%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM612+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 : n011.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 07:56:36 PM UTC 2025
% Result : Theorem 12.81s 4.06s
% Output : CNFRefutation 12.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 16
% Syntax : Number of formulae : 70 ( 36 unt; 0 typ; 2 def)
% Number of atoms : 142 ( 25 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 131 ( 59 ~; 49 |; 11 &)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 61 ( 61 usr; 16 con; 0-4 aty)
% Number of variables : 33 ( 33 !; 0 ?; 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 > xp > xk > xe > xd > xc > xT > xS > xQ > xP > xO > xN > xK > xC > szNzAzT0 > sz00 > slcrc0 > #skF_26 > #skF_7 > #skF_11 > #skF_17 > #skF_6 > #skF_27 > #skF_1 > #skF_31 > #skF_18 > #skF_4 > #skF_29 > #skF_12 > #skF_23 > #skF_28 > #skF_5 > #skF_19 > #skF_10 > #skF_8 > #skF_20 > #skF_24 > #skF_15 > #skF_13 > #skF_14 > #skF_25 > #skF_3 > #skF_2 > #skF_21 > #skF_9 > #skF_22 > #skF_30 > #skF_16
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(xk,type,
xk: $i ).
tff('#skF_26',type,
'#skF_26': ( $i * $i * $i ) > $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(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(xd,type,
xd: $i ).
tff('#skF_27',type,
'#skF_27': ( $i * $i * $i ) > $i ).
tff(sdtmndt0,type,
sdtmndt0: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff('#skF_31',type,
'#skF_31': $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(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(xe,type,
xe: $i ).
tff(xP,type,
xP: $i ).
tff('#skF_29',type,
'#skF_29': $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('#skF_23',type,
'#skF_23': ( $i * $i * $i ) > $i ).
tff('#skF_28',type,
'#skF_28': $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(xC,type,
xC: $i ).
tff('#skF_20',type,
'#skF_20': ( $i * $i * $i ) > $i ).
tff(szDzizrdt0,type,
szDzizrdt0: $i > $i ).
tff('#skF_24',type,
'#skF_24': ( $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': ( $i * $i * $i ) > $i ).
tff('#skF_13',type,
'#skF_13': $i > $i ).
tff(xO,type,
xO: $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(xQ,type,
xQ: $i ).
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(xp,type,
xp: $i ).
tff(iLess0,type,
iLess0: ( $i * $i ) > $o ).
tff(szmzizndt0,type,
szmzizndt0: $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_30',type,
'#skF_30': $i > $i ).
tff('#skF_16',type,
'#skF_16': ( $i * $i * $i ) > $i ).
tff(f_873,hypothesis,
( aSet0(xP)
& ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5164) ).
tff(f_324,axiom,
! [W0] :
( aSet0(W0)
=> ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardNum) ).
tff(f_852,hypothesis,
( aSet0(xO)
& isCountable0(xO) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4908) ).
tff(f_664,hypothesis,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).
tff(f_863,hypothesis,
aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5078) ).
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_881,negated_conjecture,
~ ( ( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) )
& aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(f_211,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
tff(f_868,hypothesis,
aSubsetOf0(xQ,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5106) ).
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_876,hypothesis,
aSubsetOf0(xP,xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5195) ).
tff(f_93,axiom,
! [W0] :
( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1] :
( aSubsetOf0(W1,W0)
=> isFinite0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubFSet) ).
tff(f_874,hypothesis,
aElementOf0(xp,xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5173) ).
tff(f_870,hypothesis,
xp = szmzizndt0(xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5147) ).
tff(f_351,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( ( isFinite0(W0)
& aElementOf0(W1,W0) )
=> ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardDiff) ).
tff(f_867,hypothesis,
( aSubsetOf0(xQ,xO)
& ( xQ != slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5093) ).
tff(c_458,plain,
aSet0(xP),
inference(cnfTransformation,[status(thm)],[f_873]) ).
tff(c_6215,plain,
! [W0_801] :
( aElementOf0(sbrdtbr0(W0_801),szNzAzT0)
| ~ isFinite0(W0_801)
| ~ aSet0(W0_801) ),
inference(cnfTransformation,[status(thm)],[f_324]) ).
tff(c_434,plain,
aSet0(xO),
inference(cnfTransformation,[status(thm)],[f_852]) ).
tff(c_336,plain,
aElementOf0(xK,szNzAzT0),
inference(cnfTransformation,[status(thm)],[f_664]) ).
tff(c_444,plain,
aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
inference(cnfTransformation,[status(thm)],[f_863]) ).
tff(c_5591,plain,
! [W3_759,W1_760,W0_761] :
( ( sbrdtbr0(W3_759) = W1_760 )
| ~ aElementOf0(W3_759,slbdtsldtrb0(W0_761,W1_760))
| ~ aElementOf0(W1_760,szNzAzT0)
| ~ aSet0(W0_761) ),
inference(cnfTransformation,[status(thm)],[f_487]) ).
tff(c_5614,plain,
( ( sbrdtbr0(xQ) = xK )
| ~ aElementOf0(xK,szNzAzT0)
| ~ aSet0(xO) ),
inference(resolution,[status(thm)],[c_444,c_5591]) ).
tff(c_5625,plain,
sbrdtbr0(xQ) = xK,
inference(demodulation,[status(thm),theory(equality)],[c_434,c_336,c_5614]) ).
tff(c_468,plain,
( ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| ( szszuzczcdt0(sbrdtbr0(xP)) != sbrdtbr0(xQ) ) ),
inference(cnfTransformation,[status(thm)],[f_881]) ).
tff(c_477,plain,
szszuzczcdt0(sbrdtbr0(xP)) != sbrdtbr0(xQ),
inference(splitLeft,[status(thm)],[c_468]) ).
tff(c_5629,plain,
szszuzczcdt0(sbrdtbr0(xP)) != xK,
inference(demodulation,[status(thm),theory(equality)],[c_5625,c_477]) ).
tff(c_108,plain,
aSet0(szNzAzT0),
inference(cnfTransformation,[status(thm)],[f_211]) ).
tff(c_450,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(cnfTransformation,[status(thm)],[f_868]) ).
tff(c_631,plain,
! [W1_440,W0_441] :
( aSet0(W1_440)
| ~ aSubsetOf0(W1_440,W0_441)
| ~ aSet0(W0_441) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_643,plain,
( aSet0(xQ)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[status(thm)],[c_450,c_631]) ).
tff(c_668,plain,
aSet0(xQ),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_643]) ).
tff(c_464,plain,
aSubsetOf0(xP,xQ),
inference(cnfTransformation,[status(thm)],[f_876]) ).
tff(c_1345,plain,
! [W1_492,W0_493] :
( isFinite0(W1_492)
| ~ aSubsetOf0(W1_492,W0_493)
| ~ isFinite0(W0_493)
| ~ aSet0(W0_493) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_1369,plain,
( isFinite0(xP)
| ~ isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(resolution,[status(thm)],[c_464,c_1345]) ).
tff(c_1400,plain,
( isFinite0(xP)
| ~ isFinite0(xQ) ),
inference(demodulation,[status(thm),theory(equality)],[c_668,c_1369]) ).
tff(c_1423,plain,
~ isFinite0(xQ),
inference(splitLeft,[status(thm)],[c_1400]) ).
tff(c_3372,plain,
! [W3_617,W1_618,W0_619] :
( ( sbrdtbr0(W3_617) = W1_618 )
| ~ aElementOf0(W3_617,slbdtsldtrb0(W0_619,W1_618))
| ~ aElementOf0(W1_618,szNzAzT0)
| ~ aSet0(W0_619) ),
inference(cnfTransformation,[status(thm)],[f_487]) ).
tff(c_3395,plain,
( ( sbrdtbr0(xQ) = xK )
| ~ aElementOf0(xK,szNzAzT0)
| ~ aSet0(xO) ),
inference(resolution,[status(thm)],[c_444,c_3372]) ).
tff(c_3406,plain,
sbrdtbr0(xQ) = xK,
inference(demodulation,[status(thm),theory(equality)],[c_434,c_336,c_3395]) ).
tff(c_152,plain,
! [W0_97] :
( isFinite0(W0_97)
| ~ aElementOf0(sbrdtbr0(W0_97),szNzAzT0)
| ~ aSet0(W0_97) ),
inference(cnfTransformation,[status(thm)],[f_324]) ).
tff(c_3429,plain,
( isFinite0(xQ)
| ~ aElementOf0(xK,szNzAzT0)
| ~ aSet0(xQ) ),
inference(superposition,[status(thm),theory(equality)],[c_3406,c_152]) ).
tff(c_3446,plain,
isFinite0(xQ),
inference(demodulation,[status(thm),theory(equality)],[c_668,c_336,c_3429]) ).
tff(c_3448,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1423,c_3446]) ).
tff(c_3450,plain,
isFinite0(xQ),
inference(splitRight,[status(thm)],[c_1400]) ).
tff(c_460,plain,
aElementOf0(xp,xQ),
inference(cnfTransformation,[status(thm)],[f_874]) ).
tff(c_454,plain,
szmzizndt0(xQ) = xp,
inference(cnfTransformation,[status(thm)],[f_870]) ).
tff(c_456,plain,
sdtmndt0(xQ,szmzizndt0(xQ)) = xP,
inference(cnfTransformation,[status(thm)],[f_873]) ).
tff(c_469,plain,
sdtmndt0(xQ,xp) = xP,
inference(demodulation,[status(thm),theory(equality)],[c_454,c_456]) ).
tff(c_5671,plain,
! [W0_762,W1_763] :
( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0_762,W1_763))) = sbrdtbr0(W0_762) )
| ~ aElementOf0(W1_763,W0_762)
| ~ isFinite0(W0_762)
| ~ aSet0(W0_762) ),
inference(cnfTransformation,[status(thm)],[f_351]) ).
tff(c_5723,plain,
( ( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) )
| ~ aElementOf0(xp,xQ)
| ~ isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(superposition,[status(thm),theory(equality)],[c_469,c_5671]) ).
tff(c_5727,plain,
szszuzczcdt0(sbrdtbr0(xP)) = xK,
inference(demodulation,[status(thm),theory(equality)],[c_668,c_3450,c_460,c_5625,c_5723]) ).
tff(c_5729,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_5629,c_5727]) ).
tff(c_5730,plain,
~ aElementOf0(sbrdtbr0(xP),szNzAzT0),
inference(splitRight,[status(thm)],[c_468]) ).
tff(c_6230,plain,
( ~ isFinite0(xP)
| ~ aSet0(xP) ),
inference(resolution,[status(thm)],[c_6215,c_5730]) ).
tff(c_6245,plain,
~ isFinite0(xP),
inference(demodulation,[status(thm),theory(equality)],[c_458,c_6230]) ).
tff(c_448,plain,
aSubsetOf0(xQ,xO),
inference(cnfTransformation,[status(thm)],[f_867]) ).
tff(c_5922,plain,
! [W1_781,W0_782] :
( aSet0(W1_781)
| ~ aSubsetOf0(W1_781,W0_782)
| ~ aSet0(W0_782) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_5940,plain,
( aSet0(xQ)
| ~ aSet0(xO) ),
inference(resolution,[status(thm)],[c_448,c_5922]) ).
tff(c_5964,plain,
aSet0(xQ),
inference(demodulation,[status(thm),theory(equality)],[c_434,c_5940]) ).
tff(c_6521,plain,
! [W1_820,W0_821] :
( isFinite0(W1_820)
| ~ aSubsetOf0(W1_820,W0_821)
| ~ isFinite0(W0_821)
| ~ aSet0(W0_821) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_6539,plain,
( isFinite0(xP)
| ~ isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(resolution,[status(thm)],[c_464,c_6521]) ).
tff(c_6568,plain,
( isFinite0(xP)
| ~ isFinite0(xQ) ),
inference(demodulation,[status(thm),theory(equality)],[c_5964,c_6539]) ).
tff(c_6569,plain,
~ isFinite0(xQ),
inference(negUnitSimplification,[status(thm)],[c_6245,c_6568]) ).
tff(c_8422,plain,
! [W3_942,W1_943,W0_944] :
( ( sbrdtbr0(W3_942) = W1_943 )
| ~ aElementOf0(W3_942,slbdtsldtrb0(W0_944,W1_943))
| ~ aElementOf0(W1_943,szNzAzT0)
| ~ aSet0(W0_944) ),
inference(cnfTransformation,[status(thm)],[f_487]) ).
tff(c_8441,plain,
( ( sbrdtbr0(xQ) = xK )
| ~ aElementOf0(xK,szNzAzT0)
| ~ aSet0(xO) ),
inference(resolution,[status(thm)],[c_444,c_8422]) ).
tff(c_8451,plain,
sbrdtbr0(xQ) = xK,
inference(demodulation,[status(thm),theory(equality)],[c_434,c_336,c_8441]) ).
tff(c_8478,plain,
( isFinite0(xQ)
| ~ aElementOf0(xK,szNzAzT0)
| ~ aSet0(xQ) ),
inference(superposition,[status(thm),theory(equality)],[c_8451,c_152]) ).
tff(c_8494,plain,
isFinite0(xQ),
inference(demodulation,[status(thm),theory(equality)],[c_5964,c_336,c_8478]) ).
tff(c_8496,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6569,c_8494]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : NUM612+1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.15 % 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
% 0.12/0.36 % Computer : n011.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8042.1875MB
% 0.12/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Tue Apr 8 14:06:33 EDT 2025
% 0.19/0.37 % CPUTime :
% 12.81/4.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.96/4.07
% 12.96/4.07 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------