%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWC239-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n019.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 09:19:44 PM UTC 2025
% Result : Timeout 297.69s 272.89s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 68 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 169 ( 43 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 207 ( 106 ~; 101 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 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 : 55 ( 55 usr; 8 con; 0-3 aty)
% Number of variables : 75 ( 75 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ segmentP > rearsegP > neq > memberP > lt > leq > gt > geq > frontsegP > totalorderedP > totalorderP > strictorderedP > strictorderP > ssList > ssItem > singletonP > equalelemsP > duplicatefreeP > cyclefreeP > sk5 > 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 > sk6 > 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(sk5,type,
sk5: ( $i * $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_1652,axiom,
nil != sk1,
file(unknown,unknown) ).
tff(f_1650,axiom,
sk1 = sk3,
file(unknown,unknown) ).
tff(f_1729,axiom,
( ssItem(sk6)
| ( nil = sk3 ) ),
file(unknown,unknown) ).
tff(f_1647,axiom,
ssList(sk3),
file(unknown,unknown) ).
tff(f_1751,axiom,
( ( cons(sk6,nil) = sk3 )
| ( nil = sk3 ) ),
file(unknown,unknown) ).
tff(f_666,axiom,
! [U,V] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
file(unknown,unknown) ).
tff(f_342,axiom,
! [U,V] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file(unknown,unknown) ).
tff(f_240,axiom,
! [U,V] :
( ~ ssList(U)
| duplicatefreeP(U)
| ssItem(V) ),
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_1175,axiom,
! [U,V,W] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) ),
file(unknown,unknown) ).
tff(f_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_233,axiom,
! [U] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
file(unknown,unknown) ).
tff(f_1680,axiom,
! [A,B,C] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) ),
file(unknown,unknown) ).
tff(c_16,plain,
ssList(nil),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_384,plain,
sk1 != nil,
inference(cnfTransformation,[status(thm)],[f_1652]) ).
tff(c_382,plain,
sk3 = sk1,
inference(cnfTransformation,[status(thm)],[f_1650]) ).
tff(c_398,plain,
( ( sk3 = nil )
| ssItem(sk6) ),
inference(cnfTransformation,[status(thm)],[f_1729]) ).
tff(c_411,plain,
( ( sk1 = nil )
| ssItem(sk6) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_398]) ).
tff(c_416,plain,
ssItem(sk6),
inference(negUnitSimplification,[status(thm)],[c_384,c_411]) ).
tff(c_376,plain,
ssList(sk3),
inference(cnfTransformation,[status(thm)],[f_1647]) ).
tff(c_426,plain,
ssList(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_376]) ).
tff(c_406,plain,
( ( sk3 = nil )
| ( cons(sk6,nil) = sk3 ) ),
inference(cnfTransformation,[status(thm)],[f_1751]) ).
tff(c_415,plain,
( ( sk1 = nil )
| ( cons(sk6,nil) = sk1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_382,c_406]) ).
tff(c_421,plain,
cons(sk6,nil) = sk1,
inference(negUnitSimplification,[status(thm)],[c_384,c_415]) ).
tff(c_3765,plain,
! [U_658,V_659] :
( ( app(cons(U_658,nil),V_659) = cons(U_658,V_659) )
| ~ ssList(V_659)
| ~ ssItem(U_658) ),
inference(cnfTransformation,[status(thm)],[f_666]) ).
tff(c_3783,plain,
! [V_659] :
( ( cons(sk6,V_659) = app(sk1,V_659) )
| ~ ssList(V_659)
| ~ ssItem(sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_421,c_3765]) ).
tff(c_12797,plain,
! [V_1254] :
( ( cons(sk6,V_1254) = app(sk1,V_1254) )
| ~ ssList(V_1254) ),
inference(demodulation,[status(thm),theory(equality)],[c_416,c_3783]) ).
tff(c_12930,plain,
cons(sk6,sk1) = app(sk1,sk1),
inference(resolution,[status(thm)],[c_426,c_12797]) ).
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_13429,plain,
( ssList(app(sk1,sk1))
| ~ ssList(sk1)
| ~ ssItem(sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_12930,c_172]) ).
tff(c_13489,plain,
ssList(app(sk1,sk1)),
inference(demodulation,[status(thm),theory(equality)],[c_416,c_426,c_13429]) ).
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_782,plain,
! [U_66] :
( duplicatefreeP(U_66)
| ~ ssList(U_66) ),
inference(splitLeft,[status(thm)],[c_144]) ).
tff(c_13579,plain,
duplicatefreeP(app(sk1,sk1)),
inference(resolution,[status(thm)],[c_13489,c_782]) ).
tff(c_640,plain,
! [U_407] :
( ( app(nil,U_407) = U_407 )
| ~ ssList(U_407) ),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_761,plain,
app(nil,sk1) = sk1,
inference(resolution,[status(thm)],[c_426,c_640]) ).
tff(c_495,plain,
! [U_404] :
( ( app(U_404,nil) = U_404 )
| ~ ssList(U_404) ),
inference(cnfTransformation,[status(thm)],[f_245]) ).
tff(c_613,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[c_16,c_495]) ).
tff(c_7670,plain,
! [U_856,V_857,W_858] :
( ( cons(U_856,app(V_857,W_858)) = app(cons(U_856,V_857),W_858) )
| ~ ssList(W_858)
| ~ ssList(V_857)
| ~ ssItem(U_856) ),
inference(cnfTransformation,[status(thm)],[f_1175]) ).
tff(c_7865,plain,
! [U_856] :
( ( app(cons(U_856,nil),nil) = cons(U_856,nil) )
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssItem(U_856) ),
inference(superposition,[status(thm),theory(equality)],[c_613,c_7670]) ).
tff(c_161933,plain,
! [U_5302] :
( ( app(cons(U_5302,nil),nil) = cons(U_5302,nil) )
| ~ ssItem(U_5302) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_7865]) ).
tff(c_7703,plain,
! [U_856,V_857,W_858] :
( ssList(app(cons(U_856,V_857),W_858))
| ~ ssList(app(V_857,W_858))
| ~ ssItem(U_856)
| ~ ssList(W_858)
| ~ ssList(V_857)
| ~ ssItem(U_856) ),
inference(superposition,[status(thm),theory(equality)],[c_7670,c_172]) ).
tff(c_161960,plain,
! [U_5302] :
( ssList(cons(U_5302,nil))
| ~ ssList(app(nil,nil))
| ~ ssItem(U_5302)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssItem(U_5302)
| ~ ssItem(U_5302) ),
inference(superposition,[status(thm),theory(equality)],[c_161933,c_7703]) ).
tff(c_162193,plain,
! [U_5304] :
( ssList(cons(U_5304,nil))
| ~ ssItem(U_5304) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_613,c_161960]) ).
tff(c_148,plain,
! [U_69] :
( ( app(nil,U_69) = U_69 )
| ~ ssList(U_69) ),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_293595,plain,
! [U_7462] :
( ( app(nil,cons(U_7462,nil)) = cons(U_7462,nil) )
| ~ ssItem(U_7462) ),
inference(resolution,[status(thm)],[c_162193,c_148]) ).
tff(c_10162,plain,
! [U_1024,V_1025,W_1026,X_1027] :
( ~ ssList(app(app(U_1024,cons(V_1025,W_1026)),cons(V_1025,X_1027)))
| ~ duplicatefreeP(app(app(U_1024,cons(V_1025,W_1026)),cons(V_1025,X_1027)))
| ~ ssItem(V_1025)
| ~ ssList(U_1024)
| ~ ssList(W_1026)
| ~ ssList(X_1027) ),
inference(cnfTransformation,[status(thm)],[f_1481]) ).
tff(c_10236,plain,
! [U_1024,W_1026] :
( ~ ssList(app(app(U_1024,cons(sk6,W_1026)),sk1))
| ~ duplicatefreeP(app(app(U_1024,cons(sk6,W_1026)),cons(sk6,nil)))
| ~ ssItem(sk6)
| ~ ssList(U_1024)
| ~ ssList(W_1026)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_421,c_10162]) ).
tff(c_10265,plain,
! [U_1024,W_1026] :
( ~ ssList(app(app(U_1024,cons(sk6,W_1026)),sk1))
| ~ duplicatefreeP(app(app(U_1024,cons(sk6,W_1026)),sk1))
| ~ ssList(U_1024)
| ~ ssList(W_1026) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_416,c_421,c_10236]) ).
tff(c_293741,plain,
( ~ ssList(app(cons(sk6,nil),sk1))
| ~ duplicatefreeP(app(app(nil,cons(sk6,nil)),sk1))
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssItem(sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_293595,c_10265]) ).
tff(c_294022,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_416,c_16,c_16,c_13579,c_761,c_421,c_13489,c_421,c_293741]) ).
tff(c_294023,plain,
! [V_67] : ssItem(V_67),
inference(splitRight,[status(thm)],[c_144]) ).
tff(c_294322,plain,
! [U_7498,V_7499] :
( ssList(cons(U_7498,V_7499))
| ~ ssList(V_7499) ),
inference(demodulation,[status(thm),theory(equality)],[c_294023,c_172]) ).
tff(c_146,plain,
! [U_68] :
( ( app(U_68,nil) = U_68 )
| ~ ssList(U_68) ),
inference(cnfTransformation,[status(thm)],[f_245]) ).
tff(c_294333,plain,
! [U_7498,V_7499] :
( ( app(cons(U_7498,V_7499),nil) = cons(U_7498,V_7499) )
| ~ ssList(V_7499) ),
inference(resolution,[status(thm)],[c_294322,c_146]) ).
tff(c_142,plain,
! [U_65] :
( ~ ssItem(U_65)
| ~ memberP(nil,U_65) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_294039,plain,
! [U_65] : ~ memberP(nil,U_65),
inference(demodulation,[status(thm),theory(equality)],[c_294023,c_142]) ).
tff(c_329706,plain,
! [U_9342,V_9343] :
( ( app(nil,cons(U_9342,V_9343)) = cons(U_9342,V_9343) )
| ~ ssList(V_9343) ),
inference(resolution,[status(thm)],[c_294322,c_148]) ).
tff(c_388,plain,
! [B_331,C_332,A_330] :
( memberP(B_331,sk5(C_332,B_331,A_330))
| ( app(app(B_331,cons(A_330,nil)),C_332) != sk1 )
| ~ ssList(C_332)
| ~ ssList(B_331)
| ~ ssItem(A_330) ),
inference(cnfTransformation,[status(thm)],[f_1680]) ).
tff(c_303268,plain,
! [B_331,C_332,A_330] :
( memberP(B_331,sk5(C_332,B_331,A_330))
| ( app(app(B_331,cons(A_330,nil)),C_332) != sk1 )
| ~ ssList(C_332)
| ~ ssList(B_331) ),
inference(demodulation,[status(thm),theory(equality)],[c_294023,c_388]) ).
tff(c_329740,plain,
! [C_332,U_9342] :
( memberP(nil,sk5(C_332,nil,U_9342))
| ( app(cons(U_9342,nil),C_332) != sk1 )
| ~ ssList(C_332)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_329706,c_303268]) ).
tff(c_329896,plain,
! [C_332,U_9342] :
( memberP(nil,sk5(C_332,nil,U_9342))
| ( app(cons(U_9342,nil),C_332) != sk1 )
| ~ ssList(C_332) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_329740]) ).
tff(c_329985,plain,
! [U_9344,C_9345] :
( ( app(cons(U_9344,nil),C_9345) != sk1 )
| ~ ssList(C_9345) ),
inference(negUnitSimplification,[status(thm)],[c_294039,c_329896]) ).
tff(c_329989,plain,
! [U_7498] :
( ( cons(U_7498,nil) != sk1 )
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_294333,c_329985]) ).
tff(c_330011,plain,
! [U_7498] : ( cons(U_7498,nil) != sk1 ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_329989]) ).
tff(c_330021,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_330011,c_421]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC239-1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.13 % 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 : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Apr 9 01:57:02 EDT 2025
% 0.13/0.34 % CPUTime :
% 297.69/272.89 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 297.69/272.90
% 297.69/272.90 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
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