TSTP Solution File: LCL197-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL197-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 12:50:29 EDT 2022
% Result : Unsatisfiable 3.03s 3.26s
% Output : CNFRefutation 3.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 31
% Syntax : Number of clauses : 159 ( 84 unt; 0 nHn; 70 RR)
% Number of literals : 260 ( 79 equ; 102 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 : 403 ( 25 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1_2,axiom,
axiom(implies(or(A,A),A)) ).
cnf(axiom_1_3,axiom,
axiom(implies(A,or(B,A))) ).
cnf(axiom_1_4,axiom,
axiom(implies(or(A,B),or(B,A))) ).
cnf(axiom_1_5,axiom,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) ).
cnf(axiom_1_6,axiom,
axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) ).
cnf(implies_definition,axiom,
implies(X,Y) = or(not(X),Y) ).
cnf(rule_1,axiom,
( theorem(X)
| ~ axiom(X) ) ).
cnf(rule_2,axiom,
( theorem(X)
| ~ theorem(implies(Y,X))
| ~ theorem(Y) ) ).
cnf(prove_this,negated_conjecture,
~ theorem(implies(or(q,or(p,q)),or(p,q))) ).
cnf(refute_0_0,plain,
( ~ theorem(implies(X_2423,or(X_2424,X_2424)))
| ~ theorem(implies(implies(X_2423,or(X_2424,X_2424)),implies(X_2423,X_2424)))
| theorem(implies(X_2423,X_2424)) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_2423,X_2424))),bind(Y,$fot(implies(X_2423,or(X_2424,X_2424))))]]) ).
cnf(refute_0_1,plain,
( ~ axiom(implies(or(A,A),A))
| theorem(implies(or(A,A),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_2,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[$cnf( axiom(implies(or(A,A),A)) )],[axiom_1_2,refute_0_1]) ).
cnf(refute_0_3,plain,
theorem(implies(or(X_2417,X_2417),X_2417)),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_2417))]]) ).
cnf(refute_0_4,plain,
( ~ axiom(implies(implies(X_43,X_44),implies(or(X_45,X_43),or(X_45,X_44))))
| theorem(implies(implies(X_43,X_44),implies(or(X_45,X_43),or(X_45,X_44)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_43,X_44),implies(or(X_45,X_43),or(X_45,X_44)))))]]) ).
cnf(refute_0_5,plain,
axiom(implies(implies(X_43,X_44),implies(or(X_45,X_43),or(X_45,X_44)))),
inference(subst,[],[axiom_1_6:[bind(A,$fot(X_43)),bind(B,$fot(X_44)),bind(C,$fot(X_45))]]) ).
cnf(refute_0_6,plain,
theorem(implies(implies(X_43,X_44),implies(or(X_45,X_43),or(X_45,X_44)))),
inference(resolve,[$cnf( axiom(implies(implies(X_43,X_44),implies(or(X_45,X_43),or(X_45,X_44)))) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
( ~ theorem(implies(X_43,X_44))
| ~ theorem(implies(implies(X_43,X_44),implies(or(X_45,X_43),or(X_45,X_44))))
| theorem(implies(or(X_45,X_43),or(X_45,X_44))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(or(X_45,X_43),or(X_45,X_44)))),bind(Y,$fot(implies(X_43,X_44)))]]) ).
cnf(refute_0_8,plain,
( ~ theorem(implies(X_43,X_44))
| theorem(implies(or(X_45,X_43),or(X_45,X_44))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_43,X_44),implies(or(X_45,X_43),or(X_45,X_44)))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ theorem(implies(or(X_2417,X_2417),X_2417))
| theorem(implies(or(X_2418,or(X_2417,X_2417)),or(X_2418,X_2417))) ),
inference(subst,[],[refute_0_8:[bind(X_43,$fot(or(X_2417,X_2417))),bind(X_44,$fot(X_2417)),bind(X_45,$fot(X_2418))]]) ).
cnf(refute_0_10,plain,
theorem(implies(or(X_2418,or(X_2417,X_2417)),or(X_2418,X_2417))),
inference(resolve,[$cnf( theorem(implies(or(X_2417,X_2417),X_2417)) )],[refute_0_3,refute_0_9]) ).
cnf(refute_0_11,plain,
theorem(implies(or(not(X),or(X_2421,X_2421)),or(not(X),X_2421))),
inference(subst,[],[refute_0_10:[bind(X_2417,$fot(X_2421)),bind(X_2418,$fot(not(X)))]]) ).
cnf(refute_0_12,plain,
implies(X,X_2421) = or(not(X),X_2421),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_2421))]]) ).
cnf(refute_0_13,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_14,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_15,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( implies(X,X_2421) != or(not(X),X_2421)
| or(not(X),X_2421) = implies(X,X_2421) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,X_2421))),bind(Y0,$fot(or(not(X),X_2421)))]]) ).
cnf(refute_0_17,plain,
or(not(X),X_2421) = implies(X,X_2421),
inference(resolve,[$cnf( $equal(implies(X,X_2421),or(not(X),X_2421)) )],[refute_0_12,refute_0_16]) ).
cnf(refute_0_18,plain,
( or(not(X),X_2421) != implies(X,X_2421)
| ~ theorem(implies(or(not(X),or(X_2421,X_2421)),or(not(X),X_2421)))
| theorem(implies(or(not(X),or(X_2421,X_2421)),implies(X,X_2421))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),or(X_2421,X_2421)),or(not(X),X_2421))) ),[0,1],$fot(implies(X,X_2421))]]) ).
cnf(refute_0_19,plain,
( ~ theorem(implies(or(not(X),or(X_2421,X_2421)),or(not(X),X_2421)))
| theorem(implies(or(not(X),or(X_2421,X_2421)),implies(X,X_2421))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_2421),implies(X,X_2421)) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
theorem(implies(or(not(X),or(X_2421,X_2421)),implies(X,X_2421))),
inference(resolve,[$cnf( theorem(implies(or(not(X),or(X_2421,X_2421)),or(not(X),X_2421))) )],[refute_0_11,refute_0_19]) ).
cnf(refute_0_21,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_22,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_21]) ).
cnf(refute_0_23,plain,
or(not(X),or(X_2421,X_2421)) = implies(X,or(X_2421,X_2421)),
inference(subst,[],[refute_0_22:[bind(Y,$fot(or(X_2421,X_2421)))]]) ).
cnf(refute_0_24,plain,
implies(or(not(X),or(X_2421,X_2421)),implies(X,X_2421)) = implies(or(not(X),or(X_2421,X_2421)),implies(X,X_2421)),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_2421,X_2421)),implies(X,X_2421)))]]) ).
cnf(refute_0_25,plain,
( implies(or(not(X),or(X_2421,X_2421)),implies(X,X_2421)) != implies(or(not(X),or(X_2421,X_2421)),implies(X,X_2421))
| or(not(X),or(X_2421,X_2421)) != implies(X,or(X_2421,X_2421))
| implies(or(not(X),or(X_2421,X_2421)),implies(X,X_2421)) = implies(implies(X,or(X_2421,X_2421)),implies(X,X_2421)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_2421,X_2421)),implies(X,X_2421)),implies(or(not(X),or(X_2421,X_2421)),implies(X,X_2421))) ),[1,0],$fot(implies(X,or(X_2421,X_2421)))]]) ).
cnf(refute_0_26,plain,
( or(not(X),or(X_2421,X_2421)) != implies(X,or(X_2421,X_2421))
| implies(or(not(X),or(X_2421,X_2421)),implies(X,X_2421)) = implies(implies(X,or(X_2421,X_2421)),implies(X,X_2421)) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_2421,X_2421)),implies(X,X_2421)),implies(or(not(X),or(X_2421,X_2421)),implies(X,X_2421))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
implies(or(not(X),or(X_2421,X_2421)),implies(X,X_2421)) = implies(implies(X,or(X_2421,X_2421)),implies(X,X_2421)),
inference(resolve,[$cnf( $equal(or(not(X),or(X_2421,X_2421)),implies(X,or(X_2421,X_2421))) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
( implies(or(not(X),or(X_2421,X_2421)),implies(X,X_2421)) != implies(implies(X,or(X_2421,X_2421)),implies(X,X_2421))
| ~ theorem(implies(or(not(X),or(X_2421,X_2421)),implies(X,X_2421)))
| theorem(implies(implies(X,or(X_2421,X_2421)),implies(X,X_2421))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),or(X_2421,X_2421)),implies(X,X_2421))) ),[0],$fot(implies(implies(X,or(X_2421,X_2421)),implies(X,X_2421)))]]) ).
cnf(refute_0_29,plain,
( ~ theorem(implies(or(not(X),or(X_2421,X_2421)),implies(X,X_2421)))
| theorem(implies(implies(X,or(X_2421,X_2421)),implies(X,X_2421))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_2421,X_2421)),implies(X,X_2421)),implies(implies(X,or(X_2421,X_2421)),implies(X,X_2421))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
theorem(implies(implies(X,or(X_2421,X_2421)),implies(X,X_2421))),
inference(resolve,[$cnf( theorem(implies(or(not(X),or(X_2421,X_2421)),implies(X,X_2421))) )],[refute_0_20,refute_0_29]) ).
cnf(refute_0_31,plain,
theorem(implies(implies(X_2423,or(X_2424,X_2424)),implies(X_2423,X_2424))),
inference(subst,[],[refute_0_30:[bind(X,$fot(X_2423)),bind(X_2421,$fot(X_2424))]]) ).
cnf(refute_0_32,plain,
( ~ theorem(implies(X_2423,or(X_2424,X_2424)))
| theorem(implies(X_2423,X_2424)) ),
inference(resolve,[$cnf( theorem(implies(implies(X_2423,or(X_2424,X_2424)),implies(X_2423,X_2424))) )],[refute_0_31,refute_0_0]) ).
cnf(refute_0_33,plain,
( ~ theorem(implies(or(X_7786,or(X_7785,X_7786)),or(or(X_7785,X_7786),or(X_7785,X_7786))))
| theorem(implies(or(X_7786,or(X_7785,X_7786)),or(X_7785,X_7786))) ),
inference(subst,[],[refute_0_32:[bind(X_2423,$fot(or(X_7786,or(X_7785,X_7786)))),bind(X_2424,$fot(or(X_7785,X_7786)))]]) ).
cnf(refute_0_34,plain,
( ~ axiom(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27))))
| theorem(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))))]]) ).
cnf(refute_0_35,plain,
axiom(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_25)),bind(B,$fot(X_26)),bind(C,$fot(X_27))]]) ).
cnf(refute_0_36,plain,
theorem(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))),
inference(resolve,[$cnf( axiom(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))) )],[refute_0_35,refute_0_34]) ).
cnf(refute_0_37,plain,
theorem(implies(or(X_34,or(not(X),X_36)),or(not(X),or(X_34,X_36)))),
inference(subst,[],[refute_0_36:[bind(X_25,$fot(X_34)),bind(X_26,$fot(not(X))),bind(X_27,$fot(X_36))]]) ).
cnf(refute_0_38,plain,
implies(X,or(X_34,X_36)) = or(not(X),or(X_34,X_36)),
inference(subst,[],[implies_definition:[bind(Y,$fot(or(X_34,X_36)))]]) ).
cnf(refute_0_39,plain,
( implies(X,or(X_34,X_36)) != or(not(X),or(X_34,X_36))
| or(not(X),or(X_34,X_36)) = implies(X,or(X_34,X_36)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,or(X_34,X_36)))),bind(Y0,$fot(or(not(X),or(X_34,X_36))))]]) ).
cnf(refute_0_40,plain,
or(not(X),or(X_34,X_36)) = implies(X,or(X_34,X_36)),
inference(resolve,[$cnf( $equal(implies(X,or(X_34,X_36)),or(not(X),or(X_34,X_36))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( or(not(X),or(X_34,X_36)) != implies(X,or(X_34,X_36))
| ~ theorem(implies(or(X_34,or(not(X),X_36)),or(not(X),or(X_34,X_36))))
| theorem(implies(or(X_34,or(not(X),X_36)),implies(X,or(X_34,X_36)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(X_34,or(not(X),X_36)),or(not(X),or(X_34,X_36)))) ),[0,1],$fot(implies(X,or(X_34,X_36)))]]) ).
cnf(refute_0_42,plain,
( ~ theorem(implies(or(X_34,or(not(X),X_36)),or(not(X),or(X_34,X_36))))
| theorem(implies(or(X_34,or(not(X),X_36)),implies(X,or(X_34,X_36)))) ),
inference(resolve,[$cnf( $equal(or(not(X),or(X_34,X_36)),implies(X,or(X_34,X_36))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
theorem(implies(or(X_34,or(not(X),X_36)),implies(X,or(X_34,X_36)))),
inference(resolve,[$cnf( theorem(implies(or(X_34,or(not(X),X_36)),or(not(X),or(X_34,X_36)))) )],[refute_0_37,refute_0_42]) ).
cnf(refute_0_44,plain,
or(not(X),X_36) = implies(X,X_36),
inference(subst,[],[refute_0_22:[bind(Y,$fot(X_36))]]) ).
cnf(refute_0_45,plain,
or(X_34,or(not(X),X_36)) = or(X_34,or(not(X),X_36)),
introduced(tautology,[refl,[$fot(or(X_34,or(not(X),X_36)))]]) ).
cnf(refute_0_46,plain,
( or(X_34,or(not(X),X_36)) != or(X_34,or(not(X),X_36))
| or(not(X),X_36) != implies(X,X_36)
| or(X_34,or(not(X),X_36)) = or(X_34,implies(X,X_36)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_34,or(not(X),X_36)),or(X_34,or(not(X),X_36))) ),[1,1],$fot(implies(X,X_36))]]) ).
cnf(refute_0_47,plain,
( or(not(X),X_36) != implies(X,X_36)
| or(X_34,or(not(X),X_36)) = or(X_34,implies(X,X_36)) ),
inference(resolve,[$cnf( $equal(or(X_34,or(not(X),X_36)),or(X_34,or(not(X),X_36))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
or(X_34,or(not(X),X_36)) = or(X_34,implies(X,X_36)),
inference(resolve,[$cnf( $equal(or(not(X),X_36),implies(X,X_36)) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
implies(or(X_34,or(not(X),X_36)),implies(X,or(X_34,X_36))) = implies(or(X_34,or(not(X),X_36)),implies(X,or(X_34,X_36))),
introduced(tautology,[refl,[$fot(implies(or(X_34,or(not(X),X_36)),implies(X,or(X_34,X_36))))]]) ).
cnf(refute_0_50,plain,
( implies(or(X_34,or(not(X),X_36)),implies(X,or(X_34,X_36))) != implies(or(X_34,or(not(X),X_36)),implies(X,or(X_34,X_36)))
| or(X_34,or(not(X),X_36)) != or(X_34,implies(X,X_36))
| implies(or(X_34,or(not(X),X_36)),implies(X,or(X_34,X_36))) = implies(or(X_34,implies(X,X_36)),implies(X,or(X_34,X_36))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_34,or(not(X),X_36)),implies(X,or(X_34,X_36))),implies(or(X_34,or(not(X),X_36)),implies(X,or(X_34,X_36)))) ),[1,0],$fot(or(X_34,implies(X,X_36)))]]) ).
cnf(refute_0_51,plain,
( or(X_34,or(not(X),X_36)) != or(X_34,implies(X,X_36))
| implies(or(X_34,or(not(X),X_36)),implies(X,or(X_34,X_36))) = implies(or(X_34,implies(X,X_36)),implies(X,or(X_34,X_36))) ),
inference(resolve,[$cnf( $equal(implies(or(X_34,or(not(X),X_36)),implies(X,or(X_34,X_36))),implies(or(X_34,or(not(X),X_36)),implies(X,or(X_34,X_36)))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
implies(or(X_34,or(not(X),X_36)),implies(X,or(X_34,X_36))) = implies(or(X_34,implies(X,X_36)),implies(X,or(X_34,X_36))),
inference(resolve,[$cnf( $equal(or(X_34,or(not(X),X_36)),or(X_34,implies(X,X_36))) )],[refute_0_48,refute_0_51]) ).
cnf(refute_0_53,plain,
( implies(or(X_34,or(not(X),X_36)),implies(X,or(X_34,X_36))) != implies(or(X_34,implies(X,X_36)),implies(X,or(X_34,X_36)))
| ~ theorem(implies(or(X_34,or(not(X),X_36)),implies(X,or(X_34,X_36))))
| theorem(implies(or(X_34,implies(X,X_36)),implies(X,or(X_34,X_36)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(X_34,or(not(X),X_36)),implies(X,or(X_34,X_36)))) ),[0],$fot(implies(or(X_34,implies(X,X_36)),implies(X,or(X_34,X_36))))]]) ).
cnf(refute_0_54,plain,
( ~ theorem(implies(or(X_34,or(not(X),X_36)),implies(X,or(X_34,X_36))))
| theorem(implies(or(X_34,implies(X,X_36)),implies(X,or(X_34,X_36)))) ),
inference(resolve,[$cnf( $equal(implies(or(X_34,or(not(X),X_36)),implies(X,or(X_34,X_36))),implies(or(X_34,implies(X,X_36)),implies(X,or(X_34,X_36)))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
theorem(implies(or(X_34,implies(X,X_36)),implies(X,or(X_34,X_36)))),
inference(resolve,[$cnf( theorem(implies(or(X_34,or(not(X),X_36)),implies(X,or(X_34,X_36)))) )],[refute_0_43,refute_0_54]) ).
cnf(refute_0_56,plain,
( ~ theorem(implies(or(X_34,implies(X,X_36)),implies(X,or(X_34,X_36))))
| ~ theorem(or(X_34,implies(X,X_36)))
| theorem(implies(X,or(X_34,X_36))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X,or(X_34,X_36)))),bind(Y,$fot(or(X_34,implies(X,X_36))))]]) ).
cnf(refute_0_57,plain,
( ~ theorem(or(X_34,implies(X,X_36)))
| theorem(implies(X,or(X_34,X_36))) ),
inference(resolve,[$cnf( theorem(implies(or(X_34,implies(X,X_36)),implies(X,or(X_34,X_36)))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
( ~ theorem(or(or(X_7782,X_7783),implies(or(X_7783,X_7781),X_7781)))
| theorem(implies(or(X_7783,X_7781),or(or(X_7782,X_7783),X_7781))) ),
inference(subst,[],[refute_0_57:[bind(X,$fot(or(X_7783,X_7781))),bind(X_34,$fot(or(X_7782,X_7783))),bind(X_36,$fot(X_7781))]]) ).
cnf(refute_0_59,plain,
( ~ axiom(implies(or(X_7,X_8),or(X_8,X_7)))
| theorem(implies(or(X_7,X_8),or(X_8,X_7))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_7,X_8),or(X_8,X_7))))]]) ).
cnf(refute_0_60,plain,
axiom(implies(or(X_7,X_8),or(X_8,X_7))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_7)),bind(B,$fot(X_8))]]) ).
cnf(refute_0_61,plain,
theorem(implies(or(X_7,X_8),or(X_8,X_7))),
inference(resolve,[$cnf( axiom(implies(or(X_7,X_8),or(X_8,X_7))) )],[refute_0_60,refute_0_59]) ).
cnf(refute_0_62,plain,
( ~ theorem(implies(or(X_7,X_8),or(X_8,X_7)))
| ~ theorem(or(X_7,X_8))
| theorem(or(X_8,X_7)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_8,X_7))),bind(Y,$fot(or(X_7,X_8)))]]) ).
cnf(refute_0_63,plain,
( ~ theorem(or(X_7,X_8))
| theorem(or(X_8,X_7)) ),
inference(resolve,[$cnf( theorem(implies(or(X_7,X_8),or(X_8,X_7))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
( ~ theorem(or(implies(or(X_6998,X_6996),X_6996),or(X_6997,X_6998)))
| theorem(or(or(X_6997,X_6998),implies(or(X_6998,X_6996),X_6996))) ),
inference(subst,[],[refute_0_63:[bind(X_7,$fot(implies(or(X_6998,X_6996),X_6996))),bind(X_8,$fot(or(X_6997,X_6998)))]]) ).
cnf(refute_0_65,plain,
( ~ axiom(implies(A,or(B,A)))
| theorem(implies(A,or(B,A))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(A,or(B,A))))]]) ).
cnf(refute_0_66,plain,
theorem(implies(A,or(B,A))),
inference(resolve,[$cnf( axiom(implies(A,or(B,A))) )],[axiom_1_3,refute_0_65]) ).
cnf(refute_0_67,plain,
theorem(implies(X_68,or(B,X_68))),
inference(subst,[],[refute_0_66:[bind(A,$fot(X_68))]]) ).
cnf(refute_0_68,plain,
( ~ theorem(X_68)
| ~ theorem(implies(X_68,or(B,X_68)))
| theorem(or(B,X_68)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(B,X_68))),bind(Y,$fot(X_68))]]) ).
cnf(refute_0_69,plain,
( ~ theorem(X_68)
| theorem(or(B,X_68)) ),
inference(resolve,[$cnf( theorem(implies(X_68,or(B,X_68))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
( ~ theorem(or(implies(or(X_4625,X_4626),X_4626),X_4625))
| theorem(or(B,or(implies(or(X_4625,X_4626),X_4626),X_4625))) ),
inference(subst,[],[refute_0_69:[bind(X_68,$fot(or(implies(or(X_4625,X_4626),X_4626),X_4625)))]]) ).
cnf(refute_0_71,plain,
( ~ theorem(or(X_4623,implies(or(X_4623,X_4624),X_4624)))
| theorem(or(implies(or(X_4623,X_4624),X_4624),X_4623)) ),
inference(subst,[],[refute_0_63:[bind(X_7,$fot(X_4623)),bind(X_8,$fot(implies(or(X_4623,X_4624),X_4624)))]]) ).
cnf(refute_0_72,plain,
theorem(implies(or(not(X),implies(X_40,X_42)),implies(X_40,or(not(X),X_42)))),
inference(subst,[],[refute_0_55:[bind(X,$fot(X_40)),bind(X_34,$fot(not(X))),bind(X_36,$fot(X_42))]]) ).
cnf(refute_0_73,plain,
implies(X,X_42) = or(not(X),X_42),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_42))]]) ).
cnf(refute_0_74,plain,
( implies(X,X_42) != or(not(X),X_42)
| or(not(X),X_42) = implies(X,X_42) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,X_42))),bind(Y0,$fot(or(not(X),X_42)))]]) ).
cnf(refute_0_75,plain,
or(not(X),X_42) = implies(X,X_42),
inference(resolve,[$cnf( $equal(implies(X,X_42),or(not(X),X_42)) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
( or(not(X),X_42) != implies(X,X_42)
| ~ theorem(implies(or(not(X),implies(X_40,X_42)),implies(X_40,or(not(X),X_42))))
| theorem(implies(or(not(X),implies(X_40,X_42)),implies(X_40,implies(X,X_42)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),implies(X_40,X_42)),implies(X_40,or(not(X),X_42)))) ),[0,1,1],$fot(implies(X,X_42))]]) ).
cnf(refute_0_77,plain,
( ~ theorem(implies(or(not(X),implies(X_40,X_42)),implies(X_40,or(not(X),X_42))))
| theorem(implies(or(not(X),implies(X_40,X_42)),implies(X_40,implies(X,X_42)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_42),implies(X,X_42)) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
theorem(implies(or(not(X),implies(X_40,X_42)),implies(X_40,implies(X,X_42)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),implies(X_40,X_42)),implies(X_40,or(not(X),X_42)))) )],[refute_0_72,refute_0_77]) ).
cnf(refute_0_79,plain,
or(not(X),implies(X_40,X_42)) = implies(X,implies(X_40,X_42)),
inference(subst,[],[refute_0_22:[bind(Y,$fot(implies(X_40,X_42)))]]) ).
cnf(refute_0_80,plain,
implies(or(not(X),implies(X_40,X_42)),implies(X_40,implies(X,X_42))) = implies(or(not(X),implies(X_40,X_42)),implies(X_40,implies(X,X_42))),
introduced(tautology,[refl,[$fot(implies(or(not(X),implies(X_40,X_42)),implies(X_40,implies(X,X_42))))]]) ).
cnf(refute_0_81,plain,
( implies(or(not(X),implies(X_40,X_42)),implies(X_40,implies(X,X_42))) != implies(or(not(X),implies(X_40,X_42)),implies(X_40,implies(X,X_42)))
| or(not(X),implies(X_40,X_42)) != implies(X,implies(X_40,X_42))
| implies(or(not(X),implies(X_40,X_42)),implies(X_40,implies(X,X_42))) = implies(implies(X,implies(X_40,X_42)),implies(X_40,implies(X,X_42))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),implies(X_40,X_42)),implies(X_40,implies(X,X_42))),implies(or(not(X),implies(X_40,X_42)),implies(X_40,implies(X,X_42)))) ),[1,0],$fot(implies(X,implies(X_40,X_42)))]]) ).
cnf(refute_0_82,plain,
( or(not(X),implies(X_40,X_42)) != implies(X,implies(X_40,X_42))
| implies(or(not(X),implies(X_40,X_42)),implies(X_40,implies(X,X_42))) = implies(implies(X,implies(X_40,X_42)),implies(X_40,implies(X,X_42))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),implies(X_40,X_42)),implies(X_40,implies(X,X_42))),implies(or(not(X),implies(X_40,X_42)),implies(X_40,implies(X,X_42)))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
implies(or(not(X),implies(X_40,X_42)),implies(X_40,implies(X,X_42))) = implies(implies(X,implies(X_40,X_42)),implies(X_40,implies(X,X_42))),
inference(resolve,[$cnf( $equal(or(not(X),implies(X_40,X_42)),implies(X,implies(X_40,X_42))) )],[refute_0_79,refute_0_82]) ).
cnf(refute_0_84,plain,
( implies(or(not(X),implies(X_40,X_42)),implies(X_40,implies(X,X_42))) != implies(implies(X,implies(X_40,X_42)),implies(X_40,implies(X,X_42)))
| ~ theorem(implies(or(not(X),implies(X_40,X_42)),implies(X_40,implies(X,X_42))))
| theorem(implies(implies(X,implies(X_40,X_42)),implies(X_40,implies(X,X_42)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),implies(X_40,X_42)),implies(X_40,implies(X,X_42)))) ),[0],$fot(implies(implies(X,implies(X_40,X_42)),implies(X_40,implies(X,X_42))))]]) ).
cnf(refute_0_85,plain,
( ~ theorem(implies(or(not(X),implies(X_40,X_42)),implies(X_40,implies(X,X_42))))
| theorem(implies(implies(X,implies(X_40,X_42)),implies(X_40,implies(X,X_42)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),implies(X_40,X_42)),implies(X_40,implies(X,X_42))),implies(implies(X,implies(X_40,X_42)),implies(X_40,implies(X,X_42)))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
theorem(implies(implies(X,implies(X_40,X_42)),implies(X_40,implies(X,X_42)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),implies(X_40,X_42)),implies(X_40,implies(X,X_42)))) )],[refute_0_78,refute_0_85]) ).
cnf(refute_0_87,plain,
( ~ theorem(implies(implies(X,implies(X_40,X_42)),implies(X_40,implies(X,X_42))))
| theorem(or(X_83,implies(implies(X,implies(X_40,X_42)),implies(X_40,implies(X,X_42))))) ),
inference(subst,[],[refute_0_69:[bind(B,$fot(X_83)),bind(X_68,$fot(implies(implies(X,implies(X_40,X_42)),implies(X_40,implies(X,X_42)))))]]) ).
cnf(refute_0_88,plain,
theorem(or(X_83,implies(implies(X,implies(X_40,X_42)),implies(X_40,implies(X,X_42))))),
inference(resolve,[$cnf( theorem(implies(implies(X,implies(X_40,X_42)),implies(X_40,implies(X,X_42)))) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
theorem(or(not(X),implies(implies(X_406,implies(X_407,X_408)),implies(X_407,implies(X_406,X_408))))),
inference(subst,[],[refute_0_88:[bind(X,$fot(X_406)),bind(X_40,$fot(X_407)),bind(X_42,$fot(X_408)),bind(X_83,$fot(not(X)))]]) ).
cnf(refute_0_90,plain,
implies(X,implies(implies(X_406,implies(X_407,X_408)),implies(X_407,implies(X_406,X_408)))) = or(not(X),implies(implies(X_406,implies(X_407,X_408)),implies(X_407,implies(X_406,X_408)))),
inference(subst,[],[implies_definition:[bind(Y,$fot(implies(implies(X_406,implies(X_407,X_408)),implies(X_407,implies(X_406,X_408)))))]]) ).
cnf(refute_0_91,plain,
( implies(X,implies(implies(X_406,implies(X_407,X_408)),implies(X_407,implies(X_406,X_408)))) != or(not(X),implies(implies(X_406,implies(X_407,X_408)),implies(X_407,implies(X_406,X_408))))
| or(not(X),implies(implies(X_406,implies(X_407,X_408)),implies(X_407,implies(X_406,X_408)))) = implies(X,implies(implies(X_406,implies(X_407,X_408)),implies(X_407,implies(X_406,X_408)))) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,implies(implies(X_406,implies(X_407,X_408)),implies(X_407,implies(X_406,X_408)))))),bind(Y0,$fot(or(not(X),implies(implies(X_406,implies(X_407,X_408)),implies(X_407,implies(X_406,X_408))))))]]) ).
cnf(refute_0_92,plain,
or(not(X),implies(implies(X_406,implies(X_407,X_408)),implies(X_407,implies(X_406,X_408)))) = implies(X,implies(implies(X_406,implies(X_407,X_408)),implies(X_407,implies(X_406,X_408)))),
inference(resolve,[$cnf( $equal(implies(X,implies(implies(X_406,implies(X_407,X_408)),implies(X_407,implies(X_406,X_408)))),or(not(X),implies(implies(X_406,implies(X_407,X_408)),implies(X_407,implies(X_406,X_408))))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
( or(not(X),implies(implies(X_406,implies(X_407,X_408)),implies(X_407,implies(X_406,X_408)))) != implies(X,implies(implies(X_406,implies(X_407,X_408)),implies(X_407,implies(X_406,X_408))))
| ~ theorem(or(not(X),implies(implies(X_406,implies(X_407,X_408)),implies(X_407,implies(X_406,X_408)))))
| theorem(implies(X,implies(implies(X_406,implies(X_407,X_408)),implies(X_407,implies(X_406,X_408))))) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(X),implies(implies(X_406,implies(X_407,X_408)),implies(X_407,implies(X_406,X_408))))) ),[0],$fot(implies(X,implies(implies(X_406,implies(X_407,X_408)),implies(X_407,implies(X_406,X_408)))))]]) ).
cnf(refute_0_94,plain,
( ~ theorem(or(not(X),implies(implies(X_406,implies(X_407,X_408)),implies(X_407,implies(X_406,X_408)))))
| theorem(implies(X,implies(implies(X_406,implies(X_407,X_408)),implies(X_407,implies(X_406,X_408))))) ),
inference(resolve,[$cnf( $equal(or(not(X),implies(implies(X_406,implies(X_407,X_408)),implies(X_407,implies(X_406,X_408)))),implies(X,implies(implies(X_406,implies(X_407,X_408)),implies(X_407,implies(X_406,X_408))))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
theorem(implies(X,implies(implies(X_406,implies(X_407,X_408)),implies(X_407,implies(X_406,X_408))))),
inference(resolve,[$cnf( theorem(or(not(X),implies(implies(X_406,implies(X_407,X_408)),implies(X_407,implies(X_406,X_408))))) )],[refute_0_89,refute_0_94]) ).
cnf(refute_0_96,plain,
theorem(implies(X_736,implies(implies(X_406,implies(X_407,X_408)),implies(X_407,implies(X_406,X_408))))),
inference(subst,[],[refute_0_95:[bind(X,$fot(X_736))]]) ).
cnf(refute_0_97,plain,
( ~ theorem(implies(X,implies(X_40,X_42)))
| ~ theorem(implies(implies(X,implies(X_40,X_42)),implies(X_40,implies(X,X_42))))
| theorem(implies(X_40,implies(X,X_42))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_40,implies(X,X_42)))),bind(Y,$fot(implies(X,implies(X_40,X_42))))]]) ).
cnf(refute_0_98,plain,
( ~ theorem(implies(X,implies(X_40,X_42)))
| theorem(implies(X_40,implies(X,X_42))) ),
inference(resolve,[$cnf( theorem(implies(implies(X,implies(X_40,X_42)),implies(X_40,implies(X,X_42)))) )],[refute_0_86,refute_0_97]) ).
cnf(refute_0_99,plain,
( ~ theorem(implies(X_736,implies(implies(X_406,implies(X_407,X_408)),implies(X_407,implies(X_406,X_408)))))
| theorem(implies(implies(X_406,implies(X_407,X_408)),implies(X_736,implies(X_407,implies(X_406,X_408))))) ),
inference(subst,[],[refute_0_98:[bind(X,$fot(X_736)),bind(X_40,$fot(implies(X_406,implies(X_407,X_408)))),bind(X_42,$fot(implies(X_407,implies(X_406,X_408))))]]) ).
cnf(refute_0_100,plain,
theorem(implies(implies(X_406,implies(X_407,X_408)),implies(X_736,implies(X_407,implies(X_406,X_408))))),
inference(resolve,[$cnf( theorem(implies(X_736,implies(implies(X_406,implies(X_407,X_408)),implies(X_407,implies(X_406,X_408))))) )],[refute_0_96,refute_0_99]) ).
cnf(refute_0_101,plain,
( ~ theorem(X_739)
| ~ theorem(implies(X_739,implies(X_740,X_740)))
| theorem(implies(X_740,X_740)) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_740,X_740))),bind(Y,$fot(X_739))]]) ).
cnf(refute_0_102,plain,
theorem(implies(A,or(not(X_9),A))),
inference(subst,[],[refute_0_66:[bind(B,$fot(not(X_9)))]]) ).
cnf(refute_0_103,plain,
implies(X_9,A) = or(not(X_9),A),
inference(subst,[],[implies_definition:[bind(X,$fot(X_9)),bind(Y,$fot(A))]]) ).
cnf(refute_0_104,plain,
( implies(X_9,A) != or(not(X_9),A)
| or(not(X_9),A) = implies(X_9,A) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X_9,A))),bind(Y0,$fot(or(not(X_9),A)))]]) ).
cnf(refute_0_105,plain,
or(not(X_9),A) = implies(X_9,A),
inference(resolve,[$cnf( $equal(implies(X_9,A),or(not(X_9),A)) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
( or(not(X_9),A) != implies(X_9,A)
| ~ theorem(implies(A,or(not(X_9),A)))
| theorem(implies(A,implies(X_9,A))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(A,or(not(X_9),A))) ),[0,1],$fot(implies(X_9,A))]]) ).
cnf(refute_0_107,plain,
( ~ theorem(implies(A,or(not(X_9),A)))
| theorem(implies(A,implies(X_9,A))) ),
inference(resolve,[$cnf( $equal(or(not(X_9),A),implies(X_9,A)) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
theorem(implies(A,implies(X_9,A))),
inference(resolve,[$cnf( theorem(implies(A,or(not(X_9),A))) )],[refute_0_102,refute_0_107]) ).
cnf(refute_0_109,plain,
theorem(implies(X_738,implies(X_737,X_738))),
inference(subst,[],[refute_0_108:[bind(A,$fot(X_738)),bind(X_9,$fot(X_737))]]) ).
cnf(refute_0_110,plain,
( ~ theorem(implies(X_738,implies(X_737,X_738)))
| theorem(implies(X_737,implies(X_738,X_738))) ),
inference(subst,[],[refute_0_98:[bind(X,$fot(X_738)),bind(X_40,$fot(X_737)),bind(X_42,$fot(X_738))]]) ).
cnf(refute_0_111,plain,
theorem(implies(X_737,implies(X_738,X_738))),
inference(resolve,[$cnf( theorem(implies(X_738,implies(X_737,X_738))) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
theorem(implies(X_739,implies(X_740,X_740))),
inference(subst,[],[refute_0_111:[bind(X_737,$fot(X_739)),bind(X_738,$fot(X_740))]]) ).
cnf(refute_0_113,plain,
( ~ theorem(X_739)
| theorem(implies(X_740,X_740)) ),
inference(resolve,[$cnf( theorem(implies(X_739,implies(X_740,X_740))) )],[refute_0_112,refute_0_101]) ).
cnf(refute_0_114,plain,
( ~ theorem(implies(implies(X_406,implies(X_407,X_408)),implies(X_736,implies(X_407,implies(X_406,X_408)))))
| theorem(implies(X_1028,X_1028)) ),
inference(subst,[],[refute_0_113:[bind(X_739,$fot(implies(implies(X_406,implies(X_407,X_408)),implies(X_736,implies(X_407,implies(X_406,X_408)))))),bind(X_740,$fot(X_1028))]]) ).
cnf(refute_0_115,plain,
theorem(implies(X_1028,X_1028)),
inference(resolve,[$cnf( theorem(implies(implies(X_406,implies(X_407,X_408)),implies(X_736,implies(X_407,implies(X_406,X_408))))) )],[refute_0_100,refute_0_114]) ).
cnf(refute_0_116,plain,
theorem(implies(or(X_4605,X_4606),or(X_4605,X_4606))),
inference(subst,[],[refute_0_115:[bind(X_1028,$fot(or(X_4605,X_4606)))]]) ).
cnf(refute_0_117,plain,
theorem(implies(or(not(X),or(X_35,X_36)),or(X_35,or(not(X),X_36)))),
inference(subst,[],[refute_0_36:[bind(X_25,$fot(not(X))),bind(X_26,$fot(X_35)),bind(X_27,$fot(X_36))]]) ).
cnf(refute_0_118,plain,
( or(not(X),X_36) != implies(X,X_36)
| ~ theorem(implies(or(not(X),or(X_35,X_36)),or(X_35,or(not(X),X_36))))
| theorem(implies(or(not(X),or(X_35,X_36)),or(X_35,implies(X,X_36)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),or(X_35,X_36)),or(X_35,or(not(X),X_36)))) ),[0,1,1],$fot(implies(X,X_36))]]) ).
cnf(refute_0_119,plain,
( ~ theorem(implies(or(not(X),or(X_35,X_36)),or(X_35,or(not(X),X_36))))
| theorem(implies(or(not(X),or(X_35,X_36)),or(X_35,implies(X,X_36)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_36),implies(X,X_36)) )],[refute_0_44,refute_0_118]) ).
cnf(refute_0_120,plain,
theorem(implies(or(not(X),or(X_35,X_36)),or(X_35,implies(X,X_36)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),or(X_35,X_36)),or(X_35,or(not(X),X_36)))) )],[refute_0_117,refute_0_119]) ).
cnf(refute_0_121,plain,
or(not(X),or(X_35,X_36)) = implies(X,or(X_35,X_36)),
inference(subst,[],[refute_0_22:[bind(Y,$fot(or(X_35,X_36)))]]) ).
cnf(refute_0_122,plain,
implies(or(not(X),or(X_35,X_36)),or(X_35,implies(X,X_36))) = implies(or(not(X),or(X_35,X_36)),or(X_35,implies(X,X_36))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_35,X_36)),or(X_35,implies(X,X_36))))]]) ).
cnf(refute_0_123,plain,
( implies(or(not(X),or(X_35,X_36)),or(X_35,implies(X,X_36))) != implies(or(not(X),or(X_35,X_36)),or(X_35,implies(X,X_36)))
| or(not(X),or(X_35,X_36)) != implies(X,or(X_35,X_36))
| implies(or(not(X),or(X_35,X_36)),or(X_35,implies(X,X_36))) = implies(implies(X,or(X_35,X_36)),or(X_35,implies(X,X_36))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_35,X_36)),or(X_35,implies(X,X_36))),implies(or(not(X),or(X_35,X_36)),or(X_35,implies(X,X_36)))) ),[1,0],$fot(implies(X,or(X_35,X_36)))]]) ).
cnf(refute_0_124,plain,
( or(not(X),or(X_35,X_36)) != implies(X,or(X_35,X_36))
| implies(or(not(X),or(X_35,X_36)),or(X_35,implies(X,X_36))) = implies(implies(X,or(X_35,X_36)),or(X_35,implies(X,X_36))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_35,X_36)),or(X_35,implies(X,X_36))),implies(or(not(X),or(X_35,X_36)),or(X_35,implies(X,X_36)))) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
implies(or(not(X),or(X_35,X_36)),or(X_35,implies(X,X_36))) = implies(implies(X,or(X_35,X_36)),or(X_35,implies(X,X_36))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_35,X_36)),implies(X,or(X_35,X_36))) )],[refute_0_121,refute_0_124]) ).
cnf(refute_0_126,plain,
( implies(or(not(X),or(X_35,X_36)),or(X_35,implies(X,X_36))) != implies(implies(X,or(X_35,X_36)),or(X_35,implies(X,X_36)))
| ~ theorem(implies(or(not(X),or(X_35,X_36)),or(X_35,implies(X,X_36))))
| theorem(implies(implies(X,or(X_35,X_36)),or(X_35,implies(X,X_36)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),or(X_35,X_36)),or(X_35,implies(X,X_36)))) ),[0],$fot(implies(implies(X,or(X_35,X_36)),or(X_35,implies(X,X_36))))]]) ).
cnf(refute_0_127,plain,
( ~ theorem(implies(or(not(X),or(X_35,X_36)),or(X_35,implies(X,X_36))))
| theorem(implies(implies(X,or(X_35,X_36)),or(X_35,implies(X,X_36)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_35,X_36)),or(X_35,implies(X,X_36))),implies(implies(X,or(X_35,X_36)),or(X_35,implies(X,X_36)))) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
theorem(implies(implies(X,or(X_35,X_36)),or(X_35,implies(X,X_36)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),or(X_35,X_36)),or(X_35,implies(X,X_36)))) )],[refute_0_120,refute_0_127]) ).
cnf(refute_0_129,plain,
( ~ theorem(implies(X,or(X_35,X_36)))
| ~ theorem(implies(implies(X,or(X_35,X_36)),or(X_35,implies(X,X_36))))
| theorem(or(X_35,implies(X,X_36))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_35,implies(X,X_36)))),bind(Y,$fot(implies(X,or(X_35,X_36))))]]) ).
cnf(refute_0_130,plain,
( ~ theorem(implies(X,or(X_35,X_36)))
| theorem(or(X_35,implies(X,X_36))) ),
inference(resolve,[$cnf( theorem(implies(implies(X,or(X_35,X_36)),or(X_35,implies(X,X_36)))) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
( ~ theorem(implies(or(X_4605,X_4606),or(X_4605,X_4606)))
| theorem(or(X_4605,implies(or(X_4605,X_4606),X_4606))) ),
inference(subst,[],[refute_0_130:[bind(X,$fot(or(X_4605,X_4606))),bind(X_35,$fot(X_4605)),bind(X_36,$fot(X_4606))]]) ).
cnf(refute_0_132,plain,
theorem(or(X_4605,implies(or(X_4605,X_4606),X_4606))),
inference(resolve,[$cnf( theorem(implies(or(X_4605,X_4606),or(X_4605,X_4606))) )],[refute_0_116,refute_0_131]) ).
cnf(refute_0_133,plain,
theorem(or(X_4623,implies(or(X_4623,X_4624),X_4624))),
inference(subst,[],[refute_0_132:[bind(X_4605,$fot(X_4623)),bind(X_4606,$fot(X_4624))]]) ).
cnf(refute_0_134,plain,
theorem(or(implies(or(X_4623,X_4624),X_4624),X_4623)),
inference(resolve,[$cnf( theorem(or(X_4623,implies(or(X_4623,X_4624),X_4624))) )],[refute_0_133,refute_0_71]) ).
cnf(refute_0_135,plain,
theorem(or(implies(or(X_4625,X_4626),X_4626),X_4625)),
inference(subst,[],[refute_0_134:[bind(X_4623,$fot(X_4625)),bind(X_4624,$fot(X_4626))]]) ).
cnf(refute_0_136,plain,
theorem(or(B,or(implies(or(X_4625,X_4626),X_4626),X_4625))),
inference(resolve,[$cnf( theorem(or(implies(or(X_4625,X_4626),X_4626),X_4625)) )],[refute_0_135,refute_0_70]) ).
cnf(refute_0_137,plain,
theorem(or(X_6989,or(implies(or(X_6991,X_4626),X_4626),X_6991))),
inference(subst,[],[refute_0_136:[bind(B,$fot(X_6989)),bind(X_4625,$fot(X_6991))]]) ).
cnf(refute_0_138,plain,
( ~ theorem(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27))))
| ~ theorem(or(X_25,or(X_26,X_27)))
| theorem(or(X_26,or(X_25,X_27))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_26,or(X_25,X_27)))),bind(Y,$fot(or(X_25,or(X_26,X_27))))]]) ).
cnf(refute_0_139,plain,
( ~ theorem(or(X_25,or(X_26,X_27)))
| theorem(or(X_26,or(X_25,X_27))) ),
inference(resolve,[$cnf( theorem(implies(or(X_25,or(X_26,X_27)),or(X_26,or(X_25,X_27)))) )],[refute_0_36,refute_0_138]) ).
cnf(refute_0_140,plain,
( ~ theorem(or(X_6989,or(implies(or(X_6991,X_4626),X_4626),X_6991)))
| theorem(or(implies(or(X_6991,X_4626),X_4626),or(X_6989,X_6991))) ),
inference(subst,[],[refute_0_139:[bind(X_25,$fot(X_6989)),bind(X_26,$fot(implies(or(X_6991,X_4626),X_4626))),bind(X_27,$fot(X_6991))]]) ).
cnf(refute_0_141,plain,
theorem(or(implies(or(X_6991,X_4626),X_4626),or(X_6989,X_6991))),
inference(resolve,[$cnf( theorem(or(X_6989,or(implies(or(X_6991,X_4626),X_4626),X_6991))) )],[refute_0_137,refute_0_140]) ).
cnf(refute_0_142,plain,
theorem(or(implies(or(X_6998,X_6996),X_6996),or(X_6997,X_6998))),
inference(subst,[],[refute_0_141:[bind(X_4626,$fot(X_6996)),bind(X_6989,$fot(X_6997)),bind(X_6991,$fot(X_6998))]]) ).
cnf(refute_0_143,plain,
theorem(or(or(X_6997,X_6998),implies(or(X_6998,X_6996),X_6996))),
inference(resolve,[$cnf( theorem(or(implies(or(X_6998,X_6996),X_6996),or(X_6997,X_6998))) )],[refute_0_142,refute_0_64]) ).
cnf(refute_0_144,plain,
theorem(or(or(X_7782,X_7783),implies(or(X_7783,X_7781),X_7781))),
inference(subst,[],[refute_0_143:[bind(X_6996,$fot(X_7781)),bind(X_6997,$fot(X_7782)),bind(X_6998,$fot(X_7783))]]) ).
cnf(refute_0_145,plain,
theorem(implies(or(X_7783,X_7781),or(or(X_7782,X_7783),X_7781))),
inference(resolve,[$cnf( theorem(or(or(X_7782,X_7783),implies(or(X_7783,X_7781),X_7781))) )],[refute_0_144,refute_0_58]) ).
cnf(refute_0_146,plain,
theorem(implies(or(X_7786,or(X_7785,X_7786)),or(or(X_7785,X_7786),or(X_7785,X_7786)))),
inference(subst,[],[refute_0_145:[bind(X_7781,$fot(or(X_7785,X_7786))),bind(X_7782,$fot(X_7785)),bind(X_7783,$fot(X_7786))]]) ).
cnf(refute_0_147,plain,
theorem(implies(or(X_7786,or(X_7785,X_7786)),or(X_7785,X_7786))),
inference(resolve,[$cnf( theorem(implies(or(X_7786,or(X_7785,X_7786)),or(or(X_7785,X_7786),or(X_7785,X_7786)))) )],[refute_0_146,refute_0_33]) ).
cnf(refute_0_148,plain,
theorem(implies(or(q,or(p,q)),or(p,q))),
inference(subst,[],[refute_0_147:[bind(X_7785,$fot(p)),bind(X_7786,$fot(q))]]) ).
cnf(refute_0_149,plain,
$false,
inference(resolve,[$cnf( theorem(implies(or(q,or(p,q)),or(p,q))) )],[refute_0_148,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL197-3 : TPTP v8.1.0. Released v2.3.0.
% 0.11/0.11 % Command : metis --show proof --show saturation %s
% 0.11/0.32 % Computer : n028.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Sat Jul 2 22:12:17 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 3.03/3.26 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.03/3.26
% 3.03/3.26 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.03/3.27
%------------------------------------------------------------------------------