%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM545+2 : 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/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 : Wed Apr 9 07:56:20 PM UTC 2025
% Result : Theorem 5.33s 2.16s
% Output : CNFRefutation 5.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 23 unt; 0 typ; 1 def)
% Number of atoms : 88 ( 22 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 70 ( 25 ~; 18 |; 15 &)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 4 con; 0-3 aty)
% Number of variables : 22 ( 19 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > aSubsetOf0 > aElementOf0 > isFinite0 > isCountable0 > aSet0 > aElement0 > sdtpldt0 > sdtmndt0 > #nlpp > szszuzczcdt0 > szmzizndt0 > szmzazxdt0 > slbdtrb0 > sbrdtbr0 > xS > szNzAzT0 > sz00 > slcrc0 > #skF_7 > #skF_11 > #skF_6 > #skF_1 > #skF_4 > #skF_12 > #skF_5 > #skF_10 > #skF_8 > #skF_13 > #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(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(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('#skF_13',type,
'#skF_13': $i > $i ).
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(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_52,definition,
! [W0] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1] : aElementOf0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
tff(f_497,hypothesis,
( ~ ( ~ ? [W0] : aElementOf0(W0,xS)
& ( xS = slcrc0 ) )
=> ( aElementOf0(szmzazxdt0(xS),xS)
& ! [W0] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(W0,szmzazxdt0(xS)) )
& aSet0(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& ! [W0] :
( aElementOf0(W0,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
<=> ( aElementOf0(W0,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(szmzazxdt0(xS))) ) )
& ! [W0] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) )
& aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2035) ).
tff(f_468,hypothesis,
( aSet0(xS)
& ! [W0] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& isFinite0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1986) ).
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_330,axiom,
! [W0] :
( aSet0(W0)
=> ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardEmpty) ).
tff(f_516,negated_conjecture,
~ ? [W0] :
( aElementOf0(W0,szNzAzT0)
& ( ( aSet0(slbdtrb0(W0))
& ! [W1] :
( aElementOf0(W1,slbdtrb0(W0))
<=> ( aElementOf0(W1,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(W1),W0) ) ) )
=> ( ! [W1] :
( aElementOf0(W1,xS)
=> aElementOf0(W1,slbdtrb0(W0)) )
| aSubsetOf0(xS,slbdtrb0(W0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(f_212,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).
tff(c_12,plain,
! [W1_10] : ~ aElementOf0(W1_10,slcrc0),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_256,plain,
( ( xS = slcrc0 )
| aElementOf0(szmzazxdt0(xS),xS) ),
inference(cnfTransformation,[status(thm)],[f_497]) ).
tff(c_333,plain,
aElementOf0(szmzazxdt0(xS),xS),
inference(splitLeft,[status(thm)],[c_256]) ).
tff(c_335,plain,
! [W0_168] :
( aElementOf0(W0_168,szNzAzT0)
| ~ aElementOf0(W0_168,xS) ),
inference(cnfTransformation,[status(thm)],[f_468]) ).
tff(c_342,plain,
aElementOf0(szmzazxdt0(xS),szNzAzT0),
inference(resolution,[status(thm)],[c_333,c_335]) ).
tff(c_114,plain,
! [W0_72] :
( aElementOf0(szszuzczcdt0(W0_72),szNzAzT0)
| ~ aElementOf0(W0_72,szNzAzT0) ),
inference(cnfTransformation,[status(thm)],[f_219]) ).
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_276,plain,
sbrdtbr0(slcrc0) = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_14,c_154]) ).
tff(c_226,plain,
aSet0(xS),
inference(cnfTransformation,[status(thm)],[f_468]) ).
tff(c_481,plain,
! [W0_188] :
( ( slcrc0 = W0_188 )
| aElementOf0('#skF_1'(W0_188),W0_188)
| ~ aSet0(W0_188) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_224,plain,
! [W0_148] :
( aElementOf0(W0_148,szNzAzT0)
| ~ aElementOf0(W0_148,xS) ),
inference(cnfTransformation,[status(thm)],[f_468]) ).
tff(c_492,plain,
( aElementOf0('#skF_1'(xS),szNzAzT0)
| ( xS = slcrc0 )
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c_481,c_224]) ).
tff(c_509,plain,
( aElementOf0('#skF_1'(xS),szNzAzT0)
| ( xS = slcrc0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_226,c_492]) ).
tff(c_520,plain,
xS = slcrc0,
inference(splitLeft,[status(thm)],[c_509]) ).
tff(c_372,plain,
! [W0_175] :
( ( slcrc0 = W0_175 )
| ( sbrdtbr0(W0_175) != sz00 )
| ~ aSet0(W0_175) ),
inference(cnfTransformation,[status(thm)],[f_330]) ).
tff(c_391,plain,
( ( xS = slcrc0 )
| ( sbrdtbr0(xS) != sz00 ) ),
inference(resolution,[status(thm)],[c_226,c_372]) ).
tff(c_399,plain,
sbrdtbr0(xS) != sz00,
inference(splitLeft,[status(thm)],[c_391]) ).
tff(c_531,plain,
sbrdtbr0(slcrc0) != sz00,
inference(demodulation,[status(thm),theory(equality)],[c_520,c_399]) ).
tff(c_546,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_276,c_531]) ).
tff(c_548,plain,
xS != slcrc0,
inference(splitRight,[status(thm)],[c_509]) ).
tff(c_228,plain,
( ( xS = slcrc0 )
| aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ),
inference(cnfTransformation,[status(thm)],[f_497]) ).
tff(c_579,plain,
aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))),
inference(negUnitSimplification,[status(thm)],[c_548,c_228]) ).
tff(c_260,plain,
! [W0_153] :
( ~ aSubsetOf0(xS,slbdtrb0(W0_153))
| ~ aElementOf0(W0_153,szNzAzT0) ),
inference(cnfTransformation,[status(thm)],[f_516]) ).
tff(c_589,plain,
~ aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0),
inference(resolution,[status(thm)],[c_579,c_260]) ).
tff(c_592,plain,
~ aElementOf0(szmzazxdt0(xS),szNzAzT0),
inference(resolution,[status(thm)],[c_114,c_589]) ).
tff(c_596,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_342,c_592]) ).
tff(c_597,plain,
xS = slcrc0,
inference(splitRight,[status(thm)],[c_391]) ).
tff(c_606,plain,
aElementOf0(szmzazxdt0(slcrc0),slcrc0),
inference(demodulation,[status(thm),theory(equality)],[c_597,c_597,c_333]) ).
tff(c_613,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12,c_606]) ).
tff(c_614,plain,
xS = slcrc0,
inference(splitRight,[status(thm)],[c_256]) ).
tff(c_264,plain,
! [W0_153] :
( aElementOf0('#skF_13'(W0_153),xS)
| ~ aElementOf0(W0_153,szNzAzT0) ),
inference(cnfTransformation,[status(thm)],[f_516]) ).
tff(c_617,plain,
! [W0_153] :
( aElementOf0('#skF_13'(W0_153),slcrc0)
| ~ aElementOf0(W0_153,szNzAzT0) ),
inference(demodulation,[status(thm),theory(equality)],[c_614,c_264]) ).
tff(c_621,plain,
! [W0_153] : ~ aElementOf0(W0_153,szNzAzT0),
inference(negUnitSimplification,[status(thm)],[c_12,c_617]) ).
tff(c_110,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_629,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_621,c_110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : NUM545+2 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.14 % 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
% 0.12/0.35 % Computer : n005.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Tue Apr 8 13:27:42 EDT 2025
% 0.12/0.35 % CPUTime :
% 5.33/2.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.33/2.16
% 5.33/2.16 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------