%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET012-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 : Tue Jul 19 03:31:04 EDT 2022

% Result   : Unsatisfiable 0.14s 0.37s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   21
% Syntax   : Number of clauses     :   65 (  15 unt;  20 nHn;  54 RR)
%            Number of literals    :  139 (  63 equ;  57 neg)
%            Maximal clause size   :    3 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   47 (   1 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(a2,axiom,
    ( ~ member(X,Y)
    | little_set(X) ) ).

cnf(extensionality1,axiom,
    ( little_set(f1(X,Y))
    | X = Y ) ).

cnf(extensionality2,axiom,
    ( member(f1(X,Y),X)
    | member(f1(X,Y),Y)
    | X = Y ) ).

cnf(extensionality3,axiom,
    ( ~ member(f1(X,Y),X)
    | ~ member(f1(X,Y),Y)
    | X = Y ) ).

cnf(complement1,axiom,
    ( ~ member(Z,complement(X))
    | ~ member(Z,X) ) ).

cnf(complement2,axiom,
    ( member(Z,complement(X))
    | ~ little_set(Z)
    | member(Z,X) ) ).

cnf(complement_of_a_is_b,hypothesis,
    complement(as) = bs ).

cnf(complement_of_b_is_c,hypothesis,
    complement(bs) = cs ).

cnf(prove_a_equals_c,negated_conjecture,
    as != cs ).

cnf(refute_0_0,plain,
    ( ~ member(X_9,as)
    | ~ member(X_9,complement(as)) ),
    inference(subst,[],[complement1:[bind(X,$fot(as)),bind(Z,$fot(X_9))]]) ).

cnf(refute_0_1,plain,
    ( complement(as) != bs
    | ~ member(X_9,bs)
    | member(X_9,complement(as)) ),
    introduced(tautology,[equality,[$cnf( ~ member(X_9,complement(as)) ),[1],$fot(bs)]]) ).

cnf(refute_0_2,plain,
    ( ~ member(X_9,bs)
    | member(X_9,complement(as)) ),
    inference(resolve,[$cnf( $equal(complement(as),bs) )],[complement_of_a_is_b,refute_0_1]) ).

cnf(refute_0_3,plain,
    ( ~ member(X_9,as)
    | ~ member(X_9,bs) ),
    inference(resolve,[$cnf( member(X_9,complement(as)) )],[refute_0_2,refute_0_0]) ).

cnf(refute_0_4,plain,
    ( ~ member(f1(cs,as),as)
    | ~ member(f1(cs,as),bs) ),
    inference(subst,[],[refute_0_3:[bind(X_9,$fot(f1(cs,as)))]]) ).

cnf(refute_0_5,plain,
    ( ~ member(f1(cs,as),as)
    | ~ member(f1(cs,as),cs)
    | cs = as ),
    inference(subst,[],[extensionality3:[bind(X,$fot(cs)),bind(Y,$fot(as))]]) ).

cnf(refute_0_6,plain,
    ( ~ little_set(f1(cs,as))
    | member(f1(cs,as),X)
    | member(f1(cs,as),complement(X)) ),
    inference(subst,[],[complement2:[bind(Z,$fot(f1(cs,as)))]]) ).

cnf(refute_0_7,plain,
    ( ~ member(f1(cs,as),as)
    | little_set(f1(cs,as)) ),
    inference(subst,[],[a2:[bind(X,$fot(f1(cs,as))),bind(Y,$fot(as))]]) ).

cnf(refute_0_8,plain,
    ( ~ member(f1(complement(X),X_15),X)
    | ~ member(f1(complement(X),X_15),complement(X)) ),
    inference(subst,[],[complement1:[bind(Z,$fot(f1(complement(X),X_15)))]]) ).

cnf(refute_0_9,plain,
    ( complement(X) = X_15
    | member(f1(complement(X),X_15),X_15)
    | member(f1(complement(X),X_15),complement(X)) ),
    inference(subst,[],[extensionality2:[bind(X,$fot(complement(X))),bind(Y,$fot(X_15))]]) ).

cnf(refute_0_10,plain,
    ( ~ member(f1(complement(X),X_15),X)
    | complement(X) = X_15
    | member(f1(complement(X),X_15),X_15) ),
    inference(resolve,[$cnf( member(f1(complement(X),X_15),complement(X)) )],[refute_0_9,refute_0_8]) ).

cnf(refute_0_11,plain,
    ( ~ member(f1(complement(complement(X_32)),X_31),complement(X_32))
    | complement(complement(X_32)) = X_31
    | member(f1(complement(complement(X_32)),X_31),X_31) ),
    inference(subst,[],[refute_0_10:[bind(X,$fot(complement(X_32))),bind(X_15,$fot(X_31))]]) ).

cnf(refute_0_12,plain,
    ( ~ little_set(f1(X,Y))
    | member(f1(X,Y),X_12)
    | member(f1(X,Y),complement(X_12)) ),
    inference(subst,[],[complement2:[bind(X,$fot(X_12)),bind(Z,$fot(f1(X,Y)))]]) ).

cnf(refute_0_13,plain,
    ( X = Y
    | member(f1(X,Y),X_12)
    | member(f1(X,Y),complement(X_12)) ),
    inference(resolve,[$cnf( little_set(f1(X,Y)) )],[extensionality1,refute_0_12]) ).

cnf(refute_0_14,plain,
    ( complement(complement(X_32)) = X_31
    | member(f1(complement(complement(X_32)),X_31),X_32)
    | member(f1(complement(complement(X_32)),X_31),complement(X_32)) ),
    inference(subst,[],[refute_0_13:[bind(X,$fot(complement(complement(X_32)))),bind(Y,$fot(X_31)),bind(X_12,$fot(X_32))]]) ).

cnf(refute_0_15,plain,
    ( complement(complement(X_32)) = X_31
    | member(f1(complement(complement(X_32)),X_31),X_31)
    | member(f1(complement(complement(X_32)),X_31),X_32) ),
    inference(resolve,[$cnf( member(f1(complement(complement(X_32)),X_31),complement(X_32)) )],[refute_0_14,refute_0_11]) ).

cnf(refute_0_16,plain,
    ( complement(complement(as)) = as
    | member(f1(complement(complement(as)),as),as) ),
    inference(subst,[],[refute_0_15:[bind(X_31,$fot(as)),bind(X_32,$fot(as))]]) ).

cnf(refute_0_17,plain,
    ( complement(as) != bs
    | ~ member(f1(complement(complement(as)),as),as)
    | member(f1(complement(bs),as),as) ),
    introduced(tautology,[equality,[$cnf( member(f1(complement(complement(as)),as),as) ),[0,0,0],$fot(bs)]]) ).

cnf(refute_0_18,plain,
    ( ~ member(f1(complement(complement(as)),as),as)
    | member(f1(complement(bs),as),as) ),
    inference(resolve,[$cnf( $equal(complement(as),bs) )],[complement_of_a_is_b,refute_0_17]) ).

cnf(refute_0_19,plain,
    ( complement(complement(as)) = as
    | member(f1(complement(bs),as),as) ),
    inference(resolve,[$cnf( member(f1(complement(complement(as)),as),as) )],[refute_0_16,refute_0_18]) ).

cnf(refute_0_20,plain,
    complement(complement(as)) = complement(complement(as)),
    introduced(tautology,[refl,[$fot(complement(complement(as)))]]) ).

cnf(refute_0_21,plain,
    ( complement(as) != bs
    | complement(complement(as)) != complement(complement(as))
    | complement(complement(as)) = complement(bs) ),
    introduced(tautology,[equality,[$cnf( $equal(complement(complement(as)),complement(complement(as))) ),[1,0],$fot(bs)]]) ).

cnf(refute_0_22,plain,
    ( complement(as) != bs
    | complement(complement(as)) = complement(bs) ),
    inference(resolve,[$cnf( $equal(complement(complement(as)),complement(complement(as))) )],[refute_0_20,refute_0_21]) ).

cnf(refute_0_23,plain,
    complement(complement(as)) = complement(bs),
    inference(resolve,[$cnf( $equal(complement(as),bs) )],[complement_of_a_is_b,refute_0_22]) ).

cnf(refute_0_24,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_25,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_26,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_24,refute_0_25]) ).

cnf(refute_0_27,plain,
    ( Y0 != X0
    | Y0 != Z0
    | X0 = Z0 ),
    introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).

cnf(refute_0_28,plain,
    ( X0 != Y0
    | Y0 != Z0
    | X0 = Z0 ),
    inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_26,refute_0_27]) ).

cnf(refute_0_29,plain,
    ( complement(bs) != cs
    | complement(complement(as)) != complement(bs)
    | complement(complement(as)) = cs ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(complement(complement(as)))),bind(Y0,$fot(complement(bs))),bind(Z0,$fot(cs))]]) ).

cnf(refute_0_30,plain,
    ( complement(bs) != cs
    | complement(complement(as)) = cs ),
    inference(resolve,[$cnf( $equal(complement(complement(as)),complement(bs)) )],[refute_0_23,refute_0_29]) ).

cnf(refute_0_31,plain,
    complement(complement(as)) = cs,
    inference(resolve,[$cnf( $equal(complement(bs),cs) )],[complement_of_b_is_c,refute_0_30]) ).

cnf(refute_0_32,plain,
    ( complement(complement(as)) != as
    | complement(complement(as)) != cs
    | cs = as ),
    introduced(tautology,[equality,[$cnf( $equal(complement(complement(as)),as) ),[0],$fot(cs)]]) ).

cnf(refute_0_33,plain,
    ( complement(complement(as)) != as
    | cs = as ),
    inference(resolve,[$cnf( $equal(complement(complement(as)),cs) )],[refute_0_31,refute_0_32]) ).

cnf(refute_0_34,plain,
    ( cs = as
    | member(f1(complement(bs),as),as) ),
    inference(resolve,[$cnf( $equal(complement(complement(as)),as) )],[refute_0_19,refute_0_33]) ).

cnf(refute_0_35,plain,
    f1(complement(bs),as) = f1(complement(bs),as),
    introduced(tautology,[refl,[$fot(f1(complement(bs),as))]]) ).

cnf(refute_0_36,plain,
    ( complement(bs) != cs
    | f1(complement(bs),as) != f1(complement(bs),as)
    | f1(complement(bs),as) = f1(cs,as) ),
    introduced(tautology,[equality,[$cnf( $equal(f1(complement(bs),as),f1(complement(bs),as)) ),[1,0],$fot(cs)]]) ).

cnf(refute_0_37,plain,
    ( complement(bs) != cs
    | f1(complement(bs),as) = f1(cs,as) ),
    inference(resolve,[$cnf( $equal(f1(complement(bs),as),f1(complement(bs),as)) )],[refute_0_35,refute_0_36]) ).

cnf(refute_0_38,plain,
    f1(complement(bs),as) = f1(cs,as),
    inference(resolve,[$cnf( $equal(complement(bs),cs) )],[complement_of_b_is_c,refute_0_37]) ).

cnf(refute_0_39,plain,
    ( f1(complement(bs),as) != f1(cs,as)
    | ~ member(f1(complement(bs),as),as)
    | member(f1(cs,as),as) ),
    introduced(tautology,[equality,[$cnf( member(f1(complement(bs),as),as) ),[0],$fot(f1(cs,as))]]) ).

cnf(refute_0_40,plain,
    ( ~ member(f1(complement(bs),as),as)
    | member(f1(cs,as),as) ),
    inference(resolve,[$cnf( $equal(f1(complement(bs),as),f1(cs,as)) )],[refute_0_38,refute_0_39]) ).

cnf(refute_0_41,plain,
    ( cs = as
    | member(f1(cs,as),as) ),
    inference(resolve,[$cnf( member(f1(complement(bs),as),as) )],[refute_0_34,refute_0_40]) ).

cnf(refute_0_42,plain,
    ( cs != as
    | as = cs ),
    inference(subst,[],[refute_0_26:[bind(X0,$fot(cs)),bind(Y0,$fot(as))]]) ).

cnf(refute_0_43,plain,
    cs != as,
    inference(resolve,[$cnf( $equal(as,cs) )],[refute_0_42,prove_a_equals_c]) ).

cnf(refute_0_44,plain,
    member(f1(cs,as),as),
    inference(resolve,[$cnf( $equal(cs,as) )],[refute_0_41,refute_0_43]) ).

cnf(refute_0_45,plain,
    little_set(f1(cs,as)),
    inference(resolve,[$cnf( member(f1(cs,as),as) )],[refute_0_44,refute_0_7]) ).

cnf(refute_0_46,plain,
    ( member(f1(cs,as),X)
    | member(f1(cs,as),complement(X)) ),
    inference(resolve,[$cnf( little_set(f1(cs,as)) )],[refute_0_45,refute_0_6]) ).

cnf(refute_0_47,plain,
    ( member(f1(cs,as),bs)
    | member(f1(cs,as),complement(bs)) ),
    inference(subst,[],[refute_0_46:[bind(X,$fot(bs))]]) ).

cnf(refute_0_48,plain,
    ( complement(bs) != cs
    | ~ member(f1(cs,as),complement(bs))
    | member(f1(cs,as),cs) ),
    introduced(tautology,[equality,[$cnf( member(f1(cs,as),complement(bs)) ),[1],$fot(cs)]]) ).

cnf(refute_0_49,plain,
    ( ~ member(f1(cs,as),complement(bs))
    | member(f1(cs,as),cs) ),
    inference(resolve,[$cnf( $equal(complement(bs),cs) )],[complement_of_b_is_c,refute_0_48]) ).

cnf(refute_0_50,plain,
    ( member(f1(cs,as),bs)
    | member(f1(cs,as),cs) ),
    inference(resolve,[$cnf( member(f1(cs,as),complement(bs)) )],[refute_0_47,refute_0_49]) ).

cnf(refute_0_51,plain,
    ( ~ member(f1(cs,as),as)
    | cs = as
    | member(f1(cs,as),bs) ),
    inference(resolve,[$cnf( member(f1(cs,as),cs) )],[refute_0_50,refute_0_5]) ).

cnf(refute_0_52,plain,
    ( cs = as
    | member(f1(cs,as),bs) ),
    inference(resolve,[$cnf( member(f1(cs,as),as) )],[refute_0_44,refute_0_51]) ).

cnf(refute_0_53,plain,
    member(f1(cs,as),bs),
    inference(resolve,[$cnf( $equal(cs,as) )],[refute_0_52,refute_0_43]) ).

cnf(refute_0_54,plain,
    ~ member(f1(cs,as),as),
    inference(resolve,[$cnf( member(f1(cs,as),bs) )],[refute_0_53,refute_0_4]) ).

cnf(refute_0_55,plain,
    $false,
    inference(resolve,[$cnf( member(f1(cs,as),as) )],[refute_0_44,refute_0_54]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET012-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.13  % Command  : metis --show proof --show saturation %s
% 0.14/0.34  % Computer : n029.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Sun Jul 10 19:50:31 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.37  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.37  
% 0.14/0.37  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.14/0.38  
%------------------------------------------------------------------------------