TSTP Solution File: SET047+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET047+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n006.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 14:32:30 EDT 2023

% Result   : Theorem 0.19s 0.57s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   27 (   4 unt;   5 typ;   0 def)
%            Number of atoms       :   60 (   0 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :   61 (  23   ~;  30   |;   4   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   28 (   0 sgn;  13   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_25,type,
    esk2_0: $i ).

tff(decl_26,type,
    esk3_0: $i ).

fof(pel43,conjecture,
    ! [X1,X2] :
      ( set_equal(X1,X2)
    <=> set_equal(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel43) ).

fof(pel43_1,axiom,
    ! [X1,X2] :
      ( set_equal(X1,X2)
    <=> ! [X3] :
          ( element(X3,X1)
        <=> element(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel43_1) ).

fof(c_0_2,negated_conjecture,
    ~ ! [X1,X2] :
        ( set_equal(X1,X2)
      <=> set_equal(X2,X1) ),
    inference(assume_negation,[status(cth)],[pel43]) ).

fof(c_0_3,plain,
    ! [X4,X5,X6,X7,X8,X9] :
      ( ( ~ element(X6,X4)
        | element(X6,X5)
        | ~ set_equal(X4,X5) )
      & ( ~ element(X7,X5)
        | element(X7,X4)
        | ~ set_equal(X4,X5) )
      & ( ~ element(esk1_2(X8,X9),X8)
        | ~ element(esk1_2(X8,X9),X9)
        | set_equal(X8,X9) )
      & ( element(esk1_2(X8,X9),X8)
        | element(esk1_2(X8,X9),X9)
        | set_equal(X8,X9) ) ),
    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)],[pel43_1])])])])])]) ).

fof(c_0_4,negated_conjecture,
    ( ( ~ set_equal(esk2_0,esk3_0)
      | ~ set_equal(esk3_0,esk2_0) )
    & ( set_equal(esk2_0,esk3_0)
      | set_equal(esk3_0,esk2_0) ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])]) ).

cnf(c_0_5,plain,
    ( element(X1,X3)
    | ~ element(X1,X2)
    | ~ set_equal(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

cnf(c_0_6,negated_conjecture,
    ( set_equal(esk2_0,esk3_0)
    | set_equal(esk3_0,esk2_0) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_7,plain,
    ( element(X1,X3)
    | ~ element(X1,X2)
    | ~ set_equal(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

cnf(c_0_8,negated_conjecture,
    ( element(X1,esk3_0)
    | ~ element(X1,esk2_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_7]) ).

cnf(c_0_9,plain,
    ( element(esk1_2(X1,X2),X1)
    | element(esk1_2(X1,X2),X2)
    | set_equal(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

cnf(c_0_10,negated_conjecture,
    ( element(esk1_2(esk2_0,X1),esk3_0)
    | element(esk1_2(esk2_0,X1),X1)
    | set_equal(esk2_0,X1) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_11,plain,
    ( set_equal(X1,X2)
    | ~ element(esk1_2(X1,X2),X1)
    | ~ element(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

cnf(c_0_12,negated_conjecture,
    ( element(esk1_2(esk2_0,esk3_0),esk3_0)
    | set_equal(esk2_0,esk3_0) ),
    inference(ef,[status(thm)],[c_0_10]) ).

cnf(c_0_13,negated_conjecture,
    ( set_equal(esk2_0,esk3_0)
    | ~ element(esk1_2(esk2_0,esk3_0),esk2_0) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_14,negated_conjecture,
    ( element(X1,esk2_0)
    | ~ element(X1,esk3_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_6]),c_0_5]) ).

cnf(c_0_15,negated_conjecture,
    ( ~ set_equal(esk2_0,esk3_0)
    | ~ set_equal(esk3_0,esk2_0) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_16,negated_conjecture,
    set_equal(esk2_0,esk3_0),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_12]) ).

cnf(c_0_17,negated_conjecture,
    ( element(esk1_2(X1,esk2_0),esk3_0)
    | element(esk1_2(X1,esk2_0),X1)
    | set_equal(X1,esk2_0) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_18,negated_conjecture,
    ~ set_equal(esk3_0,esk2_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]) ).

cnf(c_0_19,negated_conjecture,
    ( set_equal(X1,esk2_0)
    | ~ element(esk1_2(X1,esk2_0),esk3_0)
    | ~ element(esk1_2(X1,esk2_0),X1) ),
    inference(spm,[status(thm)],[c_0_11,c_0_14]) ).

cnf(c_0_20,negated_conjecture,
    element(esk1_2(esk3_0,esk2_0),esk3_0),
    inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_17]),c_0_18]) ).

cnf(c_0_21,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_20])]),c_0_18]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET047+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n006.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Sat Aug 26 13:17:52 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.19/0.57  % Version  : CSE_E---1.5
% 0.19/0.57  % Problem  : theBenchmark.p
% 0.19/0.57  % Proof found
% 0.19/0.57  % SZS status Theorem for theBenchmark.p
% 0.19/0.57  % SZS output start Proof
% See solution above
% 0.19/0.57  % Total time : 0.004000 s
% 0.19/0.57  % SZS output end Proof
% 0.19/0.57  % Total time : 0.007000 s
%------------------------------------------------------------------------------