TSTP Solution File: SWV381+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWV381+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : Tue Aug 22 11:03:58 EDT 2023
% Result : Theorem 44.54s 27.35s
% Output : CNFRefutation 44.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 63
% Syntax : Number of formulae : 100 ( 23 unt; 52 typ; 0 def)
% Number of atoms : 82 ( 17 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 63 ( 29 ~; 25 |; 2 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 76 ( 45 >; 31 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-3 aty)
% Number of functors : 33 ( 33 usr; 7 con; 0-3 aty)
% Number of variables : 79 (; 78 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ pair_in_list > succ_cpq > strictly_less_than > pi_sharp_removemin > pi_sharp_remove > pi_sharp_find_min > pi_remove > less_than > issmallestelement_pq > contains_slb > contains_pq > contains_cpq > pi_removemin > pi_find_min > phi > ok > isnonempty_slb > isnonempty_pq > check_cpq > triple > update_slb > removemin_pq_res > removemin_pq_eff > remove_slb > remove_pqp > remove_pq > remove_cpq > pair > lookup_slb > insert_slb > insert_pqp > insert_pq > insert_cpq > findmin_pq_res > findmin_pq_eff > #nlpp > removemin_cpq_res > removemin_cpq_eff > i > findmin_pqp_res > findmin_cpq_res > findmin_cpq_eff > create_slb > create_pq > bottom > bad > #skF_2 > #skF_4 > #skF_7 > #skF_5 > #skF_6 > #skF_3 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(bad,type,
bad: $i ).
tff(insert_cpq,type,
insert_cpq: ( $i * $i ) > $i ).
tff(pi_sharp_find_min,type,
pi_sharp_find_min: ( $i * $i ) > $o ).
tff(pi_remove,type,
pi_remove: ( $i * $i ) > $o ).
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff(succ_cpq,type,
succ_cpq: ( $i * $i ) > $o ).
tff(insert_pq,type,
insert_pq: ( $i * $i ) > $i ).
tff(pi_find_min,type,
pi_find_min: $i > $o ).
tff(i,type,
i: $i > $i ).
tff(remove_cpq,type,
remove_cpq: ( $i * $i ) > $i ).
tff(pi_sharp_removemin,type,
pi_sharp_removemin: ( $i * $i ) > $o ).
tff(pi_sharp_remove,type,
pi_sharp_remove: ( $i * $i ) > $o ).
tff(contains_slb,type,
contains_slb: ( $i * $i ) > $o ).
tff(contains_pq,type,
contains_pq: ( $i * $i ) > $o ).
tff(findmin_pq_eff,type,
findmin_pq_eff: ( $i * $i ) > $i ).
tff(lookup_slb,type,
lookup_slb: ( $i * $i ) > $i ).
tff(pi_removemin,type,
pi_removemin: $i > $o ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(phi,type,
phi: $i > $o ).
tff(pair_in_list,type,
pair_in_list: ( $i * $i * $i ) > $o ).
tff(isnonempty_pq,type,
isnonempty_pq: $i > $o ).
tff(findmin_pq_res,type,
findmin_pq_res: ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(less_than,type,
less_than: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff(issmallestelement_pq,type,
issmallestelement_pq: ( $i * $i ) > $o ).
tff(contains_cpq,type,
contains_cpq: ( $i * $i ) > $o ).
tff(strictly_less_than,type,
strictly_less_than: ( $i * $i ) > $o ).
tff(pair,type,
pair: ( $i * $i ) > $i ).
tff(ok,type,
ok: $i > $o ).
tff(insert_pqp,type,
insert_pqp: ( $i * $i ) > $i ).
tff(remove_pq,type,
remove_pq: ( $i * $i ) > $i ).
tff(findmin_pqp_res,type,
findmin_pqp_res: $i > $i ).
tff(remove_pqp,type,
remove_pqp: ( $i * $i ) > $i ).
tff(bottom,type,
bottom: $i ).
tff(removemin_pq_res,type,
removemin_pq_res: ( $i * $i ) > $i ).
tff(triple,type,
triple: ( $i * $i * $i ) > $i ).
tff(create_pq,type,
create_pq: $i ).
tff(removemin_cpq_res,type,
removemin_cpq_res: $i > $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff(isnonempty_slb,type,
isnonempty_slb: $i > $o ).
tff(check_cpq,type,
check_cpq: $i > $o ).
tff(remove_slb,type,
remove_slb: ( $i * $i ) > $i ).
tff(findmin_cpq_eff,type,
findmin_cpq_eff: $i > $i ).
tff(removemin_cpq_eff,type,
removemin_cpq_eff: $i > $i ).
tff(create_slb,type,
create_slb: $i ).
tff(removemin_pq_eff,type,
removemin_pq_eff: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(findmin_cpq_res,type,
findmin_cpq_res: $i > $i ).
tff(insert_slb,type,
insert_slb: ( $i * $i ) > $i ).
tff(update_slb,type,
update_slb: ( $i * $i ) > $i ).
tff(f_71,axiom,
! [U] : less_than(bottom,U),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax',bottom_smallest) ).
tff(f_117,axiom,
! [U,V] :
( issmallestelement_pq(U,V)
<=> ! [W] :
( contains_pq(U,W)
=> less_than(V,W) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+1.ax',ax10) ).
tff(f_104,axiom,
! [U] : ~ contains_pq(create_pq,U),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+1.ax',ax8) ).
tff(f_357,axiom,
! [U,V,W,X] :
( ( V != create_slb )
=> ( findmin_cpq_res(triple(U,V,W)) = findmin_pqp_res(U) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax51) ).
tff(f_453,negated_conjecture,
~ ! [U,V,W] :
( phi(findmin_cpq_eff(triple(U,V,W)))
=> issmallestelement_pq(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l17_co) ).
tff(f_438,lemma,
! [U,V,W,X] :
( contains_cpq(triple(U,V,W),X)
<=> contains_pq(i(triple(U,V,W)),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l17_li56) ).
tff(f_60,axiom,
! [U,V] :
( less_than(U,V)
| less_than(V,U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax',totality) ).
tff(f_69,axiom,
! [U,V] :
( strictly_less_than(U,V)
<=> ( less_than(U,V)
& ~ less_than(V,U) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax',stricly_smaller_definition) ).
tff(f_447,lemma,
! [U,V,W] :
( ? [X] :
( contains_cpq(triple(U,V,W),X)
& strictly_less_than(X,findmin_cpq_res(triple(U,V,W))) )
=> ~ phi(findmin_cpq_eff(triple(U,V,W))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l17_l18) ).
tff(f_389,axiom,
! [U,V] : ( i(triple(U,create_slb,V)) = create_pq ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+4.ax',ax54) ).
tff(f_352,axiom,
! [U,V] : ( findmin_cpq_res(triple(U,create_slb,V)) = bottom ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax50) ).
tff(c_14,plain,
! [U_9] : less_than(bottom,U_9),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_441,plain,
! [V_283,U_284] :
( ~ less_than(V_283,'#skF_1'(U_284,V_283))
| issmallestelement_pq(U_284,V_283) ),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_450,plain,
! [U_284] : issmallestelement_pq(U_284,bottom),
inference(resolution,[status(thm)],[c_14,c_441]) ).
tff(c_362,plain,
! [U_251,V_252] :
( contains_pq(U_251,'#skF_1'(U_251,V_252))
| issmallestelement_pq(U_251,V_252) ),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_20,plain,
! [U_12] : ~ contains_pq(create_pq,U_12),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_367,plain,
! [V_252] : issmallestelement_pq(create_pq,V_252),
inference(resolution,[status(thm)],[c_362,c_20]) ).
tff(c_509,plain,
! [U_301,V_302,W_303] :
( ( findmin_cpq_res(triple(U_301,V_302,W_303)) = findmin_pqp_res(U_301) )
| ( create_slb = V_302 ) ),
inference(cnfTransformation,[status(thm)],[f_357]) ).
tff(c_180,plain,
~ issmallestelement_pq(i(triple('#skF_5','#skF_6','#skF_7')),findmin_cpq_res(triple('#skF_5','#skF_6','#skF_7'))),
inference(cnfTransformation,[status(thm)],[f_453]) ).
tff(c_522,plain,
( ~ issmallestelement_pq(i(triple('#skF_5','#skF_6','#skF_7')),findmin_pqp_res('#skF_5'))
| ( create_slb = '#skF_6' ) ),
inference(superposition,[status(thm),theory(equality)],[c_509,c_180]) ).
tff(c_628,plain,
~ issmallestelement_pq(i(triple('#skF_5','#skF_6','#skF_7')),findmin_pqp_res('#skF_5')),
inference(splitLeft,[status(thm)],[c_522]) ).
tff(c_32,plain,
! [U_16,V_17] :
( contains_pq(U_16,'#skF_1'(U_16,V_17))
| issmallestelement_pq(U_16,V_17) ),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_1727,plain,
! [U_438,V_439,W_440,X_441] :
( contains_cpq(triple(U_438,V_439,W_440),X_441)
| ~ contains_pq(i(triple(U_438,V_439,W_440)),X_441) ),
inference(cnfTransformation,[status(thm)],[f_438]) ).
tff(c_1754,plain,
! [U_438,V_439,W_440,V_17] :
( contains_cpq(triple(U_438,V_439,W_440),'#skF_1'(i(triple(U_438,V_439,W_440)),V_17))
| issmallestelement_pq(i(triple(U_438,V_439,W_440)),V_17) ),
inference(resolution,[status(thm)],[c_32,c_1727]) ).
tff(c_4,plain,
! [V_5,U_4] :
( less_than(V_5,U_4)
| less_than(U_4,V_5) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_8,plain,
! [U_7,V_8] :
( strictly_less_than(U_7,V_8)
| less_than(V_8,U_7)
| ~ less_than(U_7,V_8) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_182,plain,
phi(findmin_cpq_eff(triple('#skF_5','#skF_6','#skF_7'))),
inference(cnfTransformation,[status(thm)],[f_453]) ).
tff(c_128,plain,
! [U_139,V_140,W_141] :
( ( findmin_cpq_res(triple(U_139,V_140,W_141)) = findmin_pqp_res(U_139) )
| ( create_slb = V_140 ) ),
inference(cnfTransformation,[status(thm)],[f_357]) ).
tff(c_2848,plain,
! [U_594,V_595,W_596,X_597] :
( ~ phi(findmin_cpq_eff(triple(U_594,V_595,W_596)))
| ~ strictly_less_than(X_597,findmin_cpq_res(triple(U_594,V_595,W_596)))
| ~ contains_cpq(triple(U_594,V_595,W_596),X_597) ),
inference(cnfTransformation,[status(thm)],[f_447]) ).
tff(c_156463,plain,
! [U_29763,V_29764,W_29765,X_29766] :
( ~ phi(findmin_cpq_eff(triple(U_29763,V_29764,W_29765)))
| ~ strictly_less_than(X_29766,findmin_pqp_res(U_29763))
| ~ contains_cpq(triple(U_29763,V_29764,W_29765),X_29766)
| ( create_slb = V_29764 ) ),
inference(superposition,[status(thm),theory(equality)],[c_128,c_2848]) ).
tff(c_156563,plain,
! [X_29766] :
( ~ strictly_less_than(X_29766,findmin_pqp_res('#skF_5'))
| ~ contains_cpq(triple('#skF_5','#skF_6','#skF_7'),X_29766)
| ( create_slb = '#skF_6' ) ),
inference(resolution,[status(thm)],[c_182,c_156463]) ).
tff(c_156565,plain,
! [X_29855] :
( ~ strictly_less_than(X_29855,findmin_pqp_res('#skF_5'))
| ~ contains_cpq(triple('#skF_5','#skF_6','#skF_7'),X_29855) ),
inference(splitLeft,[status(thm)],[c_156563]) ).
tff(c_279448,plain,
! [U_49614] :
( ~ contains_cpq(triple('#skF_5','#skF_6','#skF_7'),U_49614)
| less_than(findmin_pqp_res('#skF_5'),U_49614)
| ~ less_than(U_49614,findmin_pqp_res('#skF_5')) ),
inference(resolution,[status(thm)],[c_8,c_156565]) ).
tff(c_279662,plain,
! [V_49703] :
( ~ contains_cpq(triple('#skF_5','#skF_6','#skF_7'),V_49703)
| less_than(findmin_pqp_res('#skF_5'),V_49703) ),
inference(resolution,[status(thm)],[c_4,c_279448]) ).
tff(c_30,plain,
! [V_17,U_16] :
( ~ less_than(V_17,'#skF_1'(U_16,V_17))
| issmallestelement_pq(U_16,V_17) ),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_280211,plain,
! [U_50061] :
( issmallestelement_pq(U_50061,findmin_pqp_res('#skF_5'))
| ~ contains_cpq(triple('#skF_5','#skF_6','#skF_7'),'#skF_1'(U_50061,findmin_pqp_res('#skF_5'))) ),
inference(resolution,[status(thm)],[c_279662,c_30]) ).
tff(c_280215,plain,
issmallestelement_pq(i(triple('#skF_5','#skF_6','#skF_7')),findmin_pqp_res('#skF_5')),
inference(resolution,[status(thm)],[c_1754,c_280211]) ).
tff(c_280387,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_628,c_628,c_280215]) ).
tff(c_280388,plain,
create_slb = '#skF_6',
inference(splitRight,[status(thm)],[c_156563]) ).
tff(c_134,plain,
! [U_145,V_146] : ( i(triple(U_145,create_slb,V_146)) = create_pq ),
inference(cnfTransformation,[status(thm)],[f_389]) ).
tff(c_280417,plain,
! [U_145,V_146] : ( i(triple(U_145,'#skF_6',V_146)) = create_pq ),
inference(demodulation,[status(thm),theory(equality)],[c_280388,c_134]) ).
tff(c_281654,plain,
~ issmallestelement_pq(create_pq,findmin_pqp_res('#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_280417,c_628]) ).
tff(c_281658,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_367,c_281654]) ).
tff(c_281659,plain,
create_slb = '#skF_6',
inference(splitRight,[status(thm)],[c_522]) ).
tff(c_126,plain,
! [U_137,V_138] : ( findmin_cpq_res(triple(U_137,create_slb,V_138)) = bottom ),
inference(cnfTransformation,[status(thm)],[f_352]) ).
tff(c_281666,plain,
! [U_137,V_138] : ( findmin_cpq_res(triple(U_137,'#skF_6',V_138)) = bottom ),
inference(demodulation,[status(thm),theory(equality)],[c_281659,c_126]) ).
tff(c_281712,plain,
~ issmallestelement_pq(i(triple('#skF_5','#skF_6','#skF_7')),bottom),
inference(demodulation,[status(thm),theory(equality)],[c_281666,c_180]) ).
tff(c_281715,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_450,c_281712]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWV381+1 : TPTP v8.1.2. Released v3.3.0.
% 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
% 0.17/0.35 % Computer : n029.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Thu Aug 3 22:49:53 EDT 2023
% 0.17/0.35 % CPUTime :
% 44.54/27.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 44.54/27.36
% 44.54/27.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 44.54/27.39
% 44.54/27.39 Inference rules
% 44.54/27.39 ----------------------
% 44.54/27.39 #Ref : 0
% 44.54/27.39 #Sup : 50834
% 44.54/27.39 #Fact : 26
% 44.54/27.39 #Define : 0
% 44.54/27.39 #Split : 139
% 44.54/27.39 #Chain : 0
% 44.54/27.39 #Close : 0
% 44.54/27.39
% 44.54/27.39 Ordering : KBO
% 44.54/27.39
% 44.54/27.39 Simplification rules
% 44.54/27.39 ----------------------
% 44.54/27.39 #Subsume : 9024
% 44.54/27.39 #Demod : 7164
% 44.54/27.39 #Tautology : 1305
% 44.54/27.39 #SimpNegUnit : 153
% 44.54/27.39 #BackRed : 272
% 44.54/27.39
% 44.54/27.39 #Partial instantiations: 36696
% 44.54/27.39 #Strategies tried : 1
% 44.54/27.39
% 44.54/27.39 Timing (in seconds)
% 44.54/27.39 ----------------------
% 44.54/27.40 Preprocessing : 0.71
% 44.54/27.40 Parsing : 0.37
% 44.54/27.40 CNF conversion : 0.05
% 44.54/27.40 Main loop : 25.58
% 44.54/27.40 Inferencing : 3.54
% 44.54/27.40 Reduction : 10.35
% 44.54/27.40 Demodulation : 8.81
% 44.54/27.40 BG Simplification : 0.41
% 44.54/27.40 Subsumption : 7.63
% 44.54/27.40 Abstraction : 0.45
% 44.54/27.40 MUC search : 0.00
% 44.54/27.40 Cooper : 0.00
% 44.54/27.40 Total : 26.34
% 44.54/27.40 Index Insertion : 0.00
% 44.54/27.40 Index Deletion : 0.00
% 44.54/27.40 Index Matching : 0.00
% 44.54/27.40 BG Taut test : 0.00
%------------------------------------------------------------------------------