TSTP Solution File: SEU077+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU077+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 : n007.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 16:22:22 EDT 2023

% Result   : Theorem 0.20s 0.68s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   37
% Syntax   : Number of formulae    :   67 (   8 unt;  33 typ;   0 def)
%            Number of atoms       :  170 (  25 equ)
%            Maximal formula atoms :   32 (   5 avg)
%            Number of connectives :  230 (  94   ~; 100   |;  24   &)
%                                         (   5 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   33 (  21   >;  12   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   25 (  25 usr;  12 con; 0-3 aty)
%            Number of variables   :   75 (   0 sgn;  35   !;   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_inverse_image: ( $i * $i ) > $i ).

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

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

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

tff(decl_31,type,
    relation_rng: $i > $i ).

tff(decl_32,type,
    element: ( $i * $i ) > $o ).

tff(decl_33,type,
    empty_set: $i ).

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

tff(decl_35,type,
    powerset: $i > $i ).

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

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

tff(decl_38,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_39,type,
    esk4_2: ( $i * $i ) > $i ).

tff(decl_40,type,
    esk5_2: ( $i * $i ) > $i ).

tff(decl_41,type,
    esk6_1: $i > $i ).

tff(decl_42,type,
    esk7_0: $i ).

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

tff(decl_44,type,
    esk9_1: $i > $i ).

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

tff(decl_46,type,
    esk11_0: $i ).

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

tff(decl_48,type,
    esk13_1: $i > $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_0: $i ).

fof(t158_funct_1,conjecture,
    ! [X1,X2,X3] :
      ( ( relation(X3)
        & function(X3) )
     => ( ( subset(relation_inverse_image(X3,X1),relation_inverse_image(X3,X2))
          & subset(X1,relation_rng(X3)) )
       => subset(X1,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_funct_1) ).

fof(d13_funct_1,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ! [X2,X3] :
          ( X3 = relation_inverse_image(X1,X2)
        <=> ! [X4] :
              ( in(X4,X3)
            <=> ( in(X4,relation_dom(X1))
                & in(apply(X1,X4),X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).

fof(d3_tarski,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( in(X3,X1)
         => in(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

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(c_0_4,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( relation(X3)
          & function(X3) )
       => ( ( subset(relation_inverse_image(X3,X1),relation_inverse_image(X3,X2))
            & subset(X1,relation_rng(X3)) )
         => subset(X1,X2) ) ),
    inference(assume_negation,[status(cth)],[t158_funct_1]) ).

fof(c_0_5,plain,
    ! [X10,X11,X12,X13,X14,X15,X16] :
      ( ( in(X13,relation_dom(X10))
        | ~ in(X13,X12)
        | X12 != relation_inverse_image(X10,X11)
        | ~ relation(X10)
        | ~ function(X10) )
      & ( in(apply(X10,X13),X11)
        | ~ in(X13,X12)
        | X12 != relation_inverse_image(X10,X11)
        | ~ relation(X10)
        | ~ function(X10) )
      & ( ~ in(X14,relation_dom(X10))
        | ~ in(apply(X10,X14),X11)
        | in(X14,X12)
        | X12 != relation_inverse_image(X10,X11)
        | ~ relation(X10)
        | ~ function(X10) )
      & ( ~ in(esk1_3(X10,X15,X16),X16)
        | ~ in(esk1_3(X10,X15,X16),relation_dom(X10))
        | ~ in(apply(X10,esk1_3(X10,X15,X16)),X15)
        | X16 = relation_inverse_image(X10,X15)
        | ~ relation(X10)
        | ~ function(X10) )
      & ( in(esk1_3(X10,X15,X16),relation_dom(X10))
        | in(esk1_3(X10,X15,X16),X16)
        | X16 = relation_inverse_image(X10,X15)
        | ~ relation(X10)
        | ~ function(X10) )
      & ( in(apply(X10,esk1_3(X10,X15,X16)),X15)
        | in(esk1_3(X10,X15,X16),X16)
        | X16 = relation_inverse_image(X10,X15)
        | ~ 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)],[d13_funct_1])])])])])]) ).

fof(c_0_6,plain,
    ! [X18,X19,X20,X21,X22] :
      ( ( ~ subset(X18,X19)
        | ~ in(X20,X18)
        | in(X20,X19) )
      & ( in(esk2_2(X21,X22),X21)
        | subset(X21,X22) )
      & ( ~ in(esk2_2(X21,X22),X22)
        | subset(X21,X22) ) ),
    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])])])])])]) ).

fof(c_0_7,negated_conjecture,
    ( relation(esk19_0)
    & function(esk19_0)
    & subset(relation_inverse_image(esk19_0,esk17_0),relation_inverse_image(esk19_0,esk18_0))
    & subset(esk17_0,relation_rng(esk19_0))
    & ~ subset(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(apply(X1,X2),X3)
    | ~ in(X2,X4)
    | X4 != relation_inverse_image(X1,X3)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,plain,
    ( in(X3,X2)
    | ~ subset(X1,X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    subset(relation_inverse_image(esk19_0,esk17_0),relation_inverse_image(esk19_0,esk18_0)),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_11,plain,
    ! [X24,X25,X26,X28,X29,X30,X32] :
      ( ( in(esk3_3(X24,X25,X26),relation_dom(X24))
        | ~ in(X26,X25)
        | X25 != relation_rng(X24)
        | ~ relation(X24)
        | ~ function(X24) )
      & ( X26 = apply(X24,esk3_3(X24,X25,X26))
        | ~ in(X26,X25)
        | X25 != relation_rng(X24)
        | ~ relation(X24)
        | ~ function(X24) )
      & ( ~ in(X29,relation_dom(X24))
        | X28 != apply(X24,X29)
        | in(X28,X25)
        | X25 != relation_rng(X24)
        | ~ relation(X24)
        | ~ function(X24) )
      & ( ~ in(esk4_2(X24,X30),X30)
        | ~ in(X32,relation_dom(X24))
        | esk4_2(X24,X30) != apply(X24,X32)
        | X30 = relation_rng(X24)
        | ~ relation(X24)
        | ~ function(X24) )
      & ( in(esk5_2(X24,X30),relation_dom(X24))
        | in(esk4_2(X24,X30),X30)
        | X30 = relation_rng(X24)
        | ~ relation(X24)
        | ~ function(X24) )
      & ( esk4_2(X24,X30) = apply(X24,esk5_2(X24,X30))
        | in(esk4_2(X24,X30),X30)
        | X30 = relation_rng(X24)
        | ~ relation(X24)
        | ~ function(X24) ) ),
    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_12,plain,
    ( in(apply(X1,X2),X3)
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X2,relation_inverse_image(X1,X3)) ),
    inference(er,[status(thm)],[c_0_8]) ).

cnf(c_0_13,negated_conjecture,
    ( in(X1,relation_inverse_image(esk19_0,esk18_0))
    | ~ in(X1,relation_inverse_image(esk19_0,esk17_0)) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_14,negated_conjecture,
    relation(esk19_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_15,negated_conjecture,
    function(esk19_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_16,plain,
    ( X1 = apply(X2,esk3_3(X2,X3,X1))
    | ~ in(X1,X3)
    | X3 != relation_rng(X2)
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_17,plain,
    ( in(X1,X4)
    | ~ in(X1,relation_dom(X2))
    | ~ in(apply(X2,X1),X3)
    | X4 != relation_inverse_image(X2,X3)
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_18,plain,
    ( in(esk3_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_11]) ).

cnf(c_0_19,negated_conjecture,
    ( in(apply(esk19_0,X1),esk18_0)
    | ~ in(X1,relation_inverse_image(esk19_0,esk17_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]) ).

cnf(c_0_20,plain,
    ( apply(X1,esk3_3(X1,relation_rng(X1),X2)) = X2
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X2,relation_rng(X1)) ),
    inference(er,[status(thm)],[c_0_16]) ).

cnf(c_0_21,plain,
    ( in(X1,relation_inverse_image(X2,X3))
    | ~ relation(X2)
    | ~ function(X2)
    | ~ in(apply(X2,X1),X3)
    | ~ in(X1,relation_dom(X2)) ),
    inference(er,[status(thm)],[c_0_17]) ).

cnf(c_0_22,plain,
    ( in(esk3_3(X1,relation_rng(X1),X2),relation_dom(X1))
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X2,relation_rng(X1)) ),
    inference(er,[status(thm)],[c_0_18]) ).

cnf(c_0_23,negated_conjecture,
    subset(esk17_0,relation_rng(esk19_0)),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_24,negated_conjecture,
    ~ subset(esk17_0,esk18_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_25,plain,
    ( subset(X1,X2)
    | ~ in(esk2_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_26,negated_conjecture,
    ( in(X1,esk18_0)
    | ~ in(esk3_3(esk19_0,relation_rng(esk19_0),X1),relation_inverse_image(esk19_0,esk17_0))
    | ~ in(X1,relation_rng(esk19_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_14]),c_0_15])]) ).

cnf(c_0_27,plain,
    ( in(esk3_3(X1,relation_rng(X1),X2),relation_inverse_image(X1,X3))
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X2,relation_rng(X1))
    | ~ in(X2,X3) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_20]),c_0_22]) ).

cnf(c_0_28,negated_conjecture,
    ( in(X1,relation_rng(esk19_0))
    | ~ in(X1,esk17_0) ),
    inference(spm,[status(thm)],[c_0_9,c_0_23]) ).

cnf(c_0_29,plain,
    ( in(esk2_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_30,negated_conjecture,
    ~ in(esk2_2(esk17_0,esk18_0),esk18_0),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_31,negated_conjecture,
    ( in(X1,esk18_0)
    | ~ in(X1,esk17_0) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_14]),c_0_15])]),c_0_28]) ).

cnf(c_0_32,negated_conjecture,
    in(esk2_2(esk17_0,esk18_0),esk17_0),
    inference(spm,[status(thm)],[c_0_24,c_0_29]) ).

cnf(c_0_33,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU077+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n007.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Wed Aug 23 18:01:54 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 0.20/0.68  % Version  : CSE_E---1.5
% 0.20/0.68  % Problem  : theBenchmark.p
% 0.20/0.68  % Proof found
% 0.20/0.68  % SZS status Theorem for theBenchmark.p
% 0.20/0.68  % SZS output start Proof
% See solution above
% 0.20/0.69  % Total time : 0.090000 s
% 0.20/0.69  % SZS output end Proof
% 0.20/0.69  % Total time : 0.093000 s
%------------------------------------------------------------------------------