TSTP Solution File: SEU362+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU362+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 : 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 16:25:08 EDT 2023

% Result   : Theorem 0.19s 0.62s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   43
% Syntax   : Number of formulae    :   87 (  22 unt;  35 typ;   0 def)
%            Number of atoms       :  155 (   8 equ)
%            Maximal formula atoms :   13 (   2 avg)
%            Number of connectives :  164 (  61   ~;  56   |;  21   &)
%                                         (   3 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   37 (  23   >;  14   *;   0   +;   0  <<)
%            Number of predicates  :   14 (  12 usr;   1 prp; 0-3 aty)
%            Number of functors    :   23 (  23 usr;  12 con; 0-2 aty)
%            Number of variables   :   72 (   3 sgn;  46   !;   0   ?;   0   :)

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

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

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

tff(decl_25,type,
    cartesian_product2: ( $i * $i ) > $i ).

tff(decl_26,type,
    powerset: $i > $i ).

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

tff(decl_28,type,
    relation: $i > $o ).

tff(decl_29,type,
    rel_str: $i > $o ).

tff(decl_30,type,
    subrelstr: ( $i * $i ) > $o ).

tff(decl_31,type,
    the_carrier: $i > $i ).

tff(decl_32,type,
    subset: ( $i * $i ) > $o ).

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

tff(decl_34,type,
    related: ( $i * $i * $i ) > $o ).

tff(decl_35,type,
    ordered_pair: ( $i * $i ) > $i ).

tff(decl_36,type,
    one_sorted_str: $i > $o ).

tff(decl_37,type,
    relation_of2_as_subset: ( $i * $i * $i ) > $o ).

tff(decl_38,type,
    relation_of2: ( $i * $i * $i ) > $o ).

tff(decl_39,type,
    empty_set: $i ).

tff(decl_40,type,
    esk1_0: $i ).

tff(decl_41,type,
    esk2_0: $i ).

tff(decl_42,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_43,type,
    esk4_1: $i > $i ).

tff(decl_44,type,
    esk5_1: $i > $i ).

tff(decl_45,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_46,type,
    esk7_0: $i ).

tff(decl_47,type,
    esk8_0: $i ).

tff(decl_48,type,
    esk9_0: $i ).

tff(decl_49,type,
    esk10_1: $i > $i ).

tff(decl_50,type,
    esk11_1: $i > $i ).

tff(decl_51,type,
    esk12_0: $i ).

tff(decl_52,type,
    esk13_0: $i ).

tff(decl_53,type,
    esk14_0: $i ).

tff(decl_54,type,
    esk15_0: $i ).

tff(decl_55,type,
    esk16_0: $i ).

tff(decl_56,type,
    esk17_0: $i ).

fof(d13_yellow_0,axiom,
    ! [X1] :
      ( rel_str(X1)
     => ! [X2] :
          ( rel_str(X2)
         => ( subrelstr(X2,X1)
          <=> ( subset(the_carrier(X2),the_carrier(X1))
              & subset(the_InternalRel(X2),the_InternalRel(X1)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_yellow_0) ).

fof(dt_m1_yellow_0,axiom,
    ! [X1] :
      ( rel_str(X1)
     => ! [X2] :
          ( subrelstr(X2,X1)
         => rel_str(X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_yellow_0) ).

fof(t60_yellow_0,conjecture,
    ! [X1] :
      ( rel_str(X1)
     => ! [X2] :
          ( subrelstr(X2,X1)
         => ! [X3] :
              ( element(X3,the_carrier(X1))
             => ! [X4] :
                  ( element(X4,the_carrier(X1))
                 => ! [X5] :
                      ( element(X5,the_carrier(X2))
                     => ! [X6] :
                          ( element(X6,the_carrier(X2))
                         => ( ( X5 = X3
                              & X6 = X4
                              & related(X2,X5,X6) )
                           => related(X1,X3,X4) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_yellow_0) ).

fof(t3_subset,axiom,
    ! [X1,X2] :
      ( element(X1,powerset(X2))
    <=> subset(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).

fof(d9_orders_2,axiom,
    ! [X1] :
      ( rel_str(X1)
     => ! [X2] :
          ( element(X2,the_carrier(X1))
         => ! [X3] :
              ( element(X3,the_carrier(X1))
             => ( related(X1,X2,X3)
              <=> in(ordered_pair(X2,X3),the_InternalRel(X1)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_orders_2) ).

fof(t4_subset,axiom,
    ! [X1,X2,X3] :
      ( ( in(X1,X2)
        & element(X2,powerset(X3)) )
     => element(X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).

fof(t2_subset,axiom,
    ! [X1,X2] :
      ( element(X1,X2)
     => ( empty(X2)
        | in(X1,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).

fof(t5_subset,axiom,
    ! [X1,X2,X3] :
      ~ ( in(X1,X2)
        & element(X2,powerset(X3))
        & empty(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).

fof(c_0_8,plain,
    ! [X15,X16] :
      ( ( subset(the_carrier(X16),the_carrier(X15))
        | ~ subrelstr(X16,X15)
        | ~ rel_str(X16)
        | ~ rel_str(X15) )
      & ( subset(the_InternalRel(X16),the_InternalRel(X15))
        | ~ subrelstr(X16,X15)
        | ~ rel_str(X16)
        | ~ rel_str(X15) )
      & ( ~ subset(the_carrier(X16),the_carrier(X15))
        | ~ subset(the_InternalRel(X16),the_InternalRel(X15))
        | subrelstr(X16,X15)
        | ~ rel_str(X16)
        | ~ rel_str(X15) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d13_yellow_0])])])]) ).

fof(c_0_9,plain,
    ! [X21,X22] :
      ( ~ rel_str(X21)
      | ~ subrelstr(X22,X21)
      | rel_str(X22) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m1_yellow_0])])]) ).

fof(c_0_10,negated_conjecture,
    ~ ! [X1] :
        ( rel_str(X1)
       => ! [X2] :
            ( subrelstr(X2,X1)
           => ! [X3] :
                ( element(X3,the_carrier(X1))
               => ! [X4] :
                    ( element(X4,the_carrier(X1))
                   => ! [X5] :
                        ( element(X5,the_carrier(X2))
                       => ! [X6] :
                            ( element(X6,the_carrier(X2))
                           => ( ( X5 = X3
                                & X6 = X4
                                & related(X2,X5,X6) )
                             => related(X1,X3,X4) ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[t60_yellow_0]) ).

cnf(c_0_11,plain,
    ( subset(the_InternalRel(X1),the_InternalRel(X2))
    | ~ subrelstr(X1,X2)
    | ~ rel_str(X1)
    | ~ rel_str(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12,plain,
    ( rel_str(X2)
    | ~ rel_str(X1)
    | ~ subrelstr(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

fof(c_0_13,negated_conjecture,
    ( rel_str(esk12_0)
    & subrelstr(esk13_0,esk12_0)
    & element(esk14_0,the_carrier(esk12_0))
    & element(esk15_0,the_carrier(esk12_0))
    & element(esk16_0,the_carrier(esk13_0))
    & element(esk17_0,the_carrier(esk13_0))
    & esk16_0 = esk14_0
    & esk17_0 = esk15_0
    & related(esk13_0,esk16_0,esk17_0)
    & ~ related(esk12_0,esk14_0,esk15_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).

fof(c_0_14,plain,
    ! [X56,X57] :
      ( ( ~ element(X56,powerset(X57))
        | subset(X56,X57) )
      & ( ~ subset(X56,X57)
        | element(X56,powerset(X57)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).

cnf(c_0_15,plain,
    ( subset(the_InternalRel(X1),the_InternalRel(X2))
    | ~ subrelstr(X1,X2)
    | ~ rel_str(X2) ),
    inference(csr,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_16,negated_conjecture,
    subrelstr(esk13_0,esk12_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_17,negated_conjecture,
    rel_str(esk12_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_18,plain,
    ! [X17,X18,X19] :
      ( ( ~ related(X17,X18,X19)
        | in(ordered_pair(X18,X19),the_InternalRel(X17))
        | ~ element(X19,the_carrier(X17))
        | ~ element(X18,the_carrier(X17))
        | ~ rel_str(X17) )
      & ( ~ in(ordered_pair(X18,X19),the_InternalRel(X17))
        | related(X17,X18,X19)
        | ~ element(X19,the_carrier(X17))
        | ~ element(X18,the_carrier(X17))
        | ~ rel_str(X17) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_orders_2])])])]) ).

fof(c_0_19,plain,
    ! [X58,X59,X60] :
      ( ~ in(X58,X59)
      | ~ element(X59,powerset(X60))
      | element(X58,X60) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).

cnf(c_0_20,plain,
    ( element(X1,powerset(X2))
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_21,negated_conjecture,
    subset(the_InternalRel(esk13_0),the_InternalRel(esk12_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).

cnf(c_0_22,plain,
    ( in(ordered_pair(X2,X3),the_InternalRel(X1))
    | ~ related(X1,X2,X3)
    | ~ element(X3,the_carrier(X1))
    | ~ element(X2,the_carrier(X1))
    | ~ rel_str(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_23,negated_conjecture,
    element(esk17_0,the_carrier(esk13_0)),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_24,negated_conjecture,
    rel_str(esk13_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_16]),c_0_17])]) ).

cnf(c_0_25,negated_conjecture,
    related(esk13_0,esk16_0,esk17_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_26,negated_conjecture,
    esk16_0 = esk14_0,
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_27,negated_conjecture,
    element(esk16_0,the_carrier(esk13_0)),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_28,plain,
    ( element(X1,X3)
    | ~ in(X1,X2)
    | ~ element(X2,powerset(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_29,negated_conjecture,
    element(the_InternalRel(esk13_0),powerset(the_InternalRel(esk12_0))),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_30,negated_conjecture,
    ( in(ordered_pair(X1,esk17_0),the_InternalRel(esk13_0))
    | ~ related(esk13_0,X1,esk17_0)
    | ~ element(X1,the_carrier(esk13_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).

cnf(c_0_31,negated_conjecture,
    related(esk13_0,esk14_0,esk17_0),
    inference(rw,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_32,negated_conjecture,
    element(esk14_0,the_carrier(esk13_0)),
    inference(rw,[status(thm)],[c_0_27,c_0_26]) ).

fof(c_0_33,plain,
    ! [X54,X55] :
      ( ~ element(X54,X55)
      | empty(X55)
      | in(X54,X55) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).

cnf(c_0_34,negated_conjecture,
    ( element(X1,the_InternalRel(esk12_0))
    | ~ in(X1,the_InternalRel(esk13_0)) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_35,negated_conjecture,
    in(ordered_pair(esk14_0,esk17_0),the_InternalRel(esk13_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).

fof(c_0_36,plain,
    ! [X61,X62,X63] :
      ( ~ in(X61,X62)
      | ~ element(X62,powerset(X63))
      | ~ empty(X63) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).

cnf(c_0_37,plain,
    ( empty(X2)
    | in(X1,X2)
    | ~ element(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_38,negated_conjecture,
    element(ordered_pair(esk14_0,esk17_0),the_InternalRel(esk12_0)),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_39,negated_conjecture,
    element(esk15_0,the_carrier(esk12_0)),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_40,negated_conjecture,
    esk17_0 = esk15_0,
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_41,negated_conjecture,
    ~ related(esk12_0,esk14_0,esk15_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_42,plain,
    ( ~ in(X1,X2)
    | ~ element(X2,powerset(X3))
    | ~ empty(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_43,plain,
    ( related(X3,X1,X2)
    | ~ in(ordered_pair(X1,X2),the_InternalRel(X3))
    | ~ element(X2,the_carrier(X3))
    | ~ element(X1,the_carrier(X3))
    | ~ rel_str(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_44,negated_conjecture,
    ( empty(the_InternalRel(esk12_0))
    | in(ordered_pair(esk14_0,esk17_0),the_InternalRel(esk12_0)) ),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_45,negated_conjecture,
    element(esk17_0,the_carrier(esk12_0)),
    inference(rw,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_46,negated_conjecture,
    element(esk14_0,the_carrier(esk12_0)),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_47,negated_conjecture,
    ~ related(esk12_0,esk14_0,esk17_0),
    inference(rw,[status(thm)],[c_0_41,c_0_40]) ).

cnf(c_0_48,negated_conjecture,
    ( ~ empty(the_InternalRel(esk12_0))
    | ~ in(X1,the_InternalRel(esk13_0)) ),
    inference(spm,[status(thm)],[c_0_42,c_0_29]) ).

cnf(c_0_49,negated_conjecture,
    empty(the_InternalRel(esk12_0)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_17]),c_0_45]),c_0_46])]),c_0_47]) ).

cnf(c_0_50,negated_conjecture,
    ~ in(X1,the_InternalRel(esk13_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]) ).

cnf(c_0_51,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[c_0_35,c_0_50]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU362+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13  % Command    : java -jar /export/starexec/sandbox/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   : Wed Aug 23 13:54:35 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.58  start to proof: theBenchmark
% 0.19/0.62  % Version  : CSE_E---1.5
% 0.19/0.62  % Problem  : theBenchmark.p
% 0.19/0.62  % Proof found
% 0.19/0.62  % SZS status Theorem for theBenchmark.p
% 0.19/0.62  % SZS output start Proof
% See solution above
% 0.19/0.62  % Total time : 0.026000 s
% 0.19/0.62  % SZS output end Proof
% 0.19/0.62  % Total time : 0.030000 s
%------------------------------------------------------------------------------