TSTP Solution File: SWC396-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWC396-1 : 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 : n006.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 11:02:28 EDT 2023
% Result : Unsatisfiable 164.03s 143.85s
% Output : CNFRefutation 164.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 110
% Syntax : Number of formulae : 382 ( 153 unt; 73 typ; 0 def)
% Number of atoms : 682 ( 200 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 769 ( 396 ~; 373 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 5 ( 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 : 54 ( 54 usr; 8 con; 0-2 aty)
% Number of variables : 170 (; 170 !; 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 > sk5 > 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(sk5,type,
sk5: $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_1651,axiom,
ssItem(sk5),
file(unknown,unknown) ).
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_1650,axiom,
sk1 = sk3,
file(unknown,unknown) ).
tff(f_1647,axiom,
ssList(sk3),
file(unknown,unknown) ).
tff(f_1649,axiom,
sk2 = sk4,
file(unknown,unknown) ).
tff(f_1648,axiom,
ssList(sk4),
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_64,axiom,
! [U] : ssList(skaf82(U)),
file(unknown,unknown) ).
tff(f_245,axiom,
! [U] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
file(unknown,unknown) ).
tff(f_647,axiom,
! [U,V] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) ),
file(unknown,unknown) ).
tff(f_62,axiom,
! [U] : ssItem(skaf83(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_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_770,axiom,
! [U,V] :
( ~ rearsegP(U,V)
| ~ rearsegP(V,U)
| ~ ssList(U)
| ~ ssList(V)
| ( V = U ) ),
file(unknown,unknown) ).
tff(f_342,axiom,
! [U,V] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file(unknown,unknown) ).
tff(f_420,axiom,
! [U,V] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
file(unknown,unknown) ).
tff(f_1658,axiom,
( ( nil = sk3 )
| ( nil != sk4 ) ),
file(unknown,unknown) ).
tff(f_1662,axiom,
( ~ neq(sk4,nil)
| neq(sk3,nil) ),
file(unknown,unknown) ).
tff(f_1697,axiom,
! [A,B,C,D] :
( ~ neq(sk4,nil)
| ~ ssList(A)
| ( sk4 = A )
| ~ ssList(B)
| ~ ssList(C)
| ( tl(sk3) != B )
| ( app(B,C) != A )
| ~ ssItem(D)
| ( cons(D,nil) != C )
| ( hd(sk3) != D )
| ~ neq(nil,sk3)
| ~ neq(nil,sk3) ),
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_658,axiom,
! [U,V] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = 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_1652,axiom,
memberP(sk1,sk5),
file(unknown,unknown) ).
tff(f_233,axiom,
! [U] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
file(unknown,unknown) ).
tff(f_636,axiom,
! [U,V] :
( ( U != V )
| ~ neq(U,V)
| ~ ssItem(V)
| ~ ssItem(U) ),
file(unknown,unknown) ).
tff(f_1654,axiom,
~ memberP(sk2,sk5),
file(unknown,unknown) ).
tff(f_1239,axiom,
! [U,V,W] :
( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U ) ),
file(unknown,unknown) ).
tff(f_474,axiom,
! [U,V] :
( ~ ssItem(U)
| ~ ssItem(V)
| neq(V,U)
| ( V = U ) ),
file(unknown,unknown) ).
tff(f_926,axiom,
! [U,V,W] :
( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,W),V) ),
file(unknown,unknown) ).
tff(f_1405,axiom,
! [U,V,W,X] :
( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) ),
file(unknown,unknown) ).
tff(c_384,plain,
ssItem(sk5),
inference(cnfTransformation,[status(thm)],[f_1651]) ).
tff(c_16,plain,
ssList(nil),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_468,plain,
! [U_391] :
( ( app(nil,U_391) = U_391 )
| ~ ssList(U_391) ),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_586,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[c_16,c_468]) ).
tff(c_4954,plain,
! [U_770,V_771] :
( frontsegP(app(U_770,V_771),U_770)
| ~ ssList(app(U_770,V_771))
| ~ ssList(U_770)
| ~ ssList(V_771) ),
inference(cnfTransformation,[status(thm)],[f_975]) ).
tff(c_5100,plain,
( frontsegP(nil,nil)
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_586,c_4954]) ).
tff(c_5195,plain,
frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_586,c_5100]) ).
tff(c_5214,plain,
! [U_772,V_773] :
( rearsegP(app(U_772,V_773),V_773)
| ~ ssList(app(U_772,V_773))
| ~ ssList(V_773)
| ~ ssList(U_772) ),
inference(cnfTransformation,[status(thm)],[f_961]) ).
tff(c_5360,plain,
( rearsegP(nil,nil)
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_586,c_5214]) ).
tff(c_5455,plain,
rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_586,c_5360]) ).
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_402,plain,
ssList(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_376]) ).
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_401,plain,
ssList(sk2),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_378]) ).
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_2431,plain,
! [V_568,U_569] :
( ssList(app(V_568,U_569))
| ~ ssList(V_568)
| ~ ssList(U_569) ),
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_603,plain,
! [U_66] :
( duplicatefreeP(U_66)
| ~ ssList(U_66) ),
inference(splitLeft,[status(thm)],[c_144]) ).
tff(c_2526,plain,
! [V_568,U_569] :
( duplicatefreeP(app(V_568,U_569))
| ~ ssList(V_568)
| ~ ssList(U_569) ),
inference(resolution,[status(thm)],[c_2431,c_603]) ).
tff(c_26,plain,
! [U_2] : ssList(skaf82(U_2)),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_726,plain,
! [U_395] :
( ( app(U_395,nil) = U_395 )
| ~ ssList(U_395) ),
inference(cnfTransformation,[status(thm)],[f_245]) ).
tff(c_846,plain,
app(sk1,nil) = sk1,
inference(resolution,[status(thm)],[c_402,c_726]) ).
tff(c_3849,plain,
! [U_695,V_696] :
( ( nil = U_695 )
| ~ ssList(U_695)
| ~ ssList(V_696)
| ( app(U_695,V_696) != nil ) ),
inference(cnfTransformation,[status(thm)],[f_647]) ).
tff(c_3948,plain,
! [V_696] :
( ( sk1 = nil )
| ~ ssList(V_696)
| ( app(sk1,V_696) != nil ) ),
inference(resolution,[status(thm)],[c_402,c_3849]) ).
tff(c_16903,plain,
! [V_1479] :
( ~ ssList(V_1479)
| ( app(sk1,V_1479) != nil ) ),
inference(splitLeft,[status(thm)],[c_3948]) ).
tff(c_17002,plain,
app(sk1,nil) != nil,
inference(resolution,[status(thm)],[c_16,c_16903]) ).
tff(c_17042,plain,
sk1 != nil,
inference(demodulation,[status(thm),theory(equality)],[c_846,c_17002]) ).
tff(c_24,plain,
! [U_1] : ssItem(skaf83(U_1)),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_3625,plain,
! [U_664] :
( ( nil = U_664 )
| ( cons(skaf83(U_664),skaf82(U_664)) = U_664 )
| ~ ssList(U_664) ),
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_3634,plain,
! [U_664] :
( ( skaf83(U_664) = hd(U_664) )
| ~ ssList(skaf82(U_664))
| ~ ssItem(skaf83(U_664))
| ( nil = U_664 )
| ~ ssList(U_664) ),
inference(superposition,[status(thm),theory(equality)],[c_3625,c_194]) ).
tff(c_17375,plain,
! [U_1533] :
( ( skaf83(U_1533) = hd(U_1533) )
| ( nil = U_1533 )
| ~ ssList(U_1533) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_3634]) ).
tff(c_17477,plain,
( ( skaf83(sk1) = hd(sk1) )
| ( sk1 = nil ) ),
inference(resolution,[status(thm)],[c_402,c_17375]) ).
tff(c_17519,plain,
skaf83(sk1) = hd(sk1),
inference(negUnitSimplification,[status(thm)],[c_17042,c_17477]) ).
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_17530,plain,
( ( sk1 = nil )
| ( cons(hd(sk1),skaf82(sk1)) = sk1 )
| ~ ssList(sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_17519,c_218]) ).
tff(c_17542,plain,
( ( sk1 = nil )
| ( cons(hd(sk1),skaf82(sk1)) = sk1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_402,c_17530]) ).
tff(c_17543,plain,
cons(hd(sk1),skaf82(sk1)) = sk1,
inference(negUnitSimplification,[status(thm)],[c_17042,c_17542]) ).
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_12323,plain,
! [U_1229] :
( ( skaf83(U_1229) = hd(U_1229) )
| ( nil = U_1229 )
| ~ ssList(U_1229) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_3634]) ).
tff(c_12455,plain,
( ( skaf83(sk1) = hd(sk1) )
| ( sk1 = nil ) ),
inference(resolution,[status(thm)],[c_402,c_12323]) ).
tff(c_12601,plain,
sk1 = nil,
inference(splitLeft,[status(thm)],[c_12455]) ).
tff(c_5348,plain,
( rearsegP(sk1,nil)
| ~ ssList(app(sk1,nil))
| ~ ssList(nil)
| ~ ssList(sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_846,c_5214]) ).
tff(c_5447,plain,
rearsegP(sk1,nil),
inference(demodulation,[status(thm),theory(equality)],[c_402,c_16,c_402,c_846,c_5348]) ).
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_5475,plain,
( ( sk1 = nil )
| ~ ssList(sk1)
| ~ ssList(nil)
| ~ rearsegP(nil,sk1) ),
inference(resolution,[status(thm)],[c_5447,c_256]) ).
tff(c_5478,plain,
( ( sk1 = nil )
| ~ rearsegP(nil,sk1) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_402,c_5475]) ).
tff(c_8405,plain,
~ rearsegP(nil,sk1),
inference(splitLeft,[status(thm)],[c_5478]) ).
tff(c_12605,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_12601,c_8405]) ).
tff(c_12661,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5455,c_12605]) ).
tff(c_12662,plain,
skaf83(sk1) = hd(sk1),
inference(splitRight,[status(thm)],[c_12455]) ).
tff(c_12817,plain,
ssItem(hd(sk1)),
inference(superposition,[status(thm),theory(equality)],[c_12662,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_12663,plain,
sk1 != nil,
inference(splitRight,[status(thm)],[c_12455]) ).
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_3637,plain,
! [U_664] :
( ( tl(U_664) = skaf82(U_664) )
| ~ ssList(skaf82(U_664))
| ~ ssItem(skaf83(U_664))
| ( nil = U_664 )
| ~ ssList(U_664) ),
inference(superposition,[status(thm),theory(equality)],[c_3625,c_192]) ).
tff(c_12664,plain,
! [U_1238] :
( ( tl(U_1238) = skaf82(U_1238) )
| ( nil = U_1238 )
| ~ ssList(U_1238) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_3637]) ).
tff(c_12760,plain,
( ( tl(sk1) = skaf82(sk1) )
| ( sk1 = nil ) ),
inference(resolution,[status(thm)],[c_402,c_12664]) ).
tff(c_12798,plain,
tl(sk1) = skaf82(sk1),
inference(negUnitSimplification,[status(thm)],[c_12663,c_12760]) ).
tff(c_390,plain,
( ( sk4 != nil )
| ( sk3 = nil ) ),
inference(cnfTransformation,[status(thm)],[f_1658]) ).
tff(c_396,plain,
( ( sk4 != nil )
| ( sk1 = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_390]) ).
tff(c_399,plain,
( ( sk2 != nil )
| ( sk1 = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_396]) ).
tff(c_452,plain,
sk2 != nil,
inference(splitLeft,[status(thm)],[c_399]) ).
tff(c_2050,plain,
! [V_527,U_528] :
( ( V_527 = U_528 )
| neq(V_527,U_528)
| ~ ssList(V_527)
| ~ ssList(U_528) ),
inference(cnfTransformation,[status(thm)],[f_456]) ).
tff(c_392,plain,
( neq(sk3,nil)
| ~ neq(sk4,nil) ),
inference(cnfTransformation,[status(thm)],[f_1662]) ).
tff(c_397,plain,
( neq(sk1,nil)
| ~ neq(sk4,nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_392]) ).
tff(c_400,plain,
( neq(sk1,nil)
| ~ neq(sk2,nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_397]) ).
tff(c_883,plain,
~ neq(sk2,nil),
inference(splitLeft,[status(thm)],[c_400]) ).
tff(c_2053,plain,
( ( sk2 = nil )
| ~ ssList(sk2)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_2050,c_883]) ).
tff(c_2064,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_401,c_2053]) ).
tff(c_2066,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_452,c_2064]) ).
tff(c_2068,plain,
neq(sk2,nil),
inference(splitRight,[status(thm)],[c_400]) ).
tff(c_394,plain,
( ~ neq(nil,sk3)
| ~ ssItem(hd(sk3))
| ~ ssList(cons(hd(sk3),nil))
| ~ ssList(tl(sk3))
| ( app(tl(sk3),cons(hd(sk3),nil)) = sk4 )
| ~ ssList(app(tl(sk3),cons(hd(sk3),nil)))
| ~ neq(sk4,nil) ),
inference(cnfTransformation,[status(thm)],[f_1697]) ).
tff(c_395,plain,
( ~ neq(nil,sk1)
| ~ ssItem(hd(sk1))
| ~ ssList(cons(hd(sk1),nil))
| ~ ssList(tl(sk1))
| ( app(tl(sk1),cons(hd(sk1),nil)) = sk4 )
| ~ ssList(app(tl(sk1),cons(hd(sk1),nil)))
| ~ neq(sk4,nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_382,c_382,c_382,c_382,c_382,c_382,c_382,c_394]) ).
tff(c_398,plain,
( ~ neq(nil,sk1)
| ~ ssItem(hd(sk1))
| ~ ssList(cons(hd(sk1),nil))
| ~ ssList(tl(sk1))
| ( app(tl(sk1),cons(hd(sk1),nil)) = sk2 )
| ~ ssList(app(tl(sk1),cons(hd(sk1),nil)))
| ~ neq(sk2,nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_380,c_395]) ).
tff(c_11282,plain,
( ~ neq(nil,sk1)
| ~ ssItem(hd(sk1))
| ~ ssList(cons(hd(sk1),nil))
| ~ ssList(tl(sk1))
| ( app(tl(sk1),cons(hd(sk1),nil)) = sk2 )
| ~ ssList(app(tl(sk1),cons(hd(sk1),nil))) ),
inference(demodulation,[status(thm),theory(equality)],[c_2068,c_398]) ).
tff(c_11283,plain,
~ ssList(app(tl(sk1),cons(hd(sk1),nil))),
inference(splitLeft,[status(thm)],[c_11282]) ).
tff(c_11419,plain,
( ~ ssList(tl(sk1))
| ~ ssList(cons(hd(sk1),nil)) ),
inference(resolution,[status(thm)],[c_170,c_11283]) ).
tff(c_14821,plain,
~ ssList(cons(hd(sk1),nil)),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_12798,c_11419]) ).
tff(c_14824,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sk1)) ),
inference(resolution,[status(thm)],[c_172,c_14821]) ).
tff(c_14828,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12817,c_16,c_14824]) ).
tff(c_14829,plain,
( ~ ssList(tl(sk1))
| ~ ssList(cons(hd(sk1),nil))
| ~ ssItem(hd(sk1))
| ~ neq(nil,sk1)
| ( app(tl(sk1),cons(hd(sk1),nil)) = sk2 ) ),
inference(splitRight,[status(thm)],[c_11282]) ).
tff(c_15026,plain,
~ neq(nil,sk1),
inference(splitLeft,[status(thm)],[c_14829]) ).
tff(c_15032,plain,
( ( sk1 = nil )
| ~ ssList(nil)
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[c_200,c_15026]) ).
tff(c_15036,plain,
sk1 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_402,c_16,c_15032]) ).
tff(c_15039,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_15036,c_8405]) ).
tff(c_15095,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5455,c_15039]) ).
tff(c_15096,plain,
( ~ ssItem(hd(sk1))
| ~ ssList(cons(hd(sk1),nil))
| ~ ssList(tl(sk1))
| ( app(tl(sk1),cons(hd(sk1),nil)) = sk2 ) ),
inference(splitRight,[status(thm)],[c_14829]) ).
tff(c_15222,plain,
~ ssList(tl(sk1)),
inference(splitLeft,[status(thm)],[c_15096]) ).
tff(c_15225,plain,
( ( sk1 = nil )
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[c_154,c_15222]) ).
tff(c_15228,plain,
sk1 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_402,c_15225]) ).
tff(c_15232,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_15228,c_8405]) ).
tff(c_15288,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5455,c_15232]) ).
tff(c_15290,plain,
ssList(tl(sk1)),
inference(splitRight,[status(thm)],[c_15096]) ).
tff(c_156,plain,
! [U_73] :
( ( nil = U_73 )
| ssItem(hd(U_73))
| ~ ssList(U_73) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_15289,plain,
( ~ ssList(cons(hd(sk1),nil))
| ~ ssItem(hd(sk1))
| ( app(tl(sk1),cons(hd(sk1),nil)) = sk2 ) ),
inference(splitRight,[status(thm)],[c_15096]) ).
tff(c_15564,plain,
~ ssItem(hd(sk1)),
inference(splitLeft,[status(thm)],[c_15289]) ).
tff(c_15567,plain,
( ( sk1 = nil )
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[c_156,c_15564]) ).
tff(c_15570,plain,
sk1 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_402,c_15567]) ).
tff(c_15580,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_15570,c_8405]) ).
tff(c_15636,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5455,c_15580]) ).
tff(c_15638,plain,
ssItem(hd(sk1)),
inference(splitRight,[status(thm)],[c_15289]) ).
tff(c_15637,plain,
( ~ ssList(cons(hd(sk1),nil))
| ( app(tl(sk1),cons(hd(sk1),nil)) = sk2 ) ),
inference(splitRight,[status(thm)],[c_15289]) ).
tff(c_15749,plain,
~ ssList(cons(hd(sk1),nil)),
inference(splitLeft,[status(thm)],[c_15637]) ).
tff(c_15752,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sk1)) ),
inference(resolution,[status(thm)],[c_172,c_15749]) ).
tff(c_15756,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_15638,c_16,c_15752]) ).
tff(c_15757,plain,
app(tl(sk1),cons(hd(sk1),nil)) = sk2,
inference(splitRight,[status(thm)],[c_15637]) ).
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_15865,plain,
! [X_289] :
( ~ ssList(app(sk2,cons(hd(sk1),X_289)))
| ~ duplicatefreeP(app(app(tl(sk1),cons(hd(sk1),nil)),cons(hd(sk1),X_289)))
| ~ ssItem(hd(sk1))
| ~ ssList(tl(sk1))
| ~ ssList(nil)
| ~ ssList(X_289) ),
inference(superposition,[status(thm),theory(equality)],[c_15757,c_358]) ).
tff(c_83831,plain,
! [X_4785] :
( ~ ssList(app(sk2,cons(hd(sk1),X_4785)))
| ~ duplicatefreeP(app(sk2,cons(hd(sk1),X_4785)))
| ~ ssList(X_4785) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_15290,c_15638,c_15757,c_15865]) ).
tff(c_83834,plain,
( ~ ssList(app(sk2,sk1))
| ~ duplicatefreeP(app(sk2,cons(hd(sk1),skaf82(sk1))))
| ~ ssList(skaf82(sk1)) ),
inference(superposition,[status(thm),theory(equality)],[c_17543,c_83831]) ).
tff(c_83847,plain,
( ~ ssList(app(sk2,sk1))
| ~ duplicatefreeP(app(sk2,sk1)) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_17543,c_83834]) ).
tff(c_83856,plain,
~ duplicatefreeP(app(sk2,sk1)),
inference(splitLeft,[status(thm)],[c_83847]) ).
tff(c_83859,plain,
( ~ ssList(sk2)
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[c_2526,c_83856]) ).
tff(c_83863,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_402,c_401,c_83859]) ).
tff(c_83864,plain,
~ ssList(app(sk2,sk1)),
inference(splitRight,[status(thm)],[c_83847]) ).
tff(c_83995,plain,
( ~ ssList(sk2)
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[c_170,c_83864]) ).
tff(c_83999,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_402,c_401,c_83995]) ).
tff(c_84000,plain,
sk1 = nil,
inference(splitRight,[status(thm)],[c_3948]) ).
tff(c_3429,plain,
! [V_655,U_656] :
( ( nil = V_655 )
| ~ ssList(U_656)
| ~ ssList(V_655)
| ( app(U_656,V_655) != nil ) ),
inference(cnfTransformation,[status(thm)],[f_658]) ).
tff(c_16118,plain,
! [V_1442] :
( ( nil = V_1442 )
| ~ ssList(V_1442)
| ( app(sk1,V_1442) != nil ) ),
inference(resolution,[status(thm)],[c_402,c_3429]) ).
tff(c_16261,plain,
( ( sk1 = nil )
| ( app(sk1,sk1) != nil ) ),
inference(resolution,[status(thm)],[c_402,c_16118]) ).
tff(c_16265,plain,
app(sk1,sk1) != nil,
inference(splitLeft,[status(thm)],[c_16261]) ).
tff(c_84005,plain,
app(nil,nil) != nil,
inference(demodulation,[status(thm),theory(equality)],[c_84000,c_84000,c_16265]) ).
tff(c_84090,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_586,c_84005]) ).
tff(c_84091,plain,
sk1 = nil,
inference(splitRight,[status(thm)],[c_16261]) ).
tff(c_84121,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_84091,c_8405]) ).
tff(c_84178,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5455,c_84121]) ).
tff(c_84179,plain,
sk1 = nil,
inference(splitRight,[status(thm)],[c_5478]) ).
tff(c_587,plain,
app(nil,sk1) = sk1,
inference(resolution,[status(thm)],[c_402,c_468]) ).
tff(c_5097,plain,
( frontsegP(sk1,nil)
| ~ ssList(app(nil,sk1))
| ~ ssList(nil)
| ~ ssList(sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_587,c_4954]) ).
tff(c_5193,plain,
frontsegP(sk1,nil),
inference(demodulation,[status(thm),theory(equality)],[c_402,c_16,c_402,c_587,c_5097]) ).
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_5457,plain,
( ( sk1 = nil )
| ~ ssList(sk1)
| ~ ssList(nil)
| ~ frontsegP(nil,sk1) ),
inference(resolution,[status(thm)],[c_5193,c_258]) ).
tff(c_5460,plain,
( ( sk1 = nil )
| ~ frontsegP(nil,sk1) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_402,c_5457]) ).
tff(c_8404,plain,
~ frontsegP(nil,sk1),
inference(splitLeft,[status(thm)],[c_5460]) ).
tff(c_84181,plain,
~ frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_84179,c_8404]) ).
tff(c_84236,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5195,c_84181]) ).
tff(c_84237,plain,
sk1 = nil,
inference(splitRight,[status(thm)],[c_5460]) ).
tff(c_386,plain,
memberP(sk1,sk5),
inference(cnfTransformation,[status(thm)],[f_1652]) ).
tff(c_84288,plain,
memberP(nil,sk5),
inference(demodulation,[status(thm),theory(equality)],[c_84237,c_386]) ).
tff(c_142,plain,
! [U_65] :
( ~ ssItem(U_65)
| ~ memberP(nil,U_65) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_84584,plain,
~ ssItem(sk5),
inference(resolution,[status(thm)],[c_84288,c_142]) ).
tff(c_84588,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_84584]) ).
tff(c_84589,plain,
! [V_67] : ssItem(V_67),
inference(splitRight,[status(thm)],[c_144]) ).
tff(c_234,plain,
! [V_133] :
( ~ ssItem(V_133)
| ~ neq(V_133,V_133) ),
inference(cnfTransformation,[status(thm)],[f_636]) ).
tff(c_84603,plain,
! [V_133] : ~ neq(V_133,V_133),
inference(demodulation,[status(thm),theory(equality)],[c_84589,c_234]) ).
tff(c_88668,plain,
! [U_5183,V_5184] :
( frontsegP(app(U_5183,V_5184),U_5183)
| ~ ssList(app(U_5183,V_5184))
| ~ ssList(U_5183)
| ~ ssList(V_5184) ),
inference(cnfTransformation,[status(thm)],[f_975]) ).
tff(c_88814,plain,
( frontsegP(nil,nil)
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_586,c_88668]) ).
tff(c_88909,plain,
frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_586,c_88814]) ).
tff(c_388,plain,
~ memberP(sk2,sk5),
inference(cnfTransformation,[status(thm)],[f_1654]) ).
tff(c_84639,plain,
! [U_4802] :
( ( app(U_4802,nil) = U_4802 )
| ~ ssList(U_4802) ),
inference(cnfTransformation,[status(thm)],[f_245]) ).
tff(c_84759,plain,
app(sk1,nil) = sk1,
inference(resolution,[status(thm)],[c_402,c_84639]) ).
tff(c_87527,plain,
! [U_5113,V_5114] :
( ( nil = U_5113 )
| ~ ssList(U_5113)
| ~ ssList(V_5114)
| ( app(U_5113,V_5114) != nil ) ),
inference(cnfTransformation,[status(thm)],[f_647]) ).
tff(c_87626,plain,
! [V_5114] :
( ( sk1 = nil )
| ~ ssList(V_5114)
| ( app(sk1,V_5114) != nil ) ),
inference(resolution,[status(thm)],[c_402,c_87527]) ).
tff(c_99076,plain,
! [V_5717] :
( ~ ssList(V_5717)
| ( app(sk1,V_5717) != nil ) ),
inference(splitLeft,[status(thm)],[c_87626]) ).
tff(c_99175,plain,
app(sk1,nil) != nil,
inference(resolution,[status(thm)],[c_16,c_99076]) ).
tff(c_99215,plain,
sk1 != nil,
inference(demodulation,[status(thm),theory(equality)],[c_84759,c_99175]) ).
tff(c_87428,plain,
! [U_5095] :
( ( nil = U_5095 )
| ( cons(skaf83(U_5095),skaf82(U_5095)) = U_5095 )
| ~ ssList(U_5095) ),
inference(cnfTransformation,[status(thm)],[f_543]) ).
tff(c_86757,plain,
! [U_95,V_96] :
( ( hd(cons(U_95,V_96)) = U_95 )
| ~ ssList(V_96) ),
inference(demodulation,[status(thm),theory(equality)],[c_84589,c_194]) ).
tff(c_87437,plain,
! [U_5095] :
( ( skaf83(U_5095) = hd(U_5095) )
| ~ ssList(skaf82(U_5095))
| ( nil = U_5095 )
| ~ ssList(U_5095) ),
inference(superposition,[status(thm),theory(equality)],[c_87428,c_86757]) ).
tff(c_99901,plain,
! [U_5797] :
( ( skaf83(U_5797) = hd(U_5797) )
| ( nil = U_5797 )
| ~ ssList(U_5797) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_87437]) ).
tff(c_100003,plain,
( ( skaf83(sk1) = hd(sk1) )
| ( sk1 = nil ) ),
inference(resolution,[status(thm)],[c_402,c_99901]) ).
tff(c_100045,plain,
skaf83(sk1) = hd(sk1),
inference(negUnitSimplification,[status(thm)],[c_99215,c_100003]) ).
tff(c_322,plain,
! [W_242,U_240,V_241] :
( ( W_242 = U_240 )
| memberP(V_241,W_242)
| ~ ssItem(W_242)
| ~ ssItem(U_240)
| ~ ssList(V_241)
| ~ memberP(cons(U_240,V_241),W_242) ),
inference(cnfTransformation,[status(thm)],[f_1239]) ).
tff(c_92388,plain,
! [W_5361,U_5362,V_5363] :
( ( W_5361 = U_5362 )
| memberP(V_5363,W_5361)
| ~ ssList(V_5363)
| ~ memberP(cons(U_5362,V_5363),W_5361) ),
inference(demodulation,[status(thm),theory(equality)],[c_84589,c_84589,c_322]) ).
tff(c_92397,plain,
! [U_117,W_5361] :
( ( skaf83(U_117) = W_5361 )
| memberP(skaf82(U_117),W_5361)
| ~ ssList(skaf82(U_117))
| ~ memberP(U_117,W_5361)
| ( nil = U_117 )
| ~ ssList(U_117) ),
inference(superposition,[status(thm),theory(equality)],[c_218,c_92388]) ).
tff(c_187574,plain,
! [U_9319,W_9320] :
( ( skaf83(U_9319) = W_9320 )
| memberP(skaf82(U_9319),W_9320)
| ~ memberP(U_9319,W_9320)
| ( nil = U_9319 )
| ~ ssList(U_9319) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_92397]) ).
tff(c_100062,plain,
( ( sk1 = nil )
| ( cons(hd(sk1),skaf82(sk1)) = sk1 )
| ~ ssList(sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_100045,c_218]) ).
tff(c_100066,plain,
( ( sk1 = nil )
| ( cons(hd(sk1),skaf82(sk1)) = sk1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_402,c_100062]) ).
tff(c_100067,plain,
cons(hd(sk1),skaf82(sk1)) = sk1,
inference(negUnitSimplification,[status(thm)],[c_99215,c_100066]) ).
tff(c_86627,plain,
! [U_93,V_94] :
( ( tl(cons(U_93,V_94)) = V_94 )
| ~ ssList(V_94) ),
inference(demodulation,[status(thm),theory(equality)],[c_84589,c_192]) ).
tff(c_100338,plain,
( ( tl(sk1) = skaf82(sk1) )
| ~ ssList(skaf82(sk1)) ),
inference(superposition,[status(thm),theory(equality)],[c_100067,c_86627]) ).
tff(c_100400,plain,
tl(sk1) = skaf82(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_100338]) ).
tff(c_86264,plain,
! [U_82,V_83] :
( ssList(cons(U_82,V_83))
| ~ ssList(V_83) ),
inference(demodulation,[status(thm),theory(equality)],[c_84589,c_172]) ).
tff(c_88409,plain,
! [U_5181,V_5182] :
( rearsegP(app(U_5181,V_5182),V_5182)
| ~ ssList(app(U_5181,V_5182))
| ~ ssList(V_5182)
| ~ ssList(U_5181) ),
inference(cnfTransformation,[status(thm)],[f_961]) ).
tff(c_88555,plain,
( rearsegP(nil,nil)
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_586,c_88409]) ).
tff(c_88650,plain,
rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_586,c_88555]) ).
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_86908,plain,
! [V_105,U_104] :
( ( V_105 = U_104 )
| neq(V_105,U_104) ),
inference(demodulation,[status(thm),theory(equality)],[c_84589,c_84589,c_204]) ).
tff(c_95903,plain,
! [V_5559] :
( ~ ssList(V_5559)
| ( app(sk1,V_5559) != nil ) ),
inference(splitLeft,[status(thm)],[c_87626]) ).
tff(c_95996,plain,
app(sk1,nil) != nil,
inference(resolution,[status(thm)],[c_16,c_95903]) ).
tff(c_96034,plain,
sk1 != nil,
inference(demodulation,[status(thm),theory(equality)],[c_84759,c_95996]) ).
tff(c_85614,plain,
! [V_4872,U_4873] :
( ( V_4872 = U_4873 )
| neq(V_4872,U_4873)
| ~ ssList(V_4872)
| ~ ssList(U_4873) ),
inference(cnfTransformation,[status(thm)],[f_456]) ).
tff(c_84772,plain,
~ neq(sk2,nil),
inference(splitLeft,[status(thm)],[c_400]) ).
tff(c_85617,plain,
( ( sk2 = nil )
| ~ ssList(sk2)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_85614,c_84772]) ).
tff(c_85624,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_401,c_85617]) ).
tff(c_85626,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_452,c_85624]) ).
tff(c_85628,plain,
neq(sk2,nil),
inference(splitRight,[status(thm)],[c_400]) ).
tff(c_94943,plain,
( ~ neq(nil,sk1)
| ~ ssList(cons(hd(sk1),nil))
| ~ ssList(tl(sk1))
| ( app(tl(sk1),cons(hd(sk1),nil)) = sk2 )
| ~ ssList(app(tl(sk1),cons(hd(sk1),nil))) ),
inference(demodulation,[status(thm),theory(equality)],[c_85628,c_84589,c_398]) ).
tff(c_94944,plain,
~ ssList(app(tl(sk1),cons(hd(sk1),nil))),
inference(splitLeft,[status(thm)],[c_94943]) ).
tff(c_95092,plain,
( ~ ssList(tl(sk1))
| ~ ssList(cons(hd(sk1),nil)) ),
inference(resolution,[status(thm)],[c_170,c_94944]) ).
tff(c_96989,plain,
~ ssList(cons(hd(sk1),nil)),
inference(splitLeft,[status(thm)],[c_95092]) ).
tff(c_96992,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[c_86264,c_96989]) ).
tff(c_96996,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_96992]) ).
tff(c_96997,plain,
~ ssList(tl(sk1)),
inference(splitRight,[status(thm)],[c_95092]) ).
tff(c_97001,plain,
( ( sk1 = nil )
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[c_154,c_96997]) ).
tff(c_97004,plain,
sk1 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_402,c_97001]) ).
tff(c_97006,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_96034,c_97004]) ).
tff(c_97007,plain,
sk1 = nil,
inference(splitRight,[status(thm)],[c_87626]) ).
tff(c_88546,plain,
( rearsegP(sk1,nil)
| ~ ssList(app(sk1,nil))
| ~ ssList(nil)
| ~ ssList(sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_84759,c_88409]) ).
tff(c_88644,plain,
rearsegP(sk1,nil),
inference(demodulation,[status(thm),theory(equality)],[c_402,c_16,c_402,c_84759,c_88546]) ).
tff(c_88658,plain,
( ( sk1 = nil )
| ~ ssList(sk1)
| ~ ssList(nil)
| ~ rearsegP(nil,sk1) ),
inference(resolution,[status(thm)],[c_88644,c_256]) ).
tff(c_88661,plain,
( ( sk1 = nil )
| ~ rearsegP(nil,sk1) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_402,c_88658]) ).
tff(c_91895,plain,
~ rearsegP(nil,sk1),
inference(splitLeft,[status(thm)],[c_88661]) ).
tff(c_97010,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_97007,c_91895]) ).
tff(c_97029,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_88650,c_97010]) ).
tff(c_97030,plain,
( ~ ssList(tl(sk1))
| ~ ssList(cons(hd(sk1),nil))
| ~ neq(nil,sk1)
| ( app(tl(sk1),cons(hd(sk1),nil)) = sk2 ) ),
inference(splitRight,[status(thm)],[c_94943]) ).
tff(c_97246,plain,
~ neq(nil,sk1),
inference(splitLeft,[status(thm)],[c_97030]) ).
tff(c_97250,plain,
sk1 = nil,
inference(resolution,[status(thm)],[c_86908,c_97246]) ).
tff(c_97254,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_97250,c_91895]) ).
tff(c_97273,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_88650,c_97254]) ).
tff(c_97274,plain,
( ~ ssList(cons(hd(sk1),nil))
| ~ ssList(tl(sk1))
| ( app(tl(sk1),cons(hd(sk1),nil)) = sk2 ) ),
inference(splitRight,[status(thm)],[c_97030]) ).
tff(c_97578,plain,
~ ssList(tl(sk1)),
inference(splitLeft,[status(thm)],[c_97274]) ).
tff(c_97581,plain,
( ( sk1 = nil )
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[c_154,c_97578]) ).
tff(c_97584,plain,
sk1 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_402,c_97581]) ).
tff(c_97275,plain,
neq(nil,sk1),
inference(splitRight,[status(thm)],[c_97030]) ).
tff(c_97588,plain,
neq(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_97584,c_97275]) ).
tff(c_97610,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_84603,c_97588]) ).
tff(c_97611,plain,
( ~ ssList(cons(hd(sk1),nil))
| ( app(tl(sk1),cons(hd(sk1),nil)) = sk2 ) ),
inference(splitRight,[status(thm)],[c_97274]) ).
tff(c_97924,plain,
~ ssList(cons(hd(sk1),nil)),
inference(splitLeft,[status(thm)],[c_97611]) ).
tff(c_97927,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[c_86264,c_97924]) ).
tff(c_97931,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_97927]) ).
tff(c_97933,plain,
ssList(cons(hd(sk1),nil)),
inference(splitRight,[status(thm)],[c_97611]) ).
tff(c_97612,plain,
ssList(tl(sk1)),
inference(splitRight,[status(thm)],[c_97274]) ).
tff(c_97932,plain,
app(tl(sk1),cons(hd(sk1),nil)) = sk2,
inference(splitRight,[status(thm)],[c_97611]) ).
tff(c_280,plain,
! [U_182,W_184,V_183] :
( memberP(app(U_182,W_184),V_183)
| ~ ssItem(V_183)
| ~ ssList(U_182)
| ~ ssList(W_184)
| ~ memberP(U_182,V_183) ),
inference(cnfTransformation,[status(thm)],[f_926]) ).
tff(c_89120,plain,
! [U_182,W_184,V_183] :
( memberP(app(U_182,W_184),V_183)
| ~ ssList(U_182)
| ~ ssList(W_184)
| ~ memberP(U_182,V_183) ),
inference(demodulation,[status(thm),theory(equality)],[c_84589,c_280]) ).
tff(c_98175,plain,
! [V_183] :
( memberP(sk2,V_183)
| ~ ssList(tl(sk1))
| ~ ssList(cons(hd(sk1),nil))
| ~ memberP(tl(sk1),V_183) ),
inference(superposition,[status(thm),theory(equality)],[c_97932,c_89120]) ).
tff(c_98227,plain,
! [V_183] :
( memberP(sk2,V_183)
| ~ memberP(tl(sk1),V_183) ),
inference(demodulation,[status(thm),theory(equality)],[c_97933,c_97612,c_98175]) ).
tff(c_100409,plain,
! [V_183] :
( memberP(sk2,V_183)
| ~ memberP(skaf82(sk1),V_183) ),
inference(demodulation,[status(thm),theory(equality)],[c_100400,c_98227]) ).
tff(c_187592,plain,
! [W_9320] :
( memberP(sk2,W_9320)
| ( skaf83(sk1) = W_9320 )
| ~ memberP(sk1,W_9320)
| ( sk1 = nil )
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[c_187574,c_100409]) ).
tff(c_187626,plain,
! [W_9320] :
( memberP(sk2,W_9320)
| ( hd(sk1) = W_9320 )
| ~ memberP(sk1,W_9320)
| ( sk1 = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_402,c_100045,c_187592]) ).
tff(c_256676,plain,
! [W_10807] :
( memberP(sk2,W_10807)
| ( hd(sk1) = W_10807 )
| ~ memberP(sk1,W_10807) ),
inference(negUnitSimplification,[status(thm)],[c_99215,c_187626]) ).
tff(c_256686,plain,
( ( hd(sk1) = sk5 )
| ~ memberP(sk1,sk5) ),
inference(resolution,[status(thm)],[c_256676,c_388]) ).
tff(c_256698,plain,
hd(sk1) = sk5,
inference(demodulation,[status(thm),theory(equality)],[c_386,c_256686]) ).
tff(c_350,plain,
! [U_273,V_274,W_275] :
( memberP(app(U_273,cons(V_274,W_275)),V_274)
| ~ ssList(app(U_273,cons(V_274,W_275)))
| ~ ssItem(V_274)
| ~ ssList(U_273)
| ~ ssList(W_275) ),
inference(cnfTransformation,[status(thm)],[f_1405]) ).
tff(c_93891,plain,
! [U_273,V_274,W_275] :
( memberP(app(U_273,cons(V_274,W_275)),V_274)
| ~ ssList(app(U_273,cons(V_274,W_275)))
| ~ ssList(U_273)
| ~ ssList(W_275) ),
inference(demodulation,[status(thm),theory(equality)],[c_84589,c_350]) ).
tff(c_98151,plain,
( memberP(sk2,hd(sk1))
| ~ ssList(app(tl(sk1),cons(hd(sk1),nil)))
| ~ ssList(tl(sk1))
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_97932,c_93891]) ).
tff(c_98211,plain,
memberP(sk2,hd(sk1)),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_97612,c_401,c_97932,c_98151]) ).
tff(c_256751,plain,
memberP(sk2,sk5),
inference(demodulation,[status(thm),theory(equality)],[c_256698,c_98211]) ).
tff(c_256754,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_388,c_256751]) ).
tff(c_256755,plain,
sk1 = nil,
inference(splitRight,[status(thm)],[c_87626]) ).
tff(c_87237,plain,
! [V_5064,U_5065] :
( ( nil = V_5064 )
| ~ ssList(U_5065)
| ~ ssList(V_5064)
| ( app(U_5065,V_5064) != nil ) ),
inference(cnfTransformation,[status(thm)],[f_658]) ).
tff(c_97437,plain,
! [V_5670] :
( ( nil = V_5670 )
| ~ ssList(V_5670)
| ( app(sk1,V_5670) != nil ) ),
inference(resolution,[status(thm)],[c_402,c_87237]) ).
tff(c_97574,plain,
( ( sk1 = nil )
| ( app(sk1,sk1) != nil ) ),
inference(resolution,[status(thm)],[c_402,c_97437]) ).
tff(c_98124,plain,
app(sk1,sk1) != nil,
inference(splitLeft,[status(thm)],[c_97574]) ).
tff(c_256767,plain,
app(nil,nil) != nil,
inference(demodulation,[status(thm),theory(equality)],[c_256755,c_256755,c_98124]) ).
tff(c_256806,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_586,c_256767]) ).
tff(c_256807,plain,
sk1 = nil,
inference(splitRight,[status(thm)],[c_97574]) ).
tff(c_256823,plain,
neq(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_256807,c_97275]) ).
tff(c_256845,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_84603,c_256823]) ).
tff(c_256846,plain,
sk1 = nil,
inference(splitRight,[status(thm)],[c_88661]) ).
tff(c_88811,plain,
( frontsegP(sk1,nil)
| ~ ssList(app(nil,sk1))
| ~ ssList(nil)
| ~ ssList(sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_587,c_88668]) ).
tff(c_88907,plain,
frontsegP(sk1,nil),
inference(demodulation,[status(thm),theory(equality)],[c_402,c_16,c_402,c_587,c_88811]) ).
tff(c_88977,plain,
( ( sk1 = nil )
| ~ ssList(sk1)
| ~ ssList(nil)
| ~ frontsegP(nil,sk1) ),
inference(resolution,[status(thm)],[c_88907,c_258]) ).
tff(c_88980,plain,
( ( sk1 = nil )
| ~ frontsegP(nil,sk1) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_402,c_88977]) ).
tff(c_91894,plain,
~ frontsegP(nil,sk1),
inference(splitLeft,[status(thm)],[c_88980]) ).
tff(c_256848,plain,
~ frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_256846,c_91894]) ).
tff(c_256866,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_88909,c_256848]) ).
tff(c_256867,plain,
sk1 = nil,
inference(splitRight,[status(thm)],[c_88980]) ).
tff(c_85627,plain,
neq(sk1,nil),
inference(splitRight,[status(thm)],[c_400]) ).
tff(c_256878,plain,
neq(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_256867,c_85627]) ).
tff(c_256890,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_84603,c_256878]) ).
tff(c_256892,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_399]) ).
tff(c_256902,plain,
~ memberP(nil,sk5),
inference(demodulation,[status(thm),theory(equality)],[c_256892,c_388]) ).
tff(c_256891,plain,
sk1 = nil,
inference(splitRight,[status(thm)],[c_399]) ).
tff(c_256894,plain,
memberP(nil,sk5),
inference(demodulation,[status(thm),theory(equality)],[c_256891,c_386]) ).
tff(c_256918,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_256902,c_256894]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC396-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % 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 : n006.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 : Thu Aug 3 21:30:58 EDT 2023
% 0.13/0.35 % CPUTime :
% 164.03/143.85 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 164.14/143.90
% 164.14/143.90 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 164.44/143.96
% 164.44/143.96 Inference rules
% 164.44/143.96 ----------------------
% 164.44/143.96 #Ref : 42
% 164.44/143.96 #Sup : 62024
% 164.44/143.96 #Fact : 0
% 164.44/143.96 #Define : 0
% 164.44/143.96 #Split : 85
% 164.44/143.96 #Chain : 0
% 164.44/143.96 #Close : 0
% 164.44/143.96
% 164.44/143.96 Ordering : KBO
% 164.44/143.96
% 164.44/143.96 Simplification rules
% 164.44/143.96 ----------------------
% 164.44/143.96 #Subsume : 11089
% 164.44/143.96 #Demod : 42725
% 164.44/143.96 #Tautology : 8668
% 164.44/143.96 #SimpNegUnit : 2842
% 164.44/143.96 #BackRed : 915
% 164.44/143.96
% 164.44/143.96 #Partial instantiations: 0
% 164.44/143.96 #Strategies tried : 1
% 164.44/143.96
% 164.44/143.96 Timing (in seconds)
% 164.44/143.96 ----------------------
% 164.44/143.96 Preprocessing : 0.85
% 164.44/143.96 Parsing : 0.45
% 164.44/143.96 CNF conversion : 0.06
% 164.44/143.96 Main loop : 142.01
% 164.44/143.96 Inferencing : 18.84
% 164.44/143.96 Reduction : 63.39
% 164.44/143.96 Demodulation : 47.02
% 164.44/143.96 BG Simplification : 0.47
% 164.44/143.96 Subsumption : 48.52
% 164.44/143.96 Abstraction : 1.14
% 164.44/143.97 MUC search : 0.00
% 164.44/143.97 Cooper : 0.00
% 164.44/143.97 Total : 142.98
% 164.44/143.97 Index Insertion : 0.00
% 164.44/143.97 Index Deletion : 0.00
% 164.44/143.97 Index Matching : 0.00
% 164.44/143.97 BG Taut test : 0.00
%------------------------------------------------------------------------------