TSTP Solution File: SWV394+1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWV394+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 : n021.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 11:03:59 EDT 2023
% Result : Theorem 7.66s 2.92s
% Output : CNFRefutation 8.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 42
% Syntax : Number of formulae : 88 ( 23 unt; 34 typ; 0 def)
% Number of atoms : 108 ( 7 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 105 ( 51 ~; 39 |; 6 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 48 ( 26 >; 22 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 8 con; 0-3 aty)
% Number of variables : 95 (; 95 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ pair_in_list > succ_cpq > strictly_less_than > less_than > contains_slb > contains_cpq > ok > isnonempty_slb > check_cpq > triple > update_slb > remove_slb > remove_pqp > remove_cpq > pair > lookup_slb > insert_slb > insert_pqp > insert_cpq > #nlpp > removemin_cpq_res > removemin_cpq_eff > findmin_pqp_res > findmin_cpq_res > findmin_cpq_eff > create_slb > bottom > bad > #skF_1 > #skF_7 > #skF_5 > #skF_6 > #skF_3 > #skF_2 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(bad,type,
bad: $i ).
tff(insert_cpq,type,
insert_cpq: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i * $i ) > $i ).
tff(succ_cpq,type,
succ_cpq: ( $i * $i ) > $o ).
tff(remove_cpq,type,
remove_cpq: ( $i * $i ) > $i ).
tff(contains_slb,type,
contains_slb: ( $i * $i ) > $o ).
tff(lookup_slb,type,
lookup_slb: ( $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(pair_in_list,type,
pair_in_list: ( $i * $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(less_than,type,
less_than: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i * $i ) > $i ).
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(findmin_pqp_res,type,
findmin_pqp_res: $i > $i ).
tff(remove_pqp,type,
remove_pqp: ( $i * $i ) > $i ).
tff(bottom,type,
bottom: $i ).
tff(triple,type,
triple: ( $i * $i * $i ) > $i ).
tff(removemin_cpq_res,type,
removemin_cpq_res: $i > $i ).
tff('#skF_4',type,
'#skF_4': $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(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_310,negated_conjecture,
~ ! [U,V,W,X] :
( ( check_cpq(remove_cpq(triple(U,V,W),X))
& ok(remove_cpq(triple(U,V,W),X)) )
=> ! [Y] :
( pair_in_list(V,X,Y)
=> less_than(Y,X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l30_co) ).
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_290,lemma,
! [U,V,W] :
( check_cpq(triple(U,V,W))
<=> ! [X,Y] :
( pair_in_list(V,X,Y)
=> less_than(Y,X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l30_li4142) ).
tff(f_229,axiom,
! [U,V,W,X] :
( ~ contains_slb(V,X)
=> ( remove_cpq(triple(U,V,W),X) = triple(U,V,bad) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax43) ).
tff(f_241,axiom,
! [U,V,W,X] :
( ( contains_slb(V,X)
& strictly_less_than(X,lookup_slb(V,X)) )
=> ( remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),bad) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax45) ).
tff(f_299,lemma,
! [U,V,W,X,Y] :
( ( pair_in_list(V,X,Y)
& strictly_less_than(X,Y)
& ok(remove_cpq(triple(U,V,W),X)) )
=> pair_in_list(remove_slb(V,X),X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l30_li3132) ).
tff(f_235,axiom,
! [U,V,W,X] :
( ( contains_slb(V,X)
& less_than(lookup_slb(V,X),X) )
=> ( remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),W) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax44) ).
tff(c_110,plain,
~ less_than('#skF_7','#skF_6'),
inference(cnfTransformation,[status(thm)],[f_310]) ).
tff(c_166,plain,
! [V_154,U_155] :
( less_than(V_154,U_155)
| less_than(U_155,V_154) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_173,plain,
less_than('#skF_6','#skF_7'),
inference(resolution,[status(thm)],[c_166,c_110]) ).
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_112,plain,
pair_in_list('#skF_4','#skF_6','#skF_7'),
inference(cnfTransformation,[status(thm)],[f_310]) ).
tff(c_759,plain,
! [V_235,Y_239,U_236,W_237,X_238] :
( less_than(Y_239,X_238)
| ~ pair_in_list(V_235,X_238,Y_239)
| ~ check_cpq(triple(U_236,V_235,W_237)) ),
inference(cnfTransformation,[status(thm)],[f_290]) ).
tff(c_763,plain,
! [U_236,W_237] :
( less_than('#skF_7','#skF_6')
| ~ check_cpq(triple(U_236,'#skF_4',W_237)) ),
inference(resolution,[status(thm)],[c_112,c_759]) ).
tff(c_767,plain,
! [U_236,W_237] : ~ check_cpq(triple(U_236,'#skF_4',W_237)),
inference(negUnitSimplification,[status(thm)],[c_110,c_763]) ).
tff(c_785,plain,
! [U_262,V_263,W_264,X_265] :
( ( remove_cpq(triple(U_262,V_263,W_264),X_265) = triple(U_262,V_263,bad) )
| contains_slb(V_263,X_265) ),
inference(cnfTransformation,[status(thm)],[f_229]) ).
tff(c_116,plain,
check_cpq(remove_cpq(triple('#skF_3','#skF_4','#skF_5'),'#skF_6')),
inference(cnfTransformation,[status(thm)],[f_310]) ).
tff(c_798,plain,
( check_cpq(triple('#skF_3','#skF_4',bad))
| contains_slb('#skF_4','#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_785,c_116]) ).
tff(c_810,plain,
contains_slb('#skF_4','#skF_6'),
inference(negUnitSimplification,[status(thm)],[c_767,c_798]) ).
tff(c_3846,plain,
! [U_558,X_559,V_560,W_561] :
( ( triple(remove_pqp(U_558,X_559),remove_slb(V_560,X_559),bad) = remove_cpq(triple(U_558,V_560,W_561),X_559) )
| ~ strictly_less_than(X_559,lookup_slb(V_560,X_559))
| ~ contains_slb(V_560,X_559) ),
inference(cnfTransformation,[status(thm)],[f_241]) ).
tff(c_114,plain,
ok(remove_cpq(triple('#skF_3','#skF_4','#skF_5'),'#skF_6')),
inference(cnfTransformation,[status(thm)],[f_310]) ).
tff(c_3615,plain,
! [Y_541,V_539,U_542,X_540,W_543] :
( pair_in_list(remove_slb(V_539,X_540),X_540,Y_541)
| ~ ok(remove_cpq(triple(U_542,V_539,W_543),X_540))
| ~ strictly_less_than(X_540,Y_541)
| ~ pair_in_list(V_539,X_540,Y_541) ),
inference(cnfTransformation,[status(thm)],[f_299]) ).
tff(c_3627,plain,
! [Y_544] :
( pair_in_list(remove_slb('#skF_4','#skF_6'),'#skF_6',Y_544)
| ~ strictly_less_than('#skF_6',Y_544)
| ~ pair_in_list('#skF_4','#skF_6',Y_544) ),
inference(resolution,[status(thm)],[c_114,c_3615]) ).
tff(c_102,plain,
! [W_120,X_125,V_119,U_118,Y_126] :
( less_than(Y_126,X_125)
| ~ pair_in_list(V_119,X_125,Y_126)
| ~ check_cpq(triple(U_118,V_119,W_120)) ),
inference(cnfTransformation,[status(thm)],[f_290]) ).
tff(c_3630,plain,
! [Y_544,U_118,W_120] :
( less_than(Y_544,'#skF_6')
| ~ check_cpq(triple(U_118,remove_slb('#skF_4','#skF_6'),W_120))
| ~ strictly_less_than('#skF_6',Y_544)
| ~ pair_in_list('#skF_4','#skF_6',Y_544) ),
inference(resolution,[status(thm)],[c_3627,c_102]) ).
tff(c_3734,plain,
! [U_118,W_120] : ~ check_cpq(triple(U_118,remove_slb('#skF_4','#skF_6'),W_120)),
inference(splitLeft,[status(thm)],[c_3630]) ).
tff(c_3860,plain,
! [U_558,W_561] :
( ~ check_cpq(remove_cpq(triple(U_558,'#skF_4',W_561),'#skF_6'))
| ~ strictly_less_than('#skF_6',lookup_slb('#skF_4','#skF_6'))
| ~ contains_slb('#skF_4','#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_3846,c_3734]) ).
tff(c_3966,plain,
! [U_558,W_561] :
( ~ check_cpq(remove_cpq(triple(U_558,'#skF_4',W_561),'#skF_6'))
| ~ strictly_less_than('#skF_6',lookup_slb('#skF_4','#skF_6')) ),
inference(demodulation,[status(thm),theory(equality)],[c_810,c_3860]) ).
tff(c_3975,plain,
~ strictly_less_than('#skF_6',lookup_slb('#skF_4','#skF_6')),
inference(splitLeft,[status(thm)],[c_3966]) ).
tff(c_3979,plain,
( less_than(lookup_slb('#skF_4','#skF_6'),'#skF_6')
| ~ less_than('#skF_6',lookup_slb('#skF_4','#skF_6')) ),
inference(resolution,[status(thm)],[c_8,c_3975]) ).
tff(c_3980,plain,
~ less_than('#skF_6',lookup_slb('#skF_4','#skF_6')),
inference(splitLeft,[status(thm)],[c_3979]) ).
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_4121,plain,
! [U_570,X_571,V_572,W_573] :
( ( triple(remove_pqp(U_570,X_571),remove_slb(V_572,X_571),W_573) = remove_cpq(triple(U_570,V_572,W_573),X_571) )
| ~ less_than(lookup_slb(V_572,X_571),X_571)
| ~ contains_slb(V_572,X_571) ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_4141,plain,
! [U_570,W_573] :
( ~ check_cpq(remove_cpq(triple(U_570,'#skF_4',W_573),'#skF_6'))
| ~ less_than(lookup_slb('#skF_4','#skF_6'),'#skF_6')
| ~ contains_slb('#skF_4','#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_4121,c_3734]) ).
tff(c_4247,plain,
! [U_570,W_573] :
( ~ check_cpq(remove_cpq(triple(U_570,'#skF_4',W_573),'#skF_6'))
| ~ less_than(lookup_slb('#skF_4','#skF_6'),'#skF_6') ),
inference(demodulation,[status(thm),theory(equality)],[c_810,c_4141]) ).
tff(c_4251,plain,
~ less_than(lookup_slb('#skF_4','#skF_6'),'#skF_6'),
inference(splitLeft,[status(thm)],[c_4247]) ).
tff(c_4308,plain,
less_than('#skF_6',lookup_slb('#skF_4','#skF_6')),
inference(resolution,[status(thm)],[c_4,c_4251]) ).
tff(c_4339,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3980,c_4308]) ).
tff(c_4340,plain,
! [U_570,W_573] : ~ check_cpq(remove_cpq(triple(U_570,'#skF_4',W_573),'#skF_6')),
inference(splitRight,[status(thm)],[c_4247]) ).
tff(c_4466,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_4340,c_116]) ).
tff(c_4467,plain,
less_than(lookup_slb('#skF_4','#skF_6'),'#skF_6'),
inference(splitRight,[status(thm)],[c_3979]) ).
tff(c_4585,plain,
! [U_577,X_578,V_579,W_580] :
( ( triple(remove_pqp(U_577,X_578),remove_slb(V_579,X_578),W_580) = remove_cpq(triple(U_577,V_579,W_580),X_578) )
| ~ less_than(lookup_slb(V_579,X_578),X_578)
| ~ contains_slb(V_579,X_578) ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_4603,plain,
! [U_577,W_580] :
( ~ check_cpq(remove_cpq(triple(U_577,'#skF_4',W_580),'#skF_6'))
| ~ less_than(lookup_slb('#skF_4','#skF_6'),'#skF_6')
| ~ contains_slb('#skF_4','#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_4585,c_3734]) ).
tff(c_4709,plain,
! [U_577,W_580] : ~ check_cpq(remove_cpq(triple(U_577,'#skF_4',W_580),'#skF_6')),
inference(demodulation,[status(thm),theory(equality)],[c_810,c_4467,c_4603]) ).
tff(c_4714,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_4709,c_116]) ).
tff(c_4715,plain,
! [U_558,W_561] : ~ check_cpq(remove_cpq(triple(U_558,'#skF_4',W_561),'#skF_6')),
inference(splitRight,[status(thm)],[c_3966]) ).
tff(c_4847,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_4715,c_116]) ).
tff(c_4849,plain,
! [Y_581] :
( less_than(Y_581,'#skF_6')
| ~ strictly_less_than('#skF_6',Y_581)
| ~ pair_in_list('#skF_4','#skF_6',Y_581) ),
inference(splitRight,[status(thm)],[c_3630]) ).
tff(c_4852,plain,
( less_than('#skF_7','#skF_6')
| ~ strictly_less_than('#skF_6','#skF_7') ),
inference(resolution,[status(thm)],[c_112,c_4849]) ).
tff(c_4855,plain,
~ strictly_less_than('#skF_6','#skF_7'),
inference(negUnitSimplification,[status(thm)],[c_110,c_4852]) ).
tff(c_4975,plain,
( less_than('#skF_7','#skF_6')
| ~ less_than('#skF_6','#skF_7') ),
inference(resolution,[status(thm)],[c_8,c_4855]) ).
tff(c_4978,plain,
less_than('#skF_7','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_173,c_4975]) ).
tff(c_4980,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_110,c_4978]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWV394+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
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 3 22:53:37 EDT 2023
% 0.14/0.34 % CPUTime :
% 7.66/2.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.77/2.93
% 7.77/2.93 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.31/2.96
% 8.31/2.96 Inference rules
% 8.31/2.96 ----------------------
% 8.31/2.96 #Ref : 0
% 8.31/2.96 #Sup : 1139
% 8.31/2.96 #Fact : 88
% 8.31/2.96 #Define : 0
% 8.31/2.96 #Split : 4
% 8.31/2.96 #Chain : 0
% 8.31/2.96 #Close : 0
% 8.31/2.96
% 8.31/2.96 Ordering : KBO
% 8.31/2.96
% 8.31/2.96 Simplification rules
% 8.31/2.96 ----------------------
% 8.31/2.96 #Subsume : 440
% 8.31/2.96 #Demod : 281
% 8.31/2.96 #Tautology : 230
% 8.31/2.96 #SimpNegUnit : 24
% 8.31/2.96 #BackRed : 4
% 8.31/2.96
% 8.31/2.96 #Partial instantiations: 0
% 8.31/2.96 #Strategies tried : 1
% 8.31/2.96
% 8.31/2.96 Timing (in seconds)
% 8.31/2.96 ----------------------
% 8.31/2.96 Preprocessing : 0.65
% 8.31/2.96 Parsing : 0.33
% 8.31/2.96 CNF conversion : 0.05
% 8.31/2.96 Main loop : 1.24
% 8.31/2.96 Inferencing : 0.40
% 8.31/2.96 Reduction : 0.37
% 8.31/2.96 Demodulation : 0.27
% 8.31/2.96 BG Simplification : 0.05
% 8.31/2.96 Subsumption : 0.35
% 8.31/2.96 Abstraction : 0.05
% 8.31/2.96 MUC search : 0.00
% 8.31/2.96 Cooper : 0.00
% 8.31/2.96 Total : 1.95
% 8.31/2.96 Index Insertion : 0.00
% 8.31/2.96 Index Deletion : 0.00
% 8.31/2.96 Index Matching : 0.00
% 8.31/2.97 BG Taut test : 0.00
%------------------------------------------------------------------------------