%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM617+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 : n026.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 07:56:37 PM UTC 2025
% Result : Theorem 9.70s 3.73s
% Output : CNFRefutation 9.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 15 unt; 0 typ; 1 def)
% Number of atoms : 49 ( 1 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 40 ( 18 ~; 15 |; 4 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 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; 18 con; 0-4 aty)
% Number of variables : 13 ( 13 !; 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 > xx > xp > xn > 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(xx,type,
xx: $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(xn,type,
xn: $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_888,negated_conjecture,
~ aElementOf0(xx,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_852,hypothesis,
( aSet0(xO)
& isCountable0(xO) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4908) ).
tff(f_867,hypothesis,
( aSubsetOf0(xQ,xO)
& ( xQ != slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5093) ).
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_886,hypothesis,
aElementOf0(xx,xP),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5348) ).
tff(c_482,plain,
~ aElementOf0(xx,szNzAzT0),
inference(cnfTransformation,[status(thm)],[f_888]) ).
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_434,plain,
aSet0(xO),
inference(cnfTransformation,[status(thm)],[f_852]) ).
tff(c_448,plain,
aSubsetOf0(xQ,xO),
inference(cnfTransformation,[status(thm)],[f_867]) ).
tff(c_762,plain,
! [W1_444,W0_445] :
( aSet0(W1_444)
| ~ aSubsetOf0(W1_444,W0_445)
| ~ aSet0(W0_445) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_774,plain,
( aSet0(xQ)
| ~ aSet0(xO) ),
inference(resolution,[status(thm)],[c_448,c_762]) ).
tff(c_799,plain,
aSet0(xQ),
inference(demodulation,[status(thm),theory(equality)],[c_434,c_774]) ).
tff(c_464,plain,
aSubsetOf0(xP,xQ),
inference(cnfTransformation,[status(thm)],[f_876]) ).
tff(c_480,plain,
aElementOf0(xx,xP),
inference(cnfTransformation,[status(thm)],[f_886]) ).
tff(c_2370,plain,
! [W2_574,W0_575,W1_576] :
( aElementOf0(W2_574,W0_575)
| ~ aElementOf0(W2_574,W1_576)
| ~ aSubsetOf0(W1_576,W0_575)
| ~ aSet0(W0_575) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_2446,plain,
! [W0_577] :
( aElementOf0(xx,W0_577)
| ~ aSubsetOf0(xP,W0_577)
| ~ aSet0(W0_577) ),
inference(resolution,[status(thm)],[c_480,c_2370]) ).
tff(c_2457,plain,
( aElementOf0(xx,xQ)
| ~ aSet0(xQ) ),
inference(resolution,[status(thm)],[c_464,c_2446]) ).
tff(c_2469,plain,
aElementOf0(xx,xQ),
inference(demodulation,[status(thm),theory(equality)],[c_799,c_2457]) ).
tff(c_24,plain,
! [W2_23,W0_14,W1_20] :
( aElementOf0(W2_23,W0_14)
| ~ aElementOf0(W2_23,W1_20)
| ~ aSubsetOf0(W1_20,W0_14)
| ~ aSet0(W0_14) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_2984,plain,
! [W0_602] :
( aElementOf0(xx,W0_602)
| ~ aSubsetOf0(xQ,W0_602)
| ~ aSet0(W0_602) ),
inference(resolution,[status(thm)],[c_2469,c_24]) ).
tff(c_2998,plain,
( aElementOf0(xx,szNzAzT0)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[status(thm)],[c_450,c_2984]) ).
tff(c_3010,plain,
aElementOf0(xx,szNzAzT0),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_2998]) ).
tff(c_3012,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_482,c_3010]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.23 % Problem : NUM617+1 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.24 % 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
% 0.15/0.92 % Computer : n026.cluster.edu
% 0.15/0.92 % Model : x86_64 x86_64
% 0.15/0.92 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.92 % Memory : 8042.1875MB
% 0.15/0.92 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.92 % CPULimit : 300
% 0.15/0.92 % WCLimit : 300
% 0.15/0.92 % DateTime : Tue Apr 8 14:10:24 EDT 2025
% 0.15/0.92 % CPUTime :
% 9.70/3.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.70/3.73
% 9.70/3.73 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------