TSTP Solution File: NUM852+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM852+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 : n022.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 0.19s 0.59s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   38 (  14 unt;  17 typ;   0 def)
%            Number of atoms       :   28 (  12 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   14 (   7   ~;   5   |;   0   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   24 (  13   >;  11   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   4 con; 0-2 aty)
%            Number of variables   :   26 (   1 sgn;  16   !;   0   ?;   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,
    v1: $i ).

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

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

tff(decl_34,type,
    vskolem2: $i > $i ).

tff(decl_35,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_36,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_37,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_38,type,
    esk4_2: ( $i * $i ) > $i ).

fof('ass(cond(302, 0), 1)',axiom,
    ! [X3,X4] :
      ( greater(X3,X4)
     => vmul(vplus(X4,vskolem9(X3,X4)),vd469) = vplus(vmul(X4,vd469),vmul(vskolem9(X3,X4),vd469)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(302, 0), 1)') ).

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('ass(cond(302, 0), 3)',axiom,
    ! [X3,X4] :
      ( greater(X3,X4)
     => X3 = vplus(X4,vskolem9(X3,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(302, 0), 3)') ).

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('ass(cond(189, 0), 0)',axiom,
    ! [X41,X42] : greater(vplus(X41,X42),X41),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(189, 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(c_0_6,plain,
    ! [X102,X103] :
      ( ~ greater(X102,X103)
      | vmul(vplus(X103,vskolem9(X102,X103)),vd469) = vplus(vmul(X103,vd469),vmul(vskolem9(X102,X103),vd469)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(302, 0), 1)'])]) ).

fof(c_0_7,plain,
    ! [X114,X115] : vmul(X114,X115) = vmul(X115,X114),
    inference(variable_rename,[status(thm)],['ass(cond(270, 0), 0)']) ).

fof(c_0_8,plain,
    ! [X106,X107] :
      ( ~ greater(X106,X107)
      | X106 = vplus(X107,vskolem9(X106,X107)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(302, 0), 3)'])]) ).

cnf(c_0_9,plain,
    ( vmul(vplus(X2,vskolem9(X1,X2)),vd469) = vplus(vmul(X2,vd469),vmul(vskolem9(X1,X2),vd469))
    | ~ greater(X1,X2) ),
    inference(split_conjunct,[status(thm)],[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,plain,
    ( X1 = vplus(X2,vskolem9(X1,X2))
    | ~ greater(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12,plain,
    greater(vd481,vd480),
    inference(split_conjunct,[status(thm)],['holds(conseq_conjunct1(conseq(304)), 483, 0)']) ).

fof(c_0_13,plain,
    ! [X156,X157] : greater(vplus(X156,X157),X156),
    inference(variable_rename,[status(thm)],['ass(cond(189, 0), 0)']) ).

cnf(c_0_14,plain,
    ( vplus(vmul(X1,vd469),vmul(vd469,vskolem9(X2,X1))) = vmul(vd469,vplus(X1,vskolem9(X2,X1)))
    | ~ greater(X2,X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_10]) ).

cnf(c_0_15,plain,
    vplus(vd480,vskolem9(vd481,vd480)) = vd481,
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

fof(c_0_16,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_17,plain,
    greater(vplus(X1,X2),X1),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_18,plain,
    vplus(vmul(vd480,vd469),vmul(vd469,vskolem9(vd481,vd480))) = vmul(vd481,vd469),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_12]),c_0_15]),c_0_10]) ).

cnf(c_0_19,negated_conjecture,
    ~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_20,plain,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM852+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
% 0.13/0.34  % Computer : n022.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 17:21:25 EDT 2023
% 0.19/0.34  % CPUTime  : 
% 0.19/0.54  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
% 0.19/0.60  % Total time : 0.039000 s
% 0.19/0.60  % SZS output end Proof
% 0.19/0.60  % Total time : 0.043000 s
%------------------------------------------------------------------------------