TSTP Solution File: SEU044+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU044+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 : n002.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 16:22:14 EDT 2023

% Result   : Theorem 0.20s 0.60s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   33
% Syntax   : Number of formulae    :   56 (   6 unt;  29 typ;   0 def)
%            Number of atoms       :  177 (  19 equ)
%            Maximal formula atoms :   79 (   6 avg)
%            Number of connectives :  255 ( 105   ~; 115   |;  24   &)
%                                         (   4 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   26 (  17   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   21 (  21 usr;  12 con; 0-3 aty)
%            Number of variables   :   50 (   4 sgn;  25   !;   0   ?;   0   :)

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

tff(decl_23,type,
    empty_set: $i ).

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

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

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

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

tff(decl_28,type,
    function: $i > $o ).

tff(decl_29,type,
    one_to_one: $i > $o ).

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

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

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

tff(decl_33,type,
    relation_rng_restriction: ( $i * $i ) > $i ).

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

tff(decl_35,type,
    esk1_1: $i > $i ).

tff(decl_36,type,
    esk2_0: $i ).

tff(decl_37,type,
    esk3_0: $i ).

tff(decl_38,type,
    esk4_0: $i ).

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

tff(decl_40,type,
    esk6_1: $i > $i ).

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

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

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

tff(decl_44,type,
    esk10_0: $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_0: $i ).

tff(decl_49,type,
    esk15_3: ( $i * $i * $i ) > $i ).

tff(decl_50,type,
    esk16_3: ( $i * $i * $i ) > $i ).

fof(t85_funct_1,axiom,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => ! [X3] :
          ( ( relation(X3)
            & function(X3) )
         => ( X2 = relation_rng_restriction(X1,X3)
          <=> ( ! [X4] :
                  ( in(X4,relation_dom(X2))
                <=> ( in(X4,relation_dom(X3))
                    & in(apply(X3,X4),X1) ) )
              & ! [X4] :
                  ( in(X4,relation_dom(X2))
                 => apply(X2,X4) = apply(X3,X4) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_funct_1) ).

fof(dt_k8_relat_1,axiom,
    ! [X1,X2] :
      ( relation(X2)
     => relation(relation_rng_restriction(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).

fof(fc5_funct_1,axiom,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => ( relation(relation_rng_restriction(X1,X2))
        & function(relation_rng_restriction(X1,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_funct_1) ).

fof(t86_funct_1,conjecture,
    ! [X1,X2,X3] :
      ( ( relation(X3)
        & function(X3) )
     => ( in(X2,relation_dom(relation_rng_restriction(X1,X3)))
      <=> ( in(X2,relation_dom(X3))
          & in(apply(X3,X2),X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_funct_1) ).

fof(c_0_4,plain,
    ! [X52,X53,X54,X55,X56,X57] :
      ( ( in(X55,relation_dom(X54))
        | ~ in(X55,relation_dom(X53))
        | X53 != relation_rng_restriction(X52,X54)
        | ~ relation(X54)
        | ~ function(X54)
        | ~ relation(X53)
        | ~ function(X53) )
      & ( in(apply(X54,X55),X52)
        | ~ in(X55,relation_dom(X53))
        | X53 != relation_rng_restriction(X52,X54)
        | ~ relation(X54)
        | ~ function(X54)
        | ~ relation(X53)
        | ~ function(X53) )
      & ( ~ in(X56,relation_dom(X54))
        | ~ in(apply(X54,X56),X52)
        | in(X56,relation_dom(X53))
        | X53 != relation_rng_restriction(X52,X54)
        | ~ relation(X54)
        | ~ function(X54)
        | ~ relation(X53)
        | ~ function(X53) )
      & ( ~ in(X57,relation_dom(X53))
        | apply(X53,X57) = apply(X54,X57)
        | X53 != relation_rng_restriction(X52,X54)
        | ~ relation(X54)
        | ~ function(X54)
        | ~ relation(X53)
        | ~ function(X53) )
      & ( in(esk16_3(X52,X53,X54),relation_dom(X53))
        | ~ in(esk15_3(X52,X53,X54),relation_dom(X53))
        | ~ in(esk15_3(X52,X53,X54),relation_dom(X54))
        | ~ in(apply(X54,esk15_3(X52,X53,X54)),X52)
        | X53 = relation_rng_restriction(X52,X54)
        | ~ relation(X54)
        | ~ function(X54)
        | ~ relation(X53)
        | ~ function(X53) )
      & ( apply(X53,esk16_3(X52,X53,X54)) != apply(X54,esk16_3(X52,X53,X54))
        | ~ in(esk15_3(X52,X53,X54),relation_dom(X53))
        | ~ in(esk15_3(X52,X53,X54),relation_dom(X54))
        | ~ in(apply(X54,esk15_3(X52,X53,X54)),X52)
        | X53 = relation_rng_restriction(X52,X54)
        | ~ relation(X54)
        | ~ function(X54)
        | ~ relation(X53)
        | ~ function(X53) )
      & ( in(esk16_3(X52,X53,X54),relation_dom(X53))
        | in(esk15_3(X52,X53,X54),relation_dom(X54))
        | in(esk15_3(X52,X53,X54),relation_dom(X53))
        | X53 = relation_rng_restriction(X52,X54)
        | ~ relation(X54)
        | ~ function(X54)
        | ~ relation(X53)
        | ~ function(X53) )
      & ( apply(X53,esk16_3(X52,X53,X54)) != apply(X54,esk16_3(X52,X53,X54))
        | in(esk15_3(X52,X53,X54),relation_dom(X54))
        | in(esk15_3(X52,X53,X54),relation_dom(X53))
        | X53 = relation_rng_restriction(X52,X54)
        | ~ relation(X54)
        | ~ function(X54)
        | ~ relation(X53)
        | ~ function(X53) )
      & ( in(esk16_3(X52,X53,X54),relation_dom(X53))
        | in(apply(X54,esk15_3(X52,X53,X54)),X52)
        | in(esk15_3(X52,X53,X54),relation_dom(X53))
        | X53 = relation_rng_restriction(X52,X54)
        | ~ relation(X54)
        | ~ function(X54)
        | ~ relation(X53)
        | ~ function(X53) )
      & ( apply(X53,esk16_3(X52,X53,X54)) != apply(X54,esk16_3(X52,X53,X54))
        | in(apply(X54,esk15_3(X52,X53,X54)),X52)
        | in(esk15_3(X52,X53,X54),relation_dom(X53))
        | X53 = relation_rng_restriction(X52,X54)
        | ~ relation(X54)
        | ~ function(X54)
        | ~ relation(X53)
        | ~ function(X53) ) ),
    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)],[t85_funct_1])])])])])]) ).

fof(c_0_5,plain,
    ! [X29,X30] :
      ( ~ relation(X30)
      | relation(relation_rng_restriction(X29,X30)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k8_relat_1])]) ).

fof(c_0_6,plain,
    ! [X31,X32] :
      ( ( relation(relation_rng_restriction(X31,X32))
        | ~ relation(X32)
        | ~ function(X32) )
      & ( function(relation_rng_restriction(X31,X32))
        | ~ relation(X32)
        | ~ function(X32) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc5_funct_1])])]) ).

fof(c_0_7,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( relation(X3)
          & function(X3) )
       => ( in(X2,relation_dom(relation_rng_restriction(X1,X3)))
        <=> ( in(X2,relation_dom(X3))
            & in(apply(X3,X2),X1) ) ) ),
    inference(assume_negation,[status(cth)],[t86_funct_1]) ).

cnf(c_0_8,plain,
    ( in(X1,relation_dom(X2))
    | ~ in(X1,relation_dom(X3))
    | X3 != relation_rng_restriction(X4,X2)
    | ~ relation(X2)
    | ~ function(X2)
    | ~ relation(X3)
    | ~ function(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_9,plain,
    ( relation(relation_rng_restriction(X2,X1))
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_10,plain,
    ( function(relation_rng_restriction(X1,X2))
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_11,negated_conjecture,
    ( relation(esk14_0)
    & function(esk14_0)
    & ( ~ in(esk13_0,relation_dom(relation_rng_restriction(esk12_0,esk14_0)))
      | ~ in(esk13_0,relation_dom(esk14_0))
      | ~ in(apply(esk14_0,esk13_0),esk12_0) )
    & ( in(esk13_0,relation_dom(esk14_0))
      | in(esk13_0,relation_dom(relation_rng_restriction(esk12_0,esk14_0))) )
    & ( in(apply(esk14_0,esk13_0),esk12_0)
      | in(esk13_0,relation_dom(relation_rng_restriction(esk12_0,esk14_0))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).

cnf(c_0_12,plain,
    ( in(X1,relation_dom(X2))
    | ~ in(X1,relation_dom(relation_rng_restriction(X3,X2)))
    | ~ function(X2)
    | ~ relation(X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_8]),c_0_9]),c_0_10]) ).

cnf(c_0_13,negated_conjecture,
    ( in(esk13_0,relation_dom(esk14_0))
    | in(esk13_0,relation_dom(relation_rng_restriction(esk12_0,esk14_0))) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_14,negated_conjecture,
    function(esk14_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_15,negated_conjecture,
    relation(esk14_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_16,plain,
    ( in(X1,relation_dom(X4))
    | ~ in(X1,relation_dom(X2))
    | ~ in(apply(X2,X1),X3)
    | X4 != relation_rng_restriction(X3,X2)
    | ~ relation(X2)
    | ~ function(X2)
    | ~ relation(X4)
    | ~ function(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_17,negated_conjecture,
    ( ~ in(esk13_0,relation_dom(relation_rng_restriction(esk12_0,esk14_0)))
    | ~ in(esk13_0,relation_dom(esk14_0))
    | ~ in(apply(esk14_0,esk13_0),esk12_0) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_18,negated_conjecture,
    in(esk13_0,relation_dom(esk14_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_19,plain,
    ( in(X1,relation_dom(relation_rng_restriction(X2,X3)))
    | ~ in(apply(X3,X1),X2)
    | ~ in(X1,relation_dom(X3))
    | ~ function(X3)
    | ~ relation(X3) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_16]),c_0_9]),c_0_10]) ).

cnf(c_0_20,negated_conjecture,
    ( in(apply(esk14_0,esk13_0),esk12_0)
    | in(esk13_0,relation_dom(relation_rng_restriction(esk12_0,esk14_0))) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_21,plain,
    ( in(apply(X1,X2),X3)
    | ~ in(X2,relation_dom(X4))
    | X4 != relation_rng_restriction(X3,X1)
    | ~ relation(X1)
    | ~ function(X1)
    | ~ relation(X4)
    | ~ function(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_22,negated_conjecture,
    ( ~ in(esk13_0,relation_dom(relation_rng_restriction(esk12_0,esk14_0)))
    | ~ in(apply(esk14_0,esk13_0),esk12_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).

cnf(c_0_23,negated_conjecture,
    in(esk13_0,relation_dom(relation_rng_restriction(esk12_0,esk14_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_18]),c_0_14]),c_0_15])]) ).

cnf(c_0_24,plain,
    ( in(apply(X1,X2),X3)
    | ~ in(X2,relation_dom(relation_rng_restriction(X3,X1)))
    | ~ function(X1)
    | ~ relation(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_21]),c_0_9]),c_0_10]) ).

cnf(c_0_25,negated_conjecture,
    ~ in(apply(esk14_0,esk13_0),esk12_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).

cnf(c_0_26,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_23]),c_0_14]),c_0_15])]),c_0_25]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU044+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n002.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Wed Aug 23 12:46:15 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.60  % Version  : CSE_E---1.5
% 0.20/0.60  % Problem  : theBenchmark.p
% 0.20/0.60  % Proof found
% 0.20/0.60  % SZS status Theorem for theBenchmark.p
% 0.20/0.60  % SZS output start Proof
% See solution above
% 0.20/0.61  % Total time : 0.020000 s
% 0.20/0.61  % SZS output end Proof
% 0.20/0.61  % Total time : 0.023000 s
%------------------------------------------------------------------------------