TSTP Solution File: NUM852+2 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM852+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 : n003.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 10:41:02 EDT 2023

% Result   : Theorem 0.20s 0.61s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   35 (  15 unt;  11 typ;   0 def)
%            Number of atoms       :   35 (  14 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   22 (  11   ~;   8   |;   1   &)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   15 (   8   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-2 aty)
%            Number of variables   :   43 (   3 sgn;  21   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    vd481: $i ).

tff(decl_23,type,
    vd469: $i ).

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

tff(decl_25,type,
    vd480: $i ).

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

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

tff(decl_28,type,
    vskolem9: ( $i * $i ) > $i ).

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

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

tff(decl_31,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_32,type,
    esk2_2: ( $i * $i ) > $i ).

fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
    ! [X24,X25] :
      ( greater(X25,X24)
    <=> ? [X26] : X25 = vplus(X24,X26) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).

fof('ass(cond(281, 0), 0)',axiom,
    ! [X8,X9,X10] : vmul(X8,vplus(X9,X10)) = vplus(vmul(X8,X9),vmul(X8,X10)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).

fof('ass(cond(302, 0), 2)',axiom,
    ! [X3,X4] :
      ( greater(X3,X4)
     => vmul(X3,vd469) = vmul(vplus(X4,vskolem9(X3,X4)),vd469) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(302, 0), 2)') ).

fof('ass(cond(270, 0), 0)',axiom,
    ! [X11,X12] : vmul(X11,X12) = vmul(X12,X11),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).

fof('holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)',conjecture,
    greater(vmul(vd481,vd469),vmul(vd480,vd469)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)') ).

fof('holds(conseq_conjunct1(conseq(304)), 483, 0)',axiom,
    greater(vd481,vd480),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq_conjunct1(conseq(304)), 483, 0)') ).

fof(c_0_6,plain,
    ! [X65,X66,X68,X69,X70] :
      ( ( ~ greater(X66,X65)
        | X66 = vplus(X65,esk2_2(X65,X66)) )
      & ( X69 != vplus(X68,X70)
        | greater(X69,X68) ) ),
    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)), 11), 1)'])])])])]) ).

cnf(c_0_7,plain,
    ( greater(X1,X2)
    | X1 != vplus(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_8,plain,
    ! [X40,X41,X42] : vmul(X40,vplus(X41,X42)) = vplus(vmul(X40,X41),vmul(X40,X42)),
    inference(variable_rename,[status(thm)],['ass(cond(281, 0), 0)']) ).

fof(c_0_9,plain,
    ! [X33,X34] :
      ( ~ greater(X33,X34)
      | vmul(X33,vd469) = vmul(vplus(X34,vskolem9(X33,X34)),vd469) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(302, 0), 2)'])]) ).

fof(c_0_10,plain,
    ! [X43,X44] : vmul(X43,X44) = vmul(X44,X43),
    inference(variable_rename,[status(thm)],['ass(cond(270, 0), 0)']) ).

cnf(c_0_11,plain,
    greater(vplus(X1,X2),X1),
    inference(er,[status(thm)],[c_0_7]) ).

cnf(c_0_12,plain,
    vmul(X1,vplus(X2,X3)) = vplus(vmul(X1,X2),vmul(X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,plain,
    ( vmul(X1,vd469) = vmul(vplus(X2,vskolem9(X1,X2)),vd469)
    | ~ greater(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,plain,
    vmul(X1,X2) = vmul(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_15,negated_conjecture,
    ~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],['holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)'])]) ).

cnf(c_0_16,plain,
    greater(vmul(X1,vplus(X2,X3)),vmul(X1,X2)),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_17,plain,
    ( vmul(vd469,vplus(X1,vskolem9(X2,X1))) = vmul(X2,vd469)
    | ~ greater(X2,X1) ),
    inference(rw,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_18,negated_conjecture,
    ~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_19,plain,
    ( greater(vmul(X1,vd469),vmul(vd469,X2))
    | ~ greater(X1,X2) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_20,negated_conjecture,
    ~ greater(vmul(vd469,vd481),vmul(vd469,vd480)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_14]),c_0_14]) ).

cnf(c_0_21,plain,
    ( greater(vmul(vd469,X1),vmul(vd469,X2))
    | ~ greater(X1,X2) ),
    inference(spm,[status(thm)],[c_0_19,c_0_14]) ).

cnf(c_0_22,plain,
    greater(vd481,vd480),
    inference(split_conjunct,[status(thm)],['holds(conseq_conjunct1(conseq(304)), 483, 0)']) ).

cnf(c_0_23,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : NUM852+2 : TPTP v8.1.2. Released v4.1.0.
% 0.13/0.14  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n003.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri Aug 25 10:31:38 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 0.20/0.61  % Version  : CSE_E---1.5
% 0.20/0.61  % Problem  : theBenchmark.p
% 0.20/0.61  % Proof found
% 0.20/0.61  % SZS status Theorem for theBenchmark.p
% 0.20/0.61  % SZS output start Proof
% See solution above
% 0.20/0.62  % Total time : 0.024000 s
% 0.20/0.62  % SZS output end Proof
% 0.20/0.62  % Total time : 0.027000 s
%------------------------------------------------------------------------------