TSTP Solution File: SEU133+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU133+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n011.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 16:22:38 EDT 2023

% Result   : Theorem 0.19s 0.57s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   27 (   6 unt;  11 typ;   0 def)
%            Number of atoms       :   55 (   9 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :   61 (  22   ~;  24   |;   9   &)
%                                         (   5 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (   6   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-3 aty)
%            Number of variables   :   44 (   3 sgn;  28   !;   0   ?;   0   :)

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

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

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

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

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

tff(decl_27,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_28,type,
    esk2_3: ( $i * $i * $i ) > $i ).

tff(decl_29,type,
    esk3_0: $i ).

tff(decl_30,type,
    esk4_0: $i ).

tff(decl_31,type,
    esk5_0: $i ).

tff(decl_32,type,
    esk6_0: $i ).

fof(d4_xboole_0,axiom,
    ! [X1,X2,X3] :
      ( X3 = set_difference(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            & ~ in(X4,X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).

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

fof(t36_xboole_1,conjecture,
    ! [X1,X2] : subset(set_difference(X1,X2),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).

fof(c_0_3,plain,
    ! [X1,X2,X3] :
      ( X3 = set_difference(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            & ~ in(X4,X2) ) ) ),
    inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).

fof(c_0_4,plain,
    ! [X13,X14,X15,X16,X17,X18,X19,X20] :
      ( ( in(X16,X13)
        | ~ in(X16,X15)
        | X15 != set_difference(X13,X14) )
      & ( ~ in(X16,X14)
        | ~ in(X16,X15)
        | X15 != set_difference(X13,X14) )
      & ( ~ in(X17,X13)
        | in(X17,X14)
        | in(X17,X15)
        | X15 != set_difference(X13,X14) )
      & ( ~ in(esk2_3(X18,X19,X20),X20)
        | ~ in(esk2_3(X18,X19,X20),X18)
        | in(esk2_3(X18,X19,X20),X19)
        | X20 = set_difference(X18,X19) )
      & ( in(esk2_3(X18,X19,X20),X18)
        | in(esk2_3(X18,X19,X20),X20)
        | X20 = set_difference(X18,X19) )
      & ( ~ in(esk2_3(X18,X19,X20),X19)
        | in(esk2_3(X18,X19,X20),X20)
        | X20 = set_difference(X18,X19) ) ),
    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)],[c_0_3])])])])])]) ).

cnf(c_0_5,plain,
    ( in(X1,X2)
    | ~ in(X1,X3)
    | X3 != set_difference(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

fof(c_0_6,plain,
    ! [X7,X8,X9,X10,X11] :
      ( ( ~ subset(X7,X8)
        | ~ in(X9,X7)
        | in(X9,X8) )
      & ( in(esk1_2(X10,X11),X10)
        | subset(X10,X11) )
      & ( ~ in(esk1_2(X10,X11),X11)
        | subset(X10,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)],[d3_tarski])])])])])]) ).

fof(c_0_7,negated_conjecture,
    ~ ! [X1,X2] : subset(set_difference(X1,X2),X1),
    inference(assume_negation,[status(cth)],[t36_xboole_1]) ).

cnf(c_0_8,plain,
    ( in(X1,X2)
    | ~ in(X1,set_difference(X2,X3)) ),
    inference(er,[status(thm)],[c_0_5]) ).

cnf(c_0_9,plain,
    ( in(esk1_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_10,negated_conjecture,
    ~ subset(set_difference(esk5_0,esk6_0),esk5_0),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

cnf(c_0_11,plain,
    ( subset(X1,X2)
    | ~ in(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_12,plain,
    ( subset(set_difference(X1,X2),X3)
    | in(esk1_2(set_difference(X1,X2),X3),X1) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_13,negated_conjecture,
    ~ subset(set_difference(esk5_0,esk6_0),esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,plain,
    subset(set_difference(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_11,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
% 0.00/0.12  % Problem    : SEU133+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n011.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % 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   : Wed Aug 23 16:33:21 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.55  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 : 0.007000 s
% 0.19/0.57  % SZS output end Proof
% 0.19/0.57  % Total time : 0.010000 s
%------------------------------------------------------------------------------