%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM844+2 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n016.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 10:40:58 EDT 2023

% Result   : Theorem 0.20s 0.56s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   27 (  14 unt;  11 typ;   0 def)
%            Number of atoms       :   18 (  17 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    5 (   3   ~;   0   |;   2   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (   8   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   25 (   0 sgn;  14   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    vd411: $i ).

tff(decl_23,type,
    vd413: $i ).

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

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

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

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

tff(decl_28,type,
    less: ( $i * $i ) > $o ).

tff(decl_29,type,
    leq: ( $i * $i ) > $o ).

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

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

tff(decl_32,type,
    vskolem2: $i > $i ).

fof('holds(266, 415, 3)',conjecture,
    vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(266, 415, 3)') ).

fof('qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))',axiom,
    ! [X16,X17] :
      ( vplus(X16,vsucc(X17)) = vsucc(vplus(X16,X17))
      & vplus(X16,v1) = vsucc(X16) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).

fof('ass(cond(61, 0), 0)',axiom,
    ! [X8,X9] : vplus(X9,X8) = vplus(X8,X9),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).

fof('ass(cond(33, 0), 0)',axiom,
    ! [X13,X14,X15] : vplus(vplus(X13,X14),X15) = vplus(X13,vplus(X14,X15)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).

fof(c_0_4,negated_conjecture,
    vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],['holds(266, 415, 3)'])]) ).

fof(c_0_5,plain,
    ! [X37,X38] :
      ( vplus(X37,vsucc(X38)) = vsucc(vplus(X37,X38))
      & vplus(X37,v1) = vsucc(X37) ),
    inference(variable_rename,[status(thm)],['qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))']) ).

fof(c_0_6,plain,
    ! [X29,X30] : vplus(X30,X29) = vplus(X29,X30),
    inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).

fof(c_0_7,plain,
    ! [X34,X35,X36] : vplus(vplus(X34,X35),X36) = vplus(X34,vplus(X35,X36)),
    inference(variable_rename,[status(thm)],['ass(cond(33, 0), 0)']) ).

cnf(c_0_8,negated_conjecture,
    vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_9,plain,
    vplus(X1,v1) = vsucc(X1),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_10,plain,
    vplus(X1,X2) = vplus(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,plain,
    vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,negated_conjecture,
    vplus(vmul(vd411,vd413),vplus(vd413,vplus(vd411,v1))) != vplus(vmul(vd411,vd413),vplus(vplus(vd411,v1),vd413)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9]),c_0_9]) ).

cnf(c_0_13,plain,
    vplus(X1,X2) = vplus(X2,X1),
    c_0_10 ).

cnf(c_0_14,plain,
    vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
    c_0_11 ).

cnf(c_0_15,negated_conjecture,
    $false,
    inference(ar,[status(thm)],[c_0_12,c_0_13,c_0_14]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM844+2 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34  % Computer : n016.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   : Fri Aug 25 08:34:25 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.54  start to proof: theBenchmark
% 0.20/0.56  % Version  : CSE_E---1.5
% 0.20/0.56  % Problem  : theBenchmark.p
% 0.20/0.56  % Proof found
% 0.20/0.56  % SZS status Theorem for theBenchmark.p
% 0.20/0.56  % SZS output start Proof
% See solution above
% 0.20/0.56  % Total time : 0.005000 s
% 0.20/0.56  % SZS output end Proof
% 0.20/0.56  % Total time : 0.008000 s
%------------------------------------------------------------------------------