TSTP Solution File: LCL500+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL500+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 12:52:46 EDT 2022
% Result : Theorem 107.65s 107.81s
% Output : CNFRefutation 107.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 41
% Syntax : Number of formulae : 192 ( 96 unt; 0 def)
% Number of atoms : 334 ( 125 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 271 ( 129 ~; 117 |; 10 &)
% ( 10 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 13 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-2 aty)
% Number of variables : 351 ( 14 sgn 55 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(Y) ) ) ).
fof(kn2,axiom,
( kn2
<=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ) ).
fof(r2,axiom,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ) ).
fof(r3,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ) ).
fof(r5,axiom,
( r5
<=> ! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ) ).
fof(op_or,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ) ).
fof(op_and,axiom,
( op_and
=> ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ) ).
fof(op_implies_or,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) ) ).
fof(principia_op_implies_or,axiom,
op_implies_or ).
fof(principia_op_and,axiom,
op_and ).
fof(principia_modus_ponens,axiom,
modus_ponens ).
fof(principia_r2,axiom,
r2 ).
fof(principia_r3,axiom,
r3 ).
fof(principia_r5,axiom,
r5 ).
fof(rosser_op_or,axiom,
op_or ).
fof(rosser_op_implies_and,axiom,
op_implies_and ).
fof(rosser_kn2,conjecture,
kn2 ).
fof(subgoal_0,plain,
kn2,
inference(strip,[],[rosser_kn2]) ).
fof(negate_0_0,plain,
~ kn2,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ kn2
<=> ? [P,Q] : ~ is_a_theorem(implies(and(P,Q),P)) ),
inference(canonicalize,[],[kn2]) ).
fof(normalize_0_1,plain,
! [P,Q] :
( ( ~ is_a_theorem(implies(and(skolemFOFtoCNF_P_1,skolemFOFtoCNF_Q),skolemFOFtoCNF_P_1))
| kn2 )
& ( ~ kn2
| is_a_theorem(implies(and(P,Q),P)) ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ is_a_theorem(implies(and(skolemFOFtoCNF_P_1,skolemFOFtoCNF_Q),skolemFOFtoCNF_P_1))
| kn2 ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ kn2,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_4,plain,
( ~ r3
<=> ? [P,Q] : ~ is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(canonicalize,[],[r3]) ).
fof(normalize_0_5,plain,
! [P,Q] :
( ( ~ is_a_theorem(implies(or(skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_5),or(skolemFOFtoCNF_Q_5,skolemFOFtoCNF_P_8)))
| r3 )
& ( ~ r3
| is_a_theorem(implies(or(P,Q),or(Q,P))) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [P,Q] :
( ~ r3
| is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
r3,
inference(canonicalize,[],[principia_r3]) ).
fof(normalize_0_8,plain,
( ~ op_implies_or
| ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[op_implies_or]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
op_implies_or,
inference(canonicalize,[],[principia_op_implies_or]) ).
fof(normalize_0_11,plain,
( ~ op_and
| ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ),
inference(canonicalize,[],[op_and]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ~ op_and
| and(X,Y) = not(or(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
op_and,
inference(canonicalize,[],[principia_op_and]) ).
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,[],[principia_modus_ponens]) ).
fof(normalize_0_18,plain,
( ~ op_or
| ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[op_or]) ).
fof(normalize_0_19,plain,
! [X,Y] :
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
op_or,
inference(canonicalize,[],[rosser_op_or]) ).
fof(normalize_0_21,plain,
( ~ op_implies_and
| ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[op_implies_and]) ).
fof(normalize_0_22,plain,
! [X,Y] :
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(clausify,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
op_implies_and,
inference(canonicalize,[],[rosser_op_implies_and]) ).
fof(normalize_0_24,plain,
( ~ r2
<=> ? [P,Q] : ~ is_a_theorem(implies(Q,or(P,Q))) ),
inference(canonicalize,[],[r2]) ).
fof(normalize_0_25,plain,
! [P,Q] :
( ( ~ is_a_theorem(implies(skolemFOFtoCNF_Q_4,or(skolemFOFtoCNF_P_7,skolemFOFtoCNF_Q_4)))
| r2 )
& ( ~ r2
| is_a_theorem(implies(Q,or(P,Q))) ) ),
inference(clausify,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [P,Q] :
( ~ r2
| is_a_theorem(implies(Q,or(P,Q))) ),
inference(conjunct,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
r2,
inference(canonicalize,[],[principia_r2]) ).
fof(normalize_0_28,plain,
( ~ r5
<=> ? [P,Q,R] : ~ is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
inference(canonicalize,[],[r5]) ).
fof(normalize_0_29,plain,
! [P,Q,R] :
( ( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_Q_7,skolemFOFtoCNF_R_3),implies(or(skolemFOFtoCNF_P_10,skolemFOFtoCNF_Q_7),or(skolemFOFtoCNF_P_10,skolemFOFtoCNF_R_3))))
| r5 )
& ( ~ r5
| is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ) ),
inference(clausify,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [P,Q,R] :
( ~ r5
| is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
inference(conjunct,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
r5,
inference(canonicalize,[],[principia_r5]) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(and(skolemFOFtoCNF_P_1,skolemFOFtoCNF_Q),skolemFOFtoCNF_P_1))
| kn2 ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ kn2,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
~ is_a_theorem(implies(and(skolemFOFtoCNF_P_1,skolemFOFtoCNF_Q),skolemFOFtoCNF_P_1)),
inference(resolve,[$cnf( kn2 )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ r3
| is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
r3,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(or(P,Q),or(Q,P))),
inference(resolve,[$cnf( r3 )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(or(not(X),X_32),or(X_32,not(X)))),
inference(subst,[],[refute_0_5:[bind(P,$fot(not(X))),bind(Q,$fot(X_32))]]) ).
cnf(refute_0_7,plain,
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_8,plain,
op_implies_or,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
implies(X,Y) = or(not(X),Y),
inference(resolve,[$cnf( op_implies_or )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
implies(X,X_32) = or(not(X),X_32),
inference(subst,[],[refute_0_9:[bind(Y,$fot(X_32))]]) ).
cnf(refute_0_11,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_12,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_13,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( implies(X,X_32) != or(not(X),X_32)
| or(not(X),X_32) = implies(X,X_32) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,X_32))),bind(Y0,$fot(or(not(X),X_32)))]]) ).
cnf(refute_0_15,plain,
or(not(X),X_32) = implies(X,X_32),
inference(resolve,[$cnf( $equal(implies(X,X_32),or(not(X),X_32)) )],[refute_0_10,refute_0_14]) ).
cnf(refute_0_16,plain,
( or(not(X),X_32) != implies(X,X_32)
| ~ is_a_theorem(implies(or(not(X),X_32),or(X_32,not(X))))
| is_a_theorem(implies(implies(X,X_32),or(X_32,not(X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),X_32),or(X_32,not(X)))) ),[0,0],$fot(implies(X,X_32))]]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(implies(or(not(X),X_32),or(X_32,not(X))))
| is_a_theorem(implies(implies(X,X_32),or(X_32,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_32),implies(X,X_32)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
is_a_theorem(implies(implies(X,X_32),or(X_32,not(X)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),X_32),or(X_32,not(X)))) )],[refute_0_6,refute_0_17]) ).
cnf(refute_0_19,plain,
is_a_theorem(implies(implies(X,not(X_64)),or(not(X_64),not(X)))),
inference(subst,[],[refute_0_18:[bind(X_32,$fot(not(X_64)))]]) ).
cnf(refute_0_20,plain,
implies(implies(X,not(Y)),X_12) = or(not(implies(X,not(Y))),X_12),
inference(subst,[],[refute_0_9:[bind(X,$fot(implies(X,not(Y)))),bind(Y,$fot(X_12))]]) ).
cnf(refute_0_21,plain,
( ~ op_and
| and(X,Y) = not(or(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_22,plain,
op_and,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_23,plain,
and(X,Y) = not(or(not(X),not(Y))),
inference(resolve,[$cnf( op_and )],[refute_0_22,refute_0_21]) ).
cnf(refute_0_24,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_25,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[refute_0_9,refute_0_24]) ).
cnf(refute_0_26,plain,
or(not(X),not(Y)) = implies(X,not(Y)),
inference(subst,[],[refute_0_25:[bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_27,plain,
not(or(not(X),not(Y))) = not(or(not(X),not(Y))),
introduced(tautology,[refl,[$fot(not(or(not(X),not(Y))))]]) ).
cnf(refute_0_28,plain,
( not(or(not(X),not(Y))) != not(or(not(X),not(Y)))
| or(not(X),not(Y)) != implies(X,not(Y))
| not(or(not(X),not(Y))) = not(implies(X,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X),not(Y))),not(or(not(X),not(Y)))) ),[1,0],$fot(implies(X,not(Y)))]]) ).
cnf(refute_0_29,plain,
( or(not(X),not(Y)) != implies(X,not(Y))
| not(or(not(X),not(Y))) = not(implies(X,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),not(or(not(X),not(Y)))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
not(or(not(X),not(Y))) = not(implies(X,not(Y))),
inference(resolve,[$cnf( $equal(or(not(X),not(Y)),implies(X,not(Y))) )],[refute_0_26,refute_0_29]) ).
cnf(refute_0_31,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| not(or(not(X),not(Y))) != not(implies(X,not(Y)))
| and(X,Y) = not(implies(X,not(Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X,Y),not(implies(X,not(Y)))) ),[0],$fot(not(or(not(X),not(Y))))]]) ).
cnf(refute_0_32,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| and(X,Y) = not(implies(X,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),not(implies(X,not(Y)))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
and(X,Y) = not(implies(X,not(Y))),
inference(resolve,[$cnf( $equal(and(X,Y),not(or(not(X),not(Y)))) )],[refute_0_23,refute_0_32]) ).
cnf(refute_0_34,plain,
( and(X,Y) != not(implies(X,not(Y)))
| not(implies(X,not(Y))) = and(X,Y) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(X,Y))),bind(Y0,$fot(not(implies(X,not(Y)))))]]) ).
cnf(refute_0_35,plain,
not(implies(X,not(Y))) = and(X,Y),
inference(resolve,[$cnf( $equal(and(X,Y),not(implies(X,not(Y)))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( implies(implies(X,not(Y)),X_12) != or(not(implies(X,not(Y))),X_12)
| not(implies(X,not(Y))) != and(X,Y)
| implies(implies(X,not(Y)),X_12) = or(and(X,Y),X_12) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,not(Y)),X_12),or(not(implies(X,not(Y))),X_12)) ),[1,0],$fot(and(X,Y))]]) ).
cnf(refute_0_37,plain,
( implies(implies(X,not(Y)),X_12) != or(not(implies(X,not(Y))),X_12)
| implies(implies(X,not(Y)),X_12) = or(and(X,Y),X_12) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(Y))),and(X,Y)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
implies(implies(X,not(Y)),X_12) = or(and(X,Y),X_12),
inference(resolve,[$cnf( $equal(implies(implies(X,not(Y)),X_12),or(not(implies(X,not(Y))),X_12)) )],[refute_0_20,refute_0_37]) ).
cnf(refute_0_39,plain,
implies(implies(X,not(X_64)),or(not(X_64),not(X))) = or(and(X,X_64),or(not(X_64),not(X))),
inference(subst,[],[refute_0_38:[bind(Y,$fot(X_64)),bind(X_12,$fot(or(not(X_64),not(X))))]]) ).
cnf(refute_0_40,plain,
( implies(implies(X,not(X_64)),or(not(X_64),not(X))) != or(and(X,X_64),or(not(X_64),not(X)))
| ~ is_a_theorem(implies(implies(X,not(X_64)),or(not(X_64),not(X))))
| is_a_theorem(or(and(X,X_64),or(not(X_64),not(X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X,not(X_64)),or(not(X_64),not(X)))) ),[0],$fot(or(and(X,X_64),or(not(X_64),not(X))))]]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(implies(implies(X,not(X_64)),or(not(X_64),not(X))))
| is_a_theorem(or(and(X,X_64),or(not(X_64),not(X)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(X_64)),or(not(X_64),not(X))),or(and(X,X_64),or(not(X_64),not(X)))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
is_a_theorem(or(and(X,X_64),or(not(X_64),not(X)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,not(X_64)),or(not(X_64),not(X)))) )],[refute_0_19,refute_0_41]) ).
cnf(refute_0_43,plain,
or(not(X_64),not(X)) = implies(X_64,not(X)),
inference(subst,[],[refute_0_25:[bind(X,$fot(X_64)),bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_44,plain,
or(and(X,X_64),or(not(X_64),not(X))) = or(and(X,X_64),or(not(X_64),not(X))),
introduced(tautology,[refl,[$fot(or(and(X,X_64),or(not(X_64),not(X))))]]) ).
cnf(refute_0_45,plain,
( or(and(X,X_64),or(not(X_64),not(X))) != or(and(X,X_64),or(not(X_64),not(X)))
| or(not(X_64),not(X)) != implies(X_64,not(X))
| or(and(X,X_64),or(not(X_64),not(X))) = or(and(X,X_64),implies(X_64,not(X))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X,X_64),or(not(X_64),not(X))),or(and(X,X_64),or(not(X_64),not(X)))) ),[1,1],$fot(implies(X_64,not(X)))]]) ).
cnf(refute_0_46,plain,
( or(not(X_64),not(X)) != implies(X_64,not(X))
| or(and(X,X_64),or(not(X_64),not(X))) = or(and(X,X_64),implies(X_64,not(X))) ),
inference(resolve,[$cnf( $equal(or(and(X,X_64),or(not(X_64),not(X))),or(and(X,X_64),or(not(X_64),not(X)))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
or(and(X,X_64),or(not(X_64),not(X))) = or(and(X,X_64),implies(X_64,not(X))),
inference(resolve,[$cnf( $equal(or(not(X_64),not(X)),implies(X_64,not(X))) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
( or(and(X,X_64),or(not(X_64),not(X))) != or(and(X,X_64),implies(X_64,not(X)))
| ~ is_a_theorem(or(and(X,X_64),or(not(X_64),not(X))))
| is_a_theorem(or(and(X,X_64),implies(X_64,not(X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(X,X_64),or(not(X_64),not(X)))) ),[0],$fot(or(and(X,X_64),implies(X_64,not(X))))]]) ).
cnf(refute_0_49,plain,
( ~ is_a_theorem(or(and(X,X_64),or(not(X_64),not(X))))
| is_a_theorem(or(and(X,X_64),implies(X_64,not(X)))) ),
inference(resolve,[$cnf( $equal(or(and(X,X_64),or(not(X_64),not(X))),or(and(X,X_64),implies(X_64,not(X)))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
is_a_theorem(or(and(X,X_64),implies(X_64,not(X)))),
inference(resolve,[$cnf( is_a_theorem(or(and(X,X_64),or(not(X_64),not(X)))) )],[refute_0_42,refute_0_49]) ).
cnf(refute_0_51,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_52,plain,
modus_ponens,
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_53,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) ),
inference(resolve,[$cnf( modus_ponens )],[refute_0_52,refute_0_51]) ).
cnf(refute_0_54,plain,
( ~ is_a_theorem(implies(or(P,Q),or(Q,P)))
| ~ is_a_theorem(or(P,Q))
| is_a_theorem(or(Q,P)) ),
inference(subst,[],[refute_0_53:[bind(X,$fot(or(P,Q))),bind(Y,$fot(or(Q,P)))]]) ).
cnf(refute_0_55,plain,
( ~ is_a_theorem(or(P,Q))
| is_a_theorem(or(Q,P)) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(P,Q),or(Q,P))) )],[refute_0_5,refute_0_54]) ).
cnf(refute_0_56,plain,
( ~ is_a_theorem(or(and(X,X_64),implies(X_64,not(X))))
| is_a_theorem(or(implies(X_64,not(X)),and(X,X_64))) ),
inference(subst,[],[refute_0_55:[bind(P,$fot(and(X,X_64))),bind(Q,$fot(implies(X_64,not(X))))]]) ).
cnf(refute_0_57,plain,
is_a_theorem(or(implies(X_64,not(X)),and(X,X_64))),
inference(resolve,[$cnf( is_a_theorem(or(and(X,X_64),implies(X_64,not(X)))) )],[refute_0_50,refute_0_56]) ).
cnf(refute_0_58,plain,
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_59,plain,
op_or,
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_60,plain,
or(X,Y) = not(and(not(X),not(Y))),
inference(resolve,[$cnf( op_or )],[refute_0_59,refute_0_58]) ).
cnf(refute_0_61,plain,
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_62,plain,
op_implies_and,
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_63,plain,
implies(X,Y) = not(and(X,not(Y))),
inference(resolve,[$cnf( op_implies_and )],[refute_0_62,refute_0_61]) ).
cnf(refute_0_64,plain,
( implies(X,Y) != not(and(X,not(Y)))
| not(and(X,not(Y))) = implies(X,Y) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(not(and(X,not(Y)))))]]) ).
cnf(refute_0_65,plain,
not(and(X,not(Y))) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),not(and(X,not(Y)))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
not(and(not(X),not(Y))) = implies(not(X),Y),
inference(subst,[],[refute_0_65:[bind(X,$fot(not(X)))]]) ).
cnf(refute_0_67,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_68,plain,
( or(X,Y) != not(and(not(X),not(Y)))
| or(X,Y) = implies(not(X),Y) ),
inference(resolve,[$cnf( $equal(not(and(not(X),not(Y))),implies(not(X),Y)) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
or(X,Y) = implies(not(X),Y),
inference(resolve,[$cnf( $equal(or(X,Y),not(and(not(X),not(Y)))) )],[refute_0_60,refute_0_68]) ).
cnf(refute_0_70,plain,
or(implies(X_3,not(X_4)),Y) = implies(not(implies(X_3,not(X_4))),Y),
inference(subst,[],[refute_0_69:[bind(X,$fot(implies(X_3,not(X_4))))]]) ).
cnf(refute_0_71,plain,
and(X_3,X_4) = not(implies(X_3,not(X_4))),
inference(subst,[],[refute_0_33:[bind(X,$fot(X_3)),bind(Y,$fot(X_4))]]) ).
cnf(refute_0_72,plain,
( and(X_3,X_4) != not(implies(X_3,not(X_4)))
| not(implies(X_3,not(X_4))) = and(X_3,X_4) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(X_3,X_4))),bind(Y0,$fot(not(implies(X_3,not(X_4)))))]]) ).
cnf(refute_0_73,plain,
not(implies(X_3,not(X_4))) = and(X_3,X_4),
inference(resolve,[$cnf( $equal(and(X_3,X_4),not(implies(X_3,not(X_4)))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
( not(implies(X_3,not(X_4))) != and(X_3,X_4)
| or(implies(X_3,not(X_4)),Y) != implies(not(implies(X_3,not(X_4))),Y)
| or(implies(X_3,not(X_4)),Y) = implies(and(X_3,X_4),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(X_3,not(X_4)),Y),implies(not(implies(X_3,not(X_4))),Y)) ),[1,0],$fot(and(X_3,X_4))]]) ).
cnf(refute_0_75,plain,
( or(implies(X_3,not(X_4)),Y) != implies(not(implies(X_3,not(X_4))),Y)
| or(implies(X_3,not(X_4)),Y) = implies(and(X_3,X_4),Y) ),
inference(resolve,[$cnf( $equal(not(implies(X_3,not(X_4))),and(X_3,X_4)) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
or(implies(X_3,not(X_4)),Y) = implies(and(X_3,X_4),Y),
inference(resolve,[$cnf( $equal(or(implies(X_3,not(X_4)),Y),implies(not(implies(X_3,not(X_4))),Y)) )],[refute_0_70,refute_0_75]) ).
cnf(refute_0_77,plain,
or(implies(X_64,not(X)),and(X,X_64)) = implies(and(X_64,X),and(X,X_64)),
inference(subst,[],[refute_0_76:[bind(Y,$fot(and(X,X_64))),bind(X_3,$fot(X_64)),bind(X_4,$fot(X))]]) ).
cnf(refute_0_78,plain,
( or(implies(X_64,not(X)),and(X,X_64)) != implies(and(X_64,X),and(X,X_64))
| ~ is_a_theorem(or(implies(X_64,not(X)),and(X,X_64)))
| is_a_theorem(implies(and(X_64,X),and(X,X_64))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(X_64,not(X)),and(X,X_64))) ),[0],$fot(implies(and(X_64,X),and(X,X_64)))]]) ).
cnf(refute_0_79,plain,
( ~ is_a_theorem(or(implies(X_64,not(X)),and(X,X_64)))
| is_a_theorem(implies(and(X_64,X),and(X,X_64))) ),
inference(resolve,[$cnf( $equal(or(implies(X_64,not(X)),and(X,X_64)),implies(and(X_64,X),and(X,X_64))) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
is_a_theorem(implies(and(X_64,X),and(X,X_64))),
inference(resolve,[$cnf( is_a_theorem(or(implies(X_64,not(X)),and(X,X_64))) )],[refute_0_57,refute_0_79]) ).
cnf(refute_0_81,plain,
is_a_theorem(implies(and(X_25232,X_25230),and(X_25230,X_25232))),
inference(subst,[],[refute_0_80:[bind(X,$fot(X_25230)),bind(X_64,$fot(X_25232))]]) ).
cnf(refute_0_82,plain,
( ~ is_a_theorem(implies(X_6256,and(X_6255,X_6257)))
| ~ is_a_theorem(implies(implies(X_6256,and(X_6255,X_6257)),implies(X_6256,X_6257)))
| is_a_theorem(implies(X_6256,X_6257)) ),
inference(subst,[],[refute_0_53:[bind(X,$fot(implies(X_6256,and(X_6255,X_6257)))),bind(Y,$fot(implies(X_6256,X_6257)))]]) ).
cnf(refute_0_83,plain,
( ~ r2
| is_a_theorem(implies(Q,or(P,Q))) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_84,plain,
r2,
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_85,plain,
is_a_theorem(implies(Q,or(P,Q))),
inference(resolve,[$cnf( r2 )],[refute_0_84,refute_0_83]) ).
cnf(refute_0_86,plain,
is_a_theorem(implies(not(X),or(X_7,not(X)))),
inference(subst,[],[refute_0_85:[bind(P,$fot(X_7)),bind(Q,$fot(not(X)))]]) ).
cnf(refute_0_87,plain,
or(X,or(X_7,not(X))) = implies(not(X),or(X_7,not(X))),
inference(subst,[],[refute_0_69:[bind(Y,$fot(or(X_7,not(X))))]]) ).
cnf(refute_0_88,plain,
( or(X,or(X_7,not(X))) != implies(not(X),or(X_7,not(X)))
| implies(not(X),or(X_7,not(X))) = or(X,or(X_7,not(X))) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(X,or(X_7,not(X))))),bind(Y0,$fot(implies(not(X),or(X_7,not(X)))))]]) ).
cnf(refute_0_89,plain,
implies(not(X),or(X_7,not(X))) = or(X,or(X_7,not(X))),
inference(resolve,[$cnf( $equal(or(X,or(X_7,not(X))),implies(not(X),or(X_7,not(X)))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
( implies(not(X),or(X_7,not(X))) != or(X,or(X_7,not(X)))
| ~ is_a_theorem(implies(not(X),or(X_7,not(X))))
| is_a_theorem(or(X,or(X_7,not(X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(X),or(X_7,not(X)))) ),[0],$fot(or(X,or(X_7,not(X))))]]) ).
cnf(refute_0_91,plain,
( ~ is_a_theorem(implies(not(X),or(X_7,not(X))))
| is_a_theorem(or(X,or(X_7,not(X)))) ),
inference(resolve,[$cnf( $equal(implies(not(X),or(X_7,not(X))),or(X,or(X_7,not(X)))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
is_a_theorem(or(X,or(X_7,not(X)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X),or(X_7,not(X)))) )],[refute_0_86,refute_0_91]) ).
cnf(refute_0_93,plain,
is_a_theorem(or(X,or(not(X_11),not(X)))),
inference(subst,[],[refute_0_92:[bind(X_7,$fot(not(X_11)))]]) ).
cnf(refute_0_94,plain,
implies(X_11,not(X)) = or(not(X_11),not(X)),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_11)),bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_95,plain,
( implies(X_11,not(X)) != or(not(X_11),not(X))
| or(not(X_11),not(X)) = implies(X_11,not(X)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X_11,not(X)))),bind(Y0,$fot(or(not(X_11),not(X))))]]) ).
cnf(refute_0_96,plain,
or(not(X_11),not(X)) = implies(X_11,not(X)),
inference(resolve,[$cnf( $equal(implies(X_11,not(X)),or(not(X_11),not(X))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
( or(not(X_11),not(X)) != implies(X_11,not(X))
| ~ is_a_theorem(or(X,or(not(X_11),not(X))))
| is_a_theorem(or(X,implies(X_11,not(X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(X,or(not(X_11),not(X)))) ),[0,1],$fot(implies(X_11,not(X)))]]) ).
cnf(refute_0_98,plain,
( ~ is_a_theorem(or(X,or(not(X_11),not(X))))
| is_a_theorem(or(X,implies(X_11,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X_11),not(X)),implies(X_11,not(X))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
is_a_theorem(or(X,implies(X_11,not(X)))),
inference(resolve,[$cnf( is_a_theorem(or(X,or(not(X_11),not(X)))) )],[refute_0_93,refute_0_98]) ).
cnf(refute_0_100,plain,
is_a_theorem(or(X_357,implies(X_11,not(X_357)))),
inference(subst,[],[refute_0_99:[bind(X,$fot(X_357))]]) ).
cnf(refute_0_101,plain,
( ~ is_a_theorem(or(X_357,implies(X_11,not(X_357))))
| is_a_theorem(or(implies(X_11,not(X_357)),X_357)) ),
inference(subst,[],[refute_0_55:[bind(P,$fot(X_357)),bind(Q,$fot(implies(X_11,not(X_357))))]]) ).
cnf(refute_0_102,plain,
is_a_theorem(or(implies(X_11,not(X_357)),X_357)),
inference(resolve,[$cnf( is_a_theorem(or(X_357,implies(X_11,not(X_357)))) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
or(implies(X_11,not(X_357)),X_357) = implies(and(X_11,X_357),X_357),
inference(subst,[],[refute_0_76:[bind(Y,$fot(X_357)),bind(X_3,$fot(X_11)),bind(X_4,$fot(X_357))]]) ).
cnf(refute_0_104,plain,
( or(implies(X_11,not(X_357)),X_357) != implies(and(X_11,X_357),X_357)
| ~ is_a_theorem(or(implies(X_11,not(X_357)),X_357))
| is_a_theorem(implies(and(X_11,X_357),X_357)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(X_11,not(X_357)),X_357)) ),[0],$fot(implies(and(X_11,X_357),X_357))]]) ).
cnf(refute_0_105,plain,
( ~ is_a_theorem(or(implies(X_11,not(X_357)),X_357))
| is_a_theorem(implies(and(X_11,X_357),X_357)) ),
inference(resolve,[$cnf( $equal(or(implies(X_11,not(X_357)),X_357),implies(and(X_11,X_357),X_357)) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
is_a_theorem(implies(and(X_11,X_357),X_357)),
inference(resolve,[$cnf( is_a_theorem(or(implies(X_11,not(X_357)),X_357)) )],[refute_0_102,refute_0_105]) ).
cnf(refute_0_107,plain,
is_a_theorem(implies(and(X_11,X_6238),X_6238)),
inference(subst,[],[refute_0_106:[bind(X_357,$fot(X_6238))]]) ).
cnf(refute_0_108,plain,
( ~ r5
| is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_109,plain,
r5,
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_110,plain,
is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))),
inference(resolve,[$cnf( r5 )],[refute_0_109,refute_0_108]) ).
cnf(refute_0_111,plain,
is_a_theorem(implies(implies(X_73,X_74),implies(or(not(X),X_73),or(not(X),X_74)))),
inference(subst,[],[refute_0_110:[bind(P,$fot(not(X))),bind(Q,$fot(X_73)),bind(R,$fot(X_74))]]) ).
cnf(refute_0_112,plain,
implies(X,X_74) = or(not(X),X_74),
inference(subst,[],[refute_0_9:[bind(Y,$fot(X_74))]]) ).
cnf(refute_0_113,plain,
( implies(X,X_74) != or(not(X),X_74)
| or(not(X),X_74) = implies(X,X_74) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,X_74))),bind(Y0,$fot(or(not(X),X_74)))]]) ).
cnf(refute_0_114,plain,
or(not(X),X_74) = implies(X,X_74),
inference(resolve,[$cnf( $equal(implies(X,X_74),or(not(X),X_74)) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
( or(not(X),X_74) != implies(X,X_74)
| ~ is_a_theorem(implies(implies(X_73,X_74),implies(or(not(X),X_73),or(not(X),X_74))))
| is_a_theorem(implies(implies(X_73,X_74),implies(or(not(X),X_73),implies(X,X_74)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_73,X_74),implies(or(not(X),X_73),or(not(X),X_74)))) ),[0,1,1],$fot(implies(X,X_74))]]) ).
cnf(refute_0_116,plain,
( ~ is_a_theorem(implies(implies(X_73,X_74),implies(or(not(X),X_73),or(not(X),X_74))))
| is_a_theorem(implies(implies(X_73,X_74),implies(or(not(X),X_73),implies(X,X_74)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_74),implies(X,X_74)) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
is_a_theorem(implies(implies(X_73,X_74),implies(or(not(X),X_73),implies(X,X_74)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_73,X_74),implies(or(not(X),X_73),or(not(X),X_74)))) )],[refute_0_111,refute_0_116]) ).
cnf(refute_0_118,plain,
or(not(X),X_73) = implies(X,X_73),
inference(subst,[],[refute_0_25:[bind(Y,$fot(X_73))]]) ).
cnf(refute_0_119,plain,
implies(or(not(X),X_73),implies(X,X_74)) = implies(or(not(X),X_73),implies(X,X_74)),
introduced(tautology,[refl,[$fot(implies(or(not(X),X_73),implies(X,X_74)))]]) ).
cnf(refute_0_120,plain,
( implies(or(not(X),X_73),implies(X,X_74)) != implies(or(not(X),X_73),implies(X,X_74))
| or(not(X),X_73) != implies(X,X_73)
| implies(or(not(X),X_73),implies(X,X_74)) = implies(implies(X,X_73),implies(X,X_74)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),X_73),implies(X,X_74)),implies(or(not(X),X_73),implies(X,X_74))) ),[1,0],$fot(implies(X,X_73))]]) ).
cnf(refute_0_121,plain,
( or(not(X),X_73) != implies(X,X_73)
| implies(or(not(X),X_73),implies(X,X_74)) = implies(implies(X,X_73),implies(X,X_74)) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_73),implies(X,X_74)),implies(or(not(X),X_73),implies(X,X_74))) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
implies(or(not(X),X_73),implies(X,X_74)) = implies(implies(X,X_73),implies(X,X_74)),
inference(resolve,[$cnf( $equal(or(not(X),X_73),implies(X,X_73)) )],[refute_0_118,refute_0_121]) ).
cnf(refute_0_123,plain,
implies(implies(X_73,X_74),implies(or(not(X),X_73),implies(X,X_74))) = implies(implies(X_73,X_74),implies(or(not(X),X_73),implies(X,X_74))),
introduced(tautology,[refl,[$fot(implies(implies(X_73,X_74),implies(or(not(X),X_73),implies(X,X_74))))]]) ).
cnf(refute_0_124,plain,
( implies(implies(X_73,X_74),implies(or(not(X),X_73),implies(X,X_74))) != implies(implies(X_73,X_74),implies(or(not(X),X_73),implies(X,X_74)))
| implies(or(not(X),X_73),implies(X,X_74)) != implies(implies(X,X_73),implies(X,X_74))
| implies(implies(X_73,X_74),implies(or(not(X),X_73),implies(X,X_74))) = implies(implies(X_73,X_74),implies(implies(X,X_73),implies(X,X_74))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_73,X_74),implies(or(not(X),X_73),implies(X,X_74))),implies(implies(X_73,X_74),implies(or(not(X),X_73),implies(X,X_74)))) ),[1,1],$fot(implies(implies(X,X_73),implies(X,X_74)))]]) ).
cnf(refute_0_125,plain,
( implies(or(not(X),X_73),implies(X,X_74)) != implies(implies(X,X_73),implies(X,X_74))
| implies(implies(X_73,X_74),implies(or(not(X),X_73),implies(X,X_74))) = implies(implies(X_73,X_74),implies(implies(X,X_73),implies(X,X_74))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_73,X_74),implies(or(not(X),X_73),implies(X,X_74))),implies(implies(X_73,X_74),implies(or(not(X),X_73),implies(X,X_74)))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
implies(implies(X_73,X_74),implies(or(not(X),X_73),implies(X,X_74))) = implies(implies(X_73,X_74),implies(implies(X,X_73),implies(X,X_74))),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_73),implies(X,X_74)),implies(implies(X,X_73),implies(X,X_74))) )],[refute_0_122,refute_0_125]) ).
cnf(refute_0_127,plain,
( implies(implies(X_73,X_74),implies(or(not(X),X_73),implies(X,X_74))) != implies(implies(X_73,X_74),implies(implies(X,X_73),implies(X,X_74)))
| ~ is_a_theorem(implies(implies(X_73,X_74),implies(or(not(X),X_73),implies(X,X_74))))
| is_a_theorem(implies(implies(X_73,X_74),implies(implies(X,X_73),implies(X,X_74)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_73,X_74),implies(or(not(X),X_73),implies(X,X_74)))) ),[0],$fot(implies(implies(X_73,X_74),implies(implies(X,X_73),implies(X,X_74))))]]) ).
cnf(refute_0_128,plain,
( ~ is_a_theorem(implies(implies(X_73,X_74),implies(or(not(X),X_73),implies(X,X_74))))
| is_a_theorem(implies(implies(X_73,X_74),implies(implies(X,X_73),implies(X,X_74)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_73,X_74),implies(or(not(X),X_73),implies(X,X_74))),implies(implies(X_73,X_74),implies(implies(X,X_73),implies(X,X_74)))) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
is_a_theorem(implies(implies(X_73,X_74),implies(implies(X,X_73),implies(X,X_74)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_73,X_74),implies(or(not(X),X_73),implies(X,X_74)))) )],[refute_0_117,refute_0_128]) ).
cnf(refute_0_130,plain,
( ~ is_a_theorem(implies(X_73,X_74))
| ~ is_a_theorem(implies(implies(X_73,X_74),implies(implies(X,X_73),implies(X,X_74))))
| is_a_theorem(implies(implies(X,X_73),implies(X,X_74))) ),
inference(subst,[],[refute_0_53:[bind(X,$fot(implies(X_73,X_74))),bind(Y,$fot(implies(implies(X,X_73),implies(X,X_74))))]]) ).
cnf(refute_0_131,plain,
( ~ is_a_theorem(implies(X_73,X_74))
| is_a_theorem(implies(implies(X,X_73),implies(X,X_74))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_73,X_74),implies(implies(X,X_73),implies(X,X_74)))) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
( ~ is_a_theorem(implies(and(X_11,X_6238),X_6238))
| is_a_theorem(implies(implies(X_6236,and(X_11,X_6238)),implies(X_6236,X_6238))) ),
inference(subst,[],[refute_0_131:[bind(X,$fot(X_6236)),bind(X_73,$fot(and(X_11,X_6238))),bind(X_74,$fot(X_6238))]]) ).
cnf(refute_0_133,plain,
is_a_theorem(implies(implies(X_6236,and(X_11,X_6238)),implies(X_6236,X_6238))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_11,X_6238),X_6238)) )],[refute_0_107,refute_0_132]) ).
cnf(refute_0_134,plain,
is_a_theorem(implies(implies(X_6256,and(X_6255,X_6257)),implies(X_6256,X_6257))),
inference(subst,[],[refute_0_133:[bind(X_11,$fot(X_6255)),bind(X_6236,$fot(X_6256)),bind(X_6238,$fot(X_6257))]]) ).
cnf(refute_0_135,plain,
( ~ is_a_theorem(implies(X_6256,and(X_6255,X_6257)))
| is_a_theorem(implies(X_6256,X_6257)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_6256,and(X_6255,X_6257)),implies(X_6256,X_6257))) )],[refute_0_134,refute_0_82]) ).
cnf(refute_0_136,plain,
( ~ is_a_theorem(implies(and(X_25232,X_25230),and(X_25230,X_25232)))
| is_a_theorem(implies(and(X_25232,X_25230),X_25232)) ),
inference(subst,[],[refute_0_135:[bind(X_6255,$fot(X_25230)),bind(X_6256,$fot(and(X_25232,X_25230))),bind(X_6257,$fot(X_25232))]]) ).
cnf(refute_0_137,plain,
is_a_theorem(implies(and(X_25232,X_25230),X_25232)),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_25232,X_25230),and(X_25230,X_25232))) )],[refute_0_81,refute_0_136]) ).
cnf(refute_0_138,plain,
is_a_theorem(implies(and(skolemFOFtoCNF_P_1,skolemFOFtoCNF_Q),skolemFOFtoCNF_P_1)),
inference(subst,[],[refute_0_137:[bind(X_25230,$fot(skolemFOFtoCNF_Q)),bind(X_25232,$fot(skolemFOFtoCNF_P_1))]]) ).
cnf(refute_0_139,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(and(skolemFOFtoCNF_P_1,skolemFOFtoCNF_Q),skolemFOFtoCNF_P_1)) )],[refute_0_138,refute_0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LCL500+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.11/0.33 % Computer : n009.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Mon Jul 4 06:13:22 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 107.65/107.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 107.65/107.81
% 107.65/107.81 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 107.65/107.83
%------------------------------------------------------------------------------