TSTP Solution File: LCL211-10 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL211-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n005.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 12:50:39 EDT 2022
% Result : Unsatisfiable 12.57s 12.73s
% Output : CNFRefutation 12.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 82
% Syntax : Number of clauses : 287 ( 157 unt; 0 nHn; 131 RR)
% Number of literals : 480 ( 479 equ; 195 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 : 603 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ifeq_axiom,axiom,
ifeq(A,A,B,C) = B ).
cnf(axiom_1_2,axiom,
axiom(implies(or(A,A),A)) = true ).
cnf(axiom_1_3,axiom,
axiom(implies(A,or(B,A))) = true ).
cnf(axiom_1_4,axiom,
axiom(implies(or(A,B),or(B,A))) = true ).
cnf(axiom_1_5,axiom,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) = true ).
cnf(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(q),implies(or(p,q),p))) != true ).
cnf(refute_0_0,plain,
ifeq(theorem(implies(or(X_10,X_11),or(X_11,X_10))),true,ifeq(theorem(or(X_10,X_11)),true,theorem(or(X_11,X_10)),true),true) = true,
inference(subst,[],[rule_2:[bind(X,$fot(or(X_11,X_10))),bind(Y,$fot(or(X_10,X_11)))]]) ).
cnf(refute_0_1,plain,
ifeq(axiom(implies(or(X_10,X_11),or(X_11,X_10))),true,theorem(implies(or(X_10,X_11),or(X_11,X_10))),true) = true,
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_10,X_11),or(X_11,X_10))))]]) ).
cnf(refute_0_2,plain,
axiom(implies(or(X_10,X_11),or(X_11,X_10))) = true,
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_10)),bind(B,$fot(X_11))]]) ).
cnf(refute_0_3,plain,
( axiom(implies(or(X_10,X_11),or(X_11,X_10))) != true
| ifeq(axiom(implies(or(X_10,X_11),or(X_11,X_10))),true,theorem(implies(or(X_10,X_11),or(X_11,X_10))),true) != true
| ifeq(true,true,theorem(implies(or(X_10,X_11),or(X_11,X_10))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(axiom(implies(or(X_10,X_11),or(X_11,X_10))),true,theorem(implies(or(X_10,X_11),or(X_11,X_10))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_4,plain,
( ifeq(axiom(implies(or(X_10,X_11),or(X_11,X_10))),true,theorem(implies(or(X_10,X_11),or(X_11,X_10))),true) != true
| ifeq(true,true,theorem(implies(or(X_10,X_11),or(X_11,X_10))),true) = true ),
inference(resolve,[$cnf( $equal(axiom(implies(or(X_10,X_11),or(X_11,X_10))),true) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
ifeq(true,true,theorem(implies(or(X_10,X_11),or(X_11,X_10))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(axiom(implies(or(X_10,X_11),or(X_11,X_10))),true,theorem(implies(or(X_10,X_11),or(X_11,X_10))),true),true) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
ifeq(true,true,theorem(implies(or(X_10,X_11),or(X_11,X_10))),true) = theorem(implies(or(X_10,X_11),or(X_11,X_10))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(implies(or(X_10,X_11),or(X_11,X_10))))),bind(C,$fot(true))]]) ).
cnf(refute_0_7,plain,
( ifeq(true,true,theorem(implies(or(X_10,X_11),or(X_11,X_10))),true) != theorem(implies(or(X_10,X_11),or(X_11,X_10)))
| ifeq(true,true,theorem(implies(or(X_10,X_11),or(X_11,X_10))),true) != true
| theorem(implies(or(X_10,X_11),or(X_11,X_10))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(implies(or(X_10,X_11),or(X_11,X_10))),true),true) ),[0],$fot(theorem(implies(or(X_10,X_11),or(X_11,X_10))))]]) ).
cnf(refute_0_8,plain,
( ifeq(true,true,theorem(implies(or(X_10,X_11),or(X_11,X_10))),true) != true
| theorem(implies(or(X_10,X_11),or(X_11,X_10))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(or(X_10,X_11),or(X_11,X_10))),true),theorem(implies(or(X_10,X_11),or(X_11,X_10)))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
theorem(implies(or(X_10,X_11),or(X_11,X_10))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(or(X_10,X_11),or(X_11,X_10))),true),true) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( ifeq(theorem(implies(or(X_10,X_11),or(X_11,X_10))),true,ifeq(theorem(or(X_10,X_11)),true,theorem(or(X_11,X_10)),true),true) != true
| theorem(implies(or(X_10,X_11),or(X_11,X_10))) != true
| ifeq(true,true,ifeq(theorem(or(X_10,X_11)),true,theorem(or(X_11,X_10)),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(or(X_10,X_11),or(X_11,X_10))),true,ifeq(theorem(or(X_10,X_11)),true,theorem(or(X_11,X_10)),true),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_11,plain,
( ifeq(theorem(implies(or(X_10,X_11),or(X_11,X_10))),true,ifeq(theorem(or(X_10,X_11)),true,theorem(or(X_11,X_10)),true),true) != true
| ifeq(true,true,ifeq(theorem(or(X_10,X_11)),true,theorem(or(X_11,X_10)),true),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(or(X_10,X_11),or(X_11,X_10))),true) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
ifeq(true,true,ifeq(theorem(or(X_10,X_11)),true,theorem(or(X_11,X_10)),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(or(X_10,X_11),or(X_11,X_10))),true,ifeq(theorem(or(X_10,X_11)),true,theorem(or(X_11,X_10)),true),true),true) )],[refute_0_0,refute_0_11]) ).
cnf(refute_0_13,plain,
ifeq(true,true,ifeq(theorem(or(X_10,X_11)),true,theorem(or(X_11,X_10)),true),true) = ifeq(theorem(or(X_10,X_11)),true,theorem(or(X_11,X_10)),true),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(ifeq(theorem(or(X_10,X_11)),true,theorem(or(X_11,X_10)),true))),bind(C,$fot(true))]]) ).
cnf(refute_0_14,plain,
( ifeq(true,true,ifeq(theorem(or(X_10,X_11)),true,theorem(or(X_11,X_10)),true),true) != ifeq(theorem(or(X_10,X_11)),true,theorem(or(X_11,X_10)),true)
| ifeq(true,true,ifeq(theorem(or(X_10,X_11)),true,theorem(or(X_11,X_10)),true),true) != true
| ifeq(theorem(or(X_10,X_11)),true,theorem(or(X_11,X_10)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,ifeq(theorem(or(X_10,X_11)),true,theorem(or(X_11,X_10)),true),true),true) ),[0],$fot(ifeq(theorem(or(X_10,X_11)),true,theorem(or(X_11,X_10)),true))]]) ).
cnf(refute_0_15,plain,
( ifeq(true,true,ifeq(theorem(or(X_10,X_11)),true,theorem(or(X_11,X_10)),true),true) != true
| ifeq(theorem(or(X_10,X_11)),true,theorem(or(X_11,X_10)),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(theorem(or(X_10,X_11)),true,theorem(or(X_11,X_10)),true),true),ifeq(theorem(or(X_10,X_11)),true,theorem(or(X_11,X_10)),true)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
ifeq(theorem(or(X_10,X_11)),true,theorem(or(X_11,X_10)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(theorem(or(X_10,X_11)),true,theorem(or(X_11,X_10)),true),true),true) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
ifeq(theorem(or(implies(or(X_1884,X_1883),X_1884),not(not(X_1883)))),true,theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))),true) = true,
inference(subst,[],[refute_0_16:[bind(X_10,$fot(implies(or(X_1884,X_1883),X_1884))),bind(X_11,$fot(not(not(X_1883))))]]) ).
cnf(refute_0_18,plain,
ifeq(theorem(implies(or(X_293,X_292),or(X_293,not(not(X_292))))),true,ifeq(theorem(or(X_293,X_292)),true,theorem(or(X_293,not(not(X_292)))),true),true) = true,
inference(subst,[],[rule_2:[bind(X,$fot(or(X_293,not(not(X_292))))),bind(Y,$fot(or(X_293,X_292)))]]) ).
cnf(refute_0_19,plain,
ifeq(theorem(implies(implies(X_42,X_43),implies(or(X_44,X_42),or(X_44,X_43)))),true,ifeq(theorem(implies(X_42,X_43)),true,theorem(implies(or(X_44,X_42),or(X_44,X_43))),true),true) = true,
inference(subst,[],[rule_2:[bind(X,$fot(implies(or(X_44,X_42),or(X_44,X_43)))),bind(Y,$fot(implies(X_42,X_43)))]]) ).
cnf(refute_0_20,plain,
ifeq(axiom(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))),true,theorem(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))),true) = true,
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))))]]) ).
cnf(refute_0_21,plain,
axiom(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))) = true,
inference(subst,[],[axiom_1_6:[bind(A,$fot(X_28)),bind(B,$fot(X_29)),bind(C,$fot(X_30))]]) ).
cnf(refute_0_22,plain,
( axiom(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))) != true
| ifeq(axiom(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))),true,theorem(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))),true) != true
| ifeq(true,true,theorem(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(axiom(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))),true,theorem(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_23,plain,
( ifeq(axiom(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))),true,theorem(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))),true) != true
| ifeq(true,true,theorem(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))),true) = true ),
inference(resolve,[$cnf( $equal(axiom(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))),true) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
ifeq(true,true,theorem(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(axiom(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))),true,theorem(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))),true),true) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
ifeq(true,true,theorem(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))),true) = theorem(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))))),bind(C,$fot(true))]]) ).
cnf(refute_0_26,plain,
( ifeq(true,true,theorem(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))),true) != theorem(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29))))
| ifeq(true,true,theorem(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))),true) != true
| theorem(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))),true),true) ),[0],$fot(theorem(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))))]]) ).
cnf(refute_0_27,plain,
( ifeq(true,true,theorem(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))),true) != true
| theorem(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))),true),theorem(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29))))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
theorem(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(implies(X_28,X_29),implies(or(X_30,X_28),or(X_30,X_29)))),true),true) )],[refute_0_24,refute_0_27]) ).
cnf(refute_0_29,plain,
theorem(implies(implies(X_42,X_43),implies(or(X_44,X_42),or(X_44,X_43)))) = true,
inference(subst,[],[refute_0_28:[bind(X_28,$fot(X_42)),bind(X_29,$fot(X_43)),bind(X_30,$fot(X_44))]]) ).
cnf(refute_0_30,plain,
( ifeq(theorem(implies(implies(X_42,X_43),implies(or(X_44,X_42),or(X_44,X_43)))),true,ifeq(theorem(implies(X_42,X_43)),true,theorem(implies(or(X_44,X_42),or(X_44,X_43))),true),true) != true
| theorem(implies(implies(X_42,X_43),implies(or(X_44,X_42),or(X_44,X_43)))) != true
| ifeq(true,true,ifeq(theorem(implies(X_42,X_43)),true,theorem(implies(or(X_44,X_42),or(X_44,X_43))),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(X_42,X_43),implies(or(X_44,X_42),or(X_44,X_43)))),true,ifeq(theorem(implies(X_42,X_43)),true,theorem(implies(or(X_44,X_42),or(X_44,X_43))),true),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_31,plain,
( ifeq(theorem(implies(implies(X_42,X_43),implies(or(X_44,X_42),or(X_44,X_43)))),true,ifeq(theorem(implies(X_42,X_43)),true,theorem(implies(or(X_44,X_42),or(X_44,X_43))),true),true) != true
| ifeq(true,true,ifeq(theorem(implies(X_42,X_43)),true,theorem(implies(or(X_44,X_42),or(X_44,X_43))),true),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(implies(X_42,X_43),implies(or(X_44,X_42),or(X_44,X_43)))),true) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
ifeq(true,true,ifeq(theorem(implies(X_42,X_43)),true,theorem(implies(or(X_44,X_42),or(X_44,X_43))),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(X_42,X_43),implies(or(X_44,X_42),or(X_44,X_43)))),true,ifeq(theorem(implies(X_42,X_43)),true,theorem(implies(or(X_44,X_42),or(X_44,X_43))),true),true),true) )],[refute_0_19,refute_0_31]) ).
cnf(refute_0_33,plain,
ifeq(true,true,ifeq(theorem(implies(X_42,X_43)),true,theorem(implies(or(X_44,X_42),or(X_44,X_43))),true),true) = ifeq(theorem(implies(X_42,X_43)),true,theorem(implies(or(X_44,X_42),or(X_44,X_43))),true),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(ifeq(theorem(implies(X_42,X_43)),true,theorem(implies(or(X_44,X_42),or(X_44,X_43))),true))),bind(C,$fot(true))]]) ).
cnf(refute_0_34,plain,
( ifeq(true,true,ifeq(theorem(implies(X_42,X_43)),true,theorem(implies(or(X_44,X_42),or(X_44,X_43))),true),true) != ifeq(theorem(implies(X_42,X_43)),true,theorem(implies(or(X_44,X_42),or(X_44,X_43))),true)
| ifeq(true,true,ifeq(theorem(implies(X_42,X_43)),true,theorem(implies(or(X_44,X_42),or(X_44,X_43))),true),true) != true
| ifeq(theorem(implies(X_42,X_43)),true,theorem(implies(or(X_44,X_42),or(X_44,X_43))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,ifeq(theorem(implies(X_42,X_43)),true,theorem(implies(or(X_44,X_42),or(X_44,X_43))),true),true),true) ),[0],$fot(ifeq(theorem(implies(X_42,X_43)),true,theorem(implies(or(X_44,X_42),or(X_44,X_43))),true))]]) ).
cnf(refute_0_35,plain,
( ifeq(true,true,ifeq(theorem(implies(X_42,X_43)),true,theorem(implies(or(X_44,X_42),or(X_44,X_43))),true),true) != true
| ifeq(theorem(implies(X_42,X_43)),true,theorem(implies(or(X_44,X_42),or(X_44,X_43))),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(theorem(implies(X_42,X_43)),true,theorem(implies(or(X_44,X_42),or(X_44,X_43))),true),true),ifeq(theorem(implies(X_42,X_43)),true,theorem(implies(or(X_44,X_42),or(X_44,X_43))),true)) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
ifeq(theorem(implies(X_42,X_43)),true,theorem(implies(or(X_44,X_42),or(X_44,X_43))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(theorem(implies(X_42,X_43)),true,theorem(implies(or(X_44,X_42),or(X_44,X_43))),true),true),true) )],[refute_0_32,refute_0_35]) ).
cnf(refute_0_37,plain,
ifeq(theorem(implies(X_289,not(not(X_289)))),true,theorem(implies(or(X_291,X_289),or(X_291,not(not(X_289))))),true) = true,
inference(subst,[],[refute_0_36:[bind(X_42,$fot(X_289)),bind(X_43,$fot(not(not(X_289)))),bind(X_44,$fot(X_291))]]) ).
cnf(refute_0_38,plain,
ifeq(theorem(implies(implies(X_32,X_31),or(X_31,not(X_32)))),true,ifeq(theorem(implies(X_32,X_31)),true,theorem(or(X_31,not(X_32))),true),true) = true,
inference(subst,[],[rule_2:[bind(X,$fot(or(X_31,not(X_32)))),bind(Y,$fot(implies(X_32,X_31)))]]) ).
cnf(refute_0_39,plain,
theorem(implies(or(not(X_14),X_11),or(X_11,not(X_14)))) = true,
inference(subst,[],[refute_0_9:[bind(X_10,$fot(not(X_14)))]]) ).
cnf(refute_0_40,plain,
implies(X_14,X_11) = or(not(X_14),X_11),
inference(subst,[],[implies_definition:[bind(X,$fot(X_14)),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_41,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_42,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_43,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
( implies(X_14,X_11) != or(not(X_14),X_11)
| or(not(X_14),X_11) = implies(X_14,X_11) ),
inference(subst,[],[refute_0_43:[bind(X0,$fot(implies(X_14,X_11))),bind(Y0,$fot(or(not(X_14),X_11)))]]) ).
cnf(refute_0_45,plain,
or(not(X_14),X_11) = implies(X_14,X_11),
inference(resolve,[$cnf( $equal(implies(X_14,X_11),or(not(X_14),X_11)) )],[refute_0_40,refute_0_44]) ).
cnf(refute_0_46,plain,
( or(not(X_14),X_11) != implies(X_14,X_11)
| theorem(implies(or(not(X_14),X_11),or(X_11,not(X_14)))) != true
| theorem(implies(implies(X_14,X_11),or(X_11,not(X_14)))) = true ),
introduced(tautology,[equality,[$cnf( $equal(theorem(implies(or(not(X_14),X_11),or(X_11,not(X_14)))),true) ),[0,0,0],$fot(implies(X_14,X_11))]]) ).
cnf(refute_0_47,plain,
( theorem(implies(or(not(X_14),X_11),or(X_11,not(X_14)))) != true
| theorem(implies(implies(X_14,X_11),or(X_11,not(X_14)))) = true ),
inference(resolve,[$cnf( $equal(or(not(X_14),X_11),implies(X_14,X_11)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
theorem(implies(implies(X_14,X_11),or(X_11,not(X_14)))) = true,
inference(resolve,[$cnf( $equal(theorem(implies(or(not(X_14),X_11),or(X_11,not(X_14)))),true) )],[refute_0_39,refute_0_47]) ).
cnf(refute_0_49,plain,
theorem(implies(implies(X_32,X_31),or(X_31,not(X_32)))) = true,
inference(subst,[],[refute_0_48:[bind(X_11,$fot(X_31)),bind(X_14,$fot(X_32))]]) ).
cnf(refute_0_50,plain,
( ifeq(theorem(implies(implies(X_32,X_31),or(X_31,not(X_32)))),true,ifeq(theorem(implies(X_32,X_31)),true,theorem(or(X_31,not(X_32))),true),true) != true
| theorem(implies(implies(X_32,X_31),or(X_31,not(X_32)))) != true
| ifeq(true,true,ifeq(theorem(implies(X_32,X_31)),true,theorem(or(X_31,not(X_32))),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(X_32,X_31),or(X_31,not(X_32)))),true,ifeq(theorem(implies(X_32,X_31)),true,theorem(or(X_31,not(X_32))),true),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_51,plain,
( ifeq(theorem(implies(implies(X_32,X_31),or(X_31,not(X_32)))),true,ifeq(theorem(implies(X_32,X_31)),true,theorem(or(X_31,not(X_32))),true),true) != true
| ifeq(true,true,ifeq(theorem(implies(X_32,X_31)),true,theorem(or(X_31,not(X_32))),true),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(implies(X_32,X_31),or(X_31,not(X_32)))),true) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
ifeq(true,true,ifeq(theorem(implies(X_32,X_31)),true,theorem(or(X_31,not(X_32))),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(X_32,X_31),or(X_31,not(X_32)))),true,ifeq(theorem(implies(X_32,X_31)),true,theorem(or(X_31,not(X_32))),true),true),true) )],[refute_0_38,refute_0_51]) ).
cnf(refute_0_53,plain,
ifeq(true,true,ifeq(theorem(implies(X_32,X_31)),true,theorem(or(X_31,not(X_32))),true),true) = ifeq(theorem(implies(X_32,X_31)),true,theorem(or(X_31,not(X_32))),true),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(ifeq(theorem(implies(X_32,X_31)),true,theorem(or(X_31,not(X_32))),true))),bind(C,$fot(true))]]) ).
cnf(refute_0_54,plain,
( ifeq(true,true,ifeq(theorem(implies(X_32,X_31)),true,theorem(or(X_31,not(X_32))),true),true) != ifeq(theorem(implies(X_32,X_31)),true,theorem(or(X_31,not(X_32))),true)
| ifeq(true,true,ifeq(theorem(implies(X_32,X_31)),true,theorem(or(X_31,not(X_32))),true),true) != true
| ifeq(theorem(implies(X_32,X_31)),true,theorem(or(X_31,not(X_32))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,ifeq(theorem(implies(X_32,X_31)),true,theorem(or(X_31,not(X_32))),true),true),true) ),[0],$fot(ifeq(theorem(implies(X_32,X_31)),true,theorem(or(X_31,not(X_32))),true))]]) ).
cnf(refute_0_55,plain,
( ifeq(true,true,ifeq(theorem(implies(X_32,X_31)),true,theorem(or(X_31,not(X_32))),true),true) != true
| ifeq(theorem(implies(X_32,X_31)),true,theorem(or(X_31,not(X_32))),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(theorem(implies(X_32,X_31)),true,theorem(or(X_31,not(X_32))),true),true),ifeq(theorem(implies(X_32,X_31)),true,theorem(or(X_31,not(X_32))),true)) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
ifeq(theorem(implies(X_32,X_31)),true,theorem(or(X_31,not(X_32))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(theorem(implies(X_32,X_31)),true,theorem(or(X_31,not(X_32))),true),true),true) )],[refute_0_52,refute_0_55]) ).
cnf(refute_0_57,plain,
ifeq(theorem(implies(not(X_168),not(X_168))),true,theorem(or(not(X_168),not(not(X_168)))),true) = true,
inference(subst,[],[refute_0_56:[bind(X_31,$fot(not(X_168))),bind(X_32,$fot(not(X_168)))]]) ).
cnf(refute_0_58,plain,
ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,ifeq(theorem(implies(X_3,implies(X_14,X_3))),true,theorem(X_22),true),true) = true,
inference(subst,[],[rule_2:[bind(X,$fot(X_22)),bind(Y,$fot(implies(X_3,implies(X_14,X_3))))]]) ).
cnf(refute_0_59,plain,
ifeq(axiom(implies(X_3,or(X_4,X_3))),true,theorem(implies(X_3,or(X_4,X_3))),true) = true,
inference(subst,[],[rule_1:[bind(X,$fot(implies(X_3,or(X_4,X_3))))]]) ).
cnf(refute_0_60,plain,
axiom(implies(X_3,or(X_4,X_3))) = true,
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_3)),bind(B,$fot(X_4))]]) ).
cnf(refute_0_61,plain,
( axiom(implies(X_3,or(X_4,X_3))) != true
| ifeq(axiom(implies(X_3,or(X_4,X_3))),true,theorem(implies(X_3,or(X_4,X_3))),true) != true
| ifeq(true,true,theorem(implies(X_3,or(X_4,X_3))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(axiom(implies(X_3,or(X_4,X_3))),true,theorem(implies(X_3,or(X_4,X_3))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_62,plain,
( ifeq(axiom(implies(X_3,or(X_4,X_3))),true,theorem(implies(X_3,or(X_4,X_3))),true) != true
| ifeq(true,true,theorem(implies(X_3,or(X_4,X_3))),true) = true ),
inference(resolve,[$cnf( $equal(axiom(implies(X_3,or(X_4,X_3))),true) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
ifeq(true,true,theorem(implies(X_3,or(X_4,X_3))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(axiom(implies(X_3,or(X_4,X_3))),true,theorem(implies(X_3,or(X_4,X_3))),true),true) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
ifeq(true,true,theorem(implies(X_3,or(X_4,X_3))),true) = theorem(implies(X_3,or(X_4,X_3))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(implies(X_3,or(X_4,X_3))))),bind(C,$fot(true))]]) ).
cnf(refute_0_65,plain,
( ifeq(true,true,theorem(implies(X_3,or(X_4,X_3))),true) != theorem(implies(X_3,or(X_4,X_3)))
| ifeq(true,true,theorem(implies(X_3,or(X_4,X_3))),true) != true
| theorem(implies(X_3,or(X_4,X_3))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(implies(X_3,or(X_4,X_3))),true),true) ),[0],$fot(theorem(implies(X_3,or(X_4,X_3))))]]) ).
cnf(refute_0_66,plain,
( ifeq(true,true,theorem(implies(X_3,or(X_4,X_3))),true) != true
| theorem(implies(X_3,or(X_4,X_3))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(X_3,or(X_4,X_3))),true),theorem(implies(X_3,or(X_4,X_3)))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
theorem(implies(X_3,or(X_4,X_3))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(X_3,or(X_4,X_3))),true),true) )],[refute_0_63,refute_0_66]) ).
cnf(refute_0_68,plain,
theorem(implies(X_3,or(not(X_14),X_3))) = true,
inference(subst,[],[refute_0_67:[bind(X_4,$fot(not(X_14)))]]) ).
cnf(refute_0_69,plain,
implies(X_14,X_3) = or(not(X_14),X_3),
inference(subst,[],[implies_definition:[bind(X,$fot(X_14)),bind(Y,$fot(X_3))]]) ).
cnf(refute_0_70,plain,
( implies(X_14,X_3) != or(not(X_14),X_3)
| or(not(X_14),X_3) = implies(X_14,X_3) ),
inference(subst,[],[refute_0_43:[bind(X0,$fot(implies(X_14,X_3))),bind(Y0,$fot(or(not(X_14),X_3)))]]) ).
cnf(refute_0_71,plain,
or(not(X_14),X_3) = implies(X_14,X_3),
inference(resolve,[$cnf( $equal(implies(X_14,X_3),or(not(X_14),X_3)) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( or(not(X_14),X_3) != implies(X_14,X_3)
| theorem(implies(X_3,or(not(X_14),X_3))) != true
| theorem(implies(X_3,implies(X_14,X_3))) = true ),
introduced(tautology,[equality,[$cnf( $equal(theorem(implies(X_3,or(not(X_14),X_3))),true) ),[0,0,1],$fot(implies(X_14,X_3))]]) ).
cnf(refute_0_73,plain,
( theorem(implies(X_3,or(not(X_14),X_3))) != true
| theorem(implies(X_3,implies(X_14,X_3))) = true ),
inference(resolve,[$cnf( $equal(or(not(X_14),X_3),implies(X_14,X_3)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
theorem(implies(X_3,implies(X_14,X_3))) = true,
inference(resolve,[$cnf( $equal(theorem(implies(X_3,or(not(X_14),X_3))),true) )],[refute_0_68,refute_0_73]) ).
cnf(refute_0_75,plain,
( ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,ifeq(theorem(implies(X_3,implies(X_14,X_3))),true,theorem(X_22),true),true) != true
| theorem(implies(X_3,implies(X_14,X_3))) != true
| ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,ifeq(theorem(implies(X_3,implies(X_14,X_3))),true,theorem(X_22),true),true),true) ),[0,2,0],$fot(true)]]) ).
cnf(refute_0_76,plain,
( ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,ifeq(theorem(implies(X_3,implies(X_14,X_3))),true,theorem(X_22),true),true) != true
| ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(X_3,implies(X_14,X_3))),true) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,ifeq(theorem(implies(X_3,implies(X_14,X_3))),true,theorem(X_22),true),true),true) )],[refute_0_58,refute_0_76]) ).
cnf(refute_0_78,plain,
ifeq(true,true,theorem(X_22),true) = theorem(X_22),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(X_22))),bind(C,$fot(true))]]) ).
cnf(refute_0_79,plain,
ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) = ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,ifeq(true,true,theorem(X_22),true),true),
introduced(tautology,[refl,[$fot(ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,ifeq(true,true,theorem(X_22),true),true))]]) ).
cnf(refute_0_80,plain,
( ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) != ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,ifeq(true,true,theorem(X_22),true),true)
| ifeq(true,true,theorem(X_22),true) != theorem(X_22)
| ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) = ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,theorem(X_22),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,ifeq(true,true,theorem(X_22),true),true),ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,ifeq(true,true,theorem(X_22),true),true)) ),[1,2],$fot(theorem(X_22))]]) ).
cnf(refute_0_81,plain,
( ifeq(true,true,theorem(X_22),true) != theorem(X_22)
| ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) = ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,theorem(X_22),true) ),
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,ifeq(true,true,theorem(X_22),true),true),ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,ifeq(true,true,theorem(X_22),true),true)) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) = ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,theorem(X_22),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(X_22),true),theorem(X_22)) )],[refute_0_78,refute_0_81]) ).
cnf(refute_0_83,plain,
( ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) != ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,theorem(X_22),true)
| ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) != true
| ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,theorem(X_22),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,ifeq(true,true,theorem(X_22),true),true),true) ),[0],$fot(ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,theorem(X_22),true))]]) ).
cnf(refute_0_84,plain,
( ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) != true
| ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,theorem(X_22),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,ifeq(true,true,theorem(X_22),true),true),ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,theorem(X_22),true)) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,theorem(X_22),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(X_3,implies(X_14,X_3)),X_22)),true,ifeq(true,true,theorem(X_22),true),true),true) )],[refute_0_77,refute_0_84]) ).
cnf(refute_0_86,plain,
ifeq(theorem(implies(implies(not(X_165),implies(X_165,not(X_165))),implies(not(X_165),not(X_165)))),true,theorem(implies(not(X_165),not(X_165))),true) = true,
inference(subst,[],[refute_0_85:[bind(X_14,$fot(X_165)),bind(X_22,$fot(implies(not(X_165),not(X_165)))),bind(X_3,$fot(not(X_165)))]]) ).
cnf(refute_0_87,plain,
ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,ifeq(theorem(implies(implies(X_14,not(X_14)),not(X_14))),true,theorem(X_22),true),true) = true,
inference(subst,[],[rule_2:[bind(X,$fot(X_22)),bind(Y,$fot(implies(implies(X_14,not(X_14)),not(X_14))))]]) ).
cnf(refute_0_88,plain,
ifeq(axiom(implies(or(A,A),A)),true,theorem(implies(or(A,A),A)),true) = true,
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_89,plain,
( axiom(implies(or(A,A),A)) != true
| ifeq(axiom(implies(or(A,A),A)),true,theorem(implies(or(A,A),A)),true) != true
| ifeq(true,true,theorem(implies(or(A,A),A)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(axiom(implies(or(A,A),A)),true,theorem(implies(or(A,A),A)),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_90,plain,
( ifeq(axiom(implies(or(A,A),A)),true,theorem(implies(or(A,A),A)),true) != true
| ifeq(true,true,theorem(implies(or(A,A),A)),true) = true ),
inference(resolve,[$cnf( $equal(axiom(implies(or(A,A),A)),true) )],[axiom_1_2,refute_0_89]) ).
cnf(refute_0_91,plain,
ifeq(true,true,theorem(implies(or(A,A),A)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(axiom(implies(or(A,A),A)),true,theorem(implies(or(A,A),A)),true),true) )],[refute_0_88,refute_0_90]) ).
cnf(refute_0_92,plain,
ifeq(true,true,theorem(implies(or(A,A),A)),true) = theorem(implies(or(A,A),A)),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(implies(or(A,A),A)))),bind(C,$fot(true))]]) ).
cnf(refute_0_93,plain,
( ifeq(true,true,theorem(implies(or(A,A),A)),true) != theorem(implies(or(A,A),A))
| ifeq(true,true,theorem(implies(or(A,A),A)),true) != true
| theorem(implies(or(A,A),A)) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(implies(or(A,A),A)),true),true) ),[0],$fot(theorem(implies(or(A,A),A)))]]) ).
cnf(refute_0_94,plain,
( ifeq(true,true,theorem(implies(or(A,A),A)),true) != true
| theorem(implies(or(A,A),A)) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(or(A,A),A)),true),theorem(implies(or(A,A),A))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
theorem(implies(or(A,A),A)) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(or(A,A),A)),true),true) )],[refute_0_91,refute_0_94]) ).
cnf(refute_0_96,plain,
theorem(implies(or(not(X_14),not(X_14)),not(X_14))) = true,
inference(subst,[],[refute_0_95:[bind(A,$fot(not(X_14)))]]) ).
cnf(refute_0_97,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_98,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_43:[bind(X0,$fot(implies(X_14,not(X_14)))),bind(Y0,$fot(or(not(X_14),not(X_14))))]]) ).
cnf(refute_0_99,plain,
or(not(X_14),not(X_14)) = implies(X_14,not(X_14)),
inference(resolve,[$cnf( $equal(implies(X_14,not(X_14)),or(not(X_14),not(X_14))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
( or(not(X_14),not(X_14)) != implies(X_14,not(X_14))
| theorem(implies(or(not(X_14),not(X_14)),not(X_14))) != true
| theorem(implies(implies(X_14,not(X_14)),not(X_14))) = true ),
introduced(tautology,[equality,[$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_101,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( $equal(or(not(X_14),not(X_14)),implies(X_14,not(X_14))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
theorem(implies(implies(X_14,not(X_14)),not(X_14))) = true,
inference(resolve,[$cnf( $equal(theorem(implies(or(not(X_14),not(X_14)),not(X_14))),true) )],[refute_0_96,refute_0_101]) ).
cnf(refute_0_103,plain,
( ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,ifeq(theorem(implies(implies(X_14,not(X_14)),not(X_14))),true,theorem(X_22),true),true) != true
| theorem(implies(implies(X_14,not(X_14)),not(X_14))) != true
| ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,ifeq(theorem(implies(implies(X_14,not(X_14)),not(X_14))),true,theorem(X_22),true),true),true) ),[0,2,0],$fot(true)]]) ).
cnf(refute_0_104,plain,
( ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,ifeq(theorem(implies(implies(X_14,not(X_14)),not(X_14))),true,theorem(X_22),true),true) != true
| ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(implies(X_14,not(X_14)),not(X_14))),true) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,ifeq(theorem(implies(implies(X_14,not(X_14)),not(X_14))),true,theorem(X_22),true),true),true) )],[refute_0_87,refute_0_104]) ).
cnf(refute_0_106,plain,
ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) = ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,ifeq(true,true,theorem(X_22),true),true),
introduced(tautology,[refl,[$fot(ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,ifeq(true,true,theorem(X_22),true),true))]]) ).
cnf(refute_0_107,plain,
( ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) != ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,ifeq(true,true,theorem(X_22),true),true)
| ifeq(true,true,theorem(X_22),true) != theorem(X_22)
| ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) = ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,theorem(X_22),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,ifeq(true,true,theorem(X_22),true),true),ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,ifeq(true,true,theorem(X_22),true),true)) ),[1,2],$fot(theorem(X_22))]]) ).
cnf(refute_0_108,plain,
( ifeq(true,true,theorem(X_22),true) != theorem(X_22)
| ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) = ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,theorem(X_22),true) ),
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,ifeq(true,true,theorem(X_22),true),true),ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,ifeq(true,true,theorem(X_22),true),true)) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) = ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,theorem(X_22),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(X_22),true),theorem(X_22)) )],[refute_0_78,refute_0_108]) ).
cnf(refute_0_110,plain,
( ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) != ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,theorem(X_22),true)
| ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) != true
| ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,theorem(X_22),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,ifeq(true,true,theorem(X_22),true),true),true) ),[0],$fot(ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,theorem(X_22),true))]]) ).
cnf(refute_0_111,plain,
( ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) != true
| ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,theorem(X_22),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,ifeq(true,true,theorem(X_22),true),true),ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,theorem(X_22),true)) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,theorem(X_22),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(implies(X_14,not(X_14)),not(X_14)),X_22)),true,ifeq(true,true,theorem(X_22),true),true),true) )],[refute_0_105,refute_0_111]) ).
cnf(refute_0_113,plain,
ifeq(theorem(implies(implies(implies(X_125,not(X_125)),not(X_125)),implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125))))),true,theorem(implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125)))),true) = true,
inference(subst,[],[refute_0_112:[bind(X_14,$fot(X_125)),bind(X_22,$fot(implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125)))))]]) ).
cnf(refute_0_114,plain,
theorem(implies(implies(X_42,X_43),implies(or(not(X),X_42),or(not(X),X_43)))) = true,
inference(subst,[],[refute_0_28:[bind(X_28,$fot(X_42)),bind(X_29,$fot(X_43)),bind(X_30,$fot(not(X)))]]) ).
cnf(refute_0_115,plain,
implies(X,X_43) = or(not(X),X_43),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_43))]]) ).
cnf(refute_0_116,plain,
( implies(X,X_43) != or(not(X),X_43)
| or(not(X),X_43) = implies(X,X_43) ),
inference(subst,[],[refute_0_43:[bind(X0,$fot(implies(X,X_43))),bind(Y0,$fot(or(not(X),X_43)))]]) ).
cnf(refute_0_117,plain,
or(not(X),X_43) = implies(X,X_43),
inference(resolve,[$cnf( $equal(implies(X,X_43),or(not(X),X_43)) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
( or(not(X),X_43) != implies(X,X_43)
| theorem(implies(implies(X_42,X_43),implies(or(not(X),X_42),or(not(X),X_43)))) != true
| theorem(implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43)))) = true ),
introduced(tautology,[equality,[$cnf( $equal(theorem(implies(implies(X_42,X_43),implies(or(not(X),X_42),or(not(X),X_43)))),true) ),[0,0,1,1],$fot(implies(X,X_43))]]) ).
cnf(refute_0_119,plain,
( theorem(implies(implies(X_42,X_43),implies(or(not(X),X_42),or(not(X),X_43)))) != true
| theorem(implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43)))) = true ),
inference(resolve,[$cnf( $equal(or(not(X),X_43),implies(X,X_43)) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
theorem(implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43)))) = true,
inference(resolve,[$cnf( $equal(theorem(implies(implies(X_42,X_43),implies(or(not(X),X_42),or(not(X),X_43)))),true) )],[refute_0_114,refute_0_119]) ).
cnf(refute_0_121,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_43:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_122,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_121]) ).
cnf(refute_0_123,plain,
or(not(X),X_42) = implies(X,X_42),
inference(subst,[],[refute_0_122:[bind(Y,$fot(X_42))]]) ).
cnf(refute_0_124,plain,
implies(or(not(X),X_42),implies(X,X_43)) = implies(or(not(X),X_42),implies(X,X_43)),
introduced(tautology,[refl,[$fot(implies(or(not(X),X_42),implies(X,X_43)))]]) ).
cnf(refute_0_125,plain,
( implies(or(not(X),X_42),implies(X,X_43)) != implies(or(not(X),X_42),implies(X,X_43))
| or(not(X),X_42) != implies(X,X_42)
| implies(or(not(X),X_42),implies(X,X_43)) = implies(implies(X,X_42),implies(X,X_43)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),X_42),implies(X,X_43)),implies(or(not(X),X_42),implies(X,X_43))) ),[1,0],$fot(implies(X,X_42))]]) ).
cnf(refute_0_126,plain,
( or(not(X),X_42) != implies(X,X_42)
| implies(or(not(X),X_42),implies(X,X_43)) = implies(implies(X,X_42),implies(X,X_43)) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_42),implies(X,X_43)),implies(or(not(X),X_42),implies(X,X_43))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
implies(or(not(X),X_42),implies(X,X_43)) = implies(implies(X,X_42),implies(X,X_43)),
inference(resolve,[$cnf( $equal(or(not(X),X_42),implies(X,X_42)) )],[refute_0_123,refute_0_126]) ).
cnf(refute_0_128,plain,
implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43))) = implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43))),
introduced(tautology,[refl,[$fot(implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43))))]]) ).
cnf(refute_0_129,plain,
( implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43))) != implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43)))
| implies(or(not(X),X_42),implies(X,X_43)) != implies(implies(X,X_42),implies(X,X_43))
| implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43))) = implies(implies(X_42,X_43),implies(implies(X,X_42),implies(X,X_43))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43))),implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43)))) ),[1,1],$fot(implies(implies(X,X_42),implies(X,X_43)))]]) ).
cnf(refute_0_130,plain,
( implies(or(not(X),X_42),implies(X,X_43)) != implies(implies(X,X_42),implies(X,X_43))
| implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43))) = implies(implies(X_42,X_43),implies(implies(X,X_42),implies(X,X_43))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43))),implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43)))) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43))) = implies(implies(X_42,X_43),implies(implies(X,X_42),implies(X,X_43))),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_42),implies(X,X_43)),implies(implies(X,X_42),implies(X,X_43))) )],[refute_0_127,refute_0_130]) ).
cnf(refute_0_132,plain,
theorem(implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43)))) = theorem(implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43)))),
introduced(tautology,[refl,[$fot(theorem(implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43)))))]]) ).
cnf(refute_0_133,plain,
( implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43))) != implies(implies(X_42,X_43),implies(implies(X,X_42),implies(X,X_43)))
| theorem(implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43)))) != theorem(implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43))))
| theorem(implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43)))) = theorem(implies(implies(X_42,X_43),implies(implies(X,X_42),implies(X,X_43)))) ),
introduced(tautology,[equality,[$cnf( $equal(theorem(implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43)))),theorem(implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43))))) ),[1,0],$fot(implies(implies(X_42,X_43),implies(implies(X,X_42),implies(X,X_43))))]]) ).
cnf(refute_0_134,plain,
( implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43))) != implies(implies(X_42,X_43),implies(implies(X,X_42),implies(X,X_43)))
| theorem(implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43)))) = theorem(implies(implies(X_42,X_43),implies(implies(X,X_42),implies(X,X_43)))) ),
inference(resolve,[$cnf( $equal(theorem(implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43)))),theorem(implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43))))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
theorem(implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43)))) = theorem(implies(implies(X_42,X_43),implies(implies(X,X_42),implies(X,X_43)))),
inference(resolve,[$cnf( $equal(implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43))),implies(implies(X_42,X_43),implies(implies(X,X_42),implies(X,X_43)))) )],[refute_0_131,refute_0_134]) ).
cnf(refute_0_136,plain,
( theorem(implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43)))) != theorem(implies(implies(X_42,X_43),implies(implies(X,X_42),implies(X,X_43))))
| theorem(implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43)))) != true
| theorem(implies(implies(X_42,X_43),implies(implies(X,X_42),implies(X,X_43)))) = true ),
introduced(tautology,[equality,[$cnf( $equal(theorem(implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43)))),true) ),[0],$fot(theorem(implies(implies(X_42,X_43),implies(implies(X,X_42),implies(X,X_43)))))]]) ).
cnf(refute_0_137,plain,
( theorem(implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43)))) != true
| theorem(implies(implies(X_42,X_43),implies(implies(X,X_42),implies(X,X_43)))) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43)))),theorem(implies(implies(X_42,X_43),implies(implies(X,X_42),implies(X,X_43))))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
theorem(implies(implies(X_42,X_43),implies(implies(X,X_42),implies(X,X_43)))) = true,
inference(resolve,[$cnf( $equal(theorem(implies(implies(X_42,X_43),implies(or(not(X),X_42),implies(X,X_43)))),true) )],[refute_0_120,refute_0_137]) ).
cnf(refute_0_139,plain,
theorem(implies(implies(implies(X_125,not(X_125)),not(X_125)),implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125))))) = true,
inference(subst,[],[refute_0_138:[bind(X_42,$fot(implies(X_125,not(X_125)))),bind(X_43,$fot(not(X_125)))]]) ).
cnf(refute_0_140,plain,
( ifeq(theorem(implies(implies(implies(X_125,not(X_125)),not(X_125)),implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125))))),true,theorem(implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125)))),true) != true
| theorem(implies(implies(implies(X_125,not(X_125)),not(X_125)),implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125))))) != true
| ifeq(true,true,theorem(implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125)))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(implies(X_125,not(X_125)),not(X_125)),implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125))))),true,theorem(implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125)))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_141,plain,
( ifeq(theorem(implies(implies(implies(X_125,not(X_125)),not(X_125)),implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125))))),true,theorem(implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125)))),true) != true
| ifeq(true,true,theorem(implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125)))),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(implies(implies(X_125,not(X_125)),not(X_125)),implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125))))),true) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
ifeq(true,true,theorem(implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125)))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(implies(X_125,not(X_125)),not(X_125)),implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125))))),true,theorem(implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125)))),true),true) )],[refute_0_113,refute_0_141]) ).
cnf(refute_0_143,plain,
ifeq(true,true,theorem(implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125)))),true) = theorem(implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125)))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125)))))),bind(C,$fot(true))]]) ).
cnf(refute_0_144,plain,
( ifeq(true,true,theorem(implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125)))),true) != theorem(implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125))))
| ifeq(true,true,theorem(implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125)))),true) != true
| theorem(implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125)))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125)))),true),true) ),[0],$fot(theorem(implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125)))))]]) ).
cnf(refute_0_145,plain,
( ifeq(true,true,theorem(implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125)))),true) != true
| theorem(implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125)))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125)))),true),theorem(implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125))))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
theorem(implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125)))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(implies(X,implies(X_125,not(X_125))),implies(X,not(X_125)))),true),true) )],[refute_0_142,refute_0_145]) ).
cnf(refute_0_147,plain,
theorem(implies(implies(not(X_165),implies(X_165,not(X_165))),implies(not(X_165),not(X_165)))) = true,
inference(subst,[],[refute_0_146:[bind(X,$fot(not(X_165))),bind(X_125,$fot(X_165))]]) ).
cnf(refute_0_148,plain,
( ifeq(theorem(implies(implies(not(X_165),implies(X_165,not(X_165))),implies(not(X_165),not(X_165)))),true,theorem(implies(not(X_165),not(X_165))),true) != true
| theorem(implies(implies(not(X_165),implies(X_165,not(X_165))),implies(not(X_165),not(X_165)))) != true
| ifeq(true,true,theorem(implies(not(X_165),not(X_165))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(not(X_165),implies(X_165,not(X_165))),implies(not(X_165),not(X_165)))),true,theorem(implies(not(X_165),not(X_165))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_149,plain,
( ifeq(theorem(implies(implies(not(X_165),implies(X_165,not(X_165))),implies(not(X_165),not(X_165)))),true,theorem(implies(not(X_165),not(X_165))),true) != true
| ifeq(true,true,theorem(implies(not(X_165),not(X_165))),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(implies(not(X_165),implies(X_165,not(X_165))),implies(not(X_165),not(X_165)))),true) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
ifeq(true,true,theorem(implies(not(X_165),not(X_165))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(not(X_165),implies(X_165,not(X_165))),implies(not(X_165),not(X_165)))),true,theorem(implies(not(X_165),not(X_165))),true),true) )],[refute_0_86,refute_0_149]) ).
cnf(refute_0_151,plain,
ifeq(true,true,theorem(implies(not(X_165),not(X_165))),true) = theorem(implies(not(X_165),not(X_165))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(implies(not(X_165),not(X_165))))),bind(C,$fot(true))]]) ).
cnf(refute_0_152,plain,
( ifeq(true,true,theorem(implies(not(X_165),not(X_165))),true) != theorem(implies(not(X_165),not(X_165)))
| ifeq(true,true,theorem(implies(not(X_165),not(X_165))),true) != true
| theorem(implies(not(X_165),not(X_165))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(implies(not(X_165),not(X_165))),true),true) ),[0],$fot(theorem(implies(not(X_165),not(X_165))))]]) ).
cnf(refute_0_153,plain,
( ifeq(true,true,theorem(implies(not(X_165),not(X_165))),true) != true
| theorem(implies(not(X_165),not(X_165))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(not(X_165),not(X_165))),true),theorem(implies(not(X_165),not(X_165)))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
theorem(implies(not(X_165),not(X_165))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(not(X_165),not(X_165))),true),true) )],[refute_0_150,refute_0_153]) ).
cnf(refute_0_155,plain,
theorem(implies(not(X_168),not(X_168))) = true,
inference(subst,[],[refute_0_154:[bind(X_165,$fot(X_168))]]) ).
cnf(refute_0_156,plain,
( ifeq(theorem(implies(not(X_168),not(X_168))),true,theorem(or(not(X_168),not(not(X_168)))),true) != true
| theorem(implies(not(X_168),not(X_168))) != true
| ifeq(true,true,theorem(or(not(X_168),not(not(X_168)))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(not(X_168),not(X_168))),true,theorem(or(not(X_168),not(not(X_168)))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_157,plain,
( ifeq(theorem(implies(not(X_168),not(X_168))),true,theorem(or(not(X_168),not(not(X_168)))),true) != true
| ifeq(true,true,theorem(or(not(X_168),not(not(X_168)))),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(not(X_168),not(X_168))),true) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
ifeq(true,true,theorem(or(not(X_168),not(not(X_168)))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(not(X_168),not(X_168))),true,theorem(or(not(X_168),not(not(X_168)))),true),true) )],[refute_0_57,refute_0_157]) ).
cnf(refute_0_159,plain,
or(not(X_168),not(not(X_168))) = implies(X_168,not(not(X_168))),
inference(subst,[],[refute_0_122:[bind(X,$fot(X_168)),bind(Y,$fot(not(not(X_168))))]]) ).
cnf(refute_0_160,plain,
theorem(or(not(X_168),not(not(X_168)))) = theorem(or(not(X_168),not(not(X_168)))),
introduced(tautology,[refl,[$fot(theorem(or(not(X_168),not(not(X_168)))))]]) ).
cnf(refute_0_161,plain,
( or(not(X_168),not(not(X_168))) != implies(X_168,not(not(X_168)))
| theorem(or(not(X_168),not(not(X_168)))) != theorem(or(not(X_168),not(not(X_168))))
| theorem(or(not(X_168),not(not(X_168)))) = theorem(implies(X_168,not(not(X_168)))) ),
introduced(tautology,[equality,[$cnf( $equal(theorem(or(not(X_168),not(not(X_168)))),theorem(or(not(X_168),not(not(X_168))))) ),[1,0],$fot(implies(X_168,not(not(X_168))))]]) ).
cnf(refute_0_162,plain,
( or(not(X_168),not(not(X_168))) != implies(X_168,not(not(X_168)))
| theorem(or(not(X_168),not(not(X_168)))) = theorem(implies(X_168,not(not(X_168)))) ),
inference(resolve,[$cnf( $equal(theorem(or(not(X_168),not(not(X_168)))),theorem(or(not(X_168),not(not(X_168))))) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
theorem(or(not(X_168),not(not(X_168)))) = theorem(implies(X_168,not(not(X_168)))),
inference(resolve,[$cnf( $equal(or(not(X_168),not(not(X_168))),implies(X_168,not(not(X_168)))) )],[refute_0_159,refute_0_162]) ).
cnf(refute_0_164,plain,
ifeq(true,true,theorem(or(not(X_168),not(not(X_168)))),true) = theorem(or(not(X_168),not(not(X_168)))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(or(not(X_168),not(not(X_168)))))),bind(C,$fot(true))]]) ).
cnf(refute_0_165,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_166,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_43,refute_0_165]) ).
cnf(refute_0_167,plain,
( ifeq(true,true,theorem(or(not(X_168),not(not(X_168)))),true) != theorem(or(not(X_168),not(not(X_168))))
| theorem(or(not(X_168),not(not(X_168)))) != theorem(implies(X_168,not(not(X_168))))
| ifeq(true,true,theorem(or(not(X_168),not(not(X_168)))),true) = theorem(implies(X_168,not(not(X_168)))) ),
inference(subst,[],[refute_0_166:[bind(X0,$fot(ifeq(true,true,theorem(or(not(X_168),not(not(X_168)))),true))),bind(Y0,$fot(theorem(or(not(X_168),not(not(X_168)))))),bind(Z,$fot(theorem(implies(X_168,not(not(X_168))))))]]) ).
cnf(refute_0_168,plain,
( theorem(or(not(X_168),not(not(X_168)))) != theorem(implies(X_168,not(not(X_168))))
| ifeq(true,true,theorem(or(not(X_168),not(not(X_168)))),true) = theorem(implies(X_168,not(not(X_168)))) ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(not(X_168),not(not(X_168)))),true),theorem(or(not(X_168),not(not(X_168))))) )],[refute_0_164,refute_0_167]) ).
cnf(refute_0_169,plain,
ifeq(true,true,theorem(or(not(X_168),not(not(X_168)))),true) = theorem(implies(X_168,not(not(X_168)))),
inference(resolve,[$cnf( $equal(theorem(or(not(X_168),not(not(X_168)))),theorem(implies(X_168,not(not(X_168))))) )],[refute_0_163,refute_0_168]) ).
cnf(refute_0_170,plain,
( ifeq(true,true,theorem(or(not(X_168),not(not(X_168)))),true) != theorem(implies(X_168,not(not(X_168))))
| ifeq(true,true,theorem(or(not(X_168),not(not(X_168)))),true) != true
| theorem(implies(X_168,not(not(X_168)))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(or(not(X_168),not(not(X_168)))),true),true) ),[0],$fot(theorem(implies(X_168,not(not(X_168)))))]]) ).
cnf(refute_0_171,plain,
( ifeq(true,true,theorem(or(not(X_168),not(not(X_168)))),true) != true
| theorem(implies(X_168,not(not(X_168)))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(not(X_168),not(not(X_168)))),true),theorem(implies(X_168,not(not(X_168))))) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
theorem(implies(X_168,not(not(X_168)))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(not(X_168),not(not(X_168)))),true),true) )],[refute_0_158,refute_0_171]) ).
cnf(refute_0_173,plain,
theorem(implies(X_289,not(not(X_289)))) = true,
inference(subst,[],[refute_0_172:[bind(X_168,$fot(X_289))]]) ).
cnf(refute_0_174,plain,
( ifeq(theorem(implies(X_289,not(not(X_289)))),true,theorem(implies(or(X_291,X_289),or(X_291,not(not(X_289))))),true) != true
| theorem(implies(X_289,not(not(X_289)))) != true
| ifeq(true,true,theorem(implies(or(X_291,X_289),or(X_291,not(not(X_289))))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(X_289,not(not(X_289)))),true,theorem(implies(or(X_291,X_289),or(X_291,not(not(X_289))))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_175,plain,
( ifeq(theorem(implies(X_289,not(not(X_289)))),true,theorem(implies(or(X_291,X_289),or(X_291,not(not(X_289))))),true) != true
| ifeq(true,true,theorem(implies(or(X_291,X_289),or(X_291,not(not(X_289))))),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(X_289,not(not(X_289)))),true) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
ifeq(true,true,theorem(implies(or(X_291,X_289),or(X_291,not(not(X_289))))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(X_289,not(not(X_289)))),true,theorem(implies(or(X_291,X_289),or(X_291,not(not(X_289))))),true),true) )],[refute_0_37,refute_0_175]) ).
cnf(refute_0_177,plain,
ifeq(true,true,theorem(implies(or(X_291,X_289),or(X_291,not(not(X_289))))),true) = theorem(implies(or(X_291,X_289),or(X_291,not(not(X_289))))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(implies(or(X_291,X_289),or(X_291,not(not(X_289))))))),bind(C,$fot(true))]]) ).
cnf(refute_0_178,plain,
( ifeq(true,true,theorem(implies(or(X_291,X_289),or(X_291,not(not(X_289))))),true) != theorem(implies(or(X_291,X_289),or(X_291,not(not(X_289)))))
| ifeq(true,true,theorem(implies(or(X_291,X_289),or(X_291,not(not(X_289))))),true) != true
| theorem(implies(or(X_291,X_289),or(X_291,not(not(X_289))))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(implies(or(X_291,X_289),or(X_291,not(not(X_289))))),true),true) ),[0],$fot(theorem(implies(or(X_291,X_289),or(X_291,not(not(X_289))))))]]) ).
cnf(refute_0_179,plain,
( ifeq(true,true,theorem(implies(or(X_291,X_289),or(X_291,not(not(X_289))))),true) != true
| theorem(implies(or(X_291,X_289),or(X_291,not(not(X_289))))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(or(X_291,X_289),or(X_291,not(not(X_289))))),true),theorem(implies(or(X_291,X_289),or(X_291,not(not(X_289)))))) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
theorem(implies(or(X_291,X_289),or(X_291,not(not(X_289))))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(or(X_291,X_289),or(X_291,not(not(X_289))))),true),true) )],[refute_0_176,refute_0_179]) ).
cnf(refute_0_181,plain,
theorem(implies(or(X_293,X_292),or(X_293,not(not(X_292))))) = true,
inference(subst,[],[refute_0_180:[bind(X_289,$fot(X_292)),bind(X_291,$fot(X_293))]]) ).
cnf(refute_0_182,plain,
( ifeq(theorem(implies(or(X_293,X_292),or(X_293,not(not(X_292))))),true,ifeq(theorem(or(X_293,X_292)),true,theorem(or(X_293,not(not(X_292)))),true),true) != true
| theorem(implies(or(X_293,X_292),or(X_293,not(not(X_292))))) != true
| ifeq(true,true,ifeq(theorem(or(X_293,X_292)),true,theorem(or(X_293,not(not(X_292)))),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(or(X_293,X_292),or(X_293,not(not(X_292))))),true,ifeq(theorem(or(X_293,X_292)),true,theorem(or(X_293,not(not(X_292)))),true),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_183,plain,
( ifeq(theorem(implies(or(X_293,X_292),or(X_293,not(not(X_292))))),true,ifeq(theorem(or(X_293,X_292)),true,theorem(or(X_293,not(not(X_292)))),true),true) != true
| ifeq(true,true,ifeq(theorem(or(X_293,X_292)),true,theorem(or(X_293,not(not(X_292)))),true),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(or(X_293,X_292),or(X_293,not(not(X_292))))),true) )],[refute_0_181,refute_0_182]) ).
cnf(refute_0_184,plain,
ifeq(true,true,ifeq(theorem(or(X_293,X_292)),true,theorem(or(X_293,not(not(X_292)))),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(or(X_293,X_292),or(X_293,not(not(X_292))))),true,ifeq(theorem(or(X_293,X_292)),true,theorem(or(X_293,not(not(X_292)))),true),true),true) )],[refute_0_18,refute_0_183]) ).
cnf(refute_0_185,plain,
ifeq(true,true,ifeq(theorem(or(X_293,X_292)),true,theorem(or(X_293,not(not(X_292)))),true),true) = ifeq(theorem(or(X_293,X_292)),true,theorem(or(X_293,not(not(X_292)))),true),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(ifeq(theorem(or(X_293,X_292)),true,theorem(or(X_293,not(not(X_292)))),true))),bind(C,$fot(true))]]) ).
cnf(refute_0_186,plain,
( ifeq(true,true,ifeq(theorem(or(X_293,X_292)),true,theorem(or(X_293,not(not(X_292)))),true),true) != ifeq(theorem(or(X_293,X_292)),true,theorem(or(X_293,not(not(X_292)))),true)
| ifeq(true,true,ifeq(theorem(or(X_293,X_292)),true,theorem(or(X_293,not(not(X_292)))),true),true) != true
| ifeq(theorem(or(X_293,X_292)),true,theorem(or(X_293,not(not(X_292)))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,ifeq(theorem(or(X_293,X_292)),true,theorem(or(X_293,not(not(X_292)))),true),true),true) ),[0],$fot(ifeq(theorem(or(X_293,X_292)),true,theorem(or(X_293,not(not(X_292)))),true))]]) ).
cnf(refute_0_187,plain,
( ifeq(true,true,ifeq(theorem(or(X_293,X_292)),true,theorem(or(X_293,not(not(X_292)))),true),true) != true
| ifeq(theorem(or(X_293,X_292)),true,theorem(or(X_293,not(not(X_292)))),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(theorem(or(X_293,X_292)),true,theorem(or(X_293,not(not(X_292)))),true),true),ifeq(theorem(or(X_293,X_292)),true,theorem(or(X_293,not(not(X_292)))),true)) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
ifeq(theorem(or(X_293,X_292)),true,theorem(or(X_293,not(not(X_292)))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(theorem(or(X_293,X_292)),true,theorem(or(X_293,not(not(X_292)))),true),true),true) )],[refute_0_184,refute_0_187]) ).
cnf(refute_0_189,plain,
ifeq(theorem(or(implies(or(X_366,X_1779),X_366),X_1779)),true,theorem(or(implies(or(X_366,X_1779),X_366),not(not(X_1779)))),true) = true,
inference(subst,[],[refute_0_188:[bind(X_292,$fot(X_1779)),bind(X_293,$fot(implies(or(X_366,X_1779),X_366)))]]) ).
cnf(refute_0_190,plain,
ifeq(theorem(or(X_10,implies(or(X_366,X_10),X_366))),true,theorem(or(implies(or(X_366,X_10),X_366),X_10)),true) = true,
inference(subst,[],[refute_0_16:[bind(X_11,$fot(implies(or(X_366,X_10),X_366)))]]) ).
cnf(refute_0_191,plain,
ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,ifeq(theorem(implies(or(X_10,X_11),or(X_11,X_10))),true,theorem(X_22),true),true) = true,
inference(subst,[],[rule_2:[bind(X,$fot(X_22)),bind(Y,$fot(implies(or(X_10,X_11),or(X_11,X_10))))]]) ).
cnf(refute_0_192,plain,
( ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,ifeq(theorem(implies(or(X_10,X_11),or(X_11,X_10))),true,theorem(X_22),true),true) != true
| theorem(implies(or(X_10,X_11),or(X_11,X_10))) != true
| ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,ifeq(theorem(implies(or(X_10,X_11),or(X_11,X_10))),true,theorem(X_22),true),true),true) ),[0,2,0],$fot(true)]]) ).
cnf(refute_0_193,plain,
( ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,ifeq(theorem(implies(or(X_10,X_11),or(X_11,X_10))),true,theorem(X_22),true),true) != true
| ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(or(X_10,X_11),or(X_11,X_10))),true) )],[refute_0_9,refute_0_192]) ).
cnf(refute_0_194,plain,
ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,ifeq(theorem(implies(or(X_10,X_11),or(X_11,X_10))),true,theorem(X_22),true),true),true) )],[refute_0_191,refute_0_193]) ).
cnf(refute_0_195,plain,
ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) = ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,ifeq(true,true,theorem(X_22),true),true),
introduced(tautology,[refl,[$fot(ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,ifeq(true,true,theorem(X_22),true),true))]]) ).
cnf(refute_0_196,plain,
( ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) != ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,ifeq(true,true,theorem(X_22),true),true)
| ifeq(true,true,theorem(X_22),true) != theorem(X_22)
| ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) = ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,theorem(X_22),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,ifeq(true,true,theorem(X_22),true),true),ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,ifeq(true,true,theorem(X_22),true),true)) ),[1,2],$fot(theorem(X_22))]]) ).
cnf(refute_0_197,plain,
( ifeq(true,true,theorem(X_22),true) != theorem(X_22)
| ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) = ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,theorem(X_22),true) ),
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,ifeq(true,true,theorem(X_22),true),true),ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,ifeq(true,true,theorem(X_22),true),true)) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) = ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,theorem(X_22),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(X_22),true),theorem(X_22)) )],[refute_0_78,refute_0_197]) ).
cnf(refute_0_199,plain,
( ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) != ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,theorem(X_22),true)
| ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) != true
| ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,theorem(X_22),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,ifeq(true,true,theorem(X_22),true),true),true) ),[0],$fot(ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,theorem(X_22),true))]]) ).
cnf(refute_0_200,plain,
( ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,ifeq(true,true,theorem(X_22),true),true) != true
| ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,theorem(X_22),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,ifeq(true,true,theorem(X_22),true),true),ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,theorem(X_22),true)) )],[refute_0_198,refute_0_199]) ).
cnf(refute_0_201,plain,
ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,theorem(X_22),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(or(X_10,X_11),or(X_11,X_10)),X_22)),true,ifeq(true,true,theorem(X_22),true),true),true) )],[refute_0_194,refute_0_200]) ).
cnf(refute_0_202,plain,
ifeq(theorem(implies(implies(or(X_363,X_364),or(X_364,X_363)),or(X_364,implies(or(X_363,X_364),X_363)))),true,theorem(or(X_364,implies(or(X_363,X_364),X_363))),true) = true,
inference(subst,[],[refute_0_201:[bind(X_10,$fot(X_363)),bind(X_11,$fot(X_364)),bind(X_22,$fot(or(X_364,implies(or(X_363,X_364),X_363))))]]) ).
cnf(refute_0_203,plain,
ifeq(axiom(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))),true,theorem(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))),true) = true,
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))))]]) ).
cnf(refute_0_204,plain,
axiom(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))) = true,
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_25)),bind(B,$fot(X_26)),bind(C,$fot(X_27))]]) ).
cnf(refute_0_205,plain,
( axiom(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))) != true
| ifeq(axiom(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))),true,theorem(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))),true) != true
| ifeq(true,true,theorem(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(axiom(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))),true,theorem(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_206,plain,
( ifeq(axiom(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))),true,theorem(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))),true) != true
| ifeq(true,true,theorem(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))),true) = true ),
inference(resolve,[$cnf( $equal(axiom(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))),true) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
ifeq(true,true,theorem(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(axiom(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))),true,theorem(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))),true),true) )],[refute_0_203,refute_0_206]) ).
cnf(refute_0_208,plain,
ifeq(true,true,theorem(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))),true) = theorem(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))))),bind(C,$fot(true))]]) ).
cnf(refute_0_209,plain,
( ifeq(true,true,theorem(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))),true) != theorem(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27))))
| ifeq(true,true,theorem(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))),true) != true
| theorem(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))),true),true) ),[0],$fot(theorem(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))))]]) ).
cnf(refute_0_210,plain,
( ifeq(true,true,theorem(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))),true) != true
| theorem(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))),true),theorem(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27))))) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
theorem(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))),true),true) )],[refute_0_207,refute_0_210]) ).
cnf(refute_0_212,plain,
theorem(implies(or(not(X),or(X_54,X_55)),or(X_54,or(not(X),X_55)))) = true,
inference(subst,[],[refute_0_211:[bind(X_25,$fot(not(X))),bind(X_26,$fot(X_54)),bind(X_27,$fot(X_55))]]) ).
cnf(refute_0_213,plain,
implies(X,X_55) = or(not(X),X_55),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_55))]]) ).
cnf(refute_0_214,plain,
( implies(X,X_55) != or(not(X),X_55)
| or(not(X),X_55) = implies(X,X_55) ),
inference(subst,[],[refute_0_43:[bind(X0,$fot(implies(X,X_55))),bind(Y0,$fot(or(not(X),X_55)))]]) ).
cnf(refute_0_215,plain,
or(not(X),X_55) = implies(X,X_55),
inference(resolve,[$cnf( $equal(implies(X,X_55),or(not(X),X_55)) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
( or(not(X),X_55) != implies(X,X_55)
| theorem(implies(or(not(X),or(X_54,X_55)),or(X_54,or(not(X),X_55)))) != true
| theorem(implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55)))) = true ),
introduced(tautology,[equality,[$cnf( $equal(theorem(implies(or(not(X),or(X_54,X_55)),or(X_54,or(not(X),X_55)))),true) ),[0,0,1,1],$fot(implies(X,X_55))]]) ).
cnf(refute_0_217,plain,
( theorem(implies(or(not(X),or(X_54,X_55)),or(X_54,or(not(X),X_55)))) != true
| theorem(implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55)))) = true ),
inference(resolve,[$cnf( $equal(or(not(X),X_55),implies(X,X_55)) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
theorem(implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55)))) = true,
inference(resolve,[$cnf( $equal(theorem(implies(or(not(X),or(X_54,X_55)),or(X_54,or(not(X),X_55)))),true) )],[refute_0_212,refute_0_217]) ).
cnf(refute_0_219,plain,
or(not(X),or(X_54,X_55)) = implies(X,or(X_54,X_55)),
inference(subst,[],[refute_0_122:[bind(Y,$fot(or(X_54,X_55)))]]) ).
cnf(refute_0_220,plain,
implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55))) = implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55))))]]) ).
cnf(refute_0_221,plain,
( implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55))) != implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55)))
| or(not(X),or(X_54,X_55)) != implies(X,or(X_54,X_55))
| implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55))) = implies(implies(X,or(X_54,X_55)),or(X_54,implies(X,X_55))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55))),implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55)))) ),[1,0],$fot(implies(X,or(X_54,X_55)))]]) ).
cnf(refute_0_222,plain,
( or(not(X),or(X_54,X_55)) != implies(X,or(X_54,X_55))
| implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55))) = implies(implies(X,or(X_54,X_55)),or(X_54,implies(X,X_55))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55))),implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55)))) )],[refute_0_220,refute_0_221]) ).
cnf(refute_0_223,plain,
implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55))) = implies(implies(X,or(X_54,X_55)),or(X_54,implies(X,X_55))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_54,X_55)),implies(X,or(X_54,X_55))) )],[refute_0_219,refute_0_222]) ).
cnf(refute_0_224,plain,
theorem(implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55)))) = theorem(implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55)))),
introduced(tautology,[refl,[$fot(theorem(implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55)))))]]) ).
cnf(refute_0_225,plain,
( implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55))) != implies(implies(X,or(X_54,X_55)),or(X_54,implies(X,X_55)))
| theorem(implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55)))) != theorem(implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55))))
| theorem(implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55)))) = theorem(implies(implies(X,or(X_54,X_55)),or(X_54,implies(X,X_55)))) ),
introduced(tautology,[equality,[$cnf( $equal(theorem(implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55)))),theorem(implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55))))) ),[1,0],$fot(implies(implies(X,or(X_54,X_55)),or(X_54,implies(X,X_55))))]]) ).
cnf(refute_0_226,plain,
( implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55))) != implies(implies(X,or(X_54,X_55)),or(X_54,implies(X,X_55)))
| theorem(implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55)))) = theorem(implies(implies(X,or(X_54,X_55)),or(X_54,implies(X,X_55)))) ),
inference(resolve,[$cnf( $equal(theorem(implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55)))),theorem(implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55))))) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
theorem(implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55)))) = theorem(implies(implies(X,or(X_54,X_55)),or(X_54,implies(X,X_55)))),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55))),implies(implies(X,or(X_54,X_55)),or(X_54,implies(X,X_55)))) )],[refute_0_223,refute_0_226]) ).
cnf(refute_0_228,plain,
( theorem(implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55)))) != theorem(implies(implies(X,or(X_54,X_55)),or(X_54,implies(X,X_55))))
| theorem(implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55)))) != true
| theorem(implies(implies(X,or(X_54,X_55)),or(X_54,implies(X,X_55)))) = true ),
introduced(tautology,[equality,[$cnf( $equal(theorem(implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55)))),true) ),[0],$fot(theorem(implies(implies(X,or(X_54,X_55)),or(X_54,implies(X,X_55)))))]]) ).
cnf(refute_0_229,plain,
( theorem(implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55)))) != true
| theorem(implies(implies(X,or(X_54,X_55)),or(X_54,implies(X,X_55)))) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55)))),theorem(implies(implies(X,or(X_54,X_55)),or(X_54,implies(X,X_55))))) )],[refute_0_227,refute_0_228]) ).
cnf(refute_0_230,plain,
theorem(implies(implies(X,or(X_54,X_55)),or(X_54,implies(X,X_55)))) = true,
inference(resolve,[$cnf( $equal(theorem(implies(or(not(X),or(X_54,X_55)),or(X_54,implies(X,X_55)))),true) )],[refute_0_218,refute_0_229]) ).
cnf(refute_0_231,plain,
theorem(implies(implies(or(X_363,X_364),or(X_364,X_363)),or(X_364,implies(or(X_363,X_364),X_363)))) = true,
inference(subst,[],[refute_0_230:[bind(X,$fot(or(X_363,X_364))),bind(X_54,$fot(X_364)),bind(X_55,$fot(X_363))]]) ).
cnf(refute_0_232,plain,
( ifeq(theorem(implies(implies(or(X_363,X_364),or(X_364,X_363)),or(X_364,implies(or(X_363,X_364),X_363)))),true,theorem(or(X_364,implies(or(X_363,X_364),X_363))),true) != true
| theorem(implies(implies(or(X_363,X_364),or(X_364,X_363)),or(X_364,implies(or(X_363,X_364),X_363)))) != true
| ifeq(true,true,theorem(or(X_364,implies(or(X_363,X_364),X_363))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(implies(implies(or(X_363,X_364),or(X_364,X_363)),or(X_364,implies(or(X_363,X_364),X_363)))),true,theorem(or(X_364,implies(or(X_363,X_364),X_363))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_233,plain,
( ifeq(theorem(implies(implies(or(X_363,X_364),or(X_364,X_363)),or(X_364,implies(or(X_363,X_364),X_363)))),true,theorem(or(X_364,implies(or(X_363,X_364),X_363))),true) != true
| ifeq(true,true,theorem(or(X_364,implies(or(X_363,X_364),X_363))),true) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(implies(or(X_363,X_364),or(X_364,X_363)),or(X_364,implies(or(X_363,X_364),X_363)))),true) )],[refute_0_231,refute_0_232]) ).
cnf(refute_0_234,plain,
ifeq(true,true,theorem(or(X_364,implies(or(X_363,X_364),X_363))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(implies(implies(or(X_363,X_364),or(X_364,X_363)),or(X_364,implies(or(X_363,X_364),X_363)))),true,theorem(or(X_364,implies(or(X_363,X_364),X_363))),true),true) )],[refute_0_202,refute_0_233]) ).
cnf(refute_0_235,plain,
ifeq(true,true,theorem(or(X_364,implies(or(X_363,X_364),X_363))),true) = theorem(or(X_364,implies(or(X_363,X_364),X_363))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(or(X_364,implies(or(X_363,X_364),X_363))))),bind(C,$fot(true))]]) ).
cnf(refute_0_236,plain,
( ifeq(true,true,theorem(or(X_364,implies(or(X_363,X_364),X_363))),true) != theorem(or(X_364,implies(or(X_363,X_364),X_363)))
| ifeq(true,true,theorem(or(X_364,implies(or(X_363,X_364),X_363))),true) != true
| theorem(or(X_364,implies(or(X_363,X_364),X_363))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(or(X_364,implies(or(X_363,X_364),X_363))),true),true) ),[0],$fot(theorem(or(X_364,implies(or(X_363,X_364),X_363))))]]) ).
cnf(refute_0_237,plain,
( ifeq(true,true,theorem(or(X_364,implies(or(X_363,X_364),X_363))),true) != true
| theorem(or(X_364,implies(or(X_363,X_364),X_363))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(X_364,implies(or(X_363,X_364),X_363))),true),theorem(or(X_364,implies(or(X_363,X_364),X_363)))) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
theorem(or(X_364,implies(or(X_363,X_364),X_363))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(X_364,implies(or(X_363,X_364),X_363))),true),true) )],[refute_0_234,refute_0_237]) ).
cnf(refute_0_239,plain,
theorem(or(X_10,implies(or(X_366,X_10),X_366))) = true,
inference(subst,[],[refute_0_238:[bind(X_363,$fot(X_366)),bind(X_364,$fot(X_10))]]) ).
cnf(refute_0_240,plain,
( ifeq(theorem(or(X_10,implies(or(X_366,X_10),X_366))),true,theorem(or(implies(or(X_366,X_10),X_366),X_10)),true) != true
| theorem(or(X_10,implies(or(X_366,X_10),X_366))) != true
| ifeq(true,true,theorem(or(implies(or(X_366,X_10),X_366),X_10)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(or(X_10,implies(or(X_366,X_10),X_366))),true,theorem(or(implies(or(X_366,X_10),X_366),X_10)),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_241,plain,
( ifeq(theorem(or(X_10,implies(or(X_366,X_10),X_366))),true,theorem(or(implies(or(X_366,X_10),X_366),X_10)),true) != true
| ifeq(true,true,theorem(or(implies(or(X_366,X_10),X_366),X_10)),true) = true ),
inference(resolve,[$cnf( $equal(theorem(or(X_10,implies(or(X_366,X_10),X_366))),true) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
ifeq(true,true,theorem(or(implies(or(X_366,X_10),X_366),X_10)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(or(X_10,implies(or(X_366,X_10),X_366))),true,theorem(or(implies(or(X_366,X_10),X_366),X_10)),true),true) )],[refute_0_190,refute_0_241]) ).
cnf(refute_0_243,plain,
ifeq(true,true,theorem(or(implies(or(X_366,X_10),X_366),X_10)),true) = theorem(or(implies(or(X_366,X_10),X_366),X_10)),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(or(implies(or(X_366,X_10),X_366),X_10)))),bind(C,$fot(true))]]) ).
cnf(refute_0_244,plain,
( ifeq(true,true,theorem(or(implies(or(X_366,X_10),X_366),X_10)),true) != theorem(or(implies(or(X_366,X_10),X_366),X_10))
| ifeq(true,true,theorem(or(implies(or(X_366,X_10),X_366),X_10)),true) != true
| theorem(or(implies(or(X_366,X_10),X_366),X_10)) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(or(implies(or(X_366,X_10),X_366),X_10)),true),true) ),[0],$fot(theorem(or(implies(or(X_366,X_10),X_366),X_10)))]]) ).
cnf(refute_0_245,plain,
( ifeq(true,true,theorem(or(implies(or(X_366,X_10),X_366),X_10)),true) != true
| theorem(or(implies(or(X_366,X_10),X_366),X_10)) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(implies(or(X_366,X_10),X_366),X_10)),true),theorem(or(implies(or(X_366,X_10),X_366),X_10))) )],[refute_0_243,refute_0_244]) ).
cnf(refute_0_246,plain,
theorem(or(implies(or(X_366,X_10),X_366),X_10)) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(implies(or(X_366,X_10),X_366),X_10)),true),true) )],[refute_0_242,refute_0_245]) ).
cnf(refute_0_247,plain,
theorem(or(implies(or(X_366,X_1779),X_366),X_1779)) = true,
inference(subst,[],[refute_0_246:[bind(X_10,$fot(X_1779))]]) ).
cnf(refute_0_248,plain,
( ifeq(theorem(or(implies(or(X_366,X_1779),X_366),X_1779)),true,theorem(or(implies(or(X_366,X_1779),X_366),not(not(X_1779)))),true) != true
| theorem(or(implies(or(X_366,X_1779),X_366),X_1779)) != true
| ifeq(true,true,theorem(or(implies(or(X_366,X_1779),X_366),not(not(X_1779)))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(or(implies(or(X_366,X_1779),X_366),X_1779)),true,theorem(or(implies(or(X_366,X_1779),X_366),not(not(X_1779)))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_249,plain,
( ifeq(theorem(or(implies(or(X_366,X_1779),X_366),X_1779)),true,theorem(or(implies(or(X_366,X_1779),X_366),not(not(X_1779)))),true) != true
| ifeq(true,true,theorem(or(implies(or(X_366,X_1779),X_366),not(not(X_1779)))),true) = true ),
inference(resolve,[$cnf( $equal(theorem(or(implies(or(X_366,X_1779),X_366),X_1779)),true) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
ifeq(true,true,theorem(or(implies(or(X_366,X_1779),X_366),not(not(X_1779)))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(or(implies(or(X_366,X_1779),X_366),X_1779)),true,theorem(or(implies(or(X_366,X_1779),X_366),not(not(X_1779)))),true),true) )],[refute_0_189,refute_0_249]) ).
cnf(refute_0_251,plain,
ifeq(true,true,theorem(or(implies(or(X_366,X_1779),X_366),not(not(X_1779)))),true) = theorem(or(implies(or(X_366,X_1779),X_366),not(not(X_1779)))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(or(implies(or(X_366,X_1779),X_366),not(not(X_1779)))))),bind(C,$fot(true))]]) ).
cnf(refute_0_252,plain,
( ifeq(true,true,theorem(or(implies(or(X_366,X_1779),X_366),not(not(X_1779)))),true) != theorem(or(implies(or(X_366,X_1779),X_366),not(not(X_1779))))
| ifeq(true,true,theorem(or(implies(or(X_366,X_1779),X_366),not(not(X_1779)))),true) != true
| theorem(or(implies(or(X_366,X_1779),X_366),not(not(X_1779)))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(or(implies(or(X_366,X_1779),X_366),not(not(X_1779)))),true),true) ),[0],$fot(theorem(or(implies(or(X_366,X_1779),X_366),not(not(X_1779)))))]]) ).
cnf(refute_0_253,plain,
( ifeq(true,true,theorem(or(implies(or(X_366,X_1779),X_366),not(not(X_1779)))),true) != true
| theorem(or(implies(or(X_366,X_1779),X_366),not(not(X_1779)))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(implies(or(X_366,X_1779),X_366),not(not(X_1779)))),true),theorem(or(implies(or(X_366,X_1779),X_366),not(not(X_1779))))) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
theorem(or(implies(or(X_366,X_1779),X_366),not(not(X_1779)))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(implies(or(X_366,X_1779),X_366),not(not(X_1779)))),true),true) )],[refute_0_250,refute_0_253]) ).
cnf(refute_0_255,plain,
theorem(or(implies(or(X_1884,X_1883),X_1884),not(not(X_1883)))) = true,
inference(subst,[],[refute_0_254:[bind(X_1779,$fot(X_1883)),bind(X_366,$fot(X_1884))]]) ).
cnf(refute_0_256,plain,
( ifeq(theorem(or(implies(or(X_1884,X_1883),X_1884),not(not(X_1883)))),true,theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))),true) != true
| theorem(or(implies(or(X_1884,X_1883),X_1884),not(not(X_1883)))) != true
| ifeq(true,true,theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(or(implies(or(X_1884,X_1883),X_1884),not(not(X_1883)))),true,theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_257,plain,
( ifeq(theorem(or(implies(or(X_1884,X_1883),X_1884),not(not(X_1883)))),true,theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))),true) != true
| ifeq(true,true,theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))),true) = true ),
inference(resolve,[$cnf( $equal(theorem(or(implies(or(X_1884,X_1883),X_1884),not(not(X_1883)))),true) )],[refute_0_255,refute_0_256]) ).
cnf(refute_0_258,plain,
ifeq(true,true,theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(or(implies(or(X_1884,X_1883),X_1884),not(not(X_1883)))),true,theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))),true),true) )],[refute_0_17,refute_0_257]) ).
cnf(refute_0_259,plain,
or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884)) = implies(not(X_1883),implies(or(X_1884,X_1883),X_1884)),
inference(subst,[],[refute_0_122:[bind(X,$fot(not(X_1883))),bind(Y,$fot(implies(or(X_1884,X_1883),X_1884)))]]) ).
cnf(refute_0_260,plain,
theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))) = theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))),
introduced(tautology,[refl,[$fot(theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))))]]) ).
cnf(refute_0_261,plain,
( or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884)) != implies(not(X_1883),implies(or(X_1884,X_1883),X_1884))
| theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))) != theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884)))
| theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))) = theorem(implies(not(X_1883),implies(or(X_1884,X_1883),X_1884))) ),
introduced(tautology,[equality,[$cnf( $equal(theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))),theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884)))) ),[1,0],$fot(implies(not(X_1883),implies(or(X_1884,X_1883),X_1884)))]]) ).
cnf(refute_0_262,plain,
( or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884)) != implies(not(X_1883),implies(or(X_1884,X_1883),X_1884))
| theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))) = theorem(implies(not(X_1883),implies(or(X_1884,X_1883),X_1884))) ),
inference(resolve,[$cnf( $equal(theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))),theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884)))) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))) = theorem(implies(not(X_1883),implies(or(X_1884,X_1883),X_1884))),
inference(resolve,[$cnf( $equal(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884)),implies(not(X_1883),implies(or(X_1884,X_1883),X_1884))) )],[refute_0_259,refute_0_262]) ).
cnf(refute_0_264,plain,
ifeq(true,true,theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))),true) = theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))))),bind(C,$fot(true))]]) ).
cnf(refute_0_265,plain,
( ifeq(true,true,theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))),true) != theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884)))
| theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))) != theorem(implies(not(X_1883),implies(or(X_1884,X_1883),X_1884)))
| ifeq(true,true,theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))),true) = theorem(implies(not(X_1883),implies(or(X_1884,X_1883),X_1884))) ),
inference(subst,[],[refute_0_166:[bind(X0,$fot(ifeq(true,true,theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))),true))),bind(Y0,$fot(theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))))),bind(Z,$fot(theorem(implies(not(X_1883),implies(or(X_1884,X_1883),X_1884)))))]]) ).
cnf(refute_0_266,plain,
( theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))) != theorem(implies(not(X_1883),implies(or(X_1884,X_1883),X_1884)))
| ifeq(true,true,theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))),true) = theorem(implies(not(X_1883),implies(or(X_1884,X_1883),X_1884))) ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))),true),theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884)))) )],[refute_0_264,refute_0_265]) ).
cnf(refute_0_267,plain,
ifeq(true,true,theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))),true) = theorem(implies(not(X_1883),implies(or(X_1884,X_1883),X_1884))),
inference(resolve,[$cnf( $equal(theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))),theorem(implies(not(X_1883),implies(or(X_1884,X_1883),X_1884)))) )],[refute_0_263,refute_0_266]) ).
cnf(refute_0_268,plain,
( ifeq(true,true,theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))),true) != theorem(implies(not(X_1883),implies(or(X_1884,X_1883),X_1884)))
| ifeq(true,true,theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))),true) != true
| theorem(implies(not(X_1883),implies(or(X_1884,X_1883),X_1884))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))),true),true) ),[0],$fot(theorem(implies(not(X_1883),implies(or(X_1884,X_1883),X_1884))))]]) ).
cnf(refute_0_269,plain,
( ifeq(true,true,theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))),true) != true
| theorem(implies(not(X_1883),implies(or(X_1884,X_1883),X_1884))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))),true),theorem(implies(not(X_1883),implies(or(X_1884,X_1883),X_1884)))) )],[refute_0_267,refute_0_268]) ).
cnf(refute_0_270,plain,
theorem(implies(not(X_1883),implies(or(X_1884,X_1883),X_1884))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(not(not(X_1883)),implies(or(X_1884,X_1883),X_1884))),true),true) )],[refute_0_258,refute_0_269]) ).
cnf(refute_0_271,plain,
theorem(implies(not(q),implies(or(p,q),p))) = true,
inference(subst,[],[refute_0_270:[bind(X_1883,$fot(q)),bind(X_1884,$fot(p))]]) ).
cnf(refute_0_272,plain,
( theorem(implies(not(q),implies(or(p,q),p))) != true
| true != true
| theorem(implies(not(q),implies(or(p,q),p))) = true ),
introduced(tautology,[equality,[$cnf( ~ $equal(theorem(implies(not(q),implies(or(p,q),p))),true) ),[0],$fot(true)]]) ).
cnf(refute_0_273,plain,
( true != true
| theorem(implies(not(q),implies(or(p,q),p))) = true ),
inference(resolve,[$cnf( $equal(theorem(implies(not(q),implies(or(p,q),p))),true) )],[refute_0_271,refute_0_272]) ).
cnf(refute_0_274,plain,
true != true,
inference(resolve,[$cnf( $equal(theorem(implies(not(q),implies(or(p,q),p))),true) )],[refute_0_273,prove_this]) ).
cnf(refute_0_275,plain,
true = true,
introduced(tautology,[refl,[$fot(true)]]) ).
cnf(refute_0_276,plain,
$false,
inference(resolve,[$cnf( $equal(true,true) )],[refute_0_275,refute_0_274]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL211-10 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 2 21:12:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 12.57/12.73 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.57/12.73
% 12.57/12.73 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.57/12.76
%------------------------------------------------------------------------------