%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM571+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n031.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 : Wed Apr 9 07:56:26 PM UTC 2025
% Result : Theorem 69.09s 55.49s
% Output : CNFRefutation 69.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 63 ( 14 equ)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 51 ( 11 ~; 6 |; 24 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 63 ( 63 usr; 12 con; 0-4 aty)
% Number of variables : 9 ( 8 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > aSubsetOf0 > aElementOf0 > isFinite0 > isCountable0 > aSet0 > aFunction0 > aElement0 > slbdtsldtrb0 > sdtpldt0 > sdtmndt0 > sdtlpdtrp0 > sdtlcdtrc0 > sdtlbdtrb0 > sdtexdt0 > #nlpp > szszuzczcdt0 > szmzizndt0 > szmzazxdt0 > szDzozmdt0 > szDzizrdt0 > slbdtrb0 > sbrdtbr0 > xk > xi > xc > xT > xS > xN > xK > szNzAzT0 > sz00 > slcrc0 > #skF_7 > #skF_11 > #skF_17 > #skF_31 > #skF_33 > #skF_6 > #skF_1 > #skF_18 > #skF_38 > #skF_37 > #skF_4 > #skF_29 > #skF_12 > #skF_30 > #skF_32 > #skF_23 > #skF_39 > #skF_35 > #skF_5 > #skF_19 > #skF_10 > #skF_8 > #skF_20 > #skF_28 > #skF_26 > #skF_24 > #skF_34 > #skF_15 > #skF_13 > #skF_14 > #skF_25 > #skF_3 > #skF_2 > #skF_27 > #skF_36 > #skF_21 > #skF_9 > #skF_22 > #skF_16
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(xk,type,
xk: $i ).
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff('#skF_11',type,
'#skF_11': ( $i * $i ) > $i ).
tff(sbrdtbr0,type,
sbrdtbr0: $i > $i ).
tff('#skF_17',type,
'#skF_17': ( $i * $i * $i ) > $i ).
tff('#skF_31',type,
'#skF_31': ( $i * $i * $i ) > $i ).
tff('#skF_33',type,
'#skF_33': ( $i * $i * $i ) > $i ).
tff(aSet0,type,
aSet0: $i > $o ).
tff(szszuzczcdt0,type,
szszuzczcdt0: $i > $i ).
tff(sdtlbdtrb0,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(szDzozmdt0,type,
szDzozmdt0: $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('#skF_18',type,
'#skF_18': ( $i * $i * $i ) > $i ).
tff(aElement0,type,
aElement0: $i > $o ).
tff(sdtexdt0,type,
sdtexdt0: ( $i * $i ) > $i ).
tff('#skF_38',type,
'#skF_38': $i ).
tff('#skF_37',type,
'#skF_37': $i > $i ).
tff(xi,type,
xi: $i ).
tff(szNzAzT0,type,
szNzAzT0: $i ).
tff(sdtlseqdt0,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(xS,type,
xS: $i ).
tff(sz00,type,
sz00: $i ).
tff(sdtlpdtrp0,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff(xc,type,
xc: $i ).
tff('#skF_29',type,
'#skF_29': ( $i * $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i ) > $i ).
tff(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff('#skF_30',type,
'#skF_30': ( $i * $i * $i ) > $i ).
tff(slbdtsldtrb0,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff('#skF_32',type,
'#skF_32': ( $i * $i * $i * $i ) > $i ).
tff('#skF_23',type,
'#skF_23': ( $i * $i * $i ) > $i ).
tff('#skF_39',type,
'#skF_39': $i ).
tff('#skF_35',type,
'#skF_35': ( $i * $i * $i ) > $i ).
tff(aSubsetOf0,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff('#skF_19',type,
'#skF_19': ( $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(xT,type,
xT: $i ).
tff(xN,type,
xN: $i ).
tff(aElementOf0,type,
aElementOf0: ( $i * $i ) > $o ).
tff('#skF_20',type,
'#skF_20': ( $i * $i * $i ) > $i ).
tff(szDzizrdt0,type,
szDzizrdt0: $i > $i ).
tff('#skF_28',type,
'#skF_28': ( $i * $i ) > $i ).
tff('#skF_26',type,
'#skF_26': $i > $i ).
tff('#skF_24',type,
'#skF_24': ( $i * $i ) > $i ).
tff('#skF_34',type,
'#skF_34': ( $i * $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': ( $i * $i * $i ) > $i ).
tff('#skF_13',type,
'#skF_13': $i > $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i * $i ) > $i ).
tff(slcrc0,type,
slcrc0: $i ).
tff(aFunction0,type,
aFunction0: $i > $o ).
tff(isFinite0,type,
isFinite0: $i > $o ).
tff('#skF_25',type,
'#skF_25': ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff(sdtlcdtrc0,type,
sdtlcdtrc0: ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(iLess0,type,
iLess0: ( $i * $i ) > $o ).
tff('#skF_27',type,
'#skF_27': $i > $i ).
tff(szmzizndt0,type,
szmzizndt0: $i > $i ).
tff('#skF_36',type,
'#skF_36': ( $i * $i * $i * $i ) > $i ).
tff(szmzazxdt0,type,
szmzazxdt0: $i > $i ).
tff('#skF_21',type,
'#skF_21': ( $i * $i * $i ) > $i ).
tff(xK,type,
xK: $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff(slbdtrb0,type,
slbdtrb0: $i > $i ).
tff('#skF_22',type,
'#skF_22': ( $i * $i * $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': ( $i * $i * $i ) > $i ).
tff(f_674,hypothesis,
( aSet0(xS)
& ! [W0] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
tff(f_873,hypothesis,
( aFunction0(xN)
& ( szDzozmdt0(xN) = szNzAzT0 )
& ( sdtlpdtrp0(xN,sz00) = xS )
& ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( ( ( ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,W0)) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W1] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W1)
& aElementOf0(W1,sdtlpdtrp0(xN,W0))
& ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3623) ).
tff(f_907,hypothesis,
( ( xi != sz00 )
=> ( ? [W0] :
( aElementOf0(W0,szNzAzT0)
& ( szszuzczcdt0(W0) = xi ) )
& aSet0(sdtlpdtrp0(xN,xi))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> aElementOf0(W0,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,xi)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3702_02) ).
tff(f_918,negated_conjecture,
~ ( ( ( aSet0(sdtlpdtrp0(xN,xi))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> aElementOf0(W0,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,xi)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(c_340,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnfTransformation,[status(thm)],[f_674]) ).
tff(c_8322,plain,
sdtlpdtrp0(xN,sz00) = xS,
inference(cnfTransformation,[status(thm)],[f_873]) ).
tff(c_8412,plain,
( ( szszuzczcdt0('#skF_38') = xi )
| ( xi = sz00 ) ),
inference(cnfTransformation,[status(thm)],[f_907]) ).
tff(c_8581,plain,
xi = sz00,
inference(splitLeft,[status(thm)],[c_8412]) ).
tff(c_338,plain,
isCountable0(xS),
inference(cnfTransformation,[status(thm)],[f_674]) ).
tff(c_8448,plain,
xi = sz00,
inference(splitLeft,[status(thm)],[c_8412]) ).
tff(c_8416,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,xi)) ),
inference(cnfTransformation,[status(thm)],[f_918]) ).
tff(c_8425,plain,
~ isCountable0(sdtlpdtrp0(xN,xi)),
inference(splitLeft,[status(thm)],[c_8416]) ).
tff(c_8449,plain,
~ isCountable0(sdtlpdtrp0(xN,sz00)),
inference(demodulation,[status(thm),theory(equality)],[c_8448,c_8425]) ).
tff(c_8453,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_338,c_8322,c_8449]) ).
tff(c_8455,plain,
xi != sz00,
inference(splitRight,[status(thm)],[c_8412]) ).
tff(c_8404,plain,
( isCountable0(sdtlpdtrp0(xN,xi))
| ( xi = sz00 ) ),
inference(cnfTransformation,[status(thm)],[f_907]) ).
tff(c_8507,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8455,c_8425,c_8404]) ).
tff(c_8508,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0),
inference(splitRight,[status(thm)],[c_8416]) ).
tff(c_8582,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,sz00),szNzAzT0),
inference(demodulation,[status(thm),theory(equality)],[c_8581,c_8508]) ).
tff(c_8587,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_340,c_8322,c_8582]) ).
tff(c_8589,plain,
xi != sz00,
inference(splitRight,[status(thm)],[c_8412]) ).
tff(c_8406,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
| ( xi = sz00 ) ),
inference(cnfTransformation,[status(thm)],[f_907]) ).
tff(c_8859,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8589,c_8508,c_8406]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM571+3 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35 % Computer : n031.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
% 0.14/0.35 % DateTime : Tue Apr 8 13:40:37 EDT 2025
% 0.14/0.36 % CPUTime :
% 69.09/55.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 69.09/55.50
% 69.09/55.50 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------