TSTP Solution File: SWC404+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWC404+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 : n005.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 11:02:31 EDT 2023
% Result : Theorem 23.01s 10.07s
% Output : CNFRefutation 23.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 83
% Syntax : Number of formulae : 114 ( 15 unt; 78 typ; 0 def)
% Number of atoms : 141 ( 24 equ)
% Maximal formula atoms : 29 ( 3 avg)
% Number of connectives : 186 ( 81 ~; 73 |; 14 &)
% ( 3 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 6 avg)
% Maximal term depth : 3 ( 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 : 59 ( 59 usr; 10 con; 0-2 aty)
% Number of variables : 55 (; 46 !; 9 ?; 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_54 > #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_54',type,
'#skF_54': $i ).
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_1055,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(app(Y,W),Z) != X )
| ~ strictorderedP(W)
| ? [X1] :
( ssItem(X1)
& ? [X2] :
( ssList(X2)
& ( app(X2,cons(X1,nil)) = Y )
& ? [X3] :
( ssItem(X3)
& ? [X4] :
( ssList(X4)
& ( app(cons(X3,nil),X4) = W )
& lt(X1,X3) ) ) ) )
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ( app(cons(X5,nil),X6) = Z )
& ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& ( app(X8,cons(X7,nil)) = W )
& lt(X7,X5) ) ) ) ) ) ) )
| ! [X9] :
( ssItem(X9)
=> ( ~ memberP(U,X9)
| memberP(V,X9) ) )
| ( ( nil != X )
& ( nil = W ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f_498,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( memberP(app(V,W),U)
<=> ( memberP(V,U)
| memberP(W,U) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax36) ).
tff(f_399,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
tff(f_96,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( ssItem(V)
& ( cons(V,nil) = U ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax4) ).
tff(f_484,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( gt(U,V)
<=> lt(V,U) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax35) ).
tff(c_390,plain,
ssItem('#skF_54'),
inference(cnfTransformation,[status(thm)],[f_1055]) ).
tff(c_404,plain,
'#skF_48' = '#skF_50',
inference(cnfTransformation,[status(thm)],[f_1055]) ).
tff(c_388,plain,
memberP('#skF_48','#skF_54'),
inference(cnfTransformation,[status(thm)],[f_1055]) ).
tff(c_419,plain,
memberP('#skF_50','#skF_54'),
inference(demodulation,[status(thm),theory(equality)],[c_404,c_388]) ).
tff(c_402,plain,
ssList('#skF_52'),
inference(cnfTransformation,[status(thm)],[f_1055]) ).
tff(c_410,plain,
ssList('#skF_50'),
inference(cnfTransformation,[status(thm)],[f_1055]) ).
tff(c_218,plain,
! [W_940,U_934,V_938] :
( ~ memberP(W_940,U_934)
| memberP(app(V_938,W_940),U_934)
| ~ ssList(W_940)
| ~ ssList(V_938)
| ~ ssItem(U_934) ),
inference(cnfTransformation,[status(thm)],[f_498]) ).
tff(c_192,plain,
! [U_896,V_898] :
( ssList(app(U_896,V_898))
| ~ ssList(V_898)
| ~ ssList(U_896) ),
inference(cnfTransformation,[status(thm)],[f_399]) ).
tff(c_400,plain,
ssList('#skF_53'),
inference(cnfTransformation,[status(thm)],[f_1055]) ).
tff(c_398,plain,
app(app('#skF_52','#skF_50'),'#skF_53') = '#skF_51',
inference(cnfTransformation,[status(thm)],[f_1055]) ).
tff(c_22,plain,
! [U_30] :
( ( cons('#skF_5'(U_30),nil) = U_30 )
| ~ singletonP(U_30)
| ~ ssList(U_30) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_31014,plain,
! [V_4270,U_4271] :
( lt(V_4270,U_4271)
| ~ gt(U_4271,V_4270)
| ~ ssItem(V_4270)
| ~ ssItem(U_4271) ),
inference(cnfTransformation,[status(thm)],[f_484]) ).
tff(c_394,plain,
! [X1_3084,X3_3096,X4_3098,X2_3092] :
( ~ lt(X1_3084,X3_3096)
| ( app(cons(X3_3096,nil),X4_3098) != '#skF_50' )
| ~ ssList(X4_3098)
| ~ ssItem(X3_3096)
| ( app(X2_3092,cons(X1_3084,nil)) != '#skF_52' )
| ~ ssList(X2_3092)
| ~ ssItem(X1_3084) ),
inference(cnfTransformation,[status(thm)],[f_1055]) ).
tff(c_31064,plain,
! [U_4273,X4_4274,X2_4275,V_4276] :
( ( app(cons(U_4273,nil),X4_4274) != '#skF_50' )
| ~ ssList(X4_4274)
| ( app(X2_4275,cons(V_4276,nil)) != '#skF_52' )
| ~ ssList(X2_4275)
| ~ gt(U_4273,V_4276)
| ~ ssItem(V_4276)
| ~ ssItem(U_4273) ),
inference(resolution,[status(thm)],[c_31014,c_394]) ).
tff(c_31357,plain,
! [U_4288,X4_4289,X2_4290,V_4291] :
( ( app(U_4288,X4_4289) != '#skF_50' )
| ~ ssList(X4_4289)
| ( app(X2_4290,cons(V_4291,nil)) != '#skF_52' )
| ~ ssList(X2_4290)
| ~ gt('#skF_5'(U_4288),V_4291)
| ~ ssItem(V_4291)
| ~ ssItem('#skF_5'(U_4288))
| ~ singletonP(U_4288)
| ~ ssList(U_4288) ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_31064]) ).
tff(c_31401,plain,
! [X2_4290,V_4291] :
( ( '#skF_51' != '#skF_50' )
| ~ ssList('#skF_53')
| ( app(X2_4290,cons(V_4291,nil)) != '#skF_52' )
| ~ ssList(X2_4290)
| ~ gt('#skF_5'(app('#skF_52','#skF_50')),V_4291)
| ~ ssItem(V_4291)
| ~ ssItem('#skF_5'(app('#skF_52','#skF_50')))
| ~ singletonP(app('#skF_52','#skF_50'))
| ~ ssList(app('#skF_52','#skF_50')) ),
inference(superposition,[status(thm),theory(equality)],[c_398,c_31357]) ).
tff(c_31447,plain,
! [X2_4290,V_4291] :
( ( '#skF_51' != '#skF_50' )
| ( app(X2_4290,cons(V_4291,nil)) != '#skF_52' )
| ~ ssList(X2_4290)
| ~ gt('#skF_5'(app('#skF_52','#skF_50')),V_4291)
| ~ ssItem(V_4291)
| ~ ssItem('#skF_5'(app('#skF_52','#skF_50')))
| ~ singletonP(app('#skF_52','#skF_50'))
| ~ ssList(app('#skF_52','#skF_50')) ),
inference(demodulation,[status(thm),theory(equality)],[c_400,c_31401]) ).
tff(c_31753,plain,
~ ssList(app('#skF_52','#skF_50')),
inference(splitLeft,[status(thm)],[c_31447]) ).
tff(c_31756,plain,
( ~ ssList('#skF_50')
| ~ ssList('#skF_52') ),
inference(resolution,[status(thm)],[c_192,c_31753]) ).
tff(c_31760,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_402,c_410,c_31756]) ).
tff(c_31762,plain,
ssList(app('#skF_52','#skF_50')),
inference(splitRight,[status(thm)],[c_31447]) ).
tff(c_36959,plain,
! [V_4427,U_4428,W_4429] :
( ~ memberP(V_4427,U_4428)
| memberP(app(V_4427,W_4429),U_4428)
| ~ ssList(W_4429)
| ~ ssList(V_4427)
| ~ ssItem(U_4428) ),
inference(cnfTransformation,[status(thm)],[f_498]) ).
tff(c_37145,plain,
! [U_4428] :
( ~ memberP(app('#skF_52','#skF_50'),U_4428)
| memberP('#skF_51',U_4428)
| ~ ssList('#skF_53')
| ~ ssList(app('#skF_52','#skF_50'))
| ~ ssItem(U_4428) ),
inference(superposition,[status(thm),theory(equality)],[c_398,c_36959]) ).
tff(c_47897,plain,
! [U_4573] :
( ~ memberP(app('#skF_52','#skF_50'),U_4573)
| memberP('#skF_51',U_4573)
| ~ ssItem(U_4573) ),
inference(demodulation,[status(thm),theory(equality)],[c_31762,c_400,c_37145]) ).
tff(c_47901,plain,
! [U_934] :
( memberP('#skF_51',U_934)
| ~ memberP('#skF_50',U_934)
| ~ ssList('#skF_50')
| ~ ssList('#skF_52')
| ~ ssItem(U_934) ),
inference(resolution,[status(thm)],[c_218,c_47897]) ).
tff(c_47912,plain,
! [U_4574] :
( memberP('#skF_51',U_4574)
| ~ memberP('#skF_50',U_4574)
| ~ ssItem(U_4574) ),
inference(demodulation,[status(thm),theory(equality)],[c_402,c_410,c_47901]) ).
tff(c_406,plain,
'#skF_49' = '#skF_51',
inference(cnfTransformation,[status(thm)],[f_1055]) ).
tff(c_386,plain,
~ memberP('#skF_49','#skF_54'),
inference(cnfTransformation,[status(thm)],[f_1055]) ).
tff(c_420,plain,
~ memberP('#skF_51','#skF_54'),
inference(demodulation,[status(thm),theory(equality)],[c_406,c_386]) ).
tff(c_47915,plain,
( ~ memberP('#skF_50','#skF_54')
| ~ ssItem('#skF_54') ),
inference(resolution,[status(thm)],[c_47912,c_420]) ).
tff(c_47919,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_390,c_419,c_47915]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SWC404+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.15 % 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 : n005.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 21:32:56 EDT 2023
% 0.14/0.36 % CPUTime :
% 23.01/10.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.01/10.08
% 23.01/10.08 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 23.11/10.11
% 23.11/10.11 Inference rules
% 23.11/10.11 ----------------------
% 23.11/10.11 #Ref : 5
% 23.11/10.11 #Sup : 10537
% 23.11/10.11 #Fact : 0
% 23.11/10.11 #Define : 0
% 23.11/10.11 #Split : 175
% 23.11/10.11 #Chain : 0
% 23.11/10.11 #Close : 0
% 23.11/10.11
% 23.11/10.11 Ordering : KBO
% 23.11/10.11
% 23.11/10.11 Simplification rules
% 23.11/10.11 ----------------------
% 23.11/10.11 #Subsume : 1748
% 23.11/10.11 #Demod : 9377
% 23.11/10.11 #Tautology : 3183
% 23.11/10.11 #SimpNegUnit : 898
% 23.11/10.11 #BackRed : 415
% 23.11/10.11
% 23.11/10.11 #Partial instantiations: 0
% 23.11/10.11 #Strategies tried : 1
% 23.11/10.11
% 23.11/10.11 Timing (in seconds)
% 23.11/10.11 ----------------------
% 23.11/10.11 Preprocessing : 0.92
% 23.11/10.11 Parsing : 0.42
% 23.11/10.11 CNF conversion : 0.14
% 23.11/10.11 Main loop : 8.05
% 23.11/10.11 Inferencing : 2.10
% 23.11/10.11 Reduction : 3.40
% 23.11/10.11 Demodulation : 2.53
% 23.11/10.11 BG Simplification : 0.14
% 23.11/10.11 Subsumption : 1.88
% 23.11/10.11 Abstraction : 0.15
% 23.11/10.11 MUC search : 0.00
% 23.11/10.11 Cooper : 0.00
% 23.11/10.11 Total : 9.02
% 23.11/10.11 Index Insertion : 0.00
% 23.11/10.11 Index Deletion : 0.00
% 23.11/10.11 Index Matching : 0.00
% 23.11/10.11 BG Taut test : 0.00
%------------------------------------------------------------------------------