TSTP Solution File: LCL202-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL202-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 12:50:32 EDT 2022
% Result : Unsatisfiable 28.23s 28.42s
% Output : CNFRefutation 28.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 35
% Syntax : Number of clauses : 167 ( 89 unt; 0 nHn; 69 RR)
% Number of literals : 273 ( 98 equ; 107 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 421 ( 27 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1_3,axiom,
axiom(implies(A,or(B,A))) ).
cnf(axiom_1_4,axiom,
axiom(implies(or(A,B),or(B,A))) ).
cnf(axiom_1_5,axiom,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) ).
cnf(axiom_1_6,axiom,
axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) ).
cnf(implies_definition,axiom,
implies(X,Y) = or(not(X),Y) ).
cnf(rule_1,axiom,
( theorem(X)
| ~ axiom(X) ) ).
cnf(rule_2,axiom,
( theorem(X)
| ~ theorem(implies(Y,X))
| ~ theorem(Y) ) ).
cnf(prove_this,negated_conjecture,
~ theorem(implies(not(or(p,q)),or(p,not(q)))) ).
cnf(refute_0_0,plain,
( ~ axiom(implies(or(X_53,implies(X_52,X_54)),implies(X_52,or(X_53,X_54))))
| theorem(implies(or(X_53,implies(X_52,X_54)),implies(X_52,or(X_53,X_54)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_53,implies(X_52,X_54)),implies(X_52,or(X_53,X_54)))))]]) ).
cnf(refute_0_1,plain,
axiom(implies(or(X_31,or(not(X),X_33)),or(not(X),or(X_31,X_33)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_31)),bind(B,$fot(not(X))),bind(C,$fot(X_33))]]) ).
cnf(refute_0_2,plain,
implies(X,or(X_31,X_33)) = or(not(X),or(X_31,X_33)),
inference(subst,[],[implies_definition:[bind(Y,$fot(or(X_31,X_33)))]]) ).
cnf(refute_0_3,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_4,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_5,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( implies(X,or(X_31,X_33)) != or(not(X),or(X_31,X_33))
| or(not(X),or(X_31,X_33)) = implies(X,or(X_31,X_33)) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(implies(X,or(X_31,X_33)))),bind(Y0,$fot(or(not(X),or(X_31,X_33))))]]) ).
cnf(refute_0_7,plain,
or(not(X),or(X_31,X_33)) = implies(X,or(X_31,X_33)),
inference(resolve,[$cnf( $equal(implies(X,or(X_31,X_33)),or(not(X),or(X_31,X_33))) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
( or(not(X),or(X_31,X_33)) != implies(X,or(X_31,X_33))
| ~ axiom(implies(or(X_31,or(not(X),X_33)),or(not(X),or(X_31,X_33))))
| axiom(implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(X_31,or(not(X),X_33)),or(not(X),or(X_31,X_33)))) ),[0,1],$fot(implies(X,or(X_31,X_33)))]]) ).
cnf(refute_0_9,plain,
( ~ axiom(implies(or(X_31,or(not(X),X_33)),or(not(X),or(X_31,X_33))))
| axiom(implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33)))) ),
inference(resolve,[$cnf( $equal(or(not(X),or(X_31,X_33)),implies(X,or(X_31,X_33))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
axiom(implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33)))),
inference(resolve,[$cnf( axiom(implies(or(X_31,or(not(X),X_33)),or(not(X),or(X_31,X_33)))) )],[refute_0_1,refute_0_9]) ).
cnf(refute_0_11,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_12,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_11]) ).
cnf(refute_0_13,plain,
or(not(X),X_33) = implies(X,X_33),
inference(subst,[],[refute_0_12:[bind(Y,$fot(X_33))]]) ).
cnf(refute_0_14,plain,
or(X_31,or(not(X),X_33)) = or(X_31,or(not(X),X_33)),
introduced(tautology,[refl,[$fot(or(X_31,or(not(X),X_33)))]]) ).
cnf(refute_0_15,plain,
( or(X_31,or(not(X),X_33)) != or(X_31,or(not(X),X_33))
| or(not(X),X_33) != implies(X,X_33)
| or(X_31,or(not(X),X_33)) = or(X_31,implies(X,X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_31,or(not(X),X_33)),or(X_31,or(not(X),X_33))) ),[1,1],$fot(implies(X,X_33))]]) ).
cnf(refute_0_16,plain,
( or(not(X),X_33) != implies(X,X_33)
| or(X_31,or(not(X),X_33)) = or(X_31,implies(X,X_33)) ),
inference(resolve,[$cnf( $equal(or(X_31,or(not(X),X_33)),or(X_31,or(not(X),X_33))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
or(X_31,or(not(X),X_33)) = or(X_31,implies(X,X_33)),
inference(resolve,[$cnf( $equal(or(not(X),X_33),implies(X,X_33)) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33))) = implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33))),
introduced(tautology,[refl,[$fot(implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33))))]]) ).
cnf(refute_0_19,plain,
( implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33))) != implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33)))
| or(X_31,or(not(X),X_33)) != or(X_31,implies(X,X_33))
| implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33))) = implies(or(X_31,implies(X,X_33)),implies(X,or(X_31,X_33))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33))),implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33)))) ),[1,0],$fot(or(X_31,implies(X,X_33)))]]) ).
cnf(refute_0_20,plain,
( or(X_31,or(not(X),X_33)) != or(X_31,implies(X,X_33))
| implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33))) = implies(or(X_31,implies(X,X_33)),implies(X,or(X_31,X_33))) ),
inference(resolve,[$cnf( $equal(implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33))),implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33)))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33))) = implies(or(X_31,implies(X,X_33)),implies(X,or(X_31,X_33))),
inference(resolve,[$cnf( $equal(or(X_31,or(not(X),X_33)),or(X_31,implies(X,X_33))) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
( implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33))) != implies(or(X_31,implies(X,X_33)),implies(X,or(X_31,X_33)))
| ~ axiom(implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33))))
| axiom(implies(or(X_31,implies(X,X_33)),implies(X,or(X_31,X_33)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33)))) ),[0],$fot(implies(or(X_31,implies(X,X_33)),implies(X,or(X_31,X_33))))]]) ).
cnf(refute_0_23,plain,
( ~ axiom(implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33))))
| axiom(implies(or(X_31,implies(X,X_33)),implies(X,or(X_31,X_33)))) ),
inference(resolve,[$cnf( $equal(implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33))),implies(or(X_31,implies(X,X_33)),implies(X,or(X_31,X_33)))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
axiom(implies(or(X_31,implies(X,X_33)),implies(X,or(X_31,X_33)))),
inference(resolve,[$cnf( axiom(implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33)))) )],[refute_0_10,refute_0_23]) ).
cnf(refute_0_25,plain,
axiom(implies(or(X_53,implies(X_52,X_54)),implies(X_52,or(X_53,X_54)))),
inference(subst,[],[refute_0_24:[bind(X,$fot(X_52)),bind(X_31,$fot(X_53)),bind(X_33,$fot(X_54))]]) ).
cnf(refute_0_26,plain,
theorem(implies(or(X_53,implies(X_52,X_54)),implies(X_52,or(X_53,X_54)))),
inference(resolve,[$cnf( axiom(implies(or(X_53,implies(X_52,X_54)),implies(X_52,or(X_53,X_54)))) )],[refute_0_25,refute_0_0]) ).
cnf(refute_0_27,plain,
( ~ theorem(implies(or(X_53,implies(X_52,X_54)),implies(X_52,or(X_53,X_54))))
| ~ theorem(or(X_53,implies(X_52,X_54)))
| theorem(implies(X_52,or(X_53,X_54))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_52,or(X_53,X_54)))),bind(Y,$fot(or(X_53,implies(X_52,X_54))))]]) ).
cnf(refute_0_28,plain,
( ~ theorem(or(X_53,implies(X_52,X_54)))
| theorem(implies(X_52,or(X_53,X_54))) ),
inference(resolve,[$cnf( theorem(implies(or(X_53,implies(X_52,X_54)),implies(X_52,or(X_53,X_54)))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ theorem(or(X_25441,implies(not(or(X_25442,X_25440)),not(X_25440))))
| theorem(implies(not(or(X_25442,X_25440)),or(X_25441,not(X_25440)))) ),
inference(subst,[],[refute_0_28:[bind(X_52,$fot(not(or(X_25442,X_25440)))),bind(X_53,$fot(X_25441)),bind(X_54,$fot(not(X_25440)))]]) ).
cnf(refute_0_30,plain,
( ~ axiom(implies(X_3,or(X_4,X_3)))
| theorem(implies(X_3,or(X_4,X_3))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(X_3,or(X_4,X_3))))]]) ).
cnf(refute_0_31,plain,
axiom(implies(X_3,or(X_4,X_3))),
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_3)),bind(B,$fot(X_4))]]) ).
cnf(refute_0_32,plain,
theorem(implies(X_3,or(X_4,X_3))),
inference(resolve,[$cnf( axiom(implies(X_3,or(X_4,X_3))) )],[refute_0_31,refute_0_30]) ).
cnf(refute_0_33,plain,
theorem(implies(X_18889,or(X_4,X_18889))),
inference(subst,[],[refute_0_32:[bind(X_3,$fot(X_18889))]]) ).
cnf(refute_0_34,plain,
( ~ theorem(implies(X_1710,X_1711))
| ~ theorem(implies(implies(X_1710,X_1711),implies(X_1710,not(not(X_1711)))))
| theorem(implies(X_1710,not(not(X_1711)))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_1710,not(not(X_1711))))),bind(Y,$fot(implies(X_1710,X_1711)))]]) ).
cnf(refute_0_35,plain,
( ~ axiom(implies(implies(X_40,X_41),implies(or(X_42,X_40),or(X_42,X_41))))
| theorem(implies(implies(X_40,X_41),implies(or(X_42,X_40),or(X_42,X_41)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_40,X_41),implies(or(X_42,X_40),or(X_42,X_41)))))]]) ).
cnf(refute_0_36,plain,
axiom(implies(implies(X_40,X_41),implies(or(X_42,X_40),or(X_42,X_41)))),
inference(subst,[],[axiom_1_6:[bind(A,$fot(X_40)),bind(B,$fot(X_41)),bind(C,$fot(X_42))]]) ).
cnf(refute_0_37,plain,
theorem(implies(implies(X_40,X_41),implies(or(X_42,X_40),or(X_42,X_41)))),
inference(resolve,[$cnf( axiom(implies(implies(X_40,X_41),implies(or(X_42,X_40),or(X_42,X_41)))) )],[refute_0_36,refute_0_35]) ).
cnf(refute_0_38,plain,
theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),or(not(X),X_47)))),
inference(subst,[],[refute_0_37:[bind(X_40,$fot(X_46)),bind(X_41,$fot(X_47)),bind(X_42,$fot(not(X)))]]) ).
cnf(refute_0_39,plain,
implies(X,X_47) = or(not(X),X_47),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_47))]]) ).
cnf(refute_0_40,plain,
( implies(X,X_47) != or(not(X),X_47)
| or(not(X),X_47) = implies(X,X_47) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(implies(X,X_47))),bind(Y0,$fot(or(not(X),X_47)))]]) ).
cnf(refute_0_41,plain,
or(not(X),X_47) = implies(X,X_47),
inference(resolve,[$cnf( $equal(implies(X,X_47),or(not(X),X_47)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( or(not(X),X_47) != implies(X,X_47)
| ~ theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),or(not(X),X_47))))
| theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),or(not(X),X_47)))) ),[0,1,1],$fot(implies(X,X_47))]]) ).
cnf(refute_0_43,plain,
( ~ theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),or(not(X),X_47))))
| theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_47),implies(X,X_47)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47)))),
inference(resolve,[$cnf( theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),or(not(X),X_47)))) )],[refute_0_38,refute_0_43]) ).
cnf(refute_0_45,plain,
or(not(X),X_46) = implies(X,X_46),
inference(subst,[],[refute_0_12:[bind(Y,$fot(X_46))]]) ).
cnf(refute_0_46,plain,
implies(or(not(X),X_46),implies(X,X_47)) = implies(or(not(X),X_46),implies(X,X_47)),
introduced(tautology,[refl,[$fot(implies(or(not(X),X_46),implies(X,X_47)))]]) ).
cnf(refute_0_47,plain,
( implies(or(not(X),X_46),implies(X,X_47)) != implies(or(not(X),X_46),implies(X,X_47))
| or(not(X),X_46) != implies(X,X_46)
| implies(or(not(X),X_46),implies(X,X_47)) = implies(implies(X,X_46),implies(X,X_47)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),X_46),implies(X,X_47)),implies(or(not(X),X_46),implies(X,X_47))) ),[1,0],$fot(implies(X,X_46))]]) ).
cnf(refute_0_48,plain,
( or(not(X),X_46) != implies(X,X_46)
| implies(or(not(X),X_46),implies(X,X_47)) = implies(implies(X,X_46),implies(X,X_47)) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_46),implies(X,X_47)),implies(or(not(X),X_46),implies(X,X_47))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
implies(or(not(X),X_46),implies(X,X_47)) = implies(implies(X,X_46),implies(X,X_47)),
inference(resolve,[$cnf( $equal(or(not(X),X_46),implies(X,X_46)) )],[refute_0_45,refute_0_48]) ).
cnf(refute_0_50,plain,
implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))) = implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))),
introduced(tautology,[refl,[$fot(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))))]]) ).
cnf(refute_0_51,plain,
( implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))) != implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47)))
| implies(or(not(X),X_46),implies(X,X_47)) != implies(implies(X,X_46),implies(X,X_47))
| implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))) = implies(implies(X_46,X_47),implies(implies(X,X_46),implies(X,X_47))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))),implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47)))) ),[1,1],$fot(implies(implies(X,X_46),implies(X,X_47)))]]) ).
cnf(refute_0_52,plain,
( implies(or(not(X),X_46),implies(X,X_47)) != implies(implies(X,X_46),implies(X,X_47))
| implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))) = implies(implies(X_46,X_47),implies(implies(X,X_46),implies(X,X_47))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))),implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47)))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))) = implies(implies(X_46,X_47),implies(implies(X,X_46),implies(X,X_47))),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_46),implies(X,X_47)),implies(implies(X,X_46),implies(X,X_47))) )],[refute_0_49,refute_0_52]) ).
cnf(refute_0_54,plain,
( implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))) != implies(implies(X_46,X_47),implies(implies(X,X_46),implies(X,X_47)))
| ~ theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))))
| theorem(implies(implies(X_46,X_47),implies(implies(X,X_46),implies(X,X_47)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47)))) ),[0],$fot(implies(implies(X_46,X_47),implies(implies(X,X_46),implies(X,X_47))))]]) ).
cnf(refute_0_55,plain,
( ~ theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))))
| theorem(implies(implies(X_46,X_47),implies(implies(X,X_46),implies(X,X_47)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))),implies(implies(X_46,X_47),implies(implies(X,X_46),implies(X,X_47)))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
theorem(implies(implies(X_46,X_47),implies(implies(X,X_46),implies(X,X_47)))),
inference(resolve,[$cnf( theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47)))) )],[refute_0_44,refute_0_55]) ).
cnf(refute_0_57,plain,
( ~ theorem(implies(X_46,X_47))
| ~ theorem(implies(implies(X_46,X_47),implies(implies(X,X_46),implies(X,X_47))))
| theorem(implies(implies(X,X_46),implies(X,X_47))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(implies(X,X_46),implies(X,X_47)))),bind(Y,$fot(implies(X_46,X_47)))]]) ).
cnf(refute_0_58,plain,
( ~ theorem(implies(X_46,X_47))
| theorem(implies(implies(X,X_46),implies(X,X_47))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_46,X_47),implies(implies(X,X_46),implies(X,X_47)))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
( ~ theorem(implies(X_1523,not(not(X_1523))))
| theorem(implies(implies(X,X_1523),implies(X,not(not(X_1523))))) ),
inference(subst,[],[refute_0_58:[bind(X_46,$fot(X_1523)),bind(X_47,$fot(not(not(X_1523))))]]) ).
cnf(refute_0_60,plain,
( ~ axiom(implies(or(X_15,X_16),or(X_16,X_15)))
| theorem(implies(or(X_15,X_16),or(X_16,X_15))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_15,X_16),or(X_16,X_15))))]]) ).
cnf(refute_0_61,plain,
axiom(implies(or(X_15,X_16),or(X_16,X_15))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_15)),bind(B,$fot(X_16))]]) ).
cnf(refute_0_62,plain,
theorem(implies(or(X_15,X_16),or(X_16,X_15))),
inference(resolve,[$cnf( axiom(implies(or(X_15,X_16),or(X_16,X_15))) )],[refute_0_61,refute_0_60]) ).
cnf(refute_0_63,plain,
theorem(implies(or(X_21,not(X)),or(not(X),X_21))),
inference(subst,[],[refute_0_62:[bind(X_15,$fot(X_21)),bind(X_16,$fot(not(X)))]]) ).
cnf(refute_0_64,plain,
implies(X,X_21) = or(not(X),X_21),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_21))]]) ).
cnf(refute_0_65,plain,
( implies(X,X_21) != or(not(X),X_21)
| or(not(X),X_21) = implies(X,X_21) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(implies(X,X_21))),bind(Y0,$fot(or(not(X),X_21)))]]) ).
cnf(refute_0_66,plain,
or(not(X),X_21) = implies(X,X_21),
inference(resolve,[$cnf( $equal(implies(X,X_21),or(not(X),X_21)) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
( or(not(X),X_21) != implies(X,X_21)
| ~ theorem(implies(or(X_21,not(X)),or(not(X),X_21)))
| theorem(implies(or(X_21,not(X)),implies(X,X_21))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(X_21,not(X)),or(not(X),X_21))) ),[0,1],$fot(implies(X,X_21))]]) ).
cnf(refute_0_68,plain,
( ~ theorem(implies(or(X_21,not(X)),or(not(X),X_21)))
| theorem(implies(or(X_21,not(X)),implies(X,X_21))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_21),implies(X,X_21)) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
theorem(implies(or(X_21,not(X)),implies(X,X_21))),
inference(resolve,[$cnf( theorem(implies(or(X_21,not(X)),or(not(X),X_21))) )],[refute_0_63,refute_0_68]) ).
cnf(refute_0_70,plain,
theorem(implies(or(not(X),not(X_25)),implies(X_25,not(X)))),
inference(subst,[],[refute_0_69:[bind(X,$fot(X_25)),bind(X_21,$fot(not(X)))]]) ).
cnf(refute_0_71,plain,
implies(X,not(X_25)) = or(not(X),not(X_25)),
inference(subst,[],[implies_definition:[bind(Y,$fot(not(X_25)))]]) ).
cnf(refute_0_72,plain,
( implies(X,not(X_25)) != or(not(X),not(X_25))
| or(not(X),not(X_25)) = implies(X,not(X_25)) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(implies(X,not(X_25)))),bind(Y0,$fot(or(not(X),not(X_25))))]]) ).
cnf(refute_0_73,plain,
or(not(X),not(X_25)) = implies(X,not(X_25)),
inference(resolve,[$cnf( $equal(implies(X,not(X_25)),or(not(X),not(X_25))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
( or(not(X),not(X_25)) != implies(X,not(X_25))
| ~ theorem(implies(or(not(X),not(X_25)),implies(X_25,not(X))))
| theorem(implies(implies(X,not(X_25)),implies(X_25,not(X)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),not(X_25)),implies(X_25,not(X)))) ),[0,0],$fot(implies(X,not(X_25)))]]) ).
cnf(refute_0_75,plain,
( ~ theorem(implies(or(not(X),not(X_25)),implies(X_25,not(X))))
| theorem(implies(implies(X,not(X_25)),implies(X_25,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_25)),implies(X,not(X_25))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
theorem(implies(implies(X,not(X_25)),implies(X_25,not(X)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),not(X_25)),implies(X_25,not(X)))) )],[refute_0_70,refute_0_75]) ).
cnf(refute_0_77,plain,
( ~ theorem(implies(X,not(X_25)))
| ~ theorem(implies(implies(X,not(X_25)),implies(X_25,not(X))))
| theorem(implies(X_25,not(X))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_25,not(X)))),bind(Y,$fot(implies(X,not(X_25))))]]) ).
cnf(refute_0_78,plain,
( ~ theorem(implies(X,not(X_25)))
| theorem(implies(X_25,not(X))) ),
inference(resolve,[$cnf( theorem(implies(implies(X,not(X_25)),implies(X_25,not(X)))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
( ~ theorem(implies(not(X_25),not(X_25)))
| theorem(implies(X_25,not(not(X_25)))) ),
inference(subst,[],[refute_0_78:[bind(X,$fot(not(X_25)))]]) ).
cnf(refute_0_80,plain,
( ~ axiom(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36))))
| theorem(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36)))))]]) ).
cnf(refute_0_81,plain,
axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,or(not(X),X_33)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(not(X))),bind(B,$fot(X_32)),bind(C,$fot(X_33))]]) ).
cnf(refute_0_82,plain,
( or(not(X),X_33) != implies(X,X_33)
| ~ axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,or(not(X),X_33))))
| axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,or(not(X),X_33)))) ),[0,1,1],$fot(implies(X,X_33))]]) ).
cnf(refute_0_83,plain,
( ~ axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,or(not(X),X_33))))
| axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_33),implies(X,X_33)) )],[refute_0_13,refute_0_82]) ).
cnf(refute_0_84,plain,
axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,or(not(X),X_33)))) )],[refute_0_81,refute_0_83]) ).
cnf(refute_0_85,plain,
or(not(X),or(X_32,X_33)) = implies(X,or(X_32,X_33)),
inference(subst,[],[refute_0_12:[bind(Y,$fot(or(X_32,X_33)))]]) ).
cnf(refute_0_86,plain,
implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))) = implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))))]]) ).
cnf(refute_0_87,plain,
( implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))) != implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))
| or(not(X),or(X_32,X_33)) != implies(X,or(X_32,X_33))
| implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))) = implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))),implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))) ),[1,0],$fot(implies(X,or(X_32,X_33)))]]) ).
cnf(refute_0_88,plain,
( or(not(X),or(X_32,X_33)) != implies(X,or(X_32,X_33))
| implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))) = implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))),implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))) = implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_32,X_33)),implies(X,or(X_32,X_33))) )],[refute_0_85,refute_0_88]) ).
cnf(refute_0_90,plain,
( implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))) != implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33)))
| ~ axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))))
| axiom(implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))) ),[0],$fot(implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33))))]]) ).
cnf(refute_0_91,plain,
( ~ axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))))
| axiom(implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))),implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33)))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
axiom(implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))) )],[refute_0_84,refute_0_91]) ).
cnf(refute_0_93,plain,
axiom(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36)))),
inference(subst,[],[refute_0_92:[bind(X,$fot(X_34)),bind(X_32,$fot(X_35)),bind(X_33,$fot(X_36))]]) ).
cnf(refute_0_94,plain,
theorem(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36)))),
inference(resolve,[$cnf( axiom(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36)))) )],[refute_0_93,refute_0_80]) ).
cnf(refute_0_95,plain,
theorem(implies(implies(X_58,or(not(X),X_60)),or(not(X),implies(X_58,X_60)))),
inference(subst,[],[refute_0_94:[bind(X_34,$fot(X_58)),bind(X_35,$fot(not(X))),bind(X_36,$fot(X_60))]]) ).
cnf(refute_0_96,plain,
implies(X,implies(X_58,X_60)) = or(not(X),implies(X_58,X_60)),
inference(subst,[],[implies_definition:[bind(Y,$fot(implies(X_58,X_60)))]]) ).
cnf(refute_0_97,plain,
( implies(X,implies(X_58,X_60)) != or(not(X),implies(X_58,X_60))
| or(not(X),implies(X_58,X_60)) = implies(X,implies(X_58,X_60)) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(implies(X,implies(X_58,X_60)))),bind(Y0,$fot(or(not(X),implies(X_58,X_60))))]]) ).
cnf(refute_0_98,plain,
or(not(X),implies(X_58,X_60)) = implies(X,implies(X_58,X_60)),
inference(resolve,[$cnf( $equal(implies(X,implies(X_58,X_60)),or(not(X),implies(X_58,X_60))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
( or(not(X),implies(X_58,X_60)) != implies(X,implies(X_58,X_60))
| ~ theorem(implies(implies(X_58,or(not(X),X_60)),or(not(X),implies(X_58,X_60))))
| theorem(implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_58,or(not(X),X_60)),or(not(X),implies(X_58,X_60)))) ),[0,1],$fot(implies(X,implies(X_58,X_60)))]]) ).
cnf(refute_0_100,plain,
( ~ theorem(implies(implies(X_58,or(not(X),X_60)),or(not(X),implies(X_58,X_60))))
| theorem(implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60)))) ),
inference(resolve,[$cnf( $equal(or(not(X),implies(X_58,X_60)),implies(X,implies(X_58,X_60))) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
theorem(implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60)))),
inference(resolve,[$cnf( theorem(implies(implies(X_58,or(not(X),X_60)),or(not(X),implies(X_58,X_60)))) )],[refute_0_95,refute_0_100]) ).
cnf(refute_0_102,plain,
or(not(X),X_60) = implies(X,X_60),
inference(subst,[],[refute_0_12:[bind(Y,$fot(X_60))]]) ).
cnf(refute_0_103,plain,
implies(X_58,or(not(X),X_60)) = implies(X_58,or(not(X),X_60)),
introduced(tautology,[refl,[$fot(implies(X_58,or(not(X),X_60)))]]) ).
cnf(refute_0_104,plain,
( implies(X_58,or(not(X),X_60)) != implies(X_58,or(not(X),X_60))
| or(not(X),X_60) != implies(X,X_60)
| implies(X_58,or(not(X),X_60)) = implies(X_58,implies(X,X_60)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_58,or(not(X),X_60)),implies(X_58,or(not(X),X_60))) ),[1,1],$fot(implies(X,X_60))]]) ).
cnf(refute_0_105,plain,
( or(not(X),X_60) != implies(X,X_60)
| implies(X_58,or(not(X),X_60)) = implies(X_58,implies(X,X_60)) ),
inference(resolve,[$cnf( $equal(implies(X_58,or(not(X),X_60)),implies(X_58,or(not(X),X_60))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
implies(X_58,or(not(X),X_60)) = implies(X_58,implies(X,X_60)),
inference(resolve,[$cnf( $equal(or(not(X),X_60),implies(X,X_60)) )],[refute_0_102,refute_0_105]) ).
cnf(refute_0_107,plain,
implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60))) = implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60))),
introduced(tautology,[refl,[$fot(implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60))))]]) ).
cnf(refute_0_108,plain,
( implies(X_58,or(not(X),X_60)) != implies(X_58,implies(X,X_60))
| implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60))) != implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60)))
| implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60))) = implies(implies(X_58,implies(X,X_60)),implies(X,implies(X_58,X_60))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60))),implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60)))) ),[1,0],$fot(implies(X_58,implies(X,X_60)))]]) ).
cnf(refute_0_109,plain,
( implies(X_58,or(not(X),X_60)) != implies(X_58,implies(X,X_60))
| implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60))) = implies(implies(X_58,implies(X,X_60)),implies(X,implies(X_58,X_60))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60))),implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60)))) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60))) = implies(implies(X_58,implies(X,X_60)),implies(X,implies(X_58,X_60))),
inference(resolve,[$cnf( $equal(implies(X_58,or(not(X),X_60)),implies(X_58,implies(X,X_60))) )],[refute_0_106,refute_0_109]) ).
cnf(refute_0_111,plain,
( implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60))) != implies(implies(X_58,implies(X,X_60)),implies(X,implies(X_58,X_60)))
| ~ theorem(implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60))))
| theorem(implies(implies(X_58,implies(X,X_60)),implies(X,implies(X_58,X_60)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60)))) ),[0],$fot(implies(implies(X_58,implies(X,X_60)),implies(X,implies(X_58,X_60))))]]) ).
cnf(refute_0_112,plain,
( ~ theorem(implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60))))
| theorem(implies(implies(X_58,implies(X,X_60)),implies(X,implies(X_58,X_60)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60))),implies(implies(X_58,implies(X,X_60)),implies(X,implies(X_58,X_60)))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
theorem(implies(implies(X_58,implies(X,X_60)),implies(X,implies(X_58,X_60)))),
inference(resolve,[$cnf( theorem(implies(implies(X_58,or(not(X),X_60)),implies(X,implies(X_58,X_60)))) )],[refute_0_101,refute_0_112]) ).
cnf(refute_0_114,plain,
( ~ theorem(implies(implies(X_58,implies(X,X_60)),implies(X,implies(X_58,X_60))))
| theorem(implies(implies(X_744,implies(X_58,implies(X,X_60))),implies(X_744,implies(X,implies(X_58,X_60))))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(X_744)),bind(X_46,$fot(implies(X_58,implies(X,X_60)))),bind(X_47,$fot(implies(X,implies(X_58,X_60))))]]) ).
cnf(refute_0_115,plain,
theorem(implies(implies(X_744,implies(X_58,implies(X,X_60))),implies(X_744,implies(X,implies(X_58,X_60))))),
inference(resolve,[$cnf( theorem(implies(implies(X_58,implies(X,X_60)),implies(X,implies(X_58,X_60)))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
( ~ theorem(X_1347)
| ~ theorem(implies(X_1347,implies(X_1348,X_1348)))
| theorem(implies(X_1348,X_1348)) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_1348,X_1348))),bind(Y,$fot(X_1347))]]) ).
cnf(refute_0_117,plain,
theorem(implies(X_3,or(not(X_7),X_3))),
inference(subst,[],[refute_0_32:[bind(X_4,$fot(not(X_7)))]]) ).
cnf(refute_0_118,plain,
implies(X_7,X_3) = or(not(X_7),X_3),
inference(subst,[],[implies_definition:[bind(X,$fot(X_7)),bind(Y,$fot(X_3))]]) ).
cnf(refute_0_119,plain,
( implies(X_7,X_3) != or(not(X_7),X_3)
| or(not(X_7),X_3) = implies(X_7,X_3) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(implies(X_7,X_3))),bind(Y0,$fot(or(not(X_7),X_3)))]]) ).
cnf(refute_0_120,plain,
or(not(X_7),X_3) = implies(X_7,X_3),
inference(resolve,[$cnf( $equal(implies(X_7,X_3),or(not(X_7),X_3)) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
( or(not(X_7),X_3) != implies(X_7,X_3)
| ~ theorem(implies(X_3,or(not(X_7),X_3)))
| theorem(implies(X_3,implies(X_7,X_3))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(X_3,or(not(X_7),X_3))) ),[0,1],$fot(implies(X_7,X_3))]]) ).
cnf(refute_0_122,plain,
( ~ theorem(implies(X_3,or(not(X_7),X_3)))
| theorem(implies(X_3,implies(X_7,X_3))) ),
inference(resolve,[$cnf( $equal(or(not(X_7),X_3),implies(X_7,X_3)) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
theorem(implies(X_3,implies(X_7,X_3))),
inference(resolve,[$cnf( theorem(implies(X_3,or(not(X_7),X_3))) )],[refute_0_117,refute_0_122]) ).
cnf(refute_0_124,plain,
theorem(implies(X_1346,implies(X_1344,X_1346))),
inference(subst,[],[refute_0_123:[bind(X_3,$fot(X_1346)),bind(X_7,$fot(X_1344))]]) ).
cnf(refute_0_125,plain,
( ~ theorem(implies(X_58,implies(X,X_60)))
| ~ theorem(implies(implies(X_58,implies(X,X_60)),implies(X,implies(X_58,X_60))))
| theorem(implies(X,implies(X_58,X_60))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X,implies(X_58,X_60)))),bind(Y,$fot(implies(X_58,implies(X,X_60))))]]) ).
cnf(refute_0_126,plain,
( ~ theorem(implies(X_58,implies(X,X_60)))
| theorem(implies(X,implies(X_58,X_60))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_58,implies(X,X_60)),implies(X,implies(X_58,X_60)))) )],[refute_0_113,refute_0_125]) ).
cnf(refute_0_127,plain,
( ~ theorem(implies(X_1346,implies(X_1344,X_1346)))
| theorem(implies(X_1344,implies(X_1346,X_1346))) ),
inference(subst,[],[refute_0_126:[bind(X,$fot(X_1344)),bind(X_58,$fot(X_1346)),bind(X_60,$fot(X_1346))]]) ).
cnf(refute_0_128,plain,
theorem(implies(X_1344,implies(X_1346,X_1346))),
inference(resolve,[$cnf( theorem(implies(X_1346,implies(X_1344,X_1346))) )],[refute_0_124,refute_0_127]) ).
cnf(refute_0_129,plain,
theorem(implies(X_1347,implies(X_1348,X_1348))),
inference(subst,[],[refute_0_128:[bind(X_1344,$fot(X_1347)),bind(X_1346,$fot(X_1348))]]) ).
cnf(refute_0_130,plain,
( ~ theorem(X_1347)
| theorem(implies(X_1348,X_1348)) ),
inference(resolve,[$cnf( theorem(implies(X_1347,implies(X_1348,X_1348))) )],[refute_0_129,refute_0_116]) ).
cnf(refute_0_131,plain,
( ~ theorem(implies(implies(X_744,implies(X_58,implies(X,X_60))),implies(X_744,implies(X,implies(X_58,X_60)))))
| theorem(implies(X_1520,X_1520)) ),
inference(subst,[],[refute_0_130:[bind(X_1347,$fot(implies(implies(X_744,implies(X_58,implies(X,X_60))),implies(X_744,implies(X,implies(X_58,X_60)))))),bind(X_1348,$fot(X_1520))]]) ).
cnf(refute_0_132,plain,
theorem(implies(X_1520,X_1520)),
inference(resolve,[$cnf( theorem(implies(implies(X_744,implies(X_58,implies(X,X_60))),implies(X_744,implies(X,implies(X_58,X_60))))) )],[refute_0_115,refute_0_131]) ).
cnf(refute_0_133,plain,
theorem(implies(not(X_25),not(X_25))),
inference(subst,[],[refute_0_132:[bind(X_1520,$fot(not(X_25)))]]) ).
cnf(refute_0_134,plain,
theorem(implies(X_25,not(not(X_25)))),
inference(resolve,[$cnf( theorem(implies(not(X_25),not(X_25))) )],[refute_0_133,refute_0_79]) ).
cnf(refute_0_135,plain,
theorem(implies(X_1523,not(not(X_1523)))),
inference(subst,[],[refute_0_134:[bind(X_25,$fot(X_1523))]]) ).
cnf(refute_0_136,plain,
theorem(implies(implies(X,X_1523),implies(X,not(not(X_1523))))),
inference(resolve,[$cnf( theorem(implies(X_1523,not(not(X_1523)))) )],[refute_0_135,refute_0_59]) ).
cnf(refute_0_137,plain,
theorem(implies(implies(X_1710,X_1711),implies(X_1710,not(not(X_1711))))),
inference(subst,[],[refute_0_136:[bind(X,$fot(X_1710)),bind(X_1523,$fot(X_1711))]]) ).
cnf(refute_0_138,plain,
( ~ theorem(implies(X_1710,X_1711))
| theorem(implies(X_1710,not(not(X_1711)))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_1710,X_1711),implies(X_1710,not(not(X_1711))))) )],[refute_0_137,refute_0_34]) ).
cnf(refute_0_139,plain,
( ~ theorem(implies(X_18889,or(X_4,X_18889)))
| theorem(implies(X_18889,not(not(or(X_4,X_18889))))) ),
inference(subst,[],[refute_0_138:[bind(X_1710,$fot(X_18889)),bind(X_1711,$fot(or(X_4,X_18889)))]]) ).
cnf(refute_0_140,plain,
theorem(implies(X_18889,not(not(or(X_4,X_18889))))),
inference(resolve,[$cnf( theorem(implies(X_18889,or(X_4,X_18889))) )],[refute_0_33,refute_0_139]) ).
cnf(refute_0_141,plain,
theorem(implies(X_25353,not(not(or(X_4,X_25353))))),
inference(subst,[],[refute_0_140:[bind(X_18889,$fot(X_25353))]]) ).
cnf(refute_0_142,plain,
( ~ theorem(implies(X_1004,not(X_1005)))
| ~ theorem(implies(implies(X_1004,not(X_1005)),or(X_1006,implies(X_1005,not(X_1004)))))
| theorem(or(X_1006,implies(X_1005,not(X_1004)))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_1006,implies(X_1005,not(X_1004))))),bind(Y,$fot(implies(X_1004,not(X_1005))))]]) ).
cnf(refute_0_143,plain,
theorem(implies(X_68,or(X_4,X_68))),
inference(subst,[],[refute_0_32:[bind(X_3,$fot(X_68))]]) ).
cnf(refute_0_144,plain,
( ~ theorem(X_68)
| ~ theorem(implies(X_68,or(X_4,X_68)))
| theorem(or(X_4,X_68)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_4,X_68))),bind(Y,$fot(X_68))]]) ).
cnf(refute_0_145,plain,
( ~ theorem(X_68)
| theorem(or(X_4,X_68)) ),
inference(resolve,[$cnf( theorem(implies(X_68,or(X_4,X_68))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
( ~ theorem(implies(implies(X,not(X_25)),implies(X_25,not(X))))
| theorem(or(X_75,implies(implies(X,not(X_25)),implies(X_25,not(X))))) ),
inference(subst,[],[refute_0_145:[bind(X_4,$fot(X_75)),bind(X_68,$fot(implies(implies(X,not(X_25)),implies(X_25,not(X)))))]]) ).
cnf(refute_0_147,plain,
theorem(or(X_75,implies(implies(X,not(X_25)),implies(X_25,not(X))))),
inference(resolve,[$cnf( theorem(implies(implies(X,not(X_25)),implies(X_25,not(X)))) )],[refute_0_76,refute_0_146]) ).
cnf(refute_0_148,plain,
theorem(or(X_783,implies(implies(X,not(X_25)),implies(X_25,not(X))))),
inference(subst,[],[refute_0_147:[bind(X_75,$fot(X_783))]]) ).
cnf(refute_0_149,plain,
( ~ theorem(or(X_783,implies(implies(X,not(X_25)),implies(X_25,not(X)))))
| theorem(implies(implies(X,not(X_25)),or(X_783,implies(X_25,not(X))))) ),
inference(subst,[],[refute_0_28:[bind(X_52,$fot(implies(X,not(X_25)))),bind(X_53,$fot(X_783)),bind(X_54,$fot(implies(X_25,not(X))))]]) ).
cnf(refute_0_150,plain,
theorem(implies(implies(X,not(X_25)),or(X_783,implies(X_25,not(X))))),
inference(resolve,[$cnf( theorem(or(X_783,implies(implies(X,not(X_25)),implies(X_25,not(X))))) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
theorem(implies(implies(X_1004,not(X_1005)),or(X_1006,implies(X_1005,not(X_1004))))),
inference(subst,[],[refute_0_150:[bind(X,$fot(X_1004)),bind(X_25,$fot(X_1005)),bind(X_783,$fot(X_1006))]]) ).
cnf(refute_0_152,plain,
( ~ theorem(implies(X_1004,not(X_1005)))
| theorem(or(X_1006,implies(X_1005,not(X_1004)))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_1004,not(X_1005)),or(X_1006,implies(X_1005,not(X_1004))))) )],[refute_0_151,refute_0_142]) ).
cnf(refute_0_153,plain,
( ~ theorem(implies(X_25353,not(not(or(X_4,X_25353)))))
| theorem(or(X_25355,implies(not(or(X_4,X_25353)),not(X_25353)))) ),
inference(subst,[],[refute_0_152:[bind(X_1004,$fot(X_25353)),bind(X_1005,$fot(not(or(X_4,X_25353)))),bind(X_1006,$fot(X_25355))]]) ).
cnf(refute_0_154,plain,
theorem(or(X_25355,implies(not(or(X_4,X_25353)),not(X_25353)))),
inference(resolve,[$cnf( theorem(implies(X_25353,not(not(or(X_4,X_25353))))) )],[refute_0_141,refute_0_153]) ).
cnf(refute_0_155,plain,
theorem(or(X_25441,implies(not(or(X_25442,X_25440)),not(X_25440)))),
inference(subst,[],[refute_0_154:[bind(X_25353,$fot(X_25440)),bind(X_25355,$fot(X_25441)),bind(X_4,$fot(X_25442))]]) ).
cnf(refute_0_156,plain,
theorem(implies(not(or(X_25442,X_25440)),or(X_25441,not(X_25440)))),
inference(resolve,[$cnf( theorem(or(X_25441,implies(not(or(X_25442,X_25440)),not(X_25440)))) )],[refute_0_155,refute_0_29]) ).
cnf(refute_0_157,plain,
theorem(implies(not(or(p,q)),or(p,not(q)))),
inference(subst,[],[refute_0_156:[bind(X_25440,$fot(q)),bind(X_25441,$fot(p)),bind(X_25442,$fot(p))]]) ).
cnf(refute_0_158,plain,
$false,
inference(resolve,[$cnf( theorem(implies(not(or(p,q)),or(p,not(q)))) )],[refute_0_157,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL202-3 : TPTP v8.1.0. Released v2.3.0.
% 0.13/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n026.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 : Mon Jul 4 02:22:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 28.23/28.42 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.23/28.42
% 28.23/28.42 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 28.23/28.44
%------------------------------------------------------------------------------