%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SYN986+1.001 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n007.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 : Fri Sep  1 02:00:29 EDT 2023

% Result   : Theorem 0.20s 0.58s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   17 (   6 unt;   3 typ;   0 def)
%            Number of atoms       :   25 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   23 (  12   ~;   7   |;   2   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   2   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    2 (   2 usr;   1 con; 0-1 aty)
%            Number of variables   :   27 (   3 sgn;  12   !;   4   ?;   0   :)

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

tff(decl_23,type,
    succ: $i > $i ).

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

fof(ck,conjecture,
    ? [X4,X5] :
      ( r(zero,zero,X4)
      & r(zero,X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ck) ).

fof(hyp1,axiom,
    ! [X1] : r(X1,zero,succ(X1)),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN002+0.ax',hyp1) ).

fof(hyp2,axiom,
    ! [X1,X2,X3,X4] :
      ( r(X1,X2,X3)
     => ( r(X3,X2,X4)
       => r(X1,succ(X2),X4) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN002+0.ax',hyp2) ).

fof(c_0_3,negated_conjecture,
    ~ ? [X4,X5] :
        ( r(zero,zero,X4)
        & r(zero,X4,X5) ),
    inference(assume_negation,[status(cth)],[ck]) ).

fof(c_0_4,negated_conjecture,
    ! [X11,X12] :
      ( ~ r(zero,zero,X11)
      | ~ r(zero,X11,X12) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])]) ).

fof(c_0_5,plain,
    ! [X6] : r(X6,zero,succ(X6)),
    inference(variable_rename,[status(thm)],[hyp1]) ).

fof(c_0_6,plain,
    ! [X7,X8,X9,X10] :
      ( ~ r(X7,X8,X9)
      | ~ r(X9,X8,X10)
      | r(X7,succ(X8),X10) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[hyp2])]) ).

cnf(c_0_7,negated_conjecture,
    ( ~ r(zero,zero,X1)
    | ~ r(zero,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_8,plain,
    r(X1,zero,succ(X1)),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,plain,
    ( r(X1,succ(X2),X4)
    | ~ r(X1,X2,X3)
    | ~ r(X3,X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    ~ r(zero,succ(zero),X1),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_11,plain,
    ( r(X1,succ(zero),succ(X2))
    | ~ r(X1,zero,X2) ),
    inference(spm,[status(thm)],[c_0_9,c_0_8]) ).

cnf(c_0_12,negated_conjecture,
    ~ r(zero,zero,X1),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_13,negated_conjecture,
    $false,
    inference(spm,[status(thm)],[c_0_12,c_0_8]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SYN986+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n007.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   : Sat Aug 26 19:25:26 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.20/0.58  % Version  : CSE_E---1.5
% 0.20/0.58  % Problem  : theBenchmark.p
% 0.20/0.58  % Proof found
% 0.20/0.58  % SZS status Theorem for theBenchmark.p
% 0.20/0.58  % SZS output start Proof
% See solution above
% 0.20/0.58  % Total time : 0.004000 s
% 0.20/0.58  % SZS output end Proof
% 0.20/0.58  % Total time : 0.006000 s
%------------------------------------------------------------------------------