TSTP Solution File: LCL272-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL272-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 12:51:17 EDT 2022
% Result : Unsatisfiable 11.61s 11.82s
% Output : CNFRefutation 11.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 27
% Syntax : Number of clauses : 110 ( 61 unt; 0 nHn; 49 RR)
% Number of literals : 177 ( 77 equ; 68 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 218 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1_2,axiom,
axiom(implies(or(A,A),A)) ).
cnf(axiom_1_3,axiom,
axiom(implies(A,or(B,A))) ).
cnf(axiom_1_4,axiom,
axiom(implies(or(A,B),or(B,A))) ).
cnf(axiom_1_5,axiom,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) ).
cnf(implies_definition,axiom,
implies(X,Y) = or(not(X),Y) ).
cnf(rule_1,axiom,
( theorem(X)
| ~ axiom(X) ) ).
cnf(rule_2,axiom,
( theorem(X)
| ~ theorem(implies(Y,X))
| ~ theorem(Y) ) ).
cnf(and_defn,axiom,
and(P,Q) = not(or(not(P),not(Q))) ).
cnf(equivalent_defn,axiom,
equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ).
cnf(prove_this,negated_conjecture,
~ theorem(equivalent(p,or(p,p))) ).
cnf(refute_0_0,plain,
( ~ theorem(implies(X_8446,or(X_8446,X_8446)))
| ~ theorem(implies(implies(X_8446,or(X_8446,X_8446)),equivalent(X_8446,or(X_8446,X_8446))))
| theorem(equivalent(X_8446,or(X_8446,X_8446))) ),
inference(subst,[],[rule_2:[bind(X,$fot(equivalent(X_8446,or(X_8446,X_8446)))),bind(Y,$fot(implies(X_8446,or(X_8446,X_8446))))]]) ).
cnf(refute_0_1,plain,
( ~ axiom(implies(or(X_5,X_6),or(X_6,X_5)))
| theorem(implies(or(X_5,X_6),or(X_6,X_5))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_5,X_6),or(X_6,X_5))))]]) ).
cnf(refute_0_2,plain,
axiom(implies(or(X_5,X_6),or(X_6,X_5))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_5)),bind(B,$fot(X_6))]]) ).
cnf(refute_0_3,plain,
theorem(implies(or(X_5,X_6),or(X_6,X_5))),
inference(resolve,[$cnf( axiom(implies(or(X_5,X_6),or(X_6,X_5))) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
( ~ theorem(implies(or(X_5,X_6),or(X_6,X_5)))
| ~ theorem(or(X_5,X_6))
| theorem(or(X_6,X_5)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_6,X_5))),bind(Y,$fot(or(X_5,X_6)))]]) ).
cnf(refute_0_5,plain,
( ~ theorem(or(X_5,X_6))
| theorem(or(X_6,X_5)) ),
inference(resolve,[$cnf( theorem(implies(or(X_5,X_6),or(X_6,X_5))) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ theorem(or(equivalent(X_8445,or(X_8445,X_8445)),not(implies(X_8445,or(X_8445,X_8445)))))
| theorem(or(not(implies(X_8445,or(X_8445,X_8445))),equivalent(X_8445,or(X_8445,X_8445)))) ),
inference(subst,[],[refute_0_5:[bind(X_5,$fot(equivalent(X_8445,or(X_8445,X_8445)))),bind(X_6,$fot(not(implies(X_8445,or(X_8445,X_8445)))))]]) ).
cnf(refute_0_7,plain,
( ~ axiom(implies(or(A,A),A))
| theorem(implies(or(A,A),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_8,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[$cnf( axiom(implies(or(A,A),A)) )],[axiom_1_2,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ theorem(X_623)
| ~ theorem(implies(X_623,or(and(X_622,X_623),not(X_622))))
| theorem(or(and(X_622,X_623),not(X_622))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(and(X_622,X_623),not(X_622)))),bind(Y,$fot(X_623))]]) ).
cnf(refute_0_10,plain,
theorem(implies(or(not(X),X_20),or(X_20,not(X)))),
inference(subst,[],[refute_0_3:[bind(X_5,$fot(not(X))),bind(X_6,$fot(X_20))]]) ).
cnf(refute_0_11,plain,
implies(X,X_20) = or(not(X),X_20),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_20))]]) ).
cnf(refute_0_12,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_13,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_14,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( implies(X,X_20) != or(not(X),X_20)
| or(not(X),X_20) = implies(X,X_20) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(implies(X,X_20))),bind(Y0,$fot(or(not(X),X_20)))]]) ).
cnf(refute_0_16,plain,
or(not(X),X_20) = implies(X,X_20),
inference(resolve,[$cnf( $equal(implies(X,X_20),or(not(X),X_20)) )],[refute_0_11,refute_0_15]) ).
cnf(refute_0_17,plain,
( or(not(X),X_20) != implies(X,X_20)
| ~ theorem(implies(or(not(X),X_20),or(X_20,not(X))))
| theorem(implies(implies(X,X_20),or(X_20,not(X)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),X_20),or(X_20,not(X)))) ),[0,0],$fot(implies(X,X_20))]]) ).
cnf(refute_0_18,plain,
( ~ theorem(implies(or(not(X),X_20),or(X_20,not(X))))
| theorem(implies(implies(X,X_20),or(X_20,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_20),implies(X,X_20)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
theorem(implies(implies(X,X_20),or(X_20,not(X)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),X_20),or(X_20,not(X)))) )],[refute_0_10,refute_0_18]) ).
cnf(refute_0_20,plain,
theorem(implies(implies(X_21,not(X)),or(not(X),not(X_21)))),
inference(subst,[],[refute_0_19:[bind(X,$fot(X_21)),bind(X_20,$fot(not(X)))]]) ).
cnf(refute_0_21,plain,
implies(X,not(X_21)) = or(not(X),not(X_21)),
inference(subst,[],[implies_definition:[bind(Y,$fot(not(X_21)))]]) ).
cnf(refute_0_22,plain,
( implies(X,not(X_21)) != or(not(X),not(X_21))
| or(not(X),not(X_21)) = implies(X,not(X_21)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(implies(X,not(X_21)))),bind(Y0,$fot(or(not(X),not(X_21))))]]) ).
cnf(refute_0_23,plain,
or(not(X),not(X_21)) = implies(X,not(X_21)),
inference(resolve,[$cnf( $equal(implies(X,not(X_21)),or(not(X),not(X_21))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( or(not(X),not(X_21)) != implies(X,not(X_21))
| ~ theorem(implies(implies(X_21,not(X)),or(not(X),not(X_21))))
| theorem(implies(implies(X_21,not(X)),implies(X,not(X_21)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_21,not(X)),or(not(X),not(X_21)))) ),[0,1],$fot(implies(X,not(X_21)))]]) ).
cnf(refute_0_25,plain,
( ~ theorem(implies(implies(X_21,not(X)),or(not(X),not(X_21))))
| theorem(implies(implies(X_21,not(X)),implies(X,not(X_21)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_21)),implies(X,not(X_21))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
theorem(implies(implies(X_21,not(X)),implies(X,not(X_21)))),
inference(resolve,[$cnf( theorem(implies(implies(X_21,not(X)),or(not(X),not(X_21)))) )],[refute_0_20,refute_0_25]) ).
cnf(refute_0_27,plain,
implies(implies(X_23,not(X_24)),Y) = or(not(implies(X_23,not(X_24))),Y),
inference(subst,[],[implies_definition:[bind(X,$fot(implies(X_23,not(X_24))))]]) ).
cnf(refute_0_28,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_29,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_28]) ).
cnf(refute_0_30,plain,
or(not(P),not(Q)) = implies(P,not(Q)),
inference(subst,[],[refute_0_29:[bind(X,$fot(P)),bind(Y,$fot(not(Q)))]]) ).
cnf(refute_0_31,plain,
not(or(not(P),not(Q))) = not(or(not(P),not(Q))),
introduced(tautology,[refl,[$fot(not(or(not(P),not(Q))))]]) ).
cnf(refute_0_32,plain,
( not(or(not(P),not(Q))) != not(or(not(P),not(Q)))
| or(not(P),not(Q)) != implies(P,not(Q))
| not(or(not(P),not(Q))) = not(implies(P,not(Q))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(P),not(Q))),not(or(not(P),not(Q)))) ),[1,0],$fot(implies(P,not(Q)))]]) ).
cnf(refute_0_33,plain,
( or(not(P),not(Q)) != implies(P,not(Q))
| not(or(not(P),not(Q))) = not(implies(P,not(Q))) ),
inference(resolve,[$cnf( $equal(not(or(not(P),not(Q))),not(or(not(P),not(Q)))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
not(or(not(P),not(Q))) = not(implies(P,not(Q))),
inference(resolve,[$cnf( $equal(or(not(P),not(Q)),implies(P,not(Q))) )],[refute_0_30,refute_0_33]) ).
cnf(refute_0_35,plain,
( and(P,Q) != not(or(not(P),not(Q)))
| not(or(not(P),not(Q))) != not(implies(P,not(Q)))
| and(P,Q) = not(implies(P,not(Q))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(P,Q),not(implies(P,not(Q)))) ),[0],$fot(not(or(not(P),not(Q))))]]) ).
cnf(refute_0_36,plain,
( and(P,Q) != not(or(not(P),not(Q)))
| and(P,Q) = not(implies(P,not(Q))) ),
inference(resolve,[$cnf( $equal(not(or(not(P),not(Q))),not(implies(P,not(Q)))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
and(P,Q) = not(implies(P,not(Q))),
inference(resolve,[$cnf( $equal(and(P,Q),not(or(not(P),not(Q)))) )],[and_defn,refute_0_36]) ).
cnf(refute_0_38,plain,
and(X_23,X_24) = not(implies(X_23,not(X_24))),
inference(subst,[],[refute_0_37:[bind(P,$fot(X_23)),bind(Q,$fot(X_24))]]) ).
cnf(refute_0_39,plain,
( and(X_23,X_24) != not(implies(X_23,not(X_24)))
| not(implies(X_23,not(X_24))) = and(X_23,X_24) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(and(X_23,X_24))),bind(Y0,$fot(not(implies(X_23,not(X_24)))))]]) ).
cnf(refute_0_40,plain,
not(implies(X_23,not(X_24))) = and(X_23,X_24),
inference(resolve,[$cnf( $equal(and(X_23,X_24),not(implies(X_23,not(X_24)))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( implies(implies(X_23,not(X_24)),Y) != or(not(implies(X_23,not(X_24))),Y)
| not(implies(X_23,not(X_24))) != and(X_23,X_24)
| implies(implies(X_23,not(X_24)),Y) = or(and(X_23,X_24),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_23,not(X_24)),Y),or(not(implies(X_23,not(X_24))),Y)) ),[1,0],$fot(and(X_23,X_24))]]) ).
cnf(refute_0_42,plain,
( implies(implies(X_23,not(X_24)),Y) != or(not(implies(X_23,not(X_24))),Y)
| implies(implies(X_23,not(X_24)),Y) = or(and(X_23,X_24),Y) ),
inference(resolve,[$cnf( $equal(not(implies(X_23,not(X_24))),and(X_23,X_24)) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
implies(implies(X_23,not(X_24)),Y) = or(and(X_23,X_24),Y),
inference(resolve,[$cnf( $equal(implies(implies(X_23,not(X_24)),Y),or(not(implies(X_23,not(X_24))),Y)) )],[refute_0_27,refute_0_42]) ).
cnf(refute_0_44,plain,
implies(implies(X_21,not(X)),implies(X,not(X_21))) = or(and(X_21,X),implies(X,not(X_21))),
inference(subst,[],[refute_0_43:[bind(Y,$fot(implies(X,not(X_21)))),bind(X_23,$fot(X_21)),bind(X_24,$fot(X))]]) ).
cnf(refute_0_45,plain,
( implies(implies(X_21,not(X)),implies(X,not(X_21))) != or(and(X_21,X),implies(X,not(X_21)))
| ~ theorem(implies(implies(X_21,not(X)),implies(X,not(X_21))))
| theorem(or(and(X_21,X),implies(X,not(X_21)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_21,not(X)),implies(X,not(X_21)))) ),[0],$fot(or(and(X_21,X),implies(X,not(X_21))))]]) ).
cnf(refute_0_46,plain,
( ~ theorem(implies(implies(X_21,not(X)),implies(X,not(X_21))))
| theorem(or(and(X_21,X),implies(X,not(X_21)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_21,not(X)),implies(X,not(X_21))),or(and(X_21,X),implies(X,not(X_21)))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
theorem(or(and(X_21,X),implies(X,not(X_21)))),
inference(resolve,[$cnf( theorem(implies(implies(X_21,not(X)),implies(X,not(X_21)))) )],[refute_0_26,refute_0_46]) ).
cnf(refute_0_48,plain,
theorem(or(and(X_21,X_600),implies(X_600,not(X_21)))),
inference(subst,[],[refute_0_47:[bind(X,$fot(X_600))]]) ).
cnf(refute_0_49,plain,
( ~ axiom(implies(or(X_48,implies(X_47,X_49)),implies(X_47,or(X_48,X_49))))
| theorem(implies(or(X_48,implies(X_47,X_49)),implies(X_47,or(X_48,X_49)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_48,implies(X_47,X_49)),implies(X_47,or(X_48,X_49)))))]]) ).
cnf(refute_0_50,plain,
axiom(implies(or(X_41,or(not(X),X_43)),or(not(X),or(X_41,X_43)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_41)),bind(B,$fot(not(X))),bind(C,$fot(X_43))]]) ).
cnf(refute_0_51,plain,
implies(X,or(X_41,X_43)) = or(not(X),or(X_41,X_43)),
inference(subst,[],[implies_definition:[bind(Y,$fot(or(X_41,X_43)))]]) ).
cnf(refute_0_52,plain,
( implies(X,or(X_41,X_43)) != or(not(X),or(X_41,X_43))
| or(not(X),or(X_41,X_43)) = implies(X,or(X_41,X_43)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(implies(X,or(X_41,X_43)))),bind(Y0,$fot(or(not(X),or(X_41,X_43))))]]) ).
cnf(refute_0_53,plain,
or(not(X),or(X_41,X_43)) = implies(X,or(X_41,X_43)),
inference(resolve,[$cnf( $equal(implies(X,or(X_41,X_43)),or(not(X),or(X_41,X_43))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
( or(not(X),or(X_41,X_43)) != implies(X,or(X_41,X_43))
| ~ axiom(implies(or(X_41,or(not(X),X_43)),or(not(X),or(X_41,X_43))))
| axiom(implies(or(X_41,or(not(X),X_43)),implies(X,or(X_41,X_43)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(X_41,or(not(X),X_43)),or(not(X),or(X_41,X_43)))) ),[0,1],$fot(implies(X,or(X_41,X_43)))]]) ).
cnf(refute_0_55,plain,
( ~ axiom(implies(or(X_41,or(not(X),X_43)),or(not(X),or(X_41,X_43))))
| axiom(implies(or(X_41,or(not(X),X_43)),implies(X,or(X_41,X_43)))) ),
inference(resolve,[$cnf( $equal(or(not(X),or(X_41,X_43)),implies(X,or(X_41,X_43))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
axiom(implies(or(X_41,or(not(X),X_43)),implies(X,or(X_41,X_43)))),
inference(resolve,[$cnf( axiom(implies(or(X_41,or(not(X),X_43)),or(not(X),or(X_41,X_43)))) )],[refute_0_50,refute_0_55]) ).
cnf(refute_0_57,plain,
or(not(X),X_43) = implies(X,X_43),
inference(subst,[],[refute_0_29:[bind(Y,$fot(X_43))]]) ).
cnf(refute_0_58,plain,
or(X_41,or(not(X),X_43)) = or(X_41,or(not(X),X_43)),
introduced(tautology,[refl,[$fot(or(X_41,or(not(X),X_43)))]]) ).
cnf(refute_0_59,plain,
( or(X_41,or(not(X),X_43)) != or(X_41,or(not(X),X_43))
| or(not(X),X_43) != implies(X,X_43)
| or(X_41,or(not(X),X_43)) = or(X_41,implies(X,X_43)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_41,or(not(X),X_43)),or(X_41,or(not(X),X_43))) ),[1,1],$fot(implies(X,X_43))]]) ).
cnf(refute_0_60,plain,
( or(not(X),X_43) != implies(X,X_43)
| or(X_41,or(not(X),X_43)) = or(X_41,implies(X,X_43)) ),
inference(resolve,[$cnf( $equal(or(X_41,or(not(X),X_43)),or(X_41,or(not(X),X_43))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
or(X_41,or(not(X),X_43)) = or(X_41,implies(X,X_43)),
inference(resolve,[$cnf( $equal(or(not(X),X_43),implies(X,X_43)) )],[refute_0_57,refute_0_60]) ).
cnf(refute_0_62,plain,
implies(or(X_41,or(not(X),X_43)),implies(X,or(X_41,X_43))) = implies(or(X_41,or(not(X),X_43)),implies(X,or(X_41,X_43))),
introduced(tautology,[refl,[$fot(implies(or(X_41,or(not(X),X_43)),implies(X,or(X_41,X_43))))]]) ).
cnf(refute_0_63,plain,
( implies(or(X_41,or(not(X),X_43)),implies(X,or(X_41,X_43))) != implies(or(X_41,or(not(X),X_43)),implies(X,or(X_41,X_43)))
| or(X_41,or(not(X),X_43)) != or(X_41,implies(X,X_43))
| implies(or(X_41,or(not(X),X_43)),implies(X,or(X_41,X_43))) = implies(or(X_41,implies(X,X_43)),implies(X,or(X_41,X_43))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_41,or(not(X),X_43)),implies(X,or(X_41,X_43))),implies(or(X_41,or(not(X),X_43)),implies(X,or(X_41,X_43)))) ),[1,0],$fot(or(X_41,implies(X,X_43)))]]) ).
cnf(refute_0_64,plain,
( or(X_41,or(not(X),X_43)) != or(X_41,implies(X,X_43))
| implies(or(X_41,or(not(X),X_43)),implies(X,or(X_41,X_43))) = implies(or(X_41,implies(X,X_43)),implies(X,or(X_41,X_43))) ),
inference(resolve,[$cnf( $equal(implies(or(X_41,or(not(X),X_43)),implies(X,or(X_41,X_43))),implies(or(X_41,or(not(X),X_43)),implies(X,or(X_41,X_43)))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
implies(or(X_41,or(not(X),X_43)),implies(X,or(X_41,X_43))) = implies(or(X_41,implies(X,X_43)),implies(X,or(X_41,X_43))),
inference(resolve,[$cnf( $equal(or(X_41,or(not(X),X_43)),or(X_41,implies(X,X_43))) )],[refute_0_61,refute_0_64]) ).
cnf(refute_0_66,plain,
( implies(or(X_41,or(not(X),X_43)),implies(X,or(X_41,X_43))) != implies(or(X_41,implies(X,X_43)),implies(X,or(X_41,X_43)))
| ~ axiom(implies(or(X_41,or(not(X),X_43)),implies(X,or(X_41,X_43))))
| axiom(implies(or(X_41,implies(X,X_43)),implies(X,or(X_41,X_43)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(X_41,or(not(X),X_43)),implies(X,or(X_41,X_43)))) ),[0],$fot(implies(or(X_41,implies(X,X_43)),implies(X,or(X_41,X_43))))]]) ).
cnf(refute_0_67,plain,
( ~ axiom(implies(or(X_41,or(not(X),X_43)),implies(X,or(X_41,X_43))))
| axiom(implies(or(X_41,implies(X,X_43)),implies(X,or(X_41,X_43)))) ),
inference(resolve,[$cnf( $equal(implies(or(X_41,or(not(X),X_43)),implies(X,or(X_41,X_43))),implies(or(X_41,implies(X,X_43)),implies(X,or(X_41,X_43)))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
axiom(implies(or(X_41,implies(X,X_43)),implies(X,or(X_41,X_43)))),
inference(resolve,[$cnf( axiom(implies(or(X_41,or(not(X),X_43)),implies(X,or(X_41,X_43)))) )],[refute_0_56,refute_0_67]) ).
cnf(refute_0_69,plain,
axiom(implies(or(X_48,implies(X_47,X_49)),implies(X_47,or(X_48,X_49)))),
inference(subst,[],[refute_0_68:[bind(X,$fot(X_47)),bind(X_41,$fot(X_48)),bind(X_43,$fot(X_49))]]) ).
cnf(refute_0_70,plain,
theorem(implies(or(X_48,implies(X_47,X_49)),implies(X_47,or(X_48,X_49)))),
inference(resolve,[$cnf( axiom(implies(or(X_48,implies(X_47,X_49)),implies(X_47,or(X_48,X_49)))) )],[refute_0_69,refute_0_49]) ).
cnf(refute_0_71,plain,
( ~ theorem(implies(or(X_48,implies(X_47,X_49)),implies(X_47,or(X_48,X_49))))
| ~ theorem(or(X_48,implies(X_47,X_49)))
| theorem(implies(X_47,or(X_48,X_49))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_47,or(X_48,X_49)))),bind(Y,$fot(or(X_48,implies(X_47,X_49))))]]) ).
cnf(refute_0_72,plain,
( ~ theorem(or(X_48,implies(X_47,X_49)))
| theorem(implies(X_47,or(X_48,X_49))) ),
inference(resolve,[$cnf( theorem(implies(or(X_48,implies(X_47,X_49)),implies(X_47,or(X_48,X_49)))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
( ~ theorem(or(and(X_21,X_600),implies(X_600,not(X_21))))
| theorem(implies(X_600,or(and(X_21,X_600),not(X_21)))) ),
inference(subst,[],[refute_0_72:[bind(X_47,$fot(X_600)),bind(X_48,$fot(and(X_21,X_600))),bind(X_49,$fot(not(X_21)))]]) ).
cnf(refute_0_74,plain,
theorem(implies(X_600,or(and(X_21,X_600),not(X_21)))),
inference(resolve,[$cnf( theorem(or(and(X_21,X_600),implies(X_600,not(X_21)))) )],[refute_0_48,refute_0_73]) ).
cnf(refute_0_75,plain,
theorem(implies(X_623,or(and(X_622,X_623),not(X_622)))),
inference(subst,[],[refute_0_74:[bind(X_21,$fot(X_622)),bind(X_600,$fot(X_623))]]) ).
cnf(refute_0_76,plain,
( ~ theorem(X_623)
| theorem(or(and(X_622,X_623),not(X_622))) ),
inference(resolve,[$cnf( theorem(implies(X_623,or(and(X_622,X_623),not(X_622)))) )],[refute_0_75,refute_0_9]) ).
cnf(refute_0_77,plain,
( ~ theorem(implies(or(A,A),A))
| theorem(or(and(X_2200,implies(or(A,A),A)),not(X_2200))) ),
inference(subst,[],[refute_0_76:[bind(X_622,$fot(X_2200)),bind(X_623,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_78,plain,
theorem(or(and(X_2200,implies(or(A,A),A)),not(X_2200))),
inference(resolve,[$cnf( theorem(implies(or(A,A),A)) )],[refute_0_8,refute_0_77]) ).
cnf(refute_0_79,plain,
theorem(or(and(implies(X_8443,or(X_8443,X_8443)),implies(or(X_8443,X_8443),X_8443)),not(implies(X_8443,or(X_8443,X_8443))))),
inference(subst,[],[refute_0_78:[bind(A,$fot(X_8443)),bind(X_2200,$fot(implies(X_8443,or(X_8443,X_8443))))]]) ).
cnf(refute_0_80,plain,
equivalent(X_8443,or(X_8443,X_8443)) = and(implies(X_8443,or(X_8443,X_8443)),implies(or(X_8443,X_8443),X_8443)),
inference(subst,[],[equivalent_defn:[bind(P,$fot(X_8443)),bind(Q,$fot(or(X_8443,X_8443)))]]) ).
cnf(refute_0_81,plain,
( equivalent(X_8443,or(X_8443,X_8443)) != and(implies(X_8443,or(X_8443,X_8443)),implies(or(X_8443,X_8443),X_8443))
| and(implies(X_8443,or(X_8443,X_8443)),implies(or(X_8443,X_8443),X_8443)) = equivalent(X_8443,or(X_8443,X_8443)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(equivalent(X_8443,or(X_8443,X_8443)))),bind(Y0,$fot(and(implies(X_8443,or(X_8443,X_8443)),implies(or(X_8443,X_8443),X_8443))))]]) ).
cnf(refute_0_82,plain,
and(implies(X_8443,or(X_8443,X_8443)),implies(or(X_8443,X_8443),X_8443)) = equivalent(X_8443,or(X_8443,X_8443)),
inference(resolve,[$cnf( $equal(equivalent(X_8443,or(X_8443,X_8443)),and(implies(X_8443,or(X_8443,X_8443)),implies(or(X_8443,X_8443),X_8443))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
( and(implies(X_8443,or(X_8443,X_8443)),implies(or(X_8443,X_8443),X_8443)) != equivalent(X_8443,or(X_8443,X_8443))
| ~ theorem(or(and(implies(X_8443,or(X_8443,X_8443)),implies(or(X_8443,X_8443),X_8443)),not(implies(X_8443,or(X_8443,X_8443)))))
| theorem(or(equivalent(X_8443,or(X_8443,X_8443)),not(implies(X_8443,or(X_8443,X_8443))))) ),
introduced(tautology,[equality,[$cnf( theorem(or(and(implies(X_8443,or(X_8443,X_8443)),implies(or(X_8443,X_8443),X_8443)),not(implies(X_8443,or(X_8443,X_8443))))) ),[0,0],$fot(equivalent(X_8443,or(X_8443,X_8443)))]]) ).
cnf(refute_0_84,plain,
( ~ theorem(or(and(implies(X_8443,or(X_8443,X_8443)),implies(or(X_8443,X_8443),X_8443)),not(implies(X_8443,or(X_8443,X_8443)))))
| theorem(or(equivalent(X_8443,or(X_8443,X_8443)),not(implies(X_8443,or(X_8443,X_8443))))) ),
inference(resolve,[$cnf( $equal(and(implies(X_8443,or(X_8443,X_8443)),implies(or(X_8443,X_8443),X_8443)),equivalent(X_8443,or(X_8443,X_8443))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
theorem(or(equivalent(X_8443,or(X_8443,X_8443)),not(implies(X_8443,or(X_8443,X_8443))))),
inference(resolve,[$cnf( theorem(or(and(implies(X_8443,or(X_8443,X_8443)),implies(or(X_8443,X_8443),X_8443)),not(implies(X_8443,or(X_8443,X_8443))))) )],[refute_0_79,refute_0_84]) ).
cnf(refute_0_86,plain,
theorem(or(equivalent(X_8445,or(X_8445,X_8445)),not(implies(X_8445,or(X_8445,X_8445))))),
inference(subst,[],[refute_0_85:[bind(X_8443,$fot(X_8445))]]) ).
cnf(refute_0_87,plain,
theorem(or(not(implies(X_8445,or(X_8445,X_8445))),equivalent(X_8445,or(X_8445,X_8445)))),
inference(resolve,[$cnf( theorem(or(equivalent(X_8445,or(X_8445,X_8445)),not(implies(X_8445,or(X_8445,X_8445))))) )],[refute_0_86,refute_0_6]) ).
cnf(refute_0_88,plain,
or(not(implies(X_8445,or(X_8445,X_8445))),equivalent(X_8445,or(X_8445,X_8445))) = implies(implies(X_8445,or(X_8445,X_8445)),equivalent(X_8445,or(X_8445,X_8445))),
inference(subst,[],[refute_0_29:[bind(X,$fot(implies(X_8445,or(X_8445,X_8445)))),bind(Y,$fot(equivalent(X_8445,or(X_8445,X_8445))))]]) ).
cnf(refute_0_89,plain,
( or(not(implies(X_8445,or(X_8445,X_8445))),equivalent(X_8445,or(X_8445,X_8445))) != implies(implies(X_8445,or(X_8445,X_8445)),equivalent(X_8445,or(X_8445,X_8445)))
| ~ theorem(or(not(implies(X_8445,or(X_8445,X_8445))),equivalent(X_8445,or(X_8445,X_8445))))
| theorem(implies(implies(X_8445,or(X_8445,X_8445)),equivalent(X_8445,or(X_8445,X_8445)))) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(implies(X_8445,or(X_8445,X_8445))),equivalent(X_8445,or(X_8445,X_8445)))) ),[0],$fot(implies(implies(X_8445,or(X_8445,X_8445)),equivalent(X_8445,or(X_8445,X_8445))))]]) ).
cnf(refute_0_90,plain,
( ~ theorem(or(not(implies(X_8445,or(X_8445,X_8445))),equivalent(X_8445,or(X_8445,X_8445))))
| theorem(implies(implies(X_8445,or(X_8445,X_8445)),equivalent(X_8445,or(X_8445,X_8445)))) ),
inference(resolve,[$cnf( $equal(or(not(implies(X_8445,or(X_8445,X_8445))),equivalent(X_8445,or(X_8445,X_8445))),implies(implies(X_8445,or(X_8445,X_8445)),equivalent(X_8445,or(X_8445,X_8445)))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
theorem(implies(implies(X_8445,or(X_8445,X_8445)),equivalent(X_8445,or(X_8445,X_8445)))),
inference(resolve,[$cnf( theorem(or(not(implies(X_8445,or(X_8445,X_8445))),equivalent(X_8445,or(X_8445,X_8445)))) )],[refute_0_87,refute_0_90]) ).
cnf(refute_0_92,plain,
theorem(implies(implies(X_8446,or(X_8446,X_8446)),equivalent(X_8446,or(X_8446,X_8446)))),
inference(subst,[],[refute_0_91:[bind(X_8445,$fot(X_8446))]]) ).
cnf(refute_0_93,plain,
( ~ theorem(implies(X_8446,or(X_8446,X_8446)))
| theorem(equivalent(X_8446,or(X_8446,X_8446))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_8446,or(X_8446,X_8446)),equivalent(X_8446,or(X_8446,X_8446)))) )],[refute_0_92,refute_0_0]) ).
cnf(refute_0_94,plain,
( ~ axiom(implies(A,or(B,A)))
| theorem(implies(A,or(B,A))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(A,or(B,A))))]]) ).
cnf(refute_0_95,plain,
theorem(implies(A,or(B,A))),
inference(resolve,[$cnf( axiom(implies(A,or(B,A))) )],[axiom_1_3,refute_0_94]) ).
cnf(refute_0_96,plain,
theorem(implies(X_8446,or(X_8446,X_8446))),
inference(subst,[],[refute_0_95:[bind(A,$fot(X_8446)),bind(B,$fot(X_8446))]]) ).
cnf(refute_0_97,plain,
theorem(equivalent(X_8446,or(X_8446,X_8446))),
inference(resolve,[$cnf( theorem(implies(X_8446,or(X_8446,X_8446))) )],[refute_0_96,refute_0_93]) ).
cnf(refute_0_98,plain,
theorem(equivalent(p,or(p,p))),
inference(subst,[],[refute_0_97:[bind(X_8446,$fot(p))]]) ).
cnf(refute_0_99,plain,
$false,
inference(resolve,[$cnf( theorem(equivalent(p,or(p,p))) )],[refute_0_98,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL272-3 : TPTP v8.1.0. Released v2.3.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 4 17:20:46 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 11.61/11.82 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.61/11.82
% 11.61/11.82 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.61/11.83
%------------------------------------------------------------------------------