%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWC418-1 : 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 : 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 09:20:25 PM UTC 2025
% Result : Unsatisfiable 161.32s 139.71s
% Output : CNFRefutation 161.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 27
% Syntax : Number of formulae : 182 ( 78 unt; 0 typ; 0 def)
% Number of atoms : 419 ( 147 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 477 ( 240 ~; 237 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 5 ( 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 : 119 ( 119 !; 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_56,axiom,
ssList(nil),
file(unknown,unknown) ).
tff(f_1649,axiom,
sk2 = sk4,
file(unknown,unknown) ).
tff(f_1650,axiom,
sk1 = sk3,
file(unknown,unknown) ).
tff(f_1670,axiom,
( ( nil = sk3 )
| ( nil != sk4 ) ),
file(unknown,unknown) ).
tff(f_1648,axiom,
ssList(sk4),
file(unknown,unknown) ).
tff(f_64,axiom,
! [U] : ssList(skaf82(U)),
file(unknown,unknown) ).
tff(f_543,axiom,
! [U] :
( ~ ssList(U)
| ( cons(skaf83(U),skaf82(U)) = U )
| ( nil = U ) ),
file(unknown,unknown) ).
tff(f_1647,axiom,
ssList(sk3),
file(unknown,unknown) ).
tff(f_334,axiom,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file(unknown,unknown) ).
tff(f_240,axiom,
! [U,V] :
( ~ ssList(U)
| duplicatefreeP(U)
| ssItem(V) ),
file(unknown,unknown) ).
tff(f_62,axiom,
! [U] : ssItem(skaf83(U)),
file(unknown,unknown) ).
tff(f_420,axiom,
! [U,V] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
file(unknown,unknown) ).
tff(f_492,axiom,
! [U] :
( ~ ssList(U)
| ( cons(hd(U),tl(U)) = U )
| ( nil = U ) ),
file(unknown,unknown) ).
tff(f_271,axiom,
! [U] :
( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) ),
file(unknown,unknown) ).
tff(f_456,axiom,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) ),
file(unknown,unknown) ).
tff(f_428,axiom,
! [U,V] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ),
file(unknown,unknown) ).
tff(f_342,axiom,
! [U,V] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file(unknown,unknown) ).
tff(f_1651,axiom,
neq(sk2,nil),
file(unknown,unknown) ).
tff(f_1705,axiom,
! [A,B,C,D] :
( ~ ssList(A)
| ( sk3 = A )
| ~ ssList(B)
| ~ ssList(C)
| ( tl(sk4) != B )
| ( app(B,C) != A )
| ~ ssItem(D)
| ( cons(D,nil) != C )
| ( hd(sk4) != D )
| ~ neq(nil,sk4)
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
file(unknown,unknown) ).
tff(f_278,axiom,
! [U] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) ),
file(unknown,unknown) ).
tff(f_1481,axiom,
! [W,U,X,Y,V] :
( ( app(app(U,cons(V,W)),cons(V,X)) != Y )
| ~ ssList(X)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(Y) ),
file(unknown,unknown) ).
tff(f_474,axiom,
! [U,V] :
( ~ ssItem(U)
| ~ ssItem(V)
| neq(V,U)
| ( V = U ) ),
file(unknown,unknown) ).
tff(f_250,axiom,
! [U] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file(unknown,unknown) ).
tff(f_1175,axiom,
! [U,V,W] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) ),
file(unknown,unknown) ).
tff(f_245,axiom,
! [U] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
file(unknown,unknown) ).
tff(f_1666,axiom,
! [A,B,C] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(app(C,cons(A,nil)),B) != sk1 ) ),
file(unknown,unknown) ).
tff(f_613,axiom,
! [U,V] :
( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) ),
file(unknown,unknown) ).
tff(c_16,plain,
ssList(nil),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_380,plain,
sk4 = sk2,
inference(cnfTransformation,[status(thm)],[f_1649]) ).
tff(c_382,plain,
sk3 = sk1,
inference(cnfTransformation,[status(thm)],[f_1650]) ).
tff(c_388,plain,
( ( sk4 != nil )
| ( sk3 = nil ) ),
inference(cnfTransformation,[status(thm)],[f_1670]) ).
tff(c_391,plain,
( ( sk4 != nil )
| ( sk1 = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_388]) ).
tff(c_393,plain,
( ( sk2 != nil )
| ( sk1 = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_391]) ).
tff(c_448,plain,
sk2 != nil,
inference(splitLeft,[status(thm)],[c_393]) ).
tff(c_378,plain,
ssList(sk4),
inference(cnfTransformation,[status(thm)],[f_1648]) ).
tff(c_397,plain,
ssList(sk2),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_378]) ).
tff(c_26,plain,
! [U_2] : ssList(skaf82(U_2)),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_87459,plain,
! [U_5056] :
( ( nil = U_5056 )
| ( cons(skaf83(U_5056),skaf82(U_5056)) = U_5056 )
| ~ ssList(U_5056) ),
inference(cnfTransformation,[status(thm)],[f_543]) ).
tff(c_376,plain,
ssList(sk3),
inference(cnfTransformation,[status(thm)],[f_1647]) ).
tff(c_398,plain,
ssList(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_376]) ).
tff(c_170,plain,
! [V_81,U_80] :
( ssList(app(V_81,U_80))
| ~ ssList(V_81)
| ~ ssList(U_80) ),
inference(cnfTransformation,[status(thm)],[f_334]) ).
tff(c_1205,plain,
! [V_449,U_450] :
( ssList(app(V_449,U_450))
| ~ ssList(V_449)
| ~ ssList(U_450) ),
inference(cnfTransformation,[status(thm)],[f_334]) ).
tff(c_144,plain,
! [V_67,U_66] :
( ssItem(V_67)
| duplicatefreeP(U_66)
| ~ ssList(U_66) ),
inference(cnfTransformation,[status(thm)],[f_240]) ).
tff(c_729,plain,
! [U_66] :
( duplicatefreeP(U_66)
| ~ ssList(U_66) ),
inference(splitLeft,[status(thm)],[c_144]) ).
tff(c_1249,plain,
! [V_449,U_450] :
( duplicatefreeP(app(V_449,U_450))
| ~ ssList(V_449)
| ~ ssList(U_450) ),
inference(resolution,[status(thm)],[c_1205,c_729]) ).
tff(c_24,plain,
! [U_1] : ssItem(skaf83(U_1)),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_2179,plain,
! [U_558] :
( ( nil = U_558 )
| ( cons(skaf83(U_558),skaf82(U_558)) = U_558 )
| ~ ssList(U_558) ),
inference(cnfTransformation,[status(thm)],[f_543]) ).
tff(c_192,plain,
! [U_93,V_94] :
( ( tl(cons(U_93,V_94)) = V_94 )
| ~ ssList(V_94)
| ~ ssItem(U_93) ),
inference(cnfTransformation,[status(thm)],[f_420]) ).
tff(c_2191,plain,
! [U_558] :
( ( tl(U_558) = skaf82(U_558) )
| ~ ssList(skaf82(U_558))
| ~ ssItem(skaf83(U_558))
| ( nil = U_558 )
| ~ ssList(U_558) ),
inference(superposition,[status(thm),theory(equality)],[c_2179,c_192]) ).
tff(c_15751,plain,
! [U_1447] :
( ( tl(U_1447) = skaf82(U_1447) )
| ( nil = U_1447 )
| ~ ssList(U_1447) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_2191]) ).
tff(c_15853,plain,
( ( tl(sk2) = skaf82(sk2) )
| ( sk2 = nil ) ),
inference(resolution,[status(thm)],[c_397,c_15751]) ).
tff(c_15895,plain,
tl(sk2) = skaf82(sk2),
inference(negUnitSimplification,[status(thm)],[c_448,c_15853]) ).
tff(c_208,plain,
! [U_108] :
( ( nil = U_108 )
| ( cons(hd(U_108),tl(U_108)) = U_108 )
| ~ ssList(U_108) ),
inference(cnfTransformation,[status(thm)],[f_492]) ).
tff(c_15934,plain,
( ( sk2 = nil )
| ( cons(hd(sk2),skaf82(sk2)) = sk2 )
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_15895,c_208]) ).
tff(c_15947,plain,
( ( sk2 = nil )
| ( cons(hd(sk2),skaf82(sk2)) = sk2 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_397,c_15934]) ).
tff(c_15948,plain,
cons(hd(sk2),skaf82(sk2)) = sk2,
inference(negUnitSimplification,[status(thm)],[c_448,c_15947]) ).
tff(c_154,plain,
! [U_72] :
( ( nil = U_72 )
| ssList(tl(U_72))
| ~ ssList(U_72) ),
inference(cnfTransformation,[status(thm)],[f_271]) ).
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_194,plain,
! [U_95,V_96] :
( ( hd(cons(U_95,V_96)) = U_95 )
| ~ ssList(V_96)
| ~ ssItem(U_95) ),
inference(cnfTransformation,[status(thm)],[f_428]) ).
tff(c_2188,plain,
! [U_558] :
( ( skaf83(U_558) = hd(U_558) )
| ~ ssList(skaf82(U_558))
| ~ ssItem(skaf83(U_558))
| ( nil = U_558 )
| ~ ssList(U_558) ),
inference(superposition,[status(thm),theory(equality)],[c_2179,c_194]) ).
tff(c_11378,plain,
! [U_1138] :
( ( skaf83(U_1138) = hd(U_1138) )
| ( nil = U_1138 )
| ~ ssList(U_1138) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_2188]) ).
tff(c_11474,plain,
( ( skaf83(sk2) = hd(sk2) )
| ( sk2 = nil ) ),
inference(resolution,[status(thm)],[c_397,c_11378]) ).
tff(c_11512,plain,
skaf83(sk2) = hd(sk2),
inference(negUnitSimplification,[status(thm)],[c_448,c_11474]) ).
tff(c_11530,plain,
ssItem(hd(sk2)),
inference(superposition,[status(thm),theory(equality)],[c_11512,c_24]) ).
tff(c_172,plain,
! [U_82,V_83] :
( ssList(cons(U_82,V_83))
| ~ ssList(V_83)
| ~ ssItem(U_82) ),
inference(cnfTransformation,[status(thm)],[f_342]) ).
tff(c_218,plain,
! [U_117] :
( ( nil = U_117 )
| ( cons(skaf83(U_117),skaf82(U_117)) = U_117 )
| ~ ssList(U_117) ),
inference(cnfTransformation,[status(thm)],[f_543]) ).
tff(c_11520,plain,
( ( sk2 = nil )
| ( cons(hd(sk2),skaf82(sk2)) = sk2 )
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_11512,c_218]) ).
tff(c_11534,plain,
( ( sk2 = nil )
| ( cons(hd(sk2),skaf82(sk2)) = sk2 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_397,c_11520]) ).
tff(c_11535,plain,
cons(hd(sk2),skaf82(sk2)) = sk2,
inference(negUnitSimplification,[status(thm)],[c_448,c_11534]) ).
tff(c_12155,plain,
( ( tl(sk2) = skaf82(sk2) )
| ~ ssList(skaf82(sk2))
| ~ ssItem(hd(sk2)) ),
inference(superposition,[status(thm),theory(equality)],[c_11535,c_192]) ).
tff(c_12219,plain,
tl(sk2) = skaf82(sk2),
inference(demodulation,[status(thm),theory(equality)],[c_11530,c_26,c_12155]) ).
tff(c_384,plain,
neq(sk2,nil),
inference(cnfTransformation,[status(thm)],[f_1651]) ).
tff(c_390,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| ~ ssItem(hd(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(tl(sk4))
| ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 )
| ~ ssList(app(tl(sk4),cons(hd(sk4),nil))) ),
inference(cnfTransformation,[status(thm)],[f_1705]) ).
tff(c_392,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| ~ ssItem(hd(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(tl(sk4))
| ( app(tl(sk4),cons(hd(sk4),nil)) = sk1 )
| ~ ssList(app(tl(sk4),cons(hd(sk4),nil))) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_390]) ).
tff(c_394,plain,
( ~ neq(sk2,nil)
| ~ neq(nil,sk2)
| ~ ssItem(hd(sk2))
| ~ ssList(cons(hd(sk2),nil))
| ~ ssList(tl(sk2))
| ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 )
| ~ ssList(app(tl(sk2),cons(hd(sk2),nil))) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_380,c_380,c_380,c_380,c_380,c_380,c_380,c_380,c_392]) ).
tff(c_396,plain,
( ~ neq(nil,sk2)
| ~ ssItem(hd(sk2))
| ~ ssList(cons(hd(sk2),nil))
| ~ ssList(tl(sk2))
| ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 )
| ~ ssList(app(tl(sk2),cons(hd(sk2),nil))) ),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_394]) ).
tff(c_9964,plain,
~ ssList(app(tl(sk2),cons(hd(sk2),nil))),
inference(splitLeft,[status(thm)],[c_396]) ).
tff(c_10104,plain,
( ~ ssList(tl(sk2))
| ~ ssList(cons(hd(sk2),nil)) ),
inference(resolution,[status(thm)],[c_170,c_9964]) ).
tff(c_13422,plain,
~ ssList(cons(hd(sk2),nil)),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_12219,c_10104]) ).
tff(c_13425,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sk2)) ),
inference(resolution,[status(thm)],[c_172,c_13422]) ).
tff(c_13429,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_11530,c_16,c_13425]) ).
tff(c_13430,plain,
( ~ ssList(tl(sk2))
| ~ ssList(cons(hd(sk2),nil))
| ~ ssItem(hd(sk2))
| ~ neq(nil,sk2)
| ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 ) ),
inference(splitRight,[status(thm)],[c_396]) ).
tff(c_13636,plain,
~ neq(nil,sk2),
inference(splitLeft,[status(thm)],[c_13430]) ).
tff(c_13642,plain,
( ( sk2 = nil )
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_200,c_13636]) ).
tff(c_13648,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_397,c_16,c_13642]) ).
tff(c_13650,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_448,c_13648]) ).
tff(c_13651,plain,
( ~ ssItem(hd(sk2))
| ~ ssList(cons(hd(sk2),nil))
| ~ ssList(tl(sk2))
| ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 ) ),
inference(splitRight,[status(thm)],[c_13430]) ).
tff(c_13778,plain,
~ ssList(tl(sk2)),
inference(splitLeft,[status(thm)],[c_13651]) ).
tff(c_13781,plain,
( ( sk2 = nil )
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_154,c_13778]) ).
tff(c_13784,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_397,c_13781]) ).
tff(c_13786,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_448,c_13784]) ).
tff(c_13788,plain,
ssList(tl(sk2)),
inference(splitRight,[status(thm)],[c_13651]) ).
tff(c_156,plain,
! [U_73] :
( ( nil = U_73 )
| ssItem(hd(U_73))
| ~ ssList(U_73) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_13787,plain,
( ~ ssList(cons(hd(sk2),nil))
| ~ ssItem(hd(sk2))
| ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 ) ),
inference(splitRight,[status(thm)],[c_13651]) ).
tff(c_14144,plain,
~ ssItem(hd(sk2)),
inference(splitLeft,[status(thm)],[c_13787]) ).
tff(c_14147,plain,
( ( sk2 = nil )
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_156,c_14144]) ).
tff(c_14150,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_397,c_14147]) ).
tff(c_14152,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_448,c_14150]) ).
tff(c_14154,plain,
ssItem(hd(sk2)),
inference(splitRight,[status(thm)],[c_13787]) ).
tff(c_14153,plain,
( ~ ssList(cons(hd(sk2),nil))
| ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 ) ),
inference(splitRight,[status(thm)],[c_13787]) ).
tff(c_14315,plain,
~ ssList(cons(hd(sk2),nil)),
inference(splitLeft,[status(thm)],[c_14153]) ).
tff(c_14318,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sk2)) ),
inference(resolution,[status(thm)],[c_172,c_14315]) ).
tff(c_14322,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_14154,c_16,c_14318]) ).
tff(c_14323,plain,
app(tl(sk2),cons(hd(sk2),nil)) = sk1,
inference(splitRight,[status(thm)],[c_14153]) ).
tff(c_358,plain,
! [U_288,V_291,W_287,X_289] :
( ~ ssList(app(app(U_288,cons(V_291,W_287)),cons(V_291,X_289)))
| ~ duplicatefreeP(app(app(U_288,cons(V_291,W_287)),cons(V_291,X_289)))
| ~ ssItem(V_291)
| ~ ssList(U_288)
| ~ ssList(W_287)
| ~ ssList(X_289) ),
inference(cnfTransformation,[status(thm)],[f_1481]) ).
tff(c_14421,plain,
! [X_289] :
( ~ ssList(app(sk1,cons(hd(sk2),X_289)))
| ~ duplicatefreeP(app(app(tl(sk2),cons(hd(sk2),nil)),cons(hd(sk2),X_289)))
| ~ ssItem(hd(sk2))
| ~ ssList(tl(sk2))
| ~ ssList(nil)
| ~ ssList(X_289) ),
inference(superposition,[status(thm),theory(equality)],[c_14323,c_358]) ).
tff(c_85254,plain,
! [X_4839] :
( ~ ssList(app(sk1,cons(hd(sk2),X_4839)))
| ~ duplicatefreeP(app(sk1,cons(hd(sk2),X_4839)))
| ~ ssList(X_4839) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_13788,c_14154,c_14323,c_14421]) ).
tff(c_85265,plain,
( ~ ssList(app(sk1,sk2))
| ~ duplicatefreeP(app(sk1,cons(hd(sk2),tl(sk2))))
| ~ ssList(tl(sk2))
| ( sk2 = nil )
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_208,c_85254]) ).
tff(c_85274,plain,
( ~ ssList(app(sk1,sk2))
| ~ duplicatefreeP(app(sk1,sk2))
| ( sk2 = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_397,c_26,c_15895,c_15948,c_15895,c_85265]) ).
tff(c_85275,plain,
( ~ ssList(app(sk1,sk2))
| ~ duplicatefreeP(app(sk1,sk2)) ),
inference(negUnitSimplification,[status(thm)],[c_448,c_85274]) ).
tff(c_85279,plain,
~ duplicatefreeP(app(sk1,sk2)),
inference(splitLeft,[status(thm)],[c_85275]) ).
tff(c_85282,plain,
( ~ ssList(sk1)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_1249,c_85279]) ).
tff(c_85286,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_397,c_398,c_85282]) ).
tff(c_85287,plain,
~ ssList(app(sk1,sk2)),
inference(splitRight,[status(thm)],[c_85275]) ).
tff(c_85421,plain,
( ~ ssList(sk1)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_170,c_85287]) ).
tff(c_85425,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_397,c_398,c_85421]) ).
tff(c_85426,plain,
! [V_67] : ssItem(V_67),
inference(splitRight,[status(thm)],[c_144]) ).
tff(c_86762,plain,
! [U_93,V_94] :
( ( tl(cons(U_93,V_94)) = V_94 )
| ~ ssList(V_94) ),
inference(demodulation,[status(thm),theory(equality)],[c_85426,c_192]) ).
tff(c_87468,plain,
! [U_5056] :
( ( tl(U_5056) = skaf82(U_5056) )
| ~ ssList(skaf82(U_5056))
| ( nil = U_5056 )
| ~ ssList(U_5056) ),
inference(superposition,[status(thm),theory(equality)],[c_87459,c_86762]) ).
tff(c_101023,plain,
! [U_5823] :
( ( tl(U_5823) = skaf82(U_5823) )
| ( nil = U_5823 )
| ~ ssList(U_5823) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_87468]) ).
tff(c_101125,plain,
( ( tl(sk2) = skaf82(sk2) )
| ( sk2 = nil ) ),
inference(resolution,[status(thm)],[c_397,c_101023]) ).
tff(c_101169,plain,
tl(sk2) = skaf82(sk2),
inference(negUnitSimplification,[status(thm)],[c_448,c_101125]) ).
tff(c_101207,plain,
( ( sk2 = nil )
| ( cons(hd(sk2),skaf82(sk2)) = sk2 )
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_101169,c_208]) ).
tff(c_101217,plain,
( ( sk2 = nil )
| ( cons(hd(sk2),skaf82(sk2)) = sk2 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_397,c_101207]) ).
tff(c_101218,plain,
cons(hd(sk2),skaf82(sk2)) = sk2,
inference(negUnitSimplification,[status(thm)],[c_448,c_101217]) ).
tff(c_204,plain,
! [V_105,U_104] :
( ( V_105 = U_104 )
| neq(V_105,U_104)
| ~ ssItem(V_105)
| ~ ssItem(U_104) ),
inference(cnfTransformation,[status(thm)],[f_474]) ).
tff(c_86917,plain,
! [V_105,U_104] :
( ( V_105 = U_104 )
| neq(V_105,U_104) ),
inference(demodulation,[status(thm),theory(equality)],[c_85426,c_85426,c_204]) ).
tff(c_86191,plain,
! [U_82,V_83] :
( ssList(cons(U_82,V_83))
| ~ ssList(V_83) ),
inference(demodulation,[status(thm),theory(equality)],[c_85426,c_172]) ).
tff(c_97094,plain,
! [U_5611] :
( ( tl(U_5611) = skaf82(U_5611) )
| ( nil = U_5611 )
| ~ ssList(U_5611) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_87468]) ).
tff(c_97190,plain,
( ( tl(sk2) = skaf82(sk2) )
| ( sk2 = nil ) ),
inference(resolution,[status(thm)],[c_397,c_97094]) ).
tff(c_97228,plain,
tl(sk2) = skaf82(sk2),
inference(negUnitSimplification,[status(thm)],[c_448,c_97190]) ).
tff(c_94701,plain,
( ~ neq(nil,sk2)
| ~ ssList(cons(hd(sk2),nil))
| ~ ssList(tl(sk2))
| ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 )
| ~ ssList(app(tl(sk2),cons(hd(sk2),nil))) ),
inference(demodulation,[status(thm),theory(equality)],[c_85426,c_396]) ).
tff(c_94702,plain,
~ ssList(app(tl(sk2),cons(hd(sk2),nil))),
inference(splitLeft,[status(thm)],[c_94701]) ).
tff(c_94852,plain,
( ~ ssList(tl(sk2))
| ~ ssList(cons(hd(sk2),nil)) ),
inference(resolution,[status(thm)],[c_170,c_94702]) ).
tff(c_97928,plain,
~ ssList(cons(hd(sk2),nil)),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_97228,c_94852]) ).
tff(c_97931,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[c_86191,c_97928]) ).
tff(c_97935,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_97931]) ).
tff(c_97936,plain,
( ~ ssList(tl(sk2))
| ~ ssList(cons(hd(sk2),nil))
| ~ neq(nil,sk2)
| ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 ) ),
inference(splitRight,[status(thm)],[c_94701]) ).
tff(c_98151,plain,
~ neq(nil,sk2),
inference(splitLeft,[status(thm)],[c_97936]) ).
tff(c_98154,plain,
sk2 = nil,
inference(resolution,[status(thm)],[c_86917,c_98151]) ).
tff(c_98158,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_448,c_98154]) ).
tff(c_98159,plain,
( ~ ssList(cons(hd(sk2),nil))
| ~ ssList(tl(sk2))
| ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 ) ),
inference(splitRight,[status(thm)],[c_97936]) ).
tff(c_98298,plain,
~ ssList(tl(sk2)),
inference(splitLeft,[status(thm)],[c_98159]) ).
tff(c_98301,plain,
( ( sk2 = nil )
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_154,c_98298]) ).
tff(c_98304,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_397,c_98301]) ).
tff(c_98306,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_448,c_98304]) ).
tff(c_98308,plain,
ssList(tl(sk2)),
inference(splitRight,[status(thm)],[c_98159]) ).
tff(c_148,plain,
! [U_69] :
( ( app(nil,U_69) = U_69 )
| ~ ssList(U_69) ),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_98375,plain,
app(nil,tl(sk2)) = tl(sk2),
inference(resolution,[status(thm)],[c_98308,c_148]) ).
tff(c_314,plain,
! [U_230,V_231,W_232] :
( ( cons(U_230,app(V_231,W_232)) = app(cons(U_230,V_231),W_232) )
| ~ ssList(W_232)
| ~ ssList(V_231)
| ~ ssItem(U_230) ),
inference(cnfTransformation,[status(thm)],[f_1175]) ).
tff(c_91374,plain,
! [U_230,V_231,W_232] :
( ( cons(U_230,app(V_231,W_232)) = app(cons(U_230,V_231),W_232) )
| ~ ssList(W_232)
| ~ ssList(V_231) ),
inference(demodulation,[status(thm),theory(equality)],[c_85426,c_314]) ).
tff(c_98530,plain,
! [U_230] :
( ( app(cons(U_230,nil),tl(sk2)) = cons(U_230,tl(sk2)) )
| ~ ssList(tl(sk2))
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_98375,c_91374]) ).
tff(c_98567,plain,
! [U_230] : ( app(cons(U_230,nil),tl(sk2)) = cons(U_230,tl(sk2)) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_98308,c_98530]) ).
tff(c_135733,plain,
! [U_230] : ( app(cons(U_230,nil),skaf82(sk2)) = cons(U_230,skaf82(sk2)) ),
inference(demodulation,[status(thm),theory(equality)],[c_101169,c_101169,c_98567]) ).
tff(c_603,plain,
! [U_401] :
( ( app(U_401,nil) = U_401 )
| ~ ssList(U_401) ),
inference(cnfTransformation,[status(thm)],[f_245]) ).
tff(c_724,plain,
app(sk1,nil) = sk1,
inference(resolution,[status(thm)],[c_398,c_603]) ).
tff(c_464,plain,
! [U_394] :
( ( app(nil,U_394) = U_394 )
| ~ ssList(U_394) ),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_582,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[c_16,c_464]) ).
tff(c_91375,plain,
! [U_5315,V_5316,W_5317] :
( ( cons(U_5315,app(V_5316,W_5317)) = app(cons(U_5315,V_5316),W_5317) )
| ~ ssList(W_5317)
| ~ ssList(V_5316) ),
inference(demodulation,[status(thm),theory(equality)],[c_85426,c_314]) ).
tff(c_91558,plain,
! [U_5315] :
( ( app(cons(U_5315,nil),nil) = cons(U_5315,nil) )
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_582,c_91375]) ).
tff(c_91660,plain,
! [U_5315] : ( app(cons(U_5315,nil),nil) = cons(U_5315,nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_91558]) ).
tff(c_173618,plain,
! [U_9291,V_9292,W_9293] :
( ssList(app(cons(U_9291,V_9292),W_9293))
| ~ ssList(app(V_9292,W_9293))
| ~ ssList(W_9293)
| ~ ssList(V_9292) ),
inference(superposition,[status(thm),theory(equality)],[c_91375,c_86191]) ).
tff(c_174130,plain,
! [U_5315] :
( ssList(cons(U_5315,nil))
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_91660,c_173618]) ).
tff(c_175074,plain,
! [U_9295] : ssList(cons(U_9295,nil)),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_582,c_174130]) ).
tff(c_175741,plain,
! [U_9295] : ( app(nil,cons(U_9295,nil)) = cons(U_9295,nil) ),
inference(resolution,[status(thm)],[c_175074,c_148]) ).
tff(c_98307,plain,
( ~ ssList(cons(hd(sk2),nil))
| ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 ) ),
inference(splitRight,[status(thm)],[c_98159]) ).
tff(c_98615,plain,
~ ssList(cons(hd(sk2),nil)),
inference(splitLeft,[status(thm)],[c_98307]) ).
tff(c_98618,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[c_86191,c_98615]) ).
tff(c_98622,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_98618]) ).
tff(c_98623,plain,
app(tl(sk2),cons(hd(sk2),nil)) = sk1,
inference(splitRight,[status(thm)],[c_98307]) ).
tff(c_386,plain,
! [C_329,A_327,B_328] :
( ( app(app(C_329,cons(A_327,nil)),B_328) != sk1 )
| ( app(app(B_328,cons(A_327,nil)),C_329) != sk2 )
| ~ ssList(C_329)
| ~ ssList(B_328)
| ~ ssItem(A_327) ),
inference(cnfTransformation,[status(thm)],[f_1666]) ).
tff(c_94369,plain,
! [C_329,A_327,B_328] :
( ( app(app(C_329,cons(A_327,nil)),B_328) != sk1 )
| ( app(app(B_328,cons(A_327,nil)),C_329) != sk2 )
| ~ ssList(C_329)
| ~ ssList(B_328) ),
inference(demodulation,[status(thm),theory(equality)],[c_85426,c_386]) ).
tff(c_98968,plain,
! [B_328] :
( ( app(sk1,B_328) != sk1 )
| ( app(app(B_328,cons(hd(sk2),nil)),tl(sk2)) != sk2 )
| ~ ssList(tl(sk2))
| ~ ssList(B_328) ),
inference(superposition,[status(thm),theory(equality)],[c_98623,c_94369]) ).
tff(c_99032,plain,
! [B_328] :
( ( app(sk1,B_328) != sk1 )
| ( app(app(B_328,cons(hd(sk2),nil)),tl(sk2)) != sk2 )
| ~ ssList(B_328) ),
inference(demodulation,[status(thm),theory(equality)],[c_98308,c_98968]) ).
tff(c_219526,plain,
! [B_10095] :
( ( app(sk1,B_10095) != sk1 )
| ( app(app(B_10095,cons(hd(sk2),nil)),skaf82(sk2)) != sk2 )
| ~ ssList(B_10095) ),
inference(demodulation,[status(thm),theory(equality)],[c_101169,c_99032]) ).
tff(c_219530,plain,
( ( app(sk1,nil) != sk1 )
| ( app(cons(hd(sk2),nil),skaf82(sk2)) != sk2 )
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_175741,c_219526]) ).
tff(c_219563,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_101218,c_135733,c_724,c_219530]) ).
tff(c_219565,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_393]) ).
tff(c_219573,plain,
neq(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_219565,c_384]) ).
tff(c_219596,plain,
! [V_10106] :
( ~ ssList(V_10106)
| ~ neq(V_10106,V_10106) ),
inference(cnfTransformation,[status(thm)],[f_613]) ).
tff(c_219599,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[c_219573,c_219596]) ).
tff(c_219603,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_219599]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWC418-1 : TPTP v9.0.0. Released v2.4.0.
% 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
% 0.13/0.34 % 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 : Wed Apr 9 02:28:47 EDT 2025
% 0.13/0.34 % CPUTime :
% 161.32/139.71 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 161.32/139.73
% 161.32/139.73 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------