TSTP Solution File: LCL239-10 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL239-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 12:51:01 EDT 2022
% Result : Unsatisfiable 0.48s 0.63s
% Output : CNFRefutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 67
% Syntax : Number of clauses : 219 ( 120 unt; 0 nHn; 101 RR)
% Number of literals : 365 ( 364 equ; 148 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-4 aty)
% Number of variables : 430 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ifeq_axiom,axiom,
ifeq(A,A,B,C) = B ).
cnf(axiom_1_2,axiom,
axiom(implies(or(A,A),A)) = true ).
cnf(axiom_1_3,axiom,
axiom(implies(A,or(B,A))) = true ).
cnf(axiom_1_4,axiom,
axiom(implies(or(A,B),or(B,A))) = true ).
cnf(axiom_1_5,axiom,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) = true ).
cnf(implies_definition,axiom,
implies(X,Y) = or(not(X),Y) ).
cnf(rule_1,axiom,
ifeq(axiom(X),true,theorem(X),true) = true ).
cnf(rule_2,axiom,
ifeq(theorem(implies(Y,X)),true,ifeq(theorem(Y),true,theorem(X),true),true) = true ).
cnf(and_defn,axiom,
and(P,Q) = not(or(not(P),not(Q))) ).
cnf(prove_this,negated_conjecture,
theorem(not(and(p,not(p)))) != true ).
cnf(refute_0_0,plain,
ifeq(theorem(implies(Y,not(not(Y)))),true,ifeq(theorem(Y),true,theorem(not(not(Y))),true),true) = true,
inference(subst,[],[rule_2:[bind(X,$fot(not(not(Y))))]]) ).
cnf(refute_0_1,plain,
ifeq(theorem(implies(or(X_22,not(X)),implies(X,X_22))),true,ifeq(theorem(or(X_22,not(X))),true,theorem(implies(X,X_22)),true),true) = true,
inference(subst,[],[rule_2:[bind(X,$fot(implies(X,X_22))),bind(Y,$fot(or(X_22,not(X))))]]) ).
cnf(refute_0_2,plain,
ifeq(axiom(implies(or(X_20,X_21),or(X_21,X_20))),true,theorem(implies(or(X_20,X_21),or(X_21,X_20))),true) = true,
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_20,X_21),or(X_21,X_20))))]]) ).
cnf(refute_0_3,plain,
axiom(implies(or(X_20,X_21),or(X_21,X_20))) = true,
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_20)),bind(B,$fot(X_21))]]) ).
cnf(refute_0_4,plain,
( axiom(implies(or(X_20,X_21),or(X_21,X_20))) != true
| ifeq(axiom(implies(or(X_20,X_21),or(X_21,X_20))),true,theorem(implies(or(X_20,X_21),or(X_21,X_20))),true) != true
| ifeq(true,true,theorem(implies(or(X_20,X_21),or(X_21,X_20))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(axiom(implies(or(X_20,X_21),or(X_21,X_20))),true,theorem(implies(or(X_20,X_21),or(X_21,X_20))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_5,plain,
( ifeq(axiom(implies(or(X_20,X_21),or(X_21,X_20))),true,theorem(implies(or(X_20,X_21),or(X_21,X_20))),true) != true
| ifeq(true,true,theorem(implies(or(X_20,X_21),or(X_21,X_20))),true) = true ),
inference(resolve,[$cnf( $equal(axiom(implies(or(X_20,X_21),or(X_21,X_20))),true) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
ifeq(true,true,theorem(implies(or(X_20,X_21),or(X_21,X_20))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(axiom(implies(or(X_20,X_21),or(X_21,X_20))),true,theorem(implies(or(X_20,X_21),or(X_21,X_20))),true),true) )],[refute_0_2,refute_0_5]) ).
cnf(refute_0_7,plain,
ifeq(true,true,theorem(implies(or(X_20,X_21),or(X_21,X_20))),true) = theorem(implies(or(X_20,X_21),or(X_21,X_20))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(implies(or(X_20,X_21),or(X_21,X_20))))),bind(C,$fot(true))]]) ).
cnf(refute_0_8,plain,
( ifeq(true,true,theorem(implies(or(X_20,X_21),or(X_21,X_20))),true) != theorem(implies(or(X_20,X_21),or(X_21,X_20)))
| ifeq(true,true,theorem(implies(or(X_20,X_21),or(X_21,X_20))),true) != true
| theorem(implies(or(X_20,X_21),or(X_21,X_20))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(implies(or(X_20,X_21),or(X_21,X_20))),true),true) ),[0],$fot(theorem(implies(or(X_20,X_21),or(X_21,X_20))))]]) ).
cnf(refute_0_9,plain,
( ifeq(true,true,theorem(implies(or(X_20,X_21),or(X_21,X_20))),true) != true
| theorem(implies(or(X_20,X_21),or(X_21,X_20))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(or(X_20,X_21),or(X_21,X_20))),true),theorem(implies(or(X_20,X_21),or(X_21,X_20)))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
theorem(implies(or(X_20,X_21),or(X_21,X_20))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(or(X_20,X_21),or(X_21,X_20))),true),true) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
theorem(implies(or(X_22,not(X)),or(not(X),X_22))) = true,
inference(subst,[],[refute_0_10:[bind(X_20,$fot(X_22)),bind(X_21,$fot(not(X)))]]) ).
cnf(refute_0_12,plain,
implies(X,X_22) = or(not(X),X_22),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_22))]]) ).
cnf(refute_0_13,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_14,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_15,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( implies(X,X_22) != or(not(X),X_22)
| or(not(X),X_22) = implies(X,X_22) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,X_22))),bind(Y0,$fot(or(not(X),X_22)))]]) ).
cnf(refute_0_17,plain,
or(not(X),X_22) = implies(X,X_22),
inference(resolve,[$cnf( $equal(implies(X,X_22),or(not(X),X_22)) )],[refute_0_12,refute_0_16]) ).
cnf(refute_0_18,plain,
( or(not(X),X_22) != implies(X,X_22)
| theorem(implies(or(X_22,not(X)),or(not(X),X_22))) != true
| theorem(implies(or(X_22,not(X)),implies(X,X_22))) = true ),
introduced(tautology,[equality,[$cnf( $equal(theorem(implies(or(X_22,not(X)),or(not(X),X_22))),true) ),[0,0,1],$fot(implies(X,X_22))]]) ).
cnf(refute_0_19,plain,
( theorem(implies(or(X_22,not(X)),or(not(X),X_22))) != true
| theorem(implies(or(X_22,not(X)),implies(X,X_22))) = true ),
inference(resolve,[$cnf( $equal(or(not(X),X_22),implies(X,X_22)) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
theorem(implies(or(X_22,not(X)),implies(X,X_22))) = true,
inference(resolve,[$cnf( $equal(theorem(implies(or(X_22,not(X)),or(not(X),X_22))),true) )],[refute_0_11,refute_0_19]) ).
cnf(refute_0_21,plain,
( ifeq(theorem(implies(or(X_22,not(X)),implies(X,X_22))),true,ifeq(theorem(or(X_22,not(X))),true,theorem(implies(X,X_22)),true),true) != true
| theorem(implies(or(X_22,not(X)),implies(X,X_22))) != true
| ifeq(true,true,ifeq(theorem(or(X_22,not(X))),true,theorem(implies(X,X_22)),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(or(X_22,not(X)),implies(X,X_22))),true,ifeq(theorem(or(X_22,not(X))),true,theorem(implies(X,X_22)),true),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_22,plain,
( ifeq(theorem(implies(or(X_22,not(X)),implies(X,X_22))),true,ifeq(theorem(or(X_22,not(X))),true,theorem(implies(X,X_22)),true),true) != true
| ifeq(true,true,ifeq(theorem(or(X_22,not(X))),true,theorem(implies(X,X_22)),true),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(or(X_22,not(X)),implies(X,X_22))),true) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
ifeq(true,true,ifeq(theorem(or(X_22,not(X))),true,theorem(implies(X,X_22)),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(or(X_22,not(X)),implies(X,X_22))),true,ifeq(theorem(or(X_22,not(X))),true,theorem(implies(X,X_22)),true),true),true) )],[refute_0_1,refute_0_22]) ).
cnf(refute_0_24,plain,
ifeq(true,true,ifeq(theorem(or(X_22,not(X))),true,theorem(implies(X,X_22)),true),true) = ifeq(theorem(or(X_22,not(X))),true,theorem(implies(X,X_22)),true),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(ifeq(theorem(or(X_22,not(X))),true,theorem(implies(X,X_22)),true))),bind(C,$fot(true))]]) ).
cnf(refute_0_25,plain,
( ifeq(true,true,ifeq(theorem(or(X_22,not(X))),true,theorem(implies(X,X_22)),true),true) != ifeq(theorem(or(X_22,not(X))),true,theorem(implies(X,X_22)),true)
| ifeq(true,true,ifeq(theorem(or(X_22,not(X))),true,theorem(implies(X,X_22)),true),true) != true
| ifeq(theorem(or(X_22,not(X))),true,theorem(implies(X,X_22)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,ifeq(theorem(or(X_22,not(X))),true,theorem(implies(X,X_22)),true),true),true) ),[0],$fot(ifeq(theorem(or(X_22,not(X))),true,theorem(implies(X,X_22)),true))]]) ).
cnf(refute_0_26,plain,
( ifeq(true,true,ifeq(theorem(or(X_22,not(X))),true,theorem(implies(X,X_22)),true),true) != true
| ifeq(theorem(or(X_22,not(X))),true,theorem(implies(X,X_22)),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(theorem(or(X_22,not(X))),true,theorem(implies(X,X_22)),true),true),ifeq(theorem(or(X_22,not(X))),true,theorem(implies(X,X_22)),true)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
ifeq(theorem(or(X_22,not(X))),true,theorem(implies(X,X_22)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(theorem(or(X_22,not(X))),true,theorem(implies(X,X_22)),true),true),true) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
ifeq(theorem(or(not(X),not(X_89))),true,theorem(implies(X_89,not(X))),true) = true,
inference(subst,[],[refute_0_27:[bind(X,$fot(X_89)),bind(X_22,$fot(not(X)))]]) ).
cnf(refute_0_29,plain,
implies(X,not(X_89)) = or(not(X),not(X_89)),
inference(subst,[],[implies_definition:[bind(Y,$fot(not(X_89)))]]) ).
cnf(refute_0_30,plain,
( implies(X,not(X_89)) != or(not(X),not(X_89))
| or(not(X),not(X_89)) = implies(X,not(X_89)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,not(X_89)))),bind(Y0,$fot(or(not(X),not(X_89))))]]) ).
cnf(refute_0_31,plain,
or(not(X),not(X_89)) = implies(X,not(X_89)),
inference(resolve,[$cnf( $equal(implies(X,not(X_89)),or(not(X),not(X_89))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( ifeq(theorem(or(not(X),not(X_89))),true,theorem(implies(X_89,not(X))),true) != true
| or(not(X),not(X_89)) != implies(X,not(X_89))
| ifeq(theorem(implies(X,not(X_89))),true,theorem(implies(X_89,not(X))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(or(not(X),not(X_89))),true,theorem(implies(X_89,not(X))),true),true) ),[0,0,0],$fot(implies(X,not(X_89)))]]) ).
cnf(refute_0_33,plain,
( ifeq(theorem(or(not(X),not(X_89))),true,theorem(implies(X_89,not(X))),true) != true
| ifeq(theorem(implies(X,not(X_89))),true,theorem(implies(X_89,not(X))),true) = true ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_89)),implies(X,not(X_89))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
ifeq(theorem(implies(X,not(X_89))),true,theorem(implies(X_89,not(X))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(or(not(X),not(X_89))),true,theorem(implies(X_89,not(X))),true),true) )],[refute_0_28,refute_0_33]) ).
cnf(refute_0_35,plain,
ifeq(theorem(implies(not(X_89),not(X_89))),true,theorem(implies(X_89,not(not(X_89)))),true) = true,
inference(subst,[],[refute_0_34:[bind(X,$fot(not(X_89)))]]) ).
cnf(refute_0_36,plain,
ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,ifeq(theorem(implies(or(X_4,X_4),X_4)),true,theorem(X_30),true),true) = true,
inference(subst,[],[rule_2:[bind(X,$fot(X_30)),bind(Y,$fot(implies(or(X_4,X_4),X_4)))]]) ).
cnf(refute_0_37,plain,
ifeq(axiom(implies(or(X_4,X_4),X_4)),true,theorem(implies(or(X_4,X_4),X_4)),true) = true,
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_4,X_4),X_4)))]]) ).
cnf(refute_0_38,plain,
axiom(implies(or(X_4,X_4),X_4)) = true,
inference(subst,[],[axiom_1_2:[bind(A,$fot(X_4))]]) ).
cnf(refute_0_39,plain,
( axiom(implies(or(X_4,X_4),X_4)) != true
| ifeq(axiom(implies(or(X_4,X_4),X_4)),true,theorem(implies(or(X_4,X_4),X_4)),true) != true
| ifeq(true,true,theorem(implies(or(X_4,X_4),X_4)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(axiom(implies(or(X_4,X_4),X_4)),true,theorem(implies(or(X_4,X_4),X_4)),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_40,plain,
( ifeq(axiom(implies(or(X_4,X_4),X_4)),true,theorem(implies(or(X_4,X_4),X_4)),true) != true
| ifeq(true,true,theorem(implies(or(X_4,X_4),X_4)),true) = true ),
inference(resolve,[$cnf( $equal(axiom(implies(or(X_4,X_4),X_4)),true) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
ifeq(true,true,theorem(implies(or(X_4,X_4),X_4)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(axiom(implies(or(X_4,X_4),X_4)),true,theorem(implies(or(X_4,X_4),X_4)),true),true) )],[refute_0_37,refute_0_40]) ).
cnf(refute_0_42,plain,
ifeq(true,true,theorem(implies(or(X_4,X_4),X_4)),true) = theorem(implies(or(X_4,X_4),X_4)),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(implies(or(X_4,X_4),X_4)))),bind(C,$fot(true))]]) ).
cnf(refute_0_43,plain,
( ifeq(true,true,theorem(implies(or(X_4,X_4),X_4)),true) != theorem(implies(or(X_4,X_4),X_4))
| ifeq(true,true,theorem(implies(or(X_4,X_4),X_4)),true) != true
| theorem(implies(or(X_4,X_4),X_4)) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(implies(or(X_4,X_4),X_4)),true),true) ),[0],$fot(theorem(implies(or(X_4,X_4),X_4)))]]) ).
cnf(refute_0_44,plain,
( ifeq(true,true,theorem(implies(or(X_4,X_4),X_4)),true) != true
| theorem(implies(or(X_4,X_4),X_4)) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(or(X_4,X_4),X_4)),true),theorem(implies(or(X_4,X_4),X_4))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
theorem(implies(or(X_4,X_4),X_4)) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(or(X_4,X_4),X_4)),true),true) )],[refute_0_41,refute_0_44]) ).
cnf(refute_0_46,plain,
( ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,ifeq(theorem(implies(or(X_4,X_4),X_4)),true,theorem(X_30),true),true) != true
| theorem(implies(or(X_4,X_4),X_4)) != true
| ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,ifeq(true,true,theorem(X_30),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,ifeq(theorem(implies(or(X_4,X_4),X_4)),true,theorem(X_30),true),true),true) ),[0,2,0],$fot(true)]]) ).
cnf(refute_0_47,plain,
( ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,ifeq(theorem(implies(or(X_4,X_4),X_4)),true,theorem(X_30),true),true) != true
| ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,ifeq(true,true,theorem(X_30),true),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(or(X_4,X_4),X_4)),true) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,ifeq(true,true,theorem(X_30),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,ifeq(theorem(implies(or(X_4,X_4),X_4)),true,theorem(X_30),true),true),true) )],[refute_0_36,refute_0_47]) ).
cnf(refute_0_49,plain,
ifeq(true,true,theorem(X_30),true) = theorem(X_30),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(X_30))),bind(C,$fot(true))]]) ).
cnf(refute_0_50,plain,
ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,ifeq(true,true,theorem(X_30),true),true) = ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,ifeq(true,true,theorem(X_30),true),true),
introduced(tautology,[refl,[$fot(ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,ifeq(true,true,theorem(X_30),true),true))]]) ).
cnf(refute_0_51,plain,
( ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,ifeq(true,true,theorem(X_30),true),true) != ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,ifeq(true,true,theorem(X_30),true),true)
| ifeq(true,true,theorem(X_30),true) != theorem(X_30)
| ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,ifeq(true,true,theorem(X_30),true),true) = ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,theorem(X_30),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,ifeq(true,true,theorem(X_30),true),true),ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,ifeq(true,true,theorem(X_30),true),true)) ),[1,2],$fot(theorem(X_30))]]) ).
cnf(refute_0_52,plain,
( ifeq(true,true,theorem(X_30),true) != theorem(X_30)
| ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,ifeq(true,true,theorem(X_30),true),true) = ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,theorem(X_30),true) ),
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,ifeq(true,true,theorem(X_30),true),true),ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,ifeq(true,true,theorem(X_30),true),true)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,ifeq(true,true,theorem(X_30),true),true) = ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,theorem(X_30),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(X_30),true),theorem(X_30)) )],[refute_0_49,refute_0_52]) ).
cnf(refute_0_54,plain,
( ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,ifeq(true,true,theorem(X_30),true),true) != ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,theorem(X_30),true)
| ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,ifeq(true,true,theorem(X_30),true),true) != true
| ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,theorem(X_30),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,ifeq(true,true,theorem(X_30),true),true),true) ),[0],$fot(ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,theorem(X_30),true))]]) ).
cnf(refute_0_55,plain,
( ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,ifeq(true,true,theorem(X_30),true),true) != true
| ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,theorem(X_30),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,ifeq(true,true,theorem(X_30),true),true),ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,theorem(X_30),true)) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,theorem(X_30),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(or(X_4,X_4),X_4),X_30)),true,ifeq(true,true,theorem(X_30),true),true),true) )],[refute_0_48,refute_0_55]) ).
cnf(refute_0_57,plain,
ifeq(theorem(implies(implies(or(X_4,X_4),X_4),implies(X_174,X_174))),true,theorem(implies(X_174,X_174)),true) = true,
inference(subst,[],[refute_0_56:[bind(X_30,$fot(implies(X_174,X_174)))]]) ).
cnf(refute_0_58,plain,
ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,ifeq(theorem(implies(X_6,implies(X_10,X_6))),true,theorem(X_30),true),true) = true,
inference(subst,[],[rule_2:[bind(X,$fot(X_30)),bind(Y,$fot(implies(X_6,implies(X_10,X_6))))]]) ).
cnf(refute_0_59,plain,
ifeq(axiom(implies(X_6,or(X_7,X_6))),true,theorem(implies(X_6,or(X_7,X_6))),true) = true,
inference(subst,[],[rule_1:[bind(X,$fot(implies(X_6,or(X_7,X_6))))]]) ).
cnf(refute_0_60,plain,
axiom(implies(X_6,or(X_7,X_6))) = true,
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_6)),bind(B,$fot(X_7))]]) ).
cnf(refute_0_61,plain,
( axiom(implies(X_6,or(X_7,X_6))) != true
| ifeq(axiom(implies(X_6,or(X_7,X_6))),true,theorem(implies(X_6,or(X_7,X_6))),true) != true
| ifeq(true,true,theorem(implies(X_6,or(X_7,X_6))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(axiom(implies(X_6,or(X_7,X_6))),true,theorem(implies(X_6,or(X_7,X_6))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_62,plain,
( ifeq(axiom(implies(X_6,or(X_7,X_6))),true,theorem(implies(X_6,or(X_7,X_6))),true) != true
| ifeq(true,true,theorem(implies(X_6,or(X_7,X_6))),true) = true ),
inference(resolve,[$cnf( $equal(axiom(implies(X_6,or(X_7,X_6))),true) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
ifeq(true,true,theorem(implies(X_6,or(X_7,X_6))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(axiom(implies(X_6,or(X_7,X_6))),true,theorem(implies(X_6,or(X_7,X_6))),true),true) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
ifeq(true,true,theorem(implies(X_6,or(X_7,X_6))),true) = theorem(implies(X_6,or(X_7,X_6))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(implies(X_6,or(X_7,X_6))))),bind(C,$fot(true))]]) ).
cnf(refute_0_65,plain,
( ifeq(true,true,theorem(implies(X_6,or(X_7,X_6))),true) != theorem(implies(X_6,or(X_7,X_6)))
| ifeq(true,true,theorem(implies(X_6,or(X_7,X_6))),true) != true
| theorem(implies(X_6,or(X_7,X_6))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(implies(X_6,or(X_7,X_6))),true),true) ),[0],$fot(theorem(implies(X_6,or(X_7,X_6))))]]) ).
cnf(refute_0_66,plain,
( ifeq(true,true,theorem(implies(X_6,or(X_7,X_6))),true) != true
| theorem(implies(X_6,or(X_7,X_6))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(X_6,or(X_7,X_6))),true),theorem(implies(X_6,or(X_7,X_6)))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
theorem(implies(X_6,or(X_7,X_6))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(X_6,or(X_7,X_6))),true),true) )],[refute_0_63,refute_0_66]) ).
cnf(refute_0_68,plain,
theorem(implies(X_6,or(not(X_10),X_6))) = true,
inference(subst,[],[refute_0_67:[bind(X_7,$fot(not(X_10)))]]) ).
cnf(refute_0_69,plain,
implies(X_10,X_6) = or(not(X_10),X_6),
inference(subst,[],[implies_definition:[bind(X,$fot(X_10)),bind(Y,$fot(X_6))]]) ).
cnf(refute_0_70,plain,
( implies(X_10,X_6) != or(not(X_10),X_6)
| or(not(X_10),X_6) = implies(X_10,X_6) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X_10,X_6))),bind(Y0,$fot(or(not(X_10),X_6)))]]) ).
cnf(refute_0_71,plain,
or(not(X_10),X_6) = implies(X_10,X_6),
inference(resolve,[$cnf( $equal(implies(X_10,X_6),or(not(X_10),X_6)) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( or(not(X_10),X_6) != implies(X_10,X_6)
| theorem(implies(X_6,or(not(X_10),X_6))) != true
| theorem(implies(X_6,implies(X_10,X_6))) = true ),
introduced(tautology,[equality,[$cnf( $equal(theorem(implies(X_6,or(not(X_10),X_6))),true) ),[0,0,1],$fot(implies(X_10,X_6))]]) ).
cnf(refute_0_73,plain,
( theorem(implies(X_6,or(not(X_10),X_6))) != true
| theorem(implies(X_6,implies(X_10,X_6))) = true ),
inference(resolve,[$cnf( $equal(or(not(X_10),X_6),implies(X_10,X_6)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
theorem(implies(X_6,implies(X_10,X_6))) = true,
inference(resolve,[$cnf( $equal(theorem(implies(X_6,or(not(X_10),X_6))),true) )],[refute_0_68,refute_0_73]) ).
cnf(refute_0_75,plain,
( ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,ifeq(theorem(implies(X_6,implies(X_10,X_6))),true,theorem(X_30),true),true) != true
| theorem(implies(X_6,implies(X_10,X_6))) != true
| ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,ifeq(true,true,theorem(X_30),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,ifeq(theorem(implies(X_6,implies(X_10,X_6))),true,theorem(X_30),true),true),true) ),[0,2,0],$fot(true)]]) ).
cnf(refute_0_76,plain,
( ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,ifeq(theorem(implies(X_6,implies(X_10,X_6))),true,theorem(X_30),true),true) != true
| ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,ifeq(true,true,theorem(X_30),true),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(X_6,implies(X_10,X_6))),true) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,ifeq(true,true,theorem(X_30),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,ifeq(theorem(implies(X_6,implies(X_10,X_6))),true,theorem(X_30),true),true),true) )],[refute_0_58,refute_0_76]) ).
cnf(refute_0_78,plain,
ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,ifeq(true,true,theorem(X_30),true),true) = ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,ifeq(true,true,theorem(X_30),true),true),
introduced(tautology,[refl,[$fot(ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,ifeq(true,true,theorem(X_30),true),true))]]) ).
cnf(refute_0_79,plain,
( ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,ifeq(true,true,theorem(X_30),true),true) != ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,ifeq(true,true,theorem(X_30),true),true)
| ifeq(true,true,theorem(X_30),true) != theorem(X_30)
| ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,ifeq(true,true,theorem(X_30),true),true) = ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,theorem(X_30),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,ifeq(true,true,theorem(X_30),true),true),ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,ifeq(true,true,theorem(X_30),true),true)) ),[1,2],$fot(theorem(X_30))]]) ).
cnf(refute_0_80,plain,
( ifeq(true,true,theorem(X_30),true) != theorem(X_30)
| ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,ifeq(true,true,theorem(X_30),true),true) = ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,theorem(X_30),true) ),
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,ifeq(true,true,theorem(X_30),true),true),ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,ifeq(true,true,theorem(X_30),true),true)) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,ifeq(true,true,theorem(X_30),true),true) = ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,theorem(X_30),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(X_30),true),theorem(X_30)) )],[refute_0_49,refute_0_80]) ).
cnf(refute_0_82,plain,
( ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,ifeq(true,true,theorem(X_30),true),true) != ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,theorem(X_30),true)
| ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,ifeq(true,true,theorem(X_30),true),true) != true
| ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,theorem(X_30),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,ifeq(true,true,theorem(X_30),true),true),true) ),[0],$fot(ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,theorem(X_30),true))]]) ).
cnf(refute_0_83,plain,
( ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,ifeq(true,true,theorem(X_30),true),true) != true
| ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,theorem(X_30),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,ifeq(true,true,theorem(X_30),true),true),ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,theorem(X_30),true)) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,theorem(X_30),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(X_6,implies(X_10,X_6)),X_30)),true,ifeq(true,true,theorem(X_30),true),true),true) )],[refute_0_77,refute_0_83]) ).
cnf(refute_0_85,plain,
ifeq(theorem(implies(implies(X_172,implies(X_170,X_172)),implies(X_170,implies(X_172,X_172)))),true,theorem(implies(X_170,implies(X_172,X_172))),true) = true,
inference(subst,[],[refute_0_84:[bind(X_10,$fot(X_170)),bind(X_30,$fot(implies(X_170,implies(X_172,X_172)))),bind(X_6,$fot(X_172))]]) ).
cnf(refute_0_86,plain,
ifeq(axiom(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))),true,theorem(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))),true) = true,
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))))]]) ).
cnf(refute_0_87,plain,
axiom(implies(or(X_44,or(not(X),X_46)),or(not(X),or(X_44,X_46)))) = true,
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_44)),bind(B,$fot(not(X))),bind(C,$fot(X_46))]]) ).
cnf(refute_0_88,plain,
implies(X,or(X_44,X_46)) = or(not(X),or(X_44,X_46)),
inference(subst,[],[implies_definition:[bind(Y,$fot(or(X_44,X_46)))]]) ).
cnf(refute_0_89,plain,
( implies(X,or(X_44,X_46)) != or(not(X),or(X_44,X_46))
| or(not(X),or(X_44,X_46)) = implies(X,or(X_44,X_46)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,or(X_44,X_46)))),bind(Y0,$fot(or(not(X),or(X_44,X_46))))]]) ).
cnf(refute_0_90,plain,
or(not(X),or(X_44,X_46)) = implies(X,or(X_44,X_46)),
inference(resolve,[$cnf( $equal(implies(X,or(X_44,X_46)),or(not(X),or(X_44,X_46))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
( axiom(implies(or(X_44,or(not(X),X_46)),or(not(X),or(X_44,X_46)))) != true
| or(not(X),or(X_44,X_46)) != implies(X,or(X_44,X_46))
| axiom(implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46)))) = true ),
introduced(tautology,[equality,[$cnf( $equal(axiom(implies(or(X_44,or(not(X),X_46)),or(not(X),or(X_44,X_46)))),true) ),[0,0,1],$fot(implies(X,or(X_44,X_46)))]]) ).
cnf(refute_0_92,plain,
( axiom(implies(or(X_44,or(not(X),X_46)),or(not(X),or(X_44,X_46)))) != true
| axiom(implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46)))) = true ),
inference(resolve,[$cnf( $equal(or(not(X),or(X_44,X_46)),implies(X,or(X_44,X_46))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
axiom(implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46)))) = true,
inference(resolve,[$cnf( $equal(axiom(implies(or(X_44,or(not(X),X_46)),or(not(X),or(X_44,X_46)))),true) )],[refute_0_87,refute_0_92]) ).
cnf(refute_0_94,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_95,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_94]) ).
cnf(refute_0_96,plain,
or(not(X),X_46) = implies(X,X_46),
inference(subst,[],[refute_0_95:[bind(Y,$fot(X_46))]]) ).
cnf(refute_0_97,plain,
or(X_44,or(not(X),X_46)) = or(X_44,or(not(X),X_46)),
introduced(tautology,[refl,[$fot(or(X_44,or(not(X),X_46)))]]) ).
cnf(refute_0_98,plain,
( or(X_44,or(not(X),X_46)) != or(X_44,or(not(X),X_46))
| or(not(X),X_46) != implies(X,X_46)
| or(X_44,or(not(X),X_46)) = or(X_44,implies(X,X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_44,or(not(X),X_46)),or(X_44,or(not(X),X_46))) ),[1,1],$fot(implies(X,X_46))]]) ).
cnf(refute_0_99,plain,
( or(not(X),X_46) != implies(X,X_46)
| or(X_44,or(not(X),X_46)) = or(X_44,implies(X,X_46)) ),
inference(resolve,[$cnf( $equal(or(X_44,or(not(X),X_46)),or(X_44,or(not(X),X_46))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
or(X_44,or(not(X),X_46)) = or(X_44,implies(X,X_46)),
inference(resolve,[$cnf( $equal(or(not(X),X_46),implies(X,X_46)) )],[refute_0_96,refute_0_99]) ).
cnf(refute_0_101,plain,
implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46))) = implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46))),
introduced(tautology,[refl,[$fot(implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46))))]]) ).
cnf(refute_0_102,plain,
( implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46))) != implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46)))
| or(X_44,or(not(X),X_46)) != or(X_44,implies(X,X_46))
| implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46))) = implies(or(X_44,implies(X,X_46)),implies(X,or(X_44,X_46))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46))),implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46)))) ),[1,0],$fot(or(X_44,implies(X,X_46)))]]) ).
cnf(refute_0_103,plain,
( or(X_44,or(not(X),X_46)) != or(X_44,implies(X,X_46))
| implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46))) = implies(or(X_44,implies(X,X_46)),implies(X,or(X_44,X_46))) ),
inference(resolve,[$cnf( $equal(implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46))),implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46)))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46))) = implies(or(X_44,implies(X,X_46)),implies(X,or(X_44,X_46))),
inference(resolve,[$cnf( $equal(or(X_44,or(not(X),X_46)),or(X_44,implies(X,X_46))) )],[refute_0_100,refute_0_103]) ).
cnf(refute_0_105,plain,
axiom(implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46)))) = axiom(implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46)))),
introduced(tautology,[refl,[$fot(axiom(implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46)))))]]) ).
cnf(refute_0_106,plain,
( axiom(implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46)))) != axiom(implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46))))
| implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46))) != implies(or(X_44,implies(X,X_46)),implies(X,or(X_44,X_46)))
| axiom(implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46)))) = axiom(implies(or(X_44,implies(X,X_46)),implies(X,or(X_44,X_46)))) ),
introduced(tautology,[equality,[$cnf( $equal(axiom(implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46)))),axiom(implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46))))) ),[1,0],$fot(implies(or(X_44,implies(X,X_46)),implies(X,or(X_44,X_46))))]]) ).
cnf(refute_0_107,plain,
( implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46))) != implies(or(X_44,implies(X,X_46)),implies(X,or(X_44,X_46)))
| axiom(implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46)))) = axiom(implies(or(X_44,implies(X,X_46)),implies(X,or(X_44,X_46)))) ),
inference(resolve,[$cnf( $equal(axiom(implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46)))),axiom(implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46))))) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
axiom(implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46)))) = axiom(implies(or(X_44,implies(X,X_46)),implies(X,or(X_44,X_46)))),
inference(resolve,[$cnf( $equal(implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46))),implies(or(X_44,implies(X,X_46)),implies(X,or(X_44,X_46)))) )],[refute_0_104,refute_0_107]) ).
cnf(refute_0_109,plain,
( axiom(implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46)))) != axiom(implies(or(X_44,implies(X,X_46)),implies(X,or(X_44,X_46))))
| axiom(implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46)))) != true
| axiom(implies(or(X_44,implies(X,X_46)),implies(X,or(X_44,X_46)))) = true ),
introduced(tautology,[equality,[$cnf( $equal(axiom(implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46)))),true) ),[0],$fot(axiom(implies(or(X_44,implies(X,X_46)),implies(X,or(X_44,X_46)))))]]) ).
cnf(refute_0_110,plain,
( axiom(implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46)))) != true
| axiom(implies(or(X_44,implies(X,X_46)),implies(X,or(X_44,X_46)))) = true ),
inference(resolve,[$cnf( $equal(axiom(implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46)))),axiom(implies(or(X_44,implies(X,X_46)),implies(X,or(X_44,X_46))))) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
axiom(implies(or(X_44,implies(X,X_46)),implies(X,or(X_44,X_46)))) = true,
inference(resolve,[$cnf( $equal(axiom(implies(or(X_44,or(not(X),X_46)),implies(X,or(X_44,X_46)))),true) )],[refute_0_93,refute_0_110]) ).
cnf(refute_0_112,plain,
axiom(implies(or(not(X),implies(X_75,X_77)),implies(X_75,or(not(X),X_77)))) = true,
inference(subst,[],[refute_0_111:[bind(X,$fot(X_75)),bind(X_44,$fot(not(X))),bind(X_46,$fot(X_77))]]) ).
cnf(refute_0_113,plain,
implies(X,X_77) = or(not(X),X_77),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_77))]]) ).
cnf(refute_0_114,plain,
( implies(X,X_77) != or(not(X),X_77)
| or(not(X),X_77) = implies(X,X_77) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,X_77))),bind(Y0,$fot(or(not(X),X_77)))]]) ).
cnf(refute_0_115,plain,
or(not(X),X_77) = implies(X,X_77),
inference(resolve,[$cnf( $equal(implies(X,X_77),or(not(X),X_77)) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
( axiom(implies(or(not(X),implies(X_75,X_77)),implies(X_75,or(not(X),X_77)))) != true
| or(not(X),X_77) != implies(X,X_77)
| axiom(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77)))) = true ),
introduced(tautology,[equality,[$cnf( $equal(axiom(implies(or(not(X),implies(X_75,X_77)),implies(X_75,or(not(X),X_77)))),true) ),[0,0,1,1],$fot(implies(X,X_77))]]) ).
cnf(refute_0_117,plain,
( axiom(implies(or(not(X),implies(X_75,X_77)),implies(X_75,or(not(X),X_77)))) != true
| axiom(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77)))) = true ),
inference(resolve,[$cnf( $equal(or(not(X),X_77),implies(X,X_77)) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
axiom(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77)))) = true,
inference(resolve,[$cnf( $equal(axiom(implies(or(not(X),implies(X_75,X_77)),implies(X_75,or(not(X),X_77)))),true) )],[refute_0_112,refute_0_117]) ).
cnf(refute_0_119,plain,
or(not(X),implies(X_75,X_77)) = implies(X,implies(X_75,X_77)),
inference(subst,[],[refute_0_95:[bind(Y,$fot(implies(X_75,X_77)))]]) ).
cnf(refute_0_120,plain,
implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77))) = implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77))),
introduced(tautology,[refl,[$fot(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77))))]]) ).
cnf(refute_0_121,plain,
( implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77))) != implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77)))
| or(not(X),implies(X_75,X_77)) != implies(X,implies(X_75,X_77))
| implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77))) = implies(implies(X,implies(X_75,X_77)),implies(X_75,implies(X,X_77))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77))),implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77)))) ),[1,0],$fot(implies(X,implies(X_75,X_77)))]]) ).
cnf(refute_0_122,plain,
( or(not(X),implies(X_75,X_77)) != implies(X,implies(X_75,X_77))
| implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77))) = implies(implies(X,implies(X_75,X_77)),implies(X_75,implies(X,X_77))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77))),implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77)))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77))) = implies(implies(X,implies(X_75,X_77)),implies(X_75,implies(X,X_77))),
inference(resolve,[$cnf( $equal(or(not(X),implies(X_75,X_77)),implies(X,implies(X_75,X_77))) )],[refute_0_119,refute_0_122]) ).
cnf(refute_0_124,plain,
axiom(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77)))) = axiom(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77)))),
introduced(tautology,[refl,[$fot(axiom(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77)))))]]) ).
cnf(refute_0_125,plain,
( axiom(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77)))) != axiom(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77))))
| implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77))) != implies(implies(X,implies(X_75,X_77)),implies(X_75,implies(X,X_77)))
| axiom(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77)))) = axiom(implies(implies(X,implies(X_75,X_77)),implies(X_75,implies(X,X_77)))) ),
introduced(tautology,[equality,[$cnf( $equal(axiom(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77)))),axiom(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77))))) ),[1,0],$fot(implies(implies(X,implies(X_75,X_77)),implies(X_75,implies(X,X_77))))]]) ).
cnf(refute_0_126,plain,
( implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77))) != implies(implies(X,implies(X_75,X_77)),implies(X_75,implies(X,X_77)))
| axiom(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77)))) = axiom(implies(implies(X,implies(X_75,X_77)),implies(X_75,implies(X,X_77)))) ),
inference(resolve,[$cnf( $equal(axiom(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77)))),axiom(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77))))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
axiom(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77)))) = axiom(implies(implies(X,implies(X_75,X_77)),implies(X_75,implies(X,X_77)))),
inference(resolve,[$cnf( $equal(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77))),implies(implies(X,implies(X_75,X_77)),implies(X_75,implies(X,X_77)))) )],[refute_0_123,refute_0_126]) ).
cnf(refute_0_128,plain,
( axiom(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77)))) != axiom(implies(implies(X,implies(X_75,X_77)),implies(X_75,implies(X,X_77))))
| axiom(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77)))) != true
| axiom(implies(implies(X,implies(X_75,X_77)),implies(X_75,implies(X,X_77)))) = true ),
introduced(tautology,[equality,[$cnf( $equal(axiom(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77)))),true) ),[0],$fot(axiom(implies(implies(X,implies(X_75,X_77)),implies(X_75,implies(X,X_77)))))]]) ).
cnf(refute_0_129,plain,
( axiom(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77)))) != true
| axiom(implies(implies(X,implies(X_75,X_77)),implies(X_75,implies(X,X_77)))) = true ),
inference(resolve,[$cnf( $equal(axiom(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77)))),axiom(implies(implies(X,implies(X_75,X_77)),implies(X_75,implies(X,X_77))))) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
axiom(implies(implies(X,implies(X_75,X_77)),implies(X_75,implies(X,X_77)))) = true,
inference(resolve,[$cnf( $equal(axiom(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77)))),true) )],[refute_0_118,refute_0_129]) ).
cnf(refute_0_131,plain,
axiom(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))) = true,
inference(subst,[],[refute_0_130:[bind(X,$fot(X_78)),bind(X_75,$fot(X_79)),bind(X_77,$fot(X_80))]]) ).
cnf(refute_0_132,plain,
( axiom(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))) != true
| ifeq(axiom(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))),true,theorem(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))),true) != true
| ifeq(true,true,theorem(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(axiom(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))),true,theorem(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_133,plain,
( ifeq(axiom(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))),true,theorem(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))),true) != true
| ifeq(true,true,theorem(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))),true) = true ),
inference(resolve,[$cnf( $equal(axiom(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))),true) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
ifeq(true,true,theorem(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(axiom(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))),true,theorem(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))),true),true) )],[refute_0_86,refute_0_133]) ).
cnf(refute_0_135,plain,
ifeq(true,true,theorem(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))),true) = theorem(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))))),bind(C,$fot(true))]]) ).
cnf(refute_0_136,plain,
( ifeq(true,true,theorem(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))),true) != theorem(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80))))
| ifeq(true,true,theorem(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))),true) != true
| theorem(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))),true),true) ),[0],$fot(theorem(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))))]]) ).
cnf(refute_0_137,plain,
( ifeq(true,true,theorem(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))),true) != true
| theorem(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))),true),theorem(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80))))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
theorem(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(implies(X_78,implies(X_79,X_80)),implies(X_79,implies(X_78,X_80)))),true),true) )],[refute_0_134,refute_0_137]) ).
cnf(refute_0_139,plain,
theorem(implies(implies(X_172,implies(X_170,X_172)),implies(X_170,implies(X_172,X_172)))) = true,
inference(subst,[],[refute_0_138:[bind(X_78,$fot(X_172)),bind(X_79,$fot(X_170)),bind(X_80,$fot(X_172))]]) ).
cnf(refute_0_140,plain,
( ifeq(theorem(implies(implies(X_172,implies(X_170,X_172)),implies(X_170,implies(X_172,X_172)))),true,theorem(implies(X_170,implies(X_172,X_172))),true) != true
| theorem(implies(implies(X_172,implies(X_170,X_172)),implies(X_170,implies(X_172,X_172)))) != true
| ifeq(true,true,theorem(implies(X_170,implies(X_172,X_172))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(X_172,implies(X_170,X_172)),implies(X_170,implies(X_172,X_172)))),true,theorem(implies(X_170,implies(X_172,X_172))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_141,plain,
( ifeq(theorem(implies(implies(X_172,implies(X_170,X_172)),implies(X_170,implies(X_172,X_172)))),true,theorem(implies(X_170,implies(X_172,X_172))),true) != true
| ifeq(true,true,theorem(implies(X_170,implies(X_172,X_172))),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(implies(X_172,implies(X_170,X_172)),implies(X_170,implies(X_172,X_172)))),true) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
ifeq(true,true,theorem(implies(X_170,implies(X_172,X_172))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(X_172,implies(X_170,X_172)),implies(X_170,implies(X_172,X_172)))),true,theorem(implies(X_170,implies(X_172,X_172))),true),true) )],[refute_0_85,refute_0_141]) ).
cnf(refute_0_143,plain,
ifeq(true,true,theorem(implies(X_170,implies(X_172,X_172))),true) = theorem(implies(X_170,implies(X_172,X_172))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(implies(X_170,implies(X_172,X_172))))),bind(C,$fot(true))]]) ).
cnf(refute_0_144,plain,
( ifeq(true,true,theorem(implies(X_170,implies(X_172,X_172))),true) != theorem(implies(X_170,implies(X_172,X_172)))
| ifeq(true,true,theorem(implies(X_170,implies(X_172,X_172))),true) != true
| theorem(implies(X_170,implies(X_172,X_172))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(implies(X_170,implies(X_172,X_172))),true),true) ),[0],$fot(theorem(implies(X_170,implies(X_172,X_172))))]]) ).
cnf(refute_0_145,plain,
( ifeq(true,true,theorem(implies(X_170,implies(X_172,X_172))),true) != true
| theorem(implies(X_170,implies(X_172,X_172))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(X_170,implies(X_172,X_172))),true),theorem(implies(X_170,implies(X_172,X_172)))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
theorem(implies(X_170,implies(X_172,X_172))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(X_170,implies(X_172,X_172))),true),true) )],[refute_0_142,refute_0_145]) ).
cnf(refute_0_147,plain,
theorem(implies(implies(or(X_4,X_4),X_4),implies(X_174,X_174))) = true,
inference(subst,[],[refute_0_146:[bind(X_170,$fot(implies(or(X_4,X_4),X_4))),bind(X_172,$fot(X_174))]]) ).
cnf(refute_0_148,plain,
( ifeq(theorem(implies(implies(or(X_4,X_4),X_4),implies(X_174,X_174))),true,theorem(implies(X_174,X_174)),true) != true
| theorem(implies(implies(or(X_4,X_4),X_4),implies(X_174,X_174))) != true
| ifeq(true,true,theorem(implies(X_174,X_174)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(or(X_4,X_4),X_4),implies(X_174,X_174))),true,theorem(implies(X_174,X_174)),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_149,plain,
( ifeq(theorem(implies(implies(or(X_4,X_4),X_4),implies(X_174,X_174))),true,theorem(implies(X_174,X_174)),true) != true
| ifeq(true,true,theorem(implies(X_174,X_174)),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(implies(or(X_4,X_4),X_4),implies(X_174,X_174))),true) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
ifeq(true,true,theorem(implies(X_174,X_174)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(or(X_4,X_4),X_4),implies(X_174,X_174))),true,theorem(implies(X_174,X_174)),true),true) )],[refute_0_57,refute_0_149]) ).
cnf(refute_0_151,plain,
ifeq(true,true,theorem(implies(X_174,X_174)),true) = theorem(implies(X_174,X_174)),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(implies(X_174,X_174)))),bind(C,$fot(true))]]) ).
cnf(refute_0_152,plain,
( ifeq(true,true,theorem(implies(X_174,X_174)),true) != theorem(implies(X_174,X_174))
| ifeq(true,true,theorem(implies(X_174,X_174)),true) != true
| theorem(implies(X_174,X_174)) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(implies(X_174,X_174)),true),true) ),[0],$fot(theorem(implies(X_174,X_174)))]]) ).
cnf(refute_0_153,plain,
( ifeq(true,true,theorem(implies(X_174,X_174)),true) != true
| theorem(implies(X_174,X_174)) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(X_174,X_174)),true),theorem(implies(X_174,X_174))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
theorem(implies(X_174,X_174)) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(X_174,X_174)),true),true) )],[refute_0_150,refute_0_153]) ).
cnf(refute_0_155,plain,
theorem(implies(not(X_89),not(X_89))) = true,
inference(subst,[],[refute_0_154:[bind(X_174,$fot(not(X_89)))]]) ).
cnf(refute_0_156,plain,
( ifeq(theorem(implies(not(X_89),not(X_89))),true,theorem(implies(X_89,not(not(X_89)))),true) != true
| theorem(implies(not(X_89),not(X_89))) != true
| ifeq(true,true,theorem(implies(X_89,not(not(X_89)))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(not(X_89),not(X_89))),true,theorem(implies(X_89,not(not(X_89)))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_157,plain,
( ifeq(theorem(implies(not(X_89),not(X_89))),true,theorem(implies(X_89,not(not(X_89)))),true) != true
| ifeq(true,true,theorem(implies(X_89,not(not(X_89)))),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(not(X_89),not(X_89))),true) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
ifeq(true,true,theorem(implies(X_89,not(not(X_89)))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(not(X_89),not(X_89))),true,theorem(implies(X_89,not(not(X_89)))),true),true) )],[refute_0_35,refute_0_157]) ).
cnf(refute_0_159,plain,
ifeq(true,true,theorem(implies(X_89,not(not(X_89)))),true) = theorem(implies(X_89,not(not(X_89)))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(implies(X_89,not(not(X_89)))))),bind(C,$fot(true))]]) ).
cnf(refute_0_160,plain,
( ifeq(true,true,theorem(implies(X_89,not(not(X_89)))),true) != theorem(implies(X_89,not(not(X_89))))
| ifeq(true,true,theorem(implies(X_89,not(not(X_89)))),true) != true
| theorem(implies(X_89,not(not(X_89)))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(implies(X_89,not(not(X_89)))),true),true) ),[0],$fot(theorem(implies(X_89,not(not(X_89)))))]]) ).
cnf(refute_0_161,plain,
( ifeq(true,true,theorem(implies(X_89,not(not(X_89)))),true) != true
| theorem(implies(X_89,not(not(X_89)))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(X_89,not(not(X_89)))),true),theorem(implies(X_89,not(not(X_89))))) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
theorem(implies(X_89,not(not(X_89)))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(X_89,not(not(X_89)))),true),true) )],[refute_0_158,refute_0_161]) ).
cnf(refute_0_163,plain,
theorem(implies(Y,not(not(Y)))) = true,
inference(subst,[],[refute_0_162:[bind(X_89,$fot(Y))]]) ).
cnf(refute_0_164,plain,
( ifeq(theorem(implies(Y,not(not(Y)))),true,ifeq(theorem(Y),true,theorem(not(not(Y))),true),true) != true
| theorem(implies(Y,not(not(Y)))) != true
| ifeq(true,true,ifeq(theorem(Y),true,theorem(not(not(Y))),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(Y,not(not(Y)))),true,ifeq(theorem(Y),true,theorem(not(not(Y))),true),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_165,plain,
( ifeq(theorem(implies(Y,not(not(Y)))),true,ifeq(theorem(Y),true,theorem(not(not(Y))),true),true) != true
| ifeq(true,true,ifeq(theorem(Y),true,theorem(not(not(Y))),true),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(Y,not(not(Y)))),true) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
ifeq(true,true,ifeq(theorem(Y),true,theorem(not(not(Y))),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(Y,not(not(Y)))),true,ifeq(theorem(Y),true,theorem(not(not(Y))),true),true),true) )],[refute_0_0,refute_0_165]) ).
cnf(refute_0_167,plain,
ifeq(true,true,ifeq(theorem(Y),true,theorem(not(not(Y))),true),true) = ifeq(theorem(Y),true,theorem(not(not(Y))),true),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(ifeq(theorem(Y),true,theorem(not(not(Y))),true))),bind(C,$fot(true))]]) ).
cnf(refute_0_168,plain,
( ifeq(true,true,ifeq(theorem(Y),true,theorem(not(not(Y))),true),true) != ifeq(theorem(Y),true,theorem(not(not(Y))),true)
| ifeq(true,true,ifeq(theorem(Y),true,theorem(not(not(Y))),true),true) != true
| ifeq(theorem(Y),true,theorem(not(not(Y))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,ifeq(theorem(Y),true,theorem(not(not(Y))),true),true),true) ),[0],$fot(ifeq(theorem(Y),true,theorem(not(not(Y))),true))]]) ).
cnf(refute_0_169,plain,
( ifeq(true,true,ifeq(theorem(Y),true,theorem(not(not(Y))),true),true) != true
| ifeq(theorem(Y),true,theorem(not(not(Y))),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(theorem(Y),true,theorem(not(not(Y))),true),true),ifeq(theorem(Y),true,theorem(not(not(Y))),true)) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
ifeq(theorem(Y),true,theorem(not(not(Y))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(theorem(Y),true,theorem(not(not(Y))),true),true),true) )],[refute_0_166,refute_0_169]) ).
cnf(refute_0_171,plain,
ifeq(theorem(implies(X_89,not(not(X_89)))),true,theorem(not(not(implies(X_89,not(not(X_89)))))),true) = true,
inference(subst,[],[refute_0_170:[bind(Y,$fot(implies(X_89,not(not(X_89)))))]]) ).
cnf(refute_0_172,plain,
( ifeq(theorem(implies(X_89,not(not(X_89)))),true,theorem(not(not(implies(X_89,not(not(X_89)))))),true) != true
| theorem(implies(X_89,not(not(X_89)))) != true
| ifeq(true,true,theorem(not(not(implies(X_89,not(not(X_89)))))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(X_89,not(not(X_89)))),true,theorem(not(not(implies(X_89,not(not(X_89)))))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_173,plain,
( ifeq(theorem(implies(X_89,not(not(X_89)))),true,theorem(not(not(implies(X_89,not(not(X_89)))))),true) != true
| ifeq(true,true,theorem(not(not(implies(X_89,not(not(X_89)))))),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(X_89,not(not(X_89)))),true) )],[refute_0_162,refute_0_172]) ).
cnf(refute_0_174,plain,
ifeq(true,true,theorem(not(not(implies(X_89,not(not(X_89)))))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(X_89,not(not(X_89)))),true,theorem(not(not(implies(X_89,not(not(X_89)))))),true),true) )],[refute_0_171,refute_0_173]) ).
cnf(refute_0_175,plain,
or(not(P),not(Q)) = implies(P,not(Q)),
inference(subst,[],[refute_0_95:[bind(X,$fot(P)),bind(Y,$fot(not(Q)))]]) ).
cnf(refute_0_176,plain,
not(or(not(P),not(Q))) = not(or(not(P),not(Q))),
introduced(tautology,[refl,[$fot(not(or(not(P),not(Q))))]]) ).
cnf(refute_0_177,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_178,plain,
( or(not(P),not(Q)) != implies(P,not(Q))
| not(or(not(P),not(Q))) = not(implies(P,not(Q))) ),
inference(resolve,[$cnf( $equal(not(or(not(P),not(Q))),not(or(not(P),not(Q)))) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
not(or(not(P),not(Q))) = not(implies(P,not(Q))),
inference(resolve,[$cnf( $equal(or(not(P),not(Q)),implies(P,not(Q))) )],[refute_0_175,refute_0_178]) ).
cnf(refute_0_180,plain,
( and(P,Q) != not(or(not(P),not(Q)))
| not(or(not(P),not(Q))) != not(implies(P,not(Q)))
| and(P,Q) = not(implies(P,not(Q))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(P,Q),not(implies(P,not(Q)))) ),[0],$fot(not(or(not(P),not(Q))))]]) ).
cnf(refute_0_181,plain,
( and(P,Q) != not(or(not(P),not(Q)))
| and(P,Q) = not(implies(P,not(Q))) ),
inference(resolve,[$cnf( $equal(not(or(not(P),not(Q))),not(implies(P,not(Q)))) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
and(P,Q) = not(implies(P,not(Q))),
inference(resolve,[$cnf( $equal(and(P,Q),not(or(not(P),not(Q)))) )],[and_defn,refute_0_181]) ).
cnf(refute_0_183,plain,
( and(P,Q) != not(implies(P,not(Q)))
| not(implies(P,not(Q))) = and(P,Q) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(and(P,Q))),bind(Y0,$fot(not(implies(P,not(Q)))))]]) ).
cnf(refute_0_184,plain,
not(implies(P,not(Q))) = and(P,Q),
inference(resolve,[$cnf( $equal(and(P,Q),not(implies(P,not(Q)))) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
not(implies(X_89,not(not(X_89)))) = and(X_89,not(X_89)),
inference(subst,[],[refute_0_184:[bind(P,$fot(X_89)),bind(Q,$fot(not(X_89)))]]) ).
cnf(refute_0_186,plain,
not(not(implies(X_89,not(not(X_89))))) = not(not(implies(X_89,not(not(X_89))))),
introduced(tautology,[refl,[$fot(not(not(implies(X_89,not(not(X_89))))))]]) ).
cnf(refute_0_187,plain,
( not(implies(X_89,not(not(X_89)))) != and(X_89,not(X_89))
| not(not(implies(X_89,not(not(X_89))))) != not(not(implies(X_89,not(not(X_89)))))
| not(not(implies(X_89,not(not(X_89))))) = not(and(X_89,not(X_89))) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(implies(X_89,not(not(X_89))))),not(not(implies(X_89,not(not(X_89)))))) ),[1,0],$fot(and(X_89,not(X_89)))]]) ).
cnf(refute_0_188,plain,
( not(implies(X_89,not(not(X_89)))) != and(X_89,not(X_89))
| not(not(implies(X_89,not(not(X_89))))) = not(and(X_89,not(X_89))) ),
inference(resolve,[$cnf( $equal(not(not(implies(X_89,not(not(X_89))))),not(not(implies(X_89,not(not(X_89)))))) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
not(not(implies(X_89,not(not(X_89))))) = not(and(X_89,not(X_89))),
inference(resolve,[$cnf( $equal(not(implies(X_89,not(not(X_89)))),and(X_89,not(X_89))) )],[refute_0_185,refute_0_188]) ).
cnf(refute_0_190,plain,
theorem(not(not(implies(X_89,not(not(X_89)))))) = theorem(not(not(implies(X_89,not(not(X_89)))))),
introduced(tautology,[refl,[$fot(theorem(not(not(implies(X_89,not(not(X_89)))))))]]) ).
cnf(refute_0_191,plain,
( not(not(implies(X_89,not(not(X_89))))) != not(and(X_89,not(X_89)))
| theorem(not(not(implies(X_89,not(not(X_89)))))) != theorem(not(not(implies(X_89,not(not(X_89))))))
| theorem(not(not(implies(X_89,not(not(X_89)))))) = theorem(not(and(X_89,not(X_89)))) ),
introduced(tautology,[equality,[$cnf( $equal(theorem(not(not(implies(X_89,not(not(X_89)))))),theorem(not(not(implies(X_89,not(not(X_89))))))) ),[1,0],$fot(not(and(X_89,not(X_89))))]]) ).
cnf(refute_0_192,plain,
( not(not(implies(X_89,not(not(X_89))))) != not(and(X_89,not(X_89)))
| theorem(not(not(implies(X_89,not(not(X_89)))))) = theorem(not(and(X_89,not(X_89)))) ),
inference(resolve,[$cnf( $equal(theorem(not(not(implies(X_89,not(not(X_89)))))),theorem(not(not(implies(X_89,not(not(X_89))))))) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
theorem(not(not(implies(X_89,not(not(X_89)))))) = theorem(not(and(X_89,not(X_89)))),
inference(resolve,[$cnf( $equal(not(not(implies(X_89,not(not(X_89))))),not(and(X_89,not(X_89)))) )],[refute_0_189,refute_0_192]) ).
cnf(refute_0_194,plain,
ifeq(true,true,theorem(not(not(implies(X_89,not(not(X_89)))))),true) = theorem(not(not(implies(X_89,not(not(X_89)))))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(not(not(implies(X_89,not(not(X_89)))))))),bind(C,$fot(true))]]) ).
cnf(refute_0_195,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_196,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_15,refute_0_195]) ).
cnf(refute_0_197,plain,
( ifeq(true,true,theorem(not(not(implies(X_89,not(not(X_89)))))),true) != theorem(not(not(implies(X_89,not(not(X_89))))))
| theorem(not(not(implies(X_89,not(not(X_89)))))) != theorem(not(and(X_89,not(X_89))))
| ifeq(true,true,theorem(not(not(implies(X_89,not(not(X_89)))))),true) = theorem(not(and(X_89,not(X_89)))) ),
inference(subst,[],[refute_0_196:[bind(X0,$fot(ifeq(true,true,theorem(not(not(implies(X_89,not(not(X_89)))))),true))),bind(Y0,$fot(theorem(not(not(implies(X_89,not(not(X_89)))))))),bind(Z,$fot(theorem(not(and(X_89,not(X_89))))))]]) ).
cnf(refute_0_198,plain,
( theorem(not(not(implies(X_89,not(not(X_89)))))) != theorem(not(and(X_89,not(X_89))))
| ifeq(true,true,theorem(not(not(implies(X_89,not(not(X_89)))))),true) = theorem(not(and(X_89,not(X_89)))) ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(not(not(implies(X_89,not(not(X_89)))))),true),theorem(not(not(implies(X_89,not(not(X_89))))))) )],[refute_0_194,refute_0_197]) ).
cnf(refute_0_199,plain,
ifeq(true,true,theorem(not(not(implies(X_89,not(not(X_89)))))),true) = theorem(not(and(X_89,not(X_89)))),
inference(resolve,[$cnf( $equal(theorem(not(not(implies(X_89,not(not(X_89)))))),theorem(not(and(X_89,not(X_89))))) )],[refute_0_193,refute_0_198]) ).
cnf(refute_0_200,plain,
( ifeq(true,true,theorem(not(not(implies(X_89,not(not(X_89)))))),true) != theorem(not(and(X_89,not(X_89))))
| ifeq(true,true,theorem(not(not(implies(X_89,not(not(X_89)))))),true) != true
| theorem(not(and(X_89,not(X_89)))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(not(not(implies(X_89,not(not(X_89)))))),true),true) ),[0],$fot(theorem(not(and(X_89,not(X_89)))))]]) ).
cnf(refute_0_201,plain,
( ifeq(true,true,theorem(not(not(implies(X_89,not(not(X_89)))))),true) != true
| theorem(not(and(X_89,not(X_89)))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(not(not(implies(X_89,not(not(X_89)))))),true),theorem(not(and(X_89,not(X_89))))) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
theorem(not(and(X_89,not(X_89)))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(not(not(implies(X_89,not(not(X_89)))))),true),true) )],[refute_0_174,refute_0_201]) ).
cnf(refute_0_203,plain,
theorem(not(and(p,not(p)))) = true,
inference(subst,[],[refute_0_202:[bind(X_89,$fot(p))]]) ).
cnf(refute_0_204,plain,
( theorem(not(and(p,not(p)))) != true
| true != true
| theorem(not(and(p,not(p)))) = true ),
introduced(tautology,[equality,[$cnf( ~ $equal(theorem(not(and(p,not(p)))),true) ),[0],$fot(true)]]) ).
cnf(refute_0_205,plain,
( true != true
| theorem(not(and(p,not(p)))) = true ),
inference(resolve,[$cnf( $equal(theorem(not(and(p,not(p)))),true) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
true != true,
inference(resolve,[$cnf( $equal(theorem(not(and(p,not(p)))),true) )],[refute_0_205,prove_this]) ).
cnf(refute_0_207,plain,
true = true,
introduced(tautology,[refl,[$fot(true)]]) ).
cnf(refute_0_208,plain,
$false,
inference(resolve,[$cnf( $equal(true,true) )],[refute_0_207,refute_0_206]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : LCL239-10 : TPTP v8.1.0. Released v7.5.0.
% 0.14/0.15 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n026.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jul 4 15:31:22 EDT 2022
% 0.14/0.37 % CPUTime :
% 0.14/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.48/0.63 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.48/0.63
% 0.48/0.63 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.51/0.67
%------------------------------------------------------------------------------