%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWC218+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 : n022.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 09:19:40 PM UTC 2025
% Result : Theorem 14.57s 4.30s
% Output : CNFRefutation 14.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of formulae : 128 ( 72 unt; 0 typ; 0 def)
% Number of atoms : 239 ( 98 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 222 ( 111 ~; 86 |; 3 &)
% ( 3 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 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 : 59 ( 59 usr; 10 con; 0-2 aty)
% Number of variables : 50 ( 48 !; 2 ?; 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_1011,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(Y,Z) != X )
| ! [X1] :
( ssItem(X1)
=> ( app(app(Y,cons(X1,nil)),Z) != W ) ) ) ) )
| neq(U,nil) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
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_399,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
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_859,axiom,
! [U] :
( ssList(U)
=> ( app(U,nil) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
tff(f_519,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax39) ).
tff(f_855,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( nil = app(U,V) )
<=> ( ( nil = V )
& ( nil = U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
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_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_319,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
tff(c_402,plain,
ssList('#skF_50'),
inference(cnfTransformation,[status(thm)],[f_1011]) ).
tff(c_388,plain,
ssItem('#skF_54'),
inference(cnfTransformation,[status(thm)],[f_1011]) ).
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_394,plain,
ssList('#skF_52'),
inference(cnfTransformation,[status(thm)],[f_1011]) ).
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_802,plain,
! [U_1307] :
( ( hd(U_1307) = '#skF_46'(U_1307) )
| ( nil = U_1307 )
| ~ ssList(U_1307) ),
inference(cnfTransformation,[status(thm)],[f_769]) ).
tff(c_915,plain,
( ( hd('#skF_50') = '#skF_46'('#skF_50') )
| ( nil = '#skF_50' ) ),
inference(resolution,[status(thm)],[c_402,c_802]) ).
tff(c_9832,plain,
nil = '#skF_50',
inference(splitLeft,[status(thm)],[c_915]) ).
tff(c_392,plain,
ssList('#skF_53'),
inference(cnfTransformation,[status(thm)],[f_1011]) ).
tff(c_910,plain,
( ( hd('#skF_53') = '#skF_46'('#skF_53') )
| ( nil = '#skF_53' ) ),
inference(resolution,[status(thm)],[c_392,c_802]) ).
tff(c_916,plain,
nil = '#skF_53',
inference(splitLeft,[status(thm)],[c_910]) ).
tff(c_3725,plain,
( ( hd('#skF_50') = '#skF_46'('#skF_50') )
| ( '#skF_53' = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_916,c_915]) ).
tff(c_3726,plain,
'#skF_53' = '#skF_50',
inference(splitLeft,[status(thm)],[c_3725]) ).
tff(c_390,plain,
app('#skF_52','#skF_53') = '#skF_51',
inference(cnfTransformation,[status(thm)],[f_1011]) ).
tff(c_445,plain,
! [U_1259] :
( ( app(U_1259,nil) = U_1259 )
| ~ ssList(U_1259) ),
inference(cnfTransformation,[status(thm)],[f_859]) ).
tff(c_462,plain,
app('#skF_52',nil) = '#skF_52',
inference(resolution,[status(thm)],[c_394,c_445]) ).
tff(c_937,plain,
app('#skF_52','#skF_53') = '#skF_52',
inference(demodulation,[status(thm),theory(equality)],[c_916,c_462]) ).
tff(c_960,plain,
'#skF_52' = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_390,c_937]) ).
tff(c_911,plain,
( ( hd('#skF_52') = '#skF_46'('#skF_52') )
| ( nil = '#skF_52' ) ),
inference(resolution,[status(thm)],[c_394,c_802]) ).
tff(c_966,plain,
( ( hd('#skF_52') = '#skF_46'('#skF_52') )
| ( '#skF_52' = '#skF_53' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_916,c_911]) ).
tff(c_967,plain,
'#skF_52' = '#skF_53',
inference(splitLeft,[status(thm)],[c_966]) ).
tff(c_976,plain,
'#skF_53' = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_960,c_967]) ).
tff(c_982,plain,
nil = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_976,c_916]) ).
tff(c_1095,plain,
( ( hd('#skF_50') = '#skF_46'('#skF_50') )
| ( '#skF_51' = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_982,c_915]) ).
tff(c_1096,plain,
'#skF_51' = '#skF_50',
inference(splitLeft,[status(thm)],[c_1095]) ).
tff(c_1102,plain,
nil = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_1096,c_982]) ).
tff(c_230,plain,
~ singletonP(nil),
inference(cnfTransformation,[status(thm)],[f_519]) ).
tff(c_955,plain,
~ singletonP('#skF_53'),
inference(demodulation,[status(thm),theory(equality)],[c_916,c_230]) ).
tff(c_978,plain,
~ singletonP('#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_976,c_955]) ).
tff(c_1097,plain,
~ singletonP('#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_1096,c_978]) ).
tff(c_1107,plain,
'#skF_53' = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_1096,c_976]) ).
tff(c_1108,plain,
'#skF_52' = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_1096,c_960]) ).
tff(c_386,plain,
app(app('#skF_52',cons('#skF_54',nil)),'#skF_53') = '#skF_50',
inference(cnfTransformation,[status(thm)],[f_1011]) ).
tff(c_946,plain,
app(app('#skF_52',cons('#skF_54','#skF_53')),'#skF_53') = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_916,c_386]) ).
tff(c_1256,plain,
app(app('#skF_50',cons('#skF_54','#skF_50')),'#skF_50') = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_1107,c_1107,c_1108,c_946]) ).
tff(c_400,plain,
ssList('#skF_51'),
inference(cnfTransformation,[status(thm)],[f_1011]) ).
tff(c_914,plain,
( ( hd('#skF_51') = '#skF_46'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_400,c_802]) ).
tff(c_1129,plain,
( ( hd('#skF_50') = '#skF_46'('#skF_50') )
| ( nil = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1096,c_1096,c_1096,c_914]) ).
tff(c_1130,plain,
nil = '#skF_50',
inference(splitLeft,[status(thm)],[c_1129]) ).
tff(c_352,plain,
! [U_1077,V_1079] :
( ( nil = U_1077 )
| ( app(U_1077,V_1079) != nil )
| ~ ssList(V_1079)
| ~ ssList(U_1077) ),
inference(cnfTransformation,[status(thm)],[f_855]) ).
tff(c_2327,plain,
! [U_1383,V_1384] :
( ( U_1383 = '#skF_50' )
| ( app(U_1383,V_1384) != '#skF_50' )
| ~ ssList(V_1384)
| ~ ssList(U_1383) ),
inference(demodulation,[status(thm),theory(equality)],[c_1130,c_1130,c_352]) ).
tff(c_2329,plain,
( ( app('#skF_50',cons('#skF_54','#skF_50')) = '#skF_50' )
| ~ ssList('#skF_50')
| ~ ssList(app('#skF_50',cons('#skF_54','#skF_50'))) ),
inference(superposition,[status(thm),theory(equality)],[c_1256,c_2327]) ).
tff(c_2334,plain,
( ( app('#skF_50',cons('#skF_54','#skF_50')) = '#skF_50' )
| ~ ssList(app('#skF_50',cons('#skF_54','#skF_50'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_402,c_2329]) ).
tff(c_2532,plain,
~ ssList(app('#skF_50',cons('#skF_54','#skF_50'))),
inference(splitLeft,[status(thm)],[c_2334]) ).
tff(c_2535,plain,
( ~ ssList(cons('#skF_54','#skF_50'))
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_192,c_2532]) ).
tff(c_2538,plain,
~ ssList(cons('#skF_54','#skF_50')),
inference(demodulation,[status(thm),theory(equality)],[c_402,c_2535]) ).
tff(c_2541,plain,
( ~ ssItem('#skF_54')
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_166,c_2538]) ).
tff(c_2545,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_402,c_388,c_2541]) ).
tff(c_2546,plain,
app('#skF_50',cons('#skF_54','#skF_50')) = '#skF_50',
inference(splitRight,[status(thm)],[c_2334]) ).
tff(c_354,plain,
! [V_1079,U_1077] :
( ( nil = V_1079 )
| ( app(U_1077,V_1079) != nil )
| ~ ssList(V_1079)
| ~ ssList(U_1077) ),
inference(cnfTransformation,[status(thm)],[f_855]) ).
tff(c_2450,plain,
! [V_1079,U_1077] :
( ( V_1079 = '#skF_50' )
| ( app(U_1077,V_1079) != '#skF_50' )
| ~ ssList(V_1079)
| ~ ssList(U_1077) ),
inference(demodulation,[status(thm),theory(equality)],[c_1130,c_1130,c_354]) ).
tff(c_2595,plain,
( ( cons('#skF_54','#skF_50') = '#skF_50' )
| ~ ssList(cons('#skF_54','#skF_50'))
| ~ ssList('#skF_50') ),
inference(superposition,[status(thm),theory(equality)],[c_2546,c_2450]) ).
tff(c_2605,plain,
( ( cons('#skF_54','#skF_50') = '#skF_50' )
| ~ ssList(cons('#skF_54','#skF_50')) ),
inference(demodulation,[status(thm),theory(equality)],[c_402,c_2595]) ).
tff(c_2641,plain,
~ ssList(cons('#skF_54','#skF_50')),
inference(splitLeft,[status(thm)],[c_2605]) ).
tff(c_2644,plain,
( ~ ssItem('#skF_54')
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_166,c_2641]) ).
tff(c_2648,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_402,c_388,c_2644]) ).
tff(c_2649,plain,
cons('#skF_54','#skF_50') = '#skF_50',
inference(splitRight,[status(thm)],[c_2605]) ).
tff(c_20,plain,
! [V_33] :
( singletonP(cons(V_33,nil))
| ~ ssItem(V_33)
| ~ ssList(cons(V_33,nil)) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_2162,plain,
! [V_1367] :
( singletonP(cons(V_1367,'#skF_50'))
| ~ ssItem(V_1367)
| ~ ssList(cons(V_1367,'#skF_50')) ),
inference(demodulation,[status(thm),theory(equality)],[c_1130,c_1130,c_20]) ).
tff(c_2169,plain,
! [V_861] :
( singletonP(cons(V_861,'#skF_50'))
| ~ ssItem(V_861)
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_166,c_2162]) ).
tff(c_2172,plain,
! [V_861] :
( singletonP(cons(V_861,'#skF_50'))
| ~ ssItem(V_861) ),
inference(demodulation,[status(thm),theory(equality)],[c_402,c_2169]) ).
tff(c_2700,plain,
( singletonP('#skF_50')
| ~ ssItem('#skF_54') ),
inference(superposition,[status(thm),theory(equality)],[c_2649,c_2172]) ).
tff(c_2741,plain,
singletonP('#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_2700]) ).
tff(c_2743,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1097,c_2741]) ).
tff(c_2745,plain,
nil != '#skF_50',
inference(splitRight,[status(thm)],[c_1129]) ).
tff(c_2757,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1102,c_2745]) ).
tff(c_2759,plain,
'#skF_51' != '#skF_50',
inference(splitRight,[status(thm)],[c_1095]) ).
tff(c_3570,plain,
! [U_1439,V_1440] :
( neq(U_1439,V_1440)
| ( V_1440 = U_1439 )
| ~ ssList(V_1440)
| ~ ssList(U_1439) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_396,plain,
'#skF_48' = '#skF_50',
inference(cnfTransformation,[status(thm)],[f_1011]) ).
tff(c_384,plain,
~ neq('#skF_48',nil),
inference(cnfTransformation,[status(thm)],[f_1011]) ).
tff(c_411,plain,
~ neq('#skF_50',nil),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_384]) ).
tff(c_950,plain,
~ neq('#skF_50','#skF_53'),
inference(demodulation,[status(thm),theory(equality)],[c_916,c_411]) ).
tff(c_2761,plain,
~ neq('#skF_50','#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_976,c_950]) ).
tff(c_3573,plain,
( ( '#skF_51' = '#skF_50' )
| ~ ssList('#skF_51')
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_3570,c_2761]) ).
tff(c_3584,plain,
'#skF_51' = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_402,c_400,c_3573]) ).
tff(c_3586,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2759,c_3584]) ).
tff(c_3588,plain,
'#skF_52' != '#skF_53',
inference(splitRight,[status(thm)],[c_966]) ).
tff(c_3600,plain,
'#skF_53' != '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_960,c_3588]) ).
tff(c_3740,plain,
'#skF_51' != '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_3726,c_3600]) ).
tff(c_4097,plain,
app(app('#skF_51',cons('#skF_54','#skF_50')),'#skF_50') = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_3726,c_3726,c_960,c_946]) ).
tff(c_3743,plain,
nil = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_3726,c_916]) ).
tff(c_5564,plain,
! [U_1530,V_1531] :
( ( U_1530 = '#skF_50' )
| ( app(U_1530,V_1531) != '#skF_50' )
| ~ ssList(V_1531)
| ~ ssList(U_1530) ),
inference(demodulation,[status(thm),theory(equality)],[c_3743,c_3743,c_352]) ).
tff(c_5566,plain,
( ( app('#skF_51',cons('#skF_54','#skF_50')) = '#skF_50' )
| ~ ssList('#skF_50')
| ~ ssList(app('#skF_51',cons('#skF_54','#skF_50'))) ),
inference(superposition,[status(thm),theory(equality)],[c_4097,c_5564]) ).
tff(c_5575,plain,
( ( app('#skF_51',cons('#skF_54','#skF_50')) = '#skF_50' )
| ~ ssList(app('#skF_51',cons('#skF_54','#skF_50'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_402,c_5566]) ).
tff(c_5749,plain,
~ ssList(app('#skF_51',cons('#skF_54','#skF_50'))),
inference(splitLeft,[status(thm)],[c_5575]) ).
tff(c_5758,plain,
( ~ ssList(cons('#skF_54','#skF_50'))
| ~ ssList('#skF_51') ),
inference(resolution,[status(thm)],[c_192,c_5749]) ).
tff(c_5761,plain,
~ ssList(cons('#skF_54','#skF_50')),
inference(demodulation,[status(thm),theory(equality)],[c_400,c_5758]) ).
tff(c_5764,plain,
( ~ ssItem('#skF_54')
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_166,c_5761]) ).
tff(c_5768,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_402,c_388,c_5764]) ).
tff(c_5769,plain,
app('#skF_51',cons('#skF_54','#skF_50')) = '#skF_50',
inference(splitRight,[status(thm)],[c_5575]) ).
tff(c_5563,plain,
! [U_1077,V_1079] :
( ( U_1077 = '#skF_50' )
| ( app(U_1077,V_1079) != '#skF_50' )
| ~ ssList(V_1079)
| ~ ssList(U_1077) ),
inference(demodulation,[status(thm),theory(equality)],[c_3743,c_3743,c_352]) ).
tff(c_5846,plain,
( ( '#skF_51' = '#skF_50' )
| ~ ssList(cons('#skF_54','#skF_50'))
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_5769,c_5563]) ).
tff(c_5856,plain,
( ( '#skF_51' = '#skF_50' )
| ~ ssList(cons('#skF_54','#skF_50')) ),
inference(demodulation,[status(thm),theory(equality)],[c_400,c_5846]) ).
tff(c_5857,plain,
~ ssList(cons('#skF_54','#skF_50')),
inference(negUnitSimplification,[status(thm)],[c_3740,c_5856]) ).
tff(c_5866,plain,
( ~ ssItem('#skF_54')
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_166,c_5857]) ).
tff(c_5870,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_402,c_388,c_5866]) ).
tff(c_5872,plain,
'#skF_53' != '#skF_50',
inference(splitRight,[status(thm)],[c_3725]) ).
tff(c_6848,plain,
! [U_1592,V_1593] :
( neq(U_1592,V_1593)
| ( V_1593 = U_1592 )
| ~ ssList(V_1593)
| ~ ssList(U_1592) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_6851,plain,
( ( '#skF_53' = '#skF_50' )
| ~ ssList('#skF_53')
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_6848,c_950]) ).
tff(c_6862,plain,
'#skF_53' = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_402,c_392,c_6851]) ).
tff(c_6864,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_5872,c_6862]) ).
tff(c_6866,plain,
nil != '#skF_53',
inference(splitRight,[status(thm)],[c_910]) ).
tff(c_11627,plain,
'#skF_53' != '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_9832,c_6866]) ).
tff(c_11657,plain,
app(app('#skF_52',cons('#skF_54','#skF_50')),'#skF_53') = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_9832,c_386]) ).
tff(c_13817,plain,
! [V_1880,U_1881] :
( ( V_1880 = '#skF_50' )
| ( app(U_1881,V_1880) != '#skF_50' )
| ~ ssList(V_1880)
| ~ ssList(U_1881) ),
inference(demodulation,[status(thm),theory(equality)],[c_9832,c_9832,c_354]) ).
tff(c_13819,plain,
( ( '#skF_53' = '#skF_50' )
| ~ ssList('#skF_53')
| ~ ssList(app('#skF_52',cons('#skF_54','#skF_50'))) ),
inference(superposition,[status(thm),theory(equality)],[c_11657,c_13817]) ).
tff(c_13838,plain,
( ( '#skF_53' = '#skF_50' )
| ~ ssList(app('#skF_52',cons('#skF_54','#skF_50'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_392,c_13819]) ).
tff(c_13839,plain,
~ ssList(app('#skF_52',cons('#skF_54','#skF_50'))),
inference(negUnitSimplification,[status(thm)],[c_11627,c_13838]) ).
tff(c_13939,plain,
( ~ ssList(cons('#skF_54','#skF_50'))
| ~ ssList('#skF_52') ),
inference(resolution,[status(thm)],[c_192,c_13839]) ).
tff(c_13942,plain,
~ ssList(cons('#skF_54','#skF_50')),
inference(demodulation,[status(thm),theory(equality)],[c_394,c_13939]) ).
tff(c_13945,plain,
( ~ ssItem('#skF_54')
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_166,c_13942]) ).
tff(c_13949,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_402,c_388,c_13945]) ).
tff(c_13951,plain,
nil != '#skF_50',
inference(splitRight,[status(thm)],[c_915]) ).
tff(c_168,plain,
ssList(nil),
inference(cnfTransformation,[status(thm)],[f_319]) ).
tff(c_15385,plain,
! [U_1919,V_1920] :
( neq(U_1919,V_1920)
| ( V_1920 = U_1919 )
| ~ ssList(V_1920)
| ~ ssList(U_1919) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_15396,plain,
( ( nil = '#skF_50' )
| ~ ssList(nil)
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_15385,c_411]) ).
tff(c_15403,plain,
nil = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_402,c_168,c_15396]) ).
tff(c_15405,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_13951,c_15403]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC218+1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.13 % 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
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Apr 9 01:53:36 EDT 2025
% 0.13/0.34 % CPUTime :
% 14.57/4.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.57/4.32
% 14.57/4.32 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------