TSTP Solution File: SEU407+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU407+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n029.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 16:25:35 EDT 2023

% Result   : Theorem 0.18s 0.72s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   44
% Syntax   : Number of formulae    :   85 (  15 unt;  35 typ;   0 def)
%            Number of atoms       :  170 (  25 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :  204 (  84   ~;  77   |;  24   &)
%                                         (   3 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   48 (  26   >;  22   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  11 usr;   1 prp; 0-3 aty)
%            Number of functors    :   24 (  24 usr;   9 con; 0-6 aty)
%            Number of variables   :   87 (   3 sgn;  47   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    v3_struct_0: $i > $o ).

tff(decl_23,type,
    l1_orders_2: $i > $o ).

tff(decl_24,type,
    k1_latsum_1: ( $i * $i ) > $i ).

tff(decl_25,type,
    u1_struct_0: $i > $i ).

tff(decl_26,type,
    m1_subset_1: ( $i * $i ) > $o ).

tff(decl_27,type,
    r2_hidden: ( $i * $i ) > $o ).

tff(decl_28,type,
    k4_xboole_0: ( $i * $i ) > $i ).

tff(decl_29,type,
    v1_orders_2: $i > $o ).

tff(decl_30,type,
    u1_orders_2: $i > $i ).

tff(decl_31,type,
    g1_orders_2: ( $i * $i ) > $i ).

tff(decl_32,type,
    k2_zfmisc_1: ( $i * $i ) > $i ).

tff(decl_33,type,
    k1_zfmisc_1: $i > $i ).

tff(decl_34,type,
    v1_relat_1: $i > $o ).

tff(decl_35,type,
    k2_xboole_0: ( $i * $i ) > $i ).

tff(decl_36,type,
    k7_relset_1: ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_37,type,
    m1_relset_1: ( $i * $i * $i ) > $o ).

tff(decl_38,type,
    k5_relat_1: ( $i * $i ) > $i ).

tff(decl_39,type,
    m2_relset_1: ( $i * $i * $i ) > $o ).

tff(decl_40,type,
    l1_struct_0: $i > $o ).

tff(decl_41,type,
    v1_xboole_0: $i > $o ).

tff(decl_42,type,
    k1_xboole_0: $i ).

tff(decl_43,type,
    r1_tarski: ( $i * $i ) > $o ).

tff(decl_44,type,
    esk1_0: $i ).

tff(decl_45,type,
    esk2_0: $i ).

tff(decl_46,type,
    esk3_0: $i ).

tff(decl_47,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_48,type,
    esk5_0: $i ).

tff(decl_49,type,
    esk6_0: $i ).

tff(decl_50,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_51,type,
    esk8_1: $i > $i ).

tff(decl_52,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_53,type,
    esk10_0: $i ).

tff(decl_54,type,
    esk11_0: $i ).

tff(decl_55,type,
    esk12_0: $i ).

tff(decl_56,type,
    esk13_1: $i > $i ).

fof(d2_xboole_0,axiom,
    ! [X1,X2,X3] :
      ( X3 = k2_xboole_0(X1,X2)
    <=> ! [X4] :
          ( r2_hidden(X4,X3)
        <=> ( r2_hidden(X4,X1)
            | r2_hidden(X4,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).

fof(t39_xboole_1,axiom,
    ! [X1,X2] : k2_xboole_0(X1,k4_xboole_0(X2,X1)) = k2_xboole_0(X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).

fof(t7_latsum_1,conjecture,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & l1_orders_2(X1) )
     => ! [X2] :
          ( ( ~ v3_struct_0(X2)
            & l1_orders_2(X2) )
         => ! [X3] :
              ( m1_subset_1(X3,u1_struct_0(k1_latsum_1(X1,X2)))
             => ( r2_hidden(X3,u1_struct_0(X1))
                | r2_hidden(X3,k4_xboole_0(u1_struct_0(X2),u1_struct_0(X1))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_latsum_1) ).

fof(d2_latsum_1,axiom,
    ! [X1] :
      ( l1_orders_2(X1)
     => ! [X2] :
          ( l1_orders_2(X2)
         => ! [X3] :
              ( ( v1_orders_2(X3)
                & l1_orders_2(X3) )
             => ( X3 = k1_latsum_1(X1,X2)
              <=> ( u1_struct_0(X3) = k2_xboole_0(u1_struct_0(X1),u1_struct_0(X2))
                  & u1_orders_2(X3) = k2_xboole_0(k2_xboole_0(u1_orders_2(X1),u1_orders_2(X2)),k7_relset_1(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X2),u1_struct_0(X2),u1_orders_2(X1),u1_orders_2(X2))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_latsum_1) ).

fof(dt_k1_latsum_1,axiom,
    ! [X1,X2] :
      ( ( l1_orders_2(X1)
        & l1_orders_2(X2) )
     => ( v1_orders_2(k1_latsum_1(X1,X2))
        & l1_orders_2(k1_latsum_1(X1,X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_latsum_1) ).

fof(t2_subset,axiom,
    ! [X1,X2] :
      ( m1_subset_1(X1,X2)
     => ( v1_xboole_0(X2)
        | r2_hidden(X1,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

fof(fc1_struct_0,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & l1_struct_0(X1) )
     => ~ v1_xboole_0(u1_struct_0(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).

fof(fc2_xboole_0,axiom,
    ! [X1,X2] :
      ( ~ v1_xboole_0(X1)
     => ~ v1_xboole_0(k2_xboole_0(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).

fof(dt_l1_orders_2,axiom,
    ! [X1] :
      ( l1_orders_2(X1)
     => l1_struct_0(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).

fof(c_0_9,plain,
    ! [X21,X22,X23,X24,X25,X26,X27,X28] :
      ( ( ~ r2_hidden(X24,X23)
        | r2_hidden(X24,X21)
        | r2_hidden(X24,X22)
        | X23 != k2_xboole_0(X21,X22) )
      & ( ~ r2_hidden(X25,X21)
        | r2_hidden(X25,X23)
        | X23 != k2_xboole_0(X21,X22) )
      & ( ~ r2_hidden(X25,X22)
        | r2_hidden(X25,X23)
        | X23 != k2_xboole_0(X21,X22) )
      & ( ~ r2_hidden(esk4_3(X26,X27,X28),X26)
        | ~ r2_hidden(esk4_3(X26,X27,X28),X28)
        | X28 = k2_xboole_0(X26,X27) )
      & ( ~ r2_hidden(esk4_3(X26,X27,X28),X27)
        | ~ r2_hidden(esk4_3(X26,X27,X28),X28)
        | X28 = k2_xboole_0(X26,X27) )
      & ( r2_hidden(esk4_3(X26,X27,X28),X28)
        | r2_hidden(esk4_3(X26,X27,X28),X26)
        | r2_hidden(esk4_3(X26,X27,X28),X27)
        | X28 = k2_xboole_0(X26,X27) ) ),
    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_xboole_0])])])])])]) ).

cnf(c_0_10,plain,
    ( r2_hidden(X1,X3)
    | r2_hidden(X1,X4)
    | ~ r2_hidden(X1,X2)
    | X2 != k2_xboole_0(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

fof(c_0_11,plain,
    ! [X91,X92] : k2_xboole_0(X91,k4_xboole_0(X92,X91)) = k2_xboole_0(X91,X92),
    inference(variable_rename,[status(thm)],[t39_xboole_1]) ).

fof(c_0_12,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ v3_struct_0(X1)
          & l1_orders_2(X1) )
       => ! [X2] :
            ( ( ~ v3_struct_0(X2)
              & l1_orders_2(X2) )
           => ! [X3] :
                ( m1_subset_1(X3,u1_struct_0(k1_latsum_1(X1,X2)))
               => ( r2_hidden(X3,u1_struct_0(X1))
                  | r2_hidden(X3,k4_xboole_0(u1_struct_0(X2),u1_struct_0(X1))) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t7_latsum_1])]) ).

fof(c_0_13,plain,
    ! [X18,X19,X20] :
      ( ( u1_struct_0(X20) = k2_xboole_0(u1_struct_0(X18),u1_struct_0(X19))
        | X20 != k1_latsum_1(X18,X19)
        | ~ v1_orders_2(X20)
        | ~ l1_orders_2(X20)
        | ~ l1_orders_2(X19)
        | ~ l1_orders_2(X18) )
      & ( u1_orders_2(X20) = k2_xboole_0(k2_xboole_0(u1_orders_2(X18),u1_orders_2(X19)),k7_relset_1(u1_struct_0(X18),u1_struct_0(X18),u1_struct_0(X19),u1_struct_0(X19),u1_orders_2(X18),u1_orders_2(X19)))
        | X20 != k1_latsum_1(X18,X19)
        | ~ v1_orders_2(X20)
        | ~ l1_orders_2(X20)
        | ~ l1_orders_2(X19)
        | ~ l1_orders_2(X18) )
      & ( u1_struct_0(X20) != k2_xboole_0(u1_struct_0(X18),u1_struct_0(X19))
        | u1_orders_2(X20) != k2_xboole_0(k2_xboole_0(u1_orders_2(X18),u1_orders_2(X19)),k7_relset_1(u1_struct_0(X18),u1_struct_0(X18),u1_struct_0(X19),u1_struct_0(X19),u1_orders_2(X18),u1_orders_2(X19)))
        | X20 = k1_latsum_1(X18,X19)
        | ~ v1_orders_2(X20)
        | ~ l1_orders_2(X20)
        | ~ l1_orders_2(X19)
        | ~ l1_orders_2(X18) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_latsum_1])])])]) ).

fof(c_0_14,plain,
    ! [X32,X33] :
      ( ( v1_orders_2(k1_latsum_1(X32,X33))
        | ~ l1_orders_2(X32)
        | ~ l1_orders_2(X33) )
      & ( l1_orders_2(k1_latsum_1(X32,X33))
        | ~ l1_orders_2(X32)
        | ~ l1_orders_2(X33) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_latsum_1])])]) ).

cnf(c_0_15,plain,
    ( r2_hidden(X1,X2)
    | r2_hidden(X1,X3)
    | ~ r2_hidden(X1,k2_xboole_0(X3,X2)) ),
    inference(er,[status(thm)],[c_0_10]) ).

cnf(c_0_16,plain,
    k2_xboole_0(X1,k4_xboole_0(X2,X1)) = k2_xboole_0(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_17,plain,
    ( r2_hidden(X1,X3)
    | ~ r2_hidden(X1,X2)
    | X3 != k2_xboole_0(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

fof(c_0_18,plain,
    ! [X89,X90] :
      ( ~ m1_subset_1(X89,X90)
      | v1_xboole_0(X90)
      | r2_hidden(X89,X90) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).

fof(c_0_19,negated_conjecture,
    ( ~ v3_struct_0(esk1_0)
    & l1_orders_2(esk1_0)
    & ~ v3_struct_0(esk2_0)
    & l1_orders_2(esk2_0)
    & m1_subset_1(esk3_0,u1_struct_0(k1_latsum_1(esk1_0,esk2_0)))
    & ~ r2_hidden(esk3_0,u1_struct_0(esk1_0))
    & ~ r2_hidden(esk3_0,k4_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).

cnf(c_0_20,plain,
    ( u1_struct_0(X1) = k2_xboole_0(u1_struct_0(X2),u1_struct_0(X3))
    | X1 != k1_latsum_1(X2,X3)
    | ~ v1_orders_2(X1)
    | ~ l1_orders_2(X1)
    | ~ l1_orders_2(X3)
    | ~ l1_orders_2(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_21,plain,
    ( l1_orders_2(k1_latsum_1(X1,X2))
    | ~ l1_orders_2(X1)
    | ~ l1_orders_2(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_22,plain,
    ( v1_orders_2(k1_latsum_1(X1,X2))
    | ~ l1_orders_2(X1)
    | ~ l1_orders_2(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_23,plain,
    ( r2_hidden(X1,k4_xboole_0(X2,X3))
    | r2_hidden(X1,X3)
    | ~ r2_hidden(X1,k2_xboole_0(X3,X2)) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_24,plain,
    ( r2_hidden(X1,k2_xboole_0(X2,X3))
    | ~ r2_hidden(X1,X3) ),
    inference(er,[status(thm)],[c_0_17]) ).

fof(c_0_25,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & l1_struct_0(X1) )
     => ~ v1_xboole_0(u1_struct_0(X1)) ),
    inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).

fof(c_0_26,plain,
    ! [X1,X2] :
      ( ~ v1_xboole_0(X1)
     => ~ v1_xboole_0(k2_xboole_0(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[fc2_xboole_0]) ).

cnf(c_0_27,plain,
    ( v1_xboole_0(X2)
    | r2_hidden(X1,X2)
    | ~ m1_subset_1(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_28,negated_conjecture,
    m1_subset_1(esk3_0,u1_struct_0(k1_latsum_1(esk1_0,esk2_0))),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_29,plain,
    ( u1_struct_0(k1_latsum_1(X1,X2)) = k2_xboole_0(u1_struct_0(X1),u1_struct_0(X2))
    | ~ l1_orders_2(X2)
    | ~ l1_orders_2(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_20]),c_0_21]),c_0_22]) ).

cnf(c_0_30,negated_conjecture,
    l1_orders_2(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_31,negated_conjecture,
    l1_orders_2(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_32,negated_conjecture,
    ~ r2_hidden(esk3_0,k4_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_33,plain,
    ( r2_hidden(X1,k4_xboole_0(X2,X3))
    | r2_hidden(X1,X3)
    | ~ r2_hidden(X1,X2) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_34,negated_conjecture,
    ~ r2_hidden(esk3_0,u1_struct_0(esk1_0)),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

fof(c_0_35,plain,
    ! [X59] :
      ( v3_struct_0(X59)
      | ~ l1_struct_0(X59)
      | ~ v1_xboole_0(u1_struct_0(X59)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])]) ).

fof(c_0_36,plain,
    ! [X62,X63] :
      ( v1_xboole_0(X62)
      | ~ v1_xboole_0(k2_xboole_0(X62,X63)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])]) ).

cnf(c_0_37,plain,
    ( v1_xboole_0(k2_xboole_0(X1,X2))
    | r2_hidden(X3,X1)
    | r2_hidden(X3,X2)
    | ~ m1_subset_1(X3,k2_xboole_0(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_15,c_0_27]) ).

cnf(c_0_38,negated_conjecture,
    m1_subset_1(esk3_0,k2_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31])]) ).

cnf(c_0_39,negated_conjecture,
    ~ r2_hidden(esk3_0,u1_struct_0(esk2_0)),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).

cnf(c_0_40,negated_conjecture,
    ~ v3_struct_0(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_41,plain,
    ( v3_struct_0(X1)
    | ~ l1_struct_0(X1)
    | ~ v1_xboole_0(u1_struct_0(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_42,plain,
    ( v1_xboole_0(X1)
    | ~ v1_xboole_0(k2_xboole_0(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_43,negated_conjecture,
    v1_xboole_0(k2_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0))),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_34]),c_0_39]) ).

cnf(c_0_44,negated_conjecture,
    ( ~ v1_xboole_0(u1_struct_0(esk1_0))
    | ~ l1_struct_0(esk1_0) ),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_45,negated_conjecture,
    v1_xboole_0(u1_struct_0(esk1_0)),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

fof(c_0_46,plain,
    ! [X42] :
      ( ~ l1_orders_2(X42)
      | l1_struct_0(X42) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_orders_2])]) ).

cnf(c_0_47,negated_conjecture,
    ~ l1_struct_0(esk1_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]) ).

cnf(c_0_48,plain,
    ( l1_struct_0(X1)
    | ~ l1_orders_2(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_49,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_31])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.17  % Problem    : SEU407+1 : TPTP v8.1.2. Released v3.4.0.
% 0.06/0.18  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.37  % Computer : n029.cluster.edu
% 0.13/0.37  % Model    : x86_64 x86_64
% 0.13/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37  % Memory   : 8042.1875MB
% 0.13/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.37  % CPULimit   : 300
% 0.13/0.37  % WCLimit    : 300
% 0.13/0.37  % DateTime   : Wed Aug 23 15:43:52 EDT 2023
% 0.13/0.37  % CPUTime  : 
% 0.18/0.62  start to proof: theBenchmark
% 0.18/0.72  % Version  : CSE_E---1.5
% 0.18/0.72  % Problem  : theBenchmark.p
% 0.18/0.72  % Proof found
% 0.18/0.72  % SZS status Theorem for theBenchmark.p
% 0.18/0.72  % SZS output start Proof
% See solution above
% 0.18/0.72  % Total time : 0.076000 s
% 0.18/0.72  % SZS output end Proof
% 0.18/0.72  % Total time : 0.079000 s
%------------------------------------------------------------------------------