TSTP Solution File: SWV409+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWV409+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 : 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 21:38:28 EDT 2023

% Result   : Theorem 0.56s 0.62s
% Output   : CNFRefutation 0.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   51 (   8 unt;  17 typ;   0 def)
%            Number of atoms       :  100 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  107 (  41   ~;  42   |;  17   &)
%                                         (   2 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   26 (  12   >;  14   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;   5 con; 0-4 aty)
%            Number of variables   :   66 (   0 sgn;  37   !;   4   ?;   0   :)

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

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

tff(decl_24,type,
    bottom: $i ).

tff(decl_25,type,
    create_slb: $i ).

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

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

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

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

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

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

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

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

tff(decl_34,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_35,type,
    esk2_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_36,type,
    esk3_0: $i ).

tff(decl_37,type,
    esk4_0: $i ).

tff(decl_38,type,
    esk5_0: $i ).

fof(l45_co,conjecture,
    ! [X1,X2,X3] :
      ( ( contains_slb(X1,X2)
        & strictly_less_than(X2,X3) )
     => ( pair_in_list(update_slb(X1,X3),X2,X3)
        | ? [X4] :
            ( pair_in_list(update_slb(X1,X3),X2,X4)
            & less_than(X3,X4) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_co) ).

fof(l45_li4647,lemma,
    ! [X1,X2] :
      ( contains_slb(X1,X2)
     => ? [X3] : pair_in_list(X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_li4647) ).

fof(stricly_smaller_definition,axiom,
    ! [X1,X2] :
      ( strictly_less_than(X1,X2)
    <=> ( less_than(X1,X2)
        & ~ less_than(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax',stricly_smaller_definition) ).

fof(l45_l48,lemma,
    ! [X1,X2,X3,X4] :
      ( ( pair_in_list(X1,X2,X3)
        & strictly_less_than(X2,X4)
        & strictly_less_than(X3,X4) )
     => pair_in_list(update_slb(X1,X4),X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_l48) ).

fof(totality,axiom,
    ! [X1,X2] :
      ( less_than(X1,X2)
      | less_than(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax',totality) ).

fof(l45_l49,lemma,
    ! [X1,X2,X3,X4] :
      ( ( pair_in_list(X1,X2,X3)
        & strictly_less_than(X2,X4)
        & less_than(X4,X3) )
     => ? [X5] :
          ( pair_in_list(update_slb(X1,X4),X2,X5)
          & less_than(X4,X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_l49) ).

fof(c_0_6,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( contains_slb(X1,X2)
          & strictly_less_than(X2,X3) )
       => ( pair_in_list(update_slb(X1,X3),X2,X3)
          | ? [X4] :
              ( pair_in_list(update_slb(X1,X3),X2,X4)
              & less_than(X3,X4) ) ) ),
    inference(assume_negation,[status(cth)],[l45_co]) ).

fof(c_0_7,lemma,
    ! [X53,X54] :
      ( ~ contains_slb(X53,X54)
      | pair_in_list(X53,X54,esk1_2(X53,X54)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l45_li4647])])]) ).

fof(c_0_8,negated_conjecture,
    ! [X68] :
      ( contains_slb(esk3_0,esk4_0)
      & strictly_less_than(esk4_0,esk5_0)
      & ~ pair_in_list(update_slb(esk3_0,esk5_0),esk4_0,esk5_0)
      & ( ~ pair_in_list(update_slb(esk3_0,esk5_0),esk4_0,X68)
        | ~ less_than(esk5_0,X68) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).

fof(c_0_9,plain,
    ! [X1,X2] :
      ( strictly_less_than(X1,X2)
    <=> ( less_than(X1,X2)
        & ~ less_than(X2,X1) ) ),
    inference(fof_simplification,[status(thm)],[stricly_smaller_definition]) ).

fof(c_0_10,lemma,
    ! [X56,X57,X58,X59] :
      ( ~ pair_in_list(X56,X57,X58)
      | ~ strictly_less_than(X57,X59)
      | ~ strictly_less_than(X58,X59)
      | pair_in_list(update_slb(X56,X59),X57,X59) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l45_l48])]) ).

cnf(c_0_11,lemma,
    ( pair_in_list(X1,X2,esk1_2(X1,X2))
    | ~ contains_slb(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,negated_conjecture,
    contains_slb(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_13,plain,
    ! [X12,X13] :
      ( ( less_than(X12,X13)
        | ~ strictly_less_than(X12,X13) )
      & ( ~ less_than(X13,X12)
        | ~ strictly_less_than(X12,X13) )
      & ( ~ less_than(X12,X13)
        | less_than(X13,X12)
        | strictly_less_than(X12,X13) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).

fof(c_0_14,plain,
    ! [X9,X10] :
      ( less_than(X9,X10)
      | less_than(X10,X9) ),
    inference(variable_rename,[status(thm)],[totality]) ).

cnf(c_0_15,lemma,
    ( pair_in_list(update_slb(X1,X4),X2,X4)
    | ~ pair_in_list(X1,X2,X3)
    | ~ strictly_less_than(X2,X4)
    | ~ strictly_less_than(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_16,negated_conjecture,
    pair_in_list(esk3_0,esk4_0,esk1_2(esk3_0,esk4_0)),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_17,plain,
    ( less_than(X2,X1)
    | strictly_less_than(X1,X2)
    | ~ less_than(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_18,plain,
    ( less_than(X1,X2)
    | less_than(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_19,lemma,
    ! [X60,X61,X62,X63] :
      ( ( pair_in_list(update_slb(X60,X63),X61,esk2_4(X60,X61,X62,X63))
        | ~ pair_in_list(X60,X61,X62)
        | ~ strictly_less_than(X61,X63)
        | ~ less_than(X63,X62) )
      & ( less_than(X63,esk2_4(X60,X61,X62,X63))
        | ~ pair_in_list(X60,X61,X62)
        | ~ strictly_less_than(X61,X63)
        | ~ less_than(X63,X62) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l45_l49])])])]) ).

cnf(c_0_20,negated_conjecture,
    ( pair_in_list(update_slb(esk3_0,X1),esk4_0,X1)
    | ~ strictly_less_than(esk1_2(esk3_0,esk4_0),X1)
    | ~ strictly_less_than(esk4_0,X1) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_21,plain,
    ( strictly_less_than(X1,X2)
    | less_than(X2,X1) ),
    inference(csr,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_22,lemma,
    ( pair_in_list(update_slb(X1,X2),X3,esk2_4(X1,X3,X4,X2))
    | ~ pair_in_list(X1,X3,X4)
    | ~ strictly_less_than(X3,X2)
    | ~ less_than(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_23,negated_conjecture,
    ( pair_in_list(update_slb(esk3_0,X1),esk4_0,X1)
    | less_than(X1,esk1_2(esk3_0,esk4_0))
    | ~ strictly_less_than(esk4_0,X1) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_24,negated_conjecture,
    strictly_less_than(esk4_0,esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_25,negated_conjecture,
    ~ pair_in_list(update_slb(esk3_0,esk5_0),esk4_0,esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_26,lemma,
    ( less_than(X1,esk2_4(X2,X3,X4,X1))
    | ~ pair_in_list(X2,X3,X4)
    | ~ strictly_less_than(X3,X1)
    | ~ less_than(X1,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_27,negated_conjecture,
    ( pair_in_list(update_slb(esk3_0,X1),esk4_0,esk2_4(esk3_0,esk4_0,esk1_2(esk3_0,esk4_0),X1))
    | ~ strictly_less_than(esk4_0,X1)
    | ~ less_than(X1,esk1_2(esk3_0,esk4_0)) ),
    inference(spm,[status(thm)],[c_0_22,c_0_16]) ).

cnf(c_0_28,negated_conjecture,
    less_than(esk5_0,esk1_2(esk3_0,esk4_0)),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).

cnf(c_0_29,negated_conjecture,
    ( less_than(X1,esk2_4(esk3_0,esk4_0,esk1_2(esk3_0,esk4_0),X1))
    | ~ strictly_less_than(esk4_0,X1)
    | ~ less_than(X1,esk1_2(esk3_0,esk4_0)) ),
    inference(spm,[status(thm)],[c_0_26,c_0_16]) ).

cnf(c_0_30,negated_conjecture,
    ( ~ pair_in_list(update_slb(esk3_0,esk5_0),esk4_0,X1)
    | ~ less_than(esk5_0,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_31,negated_conjecture,
    pair_in_list(update_slb(esk3_0,esk5_0),esk4_0,esk2_4(esk3_0,esk4_0,esk1_2(esk3_0,esk4_0),esk5_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_24])]) ).

cnf(c_0_32,negated_conjecture,
    less_than(esk5_0,esk2_4(esk3_0,esk4_0,esk1_2(esk3_0,esk4_0),esk5_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_28]),c_0_24])]) ).

cnf(c_0_33,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SWV409+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.12  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33  % Computer : n029.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Tue Aug 29 03:37:11 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 0.56/0.62  % Version  : CSE_E---1.5
% 0.56/0.62  % Problem  : theBenchmark.p
% 0.56/0.62  % Proof found
% 0.56/0.62  % SZS status Theorem for theBenchmark.p
% 0.56/0.62  % SZS output start Proof
% See solution above
% 0.56/0.63  % Total time : 0.037000 s
% 0.56/0.63  % SZS output end Proof
% 0.56/0.63  % Total time : 0.040000 s
%------------------------------------------------------------------------------