TSTP Solution File: SEU075+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU075+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n009.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 16:22:21 EDT 2023

% Result   : Theorem 138.96s 139.26s
% Output   : CNFRefutation 138.96s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   37
% Syntax   : Number of formulae    :   70 (  17 unt;  33 typ;   0 def)
%            Number of atoms       :  172 (  59 equ)
%            Maximal formula atoms :   32 (   4 avg)
%            Number of connectives :  213 (  78   ~;  82   |;  35   &)
%                                         (   2 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   30 (  20   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   25 (  25 usr;  13 con; 0-3 aty)
%            Number of variables   :   51 (   0 sgn;  29   !;   1   ?;   0   :)

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

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

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

tff(decl_25,type,
    relation: $i > $o ).

tff(decl_26,type,
    one_to_one: $i > $o ).

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

tff(decl_28,type,
    relation_dom: $i > $i ).

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

tff(decl_30,type,
    relation_composition: ( $i * $i ) > $i ).

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

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

tff(decl_33,type,
    relation_empty_yielding: $i > $o ).

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

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

tff(decl_36,type,
    esk1_3: ( $i * $i * $i ) > $i ).

tff(decl_37,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_38,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_39,type,
    esk4_1: $i > $i ).

tff(decl_40,type,
    esk5_0: $i ).

tff(decl_41,type,
    esk6_0: $i ).

tff(decl_42,type,
    esk7_1: $i > $i ).

tff(decl_43,type,
    esk8_0: $i ).

tff(decl_44,type,
    esk9_0: $i ).

tff(decl_45,type,
    esk10_0: $i ).

tff(decl_46,type,
    esk11_1: $i > $i ).

tff(decl_47,type,
    esk12_0: $i ).

tff(decl_48,type,
    esk13_0: $i ).

tff(decl_49,type,
    esk14_0: $i ).

tff(decl_50,type,
    esk15_0: $i ).

tff(decl_51,type,
    esk16_0: $i ).

tff(decl_52,type,
    esk17_0: $i ).

tff(decl_53,type,
    esk18_0: $i ).

tff(decl_54,type,
    esk19_2: ( $i * $i ) > $i ).

fof(t156_funct_1,conjecture,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => ! [X3] :
          ( ( relation(X3)
            & function(X3) )
         => ! [X4] :
              ( ( relation(X4)
                & function(X4) )
             => ( ( X1 = relation_rng(X2)
                  & relation_dom(X3) = X1
                  & relation_dom(X4) = X1
                  & relation_composition(X2,X3) = relation_composition(X2,X4) )
               => X3 = X4 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t156_funct_1) ).

fof(d5_funct_1,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ! [X2] :
          ( X2 = relation_rng(X1)
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] :
                  ( in(X4,relation_dom(X1))
                  & X3 = apply(X1,X4) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).

fof(t9_funct_1,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ! [X2] :
          ( ( relation(X2)
            & function(X2) )
         => ( ( relation_dom(X1) = relation_dom(X2)
              & ! [X3] :
                  ( in(X3,relation_dom(X1))
                 => apply(X1,X3) = apply(X2,X3) ) )
           => X1 = X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_1) ).

fof(t23_funct_1,axiom,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => ! [X3] :
          ( ( relation(X3)
            & function(X3) )
         => ( in(X1,relation_dom(X2))
           => apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).

fof(c_0_4,negated_conjecture,
    ~ ! [X1,X2] :
        ( ( relation(X2)
          & function(X2) )
       => ! [X3] :
            ( ( relation(X3)
              & function(X3) )
           => ! [X4] :
                ( ( relation(X4)
                  & function(X4) )
               => ( ( X1 = relation_rng(X2)
                    & relation_dom(X3) = X1
                    & relation_dom(X4) = X1
                    & relation_composition(X2,X3) = relation_composition(X2,X4) )
                 => X3 = X4 ) ) ) ),
    inference(assume_negation,[status(cth)],[t156_funct_1]) ).

fof(c_0_5,plain,
    ! [X10,X11,X12,X14,X15,X16,X18] :
      ( ( in(esk1_3(X10,X11,X12),relation_dom(X10))
        | ~ in(X12,X11)
        | X11 != relation_rng(X10)
        | ~ relation(X10)
        | ~ function(X10) )
      & ( X12 = apply(X10,esk1_3(X10,X11,X12))
        | ~ in(X12,X11)
        | X11 != relation_rng(X10)
        | ~ relation(X10)
        | ~ function(X10) )
      & ( ~ in(X15,relation_dom(X10))
        | X14 != apply(X10,X15)
        | in(X14,X11)
        | X11 != relation_rng(X10)
        | ~ relation(X10)
        | ~ function(X10) )
      & ( ~ in(esk2_2(X10,X16),X16)
        | ~ in(X18,relation_dom(X10))
        | esk2_2(X10,X16) != apply(X10,X18)
        | X16 = relation_rng(X10)
        | ~ relation(X10)
        | ~ function(X10) )
      & ( in(esk3_2(X10,X16),relation_dom(X10))
        | in(esk2_2(X10,X16),X16)
        | X16 = relation_rng(X10)
        | ~ relation(X10)
        | ~ function(X10) )
      & ( esk2_2(X10,X16) = apply(X10,esk3_2(X10,X16))
        | in(esk2_2(X10,X16),X16)
        | X16 = relation_rng(X10)
        | ~ relation(X10)
        | ~ function(X10) ) ),
    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)],[d5_funct_1])])])])])]) ).

fof(c_0_6,plain,
    ! [X72,X73] :
      ( ( in(esk19_2(X72,X73),relation_dom(X72))
        | relation_dom(X72) != relation_dom(X73)
        | X72 = X73
        | ~ relation(X73)
        | ~ function(X73)
        | ~ relation(X72)
        | ~ function(X72) )
      & ( apply(X72,esk19_2(X72,X73)) != apply(X73,esk19_2(X72,X73))
        | relation_dom(X72) != relation_dom(X73)
        | X72 = X73
        | ~ relation(X73)
        | ~ function(X73)
        | ~ relation(X72)
        | ~ function(X72) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t9_funct_1])])])])]) ).

fof(c_0_7,negated_conjecture,
    ( relation(esk16_0)
    & function(esk16_0)
    & relation(esk17_0)
    & function(esk17_0)
    & relation(esk18_0)
    & function(esk18_0)
    & esk15_0 = relation_rng(esk16_0)
    & relation_dom(esk17_0) = esk15_0
    & relation_dom(esk18_0) = esk15_0
    & relation_composition(esk16_0,esk17_0) = relation_composition(esk16_0,esk18_0)
    & esk17_0 != esk18_0 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

cnf(c_0_8,plain,
    ( in(esk1_3(X1,X2,X3),relation_dom(X1))
    | ~ in(X3,X2)
    | X2 != relation_rng(X1)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,plain,
    ( in(esk19_2(X1,X2),relation_dom(X1))
    | X1 = X2
    | relation_dom(X1) != relation_dom(X2)
    | ~ relation(X2)
    | ~ function(X2)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    relation_dom(esk18_0) = esk15_0,
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,negated_conjecture,
    relation(esk18_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,negated_conjecture,
    function(esk18_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_13,plain,
    ( X1 = apply(X2,esk1_3(X2,X3,X1))
    | ~ in(X1,X3)
    | X3 != relation_rng(X2)
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_14,plain,
    ( in(esk1_3(X1,relation_rng(X1),X2),relation_dom(X1))
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X2,relation_rng(X1)) ),
    inference(er,[status(thm)],[c_0_8]) ).

cnf(c_0_15,negated_conjecture,
    esk15_0 = relation_rng(esk16_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_16,negated_conjecture,
    relation(esk16_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_17,negated_conjecture,
    function(esk16_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_18,negated_conjecture,
    ( esk18_0 = X1
    | in(esk19_2(esk18_0,X1),esk15_0)
    | relation_dom(X1) != esk15_0
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12])]) ).

cnf(c_0_19,negated_conjecture,
    relation_dom(esk17_0) = esk15_0,
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_20,negated_conjecture,
    relation(esk17_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_21,negated_conjecture,
    function(esk17_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_22,negated_conjecture,
    esk17_0 != esk18_0,
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_23,plain,
    ( apply(X1,esk1_3(X1,relation_rng(X1),X2)) = X2
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X2,relation_rng(X1)) ),
    inference(er,[status(thm)],[c_0_13]) ).

fof(c_0_24,plain,
    ! [X54,X55,X56] :
      ( ~ relation(X55)
      | ~ function(X55)
      | ~ relation(X56)
      | ~ function(X56)
      | ~ in(X54,relation_dom(X55))
      | apply(relation_composition(X55,X56),X54) = apply(X56,apply(X55,X54)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_funct_1])])]) ).

cnf(c_0_25,negated_conjecture,
    ( in(esk1_3(esk16_0,esk15_0,X1),relation_dom(esk16_0))
    | ~ in(X1,esk15_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17])]) ).

cnf(c_0_26,negated_conjecture,
    in(esk19_2(esk18_0,esk17_0),esk15_0),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]),c_0_22]) ).

cnf(c_0_27,negated_conjecture,
    ( apply(esk16_0,esk1_3(esk16_0,esk15_0,X1)) = X1
    | ~ in(X1,esk15_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_15]),c_0_16]),c_0_17])]) ).

cnf(c_0_28,plain,
    ( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
    | ~ relation(X1)
    | ~ function(X1)
    | ~ relation(X2)
    | ~ function(X2)
    | ~ in(X3,relation_dom(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_29,negated_conjecture,
    in(esk1_3(esk16_0,esk15_0,esk19_2(esk18_0,esk17_0)),relation_dom(esk16_0)),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_30,negated_conjecture,
    apply(esk16_0,esk1_3(esk16_0,esk15_0,esk19_2(esk18_0,esk17_0))) = esk19_2(esk18_0,esk17_0),
    inference(spm,[status(thm)],[c_0_27,c_0_26]) ).

cnf(c_0_31,negated_conjecture,
    ( apply(relation_composition(esk16_0,X1),esk1_3(esk16_0,esk15_0,esk19_2(esk18_0,esk17_0))) = apply(X1,esk19_2(esk18_0,esk17_0))
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_16]),c_0_17])]),c_0_30]) ).

cnf(c_0_32,negated_conjecture,
    relation_composition(esk16_0,esk17_0) = relation_composition(esk16_0,esk18_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_33,negated_conjecture,
    apply(relation_composition(esk16_0,esk17_0),esk1_3(esk16_0,esk15_0,esk19_2(esk18_0,esk17_0))) = apply(esk18_0,esk19_2(esk18_0,esk17_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_11]),c_0_12])]) ).

cnf(c_0_34,plain,
    ( X1 = X2
    | apply(X1,esk19_2(X1,X2)) != apply(X2,esk19_2(X1,X2))
    | relation_dom(X1) != relation_dom(X2)
    | ~ relation(X2)
    | ~ function(X2)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_35,negated_conjecture,
    apply(esk18_0,esk19_2(esk18_0,esk17_0)) = apply(esk17_0,esk19_2(esk18_0,esk17_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_33]),c_0_20]),c_0_21])]) ).

cnf(c_0_36,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_10]),c_0_19]),c_0_20]),c_0_11]),c_0_21]),c_0_12])]),c_0_22]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : SEU075+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n009.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Wed Aug 23 22:28:36 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 138.96/139.26  % Version  : CSE_E---1.5
% 138.96/139.26  % Problem  : theBenchmark.p
% 138.96/139.26  % Proof found
% 138.96/139.26  % SZS status Theorem for theBenchmark.p
% 138.96/139.26  % SZS output start Proof
% See solution above
% 138.96/139.26  % Total time : 138.671000 s
% 138.96/139.26  % SZS output end Proof
% 138.96/139.26  % Total time : 138.680000 s
%------------------------------------------------------------------------------