TSTP Solution File: LCL294-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL294-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 12:51:24 EDT 2022
% Result : Unsatisfiable 0.85s 1.05s
% Output : CNFRefutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 27
% Syntax : Number of clauses : 109 ( 60 unt; 0 nHn; 56 RR)
% Number of literals : 176 ( 74 equ; 69 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 : 181 ( 5 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,q),or(not(p),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( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_3]) ).
cnf(refute_0_5,plain,
or(not(p),q) = implies(p,q),
inference(subst,[],[refute_0_4:[bind(X,$fot(p)),bind(Y,$fot(q))]]) ).
cnf(refute_0_6,plain,
equivalent(implies(p,q),or(not(p),q)) = equivalent(implies(p,q),or(not(p),q)),
introduced(tautology,[refl,[$fot(equivalent(implies(p,q),or(not(p),q)))]]) ).
cnf(refute_0_7,plain,
( equivalent(implies(p,q),or(not(p),q)) != equivalent(implies(p,q),or(not(p),q))
| or(not(p),q) != implies(p,q)
| equivalent(implies(p,q),or(not(p),q)) = equivalent(implies(p,q),implies(p,q)) ),
introduced(tautology,[equality,[$cnf( $equal(equivalent(implies(p,q),or(not(p),q)),equivalent(implies(p,q),or(not(p),q))) ),[1,1],$fot(implies(p,q))]]) ).
cnf(refute_0_8,plain,
( or(not(p),q) != implies(p,q)
| equivalent(implies(p,q),or(not(p),q)) = equivalent(implies(p,q),implies(p,q)) ),
inference(resolve,[$cnf( $equal(equivalent(implies(p,q),or(not(p),q)),equivalent(implies(p,q),or(not(p),q))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
equivalent(implies(p,q),or(not(p),q)) = equivalent(implies(p,q),implies(p,q)),
inference(resolve,[$cnf( $equal(or(not(p),q),implies(p,q)) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( equivalent(implies(p,q),or(not(p),q)) != equivalent(implies(p,q),implies(p,q))
| ~ theorem(equivalent(implies(p,q),implies(p,q)))
| theorem(equivalent(implies(p,q),or(not(p),q))) ),
introduced(tautology,[equality,[$cnf( ~ theorem(equivalent(implies(p,q),or(not(p),q))) ),[0],$fot(equivalent(implies(p,q),implies(p,q)))]]) ).
cnf(refute_0_11,plain,
( ~ theorem(equivalent(implies(p,q),implies(p,q)))
| theorem(equivalent(implies(p,q),or(not(p),q))) ),
inference(resolve,[$cnf( $equal(equivalent(implies(p,q),or(not(p),q)),equivalent(implies(p,q),implies(p,q))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
~ theorem(equivalent(implies(p,q),implies(p,q))),
inference(resolve,[$cnf( theorem(equivalent(implies(p,q),or(not(p),q))) )],[refute_0_11,prove_this]) ).
cnf(refute_0_13,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_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_9),not(X_9)),not(X_9))),
inference(subst,[],[refute_0_15:[bind(A,$fot(not(X_9)))]]) ).
cnf(refute_0_17,plain,
implies(X_9,not(X_9)) = or(not(X_9),not(X_9)),
inference(subst,[],[implies_definition:[bind(X,$fot(X_9)),bind(Y,$fot(not(X_9)))]]) ).
cnf(refute_0_18,plain,
( implies(X_9,not(X_9)) != or(not(X_9),not(X_9))
| or(not(X_9),not(X_9)) = implies(X_9,not(X_9)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_9,not(X_9)))),bind(Y0,$fot(or(not(X_9),not(X_9))))]]) ).
cnf(refute_0_19,plain,
or(not(X_9),not(X_9)) = implies(X_9,not(X_9)),
inference(resolve,[$cnf( $equal(implies(X_9,not(X_9)),or(not(X_9),not(X_9))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( or(not(X_9),not(X_9)) != implies(X_9,not(X_9))
| ~ theorem(implies(or(not(X_9),not(X_9)),not(X_9)))
| theorem(implies(implies(X_9,not(X_9)),not(X_9))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X_9),not(X_9)),not(X_9))) ),[0,0],$fot(implies(X_9,not(X_9)))]]) ).
cnf(refute_0_21,plain,
( ~ theorem(implies(or(not(X_9),not(X_9)),not(X_9)))
| theorem(implies(implies(X_9,not(X_9)),not(X_9))) ),
inference(resolve,[$cnf( $equal(or(not(X_9),not(X_9)),implies(X_9,not(X_9))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
theorem(implies(implies(X_9,not(X_9)),not(X_9))),
inference(resolve,[$cnf( theorem(implies(or(not(X_9),not(X_9)),not(X_9))) )],[refute_0_16,refute_0_21]) ).
cnf(refute_0_23,plain,
implies(implies(X_25,not(X_26)),Y) = or(not(implies(X_25,not(X_26))),Y),
inference(subst,[],[implies_definition:[bind(X,$fot(implies(X_25,not(X_26))))]]) ).
cnf(refute_0_24,plain,
or(not(P),not(Q)) = implies(P,not(Q)),
inference(subst,[],[refute_0_4:[bind(X,$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( $equal(and(P,Q),not(or(not(P),not(Q)))) )],[and_defn,refute_0_30]) ).
cnf(refute_0_32,plain,
and(X_25,X_26) = not(implies(X_25,not(X_26))),
inference(subst,[],[refute_0_31:[bind(P,$fot(X_25)),bind(Q,$fot(X_26))]]) ).
cnf(refute_0_33,plain,
( and(X_25,X_26) != not(implies(X_25,not(X_26)))
| not(implies(X_25,not(X_26))) = and(X_25,X_26) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(X_25,X_26))),bind(Y0,$fot(not(implies(X_25,not(X_26)))))]]) ).
cnf(refute_0_34,plain,
not(implies(X_25,not(X_26))) = and(X_25,X_26),
inference(resolve,[$cnf( $equal(and(X_25,X_26),not(implies(X_25,not(X_26)))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( implies(implies(X_25,not(X_26)),Y) != or(not(implies(X_25,not(X_26))),Y)
| not(implies(X_25,not(X_26))) != and(X_25,X_26)
| implies(implies(X_25,not(X_26)),Y) = or(and(X_25,X_26),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_25,not(X_26)),Y),or(not(implies(X_25,not(X_26))),Y)) ),[1,0],$fot(and(X_25,X_26))]]) ).
cnf(refute_0_36,plain,
( implies(implies(X_25,not(X_26)),Y) != or(not(implies(X_25,not(X_26))),Y)
| implies(implies(X_25,not(X_26)),Y) = or(and(X_25,X_26),Y) ),
inference(resolve,[$cnf( $equal(not(implies(X_25,not(X_26))),and(X_25,X_26)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
implies(implies(X_25,not(X_26)),Y) = or(and(X_25,X_26),Y),
inference(resolve,[$cnf( $equal(implies(implies(X_25,not(X_26)),Y),or(not(implies(X_25,not(X_26))),Y)) )],[refute_0_23,refute_0_36]) ).
cnf(refute_0_38,plain,
implies(implies(X_9,not(X_9)),not(X_9)) = or(and(X_9,X_9),not(X_9)),
inference(subst,[],[refute_0_37:[bind(Y,$fot(not(X_9))),bind(X_25,$fot(X_9)),bind(X_26,$fot(X_9))]]) ).
cnf(refute_0_39,plain,
( implies(implies(X_9,not(X_9)),not(X_9)) != or(and(X_9,X_9),not(X_9))
| ~ theorem(implies(implies(X_9,not(X_9)),not(X_9)))
| theorem(or(and(X_9,X_9),not(X_9))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_9,not(X_9)),not(X_9))) ),[0],$fot(or(and(X_9,X_9),not(X_9)))]]) ).
cnf(refute_0_40,plain,
( ~ theorem(implies(implies(X_9,not(X_9)),not(X_9)))
| theorem(or(and(X_9,X_9),not(X_9))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_9,not(X_9)),not(X_9)),or(and(X_9,X_9),not(X_9))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
theorem(or(and(X_9,X_9),not(X_9))),
inference(resolve,[$cnf( theorem(implies(implies(X_9,not(X_9)),not(X_9))) )],[refute_0_22,refute_0_40]) ).
cnf(refute_0_42,plain,
( ~ axiom(implies(or(X_7,X_8),or(X_8,X_7)))
| theorem(implies(or(X_7,X_8),or(X_8,X_7))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_7,X_8),or(X_8,X_7))))]]) ).
cnf(refute_0_43,plain,
axiom(implies(or(X_7,X_8),or(X_8,X_7))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_7)),bind(B,$fot(X_8))]]) ).
cnf(refute_0_44,plain,
theorem(implies(or(X_7,X_8),or(X_8,X_7))),
inference(resolve,[$cnf( axiom(implies(or(X_7,X_8),or(X_8,X_7))) )],[refute_0_43,refute_0_42]) ).
cnf(refute_0_45,plain,
( ~ theorem(implies(or(X_7,X_8),or(X_8,X_7)))
| ~ theorem(or(X_7,X_8))
| theorem(or(X_8,X_7)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_8,X_7))),bind(Y,$fot(or(X_7,X_8)))]]) ).
cnf(refute_0_46,plain,
( ~ theorem(or(X_7,X_8))
| theorem(or(X_8,X_7)) ),
inference(resolve,[$cnf( theorem(implies(or(X_7,X_8),or(X_8,X_7))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ theorem(or(and(X_9,X_9),not(X_9)))
| theorem(or(not(X_9),and(X_9,X_9))) ),
inference(subst,[],[refute_0_46:[bind(X_7,$fot(and(X_9,X_9))),bind(X_8,$fot(not(X_9)))]]) ).
cnf(refute_0_48,plain,
theorem(or(not(X_9),and(X_9,X_9))),
inference(resolve,[$cnf( theorem(or(and(X_9,X_9),not(X_9))) )],[refute_0_41,refute_0_47]) ).
cnf(refute_0_49,plain,
or(not(X_9),and(X_9,X_9)) = implies(X_9,and(X_9,X_9)),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_9)),bind(Y,$fot(and(X_9,X_9)))]]) ).
cnf(refute_0_50,plain,
( or(not(X_9),and(X_9,X_9)) != implies(X_9,and(X_9,X_9))
| ~ theorem(or(not(X_9),and(X_9,X_9)))
| theorem(implies(X_9,and(X_9,X_9))) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(X_9),and(X_9,X_9))) ),[0],$fot(implies(X_9,and(X_9,X_9)))]]) ).
cnf(refute_0_51,plain,
( ~ theorem(or(not(X_9),and(X_9,X_9)))
| theorem(implies(X_9,and(X_9,X_9))) ),
inference(resolve,[$cnf( $equal(or(not(X_9),and(X_9,X_9)),implies(X_9,and(X_9,X_9))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
theorem(implies(X_9,and(X_9,X_9))),
inference(resolve,[$cnf( theorem(or(not(X_9),and(X_9,X_9))) )],[refute_0_48,refute_0_51]) ).
cnf(refute_0_53,plain,
theorem(implies(X_133,and(X_133,X_133))),
inference(subst,[],[refute_0_52:[bind(X_9,$fot(X_133))]]) ).
cnf(refute_0_54,plain,
( ~ theorem(X_133)
| theorem(and(X_133,X_133)) ),
inference(resolve,[$cnf( theorem(implies(X_133,and(X_133,X_133))) )],[refute_0_53,refute_0_13]) ).
cnf(refute_0_55,plain,
( ~ theorem(implies(X_856,X_856))
| theorem(and(implies(X_856,X_856),implies(X_856,X_856))) ),
inference(subst,[],[refute_0_54:[bind(X_133,$fot(implies(X_856,X_856)))]]) ).
cnf(refute_0_56,plain,
theorem(implies(or(X_111,X_111),X_111)),
inference(subst,[],[refute_0_15:[bind(A,$fot(X_111))]]) ).
cnf(refute_0_57,plain,
( ~ theorem(implies(or(X_111,X_111),X_111))
| ~ theorem(or(X_111,X_111))
| theorem(X_111) ),
inference(subst,[],[rule_2:[bind(X,$fot(X_111)),bind(Y,$fot(or(X_111,X_111)))]]) ).
cnf(refute_0_58,plain,
( ~ theorem(or(X_111,X_111))
| theorem(X_111) ),
inference(resolve,[$cnf( theorem(implies(or(X_111,X_111),X_111)) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
( ~ theorem(or(implies(X_855,X_855),implies(X_855,X_855)))
| theorem(implies(X_855,X_855)) ),
inference(subst,[],[refute_0_58:[bind(X_111,$fot(implies(X_855,X_855)))]]) ).
cnf(refute_0_60,plain,
( ~ axiom(implies(X_3,or(X_4,X_3)))
| theorem(implies(X_3,or(X_4,X_3))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(X_3,or(X_4,X_3))))]]) ).
cnf(refute_0_61,plain,
axiom(implies(X_3,or(X_4,X_3))),
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_3)),bind(B,$fot(X_4))]]) ).
cnf(refute_0_62,plain,
theorem(implies(X_3,or(X_4,X_3))),
inference(resolve,[$cnf( axiom(implies(X_3,or(X_4,X_3))) )],[refute_0_61,refute_0_60]) ).
cnf(refute_0_63,plain,
theorem(implies(X_847,or(X_846,X_847))),
inference(subst,[],[refute_0_62:[bind(X_3,$fot(X_847)),bind(X_4,$fot(X_846))]]) ).
cnf(refute_0_64,plain,
( ~ theorem(implies(X_117,or(X_118,X_119)))
| ~ theorem(implies(implies(X_117,or(X_118,X_119)),or(X_118,implies(X_117,X_119))))
| theorem(or(X_118,implies(X_117,X_119))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_118,implies(X_117,X_119)))),bind(Y,$fot(implies(X_117,or(X_118,X_119))))]]) ).
cnf(refute_0_65,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,$fot(implies(or(X_47,or(X_48,X_49)),or(X_48,or(X_47,X_49)))))]]) ).
cnf(refute_0_66,plain,
axiom(implies(or(X_47,or(X_48,X_49)),or(X_48,or(X_47,X_49)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_47)),bind(B,$fot(X_48)),bind(C,$fot(X_49))]]) ).
cnf(refute_0_67,plain,
theorem(implies(or(X_47,or(X_48,X_49)),or(X_48,or(X_47,X_49)))),
inference(resolve,[$cnf( axiom(implies(or(X_47,or(X_48,X_49)),or(X_48,or(X_47,X_49)))) )],[refute_0_66,refute_0_65]) ).
cnf(refute_0_68,plain,
theorem(implies(or(not(X),or(X_51,X_52)),or(X_51,or(not(X),X_52)))),
inference(subst,[],[refute_0_67:[bind(X_47,$fot(not(X))),bind(X_48,$fot(X_51)),bind(X_49,$fot(X_52))]]) ).
cnf(refute_0_69,plain,
implies(X,X_52) = or(not(X),X_52),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_52))]]) ).
cnf(refute_0_70,plain,
( implies(X,X_52) != or(not(X),X_52)
| or(not(X),X_52) = implies(X,X_52) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,X_52))),bind(Y0,$fot(or(not(X),X_52)))]]) ).
cnf(refute_0_71,plain,
or(not(X),X_52) = implies(X,X_52),
inference(resolve,[$cnf( $equal(implies(X,X_52),or(not(X),X_52)) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( or(not(X),X_52) != implies(X,X_52)
| ~ theorem(implies(or(not(X),or(X_51,X_52)),or(X_51,or(not(X),X_52))))
| theorem(implies(or(not(X),or(X_51,X_52)),or(X_51,implies(X,X_52)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),or(X_51,X_52)),or(X_51,or(not(X),X_52)))) ),[0,1,1],$fot(implies(X,X_52))]]) ).
cnf(refute_0_73,plain,
( ~ theorem(implies(or(not(X),or(X_51,X_52)),or(X_51,or(not(X),X_52))))
| theorem(implies(or(not(X),or(X_51,X_52)),or(X_51,implies(X,X_52)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_52),implies(X,X_52)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
theorem(implies(or(not(X),or(X_51,X_52)),or(X_51,implies(X,X_52)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),or(X_51,X_52)),or(X_51,or(not(X),X_52)))) )],[refute_0_68,refute_0_73]) ).
cnf(refute_0_75,plain,
or(not(X),or(X_51,X_52)) = implies(X,or(X_51,X_52)),
inference(subst,[],[refute_0_4:[bind(Y,$fot(or(X_51,X_52)))]]) ).
cnf(refute_0_76,plain,
implies(or(not(X),or(X_51,X_52)),or(X_51,implies(X,X_52))) = implies(or(not(X),or(X_51,X_52)),or(X_51,implies(X,X_52))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_51,X_52)),or(X_51,implies(X,X_52))))]]) ).
cnf(refute_0_77,plain,
( implies(or(not(X),or(X_51,X_52)),or(X_51,implies(X,X_52))) != implies(or(not(X),or(X_51,X_52)),or(X_51,implies(X,X_52)))
| or(not(X),or(X_51,X_52)) != implies(X,or(X_51,X_52))
| implies(or(not(X),or(X_51,X_52)),or(X_51,implies(X,X_52))) = implies(implies(X,or(X_51,X_52)),or(X_51,implies(X,X_52))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_51,X_52)),or(X_51,implies(X,X_52))),implies(or(not(X),or(X_51,X_52)),or(X_51,implies(X,X_52)))) ),[1,0],$fot(implies(X,or(X_51,X_52)))]]) ).
cnf(refute_0_78,plain,
( or(not(X),or(X_51,X_52)) != implies(X,or(X_51,X_52))
| implies(or(not(X),or(X_51,X_52)),or(X_51,implies(X,X_52))) = implies(implies(X,or(X_51,X_52)),or(X_51,implies(X,X_52))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_51,X_52)),or(X_51,implies(X,X_52))),implies(or(not(X),or(X_51,X_52)),or(X_51,implies(X,X_52)))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
implies(or(not(X),or(X_51,X_52)),or(X_51,implies(X,X_52))) = implies(implies(X,or(X_51,X_52)),or(X_51,implies(X,X_52))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_51,X_52)),implies(X,or(X_51,X_52))) )],[refute_0_75,refute_0_78]) ).
cnf(refute_0_80,plain,
( implies(or(not(X),or(X_51,X_52)),or(X_51,implies(X,X_52))) != implies(implies(X,or(X_51,X_52)),or(X_51,implies(X,X_52)))
| ~ theorem(implies(or(not(X),or(X_51,X_52)),or(X_51,implies(X,X_52))))
| theorem(implies(implies(X,or(X_51,X_52)),or(X_51,implies(X,X_52)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),or(X_51,X_52)),or(X_51,implies(X,X_52)))) ),[0],$fot(implies(implies(X,or(X_51,X_52)),or(X_51,implies(X,X_52))))]]) ).
cnf(refute_0_81,plain,
( ~ theorem(implies(or(not(X),or(X_51,X_52)),or(X_51,implies(X,X_52))))
| theorem(implies(implies(X,or(X_51,X_52)),or(X_51,implies(X,X_52)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_51,X_52)),or(X_51,implies(X,X_52))),implies(implies(X,or(X_51,X_52)),or(X_51,implies(X,X_52)))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
theorem(implies(implies(X,or(X_51,X_52)),or(X_51,implies(X,X_52)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),or(X_51,X_52)),or(X_51,implies(X,X_52)))) )],[refute_0_74,refute_0_81]) ).
cnf(refute_0_83,plain,
theorem(implies(implies(X_117,or(X_118,X_119)),or(X_118,implies(X_117,X_119)))),
inference(subst,[],[refute_0_82:[bind(X,$fot(X_117)),bind(X_51,$fot(X_118)),bind(X_52,$fot(X_119))]]) ).
cnf(refute_0_84,plain,
( ~ theorem(implies(X_117,or(X_118,X_119)))
| theorem(or(X_118,implies(X_117,X_119))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_117,or(X_118,X_119)),or(X_118,implies(X_117,X_119)))) )],[refute_0_83,refute_0_64]) ).
cnf(refute_0_85,plain,
( ~ theorem(implies(X_847,or(X_846,X_847)))
| theorem(or(X_846,implies(X_847,X_847))) ),
inference(subst,[],[refute_0_84:[bind(X_117,$fot(X_847)),bind(X_118,$fot(X_846)),bind(X_119,$fot(X_847))]]) ).
cnf(refute_0_86,plain,
theorem(or(X_846,implies(X_847,X_847))),
inference(resolve,[$cnf( theorem(implies(X_847,or(X_846,X_847))) )],[refute_0_63,refute_0_85]) ).
cnf(refute_0_87,plain,
theorem(or(implies(X_855,X_855),implies(X_855,X_855))),
inference(subst,[],[refute_0_86:[bind(X_846,$fot(implies(X_855,X_855))),bind(X_847,$fot(X_855))]]) ).
cnf(refute_0_88,plain,
theorem(implies(X_855,X_855)),
inference(resolve,[$cnf( theorem(or(implies(X_855,X_855),implies(X_855,X_855))) )],[refute_0_87,refute_0_59]) ).
cnf(refute_0_89,plain,
theorem(implies(X_856,X_856)),
inference(subst,[],[refute_0_88:[bind(X_855,$fot(X_856))]]) ).
cnf(refute_0_90,plain,
theorem(and(implies(X_856,X_856),implies(X_856,X_856))),
inference(resolve,[$cnf( theorem(implies(X_856,X_856)) )],[refute_0_89,refute_0_55]) ).
cnf(refute_0_91,plain,
( equivalent(P,Q) != and(implies(P,Q),implies(Q,P))
| and(implies(P,Q),implies(Q,P)) = equivalent(P,Q) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(equivalent(P,Q))),bind(Y0,$fot(and(implies(P,Q),implies(Q,P))))]]) ).
cnf(refute_0_92,plain,
and(implies(P,Q),implies(Q,P)) = equivalent(P,Q),
inference(resolve,[$cnf( $equal(equivalent(P,Q),and(implies(P,Q),implies(Q,P))) )],[equivalent_defn,refute_0_91]) ).
cnf(refute_0_93,plain,
and(implies(X_856,X_856),implies(X_856,X_856)) = equivalent(X_856,X_856),
inference(subst,[],[refute_0_92:[bind(P,$fot(X_856)),bind(Q,$fot(X_856))]]) ).
cnf(refute_0_94,plain,
( and(implies(X_856,X_856),implies(X_856,X_856)) != equivalent(X_856,X_856)
| ~ theorem(and(implies(X_856,X_856),implies(X_856,X_856)))
| theorem(equivalent(X_856,X_856)) ),
introduced(tautology,[equality,[$cnf( theorem(and(implies(X_856,X_856),implies(X_856,X_856))) ),[0],$fot(equivalent(X_856,X_856))]]) ).
cnf(refute_0_95,plain,
( ~ theorem(and(implies(X_856,X_856),implies(X_856,X_856)))
| theorem(equivalent(X_856,X_856)) ),
inference(resolve,[$cnf( $equal(and(implies(X_856,X_856),implies(X_856,X_856)),equivalent(X_856,X_856)) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
theorem(equivalent(X_856,X_856)),
inference(resolve,[$cnf( theorem(and(implies(X_856,X_856),implies(X_856,X_856))) )],[refute_0_90,refute_0_95]) ).
cnf(refute_0_97,plain,
theorem(equivalent(implies(p,q),implies(p,q))),
inference(subst,[],[refute_0_96:[bind(X_856,$fot(implies(p,q)))]]) ).
cnf(refute_0_98,plain,
$false,
inference(resolve,[$cnf( theorem(equivalent(implies(p,q),implies(p,q))) )],[refute_0_97,refute_0_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL294-3 : TPTP v8.1.0. Released v2.3.0.
% 0.13/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 3 00:51:00 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.85/1.05 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.85/1.05
% 0.85/1.05 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.85/1.06
%------------------------------------------------------------------------------