TSTP Solution File: SEU003+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU003+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n026.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 16:22:06 EDT 2023

% Result   : Theorem 2.03s 2.19s
% Output   : CNFRefutation 2.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   32
% Syntax   : Number of formulae    :   56 (   9 unt;  28 typ;   0 def)
%            Number of atoms       :  136 (  20 equ)
%            Maximal formula atoms :   32 (   4 avg)
%            Number of connectives :  177 (  69   ~;  71   |;  23   &)
%                                         (   4 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   29 (  19   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   21 (  21 usr;   9 con; 0-3 aty)
%            Number of variables   :   49 (   0 sgn;  28   !;   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,
    subset: ( $i * $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,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_36,type,
    esk2_3: ( $i * $i * $i ) > $i ).

tff(decl_37,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_38,type,
    esk4_2: ( $i * $i ) > $i ).

tff(decl_39,type,
    esk5_1: $i > $i ).

tff(decl_40,type,
    esk6_0: $i ).

tff(decl_41,type,
    esk7_0: $i ).

tff(decl_42,type,
    esk8_1: $i > $i ).

tff(decl_43,type,
    esk9_0: $i ).

tff(decl_44,type,
    esk10_0: $i ).

tff(decl_45,type,
    esk11_1: $i > $i ).

tff(decl_46,type,
    esk12_0: $i ).

tff(decl_47,type,
    esk13_0: $i ).

tff(decl_48,type,
    esk14_0: $i ).

tff(decl_49,type,
    esk15_0: $i ).

fof(t27_funct_1,conjecture,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ! [X2] :
          ( ( relation(X2)
            & function(X2) )
         => ( relation_dom(relation_composition(X2,X1)) = relation_dom(X2)
           => subset(relation_rng(X2),relation_dom(X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_funct_1) ).

fof(t21_funct_1,axiom,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => ! [X3] :
          ( ( relation(X3)
            & function(X3) )
         => ( in(X1,relation_dom(relation_composition(X3,X2)))
          <=> ( in(X1,relation_dom(X3))
              & in(apply(X3,X1),relation_dom(X2)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_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/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).

fof(d3_tarski,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( in(X3,X1)
         => in(X3,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(c_0_4,negated_conjecture,
    ~ ! [X1] :
        ( ( relation(X1)
          & function(X1) )
       => ! [X2] :
            ( ( relation(X2)
              & function(X2) )
           => ( relation_dom(relation_composition(X2,X1)) = relation_dom(X2)
             => subset(relation_rng(X2),relation_dom(X1)) ) ) ),
    inference(assume_negation,[status(cth)],[t27_funct_1]) ).

fof(c_0_5,plain,
    ! [X53,X54,X55] :
      ( ( in(X53,relation_dom(X55))
        | ~ in(X53,relation_dom(relation_composition(X55,X54)))
        | ~ relation(X55)
        | ~ function(X55)
        | ~ relation(X54)
        | ~ function(X54) )
      & ( in(apply(X55,X53),relation_dom(X54))
        | ~ in(X53,relation_dom(relation_composition(X55,X54)))
        | ~ relation(X55)
        | ~ function(X55)
        | ~ relation(X54)
        | ~ function(X54) )
      & ( ~ in(X53,relation_dom(X55))
        | ~ in(apply(X55,X53),relation_dom(X54))
        | in(X53,relation_dom(relation_composition(X55,X54)))
        | ~ relation(X55)
        | ~ function(X55)
        | ~ relation(X54)
        | ~ function(X54) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_funct_1])])])]) ).

fof(c_0_6,negated_conjecture,
    ( relation(esk14_0)
    & function(esk14_0)
    & relation(esk15_0)
    & function(esk15_0)
    & relation_dom(relation_composition(esk15_0,esk14_0)) = relation_dom(esk15_0)
    & ~ subset(relation_rng(esk15_0),relation_dom(esk14_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

fof(c_0_7,plain,
    ! [X15,X16,X17,X19,X20,X21,X23] :
      ( ( in(esk2_3(X15,X16,X17),relation_dom(X15))
        | ~ in(X17,X16)
        | X16 != relation_rng(X15)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( X17 = apply(X15,esk2_3(X15,X16,X17))
        | ~ in(X17,X16)
        | X16 != relation_rng(X15)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( ~ in(X20,relation_dom(X15))
        | X19 != apply(X15,X20)
        | in(X19,X16)
        | X16 != relation_rng(X15)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( ~ in(esk3_2(X15,X21),X21)
        | ~ in(X23,relation_dom(X15))
        | esk3_2(X15,X21) != apply(X15,X23)
        | X21 = relation_rng(X15)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( in(esk4_2(X15,X21),relation_dom(X15))
        | in(esk3_2(X15,X21),X21)
        | X21 = relation_rng(X15)
        | ~ relation(X15)
        | ~ function(X15) )
      & ( esk3_2(X15,X21) = apply(X15,esk4_2(X15,X21))
        | in(esk3_2(X15,X21),X21)
        | X21 = relation_rng(X15)
        | ~ relation(X15)
        | ~ function(X15) ) ),
    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])])])])])]) ).

cnf(c_0_8,plain,
    ( in(apply(X1,X2),relation_dom(X3))
    | ~ in(X2,relation_dom(relation_composition(X1,X3)))
    | ~ relation(X1)
    | ~ function(X1)
    | ~ relation(X3)
    | ~ function(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,negated_conjecture,
    relation_dom(relation_composition(esk15_0,esk14_0)) = relation_dom(esk15_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    relation(esk14_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,negated_conjecture,
    relation(esk15_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_12,negated_conjecture,
    function(esk14_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_13,negated_conjecture,
    function(esk15_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_14,plain,
    ( X1 = apply(X2,esk2_3(X2,X3,X1))
    | ~ in(X1,X3)
    | X3 != relation_rng(X2)
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_15,negated_conjecture,
    ( in(apply(esk15_0,X1),relation_dom(esk14_0))
    | ~ in(X1,relation_dom(esk15_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]),c_0_11]),c_0_12]),c_0_13])]) ).

cnf(c_0_16,plain,
    ( apply(X1,esk2_3(X1,relation_rng(X1),X2)) = X2
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X2,relation_rng(X1)) ),
    inference(er,[status(thm)],[c_0_14]) ).

cnf(c_0_17,plain,
    ( in(esk2_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_7]) ).

fof(c_0_18,plain,
    ! [X9,X10,X11,X12,X13] :
      ( ( ~ subset(X9,X10)
        | ~ in(X11,X9)
        | in(X11,X10) )
      & ( in(esk1_2(X12,X13),X12)
        | subset(X12,X13) )
      & ( ~ in(esk1_2(X12,X13),X13)
        | subset(X12,X13) ) ),
    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)],[d3_tarski])])])])])]) ).

cnf(c_0_19,negated_conjecture,
    ( in(X1,relation_dom(esk14_0))
    | ~ in(esk2_3(esk15_0,relation_rng(esk15_0),X1),relation_dom(esk15_0))
    | ~ in(X1,relation_rng(esk15_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_11]),c_0_13])]) ).

cnf(c_0_20,plain,
    ( in(esk2_3(X1,relation_rng(X1),X2),relation_dom(X1))
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X2,relation_rng(X1)) ),
    inference(er,[status(thm)],[c_0_17]) ).

cnf(c_0_21,negated_conjecture,
    ~ subset(relation_rng(esk15_0),relation_dom(esk14_0)),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_22,plain,
    ( in(esk1_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_23,plain,
    ( subset(X1,X2)
    | ~ in(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_24,negated_conjecture,
    ( in(X1,relation_dom(esk14_0))
    | ~ in(X1,relation_rng(esk15_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_11]),c_0_13])]) ).

cnf(c_0_25,negated_conjecture,
    in(esk1_2(relation_rng(esk15_0),relation_dom(esk14_0)),relation_rng(esk15_0)),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_26,negated_conjecture,
    ~ in(esk1_2(relation_rng(esk15_0),relation_dom(esk14_0)),relation_dom(esk14_0)),
    inference(spm,[status(thm)],[c_0_21,c_0_23]) ).

cnf(c_0_27,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU003+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n026.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 13:00:31 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.18/0.56  start to proof: theBenchmark
% 2.03/2.19  % Version  : CSE_E---1.5
% 2.03/2.19  % Problem  : theBenchmark.p
% 2.03/2.19  % Proof found
% 2.03/2.19  % SZS status Theorem for theBenchmark.p
% 2.03/2.19  % SZS output start Proof
% See solution above
% 2.03/2.19  % Total time : 1.621000 s
% 2.03/2.19  % SZS output end Proof
% 2.03/2.19  % Total time : 1.623000 s
%------------------------------------------------------------------------------