%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : LCL321-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n029.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 12:51:32 EDT 2022

% Result   : Unsatisfiable 0.48s 0.66s
% Output   : CNFRefutation 0.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   59 (  34 unt;   0 nHn;  26 RR)
%            Number of literals    :   92 (  22 equ;  34 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   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   :  126 (  21 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(axiom_1_3,axiom,
    axiom(implies(A,or(B,A))) ).

cnf(axiom_1_4,axiom,
    axiom(implies(or(A,B),or(B,A))) ).

cnf(axiom_1_5,axiom,
    axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) ).

cnf(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(or(implies(p,q),implies(p,not(q)))) ).

cnf(refute_0_0,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_1,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_2,plain,
    theorem(implies(X_3,or(X_4,X_3))),
    inference(resolve,[$cnf( axiom(implies(X_3,or(X_4,X_3))) )],[refute_0_1,refute_0_0]) ).

cnf(refute_0_3,plain,
    theorem(implies(X_59,or(X_4,X_59))),
    inference(subst,[],[refute_0_2:[bind(X_3,$fot(X_59))]]) ).

cnf(refute_0_4,plain,
    ( ~ theorem(X_59)
    | ~ theorem(implies(X_59,or(X_4,X_59)))
    | theorem(or(X_4,X_59)) ),
    inference(subst,[],[rule_2:[bind(X,$fot(or(X_4,X_59))),bind(Y,$fot(X_59))]]) ).

cnf(refute_0_5,plain,
    ( ~ theorem(X_59)
    | theorem(or(X_4,X_59)) ),
    inference(resolve,[$cnf( theorem(implies(X_59,or(X_4,X_59))) )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( ~ theorem(or(implies(X_101,X_102),not(X_102)))
    | theorem(or(X_4,or(implies(X_101,X_102),not(X_102)))) ),
    inference(subst,[],[refute_0_5:[bind(X_59,$fot(or(implies(X_101,X_102),not(X_102))))]]) ).

cnf(refute_0_7,plain,
    theorem(implies(X_3,or(not(X_7),X_3))),
    inference(subst,[],[refute_0_2:[bind(X_4,$fot(not(X_7)))]]) ).

cnf(refute_0_8,plain,
    implies(X_7,X_3) = or(not(X_7),X_3),
    inference(subst,[],[implies_definition:[bind(X,$fot(X_7)),bind(Y,$fot(X_3))]]) ).

cnf(refute_0_9,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_10,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_11,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_9,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( implies(X_7,X_3) != or(not(X_7),X_3)
    | or(not(X_7),X_3) = implies(X_7,X_3) ),
    inference(subst,[],[refute_0_11:[bind(X0,$fot(implies(X_7,X_3))),bind(Y0,$fot(or(not(X_7),X_3)))]]) ).

cnf(refute_0_13,plain,
    or(not(X_7),X_3) = implies(X_7,X_3),
    inference(resolve,[$cnf( $equal(implies(X_7,X_3),or(not(X_7),X_3)) )],[refute_0_8,refute_0_12]) ).

cnf(refute_0_14,plain,
    ( or(not(X_7),X_3) != implies(X_7,X_3)
    | ~ theorem(implies(X_3,or(not(X_7),X_3)))
    | theorem(implies(X_3,implies(X_7,X_3))) ),
    introduced(tautology,[equality,[$cnf( theorem(implies(X_3,or(not(X_7),X_3))) ),[0,1],$fot(implies(X_7,X_3))]]) ).

cnf(refute_0_15,plain,
    ( ~ theorem(implies(X_3,or(not(X_7),X_3)))
    | theorem(implies(X_3,implies(X_7,X_3))) ),
    inference(resolve,[$cnf( $equal(or(not(X_7),X_3),implies(X_7,X_3)) )],[refute_0_13,refute_0_14]) ).

cnf(refute_0_16,plain,
    theorem(implies(X_3,implies(X_7,X_3))),
    inference(resolve,[$cnf( theorem(implies(X_3,or(not(X_7),X_3))) )],[refute_0_7,refute_0_15]) ).

cnf(refute_0_17,plain,
    theorem(implies(X_95,implies(X_7,X_95))),
    inference(subst,[],[refute_0_16:[bind(X_3,$fot(X_95))]]) ).

cnf(refute_0_18,plain,
    ( ~ axiom(implies(implies(X_17,X_18),or(X_18,not(X_17))))
    | theorem(implies(implies(X_17,X_18),or(X_18,not(X_17)))) ),
    inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_17,X_18),or(X_18,not(X_17)))))]]) ).

cnf(refute_0_19,plain,
    axiom(implies(or(not(X),X_16),or(X_16,not(X)))),
    inference(subst,[],[axiom_1_4:[bind(A,$fot(not(X))),bind(B,$fot(X_16))]]) ).

cnf(refute_0_20,plain,
    implies(X,X_16) = or(not(X),X_16),
    inference(subst,[],[implies_definition:[bind(Y,$fot(X_16))]]) ).

cnf(refute_0_21,plain,
    ( implies(X,X_16) != or(not(X),X_16)
    | or(not(X),X_16) = implies(X,X_16) ),
    inference(subst,[],[refute_0_11:[bind(X0,$fot(implies(X,X_16))),bind(Y0,$fot(or(not(X),X_16)))]]) ).

cnf(refute_0_22,plain,
    or(not(X),X_16) = implies(X,X_16),
    inference(resolve,[$cnf( $equal(implies(X,X_16),or(not(X),X_16)) )],[refute_0_20,refute_0_21]) ).

cnf(refute_0_23,plain,
    ( or(not(X),X_16) != implies(X,X_16)
    | ~ axiom(implies(or(not(X),X_16),or(X_16,not(X))))
    | axiom(implies(implies(X,X_16),or(X_16,not(X)))) ),
    introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),X_16),or(X_16,not(X)))) ),[0,0],$fot(implies(X,X_16))]]) ).

cnf(refute_0_24,plain,
    ( ~ axiom(implies(or(not(X),X_16),or(X_16,not(X))))
    | axiom(implies(implies(X,X_16),or(X_16,not(X)))) ),
    inference(resolve,[$cnf( $equal(or(not(X),X_16),implies(X,X_16)) )],[refute_0_22,refute_0_23]) ).

cnf(refute_0_25,plain,
    axiom(implies(implies(X,X_16),or(X_16,not(X)))),
    inference(resolve,[$cnf( axiom(implies(or(not(X),X_16),or(X_16,not(X)))) )],[refute_0_19,refute_0_24]) ).

cnf(refute_0_26,plain,
    axiom(implies(implies(X_17,X_18),or(X_18,not(X_17)))),
    inference(subst,[],[refute_0_25:[bind(X,$fot(X_17)),bind(X_16,$fot(X_18))]]) ).

cnf(refute_0_27,plain,
    theorem(implies(implies(X_17,X_18),or(X_18,not(X_17)))),
    inference(resolve,[$cnf( axiom(implies(implies(X_17,X_18),or(X_18,not(X_17)))) )],[refute_0_26,refute_0_18]) ).

cnf(refute_0_28,plain,
    ( ~ theorem(implies(X_17,X_18))
    | ~ theorem(implies(implies(X_17,X_18),or(X_18,not(X_17))))
    | theorem(or(X_18,not(X_17))) ),
    inference(subst,[],[rule_2:[bind(X,$fot(or(X_18,not(X_17)))),bind(Y,$fot(implies(X_17,X_18)))]]) ).

cnf(refute_0_29,plain,
    ( ~ theorem(implies(X_17,X_18))
    | theorem(or(X_18,not(X_17))) ),
    inference(resolve,[$cnf( theorem(implies(implies(X_17,X_18),or(X_18,not(X_17)))) )],[refute_0_27,refute_0_28]) ).

cnf(refute_0_30,plain,
    ( ~ theorem(implies(X_95,implies(X_7,X_95)))
    | theorem(or(implies(X_7,X_95),not(X_95))) ),
    inference(subst,[],[refute_0_29:[bind(X_17,$fot(X_95)),bind(X_18,$fot(implies(X_7,X_95)))]]) ).

cnf(refute_0_31,plain,
    theorem(or(implies(X_7,X_95),not(X_95))),
    inference(resolve,[$cnf( theorem(implies(X_95,implies(X_7,X_95))) )],[refute_0_17,refute_0_30]) ).

cnf(refute_0_32,plain,
    theorem(or(implies(X_101,X_102),not(X_102))),
    inference(subst,[],[refute_0_31:[bind(X_7,$fot(X_101)),bind(X_95,$fot(X_102))]]) ).

cnf(refute_0_33,plain,
    theorem(or(X_4,or(implies(X_101,X_102),not(X_102)))),
    inference(resolve,[$cnf( theorem(or(implies(X_101,X_102),not(X_102))) )],[refute_0_32,refute_0_6]) ).

cnf(refute_0_34,plain,
    theorem(or(X_1007,or(implies(X_101,X_102),not(X_102)))),
    inference(subst,[],[refute_0_33:[bind(X_4,$fot(X_1007))]]) ).

cnf(refute_0_35,plain,
    ( ~ theorem(implies(or(X_62,or(X_63,X_64)),or(X_63,or(X_62,X_64))))
    | ~ theorem(or(X_62,or(X_63,X_64)))
    | theorem(or(X_63,or(X_62,X_64))) ),
    inference(subst,[],[rule_2:[bind(X,$fot(or(X_63,or(X_62,X_64)))),bind(Y,$fot(or(X_62,or(X_63,X_64))))]]) ).

cnf(refute_0_36,plain,
    ( ~ axiom(implies(or(X_19,or(X_20,X_21)),or(X_20,or(X_19,X_21))))
    | theorem(implies(or(X_19,or(X_20,X_21)),or(X_20,or(X_19,X_21)))) ),
    inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_19,or(X_20,X_21)),or(X_20,or(X_19,X_21)))))]]) ).

cnf(refute_0_37,plain,
    axiom(implies(or(X_19,or(X_20,X_21)),or(X_20,or(X_19,X_21)))),
    inference(subst,[],[axiom_1_5:[bind(A,$fot(X_19)),bind(B,$fot(X_20)),bind(C,$fot(X_21))]]) ).

cnf(refute_0_38,plain,
    theorem(implies(or(X_19,or(X_20,X_21)),or(X_20,or(X_19,X_21)))),
    inference(resolve,[$cnf( axiom(implies(or(X_19,or(X_20,X_21)),or(X_20,or(X_19,X_21)))) )],[refute_0_37,refute_0_36]) ).

cnf(refute_0_39,plain,
    theorem(implies(or(X_62,or(X_63,X_64)),or(X_63,or(X_62,X_64)))),
    inference(subst,[],[refute_0_38:[bind(X_19,$fot(X_62)),bind(X_20,$fot(X_63)),bind(X_21,$fot(X_64))]]) ).

cnf(refute_0_40,plain,
    ( ~ theorem(or(X_62,or(X_63,X_64)))
    | theorem(or(X_63,or(X_62,X_64))) ),
    inference(resolve,[$cnf( theorem(implies(or(X_62,or(X_63,X_64)),or(X_63,or(X_62,X_64)))) )],[refute_0_39,refute_0_35]) ).

cnf(refute_0_41,plain,
    ( ~ theorem(or(X_1007,or(implies(X_101,X_102),not(X_102))))
    | theorem(or(implies(X_101,X_102),or(X_1007,not(X_102)))) ),
    inference(subst,[],[refute_0_40:[bind(X_62,$fot(X_1007)),bind(X_63,$fot(implies(X_101,X_102))),bind(X_64,$fot(not(X_102)))]]) ).

cnf(refute_0_42,plain,
    theorem(or(implies(X_101,X_102),or(X_1007,not(X_102)))),
    inference(resolve,[$cnf( theorem(or(X_1007,or(implies(X_101,X_102),not(X_102)))) )],[refute_0_34,refute_0_41]) ).

cnf(refute_0_43,plain,
    theorem(or(implies(X_1015,X_1016),or(not(X),not(X_1016)))),
    inference(subst,[],[refute_0_42:[bind(X_1007,$fot(not(X))),bind(X_101,$fot(X_1015)),bind(X_102,$fot(X_1016))]]) ).

cnf(refute_0_44,plain,
    implies(X,not(X_1016)) = or(not(X),not(X_1016)),
    inference(subst,[],[implies_definition:[bind(Y,$fot(not(X_1016)))]]) ).

cnf(refute_0_45,plain,
    ( implies(X,not(X_1016)) != or(not(X),not(X_1016))
    | or(not(X),not(X_1016)) = implies(X,not(X_1016)) ),
    inference(subst,[],[refute_0_11:[bind(X0,$fot(implies(X,not(X_1016)))),bind(Y0,$fot(or(not(X),not(X_1016))))]]) ).

cnf(refute_0_46,plain,
    or(not(X),not(X_1016)) = implies(X,not(X_1016)),
    inference(resolve,[$cnf( $equal(implies(X,not(X_1016)),or(not(X),not(X_1016))) )],[refute_0_44,refute_0_45]) ).

cnf(refute_0_47,plain,
    ( or(not(X),not(X_1016)) != implies(X,not(X_1016))
    | ~ theorem(or(implies(X_1015,X_1016),or(not(X),not(X_1016))))
    | theorem(or(implies(X_1015,X_1016),implies(X,not(X_1016)))) ),
    introduced(tautology,[equality,[$cnf( theorem(or(implies(X_1015,X_1016),or(not(X),not(X_1016)))) ),[0,1],$fot(implies(X,not(X_1016)))]]) ).

cnf(refute_0_48,plain,
    ( ~ theorem(or(implies(X_1015,X_1016),or(not(X),not(X_1016))))
    | theorem(or(implies(X_1015,X_1016),implies(X,not(X_1016)))) ),
    inference(resolve,[$cnf( $equal(or(not(X),not(X_1016)),implies(X,not(X_1016))) )],[refute_0_46,refute_0_47]) ).

cnf(refute_0_49,plain,
    theorem(or(implies(X_1015,X_1016),implies(X,not(X_1016)))),
    inference(resolve,[$cnf( theorem(or(implies(X_1015,X_1016),or(not(X),not(X_1016)))) )],[refute_0_43,refute_0_48]) ).

cnf(refute_0_50,plain,
    theorem(or(implies(p,q),implies(p,not(q)))),
    inference(subst,[],[refute_0_49:[bind(X,$fot(p)),bind(X_1015,$fot(p)),bind(X_1016,$fot(q))]]) ).

cnf(refute_0_51,plain,
    $false,
    inference(resolve,[$cnf( theorem(or(implies(p,q),implies(p,not(q)))) )],[refute_0_50,prove_this]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : LCL321-3 : TPTP v8.1.0. Released v2.3.0.
% 0.04/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n029.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sun Jul  3 19:04:41 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.48/0.66  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.48/0.66  
% 0.48/0.66  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.48/0.66  
%------------------------------------------------------------------------------