%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM547+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 : n027.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 5.71s 2.28s
% Output : CNFRefutation 5.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 10 unt; 0 typ; 3 def)
% Number of atoms : 45 ( 8 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 41 ( 17 ~; 9 |; 8 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 30 ( 30 usr; 7 con; 0-3 aty)
% Number of variables : 16 ( 14 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > aSubsetOf0 > aElementOf0 > isFinite0 > isCountable0 > aSet0 > aElement0 > slbdtsldtrb0 > sdtpldt0 > sdtmndt0 > #nlpp > szszuzczcdt0 > szmzizndt0 > szmzazxdt0 > slbdtrb0 > sbrdtbr0 > xx > xk > xT > xS > 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('#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('#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_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_52,definition,
! [W0] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1] : aElementOf0(W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
tff(f_534,negated_conjecture,
~ ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
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(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_670,plain,
! [W0_209,W1_210] :
( aSet0(slbdtsldtrb0(W0_209,W1_210))
| ~ aElementOf0(W1_210,szNzAzT0)
| ~ aSet0(W0_209) ),
inference(cnfTransformation,[status(thm)],[f_487]) ).
tff(c_260,plain,
slbdtsldtrb0(xS,xk) != slcrc0,
inference(cnfTransformation,[status(thm)],[f_530]) ).
tff(c_421,plain,
! [W0_193] :
( ( slcrc0 = W0_193 )
| aElementOf0('#skF_1'(W0_193),W0_193)
| ~ aSet0(W0_193) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_266,plain,
! [W0_171] : ~ aElementOf0(W0_171,slbdtsldtrb0(xS,xk)),
inference(cnfTransformation,[status(thm)],[f_534]) ).
tff(c_436,plain,
( ( slbdtsldtrb0(xS,xk) = slcrc0 )
| ~ aSet0(slbdtsldtrb0(xS,xk)) ),
inference(resolution,[status(thm)],[c_421,c_266]) ).
tff(c_450,plain,
~ aSet0(slbdtsldtrb0(xS,xk)),
inference(negUnitSimplification,[status(thm)],[c_260,c_436]) ).
tff(c_262,plain,
aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)),
inference(cnfTransformation,[status(thm)],[f_530]) ).
tff(c_26,plain,
! [W1_20,W0_14] :
( aSet0(W1_20)
| ~ aSubsetOf0(W1_20,W0_14)
| ~ aSet0(W0_14) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_368,plain,
( aSet0(slbdtsldtrb0(xS,xk))
| ~ aSet0(slbdtsldtrb0(xT,xk)) ),
inference(resolution,[status(thm)],[c_262,c_26]) ).
tff(c_511,plain,
~ aSet0(slbdtsldtrb0(xT,xk)),
inference(negUnitSimplification,[status(thm)],[c_450,c_368]) ).
tff(c_673,plain,
( ~ aElementOf0(xk,szNzAzT0)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[c_670,c_511]) ).
tff(c_683,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_256,c_252,c_673]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.15 % Problem : NUM547+1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.16 % 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
% 0.14/0.38 % Computer : n027.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8042.1875MB
% 0.14/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Tue Apr 8 13:28:35 EDT 2025
% 0.14/0.38 % CPUTime :
% 5.71/2.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.71/2.29
% 5.71/2.29 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------