%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM835+2 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n008.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 10:40:53 EDT 2023

% Result   : Theorem 0.21s 0.55s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   23 (   5 unt;  10 typ;   0 def)
%            Number of atoms       :   37 (  28 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :   37 (  13   ~;  18   |;   5   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   6   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :   25 (   4 sgn;  10   !;   6   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    vd165: $i ).

tff(decl_23,type,
    vd151: $i ).

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

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

tff(decl_26,type,
    m: $i > $o ).

tff(decl_27,type,
    v1: $i ).

tff(decl_28,type,
    vskolem3: $i ).

tff(decl_29,type,
    vskolem2: $i > $i ).

tff(decl_30,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_31,type,
    esk2_2: ( $i * $i ) > $i ).

fof('def(cond(conseq(105), 0), 1)',axiom,
    ! [X3,X4] :
      ( m(X4)
    <=> ( X3 = X4
        | ? [X5] : X3 = vplus(X4,X5)
        | ? [X6] : X4 = vplus(X3,X6) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(105), 0), 1)') ).

fof('dis(case_distinction(conseq(110)))',conjecture,
    ( ? [X1] : vd165 = vplus(vd151,X1)
    | ? [X2] : vd151 = vplus(vd165,X2)
    | vd151 = vd165 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dis(case_distinction(conseq(110)))') ).

fof(c_0_2,plain,
    ! [X33,X34,X37,X38,X39,X40] :
      ( ( ~ m(X34)
        | X33 = X34
        | X33 = vplus(X34,esk1_2(X33,X34))
        | X34 = vplus(X33,esk2_2(X33,X34)) )
      & ( X37 != X38
        | m(X38) )
      & ( X37 != vplus(X38,X39)
        | m(X38) )
      & ( X38 != vplus(X37,X40)
        | m(X38) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],['def(cond(conseq(105), 0), 1)'])])])])])]) ).

fof(c_0_3,negated_conjecture,
    ~ ( ? [X1] : vd165 = vplus(vd151,X1)
      | ? [X2] : vd151 = vplus(vd165,X2)
      | vd151 = vd165 ),
    inference(assume_negation,[status(cth)],['dis(case_distinction(conseq(110)))']) ).

cnf(c_0_4,plain,
    ( m(X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

fof(c_0_5,negated_conjecture,
    ! [X19,X20] :
      ( vd165 != vplus(vd151,X19)
      & vd151 != vplus(vd165,X20)
      & vd151 != vd165 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

cnf(c_0_6,plain,
    ( X2 = X1
    | X2 = vplus(X1,esk1_2(X2,X1))
    | X1 = vplus(X2,esk2_2(X2,X1))
    | ~ m(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_7,plain,
    m(X1),
    inference(er,[status(thm)],[c_0_4]) ).

cnf(c_0_8,negated_conjecture,
    vd165 != vplus(vd151,X1),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,plain,
    ( vplus(X1,esk2_2(X1,X2)) = X2
    | vplus(X2,esk1_2(X1,X2)) = X1
    | X2 = X1 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7])]) ).

cnf(c_0_10,negated_conjecture,
    vd151 != vplus(vd165,X1),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_11,negated_conjecture,
    vd151 != vd165,
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_12,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9])]),c_0_10]),c_0_11]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : NUM835+2 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n008.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri Aug 25 11:56:48 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.21/0.54  start to proof: theBenchmark
% 0.21/0.55  % Version  : CSE_E---1.5
% 0.21/0.55  % Problem  : theBenchmark.p
% 0.21/0.55  % Proof found
% 0.21/0.55  % SZS status Theorem for theBenchmark.p
% 0.21/0.55  % SZS output start Proof
% See solution above
% 0.21/0.56  % Total time : 0.007000 s
% 0.21/0.56  % SZS output end Proof
% 0.21/0.56  % Total time : 0.010000 s
%------------------------------------------------------------------------------