%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM549+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 07:56:21 PM UTC 2025
% Result : Theorem 7.65s 3.02s
% Output : CNFRefutation 8.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 15 unt; 0 typ; 1 def)
% Number of atoms : 65 ( 21 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 51 ( 19 ~; 16 |; 10 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 35 ( 35 usr; 9 con; 0-3 aty)
% Number of variables : 14 ( 12 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > aSubsetOf0 > aElementOf0 > isFinite0 > isCountable0 > aSet0 > aElement0 > slbdtsldtrb0 > sdtpldt0 > sdtmndt0 > #nlpp > szszuzczcdt0 > szmzizndt0 > szmzazxdt0 > slbdtrb0 > sbrdtbr0 > xx > xk > xT > xS > xQ > szNzAzT0 > sz00 > slcrc0 > #skF_7 > #skF_11 > #skF_16 > #skF_18 > #skF_17 > #skF_6 > #skF_19 > #skF_1 > #skF_4 > #skF_12 > #skF_5 > #skF_10 > #skF_8 > #skF_15 > #skF_13 > #skF_14 > #skF_3 > #skF_2 > #skF_9
%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('#skF_16',type,
'#skF_16': $i > $i ).
tff(sbrdtbr0,type,
sbrdtbr0: $i > $i ).
tff(aSet0,type,
aSet0: $i > $o ).
tff(szszuzczcdt0,type,
szszuzczcdt0: $i > $i ).
tff('#skF_18',type,
'#skF_18': $i > $i ).
tff('#skF_17',type,
'#skF_17': $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff('#skF_19',type,
'#skF_19': $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(xS,type,
xS: $i ).
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(slbdtsldtrb0,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(xx,type,
xx: $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(xT,type,
xT: $i ).
tff(aElementOf0,type,
aElementOf0: ( $i * $i ) > $o ).
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(isFinite0,type,
isFinite0: $i > $o ).
tff(xQ,type,
xQ: $i ).
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(szmzizndt0,type,
szmzizndt0: $i > $i ).
tff(szmzazxdt0,type,
szmzazxdt0: $i > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff(slbdtrb0,type,
slbdtrb0: $i > $i ).
tff(f_526,hypothesis,
( aSet0(xS)
& aSet0(xT)
& ( xk != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).
tff(f_52,definition,
! [W0] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1] : aElementOf0(W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
tff(f_330,axiom,
! [W0] :
( aSet0(W0)
=> ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).
tff(f_642,hypothesis,
( aSet0(xQ)
& isFinite0(xQ)
& ( sbrdtbr0(xQ) = xk ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2291) ).
tff(f_647,negated_conjecture,
~ ? [W0] :
( aElement0(W0)
& aElementOf0(W0,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(f_637,hypothesis,
( aSet0(xQ)
& ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) )
& aSubsetOf0(xQ,xS)
& ( sbrdtbr0(xQ) = xk )
& aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2270) ).
tff(f_39,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
tff(c_254,plain,
xk != sz00,
inference(cnfTransformation,[status(thm)],[f_526]) ).
tff(c_14,plain,
aSet0(slcrc0),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_154,plain,
( ( sbrdtbr0(slcrc0) = sz00 )
| ~ aSet0(slcrc0) ),
inference(cnfTransformation,[status(thm)],[f_330]) ).
tff(c_336,plain,
sbrdtbr0(slcrc0) = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_14,c_154]) ).
tff(c_330,plain,
aSet0(xQ),
inference(cnfTransformation,[status(thm)],[f_642]) ).
tff(c_659,plain,
! [W0_222] :
( ( slcrc0 = W0_222 )
| aElementOf0('#skF_1'(W0_222),W0_222)
| ~ aSet0(W0_222) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_332,plain,
! [W0_185] :
( ~ aElementOf0(W0_185,xQ)
| ~ aElement0(W0_185) ),
inference(cnfTransformation,[status(thm)],[f_647]) ).
tff(c_702,plain,
( ~ aElement0('#skF_1'(xQ))
| ( xQ = slcrc0 )
| ~ aSet0(xQ) ),
inference(resolution,[status(thm)],[c_659,c_332]) ).
tff(c_736,plain,
( ~ aElement0('#skF_1'(xQ))
| ( xQ = slcrc0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_330,c_702]) ).
tff(c_737,plain,
~ aElement0('#skF_1'(xQ)),
inference(splitLeft,[status(thm)],[c_736]) ).
tff(c_258,plain,
aSet0(xS),
inference(cnfTransformation,[status(thm)],[f_526]) ).
tff(c_322,plain,
! [W0_184] :
( aElementOf0(W0_184,xS)
| ~ aElementOf0(W0_184,xQ) ),
inference(cnfTransformation,[status(thm)],[f_637]) ).
tff(c_518,plain,
! [W1_207,W0_208] :
( aElement0(W1_207)
| ~ aElementOf0(W1_207,W0_208)
| ~ aSet0(W0_208) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_524,plain,
! [W0_184] :
( aElement0(W0_184)
| ~ aSet0(xS)
| ~ aElementOf0(W0_184,xQ) ),
inference(resolution,[status(thm)],[c_322,c_518]) ).
tff(c_545,plain,
! [W0_184] :
( aElement0(W0_184)
| ~ aElementOf0(W0_184,xQ) ),
inference(demodulation,[status(thm),theory(equality)],[c_258,c_524]) ).
tff(c_675,plain,
( aElement0('#skF_1'(xQ))
| ( xQ = slcrc0 )
| ~ aSet0(xQ) ),
inference(resolution,[status(thm)],[c_659,c_545]) ).
tff(c_715,plain,
( aElement0('#skF_1'(xQ))
| ( xQ = slcrc0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_330,c_675]) ).
tff(c_742,plain,
xQ = slcrc0,
inference(negUnitSimplification,[status(thm)],[c_737,c_715]) ).
tff(c_326,plain,
sbrdtbr0(xQ) = xk,
inference(cnfTransformation,[status(thm)],[f_642]) ).
tff(c_749,plain,
sbrdtbr0(slcrc0) = xk,
inference(demodulation,[status(thm),theory(equality)],[c_742,c_326]) ).
tff(c_754,plain,
xk = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_336,c_749]) ).
tff(c_756,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_254,c_754]) ).
tff(c_757,plain,
xQ = slcrc0,
inference(splitRight,[status(thm)],[c_736]) ).
tff(c_764,plain,
sbrdtbr0(slcrc0) = xk,
inference(demodulation,[status(thm),theory(equality)],[c_757,c_326]) ).
tff(c_769,plain,
xk = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_336,c_764]) ).
tff(c_771,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_254,c_769]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : NUM549+3 : TPTP v9.0.0. Released v4.0.0.
% 0.05/0.11 % 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
% 0.10/0.30 % Computer : n031.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue Apr 8 13:29:07 EDT 2025
% 0.10/0.31 % CPUTime :
% 7.65/3.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.65/3.03
% 7.65/3.03 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------