TSTP Solution File: SEU280+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU280+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 : n027.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 16:24:04 EDT 2023

% Result   : Theorem 0.21s 0.64s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   55 (   7 unt;  12 typ;   0 def)
%            Number of atoms       :  191 (  59 equ)
%            Maximal formula atoms :   70 (   4 avg)
%            Number of connectives :  227 (  79   ~; 115   |;  28   &)
%                                         (   3 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   29 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   7   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   68 (   4 sgn;  14   !;   4   ?;   0   :)

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

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

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

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

tff(decl_26,type,
    esk1_0: $i ).

tff(decl_27,type,
    esk2_1: $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_1: $i > $i ).

tff(decl_33,type,
    esk8_2: ( $i * $i ) > $i ).

fof(s1_tarski__e6_22__wellord2__1,axiom,
    ! [X1] :
      ( ! [X2,X3,X4] :
          ( ( X2 = X3
            & ordinal(X3)
            & X2 = X4
            & ordinal(X4) )
         => X3 = X4 )
     => ? [X2] :
        ! [X3] :
          ( in(X3,X2)
        <=> ? [X4] :
              ( in(X4,X1)
              & X4 = X3
              & ordinal(X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e6_22__wellord2__1) ).

fof(s1_xboole_0__e6_22__wellord2,conjecture,
    ! [X1] :
    ? [X2] :
    ! [X3] :
      ( in(X3,X2)
    <=> ( in(X3,X1)
        & ordinal(X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e6_22__wellord2) ).

fof(c_0_2,plain,
    ! [X16,X18,X20,X21] :
      ( ( in(esk8_2(X16,X18),X16)
        | ~ in(X18,esk7_1(X16))
        | esk4_0 = esk5_0 )
      & ( esk8_2(X16,X18) = X18
        | ~ in(X18,esk7_1(X16))
        | esk4_0 = esk5_0 )
      & ( ordinal(X18)
        | ~ in(X18,esk7_1(X16))
        | esk4_0 = esk5_0 )
      & ( ~ in(X21,X16)
        | X21 != X20
        | ~ ordinal(X20)
        | in(X20,esk7_1(X16))
        | esk4_0 = esk5_0 )
      & ( in(esk8_2(X16,X18),X16)
        | ~ in(X18,esk7_1(X16))
        | ordinal(esk5_0) )
      & ( esk8_2(X16,X18) = X18
        | ~ in(X18,esk7_1(X16))
        | ordinal(esk5_0) )
      & ( ordinal(X18)
        | ~ in(X18,esk7_1(X16))
        | ordinal(esk5_0) )
      & ( ~ in(X21,X16)
        | X21 != X20
        | ~ ordinal(X20)
        | in(X20,esk7_1(X16))
        | ordinal(esk5_0) )
      & ( in(esk8_2(X16,X18),X16)
        | ~ in(X18,esk7_1(X16))
        | esk4_0 = esk6_0 )
      & ( esk8_2(X16,X18) = X18
        | ~ in(X18,esk7_1(X16))
        | esk4_0 = esk6_0 )
      & ( ordinal(X18)
        | ~ in(X18,esk7_1(X16))
        | esk4_0 = esk6_0 )
      & ( ~ in(X21,X16)
        | X21 != X20
        | ~ ordinal(X20)
        | in(X20,esk7_1(X16))
        | esk4_0 = esk6_0 )
      & ( in(esk8_2(X16,X18),X16)
        | ~ in(X18,esk7_1(X16))
        | ordinal(esk6_0) )
      & ( esk8_2(X16,X18) = X18
        | ~ in(X18,esk7_1(X16))
        | ordinal(esk6_0) )
      & ( ordinal(X18)
        | ~ in(X18,esk7_1(X16))
        | ordinal(esk6_0) )
      & ( ~ in(X21,X16)
        | X21 != X20
        | ~ ordinal(X20)
        | in(X20,esk7_1(X16))
        | ordinal(esk6_0) )
      & ( in(esk8_2(X16,X18),X16)
        | ~ in(X18,esk7_1(X16))
        | esk5_0 != esk6_0 )
      & ( esk8_2(X16,X18) = X18
        | ~ in(X18,esk7_1(X16))
        | esk5_0 != esk6_0 )
      & ( ordinal(X18)
        | ~ in(X18,esk7_1(X16))
        | esk5_0 != esk6_0 )
      & ( ~ in(X21,X16)
        | X21 != X20
        | ~ ordinal(X20)
        | in(X20,esk7_1(X16))
        | esk5_0 != esk6_0 ) ),
    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)],[s1_tarski__e6_22__wellord2__1])])])])])]) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1] :
      ? [X2] :
      ! [X3] :
        ( in(X3,X2)
      <=> ( in(X3,X1)
          & ordinal(X3) ) ),
    inference(assume_negation,[status(cth)],[s1_xboole_0__e6_22__wellord2]) ).

cnf(c_0_4,plain,
    ( in(X3,esk7_1(X2))
    | esk4_0 = esk5_0
    | ~ in(X1,X2)
    | X1 != X3
    | ~ ordinal(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

fof(c_0_5,negated_conjecture,
    ! [X6] :
      ( ( ~ in(esk2_1(X6),X6)
        | ~ in(esk2_1(X6),esk1_0)
        | ~ ordinal(esk2_1(X6)) )
      & ( in(esk2_1(X6),esk1_0)
        | in(esk2_1(X6),X6) )
      & ( ordinal(esk2_1(X6))
        | in(esk2_1(X6),X6) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).

cnf(c_0_6,plain,
    ( esk4_0 = esk5_0
    | in(X1,esk7_1(X2))
    | ~ ordinal(X1)
    | ~ in(X1,X2) ),
    inference(er,[status(thm)],[c_0_4]) ).

cnf(c_0_7,negated_conjecture,
    ( ordinal(esk2_1(X1))
    | in(esk2_1(X1),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,negated_conjecture,
    ( esk4_0 = esk5_0
    | in(esk2_1(X1),esk7_1(X2))
    | in(esk2_1(X1),X1)
    | ~ in(esk2_1(X1),X2) ),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_9,negated_conjecture,
    ( in(esk2_1(X1),esk1_0)
    | in(esk2_1(X1),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_10,negated_conjecture,
    ( esk4_0 = esk5_0
    | in(esk2_1(X1),esk7_1(esk1_0))
    | in(esk2_1(X1),X1) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_11,plain,
    ( esk8_2(X1,X2) = X2
    | esk4_0 = esk5_0
    | ~ in(X2,esk7_1(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_12,negated_conjecture,
    ( esk4_0 = esk5_0
    | in(esk2_1(esk7_1(esk1_0)),esk7_1(esk1_0)) ),
    inference(ef,[status(thm)],[c_0_10]) ).

cnf(c_0_13,plain,
    ( in(esk8_2(X1,X2),X1)
    | esk4_0 = esk5_0
    | ~ in(X2,esk7_1(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_14,negated_conjecture,
    ( esk8_2(esk1_0,esk2_1(esk7_1(esk1_0))) = esk2_1(esk7_1(esk1_0))
    | esk4_0 = esk5_0 ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_15,plain,
    ( ordinal(X1)
    | esk4_0 = esk5_0
    | ~ in(X1,esk7_1(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_16,plain,
    ( in(X3,esk7_1(X2))
    | esk4_0 = esk6_0
    | ~ in(X1,X2)
    | X1 != X3
    | ~ ordinal(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_17,negated_conjecture,
    ( ~ in(esk2_1(X1),X1)
    | ~ in(esk2_1(X1),esk1_0)
    | ~ ordinal(esk2_1(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_18,negated_conjecture,
    ( esk4_0 = esk5_0
    | in(esk2_1(esk7_1(esk1_0)),esk1_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_9]) ).

cnf(c_0_19,negated_conjecture,
    ( esk4_0 = esk5_0
    | ordinal(esk2_1(esk7_1(esk1_0))) ),
    inference(spm,[status(thm)],[c_0_15,c_0_12]) ).

cnf(c_0_20,plain,
    ( in(X3,esk7_1(X2))
    | ~ in(X1,X2)
    | X1 != X3
    | ~ ordinal(X3)
    | esk5_0 != esk6_0 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_21,plain,
    ( esk4_0 = esk6_0
    | in(X1,esk7_1(X2))
    | ~ ordinal(X1)
    | ~ in(X1,X2) ),
    inference(er,[status(thm)],[c_0_16]) ).

cnf(c_0_22,negated_conjecture,
    esk4_0 = esk5_0,
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_12]),c_0_19]) ).

cnf(c_0_23,plain,
    ( in(X1,esk7_1(X2))
    | esk6_0 != esk5_0
    | ~ ordinal(X1)
    | ~ in(X1,X2) ),
    inference(er,[status(thm)],[c_0_20]) ).

cnf(c_0_24,plain,
    ( in(X1,esk7_1(X2))
    | ~ ordinal(X1)
    | ~ in(X1,X2) ),
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).

cnf(c_0_25,negated_conjecture,
    ( in(esk2_1(X1),esk7_1(X2))
    | in(esk2_1(X1),X1)
    | ~ in(esk2_1(X1),X2) ),
    inference(spm,[status(thm)],[c_0_24,c_0_7]) ).

cnf(c_0_26,plain,
    ( esk8_2(X1,X2) = X2
    | esk4_0 = esk6_0
    | ~ in(X2,esk7_1(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_27,plain,
    ( esk8_2(X1,X2) = X2
    | ~ in(X2,esk7_1(X1))
    | esk5_0 != esk6_0 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_28,negated_conjecture,
    ( in(esk2_1(X1),esk7_1(esk1_0))
    | in(esk2_1(X1),X1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_9]) ).

cnf(c_0_29,plain,
    ( esk8_2(X1,X2) = X2
    | ~ in(X2,esk7_1(X1)) ),
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_22]),c_0_27]) ).

cnf(c_0_30,negated_conjecture,
    in(esk2_1(esk7_1(esk1_0)),esk7_1(esk1_0)),
    inference(ef,[status(thm)],[c_0_28]) ).

cnf(c_0_31,plain,
    ( ordinal(X1)
    | esk4_0 = esk6_0
    | ~ in(X1,esk7_1(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_32,plain,
    ( ordinal(X1)
    | ~ in(X1,esk7_1(X2))
    | esk5_0 != esk6_0 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_33,plain,
    ( in(esk8_2(X1,X2),X1)
    | ~ in(X2,esk7_1(X1))
    | esk5_0 != esk6_0 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_34,negated_conjecture,
    esk8_2(esk1_0,esk2_1(esk7_1(esk1_0))) = esk2_1(esk7_1(esk1_0)),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_35,plain,
    ( ordinal(X1)
    | ~ in(X1,esk7_1(X2)) ),
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_22]),c_0_32]) ).

cnf(c_0_36,negated_conjecture,
    ( in(esk2_1(esk7_1(esk1_0)),esk1_0)
    | esk6_0 != esk5_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_30])]) ).

cnf(c_0_37,negated_conjecture,
    ordinal(esk2_1(esk7_1(esk1_0))),
    inference(spm,[status(thm)],[c_0_35,c_0_30]) ).

cnf(c_0_38,plain,
    ( in(esk8_2(X1,X2),X1)
    | esk4_0 = esk6_0
    | ~ in(X2,esk7_1(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_39,negated_conjecture,
    esk6_0 != esk5_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_36]),c_0_37]),c_0_30])]) ).

cnf(c_0_40,plain,
    ( in(esk8_2(X1,X2),X1)
    | ~ in(X2,esk7_1(X1)) ),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_22]),c_0_39]) ).

cnf(c_0_41,negated_conjecture,
    in(esk2_1(esk7_1(esk1_0)),esk1_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_34]),c_0_30])]) ).

cnf(c_0_42,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_41]),c_0_37]),c_0_30])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU280+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
% 0.14/0.34  % Computer : n027.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Wed Aug 23 20:17:31 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.21/0.57  start to proof: theBenchmark
% 0.21/0.64  % Version  : CSE_E---1.5
% 0.21/0.64  % Problem  : theBenchmark.p
% 0.21/0.64  % Proof found
% 0.21/0.64  % SZS status Theorem for theBenchmark.p
% 0.21/0.64  % SZS output start Proof
% See solution above
% 0.21/0.65  % Total time : 0.064000 s
% 0.21/0.65  % SZS output end Proof
% 0.21/0.65  % Total time : 0.067000 s
%------------------------------------------------------------------------------