%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET850-2 : 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 : n006.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 14:35:57 EDT 2023

% Result   : Unsatisfiable 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   17 (   7 unt;   7 typ;   0 def)
%            Number of atoms       :   15 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   12 (   7   ~;   5   |;   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  :    7 (   3   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-3 aty)
%            Number of variables   :   15 (   2 sgn;   0   !;   0   ?;   0   :)

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

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

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

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

tff(decl_26,type,
    v_y: $i ).

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

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

cnf(cls_Set_Osubset__trans_0,axiom,
    ( c_lessequals(X4,X2,tc_set(X3))
    | ~ c_lessequals(X1,X2,tc_set(X3))
    | ~ c_lessequals(X4,X1,tc_set(X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__trans_0) ).

cnf(cls_conjecture_0,negated_conjecture,
    c_lessequals(v_x,v_y,tc_set(tc_set(t_a))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

cnf(cls_conjecture_1,negated_conjecture,
    ~ c_lessequals(v_x,c_Zorn_Osucc(v_S,v_y,t_a),tc_set(tc_set(t_a))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

cnf(cls_Zorn_OAbrial__axiom1_0,axiom,
    c_lessequals(X1,c_Zorn_Osucc(X2,X1,X3),tc_set(tc_set(X3))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).

cnf(c_0_4,axiom,
    ( c_lessequals(X4,X2,tc_set(X3))
    | ~ c_lessequals(X1,X2,tc_set(X3))
    | ~ c_lessequals(X4,X1,tc_set(X3)) ),
    cls_Set_Osubset__trans_0 ).

cnf(c_0_5,negated_conjecture,
    c_lessequals(v_x,v_y,tc_set(tc_set(t_a))),
    cls_conjecture_0 ).

cnf(c_0_6,negated_conjecture,
    ~ c_lessequals(v_x,c_Zorn_Osucc(v_S,v_y,t_a),tc_set(tc_set(t_a))),
    cls_conjecture_1 ).

cnf(c_0_7,negated_conjecture,
    ( c_lessequals(v_x,X1,tc_set(tc_set(t_a)))
    | ~ c_lessequals(v_y,X1,tc_set(tc_set(t_a))) ),
    inference(spm,[status(thm)],[c_0_4,c_0_5]) ).

cnf(c_0_8,axiom,
    c_lessequals(X1,c_Zorn_Osucc(X2,X1,X3),tc_set(tc_set(X3))),
    cls_Zorn_OAbrial__axiom1_0 ).

cnf(c_0_9,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET850-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34  % Computer : n006.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Sat Aug 26 14:53:07 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.59  % Version  : CSE_E---1.5
% 0.20/0.59  % Problem  : theBenchmark.p
% 0.20/0.59  % Proof found
% 0.20/0.59  % SZS status Theorem for theBenchmark.p
% 0.20/0.59  % SZS output start Proof
% See solution above
% 0.20/0.59  % Total time : 0.003000 s
% 0.20/0.59  % SZS output end Proof
% 0.20/0.59  % Total time : 0.006000 s
%------------------------------------------------------------------------------