TSTP Solution File: SWC079+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWC079+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 : 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 11:01:04 EDT 2023
% Result : Theorem 20.47s 8.00s
% Output : CNFRefutation 20.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 90
% Syntax : Number of formulae : 203 ( 59 unt; 75 typ; 0 def)
% Number of atoms : 283 ( 101 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 272 ( 117 ~; 112 |; 13 &)
% ( 2 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 3 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 : 56 ( 56 usr; 7 con; 0-2 aty)
% Number of variables : 65 (; 58 !; 7 ?; 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_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_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_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_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_319,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
tff(f_1026,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ( ( ~ neq(V,nil)
| ? [Y] :
( ssList(Y)
& neq(Y,nil)
& segmentP(V,Y)
& segmentP(U,Y) )
| ? [Z] :
( ssList(Z)
& ( W != Z )
& ? [X1] :
( ssItem(X1)
& ( cons(X1,nil) = Z )
& ( hd(X) = X1 )
& neq(nil,X) ) ) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f_371,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ssItem(hd(U)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).
tff(f_769,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ? [V] :
( ssItem(V)
& ( hd(U) = V ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax75) ).
tff(f_311,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> ( U != V ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
tff(f_779,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ? [V] :
( ssList(V)
& ( tl(U) = V ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax76) ).
tff(f_318,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
tff(f_327,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( cons(V,U) != U ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax18) ).
tff(f_859,axiom,
! [U] :
( ssList(U)
=> ( app(U,nil) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
tff(f_413,axiom,
! [U] :
( ssList(U)
=> ( app(nil,U) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
tff(f_135,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( segmentP(U,V)
<=> ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& ( app(app(W,V),X) = U ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).
tff(f_385,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ssList(tl(U)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax24) ).
tff(f_378,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( hd(cons(V,U)) = V ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax23) ).
tff(f_834,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( cons(V,U) = app(cons(V,nil),U) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax81) ).
tff(f_803,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ( cons(hd(U),tl(U)) = U ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax78) ).
tff(c_168,plain,
ssList(nil),
inference(cnfTransformation,[status(thm)],[f_319]) ).
tff(c_388,plain,
ssList('#skF_51'),
inference(cnfTransformation,[status(thm)],[f_1026]) ).
tff(c_4652,plain,
! [U_1451] :
( ssItem(hd(U_1451))
| ( nil = U_1451 )
| ~ ssList(U_1451) ),
inference(cnfTransformation,[status(thm)],[f_371]) ).
tff(c_2666,plain,
! [U_1366] :
( ( hd(U_1366) = '#skF_46'(U_1366) )
| ( nil = U_1366 )
| ~ ssList(U_1366) ),
inference(cnfTransformation,[status(thm)],[f_769]) ).
tff(c_2774,plain,
( ( hd('#skF_51') = '#skF_46'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_388,c_2666]) ).
tff(c_2776,plain,
nil = '#skF_51',
inference(splitLeft,[status(thm)],[c_2774]) ).
tff(c_386,plain,
'#skF_49' = '#skF_51',
inference(cnfTransformation,[status(thm)],[f_1026]) ).
tff(c_406,plain,
neq('#skF_49',nil),
inference(cnfTransformation,[status(thm)],[f_1026]) ).
tff(c_412,plain,
neq('#skF_51',nil),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_406]) ).
tff(c_2811,plain,
neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_2776,c_412]) ).
tff(c_164,plain,
! [V_858] :
( ~ neq(V_858,V_858)
| ~ ssList(V_858) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_2865,plain,
~ ssList('#skF_51'),
inference(resolution,[status(thm)],[c_2811,c_164]) ).
tff(c_2872,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_2865]) ).
tff(c_2874,plain,
nil != '#skF_51',
inference(splitRight,[status(thm)],[c_2774]) ).
tff(c_4495,plain,
! [U_1432,V_1433] :
( neq(U_1432,V_1433)
| ( V_1433 = U_1432 )
| ~ ssList(V_1433)
| ~ ssList(U_1432) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_823,plain,
! [U_1267] :
( ( tl(U_1267) = '#skF_47'(U_1267) )
| ( nil = U_1267 )
| ~ ssList(U_1267) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_931,plain,
( ( tl('#skF_51') = '#skF_47'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_388,c_823]) ).
tff(c_933,plain,
nil = '#skF_51',
inference(splitLeft,[status(thm)],[c_931]) ).
tff(c_966,plain,
neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_933,c_412]) ).
tff(c_1124,plain,
~ ssList('#skF_51'),
inference(resolution,[status(thm)],[c_966,c_164]) ).
tff(c_1129,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_1124]) ).
tff(c_1131,plain,
nil != '#skF_51',
inference(splitRight,[status(thm)],[c_931]) ).
tff(c_2121,plain,
! [U_1297] :
( ( hd(U_1297) = '#skF_46'(U_1297) )
| ( nil = U_1297 )
| ~ ssList(U_1297) ),
inference(cnfTransformation,[status(thm)],[f_769]) ).
tff(c_2205,plain,
( ( hd('#skF_51') = '#skF_46'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_388,c_2121]) ).
tff(c_2239,plain,
hd('#skF_51') = '#skF_46'('#skF_51'),
inference(negUnitSimplification,[status(thm)],[c_1131,c_2205]) ).
tff(c_184,plain,
! [U_888] :
( ssItem(hd(U_888))
| ( nil = U_888 )
| ~ ssList(U_888) ),
inference(cnfTransformation,[status(thm)],[f_371]) ).
tff(c_2247,plain,
( ssItem('#skF_46'('#skF_51'))
| ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_2239,c_184]) ).
tff(c_2251,plain,
( ssItem('#skF_46'('#skF_51'))
| ( nil = '#skF_51' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_2247]) ).
tff(c_2252,plain,
ssItem('#skF_46'('#skF_51')),
inference(negUnitSimplification,[status(thm)],[c_1131,c_2251]) ).
tff(c_2265,plain,
! [V_1300,U_1301] :
( ssList(cons(V_1300,U_1301))
| ~ ssItem(V_1300)
| ~ ssList(U_1301) ),
inference(cnfTransformation,[status(thm)],[f_318]) ).
tff(c_396,plain,
( ~ neq(nil,'#skF_51')
| ~ ssItem(hd('#skF_51'))
| ( cons(hd('#skF_51'),nil) = '#skF_50' )
| ~ ssList(cons(hd('#skF_51'),nil))
| ~ neq('#skF_51',nil) ),
inference(cnfTransformation,[status(thm)],[f_1026]) ).
tff(c_417,plain,
( ~ neq(nil,'#skF_51')
| ~ ssItem(hd('#skF_51'))
| ( cons(hd('#skF_51'),nil) = '#skF_50' )
| ~ ssList(cons(hd('#skF_51'),nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_412,c_396]) ).
tff(c_431,plain,
~ ssList(cons(hd('#skF_51'),nil)),
inference(splitLeft,[status(thm)],[c_417]) ).
tff(c_2243,plain,
~ ssList(cons('#skF_46'('#skF_51'),nil)),
inference(demodulation,[status(thm),theory(equality)],[c_2239,c_431]) ).
tff(c_2268,plain,
( ~ ssItem('#skF_46'('#skF_51'))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_2265,c_2243]) ).
tff(c_2290,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_168,c_2252,c_2268]) ).
tff(c_2291,plain,
( ~ ssItem(hd('#skF_51'))
| ~ neq(nil,'#skF_51')
| ( cons(hd('#skF_51'),nil) = '#skF_50' ) ),
inference(splitRight,[status(thm)],[c_417]) ).
tff(c_2303,plain,
~ neq(nil,'#skF_51'),
inference(splitLeft,[status(thm)],[c_2291]) ).
tff(c_4501,plain,
( ( nil = '#skF_51' )
| ~ ssList('#skF_51')
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_4495,c_2303]) ).
tff(c_4516,plain,
nil = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_168,c_388,c_4501]) ).
tff(c_4518,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2874,c_4516]) ).
tff(c_4519,plain,
( ~ ssItem(hd('#skF_51'))
| ( cons(hd('#skF_51'),nil) = '#skF_50' ) ),
inference(splitRight,[status(thm)],[c_2291]) ).
tff(c_4583,plain,
~ ssItem(hd('#skF_51')),
inference(splitLeft,[status(thm)],[c_4519]) ).
tff(c_4655,plain,
( ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(resolution,[status(thm)],[c_4652,c_4583]) ).
tff(c_4658,plain,
nil = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_388,c_4655]) ).
tff(c_4683,plain,
neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_4658,c_412]) ).
tff(c_4702,plain,
~ ssList('#skF_51'),
inference(resolution,[status(thm)],[c_4683,c_164]) ).
tff(c_4709,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_4702]) ).
tff(c_4711,plain,
ssItem(hd('#skF_51')),
inference(splitRight,[status(thm)],[c_4519]) ).
tff(c_4710,plain,
cons(hd('#skF_51'),nil) = '#skF_50',
inference(splitRight,[status(thm)],[c_4519]) ).
tff(c_5047,plain,
! [V_1498,U_1499] :
( ( cons(V_1498,U_1499) != U_1499 )
| ~ ssItem(V_1498)
| ~ ssList(U_1499) ),
inference(cnfTransformation,[status(thm)],[f_327]) ).
tff(c_5049,plain,
( ( nil != '#skF_50' )
| ~ ssItem(hd('#skF_51'))
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_4710,c_5047]) ).
tff(c_5051,plain,
nil != '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_168,c_4711,c_5049]) ).
tff(c_390,plain,
ssList('#skF_50'),
inference(cnfTransformation,[status(thm)],[f_1026]) ).
tff(c_162,plain,
! [U_856,V_858] :
( neq(U_856,V_858)
| ( V_858 = U_856 )
| ~ ssList(V_858)
| ~ ssList(U_856) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_4523,plain,
! [U_1436] :
( ( app(U_1436,nil) = U_1436 )
| ~ ssList(U_1436) ),
inference(cnfTransformation,[status(thm)],[f_859]) ).
tff(c_4539,plain,
app('#skF_50',nil) = '#skF_50',
inference(resolution,[status(thm)],[c_390,c_4523]) ).
tff(c_4556,plain,
! [U_1441] :
( ( app(nil,U_1441) = U_1441 )
| ~ ssList(U_1441) ),
inference(cnfTransformation,[status(thm)],[f_413]) ).
tff(c_4573,plain,
app(nil,'#skF_50') = '#skF_50',
inference(resolution,[status(thm)],[c_390,c_4556]) ).
tff(c_26319,plain,
! [W_1974,V_1975,X_1976] :
( segmentP(app(app(W_1974,V_1975),X_1976),V_1975)
| ~ ssList(X_1976)
| ~ ssList(W_1974)
| ~ ssList(V_1975)
| ~ ssList(app(app(W_1974,V_1975),X_1976)) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_26588,plain,
! [X_1976] :
( segmentP(app('#skF_50',X_1976),'#skF_50')
| ~ ssList(X_1976)
| ~ ssList(nil)
| ~ ssList('#skF_50')
| ~ ssList(app(app(nil,'#skF_50'),X_1976)) ),
inference(superposition,[status(thm),theory(equality)],[c_4573,c_26319]) ).
tff(c_29397,plain,
! [X_2094] :
( segmentP(app('#skF_50',X_2094),'#skF_50')
| ~ ssList(X_2094)
| ~ ssList(app('#skF_50',X_2094)) ),
inference(demodulation,[status(thm),theory(equality)],[c_4573,c_390,c_168,c_26588]) ).
tff(c_29414,plain,
( segmentP('#skF_50','#skF_50')
| ~ ssList(nil)
| ~ ssList(app('#skF_50',nil)) ),
inference(superposition,[status(thm),theory(equality)],[c_4539,c_29397]) ).
tff(c_29426,plain,
segmentP('#skF_50','#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_4539,c_168,c_29414]) ).
tff(c_5052,plain,
! [U_1500] :
( ( tl(U_1500) = '#skF_47'(U_1500) )
| ( nil = U_1500 )
| ~ ssList(U_1500) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_5156,plain,
( ( tl('#skF_51') = '#skF_47'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_388,c_5052]) ).
tff(c_5182,plain,
nil = '#skF_51',
inference(splitLeft,[status(thm)],[c_5156]) ).
tff(c_4520,plain,
neq(nil,'#skF_51'),
inference(splitRight,[status(thm)],[c_2291]) ).
tff(c_5322,plain,
neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_5182,c_4520]) ).
tff(c_5442,plain,
~ ssList('#skF_51'),
inference(resolution,[status(thm)],[c_5322,c_164]) ).
tff(c_5449,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_5442]) ).
tff(c_5451,plain,
nil != '#skF_51',
inference(splitRight,[status(thm)],[c_5156]) ).
tff(c_5450,plain,
tl('#skF_51') = '#skF_47'('#skF_51'),
inference(splitRight,[status(thm)],[c_5156]) ).
tff(c_188,plain,
! [U_892] :
( ssList(tl(U_892))
| ( nil = U_892 )
| ~ ssList(U_892) ),
inference(cnfTransformation,[status(thm)],[f_385]) ).
tff(c_5455,plain,
( ssList('#skF_47'('#skF_51'))
| ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_5450,c_188]) ).
tff(c_5459,plain,
( ssList('#skF_47'('#skF_51'))
| ( nil = '#skF_51' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_5455]) ).
tff(c_5460,plain,
ssList('#skF_47'('#skF_51')),
inference(negUnitSimplification,[status(thm)],[c_5451,c_5459]) ).
tff(c_7149,plain,
! [U_1561] :
( ( hd(U_1561) = '#skF_46'(U_1561) )
| ( nil = U_1561 )
| ~ ssList(U_1561) ),
inference(cnfTransformation,[status(thm)],[f_769]) ).
tff(c_7242,plain,
( ( hd('#skF_50') = '#skF_46'('#skF_50') )
| ( nil = '#skF_50' ) ),
inference(resolution,[status(thm)],[c_390,c_7149]) ).
tff(c_7280,plain,
hd('#skF_50') = '#skF_46'('#skF_50'),
inference(negUnitSimplification,[status(thm)],[c_5051,c_7242]) ).
tff(c_7424,plain,
( ssItem('#skF_46'('#skF_50'))
| ( nil = '#skF_50' )
| ~ ssList('#skF_50') ),
inference(superposition,[status(thm),theory(equality)],[c_7280,c_184]) ).
tff(c_7428,plain,
( ssItem('#skF_46'('#skF_50'))
| ( nil = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_7424]) ).
tff(c_7429,plain,
ssItem('#skF_46'('#skF_50')),
inference(negUnitSimplification,[status(thm)],[c_5051,c_7428]) ).
tff(c_7239,plain,
( ( hd('#skF_51') = '#skF_46'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_388,c_7149]) ).
tff(c_7277,plain,
hd('#skF_51') = '#skF_46'('#skF_51'),
inference(negUnitSimplification,[status(thm)],[c_5451,c_7239]) ).
tff(c_7282,plain,
ssItem('#skF_46'('#skF_51')),
inference(demodulation,[status(thm),theory(equality)],[c_7277,c_4711]) ).
tff(c_7281,plain,
cons('#skF_46'('#skF_51'),nil) = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_7277,c_4710]) ).
tff(c_7558,plain,
! [V_1566,U_1567] :
( ( hd(cons(V_1566,U_1567)) = V_1566 )
| ~ ssItem(V_1566)
| ~ ssList(U_1567) ),
inference(cnfTransformation,[status(thm)],[f_378]) ).
tff(c_7573,plain,
( ( hd('#skF_50') = '#skF_46'('#skF_51') )
| ~ ssItem('#skF_46'('#skF_51'))
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_7281,c_7558]) ).
tff(c_7579,plain,
'#skF_46'('#skF_51') = '#skF_46'('#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_168,c_7282,c_7280,c_7573]) ).
tff(c_7580,plain,
cons('#skF_46'('#skF_50'),nil) = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_7579,c_7281]) ).
tff(c_10847,plain,
! [V_1725,U_1726] :
( ( app(cons(V_1725,nil),U_1726) = cons(V_1725,U_1726) )
| ~ ssItem(V_1725)
| ~ ssList(U_1726) ),
inference(cnfTransformation,[status(thm)],[f_834]) ).
tff(c_10863,plain,
! [U_1726] :
( ( cons('#skF_46'('#skF_50'),U_1726) = app('#skF_50',U_1726) )
| ~ ssItem('#skF_46'('#skF_50'))
| ~ ssList(U_1726) ),
inference(superposition,[status(thm),theory(equality)],[c_7580,c_10847]) ).
tff(c_10871,plain,
! [U_1727] :
( ( cons('#skF_46'('#skF_50'),U_1727) = app('#skF_50',U_1727) )
| ~ ssList(U_1727) ),
inference(demodulation,[status(thm),theory(equality)],[c_7429,c_10863]) ).
tff(c_7582,plain,
hd('#skF_51') = '#skF_46'('#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_7579,c_7277]) ).
tff(c_8671,plain,
! [U_1615] :
( ( cons(hd(U_1615),tl(U_1615)) = U_1615 )
| ( nil = U_1615 )
| ~ ssList(U_1615) ),
inference(cnfTransformation,[status(thm)],[f_803]) ).
tff(c_8720,plain,
( ( cons(hd('#skF_51'),'#skF_47'('#skF_51')) = '#skF_51' )
| ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_5450,c_8671]) ).
tff(c_8744,plain,
( ( cons('#skF_46'('#skF_50'),'#skF_47'('#skF_51')) = '#skF_51' )
| ( nil = '#skF_51' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_7582,c_8720]) ).
tff(c_8745,plain,
cons('#skF_46'('#skF_50'),'#skF_47'('#skF_51')) = '#skF_51',
inference(negUnitSimplification,[status(thm)],[c_5451,c_8744]) ).
tff(c_10887,plain,
( ( app('#skF_50','#skF_47'('#skF_51')) = '#skF_51' )
| ~ ssList('#skF_47'('#skF_51')) ),
inference(superposition,[status(thm),theory(equality)],[c_10871,c_8745]) ).
tff(c_10956,plain,
app('#skF_50','#skF_47'('#skF_51')) = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_5460,c_10887]) ).
tff(c_29411,plain,
( segmentP('#skF_51','#skF_50')
| ~ ssList('#skF_47'('#skF_51'))
| ~ ssList(app('#skF_50','#skF_47'('#skF_51'))) ),
inference(superposition,[status(thm),theory(equality)],[c_10956,c_29397]) ).
tff(c_29424,plain,
segmentP('#skF_51','#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_10956,c_5460,c_29411]) ).
tff(c_384,plain,
'#skF_48' = '#skF_50',
inference(cnfTransformation,[status(thm)],[f_1026]) ).
tff(c_398,plain,
! [Y_1193] :
( ~ segmentP('#skF_48',Y_1193)
| ~ segmentP('#skF_49',Y_1193)
| ~ neq(Y_1193,nil)
| ~ ssList(Y_1193)
| ~ neq('#skF_51',nil) ),
inference(cnfTransformation,[status(thm)],[f_1026]) ).
tff(c_411,plain,
! [Y_1193] :
( ~ segmentP('#skF_48',Y_1193)
| ~ segmentP('#skF_51',Y_1193)
| ~ neq(Y_1193,nil)
| ~ ssList(Y_1193)
| ~ neq('#skF_51',nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_398]) ).
tff(c_415,plain,
! [Y_1193] :
( ~ segmentP('#skF_48',Y_1193)
| ~ segmentP('#skF_51',Y_1193)
| ~ neq(Y_1193,nil)
| ~ ssList(Y_1193) ),
inference(demodulation,[status(thm),theory(equality)],[c_412,c_411]) ).
tff(c_419,plain,
! [Y_1193] :
( ~ segmentP('#skF_50',Y_1193)
| ~ segmentP('#skF_51',Y_1193)
| ~ neq(Y_1193,nil)
| ~ ssList(Y_1193) ),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_415]) ).
tff(c_29444,plain,
( ~ segmentP('#skF_50','#skF_50')
| ~ neq('#skF_50',nil)
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_29424,c_419]) ).
tff(c_29454,plain,
~ neq('#skF_50',nil),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_29426,c_29444]) ).
tff(c_29460,plain,
( ( nil = '#skF_50' )
| ~ ssList(nil)
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_162,c_29454]) ).
tff(c_29466,plain,
nil = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_390,c_168,c_29460]) ).
tff(c_29468,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_5051,c_29466]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC079+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % 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
% 0.14/0.34 % Computer : n006.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 21:43:43 EDT 2023
% 0.20/0.34 % CPUTime :
% 20.47/8.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.47/8.01
% 20.47/8.01 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 20.74/8.05
% 20.74/8.05 Inference rules
% 20.74/8.05 ----------------------
% 20.74/8.05 #Ref : 5
% 20.74/8.05 #Sup : 6433
% 20.74/8.05 #Fact : 0
% 20.74/8.05 #Define : 0
% 20.74/8.05 #Split : 61
% 20.74/8.05 #Chain : 0
% 20.74/8.05 #Close : 0
% 20.74/8.05
% 20.74/8.05 Ordering : KBO
% 20.74/8.05
% 20.74/8.05 Simplification rules
% 20.74/8.05 ----------------------
% 20.74/8.05 #Subsume : 722
% 20.74/8.05 #Demod : 4920
% 20.74/8.05 #Tautology : 1647
% 20.74/8.05 #SimpNegUnit : 454
% 20.74/8.05 #BackRed : 348
% 20.74/8.05
% 20.74/8.05 #Partial instantiations: 0
% 20.74/8.05 #Strategies tried : 1
% 20.74/8.05
% 20.74/8.05 Timing (in seconds)
% 20.74/8.05 ----------------------
% 20.74/8.06 Preprocessing : 0.92
% 20.74/8.06 Parsing : 0.43
% 20.74/8.06 CNF conversion : 0.11
% 20.74/8.06 Main loop : 5.97
% 20.74/8.06 Inferencing : 1.55
% 20.74/8.06 Reduction : 2.34
% 20.74/8.06 Demodulation : 1.68
% 20.74/8.06 BG Simplification : 0.13
% 20.74/8.06 Subsumption : 1.56
% 20.74/8.06 Abstraction : 0.12
% 20.74/8.06 MUC search : 0.00
% 20.74/8.06 Cooper : 0.00
% 20.74/8.06 Total : 6.96
% 20.74/8.06 Index Insertion : 0.00
% 20.74/8.06 Index Deletion : 0.00
% 20.74/8.06 Index Matching : 0.00
% 20.74/8.06 BG Taut test : 0.00
%------------------------------------------------------------------------------