TSTP Solution File: SEU173+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU173+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 : 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 16:23:04 EDT 2023

% Result   : Theorem 0.21s 0.59s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   40 (   4 unt;  15 typ;   0 def)
%            Number of atoms       :   86 (   6 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :   96 (  35   ~;  33   |;  12   &)
%                                         (   7 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   15 (  10   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   5 con; 0-2 aty)
%            Number of variables   :   51 (   1 sgn;  34   !;   0   ?;   0   :)

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

tff(decl_23,type,
    powerset: $i > $i ).

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

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

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

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

tff(decl_28,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_29,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_30,type,
    esk3_1: $i > $i ).

tff(decl_31,type,
    esk4_0: $i ).

tff(decl_32,type,
    esk5_0: $i ).

tff(decl_33,type,
    esk6_1: $i > $i ).

tff(decl_34,type,
    esk7_0: $i ).

tff(decl_35,type,
    esk8_1: $i > $i ).

tff(decl_36,type,
    esk9_0: $i ).

fof(d2_subset_1,axiom,
    ! [X1,X2] :
      ( ( ~ empty(X1)
       => ( element(X2,X1)
        <=> in(X2,X1) ) )
      & ( empty(X1)
       => ( element(X2,X1)
        <=> empty(X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).

fof(l71_subset_1,conjecture,
    ! [X1,X2] :
      ( ! [X3] :
          ( in(X3,X1)
         => in(X3,X2) )
     => element(X1,powerset(X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l71_subset_1) ).

fof(t7_boole,axiom,
    ! [X1,X2] :
      ~ ( in(X1,X2)
        & empty(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).

fof(d1_zfmisc_1,axiom,
    ! [X1,X2] :
      ( X2 = powerset(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> subset(X3,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).

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(c_0_5,plain,
    ! [X1,X2] :
      ( ( ~ empty(X1)
       => ( element(X2,X1)
        <=> in(X2,X1) ) )
      & ( empty(X1)
       => ( element(X2,X1)
        <=> empty(X2) ) ) ),
    inference(fof_simplification,[status(thm)],[d2_subset_1]) ).

fof(c_0_6,negated_conjecture,
    ~ ! [X1,X2] :
        ( ! [X3] :
            ( in(X3,X1)
           => in(X3,X2) )
       => element(X1,powerset(X2)) ),
    inference(assume_negation,[status(cth)],[l71_subset_1]) ).

fof(c_0_7,plain,
    ! [X13,X14] :
      ( ( ~ element(X14,X13)
        | in(X14,X13)
        | empty(X13) )
      & ( ~ in(X14,X13)
        | element(X14,X13)
        | empty(X13) )
      & ( ~ element(X14,X13)
        | empty(X14)
        | ~ empty(X13) )
      & ( ~ empty(X14)
        | element(X14,X13)
        | ~ empty(X13) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

fof(c_0_8,plain,
    ! [X35,X36] :
      ( ~ in(X35,X36)
      | ~ empty(X36) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).

fof(c_0_9,negated_conjecture,
    ! [X26] :
      ( ( ~ in(X26,esk4_0)
        | in(X26,esk5_0) )
      & ~ element(esk4_0,powerset(esk5_0)) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).

cnf(c_0_10,plain,
    ( element(X1,X2)
    | empty(X2)
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,plain,
    ( ~ in(X1,X2)
    | ~ empty(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_12,plain,
    ! [X6,X7,X8,X9,X10,X11] :
      ( ( ~ in(X8,X7)
        | subset(X8,X6)
        | X7 != powerset(X6) )
      & ( ~ subset(X9,X6)
        | in(X9,X7)
        | X7 != powerset(X6) )
      & ( ~ in(esk1_2(X10,X11),X11)
        | ~ subset(esk1_2(X10,X11),X10)
        | X11 = powerset(X10) )
      & ( in(esk1_2(X10,X11),X11)
        | subset(esk1_2(X10,X11),X10)
        | X11 = powerset(X10) ) ),
    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_zfmisc_1])])])])])]) ).

fof(c_0_13,plain,
    ! [X15,X16,X17,X18,X19] :
      ( ( ~ subset(X15,X16)
        | ~ in(X17,X15)
        | in(X17,X16) )
      & ( in(esk2_2(X18,X19),X18)
        | subset(X18,X19) )
      & ( ~ in(esk2_2(X18,X19),X19)
        | subset(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)],[d3_tarski])])])])])]) ).

cnf(c_0_14,negated_conjecture,
    ~ element(esk4_0,powerset(esk5_0)),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_15,plain,
    ( element(X1,X2)
    | ~ in(X1,X2) ),
    inference(csr,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_16,plain,
    ( in(X1,X3)
    | ~ subset(X1,X2)
    | X3 != powerset(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_17,negated_conjecture,
    ( in(X1,esk5_0)
    | ~ in(X1,esk4_0) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_18,plain,
    ( in(esk2_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_19,negated_conjecture,
    ~ in(esk4_0,powerset(esk5_0)),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_20,plain,
    ( in(X1,powerset(X2))
    | ~ subset(X1,X2) ),
    inference(er,[status(thm)],[c_0_16]) ).

cnf(c_0_21,plain,
    ( subset(X1,X2)
    | ~ in(esk2_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_22,negated_conjecture,
    ( subset(esk4_0,X1)
    | in(esk2_2(esk4_0,X1),esk5_0) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_23,negated_conjecture,
    ~ subset(esk4_0,esk5_0),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_24,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU173+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
% 0.14/0.35  % Computer : n006.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Wed Aug 23 17:22:38 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.57  start to proof: theBenchmark
% 0.21/0.59  % Version  : CSE_E---1.5
% 0.21/0.59  % Problem  : theBenchmark.p
% 0.21/0.59  % Proof found
% 0.21/0.59  % SZS status Theorem for theBenchmark.p
% 0.21/0.59  % SZS output start Proof
% See solution above
% 0.21/0.60  % Total time : 0.011000 s
% 0.21/0.60  % SZS output end Proof
% 0.21/0.60  % Total time : 0.013000 s
%------------------------------------------------------------------------------