%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWC002-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:51:43 AM UTC 2026
% Result : Unsatisfiable 112.39s 38.36s
% Output : Refutation 104.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 213
% Syntax : Number of formulae : 1390 ( 415 unt; 0 typ; 0 def)
% Number of atoms : 4584 ( 981 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 12028 (2552 ~;2322 |; 0 &;7154 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 79 ( 76 usr; 12 con; 0-3 aty)
% Number of variables : 1875 ( 0 ^;1875 !; 0 ?;1875 :)
% Comments :
%------------------------------------------------------------------------------
thf(ssList_decl,type,
ssList: $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(neq_decl,type,
neq: $i > $i > $o ).
thf(nil_decl,type,
nil: $i ).
thf(ssItem_decl,type,
ssItem: $i > $o ).
thf(app_decl,type,
app: $i > $i > $i ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i > $i ).
thf(memberP_decl,type,
memberP: $i > $i > $o ).
thf(geq_decl,type,
geq: $i > $i > $o ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(skac3_decl,type,
skac3: $i ).
thf(skac2_decl,type,
skac2: $i ).
thf(skaf43_decl,type,
skaf43: $i > $i > $i ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(totalorderedP_decl,type,
totalorderedP: $i > $o ).
thf(lt_decl,type,
lt: $i > $i > $o ).
thf(gt_decl,type,
gt: $i > $i > $o ).
thf(skaf62_decl,type,
skaf62: $i > $i ).
thf(skaf69_decl,type,
skaf69: $i > $i ).
thf(skaf70_decl,type,
skaf70: $i > $i ).
thf(strictorderedP_decl,type,
strictorderedP: $i > $o ).
thf(cyclefreeP_decl,type,
cyclefreeP: $i > $o ).
thf(skaf49_decl,type,
skaf49: $i > $i ).
thf(skaf50_decl,type,
skaf50: $i > $i ).
thf(singletonP_decl,type,
singletonP: $i > $o ).
thf(skaf44_decl,type,
skaf44: $i > $i ).
thf(duplicatefreeP_decl,type,
duplicatefreeP: $i > $o ).
thf(skaf75_decl,type,
skaf75: $i > $i ).
thf(skaf74_decl,type,
skaf74: $i > $i ).
thf(skaf76_decl,type,
skaf76: $i > $i ).
thf(skaf77_decl,type,
skaf77: $i > $i ).
thf(skaf72_decl,type,
skaf72: $i > $i ).
thf(skaf79_decl,type,
skaf79: $i > $i ).
thf(hd_decl,type,
hd: $i > $i ).
thf(frontsegP_decl,type,
frontsegP: $i > $i > $o ).
thf(skaf71_decl,type,
skaf71: $i > $i ).
thf(skaf73_decl,type,
skaf73: $i > $i ).
thf(skaf46_decl,type,
skaf46: $i > $i > $i ).
thf(skaf64_decl,type,
skaf64: $i > $i ).
thf(tl_decl,type,
tl: $i > $i ).
thf(skaf66_decl,type,
skaf66: $i > $i ).
thf(skaf67_decl,type,
skaf67: $i > $i ).
thf(skaf65_decl,type,
skaf65: $i > $i ).
thf(skaf68_decl,type,
skaf68: $i > $i ).
thf(skaf45_decl,type,
skaf45: $i > $i > $i ).
thf(rearsegP_decl,type,
rearsegP: $i > $i > $o ).
thf(strictorderP_decl,type,
strictorderP: $i > $o ).
thf(skaf61_decl,type,
skaf61: $i > $i ).
thf(skaf59_decl,type,
skaf59: $i > $i ).
thf(skaf60_decl,type,
skaf60: $i > $i ).
thf(skaf63_decl,type,
skaf63: $i > $i ).
thf(skaf51_decl,type,
skaf51: $i > $i ).
thf(skaf52_decl,type,
skaf52: $i > $i ).
thf(skaf53_decl,type,
skaf53: $i > $i ).
thf(skaf57_decl,type,
skaf57: $i > $i ).
thf(equalelemsP_decl,type,
equalelemsP: $i > $o ).
thf(totalorderP_decl,type,
totalorderP: $i > $o ).
thf(skaf56_decl,type,
skaf56: $i > $i ).
thf(skaf54_decl,type,
skaf54: $i > $i ).
thf(skaf55_decl,type,
skaf55: $i > $i ).
thf(skaf58_decl,type,
skaf58: $i > $i ).
thf(skaf48_decl,type,
skaf48: $i > $i > $i ).
thf(segmentP_decl,type,
segmentP: $i > $i > $o ).
thf(skaf80_decl,type,
skaf80: $i > $i ).
thf(skaf47_decl,type,
skaf47: $i > $i > $i ).
thf(skaf78_decl,type,
skaf78: $i > $i ).
thf(skaf81_decl,type,
skaf81: $i > $i ).
thf(skaf83_decl,type,
skaf83: $i > $i ).
thf(skaf82_decl,type,
skaf82: $i > $i ).
thf(skaf42_decl,type,
skaf42: $i > $i > $i ).
thf(188,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D = B )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ( ( B @ ( A @ cons ) )
!= ( D @ ( C @ cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause171) ).
thf(645,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D = B )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ( ( B @ ( A @ cons ) )
!= ( D @ ( C @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(101,axiom,
! [A: $i] : ( A @ skaf69 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause26) ).
thf(452,plain,
! [A: $i] : ( A @ skaf69 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(123,axiom,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( nil @ memberP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause71) ).
thf(495,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(496,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(cnf,[status(esa)],[495]) ).
thf(1317,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[452,496]) ).
thf(1318,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1317]) ).
thf(1319,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1318:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(1322,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1319]) ).
thf(65,axiom,
! [A: $i] :
( ( ( A @ skaf53 @ ( A @ skaf50 @ cons ) @ ( A @ skaf52 @ ( A @ skaf49 @ cons ) @ ( A @ skaf51 @ app ) @ app ) )
= A )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause167) ).
thf(363,plain,
! [A: $i] :
( ( ( A @ skaf53 @ ( A @ skaf50 @ cons ) @ ( A @ skaf52 @ ( A @ skaf49 @ cons ) @ ( A @ skaf51 @ app ) @ app ) )
= A )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(364,plain,
! [A: $i] :
( ( ( A @ skaf53 @ ( A @ skaf50 @ cons ) @ ( A @ skaf52 @ ( A @ skaf49 @ cons ) @ ( A @ skaf51 @ app ) @ app ) )
= A )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[363]) ).
thf(365,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ~ ( A @ ssList )
| ( ( A @ skaf53 @ ( A @ skaf50 @ cons ) @ ( A @ skaf52 @ ( A @ skaf49 @ cons ) @ ( A @ skaf51 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[364]) ).
thf(133,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ssList )
| ~ ( E @ duplicatefreeP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ( ( D @ ( B @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause179) ).
thf(518,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ssList )
| ~ ( E @ duplicatefreeP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ( ( D @ ( B @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(24,negated_conjecture,
( ~ ( nil @ ( sk4 @ neq ) )
| ( sk7 @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_24) ).
thf(234,plain,
( ~ ( nil @ ( sk4 @ neq ) )
| ( sk7 @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(70,axiom,
! [A: $i] : ( A @ skaf57 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause38) ).
thf(375,plain,
! [A: $i] : ( A @ skaf57 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause115) ).
thf(291,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(292,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[291]) ).
thf(293,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[292]) ).
thf(294,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[293]) ).
thf(935,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[375,294]) ).
thf(936,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[935]) ).
thf(937,plain,
! [A: $i] :
~ ( A @ skaf57 @ ( A @ skaf57 @ neq ) ),
inference(pattern_uni,[status(thm)],[936:[bind(A,$thf( C )),bind(B,$thf( C @ skaf57 ))]]) ).
thf(941,plain,
! [A: $i] :
~ ( A @ skaf57 @ ( A @ skaf57 @ neq ) ),
inference(simp,[status(thm)],[937]) ).
thf(88,axiom,
! [A: $i] : ( A @ skaf44 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause47) ).
thf(419,plain,
! [A: $i] : ( A @ skaf44 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(1174,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[419,496]) ).
thf(1175,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1174]) ).
thf(1176,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1175:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(1179,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1176]) ).
thf(149,axiom,
! [A: $i] : ( A @ skaf67 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause28) ).
thf(555,plain,
! [A: $i] : ( A @ skaf67 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(199,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause86) ).
thf(666,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(66,axiom,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause82) ).
thf(366,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(367,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
inference(cnf,[status(esa)],[366]) ).
thf(368,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[367]) ).
thf(7,negated_conjecture,
( ( nil @ ( sk2 @ neq ) )
| ( nil @ ( sk2 @ neq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
thf(225,plain,
nil @ ( sk2 @ neq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(57,axiom,
nil @ ssList,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
thf(345,plain,
nil @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(709,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[345,294]) ).
thf(710,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[709]) ).
thf(711,plain,
~ ( nil @ ( nil @ neq ) ),
inference(pattern_uni,[status(thm)],[710:[bind(A,$thf( nil ))]]) ).
thf(776,plain,
( ( ( nil @ ( nil @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[225,711]) ).
thf(777,plain,
( ( nil @ ( nil @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[776]) ).
thf(778,plain,
( ( nil != nil )
| ( nil != sk2 ) ),
inference(simp,[status(thm)],[777]) ).
thf(779,plain,
nil != sk2,
inference(simp,[status(thm)],[778]) ).
thf(26613,plain,
! [A: $i] :
( ( nil != nil )
| ( A != sk2 )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[368,779]) ).
thf(26614,plain,
! [A: $i] :
( ( A != sk2 )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[26613:[]]) ).
thf(28484,plain,
( ~ ( sk2 @ ssList )
| ~ ( sk2 @ ( nil @ rearsegP ) ) ),
inference(simp,[status(thm)],[26614]) ).
thf(2,negated_conjecture,
sk2 @ ssList,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).
thf(222,plain,
sk2 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(28641,plain,
( ~ $true
| ~ ( sk2 @ ( nil @ rearsegP ) ) ),
inference(rewrite,[status(thm)],[28484,222]) ).
thf(28642,plain,
~ ( sk2 @ ( nil @ rearsegP ) ),
inference(simp,[status(thm)],[28641]) ).
thf(1,negated_conjecture,
sk1 @ ssList,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
thf(218,plain,
sk1 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(54,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause75) ).
thf(335,plain,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(336,plain,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[335]) ).
thf(337,plain,
! [A: $i] :
( ( A @ tl @ ssList )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[336]) ).
thf(17584,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[218,337]) ).
thf(17585,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[17584]) ).
thf(17586,plain,
( ( sk1 @ tl @ ssList )
| ( nil = sk1 ) ),
inference(pattern_uni,[status(thm)],[17585:[bind(A,$thf( sk1 ))]]) ).
thf(712,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[218,294]) ).
thf(713,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[712]) ).
thf(714,plain,
~ ( sk1 @ ( sk1 @ neq ) ),
inference(pattern_uni,[status(thm)],[713:[bind(A,$thf( sk1 ))]]) ).
thf(723,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk1 @ ( sk1 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[225,714]) ).
thf(724,plain,
( ( nil @ ( sk2 @ neq ) )
!= ( sk1 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[723]) ).
thf(725,plain,
( ( nil != sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[724]) ).
thf(19073,plain,
( ( nil != nil )
| ( sk1 != sk1 )
| ( sk2 != sk1 )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[17586,725]) ).
thf(19074,plain,
( ( nil != nil )
| ( sk2 != sk1 )
| ( sk1 @ tl @ ssList ) ),
inference(simp,[status(thm)],[19073]) ).
thf(19075,plain,
( ( sk2 != sk1 )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[19074:[]]) ).
thf(24713,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) )
| ( sk2 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[19075,294]) ).
thf(24714,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[24713]) ).
thf(24715,plain,
( ~ ( sk1 @ tl @ ( sk1 @ tl @ neq ) )
| ( sk2 != sk1 ) ),
inference(pattern_uni,[status(thm)],[24714:[bind(A,$thf( sk1 @ tl ))]]) ).
thf(163,axiom,
! [A: $i] : ( A @ skaf51 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause44) ).
thf(593,plain,
! [A: $i] : ( A @ skaf51 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(59,axiom,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause58) ).
thf(349,plain,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(350,plain,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[349]) ).
thf(8860,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[593,350]) ).
thf(8861,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[8860]) ).
thf(8862,plain,
! [A: $i] : ( nil @ ( A @ skaf51 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[8861:[bind(A,$thf( C )),bind(B,$thf( C @ skaf51 ))]]) ).
thf(8960,plain,
! [A: $i] : ( nil @ ( A @ skaf51 @ rearsegP ) ),
inference(simp,[status(thm)],[8862]) ).
thf(8928,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[218,350]) ).
thf(8929,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[8928]) ).
thf(8930,plain,
nil @ ( sk1 @ rearsegP ),
inference(pattern_uni,[status(thm)],[8929:[bind(A,$thf( sk1 ))]]) ).
thf(25,negated_conjecture,
( ~ ( nil @ ( sk4 @ neq ) )
| ( sk8 @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_25) ).
thf(235,plain,
( ~ ( nil @ ( sk4 @ neq ) )
| ( sk8 @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(273,plain,
( ~ ( nil @ ( sk4 @ neq ) )
| ( sk8 @ ssList ) ),
inference(cnf,[status(esa)],[235]) ).
thf(5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
thf(214,plain,
sk2 = sk4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(274,plain,
sk4 = sk2,
inference(lifteq,[status(thm)],[214]) ).
thf(1222,plain,
( ~ ( nil @ ( sk2 @ neq ) )
| ( sk8 @ ssList ) ),
inference(rewrite,[status(thm)],[273,274]) ).
thf(1223,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true
| ( sk8 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[225,1222]) ).
thf(1224,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( sk8 @ ssList ) ),
inference(simp,[status(thm)],[1223]) ).
thf(1225,plain,
sk8 @ ssList,
inference(pattern_uni,[status(thm)],[1224:[]]) ).
thf(40,axiom,
! [A: $i] :
( ( ( nil @ ( A @ skaf44 @ cons ) )
= A )
| ~ ( A @ ssList )
| ~ ( A @ singletonP ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause101) ).
thf(304,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf44 @ cons ) )
= A )
| ~ ( A @ ssList )
| ~ ( A @ singletonP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(305,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf44 @ cons ) )
= A )
| ~ ( A @ ssList )
| ~ ( A @ singletonP ) ),
inference(cnf,[status(esa)],[304]) ).
thf(306,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(lifteq,[status(thm)],[305]) ).
thf(5598,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[1225,306]) ).
thf(5599,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(simp,[status(thm)],[5598]) ).
thf(5600,plain,
( ~ ( sk8 @ singletonP )
| ( ( nil @ ( sk8 @ skaf44 @ cons ) )
= sk8 ) ),
inference(pattern_uni,[status(thm)],[5599:[bind(A,$thf( sk8 ))]]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause113) ).
thf(285,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(286,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(cnf,[status(esa)],[285]) ).
thf(287,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[286]) ).
thf(288,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[287]) ).
thf(3704,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ $true ),
inference(rewrite,[status(thm)],[288,345]) ).
thf(3705,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[3704]) ).
thf(3757,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[419,3705]) ).
thf(3758,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[3757]) ).
thf(3759,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[3758:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(3792,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[3759]) ).
thf(8029,plain,
! [A: $i] :
( ( ( nil @ ( sk8 @ skaf44 @ cons ) )
!= ( nil @ ( A @ skaf44 @ cons ) ) )
| ( sk8 @ totalorderedP )
| ~ ( sk8 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[5600,3792]) ).
thf(8030,plain,
( ( sk8 @ totalorderedP )
| ~ ( sk8 @ singletonP ) ),
inference(pattern_uni,[status(thm)],[8029:[bind(A,$thf( sk8 ))]]) ).
thf(23,negated_conjecture,
( ~ ( nil @ ( sk4 @ neq ) )
| ( sk6 @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_23) ).
thf(241,plain,
( ~ ( nil @ ( sk4 @ neq ) )
| ( sk6 @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(270,plain,
( ~ ( nil @ ( sk4 @ neq ) )
| ( sk6 @ ssItem ) ),
inference(cnf,[status(esa)],[241]) ).
thf(950,plain,
( ~ ( nil @ ( sk2 @ neq ) )
| ( sk6 @ ssItem ) ),
inference(rewrite,[status(thm)],[270,274]) ).
thf(951,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true
| ( sk6 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[225,950]) ).
thf(952,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( sk6 @ ssItem ) ),
inference(simp,[status(thm)],[951]) ).
thf(953,plain,
sk6 @ ssItem,
inference(pattern_uni,[status(thm)],[952:[]]) ).
thf(960,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[953,496]) ).
thf(961,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[960]) ).
thf(962,plain,
~ ( sk6 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[961:[bind(A,$thf( sk6 ))]]) ).
thf(85,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ skaf46 ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause131) ).
thf(408,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ skaf46 ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(83,axiom,
! [A: $i] : ( A @ skaf58 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause37) ).
thf(405,plain,
! [A: $i] : ( A @ skaf58 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(1154,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[405,294]) ).
thf(1155,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1154]) ).
thf(1156,plain,
! [A: $i] :
~ ( A @ skaf58 @ ( A @ skaf58 @ neq ) ),
inference(pattern_uni,[status(thm)],[1155:[bind(A,$thf( C )),bind(B,$thf( C @ skaf58 ))]]) ).
thf(1158,plain,
! [A: $i] :
~ ( A @ skaf58 @ ( A @ skaf58 @ neq ) ),
inference(simp,[status(thm)],[1156]) ).
thf(165,axiom,
skac3 @ ssItem,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause9) ).
thf(596,plain,
skac3 @ ssItem,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(28,negated_conjecture,
! [A: $i] :
( ~ ( nil @ ( sk4 @ neq ) )
| ~ ( sk6 @ ( A @ geq ) )
| ~ ( A @ ( sk4 @ memberP ) )
| ( sk6 = A )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_28) ).
thf(236,plain,
! [A: $i] :
( ~ ( nil @ ( sk4 @ neq ) )
| ~ ( sk6 @ ( A @ geq ) )
| ~ ( A @ ( sk4 @ memberP ) )
| ( sk6 = A )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(250,plain,
! [A: $i] :
( ~ ( nil @ ( sk4 @ neq ) )
| ~ ( sk6 @ ( A @ geq ) )
| ~ ( A @ ( sk4 @ memberP ) )
| ( sk6 = A )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[236]) ).
thf(251,plain,
! [A: $i] :
( ~ ( nil @ ( sk4 @ neq ) )
| ~ ( sk6 @ ( A @ geq ) )
| ~ ( A @ ( sk4 @ memberP ) )
| ~ ( A @ ssItem )
| ( sk6 = A ) ),
inference(lifteq,[status(thm)],[250]) ).
thf(965,plain,
! [A: $i] :
( ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk6 @ ( A @ geq ) )
| ~ ( A @ ( sk2 @ memberP ) )
| ~ ( A @ ssItem )
| ( sk6 = A ) ),
inference(rewrite,[status(thm)],[251,274]) ).
thf(242,plain,
( ~ ( nil @ ( sk4 @ neq ) )
| ( sk7 @ ssList ) ),
inference(cnf,[status(esa)],[234]) ).
thf(703,plain,
( ~ ( nil @ ( sk2 @ neq ) )
| ( sk7 @ ssList ) ),
inference(rewrite,[status(thm)],[242,274]) ).
thf(704,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true
| ( sk7 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[225,703]) ).
thf(705,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( sk7 @ ssList ) ),
inference(simp,[status(thm)],[704]) ).
thf(706,plain,
sk7 @ ssList,
inference(pattern_uni,[status(thm)],[705:[]]) ).
thf(720,plain,
! [A: $i] :
( ( ( sk7 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[706,294]) ).
thf(721,plain,
! [A: $i] :
( ( ( sk7 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[720]) ).
thf(722,plain,
~ ( sk7 @ ( sk7 @ neq ) ),
inference(pattern_uni,[status(thm)],[721:[bind(A,$thf( sk7 ))]]) ).
thf(1074,plain,
! [A: $i] :
( ( A != sk7 )
| ~ ( sk7 @ ( sk6 @ neq ) )
| ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk6 @ ( A @ geq ) )
| ~ ( A @ ( sk2 @ memberP ) )
| ~ ( A @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[965,722]) ).
thf(1075,plain,
( ~ ( sk7 @ ( sk6 @ neq ) )
| ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) )
| ~ ( sk7 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[1074:[bind(A,$thf( sk7 ))]]) ).
thf(5053,plain,
( ~ ( sk7 @ ( sk6 @ neq ) )
| ~ $true
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) )
| ~ ( sk7 @ ssItem ) ),
inference(rewrite,[status(thm)],[1075,225]) ).
thf(5054,plain,
( ~ ( sk7 @ ( sk6 @ neq ) )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) )
| ~ ( sk7 @ ssItem ) ),
inference(simp,[status(thm)],[5053]) ).
thf(5124,plain,
( ( ( skac3 @ ssItem )
!= ( sk7 @ ssItem ) )
| ~ ( sk7 @ ( sk6 @ neq ) )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[596,5054]) ).
thf(5125,plain,
( ( ( skac3 @ ssItem )
!= ( sk7 @ ssItem ) )
| ~ ( sk7 @ ( sk6 @ neq ) )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[5124]) ).
thf(5141,plain,
( ( skac3 != sk7 )
| ~ ( sk7 @ ( sk6 @ neq ) )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[5125]) ).
thf(159,axiom,
skac2 @ ssItem,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause10) ).
thf(583,plain,
skac2 @ ssItem,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(5073,plain,
( ( ( skac2 @ ssItem )
!= ( sk7 @ ssItem ) )
| ~ ( sk7 @ ( sk6 @ neq ) )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[583,5054]) ).
thf(5074,plain,
( ( ( skac2 @ ssItem )
!= ( sk7 @ ssItem ) )
| ~ ( sk7 @ ( sk6 @ neq ) )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[5073]) ).
thf(5143,plain,
( ( skac2 != sk7 )
| ~ ( sk7 @ ( sk6 @ neq ) )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[5074]) ).
thf(5795,plain,
( ( ( sk7 @ ( sk6 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( skac2 != sk7 )
| ~ $true
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[225,5143]) ).
thf(5796,plain,
( ( ( sk7 @ ( sk6 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( skac2 != sk7 )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[5795]) ).
thf(5820,plain,
( ( sk7 != nil )
| ( sk6 != sk2 )
| ( skac2 != sk7 )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[5796]) ).
thf(20,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( nil @ ( sk4 @ neq ) )
| ( A @ ( B @ ( C @ sk5 ) ) @ ( sk2 @ memberP ) )
| ( ( C @ ( B @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_20) ).
thf(217,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( nil @ ( sk4 @ neq ) )
| ( A @ ( B @ ( C @ sk5 ) ) @ ( sk2 @ memberP ) )
| ( ( C @ ( B @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(119,axiom,
! [A: $i] :
( ( nil @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause56) ).
thf(486,plain,
! [A: $i] :
( ( nil @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(487,plain,
! [A: $i] :
( ( nil @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[486]) ).
thf(15825,plain,
! [A: $i] :
( ( ( sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[706,487]) ).
thf(15826,plain,
! [A: $i] :
( ( ( sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[15825]) ).
thf(15827,plain,
nil @ ( sk7 @ segmentP ),
inference(pattern_uni,[status(thm)],[15826:[bind(A,$thf( sk7 ))]]) ).
thf(100,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause98) ).
thf(449,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(51,axiom,
! [A: $i] : ( A @ skaf64 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause31) ).
thf(329,plain,
! [A: $i] : ( A @ skaf64 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(56,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause117) ).
thf(341,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(342,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[341]) ).
thf(343,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[342]) ).
thf(344,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[343]) ).
thf(20167,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[329,344]) ).
thf(20168,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[20167]) ).
thf(20169,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( A @ skaf64 @ neq ) ),
inference(pattern_uni,[status(thm)],[20168:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(20235,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( A @ skaf64 @ neq ) ),
inference(simp,[status(thm)],[20169]) ).
thf(15794,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[555,487]) ).
thf(15795,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) ) ),
inference(simp,[status(thm)],[15794]) ).
thf(15796,plain,
! [A: $i] : ( nil @ ( A @ skaf67 @ segmentP ) ),
inference(pattern_uni,[status(thm)],[15795:[bind(A,$thf( C )),bind(B,$thf( C @ skaf67 ))]]) ).
thf(15926,plain,
! [A: $i] : ( nil @ ( A @ skaf67 @ segmentP ) ),
inference(simp,[status(thm)],[15796]) ).
thf(68,axiom,
! [B: $i,A: $i] :
( ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause72) ).
thf(371,plain,
! [B: $i,A: $i] :
( ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(372,plain,
! [B: $i,A: $i] :
( ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[371]) ).
thf(3261,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[706,372]) ).
thf(3262,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP ) ),
inference(simp,[status(thm)],[3261]) ).
thf(3263,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk7 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[3262:[bind(A,$thf( sk7 ))]]) ).
thf(3377,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk7 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[3263]) ).
thf(116,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf48 ) @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause48) ).
thf(482,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf48 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(3031,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf48 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ~ ( C @ ( C @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[482,294]) ).
thf(3032,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf48 ) @ ssList )
!= ( C @ ssList ) )
| ~ ( C @ ( C @ neq ) ) ),
inference(simp,[status(thm)],[3031]) ).
thf(3033,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf48 ) @ ( B @ ( A @ skaf48 ) @ neq ) ),
inference(pattern_uni,[status(thm)],[3032:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf48 ) ))]]) ).
thf(3040,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf48 ) @ ( B @ ( A @ skaf48 ) @ neq ) ),
inference(simp,[status(thm)],[3033]) ).
thf(147,axiom,
~ ( nil @ singletonP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause11) ).
thf(549,plain,
~ ( nil @ singletonP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(550,plain,
~ ( nil @ singletonP ),
inference(polarity_switch,[status(thm)],[549]) ).
thf(18971,plain,
( ( nil != nil )
| ~ ( sk1 @ singletonP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[17586,550]) ).
thf(18972,plain,
( ~ ( sk1 @ singletonP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[18971:[]]) ).
thf(96,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause119) ).
thf(440,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(193,axiom,
! [A: $i] : ( A @ skaf71 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause24) ).
thf(655,plain,
! [A: $i] : ( A @ skaf71 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(131,axiom,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause79) ).
thf(511,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(1242,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[1225,294]) ).
thf(1243,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[1242]) ).
thf(1244,plain,
~ ( sk8 @ ( sk8 @ neq ) ),
inference(pattern_uni,[status(thm)],[1243:[bind(A,$thf( sk8 ))]]) ).
thf(1299,plain,
( ( ( sk8 @ ( sk8 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[225,1244]) ).
thf(1300,plain,
( ( sk8 @ ( sk8 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[1299]) ).
thf(1305,plain,
( ( sk8 != nil )
| ( sk8 != sk2 ) ),
inference(simp,[status(thm)],[1300]) ).
thf(166,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause78) ).
thf(597,plain,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(183,axiom,
! [A: $i] : ( A @ skaf82 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause13) ).
thf(637,plain,
! [A: $i] : ( A @ skaf82 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(8866,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[637,350]) ).
thf(8867,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[8866]) ).
thf(8868,plain,
! [A: $i] : ( nil @ ( A @ skaf82 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[8867:[bind(A,$thf( C )),bind(B,$thf( C @ skaf82 ))]]) ).
thf(8963,plain,
! [A: $i] : ( nil @ ( A @ skaf82 @ rearsegP ) ),
inference(simp,[status(thm)],[8868]) ).
thf(139,axiom,
nil @ totalorderP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause6) ).
thf(533,plain,
nil @ totalorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(27,negated_conjecture,
( ~ ( nil @ ( sk4 @ neq ) )
| ( ( sk8 @ ( sk7 @ app ) )
= sk3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_27) ).
thf(239,plain,
( ~ ( nil @ ( sk4 @ neq ) )
| ( ( sk8 @ ( sk7 @ app ) )
= sk3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(254,plain,
( ~ ( nil @ ( sk4 @ neq ) )
| ( ( sk8 @ ( sk7 @ app ) )
= sk3 ) ),
inference(cnf,[status(esa)],[239]) ).
thf(255,plain,
( ~ ( nil @ ( sk4 @ neq ) )
| ( ( sk8 @ ( sk7 @ app ) )
= sk3 ) ),
inference(lifteq,[status(thm)],[254]) ).
thf(6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
thf(219,plain,
sk1 = sk3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(266,plain,
sk3 = sk1,
inference(lifteq,[status(thm)],[219]) ).
thf(1398,plain,
( ~ ( nil @ ( sk2 @ neq ) )
| ( ( sk8 @ ( sk7 @ app ) )
= sk1 ) ),
inference(rewrite,[status(thm)],[255,274,266]) ).
thf(1405,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true
| ( ( sk8 @ ( sk7 @ app ) )
= sk1 ) ),
inference(paramod_ordered,[status(thm)],[225,1398]) ).
thf(1406,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( ( sk8 @ ( sk7 @ app ) )
= sk1 ) ),
inference(simp,[status(thm)],[1405]) ).
thf(1407,plain,
( ( sk8 @ ( sk7 @ app ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[1406:[]]) ).
thf(26,negated_conjecture,
( ~ ( nil @ ( sk4 @ neq ) )
| ( ( sk8 @ ( nil @ ( sk6 @ cons ) @ ( sk7 @ app ) @ app ) )
= sk4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_26) ).
thf(240,plain,
( ~ ( nil @ ( sk4 @ neq ) )
| ( ( sk8 @ ( nil @ ( sk6 @ cons ) @ ( sk7 @ app ) @ app ) )
= sk4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(252,plain,
( ~ ( nil @ ( sk4 @ neq ) )
| ( ( sk8 @ ( nil @ ( sk6 @ cons ) @ ( sk7 @ app ) @ app ) )
= sk4 ) ),
inference(cnf,[status(esa)],[240]) ).
thf(253,plain,
( ~ ( nil @ ( sk4 @ neq ) )
| ( ( sk8 @ ( nil @ ( sk6 @ cons ) @ ( sk7 @ app ) @ app ) )
= sk4 ) ),
inference(lifteq,[status(thm)],[252]) ).
thf(1247,plain,
( ~ ( nil @ ( sk2 @ neq ) )
| ( ( sk8 @ ( nil @ ( sk6 @ cons ) @ ( sk7 @ app ) @ app ) )
= sk2 ) ),
inference(rewrite,[status(thm)],[253,274]) ).
thf(1250,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true
| ( ( sk8 @ ( nil @ ( sk6 @ cons ) @ ( sk7 @ app ) @ app ) )
= sk2 ) ),
inference(paramod_ordered,[status(thm)],[225,1247]) ).
thf(1251,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( ( sk8 @ ( nil @ ( sk6 @ cons ) @ ( sk7 @ app ) @ app ) )
= sk2 ) ),
inference(simp,[status(thm)],[1250]) ).
thf(1252,plain,
( ( sk8 @ ( nil @ ( sk6 @ cons ) @ ( sk7 @ app ) @ app ) )
= sk2 ),
inference(pattern_uni,[status(thm)],[1251:[]]) ).
thf(1799,plain,
( ( ( sk8 @ ( nil @ ( sk6 @ cons ) @ ( sk7 @ app ) @ app ) )
!= ( sk8 @ ( sk7 @ app ) ) )
| ( sk2 = sk1 ) ),
inference(paramod_ordered,[status(thm)],[1252,1407]) ).
thf(1832,plain,
( ( sk8 != sk8 )
| ( ( nil @ ( sk6 @ cons ) @ ( sk7 @ app ) )
!= sk7 )
| ( sk2 = sk1 ) ),
inference(simp,[status(thm)],[1799]) ).
thf(1839,plain,
( ( ( nil @ ( sk6 @ cons ) @ ( sk7 @ app ) )
!= sk7 )
| ( sk2 = sk1 ) ),
inference(simp,[status(thm)],[1832]) ).
thf(2020,plain,
( ( ( nil @ ( sk6 @ cons ) @ ( sk7 @ app ) )
!= ( sk8 @ ( sk7 @ app ) ) )
| ( sk7 != sk1 )
| ( sk2 = sk1 ) ),
inference(paramod_ordered,[status(thm)],[1407,1839]) ).
thf(2033,plain,
( ( ( nil @ ( sk6 @ cons ) )
!= sk8 )
| ( sk7 != sk7 )
| ( sk7 != sk1 )
| ( sk2 = sk1 ) ),
inference(simp,[status(thm)],[2020]) ).
thf(2035,plain,
( ( ( nil @ ( sk6 @ cons ) )
!= sk8 )
| ( sk7 != sk1 )
| ( sk2 = sk1 ) ),
inference(simp,[status(thm)],[2033]) ).
thf(138,axiom,
! [A: $i] : ( A @ skaf68 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause27) ).
thf(532,plain,
! [A: $i] : ( A @ skaf68 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(15893,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[532,487]) ).
thf(15894,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) ) ),
inference(simp,[status(thm)],[15893]) ).
thf(15895,plain,
! [A: $i] : ( nil @ ( A @ skaf68 @ segmentP ) ),
inference(pattern_uni,[status(thm)],[15894:[bind(A,$thf( C )),bind(B,$thf( C @ skaf68 ))]]) ).
thf(15916,plain,
! [A: $i] : ( nil @ ( A @ skaf68 @ segmentP ) ),
inference(simp,[status(thm)],[15895]) ).
thf(130,axiom,
! [A: $i] : ( A @ skaf75 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause20) ).
thf(510,plain,
! [A: $i] : ( A @ skaf75 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(1864,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[510,294]) ).
thf(1865,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1864]) ).
thf(1866,plain,
! [A: $i] :
~ ( A @ skaf75 @ ( A @ skaf75 @ neq ) ),
inference(pattern_uni,[status(thm)],[1865:[bind(A,$thf( C )),bind(B,$thf( C @ skaf75 ))]]) ).
thf(1872,plain,
! [A: $i] :
~ ( A @ skaf75 @ ( A @ skaf75 @ neq ) ),
inference(simp,[status(thm)],[1866]) ).
thf(108,axiom,
! [A: $i] : ( A @ skaf60 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause35) ).
thf(464,plain,
! [A: $i] : ( A @ skaf60 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(3775,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[464,3705]) ).
thf(3776,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[3775]) ).
thf(3777,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[3776:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(3781,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[3777]) ).
thf(189,axiom,
! [A: $i] : ( A @ skaf56 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause39) ).
thf(648,plain,
! [A: $i] : ( A @ skaf56 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(8900,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[648,350]) ).
thf(8901,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[8900]) ).
thf(8902,plain,
! [A: $i] : ( nil @ ( A @ skaf56 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[8901:[bind(A,$thf( C )),bind(B,$thf( C @ skaf56 ))]]) ).
thf(8947,plain,
! [A: $i] : ( nil @ ( A @ skaf56 @ rearsegP ) ),
inference(simp,[status(thm)],[8902]) ).
thf(55,axiom,
! [A: $i] :
( ( ( A @ skaf68 @ ( A @ skaf65 @ cons ) @ ( A @ skaf67 @ ( A @ skaf64 @ cons ) @ ( A @ skaf66 @ app ) @ app ) )
= A )
| ( A @ totalorderedP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause164) ).
thf(338,plain,
! [A: $i] :
( ( ( A @ skaf68 @ ( A @ skaf65 @ cons ) @ ( A @ skaf67 @ ( A @ skaf64 @ cons ) @ ( A @ skaf66 @ app ) @ app ) )
= A )
| ( A @ totalorderedP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(339,plain,
! [A: $i] :
( ( ( A @ skaf68 @ ( A @ skaf65 @ cons ) @ ( A @ skaf67 @ ( A @ skaf64 @ cons ) @ ( A @ skaf66 @ app ) @ app ) )
= A )
| ( A @ totalorderedP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[338]) ).
thf(340,plain,
! [A: $i] :
( ( A @ totalorderedP )
| ~ ( A @ ssList )
| ( ( A @ skaf68 @ ( A @ skaf65 @ cons ) @ ( A @ skaf67 @ ( A @ skaf64 @ cons ) @ ( A @ skaf66 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[339]) ).
thf(142,axiom,
nil @ cyclefreeP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause7) ).
thf(538,plain,
nil @ cyclefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(3327,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[218,372]) ).
thf(3328,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP ) ),
inference(simp,[status(thm)],[3327]) ).
thf(3329,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk1 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[3328:[bind(A,$thf( sk1 ))]]) ).
thf(3342,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[3329]) ).
thf(3715,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true
| ( sk1 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[3342,3705]) ).
thf(3716,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[3715]) ).
thf(3717,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk1 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[3716:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(201,axiom,
! [A: $i] : ( A @ skaf78 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause17) ).
thf(671,plain,
! [A: $i] : ( A @ skaf78 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(3763,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[671,3705]) ).
thf(3764,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[3763]) ).
thf(3765,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[3764:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(3794,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[3765]) ).
thf(74,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause66) ).
thf(385,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(22119,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) )
| ~ ( sk1 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[18972,294]) ).
thf(22120,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ ( sk1 @ singletonP ) ),
inference(simp,[status(thm)],[22119]) ).
thf(22121,plain,
( ~ ( sk1 @ tl @ ( sk1 @ tl @ neq ) )
| ~ ( sk1 @ singletonP ) ),
inference(pattern_uni,[status(thm)],[22120:[bind(A,$thf( sk1 @ tl ))]]) ).
thf(22801,plain,
( ( ( sk1 @ tl @ ( sk1 @ tl @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true
| ~ ( sk1 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[225,22121]) ).
thf(22802,plain,
( ( ( sk1 @ tl @ ( sk1 @ tl @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ ( sk1 @ singletonP ) ),
inference(simp,[status(thm)],[22801]) ).
thf(22824,plain,
( ( ( sk1 @ tl )
!= nil )
| ( ( sk1 @ tl )
!= sk2 )
| ~ ( sk1 @ singletonP ) ),
inference(simp,[status(thm)],[22802]) ).
thf(102,axiom,
! [A: $i] : ( A @ skaf55 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause40) ).
thf(453,plain,
! [A: $i] : ( A @ skaf55 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(1336,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[453,496]) ).
thf(1337,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1336]) ).
thf(1338,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1337:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(1342,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1338]) ).
thf(17330,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[1225,337]) ).
thf(17331,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[17330]) ).
thf(17332,plain,
( ( sk8 @ tl @ ssList )
| ( sk8 = nil ) ),
inference(pattern_uni,[status(thm)],[17331:[bind(A,$thf( sk8 ))]]) ).
thf(18776,plain,
( ( sk8 != sk8 )
| ( nil != nil )
| ( sk8 != sk2 )
| ( sk8 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[17332,1305]) ).
thf(18777,plain,
( ( sk8 != sk8 )
| ( sk8 != sk2 )
| ( sk8 @ tl @ ssList ) ),
inference(simp,[status(thm)],[18776]) ).
thf(18778,plain,
( ( sk8 != sk2 )
| ( sk8 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[18777:[]]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause126) ).
thf(332,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(333,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
inference(cnf,[status(esa)],[332]) ).
thf(334,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[333]) ).
thf(29,axiom,
skac3 != skac2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause54) ).
thf(279,plain,
skac3 != skac2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(280,plain,
skac3 != skac2,
inference(polarity_switch,[status(thm)],[279]) ).
thf(281,plain,
skac2 != skac3,
inference(lifteq,[status(thm)],[280]) ).
thf(13227,plain,
! [B: $i,A: $i] :
( ( B != skac2 )
| ( A != skac3 )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
inference(paramod_ordered,[status(thm)],[334,281]) ).
thf(13228,plain,
! [A: $i] :
( ( A != skac3 )
| ~ ( skac2 @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( A @ geq ) ) ),
inference(pattern_uni,[status(thm)],[13227:[bind(A,$thf( A )),bind(B,$thf( skac2 ))]]) ).
thf(15209,plain,
( ~ ( skac2 @ ssItem )
| ~ ( skac3 @ ssItem )
| ~ ( skac3 @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( skac3 @ geq ) ) ),
inference(simp,[status(thm)],[13228]) ).
thf(18410,plain,
( ~ $true
| ~ $true
| ~ ( skac3 @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( skac3 @ geq ) ) ),
inference(rewrite,[status(thm)],[15209,596,583]) ).
thf(18411,plain,
( ~ ( skac3 @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( skac3 @ geq ) ) ),
inference(simp,[status(thm)],[18410]) ).
thf(18460,plain,
( ~ $true
| ( ( skac3 @ ( skac2 @ geq ) )
!= ( skac2 @ ( skac3 @ geq ) ) )
| ~ ( skac2 @ ( skac3 @ geq ) ) ),
inference(eqfactor_ordered,[status(thm)],[18411]) ).
thf(18463,plain,
( ( ( skac3 @ ( skac2 @ geq ) )
!= ( skac2 @ ( skac3 @ geq ) ) )
| ~ ( skac2 @ ( skac3 @ geq ) ) ),
inference(simp,[status(thm)],[18460]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause90) ).
thf(300,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(301,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(cnf,[status(esa)],[300]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ geq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause107) ).
thf(319,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(320,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ geq ) ) ),
inference(cnf,[status(esa)],[319]) ).
thf(186,axiom,
! [A: $i] : ( A @ skaf65 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause30) ).
thf(641,plain,
! [A: $i] : ( A @ skaf65 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(20190,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[641,344]) ).
thf(20191,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[20190]) ).
thf(20192,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( A @ skaf65 @ neq ) ),
inference(pattern_uni,[status(thm)],[20191:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(20239,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( A @ skaf65 @ neq ) ),
inference(simp,[status(thm)],[20192]) ).
thf(191,axiom,
! [A: $i] : ( A @ skaf50 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause45) ).
thf(651,plain,
! [A: $i] : ( A @ skaf50 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(129,axiom,
! [A: $i] : ( A @ skaf53 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause42) ).
thf(509,plain,
! [A: $i] : ( A @ skaf53 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(15844,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[509,487]) ).
thf(15845,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) ) ),
inference(simp,[status(thm)],[15844]) ).
thf(15846,plain,
! [A: $i] : ( nil @ ( A @ skaf53 @ segmentP ) ),
inference(pattern_uni,[status(thm)],[15845:[bind(A,$thf( C )),bind(B,$thf( C @ skaf53 ))]]) ).
thf(15922,plain,
! [A: $i] : ( nil @ ( A @ skaf53 @ segmentP ) ),
inference(simp,[status(thm)],[15846]) ).
thf(8937,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[532,350]) ).
thf(8938,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[8937]) ).
thf(8939,plain,
! [A: $i] : ( nil @ ( A @ skaf68 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[8938:[bind(A,$thf( C )),bind(B,$thf( C @ skaf68 ))]]) ).
thf(8967,plain,
! [A: $i] : ( nil @ ( A @ skaf68 @ rearsegP ) ),
inference(simp,[status(thm)],[8939]) ).
thf(127,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause100) ).
thf(504,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(62,axiom,
nil @ strictorderP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause5) ).
thf(357,plain,
nil @ strictorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(4982,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ~ $true
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[222,301]) ).
thf(4983,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(simp,[status(thm)],[4982]) ).
thf(4984,plain,
( ( sk2 @ strictorderedP )
| ~ ( sk2 @ skaf70 @ ( sk2 @ skaf69 @ lt ) ) ),
inference(pattern_uni,[status(thm)],[4983:[bind(A,$thf( sk2 ))]]) ).
thf(2733,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[655,294]) ).
thf(2734,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[2733]) ).
thf(2735,plain,
! [A: $i] :
~ ( A @ skaf71 @ ( A @ skaf71 @ neq ) ),
inference(pattern_uni,[status(thm)],[2734:[bind(A,$thf( C )),bind(B,$thf( C @ skaf71 ))]]) ).
thf(2745,plain,
! [A: $i] :
~ ( A @ skaf71 @ ( A @ skaf71 @ neq ) ),
inference(simp,[status(thm)],[2735]) ).
thf(106,axiom,
! [A: $i] : ( A @ skaf61 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause34) ).
thf(460,plain,
! [A: $i] : ( A @ skaf61 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(1076,plain,
! [A: $i] :
( ( A != sk7 )
| ~ ( sk6 @ ( sk7 @ neq ) )
| ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk6 @ ( A @ geq ) )
| ~ ( A @ ( sk2 @ memberP ) )
| ~ ( A @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[965,722]) ).
thf(1077,plain,
( ~ ( sk6 @ ( sk7 @ neq ) )
| ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) )
| ~ ( sk7 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[1076:[bind(A,$thf( sk7 ))]]) ).
thf(9463,plain,
( ~ ( sk6 @ ( sk7 @ neq ) )
| ~ $true
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) )
| ~ ( sk7 @ ssItem ) ),
inference(rewrite,[status(thm)],[1077,225]) ).
thf(9464,plain,
( ~ ( sk6 @ ( sk7 @ neq ) )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) )
| ~ ( sk7 @ ssItem ) ),
inference(simp,[status(thm)],[9463]) ).
thf(42,axiom,
! [A: $i] : ( A @ skaf72 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause23) ).
thf(310,plain,
! [A: $i] : ( A @ skaf72 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(8909,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[310,350]) ).
thf(8910,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[8909]) ).
thf(8911,plain,
! [A: $i] : ( nil @ ( A @ skaf72 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[8910:[bind(A,$thf( C )),bind(B,$thf( C @ skaf72 ))]]) ).
thf(8951,plain,
! [A: $i] : ( nil @ ( A @ skaf72 @ rearsegP ) ),
inference(simp,[status(thm)],[8911]) ).
thf(175,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause122) ).
thf(619,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(20161,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[452,344]) ).
thf(20162,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[20161]) ).
thf(20163,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( A @ skaf69 @ neq ) ),
inference(pattern_uni,[status(thm)],[20162:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(20232,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( A @ skaf69 @ neq ) ),
inference(simp,[status(thm)],[20163]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause108) ).
thf(283,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(284,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[283]) ).
thf(16,negated_conjecture,
( ( nil @ ( sk2 @ neq ) )
| ( ( sk8 @ ( nil @ ( sk6 @ cons ) @ ( sk7 @ app ) @ app ) )
= sk4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
thf(228,plain,
( ( nil @ ( sk2 @ neq ) )
| ( ( sk8 @ ( nil @ ( sk6 @ cons ) @ ( sk7 @ app ) @ app ) )
= sk4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause106) ).
thf(289,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(104,axiom,
! [A: $i] : ( A @ skaf70 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause25) ).
thf(457,plain,
! [A: $i] : ( A @ skaf70 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(3742,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[457,3705]) ).
thf(3743,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[3742]) ).
thf(3744,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[3743:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(3788,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[3744]) ).
thf(812,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[310,294]) ).
thf(813,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[812]) ).
thf(814,plain,
! [A: $i] :
~ ( A @ skaf72 @ ( A @ skaf72 @ neq ) ),
inference(pattern_uni,[status(thm)],[813:[bind(A,$thf( C )),bind(B,$thf( C @ skaf72 ))]]) ).
thf(817,plain,
! [A: $i] :
~ ( A @ skaf72 @ ( A @ skaf72 @ neq ) ),
inference(simp,[status(thm)],[814]) ).
thf(20158,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[453,344]) ).
thf(20159,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[20158]) ).
thf(20160,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( A @ skaf55 @ neq ) ),
inference(pattern_uni,[status(thm)],[20159:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(20230,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( A @ skaf55 @ neq ) ),
inference(simp,[status(thm)],[20160]) ).
thf(184,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause156) ).
thf(638,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(78,axiom,
nil @ duplicatefreeP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause2) ).
thf(393,plain,
nil @ duplicatefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(19090,plain,
( ( nil != nil )
| ( sk1 @ duplicatefreeP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[17586,393]) ).
thf(19091,plain,
( ( sk1 @ duplicatefreeP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[19090:[]]) ).
thf(50,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf46 ) @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause50) ).
thf(328,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf46 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(15819,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf46 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[328,487]) ).
thf(15820,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf46 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ segmentP ) ) ),
inference(simp,[status(thm)],[15819]) ).
thf(15821,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf46 ) @ segmentP ) ),
inference(pattern_uni,[status(thm)],[15820:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf46 ) ))]]) ).
thf(15911,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf46 ) @ segmentP ) ),
inference(simp,[status(thm)],[15821]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ app ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause85) ).
thf(315,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ app ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(316,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ app ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[315]) ).
thf(1355,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[457,496]) ).
thf(1356,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1355]) ).
thf(1357,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1356:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(1362,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1357]) ).
thf(14,negated_conjecture,
( ( nil @ ( sk2 @ neq ) )
| ( sk7 @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
thf(216,plain,
( ( nil @ ( sk2 @ neq ) )
| ( sk7 @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(196,axiom,
! [A: $i] : ( A @ skaf76 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause19) ).
thf(661,plain,
! [A: $i] : ( A @ skaf76 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(8854,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[661,350]) ).
thf(8855,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[8854]) ).
thf(8856,plain,
! [A: $i] : ( nil @ ( A @ skaf76 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[8855:[bind(A,$thf( C )),bind(B,$thf( C @ skaf76 ))]]) ).
thf(8956,plain,
! [A: $i] : ( nil @ ( A @ skaf76 @ rearsegP ) ),
inference(simp,[status(thm)],[8856]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ geq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause148) ).
thf(443,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ geq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(48,axiom,
! [A: $i] :
( ( ( A @ skaf73 @ ( A @ skaf70 @ cons ) @ ( A @ skaf72 @ ( A @ skaf69 @ cons ) @ ( A @ skaf71 @ app ) @ app ) )
= A )
| ( A @ strictorderedP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause163) ).
thf(321,plain,
! [A: $i] :
( ( ( A @ skaf73 @ ( A @ skaf70 @ cons ) @ ( A @ skaf72 @ ( A @ skaf69 @ cons ) @ ( A @ skaf71 @ app ) @ app ) )
= A )
| ( A @ strictorderedP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(71,axiom,
nil @ equalelemsP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause1) ).
thf(376,plain,
nil @ equalelemsP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(22,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( nil @ ( sk4 @ neq ) )
| ( A
!= ( A @ ( B @ ( C @ sk5 ) ) ) )
| ( ( C @ ( B @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_22) ).
thf(238,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( nil @ ( sk4 @ neq ) )
| ( A
!= ( A @ ( B @ ( C @ sk5 ) ) ) )
| ( ( C @ ( B @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(58,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ( B @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause132) ).
thf(346,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ( B @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(347,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ( B @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ frontsegP ) ) ),
inference(cnf,[status(esa)],[346]) ).
thf(348,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ frontsegP ) )
| ( ( B @ ( A @ skaf45 ) @ ( B @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[347]) ).
thf(60,axiom,
! [B: $i,A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause118) ).
thf(351,plain,
! [B: $i,A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(352,plain,
! [B: $i,A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
inference(cnf,[status(esa)],[351]) ).
thf(353,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( nil = A )
| ( ( B @ ( A @ app ) )
!= nil ) ),
inference(lifteq,[status(thm)],[352]) ).
thf(3312,plain,
! [B: $i,A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1225,372]) ).
thf(3313,plain,
! [B: $i,A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP ) ),
inference(simp,[status(thm)],[3312]) ).
thf(3314,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk8 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[3313:[bind(A,$thf( sk8 ))]]) ).
thf(3368,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk8 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[3314]) ).
thf(3769,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true
| ( sk8 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[3368,3705]) ).
thf(3770,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ( sk8 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[3769]) ).
thf(3771,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk8 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[3770:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(115,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ frontsegP ) )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( D @ ( C @ cons ) @ ( B @ ( A @ cons ) @ frontsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause174) ).
thf(480,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ frontsegP ) )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( D @ ( C @ cons ) @ ( B @ ( A @ cons ) @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(64,axiom,
! [A: $i] : ( A @ skaf77 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause18) ).
thf(362,plain,
! [A: $i] : ( A @ skaf77 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(8885,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[362,350]) ).
thf(8886,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[8885]) ).
thf(8887,plain,
! [A: $i] : ( nil @ ( A @ skaf77 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[8886:[bind(A,$thf( C )),bind(B,$thf( C @ skaf77 ))]]) ).
thf(8972,plain,
! [A: $i] : ( nil @ ( A @ skaf77 @ rearsegP ) ),
inference(simp,[status(thm)],[8887]) ).
thf(1679,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[464,496]) ).
thf(1680,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1679]) ).
thf(1681,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1680:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(1682,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1681]) ).
thf(118,axiom,
! [A: $i] : ( A @ skaf49 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause46) ).
thf(485,plain,
! [A: $i] : ( A @ skaf49 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(169,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= ( C @ ( A @ app ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause150) ).
thf(602,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= ( C @ ( A @ app ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(86,axiom,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause81) ).
thf(411,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(412,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(cnf,[status(esa)],[411]) ).
thf(413,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[412]) ).
thf(414,plain,
( ( nil @ ( nil @ rearsegP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[413]) ).
thf(5400,plain,
( ( nil @ ( nil @ rearsegP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[414,345]) ).
thf(5401,plain,
nil @ ( nil @ rearsegP ),
inference(simp,[status(thm)],[5400]) ).
thf(152,axiom,
! [A: $i] : ( A @ skaf81 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause14) ).
thf(561,plain,
! [A: $i] : ( A @ skaf81 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(15813,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[561,487]) ).
thf(15814,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) ) ),
inference(simp,[status(thm)],[15813]) ).
thf(15815,plain,
! [A: $i] : ( nil @ ( A @ skaf81 @ segmentP ) ),
inference(pattern_uni,[status(thm)],[15814:[bind(A,$thf( C )),bind(B,$thf( C @ skaf81 ))]]) ).
thf(15907,plain,
! [A: $i] : ( nil @ ( A @ skaf81 @ segmentP ) ),
inference(simp,[status(thm)],[15815]) ).
thf(209,axiom,
nil @ totalorderedP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause4) ).
thf(692,plain,
nil @ totalorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(13,negated_conjecture,
( ( nil @ ( sk2 @ neq ) )
| ( sk6 @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
thf(221,plain,
( ( nil @ ( sk2 @ neq ) )
| ( sk6 @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(257,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( nil @ ( sk4 @ neq ) )
| ( A
!= ( A @ ( B @ ( C @ sk5 ) ) ) )
| ( ( C @ ( B @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[238]) ).
thf(258,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( nil @ ( sk4 @ neq ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( A @ ( B @ ( C @ sk5 ) ) )
!= A )
| ( ( C @ ( B @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 ) ),
inference(lifteq,[status(thm)],[257]) ).
thf(1447,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( nil @ ( sk2 @ neq ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( A @ ( B @ ( C @ sk5 ) ) )
!= A )
| ( ( C @ ( B @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 ) ),
inference(rewrite,[status(thm)],[258,274]) ).
thf(772,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[596,496]) ).
thf(773,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[772]) ).
thf(774,plain,
~ ( skac3 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[773:[bind(A,$thf( skac3 ))]]) ).
thf(204,axiom,
nil @ strictorderedP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause3) ).
thf(679,plain,
nil @ strictorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(19084,plain,
( ( nil != nil )
| ( sk1 @ strictorderedP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[17586,679]) ).
thf(19085,plain,
( ( sk1 @ strictorderedP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[19084:[]]) ).
thf(91,axiom,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf54 @ ( A @ skaf55 @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause94) ).
thf(428,plain,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf54 @ ( A @ skaf55 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(21969,plain,
! [A: $i] :
( ( ( sk8 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) )
| ( sk8 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[18778,294]) ).
thf(21970,plain,
! [A: $i] :
( ( ( sk8 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ( sk8 != sk2 ) ),
inference(simp,[status(thm)],[21969]) ).
thf(21971,plain,
( ~ ( sk8 @ tl @ ( sk8 @ tl @ neq ) )
| ( sk8 != sk2 ) ),
inference(pattern_uni,[status(thm)],[21970:[bind(A,$thf( sk8 @ tl ))]]) ).
thf(22736,plain,
( ( ( sk8 @ tl @ ( sk8 @ tl @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true
| ( sk8 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[225,21971]) ).
thf(22737,plain,
( ( ( sk8 @ tl @ ( sk8 @ tl @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( sk8 != sk2 ) ),
inference(simp,[status(thm)],[22736]) ).
thf(22774,plain,
( ( ( sk8 @ tl )
!= nil )
| ( ( sk8 @ tl )
!= sk2 )
| ( sk8 != sk2 ) ),
inference(simp,[status(thm)],[22737]) ).
thf(128,axiom,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf55 @ ( A @ skaf54 @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause95) ).
thf(507,plain,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf55 @ ( A @ skaf54 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause134) ).
thf(312,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(87,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ app ) )
= nil )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( nil != B )
| ( nil != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause145) ).
thf(415,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ app ) )
= nil )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( nil != B )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(416,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ app ) )
= nil )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( nil != B )
| ( nil != A ) ),
inference(cnf,[status(esa)],[415]) ).
thf(417,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
= nil )
| ( nil != B )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[416]) ).
thf(418,plain,
( ~ ( nil @ ssList )
| ( ( nil @ ( nil @ app ) )
= nil ) ),
inference(simp,[status(thm)],[417]) ).
thf(5737,plain,
( ~ $true
| ( ( nil @ ( nil @ app ) )
= nil ) ),
inference(rewrite,[status(thm)],[418,345]) ).
thf(5738,plain,
( ( nil @ ( nil @ app ) )
= nil ),
inference(simp,[status(thm)],[5737]) ).
thf(80,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause103) ).
thf(397,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(207,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ segmentP ) )
| ~ ( B @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause127) ).
thf(687,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ segmentP ) )
| ~ ( B @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(41,axiom,
! [A: $i] :
( ( ( A @ skaf77 @ ( A @ skaf74 @ cons ) @ ( A @ skaf76 @ ( A @ skaf74 @ cons ) @ ( A @ skaf75 @ app ) @ app ) )
= A )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause162) ).
thf(307,plain,
! [A: $i] :
( ( ( A @ skaf77 @ ( A @ skaf74 @ cons ) @ ( A @ skaf76 @ ( A @ skaf74 @ cons ) @ ( A @ skaf75 @ app ) @ app ) )
= A )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(137,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause99) ).
thf(529,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(140,axiom,
! [A: $i] :
( ( nil @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause60) ).
thf(534,plain,
! [A: $i] :
( ( nil @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(180,axiom,
! [A: $i] : ( A @ skaf83 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause12) ).
thf(632,plain,
! [A: $i] : ( A @ skaf83 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(3766,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[632,3705]) ).
thf(3767,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[3766]) ).
thf(3768,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[3767:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(3795,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[3768]) ).
thf(15,negated_conjecture,
( ( nil @ ( sk2 @ neq ) )
| ( sk8 @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
thf(233,plain,
( ( nil @ ( sk2 @ neq ) )
| ( sk8 @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(98,axiom,
! [A: $i] : ( A @ skaf73 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause22) ).
thf(445,plain,
! [A: $i] : ( A @ skaf73 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(15838,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[445,487]) ).
thf(15839,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) ) ),
inference(simp,[status(thm)],[15838]) ).
thf(15840,plain,
! [A: $i] : ( nil @ ( A @ skaf73 @ segmentP ) ),
inference(pattern_uni,[status(thm)],[15839:[bind(A,$thf( C )),bind(B,$thf( C @ skaf73 ))]]) ).
thf(15920,plain,
! [A: $i] : ( nil @ ( A @ skaf73 @ segmentP ) ),
inference(simp,[status(thm)],[15840]) ).
thf(73,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ rearsegP ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
!= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause143) ).
thf(381,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ rearsegP ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
!= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(9,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( nil @ ( sk2 @ neq ) )
| ( A @ ( B @ ( C @ sk5 ) ) @ ssItem )
| ( ( C @ ( B @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
thf(220,plain,
! [C: $i,B: $i,A: $i] :
( ( nil @ ( sk2 @ neq ) )
| ( A @ ( B @ ( C @ sk5 ) ) @ ssItem )
| ( ( C @ ( B @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(19025,plain,
( ( nil != nil )
| ( sk1 @ totalorderedP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[17586,692]) ).
thf(19026,plain,
( ( sk1 @ totalorderedP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[19025:[]]) ).
thf(203,axiom,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause83) ).
thf(675,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(676,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(cnf,[status(esa)],[675]) ).
thf(677,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[676]) ).
thf(678,plain,
( ( nil @ ( nil @ frontsegP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[677]) ).
thf(5733,plain,
( ( nil @ ( nil @ frontsegP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[678,345]) ).
thf(5734,plain,
nil @ ( nil @ frontsegP ),
inference(simp,[status(thm)],[5733]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause88) ).
thf(302,plain,
! [A: $i] :
( ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(2144,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[632,496]) ).
thf(2145,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2144]) ).
thf(2146,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2145:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(2147,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2146]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ lt ) )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause147) ).
thf(296,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ lt ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(297,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ lt ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[296]) ).
thf(90,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ cons ) @ ( A @ ( C @ cons ) @ frontsegP ) )
| ~ ( C @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( C != D )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause178) ).
thf(424,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ cons ) @ ( A @ ( C @ cons ) @ frontsegP ) )
| ~ ( C @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( C != D )
| ~ ( B @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(1041,plain,
! [A: $i] :
( ( A != skac2 )
| ( skac3 != sk6 )
| ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk6 @ ( A @ geq ) )
| ~ ( A @ ( sk2 @ memberP ) )
| ~ ( A @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[965,281]) ).
thf(1042,plain,
( ( skac3 != sk6 )
| ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk6 @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( sk2 @ memberP ) )
| ~ ( skac2 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[1041:[bind(A,$thf( skac2 ))]]) ).
thf(3153,plain,
( ( skac3 != sk6 )
| ~ $true
| ~ ( sk6 @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( sk2 @ memberP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[1042,225,583]) ).
thf(3154,plain,
( ( skac3 != sk6 )
| ~ ( sk6 @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[3153]) ).
thf(20187,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[953,344]) ).
thf(20188,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[20187]) ).
thf(20189,plain,
~ ( sk6 @ ( sk6 @ neq ) ),
inference(pattern_uni,[status(thm)],[20188:[bind(A,$thf( sk6 ))]]) ).
thf(210,axiom,
! [A: $i] : ( A @ skaf59 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause36) ).
thf(693,plain,
! [A: $i] : ( A @ skaf59 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(179,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ rearsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ rearsegP ) )
| ~ ( B @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause153) ).
thf(630,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ rearsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ rearsegP ) )
| ~ ( B @ ( A @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(110,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ strictorderedP )
| ~ ( B @ hd @ ( A @ lt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause160) ).
thf(467,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ strictorderedP )
| ~ ( B @ hd @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(15884,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[218,487]) ).
thf(15885,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[15884]) ).
thf(15886,plain,
nil @ ( sk1 @ segmentP ),
inference(pattern_uni,[status(thm)],[15885:[bind(A,$thf( sk1 ))]]) ).
thf(63,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ssList )
| ~ ( F @ cyclefreeP )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) )
!= F )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause185) ).
thf(358,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ssList )
| ~ ( F @ cyclefreeP )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) )
!= F )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(359,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ssList )
| ~ ( F @ cyclefreeP )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) )
!= F )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[358]) ).
thf(360,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ssList )
| ~ ( F @ cyclefreeP )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ~ ( E @ ssList )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ( ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) )
!= F ) ),
inference(lifteq,[status(thm)],[359]) ).
thf(361,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) @ ssList )
| ~ ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) @ cyclefreeP )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ~ ( E @ ssList )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[360]) ).
thf(177,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause69) ).
thf(625,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ app ) @ rearsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause136) ).
thf(435,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ app ) @ rearsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(303,plain,
! [A: $i] :
( ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[302]) ).
thf(5339,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[222,303]) ).
thf(5340,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP ) ),
inference(simp,[status(thm)],[5339]) ).
thf(5341,plain,
( ( sk2 @ skaf50 @ ( sk2 @ skaf49 @ leq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5340:[bind(A,$thf( sk2 ))]]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
!= ( B @ ( C @ app ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause151) ).
thf(461,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
!= ( B @ ( C @ app ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(8931,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[510,350]) ).
thf(8932,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[8931]) ).
thf(8933,plain,
! [A: $i] : ( nil @ ( A @ skaf75 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[8932:[bind(A,$thf( C )),bind(B,$thf( C @ skaf75 ))]]) ).
thf(8964,plain,
! [A: $i] : ( nil @ ( A @ skaf75 @ rearsegP ) ),
inference(simp,[status(thm)],[8933]) ).
thf(148,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause111) ).
thf(551,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(15899,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[222,487]) ).
thf(15900,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[15899]) ).
thf(15901,plain,
nil @ ( sk2 @ segmentP ),
inference(pattern_uni,[status(thm)],[15900:[bind(A,$thf( sk2 ))]]) ).
thf(49,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( F @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause181) ).
thf(324,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( F @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(11,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( nil @ ( sk2 @ neq ) )
| ( A @ ( A @ ( B @ ( C @ sk5 ) ) @ geq ) )
| ( ( C @ ( B @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
thf(229,plain,
! [C: $i,B: $i,A: $i] :
( ( nil @ ( sk2 @ neq ) )
| ( A @ ( A @ ( B @ ( C @ sk5 ) ) @ geq ) )
| ( ( C @ ( B @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(35,axiom,
! [A: $i] : ( A @ skaf62 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause33) ).
thf(295,plain,
! [A: $i] : ( A @ skaf62 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(8903,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[295,350]) ).
thf(8904,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[8903]) ).
thf(8905,plain,
! [A: $i] : ( nil @ ( A @ skaf62 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[8904:[bind(A,$thf( C )),bind(B,$thf( C @ skaf62 ))]]) ).
thf(8948,plain,
! [A: $i] : ( nil @ ( A @ skaf62 @ rearsegP ) ),
inference(simp,[status(thm)],[8905]) ).
thf(154,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause65) ).
thf(566,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(3748,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[953,3705]) ).
thf(3749,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[3748]) ).
thf(3750,plain,
nil @ ( sk6 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[3749:[bind(A,$thf( sk6 ))]]) ).
thf(168,axiom,
! [A: $i] : ( A @ skaf66 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause29) ).
thf(601,plain,
! [A: $i] : ( A @ skaf66 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(3276,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ( C @ ssItem )
| ( B @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[601,372]) ).
thf(3277,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ( C @ ssItem )
| ( B @ duplicatefreeP ) ),
inference(simp,[status(thm)],[3276]) ).
thf(3278,plain,
! [B: $i,A: $i] :
( ( A @ ssItem )
| ( B @ skaf66 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[3277:[bind(A,$thf( D )),bind(B,$thf( D @ skaf66 ))]]) ).
thf(3349,plain,
! [B: $i,A: $i] :
( ( A @ ssItem )
| ( B @ skaf66 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[3278]) ).
thf(134,axiom,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause62) ).
thf(522,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(12,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( nil @ ( sk2 @ neq ) )
| ( A
!= ( A @ ( B @ ( C @ sk5 ) ) ) )
| ( ( C @ ( B @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
thf(224,plain,
! [C: $i,B: $i,A: $i] :
( ( nil @ ( sk2 @ neq ) )
| ( A
!= ( A @ ( B @ ( C @ sk5 ) ) ) )
| ( ( C @ ( B @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(197,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf42 ) @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause53) ).
thf(662,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf42 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(15828,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf42 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[662,487]) ).
thf(15829,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf42 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ segmentP ) ) ),
inference(simp,[status(thm)],[15828]) ).
thf(15830,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf42 ) @ segmentP ) ),
inference(pattern_uni,[status(thm)],[15829:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf42 ) ))]]) ).
thf(15915,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf42 ) @ segmentP ) ),
inference(simp,[status(thm)],[15830]) ).
thf(3727,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[452,3705]) ).
thf(3728,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[3727]) ).
thf(3729,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[3728:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(3784,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[3729]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ frontsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause154) ).
thf(317,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ frontsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(5083,plain,
( ( ( sk7 @ ssItem )
!= ( sk6 @ ssItem ) )
| ~ ( sk7 @ ( sk6 @ neq ) )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[953,5054]) ).
thf(5084,plain,
( ( ( sk7 @ ssItem )
!= ( sk6 @ ssItem ) )
| ~ ( sk7 @ ( sk6 @ neq ) )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[5083]) ).
thf(5129,plain,
( ( sk7 != sk6 )
| ~ ( sk7 @ ( sk6 @ neq ) )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[5084]) ).
thf(5404,plain,
( ( ( sk7 @ ( sk6 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( sk7 != sk6 )
| ~ $true
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[225,5129]) ).
thf(5405,plain,
( ( ( sk7 @ ( sk6 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( sk7 != sk6 )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[5404]) ).
thf(5428,plain,
( ( sk7 != nil )
| ( sk6 != sk2 )
| ( sk7 != sk6 )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[5405]) ).
thf(76,axiom,
! [A: $i] :
( ( ( A @ skaf58 @ ( A @ skaf55 @ cons ) @ ( A @ skaf57 @ ( A @ skaf54 @ cons ) @ ( A @ skaf56 @ app ) @ app ) )
= A )
| ( A @ totalorderP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause166) ).
thf(388,plain,
! [A: $i] :
( ( ( A @ skaf58 @ ( A @ skaf55 @ cons ) @ ( A @ skaf57 @ ( A @ skaf54 @ cons ) @ ( A @ skaf56 @ app ) @ app ) )
= A )
| ( A @ totalorderP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(61,axiom,
! [A: $i] :
( ( ( A @ skaf63 @ ( A @ skaf60 @ cons ) @ ( A @ skaf62 @ ( A @ skaf59 @ cons ) @ ( A @ skaf61 @ app ) @ app ) )
= A )
| ( A @ strictorderP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause165) ).
thf(354,plain,
! [A: $i] :
( ( ( A @ skaf63 @ ( A @ skaf60 @ cons ) @ ( A @ skaf62 @ ( A @ skaf59 @ cons ) @ ( A @ skaf61 @ app ) @ app ) )
= A )
| ( A @ strictorderP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(355,plain,
! [A: $i] :
( ( ( A @ skaf63 @ ( A @ skaf60 @ cons ) @ ( A @ skaf62 @ ( A @ skaf59 @ cons ) @ ( A @ skaf61 @ app ) @ app ) )
= A )
| ( A @ strictorderP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[354]) ).
thf(356,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ( ( A @ skaf63 @ ( A @ skaf60 @ cons ) @ ( A @ skaf62 @ ( A @ skaf59 @ cons ) @ ( A @ skaf61 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[355]) ).
thf(18993,plain,
( ( nil != nil )
| ( sk1 @ strictorderP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[17586,357]) ).
thf(18994,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[18993:[]]) ).
thf(15865,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[310,487]) ).
thf(15866,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) ) ),
inference(simp,[status(thm)],[15865]) ).
thf(15867,plain,
! [A: $i] : ( nil @ ( A @ skaf72 @ segmentP ) ),
inference(pattern_uni,[status(thm)],[15866:[bind(A,$thf( C )),bind(B,$thf( C @ skaf72 ))]]) ).
thf(15930,plain,
! [A: $i] : ( nil @ ( A @ skaf72 @ segmentP ) ),
inference(simp,[status(thm)],[15867]) ).
thf(172,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause77) ).
thf(610,plain,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(89,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( E @ ssList )
| ~ ( E @ equalelemsP )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( D @ ssList )
| ( ( D @ ( C @ cons ) @ ( B @ cons ) @ ( A @ app ) )
!= E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause180) ).
thf(420,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( E @ ssList )
| ~ ( E @ equalelemsP )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( D @ ssList )
| ( ( D @ ( C @ cons ) @ ( B @ cons ) @ ( A @ app ) )
!= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ segmentP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ segmentP ) )
| ~ ( B @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause152) ).
thf(499,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ segmentP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ segmentP ) )
| ~ ( B @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(212,axiom,
! [A: $i] :
( ( A @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause61) ).
thf(697,plain,
! [A: $i] :
( ( A @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(3721,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[485,3705]) ).
thf(3722,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[3721]) ).
thf(3723,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[3722:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(3782,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[3723]) ).
thf(3135,plain,
! [A: $i] :
( ( ( A @ skaf58 @ ( A @ skaf58 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[225,1158]) ).
thf(3136,plain,
! [A: $i] :
( ( A @ skaf58 @ ( A @ skaf58 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[3135]) ).
thf(3141,plain,
! [A: $i] :
( ( ( A @ skaf58 )
!= nil )
| ( ( A @ skaf58 )
!= sk2 ) ),
inference(simp,[status(thm)],[3136]) ).
thf(120,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause76) ).
thf(488,plain,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(145,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf47 ) @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause49) ).
thf(544,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf47 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(3083,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf47 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ~ ( C @ ( C @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[544,294]) ).
thf(3084,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf47 ) @ ssList )
!= ( C @ ssList ) )
| ~ ( C @ ( C @ neq ) ) ),
inference(simp,[status(thm)],[3083]) ).
thf(3085,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf47 ) @ ( B @ ( A @ skaf47 ) @ neq ) ),
inference(pattern_uni,[status(thm)],[3084:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf47 ) ))]]) ).
thf(3094,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf47 ) @ ( B @ ( A @ skaf47 ) @ neq ) ),
inference(simp,[status(thm)],[3085]) ).
thf(3712,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true
| ( sk7 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[3377,3705]) ).
thf(3713,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ( sk7 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[3712]) ).
thf(3714,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk7 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[3713:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(187,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ app ) @ hd )
= ( B @ hd ) )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause123) ).
thf(642,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ app ) @ hd )
= ( B @ hd ) )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(136,axiom,
! [A: $i] :
( ( nil = A )
| ( ( A @ tl @ ( A @ hd @ cons ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause104) ).
thf(526,plain,
! [A: $i] :
( ( nil = A )
| ( ( A @ tl @ ( A @ hd @ cons ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(5545,plain,
! [A: $i] :
( ( ( sk7 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[706,306]) ).
thf(5546,plain,
! [A: $i] :
( ( ( sk7 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(simp,[status(thm)],[5545]) ).
thf(5547,plain,
( ~ ( sk7 @ singletonP )
| ( ( nil @ ( sk7 @ skaf44 @ cons ) )
= sk7 ) ),
inference(pattern_uni,[status(thm)],[5546:[bind(A,$thf( sk7 ))]]) ).
thf(162,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ app ) @ tl )
= ( A @ ( B @ tl @ app ) ) )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause133) ).
thf(590,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ app ) @ tl )
= ( A @ ( B @ tl @ app ) ) )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(8848,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[460,350]) ).
thf(8849,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[8848]) ).
thf(8850,plain,
! [A: $i] : ( nil @ ( A @ skaf61 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[8849:[bind(A,$thf( C )),bind(B,$thf( C @ skaf61 ))]]) ).
thf(8952,plain,
! [A: $i] : ( nil @ ( A @ skaf61 @ rearsegP ) ),
inference(simp,[status(thm)],[8850]) ).
thf(1957,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[555,294]) ).
thf(1958,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1957]) ).
thf(1959,plain,
! [A: $i] :
~ ( A @ skaf67 @ ( A @ skaf67 @ neq ) ),
inference(pattern_uni,[status(thm)],[1958:[bind(A,$thf( C )),bind(B,$thf( C @ skaf67 ))]]) ).
thf(1964,plain,
! [A: $i] :
~ ( A @ skaf67 @ ( A @ skaf67 @ neq ) ),
inference(simp,[status(thm)],[1959]) ).
thf(897,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[329,496]) ).
thf(898,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[897]) ).
thf(899,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[898:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(901,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[899]) ).
thf(113,axiom,
! [A: $i] :
( ( A @ skaf49 @ ( A @ skaf50 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause87) ).
thf(476,plain,
! [A: $i] :
( ( A @ skaf49 @ ( A @ skaf50 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(8876,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[375,350]) ).
thf(8877,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[8876]) ).
thf(8878,plain,
! [A: $i] : ( nil @ ( A @ skaf57 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[8877:[bind(A,$thf( C )),bind(B,$thf( C @ skaf57 ))]]) ).
thf(8968,plain,
! [A: $i] : ( nil @ ( A @ skaf57 @ rearsegP ) ),
inference(simp,[status(thm)],[8878]) ).
thf(15822,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[637,487]) ).
thf(15823,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) ) ),
inference(simp,[status(thm)],[15822]) ).
thf(15824,plain,
! [A: $i] : ( nil @ ( A @ skaf82 @ segmentP ) ),
inference(pattern_uni,[status(thm)],[15823:[bind(A,$thf( C )),bind(B,$thf( C @ skaf82 ))]]) ).
thf(15912,plain,
! [A: $i] : ( nil @ ( A @ skaf82 @ segmentP ) ),
inference(simp,[status(thm)],[15824]) ).
thf(176,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ totalorderedP ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause125) ).
thf(622,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ totalorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(132,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = A )
| ( C @ ( B @ memberP ) )
| ~ ( C @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( C @ ( B @ ( A @ cons ) @ memberP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause161) ).
thf(515,plain,
! [C: $i,B: $i,A: $i] :
( ( C = A )
| ( C @ ( B @ memberP ) )
| ~ ( C @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( C @ ( B @ ( A @ cons ) @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(15859,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[295,487]) ).
thf(15860,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) ) ),
inference(simp,[status(thm)],[15859]) ).
thf(15861,plain,
! [A: $i] : ( nil @ ( A @ skaf62 @ segmentP ) ),
inference(pattern_uni,[status(thm)],[15860:[bind(A,$thf( C )),bind(B,$thf( C @ skaf62 ))]]) ).
thf(15927,plain,
! [A: $i] : ( nil @ ( A @ skaf62 @ segmentP ) ),
inference(simp,[status(thm)],[15861]) ).
thf(19,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( nil @ ( sk4 @ neq ) )
| ( A @ ( B @ ( C @ sk5 ) ) @ ssItem )
| ( ( C @ ( B @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_19) ).
thf(231,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( nil @ ( sk4 @ neq ) )
| ( A @ ( B @ ( C @ sk5 ) ) @ ssItem )
| ( ( C @ ( B @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(271,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( nil @ ( sk4 @ neq ) )
| ( A @ ( B @ ( C @ sk5 ) ) @ ssItem )
| ( ( C @ ( B @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[231]) ).
thf(272,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( nil @ ( sk4 @ neq ) )
| ( A @ ( B @ ( C @ sk5 ) ) @ ssItem )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( C @ ( B @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 ) ),
inference(lifteq,[status(thm)],[271]) ).
thf(2387,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( nil @ ( sk2 @ neq ) )
| ( A @ ( B @ ( C @ sk5 ) ) @ ssItem )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( C @ ( B @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 ) ),
inference(rewrite,[status(thm)],[272,274]) ).
thf(17881,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[222,337]) ).
thf(17882,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[17881]) ).
thf(17883,plain,
( ( sk2 @ tl @ ssList )
| ( nil = sk2 ) ),
inference(pattern_uni,[status(thm)],[17882:[bind(A,$thf( sk2 ))]]) ).
thf(19948,plain,
sk2 @ tl @ ssList,
inference(simplifyReflect,[status(thm)],[17883,779]) ).
thf(20026,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19948,487]) ).
thf(20027,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[20026]) ).
thf(20028,plain,
nil @ ( sk2 @ tl @ segmentP ),
inference(pattern_uni,[status(thm)],[20027:[bind(A,$thf( sk2 @ tl ))]]) ).
thf(170,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ( ( B @ ( A @ cons ) )
!= ( D @ ( C @ cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause170) ).
thf(605,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ( ( B @ ( A @ cons ) )
!= ( D @ ( C @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(9483,plain,
( ( ( skac2 @ ssItem )
!= ( sk7 @ ssItem ) )
| ~ ( sk6 @ ( sk7 @ neq ) )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[583,9464]) ).
thf(9484,plain,
( ( ( skac2 @ ssItem )
!= ( sk7 @ ssItem ) )
| ~ ( sk6 @ ( sk7 @ neq ) )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[9483]) ).
thf(9562,plain,
( ( skac2 != sk7 )
| ~ ( sk6 @ ( sk7 @ neq ) )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[9484]) ).
thf(9905,plain,
( ( ( sk6 @ ( sk7 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( skac2 != sk7 )
| ~ $true
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[225,9562]) ).
thf(9906,plain,
( ( ( sk6 @ ( sk7 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( skac2 != sk7 )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[9905]) ).
thf(9942,plain,
( ( sk6 != nil )
| ( sk7 != sk2 )
| ( skac2 != sk7 )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[9906]) ).
thf(8882,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[445,350]) ).
thf(8883,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[8882]) ).
thf(8884,plain,
! [A: $i] : ( nil @ ( A @ skaf73 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[8883:[bind(A,$thf( C )),bind(B,$thf( C @ skaf73 ))]]) ).
thf(8971,plain,
! [A: $i] : ( nil @ ( A @ skaf73 @ rearsegP ) ),
inference(simp,[status(thm)],[8884]) ).
thf(21,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( nil @ ( sk4 @ neq ) )
| ( A @ ( A @ ( B @ ( C @ sk5 ) ) @ geq ) )
| ( ( C @ ( B @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_21) ).
thf(237,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( nil @ ( sk4 @ neq ) )
| ( A @ ( A @ ( B @ ( C @ sk5 ) ) @ geq ) )
| ( ( C @ ( B @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(181,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause121) ).
thf(633,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(43,axiom,
! [A: $i] : ( A @ skaf79 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause16) ).
thf(311,plain,
! [A: $i] : ( A @ skaf79 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(8869,plain,
! [A: $i] :
( ( ( sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[706,350]) ).
thf(8870,plain,
! [A: $i] :
( ( ( sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[8869]) ).
thf(8871,plain,
nil @ ( sk7 @ rearsegP ),
inference(pattern_uni,[status(thm)],[8870:[bind(A,$thf( sk7 ))]]) ).
thf(20170,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[583,344]) ).
thf(20171,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[20170]) ).
thf(20172,plain,
~ ( skac2 @ ( skac2 @ neq ) ),
inference(pattern_uni,[status(thm)],[20171:[bind(A,$thf( skac2 ))]]) ).
thf(8943,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[222,350]) ).
thf(8944,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[8943]) ).
thf(8945,plain,
nil @ ( sk2 @ rearsegP ),
inference(pattern_uni,[status(thm)],[8944:[bind(A,$thf( sk2 ))]]) ).
thf(182,axiom,
! [A: $i] : ( A @ skaf74 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause21) ).
thf(636,plain,
! [A: $i] : ( A @ skaf74 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(2183,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[636,496]) ).
thf(2184,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2183]) ).
thf(2185,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2184:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(2189,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2185]) ).
thf(30,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf43 ) @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause52) ).
thf(282,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf43 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(2879,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf43 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ~ ( C @ ( C @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[282,294]) ).
thf(2880,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf43 ) @ ssList )
!= ( C @ ssList ) )
| ~ ( C @ ( C @ neq ) ) ),
inference(simp,[status(thm)],[2879]) ).
thf(2881,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf43 ) @ ( B @ ( A @ skaf43 ) @ neq ) ),
inference(pattern_uni,[status(thm)],[2880:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf43 ) ))]]) ).
thf(2883,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf43 ) @ ( B @ ( A @ skaf43 ) @ neq ) ),
inference(simp,[status(thm)],[2881]) ).
thf(981,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk6 @ ( A @ geq ) )
| ~ ( A @ ( sk2 @ memberP ) )
| ~ $true
| ( sk6 = A ) ),
inference(paramod_ordered,[status(thm)],[596,965]) ).
thf(982,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk6 @ ( A @ geq ) )
| ~ ( A @ ( sk2 @ memberP ) )
| ( sk6 = A ) ),
inference(simp,[status(thm)],[981]) ).
thf(983,plain,
( ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk6 @ ( skac3 @ geq ) )
| ~ ( skac3 @ ( sk2 @ memberP ) )
| ( skac3 = sk6 ) ),
inference(pattern_uni,[status(thm)],[982:[bind(A,$thf( skac3 ))]]) ).
thf(2353,plain,
( ~ $true
| ~ ( sk6 @ ( skac3 @ geq ) )
| ~ ( skac3 @ ( sk2 @ memberP ) )
| ( skac3 = sk6 ) ),
inference(rewrite,[status(thm)],[983,225]) ).
thf(2354,plain,
( ~ ( sk6 @ ( skac3 @ geq ) )
| ~ ( skac3 @ ( sk2 @ memberP ) )
| ( skac3 = sk6 ) ),
inference(simp,[status(thm)],[2353]) ).
thf(3171,plain,
( ( skac3 != skac3 )
| ( sk6 != sk6 )
| ~ ( sk6 @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( sk2 @ memberP ) )
| ~ ( sk6 @ ( skac3 @ geq ) )
| ~ ( skac3 @ ( sk2 @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[2354,3154]) ).
thf(3172,plain,
( ( skac3 != skac3 )
| ~ ( sk6 @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( sk2 @ memberP ) )
| ~ ( sk6 @ ( skac3 @ geq ) )
| ~ ( skac3 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[3171]) ).
thf(3173,plain,
( ~ ( sk6 @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( sk2 @ memberP ) )
| ~ ( sk6 @ ( skac3 @ geq ) )
| ~ ( skac3 @ ( sk2 @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[3172:[]]) ).
thf(8915,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf47 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[544,350]) ).
thf(8916,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf47 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[8915]) ).
thf(8917,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf47 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[8916:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf47 ) ))]]) ).
thf(8955,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf47 ) @ rearsegP ) ),
inference(simp,[status(thm)],[8917]) ).
thf(151,axiom,
! [A: $i] :
( ( ( A @ skaf81 @ ( A @ skaf79 @ cons ) @ ( A @ skaf78 @ cons ) @ ( A @ skaf80 @ app ) )
= A )
| ( A @ equalelemsP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause142) ).
thf(558,plain,
! [A: $i] :
( ( ( A @ skaf81 @ ( A @ skaf79 @ cons ) @ ( A @ skaf78 @ cons ) @ ( A @ skaf80 @ app ) )
= A )
| ( A @ equalelemsP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(37,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ memberP ) )
| ( C @ ( B @ memberP ) )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ( B @ ( A @ app ) @ memberP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause158) ).
thf(298,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ memberP ) )
| ( C @ ( B @ memberP ) )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ( B @ ( A @ app ) @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(92,axiom,
! [A: $i] :
( ( A @ ( A @ geq ) )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause55) ).
thf(430,plain,
! [A: $i] :
( ( A @ ( A @ geq ) )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(185,axiom,
! [A: $i] : ( A @ skaf54 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause41) ).
thf(640,plain,
! [A: $i] : ( A @ skaf54 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(2247,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[640,496]) ).
thf(2248,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2247]) ).
thf(2249,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2248:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(2253,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2249]) ).
thf(18967,plain,
( ( nil != nil )
| ( sk1 @ totalorderP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[17586,533]) ).
thf(18968,plain,
( ( sk1 @ totalorderP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[18967:[]]) ).
thf(75,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf45 ) @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause51) ).
thf(387,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf45 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(15847,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[387,487]) ).
thf(15848,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ segmentP ) ) ),
inference(simp,[status(thm)],[15847]) ).
thf(15849,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf45 ) @ segmentP ) ),
inference(pattern_uni,[status(thm)],[15848:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf45 ) ))]]) ).
thf(15923,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf45 ) @ segmentP ) ),
inference(simp,[status(thm)],[15849]) ).
thf(3736,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[583,3705]) ).
thf(3737,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[3736]) ).
thf(3738,plain,
nil @ ( skac2 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[3737:[bind(A,$thf( skac2 ))]]) ).
thf(3394,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) )
| ( sk1 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[3342,496]) ).
thf(3395,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[3394]) ).
thf(3396,plain,
! [A: $i] :
( ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[3395:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(160,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ leq ) )
| ~ ( F @ ssList )
| ~ ( F @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause182) ).
thf(584,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ leq ) )
| ~ ( F @ ssList )
| ~ ( F @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(153,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ segmentP ) )
| ~ ( D @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ( ( C @ ( B @ ( A @ app ) @ app ) )
!= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause173) ).
thf(562,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ segmentP ) )
| ~ ( D @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ( ( C @ ( B @ ( A @ app ) @ app ) )
!= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(211,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ strictorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause124) ).
thf(694,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ strictorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(82,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ totalorderedP )
| ~ ( B @ hd @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause159) ).
thf(402,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ totalorderedP )
| ~ ( B @ hd @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(15816,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[593,487]) ).
thf(15817,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) ) ),
inference(simp,[status(thm)],[15816]) ).
thf(15818,plain,
! [A: $i] : ( nil @ ( A @ skaf51 @ segmentP ) ),
inference(pattern_uni,[status(thm)],[15817:[bind(A,$thf( C )),bind(B,$thf( C @ skaf51 ))]]) ).
thf(15909,plain,
! [A: $i] : ( nil @ ( A @ skaf51 @ segmentP ) ),
inference(simp,[status(thm)],[15818]) ).
thf(2222,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[637,294]) ).
thf(2223,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[2222]) ).
thf(2224,plain,
! [A: $i] :
~ ( A @ skaf82 @ ( A @ skaf82 @ neq ) ),
inference(pattern_uni,[status(thm)],[2223:[bind(A,$thf( C )),bind(B,$thf( C @ skaf82 ))]]) ).
thf(2225,plain,
! [A: $i] :
~ ( A @ skaf82 @ ( A @ skaf82 @ neq ) ),
inference(simp,[status(thm)],[2224]) ).
thf(16747,plain,
! [A: $i] :
( ( ( sk7 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[706,337]) ).
thf(16748,plain,
! [A: $i] :
( ( ( sk7 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[16747]) ).
thf(16749,plain,
( ( sk7 @ tl @ ssList )
| ( sk7 = nil ) ),
inference(pattern_uni,[status(thm)],[16748:[bind(A,$thf( sk7 ))]]) ).
thf(784,plain,
( ( ( sk7 @ ( sk7 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[225,722]) ).
thf(785,plain,
( ( sk7 @ ( sk7 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[784]) ).
thf(786,plain,
( ( sk7 != nil )
| ( sk7 != sk2 ) ),
inference(simp,[status(thm)],[785]) ).
thf(18705,plain,
( ( sk7 != sk7 )
| ( nil != nil )
| ( sk7 != sk2 )
| ( sk7 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[16749,786]) ).
thf(18706,plain,
( ( sk7 != sk7 )
| ( sk7 != sk2 )
| ( sk7 @ tl @ ssList ) ),
inference(simp,[status(thm)],[18705]) ).
thf(18707,plain,
( ( sk7 != sk2 )
| ( sk7 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[18706:[]]) ).
thf(21199,plain,
! [A: $i] :
( ( ( sk7 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) )
| ( sk7 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[18707,294]) ).
thf(21200,plain,
! [A: $i] :
( ( ( sk7 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ( sk7 != sk2 ) ),
inference(simp,[status(thm)],[21199]) ).
thf(21201,plain,
( ~ ( sk7 @ tl @ ( sk7 @ tl @ neq ) )
| ( sk7 != sk2 ) ),
inference(pattern_uni,[status(thm)],[21200:[bind(A,$thf( sk7 @ tl ))]]) ).
thf(20181,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[457,344]) ).
thf(20182,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[20181]) ).
thf(20183,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( A @ skaf70 @ neq ) ),
inference(pattern_uni,[status(thm)],[20182:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(20237,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( A @ skaf70 @ neq ) ),
inference(simp,[status(thm)],[20183]) ).
thf(146,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ lt ) )
| ( D @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( F @ strictorderP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause183) ).
thf(545,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ lt ) )
| ( D @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( F @ strictorderP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(158,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ frontsegP ) )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause144) ).
thf(579,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ frontsegP ) )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(15835,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[601,487]) ).
thf(15836,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) ) ),
inference(simp,[status(thm)],[15835]) ).
thf(15837,plain,
! [A: $i] : ( nil @ ( A @ skaf66 @ segmentP ) ),
inference(pattern_uni,[status(thm)],[15836:[bind(A,$thf( C )),bind(B,$thf( C @ skaf66 ))]]) ).
thf(15919,plain,
! [A: $i] : ( nil @ ( A @ skaf66 @ segmentP ) ),
inference(simp,[status(thm)],[15837]) ).
thf(156,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ memberP ) )
| ~ ( D @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ( ( C @ ( B @ cons ) @ ( A @ app ) )
!= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause175) ).
thf(572,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ memberP ) )
| ~ ( D @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ( ( C @ ( B @ cons ) @ ( A @ app ) )
!= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(1702,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[485,496]) ).
thf(1703,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1702]) ).
thf(1704,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1703:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(1707,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1704]) ).
thf(2299,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[648,294]) ).
thf(2300,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[2299]) ).
thf(2301,plain,
! [A: $i] :
~ ( A @ skaf56 @ ( A @ skaf56 @ neq ) ),
inference(pattern_uni,[status(thm)],[2300:[bind(A,$thf( C )),bind(B,$thf( C @ skaf56 ))]]) ).
thf(2308,plain,
! [A: $i] :
~ ( A @ skaf56 @ ( A @ skaf56 @ neq ) ),
inference(simp,[status(thm)],[2301]) ).
thf(2996,plain,
! [A: $i] :
( ( ( A @ skaf57 @ ( A @ skaf57 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[225,941]) ).
thf(2997,plain,
! [A: $i] :
( ( A @ skaf57 @ ( A @ skaf57 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[2996]) ).
thf(3002,plain,
! [A: $i] :
( ( ( A @ skaf57 )
!= nil )
| ( ( A @ skaf57 )
!= sk2 ) ),
inference(simp,[status(thm)],[2997]) ).
thf(3724,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[453,3705]) ).
thf(3725,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[3724]) ).
thf(3726,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[3725:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(3783,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[3726]) ).
thf(915,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[362,294]) ).
thf(916,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[915]) ).
thf(917,plain,
! [A: $i] :
~ ( A @ skaf77 @ ( A @ skaf77 @ neq ) ),
inference(pattern_uni,[status(thm)],[916:[bind(A,$thf( C )),bind(B,$thf( C @ skaf77 ))]]) ).
thf(919,plain,
! [A: $i] :
~ ( A @ skaf77 @ ( A @ skaf77 @ neq ) ),
inference(simp,[status(thm)],[917]) ).
thf(202,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ skaf48 ) @ ( B @ ( B @ ( A @ skaf47 ) @ app ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause168) ).
thf(672,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ skaf48 ) @ ( B @ ( B @ ( A @ skaf47 ) @ app ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(77,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ gt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause105) ).
thf(391,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(3706,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[651,3705]) ).
thf(3707,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[3706]) ).
thf(3708,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[3707:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(3796,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[3708]) ).
thf(2160,plain,
! [A: $i] :
( ( ( A @ skaf72 @ ( A @ skaf72 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[225,817]) ).
thf(2161,plain,
! [A: $i] :
( ( A @ skaf72 @ ( A @ skaf72 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[2160]) ).
thf(2166,plain,
! [A: $i] :
( ( ( A @ skaf72 )
!= nil )
| ( ( A @ skaf72 )
!= sk2 ) ),
inference(simp,[status(thm)],[2161]) ).
thf(15806,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[661,487]) ).
thf(15807,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) ) ),
inference(simp,[status(thm)],[15806]) ).
thf(15808,plain,
! [A: $i] : ( nil @ ( A @ skaf76 @ segmentP ) ),
inference(pattern_uni,[status(thm)],[15807:[bind(A,$thf( C )),bind(B,$thf( C @ skaf76 ))]]) ).
thf(15902,plain,
! [A: $i] : ( nil @ ( A @ skaf76 @ segmentP ) ),
inference(simp,[status(thm)],[15808]) ).
thf(3336,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[222,372]) ).
thf(3337,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP ) ),
inference(simp,[status(thm)],[3336]) ).
thf(3338,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk2 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[3337:[bind(A,$thf( sk2 ))]]) ).
thf(3347,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[3338]) ).
thf(3417,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) )
| ( sk2 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[3347,496]) ).
thf(3418,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[3417]) ).
thf(3419,plain,
! [A: $i] :
( ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[3418:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(8,negated_conjecture,
( ~ ( nil @ ( sk4 @ neq ) )
| ( nil @ ( sk2 @ neq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
thf(230,plain,
( ~ ( nil @ ( sk4 @ neq ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(318,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ frontsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) ) ),
inference(cnf,[status(esa)],[317]) ).
thf(2057,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[593,294]) ).
thf(2058,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[2057]) ).
thf(2059,plain,
! [A: $i] :
~ ( A @ skaf51 @ ( A @ skaf51 @ neq ) ),
inference(pattern_uni,[status(thm)],[2058:[bind(A,$thf( C )),bind(B,$thf( C @ skaf51 ))]]) ).
thf(2065,plain,
! [A: $i] :
~ ( A @ skaf51 @ ( A @ skaf51 @ neq ) ),
inference(simp,[status(thm)],[2059]) ).
thf(20226,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[596,344]) ).
thf(20227,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[20226]) ).
thf(20228,plain,
~ ( skac3 @ ( skac3 @ neq ) ),
inference(pattern_uni,[status(thm)],[20227:[bind(A,$thf( skac3 ))]]) ).
thf(20309,plain,
( ( ( skac3 @ ( skac3 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[225,20228]) ).
thf(20310,plain,
( ( skac3 @ ( skac3 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[20309]) ).
thf(20327,plain,
( ( skac3 != nil )
| ( skac3 != sk2 ) ),
inference(simp,[status(thm)],[20310]) ).
thf(9553,plain,
( ( ( skac3 @ ssItem )
!= ( sk7 @ ssItem ) )
| ~ ( sk6 @ ( sk7 @ neq ) )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[596,9464]) ).
thf(9554,plain,
( ( ( skac3 @ ssItem )
!= ( sk7 @ ssItem ) )
| ~ ( sk6 @ ( sk7 @ neq ) )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[9553]) ).
thf(9559,plain,
( ( skac3 != sk7 )
| ~ ( sk6 @ ( sk7 @ neq ) )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[9554]) ).
thf(9583,plain,
( ( ( sk6 @ ( sk7 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( skac3 != sk7 )
| ~ $true
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[225,9559]) ).
thf(9584,plain,
( ( ( sk6 @ ( sk7 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( skac3 != sk7 )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[9583]) ).
thf(9623,plain,
( ( sk6 != nil )
| ( sk7 != sk2 )
| ( skac3 != sk7 )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[9584]) ).
thf(84,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ gt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause146) ).
thf(406,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ gt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(15800,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[460,487]) ).
thf(15801,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) ) ),
inference(simp,[status(thm)],[15800]) ).
thf(15802,plain,
! [A: $i] : ( nil @ ( A @ skaf61 @ segmentP ) ),
inference(pattern_uni,[status(thm)],[15801:[bind(A,$thf( C )),bind(B,$thf( C @ skaf61 ))]]) ).
thf(15929,plain,
! [A: $i] : ( nil @ ( A @ skaf61 @ segmentP ) ),
inference(simp,[status(thm)],[15802]) ).
thf(20046,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[19948,294]) ).
thf(20047,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[20046]) ).
thf(20048,plain,
~ ( sk2 @ tl @ ( sk2 @ tl @ neq ) ),
inference(pattern_uni,[status(thm)],[20047:[bind(A,$thf( sk2 @ tl ))]]) ).
thf(20346,plain,
( ( ( sk2 @ tl @ ( sk2 @ tl @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[225,20048]) ).
thf(20347,plain,
( ( sk2 @ tl @ ( sk2 @ tl @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[20346]) ).
thf(20366,plain,
( ( ( sk2 @ tl )
!= nil )
| ( ( sk2 @ tl )
!= sk2 ) ),
inference(simp,[status(thm)],[20347]) ).
thf(8879,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[601,350]) ).
thf(8880,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[8879]) ).
thf(8881,plain,
! [A: $i] : ( nil @ ( A @ skaf66 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[8880:[bind(A,$thf( C )),bind(B,$thf( C @ skaf66 ))]]) ).
thf(8970,plain,
! [A: $i] : ( nil @ ( A @ skaf66 @ rearsegP ) ),
inference(simp,[status(thm)],[8881]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ( B @ singletonP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( nil @ ( A @ cons ) )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause116) ).
thf(377,plain,
! [B: $i,A: $i] :
( ( B @ singletonP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( nil @ ( A @ cons ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(144,axiom,
! [A: $i] : ( A @ skaf52 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause43) ).
thf(543,plain,
! [A: $i] : ( A @ skaf52 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(1926,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[543,294]) ).
thf(1927,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1926]) ).
thf(1928,plain,
! [A: $i] :
~ ( A @ skaf52 @ ( A @ skaf52 @ neq ) ),
inference(pattern_uni,[status(thm)],[1927:[bind(A,$thf( C )),bind(B,$thf( C @ skaf52 ))]]) ).
thf(1933,plain,
! [A: $i] :
~ ( A @ skaf52 @ ( A @ skaf52 @ neq ) ),
inference(simp,[status(thm)],[1928]) ).
thf(190,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ ( D @ app ) @ app ) @ segmentP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause172) ).
thf(649,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ ( D @ app ) @ app ) @ segmentP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(174,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ tl )
= B )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause96) ).
thf(616,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ tl )
= B )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(885,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[311,496]) ).
thf(886,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[885]) ).
thf(887,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[886:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(890,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[887]) ).
thf(512,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(cnf,[status(esa)],[511]) ).
thf(513,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[512]) ).
thf(514,plain,
( ( nil @ ( nil @ segmentP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[513]) ).
thf(5729,plain,
( ( nil @ ( nil @ segmentP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[514,345]) ).
thf(5730,plain,
nil @ ( nil @ segmentP ),
inference(simp,[status(thm)],[5729]) ).
thf(4909,plain,
! [A: $i] :
( ( ( sk7 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ~ $true
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[706,301]) ).
thf(4910,plain,
! [A: $i] :
( ( ( sk7 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(simp,[status(thm)],[4909]) ).
thf(4911,plain,
( ( sk7 @ strictorderedP )
| ~ ( sk7 @ skaf70 @ ( sk7 @ skaf69 @ lt ) ) ),
inference(pattern_uni,[status(thm)],[4910:[bind(A,$thf( sk7 ))]]) ).
thf(322,plain,
! [A: $i] :
( ( ( A @ skaf73 @ ( A @ skaf70 @ cons ) @ ( A @ skaf72 @ ( A @ skaf69 @ cons ) @ ( A @ skaf71 @ app ) @ app ) )
= A )
| ( A @ strictorderedP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[321]) ).
thf(323,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ( ( A @ skaf73 @ ( A @ skaf70 @ cons ) @ ( A @ skaf72 @ ( A @ skaf69 @ cons ) @ ( A @ skaf71 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[322]) ).
thf(164,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause68) ).
thf(594,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(243,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( nil @ ( sk4 @ neq ) )
| ( A @ ( B @ ( C @ sk5 ) ) @ ( sk2 @ memberP ) )
| ( ( C @ ( B @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[217]) ).
thf(244,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( nil @ ( sk4 @ neq ) )
| ( A @ ( B @ ( C @ sk5 ) ) @ ( sk2 @ memberP ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( C @ ( B @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 ) ),
inference(lifteq,[status(thm)],[243]) ).
thf(726,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( nil @ ( sk2 @ neq ) )
| ( A @ ( B @ ( C @ sk5 ) ) @ ( sk2 @ memberP ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( C @ ( B @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 ) ),
inference(rewrite,[status(thm)],[244,274]) ).
thf(20280,plain,
( ( ( sk6 @ ( sk6 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[225,20189]) ).
thf(20281,plain,
( ( sk6 @ ( sk6 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[20280]) ).
thf(20298,plain,
( ( sk6 != nil )
| ( sk6 != sk2 ) ),
inference(simp,[status(thm)],[20281]) ).
thf(117,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause110) ).
thf(483,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(8891,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[387,350]) ).
thf(8892,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[8891]) ).
thf(8893,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf45 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[8892:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf45 ) ))]]) ).
thf(8974,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf45 ) @ rearsegP ) ),
inference(simp,[status(thm)],[8893]) ).
thf(15890,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[405,487]) ).
thf(15891,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) ) ),
inference(simp,[status(thm)],[15890]) ).
thf(15892,plain,
! [A: $i] : ( nil @ ( A @ skaf58 @ segmentP ) ),
inference(pattern_uni,[status(thm)],[15891:[bind(A,$thf( C )),bind(B,$thf( C @ skaf58 ))]]) ).
thf(15914,plain,
! [A: $i] : ( nil @ ( A @ skaf58 @ segmentP ) ),
inference(simp,[status(thm)],[15892]) ).
thf(200,axiom,
! [A: $i] :
( ( A @ equalelemsP )
| ~ ( A @ ssList )
| ( ( A @ skaf79 )
!= ( A @ skaf78 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause89) ).
thf(668,plain,
! [A: $i] :
( ( A @ equalelemsP )
| ~ ( A @ ssList )
| ( ( A @ skaf79 )
!= ( A @ skaf78 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(52,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause155) ).
thf(330,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(122,axiom,
! [A: $i] : ( A @ skaf80 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause15) ).
thf(494,plain,
! [A: $i] : ( A @ skaf80 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(8857,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[561,350]) ).
thf(8858,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[8857]) ).
thf(8859,plain,
! [A: $i] : ( nil @ ( A @ skaf81 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[8858:[bind(A,$thf( C )),bind(B,$thf( C @ skaf81 ))]]) ).
thf(8958,plain,
! [A: $i] : ( nil @ ( A @ skaf81 @ rearsegP ) ),
inference(simp,[status(thm)],[8859]) ).
thf(1800,plain,
( ( ( nil @ ( sk6 @ cons ) @ ( sk7 @ app ) )
!= ( sk8 @ ( sk7 @ app ) ) )
| ( ( sk8 @ ( sk1 @ app ) )
= sk2 ) ),
inference(paramod_ordered,[status(thm)],[1407,1252]) ).
thf(1831,plain,
( ( ( nil @ ( sk6 @ cons ) )
!= sk8 )
| ( sk7 != sk7 )
| ( ( sk8 @ ( sk1 @ app ) )
= sk2 ) ),
inference(simp,[status(thm)],[1800]) ).
thf(1838,plain,
( ( ( nil @ ( sk6 @ cons ) )
!= sk8 )
| ( ( sk8 @ ( sk1 @ app ) )
= sk2 ) ),
inference(simp,[status(thm)],[1831]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ hd )
= A )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause97) ).
thf(399,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ hd )
= A )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(5644,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[222,306]) ).
thf(5645,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(simp,[status(thm)],[5644]) ).
thf(5646,plain,
( ~ ( sk2 @ singletonP )
| ( ( nil @ ( sk2 @ skaf44 @ cons ) )
= sk2 ) ),
inference(pattern_uni,[status(thm)],[5645:[bind(A,$thf( sk2 ))]]) ).
thf(299,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ memberP ) )
| ( C @ ( B @ memberP ) )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ( B @ ( A @ app ) @ memberP ) ) ),
inference(cnf,[status(esa)],[298]) ).
thf(3273,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ( C @ ssItem )
| ( B @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[375,372]) ).
thf(3274,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ( C @ ssItem )
| ( B @ duplicatefreeP ) ),
inference(simp,[status(thm)],[3273]) ).
thf(3275,plain,
! [B: $i,A: $i] :
( ( A @ ssItem )
| ( B @ skaf57 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[3274:[bind(A,$thf( D )),bind(B,$thf( D @ skaf57 ))]]) ).
thf(3348,plain,
! [B: $i,A: $i] :
( ( A @ ssItem )
| ( B @ skaf57 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[3275]) ).
thf(5324,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[218,303]) ).
thf(5325,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP ) ),
inference(simp,[status(thm)],[5324]) ).
thf(5326,plain,
( ( sk1 @ skaf50 @ ( sk1 @ skaf49 @ leq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5325:[bind(A,$thf( sk1 ))]]) ).
thf(17,negated_conjecture,
( ( nil @ ( sk2 @ neq ) )
| ( ( sk8 @ ( sk7 @ app ) )
= sk3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
thf(223,plain,
( ( nil @ ( sk2 @ neq ) )
| ( ( sk8 @ ( sk7 @ app ) )
= sk3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(171,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ app ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause140) ).
thf(608,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ app ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(79,axiom,
! [A: $i] :
( ( ( A @ ( nil @ app ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause74) ).
thf(394,plain,
! [A: $i] :
( ( ( A @ ( nil @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(3,negated_conjecture,
sk3 @ ssList,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
thf(226,plain,
sk3 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4952,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ~ $true
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[1225,301]) ).
thf(4953,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(simp,[status(thm)],[4952]) ).
thf(4954,plain,
( ( sk8 @ strictorderedP )
| ~ ( sk8 @ skaf70 @ ( sk8 @ skaf69 @ lt ) ) ),
inference(pattern_uni,[status(thm)],[4953:[bind(A,$thf( sk8 ))]]) ).
thf(15797,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[655,487]) ).
thf(15798,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) ) ),
inference(simp,[status(thm)],[15797]) ).
thf(15799,plain,
! [A: $i] : ( nil @ ( A @ skaf71 @ segmentP ) ),
inference(pattern_uni,[status(thm)],[15798:[bind(A,$thf( C )),bind(B,$thf( C @ skaf71 ))]]) ).
thf(15928,plain,
! [A: $i] : ( nil @ ( A @ skaf71 @ segmentP ) ),
inference(simp,[status(thm)],[15799]) ).
thf(112,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( nil @ ( A @ cons ) @ app ) )
= ( B @ ( A @ cons ) ) )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause120) ).
thf(473,plain,
! [B: $i,A: $i] :
( ( ( B @ ( nil @ ( A @ cons ) @ app ) )
= ( B @ ( A @ cons ) ) )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(5437,plain,
( ( ( sk7 @ ( sk6 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( skac3 != sk7 )
| ~ $true
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[225,5141]) ).
thf(5438,plain,
( ( ( sk7 @ ( sk6 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( skac3 != sk7 )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[5437]) ).
thf(5463,plain,
( ( sk7 != nil )
| ( sk6 != sk2 )
| ( skac3 != sk7 )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[5438]) ).
thf(8934,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[405,350]) ).
thf(8935,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[8934]) ).
thf(8936,plain,
! [A: $i] : ( nil @ ( A @ skaf58 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[8935:[bind(A,$thf( C )),bind(B,$thf( C @ skaf58 ))]]) ).
thf(8965,plain,
! [A: $i] : ( nil @ ( A @ skaf58 @ rearsegP ) ),
inference(simp,[status(thm)],[8936]) ).
thf(167,axiom,
! [A: $i] : ( A @ skaf63 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause32) ).
thf(600,plain,
! [A: $i] : ( A @ skaf63 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(2088,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[600,294]) ).
thf(2089,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[2088]) ).
thf(2090,plain,
! [A: $i] :
~ ( A @ skaf63 @ ( A @ skaf63 @ neq ) ),
inference(pattern_uni,[status(thm)],[2089:[bind(A,$thf( C )),bind(B,$thf( C @ skaf63 ))]]) ).
thf(2096,plain,
! [A: $i] :
~ ( A @ skaf63 @ ( A @ skaf63 @ neq ) ),
inference(simp,[status(thm)],[2090]) ).
thf(1196,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[445,294]) ).
thf(1197,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1196]) ).
thf(1198,plain,
! [A: $i] :
~ ( A @ skaf73 @ ( A @ skaf73 @ neq ) ),
inference(pattern_uni,[status(thm)],[1197:[bind(A,$thf( C )),bind(B,$thf( C @ skaf73 ))]]) ).
thf(1203,plain,
! [A: $i] :
~ ( A @ skaf73 @ ( A @ skaf73 @ neq ) ),
inference(simp,[status(thm)],[1198]) ).
thf(205,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause112) ).
thf(680,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(198,axiom,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ frontsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause84) ).
thf(663,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(15896,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[543,487]) ).
thf(15897,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) ) ),
inference(simp,[status(thm)],[15896]) ).
thf(15898,plain,
! [A: $i] : ( nil @ ( A @ skaf52 @ segmentP ) ),
inference(pattern_uni,[status(thm)],[15897:[bind(A,$thf( C )),bind(B,$thf( C @ skaf52 ))]]) ).
thf(15918,plain,
! [A: $i] : ( nil @ ( A @ skaf52 @ segmentP ) ),
inference(simp,[status(thm)],[15898]) ).
thf(8842,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[555,350]) ).
thf(8843,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[8842]) ).
thf(8844,plain,
! [A: $i] : ( nil @ ( A @ skaf67 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[8843:[bind(A,$thf( C )),bind(B,$thf( C @ skaf67 ))]]) ).
thf(8949,plain,
! [A: $i] : ( nil @ ( A @ skaf67 @ rearsegP ) ),
inference(simp,[status(thm)],[8844]) ).
thf(105,axiom,
! [A: $i] :
( ( A @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause59) ).
thf(458,plain,
! [A: $i] :
( ( A @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(248,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( nil @ ( sk4 @ neq ) )
| ( A @ ( A @ ( B @ ( C @ sk5 ) ) @ geq ) )
| ( ( C @ ( B @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[237]) ).
thf(249,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( nil @ ( sk4 @ neq ) )
| ( A @ ( A @ ( B @ ( C @ sk5 ) ) @ geq ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( C @ ( B @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 ) ),
inference(lifteq,[status(thm)],[248]) ).
thf(823,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( nil @ ( sk2 @ neq ) )
| ( A @ ( A @ ( B @ ( C @ sk5 ) ) @ geq ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( C @ ( B @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 ) ),
inference(rewrite,[status(thm)],[249,274]) ).
thf(5622,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[218,306]) ).
thf(5623,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(simp,[status(thm)],[5622]) ).
thf(5624,plain,
( ~ ( sk1 @ singletonP )
| ( ( nil @ ( sk1 @ skaf44 @ cons ) )
= sk1 ) ),
inference(pattern_uni,[status(thm)],[5623:[bind(A,$thf( sk1 ))]]) ).
thf(208,axiom,
! [A: $i] :
( ( A @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause57) ).
thf(690,plain,
! [A: $i] :
( ( A @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(325,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( F @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
inference(cnf,[status(esa)],[324]) ).
thf(326,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( F @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
inference(lifteq,[status(thm)],[325]) ).
thf(327,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ lt ) )
| ~ ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) @ ssList )
| ~ ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList ) ),
inference(simp,[status(thm)],[326]) ).
thf(1776,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[509,294]) ).
thf(1777,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1776]) ).
thf(1778,plain,
! [A: $i] :
~ ( A @ skaf53 @ ( A @ skaf53 @ neq ) ),
inference(pattern_uni,[status(thm)],[1777:[bind(A,$thf( C )),bind(B,$thf( C @ skaf53 ))]]) ).
thf(1780,plain,
! [A: $i] :
~ ( A @ skaf53 @ ( A @ skaf53 @ neq ) ),
inference(simp,[status(thm)],[1778]) ).
thf(3733,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[329,3705]) ).
thf(3734,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[3733]) ).
thf(3735,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[3734:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(3786,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[3735]) ).
thf(15853,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[494,487]) ).
thf(15854,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) ) ),
inference(simp,[status(thm)],[15853]) ).
thf(15855,plain,
! [A: $i] : ( nil @ ( A @ skaf80 @ segmentP ) ),
inference(pattern_uni,[status(thm)],[15854:[bind(A,$thf( C )),bind(B,$thf( C @ skaf80 ))]]) ).
thf(15924,plain,
! [A: $i] : ( nil @ ( A @ skaf80 @ segmentP ) ),
inference(simp,[status(thm)],[15855]) ).
thf(2974,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ~ ( C @ ( C @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[387,294]) ).
thf(2975,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ssList )
!= ( C @ ssList ) )
| ~ ( C @ ( C @ neq ) ) ),
inference(simp,[status(thm)],[2974]) ).
thf(2976,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf45 ) @ ( B @ ( A @ skaf45 ) @ neq ) ),
inference(pattern_uni,[status(thm)],[2975:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf45 ) ))]]) ).
thf(2977,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf45 ) @ ( B @ ( A @ skaf45 ) @ neq ) ),
inference(simp,[status(thm)],[2976]) ).
thf(3754,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[641,3705]) ).
thf(3755,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[3754]) ).
thf(3756,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[3755:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(3791,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[3756]) ).
thf(331,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
inference(cnf,[status(esa)],[330]) ).
thf(9493,plain,
( ( ( sk7 @ ssItem )
!= ( sk6 @ ssItem ) )
| ~ ( sk6 @ ( sk7 @ neq ) )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[953,9464]) ).
thf(9494,plain,
( ( ( sk7 @ ssItem )
!= ( sk6 @ ssItem ) )
| ~ ( sk6 @ ( sk7 @ neq ) )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[9493]) ).
thf(9567,plain,
( ( sk7 != sk6 )
| ~ ( sk6 @ ( sk7 @ neq ) )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[9494]) ).
thf(3772,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true
| ( sk2 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[3347,3705]) ).
thf(3773,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[3772]) ).
thf(3774,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk2 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[3773:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(800,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[295,294]) ).
thf(801,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[800]) ).
thf(802,plain,
! [A: $i] :
~ ( A @ skaf62 @ ( A @ skaf62 @ neq ) ),
inference(pattern_uni,[status(thm)],[801:[bind(A,$thf( C )),bind(B,$thf( C @ skaf62 ))]]) ).
thf(803,plain,
! [A: $i] :
~ ( A @ skaf62 @ ( A @ skaf62 @ neq ) ),
inference(simp,[status(thm)],[802]) ).
thf(1212,plain,
! [A: $i] :
( ( ( A @ skaf62 @ ( A @ skaf62 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[225,803]) ).
thf(1213,plain,
! [A: $i] :
( ( A @ skaf62 @ ( A @ skaf62 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[1212]) ).
thf(1218,plain,
! [A: $i] :
( ( ( A @ skaf62 )
!= nil )
| ( ( A @ skaf62 )
!= sk2 ) ),
inference(simp,[status(thm)],[1213]) ).
thf(9949,plain,
( ( ( sk6 @ ( sk7 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( sk7 != sk6 )
| ~ $true
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[225,9567]) ).
thf(9950,plain,
( ( ( sk6 @ ( sk7 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( sk7 != sk6 )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[9949]) ).
thf(9986,plain,
( ( sk6 != nil )
| ( sk7 != sk2 )
| ( sk7 != sk6 )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[9950]) ).
thf(715,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,294]) ).
thf(716,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[715]) ).
thf(717,plain,
~ ( sk2 @ ( sk2 @ neq ) ),
inference(pattern_uni,[status(thm)],[716:[bind(A,$thf( sk2 ))]]) ).
thf(21726,plain,
( ( ( sk7 @ tl @ ( sk7 @ tl @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true
| ( sk7 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[225,21201]) ).
thf(21727,plain,
( ( ( sk7 @ tl @ ( sk7 @ tl @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( sk7 != sk2 ) ),
inference(simp,[status(thm)],[21726]) ).
thf(21764,plain,
( ( ( sk7 @ tl )
!= nil )
| ( ( sk7 @ tl )
!= sk2 )
| ( sk7 != sk2 ) ),
inference(simp,[status(thm)],[21727]) ).
thf(3330,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ( C @ ssItem )
| ( B @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[532,372]) ).
thf(3331,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ( C @ ssItem )
| ( B @ duplicatefreeP ) ),
inference(simp,[status(thm)],[3330]) ).
thf(3332,plain,
! [B: $i,A: $i] :
( ( A @ ssItem )
| ( B @ skaf68 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[3331:[bind(A,$thf( D )),bind(B,$thf( D @ skaf68 ))]]) ).
thf(3344,plain,
! [B: $i,A: $i] :
( ( A @ ssItem )
| ( B @ skaf68 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[3332]) ).
thf(111,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause129) ).
thf(470,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(157,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ app ) @ ( A @ cons ) )
= ( C @ ( B @ ( A @ cons ) @ app ) ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause157) ).
thf(576,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ app ) @ ( A @ cons ) )
= ( C @ ( B @ ( A @ cons ) @ app ) ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(3695,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) )
| ( sk7 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[3377,496]) ).
thf(3696,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) )
| ( sk7 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[3695]) ).
thf(3697,plain,
! [A: $i] :
( ~ ( A @ ( nil @ memberP ) )
| ( sk7 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[3696:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(19987,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19948,350]) ).
thf(19988,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[19987]) ).
thf(19989,plain,
nil @ ( sk2 @ tl @ rearsegP ),
inference(pattern_uni,[status(thm)],[19988:[bind(A,$thf( sk2 @ tl ))]]) ).
thf(2829,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[693,496]) ).
thf(2830,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2829]) ).
thf(2831,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2830:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(2838,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2831]) ).
thf(194,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ skaf43 ) @ ( B @ cons ) @ ( B @ ( A @ skaf42 ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ memberP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause169) ).
thf(656,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ skaf43 ) @ ( B @ cons ) @ ( B @ ( A @ skaf42 ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(20184,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[311,344]) ).
thf(20185,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[20184]) ).
thf(20186,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( A @ skaf79 @ neq ) ),
inference(pattern_uni,[status(thm)],[20185:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(20238,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( A @ skaf79 @ neq ) ),
inference(simp,[status(thm)],[20186]) ).
thf(313,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP ) ),
inference(cnf,[status(esa)],[312]) ).
thf(314,plain,
! [B: $i,A: $i] :
( ( B @ hd @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP )
| ( nil = B ) ),
inference(lifteq,[status(thm)],[313]) ).
thf(2802,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[671,496]) ).
thf(2803,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2802]) ).
thf(2804,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2803:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(2807,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2804]) ).
thf(124,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ equalelemsP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause64) ).
thf(497,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ equalelemsP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(173,axiom,
! [A: $i] :
( ( nil = A )
| ( ( A @ skaf82 @ ( A @ skaf83 @ cons ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause109) ).
thf(613,plain,
! [A: $i] :
( ( nil = A )
| ( ( A @ skaf82 @ ( A @ skaf83 @ cons ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(15856,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[648,487]) ).
thf(15857,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) ) ),
inference(simp,[status(thm)],[15856]) ).
thf(15858,plain,
! [A: $i] : ( nil @ ( A @ skaf56 @ segmentP ) ),
inference(pattern_uni,[status(thm)],[15857:[bind(A,$thf( C )),bind(B,$thf( C @ skaf56 ))]]) ).
thf(15925,plain,
! [A: $i] : ( nil @ ( A @ skaf56 @ segmentP ) ),
inference(simp,[status(thm)],[15858]) ).
thf(25535,plain,
( ( ( sk1 @ tl @ ( sk1 @ tl @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true
| ( sk2 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[225,24715]) ).
thf(25536,plain,
( ( ( sk1 @ tl @ ( sk1 @ tl @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[25535]) ).
thf(25558,plain,
( ( ( sk1 @ tl )
!= nil )
| ( ( sk1 @ tl )
!= sk2 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[25536]) ).
thf(99,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ rearsegP ) )
| ~ ( B @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause128) ).
thf(446,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ rearsegP ) )
| ~ ( B @ ( A @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(9485,plain,
( ( ( sk6 @ ( sk7 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) )
| ~ ( sk7 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[225,9464]) ).
thf(9486,plain,
( ( ( sk6 @ ( sk7 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) )
| ~ ( sk7 @ ssItem ) ),
inference(simp,[status(thm)],[9485]) ).
thf(9574,plain,
( ( sk6 != nil )
| ( sk7 != sk2 )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) )
| ~ ( sk7 @ ssItem ) ),
inference(simp,[status(thm)],[9486]) ).
thf(8888,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[509,350]) ).
thf(8889,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[8888]) ).
thf(8890,plain,
! [A: $i] : ( nil @ ( A @ skaf53 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[8889:[bind(A,$thf( C )),bind(B,$thf( C @ skaf53 ))]]) ).
thf(8973,plain,
! [A: $i] : ( nil @ ( A @ skaf53 @ rearsegP ) ),
inference(simp,[status(thm)],[8890]) ).
thf(178,axiom,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ segmentP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause80) ).
thf(627,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(8894,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[494,350]) ).
thf(8895,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[8894]) ).
thf(8896,plain,
! [A: $i] : ( nil @ ( A @ skaf80 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[8895:[bind(A,$thf( C )),bind(B,$thf( C @ skaf80 ))]]) ).
thf(8946,plain,
! [A: $i] : ( nil @ ( A @ skaf80 @ rearsegP ) ),
inference(simp,[status(thm)],[8896]) ).
thf(143,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ leq ) )
| ( D @ ( B @ leq ) )
| ~ ( F @ ssList )
| ~ ( F @ totalorderP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause184) ).
thf(539,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ leq ) )
| ( D @ ( B @ leq ) )
| ~ ( F @ ssList )
| ~ ( F @ totalorderP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(15881,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf48 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[482,487]) ).
thf(15882,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf48 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ segmentP ) ) ),
inference(simp,[status(thm)],[15881]) ).
thf(15883,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf48 ) @ segmentP ) ),
inference(pattern_uni,[status(thm)],[15882:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf48 ) ))]]) ).
thf(15910,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf48 ) @ segmentP ) ),
inference(simp,[status(thm)],[15883]) ).
thf(3333,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ( C @ ssItem )
| ( B @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[543,372]) ).
thf(3334,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ( C @ ssItem )
| ( B @ duplicatefreeP ) ),
inference(simp,[status(thm)],[3333]) ).
thf(3335,plain,
! [B: $i,A: $i] :
( ( A @ ssItem )
| ( B @ skaf52 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[3334:[bind(A,$thf( D )),bind(B,$thf( D @ skaf52 ))]]) ).
thf(3346,plain,
! [B: $i,A: $i] :
( ( A @ ssItem )
| ( B @ skaf52 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[3335]) ).
thf(2338,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[651,496]) ).
thf(2339,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2338]) ).
thf(2340,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2339:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(2342,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2340]) ).
thf(3663,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) )
| ( sk8 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[3368,496]) ).
thf(3664,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) )
| ( sk8 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[3663]) ).
thf(3665,plain,
! [A: $i] :
( ~ ( A @ ( nil @ memberP ) )
| ( sk8 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[3664:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(3709,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[636,3705]) ).
thf(3710,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[3709]) ).
thf(3711,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[3710:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(3797,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[3711]) ).
thf(109,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ app ) @ frontsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause137) ).
thf(465,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ app ) @ frontsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(150,axiom,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf60 @ ( A @ skaf59 @ lt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause93) ).
thf(556,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf60 @ ( A @ skaf59 @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(135,axiom,
! [A: $i] :
( ( A @ totalorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf65 @ ( A @ skaf64 @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause91) ).
thf(524,plain,
! [A: $i] :
( ( A @ totalorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf65 @ ( A @ skaf64 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(8863,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf46 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[328,350]) ).
thf(8864,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf46 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[8863]) ).
thf(8865,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf46 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[8864:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf46 ) ))]]) ).
thf(8962,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf46 ) @ rearsegP ) ),
inference(simp,[status(thm)],[8865]) ).
thf(8918,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[600,350]) ).
thf(8919,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[8918]) ).
thf(8920,plain,
! [A: $i] : ( nil @ ( A @ skaf63 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[8919:[bind(A,$thf( C )),bind(B,$thf( C @ skaf63 ))]]) ).
thf(8957,plain,
! [A: $i] : ( nil @ ( A @ skaf63 @ rearsegP ) ),
inference(simp,[status(thm)],[8920]) ).
thf(15871,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf47 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[544,487]) ).
thf(15872,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf47 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ segmentP ) ) ),
inference(simp,[status(thm)],[15871]) ).
thf(15873,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf47 ) @ segmentP ) ),
inference(pattern_uni,[status(thm)],[15872:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf47 ) ))]]) ).
thf(15903,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf47 ) @ segmentP ) ),
inference(simp,[status(thm)],[15873]) ).
thf(5306,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1225,303]) ).
thf(5307,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP ) ),
inference(simp,[status(thm)],[5306]) ).
thf(5308,plain,
( ( sk8 @ skaf50 @ ( sk8 @ skaf49 @ leq ) )
| ( sk8 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5307:[bind(A,$thf( sk8 ))]]) ).
thf(2270,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[641,496]) ).
thf(2271,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2270]) ).
thf(2272,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2271:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(2273,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2272]) ).
thf(1895,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[532,294]) ).
thf(1896,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1895]) ).
thf(1897,plain,
! [A: $i] :
~ ( A @ skaf68 @ ( A @ skaf68 @ neq ) ),
inference(pattern_uni,[status(thm)],[1896:[bind(A,$thf( C )),bind(B,$thf( C @ skaf68 ))]]) ).
thf(1903,plain,
! [A: $i] :
~ ( A @ skaf68 @ ( A @ skaf68 @ neq ) ),
inference(simp,[status(thm)],[1897]) ).
thf(12979,plain,
! [B: $i,A: $i] :
( ( B != nil )
| ( A != sk2 )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
inference(paramod_ordered,[status(thm)],[334,779]) ).
thf(12980,plain,
! [A: $i] :
( ( A != sk2 )
| ~ ( nil @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( nil @ geq ) )
| ~ ( nil @ ( A @ geq ) ) ),
inference(pattern_uni,[status(thm)],[12979:[bind(A,$thf( A )),bind(B,$thf( nil ))]]) ).
thf(15120,plain,
( ~ ( nil @ ssItem )
| ~ ( sk2 @ ssItem )
| ~ ( sk2 @ ( nil @ geq ) )
| ~ ( nil @ ( sk2 @ geq ) ) ),
inference(simp,[status(thm)],[12980]) ).
thf(15862,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1225,487]) ).
thf(15863,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[15862]) ).
thf(15864,plain,
nil @ ( sk8 @ segmentP ),
inference(pattern_uni,[status(thm)],[15863:[bind(A,$thf( sk8 ))]]) ).
thf(4967,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ~ $true
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[218,301]) ).
thf(4968,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(simp,[status(thm)],[4967]) ).
thf(4969,plain,
( ( sk1 @ strictorderedP )
| ~ ( sk1 @ skaf70 @ ( sk1 @ skaf69 @ lt ) ) ),
inference(pattern_uni,[status(thm)],[4968:[bind(A,$thf( sk1 ))]]) ).
thf(161,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ app ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause141) ).
thf(588,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ app ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(213,axiom,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( A @ lt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause63) ).
thf(699,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(15887,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[510,487]) ).
thf(15888,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) ) ),
inference(simp,[status(thm)],[15887]) ).
thf(15889,plain,
! [A: $i] : ( nil @ ( A @ skaf75 @ segmentP ) ),
inference(pattern_uni,[status(thm)],[15888:[bind(A,$thf( C )),bind(B,$thf( C @ skaf75 ))]]) ).
thf(15913,plain,
! [A: $i] : ( nil @ ( A @ skaf75 @ segmentP ) ),
inference(simp,[status(thm)],[15889]) ).
thf(3745,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[311,3705]) ).
thf(3746,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[3745]) ).
thf(3747,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[3746:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(3789,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[3747]) ).
thf(20164,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[693,344]) ).
thf(20165,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[20164]) ).
thf(20166,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( A @ skaf59 @ neq ) ),
inference(pattern_uni,[status(thm)],[20165:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(20234,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( A @ skaf59 @ neq ) ),
inference(simp,[status(thm)],[20166]) ).
thf(192,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( D @ ( C @ cons ) @ ( B @ ( A @ cons ) @ frontsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause176) ).
thf(652,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( D @ ( C @ cons ) @ ( B @ ( A @ cons ) @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(15868,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf43 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[282,487]) ).
thf(15869,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf43 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ segmentP ) ) ),
inference(simp,[status(thm)],[15868]) ).
thf(15870,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf43 ) @ segmentP ) ),
inference(pattern_uni,[status(thm)],[15869:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf43 ) ))]]) ).
thf(15932,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf43 ) @ segmentP ) ),
inference(simp,[status(thm)],[15870]) ).
thf(3778,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[596,3705]) ).
thf(3779,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[3778]) ).
thf(3780,plain,
nil @ ( skac3 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[3779:[bind(A,$thf( skac3 ))]]) ).
thf(2935,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf46 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ~ ( C @ ( C @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[328,294]) ).
thf(2936,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf46 ) @ ssList )
!= ( C @ ssList ) )
| ~ ( C @ ( C @ neq ) ) ),
inference(simp,[status(thm)],[2935]) ).
thf(2937,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf46 ) @ ( B @ ( A @ skaf46 ) @ neq ) ),
inference(pattern_uni,[status(thm)],[2936:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf46 ) ))]]) ).
thf(2944,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf46 ) @ ( B @ ( A @ skaf46 ) @ neq ) ),
inference(simp,[status(thm)],[2937]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ cons ) @ memberP ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause138) ).
thf(568,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ cons ) @ memberP ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(290,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
inference(cnf,[status(esa)],[289]) ).
thf(114,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ cons ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause139) ).
thf(478,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ cons ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(3760,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[640,3705]) ).
thf(3761,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[3760]) ).
thf(3762,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[3761:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(3793,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[3762]) ).
thf(8912,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf43 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[282,350]) ).
thf(8913,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf43 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[8912]) ).
thf(8914,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf43 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[8913:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf43 ) ))]]) ).
thf(8953,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf43 ) @ rearsegP ) ),
inference(simp,[status(thm)],[8914]) ).
thf(206,axiom,
! [B: $i,A: $i] :
( ( nil = A )
| ( A = B )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( A @ hd )
!= ( B @ hd ) )
| ( ( A @ tl )
!= ( B @ tl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause177) ).
thf(684,plain,
! [B: $i,A: $i] :
( ( nil = A )
| ( A = B )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( A @ hd )
!= ( B @ hd ) )
| ( ( A @ tl )
!= ( B @ tl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(5075,plain,
( ( ( sk7 @ ( sk6 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) )
| ~ ( sk7 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[225,5054]) ).
thf(5076,plain,
( ( ( sk7 @ ( sk6 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) )
| ~ ( sk7 @ ssItem ) ),
inference(simp,[status(thm)],[5075]) ).
thf(5128,plain,
( ( sk7 != nil )
| ( sk6 != sk2 )
| ~ ( sk6 @ ( sk7 @ geq ) )
| ~ ( sk7 @ ( sk2 @ memberP ) )
| ~ ( sk7 @ ssItem ) ),
inference(simp,[status(thm)],[5076]) ).
thf(8940,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[543,350]) ).
thf(8941,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[8940]) ).
thf(8942,plain,
! [A: $i] : ( nil @ ( A @ skaf52 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[8941:[bind(A,$thf( C )),bind(B,$thf( C @ skaf52 ))]]) ).
thf(8969,plain,
! [A: $i] : ( nil @ ( A @ skaf52 @ rearsegP ) ),
inference(simp,[status(thm)],[8942]) ).
thf(2772,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[661,294]) ).
thf(2773,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[2772]) ).
thf(2774,plain,
! [A: $i] :
~ ( A @ skaf76 @ ( A @ skaf76 @ neq ) ),
inference(pattern_uni,[status(thm)],[2773:[bind(A,$thf( C )),bind(B,$thf( C @ skaf76 ))]]) ).
thf(2779,plain,
! [A: $i] :
~ ( A @ skaf76 @ ( A @ skaf76 @ neq ) ),
inference(simp,[status(thm)],[2774]) ).
thf(141,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause70) ).
thf(536,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(15832,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[375,487]) ).
thf(15833,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) ) ),
inference(simp,[status(thm)],[15832]) ).
thf(15834,plain,
! [A: $i] : ( nil @ ( A @ skaf57 @ segmentP ) ),
inference(pattern_uni,[status(thm)],[15833:[bind(A,$thf( C )),bind(B,$thf( C @ skaf57 ))]]) ).
thf(15917,plain,
! [A: $i] : ( nil @ ( A @ skaf57 @ segmentP ) ),
inference(simp,[status(thm)],[15834]) ).
thf(3730,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[693,3705]) ).
thf(3731,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[3730]) ).
thf(3732,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[3731:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(3785,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[3732]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ app ) @ app ) )
= ( A @ ( B @ app ) @ ( C @ app ) ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause149) ).
thf(432,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ app ) @ app ) )
= ( A @ ( B @ app ) @ ( C @ app ) ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(5266,plain,
! [A: $i] :
( ( ( sk7 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[706,303]) ).
thf(5267,plain,
! [A: $i] :
( ( ( sk7 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP ) ),
inference(simp,[status(thm)],[5266]) ).
thf(5268,plain,
( ( sk7 @ skaf50 @ ( sk7 @ skaf49 @ leq ) )
| ( sk7 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5267:[bind(A,$thf( sk7 ))]]) ).
thf(8906,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1225,350]) ).
thf(8907,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[8906]) ).
thf(8908,plain,
nil @ ( sk8 @ rearsegP ),
inference(pattern_uni,[status(thm)],[8907:[bind(A,$thf( sk8 ))]]) ).
thf(1388,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[460,294]) ).
thf(1389,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1388]) ).
thf(1390,plain,
! [A: $i] :
~ ( A @ skaf61 @ ( A @ skaf61 @ neq ) ),
inference(pattern_uni,[status(thm)],[1389:[bind(A,$thf( C )),bind(B,$thf( C @ skaf61 ))]]) ).
thf(1395,plain,
! [A: $i] :
~ ( A @ skaf61 @ ( A @ skaf61 @ neq ) ),
inference(simp,[status(thm)],[1390]) ).
thf(19007,plain,
( ( nil != nil )
| ( sk1 @ equalelemsP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[17586,376]) ).
thf(19008,plain,
( ( sk1 @ equalelemsP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[19007:[]]) ).
thf(2002,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[561,294]) ).
thf(2003,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[2002]) ).
thf(2004,plain,
! [A: $i] :
~ ( A @ skaf81 @ ( A @ skaf81 @ neq ) ),
inference(pattern_uni,[status(thm)],[2003:[bind(A,$thf( C )),bind(B,$thf( C @ skaf81 ))]]) ).
thf(2008,plain,
! [A: $i] :
~ ( A @ skaf81 @ ( A @ skaf81 @ neq ) ),
inference(simp,[status(thm)],[2004]) ).
thf(6225,plain,
! [A: $i] :
( ( ( nil @ ( sk7 @ skaf44 @ cons ) )
!= ( nil @ ( A @ skaf44 @ cons ) ) )
| ( sk7 @ totalorderedP )
| ~ ( sk7 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[5547,3792]) ).
thf(6226,plain,
( ( sk7 @ totalorderedP )
| ~ ( sk7 @ singletonP ) ),
inference(pattern_uni,[status(thm)],[6225:[bind(A,$thf( sk7 ))]]) ).
thf(69,axiom,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf59 @ ( A @ skaf60 @ lt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause92) ).
thf(373,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf59 @ ( A @ skaf60 @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(95,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause102) ).
thf(437,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(765,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[583,496]) ).
thf(766,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[765]) ).
thf(767,plain,
~ ( skac2 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[766:[bind(A,$thf( skac2 ))]]) ).
thf(18979,plain,
( ( nil != nil )
| ( sk1 @ cyclefreeP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[17586,538]) ).
thf(18980,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[18979:[]]) ).
thf(8736,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ skaf44 @ cons ) )
!= ( nil @ ( A @ skaf44 @ cons ) ) )
| ( sk2 @ totalorderedP )
| ~ ( sk2 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[5646,3792]) ).
thf(8737,plain,
( ( sk2 @ totalorderedP )
| ~ ( sk2 @ singletonP ) ),
inference(pattern_uni,[status(thm)],[8736:[bind(A,$thf( sk2 ))]]) ).
thf(2119,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[601,294]) ).
thf(2120,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[2119]) ).
thf(2121,plain,
! [A: $i] :
~ ( A @ skaf66 @ ( A @ skaf66 @ neq ) ),
inference(pattern_uni,[status(thm)],[2120:[bind(A,$thf( C )),bind(B,$thf( C @ skaf66 ))]]) ).
thf(2127,plain,
! [A: $i] :
~ ( A @ skaf66 @ ( A @ skaf66 @ neq ) ),
inference(simp,[status(thm)],[2121]) ).
thf(20223,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[464,344]) ).
thf(20224,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[20223]) ).
thf(20225,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( A @ skaf60 @ neq ) ),
inference(pattern_uni,[status(thm)],[20224:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(20231,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( A @ skaf60 @ neq ) ),
inference(simp,[status(thm)],[20225]) ).
thf(5743,plain,
( ( ( sk8 @ ( sk7 @ app ) )
!= ( nil @ ( nil @ app ) ) )
| ( nil = sk1 ) ),
inference(paramod_ordered,[status(thm)],[5738,1407]) ).
thf(5768,plain,
( ( sk8 != nil )
| ( sk7 != nil )
| ( nil = sk1 ) ),
inference(simp,[status(thm)],[5743]) ).
thf(15841,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[362,487]) ).
thf(15842,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) ) ),
inference(simp,[status(thm)],[15841]) ).
thf(15843,plain,
! [A: $i] : ( nil @ ( A @ skaf77 @ segmentP ) ),
inference(pattern_uni,[status(thm)],[15842:[bind(A,$thf( C )),bind(B,$thf( C @ skaf77 ))]]) ).
thf(15921,plain,
! [A: $i] : ( nil @ ( A @ skaf77 @ segmentP ) ),
inference(simp,[status(thm)],[15843]) ).
thf(126,axiom,
! [A: $i] :
( ( ( nil @ ( A @ app ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause73) ).
thf(501,plain,
! [A: $i] :
( ( ( nil @ ( A @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(67,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause67) ).
thf(369,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(3122,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf42 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ~ ( C @ ( C @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[662,294]) ).
thf(3123,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf42 ) @ ssList )
!= ( C @ ssList ) )
| ~ ( C @ ( C @ neq ) ) ),
inference(simp,[status(thm)],[3122]) ).
thf(3124,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf42 ) @ ( B @ ( A @ skaf42 ) @ neq ) ),
inference(pattern_uni,[status(thm)],[3123:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf42 ) ))]]) ).
thf(3128,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf42 ) @ ( B @ ( A @ skaf42 ) @ neq ) ),
inference(simp,[status(thm)],[3124]) ).
thf(18,negated_conjecture,
! [A: $i] :
( ( nil @ ( sk2 @ neq ) )
| ~ ( sk6 @ ( A @ geq ) )
| ~ ( A @ ( sk4 @ memberP ) )
| ( sk6 = A )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
thf(227,plain,
! [A: $i] :
( ( nil @ ( sk2 @ neq ) )
| ~ ( sk6 @ ( A @ geq ) )
| ~ ( A @ ( sk4 @ memberP ) )
| ( sk6 = A )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1731,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[494,294]) ).
thf(1732,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1731]) ).
thf(1733,plain,
! [A: $i] :
~ ( A @ skaf80 @ ( A @ skaf80 @ neq ) ),
inference(pattern_uni,[status(thm)],[1732:[bind(A,$thf( C )),bind(B,$thf( C @ skaf80 ))]]) ).
thf(1737,plain,
! [A: $i] :
~ ( A @ skaf80 @ ( A @ skaf80 @ neq ) ),
inference(simp,[status(thm)],[1733]) ).
thf(10,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( nil @ ( sk2 @ neq ) )
| ( A @ ( B @ ( C @ sk5 ) ) @ ( sk2 @ memberP ) )
| ( ( C @ ( B @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
thf(215,plain,
! [C: $i,B: $i,A: $i] :
( ( nil @ ( sk2 @ neq ) )
| ( A @ ( B @ ( C @ sk5 ) ) @ ( sk2 @ memberP ) )
| ( ( C @ ( B @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8872,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf42 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[662,350]) ).
thf(8873,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf42 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[8872]) ).
thf(8874,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf42 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[8873:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf42 ) ))]]) ).
thf(8966,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf42 ) @ rearsegP ) ),
inference(simp,[status(thm)],[8874]) ).
thf(121,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ totalorderedP ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause135) ).
thf(491,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ totalorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(8925,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf48 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[482,350]) ).
thf(8926,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf48 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[8925]) ).
thf(8927,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf48 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[8926:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf48 ) ))]]) ).
thf(8961,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf48 ) @ rearsegP ) ),
inference(simp,[status(thm)],[8927]) ).
thf(4,negated_conjecture,
sk4 @ ssList,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).
thf(232,plain,
sk4 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8845,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[655,350]) ).
thf(8846,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[8845]) ).
thf(8847,plain,
! [A: $i] : ( nil @ ( A @ skaf71 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[8846:[bind(A,$thf( C )),bind(B,$thf( C @ skaf71 ))]]) ).
thf(8950,plain,
! [A: $i] : ( nil @ ( A @ skaf71 @ rearsegP ) ),
inference(simp,[status(thm)],[8847]) ).
thf(308,plain,
! [A: $i] :
( ( ( A @ skaf77 @ ( A @ skaf74 @ cons ) @ ( A @ skaf76 @ ( A @ skaf74 @ cons ) @ ( A @ skaf75 @ app ) @ app ) )
= A )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[307]) ).
thf(309,plain,
! [A: $i] :
( ( A @ duplicatefreeP )
| ~ ( A @ ssList )
| ( ( A @ skaf77 @ ( A @ skaf74 @ cons ) @ ( A @ skaf76 @ ( A @ skaf74 @ cons ) @ ( A @ skaf75 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[308]) ).
thf(195,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause114) ).
thf(659,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(2987,plain,
! [A: $i] :
( ( ( A @ skaf77 @ ( A @ skaf77 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[225,919]) ).
thf(2988,plain,
! [A: $i] :
( ( A @ skaf77 @ ( A @ skaf77 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[2987]) ).
thf(2993,plain,
! [A: $i] :
( ( ( A @ skaf77 )
!= nil )
| ( ( A @ skaf77 )
!= sk2 ) ),
inference(simp,[status(thm)],[2988]) ).
thf(15874,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[600,487]) ).
thf(15875,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ segmentP ) ) ),
inference(simp,[status(thm)],[15874]) ).
thf(15876,plain,
! [A: $i] : ( nil @ ( A @ skaf63 @ segmentP ) ),
inference(pattern_uni,[status(thm)],[15875:[bind(A,$thf( C )),bind(B,$thf( C @ skaf63 ))]]) ).
thf(15906,plain,
! [A: $i] : ( nil @ ( A @ skaf63 @ segmentP ) ),
inference(simp,[status(thm)],[15876]) ).
thf(103,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause130) ).
thf(454,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(8156,plain,
! [A: $i] :
( ( ( nil @ ( sk1 @ skaf44 @ cons ) )
!= ( nil @ ( A @ skaf44 @ cons ) ) )
| ( sk1 @ totalorderedP )
| ~ ( sk1 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[5624,3792]) ).
thf(8157,plain,
( ( sk1 @ totalorderedP )
| ~ ( sk1 @ singletonP ) ),
inference(pattern_uni,[status(thm)],[8156:[bind(A,$thf( sk1 ))]]) ).
thf(20255,plain,
( ( ( skac2 @ ( skac2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[225,20172]) ).
thf(20256,plain,
( ( skac2 @ ( skac2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[20255]) ).
thf(20269,plain,
( ( skac2 != nil )
| ( skac2 != sk2 ) ),
inference(simp,[status(thm)],[20256]) ).
thf(55769,plain,
$false,
inference(e,[status(thm)],[645,1322,365,518,234,941,1179,555,666,28642,24715,8960,8930,8030,962,408,1158,5141,5820,217,15827,449,20235,15926,3377,3040,18972,440,655,511,1305,597,8963,533,2035,15916,1872,3781,8947,340,538,3717,3794,385,550,22824,1342,18778,18463,301,320,20239,651,15922,8967,372,504,344,357,4984,2745,460,22121,9464,3342,8951,619,20232,284,228,289,3788,817,20230,638,19091,15911,316,1362,216,8956,443,321,376,238,348,353,3771,480,8972,1682,485,602,5401,15907,692,221,1447,453,774,19085,411,428,22774,507,312,5738,397,687,307,529,661,18411,534,714,3795,233,452,15920,381,220,366,334,19026,5734,302,349,2147,561,297,424,3154,20189,693,630,467,15886,361,625,435,329,5341,461,8964,1407,551,15901,324,229,8948,566,3750,3349,583,522,285,224,15915,3784,317,725,5428,388,356,18994,593,15930,610,420,499,697,3782,328,3141,488,19075,3094,3714,642,526,637,5547,590,679,8952,706,1964,225,901,476,8968,15912,622,393,515,15927,2387,457,20028,779,605,371,9942,8971,237,266,633,311,8871,20172,8945,2189,953,2883,3173,8955,558,662,9562,298,965,430,2253,18968,15923,279,3738,3792,296,3396,375,601,584,562,694,402,15909,2225,711,21201,20237,281,545,579,291,641,445,15919,572,1707,2308,3002,3783,335,919,350,672,391,3796,2166,236,17332,219,15902,274,3419,230,362,318,2065,20327,20228,9623,406,5143,15929,20366,8970,419,377,1933,5054,20048,509,649,616,303,890,387,345,5730,4911,323,594,726,20298,483,8974,15914,668,330,494,8958,240,1838,399,636,5646,299,3348,5326,223,608,394,306,226,4954,241,15928,473,5463,722,675,8965,2096,1203,680,663,15918,648,487,8949,458,823,5624,690,640,295,1225,327,1252,1780,3786,15924,310,282,2977,3791,331,9567,3774,338,1218,9986,17586,717,21764,3344,470,576,2354,544,3697,19989,2838,656,20238,600,16749,314,2807,497,18707,613,15925,25558,446,9574,8973,1839,627,8946,539,482,671,15910,3346,2342,368,3665,3797,465,231,363,556,524,8962,495,8957,218,15903,5308,2273,1903,304,15120,632,15864,1244,4969,5600,588,699,319,15913,3789,20234,652,351,786,3368,15932,3780,2944,568,290,235,510,478,3793,9559,8953,684,346,5128,549,8969,214,2779,536,15917,300,5129,3785,432,5268,8908,1395,19008,405,2008,6226,373,315,3705,239,294,341,358,437,767,532,18980,283,415,3347,8737,19948,2127,464,596,21971,20231,5768,15921,501,369,3128,332,227,803,337,354,1737,543,215,8966,491,222,8961,232,486,8950,309,659,2993,15906,496,454,8157,20269]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC002-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.07/10.34 % Computer : n012.cluster.edu
% 0.07/10.34 % Model : x86_64 x86_64
% 0.07/10.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/10.34 % Memory : 8046.5625MB
% 0.07/10.34 % OS : Linux 6.8.0-71-generic
% 0.07/10.34 % CPULimit : 300
% 0.07/10.34 % WCLimit : 300
% 0.07/10.34 % DateTime : Sat Sep 26 12:02:31 UTC 2026
% 0.07/10.34 % CPUTime :
% 0.07/10.34 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.11/10.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.45/11.05 % [INFO] Parsing done (244ms).
% 1.45/11.07 % [INFO] Running in sequential loop mode.
% 1.97/11.39 % [INFO] eprover registered as external prover.
% 1.97/11.39 % [INFO] Scanning for conjecture ...
% 2.38/11.55 % [INFO] Found a conjecture (or negated_conjecture) and 185 axioms. Running axiom selection ...
% 2.62/11.69 % [INFO] Axiom selection finished. Selected 185 axioms (removed 0 axioms).
% 2.97/11.79 % [INFO] Problem is propositional (TPTP CNF).
% 3.26/11.80 % [INFO] Type checking passed.
% 3.26/11.81 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 112.39/38.35 % External prover 'e' found a proof!
% 112.39/38.35 % [INFO] Killing All external provers ...
% 112.39/38.35 % Time passed: 27892ms (effective reasoning time: 27283ms)
% 112.39/38.36 % Axioms used in derivation (185): clause144, clause82, clause60, clause65, clause128, clause171, clause71, clause113, clause139, clause3, clause29, clause160, clause43, clause32, clause18, clause54, clause117, clause88, clause59, clause99, clause48, clause146, clause37, clause165, clause108, clause93, clause105, clause185, clause77, clause135, clause95, clause101, clause168, clause129, clause81, clause55, clause164, clause154, clause66, clause17, clause70, clause118, clause181, clause22, clause124, clause92, clause157, clause87, clause84, clause7, clause25, clause11, clause14, clause112, clause76, clause130, clause49, clause169, clause13, clause31, clause24, clause132, clause121, clause42, clause109, clause104, clause2, clause158, clause141, clause143, clause64, clause166, clause38, clause16, clause28, clause98, clause53, clause176, clause152, clause170, clause155, clause136, clause12, clause179, clause111, clause79, clause97, clause147, clause180, clause163, clause75, clause125, clause100, clause23, clause114, clause6, clause174, clause86, clause184, clause133, clause122, clause103, clause1, clause151, clause167, clause34, clause159, clause140, clause177, clause5, clause69, clause68, clause148, clause134, clause27, clause110, clause41, clause39, clause173, clause57, clause162, clause137, clause35, clause8, clause183, clause30, clause145, clause20, clause52, clause46, clause156, clause90, clause126, clause115, clause63, clause89, clause44, clause50, clause150, clause102, clause182, clause72, clause33, clause94, clause73, clause83, clause175, clause107, clause19, clause123, clause178, clause78, clause116, clause4, clause26, clause149, clause58, clause96, clause172, clause142, clause9, clause131, clause120, clause80, clause56, clause10, clause161, clause67, clause138, clause21, clause127, clause119, clause15, clause153, clause45, clause40, clause85, clause91, clause51, clause106, clause61, clause62, clause74, clause47, clause36
% 112.39/38.36 % No. of inferences in proof: 1390
% 112.39/38.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 27892 ms resp. 27283 ms w/o parsing
% 104.13/38.62 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 104.13/38.63 % [INFO] Killing All external provers ...
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