TSTP Solution File: NUM841+2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM841+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 : n017.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 10:40:57 EDT 2023

% Result   : Theorem 0.20s 0.63s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   26
% Syntax   : Number of formulae    :   72 (  41 unt;  11 typ;   0 def)
%            Number of atoms       :   87 (  35 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   59 (  33   ~;  22   |;   1   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (   6   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :   89 (  11 sgn;  44   !;   2   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    vd344: $i ).

tff(decl_23,type,
    vd347: $i ).

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

tff(decl_25,type,
    vd345: $i ).

tff(decl_26,type,
    vd348: $i ).

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

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

tff(decl_29,type,
    vsucc: $i > $i ).

tff(decl_30,type,
    v1: $i ).

tff(decl_31,type,
    vskolem2: $i > $i ).

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

fof('ass(cond(goal(130), 0), 2)',axiom,
    ! [X13,X14] :
      ( ~ greater(X13,X14)
      | ~ less(X13,X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).

fof('ass(cond(140, 0), 0)',axiom,
    ! [X11,X12] :
      ( greater(X11,X12)
     => less(X12,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).

fof('ass(cond(189, 0), 0)',axiom,
    ! [X7,X8] : greater(vplus(X7,X8),X7),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).

fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
    ! [X15,X16] :
      ( greater(X16,X15)
    <=> ? [X17] : X16 = vplus(X15,X17) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).

fof('holds(213, 351, 1)',axiom,
    greater(vplus(vd347,vd345),vplus(vd348,vd345)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(213, 351, 1)') ).

fof('holds(213, 351, 0)',axiom,
    vplus(vd345,vd347) = vplus(vd347,vd345),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(213, 351, 0)') ).

fof('holds(213, 351, 2)',axiom,
    vplus(vd348,vd345) = vplus(vd345,vd348),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(213, 351, 2)') ).

fof('ass(cond(33, 0), 0)',axiom,
    ! [X26,X27,X28] : vplus(vplus(X26,X27),X28) = vplus(X26,vplus(X27,X28)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).

fof('ass(cond(goal(88), 0), 3)',axiom,
    ! [X18,X19] :
      ( X18 != X19
      | ~ ? [X20] : X18 = vplus(X19,X20) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).

fof('holds(conjunct2(211), 349, 0)',axiom,
    greater(vd347,vd348),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct2(211), 349, 0)') ).

fof('ass(cond(61, 0), 0)',axiom,
    ! [X21,X22] : vplus(X22,X21) = vplus(X21,X22),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).

fof('holds(conjunct1(211), 346, 0)',axiom,
    greater(vd344,vd345),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct1(211), 346, 0)') ).

fof('ass(cond(147, 0), 0)',axiom,
    ! [X9,X10] :
      ( less(X9,X10)
     => greater(X10,X9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).

fof('ass(cond(goal(130), 0), 0)',axiom,
    ! [X13,X14] :
      ( X13 = X14
      | greater(X13,X14)
      | less(X13,X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).

fof('holds(214, 352, 0)',conjecture,
    greater(vplus(vd344,vd347),vplus(vd345,vd348)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(214, 352, 0)') ).

fof(c_0_15,plain,
    ! [X13,X14] :
      ( ~ greater(X13,X14)
      | ~ less(X13,X14) ),
    inference(fof_simplification,[status(thm)],['ass(cond(goal(130), 0), 2)']) ).

fof(c_0_16,plain,
    ! [X54,X55] :
      ( ~ greater(X54,X55)
      | less(X55,X54) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(140, 0), 0)'])]) ).

fof(c_0_17,plain,
    ! [X50,X51] : greater(vplus(X50,X51),X50),
    inference(variable_rename,[status(thm)],['ass(cond(189, 0), 0)']) ).

fof(c_0_18,plain,
    ! [X58,X59] :
      ( ~ greater(X58,X59)
      | ~ less(X58,X59) ),
    inference(variable_rename,[status(thm)],[c_0_15]) ).

cnf(c_0_19,plain,
    ( less(X2,X1)
    | ~ greater(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_20,plain,
    greater(vplus(X1,X2),X1),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

fof(c_0_21,plain,
    ! [X60,X61,X63,X64,X65] :
      ( ( ~ greater(X61,X60)
        | X61 = vplus(X60,esk1_2(X60,X61)) )
      & ( X64 != vplus(X63,X65)
        | greater(X64,X63) ) ),
    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_22,plain,
    greater(vplus(vd347,vd345),vplus(vd348,vd345)),
    inference(split_conjunct,[status(thm)],['holds(213, 351, 1)']) ).

cnf(c_0_23,plain,
    vplus(vd345,vd347) = vplus(vd347,vd345),
    inference(split_conjunct,[status(thm)],['holds(213, 351, 0)']) ).

cnf(c_0_24,plain,
    vplus(vd348,vd345) = vplus(vd345,vd348),
    inference(split_conjunct,[status(thm)],['holds(213, 351, 2)']) ).

fof(c_0_25,plain,
    ! [X74,X75,X76] : vplus(vplus(X74,X75),X76) = vplus(X74,vplus(X75,X76)),
    inference(variable_rename,[status(thm)],['ass(cond(33, 0), 0)']) ).

fof(c_0_26,plain,
    ! [X66,X67,X68] :
      ( X66 != X67
      | X66 != vplus(X67,X68) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(goal(88), 0), 3)'])])]) ).

cnf(c_0_27,plain,
    ( ~ greater(X1,X2)
    | ~ less(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_28,plain,
    less(X1,vplus(X1,X2)),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_29,plain,
    ( X1 = vplus(X2,esk1_2(X2,X1))
    | ~ greater(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_30,plain,
    greater(vplus(vd345,vd347),vplus(vd345,vd348)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).

cnf(c_0_31,plain,
    vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_32,plain,
    ( X1 != X2
    | X1 != vplus(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_33,plain,
    greater(vd347,vd348),
    inference(split_conjunct,[status(thm)],['holds(conjunct2(211), 349, 0)']) ).

cnf(c_0_34,plain,
    ~ greater(X1,vplus(X1,X2)),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_35,plain,
    vplus(vd345,vplus(vd348,esk1_2(vplus(vd345,vd348),vplus(vd345,vd347)))) = vplus(vd345,vd347),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).

cnf(c_0_36,plain,
    vplus(X1,X2) != X1,
    inference(er,[status(thm)],[c_0_32]) ).

cnf(c_0_37,plain,
    vplus(vd348,esk1_2(vd348,vd347)) = vd347,
    inference(spm,[status(thm)],[c_0_29,c_0_33]) ).

cnf(c_0_38,plain,
    ~ greater(vplus(X1,X2),vplus(X1,vplus(X2,X3))),
    inference(spm,[status(thm)],[c_0_34,c_0_31]) ).

cnf(c_0_39,plain,
    vplus(vd345,vplus(vd348,vplus(esk1_2(vplus(vd345,vd348),vplus(vd345,vd347)),X1))) = vplus(vd345,vplus(vd347,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_35]),c_0_31]),c_0_31]) ).

fof(c_0_40,plain,
    ! [X69,X70] : vplus(X70,X69) = vplus(X69,X70),
    inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).

cnf(c_0_41,plain,
    greater(vd344,vd345),
    inference(split_conjunct,[status(thm)],['holds(conjunct1(211), 346, 0)']) ).

cnf(c_0_42,plain,
    vplus(X1,vplus(X2,X3)) != vplus(X1,X2),
    inference(spm,[status(thm)],[c_0_36,c_0_31]) ).

cnf(c_0_43,plain,
    vplus(vd348,vplus(esk1_2(vd348,vd347),X1)) = vplus(vd347,X1),
    inference(spm,[status(thm)],[c_0_31,c_0_37]) ).

cnf(c_0_44,plain,
    ~ greater(vplus(vd345,vd348),vplus(vd345,vplus(vd347,X1))),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_45,plain,
    vplus(X1,X2) = vplus(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_46,plain,
    vplus(vd345,esk1_2(vd345,vd344)) = vd344,
    inference(spm,[status(thm)],[c_0_29,c_0_41]) ).

fof(c_0_47,plain,
    ! [X52,X53] :
      ( ~ less(X52,X53)
      | greater(X53,X52) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(147, 0), 0)'])]) ).

fof(c_0_48,plain,
    ! [X56,X57] :
      ( X56 = X57
      | greater(X56,X57)
      | less(X56,X57) ),
    inference(variable_rename,[status(thm)],['ass(cond(goal(130), 0), 0)']) ).

cnf(c_0_49,plain,
    vplus(X1,vplus(vd347,X2)) != vplus(X1,vd348),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_50,plain,
    ~ greater(vplus(vd345,vd348),vplus(vd345,vplus(X1,vd347))),
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_51,plain,
    vplus(vd345,vplus(esk1_2(vd345,vd344),X1)) = vplus(vd344,X1),
    inference(spm,[status(thm)],[c_0_31,c_0_46]) ).

cnf(c_0_52,plain,
    ( greater(X2,X1)
    | ~ less(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

cnf(c_0_53,plain,
    ( X1 = X2
    | greater(X1,X2)
    | less(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

cnf(c_0_54,plain,
    vplus(X1,vplus(X2,vd347)) != vplus(X1,vd348),
    inference(spm,[status(thm)],[c_0_49,c_0_45]) ).

fof(c_0_55,negated_conjecture,
    ~ greater(vplus(vd344,vd347),vplus(vd345,vd348)),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],['holds(214, 352, 0)'])]) ).

cnf(c_0_56,plain,
    ~ greater(vplus(vd345,vd348),vplus(vd344,vd347)),
    inference(spm,[status(thm)],[c_0_50,c_0_51]) ).

cnf(c_0_57,plain,
    ( X1 = X2
    | greater(X1,X2)
    | greater(X2,X1) ),
    inference(spm,[status(thm)],[c_0_52,c_0_53]) ).

cnf(c_0_58,plain,
    vplus(vd345,vd348) != vplus(vd344,vd347),
    inference(spm,[status(thm)],[c_0_54,c_0_51]) ).

cnf(c_0_59,negated_conjecture,
    ~ greater(vplus(vd344,vd347),vplus(vd345,vd348)),
    inference(split_conjunct,[status(thm)],[c_0_55]) ).

cnf(c_0_60,plain,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),c_0_59]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : NUM841+2 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.12  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n017.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Fri Aug 25 15:15:55 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.20/0.54  start to proof: theBenchmark
% 0.20/0.63  % Version  : CSE_E---1.5
% 0.20/0.63  % Problem  : theBenchmark.p
% 0.20/0.63  % Proof found
% 0.20/0.63  % SZS status Theorem for theBenchmark.p
% 0.20/0.63  % SZS output start Proof
% See solution above
% 0.20/0.63  % Total time : 0.077000 s
% 0.20/0.63  % SZS output end Proof
% 0.20/0.63  % Total time : 0.080000 s
%------------------------------------------------------------------------------