%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWC068-1 : TPTP v9.0.0. Released v2.4.0.
% 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 : n012.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 09:19:07 PM UTC 2025
% Result : Unsatisfiable 23.01s 10.36s
% Output : CNFRefutation 23.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 49 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 91 ( 27 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 92 ( 50 ~; 42 |; 0 &)
% ( 0 <=>; 0 =>; 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 : 21 ( 19 usr; 1 prp; 0-2 aty)
% Number of functors : 53 ( 53 usr; 7 con; 0-2 aty)
% Number of variables : 21 ( 21 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ segmentP > rearsegP > neq > memberP > lt > leq > gt > geq > frontsegP > totalorderedP > totalorderP > strictorderedP > strictorderP > ssList > ssItem > singletonP > equalelemsP > duplicatefreeP > cyclefreeP > skaf48 > skaf47 > skaf46 > skaf45 > skaf43 > skaf42 > cons > app > #nlpp > tl > skaf83 > skaf82 > skaf81 > skaf80 > skaf79 > skaf78 > skaf77 > skaf76 > skaf75 > skaf74 > skaf73 > skaf72 > skaf71 > skaf70 > skaf69 > skaf68 > skaf67 > skaf66 > skaf65 > skaf64 > skaf63 > skaf62 > skaf61 > skaf60 > skaf59 > skaf58 > skaf57 > skaf56 > skaf55 > skaf54 > skaf53 > skaf52 > skaf51 > skaf50 > skaf49 > skaf44 > hd > skac3 > skac2 > sk4 > sk3 > sk2 > sk1 > nil
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(skaf56,type,
skaf56: $i > $i ).
tff(segmentP,type,
segmentP: ( $i * $i ) > $o ).
tff(totalorderedP,type,
totalorderedP: $i > $o ).
tff(equalelemsP,type,
equalelemsP: $i > $o ).
tff(skaf74,type,
skaf74: $i > $i ).
tff(skaf61,type,
skaf61: $i > $i ).
tff(skaf51,type,
skaf51: $i > $i ).
tff(skaf83,type,
skaf83: $i > $i ).
tff(skac2,type,
skac2: $i ).
tff(skaf63,type,
skaf63: $i > $i ).
tff(skaf62,type,
skaf62: $i > $i ).
tff(sk2,type,
sk2: $i ).
tff(skaf52,type,
skaf52: $i > $i ).
tff(skaf50,type,
skaf50: $i > $i ).
tff(skaf42,type,
skaf42: ( $i * $i ) > $i ).
tff(skaf44,type,
skaf44: $i > $i ).
tff(singletonP,type,
singletonP: $i > $o ).
tff(skaf67,type,
skaf67: $i > $i ).
tff(skaf75,type,
skaf75: $i > $i ).
tff(sk1,type,
sk1: $i ).
tff(skaf58,type,
skaf58: $i > $i ).
tff(skaf46,type,
skaf46: ( $i * $i ) > $i ).
tff(frontsegP,type,
frontsegP: ( $i * $i ) > $o ).
tff(skaf70,type,
skaf70: $i > $i ).
tff(totalorderP,type,
totalorderP: $i > $o ).
tff(ssItem,type,
ssItem: $i > $o ).
tff(skaf82,type,
skaf82: $i > $i ).
tff(skaf47,type,
skaf47: ( $i * $i ) > $i ).
tff(skaf76,type,
skaf76: $i > $i ).
tff(skac3,type,
skac3: $i ).
tff(skaf80,type,
skaf80: $i > $i ).
tff(skaf59,type,
skaf59: $i > $i ).
tff(skaf53,type,
skaf53: $i > $i ).
tff(skaf45,type,
skaf45: ( $i * $i ) > $i ).
tff(hd,type,
hd: $i > $i ).
tff(app,type,
app: ( $i * $i ) > $i ).
tff(skaf72,type,
skaf72: $i > $i ).
tff(duplicatefreeP,type,
duplicatefreeP: $i > $o ).
tff(skaf64,type,
skaf64: $i > $i ).
tff(sk4,type,
sk4: $i ).
tff(gt,type,
gt: ( $i * $i ) > $o ).
tff(skaf71,type,
skaf71: $i > $i ).
tff(skaf78,type,
skaf78: $i > $i ).
tff(skaf79,type,
skaf79: $i > $i ).
tff(rearsegP,type,
rearsegP: ( $i * $i ) > $o ).
tff(memberP,type,
memberP: ( $i * $i ) > $o ).
tff(skaf73,type,
skaf73: $i > $i ).
tff(ssList,type,
ssList: $i > $o ).
tff(cons,type,
cons: ( $i * $i ) > $i ).
tff(skaf54,type,
skaf54: $i > $i ).
tff(skaf77,type,
skaf77: $i > $i ).
tff(sk3,type,
sk3: $i ).
tff(skaf66,type,
skaf66: $i > $i ).
tff(strictorderP,type,
strictorderP: $i > $o ).
tff(skaf81,type,
skaf81: $i > $i ).
tff(geq,type,
geq: ( $i * $i ) > $o ).
tff(skaf60,type,
skaf60: $i > $i ).
tff(leq,type,
leq: ( $i * $i ) > $o ).
tff(lt,type,
lt: ( $i * $i ) > $o ).
tff(skaf69,type,
skaf69: $i > $i ).
tff(tl,type,
tl: $i > $i ).
tff(neq,type,
neq: ( $i * $i ) > $o ).
tff(skaf43,type,
skaf43: ( $i * $i ) > $i ).
tff(skaf48,type,
skaf48: ( $i * $i ) > $i ).
tff(skaf65,type,
skaf65: $i > $i ).
tff(skaf57,type,
skaf57: $i > $i ).
tff(nil,type,
nil: $i ).
tff(skaf49,type,
skaf49: $i > $i ).
tff(skaf55,type,
skaf55: $i > $i ).
tff(skaf68,type,
skaf68: $i > $i ).
tff(strictorderedP,type,
strictorderedP: $i > $o ).
tff(cyclefreeP,type,
cyclefreeP: $i > $o ).
tff(f_1668,axiom,
( ( nil != sk2 )
| ( nil != sk1 ) ),
file(unknown,unknown) ).
tff(f_56,axiom,
ssList(nil),
file(unknown,unknown) ).
tff(f_1650,axiom,
sk2 = sk4,
file(unknown,unknown) ).
tff(f_1648,axiom,
ssList(sk4),
file(unknown,unknown) ).
tff(f_456,axiom,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) ),
file(unknown,unknown) ).
tff(f_161,axiom,
! [U] :
( ~ ssList(U)
| segmentP(U,U) ),
file(unknown,unknown) ).
tff(f_1663,axiom,
! [A] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A) ),
file(unknown,unknown) ).
tff(f_1651,axiom,
sk1 = sk3,
file(unknown,unknown) ).
tff(f_1647,axiom,
ssList(sk3),
file(unknown,unknown) ).
tff(f_245,axiom,
! [U] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
file(unknown,unknown) ).
tff(f_1649,axiom,
app(sk4,sk4) = sk3,
file(unknown,unknown) ).
tff(f_1371,axiom,
! [U,V,W,X] :
( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X)
| segmentP(X,V) ),
file(unknown,unknown) ).
tff(f_250,axiom,
! [U] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file(unknown,unknown) ).
tff(c_388,plain,
( ( sk1 != nil )
| ( sk2 != nil ) ),
inference(cnfTransformation,[status(thm)],[f_1668]) ).
tff(c_442,plain,
sk2 != nil,
inference(splitLeft,[status(thm)],[c_388]) ).
tff(c_16,plain,
ssList(nil),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_382,plain,
sk4 = sk2,
inference(cnfTransformation,[status(thm)],[f_1650]) ).
tff(c_378,plain,
ssList(sk4),
inference(cnfTransformation,[status(thm)],[f_1648]) ).
tff(c_390,plain,
ssList(sk2),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_378]) ).
tff(c_200,plain,
! [V_102,U_101] :
( ( V_102 = U_101 )
| neq(V_102,U_101)
| ~ ssList(V_102)
| ~ ssList(U_101) ),
inference(cnfTransformation,[status(thm)],[f_456]) ).
tff(c_114,plain,
! [U_51] :
( segmentP(U_51,U_51)
| ~ ssList(U_51) ),
inference(cnfTransformation,[status(thm)],[f_161]) ).
tff(c_2913,plain,
! [A_606] :
( ~ segmentP(sk1,A_606)
| ~ segmentP(sk2,A_606)
| ~ neq(A_606,nil)
| ~ ssList(A_606) ),
inference(cnfTransformation,[status(thm)],[f_1663]) ).
tff(c_2917,plain,
( ~ segmentP(sk1,sk2)
| ~ neq(sk2,nil)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_114,c_2913]) ).
tff(c_2924,plain,
( ~ segmentP(sk1,sk2)
| ~ neq(sk2,nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_2917]) ).
tff(c_2942,plain,
~ neq(sk2,nil),
inference(splitLeft,[status(thm)],[c_2924]) ).
tff(c_2966,plain,
( ( sk2 = nil )
| ~ ssList(sk2)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_200,c_2942]) ).
tff(c_2972,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_390,c_2966]) ).
tff(c_2974,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_442,c_2972]) ).
tff(c_2975,plain,
~ segmentP(sk1,sk2),
inference(splitRight,[status(thm)],[c_2924]) ).
tff(c_384,plain,
sk3 = sk1,
inference(cnfTransformation,[status(thm)],[f_1651]) ).
tff(c_376,plain,
ssList(sk3),
inference(cnfTransformation,[status(thm)],[f_1647]) ).
tff(c_391,plain,
ssList(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_376]) ).
tff(c_721,plain,
! [U_394] :
( ( app(U_394,nil) = U_394 )
| ~ ssList(U_394) ),
inference(cnfTransformation,[status(thm)],[f_245]) ).
tff(c_842,plain,
app(sk1,nil) = sk1,
inference(resolution,[status(thm)],[c_391,c_721]) ).
tff(c_380,plain,
app(sk4,sk4) = sk3,
inference(cnfTransformation,[status(thm)],[f_1649]) ).
tff(c_389,plain,
app(sk2,sk2) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_382,c_382,c_384,c_380]) ).
tff(c_9199,plain,
! [U_909,V_910,W_911] :
( segmentP(app(app(U_909,V_910),W_911),V_910)
| ~ ssList(app(app(U_909,V_910),W_911))
| ~ ssList(V_910)
| ~ ssList(U_909)
| ~ ssList(W_911) ),
inference(cnfTransformation,[status(thm)],[f_1371]) ).
tff(c_9393,plain,
! [W_911] :
( segmentP(app(sk1,W_911),sk2)
| ~ ssList(app(app(sk2,sk2),W_911))
| ~ ssList(sk2)
| ~ ssList(sk2)
| ~ ssList(W_911) ),
inference(superposition,[status(thm),theory(equality)],[c_389,c_9199]) ).
tff(c_25162,plain,
! [W_1786] :
( segmentP(app(sk1,W_1786),sk2)
| ~ ssList(app(sk1,W_1786))
| ~ ssList(W_1786) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_390,c_389,c_9393]) ).
tff(c_25173,plain,
( segmentP(sk1,sk2)
| ~ ssList(app(sk1,nil))
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_842,c_25162]) ).
tff(c_25183,plain,
segmentP(sk1,sk2),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_391,c_842,c_25173]) ).
tff(c_25185,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2975,c_25183]) ).
tff(c_25186,plain,
sk1 != nil,
inference(splitRight,[status(thm)],[c_388]) ).
tff(c_25218,plain,
! [U_1803] :
( ( app(nil,U_1803) = U_1803 )
| ~ ssList(U_1803) ),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_25333,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[c_16,c_25218]) ).
tff(c_25187,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_388]) ).
tff(c_25201,plain,
app(nil,nil) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_25187,c_25187,c_389]) ).
tff(c_25336,plain,
sk1 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_25333,c_25201]) ).
tff(c_25338,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_25186,c_25336]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWC068-1 : TPTP v9.0.0. Released v2.4.0.
% 0.10/0.12 % 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
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Apr 9 01:24:29 EDT 2025
% 0.12/0.33 % CPUTime :
% 23.01/10.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.01/10.36
% 23.01/10.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------