TSTP Solution File: SET580+3 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET580+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n021.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 14:34:36 EDT 2023

% Result   : Theorem 0.20s 0.60s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   41 (   9 unt;   8 typ;   0 def)
%            Number of atoms       :   92 (   3 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  102 (  43   ~;  43   |;   9   &)
%                                         (   7 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (   5   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   45 (   4 sgn;  25   !;   0   ?;   0   :)

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

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

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

tff(decl_25,type,
    symmetric_difference: ( $i * $i ) > $i ).

tff(decl_26,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_27,type,
    esk2_0: $i ).

tff(decl_28,type,
    esk3_0: $i ).

tff(decl_29,type,
    esk4_0: $i ).

fof(prove_th23,conjecture,
    ! [X1,X2,X3] :
      ( member(X1,symmetric_difference(X2,X3))
    <=> ~ ( member(X1,X2)
        <=> member(X1,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th23) ).

fof(symmetric_difference_defn,axiom,
    ! [X1,X2] : symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).

fof(difference_defn,axiom,
    ! [X1,X2,X3] :
      ( member(X3,difference(X1,X2))
    <=> ( member(X3,X1)
        & ~ member(X3,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).

fof(union_defn,axiom,
    ! [X1,X2,X3] :
      ( member(X3,union(X1,X2))
    <=> ( member(X3,X1)
        | member(X3,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).

fof(c_0_4,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( member(X1,symmetric_difference(X2,X3))
      <=> ~ ( member(X1,X2)
          <=> member(X1,X3) ) ),
    inference(assume_negation,[status(cth)],[prove_th23]) ).

fof(c_0_5,negated_conjecture,
    ( ( ~ member(esk2_0,esk3_0)
      | member(esk2_0,esk4_0)
      | ~ member(esk2_0,symmetric_difference(esk3_0,esk4_0)) )
    & ( ~ member(esk2_0,esk4_0)
      | member(esk2_0,esk3_0)
      | ~ member(esk2_0,symmetric_difference(esk3_0,esk4_0)) )
    & ( ~ member(esk2_0,esk3_0)
      | ~ member(esk2_0,esk4_0)
      | member(esk2_0,symmetric_difference(esk3_0,esk4_0)) )
    & ( member(esk2_0,esk3_0)
      | member(esk2_0,esk4_0)
      | member(esk2_0,symmetric_difference(esk3_0,esk4_0)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).

fof(c_0_6,plain,
    ! [X10,X11] : symmetric_difference(X10,X11) = union(difference(X10,X11),difference(X11,X10)),
    inference(variable_rename,[status(thm)],[symmetric_difference_defn]) ).

fof(c_0_7,plain,
    ! [X1,X2,X3] :
      ( member(X3,difference(X1,X2))
    <=> ( member(X3,X1)
        & ~ member(X3,X2) ) ),
    inference(fof_simplification,[status(thm)],[difference_defn]) ).

cnf(c_0_8,negated_conjecture,
    ( member(esk2_0,esk3_0)
    | ~ member(esk2_0,esk4_0)
    | ~ member(esk2_0,symmetric_difference(esk3_0,esk4_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,plain,
    symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_10,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,union(X4,X5))
        | member(X6,X4)
        | member(X6,X5) )
      & ( ~ member(X6,X4)
        | member(X6,union(X4,X5)) )
      & ( ~ member(X6,X5)
        | member(X6,union(X4,X5)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])]) ).

fof(c_0_11,plain,
    ! [X7,X8,X9] :
      ( ( member(X9,X7)
        | ~ member(X9,difference(X7,X8)) )
      & ( ~ member(X9,X8)
        | ~ member(X9,difference(X7,X8)) )
      & ( ~ member(X9,X7)
        | member(X9,X8)
        | member(X9,difference(X7,X8)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

cnf(c_0_12,negated_conjecture,
    ( member(esk2_0,esk3_0)
    | ~ member(esk2_0,esk4_0)
    | ~ member(esk2_0,union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0))) ),
    inference(rw,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_13,plain,
    ( member(X1,union(X3,X2))
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,plain,
    ( member(X1,X2)
    | ~ member(X1,difference(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_15,plain,
    ( ~ member(X1,X2)
    | ~ member(X1,difference(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_16,negated_conjecture,
    ( member(esk2_0,symmetric_difference(esk3_0,esk4_0))
    | ~ member(esk2_0,esk3_0)
    | ~ member(esk2_0,esk4_0) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_17,negated_conjecture,
    ~ member(esk2_0,difference(esk4_0,esk3_0)),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15]) ).

cnf(c_0_18,plain,
    ( member(X1,X3)
    | member(X1,difference(X2,X3))
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_19,negated_conjecture,
    ( member(esk2_0,esk3_0)
    | member(esk2_0,esk4_0)
    | member(esk2_0,symmetric_difference(esk3_0,esk4_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_20,negated_conjecture,
    ( member(esk2_0,union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0)))
    | ~ member(esk2_0,esk3_0)
    | ~ member(esk2_0,esk4_0) ),
    inference(rw,[status(thm)],[c_0_16,c_0_9]) ).

cnf(c_0_21,negated_conjecture,
    ( member(esk2_0,esk3_0)
    | ~ member(esk2_0,esk4_0) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_22,negated_conjecture,
    ( member(esk2_0,esk4_0)
    | ~ member(esk2_0,esk3_0)
    | ~ member(esk2_0,symmetric_difference(esk3_0,esk4_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_23,plain,
    ( member(X1,X2)
    | member(X1,X3)
    | ~ member(X1,union(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_24,negated_conjecture,
    ( member(esk2_0,esk3_0)
    | member(esk2_0,esk4_0)
    | member(esk2_0,union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0))) ),
    inference(rw,[status(thm)],[c_0_19,c_0_9]) ).

cnf(c_0_25,negated_conjecture,
    ( member(esk2_0,union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0)))
    | ~ member(esk2_0,esk4_0) ),
    inference(csr,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_26,negated_conjecture,
    ( member(esk2_0,esk4_0)
    | ~ member(esk2_0,esk3_0)
    | ~ member(esk2_0,union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0))) ),
    inference(rw,[status(thm)],[c_0_22,c_0_9]) ).

cnf(c_0_27,negated_conjecture,
    member(esk2_0,esk3_0),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_17]),c_0_21]),c_0_14]) ).

cnf(c_0_28,negated_conjecture,
    ~ member(esk2_0,esk4_0),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_25]),c_0_17]),c_0_15]) ).

cnf(c_0_29,negated_conjecture,
    ~ member(esk2_0,union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0))),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]),c_0_28]) ).

cnf(c_0_30,plain,
    ( member(X1,union(X2,X3))
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_31,negated_conjecture,
    ~ member(esk2_0,difference(esk3_0,esk4_0)),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_32,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_18]),c_0_27])]),c_0_28]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET580+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n021.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sat Aug 26 10:14:26 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.59  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 : 0.007000 s
% 0.20/0.61  % SZS output end Proof
% 0.20/0.61  % Total time : 0.010000 s
%------------------------------------------------------------------------------