TSTP Solution File: SEU159+3 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU159+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n010.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 16:22:54 EDT 2023

% Result   : Theorem 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   40 (   6 unt;  11 typ;   0 def)
%            Number of atoms       :   97 (  29 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :  106 (  38   ~;  51   |;  11   &)
%                                         (   5 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 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   :   63 (   4 sgn;  26   !;   0   ?;   0   :)

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

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

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

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

tff(decl_26,type,
    esk1_3: ( $i * $i * $i ) > $i ).

tff(decl_27,type,
    esk2_2: ( $i * $i ) > $i ).

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

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

tff(decl_30,type,
    esk5_0: $i ).

tff(decl_31,type,
    esk6_0: $i ).

tff(decl_32,type,
    esk7_0: $i ).

fof(t38_zfmisc_1,conjecture,
    ! [X1,X2,X3] :
      ( subset(unordered_pair(X1,X2),X3)
    <=> ( in(X1,X3)
        & in(X2,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_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(d2_tarski,axiom,
    ! [X1,X2,X3] :
      ( X3 = unordered_pair(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( X4 = X1
            | X4 = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( subset(unordered_pair(X1,X2),X3)
      <=> ( in(X1,X3)
          & in(X2,X3) ) ),
    inference(assume_negation,[status(cth)],[t38_zfmisc_1]) ).

fof(c_0_4,plain,
    ! [X18,X19,X20,X21,X22] :
      ( ( ~ subset(X18,X19)
        | ~ in(X20,X18)
        | in(X20,X19) )
      & ( in(esk2_2(X21,X22),X21)
        | subset(X21,X22) )
      & ( ~ in(esk2_2(X21,X22),X22)
        | subset(X21,X22) ) ),
    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_5,negated_conjecture,
    ( ( ~ subset(unordered_pair(esk5_0,esk6_0),esk7_0)
      | ~ in(esk5_0,esk7_0)
      | ~ in(esk6_0,esk7_0) )
    & ( in(esk5_0,esk7_0)
      | subset(unordered_pair(esk5_0,esk6_0),esk7_0) )
    & ( in(esk6_0,esk7_0)
      | subset(unordered_pair(esk5_0,esk6_0),esk7_0) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).

fof(c_0_6,plain,
    ! [X9,X10,X11,X12,X13,X14,X15,X16] :
      ( ( ~ in(X12,X11)
        | X12 = X9
        | X12 = X10
        | X11 != unordered_pair(X9,X10) )
      & ( X13 != X9
        | in(X13,X11)
        | X11 != unordered_pair(X9,X10) )
      & ( X13 != X10
        | in(X13,X11)
        | X11 != unordered_pair(X9,X10) )
      & ( esk1_3(X14,X15,X16) != X14
        | ~ in(esk1_3(X14,X15,X16),X16)
        | X16 = unordered_pair(X14,X15) )
      & ( esk1_3(X14,X15,X16) != X15
        | ~ in(esk1_3(X14,X15,X16),X16)
        | X16 = unordered_pair(X14,X15) )
      & ( in(esk1_3(X14,X15,X16),X16)
        | esk1_3(X14,X15,X16) = X14
        | esk1_3(X14,X15,X16) = X15
        | X16 = unordered_pair(X14,X15) ) ),
    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_7,plain,
    ( in(X3,X2)
    | ~ subset(X1,X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_8,negated_conjecture,
    ( in(esk5_0,esk7_0)
    | subset(unordered_pair(esk5_0,esk6_0),esk7_0) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,plain,
    ( in(X1,X3)
    | X1 != X2
    | X3 != unordered_pair(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,plain,
    ( X1 = X3
    | X1 = X4
    | ~ in(X1,X2)
    | X2 != unordered_pair(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,negated_conjecture,
    ( in(esk5_0,esk7_0)
    | in(X1,esk7_0)
    | ~ in(X1,unordered_pair(esk5_0,esk6_0)) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_12,plain,
    in(X1,unordered_pair(X1,X2)),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_9])]) ).

cnf(c_0_13,negated_conjecture,
    ( in(esk6_0,esk7_0)
    | subset(unordered_pair(esk5_0,esk6_0),esk7_0) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_14,plain,
    ( in(X1,X3)
    | X1 != X2
    | X3 != unordered_pair(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_15,plain,
    ( X1 = X2
    | X1 = X3
    | ~ in(X1,unordered_pair(X3,X2)) ),
    inference(er,[status(thm)],[c_0_10]) ).

cnf(c_0_16,plain,
    ( in(esk2_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_17,negated_conjecture,
    ( ~ subset(unordered_pair(esk5_0,esk6_0),esk7_0)
    | ~ in(esk5_0,esk7_0)
    | ~ in(esk6_0,esk7_0) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_18,negated_conjecture,
    in(esk5_0,esk7_0),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_19,negated_conjecture,
    ( in(esk6_0,esk7_0)
    | in(X1,esk7_0)
    | ~ in(X1,unordered_pair(esk5_0,esk6_0)) ),
    inference(spm,[status(thm)],[c_0_7,c_0_13]) ).

cnf(c_0_20,plain,
    in(X1,unordered_pair(X2,X1)),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_14])]) ).

cnf(c_0_21,plain,
    ( subset(X1,X2)
    | ~ in(esk2_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_22,plain,
    ( esk2_2(unordered_pair(X1,X2),X3) = X2
    | esk2_2(unordered_pair(X1,X2),X3) = X1
    | subset(unordered_pair(X1,X2),X3) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_23,negated_conjecture,
    ( ~ subset(unordered_pair(esk5_0,esk6_0),esk7_0)
    | ~ in(esk6_0,esk7_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).

cnf(c_0_24,negated_conjecture,
    in(esk6_0,esk7_0),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_25,plain,
    ( esk2_2(unordered_pair(X1,X2),X3) = X2
    | subset(unordered_pair(X1,X2),X3)
    | ~ in(X1,X3) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_26,negated_conjecture,
    ~ subset(unordered_pair(esk5_0,esk6_0),esk7_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]) ).

cnf(c_0_27,plain,
    ( subset(unordered_pair(X1,X2),X3)
    | ~ in(X2,X3)
    | ~ in(X1,X3) ),
    inference(spm,[status(thm)],[c_0_21,c_0_25]) ).

cnf(c_0_28,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_24]),c_0_18])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU159+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n010.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   : Wed Aug 23 13:23:06 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 0.20/0.59  % Version  : CSE_E---1.5
% 0.20/0.59  % Problem  : theBenchmark.p
% 0.20/0.59  % Proof found
% 0.20/0.59  % SZS status Theorem for theBenchmark.p
% 0.20/0.59  % SZS output start Proof
% See solution above
% 0.20/0.60  % Total time : 0.007000 s
% 0.20/0.60  % SZS output end Proof
% 0.20/0.60  % Total time : 0.010000 s
%------------------------------------------------------------------------------