%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWV262-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n009.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 21:37:21 EDT 2023

% Result   : Unsatisfiable 0.20s 0.57s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   21 (  13 unt;   8 typ;   0 def)
%            Number of atoms       :   13 (  12 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    4 (   4   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    7 (   3   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-3 aty)
%            Number of variables   :   23 (   2 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    v_X: $i ).

tff(decl_23,type,
    v_Y: $i ).

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

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

tff(decl_26,type,
    c_insert: ( $i * $i * $i ) > $i ).

tff(decl_27,type,
    c_Message_Oparts: $i > $i ).

tff(decl_28,type,
    c_emptyset: $i ).

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

cnf(cls_conjecture_0,negated_conjecture,
    c_Message_Oparts(c_insert(v_X,c_insert(v_Y,v_H,tc_Message_Omsg),tc_Message_Omsg)) != c_union(c_union(c_Message_Oparts(c_insert(v_X,c_emptyset,tc_Message_Omsg)),c_Message_Oparts(c_insert(v_Y,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Oparts(v_H),tc_Message_Omsg),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

cnf(cls_Message_Oparts__Un_0,axiom,
    c_Message_Oparts(c_union(X1,X2,tc_Message_Omsg)) = c_union(c_Message_Oparts(X1),c_Message_Oparts(X2),tc_Message_Omsg),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__Un_0) ).

cnf(cls_Set_OUn__insert__left_0,axiom,
    c_union(c_insert(X1,X2,X3),X4,X3) = c_insert(X1,c_union(X2,X4,X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__insert__left_0) ).

cnf(cls_Set_OUn__empty__left_0,axiom,
    c_union(c_emptyset,X1,X2) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).

cnf(c_0_4,negated_conjecture,
    c_Message_Oparts(c_insert(v_X,c_insert(v_Y,v_H,tc_Message_Omsg),tc_Message_Omsg)) != c_union(c_union(c_Message_Oparts(c_insert(v_X,c_emptyset,tc_Message_Omsg)),c_Message_Oparts(c_insert(v_Y,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Oparts(v_H),tc_Message_Omsg),
    cls_conjecture_0 ).

cnf(c_0_5,axiom,
    c_Message_Oparts(c_union(X1,X2,tc_Message_Omsg)) = c_union(c_Message_Oparts(X1),c_Message_Oparts(X2),tc_Message_Omsg),
    cls_Message_Oparts__Un_0 ).

cnf(c_0_6,axiom,
    c_union(c_insert(X1,X2,X3),X4,X3) = c_insert(X1,c_union(X2,X4,X3),X3),
    cls_Set_OUn__insert__left_0 ).

cnf(c_0_7,axiom,
    c_union(c_emptyset,X1,X2) = X1,
    cls_Set_OUn__empty__left_0 ).

cnf(c_0_8,negated_conjecture,
    c_Message_Oparts(c_union(c_union(c_insert(v_X,c_emptyset,tc_Message_Omsg),c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg)) != c_Message_Oparts(c_insert(v_X,c_insert(v_Y,v_H,tc_Message_Omsg),tc_Message_Omsg)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4,c_0_5]),c_0_5]) ).

cnf(c_0_9,plain,
    c_union(c_insert(X1,c_emptyset,X2),X3,X2) = c_insert(X1,X3,X2),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_10,negated_conjecture,
    c_Message_Oparts(c_union(c_insert(v_X,c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg)) != c_Message_Oparts(c_insert(v_X,c_insert(v_Y,v_H,tc_Message_Omsg),tc_Message_Omsg)),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_11,plain,
    c_union(c_insert(X1,c_insert(X2,c_emptyset,X3),X3),X4,X3) = c_insert(X1,c_insert(X2,X4,X3),X3),
    inference(spm,[status(thm)],[c_0_6,c_0_9]) ).

cnf(c_0_12,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWV262-2 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n009.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 29 09:46:35 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.20/0.57  % Version  : CSE_E---1.5
% 0.20/0.57  % Problem  : theBenchmark.p
% 0.20/0.57  % Proof found
% 0.20/0.57  % SZS status Theorem for theBenchmark.p
% 0.20/0.57  % SZS output start Proof
% See solution above
% 0.20/0.58  % Total time : 0.003000 s
% 0.20/0.58  % SZS output end Proof
% 0.20/0.58  % Total time : 0.006000 s
%------------------------------------------------------------------------------