%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWV402+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 : n032.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 21:38:25 EDT 2023

% Result   : Theorem 0.16s 0.50s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   24 (   6 unt;  15 typ;   0 def)
%            Number of atoms       :   15 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   12 (   6   ~;   0   |;   4   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   20 (  10   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-2 aty)
%            Number of variables   :   16 (   4 sgn;  14   !;   0   ?;   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_0: $i ).

tff(decl_35,type,
    esk2_0: $i ).

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

fof(l38_co,conjecture,
    ! [X1,X2,X3,X4] :
      ( ( pair_in_list(create_slb,X2,X3)
        & strictly_less_than(X3,X4) )
     => pair_in_list(update_slb(create_slb,X4),X2,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l38_co) ).

fof(ax22,axiom,
    ! [X1,X2] : ~ pair_in_list(create_slb,X1,X2),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax',ax22) ).

fof(c_0_2,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( ( pair_in_list(create_slb,X2,X3)
          & strictly_less_than(X3,X4) )
       => pair_in_list(update_slb(create_slb,X4),X2,X4) ),
    inference(assume_negation,[status(cth)],[l38_co]) ).

fof(c_0_3,plain,
    ! [X1,X2] : ~ pair_in_list(create_slb,X1,X2),
    inference(fof_simplification,[status(thm)],[ax22]) ).

fof(c_0_4,negated_conjecture,
    ( pair_in_list(create_slb,esk1_0,esk2_0)
    & strictly_less_than(esk2_0,esk3_0)
    & ~ pair_in_list(update_slb(create_slb,esk3_0),esk1_0,esk3_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_2])])])]) ).

fof(c_0_5,plain,
    ! [X23,X24] : ~ pair_in_list(create_slb,X23,X24),
    inference(variable_rename,[status(thm)],[c_0_3]) ).

cnf(c_0_6,negated_conjecture,
    pair_in_list(create_slb,esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_7,plain,
    ~ pair_in_list(create_slb,X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[c_0_6,c_0_7]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem    : SWV402+1 : TPTP v8.1.2. Released v3.3.0.
% 0.09/0.11  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.30  % Computer : n032.cluster.edu
% 0.11/0.30  % Model    : x86_64 x86_64
% 0.11/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30  % Memory   : 8042.1875MB
% 0.11/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30  % CPULimit   : 300
% 0.11/0.30  % WCLimit    : 300
% 0.11/0.30  % DateTime   : Tue Aug 29 09:46:46 EDT 2023
% 0.11/0.30  % CPUTime  : 
% 0.16/0.49  start to proof: theBenchmark
% 0.16/0.50  % Version  : CSE_E---1.5
% 0.16/0.50  % Problem  : theBenchmark.p
% 0.16/0.50  % Proof found
% 0.16/0.50  % SZS status Theorem for theBenchmark.p
% 0.16/0.50  % SZS output start Proof
% See solution above
% 0.16/0.50  % Total time : 0.006000 s
% 0.16/0.50  % SZS output end Proof
% 0.16/0.50  % Total time : 0.009000 s
%------------------------------------------------------------------------------