%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM837+1 : 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 : n014.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 0.60s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   25 (   7 unt;  15 typ;   0 def)
%            Number of atoms       :   15 (   8 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   11 (   6   ~;   3   |;   1   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   20 (  11   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   4 con; 0-2 aty)
%            Number of variables   :   14 (   1 sgn;   8   !;   3   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    vd269: $i ).

tff(decl_23,type,
    vd268: $i ).

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

tff(decl_25,type,
    vd271: $i ).

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

tff(decl_27,type,
    leq: ( $i * $i ) > $o ).

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

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

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

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

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

tff(decl_33,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_34,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_35,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_36,type,
    esk4_2: ( $i * $i ) > $i ).

fof('qe(171)',conjecture,
    ? [X1] : vd269 = vplus(vd268,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','qe(171)') ).

fof('def(cond(conseq(axiom(3)), 12), 1)',axiom,
    ! [X16,X17] :
      ( less(X17,X16)
    <=> ? [X18] : X16 = vplus(X17,X18) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).

fof('holds(conjunct1(170), 270, 0)',axiom,
    less(vd268,vd269),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct1(170), 270, 0)') ).

fof(c_0_3,negated_conjecture,
    ~ ? [X1] : vd269 = vplus(vd268,X1),
    inference(assume_negation,[status(cth)],['qe(171)']) ).

fof(c_0_4,plain,
    ! [X69,X70,X72,X73,X74] :
      ( ( ~ less(X70,X69)
        | X69 = vplus(X70,esk1_2(X69,X70)) )
      & ( X72 != vplus(X73,X74)
        | less(X73,X72) ) ),
    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(axiom(3)), 12), 1)'])])])])]) ).

fof(c_0_5,negated_conjecture,
    ! [X48] : vd269 != vplus(vd268,X48),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])]) ).

cnf(c_0_6,plain,
    ( X2 = vplus(X1,esk1_2(X2,X1))
    | ~ less(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_7,plain,
    less(vd268,vd269),
    inference(split_conjunct,[status(thm)],['holds(conjunct1(170), 270, 0)']) ).

cnf(c_0_8,negated_conjecture,
    vd269 != vplus(vd268,X1),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,plain,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM837+1 : 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
% 0.14/0.35  % Computer : n014.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Fri Aug 25 16:18:17 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.57  start to proof: theBenchmark
% 0.21/0.60  % Version  : CSE_E---1.5
% 0.21/0.60  % Problem  : theBenchmark.p
% 0.21/0.60  % Proof found
% 0.21/0.60  % SZS status Theorem for theBenchmark.p
% 0.21/0.60  % SZS output start Proof
% See solution above
% 0.21/0.60  % Total time : 0.011000 s
% 0.21/0.60  % SZS output end Proof
% 0.21/0.60  % Total time : 0.013000 s
%------------------------------------------------------------------------------