TSTP Solution File: LCL248-3 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : LCL248-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Sun Jul 17 12:51:07 EDT 2022

% Result   : Unsatisfiable 9.36s 9.55s
% Output   : CNFRefutation 9.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :   30
% Syntax   : Number of clauses     :  155 (  82 unt;   0 nHn;  71 RR)
%            Number of literals    :  252 (  85 equ;  98 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :  345 (  35 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(and_defn,axiom,
    and(P,Q) = not(or(not(P),not(Q))) ).

cnf(prove_this,negated_conjecture,
    ~ theorem(implies(and(p,q),implies(p,q))) ).

cnf(refute_0_0,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_1,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_2,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_1,refute_0_0]) ).

cnf(refute_0_3,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_4,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_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( ~ theorem(or(implies(X_14001,X_14003),not(and(X_14002,X_14003))))
    | theorem(or(not(and(X_14002,X_14003)),implies(X_14001,X_14003))) ),
    inference(subst,[],[refute_0_4:[bind(X_7,$fot(implies(X_14001,X_14003))),bind(X_8,$fot(not(and(X_14002,X_14003))))]]) ).

cnf(refute_0_6,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_7,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_8,plain,
    theorem(implies(X_3,or(X_4,X_3))),
    inference(resolve,[$cnf( axiom(implies(X_3,or(X_4,X_3))) )],[refute_0_7,refute_0_6]) ).

cnf(refute_0_9,plain,
    theorem(implies(X_75,or(X_4,X_75))),
    inference(subst,[],[refute_0_8:[bind(X_3,$fot(X_75))]]) ).

cnf(refute_0_10,plain,
    ( ~ theorem(X_75)
    | ~ theorem(implies(X_75,or(X_4,X_75)))
    | theorem(or(X_4,X_75)) ),
    inference(subst,[],[rule_2:[bind(X,$fot(or(X_4,X_75))),bind(Y,$fot(X_75))]]) ).

cnf(refute_0_11,plain,
    ( ~ theorem(X_75)
    | theorem(or(X_4,X_75)) ),
    inference(resolve,[$cnf( theorem(implies(X_75,or(X_4,X_75))) )],[refute_0_9,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( ~ theorem(or(or(X_134,X_133),not(X_133)))
    | theorem(or(X_4,or(or(X_134,X_133),not(X_133)))) ),
    inference(subst,[],[refute_0_11:[bind(X_75,$fot(or(or(X_134,X_133),not(X_133))))]]) ).

cnf(refute_0_13,plain,
    theorem(implies(X_121,or(X_4,X_121))),
    inference(subst,[],[refute_0_8:[bind(X_3,$fot(X_121))]]) ).

cnf(refute_0_14,plain,
    theorem(implies(or(not(X_11),X_8),or(X_8,not(X_11)))),
    inference(subst,[],[refute_0_2:[bind(X_7,$fot(not(X_11)))]]) ).

cnf(refute_0_15,plain,
    implies(X_11,X_8) = or(not(X_11),X_8),
    inference(subst,[],[implies_definition:[bind(X,$fot(X_11)),bind(Y,$fot(X_8))]]) ).

cnf(refute_0_16,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_17,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_18,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_16,refute_0_17]) ).

cnf(refute_0_19,plain,
    ( implies(X_11,X_8) != or(not(X_11),X_8)
    | or(not(X_11),X_8) = implies(X_11,X_8) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(implies(X_11,X_8))),bind(Y0,$fot(or(not(X_11),X_8)))]]) ).

cnf(refute_0_20,plain,
    or(not(X_11),X_8) = implies(X_11,X_8),
    inference(resolve,[$cnf( $equal(implies(X_11,X_8),or(not(X_11),X_8)) )],[refute_0_15,refute_0_19]) ).

cnf(refute_0_21,plain,
    ( or(not(X_11),X_8) != implies(X_11,X_8)
    | ~ theorem(implies(or(not(X_11),X_8),or(X_8,not(X_11))))
    | theorem(implies(implies(X_11,X_8),or(X_8,not(X_11)))) ),
    introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X_11),X_8),or(X_8,not(X_11)))) ),[0,0],$fot(implies(X_11,X_8))]]) ).

cnf(refute_0_22,plain,
    ( ~ theorem(implies(or(not(X_11),X_8),or(X_8,not(X_11))))
    | theorem(implies(implies(X_11,X_8),or(X_8,not(X_11)))) ),
    inference(resolve,[$cnf( $equal(or(not(X_11),X_8),implies(X_11,X_8)) )],[refute_0_20,refute_0_21]) ).

cnf(refute_0_23,plain,
    theorem(implies(implies(X_11,X_8),or(X_8,not(X_11)))),
    inference(resolve,[$cnf( theorem(implies(or(not(X_11),X_8),or(X_8,not(X_11)))) )],[refute_0_14,refute_0_22]) ).

cnf(refute_0_24,plain,
    ( ~ theorem(implies(X_11,X_8))
    | ~ theorem(implies(implies(X_11,X_8),or(X_8,not(X_11))))
    | theorem(or(X_8,not(X_11))) ),
    inference(subst,[],[rule_2:[bind(X,$fot(or(X_8,not(X_11)))),bind(Y,$fot(implies(X_11,X_8)))]]) ).

cnf(refute_0_25,plain,
    ( ~ theorem(implies(X_11,X_8))
    | theorem(or(X_8,not(X_11))) ),
    inference(resolve,[$cnf( theorem(implies(implies(X_11,X_8),or(X_8,not(X_11)))) )],[refute_0_23,refute_0_24]) ).

cnf(refute_0_26,plain,
    ( ~ theorem(implies(X_121,or(X_4,X_121)))
    | theorem(or(or(X_4,X_121),not(X_121))) ),
    inference(subst,[],[refute_0_25:[bind(X_11,$fot(X_121)),bind(X_8,$fot(or(X_4,X_121)))]]) ).

cnf(refute_0_27,plain,
    theorem(or(or(X_4,X_121),not(X_121))),
    inference(resolve,[$cnf( theorem(implies(X_121,or(X_4,X_121))) )],[refute_0_13,refute_0_26]) ).

cnf(refute_0_28,plain,
    theorem(or(or(X_134,X_133),not(X_133))),
    inference(subst,[],[refute_0_27:[bind(X_121,$fot(X_133)),bind(X_4,$fot(X_134))]]) ).

cnf(refute_0_29,plain,
    theorem(or(X_4,or(or(X_134,X_133),not(X_133)))),
    inference(resolve,[$cnf( theorem(or(or(X_134,X_133),not(X_133))) )],[refute_0_28,refute_0_12]) ).

cnf(refute_0_30,plain,
    theorem(or(not(X),or(or(X_272,X_271),not(X_271)))),
    inference(subst,[],[refute_0_29:[bind(X_133,$fot(X_271)),bind(X_134,$fot(X_272)),bind(X_4,$fot(not(X)))]]) ).

cnf(refute_0_31,plain,
    implies(X,or(or(X_272,X_271),not(X_271))) = or(not(X),or(or(X_272,X_271),not(X_271))),
    inference(subst,[],[implies_definition:[bind(Y,$fot(or(or(X_272,X_271),not(X_271))))]]) ).

cnf(refute_0_32,plain,
    ( implies(X,or(or(X_272,X_271),not(X_271))) != or(not(X),or(or(X_272,X_271),not(X_271)))
    | or(not(X),or(or(X_272,X_271),not(X_271))) = implies(X,or(or(X_272,X_271),not(X_271))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(implies(X,or(or(X_272,X_271),not(X_271))))),bind(Y0,$fot(or(not(X),or(or(X_272,X_271),not(X_271)))))]]) ).

cnf(refute_0_33,plain,
    or(not(X),or(or(X_272,X_271),not(X_271))) = implies(X,or(or(X_272,X_271),not(X_271))),
    inference(resolve,[$cnf( $equal(implies(X,or(or(X_272,X_271),not(X_271))),or(not(X),or(or(X_272,X_271),not(X_271)))) )],[refute_0_31,refute_0_32]) ).

cnf(refute_0_34,plain,
    ( or(not(X),or(or(X_272,X_271),not(X_271))) != implies(X,or(or(X_272,X_271),not(X_271)))
    | ~ theorem(or(not(X),or(or(X_272,X_271),not(X_271))))
    | theorem(implies(X,or(or(X_272,X_271),not(X_271)))) ),
    introduced(tautology,[equality,[$cnf( theorem(or(not(X),or(or(X_272,X_271),not(X_271)))) ),[0],$fot(implies(X,or(or(X_272,X_271),not(X_271))))]]) ).

cnf(refute_0_35,plain,
    ( ~ theorem(or(not(X),or(or(X_272,X_271),not(X_271))))
    | theorem(implies(X,or(or(X_272,X_271),not(X_271)))) ),
    inference(resolve,[$cnf( $equal(or(not(X),or(or(X_272,X_271),not(X_271))),implies(X,or(or(X_272,X_271),not(X_271)))) )],[refute_0_33,refute_0_34]) ).

cnf(refute_0_36,plain,
    theorem(implies(X,or(or(X_272,X_271),not(X_271)))),
    inference(resolve,[$cnf( theorem(or(not(X),or(or(X_272,X_271),not(X_271)))) )],[refute_0_30,refute_0_35]) ).

cnf(refute_0_37,plain,
    theorem(implies(X_1540,or(or(X_272,X_271),not(X_271)))),
    inference(subst,[],[refute_0_36:[bind(X,$fot(X_1540))]]) ).

cnf(refute_0_38,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_39,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_40,plain,
    implies(X,X_33) = or(not(X),X_33),
    inference(subst,[],[implies_definition:[bind(Y,$fot(X_33))]]) ).

cnf(refute_0_41,plain,
    ( implies(X,X_33) != or(not(X),X_33)
    | or(not(X),X_33) = implies(X,X_33) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(implies(X,X_33))),bind(Y0,$fot(or(not(X),X_33)))]]) ).

cnf(refute_0_42,plain,
    or(not(X),X_33) = implies(X,X_33),
    inference(resolve,[$cnf( $equal(implies(X,X_33),or(not(X),X_33)) )],[refute_0_40,refute_0_41]) ).

cnf(refute_0_43,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_44,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_42,refute_0_43]) ).

cnf(refute_0_45,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_39,refute_0_44]) ).

cnf(refute_0_46,plain,
    ( implies(X,Y) != or(not(X),Y)
    | or(not(X),Y) = implies(X,Y) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).

cnf(refute_0_47,plain,
    or(not(X),Y) = implies(X,Y),
    inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_46]) ).

cnf(refute_0_48,plain,
    or(not(X),or(X_32,X_33)) = implies(X,or(X_32,X_33)),
    inference(subst,[],[refute_0_47:[bind(Y,$fot(or(X_32,X_33)))]]) ).

cnf(refute_0_49,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_50,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_51,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_49,refute_0_50]) ).

cnf(refute_0_52,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_48,refute_0_51]) ).

cnf(refute_0_53,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_54,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_52,refute_0_53]) ).

cnf(refute_0_55,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_45,refute_0_54]) ).

cnf(refute_0_56,plain,
    axiom(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36)))),
    inference(subst,[],[refute_0_55:[bind(X,$fot(X_34)),bind(X_32,$fot(X_35)),bind(X_33,$fot(X_36))]]) ).

cnf(refute_0_57,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_56,refute_0_38]) ).

cnf(refute_0_58,plain,
    ( ~ theorem(implies(X_34,or(X_35,X_36)))
    | ~ theorem(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36))))
    | theorem(or(X_35,implies(X_34,X_36))) ),
    inference(subst,[],[rule_2:[bind(X,$fot(or(X_35,implies(X_34,X_36)))),bind(Y,$fot(implies(X_34,or(X_35,X_36))))]]) ).

cnf(refute_0_59,plain,
    ( ~ theorem(implies(X_34,or(X_35,X_36)))
    | theorem(or(X_35,implies(X_34,X_36))) ),
    inference(resolve,[$cnf( theorem(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36)))) )],[refute_0_57,refute_0_58]) ).

cnf(refute_0_60,plain,
    ( ~ theorem(implies(X_1540,or(or(X_272,X_271),not(X_271))))
    | theorem(or(or(X_272,X_271),implies(X_1540,not(X_271)))) ),
    inference(subst,[],[refute_0_59:[bind(X_34,$fot(X_1540)),bind(X_35,$fot(or(X_272,X_271))),bind(X_36,$fot(not(X_271)))]]) ).

cnf(refute_0_61,plain,
    theorem(or(or(X_272,X_271),implies(X_1540,not(X_271)))),
    inference(resolve,[$cnf( theorem(implies(X_1540,or(or(X_272,X_271),not(X_271)))) )],[refute_0_37,refute_0_60]) ).

cnf(refute_0_62,plain,
    theorem(or(or(not(X),X_1589),implies(X_1588,not(X_1589)))),
    inference(subst,[],[refute_0_61:[bind(X_1540,$fot(X_1588)),bind(X_271,$fot(X_1589)),bind(X_272,$fot(not(X)))]]) ).

cnf(refute_0_63,plain,
    implies(X,X_1589) = or(not(X),X_1589),
    inference(subst,[],[implies_definition:[bind(Y,$fot(X_1589))]]) ).

cnf(refute_0_64,plain,
    ( implies(X,X_1589) != or(not(X),X_1589)
    | or(not(X),X_1589) = implies(X,X_1589) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(implies(X,X_1589))),bind(Y0,$fot(or(not(X),X_1589)))]]) ).

cnf(refute_0_65,plain,
    or(not(X),X_1589) = implies(X,X_1589),
    inference(resolve,[$cnf( $equal(implies(X,X_1589),or(not(X),X_1589)) )],[refute_0_63,refute_0_64]) ).

cnf(refute_0_66,plain,
    ( or(not(X),X_1589) != implies(X,X_1589)
    | ~ theorem(or(or(not(X),X_1589),implies(X_1588,not(X_1589))))
    | theorem(or(implies(X,X_1589),implies(X_1588,not(X_1589)))) ),
    introduced(tautology,[equality,[$cnf( theorem(or(or(not(X),X_1589),implies(X_1588,not(X_1589)))) ),[0,0],$fot(implies(X,X_1589))]]) ).

cnf(refute_0_67,plain,
    ( ~ theorem(or(or(not(X),X_1589),implies(X_1588,not(X_1589))))
    | theorem(or(implies(X,X_1589),implies(X_1588,not(X_1589)))) ),
    inference(resolve,[$cnf( $equal(or(not(X),X_1589),implies(X,X_1589)) )],[refute_0_65,refute_0_66]) ).

cnf(refute_0_68,plain,
    theorem(or(implies(X,X_1589),implies(X_1588,not(X_1589)))),
    inference(resolve,[$cnf( theorem(or(or(not(X),X_1589),implies(X_1588,not(X_1589)))) )],[refute_0_62,refute_0_67]) ).

cnf(refute_0_69,plain,
    ( ~ theorem(implies(or(X_2810,X_2809),or(X_2810,not(not(X_2809)))))
    | ~ theorem(or(X_2810,X_2809))
    | theorem(or(X_2810,not(not(X_2809)))) ),
    inference(subst,[],[rule_2:[bind(X,$fot(or(X_2810,not(not(X_2809))))),bind(Y,$fot(or(X_2810,X_2809)))]]) ).

cnf(refute_0_70,plain,
    ( ~ axiom(implies(or(X_27,not(X_28)),implies(X_28,X_27)))
    | theorem(implies(or(X_27,not(X_28)),implies(X_28,X_27))) ),
    inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_27,not(X_28)),implies(X_28,X_27))))]]) ).

cnf(refute_0_71,plain,
    axiom(implies(or(A,not(X_11)),or(not(X_11),A))),
    inference(subst,[],[axiom_1_4:[bind(B,$fot(not(X_11)))]]) ).

cnf(refute_0_72,plain,
    implies(X_11,A) = or(not(X_11),A),
    inference(subst,[],[implies_definition:[bind(X,$fot(X_11)),bind(Y,$fot(A))]]) ).

cnf(refute_0_73,plain,
    ( implies(X_11,A) != or(not(X_11),A)
    | or(not(X_11),A) = implies(X_11,A) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(implies(X_11,A))),bind(Y0,$fot(or(not(X_11),A)))]]) ).

cnf(refute_0_74,plain,
    or(not(X_11),A) = implies(X_11,A),
    inference(resolve,[$cnf( $equal(implies(X_11,A),or(not(X_11),A)) )],[refute_0_72,refute_0_73]) ).

cnf(refute_0_75,plain,
    ( or(not(X_11),A) != implies(X_11,A)
    | ~ axiom(implies(or(A,not(X_11)),or(not(X_11),A)))
    | axiom(implies(or(A,not(X_11)),implies(X_11,A))) ),
    introduced(tautology,[equality,[$cnf( axiom(implies(or(A,not(X_11)),or(not(X_11),A))) ),[0,1],$fot(implies(X_11,A))]]) ).

cnf(refute_0_76,plain,
    ( ~ axiom(implies(or(A,not(X_11)),or(not(X_11),A)))
    | axiom(implies(or(A,not(X_11)),implies(X_11,A))) ),
    inference(resolve,[$cnf( $equal(or(not(X_11),A),implies(X_11,A)) )],[refute_0_74,refute_0_75]) ).

cnf(refute_0_77,plain,
    axiom(implies(or(A,not(X_11)),implies(X_11,A))),
    inference(resolve,[$cnf( axiom(implies(or(A,not(X_11)),or(not(X_11),A))) )],[refute_0_71,refute_0_76]) ).

cnf(refute_0_78,plain,
    axiom(implies(or(X_27,not(X_28)),implies(X_28,X_27))),
    inference(subst,[],[refute_0_77:[bind(A,$fot(X_27)),bind(X_11,$fot(X_28))]]) ).

cnf(refute_0_79,plain,
    theorem(implies(or(X_27,not(X_28)),implies(X_28,X_27))),
    inference(resolve,[$cnf( axiom(implies(or(X_27,not(X_28)),implies(X_28,X_27))) )],[refute_0_78,refute_0_70]) ).

cnf(refute_0_80,plain,
    ( ~ theorem(implies(or(X_27,not(X_28)),implies(X_28,X_27)))
    | ~ theorem(or(X_27,not(X_28)))
    | theorem(implies(X_28,X_27)) ),
    inference(subst,[],[rule_2:[bind(X,$fot(implies(X_28,X_27))),bind(Y,$fot(or(X_27,not(X_28))))]]) ).

cnf(refute_0_81,plain,
    ( ~ theorem(or(X_27,not(X_28)))
    | theorem(implies(X_28,X_27)) ),
    inference(resolve,[$cnf( theorem(implies(or(X_27,not(X_28)),implies(X_28,X_27))) )],[refute_0_79,refute_0_80]) ).

cnf(refute_0_82,plain,
    ( ~ theorem(or(not(X),not(X_151)))
    | theorem(implies(X_151,not(X))) ),
    inference(subst,[],[refute_0_81:[bind(X_27,$fot(not(X))),bind(X_28,$fot(X_151))]]) ).

cnf(refute_0_83,plain,
    implies(X,not(X_151)) = or(not(X),not(X_151)),
    inference(subst,[],[implies_definition:[bind(Y,$fot(not(X_151)))]]) ).

cnf(refute_0_84,plain,
    ( implies(X,not(X_151)) != or(not(X),not(X_151))
    | or(not(X),not(X_151)) = implies(X,not(X_151)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(implies(X,not(X_151)))),bind(Y0,$fot(or(not(X),not(X_151))))]]) ).

cnf(refute_0_85,plain,
    or(not(X),not(X_151)) = implies(X,not(X_151)),
    inference(resolve,[$cnf( $equal(implies(X,not(X_151)),or(not(X),not(X_151))) )],[refute_0_83,refute_0_84]) ).

cnf(refute_0_86,plain,
    ( or(not(X),not(X_151)) != implies(X,not(X_151))
    | ~ theorem(implies(X,not(X_151)))
    | theorem(or(not(X),not(X_151))) ),
    introduced(tautology,[equality,[$cnf( ~ theorem(or(not(X),not(X_151))) ),[0],$fot(implies(X,not(X_151)))]]) ).

cnf(refute_0_87,plain,
    ( ~ theorem(implies(X,not(X_151)))
    | theorem(or(not(X),not(X_151))) ),
    inference(resolve,[$cnf( $equal(or(not(X),not(X_151)),implies(X,not(X_151))) )],[refute_0_85,refute_0_86]) ).

cnf(refute_0_88,plain,
    ( ~ theorem(implies(X,not(X_151)))
    | theorem(implies(X_151,not(X))) ),
    inference(resolve,[$cnf( theorem(or(not(X),not(X_151))) )],[refute_0_87,refute_0_82]) ).

cnf(refute_0_89,plain,
    ( ~ theorem(implies(not(X_151),not(X_151)))
    | theorem(implies(X_151,not(not(X_151)))) ),
    inference(subst,[],[refute_0_88:[bind(X,$fot(not(X_151)))]]) ).

cnf(refute_0_90,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_91,plain,
    theorem(implies(or(A,A),A)),
    inference(resolve,[$cnf( axiom(implies(or(A,A),A)) )],[axiom_1_2,refute_0_90]) ).

cnf(refute_0_92,plain,
    theorem(implies(or(X_74,X_74),X_74)),
    inference(subst,[],[refute_0_91:[bind(A,$fot(X_74))]]) ).

cnf(refute_0_93,plain,
    ( ~ theorem(implies(or(X_74,X_74),X_74))
    | ~ theorem(or(X_74,X_74))
    | theorem(X_74) ),
    inference(subst,[],[rule_2:[bind(X,$fot(X_74)),bind(Y,$fot(or(X_74,X_74)))]]) ).

cnf(refute_0_94,plain,
    ( ~ theorem(or(X_74,X_74))
    | theorem(X_74) ),
    inference(resolve,[$cnf( theorem(implies(or(X_74,X_74),X_74)) )],[refute_0_92,refute_0_93]) ).

cnf(refute_0_95,plain,
    ( ~ theorem(or(implies(X_1544,X_1544),implies(X_1544,X_1544)))
    | theorem(implies(X_1544,X_1544)) ),
    inference(subst,[],[refute_0_94:[bind(X_74,$fot(implies(X_1544,X_1544)))]]) ).

cnf(refute_0_96,plain,
    theorem(implies(X_1542,or(X_1541,X_1542))),
    inference(subst,[],[refute_0_8:[bind(X_3,$fot(X_1542)),bind(X_4,$fot(X_1541))]]) ).

cnf(refute_0_97,plain,
    ( ~ theorem(implies(X_1542,or(X_1541,X_1542)))
    | theorem(or(X_1541,implies(X_1542,X_1542))) ),
    inference(subst,[],[refute_0_59:[bind(X_34,$fot(X_1542)),bind(X_35,$fot(X_1541)),bind(X_36,$fot(X_1542))]]) ).

cnf(refute_0_98,plain,
    theorem(or(X_1541,implies(X_1542,X_1542))),
    inference(resolve,[$cnf( theorem(implies(X_1542,or(X_1541,X_1542))) )],[refute_0_96,refute_0_97]) ).

cnf(refute_0_99,plain,
    theorem(or(implies(X_1544,X_1544),implies(X_1544,X_1544))),
    inference(subst,[],[refute_0_98:[bind(X_1541,$fot(implies(X_1544,X_1544))),bind(X_1542,$fot(X_1544))]]) ).

cnf(refute_0_100,plain,
    theorem(implies(X_1544,X_1544)),
    inference(resolve,[$cnf( theorem(or(implies(X_1544,X_1544),implies(X_1544,X_1544))) )],[refute_0_99,refute_0_95]) ).

cnf(refute_0_101,plain,
    theorem(implies(not(X_151),not(X_151))),
    inference(subst,[],[refute_0_100:[bind(X_1544,$fot(not(X_151)))]]) ).

cnf(refute_0_102,plain,
    theorem(implies(X_151,not(not(X_151)))),
    inference(resolve,[$cnf( theorem(implies(not(X_151),not(X_151))) )],[refute_0_101,refute_0_89]) ).

cnf(refute_0_103,plain,
    theorem(implies(X_2804,not(not(X_2804)))),
    inference(subst,[],[refute_0_102:[bind(X_151,$fot(X_2804))]]) ).

cnf(refute_0_104,plain,
    ( ~ axiom(implies(implies(X_39,X_40),implies(or(X_41,X_39),or(X_41,X_40))))
    | theorem(implies(implies(X_39,X_40),implies(or(X_41,X_39),or(X_41,X_40)))) ),
    inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_39,X_40),implies(or(X_41,X_39),or(X_41,X_40)))))]]) ).

cnf(refute_0_105,plain,
    axiom(implies(implies(X_39,X_40),implies(or(X_41,X_39),or(X_41,X_40)))),
    inference(subst,[],[axiom_1_6:[bind(A,$fot(X_39)),bind(B,$fot(X_40)),bind(C,$fot(X_41))]]) ).

cnf(refute_0_106,plain,
    theorem(implies(implies(X_39,X_40),implies(or(X_41,X_39),or(X_41,X_40)))),
    inference(resolve,[$cnf( axiom(implies(implies(X_39,X_40),implies(or(X_41,X_39),or(X_41,X_40)))) )],[refute_0_105,refute_0_104]) ).

cnf(refute_0_107,plain,
    ( ~ theorem(implies(X_39,X_40))
    | ~ theorem(implies(implies(X_39,X_40),implies(or(X_41,X_39),or(X_41,X_40))))
    | theorem(implies(or(X_41,X_39),or(X_41,X_40))) ),
    inference(subst,[],[rule_2:[bind(X,$fot(implies(or(X_41,X_39),or(X_41,X_40)))),bind(Y,$fot(implies(X_39,X_40)))]]) ).

cnf(refute_0_108,plain,
    ( ~ theorem(implies(X_39,X_40))
    | theorem(implies(or(X_41,X_39),or(X_41,X_40))) ),
    inference(resolve,[$cnf( theorem(implies(implies(X_39,X_40),implies(or(X_41,X_39),or(X_41,X_40)))) )],[refute_0_106,refute_0_107]) ).

cnf(refute_0_109,plain,
    ( ~ theorem(implies(X_2804,not(not(X_2804))))
    | theorem(implies(or(X_2806,X_2804),or(X_2806,not(not(X_2804))))) ),
    inference(subst,[],[refute_0_108:[bind(X_39,$fot(X_2804)),bind(X_40,$fot(not(not(X_2804)))),bind(X_41,$fot(X_2806))]]) ).

cnf(refute_0_110,plain,
    theorem(implies(or(X_2806,X_2804),or(X_2806,not(not(X_2804))))),
    inference(resolve,[$cnf( theorem(implies(X_2804,not(not(X_2804)))) )],[refute_0_103,refute_0_109]) ).

cnf(refute_0_111,plain,
    theorem(implies(or(X_2810,X_2809),or(X_2810,not(not(X_2809))))),
    inference(subst,[],[refute_0_110:[bind(X_2804,$fot(X_2809)),bind(X_2806,$fot(X_2810))]]) ).

cnf(refute_0_112,plain,
    ( ~ theorem(or(X_2810,X_2809))
    | theorem(or(X_2810,not(not(X_2809)))) ),
    inference(resolve,[$cnf( theorem(implies(or(X_2810,X_2809),or(X_2810,not(not(X_2809))))) )],[refute_0_111,refute_0_69]) ).

cnf(refute_0_113,plain,
    ( ~ theorem(or(implies(X,X_1589),implies(X_1588,not(X_1589))))
    | theorem(or(implies(X,X_1589),not(not(implies(X_1588,not(X_1589)))))) ),
    inference(subst,[],[refute_0_112:[bind(X_2809,$fot(implies(X_1588,not(X_1589)))),bind(X_2810,$fot(implies(X,X_1589)))]]) ).

cnf(refute_0_114,plain,
    theorem(or(implies(X,X_1589),not(not(implies(X_1588,not(X_1589)))))),
    inference(resolve,[$cnf( theorem(or(implies(X,X_1589),implies(X_1588,not(X_1589)))) )],[refute_0_68,refute_0_113]) ).

cnf(refute_0_115,plain,
    or(not(P),not(Q)) = implies(P,not(Q)),
    inference(subst,[],[refute_0_47:[bind(X,$fot(P)),bind(Y,$fot(not(Q)))]]) ).

cnf(refute_0_116,plain,
    not(or(not(P),not(Q))) = not(or(not(P),not(Q))),
    introduced(tautology,[refl,[$fot(not(or(not(P),not(Q))))]]) ).

cnf(refute_0_117,plain,
    ( not(or(not(P),not(Q))) != not(or(not(P),not(Q)))
    | or(not(P),not(Q)) != implies(P,not(Q))
    | not(or(not(P),not(Q))) = not(implies(P,not(Q))) ),
    introduced(tautology,[equality,[$cnf( $equal(not(or(not(P),not(Q))),not(or(not(P),not(Q)))) ),[1,0],$fot(implies(P,not(Q)))]]) ).

cnf(refute_0_118,plain,
    ( or(not(P),not(Q)) != implies(P,not(Q))
    | not(or(not(P),not(Q))) = not(implies(P,not(Q))) ),
    inference(resolve,[$cnf( $equal(not(or(not(P),not(Q))),not(or(not(P),not(Q)))) )],[refute_0_116,refute_0_117]) ).

cnf(refute_0_119,plain,
    not(or(not(P),not(Q))) = not(implies(P,not(Q))),
    inference(resolve,[$cnf( $equal(or(not(P),not(Q)),implies(P,not(Q))) )],[refute_0_115,refute_0_118]) ).

cnf(refute_0_120,plain,
    ( and(P,Q) != not(or(not(P),not(Q)))
    | not(or(not(P),not(Q))) != not(implies(P,not(Q)))
    | and(P,Q) = not(implies(P,not(Q))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(and(P,Q),not(implies(P,not(Q)))) ),[0],$fot(not(or(not(P),not(Q))))]]) ).

cnf(refute_0_121,plain,
    ( and(P,Q) != not(or(not(P),not(Q)))
    | and(P,Q) = not(implies(P,not(Q))) ),
    inference(resolve,[$cnf( $equal(not(or(not(P),not(Q))),not(implies(P,not(Q)))) )],[refute_0_119,refute_0_120]) ).

cnf(refute_0_122,plain,
    and(P,Q) = not(implies(P,not(Q))),
    inference(resolve,[$cnf( $equal(and(P,Q),not(or(not(P),not(Q)))) )],[and_defn,refute_0_121]) ).

cnf(refute_0_123,plain,
    ( and(P,Q) != not(implies(P,not(Q)))
    | not(implies(P,not(Q))) = and(P,Q) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(and(P,Q))),bind(Y0,$fot(not(implies(P,not(Q)))))]]) ).

cnf(refute_0_124,plain,
    not(implies(P,not(Q))) = and(P,Q),
    inference(resolve,[$cnf( $equal(and(P,Q),not(implies(P,not(Q)))) )],[refute_0_122,refute_0_123]) ).

cnf(refute_0_125,plain,
    not(implies(X_1588,not(X_1589))) = and(X_1588,X_1589),
    inference(subst,[],[refute_0_124:[bind(P,$fot(X_1588)),bind(Q,$fot(X_1589))]]) ).

cnf(refute_0_126,plain,
    not(not(implies(X_1588,not(X_1589)))) = not(not(implies(X_1588,not(X_1589)))),
    introduced(tautology,[refl,[$fot(not(not(implies(X_1588,not(X_1589)))))]]) ).

cnf(refute_0_127,plain,
    ( not(implies(X_1588,not(X_1589))) != and(X_1588,X_1589)
    | not(not(implies(X_1588,not(X_1589)))) != not(not(implies(X_1588,not(X_1589))))
    | not(not(implies(X_1588,not(X_1589)))) = not(and(X_1588,X_1589)) ),
    introduced(tautology,[equality,[$cnf( $equal(not(not(implies(X_1588,not(X_1589)))),not(not(implies(X_1588,not(X_1589))))) ),[1,0],$fot(and(X_1588,X_1589))]]) ).

cnf(refute_0_128,plain,
    ( not(implies(X_1588,not(X_1589))) != and(X_1588,X_1589)
    | not(not(implies(X_1588,not(X_1589)))) = not(and(X_1588,X_1589)) ),
    inference(resolve,[$cnf( $equal(not(not(implies(X_1588,not(X_1589)))),not(not(implies(X_1588,not(X_1589))))) )],[refute_0_126,refute_0_127]) ).

cnf(refute_0_129,plain,
    not(not(implies(X_1588,not(X_1589)))) = not(and(X_1588,X_1589)),
    inference(resolve,[$cnf( $equal(not(implies(X_1588,not(X_1589))),and(X_1588,X_1589)) )],[refute_0_125,refute_0_128]) ).

cnf(refute_0_130,plain,
    or(implies(X,X_1589),not(not(implies(X_1588,not(X_1589))))) = or(implies(X,X_1589),not(not(implies(X_1588,not(X_1589))))),
    introduced(tautology,[refl,[$fot(or(implies(X,X_1589),not(not(implies(X_1588,not(X_1589))))))]]) ).

cnf(refute_0_131,plain,
    ( not(not(implies(X_1588,not(X_1589)))) != not(and(X_1588,X_1589))
    | or(implies(X,X_1589),not(not(implies(X_1588,not(X_1589))))) != or(implies(X,X_1589),not(not(implies(X_1588,not(X_1589)))))
    | or(implies(X,X_1589),not(not(implies(X_1588,not(X_1589))))) = or(implies(X,X_1589),not(and(X_1588,X_1589))) ),
    introduced(tautology,[equality,[$cnf( $equal(or(implies(X,X_1589),not(not(implies(X_1588,not(X_1589))))),or(implies(X,X_1589),not(not(implies(X_1588,not(X_1589)))))) ),[1,1],$fot(not(and(X_1588,X_1589)))]]) ).

cnf(refute_0_132,plain,
    ( not(not(implies(X_1588,not(X_1589)))) != not(and(X_1588,X_1589))
    | or(implies(X,X_1589),not(not(implies(X_1588,not(X_1589))))) = or(implies(X,X_1589),not(and(X_1588,X_1589))) ),
    inference(resolve,[$cnf( $equal(or(implies(X,X_1589),not(not(implies(X_1588,not(X_1589))))),or(implies(X,X_1589),not(not(implies(X_1588,not(X_1589)))))) )],[refute_0_130,refute_0_131]) ).

cnf(refute_0_133,plain,
    or(implies(X,X_1589),not(not(implies(X_1588,not(X_1589))))) = or(implies(X,X_1589),not(and(X_1588,X_1589))),
    inference(resolve,[$cnf( $equal(not(not(implies(X_1588,not(X_1589)))),not(and(X_1588,X_1589))) )],[refute_0_129,refute_0_132]) ).

cnf(refute_0_134,plain,
    ( or(implies(X,X_1589),not(not(implies(X_1588,not(X_1589))))) != or(implies(X,X_1589),not(and(X_1588,X_1589)))
    | ~ theorem(or(implies(X,X_1589),not(not(implies(X_1588,not(X_1589))))))
    | theorem(or(implies(X,X_1589),not(and(X_1588,X_1589)))) ),
    introduced(tautology,[equality,[$cnf( theorem(or(implies(X,X_1589),not(not(implies(X_1588,not(X_1589)))))) ),[0],$fot(or(implies(X,X_1589),not(and(X_1588,X_1589))))]]) ).

cnf(refute_0_135,plain,
    ( ~ theorem(or(implies(X,X_1589),not(not(implies(X_1588,not(X_1589))))))
    | theorem(or(implies(X,X_1589),not(and(X_1588,X_1589)))) ),
    inference(resolve,[$cnf( $equal(or(implies(X,X_1589),not(not(implies(X_1588,not(X_1589))))),or(implies(X,X_1589),not(and(X_1588,X_1589)))) )],[refute_0_133,refute_0_134]) ).

cnf(refute_0_136,plain,
    theorem(or(implies(X,X_1589),not(and(X_1588,X_1589)))),
    inference(resolve,[$cnf( theorem(or(implies(X,X_1589),not(not(implies(X_1588,not(X_1589)))))) )],[refute_0_114,refute_0_135]) ).

cnf(refute_0_137,plain,
    theorem(or(implies(X_14001,X_14003),not(and(X_14002,X_14003)))),
    inference(subst,[],[refute_0_136:[bind(X,$fot(X_14001)),bind(X_1588,$fot(X_14002)),bind(X_1589,$fot(X_14003))]]) ).

cnf(refute_0_138,plain,
    theorem(or(not(and(X_14002,X_14003)),implies(X_14001,X_14003))),
    inference(resolve,[$cnf( theorem(or(implies(X_14001,X_14003),not(and(X_14002,X_14003)))) )],[refute_0_137,refute_0_5]) ).

cnf(refute_0_139,plain,
    or(not(and(X_14002,X_14003)),implies(X_14001,X_14003)) = implies(and(X_14002,X_14003),implies(X_14001,X_14003)),
    inference(subst,[],[refute_0_47:[bind(X,$fot(and(X_14002,X_14003))),bind(Y,$fot(implies(X_14001,X_14003)))]]) ).

cnf(refute_0_140,plain,
    ( or(not(and(X_14002,X_14003)),implies(X_14001,X_14003)) != implies(and(X_14002,X_14003),implies(X_14001,X_14003))
    | ~ theorem(or(not(and(X_14002,X_14003)),implies(X_14001,X_14003)))
    | theorem(implies(and(X_14002,X_14003),implies(X_14001,X_14003))) ),
    introduced(tautology,[equality,[$cnf( theorem(or(not(and(X_14002,X_14003)),implies(X_14001,X_14003))) ),[0],$fot(implies(and(X_14002,X_14003),implies(X_14001,X_14003)))]]) ).

cnf(refute_0_141,plain,
    ( ~ theorem(or(not(and(X_14002,X_14003)),implies(X_14001,X_14003)))
    | theorem(implies(and(X_14002,X_14003),implies(X_14001,X_14003))) ),
    inference(resolve,[$cnf( $equal(or(not(and(X_14002,X_14003)),implies(X_14001,X_14003)),implies(and(X_14002,X_14003),implies(X_14001,X_14003))) )],[refute_0_139,refute_0_140]) ).

cnf(refute_0_142,plain,
    theorem(implies(and(X_14002,X_14003),implies(X_14001,X_14003))),
    inference(resolve,[$cnf( theorem(or(not(and(X_14002,X_14003)),implies(X_14001,X_14003))) )],[refute_0_138,refute_0_141]) ).

cnf(refute_0_143,plain,
    theorem(implies(and(p,q),implies(p,q))),
    inference(subst,[],[refute_0_142:[bind(X_14001,$fot(p)),bind(X_14002,$fot(p)),bind(X_14003,$fot(q))]]) ).

cnf(refute_0_144,plain,
    $false,
    inference(resolve,[$cnf( theorem(implies(and(p,q),implies(p,q))) )],[refute_0_143,prove_this]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : LCL248-3 : TPTP v8.1.0. Released v2.3.0.
% 0.04/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.33  % Computer : n006.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Mon Jul  4 01:10:22 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 9.36/9.55  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.36/9.55  
% 9.36/9.55  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.41/9.57  
%------------------------------------------------------------------------------