%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWV254-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n018.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 21:37:17 EDT 2023

% Result   : Unsatisfiable 0.17s 0.55s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   24 (  13 unt;   9 typ;   0 def)
%            Number of atoms       :   19 (   9 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   10 (   6   ~;   4   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (   6   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :   20 (  10 sgn;   0   !;   0   ?;   0   :)

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

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

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

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

tff(decl_26,type,
    c_Suc: $i > $i ).

tff(decl_27,type,
    tc_nat: $i ).

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

tff(decl_29,type,
    v_x: $i > $i ).

tff(decl_30,type,
    v_nat: $i ).

cnf(cls_conjecture_0,negated_conjecture,
    c_lessequals(X1,v_x(X1),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

cnf(cls_conjecture_1,negated_conjecture,
    v_x(X1) = v_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

cnf(cls_SetInterval_OatLeastLessThan__empty_0,axiom,
    ( c_SetInterval_OatLeastLessThan(X3,X2,X1) = c_emptyset
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).

cnf(clsarity_nat_3,axiom,
    class_Orderings_Oorder(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_3) ).

cnf(cls_SetInterval_OatLeastLessThan__singleton_0,axiom,
    c_SetInterval_OatLeastLessThan(X1,c_Suc(X1),tc_nat) = c_insert(X1,c_emptyset,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__singleton_0) ).

cnf(cls_Set_Oempty__not__insert_0,axiom,
    c_emptyset != c_insert(X1,X2,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__not__insert_0) ).

cnf(c_0_6,negated_conjecture,
    c_lessequals(X1,v_x(X1),tc_nat),
    cls_conjecture_0 ).

cnf(c_0_7,negated_conjecture,
    v_x(X1) = v_nat,
    cls_conjecture_1 ).

cnf(c_0_8,axiom,
    ( c_SetInterval_OatLeastLessThan(X3,X2,X1) = c_emptyset
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_SetInterval_OatLeastLessThan__empty_0 ).

cnf(c_0_9,negated_conjecture,
    c_lessequals(X1,v_nat,tc_nat),
    inference(rw,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_10,axiom,
    class_Orderings_Oorder(tc_nat),
    clsarity_nat_3 ).

cnf(c_0_11,axiom,
    c_SetInterval_OatLeastLessThan(X1,c_Suc(X1),tc_nat) = c_insert(X1,c_emptyset,tc_nat),
    cls_SetInterval_OatLeastLessThan__singleton_0 ).

cnf(c_0_12,negated_conjecture,
    c_SetInterval_OatLeastLessThan(v_nat,X1,tc_nat) = c_emptyset,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10])]) ).

cnf(c_0_13,axiom,
    c_emptyset != c_insert(X1,X2,X3),
    cls_Set_Oempty__not__insert_0 ).

cnf(c_0_14,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem    : SWV254-2 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.11  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.32  % Computer : n018.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Tue Aug 29 08:48:02 EDT 2023
% 0.11/0.32  % CPUTime  : 
% 0.17/0.54  start to proof: theBenchmark
% 0.17/0.55  % Version  : CSE_E---1.5
% 0.17/0.55  % Problem  : theBenchmark.p
% 0.17/0.55  % Proof found
% 0.17/0.55  % SZS status Theorem for theBenchmark.p
% 0.17/0.55  % SZS output start Proof
% See solution above
% 0.17/0.55  % Total time : 0.003000 s
% 0.17/0.55  % SZS output end Proof
% 0.17/0.55  % Total time : 0.005000 s
%------------------------------------------------------------------------------