TSTP Solution File: LCL287-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL287-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n014.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 12:51:22 EDT 2022
% Result : Unsatisfiable 1.12s 1.33s
% Output : CNFRefutation 1.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 30
% Syntax : Number of clauses : 119 ( 63 unt; 0 nHn; 67 RR)
% Number of literals : 197 ( 97 equ; 80 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 : 186 ( 4 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(and(p,q),not(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,$fot(not(Q)))]]) ).
cnf(refute_0_6,plain,
not(or(not(P),not(Q))) = not(or(not(P),not(Q))),
introduced(tautology,[refl,[$fot(not(or(not(P),not(Q))))]]) ).
cnf(refute_0_7,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_8,plain,
( or(not(P),not(Q)) != implies(P,not(Q))
| not(or(not(P),not(Q))) = not(implies(P,not(Q))) ),
inference(resolve,[$cnf( $equal(not(or(not(P),not(Q))),not(or(not(P),not(Q)))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
not(or(not(P),not(Q))) = not(implies(P,not(Q))),
inference(resolve,[$cnf( $equal(or(not(P),not(Q)),implies(P,not(Q))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( and(P,Q) != not(or(not(P),not(Q)))
| not(or(not(P),not(Q))) != not(implies(P,not(Q)))
| and(P,Q) = not(implies(P,not(Q))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(P,Q),not(implies(P,not(Q)))) ),[0],$fot(not(or(not(P),not(Q))))]]) ).
cnf(refute_0_11,plain,
( and(P,Q) != not(or(not(P),not(Q)))
| and(P,Q) = not(implies(P,not(Q))) ),
inference(resolve,[$cnf( $equal(not(or(not(P),not(Q))),not(implies(P,not(Q)))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
and(P,Q) = not(implies(P,not(Q))),
inference(resolve,[$cnf( $equal(and(P,Q),not(or(not(P),not(Q)))) )],[and_defn,refute_0_11]) ).
cnf(refute_0_13,plain,
( and(P,Q) != not(implies(P,not(Q)))
| not(implies(P,not(Q))) = and(P,Q) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(P,Q))),bind(Y0,$fot(not(implies(P,not(Q)))))]]) ).
cnf(refute_0_14,plain,
not(implies(P,not(Q))) = and(P,Q),
inference(resolve,[$cnf( $equal(and(P,Q),not(implies(P,not(Q)))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
not(implies(p,not(q))) = and(p,q),
inference(subst,[],[refute_0_14:[bind(P,$fot(p)),bind(Q,$fot(q))]]) ).
cnf(refute_0_16,plain,
or(not(p),not(q)) = implies(p,not(q)),
inference(subst,[],[refute_0_4:[bind(X,$fot(p)),bind(Y,$fot(not(q)))]]) ).
cnf(refute_0_17,plain,
not(or(not(p),not(q))) = not(or(not(p),not(q))),
introduced(tautology,[refl,[$fot(not(or(not(p),not(q))))]]) ).
cnf(refute_0_18,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_19,plain,
( or(not(p),not(q)) != implies(p,not(q))
| not(or(not(p),not(q))) = not(implies(p,not(q))) ),
inference(resolve,[$cnf( $equal(not(or(not(p),not(q))),not(or(not(p),not(q)))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
not(or(not(p),not(q))) = not(implies(p,not(q))),
inference(resolve,[$cnf( $equal(or(not(p),not(q)),implies(p,not(q))) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_22,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_2,refute_0_21]) ).
cnf(refute_0_23,plain,
( not(implies(p,not(q))) != and(p,q)
| not(or(not(p),not(q))) != not(implies(p,not(q)))
| not(or(not(p),not(q))) = and(p,q) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(not(or(not(p),not(q))))),bind(Y0,$fot(not(implies(p,not(q))))),bind(Z,$fot(and(p,q)))]]) ).
cnf(refute_0_24,plain,
( not(implies(p,not(q))) != and(p,q)
| not(or(not(p),not(q))) = and(p,q) ),
inference(resolve,[$cnf( $equal(not(or(not(p),not(q))),not(implies(p,not(q)))) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
not(or(not(p),not(q))) = and(p,q),
inference(resolve,[$cnf( $equal(not(implies(p,not(q))),and(p,q)) )],[refute_0_15,refute_0_24]) ).
cnf(refute_0_26,plain,
equivalent(and(p,q),not(or(not(p),not(q)))) = equivalent(and(p,q),not(or(not(p),not(q)))),
introduced(tautology,[refl,[$fot(equivalent(and(p,q),not(or(not(p),not(q)))))]]) ).
cnf(refute_0_27,plain,
( equivalent(and(p,q),not(or(not(p),not(q)))) != equivalent(and(p,q),not(or(not(p),not(q))))
| not(or(not(p),not(q))) != and(p,q)
| equivalent(and(p,q),not(or(not(p),not(q)))) = equivalent(and(p,q),and(p,q)) ),
introduced(tautology,[equality,[$cnf( $equal(equivalent(and(p,q),not(or(not(p),not(q)))),equivalent(and(p,q),not(or(not(p),not(q))))) ),[1,1],$fot(and(p,q))]]) ).
cnf(refute_0_28,plain,
( not(or(not(p),not(q))) != and(p,q)
| equivalent(and(p,q),not(or(not(p),not(q)))) = equivalent(and(p,q),and(p,q)) ),
inference(resolve,[$cnf( $equal(equivalent(and(p,q),not(or(not(p),not(q)))),equivalent(and(p,q),not(or(not(p),not(q))))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
equivalent(and(p,q),not(or(not(p),not(q)))) = equivalent(and(p,q),and(p,q)),
inference(resolve,[$cnf( $equal(not(or(not(p),not(q))),and(p,q)) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
( equivalent(and(p,q),not(or(not(p),not(q)))) != equivalent(and(p,q),and(p,q))
| ~ theorem(equivalent(and(p,q),and(p,q)))
| theorem(equivalent(and(p,q),not(or(not(p),not(q))))) ),
introduced(tautology,[equality,[$cnf( ~ theorem(equivalent(and(p,q),not(or(not(p),not(q))))) ),[0],$fot(equivalent(and(p,q),and(p,q)))]]) ).
cnf(refute_0_31,plain,
( ~ theorem(equivalent(and(p,q),and(p,q)))
| theorem(equivalent(and(p,q),not(or(not(p),not(q))))) ),
inference(resolve,[$cnf( $equal(equivalent(and(p,q),not(or(not(p),not(q)))),equivalent(and(p,q),and(p,q))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
~ theorem(equivalent(and(p,q),and(p,q))),
inference(resolve,[$cnf( theorem(equivalent(and(p,q),not(or(not(p),not(q))))) )],[refute_0_31,prove_this]) ).
cnf(refute_0_33,plain,
( ~ theorem(X_133)
| ~ theorem(implies(X_133,and(X_133,X_133)))
| theorem(and(X_133,X_133)) ),
inference(subst,[],[rule_2:[bind(X,$fot(and(X_133,X_133))),bind(Y,$fot(X_133))]]) ).
cnf(refute_0_34,plain,
( ~ axiom(implies(or(A,A),A))
| theorem(implies(or(A,A),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_35,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[$cnf( axiom(implies(or(A,A),A)) )],[axiom_1_2,refute_0_34]) ).
cnf(refute_0_36,plain,
theorem(implies(or(not(X_7),not(X_7)),not(X_7))),
inference(subst,[],[refute_0_35:[bind(A,$fot(not(X_7)))]]) ).
cnf(refute_0_37,plain,
implies(X_7,not(X_7)) = or(not(X_7),not(X_7)),
inference(subst,[],[implies_definition:[bind(X,$fot(X_7)),bind(Y,$fot(not(X_7)))]]) ).
cnf(refute_0_38,plain,
( implies(X_7,not(X_7)) != or(not(X_7),not(X_7))
| or(not(X_7),not(X_7)) = implies(X_7,not(X_7)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_7,not(X_7)))),bind(Y0,$fot(or(not(X_7),not(X_7))))]]) ).
cnf(refute_0_39,plain,
or(not(X_7),not(X_7)) = implies(X_7,not(X_7)),
inference(resolve,[$cnf( $equal(implies(X_7,not(X_7)),or(not(X_7),not(X_7))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( or(not(X_7),not(X_7)) != implies(X_7,not(X_7))
| ~ theorem(implies(or(not(X_7),not(X_7)),not(X_7)))
| theorem(implies(implies(X_7,not(X_7)),not(X_7))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X_7),not(X_7)),not(X_7))) ),[0,0],$fot(implies(X_7,not(X_7)))]]) ).
cnf(refute_0_41,plain,
( ~ theorem(implies(or(not(X_7),not(X_7)),not(X_7)))
| theorem(implies(implies(X_7,not(X_7)),not(X_7))) ),
inference(resolve,[$cnf( $equal(or(not(X_7),not(X_7)),implies(X_7,not(X_7))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
theorem(implies(implies(X_7,not(X_7)),not(X_7))),
inference(resolve,[$cnf( theorem(implies(or(not(X_7),not(X_7)),not(X_7))) )],[refute_0_36,refute_0_41]) ).
cnf(refute_0_43,plain,
implies(implies(X_17,not(X_18)),Y) = or(not(implies(X_17,not(X_18))),Y),
inference(subst,[],[implies_definition:[bind(X,$fot(implies(X_17,not(X_18))))]]) ).
cnf(refute_0_44,plain,
and(X_17,X_18) = not(implies(X_17,not(X_18))),
inference(subst,[],[refute_0_12:[bind(P,$fot(X_17)),bind(Q,$fot(X_18))]]) ).
cnf(refute_0_45,plain,
( and(X_17,X_18) != not(implies(X_17,not(X_18)))
| not(implies(X_17,not(X_18))) = and(X_17,X_18) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(X_17,X_18))),bind(Y0,$fot(not(implies(X_17,not(X_18)))))]]) ).
cnf(refute_0_46,plain,
not(implies(X_17,not(X_18))) = and(X_17,X_18),
inference(resolve,[$cnf( $equal(and(X_17,X_18),not(implies(X_17,not(X_18)))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( implies(implies(X_17,not(X_18)),Y) != or(not(implies(X_17,not(X_18))),Y)
| not(implies(X_17,not(X_18))) != and(X_17,X_18)
| implies(implies(X_17,not(X_18)),Y) = or(and(X_17,X_18),Y) ),
introduced(tautology,[equality,[$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_48,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( $equal(not(implies(X_17,not(X_18))),and(X_17,X_18)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
implies(implies(X_17,not(X_18)),Y) = or(and(X_17,X_18),Y),
inference(resolve,[$cnf( $equal(implies(implies(X_17,not(X_18)),Y),or(not(implies(X_17,not(X_18))),Y)) )],[refute_0_43,refute_0_48]) ).
cnf(refute_0_50,plain,
implies(implies(X_7,not(X_7)),not(X_7)) = or(and(X_7,X_7),not(X_7)),
inference(subst,[],[refute_0_49:[bind(Y,$fot(not(X_7))),bind(X_17,$fot(X_7)),bind(X_18,$fot(X_7))]]) ).
cnf(refute_0_51,plain,
( implies(implies(X_7,not(X_7)),not(X_7)) != or(and(X_7,X_7),not(X_7))
| ~ theorem(implies(implies(X_7,not(X_7)),not(X_7)))
| theorem(or(and(X_7,X_7),not(X_7))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_7,not(X_7)),not(X_7))) ),[0],$fot(or(and(X_7,X_7),not(X_7)))]]) ).
cnf(refute_0_52,plain,
( ~ theorem(implies(implies(X_7,not(X_7)),not(X_7)))
| theorem(or(and(X_7,X_7),not(X_7))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_7,not(X_7)),not(X_7)),or(and(X_7,X_7),not(X_7))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
theorem(or(and(X_7,X_7),not(X_7))),
inference(resolve,[$cnf( theorem(implies(implies(X_7,not(X_7)),not(X_7))) )],[refute_0_42,refute_0_52]) ).
cnf(refute_0_54,plain,
( ~ axiom(implies(or(X_15,X_16),or(X_16,X_15)))
| theorem(implies(or(X_15,X_16),or(X_16,X_15))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_15,X_16),or(X_16,X_15))))]]) ).
cnf(refute_0_55,plain,
axiom(implies(or(X_15,X_16),or(X_16,X_15))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_15)),bind(B,$fot(X_16))]]) ).
cnf(refute_0_56,plain,
theorem(implies(or(X_15,X_16),or(X_16,X_15))),
inference(resolve,[$cnf( axiom(implies(or(X_15,X_16),or(X_16,X_15))) )],[refute_0_55,refute_0_54]) ).
cnf(refute_0_57,plain,
( ~ theorem(implies(or(X_15,X_16),or(X_16,X_15)))
| ~ theorem(or(X_15,X_16))
| theorem(or(X_16,X_15)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_16,X_15))),bind(Y,$fot(or(X_15,X_16)))]]) ).
cnf(refute_0_58,plain,
( ~ theorem(or(X_15,X_16))
| theorem(or(X_16,X_15)) ),
inference(resolve,[$cnf( theorem(implies(or(X_15,X_16),or(X_16,X_15))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
( ~ theorem(or(and(X_7,X_7),not(X_7)))
| theorem(or(not(X_7),and(X_7,X_7))) ),
inference(subst,[],[refute_0_58:[bind(X_15,$fot(and(X_7,X_7))),bind(X_16,$fot(not(X_7)))]]) ).
cnf(refute_0_60,plain,
theorem(or(not(X_7),and(X_7,X_7))),
inference(resolve,[$cnf( theorem(or(and(X_7,X_7),not(X_7))) )],[refute_0_53,refute_0_59]) ).
cnf(refute_0_61,plain,
or(not(X_7),and(X_7,X_7)) = implies(X_7,and(X_7,X_7)),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_7)),bind(Y,$fot(and(X_7,X_7)))]]) ).
cnf(refute_0_62,plain,
( or(not(X_7),and(X_7,X_7)) != implies(X_7,and(X_7,X_7))
| ~ theorem(or(not(X_7),and(X_7,X_7)))
| theorem(implies(X_7,and(X_7,X_7))) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(X_7),and(X_7,X_7))) ),[0],$fot(implies(X_7,and(X_7,X_7)))]]) ).
cnf(refute_0_63,plain,
( ~ theorem(or(not(X_7),and(X_7,X_7)))
| theorem(implies(X_7,and(X_7,X_7))) ),
inference(resolve,[$cnf( $equal(or(not(X_7),and(X_7,X_7)),implies(X_7,and(X_7,X_7))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
theorem(implies(X_7,and(X_7,X_7))),
inference(resolve,[$cnf( theorem(or(not(X_7),and(X_7,X_7))) )],[refute_0_60,refute_0_63]) ).
cnf(refute_0_65,plain,
theorem(implies(X_133,and(X_133,X_133))),
inference(subst,[],[refute_0_64:[bind(X_7,$fot(X_133))]]) ).
cnf(refute_0_66,plain,
( ~ theorem(X_133)
| theorem(and(X_133,X_133)) ),
inference(resolve,[$cnf( theorem(implies(X_133,and(X_133,X_133))) )],[refute_0_65,refute_0_33]) ).
cnf(refute_0_67,plain,
( ~ theorem(implies(X_1239,X_1239))
| theorem(and(implies(X_1239,X_1239),implies(X_1239,X_1239))) ),
inference(subst,[],[refute_0_66:[bind(X_133,$fot(implies(X_1239,X_1239)))]]) ).
cnf(refute_0_68,plain,
theorem(implies(or(X_112,X_112),X_112)),
inference(subst,[],[refute_0_35:[bind(A,$fot(X_112))]]) ).
cnf(refute_0_69,plain,
( ~ theorem(implies(or(X_112,X_112),X_112))
| ~ theorem(or(X_112,X_112))
| theorem(X_112) ),
inference(subst,[],[rule_2:[bind(X,$fot(X_112)),bind(Y,$fot(or(X_112,X_112)))]]) ).
cnf(refute_0_70,plain,
( ~ theorem(or(X_112,X_112))
| theorem(X_112) ),
inference(resolve,[$cnf( theorem(implies(or(X_112,X_112),X_112)) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
( ~ theorem(or(implies(X_1238,X_1238),implies(X_1238,X_1238)))
| theorem(implies(X_1238,X_1238)) ),
inference(subst,[],[refute_0_70:[bind(X_112,$fot(implies(X_1238,X_1238)))]]) ).
cnf(refute_0_72,plain,
( ~ axiom(implies(A,or(B,A)))
| theorem(implies(A,or(B,A))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(A,or(B,A))))]]) ).
cnf(refute_0_73,plain,
theorem(implies(A,or(B,A))),
inference(resolve,[$cnf( axiom(implies(A,or(B,A))) )],[axiom_1_3,refute_0_72]) ).
cnf(refute_0_74,plain,
theorem(implies(X_1236,or(X_1235,X_1236))),
inference(subst,[],[refute_0_73:[bind(A,$fot(X_1236)),bind(B,$fot(X_1235))]]) ).
cnf(refute_0_75,plain,
( ~ axiom(implies(or(X_47,or(X_48,X_49)),or(X_48,or(X_47,X_49))))
| theorem(implies(or(X_47,or(X_48,X_49)),or(X_48,or(X_47,X_49)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_47,or(X_48,X_49)),or(X_48,or(X_47,X_49)))))]]) ).
cnf(refute_0_76,plain,
axiom(implies(or(X_47,or(X_48,X_49)),or(X_48,or(X_47,X_49)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_47)),bind(B,$fot(X_48)),bind(C,$fot(X_49))]]) ).
cnf(refute_0_77,plain,
theorem(implies(or(X_47,or(X_48,X_49)),or(X_48,or(X_47,X_49)))),
inference(resolve,[$cnf( axiom(implies(or(X_47,or(X_48,X_49)),or(X_48,or(X_47,X_49)))) )],[refute_0_76,refute_0_75]) ).
cnf(refute_0_78,plain,
theorem(implies(or(not(X),or(X_77,X_78)),or(X_77,or(not(X),X_78)))),
inference(subst,[],[refute_0_77:[bind(X_47,$fot(not(X))),bind(X_48,$fot(X_77)),bind(X_49,$fot(X_78))]]) ).
cnf(refute_0_79,plain,
implies(X,X_78) = or(not(X),X_78),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_78))]]) ).
cnf(refute_0_80,plain,
( implies(X,X_78) != or(not(X),X_78)
| or(not(X),X_78) = implies(X,X_78) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,X_78))),bind(Y0,$fot(or(not(X),X_78)))]]) ).
cnf(refute_0_81,plain,
or(not(X),X_78) = implies(X,X_78),
inference(resolve,[$cnf( $equal(implies(X,X_78),or(not(X),X_78)) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
( or(not(X),X_78) != implies(X,X_78)
| ~ theorem(implies(or(not(X),or(X_77,X_78)),or(X_77,or(not(X),X_78))))
| theorem(implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),or(X_77,X_78)),or(X_77,or(not(X),X_78)))) ),[0,1,1],$fot(implies(X,X_78))]]) ).
cnf(refute_0_83,plain,
( ~ theorem(implies(or(not(X),or(X_77,X_78)),or(X_77,or(not(X),X_78))))
| theorem(implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_78),implies(X,X_78)) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
theorem(implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),or(X_77,X_78)),or(X_77,or(not(X),X_78)))) )],[refute_0_78,refute_0_83]) ).
cnf(refute_0_85,plain,
or(not(X),or(X_77,X_78)) = implies(X,or(X_77,X_78)),
inference(subst,[],[refute_0_4:[bind(Y,$fot(or(X_77,X_78)))]]) ).
cnf(refute_0_86,plain,
implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78))) = implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78))))]]) ).
cnf(refute_0_87,plain,
( implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78))) != implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78)))
| or(not(X),or(X_77,X_78)) != implies(X,or(X_77,X_78))
| implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78))) = implies(implies(X,or(X_77,X_78)),or(X_77,implies(X,X_78))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78))),implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78)))) ),[1,0],$fot(implies(X,or(X_77,X_78)))]]) ).
cnf(refute_0_88,plain,
( or(not(X),or(X_77,X_78)) != implies(X,or(X_77,X_78))
| implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78))) = implies(implies(X,or(X_77,X_78)),or(X_77,implies(X,X_78))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78))),implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78)))) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78))) = implies(implies(X,or(X_77,X_78)),or(X_77,implies(X,X_78))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_77,X_78)),implies(X,or(X_77,X_78))) )],[refute_0_85,refute_0_88]) ).
cnf(refute_0_90,plain,
( implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78))) != implies(implies(X,or(X_77,X_78)),or(X_77,implies(X,X_78)))
| ~ theorem(implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78))))
| theorem(implies(implies(X,or(X_77,X_78)),or(X_77,implies(X,X_78)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78)))) ),[0],$fot(implies(implies(X,or(X_77,X_78)),or(X_77,implies(X,X_78))))]]) ).
cnf(refute_0_91,plain,
( ~ theorem(implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78))))
| theorem(implies(implies(X,or(X_77,X_78)),or(X_77,implies(X,X_78)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78))),implies(implies(X,or(X_77,X_78)),or(X_77,implies(X,X_78)))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
theorem(implies(implies(X,or(X_77,X_78)),or(X_77,implies(X,X_78)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),or(X_77,X_78)),or(X_77,implies(X,X_78)))) )],[refute_0_84,refute_0_91]) ).
cnf(refute_0_93,plain,
( ~ theorem(implies(X,or(X_77,X_78)))
| ~ theorem(implies(implies(X,or(X_77,X_78)),or(X_77,implies(X,X_78))))
| theorem(or(X_77,implies(X,X_78))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_77,implies(X,X_78)))),bind(Y,$fot(implies(X,or(X_77,X_78))))]]) ).
cnf(refute_0_94,plain,
( ~ theorem(implies(X,or(X_77,X_78)))
| theorem(or(X_77,implies(X,X_78))) ),
inference(resolve,[$cnf( theorem(implies(implies(X,or(X_77,X_78)),or(X_77,implies(X,X_78)))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
( ~ theorem(implies(X_1236,or(X_1235,X_1236)))
| theorem(or(X_1235,implies(X_1236,X_1236))) ),
inference(subst,[],[refute_0_94:[bind(X,$fot(X_1236)),bind(X_77,$fot(X_1235)),bind(X_78,$fot(X_1236))]]) ).
cnf(refute_0_96,plain,
theorem(or(X_1235,implies(X_1236,X_1236))),
inference(resolve,[$cnf( theorem(implies(X_1236,or(X_1235,X_1236))) )],[refute_0_74,refute_0_95]) ).
cnf(refute_0_97,plain,
theorem(or(implies(X_1238,X_1238),implies(X_1238,X_1238))),
inference(subst,[],[refute_0_96:[bind(X_1235,$fot(implies(X_1238,X_1238))),bind(X_1236,$fot(X_1238))]]) ).
cnf(refute_0_98,plain,
theorem(implies(X_1238,X_1238)),
inference(resolve,[$cnf( theorem(or(implies(X_1238,X_1238),implies(X_1238,X_1238))) )],[refute_0_97,refute_0_71]) ).
cnf(refute_0_99,plain,
theorem(implies(X_1239,X_1239)),
inference(subst,[],[refute_0_98:[bind(X_1238,$fot(X_1239))]]) ).
cnf(refute_0_100,plain,
theorem(and(implies(X_1239,X_1239),implies(X_1239,X_1239))),
inference(resolve,[$cnf( theorem(implies(X_1239,X_1239)) )],[refute_0_99,refute_0_67]) ).
cnf(refute_0_101,plain,
( equivalent(P,Q) != and(implies(P,Q),implies(Q,P))
| and(implies(P,Q),implies(Q,P)) = equivalent(P,Q) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(equivalent(P,Q))),bind(Y0,$fot(and(implies(P,Q),implies(Q,P))))]]) ).
cnf(refute_0_102,plain,
and(implies(P,Q),implies(Q,P)) = equivalent(P,Q),
inference(resolve,[$cnf( $equal(equivalent(P,Q),and(implies(P,Q),implies(Q,P))) )],[equivalent_defn,refute_0_101]) ).
cnf(refute_0_103,plain,
and(implies(X_1239,X_1239),implies(X_1239,X_1239)) = equivalent(X_1239,X_1239),
inference(subst,[],[refute_0_102:[bind(P,$fot(X_1239)),bind(Q,$fot(X_1239))]]) ).
cnf(refute_0_104,plain,
( and(implies(X_1239,X_1239),implies(X_1239,X_1239)) != equivalent(X_1239,X_1239)
| ~ theorem(and(implies(X_1239,X_1239),implies(X_1239,X_1239)))
| theorem(equivalent(X_1239,X_1239)) ),
introduced(tautology,[equality,[$cnf( theorem(and(implies(X_1239,X_1239),implies(X_1239,X_1239))) ),[0],$fot(equivalent(X_1239,X_1239))]]) ).
cnf(refute_0_105,plain,
( ~ theorem(and(implies(X_1239,X_1239),implies(X_1239,X_1239)))
| theorem(equivalent(X_1239,X_1239)) ),
inference(resolve,[$cnf( $equal(and(implies(X_1239,X_1239),implies(X_1239,X_1239)),equivalent(X_1239,X_1239)) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
theorem(equivalent(X_1239,X_1239)),
inference(resolve,[$cnf( theorem(and(implies(X_1239,X_1239),implies(X_1239,X_1239))) )],[refute_0_100,refute_0_105]) ).
cnf(refute_0_107,plain,
theorem(equivalent(and(p,q),and(p,q))),
inference(subst,[],[refute_0_106:[bind(X_1239,$fot(and(p,q)))]]) ).
cnf(refute_0_108,plain,
$false,
inference(resolve,[$cnf( theorem(equivalent(and(p,q),and(p,q))) )],[refute_0_107,refute_0_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL287-3 : TPTP v8.1.0. Released v2.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n014.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 : Sat Jul 2 15:49:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.12/1.33 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.12/1.33
% 1.12/1.33 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.12/1.34
%------------------------------------------------------------------------------