TSTP Solution File: SWC030+1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWC030+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/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 : 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 11:00:50 EDT 2023
% Result : Theorem 7.95s 2.95s
% Output : CNFRefutation 8.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 83
% Syntax : Number of formulae : 140 ( 34 unt; 77 typ; 0 def)
% Number of atoms : 123 ( 82 equ)
% Maximal formula atoms : 14 ( 1 avg)
% Number of connectives : 103 ( 43 ~; 41 |; 4 &)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 85 ( 68 >; 17 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-2 aty)
% Number of functors : 58 ( 58 usr; 9 con; 0-2 aty)
% Number of variables : 30 (; 28 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ segmentP > rearsegP > neq > memberP > lt > leq > gt > geq > frontsegP > totalorderedP > totalorderP > strictorderedP > strictorderP > ssList > ssItem > singletonP > equalelemsP > duplicatefreeP > cyclefreeP > cons > app > #nlpp > tl > hd > nil > #skF_36 > #skF_25 > #skF_5 > #skF_52 > #skF_44 > #skF_21 > #skF_16 > #skF_6 > #skF_49 > #skF_18 > #skF_24 > #skF_35 > #skF_19 > #skF_31 > #skF_22 > #skF_37 > #skF_40 > #skF_48 > #skF_3 > #skF_34 > #skF_29 > #skF_15 > #skF_32 > #skF_53 > #skF_51 > #skF_28 > #skF_10 > #skF_41 > #skF_2 > #skF_38 > #skF_43 > #skF_1 > #skF_8 > #skF_39 > #skF_23 > #skF_33 > #skF_26 > #skF_50 > #skF_13 > #skF_17 > #skF_11 > #skF_14 > #skF_27 > #skF_12 > #skF_7 > #skF_46 > #skF_42 > #skF_45 > #skF_9 > #skF_30 > #skF_4 > #skF_20 > #skF_47
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_36',type,
'#skF_36': $i > $i ).
tff(segmentP,type,
segmentP: ( $i * $i ) > $o ).
tff('#skF_25',type,
'#skF_25': $i > $i ).
tff(totalorderedP,type,
totalorderedP: $i > $o ).
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(equalelemsP,type,
equalelemsP: $i > $o ).
tff('#skF_52',type,
'#skF_52': $i ).
tff('#skF_44',type,
'#skF_44': $i > $i ).
tff('#skF_21',type,
'#skF_21': $i > $i ).
tff('#skF_16',type,
'#skF_16': $i > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i ) > $i ).
tff('#skF_49',type,
'#skF_49': $i ).
tff('#skF_18',type,
'#skF_18': $i > $i ).
tff('#skF_24',type,
'#skF_24': $i > $i ).
tff('#skF_35',type,
'#skF_35': $i > $i ).
tff(singletonP,type,
singletonP: $i > $o ).
tff('#skF_19',type,
'#skF_19': $i > $i ).
tff('#skF_31',type,
'#skF_31': $i > $i ).
tff('#skF_22',type,
'#skF_22': $i > $i ).
tff(frontsegP,type,
frontsegP: ( $i * $i ) > $o ).
tff('#skF_37',type,
'#skF_37': $i > $i ).
tff(totalorderP,type,
totalorderP: $i > $o ).
tff(ssItem,type,
ssItem: $i > $o ).
tff('#skF_40',type,
'#skF_40': $i > $i ).
tff('#skF_48',type,
'#skF_48': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_34',type,
'#skF_34': $i > $i ).
tff('#skF_29',type,
'#skF_29': $i > $i ).
tff('#skF_15',type,
'#skF_15': $i > $i ).
tff('#skF_32',type,
'#skF_32': $i > $i ).
tff('#skF_53',type,
'#skF_53': $i ).
tff('#skF_51',type,
'#skF_51': $i ).
tff('#skF_28',type,
'#skF_28': $i > $i ).
tff('#skF_10',type,
'#skF_10': $i > $i ).
tff('#skF_41',type,
'#skF_41': $i > $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_38',type,
'#skF_38': $i > $i ).
tff('#skF_43',type,
'#skF_43': $i > $i ).
tff(hd,type,
hd: $i > $i ).
tff(app,type,
app: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff(duplicatefreeP,type,
duplicatefreeP: $i > $o ).
tff(gt,type,
gt: ( $i * $i ) > $o ).
tff('#skF_39',type,
'#skF_39': $i > $i ).
tff('#skF_23',type,
'#skF_23': $i > $i ).
tff(rearsegP,type,
rearsegP: ( $i * $i ) > $o ).
tff('#skF_33',type,
'#skF_33': $i > $i ).
tff(memberP,type,
memberP: ( $i * $i ) > $o ).
tff('#skF_26',type,
'#skF_26': $i > $i ).
tff('#skF_50',type,
'#skF_50': $i ).
tff('#skF_13',type,
'#skF_13': $i > $i ).
tff(ssList,type,
ssList: $i > $o ).
tff(cons,type,
cons: ( $i * $i ) > $i ).
tff(strictorderP,type,
strictorderP: $i > $o ).
tff('#skF_17',type,
'#skF_17': $i > $i ).
tff(geq,type,
geq: ( $i * $i ) > $o ).
tff('#skF_11',type,
'#skF_11': $i > $i ).
tff(leq,type,
leq: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i > $i ).
tff(lt,type,
lt: ( $i * $i ) > $o ).
tff(tl,type,
tl: $i > $i ).
tff(neq,type,
neq: ( $i * $i ) > $o ).
tff('#skF_27',type,
'#skF_27': $i > $i ).
tff('#skF_12',type,
'#skF_12': $i > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i ) > $i ).
tff('#skF_46',type,
'#skF_46': $i > $i ).
tff(nil,type,
nil: $i ).
tff('#skF_42',type,
'#skF_42': $i > $i ).
tff('#skF_45',type,
'#skF_45': $i > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff(strictorderedP,type,
strictorderedP: $i > $o ).
tff('#skF_30',type,
'#skF_30': $i > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff('#skF_20',type,
'#skF_20': $i > $i ).
tff(cyclefreeP,type,
cyclefreeP: $i > $o ).
tff('#skF_47',type,
'#skF_47': $i > $i ).
tff(f_1016,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( ( app(Y,Z) != X )
| ( app(Z,Y) != W ) ) ) )
| ( ( ( nil != V )
| ( nil = U ) )
& ( ( nil != U )
| ( nil = V ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f_859,axiom,
! [U] :
( ssList(U)
=> ( app(U,nil) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
tff(f_779,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ? [V] :
( ssList(V)
& ( tl(U) = V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax76) ).
tff(f_413,axiom,
! [U] :
( ssList(U)
=> ( app(nil,U) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
tff(f_855,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( nil = app(U,V) )
<=> ( ( nil = V )
& ( nil = U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
tff(f_769,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ? [V] :
( ssItem(V)
& ( hd(U) = V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax75) ).
tff(c_392,plain,
'#skF_48' = '#skF_50',
inference(cnfTransformation,[status(thm)],[f_1016]) ).
tff(c_394,plain,
'#skF_49' = '#skF_51',
inference(cnfTransformation,[status(thm)],[f_1016]) ).
tff(c_410,plain,
( ( nil = '#skF_49' )
| ( nil = '#skF_48' ) ),
inference(cnfTransformation,[status(thm)],[f_1016]) ).
tff(c_413,plain,
( ( nil = '#skF_51' )
| ( nil = '#skF_48' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_394,c_410]) ).
tff(c_417,plain,
( ( nil = '#skF_51' )
| ( nil = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_392,c_413]) ).
tff(c_427,plain,
nil = '#skF_50',
inference(splitLeft,[status(thm)],[c_417]) ).
tff(c_404,plain,
( ( nil != '#skF_48' )
| ( nil != '#skF_49' ) ),
inference(cnfTransformation,[status(thm)],[f_1016]) ).
tff(c_412,plain,
( ( nil != '#skF_48' )
| ( nil != '#skF_51' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_394,c_404]) ).
tff(c_416,plain,
( ( nil != '#skF_50' )
| ( nil != '#skF_51' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_392,c_412]) ).
tff(c_451,plain,
'#skF_51' != '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_427,c_427,c_416]) ).
tff(c_396,plain,
ssList('#skF_51'),
inference(cnfTransformation,[status(thm)],[f_1016]) ).
tff(c_356,plain,
! [U_1080] :
( ( app(U_1080,nil) = U_1080 )
| ~ ssList(U_1080) ),
inference(cnfTransformation,[status(thm)],[f_859]) ).
tff(c_517,plain,
! [U_1199] :
( ( app(U_1199,'#skF_50') = U_1199 )
| ~ ssList(U_1199) ),
inference(demodulation,[status(thm),theory(equality)],[c_427,c_356]) ).
tff(c_534,plain,
app('#skF_51','#skF_50') = '#skF_51',
inference(resolution,[status(thm)],[c_396,c_517]) ).
tff(c_390,plain,
ssList('#skF_52'),
inference(cnfTransformation,[status(thm)],[f_1016]) ).
tff(c_334,plain,
! [U_1047] :
( ( tl(U_1047) = '#skF_47'(U_1047) )
| ( nil = U_1047 )
| ~ ssList(U_1047) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_1139,plain,
! [U_1252] :
( ( tl(U_1252) = '#skF_47'(U_1252) )
| ( U_1252 = '#skF_50' )
| ~ ssList(U_1252) ),
inference(demodulation,[status(thm),theory(equality)],[c_427,c_334]) ).
tff(c_1252,plain,
( ( tl('#skF_52') = '#skF_47'('#skF_52') )
| ( '#skF_52' = '#skF_50' ) ),
inference(resolution,[status(thm)],[c_390,c_1139]) ).
tff(c_1289,plain,
'#skF_52' = '#skF_50',
inference(splitLeft,[status(thm)],[c_1252]) ).
tff(c_386,plain,
app('#skF_52','#skF_53') = '#skF_51',
inference(cnfTransformation,[status(thm)],[f_1016]) ).
tff(c_1294,plain,
app('#skF_50','#skF_53') = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_1289,c_386]) ).
tff(c_388,plain,
ssList('#skF_53'),
inference(cnfTransformation,[status(thm)],[f_1016]) ).
tff(c_196,plain,
! [U_906] :
( ( app(nil,U_906) = U_906 )
| ~ ssList(U_906) ),
inference(cnfTransformation,[status(thm)],[f_413]) ).
tff(c_469,plain,
! [U_1191] :
( ( app('#skF_50',U_1191) = U_1191 )
| ~ ssList(U_1191) ),
inference(demodulation,[status(thm),theory(equality)],[c_427,c_196]) ).
tff(c_483,plain,
app('#skF_50','#skF_53') = '#skF_53',
inference(resolution,[status(thm)],[c_388,c_469]) ).
tff(c_1307,plain,
'#skF_53' = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_1294,c_483]) ).
tff(c_384,plain,
app('#skF_53','#skF_52') = '#skF_50',
inference(cnfTransformation,[status(thm)],[f_1016]) ).
tff(c_1295,plain,
app('#skF_53','#skF_50') = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_1289,c_384]) ).
tff(c_1330,plain,
'#skF_51' = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_534,c_1307,c_1295]) ).
tff(c_1331,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_451,c_1330]) ).
tff(c_1333,plain,
'#skF_52' != '#skF_50',
inference(splitRight,[status(thm)],[c_1252]) ).
tff(c_354,plain,
! [V_1079,U_1077] :
( ( nil = V_1079 )
| ( app(U_1077,V_1079) != nil )
| ~ ssList(V_1079)
| ~ ssList(U_1077) ),
inference(cnfTransformation,[status(thm)],[f_855]) ).
tff(c_2129,plain,
! [V_1283,U_1284] :
( ( V_1283 = '#skF_50' )
| ( app(U_1284,V_1283) != '#skF_50' )
| ~ ssList(V_1283)
| ~ ssList(U_1284) ),
inference(demodulation,[status(thm),theory(equality)],[c_427,c_427,c_354]) ).
tff(c_2151,plain,
( ( '#skF_52' = '#skF_50' )
| ~ ssList('#skF_52')
| ~ ssList('#skF_53') ),
inference(superposition,[status(thm),theory(equality)],[c_384,c_2129]) ).
tff(c_2181,plain,
'#skF_52' = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_388,c_390,c_2151]) ).
tff(c_2183,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1333,c_2181]) ).
tff(c_2184,plain,
nil = '#skF_51',
inference(splitRight,[status(thm)],[c_417]) ).
tff(c_2185,plain,
nil != '#skF_50',
inference(splitRight,[status(thm)],[c_417]) ).
tff(c_2200,plain,
'#skF_51' != '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_2184,c_2185]) ).
tff(c_2228,plain,
! [U_1297] :
( ( app('#skF_51',U_1297) = U_1297 )
| ~ ssList(U_1297) ),
inference(demodulation,[status(thm),theory(equality)],[c_2184,c_196]) ).
tff(c_2244,plain,
app('#skF_51','#skF_51') = '#skF_51',
inference(resolution,[status(thm)],[c_396,c_2228]) ).
tff(c_330,plain,
! [U_1045] :
( ( hd(U_1045) = '#skF_46'(U_1045) )
| ( nil = U_1045 )
| ~ ssList(U_1045) ),
inference(cnfTransformation,[status(thm)],[f_769]) ).
tff(c_2704,plain,
! [U_1351] :
( ( hd(U_1351) = '#skF_46'(U_1351) )
| ( U_1351 = '#skF_51' )
| ~ ssList(U_1351) ),
inference(demodulation,[status(thm),theory(equality)],[c_2184,c_330]) ).
tff(c_2810,plain,
( ( hd('#skF_53') = '#skF_46'('#skF_53') )
| ( '#skF_53' = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_388,c_2704]) ).
tff(c_2827,plain,
'#skF_53' = '#skF_51',
inference(splitLeft,[status(thm)],[c_2810]) ).
tff(c_2831,plain,
app('#skF_52','#skF_51') = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_2827,c_386]) ).
tff(c_2266,plain,
! [U_1300] :
( ( app(U_1300,'#skF_51') = U_1300 )
| ~ ssList(U_1300) ),
inference(demodulation,[status(thm),theory(equality)],[c_2184,c_356]) ).
tff(c_2279,plain,
app('#skF_52','#skF_51') = '#skF_52',
inference(resolution,[status(thm)],[c_390,c_2266]) ).
tff(c_2842,plain,
'#skF_52' = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_2831,c_2279]) ).
tff(c_2832,plain,
app('#skF_51','#skF_52') = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_2827,c_384]) ).
tff(c_2876,plain,
'#skF_51' = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_2244,c_2842,c_2832]) ).
tff(c_2877,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2200,c_2876]) ).
tff(c_2879,plain,
'#skF_53' != '#skF_51',
inference(splitRight,[status(thm)],[c_2810]) ).
tff(c_3685,plain,
! [V_1385,U_1386] :
( ( V_1385 = '#skF_51' )
| ( app(U_1386,V_1385) != '#skF_51' )
| ~ ssList(V_1385)
| ~ ssList(U_1386) ),
inference(demodulation,[status(thm),theory(equality)],[c_2184,c_2184,c_354]) ).
tff(c_3709,plain,
( ( '#skF_53' = '#skF_51' )
| ~ ssList('#skF_53')
| ~ ssList('#skF_52') ),
inference(superposition,[status(thm),theory(equality)],[c_386,c_3685]) ).
tff(c_3743,plain,
'#skF_53' = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_390,c_388,c_3709]) ).
tff(c_3745,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2879,c_3743]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWC030+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/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
% 0.14/0.35 % Computer : n006.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 21:16:13 EDT 2023
% 0.14/0.35 % CPUTime :
% 7.95/2.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.41/2.96
% 8.41/2.96 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.41/2.99
% 8.41/2.99 Inference rules
% 8.41/2.99 ----------------------
% 8.41/2.99 #Ref : 0
% 8.41/2.99 #Sup : 750
% 8.41/2.99 #Fact : 0
% 8.41/2.99 #Define : 0
% 8.41/2.99 #Split : 23
% 8.41/2.99 #Chain : 0
% 8.41/2.99 #Close : 0
% 8.41/2.99
% 8.41/2.99 Ordering : KBO
% 8.41/2.99
% 8.41/2.99 Simplification rules
% 8.41/2.99 ----------------------
% 8.41/2.99 #Subsume : 36
% 8.41/2.99 #Demod : 426
% 8.41/2.99 #Tautology : 269
% 8.41/2.99 #SimpNegUnit : 40
% 8.96/2.99 #BackRed : 77
% 8.96/2.99
% 8.96/2.99 #Partial instantiations: 0
% 8.96/2.99 #Strategies tried : 1
% 8.96/2.99
% 8.96/2.99 Timing (in seconds)
% 8.96/2.99 ----------------------
% 8.96/2.99 Preprocessing : 0.86
% 8.96/2.99 Parsing : 0.40
% 8.96/2.99 CNF conversion : 0.11
% 8.96/2.99 Main loop : 1.03
% 8.96/2.99 Inferencing : 0.33
% 8.96/2.99 Reduction : 0.32
% 8.96/2.99 Demodulation : 0.22
% 8.96/2.99 BG Simplification : 0.08
% 8.96/3.00 Subsumption : 0.20
% 8.96/3.00 Abstraction : 0.04
% 8.96/3.00 MUC search : 0.00
% 8.96/3.00 Cooper : 0.00
% 8.96/3.00 Total : 1.95
% 8.96/3.00 Index Insertion : 0.00
% 8.96/3.00 Index Deletion : 0.00
% 8.96/3.00 Index Matching : 0.00
% 8.96/3.00 BG Taut test : 0.00
%------------------------------------------------------------------------------