TSTP Solution File: SET038-3 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET038-3 : 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 : n019.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 14:32:25 EDT 2023

% Result   : Unsatisfiable 2.61s 2.72s
% Output   : CNFRefutation 2.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   97
% Syntax   : Number of formulae    :  143 (  23 unt;  76 typ;   0 def)
%            Number of atoms       :  139 (  32 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  146 (  74   ~;  72   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    4 (   1 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    :   63 (  63 usr;  10 con; 0-5 aty)
%            Number of variables   :   91 (   8 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_function: $i ).

tff(decl_95,type,
    a_domain: $i ).

tff(decl_96,type,
    a_range: $i ).

tff(decl_97,type,
    a: $i ).

cnf(maps2,axiom,
    ( domain_of(X1) = X2
    | ~ maps(X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',maps2) ).

cnf(a_mapping,hypothesis,
    maps(a_function,a_domain,a_range),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_mapping) ).

cnf(domain2,axiom,
    ( member(f8(X1,X2),X2)
    | ~ member(X1,domain_of(X2)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',domain2) ).

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(member_of_domain,hypothesis,
    member(a,a_domain),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_domain) ).

cnf(apply_for_functions1,axiom,
    ( apply(X3,X1) = X2
    | ~ little_set(X1)
    | ~ little_set(X2)
    | ~ function(X3)
    | ~ member(ordered_pair(X1,X2),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply_for_functions1) ).

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(relation1,axiom,
    ( ordered_pair_predicate(X2)
    | ~ relation(X1)
    | ~ member(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',relation1) ).

cnf(maps1,axiom,
    ( function(X1)
    | ~ maps(X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',maps1) ).

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(function1,axiom,
    ( relation(X1)
    | ~ function(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',function1) ).

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

cnf(domain3,axiom,
    ( X1 = first(f8(X1,X2))
    | ~ member(X1,domain_of(X2)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',domain3) ).

cnf(maps3,axiom,
    ( subset(range_of(X1),X3)
    | ~ maps(X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',maps3) ).

cnf(range_of4,axiom,
    ( member(X1,range_of(X2))
    | ~ little_set(X1)
    | ~ ordered_pair_predicate(X3)
    | ~ member(X3,X2)
    | X1 != second(X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',range_of4) ).

cnf(second_component_is_small,axiom,
    ( little_set(second(X1))
    | ~ ordered_pair_predicate(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',second_component_is_small) ).

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(subset1,axiom,
    ( member(X3,X2)
    | ~ subset(X1,X2)
    | ~ member(X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',subset1) ).

cnf(prove_mapping_in_range,negated_conjecture,
    ~ member(apply(a_function,a),a_range),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_mapping_in_range) ).

cnf(c_0_21,axiom,
    ( domain_of(X1) = X2
    | ~ maps(X1,X2,X3) ),
    maps2 ).

cnf(c_0_22,hypothesis,
    maps(a_function,a_domain,a_range),
    a_mapping ).

cnf(c_0_23,axiom,
    ( member(f8(X1,X2),X2)
    | ~ member(X1,domain_of(X2)) ),
    domain2 ).

cnf(c_0_24,hypothesis,
    domain_of(a_function) = a_domain,
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_25,axiom,
    ordered_pair(X1,X2) = non_ordered_pair(singleton_set(X1),non_ordered_pair(X1,X2)),
    ordered_pair ).

cnf(c_0_26,axiom,
    singleton_set(X1) = non_ordered_pair(X1,X1),
    singleton_set ).

cnf(c_0_27,hypothesis,
    ( member(f8(X1,a_function),a_function)
    | ~ member(X1,a_domain) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_28,hypothesis,
    member(a,a_domain),
    member_of_domain ).

cnf(c_0_29,axiom,
    ( apply(X3,X1) = X2
    | ~ little_set(X1)
    | ~ little_set(X2)
    | ~ function(X3)
    | ~ member(ordered_pair(X1,X2),X3) ),
    apply_for_functions1 ).

cnf(c_0_30,plain,
    ordered_pair(X1,X2) = non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)),
    inference(rw,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_31,axiom,
    ( X1 = ordered_pair(f2(X1),f3(X1))
    | ~ ordered_pair_predicate(X1) ),
    ordered_pair_predicate3 ).

cnf(c_0_32,axiom,
    ( ordered_pair_predicate(X2)
    | ~ relation(X1)
    | ~ member(X2,X1) ),
    relation1 ).

cnf(c_0_33,hypothesis,
    member(f8(a,a_function),a_function),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_34,axiom,
    ( function(X1)
    | ~ maps(X1,X2,X3) ),
    maps1 ).

cnf(c_0_35,plain,
    ( apply(X3,X1) = X2
    | ~ little_set(X2)
    | ~ little_set(X1)
    | ~ function(X3)
    | ~ member(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)),X3) ),
    inference(rw,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_36,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_31,c_0_30]) ).

cnf(c_0_37,axiom,
    ( little_set(f2(X1))
    | ~ ordered_pair_predicate(X1) ),
    ordered_pair_predicate1 ).

cnf(c_0_38,axiom,
    ( little_set(f3(X1))
    | ~ ordered_pair_predicate(X1) ),
    ordered_pair_predicate2 ).

cnf(c_0_39,hypothesis,
    ( ordered_pair_predicate(f8(a,a_function))
    | ~ relation(a_function) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_40,axiom,
    ( relation(X1)
    | ~ function(X1) ),
    function1 ).

cnf(c_0_41,hypothesis,
    function(a_function),
    inference(spm,[status(thm)],[c_0_34,c_0_22]) ).

cnf(c_0_42,axiom,
    ( first(ordered_pair(X1,X2)) = X1
    | ~ little_set(X1)
    | ~ little_set(X2) ),
    property_of_first ).

cnf(c_0_43,axiom,
    ( X1 = first(f8(X1,X2))
    | ~ member(X1,domain_of(X2)) ),
    domain3 ).

cnf(c_0_44,axiom,
    ( subset(range_of(X1),X3)
    | ~ maps(X1,X2,X3) ),
    maps3 ).

cnf(c_0_45,axiom,
    ( member(X1,range_of(X2))
    | ~ little_set(X1)
    | ~ ordered_pair_predicate(X3)
    | ~ member(X3,X2)
    | X1 != second(X3) ),
    range_of4 ).

cnf(c_0_46,axiom,
    ( little_set(second(X1))
    | ~ ordered_pair_predicate(X1) ),
    second_component_is_small ).

cnf(c_0_47,axiom,
    ( second(ordered_pair(X1,X2)) = X2
    | ~ little_set(X1)
    | ~ little_set(X2) ),
    property_of_second ).

cnf(c_0_48,plain,
    ( apply(X1,f2(X2)) = f3(X2)
    | ~ function(X1)
    | ~ ordered_pair_predicate(X2)
    | ~ member(X2,X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_38]) ).

cnf(c_0_49,hypothesis,
    ordered_pair_predicate(f8(a,a_function)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]) ).

cnf(c_0_50,plain,
    ( first(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))) = X1
    | ~ little_set(X2)
    | ~ little_set(X1) ),
    inference(rw,[status(thm)],[c_0_42,c_0_30]) ).

cnf(c_0_51,hypothesis,
    ( first(f8(X1,a_function)) = X1
    | ~ member(X1,a_domain) ),
    inference(spm,[status(thm)],[c_0_43,c_0_24]) ).

cnf(c_0_52,axiom,
    ( member(X3,X2)
    | ~ subset(X1,X2)
    | ~ member(X3,X1) ),
    subset1 ).

cnf(c_0_53,hypothesis,
    subset(range_of(a_function),a_range),
    inference(spm,[status(thm)],[c_0_44,c_0_22]) ).

cnf(c_0_54,plain,
    ( member(second(X1),range_of(X2))
    | ~ ordered_pair_predicate(X1)
    | ~ member(X1,X2) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_45]),c_0_46]) ).

cnf(c_0_55,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_47,c_0_30]) ).

cnf(c_0_56,hypothesis,
    apply(a_function,f2(f8(a,a_function))) = f3(f8(a,a_function)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_33]),c_0_41]),c_0_49])]) ).

cnf(c_0_57,plain,
    ( f2(X1) = first(X1)
    | ~ ordered_pair_predicate(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_36]),c_0_37]),c_0_38]) ).

cnf(c_0_58,hypothesis,
    first(f8(a,a_function)) = a,
    inference(spm,[status(thm)],[c_0_51,c_0_28]) ).

cnf(c_0_59,hypothesis,
    ( member(X1,a_range)
    | ~ member(X1,range_of(a_function)) ),
    inference(spm,[status(thm)],[c_0_52,c_0_53]) ).

cnf(c_0_60,hypothesis,
    member(second(f8(a,a_function)),range_of(a_function)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_33]),c_0_49])]) ).

cnf(c_0_61,plain,
    ( f3(X1) = second(X1)
    | ~ ordered_pair_predicate(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_36]),c_0_37]),c_0_38]) ).

cnf(c_0_62,hypothesis,
    f3(f8(a,a_function)) = apply(a_function,a),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),c_0_49])]) ).

cnf(c_0_63,hypothesis,
    member(second(f8(a,a_function)),a_range),
    inference(spm,[status(thm)],[c_0_59,c_0_60]) ).

cnf(c_0_64,hypothesis,
    second(f8(a,a_function)) = apply(a_function,a),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_49])]) ).

cnf(c_0_65,negated_conjecture,
    ~ member(apply(a_function,a),a_range),
    prove_mapping_in_range ).

cnf(c_0_66,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64]),c_0_65]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET038-3 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n019.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 08:59:28 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 2.61/2.72  % Version  : CSE_E---1.5
% 2.61/2.72  % Problem  : theBenchmark.p
% 2.61/2.72  % Proof found
% 2.61/2.72  % SZS status Theorem for theBenchmark.p
% 2.61/2.72  % SZS output start Proof
% See solution above
% 2.61/2.73  % Total time : 2.144000 s
% 2.61/2.73  % SZS output end Proof
% 2.61/2.73  % Total time : 2.150000 s
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