%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWC253+1 : TPTP v9.0.0. Released v2.4.0.
% 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 : n031.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 : Wed Apr 9 09:19:46 PM UTC 2025
% Result : Theorem 17.54s 5.65s
% Output : CNFRefutation 17.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 139 ( 66 unt; 0 typ; 0 def)
% Number of atoms : 291 ( 128 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 256 ( 104 ~; 110 |; 9 &)
% ( 2 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 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 : 64 ( 59 !; 5 ?; 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_1019,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ( ( ~ neq(V,nil)
| ? [Y] :
( ssList(Y)
& ( X != Y )
& ? [Z] :
( ssList(Z)
& ( tl(X) = Z )
& ( app(W,Z) = Y )
& neq(nil,X) ) )
| singletonP(U) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f_769,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ? [V] :
( ssItem(V)
& ( hd(U) = V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax75) ).
tff(f_311,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> ( U != V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
tff(f_371,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ssItem(hd(U)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
tff(f_385,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ssList(tl(U)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
tff(f_779,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ? [V] :
( ssList(V)
& ( tl(U) = V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax76) ).
tff(f_319,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
tff(f_399,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
tff(f_413,axiom,
! [U] :
( ssList(U)
=> ( app(nil,U) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
tff(f_803,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ( cons(hd(U),tl(U)) = U ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).
tff(f_327,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( cons(V,U) != U ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).
tff(f_318,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
tff(f_96,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( ssItem(V)
& ( cons(V,nil) = U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax4) ).
tff(f_879,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( nil != U )
=> ( tl(app(U,V)) = app(tl(U),V) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax86) ).
tff(f_815,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( app(W,V) = app(U,V) )
=> ( W = U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax79) ).
tff(c_384,plain,
'#skF_48' = '#skF_50',
inference(cnfTransformation,[status(thm)],[f_1019]) ).
tff(c_386,plain,
'#skF_49' = '#skF_51',
inference(cnfTransformation,[status(thm)],[f_1019]) ).
tff(c_406,plain,
neq('#skF_49',nil),
inference(cnfTransformation,[status(thm)],[f_1019]) ).
tff(c_411,plain,
neq('#skF_51',nil),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_406]) ).
tff(c_396,plain,
( ~ singletonP('#skF_48')
| ~ neq('#skF_51',nil) ),
inference(cnfTransformation,[status(thm)],[f_1019]) ).
tff(c_414,plain,
~ singletonP('#skF_48'),
inference(demodulation,[status(thm),theory(equality)],[c_411,c_396]) ).
tff(c_418,plain,
~ singletonP('#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_414]) ).
tff(c_388,plain,
ssList('#skF_51'),
inference(cnfTransformation,[status(thm)],[f_1019]) ).
tff(c_5287,plain,
! [U_1554] :
( ( hd(U_1554) = '#skF_46'(U_1554) )
| ( nil = U_1554 )
| ~ ssList(U_1554) ),
inference(cnfTransformation,[status(thm)],[f_769]) ).
tff(c_5397,plain,
( ( hd('#skF_51') = '#skF_46'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_388,c_5287]) ).
tff(c_5401,plain,
nil = '#skF_51',
inference(splitLeft,[status(thm)],[c_5397]) ).
tff(c_5434,plain,
neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_5401,c_411]) ).
tff(c_164,plain,
! [V_858] :
( ~ neq(V_858,V_858)
| ~ ssList(V_858) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_5460,plain,
~ ssList('#skF_51'),
inference(resolution,[status(thm)],[c_5434,c_164]) ).
tff(c_5465,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_5460]) ).
tff(c_5467,plain,
nil != '#skF_51',
inference(splitRight,[status(thm)],[c_5397]) ).
tff(c_5466,plain,
hd('#skF_51') = '#skF_46'('#skF_51'),
inference(splitRight,[status(thm)],[c_5397]) ).
tff(c_184,plain,
! [U_888] :
( ssItem(hd(U_888))
| ( nil = U_888 )
| ~ ssList(U_888) ),
inference(cnfTransformation,[status(thm)],[f_371]) ).
tff(c_5471,plain,
( ssItem('#skF_46'('#skF_51'))
| ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_5466,c_184]) ).
tff(c_5475,plain,
( ssItem('#skF_46'('#skF_51'))
| ( nil = '#skF_51' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_5471]) ).
tff(c_5476,plain,
ssItem('#skF_46'('#skF_51')),
inference(negUnitSimplification,[status(thm)],[c_5467,c_5475]) ).
tff(c_390,plain,
ssList('#skF_50'),
inference(cnfTransformation,[status(thm)],[f_1019]) ).
tff(c_5400,plain,
( ( hd('#skF_50') = '#skF_46'('#skF_50') )
| ( nil = '#skF_50' ) ),
inference(resolution,[status(thm)],[c_390,c_5287]) ).
tff(c_5478,plain,
nil = '#skF_50',
inference(splitLeft,[status(thm)],[c_5400]) ).
tff(c_5479,plain,
'#skF_51' != '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_5478,c_5467]) ).
tff(c_4809,plain,
! [U_1493] :
( ssList(tl(U_1493))
| ( nil = U_1493 )
| ~ ssList(U_1493) ),
inference(cnfTransformation,[status(thm)],[f_385]) ).
tff(c_2501,plain,
! [U_1357] :
( ( tl(U_1357) = '#skF_47'(U_1357) )
| ( nil = U_1357 )
| ~ ssList(U_1357) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_2607,plain,
( ( tl('#skF_51') = '#skF_47'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_388,c_2501]) ).
tff(c_2611,plain,
nil = '#skF_51',
inference(splitLeft,[status(thm)],[c_2607]) ).
tff(c_2643,plain,
neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_2611,c_411]) ).
tff(c_2804,plain,
~ ssList('#skF_51'),
inference(resolution,[status(thm)],[c_2643,c_164]) ).
tff(c_2809,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_2804]) ).
tff(c_2811,plain,
nil != '#skF_51',
inference(splitRight,[status(thm)],[c_2607]) ).
tff(c_168,plain,
ssList(nil),
inference(cnfTransformation,[status(thm)],[f_319]) ).
tff(c_4464,plain,
! [U_1437,V_1438] :
( neq(U_1437,V_1438)
| ( V_1438 = U_1437 )
| ~ ssList(V_1438)
| ~ ssList(U_1437) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_772,plain,
! [U_1248] :
( ( hd(U_1248) = '#skF_46'(U_1248) )
| ( nil = U_1248 )
| ~ ssList(U_1248) ),
inference(cnfTransformation,[status(thm)],[f_769]) ).
tff(c_874,plain,
( ( hd('#skF_51') = '#skF_46'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_388,c_772]) ).
tff(c_878,plain,
nil = '#skF_51',
inference(splitLeft,[status(thm)],[c_874]) ).
tff(c_907,plain,
neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_878,c_411]) ).
tff(c_1059,plain,
~ ssList('#skF_51'),
inference(resolution,[status(thm)],[c_907,c_164]) ).
tff(c_1064,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_1059]) ).
tff(c_1066,plain,
nil != '#skF_51',
inference(splitRight,[status(thm)],[c_874]) ).
tff(c_1883,plain,
! [U_1288] :
( ( tl(U_1288) = '#skF_47'(U_1288) )
| ( nil = U_1288 )
| ~ ssList(U_1288) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_1955,plain,
( ( tl('#skF_51') = '#skF_47'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_388,c_1883]) ).
tff(c_1987,plain,
tl('#skF_51') = '#skF_47'('#skF_51'),
inference(negUnitSimplification,[status(thm)],[c_1066,c_1955]) ).
tff(c_188,plain,
! [U_892] :
( ssList(tl(U_892))
| ( nil = U_892 )
| ~ ssList(U_892) ),
inference(cnfTransformation,[status(thm)],[f_385]) ).
tff(c_1997,plain,
( ssList('#skF_47'('#skF_51'))
| ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_1987,c_188]) ).
tff(c_2001,plain,
( ssList('#skF_47'('#skF_51'))
| ( nil = '#skF_51' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_1997]) ).
tff(c_2002,plain,
ssList('#skF_47'('#skF_51')),
inference(negUnitSimplification,[status(thm)],[c_1066,c_2001]) ).
tff(c_2091,plain,
! [U_1291,V_1292] :
( ssList(app(U_1291,V_1292))
| ~ ssList(V_1292)
| ~ ssList(U_1291) ),
inference(cnfTransformation,[status(thm)],[f_399]) ).
tff(c_398,plain,
( ~ neq(nil,'#skF_51')
| ~ ssList(tl('#skF_51'))
| ( app('#skF_50',tl('#skF_51')) = '#skF_51' )
| ~ ssList(app('#skF_50',tl('#skF_51')))
| ~ neq('#skF_51',nil) ),
inference(cnfTransformation,[status(thm)],[f_1019]) ).
tff(c_416,plain,
( ~ neq(nil,'#skF_51')
| ~ ssList(tl('#skF_51'))
| ( app('#skF_50',tl('#skF_51')) = '#skF_51' )
| ~ ssList(app('#skF_50',tl('#skF_51'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_411,c_398]) ).
tff(c_429,plain,
~ ssList(app('#skF_50',tl('#skF_51'))),
inference(splitLeft,[status(thm)],[c_416]) ).
tff(c_1993,plain,
~ ssList(app('#skF_50','#skF_47'('#skF_51'))),
inference(demodulation,[status(thm),theory(equality)],[c_1987,c_429]) ).
tff(c_2094,plain,
( ~ ssList('#skF_47'('#skF_51'))
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_2091,c_1993]) ).
tff(c_2140,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_390,c_2002,c_2094]) ).
tff(c_2141,plain,
( ~ ssList(tl('#skF_51'))
| ~ neq(nil,'#skF_51')
| ( app('#skF_50',tl('#skF_51')) = '#skF_51' ) ),
inference(splitRight,[status(thm)],[c_416]) ).
tff(c_2146,plain,
~ neq(nil,'#skF_51'),
inference(splitLeft,[status(thm)],[c_2141]) ).
tff(c_4471,plain,
( ( nil = '#skF_51' )
| ~ ssList('#skF_51')
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_4464,c_2146]) ).
tff(c_4480,plain,
nil = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_168,c_388,c_4471]) ).
tff(c_4482,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2811,c_4480]) ).
tff(c_4483,plain,
( ~ ssList(tl('#skF_51'))
| ( app('#skF_50',tl('#skF_51')) = '#skF_51' ) ),
inference(splitRight,[status(thm)],[c_2141]) ).
tff(c_4489,plain,
~ ssList(tl('#skF_51')),
inference(splitLeft,[status(thm)],[c_4483]) ).
tff(c_4818,plain,
( ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(resolution,[status(thm)],[c_4809,c_4489]) ).
tff(c_4823,plain,
nil = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_388,c_4818]) ).
tff(c_4853,plain,
neq('#skF_51','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_4823,c_411]) ).
tff(c_4874,plain,
~ ssList('#skF_51'),
inference(resolution,[status(thm)],[c_4853,c_164]) ).
tff(c_4879,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_4874]) ).
tff(c_4880,plain,
app('#skF_50',tl('#skF_51')) = '#skF_51',
inference(splitRight,[status(thm)],[c_4483]) ).
tff(c_4881,plain,
ssList(tl('#skF_51')),
inference(splitRight,[status(thm)],[c_4483]) ).
tff(c_4895,plain,
! [U_1502] :
( ( app(nil,U_1502) = U_1502 )
| ~ ssList(U_1502) ),
inference(cnfTransformation,[status(thm)],[f_413]) ).
tff(c_4908,plain,
app(nil,tl('#skF_51')) = tl('#skF_51'),
inference(resolution,[status(thm)],[c_4881,c_4895]) ).
tff(c_5490,plain,
app('#skF_50',tl('#skF_51')) = tl('#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_5478,c_4908]) ).
tff(c_5521,plain,
tl('#skF_51') = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_4880,c_5490]) ).
tff(c_340,plain,
! [U_1052] :
( ( cons(hd(U_1052),tl(U_1052)) = U_1052 )
| ( nil = U_1052 )
| ~ ssList(U_1052) ),
inference(cnfTransformation,[status(thm)],[f_803]) ).
tff(c_6833,plain,
! [U_1618] :
( ( cons(hd(U_1618),tl(U_1618)) = U_1618 )
| ( U_1618 = '#skF_50' )
| ~ ssList(U_1618) ),
inference(demodulation,[status(thm),theory(equality)],[c_5478,c_340]) ).
tff(c_6864,plain,
( ( cons(hd('#skF_51'),'#skF_51') = '#skF_51' )
| ( '#skF_51' = '#skF_50' )
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_5521,c_6833]) ).
tff(c_6873,plain,
( ( cons('#skF_46'('#skF_51'),'#skF_51') = '#skF_51' )
| ( '#skF_51' = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_5466,c_6864]) ).
tff(c_6874,plain,
cons('#skF_46'('#skF_51'),'#skF_51') = '#skF_51',
inference(negUnitSimplification,[status(thm)],[c_5479,c_6873]) ).
tff(c_170,plain,
! [V_864,U_862] :
( ( cons(V_864,U_862) != U_862 )
| ~ ssItem(V_864)
| ~ ssList(U_862) ),
inference(cnfTransformation,[status(thm)],[f_327]) ).
tff(c_6894,plain,
( ~ ssItem('#skF_46'('#skF_51'))
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_6874,c_170]) ).
tff(c_6910,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_5476,c_6894]) ).
tff(c_6912,plain,
nil != '#skF_50',
inference(splitRight,[status(thm)],[c_5400]) ).
tff(c_6911,plain,
hd('#skF_50') = '#skF_46'('#skF_50'),
inference(splitRight,[status(thm)],[c_5400]) ).
tff(c_6916,plain,
( ssItem('#skF_46'('#skF_50'))
| ( nil = '#skF_50' )
| ~ ssList('#skF_50') ),
inference(superposition,[status(thm),theory(equality)],[c_6911,c_184]) ).
tff(c_6920,plain,
( ssItem('#skF_46'('#skF_50'))
| ( nil = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_6916]) ).
tff(c_6921,plain,
ssItem('#skF_46'('#skF_50')),
inference(negUnitSimplification,[status(thm)],[c_6912,c_6920]) ).
tff(c_6923,plain,
! [U_1619] :
( ( tl(U_1619) = '#skF_47'(U_1619) )
| ( nil = U_1619 )
| ~ ssList(U_1619) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_7007,plain,
( ( tl('#skF_50') = '#skF_47'('#skF_50') )
| ( nil = '#skF_50' ) ),
inference(resolution,[status(thm)],[c_390,c_6923]) ).
tff(c_7040,plain,
tl('#skF_50') = '#skF_47'('#skF_50'),
inference(negUnitSimplification,[status(thm)],[c_6912,c_7007]) ).
tff(c_7075,plain,
( ssList('#skF_47'('#skF_50'))
| ( nil = '#skF_50' )
| ~ ssList('#skF_50') ),
inference(superposition,[status(thm),theory(equality)],[c_7040,c_188]) ).
tff(c_7079,plain,
( ssList('#skF_47'('#skF_50'))
| ( nil = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_7075]) ).
tff(c_7080,plain,
ssList('#skF_47'('#skF_50')),
inference(negUnitSimplification,[status(thm)],[c_6912,c_7079]) ).
tff(c_334,plain,
! [U_1047] :
( ( tl(U_1047) = '#skF_47'(U_1047) )
| ( nil = U_1047 )
| ~ ssList(U_1047) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_7095,plain,
( ( tl('#skF_47'('#skF_50')) = '#skF_47'('#skF_47'('#skF_50')) )
| ( '#skF_47'('#skF_50') = nil ) ),
inference(resolution,[status(thm)],[c_7080,c_334]) ).
tff(c_7511,plain,
'#skF_47'('#skF_50') = nil,
inference(splitLeft,[status(thm)],[c_7095]) ).
tff(c_7516,plain,
tl('#skF_50') = nil,
inference(demodulation,[status(thm),theory(equality)],[c_7511,c_7040]) ).
tff(c_8280,plain,
! [U_1683] :
( ( cons(hd(U_1683),tl(U_1683)) = U_1683 )
| ( nil = U_1683 )
| ~ ssList(U_1683) ),
inference(cnfTransformation,[status(thm)],[f_803]) ).
tff(c_8314,plain,
( ( cons('#skF_46'('#skF_50'),tl('#skF_50')) = '#skF_50' )
| ( nil = '#skF_50' )
| ~ ssList('#skF_50') ),
inference(superposition,[status(thm),theory(equality)],[c_6911,c_8280]) ).
tff(c_8323,plain,
( ( cons('#skF_46'('#skF_50'),nil) = '#skF_50' )
| ( nil = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_7516,c_8314]) ).
tff(c_8324,plain,
cons('#skF_46'('#skF_50'),nil) = '#skF_50',
inference(negUnitSimplification,[status(thm)],[c_6912,c_8323]) ).
tff(c_166,plain,
! [V_861,U_859] :
( ssList(cons(V_861,U_859))
| ~ ssItem(V_861)
| ~ ssList(U_859) ),
inference(cnfTransformation,[status(thm)],[f_318]) ).
tff(c_8056,plain,
! [V_1665] :
( singletonP(cons(V_1665,nil))
| ~ ssItem(V_1665)
| ~ ssList(cons(V_1665,nil)) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_8063,plain,
! [V_861] :
( singletonP(cons(V_861,nil))
| ~ ssItem(V_861)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_166,c_8056]) ).
tff(c_8066,plain,
! [V_861] :
( singletonP(cons(V_861,nil))
| ~ ssItem(V_861) ),
inference(demodulation,[status(thm),theory(equality)],[c_168,c_8063]) ).
tff(c_8328,plain,
( singletonP('#skF_50')
| ~ ssItem('#skF_46'('#skF_50')) ),
inference(superposition,[status(thm),theory(equality)],[c_8324,c_8066]) ).
tff(c_8369,plain,
singletonP('#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_6921,c_8328]) ).
tff(c_8371,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_418,c_8369]) ).
tff(c_8373,plain,
'#skF_47'('#skF_50') != nil,
inference(splitRight,[status(thm)],[c_7095]) ).
tff(c_7001,plain,
( ( tl('#skF_51') = '#skF_47'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_388,c_6923]) ).
tff(c_7035,plain,
tl('#skF_51') = '#skF_47'('#skF_51'),
inference(negUnitSimplification,[status(thm)],[c_5467,c_7001]) ).
tff(c_7044,plain,
ssList('#skF_47'('#skF_51')),
inference(demodulation,[status(thm),theory(equality)],[c_7035,c_4881]) ).
tff(c_7043,plain,
app('#skF_50','#skF_47'('#skF_51')) = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_7035,c_4880]) ).
tff(c_17734,plain,
! [U_1922,V_1923] :
( ( app(tl(U_1922),V_1923) = tl(app(U_1922,V_1923)) )
| ( nil = U_1922 )
| ~ ssList(V_1923)
| ~ ssList(U_1922) ),
inference(cnfTransformation,[status(thm)],[f_879]) ).
tff(c_17813,plain,
! [V_1923] :
( ( app('#skF_47'('#skF_50'),V_1923) = tl(app('#skF_50',V_1923)) )
| ( nil = '#skF_50' )
| ~ ssList(V_1923)
| ~ ssList('#skF_50') ),
inference(superposition,[status(thm),theory(equality)],[c_7040,c_17734]) ).
tff(c_17838,plain,
! [V_1923] :
( ( app('#skF_47'('#skF_50'),V_1923) = tl(app('#skF_50',V_1923)) )
| ( nil = '#skF_50' )
| ~ ssList(V_1923) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_17813]) ).
tff(c_17839,plain,
! [V_1923] :
( ( app('#skF_47'('#skF_50'),V_1923) = tl(app('#skF_50',V_1923)) )
| ~ ssList(V_1923) ),
inference(negUnitSimplification,[status(thm)],[c_6912,c_17838]) ).
tff(c_7041,plain,
app(nil,'#skF_47'('#skF_51')) = '#skF_47'('#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_7035,c_7035,c_4908]) ).
tff(c_13793,plain,
! [W_1882,U_1883,V_1884] :
( ( W_1882 = U_1883 )
| ( app(W_1882,V_1884) != app(U_1883,V_1884) )
| ~ ssList(W_1882)
| ~ ssList(V_1884)
| ~ ssList(U_1883) ),
inference(cnfTransformation,[status(thm)],[f_815]) ).
tff(c_14021,plain,
! [W_1882] :
( ( nil = W_1882 )
| ( app(W_1882,'#skF_47'('#skF_51')) != '#skF_47'('#skF_51') )
| ~ ssList(W_1882)
| ~ ssList('#skF_47'('#skF_51'))
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_7041,c_13793]) ).
tff(c_19204,plain,
! [W_1947] :
( ( nil = W_1947 )
| ( app(W_1947,'#skF_47'('#skF_51')) != '#skF_47'('#skF_51') )
| ~ ssList(W_1947) ),
inference(demodulation,[status(thm),theory(equality)],[c_168,c_7044,c_14021]) ).
tff(c_19212,plain,
( ( '#skF_47'('#skF_50') = nil )
| ( tl(app('#skF_50','#skF_47'('#skF_51'))) != '#skF_47'('#skF_51') )
| ~ ssList('#skF_47'('#skF_50'))
| ~ ssList('#skF_47'('#skF_51')) ),
inference(superposition,[status(thm),theory(equality)],[c_17839,c_19204]) ).
tff(c_19239,plain,
'#skF_47'('#skF_50') = nil,
inference(demodulation,[status(thm),theory(equality)],[c_7044,c_7080,c_7035,c_7043,c_19212]) ).
tff(c_19241,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8373,c_19239]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWC253+1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.14 % 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
% 0.14/0.35 % Computer : n031.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % 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 : Wed Apr 9 02:00:22 EDT 2025
% 0.14/0.36 % CPUTime :
% 17.54/5.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.68/5.66
% 17.68/5.66 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------