%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : RNG104+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/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 : 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 08:31:34 PM UTC 2025
% Result : Theorem 18.28s 7.55s
% Output : CNFRefutation 18.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 16 unt; 0 typ; 1 def)
% Number of atoms : 63 ( 17 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 53 ( 20 ~; 14 |; 12 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 40 ( 40 usr; 10 con; 0-4 aty)
% Number of variables : 24 ( 21 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdteqdtlpzmzozddtrp0 > aGcdOfAnd0 > misRelativelyPrime0 > iLess0 > doDivides0 > aElementOf0 > aDivisorOf0 > aSet0 > aNaturalNumber0 > aIdeal0 > aElement0 > sdtpldt1 > sdtpldt0 > sdtasdt0 > sdtasasdt0 > #nlpp > smndt0 > slsdtgt0 > sbrdtbr0 > xz > xy > xx > xv > xu > xc > sz10 > sz00 > #skF_22 > #skF_6 > #skF_17 > #skF_25 > #skF_20 > #skF_4 > #skF_8 > #skF_14 > #skF_15 > #skF_18 > #skF_23 > #skF_5 > #skF_19 > #skF_7 > #skF_9 > #skF_13 > #skF_11 > #skF_3 > #skF_2 > #skF_24 > #skF_12 > #skF_1 > #skF_16 > #skF_21 > #skF_10
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_22',type,
'#skF_22': ( $i * $i ) > $i ).
tff(sbrdtbr0,type,
sbrdtbr0: $i > $i ).
tff(sdtasdt0,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(aSet0,type,
aSet0: $i > $o ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff(sz10,type,
sz10: $i ).
tff(sdtpldt1,type,
sdtpldt1: ( $i * $i ) > $i ).
tff('#skF_17',type,
'#skF_17': ( $i * $i ) > $i ).
tff('#skF_25',type,
'#skF_25': $i ).
tff('#skF_20',type,
'#skF_20': ( $i * $i ) > $i ).
tff(aElement0,type,
aElement0: $i > $o ).
tff(sz00,type,
sz00: $i ).
tff(misRelativelyPrime0,type,
misRelativelyPrime0: ( $i * $i ) > $o ).
tff(xu,type,
xu: $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff(aIdeal0,type,
aIdeal0: $i > $o ).
tff(xc,type,
xc: $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i * $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': ( $i * $i * $i * $i ) > $i ).
tff(xy,type,
xy: $i ).
tff(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff('#skF_18',type,
'#skF_18': ( $i * $i ) > $i ).
tff(xx,type,
xx: $i ).
tff('#skF_23',type,
'#skF_23': ( $i * $i * $i ) > $i ).
tff(aNaturalNumber0,type,
aNaturalNumber0: $i > $o ).
tff(slsdtgt0,type,
slsdtgt0: $i > $i ).
tff(smndt0,type,
smndt0: $i > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff('#skF_19',type,
'#skF_19': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i * $i * $i ) > $i ).
tff(doDivides0,type,
doDivides0: ( $i * $i ) > $o ).
tff(aGcdOfAnd0,type,
aGcdOfAnd0: ( $i * $i * $i ) > $o ).
tff(aElementOf0,type,
aElementOf0: ( $i * $i ) > $o ).
tff(xz,type,
xz: $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(aDivisorOf0,type,
aDivisorOf0: ( $i * $i ) > $o ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff('#skF_24',type,
'#skF_24': $i ).
tff(sdtasasdt0,type,
sdtasasdt0: ( $i * $i ) > $i ).
tff(iLess0,type,
iLess0: ( $i * $i ) > $o ).
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_16',type,
'#skF_16': ( $i * $i ) > $i ).
tff('#skF_21',type,
'#skF_21': ( $i * $i ) > $i ).
tff(xv,type,
xv: $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i * $i ) > $i ).
tff(f_361,hypothesis,
( ? [W0] :
( aElement0(W0)
& ( sdtasdt0(xc,W0) = xx ) )
& aElementOf0(xx,slsdtgt0(xc))
& ? [W0] :
( aElement0(W0)
& ( sdtasdt0(xc,W0) = xy ) )
& aElementOf0(xy,slsdtgt0(xc))
& aElement0(xz) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1933) ).
tff(f_346,hypothesis,
aElement0(xc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1905) ).
tff(f_364,hypothesis,
( aElement0(xu)
& ( sdtasdt0(xc,xu) = xx ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1956) ).
tff(f_87,axiom,
! [W0,W1,W2] :
( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
=> ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
tff(f_345,definition,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( ( W1 = slsdtgt0(W0) )
<=> ( aSet0(W1)
& ! [W2] :
( aElementOf0(W2,W1)
<=> ? [W3] :
( aElement0(W3)
& ( sdtasdt0(W0,W3) = W2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrIdeal) ).
tff(f_137,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
tff(f_79,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
tff(f_370,negated_conjecture,
sdtasdt0(xz,xx) != sdtasdt0(xc,sdtasdt0(xu,xz)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(c_208,plain,
aElement0(xz),
inference(cnfTransformation,[status(thm)],[f_361]) ).
tff(c_206,plain,
aElement0(xc),
inference(cnfTransformation,[status(thm)],[f_346]) ).
tff(c_224,plain,
aElement0(xu),
inference(cnfTransformation,[status(thm)],[f_364]) ).
tff(c_222,plain,
sdtasdt0(xc,xu) = xx,
inference(cnfTransformation,[status(thm)],[f_364]) ).
tff(c_3783,plain,
! [W0_317,W1_318,W2_319] :
( ( sdtasdt0(sdtasdt0(W0_317,W1_318),W2_319) = sdtasdt0(W0_317,sdtasdt0(W1_318,W2_319)) )
| ~ aElement0(W2_319)
| ~ aElement0(W1_318)
| ~ aElement0(W0_317) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_3989,plain,
! [W2_319] :
( ( sdtasdt0(xc,sdtasdt0(xu,W2_319)) = sdtasdt0(xx,W2_319) )
| ~ aElement0(W2_319)
| ~ aElement0(xu)
| ~ aElement0(xc) ),
inference(superposition,[status(thm),theory(equality)],[c_222,c_3783]) ).
tff(c_21413,plain,
! [W2_482] :
( ( sdtasdt0(xc,sdtasdt0(xu,W2_482)) = sdtasdt0(xx,W2_482) )
| ~ aElement0(W2_482) ),
inference(demodulation,[status(thm),theory(equality)],[c_206,c_224,c_3989]) ).
tff(c_188,plain,
! [W0_181] :
( aSet0(slsdtgt0(W0_181))
| ~ aElement0(W0_181) ),
inference(cnfTransformation,[status(thm)],[f_345]) ).
tff(c_216,plain,
aElementOf0(xx,slsdtgt0(xc)),
inference(cnfTransformation,[status(thm)],[f_361]) ).
tff(c_652,plain,
! [W1_235,W0_236] :
( aElement0(W1_235)
| ~ aElementOf0(W1_235,W0_236)
| ~ aSet0(W0_236) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_660,plain,
( aElement0(xx)
| ~ aSet0(slsdtgt0(xc)) ),
inference(resolution,[status(thm)],[c_216,c_652]) ).
tff(c_684,plain,
~ aSet0(slsdtgt0(xc)),
inference(splitLeft,[status(thm)],[c_660]) ).
tff(c_692,plain,
~ aElement0(xc),
inference(resolution,[status(thm)],[c_188,c_684]) ).
tff(c_699,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_206,c_692]) ).
tff(c_700,plain,
aElement0(xx),
inference(splitRight,[status(thm)],[c_660]) ).
tff(c_1910,plain,
! [W1_270,W0_271] :
( ( sdtasdt0(W1_270,W0_271) = sdtasdt0(W0_271,W1_270) )
| ~ aElement0(W1_270)
| ~ aElement0(W0_271) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_7374,plain,
! [W0_377] :
( ( sdtasdt0(xz,W0_377) = sdtasdt0(W0_377,xz) )
| ~ aElement0(W0_377) ),
inference(resolution,[status(thm)],[c_208,c_1910]) ).
tff(c_7481,plain,
sdtasdt0(xz,xx) = sdtasdt0(xx,xz),
inference(resolution,[status(thm)],[c_700,c_7374]) ).
tff(c_232,plain,
sdtasdt0(xc,sdtasdt0(xu,xz)) != sdtasdt0(xz,xx),
inference(cnfTransformation,[status(thm)],[f_370]) ).
tff(c_8142,plain,
sdtasdt0(xc,sdtasdt0(xu,xz)) != sdtasdt0(xx,xz),
inference(demodulation,[status(thm),theory(equality)],[c_7481,c_232]) ).
tff(c_21421,plain,
~ aElement0(xz),
inference(superposition,[status(thm),theory(equality)],[c_21413,c_8142]) ).
tff(c_21491,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_208,c_21421]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : RNG104+2 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.13 % 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
% 0.13/0.34 % 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 18:50:02 EDT 2025
% 0.13/0.34 % CPUTime :
% 18.28/7.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.28/7.55
% 18.28/7.55 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------