( is_a_theorem(implies(necessarily(X_455),X_455)) )],[refute_0_9,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ is_a_theorem(necessarily(strict_implies(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17),equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18))))
| is_a_theorem(strict_implies(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17),equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18))) ),
inference(subst,[],[refute_0_14:[bind(X_455,$fot(strict_implies(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17),equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18))))]]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(X)
| ~ necessitation
| is_a_theorem(necessarily(X)) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_17,plain,
necessitation,
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(X)
| is_a_theorem(necessarily(X)) ),
inference(resolve,[$cnf( necessitation )],[refute_0_17,refute_0_16]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(necessarily(or(X_9666,and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),not(X_9666)))))
| is_a_theorem(necessarily(necessarily(or(X_9666,and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),not(X_9666)))))) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(necessarily(or(X_9666,and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),not(X_9666))))))]]) ).
cnf(refute_0_20,plain,
( ~ is_a_theorem(or(X_9539,and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),not(X_9539))))
| is_a_theorem(necessarily(or(X_9539,and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),not(X_9539))))) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(or(X_9539,and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),not(X_9539)))))]]) ).
cnf(refute_0_21,plain,
( ~ and_3
| is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_22,plain,
and_3,
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_23,plain,
is_a_theorem(implies(X,implies(Y,and(X,Y)))),
inference(resolve,[$cnf( and_3 )],[refute_0_22,refute_0_21]) ).
cnf(refute_0_24,plain,
is_a_theorem(implies(X_69,implies(not(X),and(X_69,not(X))))),
inference(subst,[],[refute_0_23:[bind(X,$fot(X_69)),bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_25,plain,
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_26,plain,
op_or,
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_27,plain,
or(X,Y) = not(and(not(X),not(Y))),
inference(resolve,[$cnf( op_or )],[refute_0_26,refute_0_25]) ).
cnf(refute_0_28,plain,
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_29,plain,
op_implies_and,
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_30,plain,
implies(X,Y) = not(and(X,not(Y))),
inference(resolve,[$cnf( op_implies_and )],[refute_0_29,refute_0_28]) ).
cnf(refute_0_31,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_32,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_33,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( implies(X,Y) != not(and(X,not(Y)))
| not(and(X,not(Y))) = implies(X,Y) ),
inference(subst,[],[refute_0_33:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(not(and(X,not(Y)))))]]) ).
cnf(refute_0_35,plain,
not(and(X,not(Y))) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),not(and(X,not(Y)))) )],[refute_0_30,refute_0_34]) ).
cnf(refute_0_36,plain,
not(and(not(X),not(Y))) = implies(not(X),Y),
inference(subst,[],[refute_0_35:[bind(X,$fot(not(X)))]]) ).
cnf(refute_0_37,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_38,plain,
( or(X,Y) != not(and(not(X),not(Y)))
| or(X,Y) = implies(not(X),Y) ),
inference(resolve,[$cnf( $equal(not(and(not(X),not(Y))),implies(not(X),Y)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
or(X,Y) = implies(not(X),Y),
inference(resolve,[$cnf( $equal(or(X,Y),not(and(not(X),not(Y)))) )],[refute_0_27,refute_0_38]) ).
cnf(refute_0_40,plain,
or(X,and(X_69,not(X))) = implies(not(X),and(X_69,not(X))),
inference(subst,[],[refute_0_39:[bind(Y,$fot(and(X_69,not(X))))]]) ).
cnf(refute_0_41,plain,
( or(X,and(X_69,not(X))) != implies(not(X),and(X_69,not(X)))
| implies(not(X),and(X_69,not(X))) = or(X,and(X_69,not(X))) ),
inference(subst,[],[refute_0_33:[bind(X0,$fot(or(X,and(X_69,not(X))))),bind(Y0,$fot(implies(not(X),and(X_69,not(X)))))]]) ).
cnf(refute_0_42,plain,
implies(not(X),and(X_69,not(X))) = or(X,and(X_69,not(X))),
inference(resolve,[$cnf( $equal(or(X,and(X_69,not(X))),implies(not(X),and(X_69,not(X)))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( implies(not(X),and(X_69,not(X))) != or(X,and(X_69,not(X)))
| ~ is_a_theorem(implies(X_69,implies(not(X),and(X_69,not(X)))))
| is_a_theorem(implies(X_69,or(X,and(X_69,not(X))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_69,implies(not(X),and(X_69,not(X))))) ),[0,1],$fot(or(X,and(X_69,not(X))))]]) ).
cnf(refute_0_44,plain,
( ~ is_a_theorem(implies(X_69,implies(not(X),and(X_69,not(X)))))
| is_a_theorem(implies(X_69,or(X,and(X_69,not(X))))) ),
inference(resolve,[$cnf( $equal(implies(not(X),and(X_69,not(X))),or(X,and(X_69,not(X)))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
is_a_theorem(implies(X_69,or(X,and(X_69,not(X))))),
inference(resolve,[$cnf( is_a_theorem(implies(X_69,implies(not(X),and(X_69,not(X))))) )],[refute_0_24,refute_0_44]) ).
cnf(refute_0_46,plain,
is_a_theorem(implies(X_454,or(X,and(X_454,not(X))))),
inference(subst,[],[refute_0_45:[bind(X_69,$fot(X_454))]]) ).
cnf(refute_0_47,plain,
( ~ is_a_theorem(X_454)
| ~ is_a_theorem(implies(X_454,or(X,and(X_454,not(X)))))
| is_a_theorem(or(X,and(X_454,not(X)))) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_454)),bind(Y,$fot(or(X,and(X_454,not(X)))))]]) ).
cnf(refute_0_48,plain,
( ~ is_a_theorem(X_454)
| is_a_theorem(or(X,and(X_454,not(X)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_454,or(X,and(X_454,not(X))))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( ~ is_a_theorem(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18))
| is_a_theorem(or(X,and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),not(X)))) ),
inference(subst,[],[refute_0_48:[bind(X_454,$fot(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)))]]) ).
cnf(refute_0_50,plain,
( is_a_theorem(strict_equiv(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17))
| substitution_strict_equiv ),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_51,plain,
~ substitution_strict_equiv,
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_52,plain,
is_a_theorem(strict_equiv(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)),
inference(resolve,[$cnf( substitution_strict_equiv )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
( ~ and_2
| is_a_theorem(implies(and(X,Y),Y)) ),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_54,plain,
and_2,
inference(canonicalize,[],[normalize_0_36]) ).
cnf(refute_0_55,plain,
is_a_theorem(implies(and(X,Y),Y)),
inference(resolve,[$cnf( and_2 )],[refute_0_54,refute_0_53]) ).
cnf(refute_0_56,plain,
is_a_theorem(implies(and(strict_implies(X_79,X_80),strict_implies(X_80,X_79)),strict_implies(X_80,X_79))),
inference(subst,[],[refute_0_55:[bind(X,$fot(strict_implies(X_79,X_80))),bind(Y,$fot(strict_implies(X_80,X_79)))]]) ).
cnf(refute_0_57,plain,
( ~ op_strict_equiv
| strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X)) ),
inference(canonicalize,[],[normalize_0_38]) ).
cnf(refute_0_58,plain,
op_strict_equiv,
inference(canonicalize,[],[normalize_0_39]) ).
cnf(refute_0_59,plain,
strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X)),
inference(resolve,[$cnf( op_strict_equiv )],[refute_0_58,refute_0_57]) ).
cnf(refute_0_60,plain,
strict_equiv(X_79,X_80) = and(strict_implies(X_79,X_80),strict_implies(X_80,X_79)),
inference(subst,[],[refute_0_59:[bind(X,$fot(X_79)),bind(Y,$fot(X_80))]]) ).
cnf(refute_0_61,plain,
( strict_equiv(X_79,X_80) != and(strict_implies(X_79,X_80),strict_implies(X_80,X_79))
| and(strict_implies(X_79,X_80),strict_implies(X_80,X_79)) = strict_equiv(X_79,X_80) ),
inference(subst,[],[refute_0_33:[bind(X0,$fot(strict_equiv(X_79,X_80))),bind(Y0,$fot(and(strict_implies(X_79,X_80),strict_implies(X_80,X_79))))]]) ).
cnf(refute_0_62,plain,
and(strict_implies(X_79,X_80),strict_implies(X_80,X_79)) = strict_equiv(X_79,X_80),
inference(resolve,[$cnf( $equal(strict_equiv(X_79,X_80),and(strict_implies(X_79,X_80),strict_implies(X_80,X_79))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
( and(strict_implies(X_79,X_80),strict_implies(X_80,X_79)) != strict_equiv(X_79,X_80)
| ~ is_a_theorem(implies(and(strict_implies(X_79,X_80),strict_implies(X_80,X_79)),strict_implies(X_80,X_79)))
| is_a_theorem(implies(strict_equiv(X_79,X_80),strict_implies(X_80,X_79))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(and(strict_implies(X_79,X_80),strict_implies(X_80,X_79)),strict_implies(X_80,X_79))) ),[0,0],$fot(strict_equiv(X_79,X_80))]]) ).
cnf(refute_0_64,plain,
( ~ is_a_theorem(implies(and(strict_implies(X_79,X_80),strict_implies(X_80,X_79)),strict_implies(X_80,X_79)))
| is_a_theorem(implies(strict_equiv(X_79,X_80),strict_implies(X_80,X_79))) ),
inference(resolve,[$cnf( $equal(and(strict_implies(X_79,X_80),strict_implies(X_80,X_79)),strict_equiv(X_79,X_80)) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
is_a_theorem(implies(strict_equiv(X_79,X_80),strict_implies(X_80,X_79))),
inference(resolve,[$cnf( is_a_theorem(implies(and(strict_implies(X_79,X_80),strict_implies(X_80,X_79)),strict_implies(X_80,X_79))) )],[refute_0_56,refute_0_64]) ).
cnf(refute_0_66,plain,
( ~ is_a_theorem(implies(strict_equiv(X_79,X_80),strict_implies(X_80,X_79)))
| ~ is_a_theorem(strict_equiv(X_79,X_80))
| is_a_theorem(strict_implies(X_80,X_79)) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(strict_equiv(X_79,X_80))),bind(Y,$fot(strict_implies(X_80,X_79)))]]) ).
cnf(refute_0_67,plain,
( ~ is_a_theorem(strict_equiv(X_79,X_80))
| is_a_theorem(strict_implies(X_80,X_79)) ),
inference(resolve,[$cnf( is_a_theorem(implies(strict_equiv(X_79,X_80),strict_implies(X_80,X_79))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
( ~ is_a_theorem(strict_equiv(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17))
| is_a_theorem(strict_implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)) ),
inference(subst,[],[refute_0_67:[bind(X_79,$fot(skolemFOFtoCNF_X_18)),bind(X_80,$fot(skolemFOFtoCNF_Y_17))]]) ).
cnf(refute_0_69,plain,
is_a_theorem(strict_implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)),
inference(resolve,[$cnf( is_a_theorem(strict_equiv(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)) )],[refute_0_52,refute_0_68]) ).
cnf(refute_0_70,plain,
is_a_theorem(implies(necessarily(implies(X_3,X_4)),implies(X_3,X_4))),
inference(subst,[],[refute_0_8:[bind(X,$fot(implies(X_3,X_4)))]]) ).
cnf(refute_0_71,plain,
( ~ op_strict_implies
| strict_implies(X,Y) = necessarily(implies(X,Y)) ),
inference(canonicalize,[],[normalize_0_41]) ).
cnf(refute_0_72,plain,
op_strict_implies,
inference(canonicalize,[],[normalize_0_42]) ).
cnf(refute_0_73,plain,
strict_implies(X,Y) = necessarily(implies(X,Y)),
inference(resolve,[$cnf( op_strict_implies )],[refute_0_72,refute_0_71]) ).
cnf(refute_0_74,plain,
strict_implies(X_3,X_4) = necessarily(implies(X_3,X_4)),
inference(subst,[],[refute_0_73:[bind(X,$fot(X_3)),bind(Y,$fot(X_4))]]) ).
cnf(refute_0_75,plain,
( strict_implies(X_3,X_4) != necessarily(implies(X_3,X_4))
| necessarily(implies(X_3,X_4)) = strict_implies(X_3,X_4) ),
inference(subst,[],[refute_0_33:[bind(X0,$fot(strict_implies(X_3,X_4))),bind(Y0,$fot(necessarily(implies(X_3,X_4))))]]) ).
cnf(refute_0_76,plain,
necessarily(implies(X_3,X_4)) = strict_implies(X_3,X_4),
inference(resolve,[$cnf( $equal(strict_implies(X_3,X_4),necessarily(implies(X_3,X_4))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
( necessarily(implies(X_3,X_4)) != strict_implies(X_3,X_4)
| ~ is_a_theorem(implies(necessarily(implies(X_3,X_4)),implies(X_3,X_4)))
| is_a_theorem(implies(strict_implies(X_3,X_4),implies(X_3,X_4))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(necessarily(implies(X_3,X_4)),implies(X_3,X_4))) ),[0,0],$fot(strict_implies(X_3,X_4))]]) ).
cnf(refute_0_78,plain,
( ~ is_a_theorem(implies(necessarily(implies(X_3,X_4)),implies(X_3,X_4)))
| is_a_theorem(implies(strict_implies(X_3,X_4),implies(X_3,X_4))) ),
inference(resolve,[$cnf( $equal(necessarily(implies(X_3,X_4)),strict_implies(X_3,X_4)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
is_a_theorem(implies(strict_implies(X_3,X_4),implies(X_3,X_4))),
inference(resolve,[$cnf( is_a_theorem(implies(necessarily(implies(X_3,X_4)),implies(X_3,X_4))) )],[refute_0_70,refute_0_78]) ).
cnf(refute_0_80,plain,
( ~ is_a_theorem(implies(strict_implies(X_3,X_4),implies(X_3,X_4)))
| ~ is_a_theorem(strict_implies(X_3,X_4))
| is_a_theorem(implies(X_3,X_4)) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(strict_implies(X_3,X_4))),bind(Y,$fot(implies(X_3,X_4)))]]) ).
cnf(refute_0_81,plain,
( ~ is_a_theorem(strict_implies(X_3,X_4))
| is_a_theorem(implies(X_3,X_4)) ),
inference(resolve,[$cnf( is_a_theorem(implies(strict_implies(X_3,X_4),implies(X_3,X_4))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
( ~ is_a_theorem(strict_implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18))
| is_a_theorem(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)) ),
inference(subst,[],[refute_0_81:[bind(X_3,$fot(skolemFOFtoCNF_Y_17)),bind(X_4,$fot(skolemFOFtoCNF_X_18))]]) ).
cnf(refute_0_83,plain,
is_a_theorem(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)),
inference(resolve,[$cnf( is_a_theorem(strict_implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)) )],[refute_0_69,refute_0_82]) ).
cnf(refute_0_84,plain,
is_a_theorem(or(X,and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),not(X)))),
inference(resolve,[$cnf( is_a_theorem(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)) )],[refute_0_83,refute_0_49]) ).
cnf(refute_0_85,plain,
is_a_theorem(or(X_9539,and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),not(X_9539)))),
inference(subst,[],[refute_0_84:[bind(X,$fot(X_9539))]]) ).
cnf(refute_0_86,plain,
is_a_theorem(necessarily(or(X_9539,and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),not(X_9539))))),
inference(resolve,[$cnf( is_a_theorem(or(X_9539,and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),not(X_9539)))) )],[refute_0_85,refute_0_20]) ).
cnf(refute_0_87,plain,
is_a_theorem(necessarily(or(X_9666,and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),not(X_9666))))),
inference(subst,[],[refute_0_86:[bind(X_9539,$fot(X_9666))]]) ).
cnf(refute_0_88,plain,
is_a_theorem(necessarily(necessarily(or(X_9666,and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),not(X_9666)))))),
inference(resolve,[$cnf( is_a_theorem(necessarily(or(X_9666,and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),not(X_9666))))) )],[refute_0_87,refute_0_19]) ).
cnf(refute_0_89,plain,
is_a_theorem(necessarily(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),not(and(X,not(Y)))))))),
inference(subst,[],[refute_0_88:[bind(X_9666,$fot(and(X,not(Y))))]]) ).
cnf(refute_0_90,plain,
( not(and(X,not(Y))) != implies(X,Y)
| ~ is_a_theorem(necessarily(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),not(and(X,not(Y))))))))
| is_a_theorem(necessarily(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(necessarily(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),not(and(X,not(Y)))))))) ),[0,0,0,1,1],$fot(implies(X,Y))]]) ).
cnf(refute_0_91,plain,
( ~ is_a_theorem(necessarily(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),not(and(X,not(Y))))))))
| is_a_theorem(necessarily(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))))) ),
inference(resolve,[$cnf( $equal(not(and(X,not(Y))),implies(X,Y)) )],[refute_0_35,refute_0_90]) ).
cnf(refute_0_92,plain,
is_a_theorem(necessarily(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))))),
inference(resolve,[$cnf( is_a_theorem(necessarily(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),not(and(X,not(Y)))))))) )],[refute_0_89,refute_0_91]) ).
cnf(refute_0_93,plain,
( strict_implies(X,Y) != necessarily(implies(X,Y))
| necessarily(implies(X,Y)) = strict_implies(X,Y) ),
inference(subst,[],[refute_0_33:[bind(X0,$fot(strict_implies(X,Y))),bind(Y0,$fot(necessarily(implies(X,Y))))]]) ).
cnf(refute_0_94,plain,
necessarily(implies(X,Y)) = strict_implies(X,Y),
inference(resolve,[$cnf( $equal(strict_implies(X,Y),necessarily(implies(X,Y))) )],[refute_0_73,refute_0_93]) ).
cnf(refute_0_95,plain,
necessarily(implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))) = strict_implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))),
inference(subst,[],[refute_0_94:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))))]]) ).
cnf(refute_0_96,plain,
or(and(X,not(Y)),X_58) = implies(not(and(X,not(Y))),X_58),
inference(subst,[],[refute_0_39:[bind(X,$fot(and(X,not(Y)))),bind(Y,$fot(X_58))]]) ).
cnf(refute_0_97,plain,
( not(and(X,not(Y))) != implies(X,Y)
| or(and(X,not(Y)),X_58) != implies(not(and(X,not(Y))),X_58)
| or(and(X,not(Y)),X_58) = implies(implies(X,Y),X_58) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X,not(Y)),X_58),implies(not(and(X,not(Y))),X_58)) ),[1,0],$fot(implies(X,Y))]]) ).
cnf(refute_0_98,plain,
( or(and(X,not(Y)),X_58) != implies(not(and(X,not(Y))),X_58)
| or(and(X,not(Y)),X_58) = implies(implies(X,Y),X_58) ),
inference(resolve,[$cnf( $equal(not(and(X,not(Y))),implies(X,Y)) )],[refute_0_35,refute_0_97]) ).
cnf(refute_0_99,plain,
or(and(X,not(Y)),X_58) = implies(implies(X,Y),X_58),
inference(resolve,[$cnf( $equal(or(and(X,not(Y)),X_58),implies(not(and(X,not(Y))),X_58)) )],[refute_0_96,refute_0_98]) ).
cnf(refute_0_100,plain,
or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))) = implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))),
inference(subst,[],[refute_0_99:[bind(X_58,$fot(and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))))]]) ).
cnf(refute_0_101,plain,
necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))) = necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))),
introduced(tautology,[refl,[$fot(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))))]]) ).
cnf(refute_0_102,plain,
( necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))) != necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))))
| or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))) != implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))
| necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))) = necessarily(implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))),necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))))) ),[1,0],$fot(implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))))]]) ).
cnf(refute_0_103,plain,
( or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))) != implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))
| necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))) = necessarily(implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))) ),
inference(resolve,[$cnf( $equal(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))),necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))) = necessarily(implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))),
inference(resolve,[$cnf( $equal(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))),implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))) )],[refute_0_100,refute_0_103]) ).
cnf(refute_0_105,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_106,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_33,refute_0_105]) ).
cnf(refute_0_107,plain,
( necessarily(implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))) != strict_implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))
| necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))) != necessarily(implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))))
| necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))) = strict_implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))) ),
inference(subst,[],[refute_0_106:[bind(X0,$fot(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))))),bind(Y0,$fot(necessarily(implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))))),bind(Z,$fot(strict_implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))))]]) ).
cnf(refute_0_108,plain,
( necessarily(implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))) != strict_implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))
| necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))) = strict_implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))) ),
inference(resolve,[$cnf( $equal(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))),necessarily(implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))))) )],[refute_0_104,refute_0_107]) ).
cnf(refute_0_109,plain,
necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))) = strict_implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))),
inference(resolve,[$cnf( $equal(necessarily(implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))),strict_implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))) )],[refute_0_95,refute_0_108]) ).
cnf(refute_0_110,plain,
necessarily(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))))) = necessarily(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))))),
introduced(tautology,[refl,[$fot(necessarily(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))))))]]) ).
cnf(refute_0_111,plain,
( necessarily(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))))) != necessarily(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))))
| necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))) != strict_implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))
| necessarily(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))))) = necessarily(strict_implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(necessarily(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))))),necessarily(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))))) ),[1,0],$fot(strict_implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))))]]) ).
cnf(refute_0_112,plain,
( necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))) != strict_implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))
| necessarily(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))))) = necessarily(strict_implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))) ),
inference(resolve,[$cnf( $equal(necessarily(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))))),necessarily(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
necessarily(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))))) = necessarily(strict_implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))),
inference(resolve,[$cnf( $equal(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))),strict_implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))) )],[refute_0_109,refute_0_112]) ).
cnf(refute_0_114,plain,
( necessarily(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))))) != necessarily(strict_implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))))
| ~ is_a_theorem(necessarily(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))))))
| is_a_theorem(necessarily(strict_implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(necessarily(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))))) ),[0],$fot(necessarily(strict_implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))))]]) ).
cnf(refute_0_115,plain,
( ~ is_a_theorem(necessarily(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))))))
| is_a_theorem(necessarily(strict_implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))))) ),
inference(resolve,[$cnf( $equal(necessarily(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))))),necessarily(strict_implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
is_a_theorem(necessarily(strict_implies(implies(X,Y),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y))))),
inference(resolve,[$cnf( is_a_theorem(necessarily(necessarily(or(and(X,not(Y)),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(X,Y)))))) )],[refute_0_92,refute_0_115]) ).
cnf(refute_0_117,plain,
is_a_theorem(necessarily(strict_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_116:[bind(X,$fot(skolemFOFtoCNF_X_18)),bind(Y,$fot(skolemFOFtoCNF_Y_17))]]) ).
cnf(refute_0_118,plain,
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[normalize_0_44]) ).
cnf(refute_0_119,plain,
op_equiv,
inference(canonicalize,[],[normalize_0_45]) ).
cnf(refute_0_120,plain,
equiv(X,Y) = and(implies(X,Y),implies(Y,X)),
inference(resolve,[$cnf( op_equiv )],[refute_0_119,refute_0_118]) ).
cnf(refute_0_121,plain,
equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18) = and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)),
inference(subst,[],[refute_0_120:[bind(X,$fot(skolemFOFtoCNF_Y_17)),bind(Y,$fot(skolemFOFtoCNF_X_18))]]) ).
cnf(refute_0_122,plain,
( equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18) != and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17))
| and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)) = equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18) ),
inference(subst,[],[refute_0_33:[bind(X0,$fot(equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18))),bind(Y0,$fot(and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17))))]]) ).
cnf(refute_0_123,plain,
and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)) = equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),
inference(resolve,[$cnf( $equal(equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17))) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
( and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)) != equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)
| ~ is_a_theorem(necessarily(strict_implies(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)))))
| is_a_theorem(necessarily(strict_implies(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17),equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(necessarily(strict_implies(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17))))) ),[0,0,1],$fot(equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18))]]) ).
cnf(refute_0_125,plain,
( ~ is_a_theorem(necessarily(strict_implies(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17),and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)))))
| is_a_theorem(necessarily(strict_implies(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17),equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)))) ),
inference(resolve,[$cnf( $equal(and(implies(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18),implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)),equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
is_a_theorem(necessarily(strict_implies(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17),equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)))),
inference(resolve,[$cnf( is_a_theorem(necessarily(strict_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_117,refute_0_125]) ).
cnf(refute_0_127,plain,
is_a_theorem(strict_implies(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17),equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18))),
inference(resolve,[$cnf( is_a_theorem(necessarily(strict_implies(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17),equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)))) )],[refute_0_126,refute_0_15]) ).
cnf(refute_0_128,plain,
( ~ is_a_theorem(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17))
| ~ modus_ponens_strict_implies
| is_a_theorem(equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)) ),
inference(resolve,[$cnf( is_a_theorem(strict_implies(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17),equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18))) )],[refute_0_127,refute_0_5]) ).
cnf(refute_0_129,plain,
( ~ and_1
| is_a_theorem(implies(and(X,Y),X)) ),
inference(canonicalize,[],[normalize_0_48]) ).
cnf(refute_0_130,plain,
and_1,
inference(canonicalize,[],[normalize_0_49]) ).
cnf(refute_0_131,plain,
is_a_theorem(implies(and(X,Y),X)),
inference(resolve,[$cnf( and_1 )],[refute_0_130,refute_0_129]) ).
cnf(refute_0_132,plain,
is_a_theorem(implies(and(strict_implies(X_79,X_80),strict_implies(X_80,X_79)),strict_implies(X_79,X_80))),
inference(subst,[],[refute_0_131:[bind(X,$fot(strict_implies(X_79,X_80))),bind(Y,$fot(strict_implies(X_80,X_79)))]]) ).
cnf(refute_0_133,plain,
( and(strict_implies(X_79,X_80),strict_implies(X_80,X_79)) != strict_equiv(X_79,X_80)
| ~ is_a_theorem(implies(and(strict_implies(X_79,X_80),strict_implies(X_80,X_79)),strict_implies(X_79,X_80)))
| is_a_theorem(implies(strict_equiv(X_79,X_80),strict_implies(X_79,X_80))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(and(strict_implies(X_79,X_80),strict_implies(X_80,X_79)),strict_implies(X_79,X_80))) ),[0,0],$fot(strict_equiv(X_79,X_80))]]) ).
cnf(refute_0_134,plain,
( ~ is_a_theorem(implies(and(strict_implies(X_79,X_80),strict_implies(X_80,X_79)),strict_implies(X_79,X_80)))
| is_a_theorem(implies(strict_equiv(X_79,X_80),strict_implies(X_79,X_80))) ),
inference(resolve,[$cnf( $equal(and(strict_implies(X_79,X_80),strict_implies(X_80,X_79)),strict_equiv(X_79,X_80)) )],[refute_0_62,refute_0_133]) ).
cnf(refute_0_135,plain,
is_a_theorem(implies(strict_equiv(X_79,X_80),strict_implies(X_79,X_80))),
inference(resolve,[$cnf( is_a_theorem(implies(and(strict_implies(X_79,X_80),strict_implies(X_80,X_79)),strict_implies(X_79,X_80))) )],[refute_0_132,refute_0_134]) ).
cnf(refute_0_136,plain,
( ~ is_a_theorem(implies(strict_equiv(X_79,X_80),strict_implies(X_79,X_80)))
| ~ is_a_theorem(strict_equiv(X_79,X_80))
| is_a_theorem(strict_implies(X_79,X_80)) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(strict_equiv(X_79,X_80))),bind(Y,$fot(strict_implies(X_79,X_80)))]]) ).
cnf(refute_0_137,plain,
( ~ is_a_theorem(strict_equiv(X_79,X_80))
| is_a_theorem(strict_implies(X_79,X_80)) ),
inference(resolve,[$cnf( is_a_theorem(implies(strict_equiv(X_79,X_80),strict_implies(X_79,X_80))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
( ~ is_a_theorem(strict_equiv(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17))
| is_a_theorem(strict_implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)) ),
inference(subst,[],[refute_0_137:[bind(X_79,$fot(skolemFOFtoCNF_X_18)),bind(X_80,$fot(skolemFOFtoCNF_Y_17))]]) ).
cnf(refute_0_139,plain,
is_a_theorem(strict_implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)),
inference(resolve,[$cnf( is_a_theorem(strict_equiv(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)) )],[refute_0_52,refute_0_138]) ).
cnf(refute_0_140,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_81:[bind(X_3,$fot(skolemFOFtoCNF_X_18)),bind(X_4,$fot(skolemFOFtoCNF_Y_17))]]) ).
cnf(refute_0_141,plain,
is_a_theorem(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)),
inference(resolve,[$cnf( is_a_theorem(strict_implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
( ~ modus_ponens_strict_implies
| is_a_theorem(equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)) ),
inference(resolve,[$cnf( is_a_theorem(implies(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17)) )],[refute_0_141,refute_0_128]) ).
cnf(refute_0_143,plain,
( ~ is_a_theorem(skolemFOFtoCNF_Y_15)
| modus_ponens_strict_implies ),
inference(canonicalize,[],[normalize_0_50]) ).
cnf(refute_0_144,plain,
( is_a_theorem(skolemFOFtoCNF_X_16)
| modus_ponens_strict_implies ),
inference(canonicalize,[],[normalize_0_51]) ).
cnf(refute_0_145,plain,
( ~ is_a_theorem(implies(skolemFOFtoCNF_X_16,skolemFOFtoCNF_Y_15))
| ~ is_a_theorem(skolemFOFtoCNF_X_16)
| is_a_theorem(skolemFOFtoCNF_Y_15) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(skolemFOFtoCNF_X_16)),bind(Y,$fot(skolemFOFtoCNF_Y_15))]]) ).
cnf(refute_0_146,plain,
( is_a_theorem(strict_implies(skolemFOFtoCNF_X_16,skolemFOFtoCNF_Y_15))
| modus_ponens_strict_implies ),
inference(canonicalize,[],[normalize_0_52]) ).
cnf(refute_0_147,plain,
( ~ is_a_theorem(strict_implies(skolemFOFtoCNF_X_16,skolemFOFtoCNF_Y_15))
| is_a_theorem(implies(skolemFOFtoCNF_X_16,skolemFOFtoCNF_Y_15)) ),
inference(subst,[],[refute_0_81:[bind(X_3,$fot(skolemFOFtoCNF_X_16)),bind(X_4,$fot(skolemFOFtoCNF_Y_15))]]) ).
cnf(refute_0_148,plain,
( is_a_theorem(implies(skolemFOFtoCNF_X_16,skolemFOFtoCNF_Y_15))
| modus_ponens_strict_implies ),
inference(resolve,[$cnf( is_a_theorem(strict_implies(skolemFOFtoCNF_X_16,skolemFOFtoCNF_Y_15)) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
( ~ is_a_theorem(skolemFOFtoCNF_X_16)
| is_a_theorem(skolemFOFtoCNF_Y_15)
| modus_ponens_strict_implies ),
inference(resolve,[$cnf( is_a_theorem(implies(skolemFOFtoCNF_X_16,skolemFOFtoCNF_Y_15)) )],[refute_0_148,refute_0_145]) ).
cnf(refute_0_150,plain,
( is_a_theorem(skolemFOFtoCNF_Y_15)
| modus_ponens_strict_implies ),
inference(resolve,[$cnf( is_a_theorem(skolemFOFtoCNF_X_16) )],[refute_0_144,refute_0_149]) ).
cnf(refute_0_151,plain,
modus_ponens_strict_implies,
inference(resolve,[$cnf( is_a_theorem(skolemFOFtoCNF_Y_15) )],[refute_0_150,refute_0_143]) ).
cnf(refute_0_152,plain,
is_a_theorem(equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)),
inference(resolve,[$cnf( modus_ponens_strict_implies )],[refute_0_151,refute_0_142]) ).
cnf(refute_0_153,plain,
skolemFOFtoCNF_Y_17 = skolemFOFtoCNF_X_18,
inference(resolve,[$cnf( is_a_theorem(equiv(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18)) )],[refute_0_152,refute_0_3]) ).
cnf(refute_0_154,plain,
( skolemFOFtoCNF_X_18 != skolemFOFtoCNF_Y_17
| substitution_strict_equiv ),
inference(canonicalize,[],[normalize_0_53]) ).
cnf(refute_0_155,plain,
skolemFOFtoCNF_X_18 != skolemFOFtoCNF_Y_17,
inference(resolve,[$cnf( substitution_strict_equiv )],[refute_0_154,refute_0_51]) ).
cnf(refute_0_156,plain,
( skolemFOFtoCNF_Y_17 != skolemFOFtoCNF_X_18
| skolemFOFtoCNF_X_18 = skolemFOFtoCNF_Y_17 ),
inference(subst,[],[refute_0_33:[bind(X0,$fot(skolemFOFtoCNF_Y_17)),bind(Y0,$fot(skolemFOFtoCNF_X_18))]]) ).
cnf(refute_0_157,plain,
skolemFOFtoCNF_Y_17 != skolemFOFtoCNF_X_18,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_18,skolemFOFtoCNF_Y_17) )],[refute_0_156,refute_0_155]) ).
cnf(refute_0_158,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_17,skolemFOFtoCNF_X_18) )],[refute_0_153,refute_0_157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LCL539+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.11 % Command : metis --show proof --show saturation %s
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Mon Jul 4 00:15:47 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 45.75/45.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 45.75/45.94
% 45.75/45.94 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 45.75/45.96
%------------------------------------------------------------------------------