TSTP Solution File: SWC311+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWC311+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 11:02:04 EDT 2023
% Result : Theorem 12.80s 3.98s
% Output : CNFRefutation 12.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 86
% Syntax : Number of formulae : 178 ( 46 unt; 75 typ; 0 def)
% Number of atoms : 242 ( 100 equ)
% Maximal formula atoms : 27 ( 2 avg)
% Number of connectives : 243 ( 104 ~; 98 |; 18 &)
% ( 1 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 3 avg)
% Maximal term depth : 4 ( 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 : 51 (; 43 !; 8 ?; 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_1046,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ( ( nil != W )
& ( nil = X ) )
| ( ? [Y] :
( ssList(Y)
& ( W != Y )
& ? [Z] :
( ssList(Z)
& ? [X1] :
( ssList(X1)
& ( tl(X) = Z )
& ( app(Z,X1) = Y )
& ? [X2] :
( ssItem(X2)
& ( cons(X2,nil) = X1 )
& ( hd(X) = X2 )
& neq(nil,X) )
& neq(nil,X) ) ) )
& neq(X,nil) )
| ( ( ( nil != V )
| ( nil = U ) )
& ( ~ neq(V,nil)
| ? [X3] :
( ssItem(X3)
& ? [X4] :
( ssList(X4)
& ( app(cons(X3,nil),X4) = V )
& ( app(X4,cons(X3,nil)) = U ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
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_385,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ssList(tl(U)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax24) ).
tff(f_319,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
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_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_371,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ssItem(hd(U)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).
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_399,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
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(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(c_394,plain,
ssList('#skF_50'),
inference(cnfTransformation,[status(thm)],[f_1046]) ).
tff(c_386,plain,
( ( nil != '#skF_51' )
| ( nil = '#skF_50' ) ),
inference(cnfTransformation,[status(thm)],[f_1046]) ).
tff(c_426,plain,
nil != '#skF_51',
inference(splitLeft,[status(thm)],[c_386]) ).
tff(c_392,plain,
ssList('#skF_51'),
inference(cnfTransformation,[status(thm)],[f_1046]) ).
tff(c_3981,plain,
! [U_1696] :
( ( tl(U_1696) = '#skF_47'(U_1696) )
| ( nil = U_1696 )
| ~ ssList(U_1696) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_4074,plain,
( ( tl('#skF_51') = '#skF_47'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_392,c_3981]) ).
tff(c_4108,plain,
tl('#skF_51') = '#skF_47'('#skF_51'),
inference(negUnitSimplification,[status(thm)],[c_426,c_4074]) ).
tff(c_188,plain,
! [U_892] :
( ssList(tl(U_892))
| ( nil = U_892 )
| ~ ssList(U_892) ),
inference(cnfTransformation,[status(thm)],[f_385]) ).
tff(c_168,plain,
ssList(nil),
inference(cnfTransformation,[status(thm)],[f_319]) ).
tff(c_3209,plain,
! [U_1621,V_1622] :
( neq(U_1621,V_1622)
| ( V_1622 = U_1621 )
| ~ ssList(V_1622)
| ~ ssList(U_1621) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_390,plain,
'#skF_49' = '#skF_51',
inference(cnfTransformation,[status(thm)],[f_1046]) ).
tff(c_406,plain,
( ( nil = '#skF_49' )
| neq('#skF_49',nil) ),
inference(cnfTransformation,[status(thm)],[f_1046]) ).
tff(c_408,plain,
( ( nil = '#skF_51' )
| neq('#skF_51',nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_390,c_406]) ).
tff(c_1429,plain,
neq('#skF_51',nil),
inference(negUnitSimplification,[status(thm)],[c_426,c_408]) ).
tff(c_1267,plain,
! [U_1499] :
( ( hd(U_1499) = '#skF_46'(U_1499) )
| ( nil = U_1499 )
| ~ ssList(U_1499) ),
inference(cnfTransformation,[status(thm)],[f_769]) ).
tff(c_1357,plain,
( ( hd('#skF_51') = '#skF_46'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_392,c_1267]) ).
tff(c_1392,plain,
hd('#skF_51') = '#skF_46'('#skF_51'),
inference(negUnitSimplification,[status(thm)],[c_426,c_1357]) ).
tff(c_184,plain,
! [U_888] :
( ssItem(hd(U_888))
| ( nil = U_888 )
| ~ ssList(U_888) ),
inference(cnfTransformation,[status(thm)],[f_371]) ).
tff(c_1406,plain,
( ssItem('#skF_46'('#skF_51'))
| ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_1392,c_184]) ).
tff(c_1410,plain,
( ssItem('#skF_46'('#skF_51'))
| ( nil = '#skF_51' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_392,c_1406]) ).
tff(c_1411,plain,
ssItem('#skF_46'('#skF_51')),
inference(negUnitSimplification,[status(thm)],[c_426,c_1410]) ).
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_897,plain,
! [U_1493] :
( ( tl(U_1493) = '#skF_47'(U_1493) )
| ( nil = U_1493 )
| ~ ssList(U_1493) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_978,plain,
( ( tl('#skF_51') = '#skF_47'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_392,c_897]) ).
tff(c_1010,plain,
tl('#skF_51') = '#skF_47'('#skF_51'),
inference(negUnitSimplification,[status(thm)],[c_426,c_978]) ).
tff(c_1155,plain,
( ssList('#skF_47'('#skF_51'))
| ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_1010,c_188]) ).
tff(c_1159,plain,
( ssList('#skF_47'('#skF_51'))
| ( nil = '#skF_51' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_392,c_1155]) ).
tff(c_1160,plain,
ssList('#skF_47'('#skF_51')),
inference(negUnitSimplification,[status(thm)],[c_426,c_1159]) ).
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_384,plain,
( ~ neq('#skF_51',nil)
| ~ neq(nil,'#skF_51')
| ~ ssItem(hd('#skF_51'))
| ~ ssList(cons(hd('#skF_51'),nil))
| ~ ssList(tl('#skF_51'))
| ( app(tl('#skF_51'),cons(hd('#skF_51'),nil)) = '#skF_50' )
| ~ ssList(app(tl('#skF_51'),cons(hd('#skF_51'),nil))) ),
inference(cnfTransformation,[status(thm)],[f_1046]) ).
tff(c_428,plain,
~ ssList(app(tl('#skF_51'),cons(hd('#skF_51'),nil))),
inference(splitLeft,[status(thm)],[c_384]) ).
tff(c_1151,plain,
~ ssList(app('#skF_47'('#skF_51'),cons(hd('#skF_51'),nil))),
inference(demodulation,[status(thm),theory(equality)],[c_1010,c_428]) ).
tff(c_1413,plain,
~ ssList(app('#skF_47'('#skF_51'),cons('#skF_46'('#skF_51'),nil))),
inference(demodulation,[status(thm),theory(equality)],[c_1392,c_1151]) ).
tff(c_1416,plain,
( ~ ssList(cons('#skF_46'('#skF_51'),nil))
| ~ ssList('#skF_47'('#skF_51')) ),
inference(resolution,[status(thm)],[c_192,c_1413]) ).
tff(c_1419,plain,
~ ssList(cons('#skF_46'('#skF_51'),nil)),
inference(demodulation,[status(thm),theory(equality)],[c_1160,c_1416]) ).
tff(c_1422,plain,
( ~ ssItem('#skF_46'('#skF_51'))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_166,c_1419]) ).
tff(c_1426,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_168,c_1411,c_1422]) ).
tff(c_1427,plain,
( ~ ssList(tl('#skF_51'))
| ~ ssList(cons(hd('#skF_51'),nil))
| ~ ssItem(hd('#skF_51'))
| ~ neq(nil,'#skF_51')
| ~ neq('#skF_51',nil)
| ( app(tl('#skF_51'),cons(hd('#skF_51'),nil)) = '#skF_50' ) ),
inference(splitRight,[status(thm)],[c_384]) ).
tff(c_1443,plain,
( ~ ssList(tl('#skF_51'))
| ~ ssList(cons(hd('#skF_51'),nil))
| ~ ssItem(hd('#skF_51'))
| ~ neq(nil,'#skF_51')
| ( app(tl('#skF_51'),cons(hd('#skF_51'),nil)) = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1429,c_1427]) ).
tff(c_1444,plain,
~ neq(nil,'#skF_51'),
inference(splitLeft,[status(thm)],[c_1443]) ).
tff(c_3212,plain,
( ( nil = '#skF_51' )
| ~ ssList('#skF_51')
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_3209,c_1444]) ).
tff(c_3223,plain,
nil = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_168,c_392,c_3212]) ).
tff(c_3225,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_426,c_3223]) ).
tff(c_3226,plain,
( ~ ssItem(hd('#skF_51'))
| ~ ssList(cons(hd('#skF_51'),nil))
| ~ ssList(tl('#skF_51'))
| ( app(tl('#skF_51'),cons(hd('#skF_51'),nil)) = '#skF_50' ) ),
inference(splitRight,[status(thm)],[c_1443]) ).
tff(c_3480,plain,
~ ssList(tl('#skF_51')),
inference(splitLeft,[status(thm)],[c_3226]) ).
tff(c_3483,plain,
( ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(resolution,[status(thm)],[c_188,c_3480]) ).
tff(c_3486,plain,
nil = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_392,c_3483]) ).
tff(c_3488,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_426,c_3486]) ).
tff(c_3490,plain,
ssList(tl('#skF_51')),
inference(splitRight,[status(thm)],[c_3226]) ).
tff(c_4111,plain,
ssList('#skF_47'('#skF_51')),
inference(demodulation,[status(thm),theory(equality)],[c_4108,c_3490]) ).
tff(c_6787,plain,
! [U_1797] :
( ( hd(U_1797) = '#skF_46'(U_1797) )
| ( nil = U_1797 )
| ~ ssList(U_1797) ),
inference(cnfTransformation,[status(thm)],[f_769]) ).
tff(c_6880,plain,
( ( hd('#skF_51') = '#skF_46'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_392,c_6787]) ).
tff(c_6916,plain,
hd('#skF_51') = '#skF_46'('#skF_51'),
inference(negUnitSimplification,[status(thm)],[c_426,c_6880]) ).
tff(c_3489,plain,
( ~ ssList(cons(hd('#skF_51'),nil))
| ~ ssItem(hd('#skF_51'))
| ( app(tl('#skF_51'),cons(hd('#skF_51'),nil)) = '#skF_50' ) ),
inference(splitRight,[status(thm)],[c_3226]) ).
tff(c_3528,plain,
~ ssItem(hd('#skF_51')),
inference(splitLeft,[status(thm)],[c_3489]) ).
tff(c_3531,plain,
( ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(resolution,[status(thm)],[c_184,c_3528]) ).
tff(c_3534,plain,
nil = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_392,c_3531]) ).
tff(c_3536,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_426,c_3534]) ).
tff(c_3538,plain,
ssItem(hd('#skF_51')),
inference(splitRight,[status(thm)],[c_3489]) ).
tff(c_6944,plain,
ssItem('#skF_46'('#skF_51')),
inference(demodulation,[status(thm),theory(equality)],[c_6916,c_3538]) ).
tff(c_7421,plain,
! [U_1825] :
( ( cons(hd(U_1825),tl(U_1825)) = U_1825 )
| ( nil = U_1825 )
| ~ ssList(U_1825) ),
inference(cnfTransformation,[status(thm)],[f_803]) ).
tff(c_7452,plain,
( ( cons('#skF_46'('#skF_51'),tl('#skF_51')) = '#skF_51' )
| ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_6916,c_7421]) ).
tff(c_7467,plain,
( ( cons('#skF_46'('#skF_51'),'#skF_47'('#skF_51')) = '#skF_51' )
| ( nil = '#skF_51' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_392,c_4108,c_7452]) ).
tff(c_7468,plain,
cons('#skF_46'('#skF_51'),'#skF_47'('#skF_51')) = '#skF_51',
inference(negUnitSimplification,[status(thm)],[c_426,c_7467]) ).
tff(c_10895,plain,
! [V_1943,U_1944] :
( ( app(cons(V_1943,nil),U_1944) = cons(V_1943,U_1944) )
| ~ ssItem(V_1943)
| ~ ssList(U_1944) ),
inference(cnfTransformation,[status(thm)],[f_834]) ).
tff(c_3732,plain,
! [V_1681,U_1682] :
( ssList(cons(V_1681,U_1682))
| ~ ssItem(V_1681)
| ~ ssList(U_1682) ),
inference(cnfTransformation,[status(thm)],[f_318]) ).
tff(c_3537,plain,
( ~ ssList(cons(hd('#skF_51'),nil))
| ( app(tl('#skF_51'),cons(hd('#skF_51'),nil)) = '#skF_50' ) ),
inference(splitRight,[status(thm)],[c_3489]) ).
tff(c_3586,plain,
~ ssList(cons(hd('#skF_51'),nil)),
inference(splitLeft,[status(thm)],[c_3537]) ).
tff(c_3738,plain,
( ~ ssItem(hd('#skF_51'))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_3732,c_3586]) ).
tff(c_3749,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_168,c_3538,c_3738]) ).
tff(c_3750,plain,
app(tl('#skF_51'),cons(hd('#skF_51'),nil)) = '#skF_50',
inference(splitRight,[status(thm)],[c_3537]) ).
tff(c_6927,plain,
app('#skF_47'('#skF_51'),cons(hd('#skF_51'),nil)) = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_4108,c_3750]) ).
tff(c_388,plain,
'#skF_48' = '#skF_50',
inference(cnfTransformation,[status(thm)],[f_1046]) ).
tff(c_402,plain,
! [X4_1420,X3_1418] :
( ( nil = '#skF_49' )
| ( app(X4_1420,cons(X3_1418,nil)) != '#skF_48' )
| ( app(cons(X3_1418,nil),X4_1420) != '#skF_49' )
| ~ ssList(X4_1420)
| ~ ssItem(X3_1418) ),
inference(cnfTransformation,[status(thm)],[f_1046]) ).
tff(c_410,plain,
! [X4_1420,X3_1418] :
( ( nil = '#skF_51' )
| ( app(X4_1420,cons(X3_1418,nil)) != '#skF_48' )
| ( app(cons(X3_1418,nil),X4_1420) != '#skF_51' )
| ~ ssList(X4_1420)
| ~ ssItem(X3_1418) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_390,c_402]) ).
tff(c_415,plain,
! [X4_1420,X3_1418] :
( ( nil = '#skF_51' )
| ( app(X4_1420,cons(X3_1418,nil)) != '#skF_50' )
| ( app(cons(X3_1418,nil),X4_1420) != '#skF_51' )
| ~ ssList(X4_1420)
| ~ ssItem(X3_1418) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_410]) ).
tff(c_3234,plain,
! [X4_1420,X3_1418] :
( ( app(X4_1420,cons(X3_1418,nil)) != '#skF_50' )
| ( app(cons(X3_1418,nil),X4_1420) != '#skF_51' )
| ~ ssList(X4_1420)
| ~ ssItem(X3_1418) ),
inference(negUnitSimplification,[status(thm)],[c_426,c_415]) ).
tff(c_6933,plain,
( ( app(cons(hd('#skF_51'),nil),'#skF_47'('#skF_51')) != '#skF_51' )
| ~ ssList('#skF_47'('#skF_51'))
| ~ ssItem(hd('#skF_51')) ),
inference(superposition,[status(thm),theory(equality)],[c_6927,c_3234]) ).
tff(c_6940,plain,
app(cons(hd('#skF_51'),nil),'#skF_47'('#skF_51')) != '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_3538,c_4111,c_6933]) ).
tff(c_7021,plain,
app(cons('#skF_46'('#skF_51'),nil),'#skF_47'('#skF_51')) != '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_6916,c_6940]) ).
tff(c_10914,plain,
( ( cons('#skF_46'('#skF_51'),'#skF_47'('#skF_51')) != '#skF_51' )
| ~ ssItem('#skF_46'('#skF_51'))
| ~ ssList('#skF_47'('#skF_51')) ),
inference(superposition,[status(thm),theory(equality)],[c_10895,c_7021]) ).
tff(c_10936,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4111,c_6944,c_7468,c_10914]) ).
tff(c_10937,plain,
nil = '#skF_50',
inference(splitRight,[status(thm)],[c_386]) ).
tff(c_10938,plain,
nil = '#skF_51',
inference(splitRight,[status(thm)],[c_386]) ).
tff(c_10953,plain,
'#skF_51' = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_10937,c_10938]) ).
tff(c_404,plain,
( ( nil != '#skF_48' )
| neq('#skF_49',nil) ),
inference(cnfTransformation,[status(thm)],[f_1046]) ).
tff(c_409,plain,
( ( nil != '#skF_48' )
| neq('#skF_51',nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_404]) ).
tff(c_414,plain,
( ( nil != '#skF_50' )
| neq('#skF_51',nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_409]) ).
tff(c_10982,plain,
neq('#skF_50','#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_10953,c_10937,c_10937,c_414]) ).
tff(c_164,plain,
! [V_858] :
( ~ neq(V_858,V_858)
| ~ ssList(V_858) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_10988,plain,
~ ssList('#skF_50'),
inference(resolution,[status(thm)],[c_10982,c_164]) ).
tff(c_10993,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_394,c_10988]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWC311+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14 % 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
% 0.14/0.35 % Computer : n006.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
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 21:28:13 EDT 2023
% 0.14/0.35 % CPUTime :
% 12.80/3.98 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.80/3.99
% 12.80/3.99 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.80/4.04
% 12.80/4.04 Inference rules
% 12.80/4.04 ----------------------
% 12.80/4.04 #Ref : 0
% 12.80/4.04 #Sup : 2370
% 12.80/4.04 #Fact : 0
% 12.80/4.04 #Define : 0
% 12.80/4.04 #Split : 52
% 12.80/4.04 #Chain : 0
% 12.80/4.04 #Close : 0
% 12.80/4.04
% 12.80/4.04 Ordering : KBO
% 12.80/4.04
% 12.80/4.04 Simplification rules
% 12.80/4.04 ----------------------
% 12.80/4.04 #Subsume : 209
% 12.80/4.04 #Demod : 1520
% 12.80/4.04 #Tautology : 792
% 12.80/4.04 #SimpNegUnit : 118
% 12.80/4.04 #BackRed : 189
% 12.80/4.04
% 12.80/4.04 #Partial instantiations: 0
% 12.80/4.04 #Strategies tried : 1
% 12.80/4.04
% 12.80/4.04 Timing (in seconds)
% 12.80/4.04 ----------------------
% 12.80/4.04 Preprocessing : 0.89
% 12.80/4.04 Parsing : 0.41
% 12.80/4.04 CNF conversion : 0.11
% 12.80/4.04 Main loop : 2.06
% 12.80/4.04 Inferencing : 0.68
% 12.80/4.04 Reduction : 0.65
% 12.80/4.04 Demodulation : 0.45
% 12.80/4.04 BG Simplification : 0.10
% 12.80/4.04 Subsumption : 0.44
% 12.80/4.04 Abstraction : 0.07
% 12.80/4.04 MUC search : 0.00
% 12.80/4.04 Cooper : 0.00
% 12.80/4.04 Total : 3.02
% 12.80/4.04 Index Insertion : 0.00
% 12.80/4.04 Index Deletion : 0.00
% 12.80/4.04 Index Matching : 0.00
% 12.80/4.04 BG Taut test : 0.00
%------------------------------------------------------------------------------