%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWV412+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 : 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 21:38:28 EDT 2023

% Result   : Theorem 0.21s 0.57s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   27 (   4 unt;  16 typ;   0 def)
%            Number of atoms       :   27 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   24 (   8   ~;   5   |;   8   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   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    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :   21 (   0 sgn;  16   !;   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 ).

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

fof(l48_co,conjecture,
    ! [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',l48_co) ).

fof(l48_li3839,lemma,
    ! [X1,X2,X3,X4] :
      ( ( pair_in_list(X1,X2,X3)
        & strictly_less_than(X3,X4) )
     => pair_in_list(update_slb(X1,X4),X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l48_li3839) ).

fof(c_0_2,negated_conjecture,
    ~ ! [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) ),
    inference(assume_negation,[status(cth)],[l48_co]) ).

fof(c_0_3,lemma,
    ! [X53,X54,X55,X56] :
      ( ~ pair_in_list(X53,X54,X55)
      | ~ strictly_less_than(X55,X56)
      | pair_in_list(update_slb(X53,X56),X54,X56) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l48_li3839])]) ).

fof(c_0_4,negated_conjecture,
    ( pair_in_list(esk1_0,esk2_0,esk3_0)
    & strictly_less_than(esk2_0,esk4_0)
    & strictly_less_than(esk3_0,esk4_0)
    & ~ pair_in_list(update_slb(esk1_0,esk4_0),esk2_0,esk4_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])]) ).

cnf(c_0_5,lemma,
    ( pair_in_list(update_slb(X1,X4),X2,X4)
    | ~ pair_in_list(X1,X2,X3)
    | ~ strictly_less_than(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

cnf(c_0_6,negated_conjecture,
    pair_in_list(esk1_0,esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_7,negated_conjecture,
    ~ pair_in_list(update_slb(esk1_0,esk4_0),esk2_0,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_8,negated_conjecture,
    ( pair_in_list(update_slb(esk1_0,X1),esk2_0,X1)
    | ~ strictly_less_than(esk3_0,X1) ),
    inference(spm,[status(thm)],[c_0_5,c_0_6]) ).

cnf(c_0_9,negated_conjecture,
    strictly_less_than(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_10,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWV412+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n031.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 29 09:22:26 EDT 2023
% 0.12/0.35  % CPUTime  : 
% 0.21/0.55  start to proof: theBenchmark
% 0.21/0.57  % Version  : CSE_E---1.5
% 0.21/0.57  % Problem  : theBenchmark.p
% 0.21/0.57  % Proof found
% 0.21/0.57  % SZS status Theorem for theBenchmark.p
% 0.21/0.57  % SZS output start Proof
% See solution above
% 0.21/0.57  % Total time : 0.008000 s
% 0.21/0.57  % SZS output end Proof
% 0.21/0.57  % Total time : 0.011000 s
%------------------------------------------------------------------------------