%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : MSC012+1 : 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 : n011.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 09:21:04 EDT 2023

% Result   : Theorem 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   26 (   8 unt;   5 typ;   0 def)
%            Number of atoms       :   48 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   46 (  19   ~;  20   |;   5   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   4   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   2 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   0 con; 1-1 aty)
%            Number of variables   :   31 (   2 sgn;  14   !;   2   ?;   0   :)

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

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

tff(decl_24,type,
    goal: $o ).

tff(decl_25,type,
    esk1_1: $i > $i ).

tff(decl_26,type,
    esk2_1: $i > $i ).

fof(left_to_right,axiom,
    ! [X1,X2] :
      ( ( p(X1)
        & less(X1,X2)
        & p(X2) )
     => goal ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_to_right) ).

fof(goal_to_be_proved,conjecture,
    goal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_to_be_proved) ).

fof(transitive_less,axiom,
    ! [X1,X2,X3] :
      ( ( less(X1,X2)
        & less(X2,X3) )
     => less(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive_less) ).

fof(right_to_left,axiom,
    ! [X1] :
      ( p(X1)
      | ? [X2] :
          ( less(X1,X2)
          & p(X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_to_left) ).

fof(serial_less,axiom,
    ! [X1] :
    ? [X2] : less(X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',serial_less) ).

fof(c_0_5,plain,
    ! [X4,X5] :
      ( ~ p(X4)
      | ~ less(X4,X5)
      | ~ p(X5)
      | goal ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[left_to_right])]) ).

fof(c_0_6,negated_conjecture,
    ~ goal,
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[goal_to_be_proved])]) ).

fof(c_0_7,plain,
    ! [X8,X9,X10] :
      ( ~ less(X8,X9)
      | ~ less(X9,X10)
      | less(X8,X10) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[transitive_less])]) ).

fof(c_0_8,plain,
    ! [X6] :
      ( ( less(X6,esk1_1(X6))
        | p(X6) )
      & ( p(esk1_1(X6))
        | p(X6) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[right_to_left])])]) ).

cnf(c_0_9,plain,
    ( goal
    | ~ p(X1)
    | ~ less(X1,X2)
    | ~ p(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_10,negated_conjecture,
    ~ goal,
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,plain,
    ( less(X1,X3)
    | ~ less(X1,X2)
    | ~ less(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,plain,
    ( less(X1,esk1_1(X1))
    | p(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,plain,
    ( ~ less(X1,X2)
    | ~ p(X2)
    | ~ p(X1) ),
    inference(sr,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_14,plain,
    ( less(X1,esk1_1(X2))
    | p(X2)
    | ~ less(X1,X2) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_15,plain,
    ( p(esk1_1(X1))
    | p(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_16,plain,
    ! [X11] : less(X11,esk2_1(X11)),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[serial_less])]) ).

cnf(c_0_17,plain,
    ( ~ less(X1,X2)
    | ~ p(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_13]) ).

cnf(c_0_18,plain,
    less(X1,esk2_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_19,plain,
    ~ p(X1),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_20,plain,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_15,c_0_19]),c_0_19]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : MSC012+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34  % Computer : n011.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   : Thu Aug 24 13:53:22 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 : 0.005000 s
% 0.20/0.59  % SZS output end Proof
% 0.20/0.59  % Total time : 0.007000 s
%------------------------------------------------------------------------------