TSTP Solution File: SET016-1 by Metis---2.4

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET016-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n011.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 03:31:11 EDT 2022

% Result   : Unsatisfiable 0.13s 0.39s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   14
% Syntax   : Number of clauses     :   49 (  21 unt;   9 nHn;  40 RR)
%            Number of literals    :   88 (  50 equ;  32 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   45 (   3 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(singleton_1,axiom,
    member(X,singleton_set(X)) ).

cnf(singleton_2,axiom,
    ( ~ member(X,singleton_set(Y))
    | X = Y ) ).

cnf(unordered_pair_1,axiom,
    member(X,unordered_pair(X,Y)) ).

cnf(unordered_pair_3,axiom,
    ( ~ member(X,unordered_pair(Y,Z))
    | X = Y
    | X = Z ) ).

cnf(ordered_pair,axiom,
    ordered_pair(X,Y) = unordered_pair(singleton_set(X),unordered_pair(X,Y)) ).

cnf(equal_ordered_pairs,hypothesis,
    ordered_pair(m1,r1) = ordered_pair(m2,r2) ).

cnf(prove_first_components_equal,negated_conjecture,
    m1 != m2 ).

cnf(refute_0_0,plain,
    ( ~ member(m2,singleton_set(m1))
    | m2 = m1 ),
    inference(subst,[],[singleton_2:[bind(X,$fot(m2)),bind(Y,$fot(m1))]]) ).

cnf(refute_0_1,plain,
    member(m2,singleton_set(m2)),
    inference(subst,[],[singleton_1:[bind(X,$fot(m2))]]) ).

cnf(refute_0_2,plain,
    ( ~ member(m1,singleton_set(m2))
    | m1 = m2 ),
    inference(subst,[],[singleton_2:[bind(X,$fot(m1)),bind(Y,$fot(m2))]]) ).

cnf(refute_0_3,plain,
    member(m1,unordered_pair(m1,r1)),
    inference(subst,[],[unordered_pair_1:[bind(X,$fot(m1)),bind(Y,$fot(r1))]]) ).

cnf(refute_0_4,plain,
    member(singleton_set(X_5),unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6))),
    inference(subst,[],[unordered_pair_1:[bind(X,$fot(singleton_set(X_5))),bind(Y,$fot(unordered_pair(X_5,X_6)))]]) ).

cnf(refute_0_5,plain,
    ordered_pair(X_5,X_6) = unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6)),
    inference(subst,[],[ordered_pair:[bind(X,$fot(X_5)),bind(Y,$fot(X_6))]]) ).

cnf(refute_0_6,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_7,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_8,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( ordered_pair(X_5,X_6) != unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6))
    | unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6)) = ordered_pair(X_5,X_6) ),
    inference(subst,[],[refute_0_8:[bind(X0,$fot(ordered_pair(X_5,X_6))),bind(Y0,$fot(unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6))))]]) ).

cnf(refute_0_10,plain,
    unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6)) = ordered_pair(X_5,X_6),
    inference(resolve,[$cnf( $equal(ordered_pair(X_5,X_6),unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6))) )],[refute_0_5,refute_0_9]) ).

cnf(refute_0_11,plain,
    ( unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6)) != ordered_pair(X_5,X_6)
    | ~ member(singleton_set(X_5),unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6)))
    | member(singleton_set(X_5),ordered_pair(X_5,X_6)) ),
    introduced(tautology,[equality,[$cnf( member(singleton_set(X_5),unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6))) ),[1],$fot(ordered_pair(X_5,X_6))]]) ).

cnf(refute_0_12,plain,
    ( ~ member(singleton_set(X_5),unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6)))
    | member(singleton_set(X_5),ordered_pair(X_5,X_6)) ),
    inference(resolve,[$cnf( $equal(unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6)),ordered_pair(X_5,X_6)) )],[refute_0_10,refute_0_11]) ).

cnf(refute_0_13,plain,
    member(singleton_set(X_5),ordered_pair(X_5,X_6)),
    inference(resolve,[$cnf( member(singleton_set(X_5),unordered_pair(singleton_set(X_5),unordered_pair(X_5,X_6))) )],[refute_0_4,refute_0_12]) ).

cnf(refute_0_14,plain,
    member(singleton_set(m2),ordered_pair(m2,r2)),
    inference(subst,[],[refute_0_13:[bind(X_5,$fot(m2)),bind(X_6,$fot(r2))]]) ).

cnf(refute_0_15,plain,
    ( ordered_pair(m1,r1) != ordered_pair(m2,r2)
    | ordered_pair(m2,r2) = ordered_pair(m1,r1) ),
    inference(subst,[],[refute_0_8:[bind(X0,$fot(ordered_pair(m1,r1))),bind(Y0,$fot(ordered_pair(m2,r2)))]]) ).

cnf(refute_0_16,plain,
    ordered_pair(m2,r2) = ordered_pair(m1,r1),
    inference(resolve,[$cnf( $equal(ordered_pair(m1,r1),ordered_pair(m2,r2)) )],[equal_ordered_pairs,refute_0_15]) ).

cnf(refute_0_17,plain,
    ( ordered_pair(m2,r2) != ordered_pair(m1,r1)
    | ~ member(singleton_set(m2),ordered_pair(m2,r2))
    | member(singleton_set(m2),ordered_pair(m1,r1)) ),
    introduced(tautology,[equality,[$cnf( member(singleton_set(m2),ordered_pair(m2,r2)) ),[1],$fot(ordered_pair(m1,r1))]]) ).

cnf(refute_0_18,plain,
    ( ~ member(singleton_set(m2),ordered_pair(m2,r2))
    | member(singleton_set(m2),ordered_pair(m1,r1)) ),
    inference(resolve,[$cnf( $equal(ordered_pair(m2,r2),ordered_pair(m1,r1)) )],[refute_0_16,refute_0_17]) ).

cnf(refute_0_19,plain,
    member(singleton_set(m2),ordered_pair(m1,r1)),
    inference(resolve,[$cnf( member(singleton_set(m2),ordered_pair(m2,r2)) )],[refute_0_14,refute_0_18]) ).

cnf(refute_0_20,plain,
    ( ~ member(X_21,unordered_pair(singleton_set(X),unordered_pair(X,Y)))
    | X_21 = singleton_set(X)
    | X_21 = unordered_pair(X,Y) ),
    inference(subst,[],[unordered_pair_3:[bind(X,$fot(X_21)),bind(Y,$fot(singleton_set(X))),bind(Z,$fot(unordered_pair(X,Y)))]]) ).

cnf(refute_0_21,plain,
    ( ordered_pair(X,Y) != unordered_pair(singleton_set(X),unordered_pair(X,Y))
    | unordered_pair(singleton_set(X),unordered_pair(X,Y)) = ordered_pair(X,Y) ),
    inference(subst,[],[refute_0_8:[bind(X0,$fot(ordered_pair(X,Y))),bind(Y0,$fot(unordered_pair(singleton_set(X),unordered_pair(X,Y))))]]) ).

cnf(refute_0_22,plain,
    unordered_pair(singleton_set(X),unordered_pair(X,Y)) = ordered_pair(X,Y),
    inference(resolve,[$cnf( $equal(ordered_pair(X,Y),unordered_pair(singleton_set(X),unordered_pair(X,Y))) )],[ordered_pair,refute_0_21]) ).

cnf(refute_0_23,plain,
    ( unordered_pair(singleton_set(X),unordered_pair(X,Y)) != ordered_pair(X,Y)
    | ~ member(X_21,ordered_pair(X,Y))
    | member(X_21,unordered_pair(singleton_set(X),unordered_pair(X,Y))) ),
    introduced(tautology,[equality,[$cnf( ~ member(X_21,unordered_pair(singleton_set(X),unordered_pair(X,Y))) ),[1],$fot(ordered_pair(X,Y))]]) ).

cnf(refute_0_24,plain,
    ( ~ member(X_21,ordered_pair(X,Y))
    | member(X_21,unordered_pair(singleton_set(X),unordered_pair(X,Y))) ),
    inference(resolve,[$cnf( $equal(unordered_pair(singleton_set(X),unordered_pair(X,Y)),ordered_pair(X,Y)) )],[refute_0_22,refute_0_23]) ).

cnf(refute_0_25,plain,
    ( ~ member(X_21,ordered_pair(X,Y))
    | X_21 = singleton_set(X)
    | X_21 = unordered_pair(X,Y) ),
    inference(resolve,[$cnf( member(X_21,unordered_pair(singleton_set(X),unordered_pair(X,Y))) )],[refute_0_24,refute_0_20]) ).

cnf(refute_0_26,plain,
    ( ~ member(singleton_set(m2),ordered_pair(m1,r1))
    | singleton_set(m2) = singleton_set(m1)
    | singleton_set(m2) = unordered_pair(m1,r1) ),
    inference(subst,[],[refute_0_25:[bind(X,$fot(m1)),bind(Y,$fot(r1)),bind(X_21,$fot(singleton_set(m2)))]]) ).

cnf(refute_0_27,plain,
    ( singleton_set(m2) = singleton_set(m1)
    | singleton_set(m2) = unordered_pair(m1,r1) ),
    inference(resolve,[$cnf( member(singleton_set(m2),ordered_pair(m1,r1)) )],[refute_0_19,refute_0_26]) ).

cnf(refute_0_28,plain,
    ( singleton_set(m2) != unordered_pair(m1,r1)
    | unordered_pair(m1,r1) = singleton_set(m2) ),
    inference(subst,[],[refute_0_8:[bind(X0,$fot(singleton_set(m2))),bind(Y0,$fot(unordered_pair(m1,r1)))]]) ).

cnf(refute_0_29,plain,
    ( singleton_set(m2) = singleton_set(m1)
    | unordered_pair(m1,r1) = singleton_set(m2) ),
    inference(resolve,[$cnf( $equal(singleton_set(m2),unordered_pair(m1,r1)) )],[refute_0_27,refute_0_28]) ).

cnf(refute_0_30,plain,
    ( unordered_pair(m1,r1) != singleton_set(m2)
    | ~ member(m1,unordered_pair(m1,r1))
    | member(m1,singleton_set(m2)) ),
    introduced(tautology,[equality,[$cnf( member(m1,unordered_pair(m1,r1)) ),[1],$fot(singleton_set(m2))]]) ).

cnf(refute_0_31,plain,
    ( ~ member(m1,unordered_pair(m1,r1))
    | singleton_set(m2) = singleton_set(m1)
    | member(m1,singleton_set(m2)) ),
    inference(resolve,[$cnf( $equal(unordered_pair(m1,r1),singleton_set(m2)) )],[refute_0_29,refute_0_30]) ).

cnf(refute_0_32,plain,
    ( singleton_set(m2) = singleton_set(m1)
    | member(m1,singleton_set(m2)) ),
    inference(resolve,[$cnf( member(m1,unordered_pair(m1,r1)) )],[refute_0_3,refute_0_31]) ).

cnf(refute_0_33,plain,
    ( m1 = m2
    | singleton_set(m2) = singleton_set(m1) ),
    inference(resolve,[$cnf( member(m1,singleton_set(m2)) )],[refute_0_32,refute_0_2]) ).

cnf(refute_0_34,plain,
    singleton_set(m2) = singleton_set(m1),
    inference(resolve,[$cnf( $equal(m1,m2) )],[refute_0_33,prove_first_components_equal]) ).

cnf(refute_0_35,plain,
    ( singleton_set(m2) != singleton_set(m1)
    | ~ member(m2,singleton_set(m2))
    | member(m2,singleton_set(m1)) ),
    introduced(tautology,[equality,[$cnf( member(m2,singleton_set(m2)) ),[1],$fot(singleton_set(m1))]]) ).

cnf(refute_0_36,plain,
    ( ~ member(m2,singleton_set(m2))
    | member(m2,singleton_set(m1)) ),
    inference(resolve,[$cnf( $equal(singleton_set(m2),singleton_set(m1)) )],[refute_0_34,refute_0_35]) ).

cnf(refute_0_37,plain,
    member(m2,singleton_set(m1)),
    inference(resolve,[$cnf( member(m2,singleton_set(m2)) )],[refute_0_1,refute_0_36]) ).

cnf(refute_0_38,plain,
    m2 = m1,
    inference(resolve,[$cnf( member(m2,singleton_set(m1)) )],[refute_0_37,refute_0_0]) ).

cnf(refute_0_39,plain,
    ( m2 != m1
    | m1 = m2 ),
    inference(subst,[],[refute_0_8:[bind(X0,$fot(m2)),bind(Y0,$fot(m1))]]) ).

cnf(refute_0_40,plain,
    m2 != m1,
    inference(resolve,[$cnf( $equal(m1,m2) )],[refute_0_39,prove_first_components_equal]) ).

cnf(refute_0_41,plain,
    $false,
    inference(resolve,[$cnf( $equal(m2,m1) )],[refute_0_38,refute_0_40]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SET016-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12  % Command  : metis --show proof --show saturation %s
% 0.13/0.33  % Computer : n011.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 : Sun Jul 10 16:40:41 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.39  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.39  
% 0.13/0.39  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.40  
%------------------------------------------------------------------------------