%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM854+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 : n027.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 10:41:03 EDT 2023

% Result   : Theorem 0.19s 0.59s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   30 (  13 unt;  14 typ;   0 def)
%            Number of atoms       :   19 (   3 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    8 (   5   ~;   2   |;   0   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (   9   >;   8   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   5 con; 0-2 aty)
%            Number of variables   :   18 (   0 sgn;  10   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    vd508: $i ).

tff(decl_23,type,
    vd511: $i ).

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

tff(decl_25,type,
    vd509: $i ).

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

tff(decl_27,type,
    vd512: $i ).

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

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

tff(decl_30,type,
    vsucc: $i > $i ).

tff(decl_31,type,
    v1: $i ).

tff(decl_32,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_33,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_34,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_35,type,
    esk4_2: ( $i * $i ) > $i ).

fof('ass(cond(299, 0), 2)',axiom,
    ! [X10,X15,X16] :
      ( greater(X15,X16)
     => greater(vmul(X15,X10),vmul(X16,X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(299, 0), 2)') ).

fof('holds(conjunct1(314), 510, 0)',axiom,
    greater(vd508,vd509),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct1(314), 510, 0)') ).

fof('ass(cond(270, 0), 0)',axiom,
    ! [X23,X24] : vmul(X23,X24) = vmul(X24,X23),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).

fof('holds(conjunct1(315), 514, 0)',conjecture,
    greater(vmul(vd508,vd511),vmul(vd509,vd511)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct1(315), 514, 0)') ).

fof(c_0_4,plain,
    ! [X61,X62,X63] :
      ( ~ greater(X62,X63)
      | greater(vmul(X62,X61),vmul(X63,X61)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(299, 0), 2)'])]) ).

cnf(c_0_5,plain,
    ( greater(vmul(X1,X3),vmul(X2,X3))
    | ~ greater(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_6,plain,
    greater(vd508,vd509),
    inference(split_conjunct,[status(thm)],['holds(conjunct1(314), 510, 0)']) ).

fof(c_0_7,plain,
    ! [X70,X71] : vmul(X70,X71) = vmul(X71,X70),
    inference(variable_rename,[status(thm)],['ass(cond(270, 0), 0)']) ).

fof(c_0_8,negated_conjecture,
    ~ greater(vmul(vd508,vd511),vmul(vd509,vd511)),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],['holds(conjunct1(315), 514, 0)'])]) ).

cnf(c_0_9,plain,
    greater(vmul(vd508,X1),vmul(vd509,X1)),
    inference(spm,[status(thm)],[c_0_5,c_0_6]) ).

cnf(c_0_10,plain,
    vmul(X1,X2) = vmul(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,negated_conjecture,
    ~ greater(vmul(vd508,vd511),vmul(vd509,vd511)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12,plain,
    greater(vmul(vd508,X1),vmul(X1,vd509)),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_13,negated_conjecture,
    ~ greater(vmul(vd511,vd508),vmul(vd511,vd509)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_10]),c_0_10]) ).

cnf(c_0_14,plain,
    greater(vmul(X1,vd508),vmul(X1,vd509)),
    inference(spm,[status(thm)],[c_0_12,c_0_10]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM854+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
% 0.13/0.34  % Computer : n027.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   : Fri Aug 25 14:32:34 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.19/0.59  % Version  : CSE_E---1.5
% 0.19/0.59  % Problem  : theBenchmark.p
% 0.19/0.59  % Proof found
% 0.19/0.59  % SZS status Theorem for theBenchmark.p
% 0.19/0.59  % SZS output start Proof
% See solution above
% 0.19/0.59  % Total time : 0.012000 s
% 0.19/0.59  % SZS output end Proof
% 0.19/0.59  % Total time : 0.015000 s
%------------------------------------------------------------------------------