TSTP Solution File: SWC418+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWC418+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 : n032.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 11:02:35 EDT 2023
% Result : Theorem 18.89s 6.60s
% Output : CNFRefutation 19.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 88
% Syntax : Number of formulae : 202 ( 62 unt; 75 typ; 0 def)
% Number of atoms : 278 ( 120 equ)
% Maximal formula atoms : 26 ( 2 avg)
% Number of connectives : 267 ( 116 ~; 108 |; 18 &)
% ( 1 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 3 avg)
% Maximal term depth : 5 ( 2 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 : 59 (; 50 !; 9 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ segmentP > rearsegP > neq > memberP > lt > leq > gt > geq > frontsegP > totalorderedP > totalorderP > strictorderedP > strictorderP > ssList > ssItem > singletonP > equalelemsP > duplicatefreeP > cyclefreeP > cons > app > #nlpp > tl > hd > nil > #skF_36 > #skF_25 > #skF_5 > #skF_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_1044,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ~ neq(V,nil)
| ? [Y] :
( ssItem(Y)
& ? [Z] :
( ssList(Z)
& ? [X1] :
( ssList(X1)
& ( app(app(Z,cons(Y,nil)),X1) = V )
& ( app(app(X1,cons(Y,nil)),Z) = U ) ) ) )
| ( ( nil != W )
& ( nil = X ) )
| ( ? [X2] :
( ssList(X2)
& ( W != X2 )
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& ( tl(X) = X3 )
& ( app(X3,X4) = X2 )
& ? [X5] :
( ssItem(X5)
& ( cons(X5,nil) = X4 )
& ( hd(X) = X5 )
& neq(nil,X) )
& neq(nil,X) ) ) )
& neq(X,nil) ) ) ) ) ) ),
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_859,axiom,
! [U] :
( ssList(U)
=> ( app(U,nil) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
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(f_413,axiom,
! [U] :
( ssList(U)
=> ( app(nil,U) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
tff(c_398,plain,
ssList('#skF_50'),
inference(cnfTransformation,[status(thm)],[f_1044]) ).
tff(c_386,plain,
( ( nil != '#skF_51' )
| ( nil = '#skF_50' ) ),
inference(cnfTransformation,[status(thm)],[f_1044]) ).
tff(c_419,plain,
nil != '#skF_51',
inference(splitLeft,[status(thm)],[c_386]) ).
tff(c_396,plain,
ssList('#skF_51'),
inference(cnfTransformation,[status(thm)],[f_1044]) ).
tff(c_7271,plain,
! [U_1878] :
( ( tl(U_1878) = '#skF_47'(U_1878) )
| ( nil = U_1878 )
| ~ ssList(U_1878) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_7355,plain,
( ( tl('#skF_51') = '#skF_47'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_396,c_7271]) ).
tff(c_7389,plain,
tl('#skF_51') = '#skF_47'('#skF_51'),
inference(negUnitSimplification,[status(thm)],[c_419,c_7355]) ).
tff(c_4134,plain,
! [U_1741] :
( ssList(tl(U_1741))
| ( nil = U_1741 )
| ~ ssList(U_1741) ),
inference(cnfTransformation,[status(thm)],[f_385]) ).
tff(c_168,plain,
ssList(nil),
inference(cnfTransformation,[status(thm)],[f_319]) ).
tff(c_3864,plain,
! [U_1701,V_1702] :
( neq(U_1701,V_1702)
| ( V_1702 = U_1701 )
| ~ ssList(V_1702)
| ~ ssList(U_1701) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_895,plain,
! [U_1554] :
( ( hd(U_1554) = '#skF_46'(U_1554) )
| ( nil = U_1554 )
| ~ ssList(U_1554) ),
inference(cnfTransformation,[status(thm)],[f_769]) ).
tff(c_973,plain,
( ( hd('#skF_51') = '#skF_46'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_396,c_895]) ).
tff(c_1005,plain,
hd('#skF_51') = '#skF_46'('#skF_51'),
inference(negUnitSimplification,[status(thm)],[c_419,c_973]) ).
tff(c_184,plain,
! [U_888] :
( ssItem(hd(U_888))
| ( nil = U_888 )
| ~ ssList(U_888) ),
inference(cnfTransformation,[status(thm)],[f_371]) ).
tff(c_1010,plain,
( ssItem('#skF_46'('#skF_51'))
| ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_1005,c_184]) ).
tff(c_1014,plain,
( ssItem('#skF_46'('#skF_51'))
| ( nil = '#skF_51' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_1010]) ).
tff(c_1015,plain,
ssItem('#skF_46'('#skF_51')),
inference(negUnitSimplification,[status(thm)],[c_419,c_1014]) ).
tff(c_1887,plain,
! [V_1590,U_1591] :
( ssList(cons(V_1590,U_1591))
| ~ ssItem(V_1590)
| ~ ssList(U_1591) ),
inference(cnfTransformation,[status(thm)],[f_318]) ).
tff(c_764,plain,
! [U_1553] :
( ( tl(U_1553) = '#skF_47'(U_1553) )
| ( nil = U_1553 )
| ~ ssList(U_1553) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_839,plain,
( ( tl('#skF_51') = '#skF_47'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_396,c_764]) ).
tff(c_870,plain,
tl('#skF_51') = '#skF_47'('#skF_51'),
inference(negUnitSimplification,[status(thm)],[c_419,c_839]) ).
tff(c_188,plain,
! [U_892] :
( ssList(tl(U_892))
| ( nil = U_892 )
| ~ ssList(U_892) ),
inference(cnfTransformation,[status(thm)],[f_385]) ).
tff(c_876,plain,
( ssList('#skF_47'('#skF_51'))
| ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_870,c_188]) ).
tff(c_880,plain,
( ssList('#skF_47'('#skF_51'))
| ( nil = '#skF_51' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_876]) ).
tff(c_881,plain,
ssList('#skF_47'('#skF_51')),
inference(negUnitSimplification,[status(thm)],[c_419,c_880]) ).
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_394,plain,
'#skF_49' = '#skF_51',
inference(cnfTransformation,[status(thm)],[f_1044]) ).
tff(c_390,plain,
neq('#skF_49',nil),
inference(cnfTransformation,[status(thm)],[f_1044]) ).
tff(c_407,plain,
neq('#skF_51',nil),
inference(demodulation,[status(thm),theory(equality)],[c_394,c_390]) ).
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_1044]) ).
tff(c_410,plain,
( ~ 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(demodulation,[status(thm),theory(equality)],[c_407,c_384]) ).
tff(c_430,plain,
~ ssList(app(tl('#skF_51'),cons(hd('#skF_51'),nil))),
inference(splitLeft,[status(thm)],[c_410]) ).
tff(c_872,plain,
~ ssList(app('#skF_47'('#skF_51'),cons(hd('#skF_51'),nil))),
inference(demodulation,[status(thm),theory(equality)],[c_870,c_430]) ).
tff(c_1740,plain,
~ ssList(app('#skF_47'('#skF_51'),cons('#skF_46'('#skF_51'),nil))),
inference(demodulation,[status(thm),theory(equality)],[c_1005,c_872]) ).
tff(c_1743,plain,
( ~ ssList(cons('#skF_46'('#skF_51'),nil))
| ~ ssList('#skF_47'('#skF_51')) ),
inference(resolution,[status(thm)],[c_192,c_1740]) ).
tff(c_1746,plain,
~ ssList(cons('#skF_46'('#skF_51'),nil)),
inference(demodulation,[status(thm),theory(equality)],[c_881,c_1743]) ).
tff(c_1893,plain,
( ~ ssItem('#skF_46'('#skF_51'))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_1887,c_1746]) ).
tff(c_1910,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_168,c_1015,c_1893]) ).
tff(c_1911,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(splitRight,[status(thm)],[c_410]) ).
tff(c_1977,plain,
~ neq(nil,'#skF_51'),
inference(splitLeft,[status(thm)],[c_1911]) ).
tff(c_3867,plain,
( ( nil = '#skF_51' )
| ~ ssList('#skF_51')
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_3864,c_1977]) ).
tff(c_3878,plain,
nil = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_168,c_396,c_3867]) ).
tff(c_3880,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_419,c_3878]) ).
tff(c_3881,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_1911]) ).
tff(c_4011,plain,
~ ssList(tl('#skF_51')),
inference(splitLeft,[status(thm)],[c_3881]) ).
tff(c_4137,plain,
( ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(resolution,[status(thm)],[c_4134,c_4011]) ).
tff(c_4146,plain,
nil = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_396,c_4137]) ).
tff(c_4148,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_419,c_4146]) ).
tff(c_4150,plain,
ssList(tl('#skF_51')),
inference(splitRight,[status(thm)],[c_3881]) ).
tff(c_7394,plain,
ssList('#skF_47'('#skF_51')),
inference(demodulation,[status(thm),theory(equality)],[c_7389,c_4150]) ).
tff(c_7133,plain,
! [U_1877] :
( ( hd(U_1877) = '#skF_46'(U_1877) )
| ( nil = U_1877 )
| ~ ssList(U_1877) ),
inference(cnfTransformation,[status(thm)],[f_769]) ).
tff(c_7220,plain,
( ( hd('#skF_51') = '#skF_46'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_396,c_7133]) ).
tff(c_7255,plain,
hd('#skF_51') = '#skF_46'('#skF_51'),
inference(negUnitSimplification,[status(thm)],[c_419,c_7220]) ).
tff(c_4233,plain,
! [U_1749] :
( ssItem(hd(U_1749))
| ( nil = U_1749 )
| ~ ssList(U_1749) ),
inference(cnfTransformation,[status(thm)],[f_371]) ).
tff(c_1912,plain,
ssList(app(tl('#skF_51'),cons(hd('#skF_51'),nil))),
inference(splitRight,[status(thm)],[c_410]) ).
tff(c_356,plain,
! [U_1080] :
( ( app(U_1080,nil) = U_1080 )
| ~ ssList(U_1080) ),
inference(cnfTransformation,[status(thm)],[f_859]) ).
tff(c_1944,plain,
app(app(tl('#skF_51'),cons(hd('#skF_51'),nil)),nil) = app(tl('#skF_51'),cons(hd('#skF_51'),nil)),
inference(resolution,[status(thm)],[c_1912,c_356]) ).
tff(c_392,plain,
'#skF_48' = '#skF_50',
inference(cnfTransformation,[status(thm)],[f_1044]) ).
tff(c_388,plain,
! [X1_1469,Y_1463,Z_1467] :
( ( app(app(X1_1469,cons(Y_1463,nil)),Z_1467) != '#skF_48' )
| ( app(app(Z_1467,cons(Y_1463,nil)),X1_1469) != '#skF_49' )
| ~ ssList(X1_1469)
| ~ ssList(Z_1467)
| ~ ssItem(Y_1463) ),
inference(cnfTransformation,[status(thm)],[f_1044]) ).
tff(c_408,plain,
! [X1_1469,Y_1463,Z_1467] :
( ( app(app(X1_1469,cons(Y_1463,nil)),Z_1467) != '#skF_50' )
| ( app(app(Z_1467,cons(Y_1463,nil)),X1_1469) != '#skF_51' )
| ~ ssList(X1_1469)
| ~ ssList(Z_1467)
| ~ ssItem(Y_1463) ),
inference(demodulation,[status(thm),theory(equality)],[c_394,c_392,c_388]) ).
tff(c_3903,plain,
( ( app(tl('#skF_51'),cons(hd('#skF_51'),nil)) != '#skF_50' )
| ( app(app(nil,cons(hd('#skF_51'),nil)),tl('#skF_51')) != '#skF_51' )
| ~ ssList(tl('#skF_51'))
| ~ ssList(nil)
| ~ ssItem(hd('#skF_51')) ),
inference(superposition,[status(thm),theory(equality)],[c_1944,c_408]) ).
tff(c_3907,plain,
( ( app(tl('#skF_51'),cons(hd('#skF_51'),nil)) != '#skF_50' )
| ( app(app(nil,cons(hd('#skF_51'),nil)),tl('#skF_51')) != '#skF_51' )
| ~ ssList(tl('#skF_51'))
| ~ ssItem(hd('#skF_51')) ),
inference(demodulation,[status(thm),theory(equality)],[c_168,c_3903]) ).
tff(c_4213,plain,
( ( app(tl('#skF_51'),cons(hd('#skF_51'),nil)) != '#skF_50' )
| ( app(app(nil,cons(hd('#skF_51'),nil)),tl('#skF_51')) != '#skF_51' )
| ~ ssItem(hd('#skF_51')) ),
inference(demodulation,[status(thm),theory(equality)],[c_4150,c_3907]) ).
tff(c_4214,plain,
~ ssItem(hd('#skF_51')),
inference(splitLeft,[status(thm)],[c_4213]) ).
tff(c_4236,plain,
( ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(resolution,[status(thm)],[c_4233,c_4214]) ).
tff(c_4239,plain,
nil = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_396,c_4236]) ).
tff(c_4241,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_419,c_4239]) ).
tff(c_4243,plain,
ssItem(hd('#skF_51')),
inference(splitRight,[status(thm)],[c_4213]) ).
tff(c_7260,plain,
ssItem('#skF_46'('#skF_51')),
inference(demodulation,[status(thm),theory(equality)],[c_7255,c_4243]) ).
tff(c_10462,plain,
! [U_2024] :
( ( cons(hd(U_2024),tl(U_2024)) = U_2024 )
| ( nil = U_2024 )
| ~ ssList(U_2024) ),
inference(cnfTransformation,[status(thm)],[f_803]) ).
tff(c_10499,plain,
( ( cons(hd('#skF_51'),'#skF_47'('#skF_51')) = '#skF_51' )
| ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_7389,c_10462]) ).
tff(c_10514,plain,
( ( cons('#skF_46'('#skF_51'),'#skF_47'('#skF_51')) = '#skF_51' )
| ( nil = '#skF_51' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_7255,c_10499]) ).
tff(c_10515,plain,
cons('#skF_46'('#skF_51'),'#skF_47'('#skF_51')) = '#skF_51',
inference(negUnitSimplification,[status(thm)],[c_419,c_10514]) ).
tff(c_346,plain,
! [V_1069,U_1067] :
( ( app(cons(V_1069,nil),U_1067) = cons(V_1069,U_1067) )
| ~ ssItem(V_1069)
| ~ ssList(U_1067) ),
inference(cnfTransformation,[status(thm)],[f_834]) ).
tff(c_4364,plain,
! [U_1770] :
( ( hd(U_1770) = '#skF_46'(U_1770) )
| ( nil = U_1770 )
| ~ ssList(U_1770) ),
inference(cnfTransformation,[status(thm)],[f_769]) ).
tff(c_4445,plain,
( ( hd('#skF_51') = '#skF_46'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_396,c_4364]) ).
tff(c_4478,plain,
hd('#skF_51') = '#skF_46'('#skF_51'),
inference(negUnitSimplification,[status(thm)],[c_419,c_4445]) ).
tff(c_4679,plain,
ssItem('#skF_46'('#skF_51')),
inference(demodulation,[status(thm),theory(equality)],[c_4478,c_4243]) ).
tff(c_5081,plain,
! [V_1788,U_1789] :
( ssList(cons(V_1788,U_1789))
| ~ ssItem(V_1788)
| ~ ssList(U_1789) ),
inference(cnfTransformation,[status(thm)],[f_318]) ).
tff(c_4149,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_3881]) ).
tff(c_4265,plain,
( ~ ssList(cons(hd('#skF_51'),nil))
| ( app(tl('#skF_51'),cons(hd('#skF_51'),nil)) = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_4243,c_4149]) ).
tff(c_4266,plain,
~ ssList(cons(hd('#skF_51'),nil)),
inference(splitLeft,[status(thm)],[c_4265]) ).
tff(c_4678,plain,
~ ssList(cons('#skF_46'('#skF_51'),nil)),
inference(demodulation,[status(thm),theory(equality)],[c_4478,c_4266]) ).
tff(c_5090,plain,
( ~ ssItem('#skF_46'('#skF_51'))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_5081,c_4678]) ).
tff(c_5105,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_168,c_4679,c_5090]) ).
tff(c_5107,plain,
ssList(cons(hd('#skF_51'),nil)),
inference(splitRight,[status(thm)],[c_4265]) ).
tff(c_196,plain,
! [U_906] :
( ( app(nil,U_906) = U_906 )
| ~ ssList(U_906) ),
inference(cnfTransformation,[status(thm)],[f_413]) ).
tff(c_5114,plain,
app(nil,cons(hd('#skF_51'),nil)) = cons(hd('#skF_51'),nil),
inference(resolution,[status(thm)],[c_5107,c_196]) ).
tff(c_23711,plain,
app(nil,cons('#skF_46'('#skF_51'),nil)) = cons('#skF_46'('#skF_51'),nil),
inference(demodulation,[status(thm),theory(equality)],[c_7255,c_7255,c_5114]) ).
tff(c_6494,plain,
! [U_1854] :
( ( hd(U_1854) = '#skF_46'(U_1854) )
| ( nil = U_1854 )
| ~ ssList(U_1854) ),
inference(cnfTransformation,[status(thm)],[f_769]) ).
tff(c_6587,plain,
( ( hd('#skF_51') = '#skF_46'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_396,c_6494]) ).
tff(c_6624,plain,
hd('#skF_51') = '#skF_46'('#skF_51'),
inference(negUnitSimplification,[status(thm)],[c_419,c_6587]) ).
tff(c_5333,plain,
! [U_1807] :
( ( tl(U_1807) = '#skF_47'(U_1807) )
| ( nil = U_1807 )
| ~ ssList(U_1807) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_5417,plain,
( ( tl('#skF_51') = '#skF_47'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_396,c_5333]) ).
tff(c_5451,plain,
tl('#skF_51') = '#skF_47'('#skF_51'),
inference(negUnitSimplification,[status(thm)],[c_419,c_5417]) ).
tff(c_5106,plain,
app(tl('#skF_51'),cons(hd('#skF_51'),nil)) = '#skF_50',
inference(splitRight,[status(thm)],[c_4265]) ).
tff(c_6825,plain,
app('#skF_47'('#skF_51'),cons('#skF_46'('#skF_51'),nil)) = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_6624,c_5451,c_5106]) ).
tff(c_4242,plain,
( ( app(app(nil,cons(hd('#skF_51'),nil)),tl('#skF_51')) != '#skF_51' )
| ( app(tl('#skF_51'),cons(hd('#skF_51'),nil)) != '#skF_50' ) ),
inference(splitRight,[status(thm)],[c_4213]) ).
tff(c_5126,plain,
app(tl('#skF_51'),cons(hd('#skF_51'),nil)) != '#skF_50',
inference(splitLeft,[status(thm)],[c_4242]) ).
tff(c_5453,plain,
app('#skF_47'('#skF_51'),cons(hd('#skF_51'),nil)) != '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_5451,c_5126]) ).
tff(c_6842,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6825,c_6624,c_5453]) ).
tff(c_6843,plain,
app(app(nil,cons(hd('#skF_51'),nil)),tl('#skF_51')) != '#skF_51',
inference(splitRight,[status(thm)],[c_4242]) ).
tff(c_14016,plain,
app(app(nil,cons('#skF_46'('#skF_51'),nil)),'#skF_47'('#skF_51')) != '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_7255,c_7389,c_6843]) ).
tff(c_23712,plain,
app(cons('#skF_46'('#skF_51'),nil),'#skF_47'('#skF_51')) != '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_23711,c_14016]) ).
tff(c_23851,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_346,c_23712]) ).
tff(c_23854,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_7394,c_7260,c_10515,c_23851]) ).
tff(c_23855,plain,
nil = '#skF_50',
inference(splitRight,[status(thm)],[c_386]) ).
tff(c_23856,plain,
nil = '#skF_51',
inference(splitRight,[status(thm)],[c_386]) ).
tff(c_23872,plain,
'#skF_51' = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_23855,c_23856]) ).
tff(c_23857,plain,
neq('#skF_51','#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_23855,c_407]) ).
tff(c_23884,plain,
neq('#skF_50','#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_23872,c_23857]) ).
tff(c_23907,plain,
! [V_2424] :
( ~ neq(V_2424,V_2424)
| ~ ssList(V_2424) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_23910,plain,
~ ssList('#skF_50'),
inference(resolution,[status(thm)],[c_23884,c_23907]) ).
tff(c_23914,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_398,c_23910]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SWC418+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.11 % 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
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Thu Aug 3 21:48:51 EDT 2023
% 0.11/0.30 % CPUTime :
% 18.89/6.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.97/6.62
% 18.97/6.62 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 19.10/6.66
% 19.10/6.66 Inference rules
% 19.10/6.66 ----------------------
% 19.10/6.66 #Ref : 2
% 19.10/6.66 #Sup : 5193
% 19.10/6.66 #Fact : 0
% 19.10/6.66 #Define : 0
% 19.10/6.66 #Split : 74
% 19.10/6.66 #Chain : 0
% 19.10/6.66 #Close : 0
% 19.10/6.66
% 19.10/6.66 Ordering : KBO
% 19.10/6.66
% 19.10/6.66 Simplification rules
% 19.10/6.66 ----------------------
% 19.10/6.66 #Subsume : 684
% 19.10/6.66 #Demod : 4054
% 19.10/6.66 #Tautology : 1323
% 19.10/6.66 #SimpNegUnit : 264
% 19.10/6.66 #BackRed : 337
% 19.10/6.66
% 19.10/6.66 #Partial instantiations: 0
% 19.10/6.66 #Strategies tried : 1
% 19.10/6.66
% 19.10/6.66 Timing (in seconds)
% 19.10/6.66 ----------------------
% 19.10/6.66 Preprocessing : 1.03
% 19.10/6.66 Parsing : 0.41
% 19.10/6.66 CNF conversion : 0.16
% 19.10/6.66 Main loop : 4.68
% 19.10/6.66 Inferencing : 1.36
% 19.10/6.66 Reduction : 1.73
% 19.10/6.66 Demodulation : 1.29
% 19.10/6.66 BG Simplification : 0.16
% 19.10/6.66 Subsumption : 1.12
% 19.10/6.66 Abstraction : 0.11
% 19.10/6.66 MUC search : 0.00
% 19.10/6.66 Cooper : 0.00
% 19.10/6.66 Total : 5.78
% 19.10/6.66 Index Insertion : 0.00
% 19.10/6.66 Index Deletion : 0.00
% 19.10/6.66 Index Matching : 0.00
% 19.10/6.66 BG Taut test : 0.00
%------------------------------------------------------------------------------