%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SYO614-1 : TPTP v8.1.2. Released v7.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n020.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 04:12:05 EDT 2023

% Result   : Unsatisfiable 0.20s 0.58s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   33 (   8 unt;   7 typ;   0 def)
%            Number of atoms       :   48 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   53 (  31   ~;  22   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   5   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   48 (  19 sgn;   0   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    f: $i > $i ).

tff(decl_25,type,
    a0: $i ).

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

tff(decl_27,type,
    a1: $i ).

tff(decl_28,type,
    s: $i > $i ).

cnf(sos_03,axiom,
    ( le(X2,X3)
    | ~ le(max(X1,X2),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_03) ).

cnf(sos_01,axiom,
    le(X1,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_01) ).

cnf(sos_02,axiom,
    ( le(X1,X3)
    | ~ le(max(X1,X2),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_02) ).

cnf(sos_06,axiom,
    ( ~ eq(f(X1),a1)
    | ~ eq(f(X2),a1)
    | ~ le(s(X1),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_06) ).

cnf(sos_05,axiom,
    ( ~ eq(f(X1),a0)
    | ~ eq(f(X2),a0)
    | ~ le(s(X1),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_05) ).

cnf(sos_04,axiom,
    ( eq(f(X1),a0)
    | eq(f(X1),a1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_04) ).

cnf(c_0_6,axiom,
    ( le(X2,X3)
    | ~ le(max(X1,X2),X3) ),
    sos_03 ).

cnf(c_0_7,axiom,
    le(X1,X1),
    sos_01 ).

cnf(c_0_8,axiom,
    ( le(X1,X3)
    | ~ le(max(X1,X2),X3) ),
    sos_02 ).

cnf(c_0_9,axiom,
    ( ~ eq(f(X1),a1)
    | ~ eq(f(X2),a1)
    | ~ le(s(X1),X2) ),
    sos_06 ).

cnf(c_0_10,plain,
    le(X1,max(X2,X1)),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_11,axiom,
    ( ~ eq(f(X1),a0)
    | ~ eq(f(X2),a0)
    | ~ le(s(X1),X2) ),
    sos_05 ).

cnf(c_0_12,plain,
    le(X1,max(X1,X2)),
    inference(spm,[status(thm)],[c_0_8,c_0_7]) ).

cnf(c_0_13,plain,
    ( ~ eq(f(max(X1,s(X2))),a1)
    | ~ eq(f(X2),a1) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_14,axiom,
    ( eq(f(X1),a0)
    | eq(f(X1),a1) ),
    sos_04 ).

cnf(c_0_15,plain,
    ( ~ eq(f(max(s(X1),X2)),a0)
    | ~ eq(f(X1),a0) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_16,plain,
    ( eq(f(max(X1,s(X2))),a0)
    | ~ eq(f(X2),a1) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_17,plain,
    ( ~ eq(f(s(X1)),a1)
    | ~ eq(f(X1),a1) ),
    inference(spm,[status(thm)],[c_0_9,c_0_7]) ).

cnf(c_0_18,plain,
    ( ~ eq(f(X1),a0)
    | ~ eq(f(X2),a1) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_19,plain,
    ( eq(f(s(X1)),a0)
    | ~ eq(f(X1),a1) ),
    inference(spm,[status(thm)],[c_0_17,c_0_14]) ).

cnf(c_0_20,plain,
    ( ~ eq(f(X1),a1)
    | ~ eq(f(X2),a1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_21,plain,
    le(X1,max(max(X2,X1),X3)),
    inference(spm,[status(thm)],[c_0_6,c_0_12]) ).

cnf(c_0_22,plain,
    ~ eq(f(X1),a1),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_14]),c_0_18]) ).

cnf(c_0_23,plain,
    ( ~ eq(f(max(max(X1,s(X2)),X3)),a0)
    | ~ eq(f(X2),a0) ),
    inference(spm,[status(thm)],[c_0_11,c_0_21]) ).

cnf(c_0_24,plain,
    eq(f(X1),a0),
    inference(sr,[status(thm)],[c_0_14,c_0_22]) ).

cnf(c_0_25,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_24])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SYO614-1 : TPTP v8.1.2. Released v7.1.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n020.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 07:09:15 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.57  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 : 0.007000 s
%------------------------------------------------------------------------------