TSTP Solution File: NUM541+2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM541+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n005.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 : Tue Aug 22 10:52:03 EDT 2023

% Result   : Theorem 10.35s 3.53s
% Output   : CNFRefutation 10.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   45
% Syntax   : Number of formulae    :  120 (  41 unt;  32 typ;   2 def)
%            Number of atoms       :  199 (  24 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  202 (  91   ~;  76   |;  16   &)
%                                         (   3 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   47 (  27   >;  20   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   24 (  24 usr;   5 con; 0-3 aty)
%            Number of variables   :   45 (;  45   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > aSubsetOf0 > aElementOf0 > isFinite0 > isCountable0 > aSet0 > aElement0 > sdtpldt0 > sdtmndt0 > #nlpp > szszuzczcdt0 > szmzizndt0 > szmzazxdt0 > slbdtrb0 > sbrdtbr0 > xn > xm > szNzAzT0 > sz00 > slcrc0 > #skF_7 > #skF_11 > #skF_6 > #skF_1 > #skF_4 > #skF_12 > #skF_5 > #skF_10 > #skF_8 > #skF_3 > #skF_2 > #skF_9

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_7',type,
    '#skF_7': $i > $i ).

tff('#skF_11',type,
    '#skF_11': ( $i * $i ) > $i ).

tff(sbrdtbr0,type,
    sbrdtbr0: $i > $i ).

tff(aSet0,type,
    aSet0: $i > $o ).

tff(szszuzczcdt0,type,
    szszuzczcdt0: $i > $i ).

tff('#skF_6',type,
    '#skF_6': ( $i * $i * $i ) > $i ).

tff(sdtmndt0,type,
    sdtmndt0: ( $i * $i ) > $i ).

tff('#skF_1',type,
    '#skF_1': $i > $i ).

tff(aElement0,type,
    aElement0: $i > $o ).

tff(szNzAzT0,type,
    szNzAzT0: $i ).

tff(sdtlseqdt0,type,
    sdtlseqdt0: ( $i * $i ) > $o ).

tff(sz00,type,
    sz00: $i ).

tff('#skF_4',type,
    '#skF_4': ( $i * $i * $i ) > $i ).

tff('#skF_12',type,
    '#skF_12': ( $i * $i ) > $i ).

tff(sdtpldt0,type,
    sdtpldt0: ( $i * $i ) > $i ).

tff(aSubsetOf0,type,
    aSubsetOf0: ( $i * $i ) > $o ).

tff('#skF_5',type,
    '#skF_5': ( $i * $i * $i ) > $i ).

tff(isCountable0,type,
    isCountable0: $i > $o ).

tff('#skF_10',type,
    '#skF_10': ( $i * $i ) > $i ).

tff('#skF_8',type,
    '#skF_8': ( $i * $i ) > $i ).

tff(aElementOf0,type,
    aElementOf0: ( $i * $i ) > $o ).

tff(slcrc0,type,
    slcrc0: $i ).

tff(isFinite0,type,
    isFinite0: $i > $o ).

tff('#skF_3',type,
    '#skF_3': ( $i * $i * $i ) > $i ).

tff('#skF_2',type,
    '#skF_2': ( $i * $i ) > $i ).

tff(iLess0,type,
    iLess0: ( $i * $i ) > $o ).

tff(xm,type,
    xm: $i ).

tff(szmzizndt0,type,
    szmzizndt0: $i > $i ).

tff(xn,type,
    xn: $i ).

tff(szmzazxdt0,type,
    szmzazxdt0: $i > $i ).

tff('#skF_9',type,
    '#skF_9': ( $i * $i ) > $i ).

tff(slbdtrb0,type,
    slbdtrb0: $i > $i ).

tff(f_463,negated_conjecture,
    ~ ( ( ( sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
          & aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) )
       => ( sdtlseqdt0(szszuzczcdt0(xm),xn)
          | aElementOf0(xm,slbdtrb0(xn))
          | ( xm = xn ) ) )
      & ( ( ( sdtlseqdt0(szszuzczcdt0(xm),xn)
            & aElementOf0(xm,slbdtrb0(xn)) )
          | ( xm = xn ) )
       => ( sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
          | aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

tff(f_443,hypothesis,
    ( aElementOf0(xm,szNzAzT0)
    & aElementOf0(xn,szNzAzT0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1936) ).

tff(f_219,axiom,
    ! [W0] :
      ( aElementOf0(W0,szNzAzT0)
     => ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
        & ( szszuzczcdt0(W0) != sz00 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNum) ).

tff(f_273,axiom,
    ! [W0] :
      ( aElementOf0(W0,szNzAzT0)
     => sdtlseqdt0(W0,W0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessRefl) ).

tff(f_265,axiom,
    ! [W0,W1] :
      ( ( aElementOf0(W0,szNzAzT0)
        & aElementOf0(W1,szNzAzT0) )
     => ( sdtlseqdt0(W0,W1)
      <=> sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(W1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccLess) ).

tff(f_269,axiom,
    ! [W0] :
      ( aElementOf0(W0,szNzAzT0)
     => sdtlseqdt0(W0,szszuzczcdt0(W0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessSucc) ).

tff(f_211,axiom,
    ( aSet0(szNzAzT0)
    & isCountable0(szNzAzT0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).

tff(f_97,axiom,
    ! [W0] :
      ( aSet0(W0)
     => aSubsetOf0(W0,W0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubRefl) ).

tff(f_388,definition,
    ! [W0] :
      ( ( aSubsetOf0(W0,szNzAzT0)
        & ( W0 != slcrc0 ) )
     => ! [W1] :
          ( ( W1 = szmzizndt0(W0) )
        <=> ( aElementOf0(W1,W0)
            & ! [W2] :
                ( aElementOf0(W2,W0)
               => sdtlseqdt0(W1,W2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefMin) ).

tff(f_84,definition,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( aSubsetOf0(W1,W0)
        <=> ( aSet0(W1)
            & ! [W2] :
                ( aElementOf0(W2,W1)
               => aElementOf0(W2,W0) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).

tff(f_283,axiom,
    ! [W0,W1] :
      ( ( aElementOf0(W0,szNzAzT0)
        & aElementOf0(W1,szNzAzT0) )
     => ( ( sdtlseqdt0(W0,W1)
          & sdtlseqdt0(W1,W0) )
       => ( W0 = W1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessASymm) ).

tff(f_295,axiom,
    ! [W0,W1,W2] :
      ( ( aElementOf0(W0,szNzAzT0)
        & aElementOf0(W1,szNzAzT0)
        & aElementOf0(W2,szNzAzT0) )
     => ( ( sdtlseqdt0(W0,W1)
          & sdtlseqdt0(W1,W2) )
       => sdtlseqdt0(W0,W2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessTrans) ).

tff(f_303,axiom,
    ! [W0,W1] :
      ( ( aElementOf0(W0,szNzAzT0)
        & aElementOf0(W1,szNzAzT0) )
     => ( sdtlseqdt0(W0,W1)
        | sdtlseqdt0(szszuzczcdt0(W1),W0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessTotal) ).

tff(c_214,plain,
    ( ( xn != xm )
    | ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) ),
    inference(cnfTransformation,[status(thm)],[f_463]) ).

tff(c_262,plain,
    ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))),
    inference(splitLeft,[status(thm)],[c_214]) ).

tff(c_212,plain,
    aElementOf0(xm,szNzAzT0),
    inference(cnfTransformation,[status(thm)],[f_443]) ).

tff(c_114,plain,
    ! [W0_72] :
      ( aElementOf0(szszuzczcdt0(W0_72),szNzAzT0)
      | ~ aElementOf0(W0_72,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_219]) ).

tff(c_136,plain,
    ! [W0_85] :
      ( sdtlseqdt0(W0_85,W0_85)
      | ~ aElementOf0(W0_85,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_273]) ).

tff(c_210,plain,
    aElementOf0(xn,szNzAzT0),
    inference(cnfTransformation,[status(thm)],[f_443]) ).

tff(c_2642,plain,
    ! [W0_319,W1_320] :
      ( sdtlseqdt0(szszuzczcdt0(W0_319),szszuzczcdt0(W1_320))
      | ~ sdtlseqdt0(W0_319,W1_320)
      | ~ aElementOf0(W1_320,szNzAzT0)
      | ~ aElementOf0(W0_319,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_265]) ).

tff(c_224,plain,
    ( ( xn != xm )
    | ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) ),
    inference(cnfTransformation,[status(thm)],[f_463]) ).

tff(c_287,plain,
    ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)),
    inference(splitLeft,[status(thm)],[c_224]) ).

tff(c_2653,plain,
    ( ~ sdtlseqdt0(xm,xn)
    | ~ aElementOf0(xn,szNzAzT0)
    | ~ aElementOf0(xm,szNzAzT0) ),
    inference(resolution,[status(thm)],[c_2642,c_287]) ).

tff(c_2671,plain,
    ~ sdtlseqdt0(xm,xn),
    inference(demodulation,[status(thm),theory(equality)],[c_212,c_210,c_2653]) ).

tff(c_134,plain,
    ! [W0_84] :
      ( sdtlseqdt0(W0_84,szszuzczcdt0(W0_84))
      | ~ aElementOf0(W0_84,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_269]) ).

tff(c_108,plain,
    aSet0(szNzAzT0),
    inference(cnfTransformation,[status(thm)],[f_211]) ).

tff(c_34,plain,
    ! [W0_27] :
      ( aSubsetOf0(W0_27,W0_27)
      | ~ aSet0(W0_27) ),
    inference(cnfTransformation,[status(thm)],[f_97]) ).

tff(c_465,plain,
    ! [W0_177] :
      ( aElementOf0(szmzizndt0(W0_177),W0_177)
      | ( slcrc0 = W0_177 )
      | ~ aSubsetOf0(W0_177,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_388]) ).

tff(c_112,plain,
    ! [W0_72] :
      ( ( szszuzczcdt0(W0_72) != sz00 )
      | ~ aElementOf0(W0_72,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_219]) ).

tff(c_483,plain,
    ( ( szszuzczcdt0(szmzizndt0(szNzAzT0)) != sz00 )
    | ( szNzAzT0 = slcrc0 )
    | ~ aSubsetOf0(szNzAzT0,szNzAzT0) ),
    inference(resolution,[status(thm)],[c_465,c_112]) ).

tff(c_547,plain,
    ~ aSubsetOf0(szNzAzT0,szNzAzT0),
    inference(splitLeft,[status(thm)],[c_483]) ).

tff(c_550,plain,
    ~ aSet0(szNzAzT0),
    inference(resolution,[status(thm)],[c_34,c_547]) ).

tff(c_554,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_108,c_550]) ).

tff(c_556,plain,
    aSubsetOf0(szNzAzT0,szNzAzT0),
    inference(splitRight,[status(thm)],[c_483]) ).

tff(c_792,plain,
    ! [W2_220,W0_221,W1_222] :
      ( aElementOf0(W2_220,W0_221)
      | ~ aElementOf0(W2_220,W1_222)
      | ~ aSubsetOf0(W1_222,W0_221)
      | ~ aSet0(W0_221) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_822,plain,
    ! [W0_72,W0_221] :
      ( aElementOf0(szszuzczcdt0(W0_72),W0_221)
      | ~ aSubsetOf0(szNzAzT0,W0_221)
      | ~ aSet0(W0_221)
      | ~ aElementOf0(W0_72,szNzAzT0) ),
    inference(resolution,[status(thm)],[c_114,c_792]) ).

tff(c_246,plain,
    ( ~ aElementOf0(xm,slbdtrb0(xn))
    | sdtlseqdt0(szszuzczcdt0(xm),xn)
    | ( xn = xm ) ),
    inference(cnfTransformation,[status(thm)],[f_463]) ).

tff(c_583,plain,
    ~ aElementOf0(xm,slbdtrb0(xn)),
    inference(splitLeft,[status(thm)],[c_246]) ).

tff(c_242,plain,
    ( sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
    | aElementOf0(xm,slbdtrb0(xn))
    | ( xn = xm ) ),
    inference(cnfTransformation,[status(thm)],[f_463]) ).

tff(c_615,plain,
    xn = xm,
    inference(negUnitSimplification,[status(thm)],[c_583,c_287,c_242]) ).

tff(c_620,plain,
    ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xm)),
    inference(demodulation,[status(thm),theory(equality)],[c_615,c_287]) ).

tff(c_633,plain,
    ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0),
    inference(resolution,[status(thm)],[c_136,c_620]) ).

tff(c_638,plain,
    ~ aElementOf0(xm,szNzAzT0),
    inference(resolution,[status(thm)],[c_114,c_633]) ).

tff(c_642,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_212,c_638]) ).

tff(c_643,plain,
    ( ( xn = xm )
    | sdtlseqdt0(szszuzczcdt0(xm),xn) ),
    inference(splitRight,[status(thm)],[c_246]) ).

tff(c_650,plain,
    sdtlseqdt0(szszuzczcdt0(xm),xn),
    inference(splitLeft,[status(thm)],[c_643]) ).

tff(c_1666,plain,
    ! [W1_279,W0_280] :
      ( ( W1_279 = W0_280 )
      | ~ sdtlseqdt0(W1_279,W0_280)
      | ~ sdtlseqdt0(W0_280,W1_279)
      | ~ aElementOf0(W1_279,szNzAzT0)
      | ~ aElementOf0(W0_280,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_283]) ).

tff(c_1686,plain,
    ( ( szszuzczcdt0(xm) = xn )
    | ~ sdtlseqdt0(xn,szszuzczcdt0(xm))
    | ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0)
    | ~ aElementOf0(xn,szNzAzT0) ),
    inference(resolution,[status(thm)],[c_650,c_1666]) ).

tff(c_1713,plain,
    ( ( szszuzczcdt0(xm) = xn )
    | ~ sdtlseqdt0(xn,szszuzczcdt0(xm))
    | ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0) ),
    inference(demodulation,[status(thm),theory(equality)],[c_210,c_1686]) ).

tff(c_1721,plain,
    ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0),
    inference(splitLeft,[status(thm)],[c_1713]) ).

tff(c_1724,plain,
    ( ~ aSubsetOf0(szNzAzT0,szNzAzT0)
    | ~ aSet0(szNzAzT0)
    | ~ aElementOf0(xm,szNzAzT0) ),
    inference(resolution,[status(thm)],[c_822,c_1721]) ).

tff(c_1731,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_212,c_108,c_556,c_1724]) ).

tff(c_1733,plain,
    aElementOf0(szszuzczcdt0(xm),szNzAzT0),
    inference(splitRight,[status(thm)],[c_1713]) ).

tff(c_4795,plain,
    ! [W0_416,W2_417,W1_418] :
      ( sdtlseqdt0(W0_416,W2_417)
      | ~ sdtlseqdt0(W1_418,W2_417)
      | ~ sdtlseqdt0(W0_416,W1_418)
      | ~ aElementOf0(W2_417,szNzAzT0)
      | ~ aElementOf0(W1_418,szNzAzT0)
      | ~ aElementOf0(W0_416,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_295]) ).

tff(c_4823,plain,
    ! [W0_416] :
      ( sdtlseqdt0(W0_416,xn)
      | ~ sdtlseqdt0(W0_416,szszuzczcdt0(xm))
      | ~ aElementOf0(xn,szNzAzT0)
      | ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0)
      | ~ aElementOf0(W0_416,szNzAzT0) ),
    inference(resolution,[status(thm)],[c_650,c_4795]) ).

tff(c_4877,plain,
    ! [W0_419] :
      ( sdtlseqdt0(W0_419,xn)
      | ~ sdtlseqdt0(W0_419,szszuzczcdt0(xm))
      | ~ aElementOf0(W0_419,szNzAzT0) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1733,c_210,c_4823]) ).

tff(c_4901,plain,
    ( sdtlseqdt0(xm,xn)
    | ~ aElementOf0(xm,szNzAzT0) ),
    inference(resolution,[status(thm)],[c_134,c_4877]) ).

tff(c_4926,plain,
    sdtlseqdt0(xm,xn),
    inference(demodulation,[status(thm),theory(equality)],[c_212,c_4901]) ).

tff(c_4928,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2671,c_4926]) ).

tff(c_4929,plain,
    xn = xm,
    inference(splitRight,[status(thm)],[c_643]) ).

tff(c_4934,plain,
    ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xm)),
    inference(demodulation,[status(thm),theory(equality)],[c_4929,c_287]) ).

tff(c_4953,plain,
    ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0),
    inference(resolution,[status(thm)],[c_136,c_4934]) ).

tff(c_4956,plain,
    ~ aElementOf0(xm,szNzAzT0),
    inference(resolution,[status(thm)],[c_114,c_4953]) ).

tff(c_4960,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_212,c_4956]) ).

tff(c_4962,plain,
    sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)),
    inference(splitRight,[status(thm)],[c_224]) ).

tff(c_230,plain,
    ( aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
    | ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) ),
    inference(cnfTransformation,[status(thm)],[f_463]) ).

tff(c_5266,plain,
    aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))),
    inference(demodulation,[status(thm),theory(equality)],[c_4962,c_230]) ).

tff(c_5267,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_262,c_5266]) ).

tff(c_5268,plain,
    xn != xm,
    inference(splitRight,[status(thm)],[c_214]) ).

tff(c_6414,plain,
    ! [W1_592,W0_593] :
      ( sdtlseqdt0(szszuzczcdt0(W1_592),W0_593)
      | sdtlseqdt0(W0_593,W1_592)
      | ~ aElementOf0(W1_592,szNzAzT0)
      | ~ aElementOf0(W0_593,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_303]) ).

tff(c_228,plain,
    ( ~ sdtlseqdt0(szszuzczcdt0(xm),xn)
    | ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) ),
    inference(cnfTransformation,[status(thm)],[f_463]) ).

tff(c_5296,plain,
    ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)),
    inference(splitLeft,[status(thm)],[c_228]) ).

tff(c_5269,plain,
    aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))),
    inference(splitRight,[status(thm)],[c_214]) ).

tff(c_222,plain,
    ( sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
    | ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) ),
    inference(cnfTransformation,[status(thm)],[f_463]) ).

tff(c_5582,plain,
    sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)),
    inference(demodulation,[status(thm),theory(equality)],[c_5269,c_222]) ).

tff(c_5583,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_5296,c_5582]) ).

tff(c_5584,plain,
    ~ sdtlseqdt0(szszuzczcdt0(xm),xn),
    inference(splitRight,[status(thm)],[c_228]) ).

tff(c_6421,plain,
    ( sdtlseqdt0(xn,xm)
    | ~ aElementOf0(xm,szNzAzT0)
    | ~ aElementOf0(xn,szNzAzT0) ),
    inference(resolution,[status(thm)],[c_6414,c_5584]) ).

tff(c_6430,plain,
    sdtlseqdt0(xn,xm),
    inference(demodulation,[status(thm),theory(equality)],[c_210,c_212,c_6421]) ).

tff(c_6970,plain,
    ! [W1_633,W0_634] :
      ( ( W1_633 = W0_634 )
      | ~ sdtlseqdt0(W1_633,W0_634)
      | ~ sdtlseqdt0(W0_634,W1_633)
      | ~ aElementOf0(W1_633,szNzAzT0)
      | ~ aElementOf0(W0_634,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_283]) ).

tff(c_6978,plain,
    ( ( xn = xm )
    | ~ sdtlseqdt0(xm,xn)
    | ~ aElementOf0(xn,szNzAzT0)
    | ~ aElementOf0(xm,szNzAzT0) ),
    inference(resolution,[status(thm)],[c_6430,c_6970]) ).

tff(c_7006,plain,
    ( ( xn = xm )
    | ~ sdtlseqdt0(xm,xn) ),
    inference(demodulation,[status(thm),theory(equality)],[c_212,c_210,c_6978]) ).

tff(c_7007,plain,
    ~ sdtlseqdt0(xm,xn),
    inference(negUnitSimplification,[status(thm)],[c_5268,c_7006]) ).

tff(c_5585,plain,
    sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)),
    inference(splitRight,[status(thm)],[c_228]) ).

tff(c_7143,plain,
    ! [W0_636,W1_637] :
      ( sdtlseqdt0(W0_636,W1_637)
      | ~ sdtlseqdt0(szszuzczcdt0(W0_636),szszuzczcdt0(W1_637))
      | ~ aElementOf0(W1_637,szNzAzT0)
      | ~ aElementOf0(W0_636,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_265]) ).

tff(c_7167,plain,
    ( sdtlseqdt0(xm,xn)
    | ~ aElementOf0(xn,szNzAzT0)
    | ~ aElementOf0(xm,szNzAzT0) ),
    inference(resolution,[status(thm)],[c_5585,c_7143]) ).

tff(c_7178,plain,
    sdtlseqdt0(xm,xn),
    inference(demodulation,[status(thm),theory(equality)],[c_212,c_210,c_7167]) ).

tff(c_7180,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_7007,c_7178]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUM541+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35  % Computer : n005.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
% 0.14/0.36  % DateTime : Thu Aug  3 15:21:26 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 10.35/3.53  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.57/3.54  
% 10.57/3.54  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.65/3.60  
% 10.65/3.60  Inference rules
% 10.65/3.60  ----------------------
% 10.65/3.60  #Ref     : 2
% 10.65/3.60  #Sup     : 1339
% 10.65/3.60  #Fact    : 0
% 10.65/3.60  #Define  : 0
% 10.65/3.60  #Split   : 54
% 10.65/3.60  #Chain   : 0
% 10.65/3.60  #Close   : 0
% 10.65/3.60  
% 10.65/3.60  Ordering : KBO
% 10.65/3.60  
% 10.65/3.60  Simplification rules
% 10.65/3.60  ----------------------
% 10.65/3.60  #Subsume      : 340
% 10.65/3.60  #Demod        : 1122
% 10.65/3.60  #Tautology    : 373
% 10.65/3.60  #SimpNegUnit  : 114
% 10.65/3.60  #BackRed      : 122
% 10.65/3.60  
% 10.65/3.60  #Partial instantiations: 0
% 10.65/3.60  #Strategies tried      : 1
% 10.65/3.60  
% 10.65/3.60  Timing (in seconds)
% 10.65/3.60  ----------------------
% 10.65/3.60  Preprocessing        : 0.73
% 10.65/3.60  Parsing              : 0.36
% 10.65/3.60  CNF conversion       : 0.06
% 10.65/3.60  Main loop            : 1.69
% 10.65/3.60  Inferencing          : 0.62
% 10.65/3.60  Reduction            : 0.50
% 10.65/3.60  Demodulation         : 0.33
% 10.65/3.60  BG Simplification    : 0.07
% 10.65/3.60  Subsumption          : 0.38
% 10.65/3.60  Abstraction          : 0.06
% 10.65/3.60  MUC search           : 0.00
% 10.65/3.61  Cooper               : 0.00
% 10.65/3.61  Total                : 2.50
% 10.65/3.61  Index Insertion      : 0.00
% 10.65/3.61  Index Deletion       : 0.00
% 10.65/3.61  Index Matching       : 0.00
% 10.65/3.61  BG Taut test         : 0.00
%------------------------------------------------------------------------------