TSTP Solution File: SWW629_2 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWW629_2 : TPTP v8.1.2. Released v6.1.0.
% 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 11:07:50 EDT 2023
% Result : Theorem 23.25s 7.74s
% Output : CNFRefutation 23.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 78
% Syntax : Number of formulae : 110 ( 19 unt; 74 typ; 0 def)
% Number of atoms : 81 ( 10 equ)
% Maximal formula atoms : 23 ( 2 avg)
% Number of connectives : 69 ( 24 ~; 19 |; 8 &)
% ( 1 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 5 ( 1 atm; 1 fun; 3 num; 0 var)
% Number of types : 8 ( 6 usr; 1 ari)
% Number of type conns : 70 ( 35 >; 35 *; 0 +; 0 <<)
% Number of predicates : 8 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 66 ( 63 usr; 35 con; 0-5 aty)
% Number of variables : 52 (; 52 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
%$ permut > mem > sort1 > le1 > sorted1 > match_list1 > match_bool1 > num_occ1 > infix_plpl > cons > reverse > mk_t > length3 > length2 > elts > cons_proj_21 > cons_proj_11 > #nlpp > witness1 > tb2t1 > tb2t > t2tb1 > t2tb > t > nil > list > tuple03 > tuple0 > true1 > real > qtmark > int > false1 > elt > bool > #skF_3 > #skF_19 > #skF_9 > #skF_5 > #skF_4 > #skF_16 > #skF_17 > #skF_20 > #skF_18 > #skF_11 > #skF_15 > #skF_12 > #skF_8 > #skF_1 > #skF_10 > #skF_7 > #skF_6 > #skF_13 > #skF_14 > #skF_2
%Foreground sorts:
tff(elt1,type,
elt1: $tType ).
tff(tuple02,type,
tuple02: $tType ).
tff(bool1,type,
bool1: $tType ).
tff(list_elt,type,
list_elt: $tType ).
tff(ty,type,
ty: $tType ).
tff(uni,type,
uni: $tType ).
%Background operators:
tff('#skE_7',type,
'#skE_7': $int ).
tff('#skE_11',type,
'#skE_11': $int ).
tff('#skE_12',type,
'#skE_12': $int ).
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skE_6',type,
'#skE_6': $int ).
tff('#skE_13',type,
'#skE_13': $int ).
tff('#skE_10',type,
'#skE_10': $int ).
tff('#skE_5',type,
'#skE_5': $int ).
tff('#skE_8',type,
'#skE_8': $int ).
tff('#skE_4',type,
'#skE_4': $int ).
tff('#skE_3',type,
'#skE_3': $int ).
tff('#skE_9',type,
'#skE_9': $int ).
tff('#skE_14',type,
'#skE_14': $int ).
%Foreground operators:
tff(list,type,
list: ty > ty ).
tff('#skF_3',type,
'#skF_3': ( ty * uni * uni ) > uni ).
tff(length3,type,
length3: ( ty * uni ) > $int ).
tff(num_occ1,type,
num_occ1: ( ty * uni * uni ) > $int ).
tff('#skF_19',type,
'#skF_19': list_elt ).
tff('#skF_9',type,
'#skF_9': ( list_elt * list_elt ) > elt1 ).
tff(cons,type,
cons: ( ty * uni * uni ) > uni ).
tff('#skF_5',type,
'#skF_5': list_elt > elt1 ).
tff(t2tb,type,
t2tb: list_elt > uni ).
tff(t,type,
t: ty > ty ).
tff(nil,type,
nil: ty > uni ).
tff(permut,type,
permut: ( ty * uni * uni ) > $o ).
tff(true1,type,
true1: bool1 ).
tff(match_list1,type,
match_list1: ( ty * ty * uni * uni * uni ) > uni ).
tff(elts,type,
elts: ( ty * uni ) > uni ).
tff(int,type,
int: ty ).
tff(length2,type,
length2: ( ty * uni ) > $int ).
tff(false1,type,
false1: bool1 ).
tff(mk_t,type,
mk_t: ( ty * uni ) > uni ).
tff(sort1,type,
sort1: ( ty * uni ) > $o ).
tff('#skF_4',type,
'#skF_4': list_elt > elt1 ).
tff(witness1,type,
witness1: ty > uni ).
tff(real,type,
real: ty ).
tff('#skF_16',type,
'#skF_16': list_elt ).
tff(match_bool1,type,
match_bool1: ( ty * bool1 * uni * uni ) > uni ).
tff(tb2t1,type,
tb2t1: uni > elt1 ).
tff(tb2t,type,
tb2t: uni > list_elt ).
tff(reverse,type,
reverse: ( ty * uni ) > uni ).
tff(sorted1,type,
sorted1: list_elt > $o ).
tff('#skF_17',type,
'#skF_17': bool1 ).
tff('#skF_20',type,
'#skF_20': list_elt ).
tff(t2tb1,type,
t2tb1: elt1 > uni ).
tff(tuple0,type,
tuple0: ty ).
tff(qtmark,type,
qtmark: ty ).
tff(le1,type,
le1: ( elt1 * elt1 ) > $o ).
tff(bool,type,
bool: ty ).
tff('#skF_18',type,
'#skF_18': list_elt ).
tff('#skF_11',type,
'#skF_11': list_elt ).
tff('#skF_15',type,
'#skF_15': list_elt ).
tff('#skF_12',type,
'#skF_12': list_elt ).
tff('#skF_8',type,
'#skF_8': ( elt1 * list_elt ) > elt1 ).
tff('#skF_1',type,
'#skF_1': ( ty * uni * uni ) > uni ).
tff(tuple03,type,
tuple03: tuple02 ).
tff('#skF_10',type,
'#skF_10': ( list_elt * list_elt ) > elt1 ).
tff('#skF_7',type,
'#skF_7': list_elt > list_elt ).
tff(elt,type,
elt: ty ).
tff(cons_proj_11,type,
cons_proj_11: ( ty * uni ) > uni ).
tff('#skF_6',type,
'#skF_6': list_elt > elt1 ).
tff('#skF_13',type,
'#skF_13': list_elt ).
tff(mem,type,
mem: ( ty * uni * uni ) > $o ).
tff(cons_proj_21,type,
cons_proj_21: ( ty * uni ) > uni ).
tff('#skF_14',type,
'#skF_14': list_elt ).
tff(infix_plpl,type,
infix_plpl: ( ty * uni * uni ) > uni ).
tff('#skF_2',type,
'#skF_2': ( ty * uni * uni ) > uni ).
tff(f_370,negated_conjecture,
~ ! [Q: list_elt] :
( $less(1,length2(elt,t2tb(Q)))
=> ! [Q1: list_elt] :
( ( Q1 = tb2t(nil(elt)) )
=> ! [Q2: list_elt] :
( ( Q2 = tb2t(nil(elt)) )
=> ! [Q21: list_elt,Q11: list_elt,Q3: list_elt] :
( ( permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(Q11),t2tb(Q21)),t2tb(Q3)),t2tb(Q))
& ( ( length2(elt,t2tb(Q11)) = length2(elt,t2tb(Q21)) )
| ( ( length2(elt,t2tb(Q3)) = 0 )
& ( length2(elt,t2tb(Q11)) = $sum(length2(elt,t2tb(Q21)),1) ) ) ) )
=> ! [O: bool1] :
( ( ( O = true1 )
<=> ( Q3 = tb2t(nil(elt)) ) )
=> ( ( O != true1 )
=> ( ( Q3 = tb2t(nil(elt)) )
=> ( permut(elt,infix_plpl(elt,t2tb(Q11),t2tb(Q21)),t2tb(Q))
=> ! [Q12: list_elt] :
( ( sorted1(Q12)
& permut(elt,t2tb(Q12),t2tb(Q11)) )
=> ! [Q22: list_elt] :
( ( sorted1(Q22)
& permut(elt,t2tb(Q22),t2tb(Q21)) )
=> ( ( ( Q3 = tb2t(nil(elt)) )
& sorted1(Q12)
& sorted1(Q22) )
=> ! [Q4: list_elt] :
( ( sorted1(Q4)
& permut(elt,t2tb(Q4),infix_plpl(elt,t2tb(Q12),t2tb(Q22))) )
=> ( sorted1(Q4)
& permut(elt,t2tb(Q4),t2tb(Q)) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wP_parameter_mergesort) ).
tff(f_205,axiom,
! [A: ty,L1: uni,L2: uni,L3: uni] :
( permut(A,L1,L2)
=> ( permut(A,L2,L3)
=> permut(A,L1,L3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',permut_trans) ).
tff(f_199,axiom,
! [A: ty,L1: uni,L2: uni] :
( permut(A,L1,L2)
=> permut(A,L2,L1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',permut_sym) ).
tff(f_221,axiom,
! [A: ty,L1: uni,L2: uni,K1: uni,K2: uni] :
( permut(A,L1,K1)
=> ( permut(A,L2,K2)
=> permut(A,infix_plpl(A,L1,L2),infix_plpl(A,K1,K2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',permut_append) ).
tff(c_208,plain,
sorted1('#skF_20'),
inference(cnfTransformation,[status(thm)],[f_370]) ).
tff(c_204,plain,
( ~ permut(elt,t2tb('#skF_20'),t2tb('#skF_11'))
| ~ sorted1('#skF_20') ),
inference(cnfTransformation,[status(thm)],[f_370]) ).
tff(c_317,plain,
~ permut(elt,t2tb('#skF_20'),t2tb('#skF_11')),
inference(demodulation,[status(thm),theory(equality)],[c_208,c_204]) ).
tff(c_224,plain,
permut(elt,infix_plpl(elt,t2tb('#skF_15'),t2tb('#skF_14')),t2tb('#skF_11')),
inference(cnfTransformation,[status(thm)],[f_370]) ).
tff(c_206,plain,
permut(elt,t2tb('#skF_20'),infix_plpl(elt,t2tb('#skF_18'),t2tb('#skF_19'))),
inference(cnfTransformation,[status(thm)],[f_370]) ).
tff(c_2248,plain,
! [A_1095: ty,L1_1096: uni,L3_1097: uni,L2_1098: uni] :
( permut(A_1095,L1_1096,L3_1097)
| ~ permut(A_1095,L2_1098,L3_1097)
| ~ permut(A_1095,L1_1096,L2_1098) ),
inference(cnfTransformation,[status(thm)],[f_205]) ).
tff(c_2590,plain,
! [L1_1114: uni] :
( permut(elt,L1_1114,infix_plpl(elt,t2tb('#skF_18'),t2tb('#skF_19')))
| ~ permut(elt,L1_1114,t2tb('#skF_20')) ),
inference(resolution,[status(thm)],[c_206,c_2248]) ).
tff(c_126,plain,
! [A_141: ty,L1_142: uni,L3_144: uni,L2_143: uni] :
( permut(A_141,L1_142,L3_144)
| ~ permut(A_141,L2_143,L3_144)
| ~ permut(A_141,L1_142,L2_143) ),
inference(cnfTransformation,[status(thm)],[f_205]) ).
tff(c_5614,plain,
! [L1_1466: uni,L1_1467: uni] :
( permut(elt,L1_1466,infix_plpl(elt,t2tb('#skF_18'),t2tb('#skF_19')))
| ~ permut(elt,L1_1466,L1_1467)
| ~ permut(elt,L1_1467,t2tb('#skF_20')) ),
inference(resolution,[status(thm)],[c_2590,c_126]) ).
tff(c_5719,plain,
( permut(elt,infix_plpl(elt,t2tb('#skF_15'),t2tb('#skF_14')),infix_plpl(elt,t2tb('#skF_18'),t2tb('#skF_19')))
| ~ permut(elt,t2tb('#skF_11'),t2tb('#skF_20')) ),
inference(resolution,[status(thm)],[c_224,c_5614]) ).
tff(c_6004,plain,
~ permut(elt,t2tb('#skF_11'),t2tb('#skF_20')),
inference(splitLeft,[status(thm)],[c_5719]) ).
tff(c_660,plain,
! [A_712: ty,L2_713: uni,L1_714: uni] :
( permut(A_712,L2_713,L1_714)
| ~ permut(A_712,L1_714,L2_713) ),
inference(cnfTransformation,[status(thm)],[f_199]) ).
tff(c_671,plain,
permut(elt,t2tb('#skF_11'),infix_plpl(elt,t2tb('#skF_15'),t2tb('#skF_14'))),
inference(resolution,[status(thm)],[c_224,c_660]) ).
tff(c_5713,plain,
( permut(elt,t2tb('#skF_11'),infix_plpl(elt,t2tb('#skF_18'),t2tb('#skF_19')))
| ~ permut(elt,infix_plpl(elt,t2tb('#skF_15'),t2tb('#skF_14')),t2tb('#skF_20')) ),
inference(resolution,[status(thm)],[c_671,c_5614]) ).
tff(c_6696,plain,
~ permut(elt,infix_plpl(elt,t2tb('#skF_15'),t2tb('#skF_14')),t2tb('#skF_20')),
inference(splitLeft,[status(thm)],[c_5713]) ).
tff(c_220,plain,
permut(elt,t2tb('#skF_18'),t2tb('#skF_15')),
inference(cnfTransformation,[status(thm)],[f_370]) ).
tff(c_216,plain,
permut(elt,t2tb('#skF_19'),t2tb('#skF_14')),
inference(cnfTransformation,[status(thm)],[f_370]) ).
tff(c_5327,plain,
! [L2_1453: uni,A_1452: ty,L1_1449: uni,K2_1450: uni,K1_1451: uni] :
( permut(A_1452,infix_plpl(A_1452,L1_1449,L2_1453),infix_plpl(A_1452,K1_1451,K2_1450))
| ~ permut(A_1452,L2_1453,K2_1450)
| ~ permut(A_1452,L1_1449,K1_1451) ),
inference(cnfTransformation,[status(thm)],[f_221]) ).
tff(c_124,plain,
! [A_138: ty,L2_140: uni,L1_139: uni] :
( permut(A_138,L2_140,L1_139)
| ~ permut(A_138,L1_139,L2_140) ),
inference(cnfTransformation,[status(thm)],[f_199]) ).
tff(c_23468,plain,
! [K2_2305: uni,L2_2304: uni,K1_2303: uni,A_2302: ty,L1_2301: uni] :
( permut(A_2302,infix_plpl(A_2302,K1_2303,K2_2305),infix_plpl(A_2302,L1_2301,L2_2304))
| ~ permut(A_2302,L2_2304,K2_2305)
| ~ permut(A_2302,L1_2301,K1_2303) ),
inference(resolution,[status(thm)],[c_5327,c_124]) ).
tff(c_24938,plain,
! [K1_2442: uni,L1_2443: uni] :
( permut(elt,infix_plpl(elt,K1_2442,t2tb('#skF_14')),infix_plpl(elt,L1_2443,t2tb('#skF_19')))
| ~ permut(elt,L1_2443,K1_2442) ),
inference(resolution,[status(thm)],[c_216,c_23468]) ).
tff(c_25189,plain,
permut(elt,infix_plpl(elt,t2tb('#skF_15'),t2tb('#skF_14')),infix_plpl(elt,t2tb('#skF_18'),t2tb('#skF_19'))),
inference(resolution,[status(thm)],[c_220,c_24938]) ).
tff(c_672,plain,
permut(elt,infix_plpl(elt,t2tb('#skF_18'),t2tb('#skF_19')),t2tb('#skF_20')),
inference(resolution,[status(thm)],[c_206,c_660]) ).
tff(c_2277,plain,
! [L1_1096: uni] :
( permut(elt,L1_1096,t2tb('#skF_20'))
| ~ permut(elt,L1_1096,infix_plpl(elt,t2tb('#skF_18'),t2tb('#skF_19'))) ),
inference(resolution,[status(thm)],[c_672,c_2248]) ).
tff(c_25737,plain,
permut(elt,infix_plpl(elt,t2tb('#skF_15'),t2tb('#skF_14')),t2tb('#skF_20')),
inference(resolution,[status(thm)],[c_25189,c_2277]) ).
tff(c_25774,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6696,c_25737]) ).
tff(c_25775,plain,
permut(elt,t2tb('#skF_11'),infix_plpl(elt,t2tb('#skF_18'),t2tb('#skF_19'))),
inference(splitRight,[status(thm)],[c_5713]) ).
tff(c_25787,plain,
permut(elt,t2tb('#skF_11'),t2tb('#skF_20')),
inference(resolution,[status(thm)],[c_25775,c_2277]) ).
tff(c_25803,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6004,c_25787]) ).
tff(c_25805,plain,
permut(elt,t2tb('#skF_11'),t2tb('#skF_20')),
inference(splitRight,[status(thm)],[c_5719]) ).
tff(c_25821,plain,
permut(elt,t2tb('#skF_20'),t2tb('#skF_11')),
inference(resolution,[status(thm)],[c_25805,c_124]) ).
tff(c_25836,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_317,c_25821]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW629_2 : TPTP v8.1.2. Released v6.1.0.
% 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
% 0.14/0.36 % Computer : n025.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 19:48:34 EDT 2023
% 0.14/0.36 % CPUTime :
% 23.25/7.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.25/7.75
% 23.25/7.75 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 23.25/7.77
% 23.25/7.77 Inference rules
% 23.25/7.77 ----------------------
% 23.25/7.77 #Ref : 0
% 23.25/7.77 #Sup : 5464
% 23.25/7.77 #Fact : 9
% 23.25/7.77 #Define : 14
% 23.25/7.77 #Split : 43
% 23.25/7.77 #Chain : 0
% 23.25/7.77 #Close : 0
% 23.25/7.77
% 23.25/7.77 Ordering : LPO
% 23.25/7.77
% 23.25/7.77 Simplification rules
% 23.25/7.77 ----------------------
% 23.25/7.77 #Subsume : 752
% 23.25/7.77 #Demod : 2631
% 23.25/7.77 #Tautology : 1286
% 23.25/7.77 #SimpNegUnit : 105
% 23.25/7.78 #BackRed : 148
% 23.25/7.78
% 23.25/7.78 #Partial instantiations: 506
% 23.25/7.78 #Strategies tried : 1
% 23.25/7.78
% 23.25/7.78 Timing (in seconds)
% 23.25/7.78 ----------------------
% 23.25/7.78 Preprocessing : 0.85
% 23.25/7.78 Parsing : 0.46
% 23.25/7.78 CNF conversion : 0.08
% 23.25/7.78 Main loop : 5.77
% 23.25/7.78 Inferencing : 1.11
% 23.25/7.78 Reduction : 2.16
% 23.25/7.78 Demodulation : 1.71
% 23.25/7.78 BG Simplification : 0.45
% 23.25/7.78 Subsumption : 1.42
% 23.25/7.78 Abstraction : 0.15
% 23.25/7.78 MUC search : 0.00
% 23.25/7.78 Cooper : 0.17
% 23.25/7.78 Total : 6.68
% 23.25/7.78 Index Insertion : 0.00
% 23.25/7.78 Index Deletion : 0.00
% 23.25/7.78 Index Matching : 0.00
% 23.25/7.78 BG Taut test : 0.00
%------------------------------------------------------------------------------