TSTP Solution File: LCL296-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL296-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.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 12:51:25 EDT 2022
% Result : Unsatisfiable 1.92s 2.09s
% Output : CNFRefutation 1.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 26
% Syntax : Number of clauses : 107 ( 59 unt; 0 nHn; 55 RR)
% Number of literals : 173 ( 78 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 : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 201 ( 6 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(implies(p,not(q)),or(not(p),not(q)))) ).
cnf(refute_0_0,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_1,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_2,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_4,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_3]) ).
cnf(refute_0_5,plain,
or(not(p),not(q)) = implies(p,not(q)),
inference(subst,[],[refute_0_4:[bind(X,$fot(p)),bind(Y,$fot(not(q)))]]) ).
cnf(refute_0_6,plain,
equivalent(implies(p,not(q)),or(not(p),not(q))) = equivalent(implies(p,not(q)),or(not(p),not(q))),
introduced(tautology,[refl,[$fot(equivalent(implies(p,not(q)),or(not(p),not(q))))]]) ).
cnf(refute_0_7,plain,
( equivalent(implies(p,not(q)),or(not(p),not(q))) != equivalent(implies(p,not(q)),or(not(p),not(q)))
| or(not(p),not(q)) != implies(p,not(q))
| equivalent(implies(p,not(q)),or(not(p),not(q))) = equivalent(implies(p,not(q)),implies(p,not(q))) ),
introduced(tautology,[equality,[$cnf( $equal(equivalent(implies(p,not(q)),or(not(p),not(q))),equivalent(implies(p,not(q)),or(not(p),not(q)))) ),[1,1],$fot(implies(p,not(q)))]]) ).
cnf(refute_0_8,plain,
( or(not(p),not(q)) != implies(p,not(q))
| equivalent(implies(p,not(q)),or(not(p),not(q))) = equivalent(implies(p,not(q)),implies(p,not(q))) ),
inference(resolve,[$cnf( $equal(equivalent(implies(p,not(q)),or(not(p),not(q))),equivalent(implies(p,not(q)),or(not(p),not(q)))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
equivalent(implies(p,not(q)),or(not(p),not(q))) = equivalent(implies(p,not(q)),implies(p,not(q))),
inference(resolve,[$cnf( $equal(or(not(p),not(q)),implies(p,not(q))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( equivalent(implies(p,not(q)),or(not(p),not(q))) != equivalent(implies(p,not(q)),implies(p,not(q)))
| ~ theorem(equivalent(implies(p,not(q)),implies(p,not(q))))
| theorem(equivalent(implies(p,not(q)),or(not(p),not(q)))) ),
introduced(tautology,[equality,[$cnf( ~ theorem(equivalent(implies(p,not(q)),or(not(p),not(q)))) ),[0],$fot(equivalent(implies(p,not(q)),implies(p,not(q))))]]) ).
cnf(refute_0_11,plain,
( ~ theorem(equivalent(implies(p,not(q)),implies(p,not(q))))
| theorem(equivalent(implies(p,not(q)),or(not(p),not(q)))) ),
inference(resolve,[$cnf( $equal(equivalent(implies(p,not(q)),or(not(p),not(q))),equivalent(implies(p,not(q)),implies(p,not(q)))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
~ theorem(equivalent(implies(p,not(q)),implies(p,not(q)))),
inference(resolve,[$cnf( theorem(equivalent(implies(p,not(q)),or(not(p),not(q)))) )],[refute_0_11,prove_this]) ).
cnf(refute_0_13,plain,
( ~ theorem(X_91)
| ~ theorem(implies(X_91,and(X_91,X_91)))
| theorem(and(X_91,X_91)) ),
inference(subst,[],[rule_2:[bind(X,$fot(and(X_91,X_91))),bind(Y,$fot(X_91))]]) ).
cnf(refute_0_14,plain,
( ~ axiom(implies(or(A,A),A))
| theorem(implies(or(A,A),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_15,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[$cnf( axiom(implies(or(A,A),A)) )],[axiom_1_2,refute_0_14]) ).
cnf(refute_0_16,plain,
theorem(implies(or(not(X_5),not(X_5)),not(X_5))),
inference(subst,[],[refute_0_15:[bind(A,$fot(not(X_5)))]]) ).
cnf(refute_0_17,plain,
implies(X_5,not(X_5)) = or(not(X_5),not(X_5)),
inference(subst,[],[implies_definition:[bind(X,$fot(X_5)),bind(Y,$fot(not(X_5)))]]) ).
cnf(refute_0_18,plain,
( implies(X_5,not(X_5)) != or(not(X_5),not(X_5))
| or(not(X_5),not(X_5)) = implies(X_5,not(X_5)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_5,not(X_5)))),bind(Y0,$fot(or(not(X_5),not(X_5))))]]) ).
cnf(refute_0_19,plain,
or(not(X_5),not(X_5)) = implies(X_5,not(X_5)),
inference(resolve,[$cnf( $equal(implies(X_5,not(X_5)),or(not(X_5),not(X_5))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( or(not(X_5),not(X_5)) != implies(X_5,not(X_5))
| ~ theorem(implies(or(not(X_5),not(X_5)),not(X_5)))
| theorem(implies(implies(X_5,not(X_5)),not(X_5))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X_5),not(X_5)),not(X_5))) ),[0,0],$fot(implies(X_5,not(X_5)))]]) ).
cnf(refute_0_21,plain,
( ~ theorem(implies(or(not(X_5),not(X_5)),not(X_5)))
| theorem(implies(implies(X_5,not(X_5)),not(X_5))) ),
inference(resolve,[$cnf( $equal(or(not(X_5),not(X_5)),implies(X_5,not(X_5))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
theorem(implies(implies(X_5,not(X_5)),not(X_5))),
inference(resolve,[$cnf( theorem(implies(or(not(X_5),not(X_5)),not(X_5))) )],[refute_0_16,refute_0_21]) ).
cnf(refute_0_23,plain,
implies(implies(X_17,not(X_18)),Y) = or(not(implies(X_17,not(X_18))),Y),
inference(subst,[],[implies_definition:[bind(X,$fot(implies(X_17,not(X_18))))]]) ).
cnf(refute_0_24,plain,
or(not(P),not(Q)) = implies(P,not(Q)),
inference(subst,[],[refute_0_4:[bind(X,$fot(P)),bind(Y,$fot(not(Q)))]]) ).
cnf(refute_0_25,plain,
not(or(not(P),not(Q))) = not(or(not(P),not(Q))),
introduced(tautology,[refl,[$fot(not(or(not(P),not(Q))))]]) ).
cnf(refute_0_26,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_27,plain,
( or(not(P),not(Q)) != implies(P,not(Q))
| not(or(not(P),not(Q))) = not(implies(P,not(Q))) ),
inference(resolve,[$cnf( $equal(not(or(not(P),not(Q))),not(or(not(P),not(Q)))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
not(or(not(P),not(Q))) = not(implies(P,not(Q))),
inference(resolve,[$cnf( $equal(or(not(P),not(Q)),implies(P,not(Q))) )],[refute_0_24,refute_0_27]) ).
cnf(refute_0_29,plain,
( and(P,Q) != not(or(not(P),not(Q)))
| not(or(not(P),not(Q))) != not(implies(P,not(Q)))
| and(P,Q) = not(implies(P,not(Q))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(P,Q),not(implies(P,not(Q)))) ),[0],$fot(not(or(not(P),not(Q))))]]) ).
cnf(refute_0_30,plain,
( and(P,Q) != not(or(not(P),not(Q)))
| and(P,Q) = not(implies(P,not(Q))) ),
inference(resolve,[$cnf( $equal(not(or(not(P),not(Q))),not(implies(P,not(Q)))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
and(P,Q) = not(implies(P,not(Q))),
inference(resolve,[$cnf( $equal(and(P,Q),not(or(not(P),not(Q)))) )],[and_defn,refute_0_30]) ).
cnf(refute_0_32,plain,
and(X_17,X_18) = not(implies(X_17,not(X_18))),
inference(subst,[],[refute_0_31:[bind(P,$fot(X_17)),bind(Q,$fot(X_18))]]) ).
cnf(refute_0_33,plain,
( and(X_17,X_18) != not(implies(X_17,not(X_18)))
| not(implies(X_17,not(X_18))) = and(X_17,X_18) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(X_17,X_18))),bind(Y0,$fot(not(implies(X_17,not(X_18)))))]]) ).
cnf(refute_0_34,plain,
not(implies(X_17,not(X_18))) = and(X_17,X_18),
inference(resolve,[$cnf( $equal(and(X_17,X_18),not(implies(X_17,not(X_18)))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( implies(implies(X_17,not(X_18)),Y) != or(not(implies(X_17,not(X_18))),Y)
| not(implies(X_17,not(X_18))) != and(X_17,X_18)
| implies(implies(X_17,not(X_18)),Y) = or(and(X_17,X_18),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_17,not(X_18)),Y),or(not(implies(X_17,not(X_18))),Y)) ),[1,0],$fot(and(X_17,X_18))]]) ).
cnf(refute_0_36,plain,
( implies(implies(X_17,not(X_18)),Y) != or(not(implies(X_17,not(X_18))),Y)
| implies(implies(X_17,not(X_18)),Y) = or(and(X_17,X_18),Y) ),
inference(resolve,[$cnf( $equal(not(implies(X_17,not(X_18))),and(X_17,X_18)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
implies(implies(X_17,not(X_18)),Y) = or(and(X_17,X_18),Y),
inference(resolve,[$cnf( $equal(implies(implies(X_17,not(X_18)),Y),or(not(implies(X_17,not(X_18))),Y)) )],[refute_0_23,refute_0_36]) ).
cnf(refute_0_38,plain,
implies(implies(X_5,not(X_5)),not(X_5)) = or(and(X_5,X_5),not(X_5)),
inference(subst,[],[refute_0_37:[bind(Y,$fot(not(X_5))),bind(X_17,$fot(X_5)),bind(X_18,$fot(X_5))]]) ).
cnf(refute_0_39,plain,
( implies(implies(X_5,not(X_5)),not(X_5)) != or(and(X_5,X_5),not(X_5))
| ~ theorem(implies(implies(X_5,not(X_5)),not(X_5)))
| theorem(or(and(X_5,X_5),not(X_5))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_5,not(X_5)),not(X_5))) ),[0],$fot(or(and(X_5,X_5),not(X_5)))]]) ).
cnf(refute_0_40,plain,
( ~ theorem(implies(implies(X_5,not(X_5)),not(X_5)))
| theorem(or(and(X_5,X_5),not(X_5))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_5,not(X_5)),not(X_5)),or(and(X_5,X_5),not(X_5))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
theorem(or(and(X_5,X_5),not(X_5))),
inference(resolve,[$cnf( theorem(implies(implies(X_5,not(X_5)),not(X_5))) )],[refute_0_22,refute_0_40]) ).
cnf(refute_0_42,plain,
( ~ axiom(implies(or(X_13,X_14),or(X_14,X_13)))
| theorem(implies(or(X_13,X_14),or(X_14,X_13))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_13,X_14),or(X_14,X_13))))]]) ).
cnf(refute_0_43,plain,
axiom(implies(or(X_13,X_14),or(X_14,X_13))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_13)),bind(B,$fot(X_14))]]) ).
cnf(refute_0_44,plain,
theorem(implies(or(X_13,X_14),or(X_14,X_13))),
inference(resolve,[$cnf( axiom(implies(or(X_13,X_14),or(X_14,X_13))) )],[refute_0_43,refute_0_42]) ).
cnf(refute_0_45,plain,
( ~ theorem(implies(or(X_13,X_14),or(X_14,X_13)))
| ~ theorem(or(X_13,X_14))
| theorem(or(X_14,X_13)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_14,X_13))),bind(Y,$fot(or(X_13,X_14)))]]) ).
cnf(refute_0_46,plain,
( ~ theorem(or(X_13,X_14))
| theorem(or(X_14,X_13)) ),
inference(resolve,[$cnf( theorem(implies(or(X_13,X_14),or(X_14,X_13))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ theorem(or(and(X_5,X_5),not(X_5)))
| theorem(or(not(X_5),and(X_5,X_5))) ),
inference(subst,[],[refute_0_46:[bind(X_13,$fot(and(X_5,X_5))),bind(X_14,$fot(not(X_5)))]]) ).
cnf(refute_0_48,plain,
theorem(or(not(X_5),and(X_5,X_5))),
inference(resolve,[$cnf( theorem(or(and(X_5,X_5),not(X_5))) )],[refute_0_41,refute_0_47]) ).
cnf(refute_0_49,plain,
or(not(X_5),and(X_5,X_5)) = implies(X_5,and(X_5,X_5)),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_5)),bind(Y,$fot(and(X_5,X_5)))]]) ).
cnf(refute_0_50,plain,
( or(not(X_5),and(X_5,X_5)) != implies(X_5,and(X_5,X_5))
| ~ theorem(or(not(X_5),and(X_5,X_5)))
| theorem(implies(X_5,and(X_5,X_5))) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(X_5),and(X_5,X_5))) ),[0],$fot(implies(X_5,and(X_5,X_5)))]]) ).
cnf(refute_0_51,plain,
( ~ theorem(or(not(X_5),and(X_5,X_5)))
| theorem(implies(X_5,and(X_5,X_5))) ),
inference(resolve,[$cnf( $equal(or(not(X_5),and(X_5,X_5)),implies(X_5,and(X_5,X_5))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
theorem(implies(X_5,and(X_5,X_5))),
inference(resolve,[$cnf( theorem(or(not(X_5),and(X_5,X_5))) )],[refute_0_48,refute_0_51]) ).
cnf(refute_0_53,plain,
theorem(implies(X_91,and(X_91,X_91))),
inference(subst,[],[refute_0_52:[bind(X_5,$fot(X_91))]]) ).
cnf(refute_0_54,plain,
( ~ theorem(X_91)
| theorem(and(X_91,X_91)) ),
inference(resolve,[$cnf( theorem(implies(X_91,and(X_91,X_91))) )],[refute_0_53,refute_0_13]) ).
cnf(refute_0_55,plain,
( ~ theorem(or(and(X_1635,X_1636),implies(X_1635,not(X_1636))))
| theorem(and(or(and(X_1635,X_1636),implies(X_1635,not(X_1636))),or(and(X_1635,X_1636),implies(X_1635,not(X_1636))))) ),
inference(subst,[],[refute_0_54:[bind(X_91,$fot(or(and(X_1635,X_1636),implies(X_1635,not(X_1636)))))]]) ).
cnf(refute_0_56,plain,
theorem(implies(or(X_85,X_85),X_85)),
inference(subst,[],[refute_0_15:[bind(A,$fot(X_85))]]) ).
cnf(refute_0_57,plain,
( ~ theorem(implies(or(X_85,X_85),X_85))
| ~ theorem(or(X_85,X_85))
| theorem(X_85) ),
inference(subst,[],[rule_2:[bind(X,$fot(X_85)),bind(Y,$fot(or(X_85,X_85)))]]) ).
cnf(refute_0_58,plain,
( ~ theorem(or(X_85,X_85))
| theorem(X_85) ),
inference(resolve,[$cnf( theorem(implies(or(X_85,X_85),X_85)) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
( ~ theorem(or(or(and(X_1633,X_1634),implies(X_1633,not(X_1634))),or(and(X_1633,X_1634),implies(X_1633,not(X_1634)))))
| theorem(or(and(X_1633,X_1634),implies(X_1633,not(X_1634)))) ),
inference(subst,[],[refute_0_58:[bind(X_85,$fot(or(and(X_1633,X_1634),implies(X_1633,not(X_1634)))))]]) ).
cnf(refute_0_60,plain,
( ~ axiom(implies(A,or(B,A)))
| theorem(implies(A,or(B,A))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(A,or(B,A))))]]) ).
cnf(refute_0_61,plain,
theorem(implies(A,or(B,A))),
inference(resolve,[$cnf( axiom(implies(A,or(B,A))) )],[axiom_1_3,refute_0_60]) ).
cnf(refute_0_62,plain,
theorem(implies(implies(X_41,not(X_42)),or(B,implies(X_41,not(X_42))))),
inference(subst,[],[refute_0_61:[bind(A,$fot(implies(X_41,not(X_42))))]]) ).
cnf(refute_0_63,plain,
implies(implies(X_41,not(X_42)),or(B,implies(X_41,not(X_42)))) = or(and(X_41,X_42),or(B,implies(X_41,not(X_42)))),
inference(subst,[],[refute_0_37:[bind(Y,$fot(or(B,implies(X_41,not(X_42))))),bind(X_17,$fot(X_41)),bind(X_18,$fot(X_42))]]) ).
cnf(refute_0_64,plain,
( implies(implies(X_41,not(X_42)),or(B,implies(X_41,not(X_42)))) != or(and(X_41,X_42),or(B,implies(X_41,not(X_42))))
| ~ theorem(implies(implies(X_41,not(X_42)),or(B,implies(X_41,not(X_42)))))
| theorem(or(and(X_41,X_42),or(B,implies(X_41,not(X_42))))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_41,not(X_42)),or(B,implies(X_41,not(X_42))))) ),[0],$fot(or(and(X_41,X_42),or(B,implies(X_41,not(X_42)))))]]) ).
cnf(refute_0_65,plain,
( ~ theorem(implies(implies(X_41,not(X_42)),or(B,implies(X_41,not(X_42)))))
| theorem(or(and(X_41,X_42),or(B,implies(X_41,not(X_42))))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_41,not(X_42)),or(B,implies(X_41,not(X_42)))),or(and(X_41,X_42),or(B,implies(X_41,not(X_42))))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
theorem(or(and(X_41,X_42),or(B,implies(X_41,not(X_42))))),
inference(resolve,[$cnf( theorem(implies(implies(X_41,not(X_42)),or(B,implies(X_41,not(X_42))))) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
theorem(or(and(X_41,X_42),or(X_1530,implies(X_41,not(X_42))))),
inference(subst,[],[refute_0_66:[bind(B,$fot(X_1530))]]) ).
cnf(refute_0_68,plain,
( ~ axiom(implies(or(X_48,or(X_49,X_50)),or(X_49,or(X_48,X_50))))
| theorem(implies(or(X_48,or(X_49,X_50)),or(X_49,or(X_48,X_50)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_48,or(X_49,X_50)),or(X_49,or(X_48,X_50)))))]]) ).
cnf(refute_0_69,plain,
axiom(implies(or(X_48,or(X_49,X_50)),or(X_49,or(X_48,X_50)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_48)),bind(B,$fot(X_49)),bind(C,$fot(X_50))]]) ).
cnf(refute_0_70,plain,
theorem(implies(or(X_48,or(X_49,X_50)),or(X_49,or(X_48,X_50)))),
inference(resolve,[$cnf( axiom(implies(or(X_48,or(X_49,X_50)),or(X_49,or(X_48,X_50)))) )],[refute_0_69,refute_0_68]) ).
cnf(refute_0_71,plain,
( ~ theorem(implies(or(X_48,or(X_49,X_50)),or(X_49,or(X_48,X_50))))
| ~ theorem(or(X_48,or(X_49,X_50)))
| theorem(or(X_49,or(X_48,X_50))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_49,or(X_48,X_50)))),bind(Y,$fot(or(X_48,or(X_49,X_50))))]]) ).
cnf(refute_0_72,plain,
( ~ theorem(or(X_48,or(X_49,X_50)))
| theorem(or(X_49,or(X_48,X_50))) ),
inference(resolve,[$cnf( theorem(implies(or(X_48,or(X_49,X_50)),or(X_49,or(X_48,X_50)))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
( ~ theorem(or(and(X_41,X_42),or(X_1530,implies(X_41,not(X_42)))))
| theorem(or(X_1530,or(and(X_41,X_42),implies(X_41,not(X_42))))) ),
inference(subst,[],[refute_0_72:[bind(X_48,$fot(and(X_41,X_42))),bind(X_49,$fot(X_1530)),bind(X_50,$fot(implies(X_41,not(X_42))))]]) ).
cnf(refute_0_74,plain,
theorem(or(X_1530,or(and(X_41,X_42),implies(X_41,not(X_42))))),
inference(resolve,[$cnf( theorem(or(and(X_41,X_42),or(X_1530,implies(X_41,not(X_42))))) )],[refute_0_67,refute_0_73]) ).
cnf(refute_0_75,plain,
theorem(or(or(and(X_1633,X_1634),implies(X_1633,not(X_1634))),or(and(X_1633,X_1634),implies(X_1633,not(X_1634))))),
inference(subst,[],[refute_0_74:[bind(X_1530,$fot(or(and(X_1633,X_1634),implies(X_1633,not(X_1634))))),bind(X_41,$fot(X_1633)),bind(X_42,$fot(X_1634))]]) ).
cnf(refute_0_76,plain,
theorem(or(and(X_1633,X_1634),implies(X_1633,not(X_1634)))),
inference(resolve,[$cnf( theorem(or(or(and(X_1633,X_1634),implies(X_1633,not(X_1634))),or(and(X_1633,X_1634),implies(X_1633,not(X_1634))))) )],[refute_0_75,refute_0_59]) ).
cnf(refute_0_77,plain,
theorem(or(and(X_1635,X_1636),implies(X_1635,not(X_1636)))),
inference(subst,[],[refute_0_76:[bind(X_1633,$fot(X_1635)),bind(X_1634,$fot(X_1636))]]) ).
cnf(refute_0_78,plain,
theorem(and(or(and(X_1635,X_1636),implies(X_1635,not(X_1636))),or(and(X_1635,X_1636),implies(X_1635,not(X_1636))))),
inference(resolve,[$cnf( theorem(or(and(X_1635,X_1636),implies(X_1635,not(X_1636)))) )],[refute_0_77,refute_0_55]) ).
cnf(refute_0_79,plain,
equivalent(P,implies(X_41,not(X_42))) = and(implies(P,implies(X_41,not(X_42))),implies(implies(X_41,not(X_42)),P)),
inference(subst,[],[equivalent_defn:[bind(Q,$fot(implies(X_41,not(X_42))))]]) ).
cnf(refute_0_80,plain,
implies(implies(X_41,not(X_42)),P) = or(and(X_41,X_42),P),
inference(subst,[],[refute_0_37:[bind(Y,$fot(P)),bind(X_17,$fot(X_41)),bind(X_18,$fot(X_42))]]) ).
cnf(refute_0_81,plain,
( equivalent(P,implies(X_41,not(X_42))) != and(implies(P,implies(X_41,not(X_42))),implies(implies(X_41,not(X_42)),P))
| implies(implies(X_41,not(X_42)),P) != or(and(X_41,X_42),P)
| equivalent(P,implies(X_41,not(X_42))) = and(implies(P,implies(X_41,not(X_42))),or(and(X_41,X_42),P)) ),
introduced(tautology,[equality,[$cnf( $equal(equivalent(P,implies(X_41,not(X_42))),and(implies(P,implies(X_41,not(X_42))),implies(implies(X_41,not(X_42)),P))) ),[1,1],$fot(or(and(X_41,X_42),P))]]) ).
cnf(refute_0_82,plain,
( equivalent(P,implies(X_41,not(X_42))) != and(implies(P,implies(X_41,not(X_42))),implies(implies(X_41,not(X_42)),P))
| equivalent(P,implies(X_41,not(X_42))) = and(implies(P,implies(X_41,not(X_42))),or(and(X_41,X_42),P)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_41,not(X_42)),P),or(and(X_41,X_42),P)) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
equivalent(P,implies(X_41,not(X_42))) = and(implies(P,implies(X_41,not(X_42))),or(and(X_41,X_42),P)),
inference(resolve,[$cnf( $equal(equivalent(P,implies(X_41,not(X_42))),and(implies(P,implies(X_41,not(X_42))),implies(implies(X_41,not(X_42)),P))) )],[refute_0_79,refute_0_82]) ).
cnf(refute_0_84,plain,
equivalent(implies(X_17,not(X_18)),implies(X_228,not(X_229))) = and(implies(implies(X_17,not(X_18)),implies(X_228,not(X_229))),or(and(X_228,X_229),implies(X_17,not(X_18)))),
inference(subst,[],[refute_0_83:[bind(P,$fot(implies(X_17,not(X_18)))),bind(X_41,$fot(X_228)),bind(X_42,$fot(X_229))]]) ).
cnf(refute_0_85,plain,
implies(implies(X_17,not(X_18)),implies(X_228,not(X_229))) = or(and(X_17,X_18),implies(X_228,not(X_229))),
inference(subst,[],[refute_0_37:[bind(Y,$fot(implies(X_228,not(X_229))))]]) ).
cnf(refute_0_86,plain,
( equivalent(implies(X_17,not(X_18)),implies(X_228,not(X_229))) != and(implies(implies(X_17,not(X_18)),implies(X_228,not(X_229))),or(and(X_228,X_229),implies(X_17,not(X_18))))
| implies(implies(X_17,not(X_18)),implies(X_228,not(X_229))) != or(and(X_17,X_18),implies(X_228,not(X_229)))
| equivalent(implies(X_17,not(X_18)),implies(X_228,not(X_229))) = and(or(and(X_17,X_18),implies(X_228,not(X_229))),or(and(X_228,X_229),implies(X_17,not(X_18)))) ),
introduced(tautology,[equality,[$cnf( $equal(equivalent(implies(X_17,not(X_18)),implies(X_228,not(X_229))),and(implies(implies(X_17,not(X_18)),implies(X_228,not(X_229))),or(and(X_228,X_229),implies(X_17,not(X_18))))) ),[1,0],$fot(or(and(X_17,X_18),implies(X_228,not(X_229))))]]) ).
cnf(refute_0_87,plain,
( equivalent(implies(X_17,not(X_18)),implies(X_228,not(X_229))) != and(implies(implies(X_17,not(X_18)),implies(X_228,not(X_229))),or(and(X_228,X_229),implies(X_17,not(X_18))))
| equivalent(implies(X_17,not(X_18)),implies(X_228,not(X_229))) = and(or(and(X_17,X_18),implies(X_228,not(X_229))),or(and(X_228,X_229),implies(X_17,not(X_18)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_17,not(X_18)),implies(X_228,not(X_229))),or(and(X_17,X_18),implies(X_228,not(X_229)))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
equivalent(implies(X_17,not(X_18)),implies(X_228,not(X_229))) = and(or(and(X_17,X_18),implies(X_228,not(X_229))),or(and(X_228,X_229),implies(X_17,not(X_18)))),
inference(resolve,[$cnf( $equal(equivalent(implies(X_17,not(X_18)),implies(X_228,not(X_229))),and(implies(implies(X_17,not(X_18)),implies(X_228,not(X_229))),or(and(X_228,X_229),implies(X_17,not(X_18))))) )],[refute_0_84,refute_0_87]) ).
cnf(refute_0_89,plain,
( equivalent(implies(X_17,not(X_18)),implies(X_228,not(X_229))) != and(or(and(X_17,X_18),implies(X_228,not(X_229))),or(and(X_228,X_229),implies(X_17,not(X_18))))
| and(or(and(X_17,X_18),implies(X_228,not(X_229))),or(and(X_228,X_229),implies(X_17,not(X_18)))) = equivalent(implies(X_17,not(X_18)),implies(X_228,not(X_229))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(equivalent(implies(X_17,not(X_18)),implies(X_228,not(X_229))))),bind(Y0,$fot(and(or(and(X_17,X_18),implies(X_228,not(X_229))),or(and(X_228,X_229),implies(X_17,not(X_18))))))]]) ).
cnf(refute_0_90,plain,
and(or(and(X_17,X_18),implies(X_228,not(X_229))),or(and(X_228,X_229),implies(X_17,not(X_18)))) = equivalent(implies(X_17,not(X_18)),implies(X_228,not(X_229))),
inference(resolve,[$cnf( $equal(equivalent(implies(X_17,not(X_18)),implies(X_228,not(X_229))),and(or(and(X_17,X_18),implies(X_228,not(X_229))),or(and(X_228,X_229),implies(X_17,not(X_18))))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
and(or(and(X_1635,X_1636),implies(X_1635,not(X_1636))),or(and(X_1635,X_1636),implies(X_1635,not(X_1636)))) = equivalent(implies(X_1635,not(X_1636)),implies(X_1635,not(X_1636))),
inference(subst,[],[refute_0_90:[bind(X_17,$fot(X_1635)),bind(X_18,$fot(X_1636)),bind(X_228,$fot(X_1635)),bind(X_229,$fot(X_1636))]]) ).
cnf(refute_0_92,plain,
( and(or(and(X_1635,X_1636),implies(X_1635,not(X_1636))),or(and(X_1635,X_1636),implies(X_1635,not(X_1636)))) != equivalent(implies(X_1635,not(X_1636)),implies(X_1635,not(X_1636)))
| ~ theorem(and(or(and(X_1635,X_1636),implies(X_1635,not(X_1636))),or(and(X_1635,X_1636),implies(X_1635,not(X_1636)))))
| theorem(equivalent(implies(X_1635,not(X_1636)),implies(X_1635,not(X_1636)))) ),
introduced(tautology,[equality,[$cnf( theorem(and(or(and(X_1635,X_1636),implies(X_1635,not(X_1636))),or(and(X_1635,X_1636),implies(X_1635,not(X_1636))))) ),[0],$fot(equivalent(implies(X_1635,not(X_1636)),implies(X_1635,not(X_1636))))]]) ).
cnf(refute_0_93,plain,
( ~ theorem(and(or(and(X_1635,X_1636),implies(X_1635,not(X_1636))),or(and(X_1635,X_1636),implies(X_1635,not(X_1636)))))
| theorem(equivalent(implies(X_1635,not(X_1636)),implies(X_1635,not(X_1636)))) ),
inference(resolve,[$cnf( $equal(and(or(and(X_1635,X_1636),implies(X_1635,not(X_1636))),or(and(X_1635,X_1636),implies(X_1635,not(X_1636)))),equivalent(implies(X_1635,not(X_1636)),implies(X_1635,not(X_1636)))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
theorem(equivalent(implies(X_1635,not(X_1636)),implies(X_1635,not(X_1636)))),
inference(resolve,[$cnf( theorem(and(or(and(X_1635,X_1636),implies(X_1635,not(X_1636))),or(and(X_1635,X_1636),implies(X_1635,not(X_1636))))) )],[refute_0_78,refute_0_93]) ).
cnf(refute_0_95,plain,
theorem(equivalent(implies(p,not(q)),implies(p,not(q)))),
inference(subst,[],[refute_0_94:[bind(X_1635,$fot(p)),bind(X_1636,$fot(q))]]) ).
cnf(refute_0_96,plain,
$false,
inference(resolve,[$cnf( theorem(equivalent(implies(p,not(q)),implies(p,not(q)))) )],[refute_0_95,refute_0_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LCL296-3 : TPTP v8.1.0. Released v2.3.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.15/0.35 % Computer : n011.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Sat Jul 2 12:35:49 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.92/2.09 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.92/2.09
% 1.92/2.09 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.92/2.10
%------------------------------------------------------------------------------