%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWC109-1 : 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/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Apr 9 09:19:16 PM UTC 2025
% Result : Unsatisfiable 25.79s 11.25s
% Output : CNFRefutation 25.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 29
% Syntax : Number of formulae : 153 ( 73 unt; 0 typ; 0 def)
% Number of atoms : 303 ( 106 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 295 ( 145 ~; 150 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-2 aty)
% Number of functors : 56 ( 56 usr; 10 con; 0-2 aty)
% Number of variables : 61 ( 61 !; 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 > sk7 > sk6 > 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(sk6,type,
sk6: $i ).
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(sk7,type,
sk7: $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_1738,axiom,
( ( nil != sk1 )
| neq(sk2,nil) ),
file(unknown,unknown) ).
tff(f_1650,axiom,
sk1 = sk3,
file(unknown,unknown) ).
tff(f_1647,axiom,
ssList(sk3),
file(unknown,unknown) ).
tff(f_456,axiom,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) ),
file(unknown,unknown) ).
tff(f_1696,axiom,
( ssList(sk7)
| ( nil = sk3 ) ),
file(unknown,unknown) ).
tff(f_647,axiom,
! [U,V] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) ),
file(unknown,unknown) ).
tff(f_250,axiom,
! [U] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file(unknown,unknown) ).
tff(f_245,axiom,
! [U] :
( ~ ssList(U)
| ( app(U,nil) = 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_334,axiom,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file(unknown,unknown) ).
tff(f_1649,axiom,
sk2 = sk4,
file(unknown,unknown) ).
tff(f_1659,axiom,
( ssList(sk6)
| ( nil = sk4 ) ),
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_784,axiom,
! [U,V] :
( ~ frontsegP(U,V)
| ~ frontsegP(V,U)
| ~ ssList(U)
| ~ ssList(V)
| ( V = U ) ),
file(unknown,unknown) ).
tff(f_1051,axiom,
! [U,V,W] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
file(unknown,unknown) ).
tff(f_1727,axiom,
( ( nil = sk2 )
| neq(sk2,nil) ),
file(unknown,unknown) ).
tff(f_1702,axiom,
( ( app(app(sk6,sk3),sk7) = sk4 )
| ( nil = sk3 ) ),
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_1734,axiom,
( ( nil = sk2 )
| ~ neq(sk1,nil)
| ~ segmentP(sk2,sk1) ),
file(unknown,unknown) ).
tff(f_1648,axiom,
ssList(sk4),
file(unknown,unknown) ).
tff(f_1371,axiom,
! [U,V,W,X] :
( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X)
| segmentP(X,V) ),
file(unknown,unknown) ).
tff(f_1665,axiom,
( ( cons(sk5,nil) = sk3 )
| ( nil = sk4 ) ),
file(unknown,unknown) ).
tff(f_1656,axiom,
( ssItem(sk5)
| ( nil = sk3 ) ),
file(unknown,unknown) ).
tff(f_437,axiom,
! [U,V] :
( ( cons(U,V) != nil )
| ~ ssItem(U)
| ~ ssList(V) ),
file(unknown,unknown) ).
tff(f_613,axiom,
! [U,V] :
( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) ),
file(unknown,unknown) ).
tff(f_1693,axiom,
( ssList(sk6)
| ( nil = sk3 ) ),
file(unknown,unknown) ).
tff(f_1662,axiom,
( ssList(sk7)
| ( nil = sk4 ) ),
file(unknown,unknown) ).
tff(f_1653,axiom,
( ssItem(sk5)
| ( nil = sk4 ) ),
file(unknown,unknown) ).
tff(c_16,plain,
ssList(nil),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_416,plain,
( neq(sk2,nil)
| ( sk1 != nil ) ),
inference(cnfTransformation,[status(thm)],[f_1738]) ).
tff(c_506,plain,
sk1 != nil,
inference(splitLeft,[status(thm)],[c_416]) ).
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_437,plain,
ssList(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_376]) ).
tff(c_10704,plain,
! [V_1004,U_1005] :
( ( V_1004 = U_1005 )
| neq(V_1004,U_1005)
| ~ ssList(V_1004)
| ~ ssList(U_1005) ),
inference(cnfTransformation,[status(thm)],[f_456]) ).
tff(c_402,plain,
( ( sk3 = nil )
| ssList(sk7) ),
inference(cnfTransformation,[status(thm)],[f_1696]) ).
tff(c_419,plain,
( ( sk1 = nil )
| ssList(sk7) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_402]) ).
tff(c_486,plain,
ssList(sk7),
inference(splitLeft,[status(thm)],[c_419]) ).
tff(c_2495,plain,
! [U_557,V_558] :
( ( nil = U_557 )
| ~ ssList(U_557)
| ~ ssList(V_558)
| ( app(U_557,V_558) != nil ) ),
inference(cnfTransformation,[status(thm)],[f_647]) ).
tff(c_2563,plain,
! [V_558] :
( ( sk1 = nil )
| ~ ssList(V_558)
| ( app(sk1,V_558) != nil ) ),
inference(resolution,[status(thm)],[c_437,c_2495]) ).
tff(c_3251,plain,
! [V_599] :
( ~ ssList(V_599)
| ( app(sk1,V_599) != nil ) ),
inference(negUnitSimplification,[status(thm)],[c_506,c_2563]) ).
tff(c_3363,plain,
app(sk1,sk7) != nil,
inference(resolution,[status(thm)],[c_486,c_3251]) ).
tff(c_676,plain,
! [U_396] :
( ( app(nil,U_396) = U_396 )
| ~ ssList(U_396) ),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_800,plain,
app(nil,sk1) = sk1,
inference(resolution,[status(thm)],[c_437,c_676]) ).
tff(c_551,plain,
! [U_395] :
( ( app(U_395,nil) = U_395 )
| ~ ssList(U_395) ),
inference(cnfTransformation,[status(thm)],[f_245]) ).
tff(c_674,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[c_16,c_551]) ).
tff(c_4433,plain,
! [U_682,V_683] :
( rearsegP(app(U_682,V_683),V_683)
| ~ ssList(app(U_682,V_683))
| ~ ssList(V_683)
| ~ ssList(U_682) ),
inference(cnfTransformation,[status(thm)],[f_961]) ).
tff(c_4591,plain,
( rearsegP(nil,nil)
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_674,c_4433]) ).
tff(c_4694,plain,
rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_674,c_4591]) ).
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_380,plain,
sk4 = sk2,
inference(cnfTransformation,[status(thm)],[f_1649]) ).
tff(c_388,plain,
( ( sk4 = nil )
| ssList(sk6) ),
inference(cnfTransformation,[status(thm)],[f_1659]) ).
tff(c_430,plain,
( ( sk2 = nil )
| ssList(sk6) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_388]) ).
tff(c_488,plain,
ssList(sk6),
inference(splitLeft,[status(thm)],[c_430]) ).
tff(c_773,plain,
app(nil,sk6) = sk6,
inference(resolution,[status(thm)],[c_488,c_676]) ).
tff(c_4146,plain,
! [U_680,V_681] :
( frontsegP(app(U_680,V_681),U_680)
| ~ ssList(app(U_680,V_681))
| ~ ssList(U_680)
| ~ ssList(V_681) ),
inference(cnfTransformation,[status(thm)],[f_975]) ).
tff(c_4292,plain,
( frontsegP(sk6,nil)
| ~ ssList(app(nil,sk6))
| ~ ssList(nil)
| ~ ssList(sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_773,c_4146]) ).
tff(c_4399,plain,
frontsegP(sk6,nil),
inference(demodulation,[status(thm),theory(equality)],[c_488,c_16,c_488,c_773,c_4292]) ).
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_4904,plain,
( ( sk6 = nil )
| ~ ssList(sk6)
| ~ ssList(nil)
| ~ frontsegP(nil,sk6) ),
inference(resolution,[status(thm)],[c_4399,c_258]) ).
tff(c_4907,plain,
( ( sk6 = nil )
| ~ frontsegP(nil,sk6) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_488,c_4904]) ).
tff(c_7874,plain,
~ frontsegP(nil,sk6),
inference(splitLeft,[status(thm)],[c_4907]) ).
tff(c_8055,plain,
! [W_841,V_842,U_843] :
( ( app(app(W_841,V_842),U_843) = app(W_841,app(V_842,U_843)) )
| ~ ssList(W_841)
| ~ ssList(V_842)
| ~ ssList(U_843) ),
inference(cnfTransformation,[status(thm)],[f_1051]) ).
tff(c_412,plain,
( neq(sk2,nil)
| ( sk2 = nil ) ),
inference(cnfTransformation,[status(thm)],[f_1727]) ).
tff(c_509,plain,
sk2 = nil,
inference(splitLeft,[status(thm)],[c_412]) ).
tff(c_406,plain,
( ( sk3 = nil )
| ( app(app(sk6,sk3),sk7) = sk4 ) ),
inference(cnfTransformation,[status(thm)],[f_1702]) ).
tff(c_426,plain,
( ( sk1 = nil )
| ( app(app(sk6,sk1),sk7) = sk4 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_382,c_406]) ).
tff(c_435,plain,
( ( sk1 = nil )
| ( app(app(sk6,sk1),sk7) = sk2 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_426]) ).
tff(c_1463,plain,
( ( sk1 = nil )
| ( app(app(sk6,sk1),sk7) = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_509,c_435]) ).
tff(c_1464,plain,
app(app(sk6,sk1),sk7) = nil,
inference(negUnitSimplification,[status(thm)],[c_506,c_1463]) ).
tff(c_8092,plain,
( ( app(sk6,app(sk1,sk7)) = nil )
| ~ ssList(sk6)
| ~ ssList(sk1)
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_8055,c_1464]) ).
tff(c_8278,plain,
app(sk6,app(sk1,sk7)) = nil,
inference(demodulation,[status(thm),theory(equality)],[c_486,c_437,c_488,c_8092]) ).
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_8644,plain,
( frontsegP(nil,sk6)
| ~ ssList(app(sk6,app(sk1,sk7)))
| ~ ssList(sk6)
| ~ ssList(app(sk1,sk7)) ),
inference(superposition,[status(thm),theory(equality)],[c_8278,c_288]) ).
tff(c_8668,plain,
( frontsegP(nil,sk6)
| ~ ssList(app(sk1,sk7)) ),
inference(demodulation,[status(thm),theory(equality)],[c_488,c_16,c_8278,c_8644]) ).
tff(c_8669,plain,
~ ssList(app(sk1,sk7)),
inference(negUnitSimplification,[status(thm)],[c_7874,c_8668]) ).
tff(c_8677,plain,
( ~ ssList(sk1)
| ~ ssList(sk7) ),
inference(resolution,[status(thm)],[c_170,c_8669]) ).
tff(c_8681,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_486,c_437,c_8677]) ).
tff(c_8682,plain,
sk6 = nil,
inference(splitRight,[status(thm)],[c_4907]) ).
tff(c_648,plain,
app(sk6,nil) = sk6,
inference(resolution,[status(thm)],[c_488,c_551]) ).
tff(c_4576,plain,
( rearsegP(sk6,nil)
| ~ ssList(app(sk6,nil))
| ~ ssList(nil)
| ~ ssList(sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_648,c_4433]) ).
tff(c_4684,plain,
rearsegP(sk6,nil),
inference(demodulation,[status(thm),theory(equality)],[c_488,c_16,c_488,c_648,c_4576]) ).
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_4786,plain,
( ( sk6 = nil )
| ~ ssList(sk6)
| ~ ssList(nil)
| ~ rearsegP(nil,sk6) ),
inference(resolution,[status(thm)],[c_4684,c_256]) ).
tff(c_4789,plain,
( ( sk6 = nil )
| ~ rearsegP(nil,sk6) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_488,c_4786]) ).
tff(c_7564,plain,
~ rearsegP(nil,sk6),
inference(splitLeft,[status(thm)],[c_4789]) ).
tff(c_8787,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_8682,c_7564]) ).
tff(c_8840,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4694,c_8787]) ).
tff(c_8841,plain,
sk6 = nil,
inference(splitRight,[status(thm)],[c_4789]) ).
tff(c_8888,plain,
app(app(nil,sk1),sk7) = nil,
inference(demodulation,[status(thm),theory(equality)],[c_8841,c_1464]) ).
tff(c_8900,plain,
app(sk1,sk7) = nil,
inference(demodulation,[status(thm),theory(equality)],[c_800,c_8888]) ).
tff(c_8902,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3363,c_8900]) ).
tff(c_8904,plain,
sk2 != nil,
inference(splitRight,[status(thm)],[c_412]) ).
tff(c_414,plain,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil)
| ( sk2 = nil ) ),
inference(cnfTransformation,[status(thm)],[f_1734]) ).
tff(c_9652,plain,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(negUnitSimplification,[status(thm)],[c_8904,c_414]) ).
tff(c_9653,plain,
~ neq(sk1,nil),
inference(splitLeft,[status(thm)],[c_9652]) ).
tff(c_10707,plain,
( ( sk1 = nil )
| ~ ssList(sk1)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_10704,c_9653]) ).
tff(c_10718,plain,
sk1 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_437,c_10707]) ).
tff(c_10720,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_506,c_10718]) ).
tff(c_10721,plain,
~ segmentP(sk2,sk1),
inference(splitRight,[status(thm)],[c_9652]) ).
tff(c_378,plain,
ssList(sk4),
inference(cnfTransformation,[status(thm)],[f_1648]) ).
tff(c_436,plain,
ssList(sk2),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_378]) ).
tff(c_11336,plain,
app(app(sk6,sk1),sk7) = sk2,
inference(negUnitSimplification,[status(thm)],[c_506,c_435]) ).
tff(c_19631,plain,
! [U_1481,V_1482,W_1483] :
( segmentP(app(app(U_1481,V_1482),W_1483),V_1482)
| ~ ssList(app(app(U_1481,V_1482),W_1483))
| ~ ssList(V_1482)
| ~ ssList(U_1481)
| ~ ssList(W_1483) ),
inference(cnfTransformation,[status(thm)],[f_1371]) ).
tff(c_19771,plain,
( segmentP(sk2,sk1)
| ~ ssList(app(app(sk6,sk1),sk7))
| ~ ssList(sk1)
| ~ ssList(sk6)
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_11336,c_19631]) ).
tff(c_19932,plain,
segmentP(sk2,sk1),
inference(demodulation,[status(thm),theory(equality)],[c_486,c_488,c_437,c_436,c_11336,c_19771]) ).
tff(c_19934,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10721,c_19932]) ).
tff(c_19936,plain,
sk1 = nil,
inference(splitRight,[status(thm)],[c_416]) ).
tff(c_392,plain,
( ( sk4 = nil )
| ( cons(sk5,nil) = sk3 ) ),
inference(cnfTransformation,[status(thm)],[f_1665]) ).
tff(c_422,plain,
( ( sk4 = nil )
| ( cons(sk5,nil) = sk1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_392]) ).
tff(c_434,plain,
( ( sk2 = nil )
| ( cons(sk5,nil) = sk1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_422]) ).
tff(c_19952,plain,
( ( sk2 = nil )
| ( cons(sk5,nil) = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_19936,c_434]) ).
tff(c_19953,plain,
cons(sk5,nil) = nil,
inference(splitLeft,[status(thm)],[c_19952]) ).
tff(c_386,plain,
( ( sk3 = nil )
| ssItem(sk5) ),
inference(cnfTransformation,[status(thm)],[f_1656]) ).
tff(c_423,plain,
( ( sk1 = nil )
| ssItem(sk5) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_386]) ).
tff(c_484,plain,
ssItem(sk5),
inference(splitLeft,[status(thm)],[c_423]) ).
tff(c_21317,plain,
! [V_1572,U_1573] :
( ~ ssList(V_1572)
| ~ ssItem(U_1573)
| ( cons(U_1573,V_1572) != nil ) ),
inference(cnfTransformation,[status(thm)],[f_437]) ).
tff(c_21457,plain,
! [U_1592] :
( ~ ssItem(U_1592)
| ( cons(U_1592,nil) != nil ) ),
inference(resolution,[status(thm)],[c_16,c_21317]) ).
tff(c_21463,plain,
cons(sk5,nil) != nil,
inference(resolution,[status(thm)],[c_484,c_21457]) ).
tff(c_21519,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_19953,c_21463]) ).
tff(c_21520,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_19952]) ).
tff(c_19935,plain,
neq(sk2,nil),
inference(splitRight,[status(thm)],[c_416]) ).
tff(c_21522,plain,
neq(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_21520,c_19935]) ).
tff(c_230,plain,
! [V_129] :
( ~ ssList(V_129)
| ~ neq(V_129,V_129) ),
inference(cnfTransformation,[status(thm)],[f_613]) ).
tff(c_21536,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[c_21522,c_230]) ).
tff(c_21543,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_21536]) ).
tff(c_21545,plain,
~ ssList(sk6),
inference(splitRight,[status(thm)],[c_430]) ).
tff(c_400,plain,
( ( sk3 = nil )
| ssList(sk6) ),
inference(cnfTransformation,[status(thm)],[f_1693]) ).
tff(c_420,plain,
( ( sk1 = nil )
| ssList(sk6) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_400]) ).
tff(c_21559,plain,
sk1 = nil,
inference(negUnitSimplification,[status(thm)],[c_21545,c_420]) ).
tff(c_21544,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_430]) ).
tff(c_21584,plain,
neq(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_21559,c_21544,c_416]) ).
tff(c_21593,plain,
! [V_1612] :
( ~ ssList(V_1612)
| ~ neq(V_1612,V_1612) ),
inference(cnfTransformation,[status(thm)],[f_613]) ).
tff(c_21596,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[c_21584,c_21593]) ).
tff(c_21600,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_21596]) ).
tff(c_21601,plain,
sk1 = nil,
inference(splitRight,[status(thm)],[c_419]) ).
tff(c_21602,plain,
~ ssList(sk7),
inference(splitRight,[status(thm)],[c_419]) ).
tff(c_390,plain,
( ( sk4 = nil )
| ssList(sk7) ),
inference(cnfTransformation,[status(thm)],[f_1662]) ).
tff(c_428,plain,
( ( sk2 = nil )
| ssList(sk7) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_390]) ).
tff(c_21620,plain,
sk2 = nil,
inference(negUnitSimplification,[status(thm)],[c_21602,c_428]) ).
tff(c_21647,plain,
neq(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_21601,c_21620,c_416]) ).
tff(c_21650,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[c_21647,c_230]) ).
tff(c_21657,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_21650]) ).
tff(c_21658,plain,
sk1 = nil,
inference(splitRight,[status(thm)],[c_423]) ).
tff(c_21659,plain,
~ ssItem(sk5),
inference(splitRight,[status(thm)],[c_423]) ).
tff(c_384,plain,
( ( sk4 = nil )
| ssItem(sk5) ),
inference(cnfTransformation,[status(thm)],[f_1653]) ).
tff(c_429,plain,
( ( sk2 = nil )
| ssItem(sk5) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_384]) ).
tff(c_21672,plain,
sk2 = nil,
inference(negUnitSimplification,[status(thm)],[c_21659,c_429]) ).
tff(c_21704,plain,
neq(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_21658,c_21672,c_416]) ).
tff(c_21710,plain,
! [V_1657] :
( ~ ssList(V_1657)
| ~ neq(V_1657,V_1657) ),
inference(cnfTransformation,[status(thm)],[f_613]) ).
tff(c_21713,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[c_21704,c_21710]) ).
tff(c_21717,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_21713]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SWC109-1 : TPTP v9.0.0. Released v2.4.0.
% 0.00/0.08 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.07/0.27 % Computer : n029.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 300
% 0.07/0.27 % DateTime : Wed Apr 9 01:32:19 EDT 2025
% 0.07/0.27 % CPUTime :
% 25.79/11.25 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.79/11.27
% 25.79/11.27 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------