%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : RNG099+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 : n013.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 08:31:33 PM UTC 2025
% Result : Theorem 5.82s 2.42s
% Output : CNFRefutation 5.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 37 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 79 ( 3 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 67 ( 25 ~; 18 |; 14 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 29 ( 29 usr; 9 con; 0-4 aty)
% Number of variables : 20 ( 19 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdteqdtlpzmzozddtrp0 > aElementOf0 > aSet0 > aIdeal0 > aElement0 > sdtpldt1 > sdtpldt0 > sdtasdt0 > sdtasasdt0 > #nlpp > smndt0 > xy > xx > xw > xb > xa > xJ > xI > sz10 > sz00 > #skF_6 > #skF_4 > #skF_8 > #skF_15 > #skF_5 > #skF_7 > #skF_9 > #skF_13 > #skF_11 > #skF_3 > #skF_14 > #skF_2 > #skF_12 > #skF_1 > #skF_10
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(sdtasdt0,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(aSet0,type,
aSet0: $i > $o ).
tff(xa,type,
xa: $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff(sz10,type,
sz10: $i ).
tff(sdtpldt1,type,
sdtpldt1: ( $i * $i ) > $i ).
tff(xw,type,
xw: $i ).
tff(aElement0,type,
aElement0: $i > $o ).
tff(sz00,type,
sz00: $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff(aIdeal0,type,
aIdeal0: $i > $o ).
tff(xI,type,
xI: $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i * $i * $i ) > $i ).
tff(xy,type,
xy: $i ).
tff('#skF_15',type,
'#skF_15': $i > $i ).
tff(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(xx,type,
xx: $i ).
tff(smndt0,type,
smndt0: $i > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i * $i * $i ) > $i ).
tff(aElementOf0,type,
aElementOf0: ( $i * $i ) > $o ).
tff(xb,type,
xb: $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i * $i ) > $i ).
tff('#skF_13',type,
'#skF_13': $i > $i ).
tff('#skF_11',type,
'#skF_11': $i > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': $i > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(xJ,type,
xJ: $i ).
tff(sdtasasdt0,type,
sdtasasdt0: ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': $i > $i ).
tff(sdteqdtlpzmzozddtrp0,type,
sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i * $i ) > $i ).
tff(f_274,hypothesis,
( aElement0(xx)
& aElement0(xy) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1217) ).
tff(f_260,hypothesis,
( aSet0(xI)
& ! [W0] :
( aElementOf0(W0,xI)
=> ( ! [W1] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [W0] :
( aElementOf0(W0,xJ)
=> ( ! [W1] :
( aElementOf0(W1,xJ)
=> aElementOf0(sdtpldt0(W0,W1),xJ) )
& ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xJ) ) ) )
& aIdeal0(xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1205) ).
tff(f_279,hypothesis,
( aElementOf0(xa,xI)
& aElementOf0(xb,xJ)
& ( sdtpldt0(xa,xb) = sz10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1294) ).
tff(f_137,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
tff(f_47,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
tff(f_281,hypothesis,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1332) ).
tff(f_282,hypothesis,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1409) ).
tff(f_293,negated_conjecture,
~ ? [W0] :
( aElement0(W0)
& ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(W0,xx,xI) )
& ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(f_280,hypothesis,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1319) ).
tff(f_41,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
tff(c_158,plain,
aElement0(xx),
inference(cnfTransformation,[status(thm)],[f_274]) ).
tff(c_134,plain,
aSet0(xJ),
inference(cnfTransformation,[status(thm)],[f_260]) ).
tff(c_162,plain,
aElementOf0(xb,xJ),
inference(cnfTransformation,[status(thm)],[f_279]) ).
tff(c_460,plain,
! [W1_172,W0_173] :
( aElement0(W1_172)
| ~ aElementOf0(W1_172,W0_173)
| ~ aSet0(W0_173) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_478,plain,
( aElement0(xb)
| ~ aSet0(xJ) ),
inference(resolution,[status(thm)],[c_162,c_460]) ).
tff(c_496,plain,
aElement0(xb),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_478]) ).
tff(c_12,plain,
! [W0_5,W1_6] :
( aElement0(sdtasdt0(W0_5,W1_6))
| ~ aElement0(W1_6)
| ~ aElement0(W0_5) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_156,plain,
aElement0(xy),
inference(cnfTransformation,[status(thm)],[f_274]) ).
tff(c_138,plain,
aSet0(xI),
inference(cnfTransformation,[status(thm)],[f_260]) ).
tff(c_164,plain,
aElementOf0(xa,xI),
inference(cnfTransformation,[status(thm)],[f_279]) ).
tff(c_475,plain,
( aElement0(xa)
| ~ aSet0(xI) ),
inference(resolution,[status(thm)],[c_164,c_460]) ).
tff(c_493,plain,
aElement0(xa),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_475]) ).
tff(c_168,plain,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(cnfTransformation,[status(thm)],[f_281]) ).
tff(c_170,plain,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
inference(cnfTransformation,[status(thm)],[f_282]) ).
tff(c_178,plain,
! [W0_155] :
( ~ aElementOf0(sdtpldt0(W0_155,smndt0(xx)),xI)
| ~ aElementOf0(sdtpldt0(W0_155,smndt0(xy)),xJ)
| ~ aElement0(W0_155) ),
inference(cnfTransformation,[status(thm)],[f_293]) ).
tff(c_403,plain,
( ~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI)
| ~ aElement0(xw) ),
inference(resolution,[status(thm)],[c_170,c_178]) ).
tff(c_409,plain,
~ aElement0(xw),
inference(demodulation,[status(thm),theory(equality)],[c_168,c_403]) ).
tff(c_166,plain,
sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)) = xw,
inference(cnfTransformation,[status(thm)],[f_280]) ).
tff(c_10,plain,
! [W0_3,W1_4] :
( aElement0(sdtpldt0(W0_3,W1_4))
| ~ aElement0(W1_4)
| ~ aElement0(W0_3) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_1492,plain,
( aElement0(xw)
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xy,xa)) ),
inference(superposition,[status(thm),theory(equality)],[c_166,c_10]) ).
tff(c_1495,plain,
( ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xy,xa)) ),
inference(negUnitSimplification,[status(thm)],[c_409,c_1492]) ).
tff(c_1627,plain,
~ aElement0(sdtasdt0(xy,xa)),
inference(splitLeft,[status(thm)],[c_1495]) ).
tff(c_1630,plain,
( ~ aElement0(xa)
| ~ aElement0(xy) ),
inference(resolution,[status(thm)],[c_12,c_1627]) ).
tff(c_1634,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_156,c_493,c_1630]) ).
tff(c_1635,plain,
~ aElement0(sdtasdt0(xx,xb)),
inference(splitRight,[status(thm)],[c_1495]) ).
tff(c_1639,plain,
( ~ aElement0(xb)
| ~ aElement0(xx) ),
inference(resolution,[status(thm)],[c_12,c_1635]) ).
tff(c_1643,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_158,c_496,c_1639]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG099+2 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.13 % 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
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 8 18:48:17 EDT 2025
% 0.13/0.34 % CPUTime :
% 5.82/2.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.82/2.42
% 5.82/2.42 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------