TSTP Solution File: SWC031+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWC031+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 : n002.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 11:00:51 EDT 2023
% Result : Theorem 242.92s 209.74s
% Output : CNFRefutation 242.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 104
% Syntax : Number of formulae : 296 ( 51 unt; 75 typ; 0 def)
% Number of atoms : 609 ( 161 equ)
% Maximal formula atoms : 17 ( 2 avg)
% Number of connectives : 695 ( 307 ~; 311 |; 16 &)
% ( 7 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 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 : 194 (; 185 !; 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_1021,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ~ frontsegP(X,W)
| ~ totalorderedP(W)
| ? [Y] :
( ssList(Y)
& neq(W,Y)
& frontsegP(X,Y)
& segmentP(Y,W)
& totalorderedP(Y) )
| ( ( ( nil != V )
| ( nil = U ) )
& ( ( nil != U )
| ( nil = V ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f_356,axiom,
! [U] :
( ssList(U)
=> ( ( nil = U )
| ? [V] :
( ssList(V)
& ? [W] :
( ssItem(W)
& ( cons(W,V) = U ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax20) ).
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_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_392,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( tl(cons(V,U)) = U ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax25) ).
tff(f_378,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( hd(cons(V,U)) = V ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax23) ).
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_96,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( ssItem(V)
& ( cons(V,nil) = U ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax4) ).
tff(f_413,axiom,
! [U] :
( ssList(U)
=> ( app(nil,U) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
tff(f_409,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssItem(W)
=> ( cons(W,app(V,U)) = app(cons(W,V),U) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax27) ).
tff(f_364,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( nil != cons(V,U) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
tff(f_371,axiom,
! [U] :
( ssList(U)
=> ( ( nil != U )
=> ssItem(hd(U)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).
tff(f_732,axiom,
! [U] :
( ssItem(U)
=> strictorderedP(cons(U,nil)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax68) ).
tff(f_749,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssList(V)
=> ( strictorderedP(cons(U,V))
<=> ( ( nil = V )
| ( ( nil != V )
& strictorderedP(V)
& lt(U,hd(V)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax70) ).
tff(f_950,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( lt(U,V)
<=> ( ( U != V )
& leq(U,V) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax93) ).
tff(f_859,axiom,
! [U] :
( ssList(U)
=> ( app(U,nil) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
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_844,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( app(app(U,V),W) = app(U,app(V,W)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax82) ).
tff(f_135,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( segmentP(U,V)
<=> ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& ( app(app(W,V),X) = U ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).
tff(f_696,axiom,
! [U] :
( ssItem(U)
=> cyclefreeP(cons(U,nil)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax59) ).
tff(f_706,axiom,
! [U] :
( ssItem(U)
=> strictorderP(cons(U,nil)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax63) ).
tff(f_711,axiom,
! [U] :
( ssItem(U)
=> totalorderedP(cons(U,nil)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax65) ).
tff(f_108,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( frontsegP(U,V)
<=> ? [W] :
( ssList(W)
& ( app(V,W) = U ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax5) ).
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_560,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( frontsegP(U,V)
=> frontsegP(app(U,W),V) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax43) ).
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_686,axiom,
! [U] :
( ssList(U)
=> segmentP(U,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax57) ).
tff(f_587,axiom,
! [U] :
( ssList(U)
=> ( frontsegP(nil,U)
<=> ( nil = U ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax46) ).
tff(c_390,plain,
'#skF_48' = '#skF_50',
inference(cnfTransformation,[status(thm)],[f_1021]) ).
tff(c_392,plain,
'#skF_49' = '#skF_51',
inference(cnfTransformation,[status(thm)],[f_1021]) ).
tff(c_408,plain,
( ( nil = '#skF_49' )
| ( nil = '#skF_48' ) ),
inference(cnfTransformation,[status(thm)],[f_1021]) ).
tff(c_411,plain,
( ( nil = '#skF_51' )
| ( nil = '#skF_48' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_392,c_408]) ).
tff(c_415,plain,
( ( nil = '#skF_51' )
| ( nil = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_411]) ).
tff(c_425,plain,
nil = '#skF_50',
inference(splitLeft,[status(thm)],[c_415]) ).
tff(c_402,plain,
( ( nil != '#skF_48' )
| ( nil != '#skF_49' ) ),
inference(cnfTransformation,[status(thm)],[f_1021]) ).
tff(c_410,plain,
( ( nil != '#skF_48' )
| ( nil != '#skF_51' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_392,c_402]) ).
tff(c_414,plain,
( ( nil != '#skF_50' )
| ( nil != '#skF_51' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_410]) ).
tff(c_443,plain,
'#skF_51' != '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_425,c_425,c_414]) ).
tff(c_394,plain,
ssList('#skF_51'),
inference(cnfTransformation,[status(thm)],[f_1021]) ).
tff(c_178,plain,
! [U_880] :
( ssItem('#skF_45'(U_880))
| ( nil = U_880 )
| ~ ssList(U_880) ),
inference(cnfTransformation,[status(thm)],[f_356]) ).
tff(c_661,plain,
! [U_880] :
( ssItem('#skF_45'(U_880))
| ( U_880 = '#skF_50' )
| ~ ssList(U_880) ),
inference(demodulation,[status(thm),theory(equality)],[c_425,c_178]) ).
tff(c_334,plain,
! [U_1047] :
( ( tl(U_1047) = '#skF_47'(U_1047) )
| ( nil = U_1047 )
| ~ ssList(U_1047) ),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_1046,plain,
! [U_1224] :
( ( tl(U_1224) = '#skF_47'(U_1224) )
| ( U_1224 = '#skF_50' )
| ~ ssList(U_1224) ),
inference(demodulation,[status(thm),theory(equality)],[c_425,c_334]) ).
tff(c_1124,plain,
( ( tl('#skF_51') = '#skF_47'('#skF_51') )
| ( '#skF_51' = '#skF_50' ) ),
inference(resolution,[status(thm)],[c_394,c_1046]) ).
tff(c_1153,plain,
tl('#skF_51') = '#skF_47'('#skF_51'),
inference(negUnitSimplification,[status(thm)],[c_443,c_1124]) ).
tff(c_188,plain,
! [U_892] :
( ssList(tl(U_892))
| ( nil = U_892 )
| ~ ssList(U_892) ),
inference(cnfTransformation,[status(thm)],[f_385]) ).
tff(c_598,plain,
! [U_892] :
( ssList(tl(U_892))
| ( U_892 = '#skF_50' )
| ~ ssList(U_892) ),
inference(demodulation,[status(thm),theory(equality)],[c_425,c_188]) ).
tff(c_1157,plain,
( ssList('#skF_47'('#skF_51'))
| ( '#skF_51' = '#skF_50' )
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_1153,c_598]) ).
tff(c_1161,plain,
( ssList('#skF_47'('#skF_51'))
| ( '#skF_51' = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_394,c_1157]) ).
tff(c_1162,plain,
ssList('#skF_47'('#skF_51')),
inference(negUnitSimplification,[status(thm)],[c_443,c_1161]) ).
tff(c_330,plain,
! [U_1045] :
( ( hd(U_1045) = '#skF_46'(U_1045) )
| ( nil = U_1045 )
| ~ ssList(U_1045) ),
inference(cnfTransformation,[status(thm)],[f_769]) ).
tff(c_1224,plain,
! [U_1227] :
( ( hd(U_1227) = '#skF_46'(U_1227) )
| ( U_1227 = '#skF_50' )
| ~ ssList(U_1227) ),
inference(demodulation,[status(thm),theory(equality)],[c_425,c_330]) ).
tff(c_1308,plain,
( ( hd('#skF_51') = '#skF_46'('#skF_51') )
| ( '#skF_51' = '#skF_50' ) ),
inference(resolution,[status(thm)],[c_394,c_1224]) ).
tff(c_1339,plain,
hd('#skF_51') = '#skF_46'('#skF_51'),
inference(negUnitSimplification,[status(thm)],[c_443,c_1308]) ).
tff(c_180,plain,
! [U_880] :
( ssList('#skF_44'(U_880))
| ( nil = U_880 )
| ~ ssList(U_880) ),
inference(cnfTransformation,[status(thm)],[f_356]) ).
tff(c_587,plain,
! [U_880] :
( ssList('#skF_44'(U_880))
| ( U_880 = '#skF_50' )
| ~ ssList(U_880) ),
inference(demodulation,[status(thm),theory(equality)],[c_425,c_180]) ).
tff(c_176,plain,
! [U_880] :
( ( cons('#skF_45'(U_880),'#skF_44'(U_880)) = U_880 )
| ( nil = U_880 )
| ~ ssList(U_880) ),
inference(cnfTransformation,[status(thm)],[f_356]) ).
tff(c_2470,plain,
! [U_1285] :
( ( cons('#skF_45'(U_1285),'#skF_44'(U_1285)) = U_1285 )
| ( U_1285 = '#skF_50' )
| ~ ssList(U_1285) ),
inference(demodulation,[status(thm),theory(equality)],[c_425,c_176]) ).
tff(c_190,plain,
! [V_895,U_893] :
( ( tl(cons(V_895,U_893)) = U_893 )
| ~ ssItem(V_895)
| ~ ssList(U_893) ),
inference(cnfTransformation,[status(thm)],[f_392]) ).
tff(c_68589,plain,
! [U_2504] :
( ( tl(U_2504) = '#skF_44'(U_2504) )
| ~ ssItem('#skF_45'(U_2504))
| ~ ssList('#skF_44'(U_2504))
| ( U_2504 = '#skF_50' )
| ~ ssList(U_2504) ),
inference(superposition,[status(thm),theory(equality)],[c_2470,c_190]) ).
tff(c_70013,plain,
! [U_2517] :
( ( tl(U_2517) = '#skF_44'(U_2517) )
| ~ ssItem('#skF_45'(U_2517))
| ( U_2517 = '#skF_50' )
| ~ ssList(U_2517) ),
inference(resolution,[status(thm)],[c_587,c_68589]) ).
tff(c_70032,plain,
! [U_2519] :
( ( tl(U_2519) = '#skF_44'(U_2519) )
| ( U_2519 = '#skF_50' )
| ~ ssList(U_2519) ),
inference(resolution,[status(thm)],[c_661,c_70013]) ).
tff(c_70302,plain,
( ( tl('#skF_51') = '#skF_44'('#skF_51') )
| ( '#skF_51' = '#skF_50' ) ),
inference(resolution,[status(thm)],[c_394,c_70032]) ).
tff(c_70430,plain,
( ( '#skF_44'('#skF_51') = '#skF_47'('#skF_51') )
| ( '#skF_51' = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1153,c_70302]) ).
tff(c_70431,plain,
'#skF_44'('#skF_51') = '#skF_47'('#skF_51'),
inference(negUnitSimplification,[status(thm)],[c_443,c_70430]) ).
tff(c_186,plain,
! [V_891,U_889] :
( ( hd(cons(V_891,U_889)) = V_891 )
| ~ ssItem(V_891)
| ~ ssList(U_889) ),
inference(cnfTransformation,[status(thm)],[f_378]) ).
tff(c_2482,plain,
! [U_1285] :
( ( hd(U_1285) = '#skF_45'(U_1285) )
| ~ ssItem('#skF_45'(U_1285))
| ~ ssList('#skF_44'(U_1285))
| ( U_1285 = '#skF_50' )
| ~ ssList(U_1285) ),
inference(superposition,[status(thm),theory(equality)],[c_2470,c_186]) ).
tff(c_70436,plain,
( ( hd('#skF_51') = '#skF_45'('#skF_51') )
| ~ ssItem('#skF_45'('#skF_51'))
| ~ ssList('#skF_47'('#skF_51'))
| ( '#skF_51' = '#skF_50' )
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_70431,c_2482]) ).
tff(c_70527,plain,
( ( '#skF_46'('#skF_51') = '#skF_45'('#skF_51') )
| ~ ssItem('#skF_45'('#skF_51'))
| ( '#skF_51' = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_394,c_1162,c_1339,c_70436]) ).
tff(c_70528,plain,
( ( '#skF_46'('#skF_51') = '#skF_45'('#skF_51') )
| ~ ssItem('#skF_45'('#skF_51')) ),
inference(negUnitSimplification,[status(thm)],[c_443,c_70527]) ).
tff(c_71078,plain,
~ ssItem('#skF_45'('#skF_51')),
inference(splitLeft,[status(thm)],[c_70528]) ).
tff(c_71088,plain,
( ( '#skF_51' = '#skF_50' )
| ~ ssList('#skF_51') ),
inference(resolution,[status(thm)],[c_661,c_71078]) ).
tff(c_71091,plain,
'#skF_51' = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_394,c_71088]) ).
tff(c_71093,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_443,c_71091]) ).
tff(c_71095,plain,
ssItem('#skF_45'('#skF_51')),
inference(splitRight,[status(thm)],[c_70528]) ).
tff(c_396,plain,
ssList('#skF_50'),
inference(cnfTransformation,[status(thm)],[f_1021]) ).
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_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_3118,plain,
! [V_1311] :
( singletonP(cons(V_1311,'#skF_50'))
| ~ ssItem(V_1311)
| ~ ssList(cons(V_1311,'#skF_50')) ),
inference(demodulation,[status(thm),theory(equality)],[c_425,c_425,c_20]) ).
tff(c_3125,plain,
! [V_861] :
( singletonP(cons(V_861,'#skF_50'))
| ~ ssItem(V_861)
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_166,c_3118]) ).
tff(c_3128,plain,
! [V_861] :
( singletonP(cons(V_861,'#skF_50'))
| ~ ssItem(V_861) ),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_3125]) ).
tff(c_196,plain,
! [U_906] :
( ( app(nil,U_906) = U_906 )
| ~ ssList(U_906) ),
inference(cnfTransformation,[status(thm)],[f_413]) ).
tff(c_472,plain,
! [U_1162] :
( ( app('#skF_50',U_1162) = U_1162 )
| ~ ssList(U_1162) ),
inference(demodulation,[status(thm),theory(equality)],[c_425,c_196]) ).
tff(c_479,plain,
app('#skF_50','#skF_50') = '#skF_50',
inference(resolution,[status(thm)],[c_396,c_472]) ).
tff(c_15236,plain,
! [W_1702,V_1703,U_1704] :
( ( cons(W_1702,app(V_1703,U_1704)) = app(cons(W_1702,V_1703),U_1704) )
| ~ ssItem(W_1702)
| ~ ssList(V_1703)
| ~ ssList(U_1704) ),
inference(cnfTransformation,[status(thm)],[f_409]) ).
tff(c_15497,plain,
! [W_1702] :
( ( app(cons(W_1702,'#skF_50'),'#skF_50') = cons(W_1702,'#skF_50') )
| ~ ssItem(W_1702)
| ~ ssList('#skF_50')
| ~ ssList('#skF_50') ),
inference(superposition,[status(thm),theory(equality)],[c_479,c_15236]) ).
tff(c_15629,plain,
! [W_1702] :
( ( app(cons(W_1702,'#skF_50'),'#skF_50') = cons(W_1702,'#skF_50') )
| ~ ssItem(W_1702) ),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_396,c_15497]) ).
tff(c_93772,plain,
! [W_2683,V_2684,U_2685] :
( ssList(app(cons(W_2683,V_2684),U_2685))
| ~ ssItem(W_2683)
| ~ ssList(app(V_2684,U_2685))
| ~ ssItem(W_2683)
| ~ ssList(V_2684)
| ~ ssList(U_2685) ),
inference(superposition,[status(thm),theory(equality)],[c_15236,c_166]) ).
tff(c_93927,plain,
! [W_1702] :
( ssList(cons(W_1702,'#skF_50'))
| ~ ssItem(W_1702)
| ~ ssList(app('#skF_50','#skF_50'))
| ~ ssItem(W_1702)
| ~ ssList('#skF_50')
| ~ ssList('#skF_50')
| ~ ssItem(W_1702) ),
inference(superposition,[status(thm),theory(equality)],[c_15629,c_93772]) ).
tff(c_94186,plain,
! [W_2687] :
( ssList(cons(W_2687,'#skF_50'))
| ~ ssItem(W_2687) ),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_396,c_396,c_479,c_93927]) ).
tff(c_24,plain,
! [U_30] :
( ssItem('#skF_5'(U_30))
| ~ singletonP(U_30)
| ~ ssList(U_30) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_22,plain,
! [U_30] :
( ( cons('#skF_5'(U_30),nil) = U_30 )
| ~ singletonP(U_30)
| ~ ssList(U_30) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_2210,plain,
! [U_1267] :
( ( cons('#skF_5'(U_1267),'#skF_50') = U_1267 )
| ~ singletonP(U_1267)
| ~ ssList(U_1267) ),
inference(demodulation,[status(thm),theory(equality)],[c_425,c_22]) ).
tff(c_182,plain,
! [V_887,U_885] :
( ( cons(V_887,U_885) != nil )
| ~ ssItem(V_887)
| ~ ssList(U_885) ),
inference(cnfTransformation,[status(thm)],[f_364]) ).
tff(c_1043,plain,
! [V_887,U_885] :
( ( cons(V_887,U_885) != '#skF_50' )
| ~ ssItem(V_887)
| ~ ssList(U_885) ),
inference(demodulation,[status(thm),theory(equality)],[c_425,c_182]) ).
tff(c_2221,plain,
! [U_1267] :
( ( U_1267 != '#skF_50' )
| ~ ssItem('#skF_5'(U_1267))
| ~ ssList('#skF_50')
| ~ singletonP(U_1267)
| ~ ssList(U_1267) ),
inference(superposition,[status(thm),theory(equality)],[c_2210,c_1043]) ).
tff(c_2660,plain,
! [U_1293] :
( ( U_1293 != '#skF_50' )
| ~ ssItem('#skF_5'(U_1293))
| ~ singletonP(U_1293)
| ~ ssList(U_1293) ),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_2221]) ).
tff(c_2664,plain,
! [U_30] :
( ( U_30 != '#skF_50' )
| ~ singletonP(U_30)
| ~ ssList(U_30) ),
inference(resolution,[status(thm)],[c_24,c_2660]) ).
tff(c_95673,plain,
! [W_2696] :
( ( cons(W_2696,'#skF_50') != '#skF_50' )
| ~ singletonP(cons(W_2696,'#skF_50'))
| ~ ssItem(W_2696) ),
inference(resolution,[status(thm)],[c_94186,c_2664]) ).
tff(c_95688,plain,
! [V_2698] :
( ( cons(V_2698,'#skF_50') != '#skF_50' )
| ~ ssItem(V_2698) ),
inference(resolution,[status(thm)],[c_3128,c_95673]) ).
tff(c_95762,plain,
cons('#skF_45'('#skF_51'),'#skF_50') != '#skF_50',
inference(resolution,[status(thm)],[c_71095,c_95688]) ).
tff(c_94015,plain,
! [W_1702] :
( ssList(cons(W_1702,'#skF_50'))
| ~ ssItem(W_1702) ),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_396,c_396,c_479,c_93927]) ).
tff(c_71094,plain,
'#skF_46'('#skF_51') = '#skF_45'('#skF_51'),
inference(splitRight,[status(thm)],[c_70528]) ).
tff(c_184,plain,
! [U_888] :
( ssItem(hd(U_888))
| ( nil = U_888 )
| ~ ssList(U_888) ),
inference(cnfTransformation,[status(thm)],[f_371]) ).
tff(c_617,plain,
! [U_888] :
( ssItem(hd(U_888))
| ( U_888 = '#skF_50' )
| ~ ssList(U_888) ),
inference(demodulation,[status(thm),theory(equality)],[c_425,c_184]) ).
tff(c_1344,plain,
( ssItem('#skF_46'('#skF_51'))
| ( '#skF_51' = '#skF_50' )
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_1339,c_617]) ).
tff(c_1348,plain,
( ssItem('#skF_46'('#skF_51'))
| ( '#skF_51' = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_394,c_1344]) ).
tff(c_1349,plain,
ssItem('#skF_46'('#skF_51')),
inference(negUnitSimplification,[status(thm)],[c_443,c_1348]) ).
tff(c_307,plain,
! [U_1039] :
( strictorderedP(cons(U_1039,nil))
| ~ ssItem(U_1039) ),
inference(cnfTransformation,[status(thm)],[f_732]) ).
tff(c_515,plain,
! [U_1039] :
( strictorderedP(cons(U_1039,'#skF_50'))
| ~ ssItem(U_1039) ),
inference(demodulation,[status(thm),theory(equality)],[c_425,c_307]) ).
tff(c_2337,plain,
! [U_1281] :
( strictorderedP(U_1281)
| ~ ssItem('#skF_5'(U_1281))
| ~ singletonP(U_1281)
| ~ ssList(U_1281) ),
inference(superposition,[status(thm),theory(equality)],[c_2210,c_515]) ).
tff(c_2341,plain,
! [U_30] :
( strictorderedP(U_30)
| ~ singletonP(U_30)
| ~ ssList(U_30) ),
inference(resolution,[status(thm)],[c_24,c_2337]) ).
tff(c_315,plain,
! [U_1040,V_1042] :
( lt(U_1040,hd(V_1042))
| ( nil = V_1042 )
| ~ strictorderedP(cons(U_1040,V_1042))
| ~ ssList(V_1042)
| ~ ssItem(U_1040) ),
inference(cnfTransformation,[status(thm)],[f_749]) ).
tff(c_6696,plain,
! [U_1495,V_1496] :
( lt(U_1495,hd(V_1496))
| ( V_1496 = '#skF_50' )
| ~ strictorderedP(cons(U_1495,V_1496))
| ~ ssList(V_1496)
| ~ ssItem(U_1495) ),
inference(demodulation,[status(thm),theory(equality)],[c_425,c_315]) ).
tff(c_6729,plain,
! [U_1495] :
( lt(U_1495,'#skF_46'('#skF_51'))
| ( '#skF_51' = '#skF_50' )
| ~ strictorderedP(cons(U_1495,'#skF_51'))
| ~ ssList('#skF_51')
| ~ ssItem(U_1495) ),
inference(superposition,[status(thm),theory(equality)],[c_1339,c_6696]) ).
tff(c_6745,plain,
! [U_1495] :
( lt(U_1495,'#skF_46'('#skF_51'))
| ( '#skF_51' = '#skF_50' )
| ~ strictorderedP(cons(U_1495,'#skF_51'))
| ~ ssItem(U_1495) ),
inference(demodulation,[status(thm),theory(equality)],[c_394,c_6729]) ).
tff(c_6759,plain,
! [U_1497] :
( lt(U_1497,'#skF_46'('#skF_51'))
| ~ strictorderedP(cons(U_1497,'#skF_51'))
| ~ ssItem(U_1497) ),
inference(negUnitSimplification,[status(thm)],[c_443,c_6745]) ).
tff(c_378,plain,
! [V_1111] :
( ~ lt(V_1111,V_1111)
| ~ ssItem(V_1111) ),
inference(cnfTransformation,[status(thm)],[f_950]) ).
tff(c_6774,plain,
( ~ strictorderedP(cons('#skF_46'('#skF_51'),'#skF_51'))
| ~ ssItem('#skF_46'('#skF_51')) ),
inference(resolution,[status(thm)],[c_6759,c_378]) ).
tff(c_6789,plain,
~ strictorderedP(cons('#skF_46'('#skF_51'),'#skF_51')),
inference(demodulation,[status(thm),theory(equality)],[c_1349,c_6774]) ).
tff(c_6793,plain,
( ~ singletonP(cons('#skF_46'('#skF_51'),'#skF_51'))
| ~ ssList(cons('#skF_46'('#skF_51'),'#skF_51')) ),
inference(resolution,[status(thm)],[c_2341,c_6789]) ).
tff(c_9589,plain,
~ ssList(cons('#skF_46'('#skF_51'),'#skF_51')),
inference(splitLeft,[status(thm)],[c_6793]) ).
tff(c_9592,plain,
( ~ ssItem('#skF_46'('#skF_51'))
| ~ ssList('#skF_51') ),
inference(resolution,[status(thm)],[c_166,c_9589]) ).
tff(c_9596,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_394,c_1349,c_9592]) ).
tff(c_9598,plain,
ssList(cons('#skF_46'('#skF_51'),'#skF_51')),
inference(splitRight,[status(thm)],[c_6793]) ).
tff(c_71171,plain,
ssList(cons('#skF_45'('#skF_51'),'#skF_51')),
inference(demodulation,[status(thm),theory(equality)],[c_71094,c_9598]) ).
tff(c_356,plain,
! [U_1080] :
( ( app(U_1080,nil) = U_1080 )
| ~ ssList(U_1080) ),
inference(cnfTransformation,[status(thm)],[f_859]) ).
tff(c_500,plain,
! [U_1080] :
( ( app(U_1080,'#skF_50') = U_1080 )
| ~ ssList(U_1080) ),
inference(demodulation,[status(thm),theory(equality)],[c_425,c_356]) ).
tff(c_9657,plain,
app(cons('#skF_46'('#skF_51'),'#skF_51'),'#skF_50') = cons('#skF_46'('#skF_51'),'#skF_51'),
inference(resolution,[status(thm)],[c_9598,c_500]) ).
tff(c_71170,plain,
app(cons('#skF_45'('#skF_51'),'#skF_51'),'#skF_50') = cons('#skF_45'('#skF_51'),'#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_71094,c_71094,c_9657]) ).
tff(c_480,plain,
app('#skF_50','#skF_51') = '#skF_51',
inference(resolution,[status(thm)],[c_394,c_472]) ).
tff(c_15494,plain,
! [W_1702] :
( ( app(cons(W_1702,'#skF_50'),'#skF_51') = cons(W_1702,'#skF_51') )
| ~ ssItem(W_1702)
| ~ ssList('#skF_50')
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_480,c_15236]) ).
tff(c_15627,plain,
! [W_1702] :
( ( app(cons(W_1702,'#skF_50'),'#skF_51') = cons(W_1702,'#skF_51') )
| ~ ssItem(W_1702) ),
inference(demodulation,[status(thm),theory(equality)],[c_394,c_396,c_15494]) ).
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_13781,plain,
! [U_1674,V_1675,W_1676] :
( ( app(app(U_1674,V_1675),W_1676) = app(U_1674,app(V_1675,W_1676)) )
| ~ ssList(W_1676)
| ~ ssList(V_1675)
| ~ ssList(U_1674) ),
inference(cnfTransformation,[status(thm)],[f_844]) ).
tff(c_95785,plain,
! [U_2699,V_2700,W_2701] :
( ssList(app(U_2699,app(V_2700,W_2701)))
| ~ ssList(W_2701)
| ~ ssList(app(U_2699,V_2700))
| ~ ssList(W_2701)
| ~ ssList(V_2700)
| ~ ssList(U_2699) ),
inference(superposition,[status(thm),theory(equality)],[c_13781,c_192]) ).
tff(c_96418,plain,
! [U_2699] :
( ssList(app(U_2699,'#skF_51'))
| ~ ssList('#skF_51')
| ~ ssList(app(U_2699,'#skF_50'))
| ~ ssList('#skF_51')
| ~ ssList('#skF_50')
| ~ ssList(U_2699) ),
inference(superposition,[status(thm),theory(equality)],[c_480,c_95785]) ).
tff(c_97328,plain,
! [U_2704] :
( ssList(app(U_2704,'#skF_51'))
| ~ ssList(app(U_2704,'#skF_50'))
| ~ ssList(U_2704) ),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_394,c_394,c_96418]) ).
tff(c_112714,plain,
! [U_2837] :
( ( app(app(U_2837,'#skF_51'),'#skF_50') = app(U_2837,'#skF_51') )
| ~ ssList(app(U_2837,'#skF_50'))
| ~ ssList(U_2837) ),
inference(resolution,[status(thm)],[c_97328,c_500]) ).
tff(c_112975,plain,
! [U_896] :
( ( app(app(U_896,'#skF_51'),'#skF_50') = app(U_896,'#skF_51') )
| ~ ssList('#skF_50')
| ~ ssList(U_896) ),
inference(resolution,[status(thm)],[c_192,c_112714]) ).
tff(c_113311,plain,
! [U_2841] :
( ( app(app(U_2841,'#skF_51'),'#skF_50') = app(U_2841,'#skF_51') )
| ~ ssList(U_2841) ),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_112975]) ).
tff(c_143791,plain,
! [W_3185] :
( ( app(cons(W_3185,'#skF_51'),'#skF_50') = app(cons(W_3185,'#skF_50'),'#skF_51') )
| ~ ssList(cons(W_3185,'#skF_50'))
| ~ ssItem(W_3185) ),
inference(superposition,[status(thm),theory(equality)],[c_15627,c_113311]) ).
tff(c_143808,plain,
! [V_861] :
( ( app(cons(V_861,'#skF_51'),'#skF_50') = app(cons(V_861,'#skF_50'),'#skF_51') )
| ~ ssItem(V_861)
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_166,c_143791]) ).
tff(c_327762,plain,
! [V_4193] :
( ( app(cons(V_4193,'#skF_51'),'#skF_50') = app(cons(V_4193,'#skF_50'),'#skF_51') )
| ~ ssItem(V_4193) ),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_143808]) ).
tff(c_328154,plain,
( ( app(cons('#skF_45'('#skF_51'),'#skF_50'),'#skF_51') = cons('#skF_45'('#skF_51'),'#skF_51') )
| ~ ssItem('#skF_45'('#skF_51')) ),
inference(superposition,[status(thm),theory(equality)],[c_327762,c_71170]) ).
tff(c_328523,plain,
app(cons('#skF_45'('#skF_51'),'#skF_50'),'#skF_51') = cons('#skF_45'('#skF_51'),'#skF_51'),
inference(demodulation,[status(thm),theory(equality)],[c_71095,c_328154]) ).
tff(c_501,plain,
! [U_1169] :
( ( app(U_1169,'#skF_50') = U_1169 )
| ~ ssList(U_1169) ),
inference(demodulation,[status(thm),theory(equality)],[c_425,c_356]) ).
tff(c_510,plain,
app('#skF_51','#skF_50') = '#skF_51',
inference(resolution,[status(thm)],[c_394,c_501]) ).
tff(c_348,plain,
! [U_1070,V_1074,W_1076] :
( ( app(app(U_1070,V_1074),W_1076) = app(U_1070,app(V_1074,W_1076)) )
| ~ ssList(W_1076)
| ~ ssList(V_1074)
| ~ ssList(U_1070) ),
inference(cnfTransformation,[status(thm)],[f_844]) ).
tff(c_19765,plain,
! [W_1841,V_1842,X_1843] :
( segmentP(app(app(W_1841,V_1842),X_1843),V_1842)
| ~ ssList(X_1843)
| ~ ssList(W_1841)
| ~ ssList(V_1842)
| ~ ssList(app(app(W_1841,V_1842),X_1843)) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_209332,plain,
! [U_3619,V_3620,W_3621] :
( segmentP(app(U_3619,app(V_3620,W_3621)),V_3620)
| ~ ssList(W_3621)
| ~ ssList(U_3619)
| ~ ssList(V_3620)
| ~ ssList(app(app(U_3619,V_3620),W_3621))
| ~ ssList(W_3621)
| ~ ssList(V_3620)
| ~ ssList(U_3619) ),
inference(superposition,[status(thm),theory(equality)],[c_348,c_19765]) ).
tff(c_209926,plain,
! [U_3619] :
( segmentP(app(U_3619,'#skF_51'),'#skF_51')
| ~ ssList('#skF_50')
| ~ ssList(U_3619)
| ~ ssList('#skF_51')
| ~ ssList(app(app(U_3619,'#skF_51'),'#skF_50'))
| ~ ssList('#skF_50')
| ~ ssList('#skF_51')
| ~ ssList(U_3619) ),
inference(superposition,[status(thm),theory(equality)],[c_510,c_209332]) ).
tff(c_210270,plain,
! [U_3619] :
( segmentP(app(U_3619,'#skF_51'),'#skF_51')
| ~ ssList(app(app(U_3619,'#skF_51'),'#skF_50'))
| ~ ssList(U_3619) ),
inference(demodulation,[status(thm),theory(equality)],[c_394,c_396,c_394,c_396,c_209926]) ).
tff(c_330523,plain,
( segmentP(app(cons('#skF_45'('#skF_51'),'#skF_50'),'#skF_51'),'#skF_51')
| ~ ssList(app(cons('#skF_45'('#skF_51'),'#skF_51'),'#skF_50'))
| ~ ssList(cons('#skF_45'('#skF_51'),'#skF_50')) ),
inference(superposition,[status(thm),theory(equality)],[c_328523,c_210270]) ).
tff(c_331014,plain,
( segmentP(cons('#skF_45'('#skF_51'),'#skF_51'),'#skF_51')
| ~ ssList(cons('#skF_45'('#skF_51'),'#skF_50')) ),
inference(demodulation,[status(thm),theory(equality)],[c_71171,c_71170,c_328523,c_330523]) ).
tff(c_331593,plain,
~ ssList(cons('#skF_45'('#skF_51'),'#skF_50')),
inference(splitLeft,[status(thm)],[c_331014]) ).
tff(c_331611,plain,
~ ssItem('#skF_45'('#skF_51')),
inference(resolution,[status(thm)],[c_94015,c_331593]) ).
tff(c_331618,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_71095,c_331611]) ).
tff(c_331620,plain,
ssList(cons('#skF_45'('#skF_51'),'#skF_50')),
inference(splitRight,[status(thm)],[c_331014]) ).
tff(c_280,plain,
! [U_1032] :
( cyclefreeP(cons(U_1032,nil))
| ~ ssItem(U_1032) ),
inference(cnfTransformation,[status(thm)],[f_696]) ).
tff(c_498,plain,
! [U_1032] :
( cyclefreeP(cons(U_1032,'#skF_50'))
| ~ ssItem(U_1032) ),
inference(demodulation,[status(thm),theory(equality)],[c_425,c_280]) ).
tff(c_2784,plain,
! [U_1295] :
( cyclefreeP(U_1295)
| ~ ssItem('#skF_5'(U_1295))
| ~ singletonP(U_1295)
| ~ ssList(U_1295) ),
inference(superposition,[status(thm),theory(equality)],[c_2210,c_498]) ).
tff(c_2788,plain,
! [U_30] :
( cyclefreeP(U_30)
| ~ singletonP(U_30)
| ~ ssList(U_30) ),
inference(resolution,[status(thm)],[c_24,c_2784]) ).
tff(c_331885,plain,
( cyclefreeP(cons('#skF_45'('#skF_51'),'#skF_50'))
| ~ singletonP(cons('#skF_45'('#skF_51'),'#skF_50')) ),
inference(resolution,[status(thm)],[c_331620,c_2788]) ).
tff(c_334053,plain,
~ singletonP(cons('#skF_45'('#skF_51'),'#skF_50')),
inference(splitLeft,[status(thm)],[c_331885]) ).
tff(c_334056,plain,
~ ssItem('#skF_45'('#skF_51')),
inference(resolution,[status(thm)],[c_3128,c_334053]) ).
tff(c_334060,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_71095,c_334056]) ).
tff(c_334062,plain,
singletonP(cons('#skF_45'('#skF_51'),'#skF_50')),
inference(splitRight,[status(thm)],[c_331885]) ).
tff(c_331897,plain,
app(cons('#skF_45'('#skF_51'),'#skF_50'),'#skF_50') = cons('#skF_45'('#skF_51'),'#skF_50'),
inference(resolution,[status(thm)],[c_331620,c_500]) ).
tff(c_2209,plain,
! [U_30] :
( ( cons('#skF_5'(U_30),'#skF_50') = U_30 )
| ~ singletonP(U_30)
| ~ ssList(U_30) ),
inference(demodulation,[status(thm),theory(equality)],[c_425,c_22]) ).
tff(c_15855,plain,
! [W_1719] :
( ( app(cons(W_1719,'#skF_50'),'#skF_50') = cons(W_1719,'#skF_50') )
| ~ ssItem(W_1719) ),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_396,c_15497]) ).
tff(c_43510,plain,
! [U_2200] :
( ( cons('#skF_5'(U_2200),'#skF_50') = app(U_2200,'#skF_50') )
| ~ ssItem('#skF_5'(U_2200))
| ~ singletonP(U_2200)
| ~ ssList(U_2200) ),
inference(superposition,[status(thm),theory(equality)],[c_2209,c_15855]) ).
tff(c_45418,plain,
! [U_2208] :
( ( cons('#skF_5'(U_2208),'#skF_50') = app(U_2208,'#skF_50') )
| ~ singletonP(U_2208)
| ~ ssList(U_2208) ),
inference(resolution,[status(thm)],[c_24,c_43510]) ).
tff(c_288,plain,
! [U_1034] :
( strictorderP(cons(U_1034,nil))
| ~ ssItem(U_1034) ),
inference(cnfTransformation,[status(thm)],[f_706]) ).
tff(c_491,plain,
! [U_1034] :
( strictorderP(cons(U_1034,'#skF_50'))
| ~ ssItem(U_1034) ),
inference(demodulation,[status(thm),theory(equality)],[c_425,c_288]) ).
tff(c_45605,plain,
! [U_2208] :
( strictorderP(app(U_2208,'#skF_50'))
| ~ ssItem('#skF_5'(U_2208))
| ~ singletonP(U_2208)
| ~ ssList(U_2208) ),
inference(superposition,[status(thm),theory(equality)],[c_45418,c_491]) ).
tff(c_334551,plain,
( strictorderP(cons('#skF_45'('#skF_51'),'#skF_50'))
| ~ ssItem('#skF_5'(cons('#skF_45'('#skF_51'),'#skF_50')))
| ~ singletonP(cons('#skF_45'('#skF_51'),'#skF_50'))
| ~ ssList(cons('#skF_45'('#skF_51'),'#skF_50')) ),
inference(superposition,[status(thm),theory(equality)],[c_331897,c_45605]) ).
tff(c_335058,plain,
( strictorderP(cons('#skF_45'('#skF_51'),'#skF_50'))
| ~ ssItem('#skF_5'(cons('#skF_45'('#skF_51'),'#skF_50'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_331620,c_334062,c_334551]) ).
tff(c_343928,plain,
~ ssItem('#skF_5'(cons('#skF_45'('#skF_51'),'#skF_50'))),
inference(splitLeft,[status(thm)],[c_335058]) ).
tff(c_343931,plain,
( ~ singletonP(cons('#skF_45'('#skF_51'),'#skF_50'))
| ~ ssList(cons('#skF_45'('#skF_51'),'#skF_50')) ),
inference(resolution,[status(thm)],[c_24,c_343928]) ).
tff(c_343935,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_331620,c_334062,c_343931]) ).
tff(c_343937,plain,
ssItem('#skF_5'(cons('#skF_45'('#skF_51'),'#skF_50'))),
inference(splitRight,[status(thm)],[c_335058]) ).
tff(c_292,plain,
! [U_1035] :
( totalorderedP(cons(U_1035,nil))
| ~ ssItem(U_1035) ),
inference(cnfTransformation,[status(thm)],[f_711]) ).
tff(c_495,plain,
! [U_1035] :
( totalorderedP(cons(U_1035,'#skF_50'))
| ~ ssItem(U_1035) ),
inference(demodulation,[status(thm),theory(equality)],[c_425,c_292]) ).
tff(c_45599,plain,
! [U_2208] :
( totalorderedP(app(U_2208,'#skF_50'))
| ~ ssItem('#skF_5'(U_2208))
| ~ singletonP(U_2208)
| ~ ssList(U_2208) ),
inference(superposition,[status(thm),theory(equality)],[c_45418,c_495]) ).
tff(c_334548,plain,
( totalorderedP(cons('#skF_45'('#skF_51'),'#skF_50'))
| ~ ssItem('#skF_5'(cons('#skF_45'('#skF_51'),'#skF_50')))
| ~ singletonP(cons('#skF_45'('#skF_51'),'#skF_50'))
| ~ ssList(cons('#skF_45'('#skF_51'),'#skF_50')) ),
inference(superposition,[status(thm),theory(equality)],[c_331897,c_45599]) ).
tff(c_335056,plain,
( totalorderedP(cons('#skF_45'('#skF_51'),'#skF_50'))
| ~ ssItem('#skF_5'(cons('#skF_45'('#skF_51'),'#skF_50'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_331620,c_334062,c_334548]) ).
tff(c_345253,plain,
totalorderedP(cons('#skF_45'('#skF_51'),'#skF_50')),
inference(demodulation,[status(thm),theory(equality)],[c_343937,c_335056]) ).
tff(c_2468,plain,
! [U_880] :
( ( cons('#skF_45'(U_880),'#skF_44'(U_880)) = U_880 )
| ( U_880 = '#skF_50' )
| ~ ssList(U_880) ),
inference(demodulation,[status(thm),theory(equality)],[c_425,c_176]) ).
tff(c_26,plain,
! [V_40,W_43] :
( frontsegP(app(V_40,W_43),V_40)
| ~ ssList(W_43)
| ~ ssList(V_40)
| ~ ssList(app(V_40,W_43)) ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_334672,plain,
( frontsegP(cons('#skF_45'('#skF_51'),'#skF_50'),cons('#skF_45'('#skF_51'),'#skF_50'))
| ~ ssList('#skF_50')
| ~ ssList(cons('#skF_45'('#skF_51'),'#skF_50'))
| ~ ssList(app(cons('#skF_45'('#skF_51'),'#skF_50'),'#skF_50')) ),
inference(superposition,[status(thm),theory(equality)],[c_331897,c_26]) ).
tff(c_335158,plain,
frontsegP(cons('#skF_45'('#skF_51'),'#skF_50'),cons('#skF_45'('#skF_51'),'#skF_50')),
inference(demodulation,[status(thm),theory(equality)],[c_331620,c_331897,c_331620,c_396,c_334672]) ).
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_5646,plain,
! [V_1069,U_1067] :
( ( app(cons(V_1069,'#skF_50'),U_1067) = cons(V_1069,U_1067) )
| ~ ssItem(V_1069)
| ~ ssList(U_1067) ),
inference(demodulation,[status(thm),theory(equality)],[c_425,c_346]) ).
tff(c_8126,plain,
! [U_1517,W_1518,V_1519] :
( frontsegP(app(U_1517,W_1518),V_1519)
| ~ frontsegP(U_1517,V_1519)
| ~ ssList(W_1518)
| ~ ssList(V_1519)
| ~ ssList(U_1517) ),
inference(cnfTransformation,[status(thm)],[f_560]) ).
tff(c_8137,plain,
! [V_1069,U_1067,V_1519] :
( frontsegP(cons(V_1069,U_1067),V_1519)
| ~ frontsegP(cons(V_1069,'#skF_50'),V_1519)
| ~ ssList(U_1067)
| ~ ssList(V_1519)
| ~ ssList(cons(V_1069,'#skF_50'))
| ~ ssItem(V_1069)
| ~ ssList(U_1067) ),
inference(superposition,[status(thm),theory(equality)],[c_5646,c_8126]) ).
tff(c_337182,plain,
! [U_1067] :
( frontsegP(cons('#skF_45'('#skF_51'),U_1067),cons('#skF_45'('#skF_51'),'#skF_50'))
| ~ ssList(cons('#skF_45'('#skF_51'),'#skF_50'))
| ~ ssItem('#skF_45'('#skF_51'))
| ~ ssList(U_1067) ),
inference(resolution,[status(thm)],[c_335158,c_8137]) ).
tff(c_349016,plain,
! [U_4308] :
( frontsegP(cons('#skF_45'('#skF_51'),U_4308),cons('#skF_45'('#skF_51'),'#skF_50'))
| ~ ssList(U_4308) ),
inference(demodulation,[status(thm),theory(equality)],[c_71095,c_331620,c_337182]) ).
tff(c_349101,plain,
( frontsegP('#skF_51',cons('#skF_45'('#skF_51'),'#skF_50'))
| ~ ssList('#skF_44'('#skF_51'))
| ( '#skF_51' = '#skF_50' )
| ~ ssList('#skF_51') ),
inference(superposition,[status(thm),theory(equality)],[c_2468,c_349016]) ).
tff(c_349182,plain,
( frontsegP('#skF_51',cons('#skF_45'('#skF_51'),'#skF_50'))
| ( '#skF_51' = '#skF_50' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_394,c_1162,c_70431,c_349101]) ).
tff(c_349183,plain,
frontsegP('#skF_51',cons('#skF_45'('#skF_51'),'#skF_50')),
inference(negUnitSimplification,[status(thm)],[c_443,c_349182]) ).
tff(c_2261,plain,
! [U_1270,V_1271] :
( neq(U_1270,V_1271)
| ( V_1271 = U_1270 )
| ~ ssList(V_1271)
| ~ ssList(U_1270) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_274,plain,
! [U_1030] :
( segmentP(U_1030,nil)
| ~ ssList(U_1030) ),
inference(cnfTransformation,[status(thm)],[f_686]) ).
tff(c_465,plain,
! [U_1160] :
( segmentP(U_1160,'#skF_50')
| ~ ssList(U_1160) ),
inference(demodulation,[status(thm),theory(equality)],[c_425,c_274]) ).
tff(c_384,plain,
! [Y_1148] :
( ~ totalorderedP(Y_1148)
| ~ segmentP(Y_1148,'#skF_50')
| ~ frontsegP('#skF_51',Y_1148)
| ~ neq('#skF_50',Y_1148)
| ~ ssList(Y_1148) ),
inference(cnfTransformation,[status(thm)],[f_1021]) ).
tff(c_469,plain,
! [U_1160] :
( ~ totalorderedP(U_1160)
| ~ frontsegP('#skF_51',U_1160)
| ~ neq('#skF_50',U_1160)
| ~ ssList(U_1160) ),
inference(resolution,[status(thm)],[c_465,c_384]) ).
tff(c_2265,plain,
! [V_1271] :
( ~ totalorderedP(V_1271)
| ~ frontsegP('#skF_51',V_1271)
| ( V_1271 = '#skF_50' )
| ~ ssList(V_1271)
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_2261,c_469]) ).
tff(c_2279,plain,
! [V_1271] :
( ~ totalorderedP(V_1271)
| ~ frontsegP('#skF_51',V_1271)
| ( V_1271 = '#skF_50' )
| ~ ssList(V_1271) ),
inference(demodulation,[status(thm),theory(equality)],[c_396,c_2265]) ).
tff(c_349214,plain,
( ~ totalorderedP(cons('#skF_45'('#skF_51'),'#skF_50'))
| ( cons('#skF_45'('#skF_51'),'#skF_50') = '#skF_50' )
| ~ ssList(cons('#skF_45'('#skF_51'),'#skF_50')) ),
inference(resolution,[status(thm)],[c_349183,c_2279]) ).
tff(c_349258,plain,
cons('#skF_45'('#skF_51'),'#skF_50') = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_331620,c_345253,c_349214]) ).
tff(c_349260,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_95762,c_349258]) ).
tff(c_349261,plain,
nil = '#skF_51',
inference(splitRight,[status(thm)],[c_415]) ).
tff(c_349262,plain,
nil != '#skF_50',
inference(splitRight,[status(thm)],[c_415]) ).
tff(c_349277,plain,
'#skF_51' != '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_349261,c_349262]) ).
tff(c_388,plain,
frontsegP('#skF_51','#skF_50'),
inference(cnfTransformation,[status(thm)],[f_1021]) ).
tff(c_250,plain,
! [U_983] :
( ( nil = U_983 )
| ~ frontsegP(nil,U_983)
| ~ ssList(U_983) ),
inference(cnfTransformation,[status(thm)],[f_587]) ).
tff(c_349352,plain,
! [U_4331] :
( ( U_4331 = '#skF_51' )
| ~ frontsegP('#skF_51',U_4331)
| ~ ssList(U_4331) ),
inference(demodulation,[status(thm),theory(equality)],[c_349261,c_349261,c_250]) ).
tff(c_349363,plain,
( ( '#skF_51' = '#skF_50' )
| ~ ssList('#skF_50') ),
inference(resolution,[status(thm)],[c_388,c_349352]) ).
tff(c_349374,plain,
'#skF_51' = '#skF_50',
inference(demodulation,[status(thm),theory(equality)],[c_396,c_349363]) ).
tff(c_349376,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_349277,c_349374]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SWC031+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.15 % 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
% 0.16/0.36 % Computer : n002.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu Aug 3 21:50:01 EDT 2023
% 0.16/0.36 % CPUTime :
% 242.92/209.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 242.92/209.77
% 242.92/209.77 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 242.92/209.82
% 242.92/209.82 Inference rules
% 242.92/209.82 ----------------------
% 242.92/209.82 #Ref : 27
% 242.92/209.82 #Sup : 77542
% 242.92/209.82 #Fact : 18
% 242.92/209.82 #Define : 0
% 242.92/209.82 #Split : 109
% 242.92/209.82 #Chain : 0
% 242.92/209.82 #Close : 0
% 242.92/209.82
% 242.92/209.83 Ordering : KBO
% 242.92/209.83
% 242.92/209.83 Simplification rules
% 242.92/209.83 ----------------------
% 242.92/209.83 #Subsume : 19221
% 242.92/209.83 #Demod : 89504
% 242.92/209.83 #Tautology : 11242
% 242.92/209.83 #SimpNegUnit : 8080
% 242.92/209.83 #BackRed : 495
% 242.92/209.83
% 242.92/209.83 #Partial instantiations: 0
% 242.92/209.83 #Strategies tried : 1
% 242.92/209.83
% 242.92/209.83 Timing (in seconds)
% 242.92/209.83 ----------------------
% 242.92/209.83 Preprocessing : 0.87
% 242.92/209.83 Parsing : 0.40
% 242.92/209.83 CNF conversion : 0.11
% 242.92/209.83 Main loop : 207.82
% 242.92/209.83 Inferencing : 21.01
% 242.92/209.83 Reduction : 98.01
% 242.92/209.83 Demodulation : 67.85
% 242.92/209.83 BG Simplification : 0.61
% 242.92/209.83 Subsumption : 67.31
% 242.92/209.83 Abstraction : 1.13
% 242.92/209.83 MUC search : 0.00
% 242.92/209.83 Cooper : 0.00
% 242.92/209.83 Total : 208.79
% 242.92/209.83 Index Insertion : 0.00
% 242.92/209.83 Index Deletion : 0.00
% 242.92/209.83 Index Matching : 0.00
% 242.92/209.83 BG Taut test : 0.00
%------------------------------------------------------------------------------