TSTP Solution File: SWC308+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWC308+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/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 : n026.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 11:02:03 EDT 2023
% Result : Theorem 15.15s 4.78s
% Output : CNFRefutation 15.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 87
% Syntax : Number of formulae : 180 ( 50 unt; 75 typ; 0 def)
% Number of atoms : 236 ( 95 equ)
% Maximal formula atoms : 24 ( 2 avg)
% Number of connectives : 228 ( 97 ~; 91 |; 16 &)
% ( 1 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 3 avg)
% Maximal term depth : 5 ( 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 : 48 (; 40 !; 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_1039,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ~ neq(V,nil)
| ? [Y] :
( ssList(Y)
& ( U = Y )
& ? [Z] :
( ssList(Z)
& ? [X1] :
( ssList(X1)
& ( tl(V) = Z )
& ( app(Z,X1) = Y )
& ? [X2] :
( ssItem(X2)
& ( cons(X2,nil) = X1 )
& ( hd(V) = X2 )
& neq(nil,V) )
& neq(nil,V) ) ) )
| ? [X3] :
( ssItem(X3)
& ? [X4] :
( ssList(X4)
& ( app(X4,cons(X3,nil)) != W )
& ( app(cons(X3,nil),X4) = X ) ) )
| ( ( nil != W )
& ( nil = X ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f_319,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
tff(f_371,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ssItem(hd(U)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
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_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_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_318,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
tff(f_385,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ssList(tl(U)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
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_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_859,axiom,
! [U] :
( ssList(U)
=> ( app(U,nil) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
tff(f_834,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( cons(V,U) = app(cons(V,nil),U) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax81) ).
tff(c_398,plain,
ssList('#skF_50'),
inference(cnfTransformation,[status(thm)],[f_1039]) ).
tff(c_168,plain,
ssList(nil),
inference(cnfTransformation,[status(thm)],[f_319]) ).
tff(c_384,plain,
( ( nil != '#skF_51' )
| ( nil = '#skF_50' ) ),
inference(cnfTransformation,[status(thm)],[f_1039]) ).
tff(c_417,plain,
nil != '#skF_51',
inference(splitLeft,[status(thm)],[c_384]) ).
tff(c_396,plain,
ssList('#skF_51'),
inference(cnfTransformation,[status(thm)],[f_1039]) ).
tff(c_184,plain,
! [U_888] :
( ssItem(hd(U_888))
| ( nil = U_888 )
| ~ ssList(U_888) ),
inference(cnfTransformation,[status(thm)],[f_371]) ).
tff(c_9755,plain,
! [U_1909] :
( ( hd(U_1909) = '#skF_46'(U_1909) )
| ( nil = U_1909 )
| ~ ssList(U_1909) ),
inference(cnfTransformation,[status(thm)],[f_769]) ).
tff(c_9839,plain,
( ( hd('#skF_51') = '#skF_46'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_396,c_9755]) ).
tff(c_9873,plain,
hd('#skF_51') = '#skF_46'('#skF_51'),
inference(negUnitSimplification,[status(thm)],[c_417,c_9839]) ).
tff(c_4188,plain,
! [U_1708] :
( ( tl(U_1708) = '#skF_47'(U_1708) )
| ( nil = U_1708 )
| ~ ssList(U_1708) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_4269,plain,
( ( tl('#skF_51') = '#skF_47'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_396,c_4188]) ).
tff(c_4302,plain,
tl('#skF_51') = '#skF_47'('#skF_51'),
inference(negUnitSimplification,[status(thm)],[c_417,c_4269]) ).
tff(c_3882,plain,
! [U_1657,V_1658] :
( neq(U_1657,V_1658)
| ( V_1658 = U_1657 )
| ~ ssList(V_1658)
| ~ ssList(U_1657) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_800,plain,
! [U_1490] :
( ( hd(U_1490) = '#skF_46'(U_1490) )
| ( nil = U_1490 )
| ~ ssList(U_1490) ),
inference(cnfTransformation,[status(thm)],[f_769]) ).
tff(c_878,plain,
( ( hd('#skF_51') = '#skF_46'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_396,c_800]) ).
tff(c_910,plain,
hd('#skF_51') = '#skF_46'('#skF_51'),
inference(negUnitSimplification,[status(thm)],[c_417,c_878]) ).
tff(c_916,plain,
( ssItem('#skF_46'('#skF_51'))
| ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_910,c_184]) ).
tff(c_920,plain,
( ssItem('#skF_46'('#skF_51'))
| ( nil = '#skF_51' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_916]) ).
tff(c_921,plain,
ssItem('#skF_46'('#skF_51')),
inference(negUnitSimplification,[status(thm)],[c_417,c_920]) ).
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_923,plain,
! [U_1491] :
( ( tl(U_1491) = '#skF_47'(U_1491) )
| ( nil = U_1491 )
| ~ ssList(U_1491) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_1001,plain,
( ( tl('#skF_51') = '#skF_47'('#skF_51') )
| ( nil = '#skF_51' ) ),
inference(resolution,[status(thm)],[c_396,c_923]) ).
tff(c_1033,plain,
tl('#skF_51') = '#skF_47'('#skF_51'),
inference(negUnitSimplification,[status(thm)],[c_417,c_1001]) ).
tff(c_188,plain,
! [U_892] :
( ssList(tl(U_892))
| ( nil = U_892 )
| ~ ssList(U_892) ),
inference(cnfTransformation,[status(thm)],[f_385]) ).
tff(c_1038,plain,
( ssList('#skF_47'('#skF_51'))
| ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_1033,c_188]) ).
tff(c_1042,plain,
( ssList('#skF_47'('#skF_51'))
| ( nil = '#skF_51' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_1038]) ).
tff(c_1043,plain,
ssList('#skF_47'('#skF_51')),
inference(negUnitSimplification,[status(thm)],[c_417,c_1042]) ).
tff(c_762,plain,
! [U_1488,V_1489] :
( ssList(app(U_1488,V_1489))
| ~ ssList(V_1489)
| ~ ssList(U_1488) ),
inference(cnfTransformation,[status(thm)],[f_399]) ).
tff(c_394,plain,
'#skF_49' = '#skF_51',
inference(cnfTransformation,[status(thm)],[f_1039]) ).
tff(c_392,plain,
'#skF_48' = '#skF_50',
inference(cnfTransformation,[status(thm)],[f_1039]) ).
tff(c_388,plain,
( ~ neq(nil,'#skF_49')
| ~ ssItem(hd('#skF_49'))
| ~ ssList(cons(hd('#skF_49'),nil))
| ~ ssList(tl('#skF_49'))
| ( app(tl('#skF_49'),cons(hd('#skF_49'),nil)) != '#skF_48' )
| ~ ssList(app(tl('#skF_49'),cons(hd('#skF_49'),nil))) ),
inference(cnfTransformation,[status(thm)],[f_1039]) ).
tff(c_408,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_394,c_394,c_392,c_394,c_394,c_394,c_394,c_394,c_394,c_388]) ).
tff(c_428,plain,
~ ssList(app(tl('#skF_51'),cons(hd('#skF_51'),nil))),
inference(splitLeft,[status(thm)],[c_408]) ).
tff(c_788,plain,
( ~ ssList(cons(hd('#skF_51'),nil))
| ~ ssList(tl('#skF_51')) ),
inference(resolution,[status(thm)],[c_762,c_428]) ).
tff(c_1789,plain,
~ ssList(cons('#skF_46'('#skF_51'),nil)),
inference(demodulation,[status(thm),theory(equality)],[c_1043,c_1033,c_910,c_788]) ).
tff(c_1792,plain,
( ~ ssItem('#skF_46'('#skF_51'))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_166,c_1789]) ).
tff(c_1796,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_168,c_921,c_1792]) ).
tff(c_1797,plain,
( ( app(tl('#skF_51'),cons(hd('#skF_51'),nil)) != '#skF_50' )
| ~ ssList(tl('#skF_51'))
| ~ ssList(cons(hd('#skF_51'),nil))
| ~ ssItem(hd('#skF_51'))
| ~ neq(nil,'#skF_51') ),
inference(splitRight,[status(thm)],[c_408]) ).
tff(c_1873,plain,
~ neq(nil,'#skF_51'),
inference(splitLeft,[status(thm)],[c_1797]) ).
tff(c_3885,plain,
( ( nil = '#skF_51' )
| ~ ssList('#skF_51')
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_3882,c_1873]) ).
tff(c_3896,plain,
nil = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_168,c_396,c_3885]) ).
tff(c_3898,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_417,c_3896]) ).
tff(c_3899,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_1797]) ).
tff(c_4041,plain,
app(tl('#skF_51'),cons(hd('#skF_51'),nil)) != '#skF_50',
inference(splitLeft,[status(thm)],[c_3899]) ).
tff(c_4304,plain,
app('#skF_47'('#skF_51'),cons(hd('#skF_51'),nil)) != '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_4302,c_4041]) ).
tff(c_9994,plain,
app('#skF_47'('#skF_51'),cons('#skF_46'('#skF_51'),nil)) != '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_9873,c_4304]) ).
tff(c_4311,plain,
( ssList('#skF_47'('#skF_51'))
| ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_4302,c_188]) ).
tff(c_4315,plain,
( ssList('#skF_47'('#skF_51'))
| ( nil = '#skF_51' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_4311]) ).
tff(c_4316,plain,
ssList('#skF_47'('#skF_51')),
inference(negUnitSimplification,[status(thm)],[c_417,c_4315]) ).
tff(c_9880,plain,
( ssItem('#skF_46'('#skF_51'))
| ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_9873,c_184]) ).
tff(c_9884,plain,
( ssItem('#skF_46'('#skF_51'))
| ( nil = '#skF_51' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_9880]) ).
tff(c_9885,plain,
ssItem('#skF_46'('#skF_51')),
inference(negUnitSimplification,[status(thm)],[c_417,c_9884]) ).
tff(c_11649,plain,
! [U_1976] :
( ( cons(hd(U_1976),tl(U_1976)) = U_1976 )
| ( nil = U_1976 )
| ~ ssList(U_1976) ),
inference(cnfTransformation,[status(thm)],[f_803]) ).
tff(c_11692,plain,
( ( cons('#skF_46'('#skF_51'),tl('#skF_51')) = '#skF_51' )
| ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_9873,c_11649]) ).
tff(c_11716,plain,
( ( cons('#skF_46'('#skF_51'),'#skF_47'('#skF_51')) = '#skF_51' )
| ( nil = '#skF_51' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_4302,c_11692]) ).
tff(c_11717,plain,
cons('#skF_46'('#skF_51'),'#skF_47'('#skF_51')) = '#skF_51',
inference(negUnitSimplification,[status(thm)],[c_417,c_11716]) ).
tff(c_1803,plain,
! [U_1527] :
( ( app(U_1527,nil) = U_1527 )
| ~ ssList(U_1527) ),
inference(cnfTransformation,[status(thm)],[f_859]) ).
tff(c_1815,plain,
app('#skF_50',nil) = '#skF_50',
inference(resolution,[status(thm)],[c_398,c_1803]) ).
tff(c_14337,plain,
! [V_2095,U_2096] :
( ( app(cons(V_2095,nil),U_2096) = cons(V_2095,U_2096) )
| ~ ssItem(V_2095)
| ~ ssList(U_2096) ),
inference(cnfTransformation,[status(thm)],[f_834]) ).
tff(c_386,plain,
! [X3_1418,X4_1420] :
( ( app(cons(X3_1418,nil),X4_1420) != '#skF_51' )
| ( app(X4_1420,cons(X3_1418,nil)) = '#skF_50' )
| ~ ssList(X4_1420)
| ~ ssItem(X3_1418) ),
inference(cnfTransformation,[status(thm)],[f_1039]) ).
tff(c_14374,plain,
! [V_2100,U_2101] :
( ( cons(V_2100,U_2101) != '#skF_51' )
| ( app(U_2101,cons(V_2100,nil)) = '#skF_50' )
| ~ ssList(U_2101)
| ~ ssItem(V_2100)
| ~ ssItem(V_2100)
| ~ ssList(U_2101) ),
inference(superposition,[status(thm),theory(equality)],[c_14337,c_386]) ).
tff(c_1798,plain,
ssList(app(tl('#skF_51'),cons(hd('#skF_51'),nil))),
inference(splitRight,[status(thm)],[c_408]) ).
tff(c_356,plain,
! [U_1080] :
( ( app(U_1080,nil) = U_1080 )
| ~ ssList(U_1080) ),
inference(cnfTransformation,[status(thm)],[f_859]) ).
tff(c_1832,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_1798,c_356]) ).
tff(c_4305,plain,
app(app('#skF_47'('#skF_51'),cons(hd('#skF_51'),nil)),nil) = app('#skF_47'('#skF_51'),cons(hd('#skF_51'),nil)),
inference(demodulation,[status(thm),theory(equality)],[c_4302,c_4302,c_1832]) ).
tff(c_11988,plain,
app(app('#skF_47'('#skF_51'),cons('#skF_46'('#skF_51'),nil)),nil) = app('#skF_47'('#skF_51'),cons('#skF_46'('#skF_51'),nil)),
inference(demodulation,[status(thm),theory(equality)],[c_9873,c_9873,c_4305]) ).
tff(c_14387,plain,
( ( app('#skF_47'('#skF_51'),cons('#skF_46'('#skF_51'),nil)) = app('#skF_50',nil) )
| ( cons('#skF_46'('#skF_51'),'#skF_47'('#skF_51')) != '#skF_51' )
| ~ ssList('#skF_47'('#skF_51'))
| ~ ssItem('#skF_46'('#skF_51'))
| ~ ssItem('#skF_46'('#skF_51'))
| ~ ssList('#skF_47'('#skF_51')) ),
inference(superposition,[status(thm),theory(equality)],[c_14374,c_11988]) ).
tff(c_14432,plain,
app('#skF_47'('#skF_51'),cons('#skF_46'('#skF_51'),nil)) = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_4316,c_9885,c_9885,c_4316,c_11717,c_1815,c_14387]) ).
tff(c_14434,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9994,c_14432]) ).
tff(c_14435,plain,
( ~ ssList(tl('#skF_51'))
| ~ ssList(cons(hd('#skF_51'),nil))
| ~ ssItem(hd('#skF_51')) ),
inference(splitRight,[status(thm)],[c_3899]) ).
tff(c_14553,plain,
~ ssItem(hd('#skF_51')),
inference(splitLeft,[status(thm)],[c_14435]) ).
tff(c_14556,plain,
( ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(resolution,[status(thm)],[c_184,c_14553]) ).
tff(c_14559,plain,
nil = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_396,c_14556]) ).
tff(c_14561,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_417,c_14559]) ).
tff(c_14563,plain,
ssItem(hd('#skF_51')),
inference(splitRight,[status(thm)],[c_14435]) ).
tff(c_14562,plain,
( ~ ssList(cons(hd('#skF_51'),nil))
| ~ ssList(tl('#skF_51')) ),
inference(splitRight,[status(thm)],[c_14435]) ).
tff(c_14603,plain,
~ ssList(tl('#skF_51')),
inference(splitLeft,[status(thm)],[c_14562]) ).
tff(c_14606,plain,
( ( nil = '#skF_51' )
| ~ ssList('#skF_51') ),
inference(resolution,[status(thm)],[c_188,c_14603]) ).
tff(c_14609,plain,
nil = '#skF_51',
inference(demodulation,[status(thm),theory(equality)],[c_396,c_14606]) ).
tff(c_14611,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_417,c_14609]) ).
tff(c_14612,plain,
~ ssList(cons(hd('#skF_51'),nil)),
inference(splitRight,[status(thm)],[c_14562]) ).
tff(c_14624,plain,
( ~ ssItem(hd('#skF_51'))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_166,c_14612]) ).
tff(c_14628,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_168,c_14563,c_14624]) ).
tff(c_14629,plain,
nil = '#skF_50',
inference(splitRight,[status(thm)],[c_384]) ).
tff(c_14630,plain,
nil = '#skF_51',
inference(splitRight,[status(thm)],[c_384]) ).
tff(c_14646,plain,
'#skF_51' = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_14629,c_14630]) ).
tff(c_390,plain,
neq('#skF_49',nil),
inference(cnfTransformation,[status(thm)],[f_1039]) ).
tff(c_407,plain,
neq('#skF_51',nil),
inference(demodulation,[status(thm),theory(equality)],[c_394,c_390]) ).
tff(c_14631,plain,
neq('#skF_51','#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_14629,c_407]) ).
tff(c_14660,plain,
neq('#skF_50','#skF_50'),
inference(demodulation,[status(thm),theory(equality)],[c_14646,c_14631]) ).
tff(c_14661,plain,
! [V_2131] :
( ~ neq(V_2131,V_2131)
| ~ ssList(V_2131) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_14664,plain,
~ ssList('#skF_50'),
inference(resolution,[status(thm)],[c_14660,c_14661]) ).
tff(c_14668,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_398,c_14664]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWC308+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/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
% 0.15/0.35 % Computer : n026.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 3 21:45:17 EDT 2023
% 0.15/0.35 % CPUTime :
% 15.15/4.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.15/4.79
% 15.15/4.79 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.36/4.83
% 15.36/4.83 Inference rules
% 15.36/4.83 ----------------------
% 15.36/4.83 #Ref : 0
% 15.36/4.83 #Sup : 3197
% 15.36/4.83 #Fact : 0
% 15.36/4.83 #Define : 0
% 15.36/4.83 #Split : 47
% 15.36/4.83 #Chain : 0
% 15.36/4.83 #Close : 0
% 15.36/4.83
% 15.36/4.83 Ordering : KBO
% 15.36/4.83
% 15.36/4.83 Simplification rules
% 15.36/4.83 ----------------------
% 15.36/4.83 #Subsume : 424
% 15.36/4.83 #Demod : 2098
% 15.36/4.83 #Tautology : 1086
% 15.36/4.83 #SimpNegUnit : 162
% 15.36/4.83 #BackRed : 191
% 15.36/4.83
% 15.36/4.83 #Partial instantiations: 0
% 15.36/4.83 #Strategies tried : 1
% 15.36/4.83
% 15.36/4.83 Timing (in seconds)
% 15.36/4.83 ----------------------
% 15.36/4.83 Preprocessing : 0.94
% 15.36/4.83 Parsing : 0.45
% 15.36/4.83 CNF conversion : 0.12
% 15.36/4.83 Main loop : 2.72
% 15.36/4.83 Inferencing : 0.95
% 15.36/4.83 Reduction : 0.88
% 15.36/4.83 Demodulation : 0.62
% 15.36/4.83 BG Simplification : 0.11
% 15.36/4.83 Subsumption : 0.56
% 15.36/4.83 Abstraction : 0.09
% 15.36/4.83 MUC search : 0.00
% 15.36/4.83 Cooper : 0.00
% 15.36/4.83 Total : 3.73
% 15.36/4.83 Index Insertion : 0.00
% 15.36/4.83 Index Deletion : 0.00
% 15.36/4.83 Index Matching : 0.00
% 15.36/4.84 BG Taut test : 0.00
%------------------------------------------------------------------------------