TSTP Solution File: SET887+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET887+1 : TPTP v8.1.2. Released v3.2.0.
% 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 14:36:09 EDT 2023

% Result   : Theorem 0.20s 0.56s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   55 (  10 unt;  14 typ;   0 def)
%            Number of atoms       :  128 (  94 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :  138 (  51   ~;  62   |;  19   &)
%                                         (   5 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   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  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-3 aty)
%            Number of variables   :   72 (   9 sgn;  39   !;   0   ?;   0   :)

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

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

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

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

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

tff(decl_27,type,
    singleton: $i > $i ).

tff(decl_28,type,
    esk1_1: $i > $i ).

tff(decl_29,type,
    esk2_3: ( $i * $i * $i ) > $i ).

tff(decl_30,type,
    esk3_0: $i ).

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

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

tff(decl_33,type,
    esk6_0: $i ).

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

tff(decl_35,type,
    esk8_0: $i ).

fof(t28_zfmisc_1,conjecture,
    ! [X1,X2,X3,X4] :
      ~ ( subset(unordered_pair(X1,X2),unordered_pair(X3,X4))
        & X1 != X3
        & X1 != X4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_zfmisc_1) ).

fof(l46_zfmisc_1,axiom,
    ! [X1,X2,X3] :
      ( subset(X1,unordered_pair(X2,X3))
    <=> ~ ( X1 != empty_set
          & X1 != singleton(X2)
          & X1 != singleton(X3)
          & X1 != unordered_pair(X2,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l46_zfmisc_1) ).

fof(t8_zfmisc_1,axiom,
    ! [X1,X2,X3] :
      ( singleton(X1) = unordered_pair(X2,X3)
     => X1 = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).

fof(d2_tarski,axiom,
    ! [X1,X2,X3] :
      ( X3 = unordered_pair(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( X4 = X1
            | X4 = X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).

fof(d1_xboole_0,axiom,
    ! [X1] :
      ( X1 = empty_set
    <=> ! [X2] : ~ in(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ~ ( subset(unordered_pair(X1,X2),unordered_pair(X3,X4))
          & X1 != X3
          & X1 != X4 ),
    inference(assume_negation,[status(cth)],[t28_zfmisc_1]) ).

fof(c_0_6,plain,
    ! [X22,X23,X24] :
      ( ( ~ subset(X22,unordered_pair(X23,X24))
        | X22 = empty_set
        | X22 = singleton(X23)
        | X22 = singleton(X24)
        | X22 = unordered_pair(X23,X24) )
      & ( X22 != empty_set
        | subset(X22,unordered_pair(X23,X24)) )
      & ( X22 != singleton(X23)
        | subset(X22,unordered_pair(X23,X24)) )
      & ( X22 != singleton(X24)
        | subset(X22,unordered_pair(X23,X24)) )
      & ( X22 != unordered_pair(X23,X24)
        | subset(X22,unordered_pair(X23,X24)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l46_zfmisc_1])])]) ).

fof(c_0_7,negated_conjecture,
    ( subset(unordered_pair(esk5_0,esk6_0),unordered_pair(esk7_0,esk8_0))
    & esk5_0 != esk7_0
    & esk5_0 != esk8_0 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

fof(c_0_8,plain,
    ! [X36,X37,X38] :
      ( singleton(X36) != unordered_pair(X37,X38)
      | X36 = X37 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_zfmisc_1])]) ).

cnf(c_0_9,plain,
    ( X1 = empty_set
    | X1 = singleton(X2)
    | X1 = singleton(X3)
    | X1 = unordered_pair(X2,X3)
    | ~ subset(X1,unordered_pair(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    subset(unordered_pair(esk5_0,esk6_0),unordered_pair(esk7_0,esk8_0)),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,plain,
    ( X1 = X2
    | singleton(X1) != unordered_pair(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12,negated_conjecture,
    ( unordered_pair(esk7_0,esk8_0) = unordered_pair(esk5_0,esk6_0)
    | singleton(esk7_0) = unordered_pair(esk5_0,esk6_0)
    | singleton(esk8_0) = unordered_pair(esk5_0,esk6_0)
    | unordered_pair(esk5_0,esk6_0) = empty_set ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_13,negated_conjecture,
    ( unordered_pair(esk7_0,esk8_0) = unordered_pair(esk5_0,esk6_0)
    | singleton(esk7_0) = unordered_pair(esk5_0,esk6_0)
    | unordered_pair(esk5_0,esk6_0) = empty_set
    | esk8_0 = X1
    | unordered_pair(esk5_0,esk6_0) != unordered_pair(X1,X2) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_14,negated_conjecture,
    esk5_0 != esk8_0,
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_15,plain,
    ! [X13,X14,X15,X16,X17,X18,X19,X20] :
      ( ( ~ in(X16,X15)
        | X16 = X13
        | X16 = X14
        | X15 != unordered_pair(X13,X14) )
      & ( X17 != X13
        | in(X17,X15)
        | X15 != unordered_pair(X13,X14) )
      & ( X17 != X14
        | in(X17,X15)
        | X15 != unordered_pair(X13,X14) )
      & ( esk2_3(X18,X19,X20) != X18
        | ~ in(esk2_3(X18,X19,X20),X20)
        | X20 = unordered_pair(X18,X19) )
      & ( esk2_3(X18,X19,X20) != X19
        | ~ in(esk2_3(X18,X19,X20),X20)
        | X20 = unordered_pair(X18,X19) )
      & ( in(esk2_3(X18,X19,X20),X20)
        | esk2_3(X18,X19,X20) = X18
        | esk2_3(X18,X19,X20) = X19
        | X20 = unordered_pair(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)],[d2_tarski])])])])])]) ).

cnf(c_0_16,negated_conjecture,
    ( unordered_pair(esk7_0,esk8_0) = unordered_pair(esk5_0,esk6_0)
    | singleton(esk7_0) = unordered_pair(esk5_0,esk6_0)
    | unordered_pair(esk5_0,esk6_0) = empty_set ),
    inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_13]),c_0_14]) ).

cnf(c_0_17,plain,
    ( in(X1,X3)
    | X1 != X2
    | X3 != unordered_pair(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_18,negated_conjecture,
    ( unordered_pair(esk7_0,esk8_0) = unordered_pair(esk5_0,esk6_0)
    | unordered_pair(esk5_0,esk6_0) = empty_set
    | esk7_0 = X1
    | unordered_pair(esk5_0,esk6_0) != unordered_pair(X1,X2) ),
    inference(spm,[status(thm)],[c_0_11,c_0_16]) ).

cnf(c_0_19,negated_conjecture,
    esk5_0 != esk7_0,
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_20,plain,
    ! [X1] :
      ( X1 = empty_set
    <=> ! [X2] : ~ in(X2,X1) ),
    inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).

cnf(c_0_21,plain,
    ( X1 = X3
    | X1 = X4
    | ~ in(X1,X2)
    | X2 != unordered_pair(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_22,plain,
    in(X1,unordered_pair(X1,X2)),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_17])]) ).

cnf(c_0_23,negated_conjecture,
    ( unordered_pair(esk7_0,esk8_0) = unordered_pair(esk5_0,esk6_0)
    | unordered_pair(esk5_0,esk6_0) = empty_set ),
    inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_18]),c_0_19]) ).

fof(c_0_24,plain,
    ! [X9,X10,X11] :
      ( ( X9 != empty_set
        | ~ in(X10,X9) )
      & ( in(esk1_1(X11),X11)
        | X11 = empty_set ) ),
    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_20])])])])]) ).

cnf(c_0_25,plain,
    ( X1 = X2
    | X1 = X3
    | ~ in(X1,unordered_pair(X3,X2)) ),
    inference(er,[status(thm)],[c_0_21]) ).

cnf(c_0_26,negated_conjecture,
    ( unordered_pair(esk5_0,esk6_0) = empty_set
    | in(esk7_0,unordered_pair(esk5_0,esk6_0)) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_27,plain,
    ( X1 != empty_set
    | ~ in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_28,negated_conjecture,
    ( unordered_pair(esk5_0,esk6_0) = empty_set
    | esk6_0 = esk7_0 ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_19]) ).

cnf(c_0_29,plain,
    ~ in(X1,empty_set),
    inference(er,[status(thm)],[c_0_27]) ).

cnf(c_0_30,plain,
    ( in(X1,X3)
    | X1 != X2
    | X3 != unordered_pair(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_31,negated_conjecture,
    esk6_0 = esk7_0,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_28]),c_0_29]) ).

cnf(c_0_32,plain,
    in(X1,unordered_pair(X2,X1)),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_30])]) ).

cnf(c_0_33,negated_conjecture,
    ( unordered_pair(esk7_0,esk8_0) = unordered_pair(esk5_0,esk7_0)
    | unordered_pair(esk5_0,esk7_0) = empty_set ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_31]),c_0_31]) ).

cnf(c_0_34,negated_conjecture,
    ( unordered_pair(esk5_0,esk7_0) = empty_set
    | in(esk8_0,unordered_pair(esk5_0,esk7_0)) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_35,negated_conjecture,
    ( unordered_pair(esk5_0,esk7_0) = empty_set
    | esk8_0 = esk7_0 ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_34]),c_0_14]) ).

cnf(c_0_36,negated_conjecture,
    esk8_0 = esk7_0,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_35]),c_0_29]) ).

cnf(c_0_37,negated_conjecture,
    ( unordered_pair(esk7_0,esk7_0) = unordered_pair(esk5_0,esk7_0)
    | unordered_pair(esk5_0,esk7_0) = empty_set ),
    inference(rw,[status(thm)],[c_0_33,c_0_36]) ).

cnf(c_0_38,negated_conjecture,
    ( unordered_pair(esk5_0,esk7_0) = empty_set
    | X1 = esk7_0
    | ~ in(X1,unordered_pair(esk5_0,esk7_0)) ),
    inference(spm,[status(thm)],[c_0_25,c_0_37]) ).

cnf(c_0_39,negated_conjecture,
    unordered_pair(esk5_0,esk7_0) = empty_set,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_22]),c_0_19]) ).

cnf(c_0_40,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_39]),c_0_29]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET887+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n031.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sat Aug 26 13:31:08 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.54  start to proof: theBenchmark
% 0.20/0.56  % Version  : CSE_E---1.5
% 0.20/0.56  % Problem  : theBenchmark.p
% 0.20/0.56  % Proof found
% 0.20/0.56  % SZS status Theorem for theBenchmark.p
% 0.20/0.56  % SZS output start Proof
% See solution above
% 0.20/0.56  % Total time : 0.009000 s
% 0.20/0.56  % SZS output end Proof
% 0.20/0.56  % Total time : 0.012000 s
%------------------------------------------------------------------------------