TSTP Solution File: NUM856+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM856+1 : 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 : n008.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 10:41:04 EDT 2023

% Result   : Theorem 0.20s 0.81s
% Output   : CNFRefutation 0.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   32
% Syntax   : Number of formulae    :   89 (  24 unt;  17 typ;   0 def)
%            Number of atoms       :  148 (  38 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  133 (  57   ~;  58   |;  10   &)
%                                         (   2 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   22 (  12   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   5 con; 0-2 aty)
%            Number of variables   :  130 (   2 sgn;  72   !;   2   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    vd517: $i ).

tff(decl_23,type,
    vd519: $i ).

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

tff(decl_25,type,
    vd518: $i ).

tff(decl_26,type,
    vd520: $i ).

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

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

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

tff(decl_30,type,
    vplus: ( $i * $i ) > $i ).

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

tff(decl_32,type,
    v1: $i ).

tff(decl_33,type,
    leq: ( $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('holds(conseq(scope(318)), 525, 0)',conjecture,
    greater(vmul(vd517,vd519),vmul(vd518,vd520)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq(scope(318)), 525, 0)') ).

fof('ass(cond(312, 0), 0)',axiom,
    ! [X1,X2,X3,X4] :
      ( ( greater(X3,X4)
        & greater(X1,X2) )
     => greater(vmul(X1,X3),vmul(X2,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(312, 0), 0)') ).

fof('def(cond(conseq(axiom(3)), 16), 1)',axiom,
    ! [X74,X75] :
      ( geq(X75,X74)
    <=> ( greater(X75,X74)
        | X75 = X74 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 16), 1)') ).

fof('dis(antec(scope(318)))',axiom,
    ( ( greater(vd519,vd520)
      & geq(vd517,vd518) )
    | ( geq(vd519,vd520)
      & greater(vd517,vd518) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dis(antec(scope(318)))') ).

fof('ass(cond(conjunct1(307), 0), 0)',axiom,
    ! [X11,X12,X13] :
      ( greater(vmul(X11,X12),vmul(X13,X12))
     => greater(X11,X13) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conjunct1(307), 0), 0)') ).

fof('ass(cond(goal(88), 0), 1)',axiom,
    ! [X88,X89] :
      ( X88 != X89
      | ~ ? [X91] : X89 = vplus(X88,X91) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).

fof('ass(cond(281, 0), 0)',axiom,
    ! [X24,X25,X26] : vmul(X24,vplus(X25,X26)) = vplus(vmul(X24,X25),vmul(X24,X26)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).

fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
    ! [X85,X86] :
      ( greater(X86,X85)
    <=> ? [X87] : X86 = vplus(X85,X87) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).

fof('ass(cond(299, 0), 2)',axiom,
    ! [X14,X19,X20] :
      ( greater(X19,X20)
     => greater(vmul(X19,X14),vmul(X20,X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(299, 0), 2)') ).

fof('ass(cond(goal(130), 0), 1)',axiom,
    ! [X80,X81] :
      ( X80 != X81
      | ~ less(X80,X81) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).

fof('ass(cond(168, 0), 0)',axiom,
    ! [X65,X66,X67] :
      ( ( less(X66,X67)
        & less(X65,X66) )
     => less(X65,X67) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(168, 0), 0)') ).

fof('ass(cond(140, 0), 0)',axiom,
    ! [X78,X79] :
      ( greater(X78,X79)
     => less(X79,X78) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).

fof('ass(cond(270, 0), 0)',axiom,
    ! [X27,X28] : vmul(X27,X28) = vmul(X28,X27),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).

fof('ass(cond(conjunct2(conjunct2(307)), 0), 0)',axiom,
    ! [X5,X6,X7] :
      ( less(vmul(X5,X6),vmul(X7,X6))
     => less(X5,X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conjunct2(conjunct2(307)), 0), 0)') ).

fof('ass(cond(goal(130), 0), 0)',axiom,
    ! [X80,X81] :
      ( X80 = X81
      | greater(X80,X81)
      | less(X80,X81) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).

fof(c_0_15,negated_conjecture,
    ~ greater(vmul(vd517,vd519),vmul(vd518,vd520)),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],['holds(conseq(scope(318)), 525, 0)'])]) ).

fof(c_0_16,plain,
    ! [X114,X115,X116,X117] :
      ( ~ greater(X116,X117)
      | ~ greater(X114,X115)
      | greater(vmul(X114,X116),vmul(X115,X117)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(312, 0), 0)'])]) ).

fof(c_0_17,plain,
    ! [X201,X202] :
      ( ( ~ geq(X202,X201)
        | greater(X202,X201)
        | X202 = X201 )
      & ( ~ greater(X202,X201)
        | geq(X202,X201) )
      & ( X202 != X201
        | geq(X202,X201) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['def(cond(conseq(axiom(3)), 16), 1)'])])]) ).

fof(c_0_18,plain,
    ( ( geq(vd519,vd520)
      | greater(vd519,vd520) )
    & ( greater(vd517,vd518)
      | greater(vd519,vd520) )
    & ( geq(vd519,vd520)
      | geq(vd517,vd518) )
    & ( greater(vd517,vd518)
      | geq(vd517,vd518) ) ),
    inference(distribute,[status(thm)],['dis(antec(scope(318)))']) ).

cnf(c_0_19,negated_conjecture,
    ~ greater(vmul(vd517,vd519),vmul(vd518,vd520)),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_20,plain,
    ( greater(vmul(X3,X1),vmul(X4,X2))
    | ~ greater(X1,X2)
    | ~ greater(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_21,plain,
    ( greater(X1,X2)
    | X1 = X2
    | ~ geq(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_22,plain,
    ( geq(vd519,vd520)
    | greater(vd519,vd520) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_23,negated_conjecture,
    ( ~ greater(vd517,vd518)
    | ~ greater(vd519,vd520) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_24,plain,
    ( vd520 = vd519
    | greater(vd519,vd520) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

fof(c_0_25,plain,
    ! [X124,X125,X126] :
      ( ~ greater(vmul(X124,X125),vmul(X126,X125))
      | greater(X124,X126) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(conjunct1(307), 0), 0)'])]) ).

fof(c_0_26,plain,
    ! [X231,X232,X233] :
      ( X231 != X232
      | X232 != vplus(X231,X233) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(goal(88), 0), 1)'])])]) ).

fof(c_0_27,plain,
    ! [X139,X140,X141] : vmul(X139,vplus(X140,X141)) = vplus(vmul(X139,X140),vmul(X139,X141)),
    inference(variable_rename,[status(thm)],['ass(cond(281, 0), 0)']) ).

fof(c_0_28,plain,
    ! [X221,X222,X224,X225,X226] :
      ( ( ~ greater(X222,X221)
        | X222 = vplus(X221,esk2_2(X221,X222)) )
      & ( X225 != vplus(X224,X226)
        | greater(X225,X224) ) ),
    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_29,negated_conjecture,
    ( vd520 = vd519
    | ~ greater(vd517,vd518) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_30,plain,
    ( greater(X1,X3)
    | ~ greater(vmul(X1,X2),vmul(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

fof(c_0_31,plain,
    ! [X133,X134,X135] :
      ( ~ greater(X134,X135)
      | greater(vmul(X134,X133),vmul(X135,X133)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(299, 0), 2)'])]) ).

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

cnf(c_0_33,plain,
    vmul(X1,vplus(X2,X3)) = vplus(vmul(X1,X2),vmul(X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_34,plain,
    ( X1 = vplus(X2,esk2_2(X2,X1))
    | ~ greater(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_35,negated_conjecture,
    ~ greater(vmul(vd517,vd519),vmul(vd518,vd519)),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_29]),c_0_30]) ).

cnf(c_0_36,plain,
    ( greater(vmul(X1,X3),vmul(X2,X3))
    | ~ greater(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

fof(c_0_37,plain,
    ! [X80,X81] :
      ( X80 != X81
      | ~ less(X80,X81) ),
    inference(fof_simplification,[status(thm)],['ass(cond(goal(130), 0), 1)']) ).

fof(c_0_38,plain,
    ! [X192,X193,X194] :
      ( ~ less(X193,X194)
      | ~ less(X192,X193)
      | less(X192,X194) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(168, 0), 0)'])]) ).

fof(c_0_39,plain,
    ! [X205,X206] :
      ( ~ greater(X205,X206)
      | less(X206,X205) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(140, 0), 0)'])]) ).

cnf(c_0_40,plain,
    vplus(X1,X2) != X1,
    inference(er,[status(thm)],[c_0_32]) ).

cnf(c_0_41,plain,
    ( vplus(vmul(X1,X2),vmul(X1,esk2_2(X2,X3))) = vmul(X1,X3)
    | ~ greater(X3,X2) ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_42,plain,
    ( greater(vd517,vd518)
    | greater(vd519,vd520) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_43,negated_conjecture,
    ~ greater(vd517,vd518),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

fof(c_0_44,plain,
    ! [X209,X210] :
      ( X209 != X210
      | ~ less(X209,X210) ),
    inference(variable_rename,[status(thm)],[c_0_37]) ).

cnf(c_0_45,plain,
    ( less(X3,X2)
    | ~ less(X1,X2)
    | ~ less(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_46,plain,
    ( less(X2,X1)
    | ~ greater(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_47,plain,
    ( vmul(X1,X2) != vmul(X1,X3)
    | ~ greater(X2,X3) ),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_48,plain,
    greater(vd519,vd520),
    inference(sr,[status(thm)],[c_0_42,c_0_43]) ).

fof(c_0_49,plain,
    ! [X142,X143] : vmul(X142,X143) = vmul(X143,X142),
    inference(variable_rename,[status(thm)],['ass(cond(270, 0), 0)']) ).

cnf(c_0_50,plain,
    ( X1 != X2
    | ~ less(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_51,plain,
    ( less(X1,X2)
    | ~ less(X3,X2)
    | ~ greater(X3,X1) ),
    inference(spm,[status(thm)],[c_0_45,c_0_46]) ).

fof(c_0_52,plain,
    ! [X118,X119,X120] :
      ( ~ less(vmul(X118,X119),vmul(X120,X119))
      | less(X118,X120) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(conjunct2(conjunct2(307)), 0), 0)'])]) ).

fof(c_0_53,plain,
    ! [X207,X208] :
      ( X207 = X208
      | greater(X207,X208)
      | less(X207,X208) ),
    inference(variable_rename,[status(thm)],['ass(cond(goal(130), 0), 0)']) ).

cnf(c_0_54,plain,
    vmul(X1,vd520) != vmul(X1,vd519),
    inference(spm,[status(thm)],[c_0_47,c_0_48]) ).

cnf(c_0_55,plain,
    vmul(X1,X2) = vmul(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

cnf(c_0_56,plain,
    ~ less(X1,X1),
    inference(er,[status(thm)],[c_0_50]) ).

cnf(c_0_57,plain,
    ( less(vd520,X1)
    | ~ less(vd519,X1) ),
    inference(spm,[status(thm)],[c_0_51,c_0_48]) ).

cnf(c_0_58,plain,
    ( less(X1,X3)
    | ~ less(vmul(X1,X2),vmul(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

cnf(c_0_59,plain,
    ( X1 = X2
    | greater(X1,X2)
    | less(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_60,plain,
    vmul(vd520,X1) != vmul(X1,vd519),
    inference(spm,[status(thm)],[c_0_54,c_0_55]) ).

cnf(c_0_61,plain,
    ( greater(vd517,vd518)
    | geq(vd517,vd518) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_62,plain,
    ~ less(vd519,vd520),
    inference(spm,[status(thm)],[c_0_56,c_0_57]) ).

cnf(c_0_63,plain,
    ( vmul(X1,X2) = vmul(X3,X2)
    | less(X1,X3)
    | greater(vmul(X1,X2),vmul(X3,X2)) ),
    inference(spm,[status(thm)],[c_0_58,c_0_59]) ).

cnf(c_0_64,plain,
    vmul(vd520,X1) != vmul(vd519,X1),
    inference(spm,[status(thm)],[c_0_60,c_0_55]) ).

cnf(c_0_65,plain,
    ( vd518 = vd517
    | greater(vd517,vd518) ),
    inference(spm,[status(thm)],[c_0_21,c_0_61]) ).

cnf(c_0_66,plain,
    greater(vmul(vd519,X1),vmul(vd520,X1)),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]) ).

cnf(c_0_67,plain,
    vd518 = vd517,
    inference(sr,[status(thm)],[c_0_65,c_0_43]) ).

cnf(c_0_68,plain,
    greater(vmul(vd519,X1),vmul(X1,vd520)),
    inference(spm,[status(thm)],[c_0_66,c_0_55]) ).

cnf(c_0_69,negated_conjecture,
    ~ greater(vmul(vd517,vd519),vmul(vd517,vd520)),
    inference(spm,[status(thm)],[c_0_19,c_0_67]) ).

cnf(c_0_70,plain,
    greater(vmul(X1,vd519),vmul(X1,vd520)),
    inference(spm,[status(thm)],[c_0_68,c_0_55]) ).

cnf(c_0_71,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : NUM856+1 : 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
% 0.13/0.35  % Computer : n008.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 16:03:17 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.60  start to proof: theBenchmark
% 0.20/0.81  % Version  : CSE_E---1.5
% 0.20/0.81  % Problem  : theBenchmark.p
% 0.20/0.81  % Proof found
% 0.20/0.81  % SZS status Theorem for theBenchmark.p
% 0.20/0.81  % SZS output start Proof
% See solution above
% 0.73/0.82  % Total time : 0.206000 s
% 0.73/0.82  % SZS output end Proof
% 0.73/0.82  % Total time : 0.210000 s
%------------------------------------------------------------------------------