TSTP Solution File: LCL205-3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL205-3 : 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 12:50:35 EDT 2022
% Result : Unsatisfiable 39.50s 39.74s
% Output : CNFRefutation 39.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 33
% Syntax : Number of clauses : 198 ( 105 unt; 0 nHn; 82 RR)
% Number of literals : 322 ( 93 equ; 125 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 478 ( 46 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(axiom_1_6,axiom,
axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) ).
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(prove_this,negated_conjecture,
~ theorem(implies(not(implies(p,q)),implies(p,not(q)))) ).
cnf(refute_0_0,plain,
( ~ theorem(implies(X_840,X_841))
| ~ theorem(implies(implies(X_840,X_841),implies(X_840,implies(X_839,X_841))))
| theorem(implies(X_840,implies(X_839,X_841))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_840,implies(X_839,X_841)))),bind(Y,$fot(implies(X_840,X_841)))]]) ).
cnf(refute_0_1,plain,
( ~ axiom(implies(A,or(B,A)))
| theorem(implies(A,or(B,A))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(A,or(B,A))))]]) ).
cnf(refute_0_2,plain,
theorem(implies(A,or(B,A))),
inference(resolve,[$cnf( axiom(implies(A,or(B,A))) )],[axiom_1_3,refute_0_1]) ).
cnf(refute_0_3,plain,
theorem(implies(A,or(not(X_11),A))),
inference(subst,[],[refute_0_2:[bind(B,$fot(not(X_11)))]]) ).
cnf(refute_0_4,plain,
implies(X_11,A) = or(not(X_11),A),
inference(subst,[],[implies_definition:[bind(X,$fot(X_11)),bind(Y,$fot(A))]]) ).
cnf(refute_0_5,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_6,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_7,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( implies(X_11,A) != or(not(X_11),A)
| or(not(X_11),A) = implies(X_11,A) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X_11,A))),bind(Y0,$fot(or(not(X_11),A)))]]) ).
cnf(refute_0_9,plain,
or(not(X_11),A) = implies(X_11,A),
inference(resolve,[$cnf( $equal(implies(X_11,A),or(not(X_11),A)) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( or(not(X_11),A) != implies(X_11,A)
| ~ theorem(implies(A,or(not(X_11),A)))
| theorem(implies(A,implies(X_11,A))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(A,or(not(X_11),A))) ),[0,1],$fot(implies(X_11,A))]]) ).
cnf(refute_0_11,plain,
( ~ theorem(implies(A,or(not(X_11),A)))
| theorem(implies(A,implies(X_11,A))) ),
inference(resolve,[$cnf( $equal(or(not(X_11),A),implies(X_11,A)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
theorem(implies(A,implies(X_11,A))),
inference(resolve,[$cnf( theorem(implies(A,or(not(X_11),A))) )],[refute_0_3,refute_0_11]) ).
cnf(refute_0_13,plain,
theorem(implies(X_833,implies(X_11,X_833))),
inference(subst,[],[refute_0_12:[bind(A,$fot(X_833))]]) ).
cnf(refute_0_14,plain,
( ~ axiom(implies(implies(X_37,X_38),implies(or(X_39,X_37),or(X_39,X_38))))
| theorem(implies(implies(X_37,X_38),implies(or(X_39,X_37),or(X_39,X_38)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_37,X_38),implies(or(X_39,X_37),or(X_39,X_38)))))]]) ).
cnf(refute_0_15,plain,
axiom(implies(implies(X_37,X_38),implies(or(X_39,X_37),or(X_39,X_38)))),
inference(subst,[],[axiom_1_6:[bind(A,$fot(X_37)),bind(B,$fot(X_38)),bind(C,$fot(X_39))]]) ).
cnf(refute_0_16,plain,
theorem(implies(implies(X_37,X_38),implies(or(X_39,X_37),or(X_39,X_38)))),
inference(resolve,[$cnf( axiom(implies(implies(X_37,X_38),implies(or(X_39,X_37),or(X_39,X_38)))) )],[refute_0_15,refute_0_14]) ).
cnf(refute_0_17,plain,
theorem(implies(implies(X_40,X_41),implies(or(not(X),X_40),or(not(X),X_41)))),
inference(subst,[],[refute_0_16:[bind(X_37,$fot(X_40)),bind(X_38,$fot(X_41)),bind(X_39,$fot(not(X)))]]) ).
cnf(refute_0_18,plain,
implies(X,X_41) = or(not(X),X_41),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_41))]]) ).
cnf(refute_0_19,plain,
( implies(X,X_41) != or(not(X),X_41)
| or(not(X),X_41) = implies(X,X_41) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,X_41))),bind(Y0,$fot(or(not(X),X_41)))]]) ).
cnf(refute_0_20,plain,
or(not(X),X_41) = implies(X,X_41),
inference(resolve,[$cnf( $equal(implies(X,X_41),or(not(X),X_41)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( or(not(X),X_41) != implies(X,X_41)
| ~ theorem(implies(implies(X_40,X_41),implies(or(not(X),X_40),or(not(X),X_41))))
| theorem(implies(implies(X_40,X_41),implies(or(not(X),X_40),implies(X,X_41)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_40,X_41),implies(or(not(X),X_40),or(not(X),X_41)))) ),[0,1,1],$fot(implies(X,X_41))]]) ).
cnf(refute_0_22,plain,
( ~ theorem(implies(implies(X_40,X_41),implies(or(not(X),X_40),or(not(X),X_41))))
| theorem(implies(implies(X_40,X_41),implies(or(not(X),X_40),implies(X,X_41)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_41),implies(X,X_41)) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
theorem(implies(implies(X_40,X_41),implies(or(not(X),X_40),implies(X,X_41)))),
inference(resolve,[$cnf( theorem(implies(implies(X_40,X_41),implies(or(not(X),X_40),or(not(X),X_41)))) )],[refute_0_17,refute_0_22]) ).
cnf(refute_0_24,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_25,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_24]) ).
cnf(refute_0_26,plain,
or(not(X),X_40) = implies(X,X_40),
inference(subst,[],[refute_0_25:[bind(Y,$fot(X_40))]]) ).
cnf(refute_0_27,plain,
implies(or(not(X),X_40),implies(X,X_41)) = implies(or(not(X),X_40),implies(X,X_41)),
introduced(tautology,[refl,[$fot(implies(or(not(X),X_40),implies(X,X_41)))]]) ).
cnf(refute_0_28,plain,
( implies(or(not(X),X_40),implies(X,X_41)) != implies(or(not(X),X_40),implies(X,X_41))
| or(not(X),X_40) != implies(X,X_40)
| implies(or(not(X),X_40),implies(X,X_41)) = implies(implies(X,X_40),implies(X,X_41)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),X_40),implies(X,X_41)),implies(or(not(X),X_40),implies(X,X_41))) ),[1,0],$fot(implies(X,X_40))]]) ).
cnf(refute_0_29,plain,
( or(not(X),X_40) != implies(X,X_40)
| implies(or(not(X),X_40),implies(X,X_41)) = implies(implies(X,X_40),implies(X,X_41)) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_40),implies(X,X_41)),implies(or(not(X),X_40),implies(X,X_41))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
implies(or(not(X),X_40),implies(X,X_41)) = implies(implies(X,X_40),implies(X,X_41)),
inference(resolve,[$cnf( $equal(or(not(X),X_40),implies(X,X_40)) )],[refute_0_26,refute_0_29]) ).
cnf(refute_0_31,plain,
implies(implies(X_40,X_41),implies(or(not(X),X_40),implies(X,X_41))) = implies(implies(X_40,X_41),implies(or(not(X),X_40),implies(X,X_41))),
introduced(tautology,[refl,[$fot(implies(implies(X_40,X_41),implies(or(not(X),X_40),implies(X,X_41))))]]) ).
cnf(refute_0_32,plain,
( implies(implies(X_40,X_41),implies(or(not(X),X_40),implies(X,X_41))) != implies(implies(X_40,X_41),implies(or(not(X),X_40),implies(X,X_41)))
| implies(or(not(X),X_40),implies(X,X_41)) != implies(implies(X,X_40),implies(X,X_41))
| implies(implies(X_40,X_41),implies(or(not(X),X_40),implies(X,X_41))) = implies(implies(X_40,X_41),implies(implies(X,X_40),implies(X,X_41))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_40,X_41),implies(or(not(X),X_40),implies(X,X_41))),implies(implies(X_40,X_41),implies(or(not(X),X_40),implies(X,X_41)))) ),[1,1],$fot(implies(implies(X,X_40),implies(X,X_41)))]]) ).
cnf(refute_0_33,plain,
( implies(or(not(X),X_40),implies(X,X_41)) != implies(implies(X,X_40),implies(X,X_41))
| implies(implies(X_40,X_41),implies(or(not(X),X_40),implies(X,X_41))) = implies(implies(X_40,X_41),implies(implies(X,X_40),implies(X,X_41))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_40,X_41),implies(or(not(X),X_40),implies(X,X_41))),implies(implies(X_40,X_41),implies(or(not(X),X_40),implies(X,X_41)))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
implies(implies(X_40,X_41),implies(or(not(X),X_40),implies(X,X_41))) = implies(implies(X_40,X_41),implies(implies(X,X_40),implies(X,X_41))),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_40),implies(X,X_41)),implies(implies(X,X_40),implies(X,X_41))) )],[refute_0_30,refute_0_33]) ).
cnf(refute_0_35,plain,
( implies(implies(X_40,X_41),implies(or(not(X),X_40),implies(X,X_41))) != implies(implies(X_40,X_41),implies(implies(X,X_40),implies(X,X_41)))
| ~ theorem(implies(implies(X_40,X_41),implies(or(not(X),X_40),implies(X,X_41))))
| theorem(implies(implies(X_40,X_41),implies(implies(X,X_40),implies(X,X_41)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_40,X_41),implies(or(not(X),X_40),implies(X,X_41)))) ),[0],$fot(implies(implies(X_40,X_41),implies(implies(X,X_40),implies(X,X_41))))]]) ).
cnf(refute_0_36,plain,
( ~ theorem(implies(implies(X_40,X_41),implies(or(not(X),X_40),implies(X,X_41))))
| theorem(implies(implies(X_40,X_41),implies(implies(X,X_40),implies(X,X_41)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_40,X_41),implies(or(not(X),X_40),implies(X,X_41))),implies(implies(X_40,X_41),implies(implies(X,X_40),implies(X,X_41)))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
theorem(implies(implies(X_40,X_41),implies(implies(X,X_40),implies(X,X_41)))),
inference(resolve,[$cnf( theorem(implies(implies(X_40,X_41),implies(or(not(X),X_40),implies(X,X_41)))) )],[refute_0_23,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ theorem(implies(X_40,X_41))
| ~ theorem(implies(implies(X_40,X_41),implies(implies(X,X_40),implies(X,X_41))))
| theorem(implies(implies(X,X_40),implies(X,X_41))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(implies(X,X_40),implies(X,X_41)))),bind(Y,$fot(implies(X_40,X_41)))]]) ).
cnf(refute_0_39,plain,
( ~ theorem(implies(X_40,X_41))
| theorem(implies(implies(X,X_40),implies(X,X_41))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_40,X_41),implies(implies(X,X_40),implies(X,X_41)))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ theorem(implies(X_833,implies(X_11,X_833)))
| theorem(implies(implies(X_832,X_833),implies(X_832,implies(X_11,X_833)))) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(X_832)),bind(X_40,$fot(X_833)),bind(X_41,$fot(implies(X_11,X_833)))]]) ).
cnf(refute_0_41,plain,
theorem(implies(implies(X_832,X_833),implies(X_832,implies(X_11,X_833)))),
inference(resolve,[$cnf( theorem(implies(X_833,implies(X_11,X_833))) )],[refute_0_13,refute_0_40]) ).
cnf(refute_0_42,plain,
theorem(implies(implies(X_840,X_841),implies(X_840,implies(X_839,X_841)))),
inference(subst,[],[refute_0_41:[bind(X_11,$fot(X_839)),bind(X_832,$fot(X_840)),bind(X_833,$fot(X_841))]]) ).
cnf(refute_0_43,plain,
( ~ theorem(implies(X_840,X_841))
| theorem(implies(X_840,implies(X_839,X_841))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_840,X_841),implies(X_840,implies(X_839,X_841)))) )],[refute_0_42,refute_0_0]) ).
cnf(refute_0_44,plain,
( ~ theorem(implies(not(implies(X_41488,X_41489)),not(X_41489)))
| theorem(implies(not(implies(X_41488,X_41489)),implies(X_839,not(X_41489)))) ),
inference(subst,[],[refute_0_43:[bind(X_840,$fot(not(implies(X_41488,X_41489)))),bind(X_841,$fot(not(X_41489)))]]) ).
cnf(refute_0_45,plain,
( ~ theorem(implies(X_835,or(X_836,X_836)))
| ~ theorem(implies(implies(X_835,or(X_836,X_836)),implies(X_835,X_836)))
| theorem(implies(X_835,X_836)) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_835,X_836))),bind(Y,$fot(implies(X_835,or(X_836,X_836))))]]) ).
cnf(refute_0_46,plain,
( ~ axiom(implies(or(A,A),A))
| theorem(implies(or(A,A),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_47,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[$cnf( axiom(implies(or(A,A),A)) )],[axiom_1_2,refute_0_46]) ).
cnf(refute_0_48,plain,
theorem(implies(or(X_834,X_834),X_834)),
inference(subst,[],[refute_0_47:[bind(A,$fot(X_834))]]) ).
cnf(refute_0_49,plain,
( ~ theorem(implies(or(X_834,X_834),X_834))
| theorem(implies(implies(X_832,or(X_834,X_834)),implies(X_832,X_834))) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(X_832)),bind(X_40,$fot(or(X_834,X_834))),bind(X_41,$fot(X_834))]]) ).
cnf(refute_0_50,plain,
theorem(implies(implies(X_832,or(X_834,X_834)),implies(X_832,X_834))),
inference(resolve,[$cnf( theorem(implies(or(X_834,X_834),X_834)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
theorem(implies(implies(X_835,or(X_836,X_836)),implies(X_835,X_836))),
inference(subst,[],[refute_0_50:[bind(X_832,$fot(X_835)),bind(X_834,$fot(X_836))]]) ).
cnf(refute_0_52,plain,
( ~ theorem(implies(X_835,or(X_836,X_836)))
| theorem(implies(X_835,X_836)) ),
inference(resolve,[$cnf( theorem(implies(implies(X_835,or(X_836,X_836)),implies(X_835,X_836))) )],[refute_0_51,refute_0_45]) ).
cnf(refute_0_53,plain,
( ~ theorem(implies(not(implies(X_41485,X_41486)),or(not(X_41486),not(X_41486))))
| theorem(implies(not(implies(X_41485,X_41486)),not(X_41486))) ),
inference(subst,[],[refute_0_52:[bind(X_835,$fot(not(implies(X_41485,X_41486)))),bind(X_836,$fot(not(X_41486)))]]) ).
cnf(refute_0_54,plain,
( ~ axiom(implies(or(X_7,X_8),or(X_8,X_7)))
| theorem(implies(or(X_7,X_8),or(X_8,X_7))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_7,X_8),or(X_8,X_7))))]]) ).
cnf(refute_0_55,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_56,plain,
theorem(implies(or(X_7,X_8),or(X_8,X_7))),
inference(resolve,[$cnf( axiom(implies(or(X_7,X_8),or(X_8,X_7))) )],[refute_0_55,refute_0_54]) ).
cnf(refute_0_57,plain,
( ~ theorem(implies(or(X_7,X_8),or(X_8,X_7)))
| ~ theorem(or(X_7,X_8))
| theorem(or(X_8,X_7)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_8,X_7))),bind(Y,$fot(or(X_7,X_8)))]]) ).
cnf(refute_0_58,plain,
( ~ theorem(or(X_7,X_8))
| theorem(or(X_8,X_7)) ),
inference(resolve,[$cnf( theorem(implies(or(X_7,X_8),or(X_8,X_7))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
( ~ theorem(or(or(X_41481,not(X_41480)),not(not(or(X_41479,X_41480)))))
| theorem(or(not(not(or(X_41479,X_41480))),or(X_41481,not(X_41480)))) ),
inference(subst,[],[refute_0_58:[bind(X_7,$fot(or(X_41481,not(X_41480)))),bind(X_8,$fot(not(not(or(X_41479,X_41480)))))]]) ).
cnf(refute_0_60,plain,
( ~ theorem(or(or(X_6238,X_6239),or(X_6240,not(X_6239))))
| theorem(or(or(X_6240,not(X_6239)),or(X_6238,X_6239))) ),
inference(subst,[],[refute_0_58:[bind(X_7,$fot(or(X_6238,X_6239))),bind(X_8,$fot(or(X_6240,not(X_6239))))]]) ).
cnf(refute_0_61,plain,
theorem(implies(X_68,or(B,X_68))),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_68))]]) ).
cnf(refute_0_62,plain,
( ~ theorem(X_68)
| ~ theorem(implies(X_68,or(B,X_68)))
| theorem(or(B,X_68)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(B,X_68))),bind(Y,$fot(X_68))]]) ).
cnf(refute_0_63,plain,
( ~ theorem(X_68)
| theorem(or(B,X_68)) ),
inference(resolve,[$cnf( theorem(implies(X_68,or(B,X_68))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
( ~ theorem(or(or(X_105,X_106),not(X_106)))
| theorem(or(B,or(or(X_105,X_106),not(X_106)))) ),
inference(subst,[],[refute_0_63:[bind(X_68,$fot(or(or(X_105,X_106),not(X_106))))]]) ).
cnf(refute_0_65,plain,
theorem(implies(X_99,or(B,X_99))),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_99))]]) ).
cnf(refute_0_66,plain,
theorem(implies(or(not(X_11),X_8),or(X_8,not(X_11)))),
inference(subst,[],[refute_0_56:[bind(X_7,$fot(not(X_11)))]]) ).
cnf(refute_0_67,plain,
implies(X_11,X_8) = or(not(X_11),X_8),
inference(subst,[],[implies_definition:[bind(X,$fot(X_11)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_68,plain,
( implies(X_11,X_8) != or(not(X_11),X_8)
| or(not(X_11),X_8) = implies(X_11,X_8) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X_11,X_8))),bind(Y0,$fot(or(not(X_11),X_8)))]]) ).
cnf(refute_0_69,plain,
or(not(X_11),X_8) = implies(X_11,X_8),
inference(resolve,[$cnf( $equal(implies(X_11,X_8),or(not(X_11),X_8)) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
( or(not(X_11),X_8) != implies(X_11,X_8)
| ~ theorem(implies(or(not(X_11),X_8),or(X_8,not(X_11))))
| theorem(implies(implies(X_11,X_8),or(X_8,not(X_11)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X_11),X_8),or(X_8,not(X_11)))) ),[0,0],$fot(implies(X_11,X_8))]]) ).
cnf(refute_0_71,plain,
( ~ theorem(implies(or(not(X_11),X_8),or(X_8,not(X_11))))
| theorem(implies(implies(X_11,X_8),or(X_8,not(X_11)))) ),
inference(resolve,[$cnf( $equal(or(not(X_11),X_8),implies(X_11,X_8)) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
theorem(implies(implies(X_11,X_8),or(X_8,not(X_11)))),
inference(resolve,[$cnf( theorem(implies(or(not(X_11),X_8),or(X_8,not(X_11)))) )],[refute_0_66,refute_0_71]) ).
cnf(refute_0_73,plain,
( ~ theorem(implies(X_11,X_8))
| ~ theorem(implies(implies(X_11,X_8),or(X_8,not(X_11))))
| theorem(or(X_8,not(X_11))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_8,not(X_11)))),bind(Y,$fot(implies(X_11,X_8)))]]) ).
cnf(refute_0_74,plain,
( ~ theorem(implies(X_11,X_8))
| theorem(or(X_8,not(X_11))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_11,X_8),or(X_8,not(X_11)))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
( ~ theorem(implies(X_99,or(B,X_99)))
| theorem(or(or(B,X_99),not(X_99))) ),
inference(subst,[],[refute_0_74:[bind(X_11,$fot(X_99)),bind(X_8,$fot(or(B,X_99)))]]) ).
cnf(refute_0_76,plain,
theorem(or(or(B,X_99),not(X_99))),
inference(resolve,[$cnf( theorem(implies(X_99,or(B,X_99))) )],[refute_0_65,refute_0_75]) ).
cnf(refute_0_77,plain,
theorem(or(or(X_105,X_106),not(X_106))),
inference(subst,[],[refute_0_76:[bind(B,$fot(X_105)),bind(X_99,$fot(X_106))]]) ).
cnf(refute_0_78,plain,
theorem(or(B,or(or(X_105,X_106),not(X_106)))),
inference(resolve,[$cnf( theorem(or(or(X_105,X_106),not(X_106))) )],[refute_0_77,refute_0_64]) ).
cnf(refute_0_79,plain,
theorem(or(X_6190,or(or(X_105,X_106),not(X_106)))),
inference(subst,[],[refute_0_78:[bind(B,$fot(X_6190))]]) ).
cnf(refute_0_80,plain,
( ~ axiom(implies(or(X_31,or(X_32,X_33)),or(X_32,or(X_31,X_33))))
| theorem(implies(or(X_31,or(X_32,X_33)),or(X_32,or(X_31,X_33)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_31,or(X_32,X_33)),or(X_32,or(X_31,X_33)))))]]) ).
cnf(refute_0_81,plain,
axiom(implies(or(X_31,or(X_32,X_33)),or(X_32,or(X_31,X_33)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_31)),bind(B,$fot(X_32)),bind(C,$fot(X_33))]]) ).
cnf(refute_0_82,plain,
theorem(implies(or(X_31,or(X_32,X_33)),or(X_32,or(X_31,X_33)))),
inference(resolve,[$cnf( axiom(implies(or(X_31,or(X_32,X_33)),or(X_32,or(X_31,X_33)))) )],[refute_0_81,refute_0_80]) ).
cnf(refute_0_83,plain,
( ~ theorem(implies(or(X_31,or(X_32,X_33)),or(X_32,or(X_31,X_33))))
| ~ theorem(or(X_31,or(X_32,X_33)))
| theorem(or(X_32,or(X_31,X_33))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_32,or(X_31,X_33)))),bind(Y,$fot(or(X_31,or(X_32,X_33))))]]) ).
cnf(refute_0_84,plain,
( ~ theorem(or(X_31,or(X_32,X_33)))
| theorem(or(X_32,or(X_31,X_33))) ),
inference(resolve,[$cnf( theorem(implies(or(X_31,or(X_32,X_33)),or(X_32,or(X_31,X_33)))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
( ~ theorem(or(X_6190,or(or(X_105,X_106),not(X_106))))
| theorem(or(or(X_105,X_106),or(X_6190,not(X_106)))) ),
inference(subst,[],[refute_0_84:[bind(X_31,$fot(X_6190)),bind(X_32,$fot(or(X_105,X_106))),bind(X_33,$fot(not(X_106)))]]) ).
cnf(refute_0_86,plain,
theorem(or(or(X_105,X_106),or(X_6190,not(X_106)))),
inference(resolve,[$cnf( theorem(or(X_6190,or(or(X_105,X_106),not(X_106)))) )],[refute_0_79,refute_0_85]) ).
cnf(refute_0_87,plain,
theorem(or(or(X_6238,X_6239),or(X_6240,not(X_6239)))),
inference(subst,[],[refute_0_86:[bind(X_105,$fot(X_6238)),bind(X_106,$fot(X_6239)),bind(X_6190,$fot(X_6240))]]) ).
cnf(refute_0_88,plain,
theorem(or(or(X_6240,not(X_6239)),or(X_6238,X_6239))),
inference(resolve,[$cnf( theorem(or(or(X_6238,X_6239),or(X_6240,not(X_6239)))) )],[refute_0_87,refute_0_60]) ).
cnf(refute_0_89,plain,
( ~ theorem(implies(or(X_3465,X_3464),or(X_3465,not(not(X_3464)))))
| ~ theorem(or(X_3465,X_3464))
| theorem(or(X_3465,not(not(X_3464)))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_3465,not(not(X_3464))))),bind(Y,$fot(or(X_3465,X_3464)))]]) ).
cnf(refute_0_90,plain,
( ~ axiom(implies(implies(X_24,not(X_23)),implies(X_23,not(X_24))))
| theorem(implies(implies(X_24,not(X_23)),implies(X_23,not(X_24)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_24,not(X_23)),implies(X_23,not(X_24)))))]]) ).
cnf(refute_0_91,plain,
axiom(implies(or(not(X_11),B),or(B,not(X_11)))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(not(X_11)))]]) ).
cnf(refute_0_92,plain,
implies(X_11,B) = or(not(X_11),B),
inference(subst,[],[implies_definition:[bind(X,$fot(X_11)),bind(Y,$fot(B))]]) ).
cnf(refute_0_93,plain,
( implies(X_11,B) != or(not(X_11),B)
| or(not(X_11),B) = implies(X_11,B) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X_11,B))),bind(Y0,$fot(or(not(X_11),B)))]]) ).
cnf(refute_0_94,plain,
or(not(X_11),B) = implies(X_11,B),
inference(resolve,[$cnf( $equal(implies(X_11,B),or(not(X_11),B)) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
( or(not(X_11),B) != implies(X_11,B)
| ~ axiom(implies(or(not(X_11),B),or(B,not(X_11))))
| axiom(implies(implies(X_11,B),or(B,not(X_11)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X_11),B),or(B,not(X_11)))) ),[0,0],$fot(implies(X_11,B))]]) ).
cnf(refute_0_96,plain,
( ~ axiom(implies(or(not(X_11),B),or(B,not(X_11))))
| axiom(implies(implies(X_11,B),or(B,not(X_11)))) ),
inference(resolve,[$cnf( $equal(or(not(X_11),B),implies(X_11,B)) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
axiom(implies(implies(X_11,B),or(B,not(X_11)))),
inference(resolve,[$cnf( axiom(implies(or(not(X_11),B),or(B,not(X_11)))) )],[refute_0_91,refute_0_96]) ).
cnf(refute_0_98,plain,
axiom(implies(implies(X_18,not(X)),or(not(X),not(X_18)))),
inference(subst,[],[refute_0_97:[bind(B,$fot(not(X))),bind(X_11,$fot(X_18))]]) ).
cnf(refute_0_99,plain,
implies(X,not(X_18)) = or(not(X),not(X_18)),
inference(subst,[],[implies_definition:[bind(Y,$fot(not(X_18)))]]) ).
cnf(refute_0_100,plain,
( implies(X,not(X_18)) != or(not(X),not(X_18))
| or(not(X),not(X_18)) = implies(X,not(X_18)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,not(X_18)))),bind(Y0,$fot(or(not(X),not(X_18))))]]) ).
cnf(refute_0_101,plain,
or(not(X),not(X_18)) = implies(X,not(X_18)),
inference(resolve,[$cnf( $equal(implies(X,not(X_18)),or(not(X),not(X_18))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
( or(not(X),not(X_18)) != implies(X,not(X_18))
| ~ axiom(implies(implies(X_18,not(X)),or(not(X),not(X_18))))
| axiom(implies(implies(X_18,not(X)),implies(X,not(X_18)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(implies(X_18,not(X)),or(not(X),not(X_18)))) ),[0,1],$fot(implies(X,not(X_18)))]]) ).
cnf(refute_0_103,plain,
( ~ axiom(implies(implies(X_18,not(X)),or(not(X),not(X_18))))
| axiom(implies(implies(X_18,not(X)),implies(X,not(X_18)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_18)),implies(X,not(X_18))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
axiom(implies(implies(X_18,not(X)),implies(X,not(X_18)))),
inference(resolve,[$cnf( axiom(implies(implies(X_18,not(X)),or(not(X),not(X_18)))) )],[refute_0_98,refute_0_103]) ).
cnf(refute_0_105,plain,
axiom(implies(implies(X_24,not(X_23)),implies(X_23,not(X_24)))),
inference(subst,[],[refute_0_104:[bind(X,$fot(X_23)),bind(X_18,$fot(X_24))]]) ).
cnf(refute_0_106,plain,
theorem(implies(implies(X_24,not(X_23)),implies(X_23,not(X_24)))),
inference(resolve,[$cnf( axiom(implies(implies(X_24,not(X_23)),implies(X_23,not(X_24)))) )],[refute_0_105,refute_0_90]) ).
cnf(refute_0_107,plain,
( ~ theorem(implies(X_24,not(X_23)))
| ~ theorem(implies(implies(X_24,not(X_23)),implies(X_23,not(X_24))))
| theorem(implies(X_23,not(X_24))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_23,not(X_24)))),bind(Y,$fot(implies(X_24,not(X_23))))]]) ).
cnf(refute_0_108,plain,
( ~ theorem(implies(X_24,not(X_23)))
| theorem(implies(X_23,not(X_24))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_24,not(X_23)),implies(X_23,not(X_24)))) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
( ~ theorem(implies(not(X_23),not(X_23)))
| theorem(implies(X_23,not(not(X_23)))) ),
inference(subst,[],[refute_0_108:[bind(X_24,$fot(not(X_23)))]]) ).
cnf(refute_0_110,plain,
( ~ axiom(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36))))
| theorem(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36)))))]]) ).
cnf(refute_0_111,plain,
axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,or(not(X),X_33)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(not(X))),bind(B,$fot(X_32)),bind(C,$fot(X_33))]]) ).
cnf(refute_0_112,plain,
implies(X,X_33) = or(not(X),X_33),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_33))]]) ).
cnf(refute_0_113,plain,
( implies(X,X_33) != or(not(X),X_33)
| or(not(X),X_33) = implies(X,X_33) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,X_33))),bind(Y0,$fot(or(not(X),X_33)))]]) ).
cnf(refute_0_114,plain,
or(not(X),X_33) = implies(X,X_33),
inference(resolve,[$cnf( $equal(implies(X,X_33),or(not(X),X_33)) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
( or(not(X),X_33) != implies(X,X_33)
| ~ axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,or(not(X),X_33))))
| axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,or(not(X),X_33)))) ),[0,1,1],$fot(implies(X,X_33))]]) ).
cnf(refute_0_116,plain,
( ~ axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,or(not(X),X_33))))
| axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_33),implies(X,X_33)) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,or(not(X),X_33)))) )],[refute_0_111,refute_0_116]) ).
cnf(refute_0_118,plain,
or(not(X),or(X_32,X_33)) = implies(X,or(X_32,X_33)),
inference(subst,[],[refute_0_25:[bind(Y,$fot(or(X_32,X_33)))]]) ).
cnf(refute_0_119,plain,
implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))) = implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))))]]) ).
cnf(refute_0_120,plain,
( implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))) != implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))
| or(not(X),or(X_32,X_33)) != implies(X,or(X_32,X_33))
| implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))) = implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))),implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))) ),[1,0],$fot(implies(X,or(X_32,X_33)))]]) ).
cnf(refute_0_121,plain,
( or(not(X),or(X_32,X_33)) != implies(X,or(X_32,X_33))
| implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))) = implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))),implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))) = implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_32,X_33)),implies(X,or(X_32,X_33))) )],[refute_0_118,refute_0_121]) ).
cnf(refute_0_123,plain,
( implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))) != implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33)))
| ~ axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))))
| axiom(implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))) ),[0],$fot(implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33))))]]) ).
cnf(refute_0_124,plain,
( ~ axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))))
| axiom(implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))),implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33)))) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
axiom(implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))) )],[refute_0_117,refute_0_124]) ).
cnf(refute_0_126,plain,
axiom(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36)))),
inference(subst,[],[refute_0_125:[bind(X,$fot(X_34)),bind(X_32,$fot(X_35)),bind(X_33,$fot(X_36))]]) ).
cnf(refute_0_127,plain,
theorem(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36)))),
inference(resolve,[$cnf( axiom(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36)))) )],[refute_0_126,refute_0_110]) ).
cnf(refute_0_128,plain,
theorem(implies(implies(X_55,or(not(X),X_57)),or(not(X),implies(X_55,X_57)))),
inference(subst,[],[refute_0_127:[bind(X_34,$fot(X_55)),bind(X_35,$fot(not(X))),bind(X_36,$fot(X_57))]]) ).
cnf(refute_0_129,plain,
implies(X,implies(X_55,X_57)) = or(not(X),implies(X_55,X_57)),
inference(subst,[],[implies_definition:[bind(Y,$fot(implies(X_55,X_57)))]]) ).
cnf(refute_0_130,plain,
( implies(X,implies(X_55,X_57)) != or(not(X),implies(X_55,X_57))
| or(not(X),implies(X_55,X_57)) = implies(X,implies(X_55,X_57)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,implies(X_55,X_57)))),bind(Y0,$fot(or(not(X),implies(X_55,X_57))))]]) ).
cnf(refute_0_131,plain,
or(not(X),implies(X_55,X_57)) = implies(X,implies(X_55,X_57)),
inference(resolve,[$cnf( $equal(implies(X,implies(X_55,X_57)),or(not(X),implies(X_55,X_57))) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
( or(not(X),implies(X_55,X_57)) != implies(X,implies(X_55,X_57))
| ~ theorem(implies(implies(X_55,or(not(X),X_57)),or(not(X),implies(X_55,X_57))))
| theorem(implies(implies(X_55,or(not(X),X_57)),implies(X,implies(X_55,X_57)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_55,or(not(X),X_57)),or(not(X),implies(X_55,X_57)))) ),[0,1],$fot(implies(X,implies(X_55,X_57)))]]) ).
cnf(refute_0_133,plain,
( ~ theorem(implies(implies(X_55,or(not(X),X_57)),or(not(X),implies(X_55,X_57))))
| theorem(implies(implies(X_55,or(not(X),X_57)),implies(X,implies(X_55,X_57)))) ),
inference(resolve,[$cnf( $equal(or(not(X),implies(X_55,X_57)),implies(X,implies(X_55,X_57))) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
theorem(implies(implies(X_55,or(not(X),X_57)),implies(X,implies(X_55,X_57)))),
inference(resolve,[$cnf( theorem(implies(implies(X_55,or(not(X),X_57)),or(not(X),implies(X_55,X_57)))) )],[refute_0_128,refute_0_133]) ).
cnf(refute_0_135,plain,
or(not(X),X_57) = implies(X,X_57),
inference(subst,[],[refute_0_25:[bind(Y,$fot(X_57))]]) ).
cnf(refute_0_136,plain,
implies(X_55,or(not(X),X_57)) = implies(X_55,or(not(X),X_57)),
introduced(tautology,[refl,[$fot(implies(X_55,or(not(X),X_57)))]]) ).
cnf(refute_0_137,plain,
( implies(X_55,or(not(X),X_57)) != implies(X_55,or(not(X),X_57))
| or(not(X),X_57) != implies(X,X_57)
| implies(X_55,or(not(X),X_57)) = implies(X_55,implies(X,X_57)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_55,or(not(X),X_57)),implies(X_55,or(not(X),X_57))) ),[1,1],$fot(implies(X,X_57))]]) ).
cnf(refute_0_138,plain,
( or(not(X),X_57) != implies(X,X_57)
| implies(X_55,or(not(X),X_57)) = implies(X_55,implies(X,X_57)) ),
inference(resolve,[$cnf( $equal(implies(X_55,or(not(X),X_57)),implies(X_55,or(not(X),X_57))) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
implies(X_55,or(not(X),X_57)) = implies(X_55,implies(X,X_57)),
inference(resolve,[$cnf( $equal(or(not(X),X_57),implies(X,X_57)) )],[refute_0_135,refute_0_138]) ).
cnf(refute_0_140,plain,
implies(implies(X_55,or(not(X),X_57)),implies(X,implies(X_55,X_57))) = implies(implies(X_55,or(not(X),X_57)),implies(X,implies(X_55,X_57))),
introduced(tautology,[refl,[$fot(implies(implies(X_55,or(not(X),X_57)),implies(X,implies(X_55,X_57))))]]) ).
cnf(refute_0_141,plain,
( implies(X_55,or(not(X),X_57)) != implies(X_55,implies(X,X_57))
| implies(implies(X_55,or(not(X),X_57)),implies(X,implies(X_55,X_57))) != implies(implies(X_55,or(not(X),X_57)),implies(X,implies(X_55,X_57)))
| implies(implies(X_55,or(not(X),X_57)),implies(X,implies(X_55,X_57))) = implies(implies(X_55,implies(X,X_57)),implies(X,implies(X_55,X_57))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_55,or(not(X),X_57)),implies(X,implies(X_55,X_57))),implies(implies(X_55,or(not(X),X_57)),implies(X,implies(X_55,X_57)))) ),[1,0],$fot(implies(X_55,implies(X,X_57)))]]) ).
cnf(refute_0_142,plain,
( implies(X_55,or(not(X),X_57)) != implies(X_55,implies(X,X_57))
| implies(implies(X_55,or(not(X),X_57)),implies(X,implies(X_55,X_57))) = implies(implies(X_55,implies(X,X_57)),implies(X,implies(X_55,X_57))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_55,or(not(X),X_57)),implies(X,implies(X_55,X_57))),implies(implies(X_55,or(not(X),X_57)),implies(X,implies(X_55,X_57)))) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
implies(implies(X_55,or(not(X),X_57)),implies(X,implies(X_55,X_57))) = implies(implies(X_55,implies(X,X_57)),implies(X,implies(X_55,X_57))),
inference(resolve,[$cnf( $equal(implies(X_55,or(not(X),X_57)),implies(X_55,implies(X,X_57))) )],[refute_0_139,refute_0_142]) ).
cnf(refute_0_144,plain,
( implies(implies(X_55,or(not(X),X_57)),implies(X,implies(X_55,X_57))) != implies(implies(X_55,implies(X,X_57)),implies(X,implies(X_55,X_57)))
| ~ theorem(implies(implies(X_55,or(not(X),X_57)),implies(X,implies(X_55,X_57))))
| theorem(implies(implies(X_55,implies(X,X_57)),implies(X,implies(X_55,X_57)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_55,or(not(X),X_57)),implies(X,implies(X_55,X_57)))) ),[0],$fot(implies(implies(X_55,implies(X,X_57)),implies(X,implies(X_55,X_57))))]]) ).
cnf(refute_0_145,plain,
( ~ theorem(implies(implies(X_55,or(not(X),X_57)),implies(X,implies(X_55,X_57))))
| theorem(implies(implies(X_55,implies(X,X_57)),implies(X,implies(X_55,X_57)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_55,or(not(X),X_57)),implies(X,implies(X_55,X_57))),implies(implies(X_55,implies(X,X_57)),implies(X,implies(X_55,X_57)))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
theorem(implies(implies(X_55,implies(X,X_57)),implies(X,implies(X_55,X_57)))),
inference(resolve,[$cnf( theorem(implies(implies(X_55,or(not(X),X_57)),implies(X,implies(X_55,X_57)))) )],[refute_0_134,refute_0_145]) ).
cnf(refute_0_147,plain,
( ~ theorem(implies(implies(X_55,implies(X,X_57)),implies(X,implies(X_55,X_57))))
| theorem(implies(implies(X_832,implies(X_55,implies(X,X_57))),implies(X_832,implies(X,implies(X_55,X_57))))) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(X_832)),bind(X_40,$fot(implies(X_55,implies(X,X_57)))),bind(X_41,$fot(implies(X,implies(X_55,X_57))))]]) ).
cnf(refute_0_148,plain,
theorem(implies(implies(X_832,implies(X_55,implies(X,X_57))),implies(X_832,implies(X,implies(X_55,X_57))))),
inference(resolve,[$cnf( theorem(implies(implies(X_55,implies(X,X_57)),implies(X,implies(X_55,X_57)))) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
( ~ theorem(X_1657)
| ~ theorem(implies(X_1657,implies(X_1658,X_1658)))
| theorem(implies(X_1658,X_1658)) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_1658,X_1658))),bind(Y,$fot(X_1657))]]) ).
cnf(refute_0_150,plain,
theorem(implies(X_1656,implies(X_1654,X_1656))),
inference(subst,[],[refute_0_12:[bind(A,$fot(X_1656)),bind(X_11,$fot(X_1654))]]) ).
cnf(refute_0_151,plain,
( ~ theorem(implies(X_55,implies(X,X_57)))
| ~ theorem(implies(implies(X_55,implies(X,X_57)),implies(X,implies(X_55,X_57))))
| theorem(implies(X,implies(X_55,X_57))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X,implies(X_55,X_57)))),bind(Y,$fot(implies(X_55,implies(X,X_57))))]]) ).
cnf(refute_0_152,plain,
( ~ theorem(implies(X_55,implies(X,X_57)))
| theorem(implies(X,implies(X_55,X_57))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_55,implies(X,X_57)),implies(X,implies(X_55,X_57)))) )],[refute_0_146,refute_0_151]) ).
cnf(refute_0_153,plain,
( ~ theorem(implies(X_1656,implies(X_1654,X_1656)))
| theorem(implies(X_1654,implies(X_1656,X_1656))) ),
inference(subst,[],[refute_0_152:[bind(X,$fot(X_1654)),bind(X_55,$fot(X_1656)),bind(X_57,$fot(X_1656))]]) ).
cnf(refute_0_154,plain,
theorem(implies(X_1654,implies(X_1656,X_1656))),
inference(resolve,[$cnf( theorem(implies(X_1656,implies(X_1654,X_1656))) )],[refute_0_150,refute_0_153]) ).
cnf(refute_0_155,plain,
theorem(implies(X_1657,implies(X_1658,X_1658))),
inference(subst,[],[refute_0_154:[bind(X_1654,$fot(X_1657)),bind(X_1656,$fot(X_1658))]]) ).
cnf(refute_0_156,plain,
( ~ theorem(X_1657)
| theorem(implies(X_1658,X_1658)) ),
inference(resolve,[$cnf( theorem(implies(X_1657,implies(X_1658,X_1658))) )],[refute_0_155,refute_0_149]) ).
cnf(refute_0_157,plain,
( ~ theorem(implies(implies(X_832,implies(X_55,implies(X,X_57))),implies(X_832,implies(X,implies(X_55,X_57)))))
| theorem(implies(X_1733,X_1733)) ),
inference(subst,[],[refute_0_156:[bind(X_1657,$fot(implies(implies(X_832,implies(X_55,implies(X,X_57))),implies(X_832,implies(X,implies(X_55,X_57)))))),bind(X_1658,$fot(X_1733))]]) ).
cnf(refute_0_158,plain,
theorem(implies(X_1733,X_1733)),
inference(resolve,[$cnf( theorem(implies(implies(X_832,implies(X_55,implies(X,X_57))),implies(X_832,implies(X,implies(X_55,X_57))))) )],[refute_0_148,refute_0_157]) ).
cnf(refute_0_159,plain,
theorem(implies(not(X_23),not(X_23))),
inference(subst,[],[refute_0_158:[bind(X_1733,$fot(not(X_23)))]]) ).
cnf(refute_0_160,plain,
theorem(implies(X_23,not(not(X_23)))),
inference(resolve,[$cnf( theorem(implies(not(X_23),not(X_23))) )],[refute_0_159,refute_0_109]) ).
cnf(refute_0_161,plain,
theorem(implies(X_3398,not(not(X_3398)))),
inference(subst,[],[refute_0_160:[bind(X_23,$fot(X_3398))]]) ).
cnf(refute_0_162,plain,
( ~ theorem(implies(X_37,X_38))
| ~ theorem(implies(implies(X_37,X_38),implies(or(X_39,X_37),or(X_39,X_38))))
| theorem(implies(or(X_39,X_37),or(X_39,X_38))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(or(X_39,X_37),or(X_39,X_38)))),bind(Y,$fot(implies(X_37,X_38)))]]) ).
cnf(refute_0_163,plain,
( ~ theorem(implies(X_37,X_38))
| theorem(implies(or(X_39,X_37),or(X_39,X_38))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_37,X_38),implies(or(X_39,X_37),or(X_39,X_38)))) )],[refute_0_16,refute_0_162]) ).
cnf(refute_0_164,plain,
( ~ theorem(implies(X_3398,not(not(X_3398))))
| theorem(implies(or(X_3400,X_3398),or(X_3400,not(not(X_3398))))) ),
inference(subst,[],[refute_0_163:[bind(X_37,$fot(X_3398)),bind(X_38,$fot(not(not(X_3398)))),bind(X_39,$fot(X_3400))]]) ).
cnf(refute_0_165,plain,
theorem(implies(or(X_3400,X_3398),or(X_3400,not(not(X_3398))))),
inference(resolve,[$cnf( theorem(implies(X_3398,not(not(X_3398)))) )],[refute_0_161,refute_0_164]) ).
cnf(refute_0_166,plain,
theorem(implies(or(X_3465,X_3464),or(X_3465,not(not(X_3464))))),
inference(subst,[],[refute_0_165:[bind(X_3398,$fot(X_3464)),bind(X_3400,$fot(X_3465))]]) ).
cnf(refute_0_167,plain,
( ~ theorem(or(X_3465,X_3464))
| theorem(or(X_3465,not(not(X_3464)))) ),
inference(resolve,[$cnf( theorem(implies(or(X_3465,X_3464),or(X_3465,not(not(X_3464))))) )],[refute_0_166,refute_0_89]) ).
cnf(refute_0_168,plain,
( ~ theorem(or(or(X_6240,not(X_6239)),or(X_6238,X_6239)))
| theorem(or(or(X_6240,not(X_6239)),not(not(or(X_6238,X_6239))))) ),
inference(subst,[],[refute_0_167:[bind(X_3464,$fot(or(X_6238,X_6239))),bind(X_3465,$fot(or(X_6240,not(X_6239))))]]) ).
cnf(refute_0_169,plain,
theorem(or(or(X_6240,not(X_6239)),not(not(or(X_6238,X_6239))))),
inference(resolve,[$cnf( theorem(or(or(X_6240,not(X_6239)),or(X_6238,X_6239))) )],[refute_0_88,refute_0_168]) ).
cnf(refute_0_170,plain,
theorem(or(or(X_41481,not(X_41480)),not(not(or(X_41479,X_41480))))),
inference(subst,[],[refute_0_169:[bind(X_6238,$fot(X_41479)),bind(X_6239,$fot(X_41480)),bind(X_6240,$fot(X_41481))]]) ).
cnf(refute_0_171,plain,
theorem(or(not(not(or(X_41479,X_41480))),or(X_41481,not(X_41480)))),
inference(resolve,[$cnf( theorem(or(or(X_41481,not(X_41480)),not(not(or(X_41479,X_41480))))) )],[refute_0_170,refute_0_59]) ).
cnf(refute_0_172,plain,
or(not(not(or(X_41479,X_41480))),or(X_41481,not(X_41480))) = implies(not(or(X_41479,X_41480)),or(X_41481,not(X_41480))),
inference(subst,[],[refute_0_25:[bind(X,$fot(not(or(X_41479,X_41480)))),bind(Y,$fot(or(X_41481,not(X_41480))))]]) ).
cnf(refute_0_173,plain,
( or(not(not(or(X_41479,X_41480))),or(X_41481,not(X_41480))) != implies(not(or(X_41479,X_41480)),or(X_41481,not(X_41480)))
| ~ theorem(or(not(not(or(X_41479,X_41480))),or(X_41481,not(X_41480))))
| theorem(implies(not(or(X_41479,X_41480)),or(X_41481,not(X_41480)))) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(not(or(X_41479,X_41480))),or(X_41481,not(X_41480)))) ),[0],$fot(implies(not(or(X_41479,X_41480)),or(X_41481,not(X_41480))))]]) ).
cnf(refute_0_174,plain,
( ~ theorem(or(not(not(or(X_41479,X_41480))),or(X_41481,not(X_41480))))
| theorem(implies(not(or(X_41479,X_41480)),or(X_41481,not(X_41480)))) ),
inference(resolve,[$cnf( $equal(or(not(not(or(X_41479,X_41480))),or(X_41481,not(X_41480))),implies(not(or(X_41479,X_41480)),or(X_41481,not(X_41480)))) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
theorem(implies(not(or(X_41479,X_41480)),or(X_41481,not(X_41480)))),
inference(resolve,[$cnf( theorem(or(not(not(or(X_41479,X_41480))),or(X_41481,not(X_41480)))) )],[refute_0_171,refute_0_174]) ).
cnf(refute_0_176,plain,
theorem(implies(not(or(not(X),X_41483)),or(X_41484,not(X_41483)))),
inference(subst,[],[refute_0_175:[bind(X_41479,$fot(not(X))),bind(X_41480,$fot(X_41483)),bind(X_41481,$fot(X_41484))]]) ).
cnf(refute_0_177,plain,
implies(X,X_41483) = or(not(X),X_41483),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_41483))]]) ).
cnf(refute_0_178,plain,
( implies(X,X_41483) != or(not(X),X_41483)
| or(not(X),X_41483) = implies(X,X_41483) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,X_41483))),bind(Y0,$fot(or(not(X),X_41483)))]]) ).
cnf(refute_0_179,plain,
or(not(X),X_41483) = implies(X,X_41483),
inference(resolve,[$cnf( $equal(implies(X,X_41483),or(not(X),X_41483)) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
( or(not(X),X_41483) != implies(X,X_41483)
| ~ theorem(implies(not(or(not(X),X_41483)),or(X_41484,not(X_41483))))
| theorem(implies(not(implies(X,X_41483)),or(X_41484,not(X_41483)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(not(or(not(X),X_41483)),or(X_41484,not(X_41483)))) ),[0,0,0],$fot(implies(X,X_41483))]]) ).
cnf(refute_0_181,plain,
( ~ theorem(implies(not(or(not(X),X_41483)),or(X_41484,not(X_41483))))
| theorem(implies(not(implies(X,X_41483)),or(X_41484,not(X_41483)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_41483),implies(X,X_41483)) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
theorem(implies(not(implies(X,X_41483)),or(X_41484,not(X_41483)))),
inference(resolve,[$cnf( theorem(implies(not(or(not(X),X_41483)),or(X_41484,not(X_41483)))) )],[refute_0_176,refute_0_181]) ).
cnf(refute_0_183,plain,
theorem(implies(not(implies(X_41485,X_41486)),or(not(X_41486),not(X_41486)))),
inference(subst,[],[refute_0_182:[bind(X,$fot(X_41485)),bind(X_41483,$fot(X_41486)),bind(X_41484,$fot(not(X_41486)))]]) ).
cnf(refute_0_184,plain,
theorem(implies(not(implies(X_41485,X_41486)),not(X_41486))),
inference(resolve,[$cnf( theorem(implies(not(implies(X_41485,X_41486)),or(not(X_41486),not(X_41486)))) )],[refute_0_183,refute_0_53]) ).
cnf(refute_0_185,plain,
theorem(implies(not(implies(X_41488,X_41489)),not(X_41489))),
inference(subst,[],[refute_0_184:[bind(X_41485,$fot(X_41488)),bind(X_41486,$fot(X_41489))]]) ).
cnf(refute_0_186,plain,
theorem(implies(not(implies(X_41488,X_41489)),implies(X_839,not(X_41489)))),
inference(resolve,[$cnf( theorem(implies(not(implies(X_41488,X_41489)),not(X_41489))) )],[refute_0_185,refute_0_44]) ).
cnf(refute_0_187,plain,
theorem(implies(not(implies(p,q)),implies(p,not(q)))),
inference(subst,[],[refute_0_186:[bind(X_41488,$fot(p)),bind(X_41489,$fot(q)),bind(X_839,$fot(p))]]) ).
cnf(refute_0_188,plain,
$false,
inference(resolve,[$cnf( theorem(implies(not(implies(p,q)),implies(p,not(q)))) )],[refute_0_187,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL205-3 : 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 10:49:46 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 39.50/39.74 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 39.50/39.74
% 39.50/39.74 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 39.50/39.76
%------------------------------------------------------------------------------