TSTP Solution File: LCL250-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL250-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 12:51:08 EDT 2022
% Result : Unsatisfiable 29.93s 30.15s
% Output : CNFRefutation 29.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 41
% Syntax : Number of clauses : 202 ( 105 unt; 0 nHn; 94 RR)
% Number of literals : 333 ( 118 equ; 132 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 475 ( 19 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(and_defn,axiom,
and(P,Q) = not(or(not(P),not(Q))) ).
cnf(prove_this,negated_conjecture,
~ theorem(implies(implies(q,r),implies(and(p,q),r))) ).
cnf(refute_0_0,plain,
( ~ axiom(implies(or(X_57,implies(X_56,X_58)),implies(X_56,or(X_57,X_58))))
| theorem(implies(or(X_57,implies(X_56,X_58)),implies(X_56,or(X_57,X_58)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_57,implies(X_56,X_58)),implies(X_56,or(X_57,X_58)))))]]) ).
cnf(refute_0_1,plain,
axiom(implies(or(X_37,or(not(X),X_39)),or(not(X),or(X_37,X_39)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_37)),bind(B,$fot(not(X))),bind(C,$fot(X_39))]]) ).
cnf(refute_0_2,plain,
implies(X,or(X_37,X_39)) = or(not(X),or(X_37,X_39)),
inference(subst,[],[implies_definition:[bind(Y,$fot(or(X_37,X_39)))]]) ).
cnf(refute_0_3,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_4,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_5,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( implies(X,or(X_37,X_39)) != or(not(X),or(X_37,X_39))
| or(not(X),or(X_37,X_39)) = implies(X,or(X_37,X_39)) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(implies(X,or(X_37,X_39)))),bind(Y0,$fot(or(not(X),or(X_37,X_39))))]]) ).
cnf(refute_0_7,plain,
or(not(X),or(X_37,X_39)) = implies(X,or(X_37,X_39)),
inference(resolve,[$cnf( $equal(implies(X,or(X_37,X_39)),or(not(X),or(X_37,X_39))) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
( or(not(X),or(X_37,X_39)) != implies(X,or(X_37,X_39))
| ~ axiom(implies(or(X_37,or(not(X),X_39)),or(not(X),or(X_37,X_39))))
| axiom(implies(or(X_37,or(not(X),X_39)),implies(X,or(X_37,X_39)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(X_37,or(not(X),X_39)),or(not(X),or(X_37,X_39)))) ),[0,1],$fot(implies(X,or(X_37,X_39)))]]) ).
cnf(refute_0_9,plain,
( ~ axiom(implies(or(X_37,or(not(X),X_39)),or(not(X),or(X_37,X_39))))
| axiom(implies(or(X_37,or(not(X),X_39)),implies(X,or(X_37,X_39)))) ),
inference(resolve,[$cnf( $equal(or(not(X),or(X_37,X_39)),implies(X,or(X_37,X_39))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
axiom(implies(or(X_37,or(not(X),X_39)),implies(X,or(X_37,X_39)))),
inference(resolve,[$cnf( axiom(implies(or(X_37,or(not(X),X_39)),or(not(X),or(X_37,X_39)))) )],[refute_0_1,refute_0_9]) ).
cnf(refute_0_11,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_12,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_11]) ).
cnf(refute_0_13,plain,
or(not(X),X_39) = implies(X,X_39),
inference(subst,[],[refute_0_12:[bind(Y,$fot(X_39))]]) ).
cnf(refute_0_14,plain,
or(X_37,or(not(X),X_39)) = or(X_37,or(not(X),X_39)),
introduced(tautology,[refl,[$fot(or(X_37,or(not(X),X_39)))]]) ).
cnf(refute_0_15,plain,
( or(X_37,or(not(X),X_39)) != or(X_37,or(not(X),X_39))
| or(not(X),X_39) != implies(X,X_39)
| or(X_37,or(not(X),X_39)) = or(X_37,implies(X,X_39)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_37,or(not(X),X_39)),or(X_37,or(not(X),X_39))) ),[1,1],$fot(implies(X,X_39))]]) ).
cnf(refute_0_16,plain,
( or(not(X),X_39) != implies(X,X_39)
| or(X_37,or(not(X),X_39)) = or(X_37,implies(X,X_39)) ),
inference(resolve,[$cnf( $equal(or(X_37,or(not(X),X_39)),or(X_37,or(not(X),X_39))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
or(X_37,or(not(X),X_39)) = or(X_37,implies(X,X_39)),
inference(resolve,[$cnf( $equal(or(not(X),X_39),implies(X,X_39)) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
implies(or(X_37,or(not(X),X_39)),implies(X,or(X_37,X_39))) = implies(or(X_37,or(not(X),X_39)),implies(X,or(X_37,X_39))),
introduced(tautology,[refl,[$fot(implies(or(X_37,or(not(X),X_39)),implies(X,or(X_37,X_39))))]]) ).
cnf(refute_0_19,plain,
( implies(or(X_37,or(not(X),X_39)),implies(X,or(X_37,X_39))) != implies(or(X_37,or(not(X),X_39)),implies(X,or(X_37,X_39)))
| or(X_37,or(not(X),X_39)) != or(X_37,implies(X,X_39))
| implies(or(X_37,or(not(X),X_39)),implies(X,or(X_37,X_39))) = implies(or(X_37,implies(X,X_39)),implies(X,or(X_37,X_39))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_37,or(not(X),X_39)),implies(X,or(X_37,X_39))),implies(or(X_37,or(not(X),X_39)),implies(X,or(X_37,X_39)))) ),[1,0],$fot(or(X_37,implies(X,X_39)))]]) ).
cnf(refute_0_20,plain,
( or(X_37,or(not(X),X_39)) != or(X_37,implies(X,X_39))
| implies(or(X_37,or(not(X),X_39)),implies(X,or(X_37,X_39))) = implies(or(X_37,implies(X,X_39)),implies(X,or(X_37,X_39))) ),
inference(resolve,[$cnf( $equal(implies(or(X_37,or(not(X),X_39)),implies(X,or(X_37,X_39))),implies(or(X_37,or(not(X),X_39)),implies(X,or(X_37,X_39)))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
implies(or(X_37,or(not(X),X_39)),implies(X,or(X_37,X_39))) = implies(or(X_37,implies(X,X_39)),implies(X,or(X_37,X_39))),
inference(resolve,[$cnf( $equal(or(X_37,or(not(X),X_39)),or(X_37,implies(X,X_39))) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
( implies(or(X_37,or(not(X),X_39)),implies(X,or(X_37,X_39))) != implies(or(X_37,implies(X,X_39)),implies(X,or(X_37,X_39)))
| ~ axiom(implies(or(X_37,or(not(X),X_39)),implies(X,or(X_37,X_39))))
| axiom(implies(or(X_37,implies(X,X_39)),implies(X,or(X_37,X_39)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(X_37,or(not(X),X_39)),implies(X,or(X_37,X_39)))) ),[0],$fot(implies(or(X_37,implies(X,X_39)),implies(X,or(X_37,X_39))))]]) ).
cnf(refute_0_23,plain,
( ~ axiom(implies(or(X_37,or(not(X),X_39)),implies(X,or(X_37,X_39))))
| axiom(implies(or(X_37,implies(X,X_39)),implies(X,or(X_37,X_39)))) ),
inference(resolve,[$cnf( $equal(implies(or(X_37,or(not(X),X_39)),implies(X,or(X_37,X_39))),implies(or(X_37,implies(X,X_39)),implies(X,or(X_37,X_39)))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
axiom(implies(or(X_37,implies(X,X_39)),implies(X,or(X_37,X_39)))),
inference(resolve,[$cnf( axiom(implies(or(X_37,or(not(X),X_39)),implies(X,or(X_37,X_39)))) )],[refute_0_10,refute_0_23]) ).
cnf(refute_0_25,plain,
axiom(implies(or(X_57,implies(X_56,X_58)),implies(X_56,or(X_57,X_58)))),
inference(subst,[],[refute_0_24:[bind(X,$fot(X_56)),bind(X_37,$fot(X_57)),bind(X_39,$fot(X_58))]]) ).
cnf(refute_0_26,plain,
theorem(implies(or(X_57,implies(X_56,X_58)),implies(X_56,or(X_57,X_58)))),
inference(resolve,[$cnf( axiom(implies(or(X_57,implies(X_56,X_58)),implies(X_56,or(X_57,X_58)))) )],[refute_0_25,refute_0_0]) ).
cnf(refute_0_27,plain,
theorem(implies(or(not(X),implies(X_59,X_61)),implies(X_59,or(not(X),X_61)))),
inference(subst,[],[refute_0_26:[bind(X_56,$fot(X_59)),bind(X_57,$fot(not(X))),bind(X_58,$fot(X_61))]]) ).
cnf(refute_0_28,plain,
implies(X,X_61) = or(not(X),X_61),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_61))]]) ).
cnf(refute_0_29,plain,
( implies(X,X_61) != or(not(X),X_61)
| or(not(X),X_61) = implies(X,X_61) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(implies(X,X_61))),bind(Y0,$fot(or(not(X),X_61)))]]) ).
cnf(refute_0_30,plain,
or(not(X),X_61) = implies(X,X_61),
inference(resolve,[$cnf( $equal(implies(X,X_61),or(not(X),X_61)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( or(not(X),X_61) != implies(X,X_61)
| ~ theorem(implies(or(not(X),implies(X_59,X_61)),implies(X_59,or(not(X),X_61))))
| theorem(implies(or(not(X),implies(X_59,X_61)),implies(X_59,implies(X,X_61)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),implies(X_59,X_61)),implies(X_59,or(not(X),X_61)))) ),[0,1,1],$fot(implies(X,X_61))]]) ).
cnf(refute_0_32,plain,
( ~ theorem(implies(or(not(X),implies(X_59,X_61)),implies(X_59,or(not(X),X_61))))
| theorem(implies(or(not(X),implies(X_59,X_61)),implies(X_59,implies(X,X_61)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_61),implies(X,X_61)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
theorem(implies(or(not(X),implies(X_59,X_61)),implies(X_59,implies(X,X_61)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),implies(X_59,X_61)),implies(X_59,or(not(X),X_61)))) )],[refute_0_27,refute_0_32]) ).
cnf(refute_0_34,plain,
or(not(X),implies(X_59,X_61)) = implies(X,implies(X_59,X_61)),
inference(subst,[],[refute_0_12:[bind(Y,$fot(implies(X_59,X_61)))]]) ).
cnf(refute_0_35,plain,
implies(or(not(X),implies(X_59,X_61)),implies(X_59,implies(X,X_61))) = implies(or(not(X),implies(X_59,X_61)),implies(X_59,implies(X,X_61))),
introduced(tautology,[refl,[$fot(implies(or(not(X),implies(X_59,X_61)),implies(X_59,implies(X,X_61))))]]) ).
cnf(refute_0_36,plain,
( implies(or(not(X),implies(X_59,X_61)),implies(X_59,implies(X,X_61))) != implies(or(not(X),implies(X_59,X_61)),implies(X_59,implies(X,X_61)))
| or(not(X),implies(X_59,X_61)) != implies(X,implies(X_59,X_61))
| implies(or(not(X),implies(X_59,X_61)),implies(X_59,implies(X,X_61))) = implies(implies(X,implies(X_59,X_61)),implies(X_59,implies(X,X_61))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),implies(X_59,X_61)),implies(X_59,implies(X,X_61))),implies(or(not(X),implies(X_59,X_61)),implies(X_59,implies(X,X_61)))) ),[1,0],$fot(implies(X,implies(X_59,X_61)))]]) ).
cnf(refute_0_37,plain,
( or(not(X),implies(X_59,X_61)) != implies(X,implies(X_59,X_61))
| implies(or(not(X),implies(X_59,X_61)),implies(X_59,implies(X,X_61))) = implies(implies(X,implies(X_59,X_61)),implies(X_59,implies(X,X_61))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),implies(X_59,X_61)),implies(X_59,implies(X,X_61))),implies(or(not(X),implies(X_59,X_61)),implies(X_59,implies(X,X_61)))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
implies(or(not(X),implies(X_59,X_61)),implies(X_59,implies(X,X_61))) = implies(implies(X,implies(X_59,X_61)),implies(X_59,implies(X,X_61))),
inference(resolve,[$cnf( $equal(or(not(X),implies(X_59,X_61)),implies(X,implies(X_59,X_61))) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
( implies(or(not(X),implies(X_59,X_61)),implies(X_59,implies(X,X_61))) != implies(implies(X,implies(X_59,X_61)),implies(X_59,implies(X,X_61)))
| ~ theorem(implies(or(not(X),implies(X_59,X_61)),implies(X_59,implies(X,X_61))))
| theorem(implies(implies(X,implies(X_59,X_61)),implies(X_59,implies(X,X_61)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),implies(X_59,X_61)),implies(X_59,implies(X,X_61)))) ),[0],$fot(implies(implies(X,implies(X_59,X_61)),implies(X_59,implies(X,X_61))))]]) ).
cnf(refute_0_40,plain,
( ~ theorem(implies(or(not(X),implies(X_59,X_61)),implies(X_59,implies(X,X_61))))
| theorem(implies(implies(X,implies(X_59,X_61)),implies(X_59,implies(X,X_61)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),implies(X_59,X_61)),implies(X_59,implies(X,X_61))),implies(implies(X,implies(X_59,X_61)),implies(X_59,implies(X,X_61)))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
theorem(implies(implies(X,implies(X_59,X_61)),implies(X_59,implies(X,X_61)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),implies(X_59,X_61)),implies(X_59,implies(X,X_61)))) )],[refute_0_33,refute_0_40]) ).
cnf(refute_0_42,plain,
( ~ theorem(implies(X,implies(X_59,X_61)))
| ~ theorem(implies(implies(X,implies(X_59,X_61)),implies(X_59,implies(X,X_61))))
| theorem(implies(X_59,implies(X,X_61))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_59,implies(X,X_61)))),bind(Y,$fot(implies(X,implies(X_59,X_61))))]]) ).
cnf(refute_0_43,plain,
( ~ theorem(implies(X,implies(X_59,X_61)))
| theorem(implies(X_59,implies(X,X_61))) ),
inference(resolve,[$cnf( theorem(implies(implies(X,implies(X_59,X_61)),implies(X_59,implies(X,X_61)))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ theorem(implies(and(X_22426,X_22427),implies(implies(X_22427,X_22428),X_22428)))
| theorem(implies(implies(X_22427,X_22428),implies(and(X_22426,X_22427),X_22428))) ),
inference(subst,[],[refute_0_43:[bind(X,$fot(and(X_22426,X_22427))),bind(X_59,$fot(implies(X_22427,X_22428))),bind(X_61,$fot(X_22428))]]) ).
cnf(refute_0_45,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,$fot(implies(or(X_7,X_8),or(X_8,X_7))))]]) ).
cnf(refute_0_46,plain,
axiom(implies(or(X_7,X_8),or(X_8,X_7))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_7)),bind(B,$fot(X_8))]]) ).
cnf(refute_0_47,plain,
theorem(implies(or(X_7,X_8),or(X_8,X_7))),
inference(resolve,[$cnf( axiom(implies(or(X_7,X_8),or(X_8,X_7))) )],[refute_0_46,refute_0_45]) ).
cnf(refute_0_48,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_49,plain,
( ~ theorem(or(X_7,X_8))
| theorem(or(X_8,X_7)) ),
inference(resolve,[$cnf( theorem(implies(or(X_7,X_8),or(X_8,X_7))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
( ~ theorem(or(implies(implies(X_22376,X_22377),X_22377),not(and(X_22375,X_22376))))
| theorem(or(not(and(X_22375,X_22376)),implies(implies(X_22376,X_22377),X_22377))) ),
inference(subst,[],[refute_0_49:[bind(X_7,$fot(implies(implies(X_22376,X_22377),X_22377))),bind(X_8,$fot(not(and(X_22375,X_22376))))]]) ).
cnf(refute_0_51,plain,
( ~ axiom(implies(A,or(B,A)))
| theorem(implies(A,or(B,A))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(A,or(B,A))))]]) ).
cnf(refute_0_52,plain,
theorem(implies(A,or(B,A))),
inference(resolve,[$cnf( axiom(implies(A,or(B,A))) )],[axiom_1_3,refute_0_51]) ).
cnf(refute_0_53,plain,
theorem(implies(X_78,or(B,X_78))),
inference(subst,[],[refute_0_52:[bind(A,$fot(X_78))]]) ).
cnf(refute_0_54,plain,
( ~ theorem(X_78)
| ~ theorem(implies(X_78,or(B,X_78)))
| theorem(or(B,X_78)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(B,X_78))),bind(Y,$fot(X_78))]]) ).
cnf(refute_0_55,plain,
( ~ theorem(X_78)
| theorem(or(B,X_78)) ),
inference(resolve,[$cnf( theorem(implies(X_78,or(B,X_78))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
( ~ theorem(or(implies(implies(X_963,X_964),X_964),not(X_963)))
| theorem(or(B,or(implies(implies(X_963,X_964),X_964),not(X_963)))) ),
inference(subst,[],[refute_0_55:[bind(X_78,$fot(or(implies(implies(X_963,X_964),X_964),not(X_963))))]]) ).
cnf(refute_0_57,plain,
theorem(implies(or(not(X_11),X_8),or(X_8,not(X_11)))),
inference(subst,[],[refute_0_47:[bind(X_7,$fot(not(X_11)))]]) ).
cnf(refute_0_58,plain,
implies(X_11,X_8) = or(not(X_11),X_8),
inference(subst,[],[implies_definition:[bind(X,$fot(X_11)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_59,plain,
( implies(X_11,X_8) != or(not(X_11),X_8)
| or(not(X_11),X_8) = implies(X_11,X_8) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(implies(X_11,X_8))),bind(Y0,$fot(or(not(X_11),X_8)))]]) ).
cnf(refute_0_60,plain,
or(not(X_11),X_8) = implies(X_11,X_8),
inference(resolve,[$cnf( $equal(implies(X_11,X_8),or(not(X_11),X_8)) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
( or(not(X_11),X_8) != implies(X_11,X_8)
| ~ theorem(implies(or(not(X_11),X_8),or(X_8,not(X_11))))
| theorem(implies(implies(X_11,X_8),or(X_8,not(X_11)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X_11),X_8),or(X_8,not(X_11)))) ),[0,0],$fot(implies(X_11,X_8))]]) ).
cnf(refute_0_62,plain,
( ~ theorem(implies(or(not(X_11),X_8),or(X_8,not(X_11))))
| theorem(implies(implies(X_11,X_8),or(X_8,not(X_11)))) ),
inference(resolve,[$cnf( $equal(or(not(X_11),X_8),implies(X_11,X_8)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
theorem(implies(implies(X_11,X_8),or(X_8,not(X_11)))),
inference(resolve,[$cnf( theorem(implies(or(not(X_11),X_8),or(X_8,not(X_11)))) )],[refute_0_57,refute_0_62]) ).
cnf(refute_0_64,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_65,plain,
( ~ theorem(implies(X_11,X_8))
| theorem(or(X_8,not(X_11))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_11,X_8),or(X_8,not(X_11)))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
( ~ theorem(implies(X_961,implies(implies(X_961,X_962),X_962)))
| theorem(or(implies(implies(X_961,X_962),X_962),not(X_961))) ),
inference(subst,[],[refute_0_65:[bind(X_11,$fot(X_961)),bind(X_8,$fot(implies(implies(X_961,X_962),X_962)))]]) ).
cnf(refute_0_67,plain,
( ~ axiom(implies(implies(X_71,or(X_72,X_73)),or(X_72,implies(X_71,X_73))))
| theorem(implies(implies(X_71,or(X_72,X_73)),or(X_72,implies(X_71,X_73)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_71,or(X_72,X_73)),or(X_72,implies(X_71,X_73)))))]]) ).
cnf(refute_0_68,plain,
axiom(implies(or(not(X),or(X_38,X_39)),or(X_38,or(not(X),X_39)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(not(X))),bind(B,$fot(X_38)),bind(C,$fot(X_39))]]) ).
cnf(refute_0_69,plain,
( or(not(X),X_39) != implies(X,X_39)
| ~ axiom(implies(or(not(X),or(X_38,X_39)),or(X_38,or(not(X),X_39))))
| axiom(implies(or(not(X),or(X_38,X_39)),or(X_38,implies(X,X_39)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_38,X_39)),or(X_38,or(not(X),X_39)))) ),[0,1,1],$fot(implies(X,X_39))]]) ).
cnf(refute_0_70,plain,
( ~ axiom(implies(or(not(X),or(X_38,X_39)),or(X_38,or(not(X),X_39))))
| axiom(implies(or(not(X),or(X_38,X_39)),or(X_38,implies(X,X_39)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_39),implies(X,X_39)) )],[refute_0_13,refute_0_69]) ).
cnf(refute_0_71,plain,
axiom(implies(or(not(X),or(X_38,X_39)),or(X_38,implies(X,X_39)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_38,X_39)),or(X_38,or(not(X),X_39)))) )],[refute_0_68,refute_0_70]) ).
cnf(refute_0_72,plain,
or(not(X),or(X_38,X_39)) = implies(X,or(X_38,X_39)),
inference(subst,[],[refute_0_12:[bind(Y,$fot(or(X_38,X_39)))]]) ).
cnf(refute_0_73,plain,
implies(or(not(X),or(X_38,X_39)),or(X_38,implies(X,X_39))) = implies(or(not(X),or(X_38,X_39)),or(X_38,implies(X,X_39))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_38,X_39)),or(X_38,implies(X,X_39))))]]) ).
cnf(refute_0_74,plain,
( implies(or(not(X),or(X_38,X_39)),or(X_38,implies(X,X_39))) != implies(or(not(X),or(X_38,X_39)),or(X_38,implies(X,X_39)))
| or(not(X),or(X_38,X_39)) != implies(X,or(X_38,X_39))
| implies(or(not(X),or(X_38,X_39)),or(X_38,implies(X,X_39))) = implies(implies(X,or(X_38,X_39)),or(X_38,implies(X,X_39))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_38,X_39)),or(X_38,implies(X,X_39))),implies(or(not(X),or(X_38,X_39)),or(X_38,implies(X,X_39)))) ),[1,0],$fot(implies(X,or(X_38,X_39)))]]) ).
cnf(refute_0_75,plain,
( or(not(X),or(X_38,X_39)) != implies(X,or(X_38,X_39))
| implies(or(not(X),or(X_38,X_39)),or(X_38,implies(X,X_39))) = implies(implies(X,or(X_38,X_39)),or(X_38,implies(X,X_39))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_38,X_39)),or(X_38,implies(X,X_39))),implies(or(not(X),or(X_38,X_39)),or(X_38,implies(X,X_39)))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
implies(or(not(X),or(X_38,X_39)),or(X_38,implies(X,X_39))) = implies(implies(X,or(X_38,X_39)),or(X_38,implies(X,X_39))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_38,X_39)),implies(X,or(X_38,X_39))) )],[refute_0_72,refute_0_75]) ).
cnf(refute_0_77,plain,
( implies(or(not(X),or(X_38,X_39)),or(X_38,implies(X,X_39))) != implies(implies(X,or(X_38,X_39)),or(X_38,implies(X,X_39)))
| ~ axiom(implies(or(not(X),or(X_38,X_39)),or(X_38,implies(X,X_39))))
| axiom(implies(implies(X,or(X_38,X_39)),or(X_38,implies(X,X_39)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_38,X_39)),or(X_38,implies(X,X_39)))) ),[0],$fot(implies(implies(X,or(X_38,X_39)),or(X_38,implies(X,X_39))))]]) ).
cnf(refute_0_78,plain,
( ~ axiom(implies(or(not(X),or(X_38,X_39)),or(X_38,implies(X,X_39))))
| axiom(implies(implies(X,or(X_38,X_39)),or(X_38,implies(X,X_39)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_38,X_39)),or(X_38,implies(X,X_39))),implies(implies(X,or(X_38,X_39)),or(X_38,implies(X,X_39)))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
axiom(implies(implies(X,or(X_38,X_39)),or(X_38,implies(X,X_39)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_38,X_39)),or(X_38,implies(X,X_39)))) )],[refute_0_71,refute_0_78]) ).
cnf(refute_0_80,plain,
axiom(implies(implies(X_71,or(X_72,X_73)),or(X_72,implies(X_71,X_73)))),
inference(subst,[],[refute_0_79:[bind(X,$fot(X_71)),bind(X_38,$fot(X_72)),bind(X_39,$fot(X_73))]]) ).
cnf(refute_0_81,plain,
theorem(implies(implies(X_71,or(X_72,X_73)),or(X_72,implies(X_71,X_73)))),
inference(resolve,[$cnf( axiom(implies(implies(X_71,or(X_72,X_73)),or(X_72,implies(X_71,X_73)))) )],[refute_0_80,refute_0_67]) ).
cnf(refute_0_82,plain,
( ~ theorem(implies(X_71,or(X_72,X_73)))
| ~ theorem(implies(implies(X_71,or(X_72,X_73)),or(X_72,implies(X_71,X_73))))
| theorem(or(X_72,implies(X_71,X_73))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_72,implies(X_71,X_73)))),bind(Y,$fot(implies(X_71,or(X_72,X_73))))]]) ).
cnf(refute_0_83,plain,
( ~ theorem(implies(X_71,or(X_72,X_73)))
| theorem(or(X_72,implies(X_71,X_73))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_71,or(X_72,X_73)),or(X_72,implies(X_71,X_73)))) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
( ~ theorem(implies(or(X_72,X_73),or(X_72,X_73)))
| theorem(or(X_72,implies(or(X_72,X_73),X_73))) ),
inference(subst,[],[refute_0_83:[bind(X_71,$fot(or(X_72,X_73)))]]) ).
cnf(refute_0_85,plain,
( ~ axiom(implies(or(A,A),A))
| theorem(implies(or(A,A),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_86,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[$cnf( axiom(implies(or(A,A),A)) )],[axiom_1_2,refute_0_85]) ).
cnf(refute_0_87,plain,
theorem(implies(or(X_77,X_77),X_77)),
inference(subst,[],[refute_0_86:[bind(A,$fot(X_77))]]) ).
cnf(refute_0_88,plain,
( ~ theorem(implies(or(X_77,X_77),X_77))
| ~ theorem(or(X_77,X_77))
| theorem(X_77) ),
inference(subst,[],[rule_2:[bind(X,$fot(X_77)),bind(Y,$fot(or(X_77,X_77)))]]) ).
cnf(refute_0_89,plain,
( ~ theorem(or(X_77,X_77))
| theorem(X_77) ),
inference(resolve,[$cnf( theorem(implies(or(X_77,X_77),X_77)) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
( ~ theorem(or(implies(X_827,X_827),implies(X_827,X_827)))
| theorem(implies(X_827,X_827)) ),
inference(subst,[],[refute_0_89:[bind(X_77,$fot(implies(X_827,X_827)))]]) ).
cnf(refute_0_91,plain,
theorem(implies(X_825,or(X_824,X_825))),
inference(subst,[],[refute_0_52:[bind(A,$fot(X_825)),bind(B,$fot(X_824))]]) ).
cnf(refute_0_92,plain,
( ~ theorem(implies(X_825,or(X_824,X_825)))
| theorem(or(X_824,implies(X_825,X_825))) ),
inference(subst,[],[refute_0_83:[bind(X_71,$fot(X_825)),bind(X_72,$fot(X_824)),bind(X_73,$fot(X_825))]]) ).
cnf(refute_0_93,plain,
theorem(or(X_824,implies(X_825,X_825))),
inference(resolve,[$cnf( theorem(implies(X_825,or(X_824,X_825))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
theorem(or(implies(X_827,X_827),implies(X_827,X_827))),
inference(subst,[],[refute_0_93:[bind(X_824,$fot(implies(X_827,X_827))),bind(X_825,$fot(X_827))]]) ).
cnf(refute_0_95,plain,
theorem(implies(X_827,X_827)),
inference(resolve,[$cnf( theorem(or(implies(X_827,X_827),implies(X_827,X_827))) )],[refute_0_94,refute_0_90]) ).
cnf(refute_0_96,plain,
theorem(implies(or(X_72,X_73),or(X_72,X_73))),
inference(subst,[],[refute_0_95:[bind(X_827,$fot(or(X_72,X_73)))]]) ).
cnf(refute_0_97,plain,
theorem(or(X_72,implies(or(X_72,X_73),X_73))),
inference(resolve,[$cnf( theorem(implies(or(X_72,X_73),or(X_72,X_73))) )],[refute_0_96,refute_0_84]) ).
cnf(refute_0_98,plain,
theorem(or(not(X),implies(or(not(X),X_960),X_960))),
inference(subst,[],[refute_0_97:[bind(X_72,$fot(not(X))),bind(X_73,$fot(X_960))]]) ).
cnf(refute_0_99,plain,
implies(X,X_960) = or(not(X),X_960),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_960))]]) ).
cnf(refute_0_100,plain,
( implies(X,X_960) != or(not(X),X_960)
| or(not(X),X_960) = implies(X,X_960) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(implies(X,X_960))),bind(Y0,$fot(or(not(X),X_960)))]]) ).
cnf(refute_0_101,plain,
or(not(X),X_960) = implies(X,X_960),
inference(resolve,[$cnf( $equal(implies(X,X_960),or(not(X),X_960)) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
( or(not(X),X_960) != implies(X,X_960)
| ~ theorem(or(not(X),implies(or(not(X),X_960),X_960)))
| theorem(or(not(X),implies(implies(X,X_960),X_960))) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(X),implies(or(not(X),X_960),X_960))) ),[0,1,0],$fot(implies(X,X_960))]]) ).
cnf(refute_0_103,plain,
( ~ theorem(or(not(X),implies(or(not(X),X_960),X_960)))
| theorem(or(not(X),implies(implies(X,X_960),X_960))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_960),implies(X,X_960)) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
theorem(or(not(X),implies(implies(X,X_960),X_960))),
inference(resolve,[$cnf( theorem(or(not(X),implies(or(not(X),X_960),X_960))) )],[refute_0_98,refute_0_103]) ).
cnf(refute_0_105,plain,
or(not(X),implies(implies(X,X_960),X_960)) = implies(X,implies(implies(X,X_960),X_960)),
inference(subst,[],[refute_0_12:[bind(Y,$fot(implies(implies(X,X_960),X_960)))]]) ).
cnf(refute_0_106,plain,
( or(not(X),implies(implies(X,X_960),X_960)) != implies(X,implies(implies(X,X_960),X_960))
| ~ theorem(or(not(X),implies(implies(X,X_960),X_960)))
| theorem(implies(X,implies(implies(X,X_960),X_960))) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(X),implies(implies(X,X_960),X_960))) ),[0],$fot(implies(X,implies(implies(X,X_960),X_960)))]]) ).
cnf(refute_0_107,plain,
( ~ theorem(or(not(X),implies(implies(X,X_960),X_960)))
| theorem(implies(X,implies(implies(X,X_960),X_960))) ),
inference(resolve,[$cnf( $equal(or(not(X),implies(implies(X,X_960),X_960)),implies(X,implies(implies(X,X_960),X_960))) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
theorem(implies(X,implies(implies(X,X_960),X_960))),
inference(resolve,[$cnf( theorem(or(not(X),implies(implies(X,X_960),X_960))) )],[refute_0_104,refute_0_107]) ).
cnf(refute_0_109,plain,
theorem(implies(X_961,implies(implies(X_961,X_962),X_962))),
inference(subst,[],[refute_0_108:[bind(X,$fot(X_961)),bind(X_960,$fot(X_962))]]) ).
cnf(refute_0_110,plain,
theorem(or(implies(implies(X_961,X_962),X_962),not(X_961))),
inference(resolve,[$cnf( theorem(implies(X_961,implies(implies(X_961,X_962),X_962))) )],[refute_0_109,refute_0_66]) ).
cnf(refute_0_111,plain,
theorem(or(implies(implies(X_963,X_964),X_964),not(X_963))),
inference(subst,[],[refute_0_110:[bind(X_961,$fot(X_963)),bind(X_962,$fot(X_964))]]) ).
cnf(refute_0_112,plain,
theorem(or(B,or(implies(implies(X_963,X_964),X_964),not(X_963)))),
inference(resolve,[$cnf( theorem(or(implies(implies(X_963,X_964),X_964),not(X_963))) )],[refute_0_111,refute_0_56]) ).
cnf(refute_0_113,plain,
theorem(or(X_7228,or(implies(implies(X_963,X_964),X_964),not(X_963)))),
inference(subst,[],[refute_0_112:[bind(B,$fot(X_7228))]]) ).
cnf(refute_0_114,plain,
( ~ axiom(implies(or(X_37,or(X_38,X_39)),or(X_38,or(X_37,X_39))))
| theorem(implies(or(X_37,or(X_38,X_39)),or(X_38,or(X_37,X_39)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_37,or(X_38,X_39)),or(X_38,or(X_37,X_39)))))]]) ).
cnf(refute_0_115,plain,
axiom(implies(or(X_37,or(X_38,X_39)),or(X_38,or(X_37,X_39)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_37)),bind(B,$fot(X_38)),bind(C,$fot(X_39))]]) ).
cnf(refute_0_116,plain,
theorem(implies(or(X_37,or(X_38,X_39)),or(X_38,or(X_37,X_39)))),
inference(resolve,[$cnf( axiom(implies(or(X_37,or(X_38,X_39)),or(X_38,or(X_37,X_39)))) )],[refute_0_115,refute_0_114]) ).
cnf(refute_0_117,plain,
( ~ theorem(implies(or(X_37,or(X_38,X_39)),or(X_38,or(X_37,X_39))))
| ~ theorem(or(X_37,or(X_38,X_39)))
| theorem(or(X_38,or(X_37,X_39))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_38,or(X_37,X_39)))),bind(Y,$fot(or(X_37,or(X_38,X_39))))]]) ).
cnf(refute_0_118,plain,
( ~ theorem(or(X_37,or(X_38,X_39)))
| theorem(or(X_38,or(X_37,X_39))) ),
inference(resolve,[$cnf( theorem(implies(or(X_37,or(X_38,X_39)),or(X_38,or(X_37,X_39)))) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
( ~ theorem(or(X_7228,or(implies(implies(X_963,X_964),X_964),not(X_963))))
| theorem(or(implies(implies(X_963,X_964),X_964),or(X_7228,not(X_963)))) ),
inference(subst,[],[refute_0_118:[bind(X_37,$fot(X_7228)),bind(X_38,$fot(implies(implies(X_963,X_964),X_964))),bind(X_39,$fot(not(X_963)))]]) ).
cnf(refute_0_120,plain,
theorem(or(implies(implies(X_963,X_964),X_964),or(X_7228,not(X_963)))),
inference(resolve,[$cnf( theorem(or(X_7228,or(implies(implies(X_963,X_964),X_964),not(X_963)))) )],[refute_0_113,refute_0_119]) ).
cnf(refute_0_121,plain,
theorem(or(implies(implies(X_7292,X_7293),X_7293),or(not(X),not(X_7292)))),
inference(subst,[],[refute_0_120:[bind(X_7228,$fot(not(X))),bind(X_963,$fot(X_7292)),bind(X_964,$fot(X_7293))]]) ).
cnf(refute_0_122,plain,
implies(X,not(X_7292)) = or(not(X),not(X_7292)),
inference(subst,[],[implies_definition:[bind(Y,$fot(not(X_7292)))]]) ).
cnf(refute_0_123,plain,
( implies(X,not(X_7292)) != or(not(X),not(X_7292))
| or(not(X),not(X_7292)) = implies(X,not(X_7292)) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(implies(X,not(X_7292)))),bind(Y0,$fot(or(not(X),not(X_7292))))]]) ).
cnf(refute_0_124,plain,
or(not(X),not(X_7292)) = implies(X,not(X_7292)),
inference(resolve,[$cnf( $equal(implies(X,not(X_7292)),or(not(X),not(X_7292))) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
( or(not(X),not(X_7292)) != implies(X,not(X_7292))
| ~ theorem(or(implies(implies(X_7292,X_7293),X_7293),or(not(X),not(X_7292))))
| theorem(or(implies(implies(X_7292,X_7293),X_7293),implies(X,not(X_7292)))) ),
introduced(tautology,[equality,[$cnf( theorem(or(implies(implies(X_7292,X_7293),X_7293),or(not(X),not(X_7292)))) ),[0,1],$fot(implies(X,not(X_7292)))]]) ).
cnf(refute_0_126,plain,
( ~ theorem(or(implies(implies(X_7292,X_7293),X_7293),or(not(X),not(X_7292))))
| theorem(or(implies(implies(X_7292,X_7293),X_7293),implies(X,not(X_7292)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_7292)),implies(X,not(X_7292))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
theorem(or(implies(implies(X_7292,X_7293),X_7293),implies(X,not(X_7292)))),
inference(resolve,[$cnf( theorem(or(implies(implies(X_7292,X_7293),X_7293),or(not(X),not(X_7292)))) )],[refute_0_121,refute_0_126]) ).
cnf(refute_0_128,plain,
( ~ theorem(implies(or(X_3114,X_3113),or(X_3114,not(not(X_3113)))))
| ~ theorem(or(X_3114,X_3113))
| theorem(or(X_3114,not(not(X_3113)))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_3114,not(not(X_3113))))),bind(Y,$fot(or(X_3114,X_3113)))]]) ).
cnf(refute_0_129,plain,
theorem(implies(or(X_7,not(X_11)),or(not(X_11),X_7))),
inference(subst,[],[refute_0_47:[bind(X_8,$fot(not(X_11)))]]) ).
cnf(refute_0_130,plain,
implies(X_11,X_7) = or(not(X_11),X_7),
inference(subst,[],[implies_definition:[bind(X,$fot(X_11)),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_131,plain,
( implies(X_11,X_7) != or(not(X_11),X_7)
| or(not(X_11),X_7) = implies(X_11,X_7) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(implies(X_11,X_7))),bind(Y0,$fot(or(not(X_11),X_7)))]]) ).
cnf(refute_0_132,plain,
or(not(X_11),X_7) = implies(X_11,X_7),
inference(resolve,[$cnf( $equal(implies(X_11,X_7),or(not(X_11),X_7)) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
( or(not(X_11),X_7) != implies(X_11,X_7)
| ~ theorem(implies(or(X_7,not(X_11)),or(not(X_11),X_7)))
| theorem(implies(or(X_7,not(X_11)),implies(X_11,X_7))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(X_7,not(X_11)),or(not(X_11),X_7))) ),[0,1],$fot(implies(X_11,X_7))]]) ).
cnf(refute_0_134,plain,
( ~ theorem(implies(or(X_7,not(X_11)),or(not(X_11),X_7)))
| theorem(implies(or(X_7,not(X_11)),implies(X_11,X_7))) ),
inference(resolve,[$cnf( $equal(or(not(X_11),X_7),implies(X_11,X_7)) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
theorem(implies(or(X_7,not(X_11)),implies(X_11,X_7))),
inference(resolve,[$cnf( theorem(implies(or(X_7,not(X_11)),or(not(X_11),X_7))) )],[refute_0_129,refute_0_134]) ).
cnf(refute_0_136,plain,
( ~ theorem(implies(or(X_7,not(X_11)),implies(X_11,X_7)))
| ~ theorem(or(X_7,not(X_11)))
| theorem(implies(X_11,X_7)) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_11,X_7))),bind(Y,$fot(or(X_7,not(X_11))))]]) ).
cnf(refute_0_137,plain,
( ~ theorem(or(X_7,not(X_11)))
| theorem(implies(X_11,X_7)) ),
inference(resolve,[$cnf( theorem(implies(or(X_7,not(X_11)),implies(X_11,X_7))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
( ~ theorem(or(not(X),not(X_346)))
| theorem(implies(X_346,not(X))) ),
inference(subst,[],[refute_0_137:[bind(X_11,$fot(X_346)),bind(X_7,$fot(not(X)))]]) ).
cnf(refute_0_139,plain,
implies(X,not(X_346)) = or(not(X),not(X_346)),
inference(subst,[],[implies_definition:[bind(Y,$fot(not(X_346)))]]) ).
cnf(refute_0_140,plain,
( implies(X,not(X_346)) != or(not(X),not(X_346))
| or(not(X),not(X_346)) = implies(X,not(X_346)) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(implies(X,not(X_346)))),bind(Y0,$fot(or(not(X),not(X_346))))]]) ).
cnf(refute_0_141,plain,
or(not(X),not(X_346)) = implies(X,not(X_346)),
inference(resolve,[$cnf( $equal(implies(X,not(X_346)),or(not(X),not(X_346))) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
( or(not(X),not(X_346)) != implies(X,not(X_346))
| ~ theorem(implies(X,not(X_346)))
| theorem(or(not(X),not(X_346))) ),
introduced(tautology,[equality,[$cnf( ~ theorem(or(not(X),not(X_346))) ),[0],$fot(implies(X,not(X_346)))]]) ).
cnf(refute_0_143,plain,
( ~ theorem(implies(X,not(X_346)))
| theorem(or(not(X),not(X_346))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_346)),implies(X,not(X_346))) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
( ~ theorem(implies(X,not(X_346)))
| theorem(implies(X_346,not(X))) ),
inference(resolve,[$cnf( theorem(or(not(X),not(X_346))) )],[refute_0_143,refute_0_138]) ).
cnf(refute_0_145,plain,
( ~ theorem(implies(not(X_346),not(X_346)))
| theorem(implies(X_346,not(not(X_346)))) ),
inference(subst,[],[refute_0_144:[bind(X,$fot(not(X_346)))]]) ).
cnf(refute_0_146,plain,
theorem(implies(not(X_346),not(X_346))),
inference(subst,[],[refute_0_95:[bind(X_827,$fot(not(X_346)))]]) ).
cnf(refute_0_147,plain,
theorem(implies(X_346,not(not(X_346)))),
inference(resolve,[$cnf( theorem(implies(not(X_346),not(X_346))) )],[refute_0_146,refute_0_145]) ).
cnf(refute_0_148,plain,
theorem(implies(X_3098,not(not(X_3098)))),
inference(subst,[],[refute_0_147:[bind(X_346,$fot(X_3098))]]) ).
cnf(refute_0_149,plain,
( ~ axiom(implies(implies(X_25,X_26),implies(or(X_27,X_25),or(X_27,X_26))))
| theorem(implies(implies(X_25,X_26),implies(or(X_27,X_25),or(X_27,X_26)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_25,X_26),implies(or(X_27,X_25),or(X_27,X_26)))))]]) ).
cnf(refute_0_150,plain,
axiom(implies(implies(X_25,X_26),implies(or(X_27,X_25),or(X_27,X_26)))),
inference(subst,[],[axiom_1_6:[bind(A,$fot(X_25)),bind(B,$fot(X_26)),bind(C,$fot(X_27))]]) ).
cnf(refute_0_151,plain,
theorem(implies(implies(X_25,X_26),implies(or(X_27,X_25),or(X_27,X_26)))),
inference(resolve,[$cnf( axiom(implies(implies(X_25,X_26),implies(or(X_27,X_25),or(X_27,X_26)))) )],[refute_0_150,refute_0_149]) ).
cnf(refute_0_152,plain,
( ~ theorem(implies(X_25,X_26))
| ~ theorem(implies(implies(X_25,X_26),implies(or(X_27,X_25),or(X_27,X_26))))
| theorem(implies(or(X_27,X_25),or(X_27,X_26))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(or(X_27,X_25),or(X_27,X_26)))),bind(Y,$fot(implies(X_25,X_26)))]]) ).
cnf(refute_0_153,plain,
( ~ theorem(implies(X_25,X_26))
| theorem(implies(or(X_27,X_25),or(X_27,X_26))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_25,X_26),implies(or(X_27,X_25),or(X_27,X_26)))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
( ~ theorem(implies(X_3098,not(not(X_3098))))
| theorem(implies(or(X_3100,X_3098),or(X_3100,not(not(X_3098))))) ),
inference(subst,[],[refute_0_153:[bind(X_25,$fot(X_3098)),bind(X_26,$fot(not(not(X_3098)))),bind(X_27,$fot(X_3100))]]) ).
cnf(refute_0_155,plain,
theorem(implies(or(X_3100,X_3098),or(X_3100,not(not(X_3098))))),
inference(resolve,[$cnf( theorem(implies(X_3098,not(not(X_3098)))) )],[refute_0_148,refute_0_154]) ).
cnf(refute_0_156,plain,
theorem(implies(or(X_3114,X_3113),or(X_3114,not(not(X_3113))))),
inference(subst,[],[refute_0_155:[bind(X_3098,$fot(X_3113)),bind(X_3100,$fot(X_3114))]]) ).
cnf(refute_0_157,plain,
( ~ theorem(or(X_3114,X_3113))
| theorem(or(X_3114,not(not(X_3113)))) ),
inference(resolve,[$cnf( theorem(implies(or(X_3114,X_3113),or(X_3114,not(not(X_3113))))) )],[refute_0_156,refute_0_128]) ).
cnf(refute_0_158,plain,
( ~ theorem(or(implies(implies(X_7292,X_7293),X_7293),implies(X,not(X_7292))))
| theorem(or(implies(implies(X_7292,X_7293),X_7293),not(not(implies(X,not(X_7292)))))) ),
inference(subst,[],[refute_0_157:[bind(X_3113,$fot(implies(X,not(X_7292)))),bind(X_3114,$fot(implies(implies(X_7292,X_7293),X_7293)))]]) ).
cnf(refute_0_159,plain,
theorem(or(implies(implies(X_7292,X_7293),X_7293),not(not(implies(X,not(X_7292)))))),
inference(resolve,[$cnf( theorem(or(implies(implies(X_7292,X_7293),X_7293),implies(X,not(X_7292)))) )],[refute_0_127,refute_0_158]) ).
cnf(refute_0_160,plain,
or(not(P),not(Q)) = implies(P,not(Q)),
inference(subst,[],[refute_0_12:[bind(X,$fot(P)),bind(Y,$fot(not(Q)))]]) ).
cnf(refute_0_161,plain,
not(or(not(P),not(Q))) = not(or(not(P),not(Q))),
introduced(tautology,[refl,[$fot(not(or(not(P),not(Q))))]]) ).
cnf(refute_0_162,plain,
( not(or(not(P),not(Q))) != not(or(not(P),not(Q)))
| or(not(P),not(Q)) != implies(P,not(Q))
| not(or(not(P),not(Q))) = not(implies(P,not(Q))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(P),not(Q))),not(or(not(P),not(Q)))) ),[1,0],$fot(implies(P,not(Q)))]]) ).
cnf(refute_0_163,plain,
( or(not(P),not(Q)) != implies(P,not(Q))
| not(or(not(P),not(Q))) = not(implies(P,not(Q))) ),
inference(resolve,[$cnf( $equal(not(or(not(P),not(Q))),not(or(not(P),not(Q)))) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
not(or(not(P),not(Q))) = not(implies(P,not(Q))),
inference(resolve,[$cnf( $equal(or(not(P),not(Q)),implies(P,not(Q))) )],[refute_0_160,refute_0_163]) ).
cnf(refute_0_165,plain,
( and(P,Q) != not(or(not(P),not(Q)))
| not(or(not(P),not(Q))) != not(implies(P,not(Q)))
| and(P,Q) = not(implies(P,not(Q))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(P,Q),not(implies(P,not(Q)))) ),[0],$fot(not(or(not(P),not(Q))))]]) ).
cnf(refute_0_166,plain,
( and(P,Q) != not(or(not(P),not(Q)))
| and(P,Q) = not(implies(P,not(Q))) ),
inference(resolve,[$cnf( $equal(not(or(not(P),not(Q))),not(implies(P,not(Q)))) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
and(P,Q) = not(implies(P,not(Q))),
inference(resolve,[$cnf( $equal(and(P,Q),not(or(not(P),not(Q)))) )],[and_defn,refute_0_166]) ).
cnf(refute_0_168,plain,
( and(P,Q) != not(implies(P,not(Q)))
| not(implies(P,not(Q))) = and(P,Q) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(and(P,Q))),bind(Y0,$fot(not(implies(P,not(Q)))))]]) ).
cnf(refute_0_169,plain,
not(implies(P,not(Q))) = and(P,Q),
inference(resolve,[$cnf( $equal(and(P,Q),not(implies(P,not(Q)))) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
not(implies(X,not(X_7292))) = and(X,X_7292),
inference(subst,[],[refute_0_169:[bind(P,$fot(X)),bind(Q,$fot(X_7292))]]) ).
cnf(refute_0_171,plain,
not(not(implies(X,not(X_7292)))) = not(not(implies(X,not(X_7292)))),
introduced(tautology,[refl,[$fot(not(not(implies(X,not(X_7292)))))]]) ).
cnf(refute_0_172,plain,
( not(implies(X,not(X_7292))) != and(X,X_7292)
| not(not(implies(X,not(X_7292)))) != not(not(implies(X,not(X_7292))))
| not(not(implies(X,not(X_7292)))) = not(and(X,X_7292)) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(implies(X,not(X_7292)))),not(not(implies(X,not(X_7292))))) ),[1,0],$fot(and(X,X_7292))]]) ).
cnf(refute_0_173,plain,
( not(implies(X,not(X_7292))) != and(X,X_7292)
| not(not(implies(X,not(X_7292)))) = not(and(X,X_7292)) ),
inference(resolve,[$cnf( $equal(not(not(implies(X,not(X_7292)))),not(not(implies(X,not(X_7292))))) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
not(not(implies(X,not(X_7292)))) = not(and(X,X_7292)),
inference(resolve,[$cnf( $equal(not(implies(X,not(X_7292))),and(X,X_7292)) )],[refute_0_170,refute_0_173]) ).
cnf(refute_0_175,plain,
or(implies(implies(X_7292,X_7293),X_7293),not(not(implies(X,not(X_7292))))) = or(implies(implies(X_7292,X_7293),X_7293),not(not(implies(X,not(X_7292))))),
introduced(tautology,[refl,[$fot(or(implies(implies(X_7292,X_7293),X_7293),not(not(implies(X,not(X_7292))))))]]) ).
cnf(refute_0_176,plain,
( not(not(implies(X,not(X_7292)))) != not(and(X,X_7292))
| or(implies(implies(X_7292,X_7293),X_7293),not(not(implies(X,not(X_7292))))) != or(implies(implies(X_7292,X_7293),X_7293),not(not(implies(X,not(X_7292)))))
| or(implies(implies(X_7292,X_7293),X_7293),not(not(implies(X,not(X_7292))))) = or(implies(implies(X_7292,X_7293),X_7293),not(and(X,X_7292))) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(implies(X_7292,X_7293),X_7293),not(not(implies(X,not(X_7292))))),or(implies(implies(X_7292,X_7293),X_7293),not(not(implies(X,not(X_7292)))))) ),[1,1],$fot(not(and(X,X_7292)))]]) ).
cnf(refute_0_177,plain,
( not(not(implies(X,not(X_7292)))) != not(and(X,X_7292))
| or(implies(implies(X_7292,X_7293),X_7293),not(not(implies(X,not(X_7292))))) = or(implies(implies(X_7292,X_7293),X_7293),not(and(X,X_7292))) ),
inference(resolve,[$cnf( $equal(or(implies(implies(X_7292,X_7293),X_7293),not(not(implies(X,not(X_7292))))),or(implies(implies(X_7292,X_7293),X_7293),not(not(implies(X,not(X_7292)))))) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
or(implies(implies(X_7292,X_7293),X_7293),not(not(implies(X,not(X_7292))))) = or(implies(implies(X_7292,X_7293),X_7293),not(and(X,X_7292))),
inference(resolve,[$cnf( $equal(not(not(implies(X,not(X_7292)))),not(and(X,X_7292))) )],[refute_0_174,refute_0_177]) ).
cnf(refute_0_179,plain,
( or(implies(implies(X_7292,X_7293),X_7293),not(not(implies(X,not(X_7292))))) != or(implies(implies(X_7292,X_7293),X_7293),not(and(X,X_7292)))
| ~ theorem(or(implies(implies(X_7292,X_7293),X_7293),not(not(implies(X,not(X_7292))))))
| theorem(or(implies(implies(X_7292,X_7293),X_7293),not(and(X,X_7292)))) ),
introduced(tautology,[equality,[$cnf( theorem(or(implies(implies(X_7292,X_7293),X_7293),not(not(implies(X,not(X_7292)))))) ),[0],$fot(or(implies(implies(X_7292,X_7293),X_7293),not(and(X,X_7292))))]]) ).
cnf(refute_0_180,plain,
( ~ theorem(or(implies(implies(X_7292,X_7293),X_7293),not(not(implies(X,not(X_7292))))))
| theorem(or(implies(implies(X_7292,X_7293),X_7293),not(and(X,X_7292)))) ),
inference(resolve,[$cnf( $equal(or(implies(implies(X_7292,X_7293),X_7293),not(not(implies(X,not(X_7292))))),or(implies(implies(X_7292,X_7293),X_7293),not(and(X,X_7292)))) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
theorem(or(implies(implies(X_7292,X_7293),X_7293),not(and(X,X_7292)))),
inference(resolve,[$cnf( theorem(or(implies(implies(X_7292,X_7293),X_7293),not(not(implies(X,not(X_7292)))))) )],[refute_0_159,refute_0_180]) ).
cnf(refute_0_182,plain,
theorem(or(implies(implies(X_22376,X_22377),X_22377),not(and(X_22375,X_22376)))),
inference(subst,[],[refute_0_181:[bind(X,$fot(X_22375)),bind(X_7292,$fot(X_22376)),bind(X_7293,$fot(X_22377))]]) ).
cnf(refute_0_183,plain,
theorem(or(not(and(X_22375,X_22376)),implies(implies(X_22376,X_22377),X_22377))),
inference(resolve,[$cnf( theorem(or(implies(implies(X_22376,X_22377),X_22377),not(and(X_22375,X_22376)))) )],[refute_0_182,refute_0_50]) ).
cnf(refute_0_184,plain,
or(not(and(X_22375,X_22376)),implies(implies(X_22376,X_22377),X_22377)) = implies(and(X_22375,X_22376),implies(implies(X_22376,X_22377),X_22377)),
inference(subst,[],[refute_0_12:[bind(X,$fot(and(X_22375,X_22376))),bind(Y,$fot(implies(implies(X_22376,X_22377),X_22377)))]]) ).
cnf(refute_0_185,plain,
( or(not(and(X_22375,X_22376)),implies(implies(X_22376,X_22377),X_22377)) != implies(and(X_22375,X_22376),implies(implies(X_22376,X_22377),X_22377))
| ~ theorem(or(not(and(X_22375,X_22376)),implies(implies(X_22376,X_22377),X_22377)))
| theorem(implies(and(X_22375,X_22376),implies(implies(X_22376,X_22377),X_22377))) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(and(X_22375,X_22376)),implies(implies(X_22376,X_22377),X_22377))) ),[0],$fot(implies(and(X_22375,X_22376),implies(implies(X_22376,X_22377),X_22377)))]]) ).
cnf(refute_0_186,plain,
( ~ theorem(or(not(and(X_22375,X_22376)),implies(implies(X_22376,X_22377),X_22377)))
| theorem(implies(and(X_22375,X_22376),implies(implies(X_22376,X_22377),X_22377))) ),
inference(resolve,[$cnf( $equal(or(not(and(X_22375,X_22376)),implies(implies(X_22376,X_22377),X_22377)),implies(and(X_22375,X_22376),implies(implies(X_22376,X_22377),X_22377))) )],[refute_0_184,refute_0_185]) ).
cnf(refute_0_187,plain,
theorem(implies(and(X_22375,X_22376),implies(implies(X_22376,X_22377),X_22377))),
inference(resolve,[$cnf( theorem(or(not(and(X_22375,X_22376)),implies(implies(X_22376,X_22377),X_22377))) )],[refute_0_183,refute_0_186]) ).
cnf(refute_0_188,plain,
theorem(implies(and(X_22426,X_22427),implies(implies(X_22427,X_22428),X_22428))),
inference(subst,[],[refute_0_187:[bind(X_22375,$fot(X_22426)),bind(X_22376,$fot(X_22427)),bind(X_22377,$fot(X_22428))]]) ).
cnf(refute_0_189,plain,
theorem(implies(implies(X_22427,X_22428),implies(and(X_22426,X_22427),X_22428))),
inference(resolve,[$cnf( theorem(implies(and(X_22426,X_22427),implies(implies(X_22427,X_22428),X_22428))) )],[refute_0_188,refute_0_44]) ).
cnf(refute_0_190,plain,
theorem(implies(implies(q,r),implies(and(p,q),r))),
inference(subst,[],[refute_0_189:[bind(X_22426,$fot(p)),bind(X_22427,$fot(q)),bind(X_22428,$fot(r))]]) ).
cnf(refute_0_191,plain,
$false,
inference(resolve,[$cnf( theorem(implies(implies(q,r),implies(and(p,q),r))) )],[refute_0_190,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL250-3 : TPTP v8.1.0. Released v2.3.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n016.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 17:21:30 EDT 2022
% 0.18/0.34 % CPUTime :
% 0.18/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 29.93/30.15 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.93/30.15
% 29.93/30.15 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 29.93/30.17
%------------------------------------------------------------------------------