TSTP Solution File: LCL226-3 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : LCL226-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n015.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 12:50:52 EDT 2022

% Result   : Unsatisfiable 1.82s 2.00s
% Output   : CNFRefutation 1.82s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   23
% Syntax   : Number of clauses     :   69 (  37 unt;   0 nHn;  40 RR)
%            Number of literals    :  114 (  61 equ;  47 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    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :  148 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
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,r),implies(or(not(r),s),or(q,s)))) ).

cnf(refute_0_0,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_1,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_2,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    ( implies(X,Y) != or(not(X),Y)
    | or(not(X),Y) = implies(X,Y) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).

cnf(refute_0_4,plain,
    or(not(X),Y) = implies(X,Y),
    inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_3]) ).

cnf(refute_0_5,plain,
    or(not(r),s) = implies(r,s),
    inference(subst,[],[refute_0_4:[bind(X,$fot(r)),bind(Y,$fot(s))]]) ).

cnf(refute_0_6,plain,
    implies(or(not(r),s),or(q,s)) = implies(or(not(r),s),or(q,s)),
    introduced(tautology,[refl,[$fot(implies(or(not(r),s),or(q,s)))]]) ).

cnf(refute_0_7,plain,
    ( implies(or(not(r),s),or(q,s)) != implies(or(not(r),s),or(q,s))
    | or(not(r),s) != implies(r,s)
    | implies(or(not(r),s),or(q,s)) = implies(implies(r,s),or(q,s)) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(or(not(r),s),or(q,s)),implies(or(not(r),s),or(q,s))) ),[1,0],$fot(implies(r,s))]]) ).

cnf(refute_0_8,plain,
    ( or(not(r),s) != implies(r,s)
    | implies(or(not(r),s),or(q,s)) = implies(implies(r,s),or(q,s)) ),
    inference(resolve,[$cnf( $equal(implies(or(not(r),s),or(q,s)),implies(or(not(r),s),or(q,s))) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    implies(or(not(r),s),or(q,s)) = implies(implies(r,s),or(q,s)),
    inference(resolve,[$cnf( $equal(or(not(r),s),implies(r,s)) )],[refute_0_5,refute_0_8]) ).

cnf(refute_0_10,plain,
    implies(or(q,r),implies(or(not(r),s),or(q,s))) = implies(or(q,r),implies(or(not(r),s),or(q,s))),
    introduced(tautology,[refl,[$fot(implies(or(q,r),implies(or(not(r),s),or(q,s))))]]) ).

cnf(refute_0_11,plain,
    ( implies(or(not(r),s),or(q,s)) != implies(implies(r,s),or(q,s))
    | implies(or(q,r),implies(or(not(r),s),or(q,s))) != implies(or(q,r),implies(or(not(r),s),or(q,s)))
    | implies(or(q,r),implies(or(not(r),s),or(q,s))) = implies(or(q,r),implies(implies(r,s),or(q,s))) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(or(q,r),implies(or(not(r),s),or(q,s))),implies(or(q,r),implies(or(not(r),s),or(q,s)))) ),[1,1],$fot(implies(implies(r,s),or(q,s)))]]) ).

cnf(refute_0_12,plain,
    ( implies(or(not(r),s),or(q,s)) != implies(implies(r,s),or(q,s))
    | implies(or(q,r),implies(or(not(r),s),or(q,s))) = implies(or(q,r),implies(implies(r,s),or(q,s))) ),
    inference(resolve,[$cnf( $equal(implies(or(q,r),implies(or(not(r),s),or(q,s))),implies(or(q,r),implies(or(not(r),s),or(q,s)))) )],[refute_0_10,refute_0_11]) ).

cnf(refute_0_13,plain,
    implies(or(q,r),implies(or(not(r),s),or(q,s))) = implies(or(q,r),implies(implies(r,s),or(q,s))),
    inference(resolve,[$cnf( $equal(implies(or(not(r),s),or(q,s)),implies(implies(r,s),or(q,s))) )],[refute_0_9,refute_0_12]) ).

cnf(refute_0_14,plain,
    ( implies(or(q,r),implies(or(not(r),s),or(q,s))) != implies(or(q,r),implies(implies(r,s),or(q,s)))
    | ~ theorem(implies(or(q,r),implies(implies(r,s),or(q,s))))
    | theorem(implies(or(q,r),implies(or(not(r),s),or(q,s)))) ),
    introduced(tautology,[equality,[$cnf( ~ theorem(implies(or(q,r),implies(or(not(r),s),or(q,s)))) ),[0],$fot(implies(or(q,r),implies(implies(r,s),or(q,s))))]]) ).

cnf(refute_0_15,plain,
    ( ~ theorem(implies(or(q,r),implies(implies(r,s),or(q,s))))
    | theorem(implies(or(q,r),implies(or(not(r),s),or(q,s)))) ),
    inference(resolve,[$cnf( $equal(implies(or(q,r),implies(or(not(r),s),or(q,s))),implies(or(q,r),implies(implies(r,s),or(q,s)))) )],[refute_0_13,refute_0_14]) ).

cnf(refute_0_16,plain,
    ~ theorem(implies(or(q,r),implies(implies(r,s),or(q,s)))),
    inference(resolve,[$cnf( theorem(implies(or(q,r),implies(or(not(r),s),or(q,s)))) )],[refute_0_15,prove_this]) ).

cnf(refute_0_17,plain,
    ( ~ axiom(implies(implies(X_31,X_32),implies(or(X_33,X_31),or(X_33,X_32))))
    | theorem(implies(implies(X_31,X_32),implies(or(X_33,X_31),or(X_33,X_32)))) ),
    inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_31,X_32),implies(or(X_33,X_31),or(X_33,X_32)))))]]) ).

cnf(refute_0_18,plain,
    axiom(implies(implies(X_31,X_32),implies(or(X_33,X_31),or(X_33,X_32)))),
    inference(subst,[],[axiom_1_6:[bind(A,$fot(X_31)),bind(B,$fot(X_32)),bind(C,$fot(X_33))]]) ).

cnf(refute_0_19,plain,
    theorem(implies(implies(X_31,X_32),implies(or(X_33,X_31),or(X_33,X_32)))),
    inference(resolve,[$cnf( axiom(implies(implies(X_31,X_32),implies(or(X_33,X_31),or(X_33,X_32)))) )],[refute_0_18,refute_0_17]) ).

cnf(refute_0_20,plain,
    ( ~ axiom(implies(implies(X_56,implies(X_55,X_57)),implies(X_55,implies(X_56,X_57))))
    | theorem(implies(implies(X_56,implies(X_55,X_57)),implies(X_55,implies(X_56,X_57)))) ),
    inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_56,implies(X_55,X_57)),implies(X_55,implies(X_56,X_57)))))]]) ).

cnf(refute_0_21,plain,
    axiom(implies(or(not(X),or(X_44,X_45)),or(X_44,or(not(X),X_45)))),
    inference(subst,[],[axiom_1_5:[bind(A,$fot(not(X))),bind(B,$fot(X_44)),bind(C,$fot(X_45))]]) ).

cnf(refute_0_22,plain,
    implies(X,X_45) = or(not(X),X_45),
    inference(subst,[],[implies_definition:[bind(Y,$fot(X_45))]]) ).

cnf(refute_0_23,plain,
    ( implies(X,X_45) != or(not(X),X_45)
    | or(not(X),X_45) = implies(X,X_45) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,X_45))),bind(Y0,$fot(or(not(X),X_45)))]]) ).

cnf(refute_0_24,plain,
    or(not(X),X_45) = implies(X,X_45),
    inference(resolve,[$cnf( $equal(implies(X,X_45),or(not(X),X_45)) )],[refute_0_22,refute_0_23]) ).

cnf(refute_0_25,plain,
    ( or(not(X),X_45) != implies(X,X_45)
    | ~ axiom(implies(or(not(X),or(X_44,X_45)),or(X_44,or(not(X),X_45))))
    | axiom(implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45)))) ),
    introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_44,X_45)),or(X_44,or(not(X),X_45)))) ),[0,1,1],$fot(implies(X,X_45))]]) ).

cnf(refute_0_26,plain,
    ( ~ axiom(implies(or(not(X),or(X_44,X_45)),or(X_44,or(not(X),X_45))))
    | axiom(implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45)))) ),
    inference(resolve,[$cnf( $equal(or(not(X),X_45),implies(X,X_45)) )],[refute_0_24,refute_0_25]) ).

cnf(refute_0_27,plain,
    axiom(implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45)))),
    inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_44,X_45)),or(X_44,or(not(X),X_45)))) )],[refute_0_21,refute_0_26]) ).

cnf(refute_0_28,plain,
    or(not(X),or(X_44,X_45)) = implies(X,or(X_44,X_45)),
    inference(subst,[],[refute_0_4:[bind(Y,$fot(or(X_44,X_45)))]]) ).

cnf(refute_0_29,plain,
    implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45))) = implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45))),
    introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45))))]]) ).

cnf(refute_0_30,plain,
    ( implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45))) != implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45)))
    | or(not(X),or(X_44,X_45)) != implies(X,or(X_44,X_45))
    | implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45))) = implies(implies(X,or(X_44,X_45)),or(X_44,implies(X,X_45))) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45))),implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45)))) ),[1,0],$fot(implies(X,or(X_44,X_45)))]]) ).

cnf(refute_0_31,plain,
    ( or(not(X),or(X_44,X_45)) != implies(X,or(X_44,X_45))
    | implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45))) = implies(implies(X,or(X_44,X_45)),or(X_44,implies(X,X_45))) ),
    inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45))),implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45)))) )],[refute_0_29,refute_0_30]) ).

cnf(refute_0_32,plain,
    implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45))) = implies(implies(X,or(X_44,X_45)),or(X_44,implies(X,X_45))),
    inference(resolve,[$cnf( $equal(or(not(X),or(X_44,X_45)),implies(X,or(X_44,X_45))) )],[refute_0_28,refute_0_31]) ).

cnf(refute_0_33,plain,
    ( implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45))) != implies(implies(X,or(X_44,X_45)),or(X_44,implies(X,X_45)))
    | ~ axiom(implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45))))
    | axiom(implies(implies(X,or(X_44,X_45)),or(X_44,implies(X,X_45)))) ),
    introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45)))) ),[0],$fot(implies(implies(X,or(X_44,X_45)),or(X_44,implies(X,X_45))))]]) ).

cnf(refute_0_34,plain,
    ( ~ axiom(implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45))))
    | axiom(implies(implies(X,or(X_44,X_45)),or(X_44,implies(X,X_45)))) ),
    inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45))),implies(implies(X,or(X_44,X_45)),or(X_44,implies(X,X_45)))) )],[refute_0_32,refute_0_33]) ).

cnf(refute_0_35,plain,
    axiom(implies(implies(X,or(X_44,X_45)),or(X_44,implies(X,X_45)))),
    inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45)))) )],[refute_0_27,refute_0_34]) ).

cnf(refute_0_36,plain,
    axiom(implies(implies(X_52,or(not(X),X_54)),or(not(X),implies(X_52,X_54)))),
    inference(subst,[],[refute_0_35:[bind(X,$fot(X_52)),bind(X_44,$fot(not(X))),bind(X_45,$fot(X_54))]]) ).

cnf(refute_0_37,plain,
    implies(X,implies(X_52,X_54)) = or(not(X),implies(X_52,X_54)),
    inference(subst,[],[implies_definition:[bind(Y,$fot(implies(X_52,X_54)))]]) ).

cnf(refute_0_38,plain,
    ( implies(X,implies(X_52,X_54)) != or(not(X),implies(X_52,X_54))
    | or(not(X),implies(X_52,X_54)) = implies(X,implies(X_52,X_54)) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,implies(X_52,X_54)))),bind(Y0,$fot(or(not(X),implies(X_52,X_54))))]]) ).

cnf(refute_0_39,plain,
    or(not(X),implies(X_52,X_54)) = implies(X,implies(X_52,X_54)),
    inference(resolve,[$cnf( $equal(implies(X,implies(X_52,X_54)),or(not(X),implies(X_52,X_54))) )],[refute_0_37,refute_0_38]) ).

cnf(refute_0_40,plain,
    ( or(not(X),implies(X_52,X_54)) != implies(X,implies(X_52,X_54))
    | ~ axiom(implies(implies(X_52,or(not(X),X_54)),or(not(X),implies(X_52,X_54))))
    | axiom(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54)))) ),
    introduced(tautology,[equality,[$cnf( axiom(implies(implies(X_52,or(not(X),X_54)),or(not(X),implies(X_52,X_54)))) ),[0,1],$fot(implies(X,implies(X_52,X_54)))]]) ).

cnf(refute_0_41,plain,
    ( ~ axiom(implies(implies(X_52,or(not(X),X_54)),or(not(X),implies(X_52,X_54))))
    | axiom(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54)))) ),
    inference(resolve,[$cnf( $equal(or(not(X),implies(X_52,X_54)),implies(X,implies(X_52,X_54))) )],[refute_0_39,refute_0_40]) ).

cnf(refute_0_42,plain,
    axiom(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54)))),
    inference(resolve,[$cnf( axiom(implies(implies(X_52,or(not(X),X_54)),or(not(X),implies(X_52,X_54)))) )],[refute_0_36,refute_0_41]) ).

cnf(refute_0_43,plain,
    or(not(X),X_54) = implies(X,X_54),
    inference(subst,[],[refute_0_4:[bind(Y,$fot(X_54))]]) ).

cnf(refute_0_44,plain,
    implies(X_52,or(not(X),X_54)) = implies(X_52,or(not(X),X_54)),
    introduced(tautology,[refl,[$fot(implies(X_52,or(not(X),X_54)))]]) ).

cnf(refute_0_45,plain,
    ( implies(X_52,or(not(X),X_54)) != implies(X_52,or(not(X),X_54))
    | or(not(X),X_54) != implies(X,X_54)
    | implies(X_52,or(not(X),X_54)) = implies(X_52,implies(X,X_54)) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(X_52,or(not(X),X_54)),implies(X_52,or(not(X),X_54))) ),[1,1],$fot(implies(X,X_54))]]) ).

cnf(refute_0_46,plain,
    ( or(not(X),X_54) != implies(X,X_54)
    | implies(X_52,or(not(X),X_54)) = implies(X_52,implies(X,X_54)) ),
    inference(resolve,[$cnf( $equal(implies(X_52,or(not(X),X_54)),implies(X_52,or(not(X),X_54))) )],[refute_0_44,refute_0_45]) ).

cnf(refute_0_47,plain,
    implies(X_52,or(not(X),X_54)) = implies(X_52,implies(X,X_54)),
    inference(resolve,[$cnf( $equal(or(not(X),X_54),implies(X,X_54)) )],[refute_0_43,refute_0_46]) ).

cnf(refute_0_48,plain,
    implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))) = implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))),
    introduced(tautology,[refl,[$fot(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))))]]) ).

cnf(refute_0_49,plain,
    ( implies(X_52,or(not(X),X_54)) != implies(X_52,implies(X,X_54))
    | implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))) != implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54)))
    | implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))) = implies(implies(X_52,implies(X,X_54)),implies(X,implies(X_52,X_54))) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))),implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54)))) ),[1,0],$fot(implies(X_52,implies(X,X_54)))]]) ).

cnf(refute_0_50,plain,
    ( implies(X_52,or(not(X),X_54)) != implies(X_52,implies(X,X_54))
    | implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))) = implies(implies(X_52,implies(X,X_54)),implies(X,implies(X_52,X_54))) ),
    inference(resolve,[$cnf( $equal(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))),implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54)))) )],[refute_0_48,refute_0_49]) ).

cnf(refute_0_51,plain,
    implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))) = implies(implies(X_52,implies(X,X_54)),implies(X,implies(X_52,X_54))),
    inference(resolve,[$cnf( $equal(implies(X_52,or(not(X),X_54)),implies(X_52,implies(X,X_54))) )],[refute_0_47,refute_0_50]) ).

cnf(refute_0_52,plain,
    ( implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))) != implies(implies(X_52,implies(X,X_54)),implies(X,implies(X_52,X_54)))
    | ~ axiom(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))))
    | axiom(implies(implies(X_52,implies(X,X_54)),implies(X,implies(X_52,X_54)))) ),
    introduced(tautology,[equality,[$cnf( axiom(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54)))) ),[0],$fot(implies(implies(X_52,implies(X,X_54)),implies(X,implies(X_52,X_54))))]]) ).

cnf(refute_0_53,plain,
    ( ~ axiom(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))))
    | axiom(implies(implies(X_52,implies(X,X_54)),implies(X,implies(X_52,X_54)))) ),
    inference(resolve,[$cnf( $equal(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))),implies(implies(X_52,implies(X,X_54)),implies(X,implies(X_52,X_54)))) )],[refute_0_51,refute_0_52]) ).

cnf(refute_0_54,plain,
    axiom(implies(implies(X_52,implies(X,X_54)),implies(X,implies(X_52,X_54)))),
    inference(resolve,[$cnf( axiom(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54)))) )],[refute_0_42,refute_0_53]) ).

cnf(refute_0_55,plain,
    axiom(implies(implies(X_56,implies(X_55,X_57)),implies(X_55,implies(X_56,X_57)))),
    inference(subst,[],[refute_0_54:[bind(X,$fot(X_55)),bind(X_52,$fot(X_56)),bind(X_54,$fot(X_57))]]) ).

cnf(refute_0_56,plain,
    theorem(implies(implies(X_56,implies(X_55,X_57)),implies(X_55,implies(X_56,X_57)))),
    inference(resolve,[$cnf( axiom(implies(implies(X_56,implies(X_55,X_57)),implies(X_55,implies(X_56,X_57)))) )],[refute_0_55,refute_0_20]) ).

cnf(refute_0_57,plain,
    ( ~ theorem(implies(X_56,implies(X_55,X_57)))
    | ~ theorem(implies(implies(X_56,implies(X_55,X_57)),implies(X_55,implies(X_56,X_57))))
    | theorem(implies(X_55,implies(X_56,X_57))) ),
    inference(subst,[],[rule_2:[bind(X,$fot(implies(X_55,implies(X_56,X_57)))),bind(Y,$fot(implies(X_56,implies(X_55,X_57))))]]) ).

cnf(refute_0_58,plain,
    ( ~ theorem(implies(X_56,implies(X_55,X_57)))
    | theorem(implies(X_55,implies(X_56,X_57))) ),
    inference(resolve,[$cnf( theorem(implies(implies(X_56,implies(X_55,X_57)),implies(X_55,implies(X_56,X_57)))) )],[refute_0_56,refute_0_57]) ).

cnf(refute_0_59,plain,
    ( ~ theorem(implies(implies(X_31,X_32),implies(or(X_33,X_31),or(X_33,X_32))))
    | theorem(implies(or(X_33,X_31),implies(implies(X_31,X_32),or(X_33,X_32)))) ),
    inference(subst,[],[refute_0_58:[bind(X_55,$fot(or(X_33,X_31))),bind(X_56,$fot(implies(X_31,X_32))),bind(X_57,$fot(or(X_33,X_32)))]]) ).

cnf(refute_0_60,plain,
    theorem(implies(or(X_33,X_31),implies(implies(X_31,X_32),or(X_33,X_32)))),
    inference(resolve,[$cnf( theorem(implies(implies(X_31,X_32),implies(or(X_33,X_31),or(X_33,X_32)))) )],[refute_0_19,refute_0_59]) ).

cnf(refute_0_61,plain,
    theorem(implies(or(q,r),implies(implies(r,s),or(q,s)))),
    inference(subst,[],[refute_0_60:[bind(X_31,$fot(r)),bind(X_32,$fot(s)),bind(X_33,$fot(q))]]) ).

cnf(refute_0_62,plain,
    $false,
    inference(resolve,[$cnf( theorem(implies(or(q,r),implies(implies(r,s),or(q,s)))) )],[refute_0_61,refute_0_16]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL226-3 : TPTP v8.1.0. Released v2.3.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n015.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 : Sun Jul  3 21:41:01 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.82/2.00  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.82/2.00  
% 1.82/2.00  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.82/2.01  
%------------------------------------------------------------------------------