%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL453+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 12:42:45 PM UTC 2026
% Result : Theorem 2.16s 2.42s
% Output : CNFRefutation 2.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 43
% Syntax : Number of formulae : 201 ( 97 unt; 0 def)
% Number of atoms : 364 ( 115 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 308 ( 145 ~; 127 |; 15 &)
% ( 16 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 15 ( 12 usr; 12 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 15 con; 0-2 aty)
% Number of variables : 234 ( 6 sgn 62 !; 15 ?)
% 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(modus_tollens,axiom,
( modus_tollens
<=> ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ) ).
fof(implies_2,axiom,
( implies_2
<=> ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ) ).
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(or_1,axiom,
( or_1
<=> ! [X,Y] : is_a_theorem(implies(X,or(X,Y))) ) ).
fof(cn3,axiom,
( cn3
<=> ! [P] : is_a_theorem(implies(implies(not(P),P),P)) ) ).
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_modus_tollens,axiom,
modus_tollens ).
fof(hilbert_implies_2,axiom,
implies_2 ).
fof(hilbert_and_2,axiom,
and_2 ).
fof(hilbert_and_3,axiom,
and_3 ).
fof(hilbert_or_1,axiom,
or_1 ).
fof(use_substitution_of_equivalents,axiom,
substitution_of_equivalents ).
fof(luka_op_or,axiom,
op_or ).
fof(luka_op_equiv,axiom,
op_equiv ).
fof(luka_cn3,conjecture,
cn3 ).
fof(subgoal_0,plain,
cn3,
inference(strip,[],[luka_cn3]) ).
fof(negate_0_0,plain,
~ cn3,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ cn3
<=> ? [P] : ~ is_a_theorem(implies(implies(not(P),P),P)) ),
inference(canonicalize,[],[cn3]) ).
fof(normalize_0_1,plain,
! [P] :
( ( ~ cn3
| is_a_theorem(implies(implies(not(P),P),P)) )
& ( ~ is_a_theorem(implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5))
| cn3 ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ is_a_theorem(implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5))
| cn3 ),
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,
~ cn3,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_10,plain,
( ~ substitution_of_equivalents
<=> ? [X,Y] :
( X != Y
& is_a_theorem(equiv(X,Y)) ) ),
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_11,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_10]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
substitution_of_equivalents,
inference(canonicalize,[],[use_substitution_of_equivalents]) ).
fof(normalize_0_14,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_15,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_14]) ).
fof(normalize_0_16,plain,
! [X,Y] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
modus_ponens,
inference(canonicalize,[],[hilbert_modus_ponens]) ).
fof(normalize_0_18,plain,
( ~ and_3
<=> ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(canonicalize,[],[and_3]) ).
fof(normalize_0_19,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_18]) ).
fof(normalize_0_20,plain,
! [X,Y] :
( ~ and_3
| is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(conjunct,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
and_3,
inference(canonicalize,[],[hilbert_and_3]) ).
fof(normalize_0_22,plain,
( ~ implies_2
<=> ? [X,Y] : ~ is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
inference(canonicalize,[],[implies_2]) ).
fof(normalize_0_23,plain,
! [X,Y] :
( ( ~ implies_2
| is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )
& ( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_X_4,implies(skolemFOFtoCNF_X_4,skolemFOFtoCNF_Y_4)),implies(skolemFOFtoCNF_X_4,skolemFOFtoCNF_Y_4)))
| implies_2 ) ),
inference(clausify,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [X,Y] :
( ~ implies_2
| is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
implies_2,
inference(canonicalize,[],[hilbert_implies_2]) ).
fof(normalize_0_26,plain,
( ~ op_equiv
| ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[op_equiv]) ).
fof(normalize_0_27,plain,
! [X,Y] :
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(clausify,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
op_equiv,
inference(canonicalize,[],[luka_op_equiv]) ).
fof(normalize_0_29,plain,
( ~ and_2
<=> ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),Y)) ),
inference(canonicalize,[],[and_2]) ).
fof(normalize_0_30,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_29]) ).
fof(normalize_0_31,plain,
! [X,Y] :
( ~ and_2
| is_a_theorem(implies(and(X,Y),Y)) ),
inference(conjunct,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
and_2,
inference(canonicalize,[],[hilbert_and_2]) ).
fof(normalize_0_33,plain,
( ~ modus_tollens
<=> ? [X,Y] : ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
inference(canonicalize,[],[modus_tollens]) ).
fof(normalize_0_34,plain,
! [X,Y] :
( ( ~ is_a_theorem(implies(implies(not(skolemFOFtoCNF_Y_2),not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2)))
| modus_tollens )
& ( ~ modus_tollens
| is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ) ),
inference(clausify,[],[normalize_0_33]) ).
fof(normalize_0_35,plain,
! [X,Y] :
( ~ modus_tollens
| is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
inference(conjunct,[],[normalize_0_34]) ).
fof(normalize_0_36,plain,
modus_tollens,
inference(canonicalize,[],[hilbert_modus_tollens]) ).
fof(normalize_0_37,plain,
( ~ or_1
<=> ? [X,Y] : ~ is_a_theorem(implies(X,or(X,Y))) ),
inference(canonicalize,[],[or_1]) ).
fof(normalize_0_38,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_37]) ).
fof(normalize_0_39,plain,
! [X,Y] :
( ~ or_1
| is_a_theorem(implies(X,or(X,Y))) ),
inference(conjunct,[],[normalize_0_38]) ).
fof(normalize_0_40,plain,
or_1,
inference(canonicalize,[],[hilbert_or_1]) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5))
| cn3 ),
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( $equal(or(X,Y),implies(not(X),Y)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) = or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),
inference(subst,[],[refute_0_17:[bind(X,$fot(skolemFOFtoCNF_P_5)),bind(Y,$fot(skolemFOFtoCNF_P_5))]]) ).
cnf(refute_0_19,plain,
implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) = implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),
introduced(tautology,[refl,[$fot(implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5))]]) ).
cnf(refute_0_20,plain,
( implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) != implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)
| implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) != or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5)
| implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) = implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)) ),[1,0],$fot(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5))]]) ).
cnf(refute_0_21,plain,
( implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) != or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5)
| implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) = implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) ),
inference(resolve,[$cnf( $equal(implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) = implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),
inference(resolve,[$cnf( $equal(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5)) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
( implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) != implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)
| ~ is_a_theorem(implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5))
| is_a_theorem(implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)) ),[0],$fot(implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5))]]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5))
| is_a_theorem(implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ is_a_theorem(implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5))
| cn3 ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)) )],[refute_0_24,refute_0_0]) ).
cnf(refute_0_26,plain,
~ cn3,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_27,plain,
~ is_a_theorem(implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)),
inference(resolve,[$cnf( cn3 )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
implies(not(not(skolemFOFtoCNF_P_5)),skolemFOFtoCNF_P_5) = or(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),
inference(subst,[],[refute_0_17:[bind(X,$fot(not(skolemFOFtoCNF_P_5))),bind(Y,$fot(skolemFOFtoCNF_P_5))]]) ).
cnf(refute_0_29,plain,
implies(not(Y),Y) = not(and(not(Y),not(Y))),
inference(subst,[],[refute_0_6:[bind(X,$fot(not(Y)))]]) ).
cnf(refute_0_30,plain,
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_31,plain,
substitution_of_equivalents,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_32,plain,
( ~ is_a_theorem(equiv(X,Y))
| X = Y ),
inference(resolve,[$cnf( substitution_of_equivalents )],[refute_0_31,refute_0_30]) ).
cnf(refute_0_33,plain,
( ~ is_a_theorem(equiv(X_689,and(X_689,X_689)))
| X_689 = and(X_689,X_689) ),
inference(subst,[],[refute_0_32:[bind(X,$fot(X_689)),bind(Y,$fot(and(X_689,X_689)))]]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_35,plain,
modus_ponens,
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_36,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) ),
inference(resolve,[$cnf( modus_ponens )],[refute_0_35,refute_0_34]) ).
cnf(refute_0_37,plain,
( ~ is_a_theorem(implies(and(X_688,X_688),X_688))
| ~ is_a_theorem(implies(implies(and(X_688,X_688),X_688),equiv(X_688,and(X_688,X_688))))
| is_a_theorem(equiv(X_688,and(X_688,X_688))) ),
inference(subst,[],[refute_0_36:[bind(X,$fot(implies(and(X_688,X_688),X_688))),bind(Y,$fot(equiv(X_688,and(X_688,X_688))))]]) ).
cnf(refute_0_38,plain,
( ~ and_3
| is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_39,plain,
and_3,
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_40,plain,
is_a_theorem(implies(X,implies(Y,and(X,Y)))),
inference(resolve,[$cnf( and_3 )],[refute_0_39,refute_0_38]) ).
cnf(refute_0_41,plain,
is_a_theorem(implies(X_119,implies(Y,and(X_119,Y)))),
inference(subst,[],[refute_0_40:[bind(X,$fot(X_119))]]) ).
cnf(refute_0_42,plain,
( ~ is_a_theorem(X_119)
| ~ is_a_theorem(implies(X_119,implies(Y,and(X_119,Y))))
| is_a_theorem(implies(Y,and(X_119,Y))) ),
inference(subst,[],[refute_0_36:[bind(X,$fot(X_119)),bind(Y,$fot(implies(Y,and(X_119,Y))))]]) ).
cnf(refute_0_43,plain,
( ~ is_a_theorem(X_119)
| is_a_theorem(implies(Y,and(X_119,Y))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_119,implies(Y,and(X_119,Y)))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ is_a_theorem(implies(X_602,and(X_602,X_602)))
| is_a_theorem(implies(Y,and(implies(X_602,and(X_602,X_602)),Y))) ),
inference(subst,[],[refute_0_43:[bind(X_119,$fot(implies(X_602,and(X_602,X_602))))]]) ).
cnf(refute_0_45,plain,
is_a_theorem(implies(X_598,implies(X_598,and(X_598,X_598)))),
inference(subst,[],[refute_0_40:[bind(X,$fot(X_598)),bind(Y,$fot(X_598))]]) ).
cnf(refute_0_46,plain,
( ~ implies_2
| is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_47,plain,
implies_2,
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_48,plain,
is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))),
inference(resolve,[$cnf( implies_2 )],[refute_0_47,refute_0_46]) ).
cnf(refute_0_49,plain,
( ~ is_a_theorem(implies(X,implies(X,Y)))
| ~ is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))
| is_a_theorem(implies(X,Y)) ),
inference(subst,[],[refute_0_36:[bind(X,$fot(implies(X,implies(X,Y)))),bind(Y,$fot(implies(X,Y)))]]) ).
cnf(refute_0_50,plain,
( ~ is_a_theorem(implies(X,implies(X,Y)))
| is_a_theorem(implies(X,Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
( ~ is_a_theorem(implies(X_598,implies(X_598,and(X_598,X_598))))
| is_a_theorem(implies(X_598,and(X_598,X_598))) ),
inference(subst,[],[refute_0_50:[bind(X,$fot(X_598)),bind(Y,$fot(and(X_598,X_598)))]]) ).
cnf(refute_0_52,plain,
is_a_theorem(implies(X_598,and(X_598,X_598))),
inference(resolve,[$cnf( is_a_theorem(implies(X_598,implies(X_598,and(X_598,X_598)))) )],[refute_0_45,refute_0_51]) ).
cnf(refute_0_53,plain,
is_a_theorem(implies(X_602,and(X_602,X_602))),
inference(subst,[],[refute_0_52:[bind(X_598,$fot(X_602))]]) ).
cnf(refute_0_54,plain,
is_a_theorem(implies(Y,and(implies(X_602,and(X_602,X_602)),Y))),
inference(resolve,[$cnf( is_a_theorem(implies(X_602,and(X_602,X_602))) )],[refute_0_53,refute_0_44]) ).
cnf(refute_0_55,plain,
is_a_theorem(implies(implies(and(X_687,X_687),X_687),and(implies(X_687,and(X_687,X_687)),implies(and(X_687,X_687),X_687)))),
inference(subst,[],[refute_0_54:[bind(Y,$fot(implies(and(X_687,X_687),X_687))),bind(X_602,$fot(X_687))]]) ).
cnf(refute_0_56,plain,
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_57,plain,
op_equiv,
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_58,plain,
equiv(X,Y) = and(implies(X,Y),implies(Y,X)),
inference(resolve,[$cnf( op_equiv )],[refute_0_57,refute_0_56]) ).
cnf(refute_0_59,plain,
equiv(X_687,and(X_687,X_687)) = and(implies(X_687,and(X_687,X_687)),implies(and(X_687,X_687),X_687)),
inference(subst,[],[refute_0_58:[bind(X,$fot(X_687)),bind(Y,$fot(and(X_687,X_687)))]]) ).
cnf(refute_0_60,plain,
( equiv(X_687,and(X_687,X_687)) != and(implies(X_687,and(X_687,X_687)),implies(and(X_687,X_687),X_687))
| and(implies(X_687,and(X_687,X_687)),implies(and(X_687,X_687),X_687)) = equiv(X_687,and(X_687,X_687)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(equiv(X_687,and(X_687,X_687)))),bind(Y0,$fot(and(implies(X_687,and(X_687,X_687)),implies(and(X_687,X_687),X_687))))]]) ).
cnf(refute_0_61,plain,
and(implies(X_687,and(X_687,X_687)),implies(and(X_687,X_687),X_687)) = equiv(X_687,and(X_687,X_687)),
inference(resolve,[$cnf( $equal(equiv(X_687,and(X_687,X_687)),and(implies(X_687,and(X_687,X_687)),implies(and(X_687,X_687),X_687))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
( and(implies(X_687,and(X_687,X_687)),implies(and(X_687,X_687),X_687)) != equiv(X_687,and(X_687,X_687))
| ~ is_a_theorem(implies(implies(and(X_687,X_687),X_687),and(implies(X_687,and(X_687,X_687)),implies(and(X_687,X_687),X_687))))
| is_a_theorem(implies(implies(and(X_687,X_687),X_687),equiv(X_687,and(X_687,X_687)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(and(X_687,X_687),X_687),and(implies(X_687,and(X_687,X_687)),implies(and(X_687,X_687),X_687)))) ),[0,1],$fot(equiv(X_687,and(X_687,X_687)))]]) ).
cnf(refute_0_63,plain,
( ~ is_a_theorem(implies(implies(and(X_687,X_687),X_687),and(implies(X_687,and(X_687,X_687)),implies(and(X_687,X_687),X_687))))
| is_a_theorem(implies(implies(and(X_687,X_687),X_687),equiv(X_687,and(X_687,X_687)))) ),
inference(resolve,[$cnf( $equal(and(implies(X_687,and(X_687,X_687)),implies(and(X_687,X_687),X_687)),equiv(X_687,and(X_687,X_687))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
is_a_theorem(implies(implies(and(X_687,X_687),X_687),equiv(X_687,and(X_687,X_687)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(and(X_687,X_687),X_687),and(implies(X_687,and(X_687,X_687)),implies(and(X_687,X_687),X_687)))) )],[refute_0_55,refute_0_63]) ).
cnf(refute_0_65,plain,
is_a_theorem(implies(implies(and(X_688,X_688),X_688),equiv(X_688,and(X_688,X_688)))),
inference(subst,[],[refute_0_64:[bind(X_687,$fot(X_688))]]) ).
cnf(refute_0_66,plain,
( ~ is_a_theorem(implies(and(X_688,X_688),X_688))
| is_a_theorem(equiv(X_688,and(X_688,X_688))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(and(X_688,X_688),X_688),equiv(X_688,and(X_688,X_688)))) )],[refute_0_65,refute_0_37]) ).
cnf(refute_0_67,plain,
( ~ and_2
| is_a_theorem(implies(and(X,Y),Y)) ),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_68,plain,
and_2,
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_69,plain,
is_a_theorem(implies(and(X,Y),Y)),
inference(resolve,[$cnf( and_2 )],[refute_0_68,refute_0_67]) ).
cnf(refute_0_70,plain,
is_a_theorem(implies(and(X_688,X_688),X_688)),
inference(subst,[],[refute_0_69:[bind(X,$fot(X_688)),bind(Y,$fot(X_688))]]) ).
cnf(refute_0_71,plain,
is_a_theorem(equiv(X_688,and(X_688,X_688))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_688,X_688),X_688)) )],[refute_0_70,refute_0_66]) ).
cnf(refute_0_72,plain,
is_a_theorem(equiv(X_689,and(X_689,X_689))),
inference(subst,[],[refute_0_71:[bind(X_688,$fot(X_689))]]) ).
cnf(refute_0_73,plain,
X_689 = and(X_689,X_689),
inference(resolve,[$cnf( is_a_theorem(equiv(X_689,and(X_689,X_689))) )],[refute_0_72,refute_0_33]) ).
cnf(refute_0_74,plain,
not(Y) = and(not(Y),not(Y)),
inference(subst,[],[refute_0_73:[bind(X_689,$fot(not(Y)))]]) ).
cnf(refute_0_75,plain,
( not(Y) != and(not(Y),not(Y))
| and(not(Y),not(Y)) = not(Y) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(not(Y))),bind(Y0,$fot(and(not(Y),not(Y))))]]) ).
cnf(refute_0_76,plain,
and(not(Y),not(Y)) = not(Y),
inference(resolve,[$cnf( $equal(not(Y),and(not(Y),not(Y))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
( and(not(Y),not(Y)) != not(Y)
| implies(not(Y),Y) != not(and(not(Y),not(Y)))
| implies(not(Y),Y) = not(not(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(Y),Y),not(and(not(Y),not(Y)))) ),[1,0],$fot(not(Y))]]) ).
cnf(refute_0_78,plain,
( implies(not(Y),Y) != not(and(not(Y),not(Y)))
| implies(not(Y),Y) = not(not(Y)) ),
inference(resolve,[$cnf( $equal(and(not(Y),not(Y)),not(Y)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
implies(not(Y),Y) = not(not(Y)),
inference(resolve,[$cnf( $equal(implies(not(Y),Y),not(and(not(Y),not(Y)))) )],[refute_0_29,refute_0_78]) ).
cnf(refute_0_80,plain,
implies(not(Y),Y) = or(Y,Y),
inference(subst,[],[refute_0_17:[bind(X,$fot(Y))]]) ).
cnf(refute_0_81,plain,
( implies(not(Y),Y) != not(not(Y))
| implies(not(Y),Y) != or(Y,Y)
| or(Y,Y) = not(not(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(Y),Y),not(not(Y))) ),[0],$fot(or(Y,Y))]]) ).
cnf(refute_0_82,plain,
( implies(not(Y),Y) != not(not(Y))
| or(Y,Y) = not(not(Y)) ),
inference(resolve,[$cnf( $equal(implies(not(Y),Y),or(Y,Y)) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
or(Y,Y) = not(not(Y)),
inference(resolve,[$cnf( $equal(implies(not(Y),Y),not(not(Y))) )],[refute_0_79,refute_0_82]) ).
cnf(refute_0_84,plain,
or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5) = not(not(skolemFOFtoCNF_P_5)),
inference(subst,[],[refute_0_83:[bind(Y,$fot(skolemFOFtoCNF_P_5))]]) ).
cnf(refute_0_85,plain,
implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) = implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),
introduced(tautology,[refl,[$fot(implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5))]]) ).
cnf(refute_0_86,plain,
( implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) != implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)
| or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5) != not(not(skolemFOFtoCNF_P_5))
| implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) = implies(not(not(skolemFOFtoCNF_P_5)),skolemFOFtoCNF_P_5) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)) ),[1,0],$fot(not(not(skolemFOFtoCNF_P_5)))]]) ).
cnf(refute_0_87,plain,
( or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5) != not(not(skolemFOFtoCNF_P_5))
| implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) = implies(not(not(skolemFOFtoCNF_P_5)),skolemFOFtoCNF_P_5) ),
inference(resolve,[$cnf( $equal(implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) = implies(not(not(skolemFOFtoCNF_P_5)),skolemFOFtoCNF_P_5),
inference(resolve,[$cnf( $equal(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),not(not(skolemFOFtoCNF_P_5))) )],[refute_0_84,refute_0_87]) ).
cnf(refute_0_89,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_90,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_9,refute_0_89]) ).
cnf(refute_0_91,plain,
( implies(not(not(skolemFOFtoCNF_P_5)),skolemFOFtoCNF_P_5) != or(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)
| implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) != implies(not(not(skolemFOFtoCNF_P_5)),skolemFOFtoCNF_P_5)
| implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) = or(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5))),bind(Y0,$fot(implies(not(not(skolemFOFtoCNF_P_5)),skolemFOFtoCNF_P_5))),bind(Z,$fot(or(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)))]]) ).
cnf(refute_0_92,plain,
( implies(not(not(skolemFOFtoCNF_P_5)),skolemFOFtoCNF_P_5) != or(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)
| implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) = or(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) ),
inference(resolve,[$cnf( $equal(implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),implies(not(not(skolemFOFtoCNF_P_5)),skolemFOFtoCNF_P_5)) )],[refute_0_88,refute_0_91]) ).
cnf(refute_0_93,plain,
implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) = or(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),
inference(resolve,[$cnf( $equal(implies(not(not(skolemFOFtoCNF_P_5)),skolemFOFtoCNF_P_5),or(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)) )],[refute_0_28,refute_0_92]) ).
cnf(refute_0_94,plain,
( implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) != or(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)
| ~ is_a_theorem(or(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5))
| is_a_theorem(implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)) ),[0],$fot(or(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5))]]) ).
cnf(refute_0_95,plain,
( ~ is_a_theorem(or(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5))
| is_a_theorem(implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)) ),
inference(resolve,[$cnf( $equal(implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),or(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
~ is_a_theorem(or(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)),
inference(resolve,[$cnf( is_a_theorem(implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)) )],[refute_0_95,refute_0_27]) ).
cnf(refute_0_97,plain,
( ~ modus_tollens
| is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_98,plain,
modus_tollens,
inference(canonicalize,[],[normalize_0_36]) ).
cnf(refute_0_99,plain,
is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))),
inference(resolve,[$cnf( modus_tollens )],[refute_0_98,refute_0_97]) ).
cnf(refute_0_100,plain,
implies(not(Y),not(X)) = or(Y,not(X)),
inference(subst,[],[refute_0_17:[bind(X,$fot(Y)),bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_101,plain,
implies(implies(not(Y),not(X)),implies(X,Y)) = implies(implies(not(Y),not(X)),implies(X,Y)),
introduced(tautology,[refl,[$fot(implies(implies(not(Y),not(X)),implies(X,Y)))]]) ).
cnf(refute_0_102,plain,
( implies(implies(not(Y),not(X)),implies(X,Y)) != implies(implies(not(Y),not(X)),implies(X,Y))
| implies(not(Y),not(X)) != or(Y,not(X))
| implies(implies(not(Y),not(X)),implies(X,Y)) = implies(or(Y,not(X)),implies(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(Y),not(X)),implies(X,Y)),implies(implies(not(Y),not(X)),implies(X,Y))) ),[1,0],$fot(or(Y,not(X)))]]) ).
cnf(refute_0_103,plain,
( implies(not(Y),not(X)) != or(Y,not(X))
| implies(implies(not(Y),not(X)),implies(X,Y)) = implies(or(Y,not(X)),implies(X,Y)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(Y),not(X)),implies(X,Y)),implies(implies(not(Y),not(X)),implies(X,Y))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
implies(implies(not(Y),not(X)),implies(X,Y)) = implies(or(Y,not(X)),implies(X,Y)),
inference(resolve,[$cnf( $equal(implies(not(Y),not(X)),or(Y,not(X))) )],[refute_0_100,refute_0_103]) ).
cnf(refute_0_105,plain,
( implies(implies(not(Y),not(X)),implies(X,Y)) != implies(or(Y,not(X)),implies(X,Y))
| ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| is_a_theorem(implies(or(Y,not(X)),implies(X,Y))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),[0],$fot(implies(or(Y,not(X)),implies(X,Y)))]]) ).
cnf(refute_0_106,plain,
( ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| is_a_theorem(implies(or(Y,not(X)),implies(X,Y))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(Y),not(X)),implies(X,Y)),implies(or(Y,not(X)),implies(X,Y))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
is_a_theorem(implies(or(Y,not(X)),implies(X,Y))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) )],[refute_0_99,refute_0_106]) ).
cnf(refute_0_108,plain,
( ~ is_a_theorem(implies(or(Y,not(X)),implies(X,Y)))
| ~ is_a_theorem(or(Y,not(X)))
| is_a_theorem(implies(X,Y)) ),
inference(subst,[],[refute_0_36:[bind(X,$fot(or(Y,not(X)))),bind(Y,$fot(implies(X,Y)))]]) ).
cnf(refute_0_109,plain,
( ~ is_a_theorem(or(Y,not(X)))
| is_a_theorem(implies(X,Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(Y,not(X)),implies(X,Y))) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
( ~ is_a_theorem(or(X_698,not(not(not(X_698)))))
| is_a_theorem(implies(not(not(X_698)),X_698)) ),
inference(subst,[],[refute_0_109:[bind(X,$fot(not(not(X_698)))),bind(Y,$fot(X_698))]]) ).
cnf(refute_0_111,plain,
( ~ or_1
| is_a_theorem(implies(X,or(X,Y))) ),
inference(canonicalize,[],[normalize_0_39]) ).
cnf(refute_0_112,plain,
or_1,
inference(canonicalize,[],[normalize_0_40]) ).
cnf(refute_0_113,plain,
is_a_theorem(implies(X,or(X,Y))),
inference(resolve,[$cnf( or_1 )],[refute_0_112,refute_0_111]) ).
cnf(refute_0_114,plain,
is_a_theorem(implies(not(X_24),or(not(X_24),Y))),
inference(subst,[],[refute_0_113:[bind(X,$fot(not(X_24)))]]) ).
cnf(refute_0_115,plain,
or(X_24,or(not(X_24),Y)) = implies(not(X_24),or(not(X_24),Y)),
inference(subst,[],[refute_0_15:[bind(X,$fot(X_24)),bind(Y,$fot(or(not(X_24),Y)))]]) ).
cnf(refute_0_116,plain,
( or(X_24,or(not(X_24),Y)) != implies(not(X_24),or(not(X_24),Y))
| implies(not(X_24),or(not(X_24),Y)) = or(X_24,or(not(X_24),Y)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(or(X_24,or(not(X_24),Y)))),bind(Y0,$fot(implies(not(X_24),or(not(X_24),Y))))]]) ).
cnf(refute_0_117,plain,
implies(not(X_24),or(not(X_24),Y)) = or(X_24,or(not(X_24),Y)),
inference(resolve,[$cnf( $equal(or(X_24,or(not(X_24),Y)),implies(not(X_24),or(not(X_24),Y))) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
( implies(not(X_24),or(not(X_24),Y)) != or(X_24,or(not(X_24),Y))
| ~ is_a_theorem(implies(not(X_24),or(not(X_24),Y)))
| is_a_theorem(or(X_24,or(not(X_24),Y))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(X_24),or(not(X_24),Y))) ),[0],$fot(or(X_24,or(not(X_24),Y)))]]) ).
cnf(refute_0_119,plain,
( ~ is_a_theorem(implies(not(X_24),or(not(X_24),Y)))
| is_a_theorem(or(X_24,or(not(X_24),Y))) ),
inference(resolve,[$cnf( $equal(implies(not(X_24),or(not(X_24),Y)),or(X_24,or(not(X_24),Y))) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
is_a_theorem(or(X_24,or(not(X_24),Y))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_24),or(not(X_24),Y))) )],[refute_0_114,refute_0_119]) ).
cnf(refute_0_121,plain,
is_a_theorem(or(X_24,or(not(X_24),not(X_24)))),
inference(subst,[],[refute_0_120:[bind(Y,$fot(not(X_24)))]]) ).
cnf(refute_0_122,plain,
or(not(X_24),not(X_24)) = not(not(not(X_24))),
inference(subst,[],[refute_0_83:[bind(Y,$fot(not(X_24)))]]) ).
cnf(refute_0_123,plain,
( or(not(X_24),not(X_24)) != not(not(not(X_24)))
| ~ is_a_theorem(or(X_24,or(not(X_24),not(X_24))))
| is_a_theorem(or(X_24,not(not(not(X_24))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(X_24,or(not(X_24),not(X_24)))) ),[0,1],$fot(not(not(not(X_24))))]]) ).
cnf(refute_0_124,plain,
( ~ is_a_theorem(or(X_24,or(not(X_24),not(X_24))))
| is_a_theorem(or(X_24,not(not(not(X_24))))) ),
inference(resolve,[$cnf( $equal(or(not(X_24),not(X_24)),not(not(not(X_24)))) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
is_a_theorem(or(X_24,not(not(not(X_24))))),
inference(resolve,[$cnf( is_a_theorem(or(X_24,or(not(X_24),not(X_24)))) )],[refute_0_121,refute_0_124]) ).
cnf(refute_0_126,plain,
is_a_theorem(or(X_698,not(not(not(X_698))))),
inference(subst,[],[refute_0_125:[bind(X_24,$fot(X_698))]]) ).
cnf(refute_0_127,plain,
is_a_theorem(implies(not(not(X_698)),X_698)),
inference(resolve,[$cnf( is_a_theorem(or(X_698,not(not(not(X_698))))) )],[refute_0_126,refute_0_110]) ).
cnf(refute_0_128,plain,
implies(not(not(X_698)),X_698) = or(not(X_698),X_698),
inference(subst,[],[refute_0_17:[bind(X,$fot(not(X_698))),bind(Y,$fot(X_698))]]) ).
cnf(refute_0_129,plain,
( implies(not(not(X_698)),X_698) != or(not(X_698),X_698)
| ~ is_a_theorem(implies(not(not(X_698)),X_698))
| is_a_theorem(or(not(X_698),X_698)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(not(X_698)),X_698)) ),[0],$fot(or(not(X_698),X_698))]]) ).
cnf(refute_0_130,plain,
( ~ is_a_theorem(implies(not(not(X_698)),X_698))
| is_a_theorem(or(not(X_698),X_698)) ),
inference(resolve,[$cnf( $equal(implies(not(not(X_698)),X_698),or(not(X_698),X_698)) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
is_a_theorem(or(not(X_698),X_698)),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(X_698)),X_698)) )],[refute_0_127,refute_0_130]) ).
cnf(refute_0_132,plain,
is_a_theorem(or(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)),
inference(subst,[],[refute_0_131:[bind(X_698,$fot(skolemFOFtoCNF_P_5))]]) ).
cnf(refute_0_133,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(or(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)) )],[refute_0_132,refute_0_96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL453+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.10/0.37 % Computer : n027.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 5 12:40:58 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.16/2.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.16/2.42
% 2.16/2.42 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.16/2.49
%------------------------------------------------------------------------------