%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM443+4 : 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 : n023.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 07:55:56 PM UTC 2025
% Result : Theorem 29.95s 14.11s
% Output : CNFRefutation 29.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 123 ( 18 equ)
% Maximal formula atoms : 34 ( 3 avg)
% Number of connectives : 135 ( 44 ~; 48 |; 33 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 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 : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 38 ( 38 usr; 8 con; 0-3 aty)
% Number of variables : 29 ( 24 !; 5 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdteqdtlpzmzozddtrp0 > aSubsetOf0 > aElementOf0 > aDivisorOf0 > isPrime0 > isOpen0 > isFinite0 > isClosed0 > aSet0 > aInteger0 > szAzrzSzezqlpdtcmdtrp0 > sdtslmnbsdt0 > sdtpldt0 > sdtbsmnsldt0 > sdtasdt0 > #nlpp > stldt0 > smndt0 > sbsmnsldt0 > xq > xc > xb > xa > sz10 > sz00 > cS1395 > #skF_11 > #skF_21 > #skF_2 > #skF_18 > #skF_6 > #skF_19 > #skF_17 > #skF_12 > #skF_8 > #skF_4 > #skF_3 > #skF_13 > #skF_14 > #skF_5 > #skF_10 > #skF_7 > #skF_23 > #skF_15 > #skF_22 > #skF_1 > #skF_9 > #skF_20 > #skF_16
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(aInteger0,type,
aInteger0: $i > $o ).
tff(sbsmnsldt0,type,
sbsmnsldt0: $i > $i ).
tff(xq,type,
xq: $i ).
tff('#skF_11',type,
'#skF_11': ( $i * $i ) > $i ).
tff(stldt0,type,
stldt0: $i > $i ).
tff('#skF_21',type,
'#skF_21': $i > $i ).
tff(sdtasdt0,type,
sdtasdt0: ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff(aSet0,type,
aSet0: $i > $o ).
tff('#skF_18',type,
'#skF_18': $i > $i ).
tff(isClosed0,type,
isClosed0: $i > $o ).
tff(xa,type,
xa: $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff(szAzrzSzezqlpdtcmdtrp0,type,
szAzrzSzezqlpdtcmdtrp0: ( $i * $i ) > $i ).
tff(sz10,type,
sz10: $i ).
tff(cS1395,type,
cS1395: $i ).
tff('#skF_19',type,
'#skF_19': $i > $i ).
tff('#skF_17',type,
'#skF_17': ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i * $i ) > $i ).
tff(sz00,type,
sz00: $i ).
tff('#skF_8',type,
'#skF_8': $i > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_13',type,
'#skF_13': ( $i * $i ) > $i ).
tff(xc,type,
xc: $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i ) > $i ).
tff(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(sdtslmnbsdt0,type,
sdtslmnbsdt0: ( $i * $i ) > $i ).
tff(isPrime0,type,
isPrime0: $i > $o ).
tff(smndt0,type,
smndt0: $i > $i ).
tff(aSubsetOf0,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(isOpen0,type,
isOpen0: $i > $o ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i * $i ) > $i ).
tff(aElementOf0,type,
aElementOf0: ( $i * $i ) > $o ).
tff('#skF_23',type,
'#skF_23': $i > $i ).
tff(xb,type,
xb: $i ).
tff(sdtbsmnsldt0,type,
sdtbsmnsldt0: ( $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': ( $i * $i * $i ) > $i ).
tff(isFinite0,type,
isFinite0: $i > $o ).
tff('#skF_22',type,
'#skF_22': $i ).
tff(aDivisorOf0,type,
aDivisorOf0: ( $i * $i ) > $o ).
tff(sdteqdtlpzmzozddtrp0,type,
sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff('#skF_20',type,
'#skF_20': $i > $i ).
tff('#skF_16',type,
'#skF_16': ( $i * $i * $i ) > $i ).
tff(f_422,hypothesis,
( aInteger0(xa)
& aInteger0(xq)
& ( xq != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1962) ).
tff(f_425,hypothesis,
( aInteger0(xb)
& aInteger0(xc) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2010) ).
tff(f_502,negated_conjecture,
~ ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [W0] :
( ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(W0)
& ? [W1] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
& ( ( aInteger0(W0)
& ( ? [W1] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) )
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
=> aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [W0] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xc,smndt0(xb)) ) )
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xc,xb,xq) )
=> ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [W0] :
( ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(W0)
& ? [W1] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
& ( ( aInteger0(W0)
& ( ? [W1] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) )
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
=> aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(f_175,axiom,
! [W0,W1,W2] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
=> sdteqdtlpzmzozddtrp0(W1,W0,W2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModSym) ).
tff(f_192,axiom,
! [W0,W1,W2,W3] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 )
& aInteger0(W3) )
=> ( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
& sdteqdtlpzmzozddtrp0(W1,W3,W2) )
=> sdteqdtlpzmzozddtrp0(W0,W3,W2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModTrn) ).
tff(c_268,plain,
xq != sz00,
inference(cnfTransformation,[status(thm)],[f_422]) ).
tff(c_276,plain,
aInteger0(xb),
inference(cnfTransformation,[status(thm)],[f_425]) ).
tff(c_801,plain,
! [W0_202] :
( ~ sdteqdtlpzmzozddtrp0(W0_202,xa,xq)
| aElementOf0(W0_202,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0_202) ),
inference(cnfTransformation,[status(thm)],[f_502]) ).
tff(c_294,plain,
~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(cnfTransformation,[status(thm)],[f_502]) ).
tff(c_816,plain,
( ~ sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ aInteger0(xb) ),
inference(resolution,[status(thm)],[c_801,c_294]) ).
tff(c_823,plain,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(demodulation,[status(thm),theory(equality)],[c_276,c_816]) ).
tff(c_272,plain,
aInteger0(xa),
inference(cnfTransformation,[status(thm)],[f_422]) ).
tff(c_270,plain,
aInteger0(xq),
inference(cnfTransformation,[status(thm)],[f_422]) ).
tff(c_274,plain,
aInteger0(xc),
inference(cnfTransformation,[status(thm)],[f_425]) ).
tff(c_280,plain,
aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(cnfTransformation,[status(thm)],[f_502]) ).
tff(c_682,plain,
! [W0_197] :
( sdteqdtlpzmzozddtrp0(W0_197,xa,xq)
| ~ aElementOf0(W0_197,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(cnfTransformation,[status(thm)],[f_502]) ).
tff(c_686,plain,
sdteqdtlpzmzozddtrp0(xc,xa,xq),
inference(resolution,[status(thm)],[c_280,c_682]) ).
tff(c_15757,plain,
! [W1_377,W0_378,W2_379] :
( sdteqdtlpzmzozddtrp0(W1_377,W0_378,W2_379)
| ~ sdteqdtlpzmzozddtrp0(W0_378,W1_377,W2_379)
| ( sz00 = W2_379 )
| ~ aInteger0(W2_379)
| ~ aInteger0(W1_377)
| ~ aInteger0(W0_378) ),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_15763,plain,
( sdteqdtlpzmzozddtrp0(xa,xc,xq)
| ( xq = sz00 )
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| ~ aInteger0(xc) ),
inference(resolution,[status(thm)],[c_686,c_15757]) ).
tff(c_15773,plain,
( sdteqdtlpzmzozddtrp0(xa,xc,xq)
| ( xq = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_274,c_272,c_270,c_15763]) ).
tff(c_15774,plain,
sdteqdtlpzmzozddtrp0(xa,xc,xq),
inference(negUnitSimplification,[status(thm)],[c_268,c_15773]) ).
tff(c_284,plain,
sdteqdtlpzmzozddtrp0(xc,xb,xq),
inference(cnfTransformation,[status(thm)],[f_502]) ).
tff(c_28070,plain,
! [W0_445,W3_446,W2_447,W1_448] :
( sdteqdtlpzmzozddtrp0(W0_445,W3_446,W2_447)
| ~ sdteqdtlpzmzozddtrp0(W1_448,W3_446,W2_447)
| ~ sdteqdtlpzmzozddtrp0(W0_445,W1_448,W2_447)
| ~ aInteger0(W3_446)
| ( sz00 = W2_447 )
| ~ aInteger0(W2_447)
| ~ aInteger0(W1_448)
| ~ aInteger0(W0_445) ),
inference(cnfTransformation,[status(thm)],[f_192]) ).
tff(c_28082,plain,
! [W0_445] :
( sdteqdtlpzmzozddtrp0(W0_445,xb,xq)
| ~ sdteqdtlpzmzozddtrp0(W0_445,xc,xq)
| ~ aInteger0(xb)
| ( xq = sz00 )
| ~ aInteger0(xq)
| ~ aInteger0(xc)
| ~ aInteger0(W0_445) ),
inference(resolution,[status(thm)],[c_284,c_28070]) ).
tff(c_28102,plain,
! [W0_445] :
( sdteqdtlpzmzozddtrp0(W0_445,xb,xq)
| ~ sdteqdtlpzmzozddtrp0(W0_445,xc,xq)
| ( xq = sz00 )
| ~ aInteger0(W0_445) ),
inference(demodulation,[status(thm),theory(equality)],[c_274,c_270,c_276,c_28082]) ).
tff(c_40468,plain,
! [W0_561] :
( sdteqdtlpzmzozddtrp0(W0_561,xb,xq)
| ~ sdteqdtlpzmzozddtrp0(W0_561,xc,xq)
| ~ aInteger0(W0_561) ),
inference(negUnitSimplification,[status(thm)],[c_268,c_28102]) ).
tff(c_40479,plain,
( sdteqdtlpzmzozddtrp0(xa,xb,xq)
| ~ aInteger0(xa) ),
inference(resolution,[status(thm)],[c_15774,c_40468]) ).
tff(c_40497,plain,
sdteqdtlpzmzozddtrp0(xa,xb,xq),
inference(demodulation,[status(thm),theory(equality)],[c_272,c_40479]) ).
tff(c_64,plain,
! [W1_43,W0_42,W2_44] :
( sdteqdtlpzmzozddtrp0(W1_43,W0_42,W2_44)
| ~ sdteqdtlpzmzozddtrp0(W0_42,W1_43,W2_44)
| ( sz00 = W2_44 )
| ~ aInteger0(W2_44)
| ~ aInteger0(W1_43)
| ~ aInteger0(W0_42) ),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_40520,plain,
( sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ( xq = sz00 )
| ~ aInteger0(xq)
| ~ aInteger0(xb)
| ~ aInteger0(xa) ),
inference(resolution,[status(thm)],[c_40497,c_64]) ).
tff(c_40527,plain,
( sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ( xq = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_272,c_276,c_270,c_40520]) ).
tff(c_40529,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_268,c_823,c_40527]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM443+4 : TPTP v9.0.0. Released v4.0.0.
% 0.04/0.13 % 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
% 0.13/0.35 % Computer : n023.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Apr 8 12:28:54 EDT 2025
% 0.13/0.35 % CPUTime :
% 29.95/14.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.95/14.11
% 29.95/14.11 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------