TSTP Solution File: SET023-3 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET023-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n021.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  : 300s
% DateTime : Thu Aug 31 14:32:15 EDT 2023

% Result   : Unsatisfiable 0.20s 0.67s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   81
% Syntax   : Number of formulae    :   95 (  10 unt;  73 typ;   0 def)
%            Number of atoms       :   37 (  12 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   32 (  17   ~;  15   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  122 (  66   >;  56   *;   0   +;   0  <<)
%            Number of predicates  :   15 (  13 usr;   1 prp; 0-5 aty)
%            Number of functors    :   60 (  60 usr;   7 con; 0-5 aty)
%            Number of variables   :   23 (   0 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    member: ( $i * $i ) > $o ).

tff(decl_23,type,
    little_set: $i > $o ).

tff(decl_24,type,
    f1: ( $i * $i ) > $i ).

tff(decl_25,type,
    non_ordered_pair: ( $i * $i ) > $i ).

tff(decl_26,type,
    singleton_set: $i > $i ).

tff(decl_27,type,
    ordered_pair: ( $i * $i ) > $i ).

tff(decl_28,type,
    ordered_pair_predicate: $i > $o ).

tff(decl_29,type,
    f2: $i > $i ).

tff(decl_30,type,
    f3: $i > $i ).

tff(decl_31,type,
    first: $i > $i ).

tff(decl_32,type,
    f4: ( $i * $i ) > $i ).

tff(decl_33,type,
    f5: ( $i * $i ) > $i ).

tff(decl_34,type,
    second: $i > $i ).

tff(decl_35,type,
    f6: ( $i * $i ) > $i ).

tff(decl_36,type,
    f7: ( $i * $i ) > $i ).

tff(decl_37,type,
    estin: $i ).

tff(decl_38,type,
    intersection: ( $i * $i ) > $i ).

tff(decl_39,type,
    complement: $i > $i ).

tff(decl_40,type,
    union: ( $i * $i ) > $i ).

tff(decl_41,type,
    domain_of: $i > $i ).

tff(decl_42,type,
    f8: ( $i * $i ) > $i ).

tff(decl_43,type,
    cross_product: ( $i * $i ) > $i ).

tff(decl_44,type,
    converse: $i > $i ).

tff(decl_45,type,
    rotate_right: $i > $i ).

tff(decl_46,type,
    f9: ( $i * $i ) > $i ).

tff(decl_47,type,
    f10: ( $i * $i ) > $i ).

tff(decl_48,type,
    f11: ( $i * $i ) > $i ).

tff(decl_49,type,
    flip_range_of: $i > $i ).

tff(decl_50,type,
    f12: ( $i * $i ) > $i ).

tff(decl_51,type,
    f13: ( $i * $i ) > $i ).

tff(decl_52,type,
    f14: ( $i * $i ) > $i ).

tff(decl_53,type,
    successor: $i > $i ).

tff(decl_54,type,
    empty_set: $i ).

tff(decl_55,type,
    universal_set: $i ).

tff(decl_56,type,
    infinity: $i ).

tff(decl_57,type,
    sigma: $i > $i ).

tff(decl_58,type,
    f16: ( $i * $i ) > $i ).

tff(decl_59,type,
    subset: ( $i * $i ) > $o ).

tff(decl_60,type,
    f17: ( $i * $i ) > $i ).

tff(decl_61,type,
    proper_subset: ( $i * $i ) > $o ).

tff(decl_62,type,
    powerset: $i > $i ).

tff(decl_63,type,
    relation: $i > $o ).

tff(decl_64,type,
    f18: $i > $i ).

tff(decl_65,type,
    single_valued_set: $i > $o ).

tff(decl_66,type,
    f19: $i > $i ).

tff(decl_67,type,
    f20: $i > $i ).

tff(decl_68,type,
    f21: $i > $i ).

tff(decl_69,type,
    function: $i > $o ).

tff(decl_70,type,
    image: ( $i * $i ) > $i ).

tff(decl_71,type,
    f22: ( $i * $i * $i ) > $i ).

tff(decl_72,type,
    disjoint: ( $i * $i ) > $o ).

tff(decl_73,type,
    f23: ( $i * $i ) > $i ).

tff(decl_74,type,
    f24: $i > $i ).

tff(decl_75,type,
    f25: $i ).

tff(decl_76,type,
    f26: $i > $i ).

tff(decl_77,type,
    range_of: $i > $i ).

tff(decl_78,type,
    f27: ( $i * $i ) > $i ).

tff(decl_79,type,
    identity_relation: $i ).

tff(decl_80,type,
    restrict: ( $i * $i ) > $i ).

tff(decl_81,type,
    one_to_one_function: $i > $o ).

tff(decl_82,type,
    apply: ( $i * $i ) > $i ).

tff(decl_83,type,
    f28: ( $i * $i * $i ) > $i ).

tff(decl_84,type,
    apply_to_two_arguments: ( $i * $i * $i ) > $i ).

tff(decl_85,type,
    maps: ( $i * $i * $i ) > $o ).

tff(decl_86,type,
    closed: ( $i * $i ) > $o ).

tff(decl_87,type,
    compose: ( $i * $i ) > $i ).

tff(decl_88,type,
    f29: ( $i * $i * $i ) > $i ).

tff(decl_89,type,
    f30: ( $i * $i * $i ) > $i ).

tff(decl_90,type,
    f31: ( $i * $i * $i ) > $i ).

tff(decl_91,type,
    homomorphism: ( $i * $i * $i * $i * $i ) > $o ).

tff(decl_92,type,
    f32: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_93,type,
    f33: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_94,type,
    a: $i ).

cnf(ordered_pair,axiom,
    ordered_pair(X1,X2) = non_ordered_pair(singleton_set(X1),non_ordered_pair(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair) ).

cnf(singleton_set,axiom,
    singleton_set(X1) = non_ordered_pair(X1,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',singleton_set) ).

cnf(property_of_second,axiom,
    ( second(ordered_pair(X1,X2)) = X2
    | ~ little_set(X1)
    | ~ little_set(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_second) ).

cnf(ordered_pair_predicate3,axiom,
    ( X1 = ordered_pair(f2(X1),f3(X1))
    | ~ ordered_pair_predicate(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair_predicate3) ).

cnf(ordered_pair_predicate1,axiom,
    ( little_set(f2(X1))
    | ~ ordered_pair_predicate(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair_predicate1) ).

cnf(ordered_pair_predicate2,axiom,
    ( little_set(f3(X1))
    | ~ ordered_pair_predicate(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair_predicate2) ).

cnf(prove_second_component_is_small,negated_conjecture,
    ~ little_set(second(a)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_second_component_is_small) ).

cnf(an_ordered_pair_predicate,hypothesis,
    ordered_pair_predicate(a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an_ordered_pair_predicate) ).

cnf(c_0_8,axiom,
    ordered_pair(X1,X2) = non_ordered_pair(singleton_set(X1),non_ordered_pair(X1,X2)),
    ordered_pair ).

cnf(c_0_9,axiom,
    singleton_set(X1) = non_ordered_pair(X1,X1),
    singleton_set ).

cnf(c_0_10,axiom,
    ( second(ordered_pair(X1,X2)) = X2
    | ~ little_set(X1)
    | ~ little_set(X2) ),
    property_of_second ).

cnf(c_0_11,plain,
    ordered_pair(X1,X2) = non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)),
    inference(rw,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_12,axiom,
    ( X1 = ordered_pair(f2(X1),f3(X1))
    | ~ ordered_pair_predicate(X1) ),
    ordered_pair_predicate3 ).

cnf(c_0_13,plain,
    ( second(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))) = X2
    | ~ little_set(X2)
    | ~ little_set(X1) ),
    inference(rw,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_14,plain,
    ( X1 = non_ordered_pair(non_ordered_pair(f2(X1),f2(X1)),non_ordered_pair(f2(X1),f3(X1)))
    | ~ ordered_pair_predicate(X1) ),
    inference(rw,[status(thm)],[c_0_12,c_0_11]) ).

cnf(c_0_15,axiom,
    ( little_set(f2(X1))
    | ~ ordered_pair_predicate(X1) ),
    ordered_pair_predicate1 ).

cnf(c_0_16,axiom,
    ( little_set(f3(X1))
    | ~ ordered_pair_predicate(X1) ),
    ordered_pair_predicate2 ).

cnf(c_0_17,plain,
    ( f3(X1) = second(X1)
    | ~ ordered_pair_predicate(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16]) ).

cnf(c_0_18,negated_conjecture,
    ~ little_set(second(a)),
    prove_second_component_is_small ).

cnf(c_0_19,plain,
    ( little_set(second(X1))
    | ~ ordered_pair_predicate(X1) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_20,hypothesis,
    ordered_pair_predicate(a),
    an_ordered_pair_predicate ).

cnf(c_0_21,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET023-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n021.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    : 300
% 0.13/0.34  % DateTime   : Sat Aug 26 14:54:12 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.61  start to proof: theBenchmark
% 0.20/0.67  % Version  : CSE_E---1.5
% 0.20/0.67  % Problem  : theBenchmark.p
% 0.20/0.67  % Proof found
% 0.20/0.67  % SZS status Theorem for theBenchmark.p
% 0.20/0.67  % SZS output start Proof
% See solution above
% 0.20/0.68  % Total time : 0.051000 s
% 0.20/0.68  % SZS output end Proof
% 0.20/0.68  % Total time : 0.057000 s
%------------------------------------------------------------------------------