TSTP Solution File: SWC253-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWC253-1 : TPTP v8.1.2. 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 : n016.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 : Tue Aug 22 11:01:47 EDT 2023
% Result : Unsatisfiable 188.05s 166.67s
% Output : CNFRefutation 188.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 108
% Syntax : Number of formulae : 355 ( 131 unt; 72 typ; 0 def)
% Number of atoms : 630 ( 222 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 695 ( 348 ~; 347 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 82 ( 65 >; 17 *; 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 : 148 (; 148 !; 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_250,axiom,
! [U] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file(unknown,unknown) ).
tff(f_975,axiom,
! [U,V,W] :
( ( app(U,V) != W )
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| frontsegP(W,U) ),
file(unknown,unknown) ).
tff(f_961,axiom,
! [U,V,W] :
( ( app(U,V) != W )
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| rearsegP(W,V) ),
file(unknown,unknown) ).
tff(f_1649,axiom,
sk2 = sk4,
file(unknown,unknown) ).
tff(f_1648,axiom,
ssList(sk4),
file(unknown,unknown) ).
tff(f_62,axiom,
! [U] : ssItem(skaf83(U)),
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_428,axiom,
! [U,V] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ),
file(unknown,unknown) ).
tff(f_245,axiom,
! [U] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
file(unknown,unknown) ).
tff(f_770,axiom,
! [U,V] :
( ~ rearsegP(U,V)
| ~ rearsegP(V,U)
| ~ ssList(U)
| ~ ssList(V)
| ( V = U ) ),
file(unknown,unknown) ).
tff(f_456,axiom,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) ),
file(unknown,unknown) ).
tff(f_446,axiom,
! [U,V] :
( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) ),
file(unknown,unknown) ).
tff(f_420,axiom,
! [U,V] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
file(unknown,unknown) ).
tff(f_271,axiom,
! [U] :
( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) ),
file(unknown,unknown) ).
tff(f_334,axiom,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file(unknown,unknown) ).
tff(f_1653,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file(unknown,unknown) ).
tff(f_1705,axiom,
( ~ singletonP(sk1)
| ~ neq(sk4,nil) ),
file(unknown,unknown) ).
tff(f_1650,axiom,
sk1 = sk3,
file(unknown,unknown) ).
tff(f_1647,axiom,
ssList(sk3),
file(unknown,unknown) ).
tff(f_1700,axiom,
! [A,B] :
( ~ ssList(A)
| ( sk4 = A )
| ~ ssList(B)
| ( tl(sk4) != B )
| ( app(sk3,B) != A )
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
file(unknown,unknown) ).
tff(f_702,axiom,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) ),
file(unknown,unknown) ).
tff(f_784,axiom,
! [U,V] :
( ~ frontsegP(U,V)
| ~ frontsegP(V,U)
| ~ ssList(U)
| ~ ssList(V)
| ( V = U ) ),
file(unknown,unknown) ).
tff(f_278,axiom,
! [U] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) ),
file(unknown,unknown) ).
tff(f_898,axiom,
! [U,V,W] :
( ( U != V )
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U)
| memberP(cons(V,W),U) ),
file(unknown,unknown) ).
tff(f_912,axiom,
! [U,V,W] :
( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssItem(W)
| ~ ssItem(V)
| memberP(cons(W,U),V) ),
file(unknown,unknown) ).
tff(f_342,axiom,
! [U,V] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file(unknown,unknown) ).
tff(f_624,axiom,
! [U,V] :
( ( cons(U,nil) != V )
| ~ ssItem(U)
| ~ ssList(V)
| singletonP(V) ),
file(unknown,unknown) ).
tff(f_830,axiom,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ),
file(unknown,unknown) ).
tff(f_1079,axiom,
! [U,V,W] :
( ( app(U,V) != app(W,V) )
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( U = W ) ),
file(unknown,unknown) ).
tff(f_658,axiom,
! [U,V] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) ),
file(unknown,unknown) ).
tff(f_492,axiom,
! [U] :
( ~ ssList(U)
| ( cons(hd(U),tl(U)) = U )
| ( nil = U ) ),
file(unknown,unknown) ).
tff(f_940,axiom,
! [U,V,W] :
( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssItem(V)
| memberP(app(W,U),V) ),
file(unknown,unknown) ).
tff(f_1065,axiom,
! [U,V,W] :
( ( app(U,V) != app(U,W) )
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| ( V = W ) ),
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_472,plain,
! [U_392] :
( ( app(nil,U_392) = U_392 )
| ~ ssList(U_392) ),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_590,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[c_16,c_472]) ).
tff(c_3893,plain,
! [U_666,V_667] :
( frontsegP(app(U_666,V_667),U_666)
| ~ ssList(app(U_666,V_667))
| ~ ssList(U_666)
| ~ ssList(V_667) ),
inference(cnfTransformation,[status(thm)],[f_975]) ).
tff(c_4042,plain,
( frontsegP(nil,nil)
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_590,c_3893]) ).
tff(c_4139,plain,
frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_590,c_4042]) ).
tff(c_3630,plain,
! [U_664,V_665] :
( rearsegP(app(U_664,V_665),V_665)
| ~ ssList(app(U_664,V_665))
| ~ ssList(V_665)
| ~ ssList(U_664) ),
inference(cnfTransformation,[status(thm)],[f_961]) ).
tff(c_3779,plain,
( rearsegP(nil,nil)
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_590,c_3630]) ).
tff(c_3876,plain,
rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_590,c_3779]) ).
tff(c_380,plain,
sk4 = sk2,
inference(cnfTransformation,[status(thm)],[f_1649]) ).
tff(c_378,plain,
ssList(sk4),
inference(cnfTransformation,[status(thm)],[f_1648]) ).
tff(c_405,plain,
ssList(sk2),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_378]) ).
tff(c_24,plain,
! [U_1] : ssItem(skaf83(U_1)),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_26,plain,
! [U_2] : ssList(skaf82(U_2)),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_2503,plain,
! [U_556] :
( ( nil = U_556 )
| ( cons(skaf83(U_556),skaf82(U_556)) = U_556 )
| ~ ssList(U_556) ),
inference(cnfTransformation,[status(thm)],[f_543]) ).
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_2515,plain,
! [U_556] :
( ( skaf83(U_556) = hd(U_556) )
| ~ ssList(skaf82(U_556))
| ~ ssItem(skaf83(U_556))
| ( nil = U_556 )
| ~ ssList(U_556) ),
inference(superposition,[status(thm),theory(equality)],[c_2503,c_194]) ).
tff(c_185673,plain,
! [U_7561] :
( ( skaf83(U_7561) = hd(U_7561) )
| ( nil = U_7561 )
| ~ ssList(U_7561) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_2515]) ).
tff(c_185806,plain,
( ( skaf83(sk2) = hd(sk2) )
| ( sk2 = nil ) ),
inference(resolution,[status(thm)],[c_405,c_185673]) ).
tff(c_185807,plain,
sk2 = nil,
inference(splitLeft,[status(thm)],[c_185806]) ).
tff(c_742,plain,
! [U_408] :
( ( app(U_408,nil) = U_408 )
| ~ ssList(U_408) ),
inference(cnfTransformation,[status(thm)],[f_245]) ).
tff(c_862,plain,
app(sk2,nil) = sk2,
inference(resolution,[status(thm)],[c_405,c_742]) ).
tff(c_3767,plain,
( rearsegP(sk2,nil)
| ~ ssList(app(sk2,nil))
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_862,c_3630]) ).
tff(c_3868,plain,
rearsegP(sk2,nil),
inference(demodulation,[status(thm),theory(equality)],[c_405,c_16,c_405,c_862,c_3767]) ).
tff(c_256,plain,
! [V_155,U_154] :
( ( V_155 = U_154 )
| ~ ssList(V_155)
| ~ ssList(U_154)
| ~ rearsegP(V_155,U_154)
| ~ rearsegP(U_154,V_155) ),
inference(cnfTransformation,[status(thm)],[f_770]) ).
tff(c_3878,plain,
( ( sk2 = nil )
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ rearsegP(nil,sk2) ),
inference(resolution,[status(thm)],[c_3868,c_256]) ).
tff(c_3881,plain,
( ( sk2 = nil )
| ~ rearsegP(nil,sk2) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_405,c_3878]) ).
tff(c_182132,plain,
~ rearsegP(nil,sk2),
inference(splitLeft,[status(thm)],[c_3881]) ).
tff(c_185810,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_185807,c_182132]) ).
tff(c_185862,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3876,c_185810]) ).
tff(c_185864,plain,
sk2 != nil,
inference(splitRight,[status(thm)],[c_185806]) ).
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_185863,plain,
skaf83(sk2) = hd(sk2),
inference(splitRight,[status(thm)],[c_185806]) ).
tff(c_185951,plain,
ssItem(hd(sk2)),
inference(superposition,[status(thm),theory(equality)],[c_185863,c_24]) ).
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_185947,plain,
( ( sk2 = nil )
| ( cons(hd(sk2),skaf82(sk2)) = sk2 )
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_185863,c_218]) ).
tff(c_185955,plain,
( ( sk2 = nil )
| ( cons(hd(sk2),skaf82(sk2)) = sk2 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_405,c_185947]) ).
tff(c_185956,plain,
cons(hd(sk2),skaf82(sk2)) = sk2,
inference(negUnitSimplification,[status(thm)],[c_185864,c_185955]) ).
tff(c_983,plain,
! [V_442,U_443] :
( ~ ssList(V_442)
| ~ ssItem(U_443)
| ( cons(U_443,V_442) != V_442 ) ),
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_186275,plain,
! [U_7579,U_7580] :
( ~ ssItem(U_7579)
| ( cons(U_7579,skaf82(U_7580)) != skaf82(U_7580) ) ),
inference(resolution,[status(thm)],[c_26,c_983]) ).
tff(c_186278,plain,
( ~ ssItem(hd(sk2))
| ( skaf82(sk2) != sk2 ) ),
inference(superposition,[status(thm),theory(equality)],[c_185956,c_186275]) ).
tff(c_186283,plain,
skaf82(sk2) != sk2,
inference(demodulation,[status(thm),theory(equality)],[c_185951,c_186278]) ).
tff(c_583,plain,
! [U_2] : ( app(nil,skaf82(U_2)) = skaf82(U_2) ),
inference(resolution,[status(thm)],[c_26,c_472]) ).
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_186150,plain,
( ( tl(sk2) = skaf82(sk2) )
| ~ ssList(skaf82(sk2))
| ~ ssItem(hd(sk2)) ),
inference(superposition,[status(thm),theory(equality)],[c_185956,c_192]) ).
tff(c_186212,plain,
tl(sk2) = skaf82(sk2),
inference(demodulation,[status(thm),theory(equality)],[c_185951,c_26,c_186150]) ).
tff(c_154,plain,
! [U_72] :
( ( nil = U_72 )
| ssList(tl(U_72))
| ~ ssList(U_72) ),
inference(cnfTransformation,[status(thm)],[f_271]) ).
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_384,plain,
neq(sk2,nil),
inference(cnfTransformation,[status(thm)],[f_1653]) ).
tff(c_394,plain,
( ~ neq(sk4,nil)
| ~ singletonP(sk1) ),
inference(cnfTransformation,[status(thm)],[f_1705]) ).
tff(c_399,plain,
( ~ neq(sk2,nil)
| ~ singletonP(sk1) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_394]) ).
tff(c_402,plain,
~ singletonP(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_399]) ).
tff(c_382,plain,
sk3 = sk1,
inference(cnfTransformation,[status(thm)],[f_1650]) ).
tff(c_376,plain,
ssList(sk3),
inference(cnfTransformation,[status(thm)],[f_1647]) ).
tff(c_406,plain,
ssList(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_376]) ).
tff(c_592,plain,
app(nil,sk1) = sk1,
inference(resolution,[status(thm)],[c_406,c_472]) ).
tff(c_4036,plain,
( frontsegP(sk1,nil)
| ~ ssList(app(nil,sk1))
| ~ ssList(nil)
| ~ ssList(sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_592,c_3893]) ).
tff(c_4135,plain,
frontsegP(sk1,nil),
inference(demodulation,[status(thm),theory(equality)],[c_406,c_16,c_406,c_592,c_4036]) ).
tff(c_392,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| ~ ssList(tl(sk4))
| ( app(sk3,tl(sk4)) = sk4 )
| ~ ssList(app(sk3,tl(sk4))) ),
inference(cnfTransformation,[status(thm)],[f_1700]) ).
tff(c_398,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| ~ ssList(tl(sk4))
| ( app(sk1,tl(sk4)) = sk4 )
| ~ ssList(app(sk1,tl(sk4))) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_382,c_392]) ).
tff(c_400,plain,
( ~ neq(sk2,nil)
| ~ neq(nil,sk2)
| ~ ssList(tl(sk2))
| ( app(sk1,tl(sk2)) = sk2 )
| ~ ssList(app(sk1,tl(sk2))) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_380,c_380,c_380,c_380,c_380,c_398]) ).
tff(c_404,plain,
( ~ neq(nil,sk2)
| ~ ssList(tl(sk2))
| ( app(sk1,tl(sk2)) = sk2 )
| ~ ssList(app(sk1,tl(sk2))) ),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_400]) ).
tff(c_7476,plain,
~ ssList(app(sk1,tl(sk2))),
inference(splitLeft,[status(thm)],[c_404]) ).
tff(c_7479,plain,
( ~ ssList(sk1)
| ~ ssList(tl(sk2)) ),
inference(resolution,[status(thm)],[c_170,c_7476]) ).
tff(c_7482,plain,
~ ssList(tl(sk2)),
inference(demodulation,[status(thm),theory(equality)],[c_406,c_7479]) ).
tff(c_7485,plain,
( ( sk2 = nil )
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_154,c_7482]) ).
tff(c_7488,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_7485]) ).
tff(c_7070,plain,
~ rearsegP(nil,sk2),
inference(splitLeft,[status(thm)],[c_3881]) ).
tff(c_7491,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_7488,c_7070]) ).
tff(c_7543,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3876,c_7491]) ).
tff(c_7544,plain,
( ~ ssList(tl(sk2))
| ~ neq(nil,sk2)
| ( app(sk1,tl(sk2)) = sk2 ) ),
inference(splitRight,[status(thm)],[c_404]) ).
tff(c_7697,plain,
~ neq(nil,sk2),
inference(splitLeft,[status(thm)],[c_7544]) ).
tff(c_7703,plain,
( ( sk2 = nil )
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_200,c_7697]) ).
tff(c_7707,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_16,c_7703]) ).
tff(c_7711,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_7707,c_7070]) ).
tff(c_7763,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3876,c_7711]) ).
tff(c_7764,plain,
( ~ ssList(tl(sk2))
| ( app(sk1,tl(sk2)) = sk2 ) ),
inference(splitRight,[status(thm)],[c_7544]) ).
tff(c_7797,plain,
~ ssList(tl(sk2)),
inference(splitLeft,[status(thm)],[c_7764]) ).
tff(c_7800,plain,
( ( sk2 = nil )
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_154,c_7797]) ).
tff(c_7803,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_7800]) ).
tff(c_7808,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_7803,c_7070]) ).
tff(c_7860,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3876,c_7808]) ).
tff(c_7862,plain,
ssList(tl(sk2)),
inference(splitRight,[status(thm)],[c_7764]) ).
tff(c_7861,plain,
app(sk1,tl(sk2)) = sk2,
inference(splitRight,[status(thm)],[c_7764]) ).
tff(c_246,plain,
! [V_145,U_144] :
( ( hd(app(V_145,U_144)) = hd(V_145) )
| ( nil = V_145 )
| ~ ssList(V_145)
| ~ ssList(U_144) ),
inference(cnfTransformation,[status(thm)],[f_702]) ).
tff(c_8213,plain,
( ( hd(sk2) = hd(sk1) )
| ( sk1 = nil )
| ~ ssList(sk1)
| ~ ssList(tl(sk2)) ),
inference(superposition,[status(thm),theory(equality)],[c_7861,c_246]) ).
tff(c_8238,plain,
( ( hd(sk2) = hd(sk1) )
| ( sk1 = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_7862,c_406,c_8213]) ).
tff(c_8554,plain,
sk1 = nil,
inference(splitLeft,[status(thm)],[c_8238]) ).
tff(c_258,plain,
! [V_157,U_156] :
( ( V_157 = U_156 )
| ~ ssList(V_157)
| ~ ssList(U_156)
| ~ frontsegP(V_157,U_156)
| ~ frontsegP(U_156,V_157) ),
inference(cnfTransformation,[status(thm)],[f_784]) ).
tff(c_4172,plain,
( ( sk1 = nil )
| ~ ssList(sk1)
| ~ ssList(nil)
| ~ frontsegP(nil,sk1) ),
inference(resolution,[status(thm)],[c_4135,c_258]) ).
tff(c_4175,plain,
( ( sk1 = nil )
| ~ frontsegP(nil,sk1) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_406,c_4172]) ).
tff(c_7015,plain,
~ frontsegP(nil,sk1),
inference(splitLeft,[status(thm)],[c_4175]) ).
tff(c_8622,plain,
~ frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_8554,c_7015]) ).
tff(c_8674,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4139,c_8622]) ).
tff(c_8675,plain,
hd(sk2) = hd(sk1),
inference(splitRight,[status(thm)],[c_8238]) ).
tff(c_156,plain,
! [U_73] :
( ( nil = U_73 )
| ssItem(hd(U_73))
| ~ ssList(U_73) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_8695,plain,
( ( sk2 = nil )
| ssItem(hd(sk1))
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_8675,c_156]) ).
tff(c_8709,plain,
( ( sk2 = nil )
| ssItem(hd(sk1)) ),
inference(demodulation,[status(thm),theory(equality)],[c_405,c_8695]) ).
tff(c_8775,plain,
ssItem(hd(sk1)),
inference(splitLeft,[status(thm)],[c_8709]) ).
tff(c_11058,plain,
! [U_1003] :
( ( skaf83(U_1003) = hd(U_1003) )
| ( nil = U_1003 )
| ~ ssList(U_1003) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_2515]) ).
tff(c_11157,plain,
( ( skaf83(sk2) = hd(sk2) )
| ( sk2 = nil ) ),
inference(resolution,[status(thm)],[c_405,c_11058]) ).
tff(c_11195,plain,
( ( skaf83(sk2) = hd(sk1) )
| ( sk2 = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8675,c_11157]) ).
tff(c_11222,plain,
sk2 = nil,
inference(splitLeft,[status(thm)],[c_11195]) ).
tff(c_288,plain,
! [U_192,V_193] :
( frontsegP(app(U_192,V_193),U_192)
| ~ ssList(app(U_192,V_193))
| ~ ssList(U_192)
| ~ ssList(V_193) ),
inference(cnfTransformation,[status(thm)],[f_975]) ).
tff(c_8207,plain,
( frontsegP(sk2,sk1)
| ~ ssList(app(sk1,tl(sk2)))
| ~ ssList(sk1)
| ~ ssList(tl(sk2)) ),
inference(superposition,[status(thm),theory(equality)],[c_7861,c_288]) ).
tff(c_8234,plain,
frontsegP(sk2,sk1),
inference(demodulation,[status(thm),theory(equality)],[c_7862,c_406,c_405,c_7861,c_8207]) ).
tff(c_8245,plain,
( ( sk2 = sk1 )
| ~ ssList(sk2)
| ~ ssList(sk1)
| ~ frontsegP(sk1,sk2) ),
inference(resolution,[status(thm)],[c_8234,c_258]) ).
tff(c_8251,plain,
( ( sk2 = sk1 )
| ~ frontsegP(sk1,sk2) ),
inference(demodulation,[status(thm),theory(equality)],[c_406,c_405,c_8245]) ).
tff(c_8262,plain,
~ frontsegP(sk1,sk2),
inference(splitLeft,[status(thm)],[c_8251]) ).
tff(c_11234,plain,
~ frontsegP(sk1,nil),
inference(demodulation,[status(thm),theory(equality)],[c_11222,c_8262]) ).
tff(c_11293,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4135,c_11234]) ).
tff(c_11295,plain,
sk2 != nil,
inference(splitRight,[status(thm)],[c_11195]) ).
tff(c_11294,plain,
skaf83(sk2) = hd(sk1),
inference(splitRight,[status(thm)],[c_11195]) ).
tff(c_11304,plain,
( ( sk2 = nil )
| ( cons(hd(sk1),skaf82(sk2)) = sk2 )
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_11294,c_218]) ).
tff(c_11316,plain,
( ( sk2 = nil )
| ( cons(hd(sk1),skaf82(sk2)) = sk2 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_405,c_11304]) ).
tff(c_11317,plain,
cons(hd(sk1),skaf82(sk2)) = sk2,
inference(negUnitSimplification,[status(thm)],[c_11295,c_11316]) ).
tff(c_11580,plain,
( ( tl(sk2) = skaf82(sk2) )
| ~ ssList(skaf82(sk2))
| ~ ssItem(hd(sk1)) ),
inference(superposition,[status(thm),theory(equality)],[c_11317,c_192]) ).
tff(c_11642,plain,
tl(sk2) = skaf82(sk2),
inference(demodulation,[status(thm),theory(equality)],[c_8775,c_26,c_11580]) ).
tff(c_11657,plain,
app(sk1,skaf82(sk2)) = sk2,
inference(demodulation,[status(thm),theory(equality)],[c_11642,c_7861]) ).
tff(c_276,plain,
! [V_177,W_178] :
( memberP(cons(V_177,W_178),V_177)
| ~ ssItem(V_177)
| ~ ssList(W_178) ),
inference(cnfTransformation,[status(thm)],[f_898]) ).
tff(c_2509,plain,
! [U_556] :
( memberP(U_556,skaf83(U_556))
| ~ ssItem(skaf83(U_556))
| ~ ssList(skaf82(U_556))
| ( nil = U_556 )
| ~ ssList(U_556) ),
inference(superposition,[status(thm),theory(equality)],[c_2503,c_276]) ).
tff(c_2524,plain,
! [U_556] :
( memberP(U_556,skaf83(U_556))
| ( nil = U_556 )
| ~ ssList(U_556) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_24,c_2509]) ).
tff(c_8676,plain,
sk1 != nil,
inference(splitRight,[status(thm)],[c_8238]) ).
tff(c_11160,plain,
( ( skaf83(sk1) = hd(sk1) )
| ( sk1 = nil ) ),
inference(resolution,[status(thm)],[c_406,c_11058]) ).
tff(c_11198,plain,
skaf83(sk1) = hd(sk1),
inference(negUnitSimplification,[status(thm)],[c_8676,c_11160]) ).
tff(c_11206,plain,
( ( sk1 = nil )
| ( cons(hd(sk1),skaf82(sk1)) = sk1 )
| ~ ssList(sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_11198,c_218]) ).
tff(c_11218,plain,
( ( sk1 = nil )
| ( cons(hd(sk1),skaf82(sk1)) = sk1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_406,c_11206]) ).
tff(c_11219,plain,
cons(hd(sk1),skaf82(sk1)) = sk1,
inference(negUnitSimplification,[status(thm)],[c_8676,c_11218]) ).
tff(c_278,plain,
! [W_181,U_179,V_180] :
( memberP(cons(W_181,U_179),V_180)
| ~ ssItem(V_180)
| ~ ssItem(W_181)
| ~ ssList(U_179)
| ~ memberP(U_179,V_180) ),
inference(cnfTransformation,[status(thm)],[f_912]) ).
tff(c_11389,plain,
! [V_180] :
( memberP(sk1,V_180)
| ~ ssItem(V_180)
| ~ ssItem(hd(sk1))
| ~ ssList(skaf82(sk1))
| ~ memberP(skaf82(sk1),V_180) ),
inference(superposition,[status(thm),theory(equality)],[c_11219,c_278]) ).
tff(c_41156,plain,
! [V_2491] :
( memberP(sk1,V_2491)
| ~ ssItem(V_2491)
| ~ memberP(skaf82(sk1),V_2491) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_8775,c_11389]) ).
tff(c_41168,plain,
( memberP(sk1,skaf83(skaf82(sk1)))
| ~ ssItem(skaf83(skaf82(sk1)))
| ( skaf82(sk1) = nil )
| ~ ssList(skaf82(sk1)) ),
inference(resolution,[status(thm)],[c_2524,c_41156]) ).
tff(c_41179,plain,
( memberP(sk1,skaf83(skaf82(sk1)))
| ( skaf82(sk1) = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_24,c_41168]) ).
tff(c_41184,plain,
skaf82(sk1) = nil,
inference(splitLeft,[status(thm)],[c_41179]) ).
tff(c_41188,plain,
cons(hd(sk1),nil) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_41184,c_11219]) ).
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_2488,plain,
! [U_554] :
( singletonP(cons(U_554,nil))
| ~ ssList(cons(U_554,nil))
| ~ ssItem(U_554) ),
inference(cnfTransformation,[status(thm)],[f_624]) ).
tff(c_2495,plain,
! [U_82] :
( singletonP(cons(U_82,nil))
| ~ ssList(nil)
| ~ ssItem(U_82) ),
inference(resolution,[status(thm)],[c_172,c_2488]) ).
tff(c_2500,plain,
! [U_82] :
( singletonP(cons(U_82,nil))
| ~ ssItem(U_82) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_2495]) ).
tff(c_41613,plain,
( singletonP(sk1)
| ~ ssItem(hd(sk1)) ),
inference(superposition,[status(thm),theory(equality)],[c_41188,c_2500]) ).
tff(c_41717,plain,
singletonP(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_8775,c_41613]) ).
tff(c_41719,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_402,c_41717]) ).
tff(c_41721,plain,
skaf82(sk1) != nil,
inference(splitRight,[status(thm)],[c_41179]) ).
tff(c_5405,plain,
! [V_719,U_720] :
( ( app(tl(V_719),U_720) = tl(app(V_719,U_720)) )
| ( nil = V_719 )
| ~ ssList(V_719)
| ~ ssList(U_720) ),
inference(cnfTransformation,[status(thm)],[f_830]) ).
tff(c_130657,plain,
! [U_5936,V_5937,U_5938] :
( ( tl(app(cons(U_5936,V_5937),U_5938)) = app(V_5937,U_5938) )
| ( cons(U_5936,V_5937) = nil )
| ~ ssList(cons(U_5936,V_5937))
| ~ ssList(U_5938)
| ~ ssList(V_5937)
| ~ ssItem(U_5936) ),
inference(superposition,[status(thm),theory(equality)],[c_192,c_5405]) ).
tff(c_130861,plain,
! [U_5938] :
( ( app(skaf82(sk1),U_5938) = tl(app(sk1,U_5938)) )
| ( cons(hd(sk1),skaf82(sk1)) = nil )
| ~ ssList(cons(hd(sk1),skaf82(sk1)))
| ~ ssList(U_5938)
| ~ ssList(skaf82(sk1))
| ~ ssItem(hd(sk1)) ),
inference(superposition,[status(thm),theory(equality)],[c_11219,c_130657]) ).
tff(c_130936,plain,
! [U_5938] :
( ( app(skaf82(sk1),U_5938) = tl(app(sk1,U_5938)) )
| ( sk1 = nil )
| ~ ssList(U_5938) ),
inference(demodulation,[status(thm),theory(equality)],[c_8775,c_26,c_406,c_11219,c_11219,c_130861]) ).
tff(c_156410,plain,
! [U_6241] :
( ( app(skaf82(sk1),U_6241) = tl(app(sk1,U_6241)) )
| ~ ssList(U_6241) ),
inference(negUnitSimplification,[status(thm)],[c_8676,c_130936]) ).
tff(c_4605,plain,
! [W_691,U_692,V_693] :
( ( W_691 = U_692 )
| ~ ssList(W_691)
| ~ ssList(V_693)
| ~ ssList(U_692)
| ( app(W_691,V_693) != app(U_692,V_693) ) ),
inference(cnfTransformation,[status(thm)],[f_1079]) ).
tff(c_28575,plain,
! [U_1908,V_1909] :
( ( nil = U_1908 )
| ~ ssList(V_1909)
| ~ ssList(U_1908)
| ( app(nil,V_1909) != app(U_1908,V_1909) ) ),
inference(resolution,[status(thm)],[c_16,c_4605]) ).
tff(c_28623,plain,
! [U_1908,U_2] :
( ( nil = U_1908 )
| ~ ssList(U_1908)
| ( app(nil,skaf82(U_2)) != app(U_1908,skaf82(U_2)) ) ),
inference(resolution,[status(thm)],[c_26,c_28575]) ).
tff(c_28686,plain,
! [U_1908,U_2] :
( ( nil = U_1908 )
| ~ ssList(U_1908)
| ( app(U_1908,skaf82(U_2)) != skaf82(U_2) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_583,c_28623]) ).
tff(c_156912,plain,
! [U_2] :
( ( skaf82(sk1) = nil )
| ~ ssList(skaf82(sk1))
| ( tl(app(sk1,skaf82(U_2))) != skaf82(U_2) )
| ~ ssList(skaf82(U_2)) ),
inference(superposition,[status(thm),theory(equality)],[c_156410,c_28686]) ).
tff(c_157470,plain,
! [U_2] :
( ( skaf82(sk1) = nil )
| ( tl(app(sk1,skaf82(U_2))) != skaf82(U_2) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_26,c_156912]) ).
tff(c_162827,plain,
! [U_6276] : ( tl(app(sk1,skaf82(U_6276))) != skaf82(U_6276) ),
inference(negUnitSimplification,[status(thm)],[c_41721,c_157470]) ).
tff(c_162830,plain,
tl(sk2) != skaf82(sk2),
inference(superposition,[status(thm),theory(equality)],[c_11657,c_162827]) ).
tff(c_162833,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_11642,c_162830]) ).
tff(c_162834,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_8709]) ).
tff(c_162843,plain,
~ frontsegP(sk1,nil),
inference(demodulation,[status(thm),theory(equality)],[c_162834,c_8262]) ).
tff(c_162902,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4135,c_162843]) ).
tff(c_162903,plain,
sk2 = sk1,
inference(splitRight,[status(thm)],[c_8251]) ).
tff(c_162907,plain,
app(sk1,tl(sk1)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_162903,c_162903,c_7861]) ).
tff(c_162909,plain,
ssList(tl(sk1)),
inference(demodulation,[status(thm),theory(equality)],[c_162903,c_7862]) ).
tff(c_2547,plain,
! [V_574,U_575] :
( ( nil = V_574 )
| ~ ssList(U_575)
| ~ ssList(V_574)
| ( app(U_575,V_574) != nil ) ),
inference(cnfTransformation,[status(thm)],[f_658]) ).
tff(c_165941,plain,
! [V_6462] :
( ( nil = V_6462 )
| ~ ssList(V_6462)
| ( app(sk1,V_6462) != nil ) ),
inference(resolution,[status(thm)],[c_406,c_2547]) ).
tff(c_165944,plain,
( ( tl(sk1) = nil )
| ( app(sk1,tl(sk1)) != nil ) ),
inference(resolution,[status(thm)],[c_162909,c_165941]) ).
tff(c_166042,plain,
( ( tl(sk1) = nil )
| ( sk1 != nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_162907,c_165944]) ).
tff(c_166077,plain,
sk1 != nil,
inference(splitLeft,[status(thm)],[c_166042]) ).
tff(c_2512,plain,
! [U_556] :
( ( tl(U_556) = skaf82(U_556) )
| ~ ssList(skaf82(U_556))
| ~ ssItem(skaf83(U_556))
| ( nil = U_556 )
| ~ ssList(U_556) ),
inference(superposition,[status(thm),theory(equality)],[c_2503,c_192]) ).
tff(c_166392,plain,
! [U_6488] :
( ( tl(U_6488) = skaf82(U_6488) )
| ( nil = U_6488 )
| ~ ssList(U_6488) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_2512]) ).
tff(c_166491,plain,
( ( tl(sk1) = skaf82(sk1) )
| ( sk1 = nil ) ),
inference(resolution,[status(thm)],[c_406,c_166392]) ).
tff(c_166527,plain,
tl(sk1) = skaf82(sk1),
inference(negUnitSimplification,[status(thm)],[c_166077,c_166491]) ).
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_166558,plain,
( ( sk1 = nil )
| ( cons(hd(sk1),skaf82(sk1)) = sk1 )
| ~ ssList(sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_166527,c_208]) ).
tff(c_166571,plain,
( ( sk1 = nil )
| ( cons(hd(sk1),skaf82(sk1)) = sk1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_406,c_166558]) ).
tff(c_166572,plain,
cons(hd(sk1),skaf82(sk1)) = sk1,
inference(negUnitSimplification,[status(thm)],[c_166077,c_166571]) ).
tff(c_166737,plain,
( memberP(sk1,hd(sk1))
| ~ ssItem(hd(sk1))
| ~ ssList(skaf82(sk1)) ),
inference(superposition,[status(thm),theory(equality)],[c_166572,c_276]) ).
tff(c_166798,plain,
( memberP(sk1,hd(sk1))
| ~ ssItem(hd(sk1)) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_166737]) ).
tff(c_166985,plain,
~ ssItem(hd(sk1)),
inference(splitLeft,[status(thm)],[c_166798]) ).
tff(c_166988,plain,
( ( sk1 = nil )
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[c_156,c_166985]) ).
tff(c_166991,plain,
sk1 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_406,c_166988]) ).
tff(c_166993,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_166077,c_166991]) ).
tff(c_166995,plain,
ssItem(hd(sk1)),
inference(splitRight,[status(thm)],[c_166798]) ).
tff(c_282,plain,
! [W_187,U_185,V_186] :
( memberP(app(W_187,U_185),V_186)
| ~ ssItem(V_186)
| ~ ssList(W_187)
| ~ ssList(U_185)
| ~ memberP(U_185,V_186) ),
inference(cnfTransformation,[status(thm)],[f_940]) ).
tff(c_8204,plain,
! [V_186] :
( memberP(sk2,V_186)
| ~ ssItem(V_186)
| ~ ssList(sk1)
| ~ ssList(tl(sk2))
| ~ memberP(tl(sk2),V_186) ),
inference(superposition,[status(thm),theory(equality)],[c_7861,c_282]) ).
tff(c_8232,plain,
! [V_186] :
( memberP(sk2,V_186)
| ~ ssItem(V_186)
| ~ memberP(tl(sk2),V_186) ),
inference(demodulation,[status(thm),theory(equality)],[c_7862,c_406,c_8204]) ).
tff(c_169137,plain,
! [V_6779] :
( memberP(sk1,V_6779)
| ~ ssItem(V_6779)
| ~ memberP(skaf82(sk1),V_6779) ),
inference(demodulation,[status(thm),theory(equality)],[c_166527,c_162903,c_162903,c_8232]) ).
tff(c_169145,plain,
( memberP(sk1,skaf83(skaf82(sk1)))
| ~ ssItem(skaf83(skaf82(sk1)))
| ( skaf82(sk1) = nil )
| ~ ssList(skaf82(sk1)) ),
inference(resolution,[status(thm)],[c_2524,c_169137]) ).
tff(c_169151,plain,
( memberP(sk1,skaf83(skaf82(sk1)))
| ( skaf82(sk1) = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_24,c_169145]) ).
tff(c_169152,plain,
skaf82(sk1) = nil,
inference(splitLeft,[status(thm)],[c_169151]) ).
tff(c_169155,plain,
cons(hd(sk1),nil) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_169152,c_166572]) ).
tff(c_169375,plain,
( singletonP(sk1)
| ~ ssItem(hd(sk1)) ),
inference(superposition,[status(thm),theory(equality)],[c_169155,c_2500]) ).
tff(c_169466,plain,
singletonP(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_166995,c_169375]) ).
tff(c_169468,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_402,c_169466]) ).
tff(c_169470,plain,
skaf82(sk1) != nil,
inference(splitRight,[status(thm)],[c_169151]) ).
tff(c_166537,plain,
app(sk1,skaf82(sk1)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_166527,c_162907]) ).
tff(c_863,plain,
app(sk1,nil) = sk1,
inference(resolution,[status(thm)],[c_406,c_742]) ).
tff(c_4723,plain,
! [W_697,V_698,U_699] :
( ( W_697 = V_698 )
| ~ ssList(W_697)
| ~ ssList(U_699)
| ~ ssList(V_698)
| ( app(U_699,W_697) != app(U_699,V_698) ) ),
inference(cnfTransformation,[status(thm)],[f_1065]) ).
tff(c_181403,plain,
! [V_7288,U_7289] :
( ( nil = V_7288 )
| ~ ssList(U_7289)
| ~ ssList(V_7288)
| ( app(U_7289,nil) != app(U_7289,V_7288) ) ),
inference(resolution,[status(thm)],[c_16,c_4723]) ).
tff(c_181467,plain,
! [V_7288] :
( ( nil = V_7288 )
| ~ ssList(V_7288)
| ( app(sk1,nil) != app(sk1,V_7288) ) ),
inference(resolution,[status(thm)],[c_406,c_181403]) ).
tff(c_181529,plain,
! [V_7290] :
( ( nil = V_7290 )
| ~ ssList(V_7290)
| ( app(sk1,V_7290) != sk1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_863,c_181467]) ).
tff(c_181769,plain,
! [U_7301] :
( ( skaf82(U_7301) = nil )
| ( app(sk1,skaf82(U_7301)) != sk1 ) ),
inference(resolution,[status(thm)],[c_26,c_181529]) ).
tff(c_181772,plain,
skaf82(sk1) = nil,
inference(superposition,[status(thm),theory(equality)],[c_166537,c_181769]) ).
tff(c_181776,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_169470,c_181772]) ).
tff(c_181778,plain,
sk1 = nil,
inference(splitRight,[status(thm)],[c_166042]) ).
tff(c_181797,plain,
~ frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_181778,c_7015]) ).
tff(c_181848,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4139,c_181797]) ).
tff(c_181849,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_3881]) ).
tff(c_591,plain,
app(nil,sk2) = sk2,
inference(resolution,[status(thm)],[c_405,c_472]) ).
tff(c_4039,plain,
( frontsegP(sk2,nil)
| ~ ssList(app(nil,sk2))
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_591,c_3893]) ).
tff(c_4137,plain,
frontsegP(sk2,nil),
inference(demodulation,[status(thm),theory(equality)],[c_405,c_16,c_405,c_591,c_4039]) ).
tff(c_4218,plain,
( ( sk2 = nil )
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ frontsegP(nil,sk2) ),
inference(resolution,[status(thm)],[c_4137,c_258]) ).
tff(c_4221,plain,
( ( sk2 = nil )
| ~ frontsegP(nil,sk2) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_405,c_4218]) ).
tff(c_6711,plain,
~ frontsegP(nil,sk2),
inference(splitLeft,[status(thm)],[c_4221]) ).
tff(c_181851,plain,
~ frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_181849,c_6711]) ).
tff(c_181902,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4139,c_181851]) ).
tff(c_181903,plain,
sk1 = nil,
inference(splitRight,[status(thm)],[c_4175]) ).
tff(c_3770,plain,
( rearsegP(sk1,nil)
| ~ ssList(app(sk1,nil))
| ~ ssList(nil)
| ~ ssList(sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_863,c_3630]) ).
tff(c_3870,plain,
rearsegP(sk1,nil),
inference(demodulation,[status(thm),theory(equality)],[c_406,c_16,c_406,c_863,c_3770]) ).
tff(c_3883,plain,
( ( sk1 = nil )
| ~ ssList(sk1)
| ~ ssList(nil)
| ~ rearsegP(nil,sk1) ),
inference(resolution,[status(thm)],[c_3870,c_256]) ).
tff(c_3886,plain,
( ( sk1 = nil )
| ~ rearsegP(nil,sk1) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_406,c_3883]) ).
tff(c_7014,plain,
~ rearsegP(nil,sk1),
inference(splitLeft,[status(thm)],[c_3886]) ).
tff(c_181959,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_181903,c_7014]) ).
tff(c_182009,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3876,c_181959]) ).
tff(c_182010,plain,
sk1 = nil,
inference(splitRight,[status(thm)],[c_3886]) ).
tff(c_182554,plain,
( ~ neq(nil,sk2)
| ~ ssList(tl(sk2))
| ( app(nil,tl(sk2)) = sk2 )
| ~ ssList(app(nil,tl(sk2))) ),
inference(demodulation,[status(thm),theory(equality)],[c_182010,c_182010,c_404]) ).
tff(c_182555,plain,
~ ssList(app(nil,tl(sk2))),
inference(splitLeft,[status(thm)],[c_182554]) ).
tff(c_182558,plain,
( ~ ssList(nil)
| ~ ssList(tl(sk2)) ),
inference(resolution,[status(thm)],[c_170,c_182555]) ).
tff(c_182561,plain,
~ ssList(tl(sk2)),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_182558]) ).
tff(c_182564,plain,
( ( sk2 = nil )
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_154,c_182561]) ).
tff(c_182567,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_182564]) ).
tff(c_182570,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_182567,c_182132]) ).
tff(c_182622,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3876,c_182570]) ).
tff(c_182623,plain,
( ~ ssList(tl(sk2))
| ~ neq(nil,sk2)
| ( app(nil,tl(sk2)) = sk2 ) ),
inference(splitRight,[status(thm)],[c_182554]) ).
tff(c_260327,plain,
( ~ neq(nil,sk2)
| ( skaf82(sk2) = sk2 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_583,c_186212,c_26,c_186212,c_182623]) ).
tff(c_260328,plain,
~ neq(nil,sk2),
inference(negUnitSimplification,[status(thm)],[c_186283,c_260327]) ).
tff(c_260334,plain,
( ( sk2 = nil )
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_200,c_260328]) ).
tff(c_260340,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_16,c_260334]) ).
tff(c_260342,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_185864,c_260340]) ).
tff(c_260343,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_3881]) ).
tff(c_260345,plain,
~ frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_260343,c_6711]) ).
tff(c_260396,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4139,c_260345]) ).
tff(c_260397,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_4221]) ).
tff(c_260444,plain,
neq(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_260397,c_384]) ).
tff(c_230,plain,
! [V_129] :
( ~ ssList(V_129)
| ~ neq(V_129,V_129) ),
inference(cnfTransformation,[status(thm)],[f_613]) ).
tff(c_260760,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[c_260444,c_230]) ).
tff(c_260765,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_260760]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWC253-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14 % 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
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 22:06:08 EDT 2023
% 0.14/0.35 % CPUTime :
% 188.05/166.67 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 188.22/166.72
% 188.22/166.72 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 188.46/166.77
% 188.46/166.77 Inference rules
% 188.46/166.77 ----------------------
% 188.46/166.77 #Ref : 57
% 188.46/166.77 #Sup : 63171
% 188.46/166.77 #Fact : 0
% 188.46/166.77 #Define : 0
% 188.46/166.77 #Split : 45
% 188.46/166.77 #Chain : 0
% 188.46/166.77 #Close : 0
% 188.46/166.77
% 188.46/166.77 Ordering : KBO
% 188.46/166.77
% 188.46/166.77 Simplification rules
% 188.46/166.77 ----------------------
% 188.46/166.77 #Subsume : 14767
% 188.46/166.77 #Demod : 54460
% 188.46/166.77 #Tautology : 9980
% 188.46/166.77 #SimpNegUnit : 877
% 188.46/166.78 #BackRed : 1083
% 188.46/166.78
% 188.46/166.78 #Partial instantiations: 0
% 188.46/166.78 #Strategies tried : 1
% 188.46/166.78
% 188.46/166.78 Timing (in seconds)
% 188.46/166.78 ----------------------
% 188.46/166.78 Preprocessing : 0.88
% 188.46/166.78 Parsing : 0.45
% 188.46/166.78 CNF conversion : 0.07
% 188.46/166.78 Main loop : 164.75
% 188.46/166.78 Inferencing : 22.84
% 188.46/166.78 Reduction : 75.90
% 188.46/166.78 Demodulation : 55.78
% 188.46/166.78 BG Simplification : 0.46
% 188.46/166.78 Subsumption : 54.36
% 188.46/166.78 Abstraction : 1.15
% 188.46/166.78 MUC search : 0.00
% 188.46/166.78 Cooper : 0.00
% 188.46/166.78 Total : 165.75
% 188.46/166.78 Index Insertion : 0.00
% 188.46/166.78 Index Deletion : 0.00
% 188.46/166.78 Index Matching : 0.00
% 188.46/166.78 BG Taut test : 0.00
%------------------------------------------------------------------------------