TSTP Solution File: SEU267+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU267+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n027.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 16:23:57 EDT 2023

% Result   : Theorem 0.21s 0.58s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   32 (   4 unt;  16 typ;   0 def)
%            Number of atoms       :   52 (  51 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :   62 (  26   ~;  24   |;   6   &)
%                                         (   2 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   18 (  11   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   5 con; 0-2 aty)
%            Number of variables   :   54 (  10 sgn;  26   !;   4   ?;   0   :)

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

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

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

tff(decl_25,type,
    empty_set: $i ).

tff(decl_26,type,
    ordered_pair: ( $i * $i ) > $i ).

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

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

tff(decl_29,type,
    esk1_1: $i > $i ).

tff(decl_30,type,
    esk2_0: $i ).

tff(decl_31,type,
    esk3_0: $i ).

tff(decl_32,type,
    esk4_0: $i ).

tff(decl_33,type,
    esk5_0: $i ).

tff(decl_34,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_35,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_36,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_37,type,
    esk9_2: ( $i * $i ) > $i ).

fof(d2_mcart_1,axiom,
    ! [X1] :
      ( ? [X2,X3] : X1 = ordered_pair(X2,X3)
     => ! [X2] :
          ( X2 = pair_second(X1)
        <=> ! [X3,X4] :
              ( X1 = ordered_pair(X3,X4)
             => X2 = X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_mcart_1) ).

fof(t7_mcart_1,conjecture,
    ! [X1,X2] :
      ( pair_first(ordered_pair(X1,X2)) = X1
      & pair_second(ordered_pair(X1,X2)) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_mcart_1) ).

fof(d1_mcart_1,axiom,
    ! [X1] :
      ( ? [X2,X3] : X1 = ordered_pair(X2,X3)
     => ! [X2] :
          ( X2 = pair_first(X1)
        <=> ! [X3,X4] :
              ( X1 = ordered_pair(X3,X4)
             => X2 = X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_mcart_1) ).

fof(c_0_3,plain,
    ! [X33,X34,X35,X36,X37,X38,X39] :
      ( ( X36 != pair_second(X33)
        | X33 != ordered_pair(X37,X38)
        | X36 = X38
        | X33 != ordered_pair(X34,X35) )
      & ( X33 = ordered_pair(esk8_2(X33,X39),esk9_2(X33,X39))
        | X39 = pair_second(X33)
        | X33 != ordered_pair(X34,X35) )
      & ( X39 != esk9_2(X33,X39)
        | X39 = pair_second(X33)
        | X33 != ordered_pair(X34,X35) ) ),
    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)],[d2_mcart_1])])])])])]) ).

fof(c_0_4,negated_conjecture,
    ~ ! [X1,X2] :
        ( pair_first(ordered_pair(X1,X2)) = X1
        & pair_second(ordered_pair(X1,X2)) = X2 ),
    inference(assume_negation,[status(cth)],[t7_mcart_1]) ).

cnf(c_0_5,plain,
    ( X1 = X4
    | X1 != pair_second(X2)
    | X2 != ordered_pair(X3,X4)
    | X2 != ordered_pair(X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

fof(c_0_6,plain,
    ! [X24,X25,X26,X27,X28,X29,X30] :
      ( ( X27 != pair_first(X24)
        | X24 != ordered_pair(X28,X29)
        | X27 = X28
        | X24 != ordered_pair(X25,X26) )
      & ( X24 = ordered_pair(esk6_2(X24,X30),esk7_2(X24,X30))
        | X30 = pair_first(X24)
        | X24 != ordered_pair(X25,X26) )
      & ( X30 != esk6_2(X24,X30)
        | X30 = pair_first(X24)
        | X24 != ordered_pair(X25,X26) ) ),
    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)],[d1_mcart_1])])])])])]) ).

fof(c_0_7,negated_conjecture,
    ( pair_first(ordered_pair(esk4_0,esk5_0)) != esk4_0
    | pair_second(ordered_pair(esk4_0,esk5_0)) != esk5_0 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

cnf(c_0_8,plain,
    ( pair_second(ordered_pair(X1,X2)) = X3
    | ordered_pair(X1,X2) != ordered_pair(X4,X3) ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_5])]) ).

cnf(c_0_9,plain,
    ( X1 = X3
    | X1 != pair_first(X2)
    | X2 != ordered_pair(X3,X4)
    | X2 != ordered_pair(X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    ( pair_first(ordered_pair(esk4_0,esk5_0)) != esk4_0
    | pair_second(ordered_pair(esk4_0,esk5_0)) != esk5_0 ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,plain,
    pair_second(ordered_pair(X1,X2)) = X2,
    inference(er,[status(thm)],[c_0_8]) ).

cnf(c_0_12,plain,
    ( pair_first(ordered_pair(X1,X2)) = X3
    | ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_9])]) ).

cnf(c_0_13,negated_conjecture,
    pair_first(ordered_pair(esk4_0,esk5_0)) != esk4_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11])]) ).

cnf(c_0_14,plain,
    pair_first(ordered_pair(X1,X2)) = X1,
    inference(er,[status(thm)],[c_0_12]) ).

cnf(c_0_15,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU267+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.17/0.35  % Computer : n027.cluster.edu
% 0.17/0.35  % Model    : x86_64 x86_64
% 0.17/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35  % Memory   : 8042.1875MB
% 0.17/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35  % CPULimit   : 300
% 0.17/0.35  % WCLimit    : 300
% 0.17/0.35  % DateTime   : Wed Aug 23 16:20:02 EDT 2023
% 0.17/0.35  % CPUTime  : 
% 0.21/0.57  start to proof: theBenchmark
% 0.21/0.58  % Version  : CSE_E---1.5
% 0.21/0.58  % Problem  : theBenchmark.p
% 0.21/0.58  % Proof found
% 0.21/0.58  % SZS status Theorem for theBenchmark.p
% 0.21/0.58  % SZS output start Proof
% See solution above
% 0.21/0.58  % Total time : 0.008000 s
% 0.21/0.58  % SZS output end Proof
% 0.21/0.58  % Total time : 0.011000 s
%------------------------------------------------------------------------------