TSTP Solution File: SET734+4 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET734+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n020.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 14:35:23 EDT 2023

% Result   : Theorem 0.95s 1.04s
% Output   : CNFRefutation 0.95s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   78
% Syntax   : Number of formulae    :   96 (   7 unt;  74 typ;   0 def)
%            Number of atoms       :   86 (   0 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  101 (  37   ~;  37   |;  19   &)
%                                         (   3 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  249 (  69   >; 180   *;   0   +;   0  <<)
%            Number of predicates  :   16 (  15 usr;   1 prp; 0-6 aty)
%            Number of functors    :   59 (  59 usr;   5 con; 0-8 aty)
%            Number of variables   :   70 (   0 sgn;  43   !;   2   ?;   0   :)

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

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

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

tff(decl_25,type,
    power_set: $i > $i ).

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

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

tff(decl_28,type,
    empty_set: $i ).

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

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

tff(decl_31,type,
    unordered_pair: ( $i * $i ) > $i ).

tff(decl_32,type,
    sum: $i > $i ).

tff(decl_33,type,
    product: $i > $i ).

tff(decl_34,type,
    maps: ( $i * $i * $i ) > $o ).

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

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

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

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

tff(decl_39,type,
    identity: ( $i * $i ) > $o ).

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

tff(decl_41,type,
    surjective: ( $i * $i * $i ) > $o ).

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

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

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

tff(decl_45,type,
    image2: ( $i * $i ) > $i ).

tff(decl_46,type,
    image3: ( $i * $i * $i ) > $i ).

tff(decl_47,type,
    inverse_image2: ( $i * $i ) > $i ).

tff(decl_48,type,
    inverse_image3: ( $i * $i * $i ) > $i ).

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

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

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

tff(decl_52,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_53,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_54,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_55,type,
    esk4_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_56,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_57,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_58,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_59,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_60,type,
    esk9_8: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_61,type,
    esk10_6: ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_62,type,
    esk11_6: ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_63,type,
    esk12_6: ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_64,type,
    esk13_7: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_65,type,
    esk14_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_66,type,
    esk15_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_67,type,
    esk16_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_68,type,
    esk17_2: ( $i * $i ) > $i ).

tff(decl_69,type,
    esk18_3: ( $i * $i * $i ) > $i ).

tff(decl_70,type,
    esk19_3: ( $i * $i * $i ) > $i ).

tff(decl_71,type,
    esk20_3: ( $i * $i * $i ) > $i ).

tff(decl_72,type,
    esk21_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_73,type,
    esk22_3: ( $i * $i * $i ) > $i ).

tff(decl_74,type,
    esk23_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_75,type,
    esk24_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_76,type,
    esk25_3: ( $i * $i * $i ) > $i ).

tff(decl_77,type,
    esk26_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_78,type,
    esk27_3: ( $i * $i * $i ) > $i ).

tff(decl_79,type,
    esk28_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_80,type,
    esk29_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_81,type,
    esk30_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_82,type,
    esk31_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_83,type,
    esk32_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_84,type,
    esk33_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_85,type,
    esk34_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_86,type,
    esk35_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_87,type,
    esk36_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_88,type,
    esk37_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_89,type,
    esk38_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_90,type,
    esk39_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_91,type,
    esk40_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_92,type,
    esk41_0: $i ).

tff(decl_93,type,
    esk42_0: $i ).

tff(decl_94,type,
    esk43_0: $i ).

tff(decl_95,type,
    esk44_0: $i ).

fof(thII25,conjecture,
    ! [X6,X10,X1,X2] :
      ( ( maps(X10,X1,X2)
        & maps(X6,X2,X1)
        & identity(compose_function(X10,X6,X2,X1,X2),X2) )
     => surjective(X10,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII25) ).

fof(identity,axiom,
    ! [X6,X1] :
      ( identity(X6,X1)
    <=> ! [X3] :
          ( member(X3,X1)
         => apply(X6,X3,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',identity) ).

fof(surjective,axiom,
    ! [X6,X1,X2] :
      ( surjective(X6,X1,X2)
    <=> ! [X5] :
          ( member(X5,X2)
         => ? [X4] :
              ( member(X4,X1)
              & apply(X6,X4,X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',surjective) ).

fof(compose_function,axiom,
    ! [X10,X6,X1,X2,X11,X3,X12] :
      ( ( member(X3,X1)
        & member(X12,X11) )
     => ( apply(compose_function(X10,X6,X1,X2,X11),X3,X12)
      <=> ? [X5] :
            ( member(X5,X2)
            & apply(X6,X3,X5)
            & apply(X10,X5,X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',compose_function) ).

fof(c_0_4,negated_conjecture,
    ~ ! [X6,X10,X1,X2] :
        ( ( maps(X10,X1,X2)
          & maps(X6,X2,X1)
          & identity(compose_function(X10,X6,X2,X1,X2),X2) )
       => surjective(X10,X1,X2) ),
    inference(assume_negation,[status(cth)],[thII25]) ).

fof(c_0_5,plain,
    ! [X113,X114,X115,X116,X117] :
      ( ( ~ identity(X113,X114)
        | ~ member(X115,X114)
        | apply(X113,X115,X115) )
      & ( member(esk17_2(X116,X117),X117)
        | identity(X116,X117) )
      & ( ~ apply(X116,esk17_2(X116,X117),esk17_2(X116,X117))
        | identity(X116,X117) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[identity])])])])])]) ).

fof(c_0_6,negated_conjecture,
    ( maps(esk42_0,esk43_0,esk44_0)
    & maps(esk41_0,esk44_0,esk43_0)
    & identity(compose_function(esk42_0,esk41_0,esk44_0,esk43_0,esk44_0),esk44_0)
    & ~ surjective(esk42_0,esk43_0,esk44_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

fof(c_0_7,plain,
    ! [X131,X132,X133,X134,X136,X137,X138,X140] :
      ( ( member(esk21_4(X131,X132,X133,X134),X132)
        | ~ member(X134,X133)
        | ~ surjective(X131,X132,X133) )
      & ( apply(X131,esk21_4(X131,X132,X133,X134),X134)
        | ~ member(X134,X133)
        | ~ surjective(X131,X132,X133) )
      & ( member(esk22_3(X136,X137,X138),X138)
        | surjective(X136,X137,X138) )
      & ( ~ member(X140,X137)
        | ~ apply(X136,X140,esk22_3(X136,X137,X138))
        | surjective(X136,X137,X138) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[surjective])])])])])]) ).

cnf(c_0_8,plain,
    ( apply(X1,X3,X3)
    | ~ identity(X1,X2)
    | ~ member(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,negated_conjecture,
    identity(compose_function(esk42_0,esk41_0,esk44_0,esk43_0,esk44_0),esk44_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    ~ surjective(esk42_0,esk43_0,esk44_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,plain,
    ( member(esk22_3(X1,X2,X3),X3)
    | surjective(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_12,plain,
    ! [X90,X91,X92,X93,X94,X95,X96,X98] :
      ( ( member(esk13_7(X90,X91,X92,X93,X94,X95,X96),X93)
        | ~ apply(compose_function(X90,X91,X92,X93,X94),X95,X96)
        | ~ member(X95,X92)
        | ~ member(X96,X94) )
      & ( apply(X91,X95,esk13_7(X90,X91,X92,X93,X94,X95,X96))
        | ~ apply(compose_function(X90,X91,X92,X93,X94),X95,X96)
        | ~ member(X95,X92)
        | ~ member(X96,X94) )
      & ( apply(X90,esk13_7(X90,X91,X92,X93,X94,X95,X96),X96)
        | ~ apply(compose_function(X90,X91,X92,X93,X94),X95,X96)
        | ~ member(X95,X92)
        | ~ member(X96,X94) )
      & ( ~ member(X98,X93)
        | ~ apply(X91,X95,X98)
        | ~ apply(X90,X98,X96)
        | apply(compose_function(X90,X91,X92,X93,X94),X95,X96)
        | ~ member(X95,X92)
        | ~ member(X96,X94) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[compose_function])])])])]) ).

cnf(c_0_13,negated_conjecture,
    ( apply(compose_function(esk42_0,esk41_0,esk44_0,esk43_0,esk44_0),X1,X1)
    | ~ member(X1,esk44_0) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_14,negated_conjecture,
    member(esk22_3(esk42_0,esk43_0,esk44_0),esk44_0),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_15,plain,
    ( apply(X1,esk13_7(X1,X2,X3,X4,X5,X6,X7),X7)
    | ~ apply(compose_function(X1,X2,X3,X4,X5),X6,X7)
    | ~ member(X6,X3)
    | ~ member(X7,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_16,negated_conjecture,
    apply(compose_function(esk42_0,esk41_0,esk44_0,esk43_0,esk44_0),esk22_3(esk42_0,esk43_0,esk44_0),esk22_3(esk42_0,esk43_0,esk44_0)),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_17,plain,
    ( member(esk13_7(X1,X2,X3,X4,X5,X6,X7),X4)
    | ~ apply(compose_function(X1,X2,X3,X4,X5),X6,X7)
    | ~ member(X6,X3)
    | ~ member(X7,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_18,plain,
    ( surjective(X3,X2,X4)
    | ~ member(X1,X2)
    | ~ apply(X3,X1,esk22_3(X3,X2,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_19,negated_conjecture,
    apply(esk42_0,esk13_7(esk42_0,esk41_0,esk44_0,esk43_0,esk44_0,esk22_3(esk42_0,esk43_0,esk44_0),esk22_3(esk42_0,esk43_0,esk44_0)),esk22_3(esk42_0,esk43_0,esk44_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_14])]) ).

cnf(c_0_20,negated_conjecture,
    member(esk13_7(esk42_0,esk41_0,esk44_0,esk43_0,esk44_0,esk22_3(esk42_0,esk43_0,esk44_0),esk22_3(esk42_0,esk43_0,esk44_0)),esk43_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_16]),c_0_14])]) ).

cnf(c_0_21,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]),c_0_10]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET734+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.17/0.34  % Computer : n020.cluster.edu
% 0.17/0.34  % Model    : x86_64 x86_64
% 0.17/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34  % Memory   : 8042.1875MB
% 0.17/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34  % CPULimit   : 300
% 0.17/0.34  % WCLimit    : 300
% 0.17/0.34  % DateTime   : Sat Aug 26 09:06:00 EDT 2023
% 0.17/0.34  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.95/1.04  % Version  : CSE_E---1.5
% 0.95/1.04  % Problem  : theBenchmark.p
% 0.95/1.04  % Proof found
% 0.95/1.04  % SZS status Theorem for theBenchmark.p
% 0.95/1.04  % SZS output start Proof
% See solution above
% 0.95/1.05  % Total time : 0.454000 s
% 0.95/1.05  % SZS output end Proof
% 0.95/1.05  % Total time : 0.458000 s
%------------------------------------------------------------------------------