TSTP Solution File: SET235-6 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET235-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n008.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 14:33:42 EDT 2023

% Result   : Unsatisfiable 0.93s 1.03s
% Output   : CNFRefutation 0.93s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   66
% Syntax   : Number of formulae    :   82 (  14 unt;  58 typ;   0 def)
%            Number of atoms       :   37 (   9 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   27 (  14   ~;  13   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   72 (  44   >;  28   *;   0   +;   0  <<)
%            Number of predicates  :   12 (  10 usr;   1 prp; 0-3 aty)
%            Number of functors    :   48 (  48 usr;  14 con; 0-3 aty)
%            Number of variables   :   32 (   6 sgn;   0   !;   0   ?;   0   :)

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

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

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

tff(decl_25,type,
    universal_class: $i ).

tff(decl_26,type,
    unordered_pair: ( $i * $i ) > $i ).

tff(decl_27,type,
    singleton: $i > $i ).

tff(decl_28,type,
    ordered_pair: ( $i * $i ) > $i ).

tff(decl_29,type,
    cross_product: ( $i * $i ) > $i ).

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

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

tff(decl_32,type,
    element_relation: $i ).

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

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

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

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

tff(decl_37,type,
    restrict: ( $i * $i * $i ) > $i ).

tff(decl_38,type,
    null_class: $i ).

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

tff(decl_40,type,
    rotate: $i > $i ).

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

tff(decl_42,type,
    inverse: $i > $i ).

tff(decl_43,type,
    range_of: $i > $i ).

tff(decl_44,type,
    domain: ( $i * $i * $i ) > $i ).

tff(decl_45,type,
    range: ( $i * $i * $i ) > $i ).

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

tff(decl_47,type,
    successor: $i > $i ).

tff(decl_48,type,
    successor_relation: $i ).

tff(decl_49,type,
    inductive: $i > $o ).

tff(decl_50,type,
    omega: $i ).

tff(decl_51,type,
    sum_class: $i > $i ).

tff(decl_52,type,
    power_class: $i > $i ).

tff(decl_53,type,
    compose: ( $i * $i ) > $i ).

tff(decl_54,type,
    single_valued_class: $i > $o ).

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

tff(decl_56,type,
    function: $i > $o ).

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

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

tff(decl_59,type,
    choice: $i ).

tff(decl_60,type,
    one_to_one: $i > $o ).

tff(decl_61,type,
    subset_relation: $i ).

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

tff(decl_63,type,
    cantor: $i > $i ).

tff(decl_64,type,
    operation: $i > $o ).

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

tff(decl_66,type,
    homomorphism: ( $i * $i * $i ) > $o ).

tff(decl_67,type,
    not_homomorphism1: ( $i * $i * $i ) > $i ).

tff(decl_68,type,
    not_homomorphism2: ( $i * $i * $i ) > $i ).

tff(decl_69,type,
    compose_class: $i > $i ).

tff(decl_70,type,
    composition_function: $i ).

tff(decl_71,type,
    domain_relation: $i ).

tff(decl_72,type,
    single_valued1: $i > $i ).

tff(decl_73,type,
    single_valued2: $i > $i ).

tff(decl_74,type,
    single_valued3: $i > $i ).

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

tff(decl_76,type,
    application_function: $i ).

tff(decl_77,type,
    maps: ( $i * $i * $i ) > $o ).

tff(decl_78,type,
    x: $i ).

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

cnf(ordered_pair,axiom,
    unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',ordered_pair) ).

cnf(singleton_set,axiom,
    unordered_pair(X1,X1) = singleton(X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).

cnf(subclass_members,axiom,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).

cnf(not_subclass_members1,axiom,
    ( member(not_subclass_element(X1,X2),X1)
    | subclass(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).

cnf(cartesian_product4,axiom,
    ( ordered_pair(first(X1),second(X1)) = X1
    | ~ member(X1,cross_product(X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).

cnf(prove_cross_product_property10_1,negated_conjecture,
    subclass(x,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cross_product_property10_1) ).

cnf(prove_cross_product_property10_2,negated_conjecture,
    ~ member(ordered_pair(first(not_subclass_element(x,y)),second(not_subclass_element(x,y))),x),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cross_product_property10_2) ).

cnf(prove_cross_product_property10_3,negated_conjecture,
    ~ subclass(x,y),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cross_product_property10_3) ).

cnf(c_0_8,axiom,
    unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
    ordered_pair ).

cnf(c_0_9,axiom,
    unordered_pair(X1,X1) = singleton(X1),
    singleton_set ).

cnf(c_0_10,axiom,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    subclass_members ).

cnf(c_0_11,axiom,
    ( member(not_subclass_element(X1,X2),X1)
    | subclass(X1,X2) ),
    not_subclass_members1 ).

cnf(c_0_12,axiom,
    ( ordered_pair(first(X1),second(X1)) = X1
    | ~ member(X1,cross_product(X2,X3)) ),
    cartesian_product4 ).

cnf(c_0_13,plain,
    unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))) = ordered_pair(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9]),c_0_9]) ).

cnf(c_0_14,plain,
    ( member(not_subclass_element(X1,X2),X3)
    | subclass(X1,X2)
    | ~ subclass(X1,X3) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_15,negated_conjecture,
    subclass(x,cross_product(universal_class,universal_class)),
    prove_cross_product_property10_1 ).

cnf(c_0_16,negated_conjecture,
    ~ member(ordered_pair(first(not_subclass_element(x,y)),second(not_subclass_element(x,y))),x),
    prove_cross_product_property10_2 ).

cnf(c_0_17,plain,
    ( unordered_pair(unordered_pair(first(X1),first(X1)),unordered_pair(first(X1),unordered_pair(second(X1),second(X1)))) = X1
    | ~ member(X1,cross_product(X2,X3)) ),
    inference(rw,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_18,negated_conjecture,
    ( member(not_subclass_element(x,X1),cross_product(universal_class,universal_class))
    | subclass(x,X1) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_19,negated_conjecture,
    ~ member(unordered_pair(unordered_pair(first(not_subclass_element(x,y)),first(not_subclass_element(x,y))),unordered_pair(first(not_subclass_element(x,y)),unordered_pair(second(not_subclass_element(x,y)),second(not_subclass_element(x,y))))),x),
    inference(rw,[status(thm)],[c_0_16,c_0_13]) ).

cnf(c_0_20,negated_conjecture,
    ( unordered_pair(unordered_pair(first(not_subclass_element(x,X1)),first(not_subclass_element(x,X1))),unordered_pair(first(not_subclass_element(x,X1)),unordered_pair(second(not_subclass_element(x,X1)),second(not_subclass_element(x,X1))))) = not_subclass_element(x,X1)
    | subclass(x,X1) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_21,negated_conjecture,
    ~ subclass(x,y),
    prove_cross_product_property10_3 ).

cnf(c_0_22,negated_conjecture,
    ~ member(not_subclass_element(x,y),x),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).

cnf(c_0_23,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_11]),c_0_21]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET235-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.18/0.35  % Computer : n008.cluster.edu
% 0.18/0.35  % Model    : x86_64 x86_64
% 0.18/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35  % Memory   : 8042.1875MB
% 0.18/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35  % CPULimit   : 300
% 0.18/0.35  % WCLimit    : 300
% 0.18/0.35  % DateTime   : Sat Aug 26 15:07:18 EDT 2023
% 0.21/0.35  % CPUTime  : 
% 0.21/0.52  start to proof: theBenchmark
% 0.93/1.03  % Version  : CSE_E---1.5
% 0.93/1.03  % Problem  : theBenchmark.p
% 0.93/1.03  % Proof found
% 0.93/1.03  % SZS status Theorem for theBenchmark.p
% 0.93/1.03  % SZS output start Proof
% See solution above
% 0.93/1.03  % Total time : 0.495000 s
% 0.93/1.03  % SZS output end Proof
% 0.93/1.03  % Total time : 0.500000 s
%------------------------------------------------------------------------------