TSTP Solution File: SEU317+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU317+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n028.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 16:24:23 EDT 2023

% Result   : Theorem 1.69s 1.75s
% Output   : CNFRefutation 1.69s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   39
% Syntax   : Number of formulae    :   81 (  17 unt;  31 typ;   0 def)
%            Number of atoms       :  142 (   0 equ)
%            Maximal formula atoms :   28 (   2 avg)
%            Number of connectives :  157 (  65   ~;  65   |;  13   &)
%                                         (   2 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   33 (  25   >;   8   *;   0   +;   0  <<)
%            Number of predicates  :   18 (  17 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   6 con; 0-3 aty)
%            Number of variables   :   74 (   4 sgn;  42   !;   1   ?;   0   :)

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

tff(decl_23,type,
    v1_membered: $i > $o ).

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

tff(decl_25,type,
    v1_xcmplx_0: $i > $o ).

tff(decl_26,type,
    v2_membered: $i > $o ).

tff(decl_27,type,
    v1_xreal_0: $i > $o ).

tff(decl_28,type,
    v3_membered: $i > $o ).

tff(decl_29,type,
    v1_rat_1: $i > $o ).

tff(decl_30,type,
    v4_membered: $i > $o ).

tff(decl_31,type,
    v1_int_1: $i > $o ).

tff(decl_32,type,
    v5_membered: $i > $o ).

tff(decl_33,type,
    natural: $i > $o ).

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

tff(decl_35,type,
    powerset: $i > $i ).

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

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

tff(decl_38,type,
    the_carrier: $i > $i ).

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

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

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

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

tff(decl_43,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_44,type,
    esk2_0: $i ).

tff(decl_45,type,
    esk3_0: $i ).

tff(decl_46,type,
    esk4_1: $i > $i ).

tff(decl_47,type,
    esk5_0: $i ).

tff(decl_48,type,
    esk6_1: $i > $i ).

tff(decl_49,type,
    esk7_1: $i > $i ).

tff(decl_50,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_51,type,
    esk9_0: $i ).

tff(decl_52,type,
    esk10_0: $i ).

fof(t48_pre_topc,conjecture,
    ! [X1] :
      ( top_str(X1)
     => ! [X2] :
          ( element(X2,powerset(the_carrier(X1)))
         => subset(X2,topstr_closure(X1,X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_pre_topc) ).

fof(d3_tarski,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( in(X3,X1)
         => in(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(t7_boole,axiom,
    ! [X1,X2] :
      ~ ( in(X1,X2)
        & empty(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

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

fof(existence_m1_subset_1,axiom,
    ! [X1] :
    ? [X2] : element(X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).

fof(t4_subset,axiom,
    ! [X1,X2,X3] :
      ( ( in(X1,X2)
        & element(X2,powerset(X3)) )
     => element(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).

fof(t5_subset,axiom,
    ! [X1,X2,X3] :
      ~ ( in(X1,X2)
        & element(X2,powerset(X3))
        & empty(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).

fof(t45_pre_topc,axiom,
    ! [X1] :
      ( top_str(X1)
     => ! [X2] :
          ( element(X2,powerset(the_carrier(X1)))
         => ! [X3] :
              ( in(X3,the_carrier(X1))
             => ( in(X3,topstr_closure(X1,X2))
              <=> ! [X4] :
                    ( element(X4,powerset(the_carrier(X1)))
                   => ( ( closed_subset(X4,X1)
                        & subset(X2,X4) )
                     => in(X3,X4) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_pre_topc) ).

fof(c_0_8,negated_conjecture,
    ~ ! [X1] :
        ( top_str(X1)
       => ! [X2] :
            ( element(X2,powerset(the_carrier(X1)))
           => subset(X2,topstr_closure(X1,X2)) ) ),
    inference(assume_negation,[status(cth)],[t48_pre_topc]) ).

fof(c_0_9,negated_conjecture,
    ( top_str(esk9_0)
    & element(esk10_0,powerset(the_carrier(esk9_0)))
    & ~ subset(esk10_0,topstr_closure(esk9_0,esk10_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).

fof(c_0_10,plain,
    ! [X32,X33,X34,X35,X36] :
      ( ( ~ subset(X32,X33)
        | ~ in(X34,X32)
        | in(X34,X33) )
      & ( in(esk1_2(X35,X36),X35)
        | subset(X35,X36) )
      & ( ~ in(esk1_2(X35,X36),X36)
        | subset(X35,X36) ) ),
    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_11,plain,
    ! [X72,X73] :
      ( ~ in(X72,X73)
      | ~ empty(X73) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).

cnf(c_0_12,negated_conjecture,
    ~ subset(esk10_0,topstr_closure(esk9_0,esk10_0)),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_13,plain,
    ( in(esk1_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_14,plain,
    ! [X54,X55] :
      ( ~ element(X54,X55)
      | empty(X55)
      | in(X54,X55) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).

fof(c_0_15,plain,
    ! [X43] : element(esk4_1(X43),X43),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).

fof(c_0_16,plain,
    ! [X65,X66,X67] :
      ( ~ in(X65,X66)
      | ~ element(X66,powerset(X67))
      | element(X65,X67) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).

cnf(c_0_17,plain,
    ( ~ in(X1,X2)
    | ~ empty(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_18,negated_conjecture,
    in(esk1_2(esk10_0,topstr_closure(esk9_0,esk10_0)),esk10_0),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_19,plain,
    ( empty(X2)
    | in(X1,X2)
    | ~ element(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_20,plain,
    element(esk4_1(X1),X1),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_21,plain,
    ( element(X1,X3)
    | ~ in(X1,X2)
    | ~ element(X2,powerset(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_22,negated_conjecture,
    element(esk10_0,powerset(the_carrier(esk9_0))),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_23,negated_conjecture,
    ~ empty(esk10_0),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_24,plain,
    ( empty(X1)
    | in(esk4_1(X1),X1) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

fof(c_0_25,plain,
    ! [X68,X69,X70] :
      ( ~ in(X68,X69)
      | ~ element(X69,powerset(X70))
      | ~ empty(X70) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).

cnf(c_0_26,negated_conjecture,
    ( element(X1,the_carrier(esk9_0))
    | ~ in(X1,esk10_0) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_27,negated_conjecture,
    in(esk4_1(esk10_0),esk10_0),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_28,plain,
    ( ~ in(X1,X2)
    | ~ element(X2,powerset(X3))
    | ~ empty(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_29,negated_conjecture,
    element(esk4_1(esk10_0),the_carrier(esk9_0)),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_30,negated_conjecture,
    ( ~ empty(the_carrier(esk9_0))
    | ~ in(X1,esk10_0) ),
    inference(spm,[status(thm)],[c_0_28,c_0_22]) ).

cnf(c_0_31,negated_conjecture,
    ( empty(the_carrier(esk9_0))
    | in(esk4_1(esk10_0),the_carrier(esk9_0)) ),
    inference(spm,[status(thm)],[c_0_19,c_0_29]) ).

cnf(c_0_32,negated_conjecture,
    ( in(esk4_1(esk10_0),the_carrier(esk9_0))
    | ~ in(X1,esk10_0) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

fof(c_0_33,plain,
    ! [X58,X59,X60,X61] :
      ( ( ~ in(X60,topstr_closure(X58,X59))
        | ~ element(X61,powerset(the_carrier(X58)))
        | ~ closed_subset(X61,X58)
        | ~ subset(X59,X61)
        | in(X60,X61)
        | ~ in(X60,the_carrier(X58))
        | ~ element(X59,powerset(the_carrier(X58)))
        | ~ top_str(X58) )
      & ( element(esk8_3(X58,X59,X60),powerset(the_carrier(X58)))
        | in(X60,topstr_closure(X58,X59))
        | ~ in(X60,the_carrier(X58))
        | ~ element(X59,powerset(the_carrier(X58)))
        | ~ top_str(X58) )
      & ( closed_subset(esk8_3(X58,X59,X60),X58)
        | in(X60,topstr_closure(X58,X59))
        | ~ in(X60,the_carrier(X58))
        | ~ element(X59,powerset(the_carrier(X58)))
        | ~ top_str(X58) )
      & ( subset(X59,esk8_3(X58,X59,X60))
        | in(X60,topstr_closure(X58,X59))
        | ~ in(X60,the_carrier(X58))
        | ~ element(X59,powerset(the_carrier(X58)))
        | ~ top_str(X58) )
      & ( ~ in(X60,esk8_3(X58,X59,X60))
        | in(X60,topstr_closure(X58,X59))
        | ~ in(X60,the_carrier(X58))
        | ~ element(X59,powerset(the_carrier(X58)))
        | ~ top_str(X58) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t45_pre_topc])])])])]) ).

cnf(c_0_34,negated_conjecture,
    element(esk1_2(esk10_0,topstr_closure(esk9_0,esk10_0)),the_carrier(esk9_0)),
    inference(spm,[status(thm)],[c_0_26,c_0_18]) ).

cnf(c_0_35,negated_conjecture,
    in(esk4_1(esk10_0),the_carrier(esk9_0)),
    inference(spm,[status(thm)],[c_0_32,c_0_27]) ).

cnf(c_0_36,plain,
    ( subset(X1,esk8_3(X2,X1,X3))
    | in(X3,topstr_closure(X2,X1))
    | ~ in(X3,the_carrier(X2))
    | ~ element(X1,powerset(the_carrier(X2)))
    | ~ top_str(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_37,negated_conjecture,
    top_str(esk9_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_38,negated_conjecture,
    ( empty(the_carrier(esk9_0))
    | in(esk1_2(esk10_0,topstr_closure(esk9_0,esk10_0)),the_carrier(esk9_0)) ),
    inference(spm,[status(thm)],[c_0_19,c_0_34]) ).

cnf(c_0_39,negated_conjecture,
    ~ empty(the_carrier(esk9_0)),
    inference(spm,[status(thm)],[c_0_17,c_0_35]) ).

cnf(c_0_40,plain,
    ( subset(X1,X2)
    | ~ in(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_41,negated_conjecture,
    ( subset(esk10_0,esk8_3(esk9_0,esk10_0,X1))
    | in(X1,topstr_closure(esk9_0,esk10_0))
    | ~ in(X1,the_carrier(esk9_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_22]),c_0_37])]) ).

cnf(c_0_42,negated_conjecture,
    in(esk1_2(esk10_0,topstr_closure(esk9_0,esk10_0)),the_carrier(esk9_0)),
    inference(sr,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_43,negated_conjecture,
    ~ in(esk1_2(esk10_0,topstr_closure(esk9_0,esk10_0)),topstr_closure(esk9_0,esk10_0)),
    inference(spm,[status(thm)],[c_0_12,c_0_40]) ).

cnf(c_0_44,plain,
    ( in(X1,topstr_closure(X2,X3))
    | ~ in(X1,esk8_3(X2,X3,X1))
    | ~ in(X1,the_carrier(X2))
    | ~ element(X3,powerset(the_carrier(X2)))
    | ~ top_str(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_45,plain,
    ( in(X3,X2)
    | ~ subset(X1,X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_46,negated_conjecture,
    subset(esk10_0,esk8_3(esk9_0,esk10_0,esk1_2(esk10_0,topstr_closure(esk9_0,esk10_0)))),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).

cnf(c_0_47,negated_conjecture,
    ( in(X1,topstr_closure(esk9_0,esk10_0))
    | ~ in(X1,esk8_3(esk9_0,esk10_0,X1))
    | ~ in(X1,the_carrier(esk9_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_22]),c_0_37])]) ).

cnf(c_0_48,negated_conjecture,
    ( in(X1,esk8_3(esk9_0,esk10_0,esk1_2(esk10_0,topstr_closure(esk9_0,esk10_0))))
    | ~ in(X1,esk10_0) ),
    inference(spm,[status(thm)],[c_0_45,c_0_46]) ).

cnf(c_0_49,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_42]),c_0_18])]),c_0_43]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU317+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n028.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Wed Aug 23 12:29:04 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 1.69/1.75  % Version  : CSE_E---1.5
% 1.69/1.75  % Problem  : theBenchmark.p
% 1.69/1.75  % Proof found
% 1.69/1.75  % SZS status Theorem for theBenchmark.p
% 1.69/1.75  % SZS output start Proof
% See solution above
% 1.69/1.76  % Total time : 1.155000 s
% 1.69/1.76  % SZS output end Proof
% 1.69/1.76  % Total time : 1.158000 s
%------------------------------------------------------------------------------