TSTP Solution File: SET018-6 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET018-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n032.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 14:32:11 EDT 2023

% Result   : Unsatisfiable 0.13s 0.54s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   60
% Syntax   : Number of formulae    :  101 (  26 unt;  51 typ;   0 def)
%            Number of atoms       :   82 (  49 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   45 (  13   ~;  32   |;   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   :   29 (   8 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,
    w: $i ).

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

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

tff(decl_72,type,
    z: $i ).

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

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

cnf(prove_ordered_pair_determines_components2_1,negated_conjecture,
    ordered_pair(w,x) = ordered_pair(y,z),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordered_pair_determines_components2_1) ).

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

cnf(unordered_pairs_in_universal,axiom,
    member(unordered_pair(X1,X2),universal_class),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pairs_in_universal) ).

cnf(unordered_pair_member,axiom,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,unordered_pair(X2,X3)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).

cnf(unordered_pair2,axiom,
    ( member(X1,unordered_pair(X1,X2))
    | ~ member(X1,universal_class) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).

cnf(prove_ordered_pair_determines_components2_2,negated_conjecture,
    member(x,universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordered_pair_determines_components2_2) ).

cnf(prove_ordered_pair_determines_components2_3,negated_conjecture,
    x != z,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordered_pair_determines_components2_3) ).

cnf(c_0_9,axiom,
    unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
    ordered_pair ).

cnf(c_0_10,axiom,
    unordered_pair(X1,X1) = singleton(X1),
    singleton_set ).

cnf(c_0_11,negated_conjecture,
    ordered_pair(w,x) = ordered_pair(y,z),
    prove_ordered_pair_determines_components2_1 ).

cnf(c_0_12,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_9,c_0_10]),c_0_10]) ).

cnf(c_0_13,axiom,
    ( member(X1,unordered_pair(X2,X1))
    | ~ member(X1,universal_class) ),
    unordered_pair3 ).

cnf(c_0_14,negated_conjecture,
    unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))) = unordered_pair(unordered_pair(w,w),unordered_pair(w,unordered_pair(x,x))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_12]) ).

cnf(c_0_15,axiom,
    member(unordered_pair(X1,X2),universal_class),
    unordered_pairs_in_universal ).

cnf(c_0_16,axiom,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,unordered_pair(X2,X3)) ),
    unordered_pair_member ).

cnf(c_0_17,negated_conjecture,
    member(unordered_pair(w,unordered_pair(x,x)),unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).

cnf(c_0_18,negated_conjecture,
    ( unordered_pair(w,unordered_pair(x,x)) = unordered_pair(y,unordered_pair(z,z))
    | unordered_pair(w,unordered_pair(x,x)) = unordered_pair(y,y) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_19,negated_conjecture,
    ( unordered_pair(w,unordered_pair(x,x)) = unordered_pair(y,y)
    | member(unordered_pair(x,x),unordered_pair(y,unordered_pair(z,z))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_18]),c_0_15])]) ).

cnf(c_0_20,axiom,
    ( member(X1,unordered_pair(X1,X2))
    | ~ member(X1,universal_class) ),
    unordered_pair2 ).

cnf(c_0_21,negated_conjecture,
    ( unordered_pair(w,unordered_pair(x,x)) = unordered_pair(y,y)
    | unordered_pair(z,z) = unordered_pair(x,x)
    | unordered_pair(x,x) = y ),
    inference(spm,[status(thm)],[c_0_16,c_0_19]) ).

cnf(c_0_22,negated_conjecture,
    member(unordered_pair(w,w),unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_14]),c_0_15])]) ).

cnf(c_0_23,negated_conjecture,
    ( unordered_pair(z,z) = unordered_pair(x,x)
    | unordered_pair(x,x) = y
    | member(unordered_pair(x,x),unordered_pair(y,y)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_21]),c_0_15])]) ).

cnf(c_0_24,negated_conjecture,
    ( unordered_pair(y,unordered_pair(z,z)) = unordered_pair(w,w)
    | unordered_pair(w,w) = unordered_pair(y,y) ),
    inference(spm,[status(thm)],[c_0_16,c_0_22]) ).

cnf(c_0_25,negated_conjecture,
    ( unordered_pair(z,z) = unordered_pair(x,x)
    | unordered_pair(x,x) = y ),
    inference(spm,[status(thm)],[c_0_16,c_0_23]) ).

cnf(c_0_26,negated_conjecture,
    ( unordered_pair(w,w) = unordered_pair(y,y)
    | member(unordered_pair(z,z),unordered_pair(w,w)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_24]),c_0_15])]) ).

cnf(c_0_27,negated_conjecture,
    ( unordered_pair(x,x) = y
    | X1 = z
    | ~ member(X1,unordered_pair(x,x)) ),
    inference(spm,[status(thm)],[c_0_16,c_0_25]) ).

cnf(c_0_28,negated_conjecture,
    member(x,universal_class),
    prove_ordered_pair_determines_components2_2 ).

cnf(c_0_29,negated_conjecture,
    x != z,
    prove_ordered_pair_determines_components2_3 ).

cnf(c_0_30,negated_conjecture,
    ( unordered_pair(w,w) = unordered_pair(y,y)
    | unordered_pair(z,z) = w ),
    inference(spm,[status(thm)],[c_0_16,c_0_26]) ).

cnf(c_0_31,negated_conjecture,
    unordered_pair(x,x) = y,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_20]),c_0_28])]),c_0_29]) ).

cnf(c_0_32,negated_conjecture,
    ( unordered_pair(z,z) = w
    | X1 = w
    | ~ member(X1,unordered_pair(y,y)) ),
    inference(spm,[status(thm)],[c_0_16,c_0_30]) ).

cnf(c_0_33,negated_conjecture,
    ( unordered_pair(w,w) = unordered_pair(y,y)
    | member(y,unordered_pair(w,w))
    | ~ member(y,universal_class) ),
    inference(spm,[status(thm)],[c_0_20,c_0_24]) ).

cnf(c_0_34,negated_conjecture,
    member(y,universal_class),
    inference(spm,[status(thm)],[c_0_15,c_0_31]) ).

cnf(c_0_35,negated_conjecture,
    ( unordered_pair(z,z) = w
    | w = y
    | ~ member(y,universal_class) ),
    inference(spm,[status(thm)],[c_0_32,c_0_20]) ).

cnf(c_0_36,negated_conjecture,
    ( unordered_pair(w,w) = unordered_pair(y,y)
    | member(y,unordered_pair(w,w)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]) ).

cnf(c_0_37,negated_conjecture,
    ( unordered_pair(z,z) = w
    | w = y ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_34])]) ).

cnf(c_0_38,negated_conjecture,
    ( unordered_pair(w,w) = unordered_pair(y,y)
    | w = y ),
    inference(spm,[status(thm)],[c_0_16,c_0_36]) ).

cnf(c_0_39,negated_conjecture,
    ( w = y
    | member(w,universal_class) ),
    inference(spm,[status(thm)],[c_0_15,c_0_37]) ).

cnf(c_0_40,negated_conjecture,
    ( w = y
    | member(w,unordered_pair(y,y)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_38]),c_0_39]) ).

cnf(c_0_41,negated_conjecture,
    w = y,
    inference(spm,[status(thm)],[c_0_16,c_0_40]) ).

cnf(c_0_42,negated_conjecture,
    unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))) = unordered_pair(unordered_pair(y,y),unordered_pair(y,y)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_31]),c_0_41]),c_0_41]),c_0_41]) ).

cnf(c_0_43,negated_conjecture,
    member(unordered_pair(y,unordered_pair(z,z)),unordered_pair(unordered_pair(y,y),unordered_pair(y,y))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_42]),c_0_15])]) ).

cnf(c_0_44,negated_conjecture,
    unordered_pair(y,unordered_pair(z,z)) = unordered_pair(y,y),
    inference(spm,[status(thm)],[c_0_16,c_0_43]) ).

cnf(c_0_45,negated_conjecture,
    member(unordered_pair(z,z),unordered_pair(y,y)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_44]),c_0_15])]) ).

cnf(c_0_46,negated_conjecture,
    unordered_pair(z,z) = y,
    inference(spm,[status(thm)],[c_0_16,c_0_45]) ).

cnf(c_0_47,negated_conjecture,
    ( X1 = z
    | ~ member(X1,y) ),
    inference(spm,[status(thm)],[c_0_16,c_0_46]) ).

cnf(c_0_48,negated_conjecture,
    member(x,y),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_31]),c_0_28])]) ).

cnf(c_0_49,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_29]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : SET018-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.09  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.28  % Computer : n032.cluster.edu
% 0.11/0.28  % Model    : x86_64 x86_64
% 0.11/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.28  % Memory   : 8042.1875MB
% 0.11/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.28  % CPULimit   : 300
% 0.11/0.28  % WCLimit    : 300
% 0.11/0.28  % DateTime   : Sat Aug 26 14:32:28 EDT 2023
% 0.11/0.29  % CPUTime  : 
% 0.13/0.48  start to proof: theBenchmark
% 0.13/0.54  % Version  : CSE_E---1.5
% 0.13/0.54  % Problem  : theBenchmark.p
% 0.13/0.54  % Proof found
% 0.13/0.54  % SZS status Theorem for theBenchmark.p
% 0.13/0.54  % SZS output start Proof
% See solution above
% 0.13/0.55  % Total time : 0.058000 s
% 0.13/0.55  % SZS output end Proof
% 0.13/0.55  % Total time : 0.062000 s
%------------------------------------------------------------------------------