%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM558+1 : 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 : n020.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 07:56:23 PM UTC 2025
% Result : Theorem 6.97s 2.55s
% Output : CNFRefutation 6.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 53 ( 26 unt; 0 typ; 4 def)
% Number of atoms : 117 ( 11 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 105 ( 41 ~; 33 |; 17 &)
% ( 7 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 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 : 33 ( 33 usr; 10 con; 0-3 aty)
% Number of variables : 35 ( 35 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > aSubsetOf0 > aElementOf0 > isFinite0 > isCountable0 > aSet0 > aElement0 > slbdtsldtrb0 > sdtpldt0 > sdtmndt0 > #nlpp > szszuzczcdt0 > szmzizndt0 > szmzazxdt0 > slbdtrb0 > sbrdtbr0 > xy > xx > xk > xT > xS > xQ > xP > szNzAzT0 > sz00 > slcrc0 > #skF_7 > #skF_11 > #skF_6 > #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(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(xP,type,
xP: $i ).
tff(xy,type,
xy: $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_548,negated_conjecture,
~ aElementOf0(xx,xT),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(f_526,hypothesis,
( aSet0(xS)
& aSet0(xT)
& ( xk != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).
tff(f_520,hypothesis,
aElementOf0(xk,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202) ).
tff(f_487,definition,
! [W0,W1] :
( ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
=> ! [W2] :
( ( W2 = slbdtsldtrb0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& ( sbrdtbr0(W3) = W1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
tff(f_530,hypothesis,
( aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ( slbdtsldtrb0(xS,xk) != slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2227) ).
tff(f_546,hypothesis,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2378) ).
tff(f_84,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
tff(f_537,hypothesis,
( aSet0(xQ)
& isFinite0(xQ)
& ( sbrdtbr0(xQ) = xk ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2291) ).
tff(f_540,hypothesis,
( aElement0(xy)
& aElementOf0(xy,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2304) ).
tff(f_156,definition,
! [W0,W1] :
( ( aSet0(W0)
& aElement0(W1) )
=> ! [W2] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
tff(f_531,hypothesis,
aElementOf0(xx,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2256) ).
tff(f_39,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
tff(f_545,hypothesis,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2357) ).
tff(f_137,definition,
! [W0,W1] :
( ( aSet0(W0)
& aElement0(W1) )
=> ! [W2] :
( ( W2 = sdtpldt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& ( aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefCons) ).
tff(c_286,plain,
~ aElementOf0(xx,xT),
inference(cnfTransformation,[status(thm)],[f_548]) ).
tff(c_256,plain,
aSet0(xT),
inference(cnfTransformation,[status(thm)],[f_526]) ).
tff(c_252,plain,
aElementOf0(xk,szNzAzT0),
inference(cnfTransformation,[status(thm)],[f_520]) ).
tff(c_228,plain,
! [W0_151,W1_152] :
( aSet0(slbdtsldtrb0(W0_151,W1_152))
| ~ aElementOf0(W1_152,szNzAzT0)
| ~ aSet0(W0_151) ),
inference(cnfTransformation,[status(thm)],[f_487]) ).
tff(c_262,plain,
aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)),
inference(cnfTransformation,[status(thm)],[f_530]) ).
tff(c_284,plain,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(cnfTransformation,[status(thm)],[f_546]) ).
tff(c_1325,plain,
! [W2_270,W0_271,W1_272] :
( aElementOf0(W2_270,W0_271)
| ~ aElementOf0(W2_270,W1_272)
| ~ aSubsetOf0(W1_272,W0_271)
| ~ aSet0(W0_271) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_1609,plain,
! [W0_288] :
( aElementOf0(xP,W0_288)
| ~ aSubsetOf0(slbdtsldtrb0(xS,xk),W0_288)
| ~ aSet0(W0_288) ),
inference(resolution,[status(thm)],[c_284,c_1325]) ).
tff(c_1622,plain,
( aElementOf0(xP,slbdtsldtrb0(xT,xk))
| ~ aSet0(slbdtsldtrb0(xT,xk)) ),
inference(resolution,[status(thm)],[c_262,c_1609]) ).
tff(c_1631,plain,
~ aSet0(slbdtsldtrb0(xT,xk)),
inference(splitLeft,[status(thm)],[c_1622]) ).
tff(c_1634,plain,
( ~ aElementOf0(xk,szNzAzT0)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[c_228,c_1631]) ).
tff(c_1638,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_256,c_252,c_1634]) ).
tff(c_1639,plain,
aElementOf0(xP,slbdtsldtrb0(xT,xk)),
inference(splitRight,[status(thm)],[c_1622]) ).
tff(c_2245,plain,
! [W3_332,W0_333,W1_334] :
( aSubsetOf0(W3_332,W0_333)
| ~ aElementOf0(W3_332,slbdtsldtrb0(W0_333,W1_334))
| ~ aElementOf0(W1_334,szNzAzT0)
| ~ aSet0(W0_333) ),
inference(cnfTransformation,[status(thm)],[f_487]) ).
tff(c_2263,plain,
( aSubsetOf0(xP,xT)
| ~ aElementOf0(xk,szNzAzT0)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[c_1639,c_2245]) ).
tff(c_2290,plain,
aSubsetOf0(xP,xT),
inference(demodulation,[status(thm),theory(equality)],[c_256,c_252,c_2263]) ).
tff(c_272,plain,
aSet0(xQ),
inference(cnfTransformation,[status(thm)],[f_537]) ).
tff(c_276,plain,
aElement0(xy),
inference(cnfTransformation,[status(thm)],[f_540]) ).
tff(c_880,plain,
! [W0_228,W1_229] :
( aSet0(sdtmndt0(W0_228,W1_229))
| ~ aElement0(W1_229)
| ~ aSet0(W0_228) ),
inference(cnfTransformation,[status(thm)],[f_156]) ).
tff(c_258,plain,
aSet0(xS),
inference(cnfTransformation,[status(thm)],[f_526]) ).
tff(c_264,plain,
aElementOf0(xx,xS),
inference(cnfTransformation,[status(thm)],[f_531]) ).
tff(c_421,plain,
! [W1_187,W0_188] :
( aElement0(W1_187)
| ~ aElementOf0(W1_187,W0_188)
| ~ aSet0(W0_188) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_436,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c_264,c_421]) ).
tff(c_453,plain,
aElement0(xx),
inference(demodulation,[status(thm),theory(equality)],[c_258,c_436]) ).
tff(c_282,plain,
sdtpldt0(sdtmndt0(xQ,xy),xx) = xP,
inference(cnfTransformation,[status(thm)],[f_545]) ).
tff(c_869,plain,
! [W0_226,W1_227] :
( aSet0(sdtpldt0(W0_226,W1_227))
| ~ aElement0(W1_227)
| ~ aSet0(W0_226) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_875,plain,
( aSet0(xP)
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(superposition,[status(thm),theory(equality)],[c_282,c_869]) ).
tff(c_878,plain,
( aSet0(xP)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(demodulation,[status(thm),theory(equality)],[c_453,c_875]) ).
tff(c_879,plain,
~ aSet0(sdtmndt0(xQ,xy)),
inference(splitLeft,[status(thm)],[c_878]) ).
tff(c_883,plain,
( ~ aElement0(xy)
| ~ aSet0(xQ) ),
inference(resolution,[status(thm)],[c_880,c_879]) ).
tff(c_890,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_272,c_276,c_883]) ).
tff(c_892,plain,
aSet0(sdtmndt0(xQ,xy)),
inference(splitRight,[status(thm)],[c_878]) ).
tff(c_925,plain,
! [W3_233,W0_234] :
( aElementOf0(W3_233,sdtpldt0(W0_234,W3_233))
| ~ aElement0(W3_233)
| ~ aSet0(W0_234) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_931,plain,
( aElementOf0(xx,xP)
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(superposition,[status(thm),theory(equality)],[c_282,c_925]) ).
tff(c_934,plain,
aElementOf0(xx,xP),
inference(demodulation,[status(thm),theory(equality)],[c_892,c_453,c_931]) ).
tff(c_1359,plain,
! [W0_271] :
( aElementOf0(xx,W0_271)
| ~ aSubsetOf0(xP,W0_271)
| ~ aSet0(W0_271) ),
inference(resolution,[status(thm)],[c_934,c_1325]) ).
tff(c_2382,plain,
( aElementOf0(xx,xT)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[c_2290,c_1359]) ).
tff(c_2394,plain,
aElementOf0(xx,xT),
inference(demodulation,[status(thm),theory(equality)],[c_256,c_2382]) ).
tff(c_2396,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_286,c_2394]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM558+1 : TPTP v9.0.0. Released v4.0.0.
% 0.10/0.12 % 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
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Apr 8 13:34:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 6.97/2.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.97/2.56
% 6.97/2.56 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------