TSTP Solution File: SET075-6 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET075-6 : 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 : n003.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 14:32:47 EDT 2023

% Result   : Unsatisfiable 0.19s 0.62s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   62
% Syntax   : Number of formulae    :   88 (  17 unt;  51 typ;   0 def)
%            Number of atoms       :   62 (  15 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   49 (  24   ~;  25   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   65 (  39   >;  26   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-3 aty)
%            Number of functors    :   42 (  42 usr;  12 con; 0-3 aty)
%            Number of variables   :   53 (  12 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,
    x: $i ).

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

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

tff(decl_72,type,
    v: $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(cartesian_product2,axiom,
    ( member(X2,X4)
    | ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).

cnf(prove_corollary_to_unordered_pair_axiom3_1,negated_conjecture,
    member(ordered_pair(x,y),cross_product(u,v)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_unordered_pair_axiom3_1) ).

cnf(intersection1,axiom,
    ( member(X1,X2)
    | ~ member(X1,intersection(X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).

cnf(regularity2,axiom,
    ( X1 = null_class
    | intersection(X1,regular(X1)) = null_class ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity2) ).

cnf(unordered_pair3,axiom,
    ( member(X1,unordered_pair(X2,X1))
    | ~ member(X1,universal_class) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).

cnf(prove_corollary_to_unordered_pair_axiom3_2,negated_conjecture,
    unordered_pair(x,y) = null_class,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_unordered_pair_axiom3_2) ).

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(class_elements_are_sets,axiom,
    subclass(X1,universal_class),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).

cnf(complement1,axiom,
    ( ~ member(X1,complement(X2))
    | ~ member(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).

cnf(c_0_11,axiom,
    unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
    ordered_pair ).

cnf(c_0_12,axiom,
    unordered_pair(X1,X1) = singleton(X1),
    singleton_set ).

cnf(c_0_13,axiom,
    ( member(X2,X4)
    | ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
    cartesian_product2 ).

cnf(c_0_14,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_11,c_0_12]),c_0_12]) ).

cnf(c_0_15,negated_conjecture,
    member(ordered_pair(x,y),cross_product(u,v)),
    prove_corollary_to_unordered_pair_axiom3_1 ).

cnf(c_0_16,plain,
    ( member(X2,X4)
    | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4)) ),
    inference(rw,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_17,negated_conjecture,
    member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),cross_product(u,v)),
    inference(rw,[status(thm)],[c_0_15,c_0_14]) ).

cnf(c_0_18,axiom,
    ( member(X1,X2)
    | ~ member(X1,intersection(X2,X3)) ),
    intersection1 ).

cnf(c_0_19,axiom,
    ( X1 = null_class
    | intersection(X1,regular(X1)) = null_class ),
    regularity2 ).

cnf(c_0_20,axiom,
    ( member(X1,unordered_pair(X2,X1))
    | ~ member(X1,universal_class) ),
    unordered_pair3 ).

cnf(c_0_21,negated_conjecture,
    unordered_pair(x,y) = null_class,
    prove_corollary_to_unordered_pair_axiom3_2 ).

cnf(c_0_22,axiom,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    subclass_members ).

cnf(c_0_23,negated_conjecture,
    member(y,v),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_24,plain,
    ( X1 = null_class
    | member(X2,X1)
    | ~ member(X2,null_class) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_25,negated_conjecture,
    ( member(y,null_class)
    | ~ member(y,universal_class) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_26,negated_conjecture,
    ( member(y,X1)
    | ~ subclass(v,X1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_27,axiom,
    subclass(X1,universal_class),
    class_elements_are_sets ).

cnf(c_0_28,negated_conjecture,
    ( X1 = null_class
    | member(y,X1)
    | ~ member(y,universal_class) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_29,negated_conjecture,
    member(y,universal_class),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_30,axiom,
    ( ~ member(X1,complement(X2))
    | ~ member(X1,X2) ),
    complement1 ).

cnf(c_0_31,negated_conjecture,
    ( X1 = null_class
    | member(y,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).

cnf(c_0_32,negated_conjecture,
    ( complement(X1) = null_class
    | ~ member(y,X1) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_33,negated_conjecture,
    ( ~ member(X1,null_class)
    | ~ member(y,X2)
    | ~ member(X1,X2) ),
    inference(spm,[status(thm)],[c_0_30,c_0_32]) ).

cnf(c_0_34,negated_conjecture,
    member(y,null_class),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_29])]) ).

cnf(c_0_35,negated_conjecture,
    ~ member(y,X1),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_36,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[c_0_23,c_0_35]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET075-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n003.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 12:52:39 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.60  start to proof: theBenchmark
% 0.19/0.62  % Version  : CSE_E---1.5
% 0.19/0.62  % Problem  : theBenchmark.p
% 0.19/0.62  % Proof found
% 0.19/0.62  % SZS status Theorem for theBenchmark.p
% 0.19/0.62  % SZS output start Proof
% See solution above
% 0.19/0.63  % Total time : 0.020000 s
% 0.19/0.63  % SZS output end Proof
% 0.19/0.63  % Total time : 0.024000 s
%------------------------------------------------------------------------------