TSTP Solution File: SET628+3 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET628+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n031.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 14:34:56 EDT 2023

% Result   : Theorem 0.20s 0.58s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   45 (   9 unt;   9 typ;   0 def)
%            Number of atoms       :   89 (  16 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :   92 (  39   ~;  36   |;   9   &)
%                                         (   8 <=>;   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  :   12 (   7   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   57 (   4 sgn;  32   !;   1   ?;   0   :)

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

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

tff(decl_24,type,
    empty_set: $i ).

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

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

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

tff(decl_28,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_29,type,
    esk3_1: $i > $i ).

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

fof(empty_set_defn,axiom,
    ! [X1] : ~ member(X1,empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).

fof(empty_defn,axiom,
    ! [X1] :
      ( empty(X1)
    <=> ! [X2] : ~ member(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_defn) ).

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

fof(intersect_defn,axiom,
    ! [X1,X2] :
      ( intersect(X1,X2)
    <=> ? [X3] :
          ( member(X3,X1)
          & member(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).

fof(prove_th110,conjecture,
    ! [X1] :
      ( intersect(X1,X1)
    <=> not_equal(X1,empty_set) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th110) ).

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

fof(c_0_6,plain,
    ! [X1] : ~ member(X1,empty_set),
    inference(fof_simplification,[status(thm)],[empty_set_defn]) ).

fof(c_0_7,plain,
    ! [X1] :
      ( empty(X1)
    <=> ! [X2] : ~ member(X2,X1) ),
    inference(fof_simplification,[status(thm)],[empty_defn]) ).

fof(c_0_8,plain,
    ! [X10] : ~ member(X10,empty_set),
    inference(variable_rename,[status(thm)],[c_0_6]) ).

fof(c_0_9,plain,
    ! [X11,X12,X13,X14,X15,X16] :
      ( ( ~ member(X13,X11)
        | member(X13,X12)
        | X11 != X12 )
      & ( ~ member(X14,X12)
        | member(X14,X11)
        | X11 != X12 )
      & ( ~ member(esk2_2(X15,X16),X15)
        | ~ member(esk2_2(X15,X16),X16)
        | X15 = X16 )
      & ( member(esk2_2(X15,X16),X15)
        | member(esk2_2(X15,X16),X16)
        | X15 = X16 ) ),
    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)],[equal_member_defn])])])])])]) ).

fof(c_0_10,plain,
    ! [X4,X5,X7,X8,X9] :
      ( ( member(esk1_2(X4,X5),X4)
        | ~ intersect(X4,X5) )
      & ( member(esk1_2(X4,X5),X5)
        | ~ intersect(X4,X5) )
      & ( ~ member(X9,X7)
        | ~ member(X9,X8)
        | intersect(X7,X8) ) ),
    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)],[intersect_defn])])])])])]) ).

fof(c_0_11,plain,
    ! [X22,X23,X24] :
      ( ( ~ empty(X22)
        | ~ member(X23,X22) )
      & ( member(esk3_1(X24),X24)
        | empty(X24) ) ),
    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_7])])])])]) ).

fof(c_0_12,negated_conjecture,
    ~ ! [X1] :
        ( intersect(X1,X1)
      <=> not_equal(X1,empty_set) ),
    inference(assume_negation,[status(cth)],[prove_th110]) ).

cnf(c_0_13,plain,
    ~ member(X1,empty_set),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,plain,
    ( member(esk2_2(X1,X2),X1)
    | member(esk2_2(X1,X2),X2)
    | X1 = X2 ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_15,plain,
    ( intersect(X2,X3)
    | ~ member(X1,X2)
    | ~ member(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_16,plain,
    ( member(esk3_1(X1),X1)
    | empty(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_17,negated_conjecture,
    ( ( ~ intersect(esk4_0,esk4_0)
      | ~ not_equal(esk4_0,empty_set) )
    & ( intersect(esk4_0,esk4_0)
      | not_equal(esk4_0,empty_set) ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).

fof(c_0_18,plain,
    ! [X18,X19] :
      ( ( ~ not_equal(X18,X19)
        | X18 != X19 )
      & ( X18 = X19
        | not_equal(X18,X19) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[not_equal_defn])]) ).

cnf(c_0_19,plain,
    ( ~ empty(X1)
    | ~ member(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_20,plain,
    ( empty_set = X1
    | member(esk2_2(empty_set,X1),X1) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_21,plain,
    ( empty(X1)
    | intersect(X2,X1)
    | ~ member(esk3_1(X1),X2) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_22,negated_conjecture,
    ( ~ intersect(esk4_0,esk4_0)
    | ~ not_equal(esk4_0,empty_set) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_23,plain,
    ( X1 = X2
    | not_equal(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_24,plain,
    ( empty_set = X1
    | ~ empty(X1) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_25,plain,
    ( empty(X1)
    | intersect(X1,X1) ),
    inference(spm,[status(thm)],[c_0_21,c_0_16]) ).

cnf(c_0_26,plain,
    ( member(esk1_2(X1,X2),X2)
    | ~ intersect(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_27,negated_conjecture,
    ( empty_set = esk4_0
    | ~ intersect(esk4_0,esk4_0) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_28,plain,
    ( empty_set = X1
    | intersect(X1,X1) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_29,plain,
    ( ~ not_equal(X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_30,plain,
    ~ intersect(X1,empty_set),
    inference(spm,[status(thm)],[c_0_13,c_0_26]) ).

cnf(c_0_31,negated_conjecture,
    empty_set = esk4_0,
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_32,negated_conjecture,
    ( intersect(esk4_0,esk4_0)
    | not_equal(esk4_0,empty_set) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_33,plain,
    ~ not_equal(X1,X1),
    inference(er,[status(thm)],[c_0_29]) ).

cnf(c_0_34,plain,
    ~ intersect(X1,esk4_0),
    inference(rw,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_35,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_31]),c_0_33]),c_0_34]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SET628+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n031.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 15:24:08 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.58  % Version  : CSE_E---1.5
% 0.20/0.58  % Problem  : theBenchmark.p
% 0.20/0.58  % Proof found
% 0.20/0.58  % SZS status Theorem for theBenchmark.p
% 0.20/0.58  % SZS output start Proof
% See solution above
% 0.20/0.59  % Total time : 0.008000 s
% 0.20/0.59  % SZS output end Proof
% 0.20/0.59  % Total time : 0.010000 s
%------------------------------------------------------------------------------