TSTP Solution File: SWC413-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWC413-1 : 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 : n025.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 11:02:34 EDT 2023
% Result : Unsatisfiable 32.89s 17.07s
% Output : CNFRefutation 32.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 113
% Syntax : Number of formulae : 227 ( 49 unt; 81 typ; 0 def)
% Number of atoms : 387 ( 121 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 464 ( 223 ~; 241 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 2 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 : 62 ( 62 usr; 16 con; 0-2 aty)
% Number of variables : 123 (; 123 !; 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 > sk9 > sk8 > sk7 > sk6 > sk5 > sk4 > sk3 > sk2 > sk13 > sk12 > sk11 > sk10 > 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(sk9,type,
sk9: $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(sk12,type,
sk12: $i ).
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(sk8,type,
sk8: $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(sk10,type,
sk10: $i ).
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(sk11,type,
sk11: $i ).
tff(skaf55,type,
skaf55: $i > $i ).
tff(skaf68,type,
skaf68: $i > $i ).
tff(strictorderedP,type,
strictorderedP: $i > $o ).
tff(sk13,type,
sk13: $i ).
tff(cyclefreeP,type,
cyclefreeP: $i > $o ).
tff(f_1937,axiom,
( ssItem(sk8)
| ssItem(sk12) ),
file(unknown,unknown) ).
tff(f_1925,axiom,
( ssItem(sk9)
| ssItem(sk11) ),
file(unknown,unknown) ).
tff(f_1964,axiom,
( ssList(sk10)
| ssList(sk13) ),
file(unknown,unknown) ).
tff(f_1649,axiom,
sk2 = sk4,
file(unknown,unknown) ).
tff(f_1931,axiom,
( ( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 )
| ssItem(sk11) ),
file(unknown,unknown) ).
tff(f_1650,axiom,
sk1 = sk3,
file(unknown,unknown) ).
tff(f_1934,axiom,
( ( app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 )
| ssItem(sk11) ),
file(unknown,unknown) ).
tff(f_1694,axiom,
! [A,B,C] :
( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ( app(app(cons(A,nil),cons(B,nil)),C) != sk2 )
| ( app(app(cons(B,nil),cons(A,nil)),C) != sk1 )
| ssItem(sk11) ),
file(unknown,unknown) ).
tff(f_1711,axiom,
! [A,B,C] :
( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ( app(app(cons(A,nil),cons(B,nil)),C) != sk2 )
| ( app(app(cons(B,nil),cons(A,nil)),C) != sk1 )
| ssItem(sk12) ),
file(unknown,unknown) ).
tff(f_1728,axiom,
! [A,B,C] :
( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ( app(app(cons(A,nil),cons(B,nil)),C) != sk2 )
| ( app(app(cons(B,nil),cons(A,nil)),C) != sk1 )
| ssList(sk13) ),
file(unknown,unknown) ).
tff(f_1745,axiom,
! [A,B,C] :
( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ( app(app(cons(A,nil),cons(B,nil)),C) != sk2 )
| ( app(app(cons(B,nil),cons(A,nil)),C) != sk1 )
| ( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2 ) ),
file(unknown,unknown) ).
tff(f_1677,axiom,
! [A,F,B,C,E,D] :
( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ( app(app(cons(A,nil),cons(B,nil)),C) != sk2 )
| ( app(app(cons(B,nil),cons(A,nil)),C) != sk1 )
| ~ ssItem(D)
| ~ ssItem(E)
| ~ ssList(F)
| ( app(app(cons(D,nil),cons(E,nil)),F) != sk4 ) ),
file(unknown,unknown) ).
tff(f_1952,axiom,
( ( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 )
| ssItem(sk12) ),
file(unknown,unknown) ).
tff(f_1967,axiom,
( ( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 )
| ssList(sk13) ),
file(unknown,unknown) ).
tff(f_1976,axiom,
( ( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 )
| ( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2 ) ),
file(unknown,unknown) ).
tff(f_1857,axiom,
! [A,B,C] :
( ( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 )
| ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ( app(app(cons(A,nil),cons(B,nil)),C) != sk4 ) ),
file(unknown,unknown) ).
tff(f_1955,axiom,
( ( app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 )
| ssItem(sk12) ),
file(unknown,unknown) ).
tff(f_1970,axiom,
( ( app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 )
| ssList(sk13) ),
file(unknown,unknown) ).
tff(f_1979,axiom,
( ( app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 )
| ( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2 ) ),
file(unknown,unknown) ).
tff(f_1871,axiom,
! [A,B,C] :
( ( app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 )
| ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ( app(app(cons(A,nil),cons(B,nil)),C) != sk4 ) ),
file(unknown,unknown) ).
tff(f_1946,axiom,
( ssItem(sk9)
| ssItem(sk12) ),
file(unknown,unknown) ).
tff(f_1958,axiom,
( ssItem(sk9)
| ssList(sk13) ),
file(unknown,unknown) ).
tff(f_1961,axiom,
( ssItem(sk9)
| ( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2 ) ),
file(unknown,unknown) ).
tff(f_1829,axiom,
! [A,B,C] :
( ssItem(sk9)
| ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ( app(app(cons(A,nil),cons(B,nil)),C) != sk4 ) ),
file(unknown,unknown) ).
tff(f_1922,axiom,
( ssItem(sk8)
| ssItem(sk11) ),
file(unknown,unknown) ).
tff(f_1940,axiom,
( ssItem(sk8)
| ssList(sk13) ),
file(unknown,unknown) ).
tff(f_1943,axiom,
( ssItem(sk8)
| ( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2 ) ),
file(unknown,unknown) ).
tff(f_1815,axiom,
! [A,B,C] :
( ssItem(sk8)
| ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ( app(app(cons(A,nil),cons(B,nil)),C) != sk4 ) ),
file(unknown,unknown) ).
tff(f_1928,axiom,
( ssList(sk10)
| ssItem(sk11) ),
file(unknown,unknown) ).
tff(f_1949,axiom,
( ssList(sk10)
| ssItem(sk12) ),
file(unknown,unknown) ).
tff(f_1973,axiom,
( ssList(sk10)
| ( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2 ) ),
file(unknown,unknown) ).
tff(f_1843,axiom,
! [A,B,C] :
( ssList(sk10)
| ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ( app(app(cons(A,nil),cons(B,nil)),C) != sk4 ) ),
file(unknown,unknown) ).
tff(c_454,plain,
( ssItem(sk12)
| ssItem(sk8) ),
inference(cnfTransformation,[status(thm)],[f_1937]) ).
tff(c_552,plain,
ssItem(sk8),
inference(splitLeft,[status(thm)],[c_454]) ).
tff(c_446,plain,
( ssItem(sk11)
| ssItem(sk9) ),
inference(cnfTransformation,[status(thm)],[f_1925]) ).
tff(c_554,plain,
ssItem(sk9),
inference(splitLeft,[status(thm)],[c_446]) ).
tff(c_472,plain,
( ssList(sk13)
| ssList(sk10) ),
inference(cnfTransformation,[status(thm)],[f_1964]) ).
tff(c_550,plain,
ssList(sk10),
inference(splitLeft,[status(thm)],[c_472]) ).
tff(c_380,plain,
sk4 = sk2,
inference(cnfTransformation,[status(thm)],[f_1649]) ).
tff(c_450,plain,
( ssItem(sk11)
| ( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 ) ),
inference(cnfTransformation,[status(thm)],[f_1931]) ).
tff(c_492,plain,
( ssItem(sk11)
| ( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk2 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_450]) ).
tff(c_3798,plain,
app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk2,
inference(splitLeft,[status(thm)],[c_492]) ).
tff(c_382,plain,
sk3 = sk1,
inference(cnfTransformation,[status(thm)],[f_1650]) ).
tff(c_452,plain,
( ssItem(sk11)
| ( app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 ) ),
inference(cnfTransformation,[status(thm)],[f_1934]) ).
tff(c_483,plain,
( ssItem(sk11)
| ( app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_452]) ).
tff(c_3472,plain,
app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk1,
inference(splitLeft,[status(thm)],[c_483]) ).
tff(c_386,plain,
! [B_334,A_333,C_335] :
( ssItem(sk11)
| ( app(app(cons(B_334,nil),cons(A_333,nil)),C_335) != sk1 )
| ( app(app(cons(A_333,nil),cons(B_334,nil)),C_335) != sk2 )
| ~ ssList(C_335)
| ~ ssItem(B_334)
| ~ ssItem(A_333) ),
inference(cnfTransformation,[status(thm)],[f_1694]) ).
tff(c_11658,plain,
! [B_1093,A_1094,C_1095] :
( ( app(app(cons(B_1093,nil),cons(A_1094,nil)),C_1095) != sk1 )
| ( app(app(cons(A_1094,nil),cons(B_1093,nil)),C_1095) != sk2 )
| ~ ssList(C_1095)
| ~ ssItem(B_1093)
| ~ ssItem(A_1094) ),
inference(splitLeft,[status(thm)],[c_386]) ).
tff(c_11668,plain,
( ( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) != sk2 )
| ~ ssList(sk10)
| ~ ssItem(sk9)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm),theory(equality)],[c_3472,c_11658]) ).
tff(c_11685,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_552,c_554,c_550,c_3798,c_11668]) ).
tff(c_11686,plain,
ssItem(sk11),
inference(splitRight,[status(thm)],[c_386]) ).
tff(c_388,plain,
! [B_337,A_336,C_338] :
( ssItem(sk12)
| ( app(app(cons(B_337,nil),cons(A_336,nil)),C_338) != sk1 )
| ( app(app(cons(A_336,nil),cons(B_337,nil)),C_338) != sk2 )
| ~ ssList(C_338)
| ~ ssItem(B_337)
| ~ ssItem(A_336) ),
inference(cnfTransformation,[status(thm)],[f_1711]) ).
tff(c_12308,plain,
! [B_1118,A_1119,C_1120] :
( ( app(app(cons(B_1118,nil),cons(A_1119,nil)),C_1120) != sk1 )
| ( app(app(cons(A_1119,nil),cons(B_1118,nil)),C_1120) != sk2 )
| ~ ssList(C_1120)
| ~ ssItem(B_1118)
| ~ ssItem(A_1119) ),
inference(splitLeft,[status(thm)],[c_388]) ).
tff(c_12318,plain,
( ( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) != sk2 )
| ~ ssList(sk10)
| ~ ssItem(sk9)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm),theory(equality)],[c_3472,c_12308]) ).
tff(c_12335,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_552,c_554,c_550,c_3798,c_12318]) ).
tff(c_12336,plain,
ssItem(sk12),
inference(splitRight,[status(thm)],[c_388]) ).
tff(c_390,plain,
! [B_340,A_339,C_341] :
( ssList(sk13)
| ( app(app(cons(B_340,nil),cons(A_339,nil)),C_341) != sk1 )
| ( app(app(cons(A_339,nil),cons(B_340,nil)),C_341) != sk2 )
| ~ ssList(C_341)
| ~ ssItem(B_340)
| ~ ssItem(A_339) ),
inference(cnfTransformation,[status(thm)],[f_1728]) ).
tff(c_11916,plain,
! [B_1110,A_1111,C_1112] :
( ( app(app(cons(B_1110,nil),cons(A_1111,nil)),C_1112) != sk1 )
| ( app(app(cons(A_1111,nil),cons(B_1110,nil)),C_1112) != sk2 )
| ~ ssList(C_1112)
| ~ ssItem(B_1110)
| ~ ssItem(A_1111) ),
inference(splitLeft,[status(thm)],[c_390]) ).
tff(c_11926,plain,
( ( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) != sk2 )
| ~ ssList(sk10)
| ~ ssItem(sk9)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm),theory(equality)],[c_3472,c_11916]) ).
tff(c_11943,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_552,c_554,c_550,c_3798,c_11926]) ).
tff(c_11944,plain,
ssList(sk13),
inference(splitRight,[status(thm)],[c_390]) ).
tff(c_392,plain,
! [B_343,A_342,C_344] :
( ( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2 )
| ( app(app(cons(B_343,nil),cons(A_342,nil)),C_344) != sk1 )
| ( app(app(cons(A_342,nil),cons(B_343,nil)),C_344) != sk2 )
| ~ ssList(C_344)
| ~ ssItem(B_343)
| ~ ssItem(A_342) ),
inference(cnfTransformation,[status(thm)],[f_1745]) ).
tff(c_13182,plain,
! [B_1147,A_1148,C_1149] :
( ( app(app(cons(B_1147,nil),cons(A_1148,nil)),C_1149) != sk1 )
| ( app(app(cons(A_1148,nil),cons(B_1147,nil)),C_1149) != sk2 )
| ~ ssList(C_1149)
| ~ ssItem(B_1147)
| ~ ssItem(A_1148) ),
inference(splitLeft,[status(thm)],[c_392]) ).
tff(c_13192,plain,
( ( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) != sk2 )
| ~ ssList(sk10)
| ~ ssItem(sk9)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm),theory(equality)],[c_3472,c_13182]) ).
tff(c_13209,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_552,c_554,c_550,c_3798,c_13192]) ).
tff(c_13210,plain,
app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2,
inference(splitRight,[status(thm)],[c_392]) ).
tff(c_384,plain,
! [D_332,E_331,C_330,B_329,F_328,A_327] :
( ( app(app(cons(D_332,nil),cons(E_331,nil)),F_328) != sk4 )
| ~ ssList(F_328)
| ~ ssItem(E_331)
| ~ ssItem(D_332)
| ( app(app(cons(B_329,nil),cons(A_327,nil)),C_330) != sk1 )
| ( app(app(cons(A_327,nil),cons(B_329,nil)),C_330) != sk2 )
| ~ ssList(C_330)
| ~ ssItem(B_329)
| ~ ssItem(A_327) ),
inference(cnfTransformation,[status(thm)],[f_1677]) ).
tff(c_500,plain,
! [D_332,E_331,C_330,B_329,F_328,A_327] :
( ( app(app(cons(D_332,nil),cons(E_331,nil)),F_328) != sk2 )
| ~ ssList(F_328)
| ~ ssItem(E_331)
| ~ ssItem(D_332)
| ( app(app(cons(B_329,nil),cons(A_327,nil)),C_330) != sk1 )
| ( app(app(cons(A_327,nil),cons(B_329,nil)),C_330) != sk2 )
| ~ ssList(C_330)
| ~ ssItem(B_329)
| ~ ssItem(A_327) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_384]) ).
tff(c_13534,plain,
! [B_1166,A_1167,C_1168] :
( ( app(app(cons(B_1166,nil),cons(A_1167,nil)),C_1168) != sk1 )
| ( app(app(cons(A_1167,nil),cons(B_1166,nil)),C_1168) != sk2 )
| ~ ssList(C_1168)
| ~ ssItem(B_1166)
| ~ ssItem(A_1167) ),
inference(splitLeft,[status(thm)],[c_500]) ).
tff(c_13546,plain,
( ( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) != sk2 )
| ~ ssList(sk10)
| ~ ssItem(sk9)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm),theory(equality)],[c_3472,c_13534]) ).
tff(c_13565,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_552,c_554,c_550,c_3798,c_13546]) ).
tff(c_13576,plain,
! [D_1178,E_1179,F_1180] :
( ( app(app(cons(D_1178,nil),cons(E_1179,nil)),F_1180) != sk2 )
| ~ ssList(F_1180)
| ~ ssItem(E_1179)
| ~ ssItem(D_1178) ),
inference(splitRight,[status(thm)],[c_500]) ).
tff(c_13579,plain,
( ~ ssList(sk13)
| ~ ssItem(sk12)
| ~ ssItem(sk11) ),
inference(superposition,[status(thm),theory(equality)],[c_13210,c_13576]) ).
tff(c_13610,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_11686,c_12336,c_11944,c_13579]) ).
tff(c_13611,plain,
ssItem(sk11),
inference(splitRight,[status(thm)],[c_492]) ).
tff(c_13612,plain,
app(app(cons(sk8,nil),cons(sk9,nil)),sk10) != sk2,
inference(splitRight,[status(thm)],[c_492]) ).
tff(c_464,plain,
( ssItem(sk12)
| ( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 ) ),
inference(cnfTransformation,[status(thm)],[f_1952]) ).
tff(c_488,plain,
( ssItem(sk12)
| ( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk2 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_464]) ).
tff(c_14635,plain,
ssItem(sk12),
inference(negUnitSimplification,[status(thm)],[c_13612,c_488]) ).
tff(c_474,plain,
( ssList(sk13)
| ( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 ) ),
inference(cnfTransformation,[status(thm)],[f_1967]) ).
tff(c_490,plain,
( ssList(sk13)
| ( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk2 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_474]) ).
tff(c_14493,plain,
ssList(sk13),
inference(negUnitSimplification,[status(thm)],[c_13612,c_490]) ).
tff(c_480,plain,
( ( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2 )
| ( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 ) ),
inference(cnfTransformation,[status(thm)],[f_1976]) ).
tff(c_491,plain,
( ( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2 )
| ( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk2 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_480]) ).
tff(c_20795,plain,
app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2,
inference(negUnitSimplification,[status(thm)],[c_13612,c_491]) ).
tff(c_408,plain,
! [A_366,B_367,C_368] :
( ( app(app(cons(A_366,nil),cons(B_367,nil)),C_368) != sk4 )
| ~ ssList(C_368)
| ~ ssItem(B_367)
| ~ ssItem(A_366)
| ( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 ) ),
inference(cnfTransformation,[status(thm)],[f_1857]) ).
tff(c_493,plain,
! [A_366,B_367,C_368] :
( ( app(app(cons(A_366,nil),cons(B_367,nil)),C_368) != sk2 )
| ~ ssList(C_368)
| ~ ssItem(B_367)
| ~ ssItem(A_366)
| ( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk2 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_380,c_408]) ).
tff(c_20974,plain,
! [A_1486,B_1487,C_1488] :
( ( app(app(cons(A_1486,nil),cons(B_1487,nil)),C_1488) != sk2 )
| ~ ssList(C_1488)
| ~ ssItem(B_1487)
| ~ ssItem(A_1486) ),
inference(negUnitSimplification,[status(thm)],[c_13612,c_493]) ).
tff(c_20977,plain,
( ~ ssList(sk13)
| ~ ssItem(sk12)
| ~ ssItem(sk11) ),
inference(superposition,[status(thm),theory(equality)],[c_20795,c_20974]) ).
tff(c_21005,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_13611,c_14635,c_14493,c_20977]) ).
tff(c_21006,plain,
ssItem(sk11),
inference(splitRight,[status(thm)],[c_483]) ).
tff(c_21007,plain,
app(app(cons(sk9,nil),cons(sk8,nil)),sk10) != sk1,
inference(splitRight,[status(thm)],[c_483]) ).
tff(c_466,plain,
( ssItem(sk12)
| ( app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 ) ),
inference(cnfTransformation,[status(thm)],[f_1955]) ).
tff(c_486,plain,
( ssItem(sk12)
| ( app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_466]) ).
tff(c_21363,plain,
ssItem(sk12),
inference(negUnitSimplification,[status(thm)],[c_21007,c_486]) ).
tff(c_476,plain,
( ssList(sk13)
| ( app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 ) ),
inference(cnfTransformation,[status(thm)],[f_1970]) ).
tff(c_484,plain,
( ssList(sk13)
| ( app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_476]) ).
tff(c_21722,plain,
ssList(sk13),
inference(negUnitSimplification,[status(thm)],[c_21007,c_484]) ).
tff(c_482,plain,
( ( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2 )
| ( app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 ) ),
inference(cnfTransformation,[status(thm)],[f_1979]) ).
tff(c_485,plain,
( ( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2 )
| ( app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_482]) ).
tff(c_28580,plain,
app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2,
inference(negUnitSimplification,[status(thm)],[c_21007,c_485]) ).
tff(c_410,plain,
! [A_369,B_370,C_371] :
( ( app(app(cons(A_369,nil),cons(B_370,nil)),C_371) != sk4 )
| ~ ssList(C_371)
| ~ ssItem(B_370)
| ~ ssItem(A_369)
| ( app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 ) ),
inference(cnfTransformation,[status(thm)],[f_1871]) ).
tff(c_487,plain,
! [A_369,B_370,C_371] :
( ( app(app(cons(A_369,nil),cons(B_370,nil)),C_371) != sk4 )
| ~ ssList(C_371)
| ~ ssItem(B_370)
| ~ ssItem(A_369)
| ( app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_410]) ).
tff(c_501,plain,
! [A_369,B_370,C_371] :
( ( app(app(cons(A_369,nil),cons(B_370,nil)),C_371) != sk2 )
| ~ ssList(C_371)
| ~ ssItem(B_370)
| ~ ssItem(A_369)
| ( app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_487]) ).
tff(c_28685,plain,
! [A_1818,B_1819,C_1820] :
( ( app(app(cons(A_1818,nil),cons(B_1819,nil)),C_1820) != sk2 )
| ~ ssList(C_1820)
| ~ ssItem(B_1819)
| ~ ssItem(A_1818) ),
inference(negUnitSimplification,[status(thm)],[c_21007,c_501]) ).
tff(c_28688,plain,
( ~ ssList(sk13)
| ~ ssItem(sk12)
| ~ ssItem(sk11) ),
inference(superposition,[status(thm),theory(equality)],[c_28580,c_28685]) ).
tff(c_28716,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_21006,c_21363,c_21722,c_28688]) ).
tff(c_28717,plain,
ssItem(sk11),
inference(splitRight,[status(thm)],[c_446]) ).
tff(c_28718,plain,
~ ssItem(sk9),
inference(splitRight,[status(thm)],[c_446]) ).
tff(c_460,plain,
( ssItem(sk12)
| ssItem(sk9) ),
inference(cnfTransformation,[status(thm)],[f_1946]) ).
tff(c_28725,plain,
ssItem(sk12),
inference(negUnitSimplification,[status(thm)],[c_28718,c_460]) ).
tff(c_468,plain,
( ssList(sk13)
| ssItem(sk9) ),
inference(cnfTransformation,[status(thm)],[f_1958]) ).
tff(c_28721,plain,
ssList(sk13),
inference(negUnitSimplification,[status(thm)],[c_28718,c_468]) ).
tff(c_470,plain,
( ( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2 )
| ssItem(sk9) ),
inference(cnfTransformation,[status(thm)],[f_1961]) ).
tff(c_32255,plain,
app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2,
inference(negUnitSimplification,[status(thm)],[c_28718,c_470]) ).
tff(c_404,plain,
! [A_360,B_361,C_362] :
( ( app(app(cons(A_360,nil),cons(B_361,nil)),C_362) != sk4 )
| ~ ssList(C_362)
| ~ ssItem(B_361)
| ~ ssItem(A_360)
| ssItem(sk9) ),
inference(cnfTransformation,[status(thm)],[f_1829]) ).
tff(c_495,plain,
! [A_360,B_361,C_362] :
( ( app(app(cons(A_360,nil),cons(B_361,nil)),C_362) != sk2 )
| ~ ssList(C_362)
| ~ ssItem(B_361)
| ~ ssItem(A_360)
| ssItem(sk9) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_404]) ).
tff(c_38229,plain,
! [A_2348,B_2349,C_2350] :
( ( app(app(cons(A_2348,nil),cons(B_2349,nil)),C_2350) != sk2 )
| ~ ssList(C_2350)
| ~ ssItem(B_2349)
| ~ ssItem(A_2348) ),
inference(negUnitSimplification,[status(thm)],[c_28718,c_495]) ).
tff(c_38240,plain,
( ~ ssList(sk13)
| ~ ssItem(sk12)
| ~ ssItem(sk11) ),
inference(superposition,[status(thm),theory(equality)],[c_32255,c_38229]) ).
tff(c_38256,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28717,c_28725,c_28721,c_38240]) ).
tff(c_38258,plain,
~ ssItem(sk8),
inference(splitRight,[status(thm)],[c_454]) ).
tff(c_444,plain,
( ssItem(sk11)
| ssItem(sk8) ),
inference(cnfTransformation,[status(thm)],[f_1922]) ).
tff(c_38269,plain,
ssItem(sk11),
inference(negUnitSimplification,[status(thm)],[c_38258,c_444]) ).
tff(c_38257,plain,
ssItem(sk12),
inference(splitRight,[status(thm)],[c_454]) ).
tff(c_456,plain,
( ssList(sk13)
| ssItem(sk8) ),
inference(cnfTransformation,[status(thm)],[f_1940]) ).
tff(c_38271,plain,
ssList(sk13),
inference(negUnitSimplification,[status(thm)],[c_38258,c_456]) ).
tff(c_458,plain,
( ( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2 )
| ssItem(sk8) ),
inference(cnfTransformation,[status(thm)],[f_1943]) ).
tff(c_40621,plain,
app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2,
inference(negUnitSimplification,[status(thm)],[c_38258,c_458]) ).
tff(c_402,plain,
! [A_357,B_358,C_359] :
( ( app(app(cons(A_357,nil),cons(B_358,nil)),C_359) != sk4 )
| ~ ssList(C_359)
| ~ ssItem(B_358)
| ~ ssItem(A_357)
| ssItem(sk8) ),
inference(cnfTransformation,[status(thm)],[f_1815]) ).
tff(c_496,plain,
! [A_357,B_358,C_359] :
( ( app(app(cons(A_357,nil),cons(B_358,nil)),C_359) != sk2 )
| ~ ssList(C_359)
| ~ ssItem(B_358)
| ~ ssItem(A_357)
| ssItem(sk8) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_402]) ).
tff(c_46997,plain,
! [A_2845,B_2846,C_2847] :
( ( app(app(cons(A_2845,nil),cons(B_2846,nil)),C_2847) != sk2 )
| ~ ssList(C_2847)
| ~ ssItem(B_2846)
| ~ ssItem(A_2845) ),
inference(negUnitSimplification,[status(thm)],[c_38258,c_496]) ).
tff(c_47012,plain,
( ~ ssList(sk13)
| ~ ssItem(sk12)
| ~ ssItem(sk11) ),
inference(superposition,[status(thm),theory(equality)],[c_40621,c_46997]) ).
tff(c_47024,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_38269,c_38257,c_38271,c_47012]) ).
tff(c_47026,plain,
~ ssList(sk10),
inference(splitRight,[status(thm)],[c_472]) ).
tff(c_448,plain,
( ssItem(sk11)
| ssList(sk10) ),
inference(cnfTransformation,[status(thm)],[f_1928]) ).
tff(c_47027,plain,
ssItem(sk11),
inference(negUnitSimplification,[status(thm)],[c_47026,c_448]) ).
tff(c_462,plain,
( ssItem(sk12)
| ssList(sk10) ),
inference(cnfTransformation,[status(thm)],[f_1949]) ).
tff(c_47044,plain,
ssItem(sk12),
inference(negUnitSimplification,[status(thm)],[c_47026,c_462]) ).
tff(c_47025,plain,
ssList(sk13),
inference(splitRight,[status(thm)],[c_472]) ).
tff(c_478,plain,
( ( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2 )
| ssList(sk10) ),
inference(cnfTransformation,[status(thm)],[f_1973]) ).
tff(c_49896,plain,
app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2,
inference(negUnitSimplification,[status(thm)],[c_47026,c_478]) ).
tff(c_406,plain,
! [A_363,B_364,C_365] :
( ( app(app(cons(A_363,nil),cons(B_364,nil)),C_365) != sk4 )
| ~ ssList(C_365)
| ~ ssItem(B_364)
| ~ ssItem(A_363)
| ssList(sk10) ),
inference(cnfTransformation,[status(thm)],[f_1843]) ).
tff(c_494,plain,
! [A_363,B_364,C_365] :
( ( app(app(cons(A_363,nil),cons(B_364,nil)),C_365) != sk2 )
| ~ ssList(C_365)
| ~ ssItem(B_364)
| ~ ssItem(A_363)
| ssList(sk10) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_406]) ).
tff(c_56152,plain,
! [A_3359,B_3360,C_3361] :
( ( app(app(cons(A_3359,nil),cons(B_3360,nil)),C_3361) != sk2 )
| ~ ssList(C_3361)
| ~ ssItem(B_3360)
| ~ ssItem(A_3359) ),
inference(negUnitSimplification,[status(thm)],[c_47026,c_494]) ).
tff(c_56163,plain,
( ~ ssList(sk13)
| ~ ssItem(sk12)
| ~ ssItem(sk11) ),
inference(superposition,[status(thm),theory(equality)],[c_49896,c_56152]) ).
tff(c_56179,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_47027,c_47044,c_47025,c_56163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWC413-1 : 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 : n025.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 21:53:49 EDT 2023
% 0.14/0.35 % CPUTime :
% 32.89/17.07 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 32.89/17.09
% 32.89/17.09 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 32.89/17.14
% 32.89/17.14 Inference rules
% 32.89/17.14 ----------------------
% 32.89/17.14 #Ref : 0
% 32.89/17.14 #Sup : 12111
% 32.89/17.14 #Fact : 0
% 32.89/17.14 #Define : 0
% 32.89/17.14 #Split : 133
% 32.89/17.14 #Chain : 0
% 32.89/17.14 #Close : 0
% 32.89/17.14
% 32.89/17.14 Ordering : KBO
% 32.89/17.14
% 32.89/17.14 Simplification rules
% 32.89/17.14 ----------------------
% 32.89/17.14 #Subsume : 888
% 32.89/17.14 #Demod : 13884
% 32.89/17.14 #Tautology : 3291
% 32.89/17.14 #SimpNegUnit : 20
% 32.89/17.14 #BackRed : 0
% 32.89/17.14
% 32.89/17.14 #Partial instantiations: 0
% 32.89/17.14 #Strategies tried : 1
% 32.89/17.14
% 32.89/17.14 Timing (in seconds)
% 32.89/17.14 ----------------------
% 32.89/17.14 Preprocessing : 0.93
% 32.89/17.14 Parsing : 0.44
% 32.89/17.14 CNF conversion : 0.07
% 32.89/17.14 Main loop : 15.11
% 32.89/17.14 Inferencing : 3.15
% 32.89/17.14 Reduction : 7.70
% 32.89/17.14 Demodulation : 5.84
% 32.89/17.14 BG Simplification : 0.15
% 32.89/17.14 Subsumption : 3.16
% 32.89/17.14 Abstraction : 0.21
% 32.89/17.14 MUC search : 0.00
% 32.89/17.14 Cooper : 0.00
% 32.89/17.14 Total : 16.12
% 32.89/17.14 Index Insertion : 0.00
% 32.89/17.14 Index Deletion : 0.00
% 32.89/17.14 Index Matching : 0.00
% 32.89/17.14 BG Taut test : 0.00
%------------------------------------------------------------------------------