TSTP Solution File: LCL203-10 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL203-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 12:50:33 EDT 2022
% Result : Unsatisfiable 193.31s 193.55s
% Output : CNFRefutation 193.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 83
% Syntax : Number of clauses : 290 ( 159 unt; 0 nHn; 138 RR)
% Number of literals : 484 ( 483 equ; 197 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; 3 con; 0-4 aty)
% Number of variables : 587 ( 30 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_6,axiom,
axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) = 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(prove_this,negated_conjecture,
theorem(implies(not(or(p,q)),or(not(p),not(q)))) != true ).
cnf(refute_0_0,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_1,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_2,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_4,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_3]) ).
cnf(refute_0_5,plain,
or(not(p),not(q)) = implies(p,not(q)),
inference(subst,[],[refute_0_4:[bind(X,$fot(p)),bind(Y,$fot(not(q)))]]) ).
cnf(refute_0_6,plain,
implies(not(or(p,q)),or(not(p),not(q))) = implies(not(or(p,q)),or(not(p),not(q))),
introduced(tautology,[refl,[$fot(implies(not(or(p,q)),or(not(p),not(q))))]]) ).
cnf(refute_0_7,plain,
( implies(not(or(p,q)),or(not(p),not(q))) != implies(not(or(p,q)),or(not(p),not(q)))
| or(not(p),not(q)) != implies(p,not(q))
| implies(not(or(p,q)),or(not(p),not(q))) = implies(not(or(p,q)),implies(p,not(q))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(or(p,q)),or(not(p),not(q))),implies(not(or(p,q)),or(not(p),not(q)))) ),[1,1],$fot(implies(p,not(q)))]]) ).
cnf(refute_0_8,plain,
( or(not(p),not(q)) != implies(p,not(q))
| implies(not(or(p,q)),or(not(p),not(q))) = implies(not(or(p,q)),implies(p,not(q))) ),
inference(resolve,[$cnf( $equal(implies(not(or(p,q)),or(not(p),not(q))),implies(not(or(p,q)),or(not(p),not(q)))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
implies(not(or(p,q)),or(not(p),not(q))) = implies(not(or(p,q)),implies(p,not(q))),
inference(resolve,[$cnf( $equal(or(not(p),not(q)),implies(p,not(q))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
theorem(implies(not(or(p,q)),or(not(p),not(q)))) = theorem(implies(not(or(p,q)),or(not(p),not(q)))),
introduced(tautology,[refl,[$fot(theorem(implies(not(or(p,q)),or(not(p),not(q)))))]]) ).
cnf(refute_0_11,plain,
( implies(not(or(p,q)),or(not(p),not(q))) != implies(not(or(p,q)),implies(p,not(q)))
| theorem(implies(not(or(p,q)),or(not(p),not(q)))) != theorem(implies(not(or(p,q)),or(not(p),not(q))))
| theorem(implies(not(or(p,q)),or(not(p),not(q)))) = theorem(implies(not(or(p,q)),implies(p,not(q)))) ),
introduced(tautology,[equality,[$cnf( $equal(theorem(implies(not(or(p,q)),or(not(p),not(q)))),theorem(implies(not(or(p,q)),or(not(p),not(q))))) ),[1,0],$fot(implies(not(or(p,q)),implies(p,not(q))))]]) ).
cnf(refute_0_12,plain,
( implies(not(or(p,q)),or(not(p),not(q))) != implies(not(or(p,q)),implies(p,not(q)))
| theorem(implies(not(or(p,q)),or(not(p),not(q)))) = theorem(implies(not(or(p,q)),implies(p,not(q)))) ),
inference(resolve,[$cnf( $equal(theorem(implies(not(or(p,q)),or(not(p),not(q)))),theorem(implies(not(or(p,q)),or(not(p),not(q))))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
theorem(implies(not(or(p,q)),or(not(p),not(q)))) = theorem(implies(not(or(p,q)),implies(p,not(q)))),
inference(resolve,[$cnf( $equal(implies(not(or(p,q)),or(not(p),not(q))),implies(not(or(p,q)),implies(p,not(q)))) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
( theorem(implies(not(or(p,q)),implies(p,not(q)))) != true
| theorem(implies(not(or(p,q)),or(not(p),not(q)))) != theorem(implies(not(or(p,q)),implies(p,not(q))))
| theorem(implies(not(or(p,q)),or(not(p),not(q)))) = true ),
introduced(tautology,[equality,[$cnf( $equal(theorem(implies(not(or(p,q)),or(not(p),not(q)))),theorem(implies(not(or(p,q)),implies(p,not(q))))) ),[1],$fot(true)]]) ).
cnf(refute_0_15,plain,
( theorem(implies(not(or(p,q)),implies(p,not(q)))) != true
| theorem(implies(not(or(p,q)),or(not(p),not(q)))) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(not(or(p,q)),or(not(p),not(q)))),theorem(implies(not(or(p,q)),implies(p,not(q))))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
theorem(implies(not(or(p,q)),implies(p,not(q)))) != true,
inference(resolve,[$cnf( $equal(theorem(implies(not(or(p,q)),or(not(p),not(q)))),true) )],[refute_0_15,prove_this]) ).
cnf(refute_0_17,plain,
ifeq(theorem(implies(implies(X_889,X_890),implies(X_889,implies(X_888,X_890)))),true,ifeq(theorem(implies(X_889,X_890)),true,theorem(implies(X_889,implies(X_888,X_890))),true),true) = true,
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_889,implies(X_888,X_890)))),bind(Y,$fot(implies(X_889,X_890)))]]) ).
cnf(refute_0_18,plain,
ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,ifeq(theorem(implies(X_10,or(X_11,X_10))),true,theorem(X_20),true),true) = true,
inference(subst,[],[rule_2:[bind(X,$fot(X_20)),bind(Y,$fot(implies(X_10,or(X_11,X_10))))]]) ).
cnf(refute_0_19,plain,
ifeq(axiom(implies(X_10,or(X_11,X_10))),true,theorem(implies(X_10,or(X_11,X_10))),true) = true,
inference(subst,[],[rule_1:[bind(X,$fot(implies(X_10,or(X_11,X_10))))]]) ).
cnf(refute_0_20,plain,
axiom(implies(X_10,or(X_11,X_10))) = true,
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_10)),bind(B,$fot(X_11))]]) ).
cnf(refute_0_21,plain,
( axiom(implies(X_10,or(X_11,X_10))) != true
| ifeq(axiom(implies(X_10,or(X_11,X_10))),true,theorem(implies(X_10,or(X_11,X_10))),true) != true
| ifeq(true,true,theorem(implies(X_10,or(X_11,X_10))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(axiom(implies(X_10,or(X_11,X_10))),true,theorem(implies(X_10,or(X_11,X_10))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_22,plain,
( ifeq(axiom(implies(X_10,or(X_11,X_10))),true,theorem(implies(X_10,or(X_11,X_10))),true) != true
| ifeq(true,true,theorem(implies(X_10,or(X_11,X_10))),true) = true ),
inference(resolve,[$cnf( $equal(axiom(implies(X_10,or(X_11,X_10))),true) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
ifeq(true,true,theorem(implies(X_10,or(X_11,X_10))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(axiom(implies(X_10,or(X_11,X_10))),true,theorem(implies(X_10,or(X_11,X_10))),true),true) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
ifeq(true,true,theorem(implies(X_10,or(X_11,X_10))),true) = theorem(implies(X_10,or(X_11,X_10))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(implies(X_10,or(X_11,X_10))))),bind(C,$fot(true))]]) ).
cnf(refute_0_25,plain,
( ifeq(true,true,theorem(implies(X_10,or(X_11,X_10))),true) != theorem(implies(X_10,or(X_11,X_10)))
| ifeq(true,true,theorem(implies(X_10,or(X_11,X_10))),true) != true
| theorem(implies(X_10,or(X_11,X_10))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(implies(X_10,or(X_11,X_10))),true),true) ),[0],$fot(theorem(implies(X_10,or(X_11,X_10))))]]) ).
cnf(refute_0_26,plain,
( ifeq(true,true,theorem(implies(X_10,or(X_11,X_10))),true) != true
| theorem(implies(X_10,or(X_11,X_10))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(X_10,or(X_11,X_10))),true),theorem(implies(X_10,or(X_11,X_10)))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
theorem(implies(X_10,or(X_11,X_10))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(X_10,or(X_11,X_10))),true),true) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
( ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,ifeq(theorem(implies(X_10,or(X_11,X_10))),true,theorem(X_20),true),true) != true
| theorem(implies(X_10,or(X_11,X_10))) != true
| ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,ifeq(true,true,theorem(X_20),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,ifeq(theorem(implies(X_10,or(X_11,X_10))),true,theorem(X_20),true),true),true) ),[0,2,0],$fot(true)]]) ).
cnf(refute_0_29,plain,
( ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,ifeq(theorem(implies(X_10,or(X_11,X_10))),true,theorem(X_20),true),true) != true
| ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,ifeq(true,true,theorem(X_20),true),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(X_10,or(X_11,X_10))),true) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,ifeq(true,true,theorem(X_20),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,ifeq(theorem(implies(X_10,or(X_11,X_10))),true,theorem(X_20),true),true),true) )],[refute_0_18,refute_0_29]) ).
cnf(refute_0_31,plain,
ifeq(true,true,theorem(X_20),true) = theorem(X_20),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(X_20))),bind(C,$fot(true))]]) ).
cnf(refute_0_32,plain,
ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,ifeq(true,true,theorem(X_20),true),true) = ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,ifeq(true,true,theorem(X_20),true),true),
introduced(tautology,[refl,[$fot(ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,ifeq(true,true,theorem(X_20),true),true))]]) ).
cnf(refute_0_33,plain,
( ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,ifeq(true,true,theorem(X_20),true),true) != ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,ifeq(true,true,theorem(X_20),true),true)
| ifeq(true,true,theorem(X_20),true) != theorem(X_20)
| ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,ifeq(true,true,theorem(X_20),true),true) = ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,theorem(X_20),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,ifeq(true,true,theorem(X_20),true),true),ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,ifeq(true,true,theorem(X_20),true),true)) ),[1,2],$fot(theorem(X_20))]]) ).
cnf(refute_0_34,plain,
( ifeq(true,true,theorem(X_20),true) != theorem(X_20)
| ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,ifeq(true,true,theorem(X_20),true),true) = ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,theorem(X_20),true) ),
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,ifeq(true,true,theorem(X_20),true),true),ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,ifeq(true,true,theorem(X_20),true),true)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,ifeq(true,true,theorem(X_20),true),true) = ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,theorem(X_20),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(X_20),true),theorem(X_20)) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
( ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,ifeq(true,true,theorem(X_20),true),true) != ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,theorem(X_20),true)
| ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,ifeq(true,true,theorem(X_20),true),true) != true
| ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,theorem(X_20),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,ifeq(true,true,theorem(X_20),true),true),true) ),[0],$fot(ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,theorem(X_20),true))]]) ).
cnf(refute_0_37,plain,
( ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,ifeq(true,true,theorem(X_20),true),true) != true
| ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,theorem(X_20),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,ifeq(true,true,theorem(X_20),true),true),ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,theorem(X_20),true)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,theorem(X_20),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),X_20)),true,ifeq(true,true,theorem(X_20),true),true),true) )],[refute_0_30,refute_0_37]) ).
cnf(refute_0_39,plain,
ifeq(theorem(implies(implies(X_128,or(X_129,X_128)),implies(implies(X,X_128),implies(X,or(X_129,X_128))))),true,theorem(implies(implies(X,X_128),implies(X,or(X_129,X_128)))),true) = true,
inference(subst,[],[refute_0_38:[bind(X_10,$fot(X_128)),bind(X_11,$fot(X_129)),bind(X_20,$fot(implies(implies(X,X_128),implies(X,or(X_129,X_128)))))]]) ).
cnf(refute_0_40,plain,
ifeq(axiom(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))),true,theorem(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))),true) = true,
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))))]]) ).
cnf(refute_0_41,plain,
axiom(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))) = true,
inference(subst,[],[axiom_1_6:[bind(A,$fot(X_17)),bind(B,$fot(X_18)),bind(C,$fot(X_19))]]) ).
cnf(refute_0_42,plain,
( axiom(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))) != true
| ifeq(axiom(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))),true,theorem(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))),true) != true
| ifeq(true,true,theorem(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(axiom(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))),true,theorem(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_43,plain,
( ifeq(axiom(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))),true,theorem(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))),true) != true
| ifeq(true,true,theorem(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))),true) = true ),
inference(resolve,[$cnf( $equal(axiom(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))),true) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
ifeq(true,true,theorem(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(axiom(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))),true,theorem(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))),true),true) )],[refute_0_40,refute_0_43]) ).
cnf(refute_0_45,plain,
ifeq(true,true,theorem(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))),true) = theorem(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))))),bind(C,$fot(true))]]) ).
cnf(refute_0_46,plain,
( ifeq(true,true,theorem(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))),true) != theorem(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18))))
| ifeq(true,true,theorem(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))),true) != true
| theorem(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))),true),true) ),[0],$fot(theorem(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))))]]) ).
cnf(refute_0_47,plain,
( ifeq(true,true,theorem(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))),true) != true
| theorem(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))),true),theorem(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18))))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
theorem(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(implies(X_17,X_18),implies(or(X_19,X_17),or(X_19,X_18)))),true),true) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
theorem(implies(implies(X_32,X_33),implies(or(not(X),X_32),or(not(X),X_33)))) = true,
inference(subst,[],[refute_0_48:[bind(X_17,$fot(X_32)),bind(X_18,$fot(X_33)),bind(X_19,$fot(not(X)))]]) ).
cnf(refute_0_50,plain,
implies(X,X_33) = or(not(X),X_33),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_33))]]) ).
cnf(refute_0_51,plain,
( implies(X,X_33) != or(not(X),X_33)
| or(not(X),X_33) = implies(X,X_33) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,X_33))),bind(Y0,$fot(or(not(X),X_33)))]]) ).
cnf(refute_0_52,plain,
or(not(X),X_33) = implies(X,X_33),
inference(resolve,[$cnf( $equal(implies(X,X_33),or(not(X),X_33)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
( or(not(X),X_33) != implies(X,X_33)
| theorem(implies(implies(X_32,X_33),implies(or(not(X),X_32),or(not(X),X_33)))) != true
| theorem(implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33)))) = true ),
introduced(tautology,[equality,[$cnf( $equal(theorem(implies(implies(X_32,X_33),implies(or(not(X),X_32),or(not(X),X_33)))),true) ),[0,0,1,1],$fot(implies(X,X_33))]]) ).
cnf(refute_0_54,plain,
( theorem(implies(implies(X_32,X_33),implies(or(not(X),X_32),or(not(X),X_33)))) != true
| theorem(implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33)))) = true ),
inference(resolve,[$cnf( $equal(or(not(X),X_33),implies(X,X_33)) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
theorem(implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33)))) = true,
inference(resolve,[$cnf( $equal(theorem(implies(implies(X_32,X_33),implies(or(not(X),X_32),or(not(X),X_33)))),true) )],[refute_0_49,refute_0_54]) ).
cnf(refute_0_56,plain,
or(not(X),X_32) = implies(X,X_32),
inference(subst,[],[refute_0_4:[bind(Y,$fot(X_32))]]) ).
cnf(refute_0_57,plain,
implies(or(not(X),X_32),implies(X,X_33)) = implies(or(not(X),X_32),implies(X,X_33)),
introduced(tautology,[refl,[$fot(implies(or(not(X),X_32),implies(X,X_33)))]]) ).
cnf(refute_0_58,plain,
( implies(or(not(X),X_32),implies(X,X_33)) != implies(or(not(X),X_32),implies(X,X_33))
| or(not(X),X_32) != implies(X,X_32)
| implies(or(not(X),X_32),implies(X,X_33)) = implies(implies(X,X_32),implies(X,X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),X_32),implies(X,X_33)),implies(or(not(X),X_32),implies(X,X_33))) ),[1,0],$fot(implies(X,X_32))]]) ).
cnf(refute_0_59,plain,
( or(not(X),X_32) != implies(X,X_32)
| implies(or(not(X),X_32),implies(X,X_33)) = implies(implies(X,X_32),implies(X,X_33)) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_32),implies(X,X_33)),implies(or(not(X),X_32),implies(X,X_33))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
implies(or(not(X),X_32),implies(X,X_33)) = implies(implies(X,X_32),implies(X,X_33)),
inference(resolve,[$cnf( $equal(or(not(X),X_32),implies(X,X_32)) )],[refute_0_56,refute_0_59]) ).
cnf(refute_0_61,plain,
implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33))) = implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33))),
introduced(tautology,[refl,[$fot(implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33))))]]) ).
cnf(refute_0_62,plain,
( implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33))) != implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33)))
| implies(or(not(X),X_32),implies(X,X_33)) != implies(implies(X,X_32),implies(X,X_33))
| implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33))) = implies(implies(X_32,X_33),implies(implies(X,X_32),implies(X,X_33))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33))),implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33)))) ),[1,1],$fot(implies(implies(X,X_32),implies(X,X_33)))]]) ).
cnf(refute_0_63,plain,
( implies(or(not(X),X_32),implies(X,X_33)) != implies(implies(X,X_32),implies(X,X_33))
| implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33))) = implies(implies(X_32,X_33),implies(implies(X,X_32),implies(X,X_33))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33))),implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33)))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33))) = implies(implies(X_32,X_33),implies(implies(X,X_32),implies(X,X_33))),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_32),implies(X,X_33)),implies(implies(X,X_32),implies(X,X_33))) )],[refute_0_60,refute_0_63]) ).
cnf(refute_0_65,plain,
theorem(implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33)))) = theorem(implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33)))),
introduced(tautology,[refl,[$fot(theorem(implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33)))))]]) ).
cnf(refute_0_66,plain,
( implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33))) != implies(implies(X_32,X_33),implies(implies(X,X_32),implies(X,X_33)))
| theorem(implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33)))) != theorem(implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33))))
| theorem(implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33)))) = theorem(implies(implies(X_32,X_33),implies(implies(X,X_32),implies(X,X_33)))) ),
introduced(tautology,[equality,[$cnf( $equal(theorem(implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33)))),theorem(implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33))))) ),[1,0],$fot(implies(implies(X_32,X_33),implies(implies(X,X_32),implies(X,X_33))))]]) ).
cnf(refute_0_67,plain,
( implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33))) != implies(implies(X_32,X_33),implies(implies(X,X_32),implies(X,X_33)))
| theorem(implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33)))) = theorem(implies(implies(X_32,X_33),implies(implies(X,X_32),implies(X,X_33)))) ),
inference(resolve,[$cnf( $equal(theorem(implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33)))),theorem(implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33))))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
theorem(implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33)))) = theorem(implies(implies(X_32,X_33),implies(implies(X,X_32),implies(X,X_33)))),
inference(resolve,[$cnf( $equal(implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33))),implies(implies(X_32,X_33),implies(implies(X,X_32),implies(X,X_33)))) )],[refute_0_64,refute_0_67]) ).
cnf(refute_0_69,plain,
( theorem(implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33)))) != theorem(implies(implies(X_32,X_33),implies(implies(X,X_32),implies(X,X_33))))
| theorem(implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33)))) != true
| theorem(implies(implies(X_32,X_33),implies(implies(X,X_32),implies(X,X_33)))) = true ),
introduced(tautology,[equality,[$cnf( $equal(theorem(implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33)))),true) ),[0],$fot(theorem(implies(implies(X_32,X_33),implies(implies(X,X_32),implies(X,X_33)))))]]) ).
cnf(refute_0_70,plain,
( theorem(implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33)))) != true
| theorem(implies(implies(X_32,X_33),implies(implies(X,X_32),implies(X,X_33)))) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33)))),theorem(implies(implies(X_32,X_33),implies(implies(X,X_32),implies(X,X_33))))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
theorem(implies(implies(X_32,X_33),implies(implies(X,X_32),implies(X,X_33)))) = true,
inference(resolve,[$cnf( $equal(theorem(implies(implies(X_32,X_33),implies(or(not(X),X_32),implies(X,X_33)))),true) )],[refute_0_55,refute_0_70]) ).
cnf(refute_0_72,plain,
theorem(implies(implies(X_128,or(X_129,X_128)),implies(implies(X,X_128),implies(X,or(X_129,X_128))))) = true,
inference(subst,[],[refute_0_71:[bind(X_32,$fot(X_128)),bind(X_33,$fot(or(X_129,X_128)))]]) ).
cnf(refute_0_73,plain,
( ifeq(theorem(implies(implies(X_128,or(X_129,X_128)),implies(implies(X,X_128),implies(X,or(X_129,X_128))))),true,theorem(implies(implies(X,X_128),implies(X,or(X_129,X_128)))),true) != true
| theorem(implies(implies(X_128,or(X_129,X_128)),implies(implies(X,X_128),implies(X,or(X_129,X_128))))) != true
| ifeq(true,true,theorem(implies(implies(X,X_128),implies(X,or(X_129,X_128)))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(X_128,or(X_129,X_128)),implies(implies(X,X_128),implies(X,or(X_129,X_128))))),true,theorem(implies(implies(X,X_128),implies(X,or(X_129,X_128)))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_74,plain,
( ifeq(theorem(implies(implies(X_128,or(X_129,X_128)),implies(implies(X,X_128),implies(X,or(X_129,X_128))))),true,theorem(implies(implies(X,X_128),implies(X,or(X_129,X_128)))),true) != true
| ifeq(true,true,theorem(implies(implies(X,X_128),implies(X,or(X_129,X_128)))),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(implies(X_128,or(X_129,X_128)),implies(implies(X,X_128),implies(X,or(X_129,X_128))))),true) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
ifeq(true,true,theorem(implies(implies(X,X_128),implies(X,or(X_129,X_128)))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(X_128,or(X_129,X_128)),implies(implies(X,X_128),implies(X,or(X_129,X_128))))),true,theorem(implies(implies(X,X_128),implies(X,or(X_129,X_128)))),true),true) )],[refute_0_39,refute_0_74]) ).
cnf(refute_0_76,plain,
ifeq(true,true,theorem(implies(implies(X,X_128),implies(X,or(X_129,X_128)))),true) = theorem(implies(implies(X,X_128),implies(X,or(X_129,X_128)))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(implies(implies(X,X_128),implies(X,or(X_129,X_128)))))),bind(C,$fot(true))]]) ).
cnf(refute_0_77,plain,
( ifeq(true,true,theorem(implies(implies(X,X_128),implies(X,or(X_129,X_128)))),true) != theorem(implies(implies(X,X_128),implies(X,or(X_129,X_128))))
| ifeq(true,true,theorem(implies(implies(X,X_128),implies(X,or(X_129,X_128)))),true) != true
| theorem(implies(implies(X,X_128),implies(X,or(X_129,X_128)))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(implies(implies(X,X_128),implies(X,or(X_129,X_128)))),true),true) ),[0],$fot(theorem(implies(implies(X,X_128),implies(X,or(X_129,X_128)))))]]) ).
cnf(refute_0_78,plain,
( ifeq(true,true,theorem(implies(implies(X,X_128),implies(X,or(X_129,X_128)))),true) != true
| theorem(implies(implies(X,X_128),implies(X,or(X_129,X_128)))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(implies(X,X_128),implies(X,or(X_129,X_128)))),true),theorem(implies(implies(X,X_128),implies(X,or(X_129,X_128))))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
theorem(implies(implies(X,X_128),implies(X,or(X_129,X_128)))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(implies(X,X_128),implies(X,or(X_129,X_128)))),true),true) )],[refute_0_75,refute_0_78]) ).
cnf(refute_0_80,plain,
theorem(implies(implies(X_131,X_132),implies(X_131,or(not(X),X_132)))) = true,
inference(subst,[],[refute_0_79:[bind(X,$fot(X_131)),bind(X_128,$fot(X_132)),bind(X_129,$fot(not(X)))]]) ).
cnf(refute_0_81,plain,
implies(X,X_132) = or(not(X),X_132),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_132))]]) ).
cnf(refute_0_82,plain,
( implies(X,X_132) != or(not(X),X_132)
| or(not(X),X_132) = implies(X,X_132) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,X_132))),bind(Y0,$fot(or(not(X),X_132)))]]) ).
cnf(refute_0_83,plain,
or(not(X),X_132) = implies(X,X_132),
inference(resolve,[$cnf( $equal(implies(X,X_132),or(not(X),X_132)) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
( or(not(X),X_132) != implies(X,X_132)
| theorem(implies(implies(X_131,X_132),implies(X_131,or(not(X),X_132)))) != true
| theorem(implies(implies(X_131,X_132),implies(X_131,implies(X,X_132)))) = true ),
introduced(tautology,[equality,[$cnf( $equal(theorem(implies(implies(X_131,X_132),implies(X_131,or(not(X),X_132)))),true) ),[0,0,1,1],$fot(implies(X,X_132))]]) ).
cnf(refute_0_85,plain,
( theorem(implies(implies(X_131,X_132),implies(X_131,or(not(X),X_132)))) != true
| theorem(implies(implies(X_131,X_132),implies(X_131,implies(X,X_132)))) = true ),
inference(resolve,[$cnf( $equal(or(not(X),X_132),implies(X,X_132)) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
theorem(implies(implies(X_131,X_132),implies(X_131,implies(X,X_132)))) = true,
inference(resolve,[$cnf( $equal(theorem(implies(implies(X_131,X_132),implies(X_131,or(not(X),X_132)))),true) )],[refute_0_80,refute_0_85]) ).
cnf(refute_0_87,plain,
theorem(implies(implies(X_889,X_890),implies(X_889,implies(X_888,X_890)))) = true,
inference(subst,[],[refute_0_86:[bind(X,$fot(X_888)),bind(X_131,$fot(X_889)),bind(X_132,$fot(X_890))]]) ).
cnf(refute_0_88,plain,
( ifeq(theorem(implies(implies(X_889,X_890),implies(X_889,implies(X_888,X_890)))),true,ifeq(theorem(implies(X_889,X_890)),true,theorem(implies(X_889,implies(X_888,X_890))),true),true) != true
| theorem(implies(implies(X_889,X_890),implies(X_889,implies(X_888,X_890)))) != true
| ifeq(true,true,ifeq(theorem(implies(X_889,X_890)),true,theorem(implies(X_889,implies(X_888,X_890))),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(X_889,X_890),implies(X_889,implies(X_888,X_890)))),true,ifeq(theorem(implies(X_889,X_890)),true,theorem(implies(X_889,implies(X_888,X_890))),true),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_89,plain,
( ifeq(theorem(implies(implies(X_889,X_890),implies(X_889,implies(X_888,X_890)))),true,ifeq(theorem(implies(X_889,X_890)),true,theorem(implies(X_889,implies(X_888,X_890))),true),true) != true
| ifeq(true,true,ifeq(theorem(implies(X_889,X_890)),true,theorem(implies(X_889,implies(X_888,X_890))),true),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(implies(X_889,X_890),implies(X_889,implies(X_888,X_890)))),true) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
ifeq(true,true,ifeq(theorem(implies(X_889,X_890)),true,theorem(implies(X_889,implies(X_888,X_890))),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(X_889,X_890),implies(X_889,implies(X_888,X_890)))),true,ifeq(theorem(implies(X_889,X_890)),true,theorem(implies(X_889,implies(X_888,X_890))),true),true),true) )],[refute_0_17,refute_0_89]) ).
cnf(refute_0_91,plain,
ifeq(true,true,ifeq(theorem(implies(X_889,X_890)),true,theorem(implies(X_889,implies(X_888,X_890))),true),true) = ifeq(theorem(implies(X_889,X_890)),true,theorem(implies(X_889,implies(X_888,X_890))),true),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(ifeq(theorem(implies(X_889,X_890)),true,theorem(implies(X_889,implies(X_888,X_890))),true))),bind(C,$fot(true))]]) ).
cnf(refute_0_92,plain,
( ifeq(true,true,ifeq(theorem(implies(X_889,X_890)),true,theorem(implies(X_889,implies(X_888,X_890))),true),true) != ifeq(theorem(implies(X_889,X_890)),true,theorem(implies(X_889,implies(X_888,X_890))),true)
| ifeq(true,true,ifeq(theorem(implies(X_889,X_890)),true,theorem(implies(X_889,implies(X_888,X_890))),true),true) != true
| ifeq(theorem(implies(X_889,X_890)),true,theorem(implies(X_889,implies(X_888,X_890))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,ifeq(theorem(implies(X_889,X_890)),true,theorem(implies(X_889,implies(X_888,X_890))),true),true),true) ),[0],$fot(ifeq(theorem(implies(X_889,X_890)),true,theorem(implies(X_889,implies(X_888,X_890))),true))]]) ).
cnf(refute_0_93,plain,
( ifeq(true,true,ifeq(theorem(implies(X_889,X_890)),true,theorem(implies(X_889,implies(X_888,X_890))),true),true) != true
| ifeq(theorem(implies(X_889,X_890)),true,theorem(implies(X_889,implies(X_888,X_890))),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(theorem(implies(X_889,X_890)),true,theorem(implies(X_889,implies(X_888,X_890))),true),true),ifeq(theorem(implies(X_889,X_890)),true,theorem(implies(X_889,implies(X_888,X_890))),true)) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
ifeq(theorem(implies(X_889,X_890)),true,theorem(implies(X_889,implies(X_888,X_890))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(theorem(implies(X_889,X_890)),true,theorem(implies(X_889,implies(X_888,X_890))),true),true),true) )],[refute_0_90,refute_0_93]) ).
cnf(refute_0_95,plain,
ifeq(theorem(implies(not(or(X_6710,X_6709)),not(X_6709))),true,theorem(implies(not(or(X_6710,X_6709)),implies(X_888,not(X_6709)))),true) = true,
inference(subst,[],[refute_0_94:[bind(X_889,$fot(not(or(X_6710,X_6709)))),bind(X_890,$fot(not(X_6709)))]]) ).
cnf(refute_0_96,plain,
ifeq(theorem(implies(or(X_6,X_7),or(X_7,X_6))),true,ifeq(theorem(or(X_6,X_7)),true,theorem(or(X_7,X_6)),true),true) = true,
inference(subst,[],[rule_2:[bind(X,$fot(or(X_7,X_6))),bind(Y,$fot(or(X_6,X_7)))]]) ).
cnf(refute_0_97,plain,
ifeq(axiom(implies(or(X_6,X_7),or(X_7,X_6))),true,theorem(implies(or(X_6,X_7),or(X_7,X_6))),true) = true,
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_6,X_7),or(X_7,X_6))))]]) ).
cnf(refute_0_98,plain,
axiom(implies(or(X_6,X_7),or(X_7,X_6))) = true,
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_6)),bind(B,$fot(X_7))]]) ).
cnf(refute_0_99,plain,
( axiom(implies(or(X_6,X_7),or(X_7,X_6))) != true
| ifeq(axiom(implies(or(X_6,X_7),or(X_7,X_6))),true,theorem(implies(or(X_6,X_7),or(X_7,X_6))),true) != true
| ifeq(true,true,theorem(implies(or(X_6,X_7),or(X_7,X_6))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(axiom(implies(or(X_6,X_7),or(X_7,X_6))),true,theorem(implies(or(X_6,X_7),or(X_7,X_6))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_100,plain,
( ifeq(axiom(implies(or(X_6,X_7),or(X_7,X_6))),true,theorem(implies(or(X_6,X_7),or(X_7,X_6))),true) != true
| ifeq(true,true,theorem(implies(or(X_6,X_7),or(X_7,X_6))),true) = true ),
inference(resolve,[$cnf( $equal(axiom(implies(or(X_6,X_7),or(X_7,X_6))),true) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
ifeq(true,true,theorem(implies(or(X_6,X_7),or(X_7,X_6))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(axiom(implies(or(X_6,X_7),or(X_7,X_6))),true,theorem(implies(or(X_6,X_7),or(X_7,X_6))),true),true) )],[refute_0_97,refute_0_100]) ).
cnf(refute_0_102,plain,
ifeq(true,true,theorem(implies(or(X_6,X_7),or(X_7,X_6))),true) = theorem(implies(or(X_6,X_7),or(X_7,X_6))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(implies(or(X_6,X_7),or(X_7,X_6))))),bind(C,$fot(true))]]) ).
cnf(refute_0_103,plain,
( ifeq(true,true,theorem(implies(or(X_6,X_7),or(X_7,X_6))),true) != theorem(implies(or(X_6,X_7),or(X_7,X_6)))
| ifeq(true,true,theorem(implies(or(X_6,X_7),or(X_7,X_6))),true) != true
| theorem(implies(or(X_6,X_7),or(X_7,X_6))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(implies(or(X_6,X_7),or(X_7,X_6))),true),true) ),[0],$fot(theorem(implies(or(X_6,X_7),or(X_7,X_6))))]]) ).
cnf(refute_0_104,plain,
( ifeq(true,true,theorem(implies(or(X_6,X_7),or(X_7,X_6))),true) != true
| theorem(implies(or(X_6,X_7),or(X_7,X_6))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(or(X_6,X_7),or(X_7,X_6))),true),theorem(implies(or(X_6,X_7),or(X_7,X_6)))) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
theorem(implies(or(X_6,X_7),or(X_7,X_6))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(or(X_6,X_7),or(X_7,X_6))),true),true) )],[refute_0_101,refute_0_104]) ).
cnf(refute_0_106,plain,
( ifeq(theorem(implies(or(X_6,X_7),or(X_7,X_6))),true,ifeq(theorem(or(X_6,X_7)),true,theorem(or(X_7,X_6)),true),true) != true
| theorem(implies(or(X_6,X_7),or(X_7,X_6))) != true
| ifeq(true,true,ifeq(theorem(or(X_6,X_7)),true,theorem(or(X_7,X_6)),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(or(X_6,X_7),or(X_7,X_6))),true,ifeq(theorem(or(X_6,X_7)),true,theorem(or(X_7,X_6)),true),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_107,plain,
( ifeq(theorem(implies(or(X_6,X_7),or(X_7,X_6))),true,ifeq(theorem(or(X_6,X_7)),true,theorem(or(X_7,X_6)),true),true) != true
| ifeq(true,true,ifeq(theorem(or(X_6,X_7)),true,theorem(or(X_7,X_6)),true),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(or(X_6,X_7),or(X_7,X_6))),true) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
ifeq(true,true,ifeq(theorem(or(X_6,X_7)),true,theorem(or(X_7,X_6)),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(or(X_6,X_7),or(X_7,X_6))),true,ifeq(theorem(or(X_6,X_7)),true,theorem(or(X_7,X_6)),true),true),true) )],[refute_0_96,refute_0_107]) ).
cnf(refute_0_109,plain,
ifeq(true,true,ifeq(theorem(or(X_6,X_7)),true,theorem(or(X_7,X_6)),true),true) = ifeq(theorem(or(X_6,X_7)),true,theorem(or(X_7,X_6)),true),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(ifeq(theorem(or(X_6,X_7)),true,theorem(or(X_7,X_6)),true))),bind(C,$fot(true))]]) ).
cnf(refute_0_110,plain,
( ifeq(true,true,ifeq(theorem(or(X_6,X_7)),true,theorem(or(X_7,X_6)),true),true) != ifeq(theorem(or(X_6,X_7)),true,theorem(or(X_7,X_6)),true)
| ifeq(true,true,ifeq(theorem(or(X_6,X_7)),true,theorem(or(X_7,X_6)),true),true) != true
| ifeq(theorem(or(X_6,X_7)),true,theorem(or(X_7,X_6)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,ifeq(theorem(or(X_6,X_7)),true,theorem(or(X_7,X_6)),true),true),true) ),[0],$fot(ifeq(theorem(or(X_6,X_7)),true,theorem(or(X_7,X_6)),true))]]) ).
cnf(refute_0_111,plain,
( ifeq(true,true,ifeq(theorem(or(X_6,X_7)),true,theorem(or(X_7,X_6)),true),true) != true
| ifeq(theorem(or(X_6,X_7)),true,theorem(or(X_7,X_6)),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(theorem(or(X_6,X_7)),true,theorem(or(X_7,X_6)),true),true),ifeq(theorem(or(X_6,X_7)),true,theorem(or(X_7,X_6)),true)) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
ifeq(theorem(or(X_6,X_7)),true,theorem(or(X_7,X_6)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(theorem(or(X_6,X_7)),true,theorem(or(X_7,X_6)),true),true),true) )],[refute_0_108,refute_0_111]) ).
cnf(refute_0_113,plain,
ifeq(theorem(or(not(X),X_46)),true,theorem(or(X_46,not(X))),true) = true,
inference(subst,[],[refute_0_112:[bind(X_6,$fot(not(X))),bind(X_7,$fot(X_46))]]) ).
cnf(refute_0_114,plain,
implies(X,X_46) = or(not(X),X_46),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_46))]]) ).
cnf(refute_0_115,plain,
( implies(X,X_46) != or(not(X),X_46)
| or(not(X),X_46) = implies(X,X_46) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,X_46))),bind(Y0,$fot(or(not(X),X_46)))]]) ).
cnf(refute_0_116,plain,
or(not(X),X_46) = implies(X,X_46),
inference(resolve,[$cnf( $equal(implies(X,X_46),or(not(X),X_46)) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
( ifeq(theorem(or(not(X),X_46)),true,theorem(or(X_46,not(X))),true) != true
| or(not(X),X_46) != implies(X,X_46)
| ifeq(theorem(implies(X,X_46)),true,theorem(or(X_46,not(X))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(or(not(X),X_46)),true,theorem(or(X_46,not(X))),true),true) ),[0,0,0],$fot(implies(X,X_46))]]) ).
cnf(refute_0_118,plain,
( ifeq(theorem(or(not(X),X_46)),true,theorem(or(X_46,not(X))),true) != true
| ifeq(theorem(implies(X,X_46)),true,theorem(or(X_46,not(X))),true) = true ),
inference(resolve,[$cnf( $equal(or(not(X),X_46),implies(X,X_46)) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
ifeq(theorem(implies(X,X_46)),true,theorem(or(X_46,not(X))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(or(not(X),X_46)),true,theorem(or(X_46,not(X))),true),true) )],[refute_0_113,refute_0_118]) ).
cnf(refute_0_120,plain,
ifeq(theorem(implies(X,not(not(or(X_2301,X))))),true,theorem(or(not(not(or(X_2301,X))),not(X))),true) = true,
inference(subst,[],[refute_0_119:[bind(X_46,$fot(not(not(or(X_2301,X)))))]]) ).
cnf(refute_0_121,plain,
ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),implies(X_10,not(not(or(X_11,X_10)))))),true,theorem(implies(X_10,not(not(or(X_11,X_10))))),true) = true,
inference(subst,[],[refute_0_38:[bind(X_20,$fot(implies(X_10,not(not(or(X_11,X_10))))))]]) ).
cnf(refute_0_122,plain,
ifeq(theorem(implies(implies(X_32,X_33),implies(or(X_34,X_32),or(X_34,X_33)))),true,ifeq(theorem(implies(X_32,X_33)),true,theorem(implies(or(X_34,X_32),or(X_34,X_33))),true),true) = true,
inference(subst,[],[rule_2:[bind(X,$fot(implies(or(X_34,X_32),or(X_34,X_33)))),bind(Y,$fot(implies(X_32,X_33)))]]) ).
cnf(refute_0_123,plain,
theorem(implies(implies(X_32,X_33),implies(or(X_34,X_32),or(X_34,X_33)))) = true,
inference(subst,[],[refute_0_48:[bind(X_17,$fot(X_32)),bind(X_18,$fot(X_33)),bind(X_19,$fot(X_34))]]) ).
cnf(refute_0_124,plain,
( ifeq(theorem(implies(implies(X_32,X_33),implies(or(X_34,X_32),or(X_34,X_33)))),true,ifeq(theorem(implies(X_32,X_33)),true,theorem(implies(or(X_34,X_32),or(X_34,X_33))),true),true) != true
| theorem(implies(implies(X_32,X_33),implies(or(X_34,X_32),or(X_34,X_33)))) != true
| ifeq(true,true,ifeq(theorem(implies(X_32,X_33)),true,theorem(implies(or(X_34,X_32),or(X_34,X_33))),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(X_32,X_33),implies(or(X_34,X_32),or(X_34,X_33)))),true,ifeq(theorem(implies(X_32,X_33)),true,theorem(implies(or(X_34,X_32),or(X_34,X_33))),true),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_125,plain,
( ifeq(theorem(implies(implies(X_32,X_33),implies(or(X_34,X_32),or(X_34,X_33)))),true,ifeq(theorem(implies(X_32,X_33)),true,theorem(implies(or(X_34,X_32),or(X_34,X_33))),true),true) != true
| ifeq(true,true,ifeq(theorem(implies(X_32,X_33)),true,theorem(implies(or(X_34,X_32),or(X_34,X_33))),true),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(implies(X_32,X_33),implies(or(X_34,X_32),or(X_34,X_33)))),true) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
ifeq(true,true,ifeq(theorem(implies(X_32,X_33)),true,theorem(implies(or(X_34,X_32),or(X_34,X_33))),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(X_32,X_33),implies(or(X_34,X_32),or(X_34,X_33)))),true,ifeq(theorem(implies(X_32,X_33)),true,theorem(implies(or(X_34,X_32),or(X_34,X_33))),true),true),true) )],[refute_0_122,refute_0_125]) ).
cnf(refute_0_127,plain,
ifeq(true,true,ifeq(theorem(implies(X_32,X_33)),true,theorem(implies(or(X_34,X_32),or(X_34,X_33))),true),true) = ifeq(theorem(implies(X_32,X_33)),true,theorem(implies(or(X_34,X_32),or(X_34,X_33))),true),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(ifeq(theorem(implies(X_32,X_33)),true,theorem(implies(or(X_34,X_32),or(X_34,X_33))),true))),bind(C,$fot(true))]]) ).
cnf(refute_0_128,plain,
( ifeq(true,true,ifeq(theorem(implies(X_32,X_33)),true,theorem(implies(or(X_34,X_32),or(X_34,X_33))),true),true) != ifeq(theorem(implies(X_32,X_33)),true,theorem(implies(or(X_34,X_32),or(X_34,X_33))),true)
| ifeq(true,true,ifeq(theorem(implies(X_32,X_33)),true,theorem(implies(or(X_34,X_32),or(X_34,X_33))),true),true) != true
| ifeq(theorem(implies(X_32,X_33)),true,theorem(implies(or(X_34,X_32),or(X_34,X_33))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,ifeq(theorem(implies(X_32,X_33)),true,theorem(implies(or(X_34,X_32),or(X_34,X_33))),true),true),true) ),[0],$fot(ifeq(theorem(implies(X_32,X_33)),true,theorem(implies(or(X_34,X_32),or(X_34,X_33))),true))]]) ).
cnf(refute_0_129,plain,
( ifeq(true,true,ifeq(theorem(implies(X_32,X_33)),true,theorem(implies(or(X_34,X_32),or(X_34,X_33))),true),true) != true
| ifeq(theorem(implies(X_32,X_33)),true,theorem(implies(or(X_34,X_32),or(X_34,X_33))),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(theorem(implies(X_32,X_33)),true,theorem(implies(or(X_34,X_32),or(X_34,X_33))),true),true),ifeq(theorem(implies(X_32,X_33)),true,theorem(implies(or(X_34,X_32),or(X_34,X_33))),true)) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
ifeq(theorem(implies(X_32,X_33)),true,theorem(implies(or(X_34,X_32),or(X_34,X_33))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(theorem(implies(X_32,X_33)),true,theorem(implies(or(X_34,X_32),or(X_34,X_33))),true),true),true) )],[refute_0_126,refute_0_129]) ).
cnf(refute_0_131,plain,
ifeq(theorem(implies(X_220,not(not(X_220)))),true,theorem(implies(or(X_222,X_220),or(X_222,not(not(X_220))))),true) = true,
inference(subst,[],[refute_0_130:[bind(X_32,$fot(X_220)),bind(X_33,$fot(not(not(X_220)))),bind(X_34,$fot(X_222))]]) ).
cnf(refute_0_132,plain,
ifeq(theorem(implies(not(X_160),not(X_160))),true,theorem(or(not(X_160),not(not(X_160)))),true) = true,
inference(subst,[],[refute_0_119:[bind(X,$fot(not(X_160))),bind(X_46,$fot(not(X_160)))]]) ).
cnf(refute_0_133,plain,
ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,ifeq(theorem(implies(X_49,implies(X_50,X_49))),true,theorem(X),true),true) = true,
inference(subst,[],[rule_2:[bind(Y,$fot(implies(X_49,implies(X_50,X_49))))]]) ).
cnf(refute_0_134,plain,
theorem(implies(X_10,or(not(X_14),X_10))) = true,
inference(subst,[],[refute_0_27:[bind(X_11,$fot(not(X_14)))]]) ).
cnf(refute_0_135,plain,
implies(X_14,X_10) = or(not(X_14),X_10),
inference(subst,[],[implies_definition:[bind(X,$fot(X_14)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_136,plain,
( implies(X_14,X_10) != or(not(X_14),X_10)
| or(not(X_14),X_10) = implies(X_14,X_10) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_14,X_10))),bind(Y0,$fot(or(not(X_14),X_10)))]]) ).
cnf(refute_0_137,plain,
or(not(X_14),X_10) = implies(X_14,X_10),
inference(resolve,[$cnf( $equal(implies(X_14,X_10),or(not(X_14),X_10)) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
( or(not(X_14),X_10) != implies(X_14,X_10)
| theorem(implies(X_10,or(not(X_14),X_10))) != true
| theorem(implies(X_10,implies(X_14,X_10))) = true ),
introduced(tautology,[equality,[$cnf( $equal(theorem(implies(X_10,or(not(X_14),X_10))),true) ),[0,0,1],$fot(implies(X_14,X_10))]]) ).
cnf(refute_0_139,plain,
( theorem(implies(X_10,or(not(X_14),X_10))) != true
| theorem(implies(X_10,implies(X_14,X_10))) = true ),
inference(resolve,[$cnf( $equal(or(not(X_14),X_10),implies(X_14,X_10)) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
theorem(implies(X_10,implies(X_14,X_10))) = true,
inference(resolve,[$cnf( $equal(theorem(implies(X_10,or(not(X_14),X_10))),true) )],[refute_0_134,refute_0_139]) ).
cnf(refute_0_141,plain,
theorem(implies(X_49,implies(X_50,X_49))) = true,
inference(subst,[],[refute_0_140:[bind(X_10,$fot(X_49)),bind(X_14,$fot(X_50))]]) ).
cnf(refute_0_142,plain,
( ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,ifeq(theorem(implies(X_49,implies(X_50,X_49))),true,theorem(X),true),true) != true
| theorem(implies(X_49,implies(X_50,X_49))) != true
| ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,ifeq(true,true,theorem(X),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,ifeq(theorem(implies(X_49,implies(X_50,X_49))),true,theorem(X),true),true),true) ),[0,2,0],$fot(true)]]) ).
cnf(refute_0_143,plain,
( ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,ifeq(theorem(implies(X_49,implies(X_50,X_49))),true,theorem(X),true),true) != true
| ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,ifeq(true,true,theorem(X),true),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(X_49,implies(X_50,X_49))),true) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,ifeq(true,true,theorem(X),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,ifeq(theorem(implies(X_49,implies(X_50,X_49))),true,theorem(X),true),true),true) )],[refute_0_133,refute_0_143]) ).
cnf(refute_0_145,plain,
ifeq(true,true,theorem(X),true) = theorem(X),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(X))),bind(C,$fot(true))]]) ).
cnf(refute_0_146,plain,
ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,ifeq(true,true,theorem(X),true),true) = ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,ifeq(true,true,theorem(X),true),true),
introduced(tautology,[refl,[$fot(ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,ifeq(true,true,theorem(X),true),true))]]) ).
cnf(refute_0_147,plain,
( ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,ifeq(true,true,theorem(X),true),true) != ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,ifeq(true,true,theorem(X),true),true)
| ifeq(true,true,theorem(X),true) != theorem(X)
| ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,ifeq(true,true,theorem(X),true),true) = ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,theorem(X),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,ifeq(true,true,theorem(X),true),true),ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,ifeq(true,true,theorem(X),true),true)) ),[1,2],$fot(theorem(X))]]) ).
cnf(refute_0_148,plain,
( ifeq(true,true,theorem(X),true) != theorem(X)
| ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,ifeq(true,true,theorem(X),true),true) = ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,theorem(X),true) ),
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,ifeq(true,true,theorem(X),true),true),ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,ifeq(true,true,theorem(X),true),true)) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,ifeq(true,true,theorem(X),true),true) = ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,theorem(X),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(X),true),theorem(X)) )],[refute_0_145,refute_0_148]) ).
cnf(refute_0_150,plain,
( ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,ifeq(true,true,theorem(X),true),true) != ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,theorem(X),true)
| ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,ifeq(true,true,theorem(X),true),true) != true
| ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,theorem(X),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,ifeq(true,true,theorem(X),true),true),true) ),[0],$fot(ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,theorem(X),true))]]) ).
cnf(refute_0_151,plain,
( ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,ifeq(true,true,theorem(X),true),true) != true
| ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,theorem(X),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,ifeq(true,true,theorem(X),true),true),ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,theorem(X),true)) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,theorem(X),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(X_49,implies(X_50,X_49)),X)),true,ifeq(true,true,theorem(X),true),true),true) )],[refute_0_144,refute_0_151]) ).
cnf(refute_0_153,plain,
ifeq(theorem(implies(implies(not(X_159),implies(X_159,not(X_159))),implies(not(X_159),not(X_159)))),true,theorem(implies(not(X_159),not(X_159))),true) = true,
inference(subst,[],[refute_0_152:[bind(X,$fot(implies(not(X_159),not(X_159)))),bind(X_49,$fot(not(X_159))),bind(X_50,$fot(X_159))]]) ).
cnf(refute_0_154,plain,
ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,ifeq(theorem(implies(implies(X_14,not(X_14)),not(X_14))),true,theorem(X_20),true),true) = true,
inference(subst,[],[rule_2:[bind(X,$fot(X_20)),bind(Y,$fot(implies(implies(X_14,not(X_14)),not(X_14))))]]) ).
cnf(refute_0_155,plain,
ifeq(axiom(implies(or(X_1,X_1),X_1)),true,theorem(implies(or(X_1,X_1),X_1)),true) = true,
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_1,X_1),X_1)))]]) ).
cnf(refute_0_156,plain,
axiom(implies(or(X_1,X_1),X_1)) = true,
inference(subst,[],[axiom_1_2:[bind(A,$fot(X_1))]]) ).
cnf(refute_0_157,plain,
( axiom(implies(or(X_1,X_1),X_1)) != true
| ifeq(axiom(implies(or(X_1,X_1),X_1)),true,theorem(implies(or(X_1,X_1),X_1)),true) != true
| ifeq(true,true,theorem(implies(or(X_1,X_1),X_1)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(axiom(implies(or(X_1,X_1),X_1)),true,theorem(implies(or(X_1,X_1),X_1)),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_158,plain,
( ifeq(axiom(implies(or(X_1,X_1),X_1)),true,theorem(implies(or(X_1,X_1),X_1)),true) != true
| ifeq(true,true,theorem(implies(or(X_1,X_1),X_1)),true) = true ),
inference(resolve,[$cnf( $equal(axiom(implies(or(X_1,X_1),X_1)),true) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
ifeq(true,true,theorem(implies(or(X_1,X_1),X_1)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(axiom(implies(or(X_1,X_1),X_1)),true,theorem(implies(or(X_1,X_1),X_1)),true),true) )],[refute_0_155,refute_0_158]) ).
cnf(refute_0_160,plain,
ifeq(true,true,theorem(implies(or(X_1,X_1),X_1)),true) = theorem(implies(or(X_1,X_1),X_1)),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(implies(or(X_1,X_1),X_1)))),bind(C,$fot(true))]]) ).
cnf(refute_0_161,plain,
( ifeq(true,true,theorem(implies(or(X_1,X_1),X_1)),true) != theorem(implies(or(X_1,X_1),X_1))
| ifeq(true,true,theorem(implies(or(X_1,X_1),X_1)),true) != true
| theorem(implies(or(X_1,X_1),X_1)) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(implies(or(X_1,X_1),X_1)),true),true) ),[0],$fot(theorem(implies(or(X_1,X_1),X_1)))]]) ).
cnf(refute_0_162,plain,
( ifeq(true,true,theorem(implies(or(X_1,X_1),X_1)),true) != true
| theorem(implies(or(X_1,X_1),X_1)) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(or(X_1,X_1),X_1)),true),theorem(implies(or(X_1,X_1),X_1))) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
theorem(implies(or(X_1,X_1),X_1)) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(or(X_1,X_1),X_1)),true),true) )],[refute_0_159,refute_0_162]) ).
cnf(refute_0_164,plain,
theorem(implies(or(not(X_14),not(X_14)),not(X_14))) = true,
inference(subst,[],[refute_0_163:[bind(X_1,$fot(not(X_14)))]]) ).
cnf(refute_0_165,plain,
implies(X_14,not(X_14)) = or(not(X_14),not(X_14)),
inference(subst,[],[implies_definition:[bind(X,$fot(X_14)),bind(Y,$fot(not(X_14)))]]) ).
cnf(refute_0_166,plain,
( implies(X_14,not(X_14)) != or(not(X_14),not(X_14))
| or(not(X_14),not(X_14)) = implies(X_14,not(X_14)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_14,not(X_14)))),bind(Y0,$fot(or(not(X_14),not(X_14))))]]) ).
cnf(refute_0_167,plain,
or(not(X_14),not(X_14)) = implies(X_14,not(X_14)),
inference(resolve,[$cnf( $equal(implies(X_14,not(X_14)),or(not(X_14),not(X_14))) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
( or(not(X_14),not(X_14)) != implies(X_14,not(X_14))
| theorem(implies(or(not(X_14),not(X_14)),not(X_14))) != true
| theorem(implies(implies(X_14,not(X_14)),not(X_14))) = true ),
introduced(tautology,[equality,[$cnf( $equal(theorem(implies(or(not(X_14),not(X_14)),not(X_14))),true) ),[0,0,0],$fot(implies(X_14,not(X_14)))]]) ).
cnf(refute_0_169,plain,
( theorem(implies(or(not(X_14),not(X_14)),not(X_14))) != true
| theorem(implies(implies(X_14,not(X_14)),not(X_14))) = true ),
inference(resolve,[$cnf( $equal(or(not(X_14),not(X_14)),implies(X_14,not(X_14))) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
theorem(implies(implies(X_14,not(X_14)),not(X_14))) = true,
inference(resolve,[$cnf( $equal(theorem(implies(or(not(X_14),not(X_14)),not(X_14))),true) )],[refute_0_164,refute_0_169]) ).
cnf(refute_0_171,plain,
( ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,ifeq(theorem(implies(implies(X_14,not(X_14)),not(X_14))),true,theorem(X_20),true),true) != true
| theorem(implies(implies(X_14,not(X_14)),not(X_14))) != true
| ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,ifeq(true,true,theorem(X_20),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,ifeq(theorem(implies(implies(X_14,not(X_14)),not(X_14))),true,theorem(X_20),true),true),true) ),[0,2,0],$fot(true)]]) ).
cnf(refute_0_172,plain,
( ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,ifeq(theorem(implies(implies(X_14,not(X_14)),not(X_14))),true,theorem(X_20),true),true) != true
| ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,ifeq(true,true,theorem(X_20),true),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(implies(X_14,not(X_14)),not(X_14))),true) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,ifeq(true,true,theorem(X_20),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,ifeq(theorem(implies(implies(X_14,not(X_14)),not(X_14))),true,theorem(X_20),true),true),true) )],[refute_0_154,refute_0_172]) ).
cnf(refute_0_174,plain,
ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,ifeq(true,true,theorem(X_20),true),true) = ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,ifeq(true,true,theorem(X_20),true),true),
introduced(tautology,[refl,[$fot(ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,ifeq(true,true,theorem(X_20),true),true))]]) ).
cnf(refute_0_175,plain,
( ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,ifeq(true,true,theorem(X_20),true),true) != ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,ifeq(true,true,theorem(X_20),true),true)
| ifeq(true,true,theorem(X_20),true) != theorem(X_20)
| ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,ifeq(true,true,theorem(X_20),true),true) = ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,theorem(X_20),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,ifeq(true,true,theorem(X_20),true),true),ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,ifeq(true,true,theorem(X_20),true),true)) ),[1,2],$fot(theorem(X_20))]]) ).
cnf(refute_0_176,plain,
( ifeq(true,true,theorem(X_20),true) != theorem(X_20)
| ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,ifeq(true,true,theorem(X_20),true),true) = ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,theorem(X_20),true) ),
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,ifeq(true,true,theorem(X_20),true),true),ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,ifeq(true,true,theorem(X_20),true),true)) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,ifeq(true,true,theorem(X_20),true),true) = ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,theorem(X_20),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(X_20),true),theorem(X_20)) )],[refute_0_31,refute_0_176]) ).
cnf(refute_0_178,plain,
( ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,ifeq(true,true,theorem(X_20),true),true) != ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,theorem(X_20),true)
| ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,ifeq(true,true,theorem(X_20),true),true) != true
| ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,theorem(X_20),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,ifeq(true,true,theorem(X_20),true),true),true) ),[0],$fot(ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,theorem(X_20),true))]]) ).
cnf(refute_0_179,plain,
( ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,ifeq(true,true,theorem(X_20),true),true) != true
| ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,theorem(X_20),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,ifeq(true,true,theorem(X_20),true),true),ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,theorem(X_20),true)) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,theorem(X_20),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_20)),true,ifeq(true,true,theorem(X_20),true),true),true) )],[refute_0_173,refute_0_179]) ).
cnf(refute_0_181,plain,
ifeq(theorem(implies(implies(implies(X_98,not(X_98)),not(X_98)),implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98))))),true,theorem(implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98)))),true) = true,
inference(subst,[],[refute_0_180:[bind(X_14,$fot(X_98)),bind(X_20,$fot(implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98)))))]]) ).
cnf(refute_0_182,plain,
theorem(implies(implies(implies(X_98,not(X_98)),not(X_98)),implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98))))) = true,
inference(subst,[],[refute_0_71:[bind(X_32,$fot(implies(X_98,not(X_98)))),bind(X_33,$fot(not(X_98)))]]) ).
cnf(refute_0_183,plain,
( ifeq(theorem(implies(implies(implies(X_98,not(X_98)),not(X_98)),implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98))))),true,theorem(implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98)))),true) != true
| theorem(implies(implies(implies(X_98,not(X_98)),not(X_98)),implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98))))) != true
| ifeq(true,true,theorem(implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98)))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(implies(X_98,not(X_98)),not(X_98)),implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98))))),true,theorem(implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98)))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_184,plain,
( ifeq(theorem(implies(implies(implies(X_98,not(X_98)),not(X_98)),implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98))))),true,theorem(implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98)))),true) != true
| ifeq(true,true,theorem(implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98)))),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(implies(implies(X_98,not(X_98)),not(X_98)),implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98))))),true) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
ifeq(true,true,theorem(implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98)))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(implies(X_98,not(X_98)),not(X_98)),implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98))))),true,theorem(implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98)))),true),true) )],[refute_0_181,refute_0_184]) ).
cnf(refute_0_186,plain,
ifeq(true,true,theorem(implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98)))),true) = theorem(implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98)))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98)))))),bind(C,$fot(true))]]) ).
cnf(refute_0_187,plain,
( ifeq(true,true,theorem(implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98)))),true) != theorem(implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98))))
| ifeq(true,true,theorem(implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98)))),true) != true
| theorem(implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98)))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98)))),true),true) ),[0],$fot(theorem(implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98)))))]]) ).
cnf(refute_0_188,plain,
( ifeq(true,true,theorem(implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98)))),true) != true
| theorem(implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98)))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98)))),true),theorem(implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98))))) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
theorem(implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98)))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(implies(X,implies(X_98,not(X_98))),implies(X,not(X_98)))),true),true) )],[refute_0_185,refute_0_188]) ).
cnf(refute_0_190,plain,
theorem(implies(implies(not(X_159),implies(X_159,not(X_159))),implies(not(X_159),not(X_159)))) = true,
inference(subst,[],[refute_0_189:[bind(X,$fot(not(X_159))),bind(X_98,$fot(X_159))]]) ).
cnf(refute_0_191,plain,
( ifeq(theorem(implies(implies(not(X_159),implies(X_159,not(X_159))),implies(not(X_159),not(X_159)))),true,theorem(implies(not(X_159),not(X_159))),true) != true
| theorem(implies(implies(not(X_159),implies(X_159,not(X_159))),implies(not(X_159),not(X_159)))) != true
| ifeq(true,true,theorem(implies(not(X_159),not(X_159))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(not(X_159),implies(X_159,not(X_159))),implies(not(X_159),not(X_159)))),true,theorem(implies(not(X_159),not(X_159))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_192,plain,
( ifeq(theorem(implies(implies(not(X_159),implies(X_159,not(X_159))),implies(not(X_159),not(X_159)))),true,theorem(implies(not(X_159),not(X_159))),true) != true
| ifeq(true,true,theorem(implies(not(X_159),not(X_159))),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(implies(not(X_159),implies(X_159,not(X_159))),implies(not(X_159),not(X_159)))),true) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
ifeq(true,true,theorem(implies(not(X_159),not(X_159))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(not(X_159),implies(X_159,not(X_159))),implies(not(X_159),not(X_159)))),true,theorem(implies(not(X_159),not(X_159))),true),true) )],[refute_0_153,refute_0_192]) ).
cnf(refute_0_194,plain,
ifeq(true,true,theorem(implies(not(X_159),not(X_159))),true) = theorem(implies(not(X_159),not(X_159))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(implies(not(X_159),not(X_159))))),bind(C,$fot(true))]]) ).
cnf(refute_0_195,plain,
( ifeq(true,true,theorem(implies(not(X_159),not(X_159))),true) != theorem(implies(not(X_159),not(X_159)))
| ifeq(true,true,theorem(implies(not(X_159),not(X_159))),true) != true
| theorem(implies(not(X_159),not(X_159))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(implies(not(X_159),not(X_159))),true),true) ),[0],$fot(theorem(implies(not(X_159),not(X_159))))]]) ).
cnf(refute_0_196,plain,
( ifeq(true,true,theorem(implies(not(X_159),not(X_159))),true) != true
| theorem(implies(not(X_159),not(X_159))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(not(X_159),not(X_159))),true),theorem(implies(not(X_159),not(X_159)))) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
theorem(implies(not(X_159),not(X_159))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(not(X_159),not(X_159))),true),true) )],[refute_0_193,refute_0_196]) ).
cnf(refute_0_198,plain,
theorem(implies(not(X_160),not(X_160))) = true,
inference(subst,[],[refute_0_197:[bind(X_159,$fot(X_160))]]) ).
cnf(refute_0_199,plain,
( ifeq(theorem(implies(not(X_160),not(X_160))),true,theorem(or(not(X_160),not(not(X_160)))),true) != true
| theorem(implies(not(X_160),not(X_160))) != true
| ifeq(true,true,theorem(or(not(X_160),not(not(X_160)))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(not(X_160),not(X_160))),true,theorem(or(not(X_160),not(not(X_160)))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_200,plain,
( ifeq(theorem(implies(not(X_160),not(X_160))),true,theorem(or(not(X_160),not(not(X_160)))),true) != true
| ifeq(true,true,theorem(or(not(X_160),not(not(X_160)))),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(not(X_160),not(X_160))),true) )],[refute_0_198,refute_0_199]) ).
cnf(refute_0_201,plain,
ifeq(true,true,theorem(or(not(X_160),not(not(X_160)))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(not(X_160),not(X_160))),true,theorem(or(not(X_160),not(not(X_160)))),true),true) )],[refute_0_132,refute_0_200]) ).
cnf(refute_0_202,plain,
or(not(X_160),not(not(X_160))) = implies(X_160,not(not(X_160))),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_160)),bind(Y,$fot(not(not(X_160))))]]) ).
cnf(refute_0_203,plain,
theorem(or(not(X_160),not(not(X_160)))) = theorem(or(not(X_160),not(not(X_160)))),
introduced(tautology,[refl,[$fot(theorem(or(not(X_160),not(not(X_160)))))]]) ).
cnf(refute_0_204,plain,
( or(not(X_160),not(not(X_160))) != implies(X_160,not(not(X_160)))
| theorem(or(not(X_160),not(not(X_160)))) != theorem(or(not(X_160),not(not(X_160))))
| theorem(or(not(X_160),not(not(X_160)))) = theorem(implies(X_160,not(not(X_160)))) ),
introduced(tautology,[equality,[$cnf( $equal(theorem(or(not(X_160),not(not(X_160)))),theorem(or(not(X_160),not(not(X_160))))) ),[1,0],$fot(implies(X_160,not(not(X_160))))]]) ).
cnf(refute_0_205,plain,
( or(not(X_160),not(not(X_160))) != implies(X_160,not(not(X_160)))
| theorem(or(not(X_160),not(not(X_160)))) = theorem(implies(X_160,not(not(X_160)))) ),
inference(resolve,[$cnf( $equal(theorem(or(not(X_160),not(not(X_160)))),theorem(or(not(X_160),not(not(X_160))))) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
theorem(or(not(X_160),not(not(X_160)))) = theorem(implies(X_160,not(not(X_160)))),
inference(resolve,[$cnf( $equal(or(not(X_160),not(not(X_160))),implies(X_160,not(not(X_160)))) )],[refute_0_202,refute_0_205]) ).
cnf(refute_0_207,plain,
ifeq(true,true,theorem(or(not(X_160),not(not(X_160)))),true) = theorem(or(not(X_160),not(not(X_160)))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(or(not(X_160),not(not(X_160)))))),bind(C,$fot(true))]]) ).
cnf(refute_0_208,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_209,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_2,refute_0_208]) ).
cnf(refute_0_210,plain,
( ifeq(true,true,theorem(or(not(X_160),not(not(X_160)))),true) != theorem(or(not(X_160),not(not(X_160))))
| theorem(or(not(X_160),not(not(X_160)))) != theorem(implies(X_160,not(not(X_160))))
| ifeq(true,true,theorem(or(not(X_160),not(not(X_160)))),true) = theorem(implies(X_160,not(not(X_160)))) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(ifeq(true,true,theorem(or(not(X_160),not(not(X_160)))),true))),bind(Y0,$fot(theorem(or(not(X_160),not(not(X_160)))))),bind(Z,$fot(theorem(implies(X_160,not(not(X_160))))))]]) ).
cnf(refute_0_211,plain,
( theorem(or(not(X_160),not(not(X_160)))) != theorem(implies(X_160,not(not(X_160))))
| ifeq(true,true,theorem(or(not(X_160),not(not(X_160)))),true) = theorem(implies(X_160,not(not(X_160)))) ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(not(X_160),not(not(X_160)))),true),theorem(or(not(X_160),not(not(X_160))))) )],[refute_0_207,refute_0_210]) ).
cnf(refute_0_212,plain,
ifeq(true,true,theorem(or(not(X_160),not(not(X_160)))),true) = theorem(implies(X_160,not(not(X_160)))),
inference(resolve,[$cnf( $equal(theorem(or(not(X_160),not(not(X_160)))),theorem(implies(X_160,not(not(X_160))))) )],[refute_0_206,refute_0_211]) ).
cnf(refute_0_213,plain,
( ifeq(true,true,theorem(or(not(X_160),not(not(X_160)))),true) != theorem(implies(X_160,not(not(X_160))))
| ifeq(true,true,theorem(or(not(X_160),not(not(X_160)))),true) != true
| theorem(implies(X_160,not(not(X_160)))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(or(not(X_160),not(not(X_160)))),true),true) ),[0],$fot(theorem(implies(X_160,not(not(X_160)))))]]) ).
cnf(refute_0_214,plain,
( ifeq(true,true,theorem(or(not(X_160),not(not(X_160)))),true) != true
| theorem(implies(X_160,not(not(X_160)))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(not(X_160),not(not(X_160)))),true),theorem(implies(X_160,not(not(X_160))))) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
theorem(implies(X_160,not(not(X_160)))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(not(X_160),not(not(X_160)))),true),true) )],[refute_0_201,refute_0_214]) ).
cnf(refute_0_216,plain,
theorem(implies(X_220,not(not(X_220)))) = true,
inference(subst,[],[refute_0_215:[bind(X_160,$fot(X_220))]]) ).
cnf(refute_0_217,plain,
( ifeq(theorem(implies(X_220,not(not(X_220)))),true,theorem(implies(or(X_222,X_220),or(X_222,not(not(X_220))))),true) != true
| theorem(implies(X_220,not(not(X_220)))) != true
| ifeq(true,true,theorem(implies(or(X_222,X_220),or(X_222,not(not(X_220))))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(X_220,not(not(X_220)))),true,theorem(implies(or(X_222,X_220),or(X_222,not(not(X_220))))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_218,plain,
( ifeq(theorem(implies(X_220,not(not(X_220)))),true,theorem(implies(or(X_222,X_220),or(X_222,not(not(X_220))))),true) != true
| ifeq(true,true,theorem(implies(or(X_222,X_220),or(X_222,not(not(X_220))))),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(X_220,not(not(X_220)))),true) )],[refute_0_216,refute_0_217]) ).
cnf(refute_0_219,plain,
ifeq(true,true,theorem(implies(or(X_222,X_220),or(X_222,not(not(X_220))))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(X_220,not(not(X_220)))),true,theorem(implies(or(X_222,X_220),or(X_222,not(not(X_220))))),true),true) )],[refute_0_131,refute_0_218]) ).
cnf(refute_0_220,plain,
ifeq(true,true,theorem(implies(or(X_222,X_220),or(X_222,not(not(X_220))))),true) = theorem(implies(or(X_222,X_220),or(X_222,not(not(X_220))))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(implies(or(X_222,X_220),or(X_222,not(not(X_220))))))),bind(C,$fot(true))]]) ).
cnf(refute_0_221,plain,
( ifeq(true,true,theorem(implies(or(X_222,X_220),or(X_222,not(not(X_220))))),true) != theorem(implies(or(X_222,X_220),or(X_222,not(not(X_220)))))
| ifeq(true,true,theorem(implies(or(X_222,X_220),or(X_222,not(not(X_220))))),true) != true
| theorem(implies(or(X_222,X_220),or(X_222,not(not(X_220))))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(implies(or(X_222,X_220),or(X_222,not(not(X_220))))),true),true) ),[0],$fot(theorem(implies(or(X_222,X_220),or(X_222,not(not(X_220))))))]]) ).
cnf(refute_0_222,plain,
( ifeq(true,true,theorem(implies(or(X_222,X_220),or(X_222,not(not(X_220))))),true) != true
| theorem(implies(or(X_222,X_220),or(X_222,not(not(X_220))))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(or(X_222,X_220),or(X_222,not(not(X_220))))),true),theorem(implies(or(X_222,X_220),or(X_222,not(not(X_220)))))) )],[refute_0_220,refute_0_221]) ).
cnf(refute_0_223,plain,
theorem(implies(or(X_222,X_220),or(X_222,not(not(X_220))))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(or(X_222,X_220),or(X_222,not(not(X_220))))),true),true) )],[refute_0_219,refute_0_222]) ).
cnf(refute_0_224,plain,
theorem(implies(or(not(X),X_454),or(not(X),not(not(X_454))))) = true,
inference(subst,[],[refute_0_223:[bind(X_220,$fot(X_454)),bind(X_222,$fot(not(X)))]]) ).
cnf(refute_0_225,plain,
implies(X,not(not(X_454))) = or(not(X),not(not(X_454))),
inference(subst,[],[implies_definition:[bind(Y,$fot(not(not(X_454))))]]) ).
cnf(refute_0_226,plain,
( implies(X,not(not(X_454))) != or(not(X),not(not(X_454)))
| or(not(X),not(not(X_454))) = implies(X,not(not(X_454))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,not(not(X_454))))),bind(Y0,$fot(or(not(X),not(not(X_454)))))]]) ).
cnf(refute_0_227,plain,
or(not(X),not(not(X_454))) = implies(X,not(not(X_454))),
inference(resolve,[$cnf( $equal(implies(X,not(not(X_454))),or(not(X),not(not(X_454)))) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
( or(not(X),not(not(X_454))) != implies(X,not(not(X_454)))
| theorem(implies(or(not(X),X_454),or(not(X),not(not(X_454))))) != true
| theorem(implies(or(not(X),X_454),implies(X,not(not(X_454))))) = true ),
introduced(tautology,[equality,[$cnf( $equal(theorem(implies(or(not(X),X_454),or(not(X),not(not(X_454))))),true) ),[0,0,1],$fot(implies(X,not(not(X_454))))]]) ).
cnf(refute_0_229,plain,
( theorem(implies(or(not(X),X_454),or(not(X),not(not(X_454))))) != true
| theorem(implies(or(not(X),X_454),implies(X,not(not(X_454))))) = true ),
inference(resolve,[$cnf( $equal(or(not(X),not(not(X_454))),implies(X,not(not(X_454)))) )],[refute_0_227,refute_0_228]) ).
cnf(refute_0_230,plain,
theorem(implies(or(not(X),X_454),implies(X,not(not(X_454))))) = true,
inference(resolve,[$cnf( $equal(theorem(implies(or(not(X),X_454),or(not(X),not(not(X_454))))),true) )],[refute_0_224,refute_0_229]) ).
cnf(refute_0_231,plain,
or(not(X),X_454) = implies(X,X_454),
inference(subst,[],[refute_0_4:[bind(Y,$fot(X_454))]]) ).
cnf(refute_0_232,plain,
implies(or(not(X),X_454),implies(X,not(not(X_454)))) = implies(or(not(X),X_454),implies(X,not(not(X_454)))),
introduced(tautology,[refl,[$fot(implies(or(not(X),X_454),implies(X,not(not(X_454)))))]]) ).
cnf(refute_0_233,plain,
( implies(or(not(X),X_454),implies(X,not(not(X_454)))) != implies(or(not(X),X_454),implies(X,not(not(X_454))))
| or(not(X),X_454) != implies(X,X_454)
| implies(or(not(X),X_454),implies(X,not(not(X_454)))) = implies(implies(X,X_454),implies(X,not(not(X_454)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),X_454),implies(X,not(not(X_454)))),implies(or(not(X),X_454),implies(X,not(not(X_454))))) ),[1,0],$fot(implies(X,X_454))]]) ).
cnf(refute_0_234,plain,
( or(not(X),X_454) != implies(X,X_454)
| implies(or(not(X),X_454),implies(X,not(not(X_454)))) = implies(implies(X,X_454),implies(X,not(not(X_454)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_454),implies(X,not(not(X_454)))),implies(or(not(X),X_454),implies(X,not(not(X_454))))) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
implies(or(not(X),X_454),implies(X,not(not(X_454)))) = implies(implies(X,X_454),implies(X,not(not(X_454)))),
inference(resolve,[$cnf( $equal(or(not(X),X_454),implies(X,X_454)) )],[refute_0_231,refute_0_234]) ).
cnf(refute_0_236,plain,
theorem(implies(or(not(X),X_454),implies(X,not(not(X_454))))) = theorem(implies(or(not(X),X_454),implies(X,not(not(X_454))))),
introduced(tautology,[refl,[$fot(theorem(implies(or(not(X),X_454),implies(X,not(not(X_454))))))]]) ).
cnf(refute_0_237,plain,
( implies(or(not(X),X_454),implies(X,not(not(X_454)))) != implies(implies(X,X_454),implies(X,not(not(X_454))))
| theorem(implies(or(not(X),X_454),implies(X,not(not(X_454))))) != theorem(implies(or(not(X),X_454),implies(X,not(not(X_454)))))
| theorem(implies(or(not(X),X_454),implies(X,not(not(X_454))))) = theorem(implies(implies(X,X_454),implies(X,not(not(X_454))))) ),
introduced(tautology,[equality,[$cnf( $equal(theorem(implies(or(not(X),X_454),implies(X,not(not(X_454))))),theorem(implies(or(not(X),X_454),implies(X,not(not(X_454)))))) ),[1,0],$fot(implies(implies(X,X_454),implies(X,not(not(X_454)))))]]) ).
cnf(refute_0_238,plain,
( implies(or(not(X),X_454),implies(X,not(not(X_454)))) != implies(implies(X,X_454),implies(X,not(not(X_454))))
| theorem(implies(or(not(X),X_454),implies(X,not(not(X_454))))) = theorem(implies(implies(X,X_454),implies(X,not(not(X_454))))) ),
inference(resolve,[$cnf( $equal(theorem(implies(or(not(X),X_454),implies(X,not(not(X_454))))),theorem(implies(or(not(X),X_454),implies(X,not(not(X_454)))))) )],[refute_0_236,refute_0_237]) ).
cnf(refute_0_239,plain,
theorem(implies(or(not(X),X_454),implies(X,not(not(X_454))))) = theorem(implies(implies(X,X_454),implies(X,not(not(X_454))))),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_454),implies(X,not(not(X_454)))),implies(implies(X,X_454),implies(X,not(not(X_454))))) )],[refute_0_235,refute_0_238]) ).
cnf(refute_0_240,plain,
( theorem(implies(or(not(X),X_454),implies(X,not(not(X_454))))) != theorem(implies(implies(X,X_454),implies(X,not(not(X_454)))))
| theorem(implies(or(not(X),X_454),implies(X,not(not(X_454))))) != true
| theorem(implies(implies(X,X_454),implies(X,not(not(X_454))))) = true ),
introduced(tautology,[equality,[$cnf( $equal(theorem(implies(or(not(X),X_454),implies(X,not(not(X_454))))),true) ),[0],$fot(theorem(implies(implies(X,X_454),implies(X,not(not(X_454))))))]]) ).
cnf(refute_0_241,plain,
( theorem(implies(or(not(X),X_454),implies(X,not(not(X_454))))) != true
| theorem(implies(implies(X,X_454),implies(X,not(not(X_454))))) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(or(not(X),X_454),implies(X,not(not(X_454))))),theorem(implies(implies(X,X_454),implies(X,not(not(X_454)))))) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
theorem(implies(implies(X,X_454),implies(X,not(not(X_454))))) = true,
inference(resolve,[$cnf( $equal(theorem(implies(or(not(X),X_454),implies(X,not(not(X_454))))),true) )],[refute_0_230,refute_0_241]) ).
cnf(refute_0_243,plain,
theorem(implies(implies(X_10,or(X_11,X_10)),implies(X_10,not(not(or(X_11,X_10)))))) = true,
inference(subst,[],[refute_0_242:[bind(X,$fot(X_10)),bind(X_454,$fot(or(X_11,X_10)))]]) ).
cnf(refute_0_244,plain,
( ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),implies(X_10,not(not(or(X_11,X_10)))))),true,theorem(implies(X_10,not(not(or(X_11,X_10))))),true) != true
| theorem(implies(implies(X_10,or(X_11,X_10)),implies(X_10,not(not(or(X_11,X_10)))))) != true
| ifeq(true,true,theorem(implies(X_10,not(not(or(X_11,X_10))))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),implies(X_10,not(not(or(X_11,X_10)))))),true,theorem(implies(X_10,not(not(or(X_11,X_10))))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_245,plain,
( ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),implies(X_10,not(not(or(X_11,X_10)))))),true,theorem(implies(X_10,not(not(or(X_11,X_10))))),true) != true
| ifeq(true,true,theorem(implies(X_10,not(not(or(X_11,X_10))))),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(implies(X_10,or(X_11,X_10)),implies(X_10,not(not(or(X_11,X_10)))))),true) )],[refute_0_243,refute_0_244]) ).
cnf(refute_0_246,plain,
ifeq(true,true,theorem(implies(X_10,not(not(or(X_11,X_10))))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(X_10,or(X_11,X_10)),implies(X_10,not(not(or(X_11,X_10)))))),true,theorem(implies(X_10,not(not(or(X_11,X_10))))),true),true) )],[refute_0_121,refute_0_245]) ).
cnf(refute_0_247,plain,
ifeq(true,true,theorem(implies(X_10,not(not(or(X_11,X_10))))),true) = theorem(implies(X_10,not(not(or(X_11,X_10))))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(implies(X_10,not(not(or(X_11,X_10))))))),bind(C,$fot(true))]]) ).
cnf(refute_0_248,plain,
( ifeq(true,true,theorem(implies(X_10,not(not(or(X_11,X_10))))),true) != theorem(implies(X_10,not(not(or(X_11,X_10)))))
| ifeq(true,true,theorem(implies(X_10,not(not(or(X_11,X_10))))),true) != true
| theorem(implies(X_10,not(not(or(X_11,X_10))))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(implies(X_10,not(not(or(X_11,X_10))))),true),true) ),[0],$fot(theorem(implies(X_10,not(not(or(X_11,X_10))))))]]) ).
cnf(refute_0_249,plain,
( ifeq(true,true,theorem(implies(X_10,not(not(or(X_11,X_10))))),true) != true
| theorem(implies(X_10,not(not(or(X_11,X_10))))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(X_10,not(not(or(X_11,X_10))))),true),theorem(implies(X_10,not(not(or(X_11,X_10)))))) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
theorem(implies(X_10,not(not(or(X_11,X_10))))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(X_10,not(not(or(X_11,X_10))))),true),true) )],[refute_0_246,refute_0_249]) ).
cnf(refute_0_251,plain,
theorem(implies(X,not(not(or(X_2301,X))))) = true,
inference(subst,[],[refute_0_250:[bind(X_10,$fot(X)),bind(X_11,$fot(X_2301))]]) ).
cnf(refute_0_252,plain,
( ifeq(theorem(implies(X,not(not(or(X_2301,X))))),true,theorem(or(not(not(or(X_2301,X))),not(X))),true) != true
| theorem(implies(X,not(not(or(X_2301,X))))) != true
| ifeq(true,true,theorem(or(not(not(or(X_2301,X))),not(X))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(X,not(not(or(X_2301,X))))),true,theorem(or(not(not(or(X_2301,X))),not(X))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_253,plain,
( ifeq(theorem(implies(X,not(not(or(X_2301,X))))),true,theorem(or(not(not(or(X_2301,X))),not(X))),true) != true
| ifeq(true,true,theorem(or(not(not(or(X_2301,X))),not(X))),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(X,not(not(or(X_2301,X))))),true) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
ifeq(true,true,theorem(or(not(not(or(X_2301,X))),not(X))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(X,not(not(or(X_2301,X))))),true,theorem(or(not(not(or(X_2301,X))),not(X))),true),true) )],[refute_0_120,refute_0_253]) ).
cnf(refute_0_255,plain,
or(not(not(or(X_2301,X))),not(X)) = implies(not(or(X_2301,X)),not(X)),
inference(subst,[],[refute_0_4:[bind(X,$fot(not(or(X_2301,X)))),bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_256,plain,
theorem(or(not(not(or(X_2301,X))),not(X))) = theorem(or(not(not(or(X_2301,X))),not(X))),
introduced(tautology,[refl,[$fot(theorem(or(not(not(or(X_2301,X))),not(X))))]]) ).
cnf(refute_0_257,plain,
( or(not(not(or(X_2301,X))),not(X)) != implies(not(or(X_2301,X)),not(X))
| theorem(or(not(not(or(X_2301,X))),not(X))) != theorem(or(not(not(or(X_2301,X))),not(X)))
| theorem(or(not(not(or(X_2301,X))),not(X))) = theorem(implies(not(or(X_2301,X)),not(X))) ),
introduced(tautology,[equality,[$cnf( $equal(theorem(or(not(not(or(X_2301,X))),not(X))),theorem(or(not(not(or(X_2301,X))),not(X)))) ),[1,0],$fot(implies(not(or(X_2301,X)),not(X)))]]) ).
cnf(refute_0_258,plain,
( or(not(not(or(X_2301,X))),not(X)) != implies(not(or(X_2301,X)),not(X))
| theorem(or(not(not(or(X_2301,X))),not(X))) = theorem(implies(not(or(X_2301,X)),not(X))) ),
inference(resolve,[$cnf( $equal(theorem(or(not(not(or(X_2301,X))),not(X))),theorem(or(not(not(or(X_2301,X))),not(X)))) )],[refute_0_256,refute_0_257]) ).
cnf(refute_0_259,plain,
theorem(or(not(not(or(X_2301,X))),not(X))) = theorem(implies(not(or(X_2301,X)),not(X))),
inference(resolve,[$cnf( $equal(or(not(not(or(X_2301,X))),not(X)),implies(not(or(X_2301,X)),not(X))) )],[refute_0_255,refute_0_258]) ).
cnf(refute_0_260,plain,
ifeq(true,true,theorem(or(not(not(or(X_2301,X))),not(X))),true) = theorem(or(not(not(or(X_2301,X))),not(X))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(or(not(not(or(X_2301,X))),not(X))))),bind(C,$fot(true))]]) ).
cnf(refute_0_261,plain,
( ifeq(true,true,theorem(or(not(not(or(X_2301,X))),not(X))),true) != theorem(or(not(not(or(X_2301,X))),not(X)))
| theorem(or(not(not(or(X_2301,X))),not(X))) != theorem(implies(not(or(X_2301,X)),not(X)))
| ifeq(true,true,theorem(or(not(not(or(X_2301,X))),not(X))),true) = theorem(implies(not(or(X_2301,X)),not(X))) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(ifeq(true,true,theorem(or(not(not(or(X_2301,X))),not(X))),true))),bind(Y0,$fot(theorem(or(not(not(or(X_2301,X))),not(X))))),bind(Z,$fot(theorem(implies(not(or(X_2301,X)),not(X)))))]]) ).
cnf(refute_0_262,plain,
( theorem(or(not(not(or(X_2301,X))),not(X))) != theorem(implies(not(or(X_2301,X)),not(X)))
| ifeq(true,true,theorem(or(not(not(or(X_2301,X))),not(X))),true) = theorem(implies(not(or(X_2301,X)),not(X))) ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(not(not(or(X_2301,X))),not(X))),true),theorem(or(not(not(or(X_2301,X))),not(X)))) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
ifeq(true,true,theorem(or(not(not(or(X_2301,X))),not(X))),true) = theorem(implies(not(or(X_2301,X)),not(X))),
inference(resolve,[$cnf( $equal(theorem(or(not(not(or(X_2301,X))),not(X))),theorem(implies(not(or(X_2301,X)),not(X)))) )],[refute_0_259,refute_0_262]) ).
cnf(refute_0_264,plain,
( ifeq(true,true,theorem(or(not(not(or(X_2301,X))),not(X))),true) != theorem(implies(not(or(X_2301,X)),not(X)))
| ifeq(true,true,theorem(or(not(not(or(X_2301,X))),not(X))),true) != true
| theorem(implies(not(or(X_2301,X)),not(X))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(or(not(not(or(X_2301,X))),not(X))),true),true) ),[0],$fot(theorem(implies(not(or(X_2301,X)),not(X))))]]) ).
cnf(refute_0_265,plain,
( ifeq(true,true,theorem(or(not(not(or(X_2301,X))),not(X))),true) != true
| theorem(implies(not(or(X_2301,X)),not(X))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(not(not(or(X_2301,X))),not(X))),true),theorem(implies(not(or(X_2301,X)),not(X)))) )],[refute_0_263,refute_0_264]) ).
cnf(refute_0_266,plain,
theorem(implies(not(or(X_2301,X)),not(X))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(not(not(or(X_2301,X))),not(X))),true),true) )],[refute_0_254,refute_0_265]) ).
cnf(refute_0_267,plain,
theorem(implies(not(or(X_6710,X_6709)),not(X_6709))) = true,
inference(subst,[],[refute_0_266:[bind(X,$fot(X_6709)),bind(X_2301,$fot(X_6710))]]) ).
cnf(refute_0_268,plain,
( ifeq(theorem(implies(not(or(X_6710,X_6709)),not(X_6709))),true,theorem(implies(not(or(X_6710,X_6709)),implies(X_888,not(X_6709)))),true) != true
| theorem(implies(not(or(X_6710,X_6709)),not(X_6709))) != true
| ifeq(true,true,theorem(implies(not(or(X_6710,X_6709)),implies(X_888,not(X_6709)))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(not(or(X_6710,X_6709)),not(X_6709))),true,theorem(implies(not(or(X_6710,X_6709)),implies(X_888,not(X_6709)))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_269,plain,
( ifeq(theorem(implies(not(or(X_6710,X_6709)),not(X_6709))),true,theorem(implies(not(or(X_6710,X_6709)),implies(X_888,not(X_6709)))),true) != true
| ifeq(true,true,theorem(implies(not(or(X_6710,X_6709)),implies(X_888,not(X_6709)))),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(not(or(X_6710,X_6709)),not(X_6709))),true) )],[refute_0_267,refute_0_268]) ).
cnf(refute_0_270,plain,
ifeq(true,true,theorem(implies(not(or(X_6710,X_6709)),implies(X_888,not(X_6709)))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(not(or(X_6710,X_6709)),not(X_6709))),true,theorem(implies(not(or(X_6710,X_6709)),implies(X_888,not(X_6709)))),true),true) )],[refute_0_95,refute_0_269]) ).
cnf(refute_0_271,plain,
ifeq(true,true,theorem(implies(not(or(X_6710,X_6709)),implies(X_888,not(X_6709)))),true) = theorem(implies(not(or(X_6710,X_6709)),implies(X_888,not(X_6709)))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(implies(not(or(X_6710,X_6709)),implies(X_888,not(X_6709)))))),bind(C,$fot(true))]]) ).
cnf(refute_0_272,plain,
( ifeq(true,true,theorem(implies(not(or(X_6710,X_6709)),implies(X_888,not(X_6709)))),true) != theorem(implies(not(or(X_6710,X_6709)),implies(X_888,not(X_6709))))
| ifeq(true,true,theorem(implies(not(or(X_6710,X_6709)),implies(X_888,not(X_6709)))),true) != true
| theorem(implies(not(or(X_6710,X_6709)),implies(X_888,not(X_6709)))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(implies(not(or(X_6710,X_6709)),implies(X_888,not(X_6709)))),true),true) ),[0],$fot(theorem(implies(not(or(X_6710,X_6709)),implies(X_888,not(X_6709)))))]]) ).
cnf(refute_0_273,plain,
( ifeq(true,true,theorem(implies(not(or(X_6710,X_6709)),implies(X_888,not(X_6709)))),true) != true
| theorem(implies(not(or(X_6710,X_6709)),implies(X_888,not(X_6709)))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(not(or(X_6710,X_6709)),implies(X_888,not(X_6709)))),true),theorem(implies(not(or(X_6710,X_6709)),implies(X_888,not(X_6709))))) )],[refute_0_271,refute_0_272]) ).
cnf(refute_0_274,plain,
theorem(implies(not(or(X_6710,X_6709)),implies(X_888,not(X_6709)))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(not(or(X_6710,X_6709)),implies(X_888,not(X_6709)))),true),true) )],[refute_0_270,refute_0_273]) ).
cnf(refute_0_275,plain,
theorem(implies(not(or(p,q)),implies(p,not(q)))) = true,
inference(subst,[],[refute_0_274:[bind(X_6709,$fot(q)),bind(X_6710,$fot(p)),bind(X_888,$fot(p))]]) ).
cnf(refute_0_276,plain,
( theorem(implies(not(or(p,q)),implies(p,not(q)))) != true
| true != true
| theorem(implies(not(or(p,q)),implies(p,not(q)))) = true ),
introduced(tautology,[equality,[$cnf( ~ $equal(theorem(implies(not(or(p,q)),implies(p,not(q)))),true) ),[0],$fot(true)]]) ).
cnf(refute_0_277,plain,
( true != true
| theorem(implies(not(or(p,q)),implies(p,not(q)))) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(not(or(p,q)),implies(p,not(q)))),true) )],[refute_0_275,refute_0_276]) ).
cnf(refute_0_278,plain,
true != true,
inference(resolve,[$cnf( $equal(theorem(implies(not(or(p,q)),implies(p,not(q)))),true) )],[refute_0_277,refute_0_16]) ).
cnf(refute_0_279,plain,
true = true,
introduced(tautology,[refl,[$fot(true)]]) ).
cnf(refute_0_280,plain,
$false,
inference(resolve,[$cnf( $equal(true,true) )],[refute_0_279,refute_0_278]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : LCL203-10 : TPTP v8.1.0. Released v7.3.0.
% 0.08/0.15 % Command : metis --show proof --show saturation %s
% 0.15/0.36 % Computer : n021.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Sun Jul 3 23:40:46 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.15/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 193.31/193.55 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 193.31/193.55
% 193.31/193.55 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 193.44/193.60
%------------------------------------------------------------------------------