TSTP Solution File: SEU076+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU076+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 : n023.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 27.61s 27.95s
% Output   : CNFRefutation 27.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   37
% Syntax   : Number of formulae    :   68 (   7 unt;  33 typ;   0 def)
%            Number of atoms       :  192 (  30 equ)
%            Maximal formula atoms :   44 (   5 avg)
%            Number of connectives :  264 ( 107   ~; 115   |;  30   &)
%                                         (   4 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   34 (  21   >;  13   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   25 (  25 usr;  12 con; 0-4 aty)
%            Number of variables   :   84 (   0 sgn;  33   !;   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_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,
    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_4: ( $i * $i * $i * $i ) > $i ).

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

tff(decl_37,type,
    esk3_3: ( $i * $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_1: $i > $i ).

tff(decl_41,type,
    esk7_1: $i > $i ).

tff(decl_42,type,
    esk8_0: $i ).

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

tff(decl_44,type,
    esk10_1: $i > $i ).

tff(decl_45,type,
    esk11_0: $i ).

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

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

tff(decl_48,type,
    esk14_1: $i > $i ).

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

tff(decl_50,type,
    esk16_0: $i ).

tff(decl_51,type,
    esk17_0: $i ).

tff(decl_52,type,
    esk18_0: $i ).

tff(decl_53,type,
    esk19_0: $i ).

tff(decl_54,type,
    esk20_0: $i ).

fof(d12_funct_1,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ! [X2,X3] :
          ( X3 = relation_image(X1,X2)
        <=> ! [X4] :
              ( in(X4,X3)
            <=> ? [X5] :
                  ( in(X5,relation_dom(X1))
                  & in(X5,X2)
                  & X4 = apply(X1,X5) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_funct_1) ).

fof(d8_funct_1,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ( one_to_one(X1)
      <=> ! [X2,X3] :
            ( ( in(X2,relation_dom(X1))
              & in(X3,relation_dom(X1))
              & apply(X1,X2) = apply(X1,X3) )
           => X2 = X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).

fof(t157_funct_1,conjecture,
    ! [X1,X2,X3] :
      ( ( relation(X3)
        & function(X3) )
     => ( ( subset(relation_image(X3,X1),relation_image(X3,X2))
          & subset(X1,relation_dom(X3))
          & one_to_one(X3) )
       => subset(X1,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t157_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(c_0_4,plain,
    ! [X11,X12,X13,X14,X16,X17,X18,X19,X21] :
      ( ( in(esk1_4(X11,X12,X13,X14),relation_dom(X11))
        | ~ in(X14,X13)
        | X13 != relation_image(X11,X12)
        | ~ relation(X11)
        | ~ function(X11) )
      & ( in(esk1_4(X11,X12,X13,X14),X12)
        | ~ in(X14,X13)
        | X13 != relation_image(X11,X12)
        | ~ relation(X11)
        | ~ function(X11) )
      & ( X14 = apply(X11,esk1_4(X11,X12,X13,X14))
        | ~ in(X14,X13)
        | X13 != relation_image(X11,X12)
        | ~ relation(X11)
        | ~ function(X11) )
      & ( ~ in(X17,relation_dom(X11))
        | ~ in(X17,X12)
        | X16 != apply(X11,X17)
        | in(X16,X13)
        | X13 != relation_image(X11,X12)
        | ~ relation(X11)
        | ~ function(X11) )
      & ( ~ in(esk2_3(X11,X18,X19),X19)
        | ~ in(X21,relation_dom(X11))
        | ~ in(X21,X18)
        | esk2_3(X11,X18,X19) != apply(X11,X21)
        | X19 = relation_image(X11,X18)
        | ~ relation(X11)
        | ~ function(X11) )
      & ( in(esk3_3(X11,X18,X19),relation_dom(X11))
        | in(esk2_3(X11,X18,X19),X19)
        | X19 = relation_image(X11,X18)
        | ~ relation(X11)
        | ~ function(X11) )
      & ( in(esk3_3(X11,X18,X19),X18)
        | in(esk2_3(X11,X18,X19),X19)
        | X19 = relation_image(X11,X18)
        | ~ relation(X11)
        | ~ function(X11) )
      & ( esk2_3(X11,X18,X19) = apply(X11,esk3_3(X11,X18,X19))
        | in(esk2_3(X11,X18,X19),X19)
        | X19 = relation_image(X11,X18)
        | ~ relation(X11)
        | ~ function(X11) ) ),
    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)],[d12_funct_1])])])])])]) ).

fof(c_0_5,plain,
    ! [X29,X30,X31] :
      ( ( ~ one_to_one(X29)
        | ~ in(X30,relation_dom(X29))
        | ~ in(X31,relation_dom(X29))
        | apply(X29,X30) != apply(X29,X31)
        | X30 = X31
        | ~ relation(X29)
        | ~ function(X29) )
      & ( in(esk5_1(X29),relation_dom(X29))
        | one_to_one(X29)
        | ~ relation(X29)
        | ~ function(X29) )
      & ( in(esk6_1(X29),relation_dom(X29))
        | one_to_one(X29)
        | ~ relation(X29)
        | ~ function(X29) )
      & ( apply(X29,esk5_1(X29)) = apply(X29,esk6_1(X29))
        | one_to_one(X29)
        | ~ relation(X29)
        | ~ function(X29) )
      & ( esk5_1(X29) != esk6_1(X29)
        | one_to_one(X29)
        | ~ relation(X29)
        | ~ function(X29) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_funct_1])])])])]) ).

cnf(c_0_6,plain,
    ( X1 = apply(X2,esk1_4(X2,X3,X4,X1))
    | ~ in(X1,X4)
    | X4 != relation_image(X2,X3)
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_7,plain,
    ( in(esk1_4(X1,X2,X3,X4),relation_dom(X1))
    | ~ in(X4,X3)
    | X3 != relation_image(X1,X2)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

fof(c_0_8,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( relation(X3)
          & function(X3) )
       => ( ( subset(relation_image(X3,X1),relation_image(X3,X2))
            & subset(X1,relation_dom(X3))
            & one_to_one(X3) )
         => subset(X1,X2) ) ),
    inference(assume_negation,[status(cth)],[t157_funct_1]) ).

cnf(c_0_9,plain,
    ( in(esk1_4(X1,X2,X3,X4),X2)
    | ~ in(X4,X3)
    | X3 != relation_image(X1,X2)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_10,plain,
    ( X2 = X3
    | ~ one_to_one(X1)
    | ~ in(X2,relation_dom(X1))
    | ~ in(X3,relation_dom(X1))
    | apply(X1,X2) != apply(X1,X3)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_11,plain,
    ( apply(X1,esk1_4(X1,X2,relation_image(X1,X2),X3)) = X3
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X3,relation_image(X1,X2)) ),
    inference(er,[status(thm)],[c_0_6]) ).

cnf(c_0_12,plain,
    ( in(esk1_4(X1,X2,relation_image(X1,X2),X3),relation_dom(X1))
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X3,relation_image(X1,X2)) ),
    inference(er,[status(thm)],[c_0_7]) ).

fof(c_0_13,plain,
    ! [X23,X24,X25,X26,X27] :
      ( ( ~ subset(X23,X24)
        | ~ in(X25,X23)
        | in(X25,X24) )
      & ( in(esk4_2(X26,X27),X26)
        | subset(X26,X27) )
      & ( ~ in(esk4_2(X26,X27),X27)
        | subset(X26,X27) ) ),
    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_14,negated_conjecture,
    ( relation(esk20_0)
    & function(esk20_0)
    & subset(relation_image(esk20_0,esk18_0),relation_image(esk20_0,esk19_0))
    & subset(esk18_0,relation_dom(esk20_0))
    & one_to_one(esk20_0)
    & ~ subset(esk18_0,esk19_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).

cnf(c_0_15,plain,
    ( in(esk1_4(X1,X2,relation_image(X1,X2),X3),X2)
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X3,relation_image(X1,X2)) ),
    inference(er,[status(thm)],[c_0_9]) ).

cnf(c_0_16,plain,
    ( esk1_4(X1,X2,relation_image(X1,X2),apply(X1,X3)) = X3
    | ~ one_to_one(X1)
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(apply(X1,X3),relation_image(X1,X2))
    | ~ in(X3,relation_dom(X1)) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11])]),c_0_12]) ).

cnf(c_0_17,plain,
    ( in(X3,X2)
    | ~ subset(X1,X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_18,negated_conjecture,
    subset(relation_image(esk20_0,esk18_0),relation_image(esk20_0,esk19_0)),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_19,plain,
    ( in(X1,X2)
    | ~ one_to_one(X3)
    | ~ relation(X3)
    | ~ function(X3)
    | ~ in(apply(X3,X1),relation_image(X3,X2))
    | ~ in(X1,relation_dom(X3)) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_20,negated_conjecture,
    ( in(X1,relation_image(esk20_0,esk19_0))
    | ~ in(X1,relation_image(esk20_0,esk18_0)) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_21,negated_conjecture,
    one_to_one(esk20_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_22,negated_conjecture,
    relation(esk20_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_23,negated_conjecture,
    function(esk20_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_24,plain,
    ( in(X4,X5)
    | ~ in(X1,relation_dom(X2))
    | ~ in(X1,X3)
    | X4 != apply(X2,X1)
    | X5 != relation_image(X2,X3)
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_25,negated_conjecture,
    subset(esk18_0,relation_dom(esk20_0)),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_26,negated_conjecture,
    ( in(X1,esk19_0)
    | ~ in(apply(esk20_0,X1),relation_image(esk20_0,esk18_0))
    | ~ in(X1,relation_dom(esk20_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22]),c_0_23])]) ).

cnf(c_0_27,plain,
    ( in(apply(X1,X2),relation_image(X1,X3))
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X2,relation_dom(X1))
    | ~ in(X2,X3) ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_24])]) ).

cnf(c_0_28,negated_conjecture,
    ( in(X1,relation_dom(esk20_0))
    | ~ in(X1,esk18_0) ),
    inference(spm,[status(thm)],[c_0_17,c_0_25]) ).

cnf(c_0_29,plain,
    ( subset(X1,X2)
    | ~ in(esk4_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_30,negated_conjecture,
    ( in(X1,esk19_0)
    | ~ in(X1,esk18_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_22]),c_0_23])]),c_0_28]) ).

cnf(c_0_31,negated_conjecture,
    ( subset(X1,esk19_0)
    | ~ in(esk4_2(X1,esk19_0),esk18_0) ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_32,plain,
    ( in(esk4_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_33,negated_conjecture,
    ~ subset(esk18_0,esk19_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_34,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU076+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n023.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   : Wed Aug 23 15:32:43 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 27.61/27.95  % Version  : CSE_E---1.5
% 27.61/27.95  % Problem  : theBenchmark.p
% 27.61/27.95  % Proof found
% 27.61/27.95  % SZS status Theorem for theBenchmark.p
% 27.61/27.95  % SZS output start Proof
% See solution above
% 27.61/27.96  % Total time : 27.389000 s
% 27.61/27.96  % SZS output end Proof
% 27.61/27.96  % Total time : 27.392000 s
%------------------------------------------------------------------------------