%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWC111-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n018.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 08:52:18 AM UTC 2026
% Result : Unsatisfiable 146.55s 41.78s
% Output : Refutation 149.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 198
% Syntax : Number of formulae : 1534 ( 472 unt; 0 typ; 0 def)
% Number of atoms : 4672 (1008 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 11858 (2519 ~;2258 |; 0 &;7081 @)
% ( 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 : 75 ( 72 usr; 9 con; 0-2 aty)
% Number of variables : 1867 ( 0 ^;1867 !; 0 ?;1867 :)
% 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(segmentP_decl,type,
segmentP: $i > $i > $o ).
thf(totalorderedP_decl,type,
totalorderedP: $i > $o ).
thf(neq_decl,type,
neq: $i > $i > $o ).
thf(nil_decl,type,
nil: $i ).
thf(skac3_decl,type,
skac3: $i ).
thf(skac2_decl,type,
skac2: $i ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(ssItem_decl,type,
ssItem: $i > $o ).
thf(geq_decl,type,
geq: $i > $i > $o ).
thf(lt_decl,type,
lt: $i > $i > $o ).
thf(gt_decl,type,
gt: $i > $i > $o ).
thf(skaf79_decl,type,
skaf79: $i > $i ).
thf(skaf64_decl,type,
skaf64: $i > $i ).
thf(skaf44_decl,type,
skaf44: $i > $i ).
thf(skaf69_decl,type,
skaf69: $i > $i ).
thf(skaf55_decl,type,
skaf55: $i > $i ).
thf(skaf70_decl,type,
skaf70: $i > $i ).
thf(skaf60_decl,type,
skaf60: $i > $i ).
thf(skaf49_decl,type,
skaf49: $i > $i ).
thf(skaf83_decl,type,
skaf83: $i > $i ).
thf(skaf74_decl,type,
skaf74: $i > $i ).
thf(skaf54_decl,type,
skaf54: $i > $i ).
thf(skaf65_decl,type,
skaf65: $i > $i ).
thf(skaf50_decl,type,
skaf50: $i > $i ).
thf(skaf78_decl,type,
skaf78: $i > $i ).
thf(skaf59_decl,type,
skaf59: $i > $i ).
thf(skaf43_decl,type,
skaf43: $i > $i > $i ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(skaf62_decl,type,
skaf62: $i > $i ).
thf(memberP_decl,type,
memberP: $i > $i > $o ).
thf(app_decl,type,
app: $i > $i > $i ).
thf(strictorderedP_decl,type,
strictorderedP: $i > $o ).
thf(cyclefreeP_decl,type,
cyclefreeP: $i > $o ).
thf(singletonP_decl,type,
singletonP: $i > $o ).
thf(duplicatefreeP_decl,type,
duplicatefreeP: $i > $o ).
thf(skaf75_decl,type,
skaf75: $i > $i ).
thf(skaf76_decl,type,
skaf76: $i > $i ).
thf(skaf77_decl,type,
skaf77: $i > $i ).
thf(skaf72_decl,type,
skaf72: $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(tl_decl,type,
tl: $i > $i ).
thf(skaf66_decl,type,
skaf66: $i > $i ).
thf(skaf67_decl,type,
skaf67: $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(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(skaf58_decl,type,
skaf58: $i > $i ).
thf(skaf48_decl,type,
skaf48: $i > $i > $i ).
thf(skaf80_decl,type,
skaf80: $i > $i ).
thf(skaf47_decl,type,
skaf47: $i > $i > $i ).
thf(skaf81_decl,type,
skaf81: $i > $i ).
thf(skaf82_decl,type,
skaf82: $i > $i ).
thf(skaf42_decl,type,
skaf42: $i > $i > $i ).
thf(147,axiom,
~ ( nil @ singletonP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause11) ).
thf(518,plain,
~ ( nil @ singletonP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(125,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ equalelemsP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause64) ).
thf(468,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ equalelemsP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(20,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/sandbox/benchmark/theBenchmark.p',clause155) ).
thf(234,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)],[20]) ).
thf(10,negated_conjecture,
( ( nil @ ( sk2 @ neq ) )
| ( nil = sk2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
thf(200,plain,
( ( nil @ ( sk2 @ neq ) )
| ( nil = sk2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(221,plain,
( ( nil @ ( sk2 @ neq ) )
| ( nil = sk2 ) ),
inference(cnf,[status(esa)],[200]) ).
thf(222,plain,
( ( nil @ ( sk2 @ neq ) )
| ( nil = sk2 ) ),
inference(lifteq,[status(thm)],[221]) ).
thf(519,plain,
~ ( nil @ singletonP ),
inference(polarity_switch,[status(thm)],[518]) ).
thf(724,plain,
( ( nil != nil )
| ~ ( sk2 @ singletonP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,519]) ).
thf(725,plain,
( ~ ( sk2 @ singletonP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[724:[]]) ).
thf(2,negated_conjecture,
sk2 @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
thf(205,plain,
sk2 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(68,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause75) ).
thf(327,plain,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(328,plain,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[327]) ).
thf(329,plain,
! [A: $i] :
( ( A @ tl @ ssList )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[328]) ).
thf(19483,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[205,329]) ).
thf(19484,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[19483]) ).
thf(19485,plain,
( ( sk2 @ tl @ ssList )
| ( nil = sk2 ) ),
inference(pattern_uni,[status(thm)],[19484:[bind(A,$thf( sk2 ))]]) ).
thf(21324,plain,
( ( nil != nil )
| ~ ( sk2 @ singletonP )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[19485,519]) ).
thf(21325,plain,
( ~ ( sk2 @ singletonP )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[21324:[]]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause115) ).
thf(294,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(295,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[294]) ).
thf(296,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[295]) ).
thf(297,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[296]) ).
thf(26041,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) )
| ~ ( sk2 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[21325,297]) ).
thf(26042,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ ( sk2 @ singletonP ) ),
inference(simp,[status(thm)],[26041]) ).
thf(26043,plain,
( ~ ( sk2 @ tl @ ( sk2 @ tl @ neq ) )
| ~ ( sk2 @ singletonP ) ),
inference(pattern_uni,[status(thm)],[26042:[bind(A,$thf( sk2 @ tl ))]]) ).
thf(26989,plain,
( ( ( sk2 @ tl @ ( sk2 @ tl @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true
| ~ ( sk2 @ singletonP )
| ~ ( sk2 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[725,26043]) ).
thf(26990,plain,
( ( ( sk2 @ tl @ ( sk2 @ tl @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ ( sk2 @ singletonP ) ),
inference(simp,[status(thm)],[26989]) ).
thf(27055,plain,
( ( ( sk2 @ tl )
!= nil )
| ( ( sk2 @ tl )
!= sk2 )
| ~ ( sk2 @ singletonP ) ),
inference(simp,[status(thm)],[26990]) ).
thf(76,axiom,
nil @ strictorderP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause5) ).
thf(349,plain,
nil @ strictorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(21298,plain,
( ( nil != nil )
| ( sk2 @ strictorderP )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[19485,349]) ).
thf(21299,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[21298:[]]) ).
thf(1,negated_conjecture,
sk1 @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
thf(201,plain,
sk1 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(73,axiom,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause58) ).
thf(341,plain,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(342,plain,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[341]) ).
thf(24430,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[201,342]) ).
thf(24431,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[24430]) ).
thf(24432,plain,
nil @ ( sk1 @ rearsegP ),
inference(pattern_uni,[status(thm)],[24431:[bind(A,$thf( sk1 ))]]) ).
thf(131,axiom,
! [A: $i] : ( A @ skaf75 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause20) ).
thf(481,plain,
! [A: $i] : ( A @ skaf75 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(83,axiom,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf59 @ ( A @ skaf60 @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause92) ).
thf(365,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf59 @ ( A @ skaf60 @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(19188,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[201,329]) ).
thf(19189,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[19188]) ).
thf(19190,plain,
( ( sk1 @ tl @ ssList )
| ( nil = sk1 ) ),
inference(pattern_uni,[status(thm)],[19189:[bind(A,$thf( sk1 ))]]) ).
thf(132,axiom,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause79) ).
thf(482,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(483,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(cnf,[status(esa)],[482]) ).
thf(484,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[483]) ).
thf(485,plain,
( ( nil @ ( nil @ segmentP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[484]) ).
thf(71,axiom,
nil @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
thf(337,plain,
nil @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(7982,plain,
( ( nil @ ( nil @ segmentP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[485,337]) ).
thf(7983,plain,
nil @ ( nil @ segmentP ),
inference(simp,[status(thm)],[7982]) ).
thf(21039,plain,
( ( nil != nil )
| ( nil @ ( sk1 @ segmentP ) )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[19190,7983]) ).
thf(21040,plain,
( ( nil @ ( sk1 @ segmentP ) )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[21039:[]]) ).
thf(70,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause117) ).
thf(333,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(27,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/sandbox/benchmark/theBenchmark.p',clause148) ).
thf(248,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)],[27]) ).
thf(249,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ geq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
inference(cnf,[status(esa)],[248]) ).
thf(145,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf47 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause49) ).
thf(513,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf47 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(24471,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf47 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[513,342]) ).
thf(24472,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf47 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[24471]) ).
thf(24473,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf47 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[24472:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf47 ) ))]]) ).
thf(24550,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf47 ) @ rearsegP ) ),
inference(simp,[status(thm)],[24473]) ).
thf(19,axiom,
! [A: $i] : ( A @ skaf64 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause31) ).
thf(233,plain,
! [A: $i] : ( A @ skaf64 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(334,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[333]) ).
thf(335,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[334]) ).
thf(336,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[335]) ).
thf(22723,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[233,336]) ).
thf(22724,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[22723]) ).
thf(22725,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( A @ skaf64 @ neq ) ),
inference(pattern_uni,[status(thm)],[22724:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(22807,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( A @ skaf64 @ neq ) ),
inference(simp,[status(thm)],[22725]) ).
thf(24460,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[205,342]) ).
thf(24461,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[24460]) ).
thf(24462,plain,
nil @ ( sk2 @ rearsegP ),
inference(pattern_uni,[status(thm)],[24461:[bind(A,$thf( sk2 ))]]) ).
thf(44,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/sandbox/benchmark/theBenchmark.p',clause147) ).
thf(275,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)],[44]) ).
thf(276,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)],[275]) ).
thf(161,axiom,
! [A: $i] : ( A @ skaf51 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause44) ).
thf(557,plain,
! [A: $i] : ( A @ skaf51 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(10004,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[557,297]) ).
thf(10005,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[10004]) ).
thf(10006,plain,
! [A: $i] :
~ ( A @ skaf51 @ ( A @ skaf51 @ neq ) ),
inference(pattern_uni,[status(thm)],[10005:[bind(A,$thf( C )),bind(B,$thf( C @ skaf51 ))]]) ).
thf(10061,plain,
! [A: $i] :
~ ( A @ skaf51 @ ( A @ skaf51 @ neq ) ),
inference(simp,[status(thm)],[10006]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ ( A @ geq ) )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause55) ).
thf(246,plain,
! [A: $i] :
( ( A @ ( A @ geq ) )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(247,plain,
! [A: $i] :
( ( A @ ( A @ geq ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[246]) ).
thf(89,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf45 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause51) ).
thf(379,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf45 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
thf(202,plain,
sk1 = sk3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(176,axiom,
! [A: $i] : ( A @ skaf82 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause13) ).
thf(592,plain,
! [A: $i] : ( A @ skaf82 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(24534,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[592,342]) ).
thf(24535,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[24534]) ).
thf(24536,plain,
! [A: $i] : ( nil @ ( A @ skaf82 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[24535:[bind(A,$thf( C )),bind(B,$thf( C @ skaf82 ))]]) ).
thf(24569,plain,
! [A: $i] : ( nil @ ( A @ skaf82 @ rearsegP ) ),
inference(simp,[status(thm)],[24536]) ).
thf(97,axiom,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause81) ).
thf(397,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(398,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(cnf,[status(esa)],[397]) ).
thf(399,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[398]) ).
thf(400,plain,
( ( nil @ ( nil @ rearsegP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[399]) ).
thf(7942,plain,
( ( nil @ ( nil @ rearsegP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[400,337]) ).
thf(7943,plain,
nil @ ( nil @ rearsegP ),
inference(simp,[status(thm)],[7942]) ).
thf(80,axiom,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause82) ).
thf(358,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(359,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
inference(cnf,[status(esa)],[358]) ).
thf(360,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[359]) ).
thf(30319,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( nil @ rearsegP ) )
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[201,360]) ).
thf(30320,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ rearsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[30319]) ).
thf(30321,plain,
( ~ ( sk1 @ ( nil @ rearsegP ) )
| ( nil = sk1 ) ),
inference(pattern_uni,[status(thm)],[30320:[bind(A,$thf( sk1 ))]]) ).
thf(10026,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[337,297]) ).
thf(10027,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[10026]) ).
thf(10028,plain,
~ ( nil @ ( nil @ neq ) ),
inference(pattern_uni,[status(thm)],[10027:[bind(A,$thf( nil ))]]) ).
thf(33905,plain,
( ( nil != nil )
| ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[30321,10028]) ).
thf(33906,plain,
( ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[33905:[]]) ).
thf(49570,plain,
( ( ( nil @ ( nil @ rearsegP ) )
!= ( sk1 @ ( nil @ rearsegP ) ) )
| ~ ( sk1 @ ( nil @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7943,33906]) ).
thf(49571,plain,
( ( ( nil @ ( nil @ rearsegP ) )
!= ( sk1 @ ( nil @ rearsegP ) ) )
| ~ ( sk1 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[49570]) ).
thf(49627,plain,
( ( nil != sk1 )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[49571]) ).
thf(49668,plain,
( ( nil != sk1 )
| ~ ( sk1 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[49627]) ).
thf(150,axiom,
! [A: $i] :
( ( ( A @ skaf81 @ ( A @ skaf79 @ cons ) @ ( A @ skaf78 @ cons ) @ ( A @ skaf80 @ app ) )
= A )
| ( A @ equalelemsP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause142) ).
thf(523,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)],[150]) ).
thf(172,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ totalorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause125) ).
thf(582,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)],[172]) ).
thf(60,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/sandbox/benchmark/theBenchmark.p',clause162) ).
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(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(40,axiom,
! [A: $i] : ( A @ skaf54 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause41) ).
thf(270,plain,
! [A: $i] : ( A @ skaf54 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause62) ).
thf(277,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(278,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[277]) ).
thf(8400,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[270,278]) ).
thf(8401,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[8400]) ).
thf(8402,plain,
! [A: $i] : ( A @ skaf54 @ ( A @ skaf54 @ leq ) ),
inference(pattern_uni,[status(thm)],[8401:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(8463,plain,
! [A: $i] : ( A @ skaf54 @ ( A @ skaf54 @ leq ) ),
inference(simp,[status(thm)],[8402]) ).
thf(187,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause86) ).
thf(614,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(47,axiom,
skac2 @ ssItem,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause10) ).
thf(283,plain,
skac2 @ ssItem,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(88,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause66) ).
thf(377,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(378,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[377]) ).
thf(39508,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[283,378]) ).
thf(39509,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[39508]) ).
thf(39510,plain,
nil @ ( skac2 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[39509:[bind(A,$thf( skac2 ))]]) ).
thf(39,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/sandbox/benchmark/theBenchmark.p',clause156) ).
thf(268,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)],[39]) ).
thf(269,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[268]) ).
thf(92,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ hd )
= A )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause97) ).
thf(384,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ hd )
= A )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ cons ) @ memberP ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause138) ).
thf(533,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)],[154]) ).
thf(34,axiom,
! [A: $i] : ( A @ skaf49 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause46) ).
thf(259,plain,
! [A: $i] : ( A @ skaf49 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(22748,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[259,336]) ).
thf(22749,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[22748]) ).
thf(22750,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( A @ skaf49 @ neq ) ),
inference(pattern_uni,[status(thm)],[22749:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(22824,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( A @ skaf49 @ neq ) ),
inference(simp,[status(thm)],[22750]) ).
thf(50,axiom,
! [A: $i] : ( A @ skaf78 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause17) ).
thf(287,plain,
! [A: $i] : ( A @ skaf78 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause111) ).
thf(279,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(280,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[279]) ).
thf(281,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[280]) ).
thf(282,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[281]) ).
thf(8901,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[287,282]) ).
thf(8902,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[8901]) ).
thf(8903,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( A @ skaf78 @ lt ) ),
inference(pattern_uni,[status(thm)],[8902:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(8915,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( A @ skaf78 @ lt ) ),
inference(simp,[status(thm)],[8903]) ).
thf(127,axiom,
! [A: $i] :
( ( ( nil @ ( A @ app ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause73) ).
thf(472,plain,
! [A: $i] :
( ( ( nil @ ( A @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(12,negated_conjecture,
( ( nil @ ( sk2 @ neq ) )
| ( nil != sk1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
thf(206,plain,
( ( nil @ ( sk2 @ neq ) )
| ( nil != sk1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(213,plain,
( ( nil @ ( sk2 @ neq ) )
| ( nil != sk1 ) ),
inference(cnf,[status(esa)],[206]) ).
thf(214,plain,
( ( nil @ ( sk2 @ neq ) )
| ( nil != sk1 ) ),
inference(lifteq,[status(thm)],[213]) ).
thf(22785,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[283,336]) ).
thf(22786,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[22785]) ).
thf(22787,plain,
~ ( skac2 @ ( skac2 @ neq ) ),
inference(pattern_uni,[status(thm)],[22786:[bind(A,$thf( skac2 ))]]) ).
thf(22953,plain,
( ( ( skac2 @ ( skac2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true
| ( nil != sk1 ) ),
inference(paramod_ordered,[status(thm)],[214,22787]) ).
thf(22954,plain,
( ( ( skac2 @ ( skac2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[22953]) ).
thf(22987,plain,
( ( skac2 != nil )
| ( skac2 != sk2 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[22954]) ).
thf(184,axiom,
! [A: $i] : ( A @ skaf76 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause19) ).
thf(609,plain,
! [A: $i] : ( A @ skaf76 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(24483,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[609,342]) ).
thf(24484,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[24483]) ).
thf(24485,plain,
! [A: $i] : ( nil @ ( A @ skaf76 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[24484:[bind(A,$thf( C )),bind(B,$thf( C @ skaf76 ))]]) ).
thf(24554,plain,
! [A: $i] : ( nil @ ( A @ skaf76 @ rearsegP ) ),
inference(simp,[status(thm)],[24485]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ( B @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause132) ).
thf(338,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)],[72]) ).
thf(339,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ( B @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ frontsegP ) ) ),
inference(cnf,[status(esa)],[338]) ).
thf(340,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ frontsegP ) )
| ( ( B @ ( A @ skaf45 ) @ ( B @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[339]) ).
thf(48,axiom,
skac3 @ ssItem,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause9) ).
thf(284,plain,
skac3 @ ssItem,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause113) ).
thf(290,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(291,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(cnf,[status(esa)],[290]) ).
thf(292,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[291]) ).
thf(293,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[292]) ).
thf(9533,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ $true ),
inference(rewrite,[status(thm)],[293,337]) ).
thf(9534,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[9533]) ).
thf(9538,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[284,9534]) ).
thf(9539,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[9538]) ).
thf(9540,plain,
nil @ ( skac3 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[9539:[bind(A,$thf( skac3 ))]]) ).
thf(36,axiom,
! [A: $i] : ( A @ skaf83 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause12) ).
thf(263,plain,
! [A: $i] : ( A @ skaf83 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(9589,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[263,9534]) ).
thf(9590,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[9589]) ).
thf(9591,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[9590:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(9644,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[9591]) ).
thf(124,axiom,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( nil @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause71) ).
thf(466,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(467,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(cnf,[status(esa)],[466]) ).
thf(654,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[283,467]) ).
thf(655,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[654]) ).
thf(656,plain,
~ ( skac2 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[655:[bind(A,$thf( skac2 ))]]) ).
thf(33897,plain,
( ( nil != nil )
| ~ ( skac2 @ ( sk1 @ memberP ) )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[30321,656]) ).
thf(33898,plain,
( ~ ( skac2 @ ( sk1 @ memberP ) )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[33897:[]]) ).
thf(46355,plain,
( ( ( nil @ ( nil @ rearsegP ) )
!= ( sk1 @ ( nil @ rearsegP ) ) )
| ~ ( skac2 @ ( sk1 @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7943,33898]) ).
thf(46356,plain,
( ( ( nil @ ( nil @ rearsegP ) )
!= ( sk1 @ ( nil @ rearsegP ) ) )
| ~ ( skac2 @ ( sk1 @ memberP ) ) ),
inference(simp,[status(thm)],[46355]) ).
thf(46390,plain,
( ( nil != sk1 )
| ( nil != nil )
| ~ ( skac2 @ ( sk1 @ memberP ) ) ),
inference(simp,[status(thm)],[46356]) ).
thf(46425,plain,
( ( nil != sk1 )
| ~ ( skac2 @ ( sk1 @ memberP ) ) ),
inference(simp,[status(thm)],[46390]) ).
thf(28,axiom,
! [A: $i] : ( A @ skaf69 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause26) ).
thf(250,plain,
! [A: $i] : ( A @ skaf69 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(8895,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[250,282]) ).
thf(8896,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[8895]) ).
thf(8897,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( A @ skaf69 @ lt ) ),
inference(pattern_uni,[status(thm)],[8896:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(8911,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( A @ skaf69 @ lt ) ),
inference(simp,[status(thm)],[8897]) ).
thf(29,axiom,
! [A: $i] : ( A @ skaf55 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause40) ).
thf(251,plain,
! [A: $i] : ( A @ skaf55 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(22763,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[251,336]) ).
thf(22764,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[22763]) ).
thf(22765,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( A @ skaf55 @ neq ) ),
inference(pattern_uni,[status(thm)],[22764:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(22829,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( A @ skaf55 @ neq ) ),
inference(simp,[status(thm)],[22765]) ).
thf(8014,plain,
( ( nil != nil )
| ( nil @ ( sk2 @ segmentP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,7983]) ).
thf(8015,plain,
( ( nil @ ( sk2 @ segmentP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[8014:[]]) ).
thf(9966,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[205,297]) ).
thf(9967,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[9966]) ).
thf(9968,plain,
~ ( sk2 @ ( sk2 @ neq ) ),
inference(pattern_uni,[status(thm)],[9967:[bind(A,$thf( sk2 ))]]) ).
thf(10177,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ~ $true
| ( nil @ ( sk2 @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[8015,9968]) ).
thf(10178,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ( nil @ ( sk2 @ segmentP ) ) ),
inference(simp,[status(thm)],[10177]) ).
thf(10214,plain,
( ( nil != sk2 )
| ( sk2 != sk2 )
| ( nil @ ( sk2 @ segmentP ) ) ),
inference(simp,[status(thm)],[10178]) ).
thf(10230,plain,
( ( nil != sk2 )
| ( nil @ ( sk2 @ segmentP ) ) ),
inference(simp,[status(thm)],[10214]) ).
thf(148,axiom,
! [A: $i] : ( A @ skaf67 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause28) ).
thf(520,plain,
! [A: $i] : ( A @ skaf67 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(94,axiom,
! [A: $i] :
( ( ( A @ ( nil @ app ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause74) ).
thf(390,plain,
! [A: $i] :
( ( ( A @ ( nil @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(391,plain,
! [A: $i] :
( ( ( A @ ( nil @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[390]) ).
thf(392,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[391]) ).
thf(46857,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[520,392]) ).
thf(46858,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[46857]) ).
thf(46859,plain,
! [A: $i] :
( ( A @ skaf67 @ ( nil @ app ) )
= ( A @ skaf67 ) ),
inference(pattern_uni,[status(thm)],[46858:[bind(A,$thf( C )),bind(B,$thf( C @ skaf67 ))]]) ).
thf(46966,plain,
! [A: $i] :
( ( A @ skaf67 @ ( nil @ app ) )
= ( A @ skaf67 ) ),
inference(simp,[status(thm)],[46859]) ).
thf(33733,plain,
( ( nil != nil )
| ~ ( sk1 @ singletonP )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[30321,519]) ).
thf(33734,plain,
( ~ ( sk1 @ singletonP )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[33733:[]]) ).
thf(34882,plain,
( ( ( nil @ ( nil @ rearsegP ) )
!= ( sk1 @ ( nil @ rearsegP ) ) )
| ~ ( sk1 @ singletonP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7943,33734]) ).
thf(34883,plain,
( ( ( nil @ ( nil @ rearsegP ) )
!= ( sk1 @ ( nil @ rearsegP ) ) )
| ~ ( sk1 @ singletonP ) ),
inference(simp,[status(thm)],[34882]) ).
thf(34917,plain,
( ( nil != sk1 )
| ( nil != nil )
| ~ ( sk1 @ singletonP ) ),
inference(simp,[status(thm)],[34883]) ).
thf(34943,plain,
( ( nil != sk1 )
| ~ ( sk1 @ singletonP ) ),
inference(simp,[status(thm)],[34917]) ).
thf(91,axiom,
nil @ duplicatefreeP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause2) ).
thf(383,plain,
nil @ duplicatefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(744,plain,
( ( nil != nil )
| ( sk2 @ duplicatefreeP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,383]) ).
thf(745,plain,
( ( sk2 @ duplicatefreeP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[744:[]]) ).
thf(10175,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ~ $true
| ( sk2 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[745,9968]) ).
thf(10176,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[10175]) ).
thf(10206,plain,
( ( nil != sk2 )
| ( sk2 != sk2 )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[10176]) ).
thf(10222,plain,
( ( nil != sk2 )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[10206]) ).
thf(21361,plain,
( ( nil != nil )
| ( sk2 != sk2 )
| ( sk2 @ duplicatefreeP )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[19485,10222]) ).
thf(21362,plain,
( ( nil != nil )
| ( sk2 @ duplicatefreeP )
| ( sk2 @ tl @ ssList ) ),
inference(simp,[status(thm)],[21361]) ).
thf(21363,plain,
( ( sk2 @ duplicatefreeP )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[21362:[]]) ).
thf(9606,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[283,9534]) ).
thf(9607,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[9606]) ).
thf(9608,plain,
nil @ ( skac2 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[9607:[bind(A,$thf( skac2 ))]]) ).
thf(9734,plain,
( ( nil != nil )
| ( sk2 @ ( skac2 @ cons ) @ totalorderedP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,9608]) ).
thf(9735,plain,
( ( sk2 @ ( skac2 @ cons ) @ totalorderedP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[9734:[]]) ).
thf(95,axiom,
! [A: $i] : ( A @ skaf58 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause37) ).
thf(393,plain,
! [A: $i] : ( A @ skaf58 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(9963,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[393,297]) ).
thf(9964,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[9963]) ).
thf(9965,plain,
! [A: $i] :
~ ( A @ skaf58 @ ( A @ skaf58 @ neq ) ),
inference(pattern_uni,[status(thm)],[9964:[bind(A,$thf( C )),bind(B,$thf( C @ skaf58 ))]]) ).
thf(10071,plain,
! [A: $i] :
~ ( A @ skaf58 @ ( A @ skaf58 @ neq ) ),
inference(simp,[status(thm)],[9965]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause90) ).
thf(301,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(166,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= ( C @ ( A @ app ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause150) ).
thf(565,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)],[166]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
!= ( B @ ( C @ app ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause151) ).
thf(436,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)],[111]) ).
thf(138,axiom,
! [A: $i] : ( A @ skaf68 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause27) ).
thf(501,plain,
! [A: $i] : ( A @ skaf68 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(24523,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[501,342]) ).
thf(24524,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[24523]) ).
thf(24525,plain,
! [A: $i] : ( nil @ ( A @ skaf68 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[24524:[bind(A,$thf( C )),bind(B,$thf( C @ skaf68 ))]]) ).
thf(24565,plain,
! [A: $i] : ( nil @ ( A @ skaf68 @ rearsegP ) ),
inference(simp,[status(thm)],[24525]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause110) ).
thf(257,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(51,axiom,
! [A: $i] : ( A @ skaf59 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause36) ).
thf(288,plain,
! [A: $i] : ( A @ skaf59 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(55,axiom,
! [A: $i] : ( A @ skaf62 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause33) ).
thf(298,plain,
! [A: $i] : ( A @ skaf62 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(9974,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[298,297]) ).
thf(9975,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[9974]) ).
thf(9976,plain,
! [A: $i] :
~ ( A @ skaf62 @ ( A @ skaf62 @ neq ) ),
inference(pattern_uni,[status(thm)],[9975:[bind(A,$thf( C )),bind(B,$thf( C @ skaf62 ))]]) ).
thf(10078,plain,
! [A: $i] :
~ ( A @ skaf62 @ ( A @ skaf62 @ neq ) ),
inference(simp,[status(thm)],[9976]) ).
thf(93,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ totalorderedP )
| ~ ( B @ hd @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause159) ).
thf(387,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)],[93]) ).
thf(388,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ totalorderedP )
| ~ ( B @ hd @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[387]) ).
thf(389,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ totalorderedP )
| ~ ( B @ hd @ ( A @ leq ) )
| ( nil = B ) ),
inference(lifteq,[status(thm)],[388]) ).
thf(85,axiom,
nil @ equalelemsP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause1) ).
thf(368,plain,
nil @ equalelemsP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(717,plain,
( ( nil != nil )
| ( sk2 @ equalelemsP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,368]) ).
thf(718,plain,
( ( sk2 @ equalelemsP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[717:[]]) ).
thf(10173,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ~ $true
| ( sk2 @ equalelemsP ) ),
inference(paramod_ordered,[status(thm)],[718,9968]) ).
thf(10174,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ( sk2 @ equalelemsP ) ),
inference(simp,[status(thm)],[10173]) ).
thf(10205,plain,
( ( nil != sk2 )
| ( sk2 != sk2 )
| ( sk2 @ equalelemsP ) ),
inference(simp,[status(thm)],[10174]) ).
thf(10221,plain,
( ( nil != sk2 )
| ( sk2 @ equalelemsP ) ),
inference(simp,[status(thm)],[10205]) ).
thf(24495,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[557,342]) ).
thf(24496,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[24495]) ).
thf(24497,plain,
! [A: $i] : ( nil @ ( A @ skaf51 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[24496:[bind(A,$thf( C )),bind(B,$thf( C @ skaf51 ))]]) ).
thf(24558,plain,
! [A: $i] : ( nil @ ( A @ skaf51 @ rearsegP ) ),
inference(simp,[status(thm)],[24497]) ).
thf(79,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/sandbox/benchmark/theBenchmark.p',clause167) ).
thf(355,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)],[79]) ).
thf(356,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)],[355]) ).
thf(357,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)],[356]) ).
thf(22715,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[288,336]) ).
thf(22716,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[22715]) ).
thf(22717,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( A @ skaf59 @ neq ) ),
inference(pattern_uni,[status(thm)],[22716:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(22834,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( A @ skaf59 @ neq ) ),
inference(simp,[status(thm)],[22717]) ).
thf(139,axiom,
nil @ totalorderP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause6) ).
thf(502,plain,
nil @ totalorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(21085,plain,
( ( nil != nil )
| ( sk1 @ totalorderP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[19190,502]) ).
thf(21086,plain,
( ( sk1 @ totalorderP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[21085:[]]) ).
thf(86,axiom,
! [B: $i,A: $i] :
( ( B @ singletonP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( nil @ ( A @ cons ) )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause116) ).
thf(369,plain,
! [B: $i,A: $i] :
( ( B @ singletonP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( nil @ ( A @ cons ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(370,plain,
! [B: $i,A: $i] :
( ( B @ singletonP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( nil @ ( A @ cons ) )
!= B ) ),
inference(cnf,[status(esa)],[369]) ).
thf(371,plain,
! [B: $i,A: $i] :
( ( B @ singletonP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( nil @ ( A @ cons ) )
!= B ) ),
inference(lifteq,[status(thm)],[370]) ).
thf(372,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ singletonP )
| ~ ( nil @ ( A @ cons ) @ ssList )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[371]) ).
thf(174,axiom,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause80) ).
thf(587,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(189,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/sandbox/benchmark/theBenchmark.p',clause168) ).
thf(619,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)],[189]) ).
thf(25,axiom,
! [A: $i] : ( A @ skaf44 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause47) ).
thf(245,plain,
! [A: $i] : ( A @ skaf44 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(799,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[245,467]) ).
thf(800,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[799]) ).
thf(801,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[800:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(802,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[801]) ).
thf(41,axiom,
! [A: $i] : ( A @ skaf65 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause30) ).
thf(271,plain,
! [A: $i] : ( A @ skaf65 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(8880,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[271,282]) ).
thf(8881,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[8880]) ).
thf(8882,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( A @ skaf65 @ lt ) ),
inference(pattern_uni,[status(thm)],[8881:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(8919,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( A @ skaf65 @ lt ) ),
inference(simp,[status(thm)],[8882]) ).
thf(22757,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[245,336]) ).
thf(22758,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[22757]) ).
thf(22759,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( A @ skaf44 @ neq ) ),
inference(pattern_uni,[status(thm)],[22758:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(22827,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( A @ skaf44 @ neq ) ),
inference(simp,[status(thm)],[22759]) ).
thf(144,axiom,
! [A: $i] : ( A @ skaf52 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause43) ).
thf(512,plain,
! [A: $i] : ( A @ skaf52 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(24427,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[512,342]) ).
thf(24428,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[24427]) ).
thf(24429,plain,
! [A: $i] : ( nil @ ( A @ skaf52 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[24428:[bind(A,$thf( C )),bind(B,$thf( C @ skaf52 ))]]) ).
thf(24577,plain,
! [A: $i] : ( nil @ ( A @ skaf52 @ rearsegP ) ),
inference(simp,[status(thm)],[24429]) ).
thf(1376,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[288,467]) ).
thf(1377,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1376]) ).
thf(1378,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1377:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(1398,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1378]) ).
thf(66,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/sandbox/benchmark/theBenchmark.p',clause181) ).
thf(322,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)],[66]) ).
thf(323,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)],[322]) ).
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(lifteq,[status(thm)],[323]) ).
thf(325,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)],[324]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause106) ).
thf(228,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(52,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf43 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause52) ).
thf(289,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf43 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(63,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause134) ).
thf(314,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)],[63]) ).
thf(315,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP ) ),
inference(cnf,[status(esa)],[314]) ).
thf(316,plain,
! [B: $i,A: $i] :
( ( B @ hd @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP )
| ( nil = B ) ),
inference(lifteq,[status(thm)],[315]) ).
thf(14,axiom,
skac3 != skac2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause54) ).
thf(223,plain,
skac3 != skac2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(224,plain,
skac3 != skac2,
inference(polarity_switch,[status(thm)],[223]) ).
thf(225,plain,
skac2 != skac3,
inference(lifteq,[status(thm)],[224]) ).
thf(30574,plain,
! [A: $i] :
( ( A != skac2 )
| ( skac3 != nil )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[360,225]) ).
thf(30575,plain,
( ( skac3 != nil )
| ~ ( skac2 @ ssList )
| ~ ( skac2 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[30574:[bind(A,$thf( skac2 ))]]) ).
thf(10034,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[592,297]) ).
thf(10035,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[10034]) ).
thf(10036,plain,
! [A: $i] :
~ ( A @ skaf82 @ ( A @ skaf82 @ neq ) ),
inference(pattern_uni,[status(thm)],[10035:[bind(A,$thf( C )),bind(B,$thf( C @ skaf82 ))]]) ).
thf(10074,plain,
! [A: $i] :
~ ( A @ skaf82 @ ( A @ skaf82 @ neq ) ),
inference(simp,[status(thm)],[10036]) ).
thf(43,axiom,
! [A: $i] : ( A @ skaf50 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause45) ).
thf(274,plain,
! [A: $i] : ( A @ skaf50 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(8409,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[274,278]) ).
thf(8410,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[8409]) ).
thf(8411,plain,
! [A: $i] : ( A @ skaf50 @ ( A @ skaf50 @ leq ) ),
inference(pattern_uni,[status(thm)],[8410:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(8468,plain,
! [A: $i] : ( A @ skaf50 @ ( A @ skaf50 @ leq ) ),
inference(simp,[status(thm)],[8411]) ).
thf(22718,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[284,336]) ).
thf(22719,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[22718]) ).
thf(22720,plain,
~ ( skac3 @ ( skac3 @ neq ) ),
inference(pattern_uni,[status(thm)],[22719:[bind(A,$thf( skac3 ))]]) ).
thf(22873,plain,
( ( ( skac3 @ ( skac3 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true
| ( nil != sk1 ) ),
inference(paramod_ordered,[status(thm)],[214,22720]) ).
thf(22874,plain,
( ( ( skac3 @ ( skac3 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[22873]) ).
thf(22902,plain,
( ( skac3 != nil )
| ( skac3 != sk2 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[22874]) ).
thf(9563,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[259,9534]) ).
thf(9564,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[9563]) ).
thf(9565,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[9564:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(9636,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[9565]) ).
thf(128,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause100) ).
thf(475,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(3246,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[270,247]) ).
thf(3247,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3246]) ).
thf(3248,plain,
! [A: $i] : ( A @ skaf54 @ ( A @ skaf54 @ geq ) ),
inference(pattern_uni,[status(thm)],[3247:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(3295,plain,
! [A: $i] : ( A @ skaf54 @ ( A @ skaf54 @ geq ) ),
inference(simp,[status(thm)],[3248]) ).
thf(65,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/sandbox/benchmark/theBenchmark.p',clause163) ).
thf(319,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)],[65]) ).
thf(320,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)],[319]) ).
thf(321,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)],[320]) ).
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/sandbox/benchmark/theBenchmark.p',clause183) ).
thf(514,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(9679,plain,
( ( nil != nil )
| ( sk2 @ ( skac3 @ cons ) @ totalorderedP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,9540]) ).
thf(9680,plain,
( ( sk2 @ ( skac3 @ cons ) @ totalorderedP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[9679:[]]) ).
thf(130,axiom,
! [A: $i] : ( A @ skaf53 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause42) ).
thf(480,plain,
! [A: $i] : ( A @ skaf53 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(24405,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf43 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[289,342]) ).
thf(24406,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf43 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[24405]) ).
thf(24407,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf43 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[24406:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf43 ) ))]]) ).
thf(24568,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf43 ) @ rearsegP ) ),
inference(simp,[status(thm)],[24407]) ).
thf(87,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ rearsegP ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
!= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause143) ).
thf(373,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)],[87]) ).
thf(374,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ rearsegP ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
!= C ) ),
inference(cnf,[status(esa)],[373]) ).
thf(375,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ rearsegP ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
!= C ) ),
inference(lifteq,[status(thm)],[374]) ).
thf(376,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ app ) @ rearsegP ) )
| ~ ( B @ ( A @ app ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[375]) ).
thf(4,negated_conjecture,
sk4 @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
thf(211,plain,
sk4 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,negated_conjecture,
sk3 @ totalorderedP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
thf(210,plain,
sk3 @ totalorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(212,plain,
sk3 = sk1,
inference(lifteq,[status(thm)],[202]) ).
thf(646,plain,
sk1 @ totalorderedP,
inference(rewrite,[status(thm)],[210,212]) ).
thf(190,axiom,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause83) ).
thf(622,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(623,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(cnf,[status(esa)],[622]) ).
thf(624,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[623]) ).
thf(625,plain,
( ( nil @ ( nil @ frontsegP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[624]) ).
thf(8042,plain,
( ( nil @ ( nil @ frontsegP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[625,337]) ).
thf(8043,plain,
nil @ ( nil @ frontsegP ),
inference(simp,[status(thm)],[8042]) ).
thf(8064,plain,
( ( nil != nil )
| ( nil @ ( sk2 @ frontsegP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,8043]) ).
thf(8065,plain,
( ( nil @ ( sk2 @ frontsegP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[8064:[]]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause126) ).
thf(236,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)],[21]) ).
thf(237,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
inference(cnf,[status(esa)],[236]) ).
thf(238,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[237]) ).
thf(142,axiom,
nil @ cyclefreeP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause7) ).
thf(507,plain,
nil @ cyclefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(20916,plain,
( ( nil != nil )
| ( sk1 @ cyclefreeP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[19190,507]) ).
thf(20917,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[20916:[]]) ).
thf(75,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/sandbox/benchmark/theBenchmark.p',clause165) ).
thf(346,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)],[75]) ).
thf(347,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)],[346]) ).
thf(348,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)],[347]) ).
thf(38,axiom,
! [A: $i] : ( A @ skaf74 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause21) ).
thf(267,plain,
! [A: $i] : ( A @ skaf74 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(3267,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[267,247]) ).
thf(3268,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3267]) ).
thf(3269,plain,
! [A: $i] : ( A @ skaf74 @ ( A @ skaf74 @ geq ) ),
inference(pattern_uni,[status(thm)],[3268:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(3290,plain,
! [A: $i] : ( A @ skaf74 @ ( A @ skaf74 @ geq ) ),
inference(simp,[status(thm)],[3269]) ).
thf(803,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[250,467]) ).
thf(804,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[803]) ).
thf(805,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[804:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(806,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[805]) ).
thf(17,axiom,
! [A: $i] : ( A @ skaf79 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause16) ).
thf(230,plain,
! [A: $i] : ( A @ skaf79 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(3255,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[230,247]) ).
thf(3256,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3255]) ).
thf(3257,plain,
! [A: $i] : ( A @ skaf79 @ ( A @ skaf79 @ geq ) ),
inference(pattern_uni,[status(thm)],[3256:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(3300,plain,
! [A: $i] : ( A @ skaf79 @ ( A @ skaf79 @ geq ) ),
inference(simp,[status(thm)],[3257]) ).
thf(151,axiom,
! [A: $i] : ( A @ skaf81 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause14) ).
thf(526,plain,
! [A: $i] : ( A @ skaf81 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(24454,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[526,342]) ).
thf(24455,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[24454]) ).
thf(24456,plain,
! [A: $i] : ( nil @ ( A @ skaf81 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[24455:[bind(A,$thf( C )),bind(B,$thf( C @ skaf81 ))]]) ).
thf(24546,plain,
! [A: $i] : ( nil @ ( A @ skaf81 @ rearsegP ) ),
inference(simp,[status(thm)],[24456]) ).
thf(77,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/sandbox/benchmark/theBenchmark.p',clause185) ).
thf(350,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)],[77]) ).
thf(351,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)],[350]) ).
thf(352,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)],[351]) ).
thf(353,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)],[352]) ).
thf(39440,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[233,378]) ).
thf(39441,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[39440]) ).
thf(39442,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[39441:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(39538,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[39442]) ).
thf(10023,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[501,297]) ).
thf(10024,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[10023]) ).
thf(10025,plain,
! [A: $i] :
~ ( A @ skaf68 @ ( A @ skaf68 @ neq ) ),
inference(pattern_uni,[status(thm)],[10024:[bind(A,$thf( C )),bind(B,$thf( C @ skaf68 ))]]) ).
thf(10070,plain,
! [A: $i] :
~ ( A @ skaf68 @ ( A @ skaf68 @ neq ) ),
inference(simp,[status(thm)],[10025]) ).
thf(96,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ skaf46 ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause131) ).
thf(394,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)],[96]) ).
thf(395,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ skaf46 ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ rearsegP ) ) ),
inference(cnf,[status(esa)],[394]) ).
thf(396,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ rearsegP ) )
| ( ( B @ ( B @ ( A @ skaf46 ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[395]) ).
thf(39412,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[284,378]) ).
thf(39413,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[39412]) ).
thf(39414,plain,
nil @ ( skac3 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[39413:[bind(A,$thf( skac3 ))]]) ).
thf(9932,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[480,297]) ).
thf(9933,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[9932]) ).
thf(9934,plain,
! [A: $i] :
~ ( A @ skaf53 @ ( A @ skaf53 @ neq ) ),
inference(pattern_uni,[status(thm)],[9933:[bind(A,$thf( C )),bind(B,$thf( C @ skaf53 ))]]) ).
thf(10057,plain,
! [A: $i] :
~ ( A @ skaf53 @ ( A @ skaf53 @ neq ) ),
inference(simp,[status(thm)],[9934]) ).
thf(8424,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[267,278]) ).
thf(8425,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[8424]) ).
thf(8426,plain,
! [A: $i] : ( A @ skaf74 @ ( A @ skaf74 @ leq ) ),
inference(pattern_uni,[status(thm)],[8425:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(8459,plain,
! [A: $i] : ( A @ skaf74 @ ( A @ skaf74 @ leq ) ),
inference(simp,[status(thm)],[8426]) ).
thf(1320,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[274,467]) ).
thf(1321,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1320]) ).
thf(1322,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1321:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(1345,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1322]) ).
thf(24,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/sandbox/benchmark/theBenchmark.p',clause146) ).
thf(243,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)],[24]) ).
thf(30694,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( nil @ rearsegP ) )
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[205,360]) ).
thf(30695,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ rearsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[30694]) ).
thf(30696,plain,
( ~ ( sk2 @ ( nil @ rearsegP ) )
| ( nil = sk2 ) ),
inference(pattern_uni,[status(thm)],[30695:[bind(A,$thf( sk2 ))]]) ).
thf(10181,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ~ $true
| ( nil != sk1 ) ),
inference(paramod_ordered,[status(thm)],[214,9968]) ).
thf(10182,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[10181]) ).
thf(10208,plain,
( ( nil != sk2 )
| ( sk2 != sk2 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[10182]) ).
thf(10224,plain,
( ( nil != sk2 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[10208]) ).
thf(35493,plain,
( ( nil != nil )
| ( sk2 != sk2 )
| ( nil != sk1 )
| ~ ( sk2 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[30696,10224]) ).
thf(35494,plain,
( ( nil != nil )
| ( nil != sk1 )
| ~ ( sk2 @ ( nil @ rearsegP ) ) ),
inference(simp,[status(thm)],[35493]) ).
thf(35495,plain,
( ( nil != sk1 )
| ~ ( sk2 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[35494:[]]) ).
thf(8382,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[288,278]) ).
thf(8383,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[8382]) ).
thf(8384,plain,
! [A: $i] : ( A @ skaf59 @ ( A @ skaf59 @ leq ) ),
inference(pattern_uni,[status(thm)],[8383:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(8454,plain,
! [A: $i] : ( A @ skaf59 @ ( A @ skaf59 @ leq ) ),
inference(simp,[status(thm)],[8384]) ).
thf(194,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ segmentP ) )
| ~ ( B @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause127) ).
thf(634,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)],[194]) ).
thf(152,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/sandbox/benchmark/theBenchmark.p',clause173) ).
thf(527,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)],[152]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ app ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause85) ).
thf(312,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ app ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(78,axiom,
! [A: $i] : ( A @ skaf77 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause18) ).
thf(354,plain,
! [A: $i] : ( A @ skaf77 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(24541,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[354,342]) ).
thf(24542,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[24541]) ).
thf(24543,plain,
! [A: $i] : ( nil @ ( A @ skaf77 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[24542:[bind(A,$thf( C )),bind(B,$thf( C @ skaf77 ))]]) ).
thf(24573,plain,
! [A: $i] : ( nil @ ( A @ skaf77 @ rearsegP ) ),
inference(simp,[status(thm)],[24543]) ).
thf(13,negated_conjecture,
( ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) )
| ( nil != sk1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
thf(204,plain,
( ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) )
| ( nil != sk1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(215,plain,
( ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) )
| ( nil != sk1 ) ),
inference(cnf,[status(esa)],[204]) ).
thf(216,plain,
( ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) )
| ( nil != sk1 ) ),
inference(lifteq,[status(thm)],[215]) ).
thf(7,negated_conjecture,
sk3 @ ( sk4 @ segmentP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
thf(207,plain,
sk3 @ ( sk4 @ segmentP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
thf(199,plain,
sk2 = sk4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(219,plain,
sk4 = sk2,
inference(lifteq,[status(thm)],[199]) ).
thf(648,plain,
sk1 @ ( sk2 @ segmentP ),
inference(rewrite,[status(thm)],[207,212,219]) ).
thf(649,plain,
( ~ $true
| ~ ( nil @ ( sk1 @ neq ) )
| ( nil != sk1 ) ),
inference(rewrite,[status(thm)],[216,648]) ).
thf(650,plain,
( ~ ( nil @ ( sk1 @ neq ) )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[649]) ).
thf(33737,plain,
( ( nil != nil )
| ~ ( nil @ ( sk1 @ neq ) )
| ( sk1 != sk1 )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[30321,650]) ).
thf(33738,plain,
( ( nil != nil )
| ~ ( nil @ ( sk1 @ neq ) )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(simp,[status(thm)],[33737]) ).
thf(33739,plain,
( ~ ( nil @ ( sk1 @ neq ) )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[33738:[]]) ).
thf(31,axiom,
! [A: $i] : ( A @ skaf70 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause25) ).
thf(255,plain,
! [A: $i] : ( A @ skaf70 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(8889,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[255,282]) ).
thf(8890,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[8889]) ).
thf(8891,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( A @ skaf70 @ lt ) ),
inference(pattern_uni,[status(thm)],[8890:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(8924,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( A @ skaf70 @ lt ) ),
inference(simp,[status(thm)],[8891]) ).
thf(39470,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[274,378]) ).
thf(39471,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[39470]) ).
thf(39472,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[39471:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(39551,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[39472]) ).
thf(59,axiom,
! [A: $i] :
( ( ( nil @ ( A @ skaf44 @ cons ) )
= A )
| ~ ( A @ ssList )
| ~ ( A @ singletonP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause101) ).
thf(305,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf44 @ cons ) )
= A )
| ~ ( A @ ssList )
| ~ ( A @ singletonP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(306,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf44 @ cons ) )
= A )
| ~ ( A @ ssList )
| ~ ( A @ singletonP ) ),
inference(cnf,[status(esa)],[305]) ).
thf(307,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(lifteq,[status(thm)],[306]) ).
thf(110,axiom,
! [A: $i] : ( A @ skaf61 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause34) ).
thf(435,plain,
! [A: $i] : ( A @ skaf61 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(9943,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[435,297]) ).
thf(9944,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[9943]) ).
thf(9945,plain,
! [A: $i] :
~ ( A @ skaf61 @ ( A @ skaf61 @ neq ) ),
inference(pattern_uni,[status(thm)],[9944:[bind(A,$thf( C )),bind(B,$thf( C @ skaf61 ))]]) ).
thf(10062,plain,
! [A: $i] :
~ ( A @ skaf61 @ ( A @ skaf61 @ neq ) ),
inference(simp,[status(thm)],[9945]) ).
thf(90,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/sandbox/benchmark/theBenchmark.p',clause166) ).
thf(380,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)],[90]) ).
thf(11,negated_conjecture,
( ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) )
| ( nil = sk2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
thf(209,plain,
( ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) )
| ( nil = sk2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(217,plain,
( ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) )
| ( nil = sk2 ) ),
inference(cnf,[status(esa)],[209]) ).
thf(218,plain,
( ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) )
| ( nil = sk2 ) ),
inference(lifteq,[status(thm)],[217]) ).
thf(661,plain,
( ~ $true
| ~ ( nil @ ( sk1 @ neq ) )
| ( nil = sk2 ) ),
inference(rewrite,[status(thm)],[218,648]) ).
thf(662,plain,
( ~ ( nil @ ( sk1 @ neq ) )
| ( nil = sk2 ) ),
inference(simp,[status(thm)],[661]) ).
thf(677,plain,
( ( nil != nil )
| ~ ( sk2 @ singletonP )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[662,519]) ).
thf(678,plain,
( ~ ( sk2 @ singletonP )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[677:[]]) ).
thf(9,negated_conjecture,
! [A: $i] :
( ~ ( A @ totalorderedP )
| ~ ( sk3 @ ( A @ segmentP ) )
| ~ ( A @ ( sk4 @ segmentP ) )
| ~ ( A @ ( sk3 @ neq ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
thf(203,plain,
! [A: $i] :
( ~ ( A @ totalorderedP )
| ~ ( sk3 @ ( A @ segmentP ) )
| ~ ( A @ ( sk4 @ segmentP ) )
| ~ ( A @ ( sk3 @ neq ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(220,plain,
! [A: $i] :
( ~ ( A @ totalorderedP )
| ~ ( sk3 @ ( A @ segmentP ) )
| ~ ( A @ ( sk4 @ segmentP ) )
| ~ ( A @ ( sk3 @ neq ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[203]) ).
thf(761,plain,
! [A: $i] :
( ~ ( A @ totalorderedP )
| ~ ( sk1 @ ( A @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( A @ ( sk1 @ neq ) )
| ~ ( A @ ssList ) ),
inference(rewrite,[status(thm)],[220,212,219]) ).
thf(21097,plain,
( ( nil != nil )
| ( nil @ ( sk1 @ frontsegP ) )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[19190,8043]) ).
thf(21098,plain,
( ( nil @ ( sk1 @ frontsegP ) )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[21097:[]]) ).
thf(713,plain,
( ( nil != nil )
| ( sk2 @ totalorderP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,502]) ).
thf(714,plain,
( ( sk2 @ totalorderP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[713:[]]) ).
thf(795,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[233,467]) ).
thf(796,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[795]) ).
thf(797,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[796:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(798,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[797]) ).
thf(117,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ cons ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause139) ).
thf(452,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)],[117]) ).
thf(112,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ app ) @ frontsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause137) ).
thf(439,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)],[112]) ).
thf(3258,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[245,247]) ).
thf(3259,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3258]) ).
thf(3260,plain,
! [A: $i] : ( A @ skaf44 @ ( A @ skaf44 @ geq ) ),
inference(pattern_uni,[status(thm)],[3259:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(3301,plain,
! [A: $i] : ( A @ skaf44 @ ( A @ skaf44 @ geq ) ),
inference(simp,[status(thm)],[3260]) ).
thf(3261,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[271,247]) ).
thf(3262,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3261]) ).
thf(3263,plain,
! [A: $i] : ( A @ skaf65 @ ( A @ skaf65 @ geq ) ),
inference(pattern_uni,[status(thm)],[3262:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(3303,plain,
! [A: $i] : ( A @ skaf65 @ ( A @ skaf65 @ geq ) ),
inference(simp,[status(thm)],[3263]) ).
thf(39488,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[255,378]) ).
thf(39489,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[39488]) ).
thf(39490,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[39489:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(39526,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[39490]) ).
thf(366,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf59 @ ( A @ skaf60 @ lt ) ) ),
inference(cnf,[status(esa)],[365]) ).
thf(22782,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[287,336]) ).
thf(22783,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[22782]) ).
thf(22784,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( A @ skaf78 @ neq ) ),
inference(pattern_uni,[status(thm)],[22783:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(22806,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( A @ skaf78 @ neq ) ),
inference(simp,[status(thm)],[22784]) ).
thf(196,axiom,
nil @ totalorderedP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause4) ).
thf(639,plain,
nil @ totalorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(753,plain,
( ( nil != nil )
| ( sk2 @ totalorderedP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,639]) ).
thf(754,plain,
( ( sk2 @ totalorderedP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[753:[]]) ).
thf(10179,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ~ $true
| ( sk2 @ totalorderedP ) ),
inference(paramod_ordered,[status(thm)],[754,9968]) ).
thf(10180,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ( sk2 @ totalorderedP ) ),
inference(simp,[status(thm)],[10179]) ).
thf(10211,plain,
( ( nil != sk2 )
| ( sk2 != sk2 )
| ( sk2 @ totalorderedP ) ),
inference(simp,[status(thm)],[10180]) ).
thf(10227,plain,
( ( nil != sk2 )
| ( sk2 @ totalorderedP ) ),
inference(simp,[status(thm)],[10211]) ).
thf(21382,plain,
( ( nil != nil )
| ( sk2 != sk2 )
| ( sk2 @ totalorderedP )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[19485,10227]) ).
thf(21383,plain,
( ( nil != nil )
| ( sk2 @ totalorderedP )
| ( sk2 @ tl @ ssList ) ),
inference(simp,[status(thm)],[21382]) ).
thf(21384,plain,
( ( sk2 @ totalorderedP )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[21383:[]]) ).
thf(39473,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[230,378]) ).
thf(39474,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[39473]) ).
thf(39475,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[39474:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(39553,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[39475]) ).
thf(22774,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[263,336]) ).
thf(22775,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[22774]) ).
thf(22776,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( A @ skaf83 @ neq ) ),
inference(pattern_uni,[status(thm)],[22775:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(22832,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( A @ skaf83 @ neq ) ),
inference(simp,[status(thm)],[22776]) ).
thf(8862,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[270,282]) ).
thf(8863,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[8862]) ).
thf(8864,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( A @ skaf54 @ lt ) ),
inference(pattern_uni,[status(thm)],[8863:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(8910,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( A @ skaf54 @ lt ) ),
inference(simp,[status(thm)],[8864]) ).
thf(10163,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ~ $true
| ( sk2 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[714,9968]) ).
thf(10164,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ( sk2 @ totalorderP ) ),
inference(simp,[status(thm)],[10163]) ).
thf(10213,plain,
( ( nil != sk2 )
| ( sk2 != sk2 )
| ( sk2 @ totalorderP ) ),
inference(simp,[status(thm)],[10164]) ).
thf(10229,plain,
( ( nil != sk2 )
| ( sk2 @ totalorderP ) ),
inference(simp,[status(thm)],[10213]) ).
thf(302,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(cnf,[status(esa)],[301]) ).
thf(35,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause122) ).
thf(260,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)],[35]) ).
thf(1107,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[263,467]) ).
thf(1108,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1107]) ).
thf(1109,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1108:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(1123,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1109]) ).
thf(3231,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[284,247]) ).
thf(3232,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) ) ),
inference(simp,[status(thm)],[3231]) ).
thf(3233,plain,
skac3 @ ( skac3 @ geq ),
inference(pattern_uni,[status(thm)],[3232:[bind(A,$thf( skac3 ))]]) ).
thf(692,plain,
( ( nil != nil )
| ( sk2 @ cyclefreeP )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[662,507]) ).
thf(693,plain,
( ( sk2 @ cyclefreeP )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[692:[]]) ).
thf(119,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf48 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause48) ).
thf(456,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf48 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(24448,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf48 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[456,342]) ).
thf(24449,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf48 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[24448]) ).
thf(24450,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf48 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[24449:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf48 ) ))]]) ).
thf(24544,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf48 ) @ rearsegP ) ),
inference(simp,[status(thm)],[24450]) ).
thf(46854,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[609,392]) ).
thf(46855,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[46854]) ).
thf(46856,plain,
! [A: $i] :
( ( A @ skaf76 @ ( nil @ app ) )
= ( A @ skaf76 ) ),
inference(pattern_uni,[status(thm)],[46855:[bind(A,$thf( C )),bind(B,$thf( C @ skaf76 ))]]) ).
thf(46965,plain,
! [A: $i] :
( ( A @ skaf76 @ ( nil @ app ) )
= ( A @ skaf76 ) ),
inference(simp,[status(thm)],[46856]) ).
thf(33915,plain,
( ( nil != nil )
| ( sk1 @ equalelemsP )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[30321,368]) ).
thf(33916,plain,
( ( sk1 @ equalelemsP )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[33915:[]]) ).
thf(229,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
inference(cnf,[status(esa)],[228]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause130) ).
thf(252,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)],[30]) ).
thf(8850,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[288,282]) ).
thf(8851,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[8850]) ).
thf(8852,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( A @ skaf59 @ lt ) ),
inference(pattern_uni,[status(thm)],[8851:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(8920,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( A @ skaf59 @ lt ) ),
inference(simp,[status(thm)],[8852]) ).
thf(81,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause67) ).
thf(361,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(32,axiom,
! [A: $i] : ( A @ skaf60 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause35) ).
thf(256,plain,
! [A: $i] : ( A @ skaf60 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(3249,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[256,247]) ).
thf(3250,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3249]) ).
thf(3251,plain,
! [A: $i] : ( A @ skaf60 @ ( A @ skaf60 @ geq ) ),
inference(pattern_uni,[status(thm)],[3250:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(3297,plain,
! [A: $i] : ( A @ skaf60 @ ( A @ skaf60 @ geq ) ),
inference(simp,[status(thm)],[3251]) ).
thf(135,axiom,
! [A: $i] :
( ( A @ totalorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf65 @ ( A @ skaf64 @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause91) ).
thf(493,plain,
! [A: $i] :
( ( A @ totalorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf65 @ ( A @ skaf64 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(21155,plain,
( ( nil != nil )
| ( nil != sk2 )
| ( sk1 != sk1 )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[19190,10224]) ).
thf(21156,plain,
( ( nil != nil )
| ( nil != sk2 )
| ( sk1 @ tl @ ssList ) ),
inference(simp,[status(thm)],[21155]) ).
thf(21157,plain,
( ( nil != sk2 )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[21156:[]]) ).
thf(24296,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) )
| ( nil != sk2 ) ),
inference(paramod_ordered,[status(thm)],[21157,297]) ).
thf(24297,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ( nil != sk2 ) ),
inference(simp,[status(thm)],[24296]) ).
thf(24298,plain,
( ~ ( sk1 @ tl @ ( sk1 @ tl @ neq ) )
| ( nil != sk2 ) ),
inference(pattern_uni,[status(thm)],[24297:[bind(A,$thf( sk1 @ tl ))]]) ).
thf(25886,plain,
( ( nil != nil )
| ~ ( sk1 @ tl @ ( sk1 @ tl @ neq ) )
| ( sk2 != sk2 )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[662,24298]) ).
thf(25887,plain,
( ( nil != nil )
| ~ ( sk1 @ tl @ ( sk1 @ tl @ neq ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[25886]) ).
thf(25888,plain,
( ~ ( sk1 @ tl @ ( sk1 @ tl @ neq ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[25887:[]]) ).
thf(191,axiom,
nil @ strictorderedP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause3) ).
thf(626,plain,
nil @ strictorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(709,plain,
( ( nil != nil )
| ( sk2 @ strictorderedP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,626]) ).
thf(710,plain,
( ( sk2 @ strictorderedP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[709:[]]) ).
thf(9578,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[251,9534]) ).
thf(9579,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[9578]) ).
thf(9580,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[9579:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(9641,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[9580]) ).
thf(49,axiom,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause63) ).
thf(285,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(8430,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[263,278]) ).
thf(8431,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[8430]) ).
thf(8432,plain,
! [A: $i] : ( A @ skaf83 @ ( A @ skaf83 @ leq ) ),
inference(pattern_uni,[status(thm)],[8431:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(8462,plain,
! [A: $i] : ( A @ skaf83 @ ( A @ skaf83 @ leq ) ),
inference(simp,[status(thm)],[8432]) ).
thf(651,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[284,467]) ).
thf(652,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[651]) ).
thf(653,plain,
~ ( skac3 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[652:[bind(A,$thf( skac3 ))]]) ).
thf(696,plain,
( ( nil != nil )
| ~ ( skac3 @ ( sk2 @ memberP ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[662,653]) ).
thf(697,plain,
( ~ ( skac3 @ ( sk2 @ memberP ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[696:[]]) ).
thf(64,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/sandbox/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)],[64]) ).
thf(24399,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[481,342]) ).
thf(24400,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[24399]) ).
thf(24401,plain,
! [A: $i] : ( nil @ ( A @ skaf75 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[24400:[bind(A,$thf( C )),bind(B,$thf( C @ skaf75 ))]]) ).
thf(24566,plain,
! [A: $i] : ( nil @ ( A @ skaf75 @ rearsegP ) ),
inference(simp,[status(thm)],[24401]) ).
thf(39454,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[256,378]) ).
thf(39455,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[39454]) ).
thf(39456,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[39455:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(39546,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[39456]) ).
thf(768,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ segmentP ) )
!= ( sk1 @ ( A @ segmentP ) ) )
| ~ ( A @ totalorderedP )
| ~ $true
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( A @ ( sk1 @ neq ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[648,761]) ).
thf(769,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ segmentP ) )
!= ( sk1 @ ( A @ segmentP ) ) )
| ~ ( A @ totalorderedP )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( A @ ( sk1 @ neq ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[768]) ).
thf(770,plain,
( ~ ( sk2 @ totalorderedP )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) )
| ~ ( sk2 @ ssList ) ),
inference(pattern_uni,[status(thm)],[769:[bind(A,$thf( sk2 ))]]) ).
thf(6318,plain,
( ~ ( sk2 @ totalorderedP )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) )
| ~ $true ),
inference(rewrite,[status(thm)],[770,205]) ).
thf(6319,plain,
( ~ ( sk2 @ totalorderedP )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[6318]) ).
thf(6380,plain,
( ( ( nil @ totalorderedP )
!= ( sk2 @ totalorderedP ) )
| ~ $true
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[639,6319]) ).
thf(6381,plain,
( ( ( nil @ totalorderedP )
!= ( sk2 @ totalorderedP ) )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[6380]) ).
thf(6404,plain,
( ( nil != sk2 )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[6381]) ).
thf(8012,plain,
( ( ( nil @ ( nil @ segmentP ) )
!= ( sk2 @ ( sk2 @ segmentP ) ) )
| ( nil != sk2 )
| ~ $true
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[7983,6404]) ).
thf(8013,plain,
( ( ( nil @ ( nil @ segmentP ) )
!= ( sk2 @ ( sk2 @ segmentP ) ) )
| ( nil != sk2 )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[8012]) ).
thf(8027,plain,
( ( nil != sk2 )
| ( nil != sk2 )
| ( nil != sk2 )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[8013]) ).
thf(8038,plain,
( ( nil != sk2 )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[8027]) ).
thf(8280,plain,
( ( nil != nil )
| ( sk2 != sk2 )
| ~ ( sk2 @ ( sk1 @ neq ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[662,8038]) ).
thf(8281,plain,
( ( nil != nil )
| ~ ( sk2 @ ( sk1 @ neq ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[8280]) ).
thf(8282,plain,
( ~ ( sk2 @ ( sk1 @ neq ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[8281:[]]) ).
thf(997,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[259,467]) ).
thf(998,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[997]) ).
thf(999,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[998:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(1006,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[999]) ).
thf(46920,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[337,392]) ).
thf(46921,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[46920]) ).
thf(46922,plain,
( ( nil @ ( nil @ app ) )
= nil ),
inference(pattern_uni,[status(thm)],[46921:[bind(A,$thf( nil ))]]) ).
thf(177,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ app ) @ hd )
= ( B @ hd ) )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause123) ).
thf(593,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)],[177]) ).
thf(737,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ~ $true
| ( nil = sk2 )
| ( nil = sk2 ) ),
inference(paramod_ordered,[status(thm)],[222,662]) ).
thf(738,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ( nil = sk2 ) ),
inference(simp,[status(thm)],[737]) ).
thf(757,plain,
( ( nil != nil )
| ( sk2 != sk1 )
| ( nil = sk2 ) ),
inference(simp,[status(thm)],[738]) ).
thf(759,plain,
( ( sk2 != sk1 )
| ( nil = sk2 ) ),
inference(simp,[status(thm)],[757]) ).
thf(657,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ~ $true
| ( nil != sk1 )
| ( nil != sk1 ) ),
inference(paramod_ordered,[status(thm)],[214,650]) ).
thf(658,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[657]) ).
thf(659,plain,
( ( nil != nil )
| ( sk2 != sk1 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[658]) ).
thf(660,plain,
( ( sk2 != sk1 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[659]) ).
thf(867,plain,
( ( nil != nil )
| ( sk2 != sk1 )
| ( sk2 != sk1 )
| ( sk2 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[759,660]) ).
thf(868,plain,
( ( nil != nil )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[867]) ).
thf(869,plain,
sk2 != sk1,
inference(pattern_uni,[status(thm)],[868:[]]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause102) ).
thf(420,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(8871,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[274,282]) ).
thf(8872,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[8871]) ).
thf(8873,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( A @ skaf50 @ lt ) ),
inference(pattern_uni,[status(thm)],[8872:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(8916,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( A @ skaf50 @ lt ) ),
inference(simp,[status(thm)],[8873]) ).
thf(84,axiom,
! [A: $i] : ( A @ skaf57 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause38) ).
thf(367,plain,
! [A: $i] : ( A @ skaf57 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(9987,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[367,297]) ).
thf(9988,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[9987]) ).
thf(9989,plain,
! [A: $i] :
~ ( A @ skaf57 @ ( A @ skaf57 @ neq ) ),
inference(pattern_uni,[status(thm)],[9988:[bind(A,$thf( C )),bind(B,$thf( C @ skaf57 ))]]) ).
thf(10052,plain,
! [A: $i] :
~ ( A @ skaf57 @ ( A @ skaf57 @ neq ) ),
inference(simp,[status(thm)],[9989]) ).
thf(21420,plain,
( ( nil != nil )
| ( sk2 @ strictorderedP )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[19485,626]) ).
thf(21421,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[21420:[]]) ).
thf(185,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf42 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause53) ).
thf(610,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf42 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(24457,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[393,342]) ).
thf(24458,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[24457]) ).
thf(24459,plain,
! [A: $i] : ( nil @ ( A @ skaf58 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[24458:[bind(A,$thf( C )),bind(B,$thf( C @ skaf58 ))]]) ).
thf(24547,plain,
! [A: $i] : ( nil @ ( A @ skaf58 @ rearsegP ) ),
inference(simp,[status(thm)],[24459]) ).
thf(9575,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[271,9534]) ).
thf(9576,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[9575]) ).
thf(9577,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[9576:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(9640,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[9577]) ).
thf(8016,plain,
( ( nil != nil )
| ( sk2 @ ( nil @ segmentP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,7983]) ).
thf(8017,plain,
( ( sk2 @ ( nil @ segmentP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[8016:[]]) ).
thf(160,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ app ) @ tl )
= ( A @ ( B @ tl @ app ) ) )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause133) ).
thf(554,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)],[160]) ).
thf(1167,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[271,467]) ).
thf(1168,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1167]) ).
thf(1169,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1168:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(1182,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1169]) ).
thf(155,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/sandbox/benchmark/theBenchmark.p',clause175) ).
thf(537,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)],[155]) ).
thf(22760,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[271,336]) ).
thf(22761,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[22760]) ).
thf(22762,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( A @ skaf65 @ neq ) ),
inference(pattern_uni,[status(thm)],[22761:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(22828,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( A @ skaf65 @ neq ) ),
inference(simp,[status(thm)],[22762]) ).
thf(33859,plain,
( ( nil != nil )
| ~ ( skac3 @ ( sk1 @ memberP ) )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[30321,653]) ).
thf(33860,plain,
( ~ ( skac3 @ ( sk1 @ memberP ) )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[33859:[]]) ).
thf(41462,plain,
( ( ( nil @ ( nil @ rearsegP ) )
!= ( sk1 @ ( nil @ rearsegP ) ) )
| ~ ( skac3 @ ( sk1 @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7943,33860]) ).
thf(41463,plain,
( ( ( nil @ ( nil @ rearsegP ) )
!= ( sk1 @ ( nil @ rearsegP ) ) )
| ~ ( skac3 @ ( sk1 @ memberP ) ) ),
inference(simp,[status(thm)],[41462]) ).
thf(41510,plain,
( ( nil != sk1 )
| ( nil != nil )
| ~ ( skac3 @ ( sk1 @ memberP ) ) ),
inference(simp,[status(thm)],[41463]) ).
thf(41532,plain,
( ( nil != sk1 )
| ~ ( skac3 @ ( sk1 @ memberP ) ) ),
inference(simp,[status(thm)],[41510]) ).
thf(195,axiom,
! [A: $i] :
( ( A @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause57) ).
thf(637,plain,
! [A: $i] :
( ( A @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(134,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/sandbox/benchmark/theBenchmark.p',clause179) ).
thf(489,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)],[134]) ).
thf(175,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/sandbox/benchmark/theBenchmark.p',clause153) ).
thf(590,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)],[175]) ).
thf(21041,plain,
( ( nil != nil )
| ( sk1 @ ( nil @ segmentP ) )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[19190,7983]) ).
thf(21042,plain,
( ( sk1 @ ( nil @ segmentP ) )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[21041:[]]) ).
thf(961,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[251,467]) ).
thf(962,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[961]) ).
thf(963,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[962:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(970,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[963]) ).
thf(24433,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[435,342]) ).
thf(24434,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[24433]) ).
thf(24435,plain,
! [A: $i] : ( nil @ ( A @ skaf61 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[24434:[bind(A,$thf( C )),bind(B,$thf( C @ skaf61 ))]]) ).
thf(24578,plain,
! [A: $i] : ( nil @ ( A @ skaf61 @ rearsegP ) ),
inference(simp,[status(thm)],[24435]) ).
thf(8406,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[259,278]) ).
thf(8407,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[8406]) ).
thf(8408,plain,
! [A: $i] : ( A @ skaf49 @ ( A @ skaf49 @ leq ) ),
inference(pattern_uni,[status(thm)],[8407:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(8467,plain,
! [A: $i] : ( A @ skaf49 @ ( A @ skaf49 @ leq ) ),
inference(simp,[status(thm)],[8408]) ).
thf(3276,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[250,247]) ).
thf(3277,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3276]) ).
thf(3278,plain,
! [A: $i] : ( A @ skaf69 @ ( A @ skaf69 @ geq ) ),
inference(pattern_uni,[status(thm)],[3277:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(3294,plain,
! [A: $i] : ( A @ skaf69 @ ( A @ skaf69 @ geq ) ),
inference(simp,[status(thm)],[3278]) ).
thf(9592,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[250,9534]) ).
thf(9593,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[9592]) ).
thf(9594,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[9593:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(9645,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[9594]) ).
thf(705,plain,
( ( nil != nil )
| ( sk2 @ strictorderP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,349]) ).
thf(706,plain,
( ( sk2 @ strictorderP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[705:[]]) ).
thf(8421,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[251,278]) ).
thf(8422,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[8421]) ).
thf(8423,plain,
! [A: $i] : ( A @ skaf55 @ ( A @ skaf55 @ leq ) ),
inference(pattern_uni,[status(thm)],[8422:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(8458,plain,
! [A: $i] : ( A @ skaf55 @ ( A @ skaf55 @ leq ) ),
inference(simp,[status(thm)],[8423]) ).
thf(700,plain,
( ( nil != nil )
| ( sk2 @ totalorderedP )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[662,639]) ).
thf(701,plain,
( ( sk2 @ totalorderedP )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[700:[]]) ).
thf(39467,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[259,378]) ).
thf(39468,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[39467]) ).
thf(39469,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[39468:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(39550,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[39469]) ).
thf(120,axiom,
! [A: $i] :
( ( nil @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause56) ).
thf(457,plain,
! [A: $i] :
( ( nil @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(9535,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[288,9534]) ).
thf(9536,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[9535]) ).
thf(9537,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[9536:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(9620,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[9537]) ).
thf(8415,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[245,278]) ).
thf(8416,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[8415]) ).
thf(8417,plain,
! [A: $i] : ( A @ skaf44 @ ( A @ skaf44 @ leq ) ),
inference(pattern_uni,[status(thm)],[8416:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(8455,plain,
! [A: $i] : ( A @ skaf44 @ ( A @ skaf44 @ leq ) ),
inference(simp,[status(thm)],[8417]) ).
thf(181,axiom,
! [A: $i] : ( A @ skaf71 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause24) ).
thf(603,plain,
! [A: $i] : ( A @ skaf71 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(24505,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[603,342]) ).
thf(24506,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[24505]) ).
thf(24507,plain,
! [A: $i] : ( nil @ ( A @ skaf71 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[24506:[bind(A,$thf( C )),bind(B,$thf( C @ skaf71 ))]]) ).
thf(24562,plain,
! [A: $i] : ( nil @ ( A @ skaf71 @ rearsegP ) ),
inference(simp,[status(thm)],[24507]) ).
thf(39476,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[245,378]) ).
thf(39477,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[39476]) ).
thf(39478,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[39477:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(39554,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[39478]) ).
thf(33702,plain,
( ( nil != nil )
| ( sk1 @ strictorderP )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[30321,349]) ).
thf(33703,plain,
( ( sk1 @ strictorderP )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[33702:[]]) ).
thf(39279,plain,
( ( ( nil @ ( nil @ rearsegP ) )
!= ( sk1 @ ( nil @ rearsegP ) ) )
| ( sk1 @ strictorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7943,33703]) ).
thf(39280,plain,
( ( ( nil @ ( nil @ rearsegP ) )
!= ( sk1 @ ( nil @ rearsegP ) ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[39279]) ).
thf(39319,plain,
( ( nil != sk1 )
| ( nil != nil )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[39280]) ).
thf(39335,plain,
( ( nil != sk1 )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[39319]) ).
thf(973,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[255,467]) ).
thf(974,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[973]) ).
thf(975,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[974:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(984,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[975]) ).
thf(9549,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[233,9534]) ).
thf(9550,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[9549]) ).
thf(9551,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[9550:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(9630,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[9551]) ).
thf(140,axiom,
! [A: $i] :
( ( nil @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause60) ).
thf(503,plain,
! [A: $i] :
( ( nil @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(10251,plain,
( ( nil != nil )
| ~ ( nil @ ( sk2 @ neq ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[662,10028]) ).
thf(10252,plain,
( ~ ( nil @ ( sk2 @ neq ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[10251:[]]) ).
thf(74,axiom,
! [B: $i,A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause118) ).
thf(343,plain,
! [B: $i,A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(244,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ gt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
inference(cnf,[status(esa)],[243]) ).
thf(61,axiom,
! [A: $i] : ( A @ skaf72 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause23) ).
thf(311,plain,
! [A: $i] : ( A @ skaf72 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(9958,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[526,297]) ).
thf(9959,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[9958]) ).
thf(9960,plain,
! [A: $i] :
~ ( A @ skaf81 @ ( A @ skaf81 @ neq ) ),
inference(pattern_uni,[status(thm)],[9959:[bind(A,$thf( C )),bind(B,$thf( C @ skaf81 ))]]) ).
thf(10069,plain,
! [A: $i] :
~ ( A @ skaf81 @ ( A @ skaf81 @ neq ) ),
inference(simp,[status(thm)],[9960]) ).
thf(162,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause68) ).
thf(558,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(21101,plain,
( ( nil != nil )
| ( sk1 @ equalelemsP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[19190,368]) ).
thf(21102,plain,
( ( sk1 @ equalelemsP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[21101:[]]) ).
thf(164,axiom,
! [A: $i] : ( A @ skaf63 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause32) ).
thf(563,plain,
! [A: $i] : ( A @ skaf63 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(9996,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[563,297]) ).
thf(9997,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[9996]) ).
thf(9998,plain,
! [A: $i] :
~ ( A @ skaf63 @ ( A @ skaf63 @ neq ) ),
inference(pattern_uni,[status(thm)],[9997:[bind(A,$thf( C )),bind(B,$thf( C @ skaf63 ))]]) ).
thf(10058,plain,
! [A: $i] :
~ ( A @ skaf63 @ ( A @ skaf63 @ neq ) ),
inference(simp,[status(thm)],[9998]) ).
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/sandbox/benchmark/theBenchmark.p',clause184) ).
thf(508,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(39494,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[250,378]) ).
thf(39495,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[39494]) ).
thf(39496,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[39495:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(39529,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[39496]) ).
thf(8886,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[267,282]) ).
thf(8887,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[8886]) ).
thf(8888,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( A @ skaf74 @ lt ) ),
inference(pattern_uni,[status(thm)],[8887:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(8923,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( A @ skaf74 @ lt ) ),
inference(simp,[status(thm)],[8888]) ).
thf(156,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/sandbox/benchmark/theBenchmark.p',clause157) ).
thf(541,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)],[156]) ).
thf(791,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[230,467]) ).
thf(792,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[791]) ).
thf(793,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[792:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(794,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[793]) ).
thf(33891,plain,
( ( nil != nil )
| ( sk1 @ totalorderP )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[30321,502]) ).
thf(33892,plain,
( ( sk1 @ totalorderP )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[33891:[]]) ).
thf(42698,plain,
( ( ( nil @ ( nil @ rearsegP ) )
!= ( sk1 @ ( nil @ rearsegP ) ) )
| ( sk1 @ totalorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7943,33892]) ).
thf(42699,plain,
( ( ( nil @ ( nil @ rearsegP ) )
!= ( sk1 @ ( nil @ rearsegP ) ) )
| ( sk1 @ totalorderP ) ),
inference(simp,[status(thm)],[42698]) ).
thf(42727,plain,
( ( nil != sk1 )
| ( nil != nil )
| ( sk1 @ totalorderP ) ),
inference(simp,[status(thm)],[42699]) ).
thf(42760,plain,
( ( nil != sk1 )
| ( sk1 @ totalorderP ) ),
inference(simp,[status(thm)],[42727]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause121) ).
thf(264,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)],[37]) ).
thf(169,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause77) ).
thf(573,plain,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(688,plain,
( ( nil != nil )
| ( sk2 @ duplicatefreeP )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[662,383]) ).
thf(689,plain,
( ( sk2 @ duplicatefreeP )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[688:[]]) ).
thf(58,axiom,
! [A: $i] :
( ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause88) ).
thf(303,plain,
! [A: $i] :
( ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(304,plain,
! [A: $i] :
( ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[303]) ).
thf(11835,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[205,304]) ).
thf(11836,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP ) ),
inference(simp,[status(thm)],[11835]) ).
thf(11837,plain,
( ( sk2 @ skaf50 @ ( sk2 @ skaf49 @ leq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[11836:[bind(A,$thf( sk2 ))]]) ).
thf(21405,plain,
( ( nil != nil )
| ( sk2 @ ( nil @ segmentP ) )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[19485,7983]) ).
thf(21406,plain,
( ( sk2 @ ( nil @ segmentP ) )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[21405:[]]) ).
thf(106,axiom,
! [A: $i] : ( A @ skaf73 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause22) ).
thf(426,plain,
! [A: $i] : ( A @ skaf73 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(24492,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[426,342]) ).
thf(24493,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[24492]) ).
thf(24494,plain,
! [A: $i] : ( nil @ ( A @ skaf73 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[24493:[bind(A,$thf( C )),bind(B,$thf( C @ skaf73 ))]]) ).
thf(24557,plain,
! [A: $i] : ( nil @ ( A @ skaf73 @ rearsegP ) ),
inference(simp,[status(thm)],[24494]) ).
thf(108,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause98) ).
thf(430,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(3234,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[259,247]) ).
thf(3235,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3234]) ).
thf(3236,plain,
! [A: $i] : ( A @ skaf49 @ ( A @ skaf49 @ geq ) ),
inference(pattern_uni,[status(thm)],[3235:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(3289,plain,
! [A: $i] : ( A @ skaf49 @ ( A @ skaf49 @ geq ) ),
inference(simp,[status(thm)],[3236]) ).
thf(9558,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[256,9534]) ).
thf(9559,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[9558]) ).
thf(9560,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[9559:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(9635,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[9560]) ).
thf(114,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause129) ).
thf(444,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)],[114]) ).
thf(21209,plain,
( ( nil != nil )
| ( sk2 != sk2 )
| ( nil @ ( sk2 @ segmentP ) )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[19485,10230]) ).
thf(21210,plain,
( ( nil != nil )
| ( nil @ ( sk2 @ segmentP ) )
| ( sk2 @ tl @ ssList ) ),
inference(simp,[status(thm)],[21209]) ).
thf(21211,plain,
( ( nil @ ( sk2 @ segmentP ) )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[21210:[]]) ).
thf(39485,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[267,378]) ).
thf(39486,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[39485]) ).
thf(39487,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[39486:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(39558,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[39487]) ).
thf(20964,plain,
( ( nil != nil )
| ~ ( sk1 @ singletonP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[19190,519]) ).
thf(20965,plain,
( ~ ( sk1 @ singletonP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[20964:[]]) ).
thf(22500,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) )
| ~ ( sk1 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[20965,297]) ).
thf(22501,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ ( sk1 @ singletonP ) ),
inference(simp,[status(thm)],[22500]) ).
thf(22502,plain,
( ~ ( sk1 @ tl @ ( sk1 @ tl @ neq ) )
| ~ ( sk1 @ singletonP ) ),
inference(pattern_uni,[status(thm)],[22501:[bind(A,$thf( sk1 @ tl ))]]) ).
thf(21464,plain,
( ( nil != nil )
| ( nil @ ( sk2 @ frontsegP ) )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[19485,8043]) ).
thf(21465,plain,
( ( nil @ ( sk2 @ frontsegP ) )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[21464:[]]) ).
thf(22769,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[255,336]) ).
thf(22770,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[22769]) ).
thf(22771,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( A @ skaf70 @ neq ) ),
inference(pattern_uni,[status(thm)],[22770:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(22831,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( A @ skaf70 @ neq ) ),
inference(simp,[status(thm)],[22771]) ).
thf(105,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause119) ).
thf(423,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(8907,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( A @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[283,282]) ).
thf(8908,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[8907]) ).
thf(8909,plain,
~ ( skac2 @ ( skac2 @ lt ) ),
inference(pattern_uni,[status(thm)],[8908:[bind(A,$thf( skac2 ))]]) ).
thf(171,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ tl )
= B )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause96) ).
thf(579,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ tl )
= B )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(24402,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[379,342]) ).
thf(24403,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[24402]) ).
thf(24404,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf45 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[24403:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf45 ) ))]]) ).
thf(24567,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf45 ) @ rearsegP ) ),
inference(simp,[status(thm)],[24404]) ).
thf(101,axiom,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf54 @ ( A @ skaf55 @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause94) ).
thf(413,plain,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf54 @ ( A @ skaf55 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(11817,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[201,304]) ).
thf(11818,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP ) ),
inference(simp,[status(thm)],[11817]) ).
thf(11819,plain,
( ( sk1 @ skaf50 @ ( sk1 @ skaf49 @ leq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[11818:[bind(A,$thf( sk1 ))]]) ).
thf(313,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ app ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[312]) ).
thf(1348,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[287,467]) ).
thf(1349,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1348]) ).
thf(1350,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1349:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(1371,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1350]) ).
thf(186,axiom,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause84) ).
thf(611,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(137,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause99) ).
thf(498,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(9923,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[481,297]) ).
thf(9924,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[9923]) ).
thf(9925,plain,
! [A: $i] :
~ ( A @ skaf75 @ ( A @ skaf75 @ neq ) ),
inference(pattern_uni,[status(thm)],[9924:[bind(A,$thf( C )),bind(B,$thf( C @ skaf75 ))]]) ).
thf(10051,plain,
! [A: $i] :
~ ( A @ skaf75 @ ( A @ skaf75 @ neq ) ),
inference(simp,[status(thm)],[9925]) ).
thf(3228,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[288,247]) ).
thf(3229,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3228]) ).
thf(3230,plain,
! [A: $i] : ( A @ skaf59 @ ( A @ skaf59 @ geq ) ),
inference(pattern_uni,[status(thm)],[3229:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(3302,plain,
! [A: $i] : ( A @ skaf59 @ ( A @ skaf59 @ geq ) ),
inference(simp,[status(thm)],[3230]) ).
thf(9993,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[520,297]) ).
thf(9994,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[9993]) ).
thf(9995,plain,
! [A: $i] :
~ ( A @ skaf67 @ ( A @ skaf67 @ neq ) ),
inference(pattern_uni,[status(thm)],[9994:[bind(A,$thf( C )),bind(B,$thf( C @ skaf67 ))]]) ).
thf(10056,plain,
! [A: $i] :
~ ( A @ skaf67 @ ( A @ skaf67 @ neq ) ),
inference(simp,[status(thm)],[9995]) ).
thf(9569,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[230,9534]) ).
thf(9570,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[9569]) ).
thf(9571,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[9570:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(9638,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[9571]) ).
thf(381,plain,
! [A: $i] :
( ( ( A @ skaf58 @ ( A @ skaf55 @ cons ) @ ( A @ skaf57 @ ( A @ skaf54 @ cons ) @ ( A @ skaf56 @ app ) @ app ) )
= A )
| ( A @ totalorderP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[380]) ).
thf(382,plain,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ( ( A @ skaf58 @ ( A @ skaf55 @ cons ) @ ( A @ skaf57 @ ( A @ skaf54 @ cons ) @ ( A @ skaf56 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[381]) ).
thf(21153,plain,
( ( nil != nil )
| ( sk1 @ ( nil @ rearsegP ) )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[19190,7943]) ).
thf(21154,plain,
( ( sk1 @ ( nil @ rearsegP ) )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[21153:[]]) ).
thf(182,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/sandbox/benchmark/theBenchmark.p',clause169) ).
thf(604,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)],[182]) ).
thf(165,axiom,
! [A: $i] : ( A @ skaf66 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause29) ).
thf(564,plain,
! [A: $i] : ( A @ skaf66 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(10015,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[564,297]) ).
thf(10016,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[10015]) ).
thf(10017,plain,
! [A: $i] :
~ ( A @ skaf66 @ ( A @ skaf66 @ neq ) ),
inference(pattern_uni,[status(thm)],[10016:[bind(A,$thf( C )),bind(B,$thf( C @ skaf66 ))]]) ).
thf(10066,plain,
! [A: $i] :
~ ( A @ skaf66 @ ( A @ skaf66 @ neq ) ),
inference(simp,[status(thm)],[10017]) ).
thf(8397,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[233,278]) ).
thf(8398,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[8397]) ).
thf(8399,plain,
! [A: $i] : ( A @ skaf64 @ ( A @ skaf64 @ leq ) ),
inference(pattern_uni,[status(thm)],[8398:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(8461,plain,
! [A: $i] : ( A @ skaf64 @ ( A @ skaf64 @ leq ) ),
inference(simp,[status(thm)],[8399]) ).
thf(1127,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[267,467]) ).
thf(1128,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1127]) ).
thf(1129,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1128:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(1144,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1129]) ).
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(188,axiom,
! [A: $i] :
( ( A @ equalelemsP )
| ~ ( A @ ssList )
| ( ( A @ skaf79 )
!= ( A @ skaf78 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause89) ).
thf(616,plain,
! [A: $i] :
( ( A @ equalelemsP )
| ~ ( A @ ssList )
| ( ( A @ skaf79 )
!= ( A @ skaf78 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(3,negated_conjecture,
sk3 @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
thf(208,plain,
sk3 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(20942,plain,
( ( nil != nil )
| ( sk1 @ strictorderP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[19190,349]) ).
thf(20943,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[20942:[]]) ).
thf(179,axiom,
! [A: $i] : ( A @ skaf56 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause39) ).
thf(599,plain,
! [A: $i] : ( A @ skaf56 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(8892,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[263,282]) ).
thf(8893,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[8892]) ).
thf(8894,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( A @ skaf83 @ lt ) ),
inference(pattern_uni,[status(thm)],[8893:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(8926,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( A @ skaf83 @ lt ) ),
inference(simp,[status(thm)],[8894]) ).
thf(33684,plain,
( ( nil != nil )
| ( sk1 @ cyclefreeP )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[30321,507]) ).
thf(33685,plain,
( ( sk1 @ cyclefreeP )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[33684:[]]) ).
thf(193,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/sandbox/benchmark/theBenchmark.p',clause177) ).
thf(631,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)],[193]) ).
thf(39491,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[263,378]) ).
thf(39492,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[39491]) ).
thf(39493,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[39492:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(39527,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[39493]) ).
thf(9583,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[267,9534]) ).
thf(9584,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[9583]) ).
thf(9585,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[9584:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(9642,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[9585]) ).
thf(46827,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[205,392]) ).
thf(46828,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[46827]) ).
thf(46829,plain,
( ( sk2 @ ( nil @ app ) )
= sk2 ),
inference(pattern_uni,[status(thm)],[46828:[bind(A,$thf( sk2 ))]]) ).
thf(667,plain,
( ( nil != nil )
| ( sk2 @ equalelemsP )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[662,368]) ).
thf(668,plain,
( ( sk2 @ equalelemsP )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[667:[]]) ).
thf(69,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/sandbox/benchmark/theBenchmark.p',clause164) ).
thf(330,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)],[69]) ).
thf(344,plain,
! [B: $i,A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
inference(cnf,[status(esa)],[343]) ).
thf(345,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( nil = A )
| ( ( B @ ( A @ app ) )
!= nil ) ),
inference(lifteq,[status(thm)],[344]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ app ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause141) ).
thf(552,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)],[159]) ).
thf(10165,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[710,9968]) ).
thf(10166,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[10165]) ).
thf(10203,plain,
( ( nil != sk2 )
| ( sk2 != sk2 )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[10166]) ).
thf(10219,plain,
( ( nil != sk2 )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[10203]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause105) ).
thf(239,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(240,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ gt ) ) ),
inference(cnf,[status(esa)],[239]) ).
thf(3252,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[274,247]) ).
thf(3253,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3252]) ).
thf(3254,plain,
! [A: $i] : ( A @ skaf50 @ ( A @ skaf50 @ geq ) ),
inference(pattern_uni,[status(thm)],[3253:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(3298,plain,
! [A: $i] : ( A @ skaf50 @ ( A @ skaf50 @ geq ) ),
inference(simp,[status(thm)],[3254]) ).
thf(22735,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[256,336]) ).
thf(22736,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[22735]) ).
thf(22737,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( A @ skaf60 @ neq ) ),
inference(pattern_uni,[status(thm)],[22736:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(22818,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( A @ skaf60 @ neq ) ),
inference(simp,[status(thm)],[22737]) ).
thf(122,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ totalorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause135) ).
thf(462,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)],[122]) ).
thf(24489,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[563,342]) ).
thf(24490,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[24489]) ).
thf(24491,plain,
! [A: $i] : ( nil @ ( A @ skaf63 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[24490:[bind(A,$thf( C )),bind(B,$thf( C @ skaf63 ))]]) ).
thf(24556,plain,
! [A: $i] : ( nil @ ( A @ skaf63 @ rearsegP ) ),
inference(simp,[status(thm)],[24491]) ).
thf(149,axiom,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf60 @ ( A @ skaf59 @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause93) ).
thf(521,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf60 @ ( A @ skaf59 @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(8418,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[271,278]) ).
thf(8419,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[8418]) ).
thf(8420,plain,
! [A: $i] : ( A @ skaf65 @ ( A @ skaf65 @ leq ) ),
inference(pattern_uni,[status(thm)],[8419:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(8456,plain,
! [A: $i] : ( A @ skaf65 @ ( A @ skaf65 @ leq ) ),
inference(simp,[status(thm)],[8420]) ).
thf(46635,plain,
( ( ( nil @ ( nil @ rearsegP ) )
!= ( sk1 @ ( nil @ rearsegP ) ) )
| ( sk1 @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7943,33916]) ).
thf(46636,plain,
( ( ( nil @ ( nil @ rearsegP ) )
!= ( sk1 @ ( nil @ rearsegP ) ) )
| ( sk1 @ equalelemsP ) ),
inference(simp,[status(thm)],[46635]) ).
thf(46664,plain,
( ( nil != sk1 )
| ( nil != nil )
| ( sk1 @ equalelemsP ) ),
inference(simp,[status(thm)],[46636]) ).
thf(46695,plain,
( ( nil != sk1 )
| ( sk1 @ equalelemsP ) ),
inference(simp,[status(thm)],[46664]) ).
thf(694,plain,
( ( nil != nil )
| ( sk2 @ strictorderedP )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[662,626]) ).
thf(695,plain,
( ( sk2 @ strictorderedP )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[694:[]]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause108) ).
thf(226,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(141,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause70) ).
thf(505,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(722,plain,
( ( nil != nil )
| ( sk2 @ cyclefreeP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,507]) ).
thf(723,plain,
( ( sk2 @ cyclefreeP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[722:[]]) ).
thf(10191,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[723,9968]) ).
thf(10192,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[10191]) ).
thf(10210,plain,
( ( nil != sk2 )
| ( sk2 != sk2 )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[10192]) ).
thf(10226,plain,
( ( nil != sk2 )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[10210]) ).
thf(123,axiom,
! [A: $i] : ( A @ skaf80 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause15) ).
thf(465,plain,
! [A: $i] : ( A @ skaf80 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(10007,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[465,297]) ).
thf(10008,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[10007]) ).
thf(10009,plain,
! [A: $i] :
~ ( A @ skaf80 @ ( A @ skaf80 @ neq ) ),
inference(pattern_uni,[status(thm)],[10008:[bind(A,$thf( C )),bind(B,$thf( C @ skaf80 ))]]) ).
thf(10063,plain,
! [A: $i] :
~ ( A @ skaf80 @ ( A @ skaf80 @ neq ) ),
inference(simp,[status(thm)],[10009]) ).
thf(56,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/sandbox/benchmark/theBenchmark.p',clause158) ).
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(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause103) ).
thf(241,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(22939,plain,
( ( ( skac2 @ ( skac2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true
| ~ ( sk2 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[725,22787]) ).
thf(22940,plain,
( ( ( skac2 @ ( skac2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ ( sk2 @ singletonP ) ),
inference(simp,[status(thm)],[22939]) ).
thf(22984,plain,
( ( skac2 != nil )
| ( skac2 != sk2 )
| ~ ( sk2 @ singletonP ) ),
inference(simp,[status(thm)],[22940]) ).
thf(153,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause65) ).
thf(531,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(10171,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[706,9968]) ).
thf(10172,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[10171]) ).
thf(10207,plain,
( ( nil != sk2 )
| ( sk2 != sk2 )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[10172]) ).
thf(10223,plain,
( ( nil != sk2 )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[10207]) ).
thf(9595,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[287,9534]) ).
thf(9596,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[9595]) ).
thf(9597,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[9596:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(9646,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[9597]) ).
thf(3273,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[263,247]) ).
thf(3274,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3273]) ).
thf(3275,plain,
! [A: $i] : ( A @ skaf83 @ ( A @ skaf83 @ geq ) ),
inference(pattern_uni,[status(thm)],[3274:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(3292,plain,
! [A: $i] : ( A @ skaf83 @ ( A @ skaf83 @ geq ) ),
inference(simp,[status(thm)],[3275]) ).
thf(24480,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[367,342]) ).
thf(24481,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[24480]) ).
thf(24482,plain,
! [A: $i] : ( nil @ ( A @ skaf57 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[24481:[bind(A,$thf( C )),bind(B,$thf( C @ skaf57 ))]]) ).
thf(24553,plain,
! [A: $i] : ( nil @ ( A @ skaf57 @ rearsegP ) ),
inference(simp,[status(thm)],[24482]) ).
thf(1147,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[270,467]) ).
thf(1148,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1147]) ).
thf(1149,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1148:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(1166,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1149]) ).
thf(3243,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[233,247]) ).
thf(3244,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3243]) ).
thf(3245,plain,
! [A: $i] : ( A @ skaf64 @ ( A @ skaf64 @ geq ) ),
inference(pattern_uni,[status(thm)],[3244:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(3293,plain,
! [A: $i] : ( A @ skaf64 @ ( A @ skaf64 @ geq ) ),
inference(simp,[status(thm)],[3245]) ).
thf(158,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/sandbox/benchmark/theBenchmark.p',clause182) ).
thf(548,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)],[158]) ).
thf(9572,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[245,9534]) ).
thf(9573,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[9572]) ).
thf(9574,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[9573:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(9639,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[9574]) ).
thf(8066,plain,
( ( nil != nil )
| ( sk2 @ ( nil @ frontsegP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,8043]) ).
thf(8067,plain,
( ( sk2 @ ( nil @ frontsegP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[8066:[]]) ).
thf(46780,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[201,392]) ).
thf(46781,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[46780]) ).
thf(46782,plain,
( ( sk1 @ ( nil @ app ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[46781:[bind(A,$thf( sk1 ))]]) ).
thf(22751,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[274,336]) ).
thf(22752,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[22751]) ).
thf(22753,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( A @ skaf50 @ neq ) ),
inference(pattern_uni,[status(thm)],[22752:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(22825,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( A @ skaf50 @ neq ) ),
inference(simp,[status(thm)],[22753]) ).
thf(197,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ strictorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause124) ).
thf(640,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)],[197]) ).
thf(46851,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[599,392]) ).
thf(46852,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[46851]) ).
thf(46853,plain,
! [A: $i] :
( ( A @ skaf56 @ ( nil @ app ) )
= ( A @ skaf56 ) ),
inference(pattern_uni,[status(thm)],[46852:[bind(A,$thf( C )),bind(B,$thf( C @ skaf56 ))]]) ).
thf(46964,plain,
! [A: $i] :
( ( A @ skaf56 @ ( nil @ app ) )
= ( A @ skaf56 ) ),
inference(simp,[status(thm)],[46853]) ).
thf(39479,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[271,378]) ).
thf(39480,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[39479]) ).
thf(39481,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[39480:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(39555,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[39481]) ).
thf(8436,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[287,278]) ).
thf(8437,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[8436]) ).
thf(8438,plain,
! [A: $i] : ( A @ skaf78 @ ( A @ skaf78 @ leq ) ),
inference(pattern_uni,[status(thm)],[8437:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(8466,plain,
! [A: $i] : ( A @ skaf78 @ ( A @ skaf78 @ leq ) ),
inference(simp,[status(thm)],[8438]) ).
thf(9935,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[512,297]) ).
thf(9936,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[9935]) ).
thf(9937,plain,
! [A: $i] :
~ ( A @ skaf52 @ ( A @ skaf52 @ neq ) ),
inference(pattern_uni,[status(thm)],[9936:[bind(A,$thf( C )),bind(B,$thf( C @ skaf52 ))]]) ).
thf(10059,plain,
! [A: $i] :
~ ( A @ skaf52 @ ( A @ skaf52 @ neq ) ),
inference(simp,[status(thm)],[9937]) ).
thf(24511,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[564,342]) ).
thf(24512,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[24511]) ).
thf(24513,plain,
! [A: $i] : ( nil @ ( A @ skaf66 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[24512:[bind(A,$thf( C )),bind(B,$thf( C @ skaf66 ))]]) ).
thf(24563,plain,
! [A: $i] : ( nil @ ( A @ skaf66 @ rearsegP ) ),
inference(simp,[status(thm)],[24513]) ).
thf(22859,plain,
( ( ( skac3 @ ( skac3 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true
| ~ ( sk2 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[725,22720]) ).
thf(22860,plain,
( ( ( skac3 @ ( skac3 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ ( sk2 @ singletonP ) ),
inference(simp,[status(thm)],[22859]) ).
thf(22908,plain,
( ( skac3 != nil )
| ( skac3 != sk2 )
| ~ ( sk2 @ singletonP ) ),
inference(simp,[status(thm)],[22860]) ).
thf(7966,plain,
( ( nil != nil )
| ( sk2 @ ( nil @ rearsegP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,7943]) ).
thf(7967,plain,
( ( sk2 @ ( nil @ rearsegP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[7966:[]]) ).
thf(21124,plain,
( ( nil != nil )
| ( nil @ ( sk2 @ neq ) )
| ( sk1 != sk1 )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[19190,214]) ).
thf(21125,plain,
( ( nil != nil )
| ( nil @ ( sk2 @ neq ) )
| ( sk1 @ tl @ ssList ) ),
inference(simp,[status(thm)],[21124]) ).
thf(21126,plain,
( ( nil @ ( sk2 @ neq ) )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[21125:[]]) ).
thf(100,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/sandbox/benchmark/theBenchmark.p',clause178) ).
thf(409,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)],[100]) ).
thf(711,plain,
( ( nil != nil )
| ~ ( skac3 @ ( sk2 @ memberP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,653]) ).
thf(712,plain,
( ~ ( skac3 @ ( sk2 @ memberP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[711:[]]) ).
thf(21290,plain,
( ( nil != nil )
| ( sk2 != sk2 )
| ( sk2 @ totalorderP )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[19485,10229]) ).
thf(21291,plain,
( ( nil != nil )
| ( sk2 @ totalorderP )
| ( sk2 @ tl @ ssList ) ),
inference(simp,[status(thm)],[21290]) ).
thf(21292,plain,
( ( sk2 @ totalorderP )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[21291:[]]) ).
thf(309,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)],[308]) ).
thf(310,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)],[309]) ).
thf(8856,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( A @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[284,282]) ).
thf(8857,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[8856]) ).
thf(8858,plain,
~ ( skac3 @ ( skac3 @ lt ) ),
inference(pattern_uni,[status(thm)],[8857:[bind(A,$thf( skac3 ))]]) ).
thf(113,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ strictorderedP )
| ~ ( B @ hd @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause160) ).
thf(441,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)],[113]) ).
thf(173,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause69) ).
thf(585,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(39497,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[287,378]) ).
thf(39498,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[39497]) ).
thf(39499,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[39498:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(39532,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[39499]) ).
thf(198,axiom,
! [A: $i] :
( ( A @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause61) ).
thf(643,plain,
! [A: $i] :
( ( A @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(157,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ frontsegP ) )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause144) ).
thf(544,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)],[157]) ).
thf(8874,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[230,282]) ).
thf(8875,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[8874]) ).
thf(8876,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( A @ skaf79 @ lt ) ),
inference(pattern_uni,[status(thm)],[8875:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(8917,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( A @ skaf79 @ lt ) ),
inference(simp,[status(thm)],[8876]) ).
thf(24463,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[311,342]) ).
thf(24464,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[24463]) ).
thf(24465,plain,
! [A: $i] : ( nil @ ( A @ skaf72 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[24464:[bind(A,$thf( C )),bind(B,$thf( C @ skaf72 ))]]) ).
thf(24548,plain,
! [A: $i] : ( nil @ ( A @ skaf72 @ rearsegP ) ),
inference(simp,[status(thm)],[24465]) ).
thf(126,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/sandbox/benchmark/theBenchmark.p',clause152) ).
thf(470,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)],[126]) ).
thf(170,axiom,
! [A: $i] :
( ( nil = A )
| ( ( A @ skaf82 @ ( A @ skaf83 @ cons ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause109) ).
thf(576,plain,
! [A: $i] :
( ( nil = A )
| ( ( A @ skaf82 @ ( A @ skaf83 @ cons ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(8433,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[250,278]) ).
thf(8434,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[8433]) ).
thf(8435,plain,
! [A: $i] : ( A @ skaf69 @ ( A @ skaf69 @ leq ) ),
inference(pattern_uni,[status(thm)],[8434:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(8464,plain,
! [A: $i] : ( A @ skaf69 @ ( A @ skaf69 @ leq ) ),
inference(simp,[status(thm)],[8435]) ).
thf(180,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/sandbox/benchmark/theBenchmark.p',clause176) ).
thf(600,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)],[180]) ).
thf(24486,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[520,342]) ).
thf(24487,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[24486]) ).
thf(24488,plain,
! [A: $i] : ( nil @ ( A @ skaf67 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[24487:[bind(A,$thf( C )),bind(B,$thf( C @ skaf67 ))]]) ).
thf(24555,plain,
! [A: $i] : ( nil @ ( A @ skaf67 @ rearsegP ) ),
inference(simp,[status(thm)],[24488]) ).
thf(9552,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[270,9534]) ).
thf(9553,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[9552]) ).
thf(9554,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[9553:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(9632,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[9554]) ).
thf(385,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ hd )
= A )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[384]) ).
thf(386,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) @ hd )
= A ) ),
inference(lifteq,[status(thm)],[385]) ).
thf(9566,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[274,9534]) ).
thf(9567,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[9566]) ).
thf(9568,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[9567:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(9637,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[9568]) ).
thf(168,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ app ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause140) ).
thf(571,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)],[168]) ).
thf(46862,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[367,392]) ).
thf(46863,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[46862]) ).
thf(46864,plain,
! [A: $i] :
( ( A @ skaf57 @ ( nil @ app ) )
= ( A @ skaf57 ) ),
inference(pattern_uni,[status(thm)],[46863:[bind(A,$thf( C )),bind(B,$thf( C @ skaf57 ))]]) ).
thf(46967,plain,
! [A: $i] :
( ( A @ skaf57 @ ( nil @ app ) )
= ( A @ skaf57 ) ),
inference(simp,[status(thm)],[46864]) ).
thf(3264,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[251,247]) ).
thf(3265,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3264]) ).
thf(3266,plain,
! [A: $i] : ( A @ skaf55 @ ( A @ skaf55 @ geq ) ),
inference(pattern_uni,[status(thm)],[3265:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(3288,plain,
! [A: $i] : ( A @ skaf55 @ ( A @ skaf55 @ geq ) ),
inference(simp,[status(thm)],[3266]) ).
thf(8868,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[259,282]) ).
thf(8869,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[8868]) ).
thf(8870,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( A @ skaf49 @ lt ) ),
inference(pattern_uni,[status(thm)],[8869:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(8914,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( A @ skaf49 @ lt ) ),
inference(simp,[status(thm)],[8870]) ).
thf(3282,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[283,247]) ).
thf(3283,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) ) ),
inference(simp,[status(thm)],[3282]) ).
thf(3284,plain,
skac2 @ ( skac2 @ geq ),
inference(pattern_uni,[status(thm)],[3283:[bind(A,$thf( skac2 ))]]) ).
thf(192,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause112) ).
thf(627,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(116,axiom,
! [A: $i] :
( ( A @ skaf49 @ ( A @ skaf50 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause87) ).
thf(450,plain,
! [A: $i] :
( ( A @ skaf49 @ ( A @ skaf50 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(24451,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf42 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[610,342]) ).
thf(24452,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf42 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[24451]) ).
thf(24453,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf42 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[24452:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf42 ) ))]]) ).
thf(24545,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf42 ) @ rearsegP ) ),
inference(simp,[status(thm)],[24453]) ).
thf(82,axiom,
! [B: $i,A: $i] :
( ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause72) ).
thf(363,plain,
! [B: $i,A: $i] :
( ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(136,axiom,
! [A: $i] :
( ( nil = A )
| ( ( A @ tl @ ( A @ hd @ cons ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause104) ).
thf(495,plain,
! [A: $i] :
( ( nil = A )
| ( ( A @ tl @ ( A @ hd @ cons ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(8412,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[230,278]) ).
thf(8413,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[8412]) ).
thf(8414,plain,
! [A: $i] : ( A @ skaf79 @ ( A @ skaf79 @ leq ) ),
inference(pattern_uni,[status(thm)],[8413:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(8469,plain,
! [A: $i] : ( A @ skaf79 @ ( A @ skaf79 @ leq ) ),
inference(simp,[status(thm)],[8414]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ geq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause107) ).
thf(231,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(33847,plain,
( ( nil != nil )
| ( sk1 @ strictorderedP )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[30321,626]) ).
thf(33848,plain,
( ( sk1 @ strictorderedP )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[33847:[]]) ).
thf(39956,plain,
( ( ( sk1 @ ( nil @ rearsegP ) )
!= ( nil @ ( sk1 @ rearsegP ) ) )
| ( sk1 @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24432,33848]) ).
thf(39957,plain,
( ( ( sk1 @ ( nil @ rearsegP ) )
!= ( nil @ ( sk1 @ rearsegP ) ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[39956]) ).
thf(40082,plain,
( ( nil != sk1 )
| ( nil != sk1 )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[39957]) ).
thf(40111,plain,
( ( nil != sk1 )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[40082]) ).
thf(10167,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ~ $true
| ~ ( sk2 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[725,9968]) ).
thf(10168,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ~ ( sk2 @ singletonP ) ),
inference(simp,[status(thm)],[10167]) ).
thf(10209,plain,
( ( nil != sk2 )
| ( sk2 != sk2 )
| ~ ( sk2 @ singletonP ) ),
inference(simp,[status(thm)],[10168]) ).
thf(10225,plain,
( ( nil != sk2 )
| ~ ( sk2 @ singletonP ) ),
inference(simp,[status(thm)],[10209]) ).
thf(98,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ app ) )
= nil )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( nil != B )
| ( nil != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause145) ).
thf(401,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)],[98]) ).
thf(232,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ geq ) ) ),
inference(cnf,[status(esa)],[231]) ).
thf(3318,plain,
! [B: $i,A: $i] :
( ( ( skac3 @ ( skac3 @ geq ) )
!= ( B @ ( A @ geq ) ) )
| ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3233,232]) ).
thf(3319,plain,
! [B: $i,A: $i] :
( ( ( skac3 @ ( skac3 @ geq ) )
!= ( B @ ( A @ geq ) ) )
| ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem ) ),
inference(simp,[status(thm)],[3318]) ).
thf(3320,plain,
( ( skac3 @ ( skac3 @ leq ) )
| ~ ( skac3 @ ssItem )
| ~ ( skac3 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[3319:[bind(A,$thf( skac3 )),bind(B,$thf( skac3 ))]]) ).
thf(3321,plain,
( ( skac3 @ ( skac3 @ leq ) )
| ~ ( skac3 @ ssItem ) ),
inference(simp,[status(thm)],[3320]) ).
thf(8082,plain,
( ( skac3 @ ( skac3 @ leq ) )
| ~ $true ),
inference(rewrite,[status(thm)],[3321,284]) ).
thf(8083,plain,
skac3 @ ( skac3 @ leq ),
inference(simp,[status(thm)],[8082]) ).
thf(39443,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[270,378]) ).
thf(39444,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[39443]) ).
thf(39445,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[39444:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(39540,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[39445]) ).
thf(10029,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[354,297]) ).
thf(10030,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[10029]) ).
thf(10031,plain,
! [A: $i] :
~ ( A @ skaf77 @ ( A @ skaf77 @ neq ) ),
inference(pattern_uni,[status(thm)],[10030:[bind(A,$thf( C )),bind(B,$thf( C @ skaf77 ))]]) ).
thf(10072,plain,
! [A: $i] :
~ ( A @ skaf77 @ ( A @ skaf77 @ neq ) ),
inference(simp,[status(thm)],[10031]) ).
thf(698,plain,
( ( nil != nil )
| ~ ( skac2 @ ( sk2 @ memberP ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[662,656]) ).
thf(699,plain,
( ~ ( skac2 @ ( sk2 @ memberP ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[698:[]]) ).
thf(10169,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ~ $true
| ( sk2 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[8017,9968]) ).
thf(10170,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ( sk2 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[10169]) ).
thf(10204,plain,
( ( nil != sk2 )
| ( sk2 != sk2 )
| ( sk2 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[10170]) ).
thf(10220,plain,
( ( nil != sk2 )
| ( sk2 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[10204]) ).
thf(22726,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[270,336]) ).
thf(22727,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[22726]) ).
thf(22728,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( A @ skaf54 @ neq ) ),
inference(pattern_uni,[status(thm)],[22727:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(22808,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( A @ skaf54 @ neq ) ),
inference(simp,[status(thm)],[22728]) ).
thf(258,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
inference(cnf,[status(esa)],[257]) ).
thf(22766,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[267,336]) ).
thf(22767,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[22766]) ).
thf(22768,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( A @ skaf74 @ neq ) ),
inference(pattern_uni,[status(thm)],[22767:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(22830,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( A @ skaf74 @ neq ) ),
inference(simp,[status(thm)],[22768]) ).
thf(8865,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[256,282]) ).
thf(8866,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[8865]) ).
thf(8867,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( A @ skaf60 @ lt ) ),
inference(pattern_uni,[status(thm)],[8866:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(8912,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( A @ skaf60 @ lt ) ),
inference(simp,[status(thm)],[8867]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ app ) @ rearsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause136) ).
thf(418,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)],[103]) ).
thf(10253,plain,
( ( nil != nil )
| ~ ( sk2 @ ( nil @ neq ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[662,10028]) ).
thf(10254,plain,
( ~ ( sk2 @ ( nil @ neq ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[10253:[]]) ).
thf(985,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[256,467]) ).
thf(986,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[985]) ).
thf(987,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[986:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(995,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[987]) ).
thf(9938,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[201,297]) ).
thf(9939,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[9938]) ).
thf(9940,plain,
~ ( sk1 @ ( sk1 @ neq ) ),
inference(pattern_uni,[status(thm)],[9939:[bind(A,$thf( sk1 ))]]) ).
thf(9984,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[599,297]) ).
thf(9985,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[9984]) ).
thf(9986,plain,
! [A: $i] :
~ ( A @ skaf56 @ ( A @ skaf56 @ neq ) ),
inference(pattern_uni,[status(thm)],[9985:[bind(A,$thf( C )),bind(B,$thf( C @ skaf56 ))]]) ).
thf(10050,plain,
! [A: $i] :
~ ( A @ skaf56 @ ( A @ skaf56 @ neq ) ),
inference(simp,[status(thm)],[9986]) ).
thf(35232,plain,
( ( nil != nil )
| ~ ( sk2 @ singletonP )
| ~ ( sk2 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[30696,519]) ).
thf(35233,plain,
( ~ ( sk2 @ singletonP )
| ~ ( sk2 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[35232:[]]) ).
thf(167,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/sandbox/benchmark/theBenchmark.p',clause170) ).
thf(568,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)],[167]) ).
thf(9906,plain,
( ( nil != nil )
| ( sk2 @ ( sk2 @ frontsegP ) )
| ( nil @ ( sk2 @ neq ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,8065]) ).
thf(9907,plain,
( ( nil != nil )
| ( sk2 @ ( sk2 @ frontsegP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[9906]) ).
thf(9908,plain,
( ( sk2 @ ( sk2 @ frontsegP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[9907:[]]) ).
thf(129,axiom,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf55 @ ( A @ skaf54 @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause95) ).
thf(478,plain,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf55 @ ( A @ skaf54 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(21526,plain,
( ( nil != nil )
| ( sk2 != sk2 )
| ( nil != sk1 )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[19485,10224]) ).
thf(21527,plain,
( ( nil != nil )
| ( nil != sk1 )
| ( sk2 @ tl @ ssList ) ),
inference(simp,[status(thm)],[21526]) ).
thf(21528,plain,
( ( nil != sk1 )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[21527:[]]) ).
thf(21099,plain,
( ( nil != nil )
| ( sk1 @ ( nil @ frontsegP ) )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[19190,8043]) ).
thf(21100,plain,
( ( sk1 @ ( nil @ frontsegP ) )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[21099:[]]) ).
thf(33975,plain,
( ( nil != nil )
| ( nil != sk2 )
| ( sk1 != sk1 )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[30321,10224]) ).
thf(33976,plain,
( ( nil != nil )
| ( nil != sk2 )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(simp,[status(thm)],[33975]) ).
thf(33977,plain,
( ( nil != sk2 )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[33976:[]]) ).
thf(9586,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[255,9534]) ).
thf(9587,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[9586]) ).
thf(9588,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[9587:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(9643,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[9588]) ).
thf(235,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)],[234]) ).
thf(109,axiom,
! [A: $i] :
( ( A @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause59) ).
thf(433,plain,
! [A: $i] :
( ( A @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(24468,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[298,342]) ).
thf(24469,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[24468]) ).
thf(24470,plain,
! [A: $i] : ( nil @ ( A @ skaf62 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[24469:[bind(A,$thf( C )),bind(B,$thf( C @ skaf62 ))]]) ).
thf(24549,plain,
! [A: $i] : ( nil @ ( A @ skaf62 @ rearsegP ) ),
inference(simp,[status(thm)],[24470]) ).
thf(8859,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[233,282]) ).
thf(8860,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[8859]) ).
thf(8861,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( A @ skaf64 @ lt ) ),
inference(pattern_uni,[status(thm)],[8860:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(8925,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( A @ skaf64 @ lt ) ),
inference(simp,[status(thm)],[8861]) ).
thf(10012,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[603,297]) ).
thf(10013,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[10012]) ).
thf(10014,plain,
! [A: $i] :
~ ( A @ skaf71 @ ( A @ skaf71 @ neq ) ),
inference(pattern_uni,[status(thm)],[10013:[bind(A,$thf( C )),bind(B,$thf( C @ skaf71 ))]]) ).
thf(10065,plain,
! [A: $i] :
~ ( A @ skaf71 @ ( A @ skaf71 @ neq ) ),
inference(simp,[status(thm)],[10014]) ).
thf(42,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause114) ).
thf(272,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(715,plain,
( ( nil != nil )
| ~ ( skac2 @ ( sk2 @ memberP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,656]) ).
thf(716,plain,
( ~ ( skac2 @ ( sk2 @ memberP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[715:[]]) ).
thf(115,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( nil @ ( A @ cons ) @ app ) )
= ( B @ ( A @ cons ) ) )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause120) ).
thf(447,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)],[115]) ).
thf(67,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf46 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause50) ).
thf(326,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf46 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(24514,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf46 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[326,342]) ).
thf(24515,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf46 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[24514]) ).
thf(24516,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf46 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[24515:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf46 ) ))]]) ).
thf(24564,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf46 ) @ rearsegP ) ),
inference(simp,[status(thm)],[24516]) ).
thf(3270,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[255,247]) ).
thf(3271,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3270]) ).
thf(3272,plain,
! [A: $i] : ( A @ skaf70 @ ( A @ skaf70 @ geq ) ),
inference(pattern_uni,[status(thm)],[3271:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(3291,plain,
! [A: $i] : ( A @ skaf70 @ ( A @ skaf70 @ geq ) ),
inference(simp,[status(thm)],[3272]) ).
thf(261,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[260]) ).
thf(262,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ leq ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[261]) ).
thf(39409,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[288,378]) ).
thf(39410,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[39409]) ).
thf(39411,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[39410:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(39552,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[39411]) ).
thf(99,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/sandbox/benchmark/theBenchmark.p',clause180) ).
thf(405,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)],[99]) ).
thf(273,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
inference(cnf,[status(esa)],[272]) ).
thf(9990,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[609,297]) ).
thf(9991,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[9990]) ).
thf(9992,plain,
! [A: $i] :
~ ( A @ skaf76 @ ( A @ skaf76 @ neq ) ),
inference(pattern_uni,[status(thm)],[9991:[bind(A,$thf( C )),bind(B,$thf( C @ skaf76 ))]]) ).
thf(10054,plain,
! [A: $i] :
~ ( A @ skaf76 @ ( A @ skaf76 @ neq ) ),
inference(simp,[status(thm)],[9992]) ).
thf(300,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)],[299]) ).
thf(39482,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[251,378]) ).
thf(39483,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[39482]) ).
thf(39484,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[39483:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(39556,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[39484]) ).
thf(9969,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[311,297]) ).
thf(9970,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[9969]) ).
thf(9971,plain,
! [A: $i] :
~ ( A @ skaf72 @ ( A @ skaf72 @ neq ) ),
inference(pattern_uni,[status(thm)],[9970:[bind(A,$thf( C )),bind(B,$thf( C @ skaf72 ))]]) ).
thf(10073,plain,
! [A: $i] :
~ ( A @ skaf72 @ ( A @ skaf72 @ neq ) ),
inference(simp,[status(thm)],[9971]) ).
thf(663,plain,
( ( nil != nil )
| ( sk2 @ strictorderP )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[662,349]) ).
thf(664,plain,
( ( sk2 @ strictorderP )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[663:[]]) ).
thf(24477,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[599,342]) ).
thf(24478,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[24477]) ).
thf(24479,plain,
! [A: $i] : ( nil @ ( A @ skaf56 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[24478:[bind(A,$thf( C )),bind(B,$thf( C @ skaf56 ))]]) ).
thf(24552,plain,
! [A: $i] : ( nil @ ( A @ skaf56 @ rearsegP ) ),
inference(simp,[status(thm)],[24479]) ).
thf(102,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/sandbox/benchmark/theBenchmark.p',clause149) ).
thf(415,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)],[102]) ).
thf(242,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
inference(cnf,[status(esa)],[241]) ).
thf(22777,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[250,336]) ).
thf(22778,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[22777]) ).
thf(22779,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( A @ skaf69 @ neq ) ),
inference(pattern_uni,[status(thm)],[22778:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(22833,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( A @ skaf69 @ neq ) ),
inference(simp,[status(thm)],[22779]) ).
thf(8883,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[251,282]) ).
thf(8884,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[8883]) ).
thf(8885,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( A @ skaf55 @ lt ) ),
inference(pattern_uni,[status(thm)],[8884:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(8921,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( A @ skaf55 @ lt ) ),
inference(simp,[status(thm)],[8885]) ).
thf(21120,plain,
( ( nil != nil )
| ( sk1 @ duplicatefreeP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[19190,383]) ).
thf(21121,plain,
( ( sk1 @ duplicatefreeP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[21120:[]]) ).
thf(8427,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[255,278]) ).
thf(8428,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[8427]) ).
thf(8429,plain,
! [A: $i] : ( A @ skaf70 @ ( A @ skaf70 @ leq ) ),
inference(pattern_uni,[status(thm)],[8428:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(8460,plain,
! [A: $i] : ( A @ skaf70 @ ( A @ skaf70 @ leq ) ),
inference(simp,[status(thm)],[8429]) ).
thf(331,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)],[330]) ).
thf(332,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)],[331]) ).
thf(178,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/sandbox/benchmark/theBenchmark.p',clause171) ).
thf(596,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)],[178]) ).
thf(24498,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[465,342]) ).
thf(24499,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[24498]) ).
thf(24500,plain,
! [A: $i] : ( nil @ ( A @ skaf80 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[24499:[bind(A,$thf( C )),bind(B,$thf( C @ skaf80 ))]]) ).
thf(24559,plain,
! [A: $i] : ( nil @ ( A @ skaf80 @ rearsegP ) ),
inference(simp,[status(thm)],[24500]) ).
thf(121,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause76) ).
thf(459,plain,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(8877,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[245,282]) ).
thf(8878,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[8877]) ).
thf(8879,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( A @ skaf44 @ lt ) ),
inference(pattern_uni,[status(thm)],[8878:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(8918,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( A @ skaf44 @ lt ) ),
inference(simp,[status(thm)],[8879]) ).
thf(21271,plain,
( ( nil != nil )
| ( sk2 @ cyclefreeP )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[19485,507]) ).
thf(21272,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[21271:[]]) ).
thf(8442,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[283,278]) ).
thf(8443,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[8442]) ).
thf(8444,plain,
skac2 @ ( skac2 @ leq ),
inference(pattern_uni,[status(thm)],[8443:[bind(A,$thf( skac2 ))]]) ).
thf(107,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ rearsegP ) )
| ~ ( B @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause128) ).
thf(427,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)],[107]) ).
thf(690,plain,
( ( nil != nil )
| ( sk2 @ totalorderP )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[662,502]) ).
thf(691,plain,
( ( sk2 @ totalorderP )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[690:[]]) ).
thf(183,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/sandbox/benchmark/theBenchmark.p',clause172) ).
thf(607,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)],[183]) ).
thf(32535,plain,
( ( ( skac2 @ ( nil @ rearsegP ) )
!= ( nil @ ( nil @ rearsegP ) ) )
| ( skac3 != nil )
| ~ ( skac2 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7943,30575]) ).
thf(32536,plain,
( ( ( skac2 @ ( nil @ rearsegP ) )
!= ( nil @ ( nil @ rearsegP ) ) )
| ( skac3 != nil )
| ~ ( skac2 @ ssList ) ),
inference(simp,[status(thm)],[32535]) ).
thf(32596,plain,
( ( skac2 != nil )
| ( nil != nil )
| ( skac3 != nil )
| ~ ( skac2 @ ssList ) ),
inference(simp,[status(thm)],[32536]) ).
thf(32661,plain,
( ( skac2 != nil )
| ( skac3 != nil )
| ~ ( skac2 @ ssList ) ),
inference(simp,[status(thm)],[32596]) ).
thf(33382,plain,
( ( ( skac2 @ ssList )
!= ( nil @ ssList ) )
| ( skac2 != nil )
| ( skac3 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[337,32661]) ).
thf(33383,plain,
( ( ( skac2 @ ssList )
!= ( nil @ ssList ) )
| ( skac2 != nil )
| ( skac3 != nil ) ),
inference(simp,[status(thm)],[33382]) ).
thf(33434,plain,
( ( skac2 != nil )
| ( skac2 != nil )
| ( skac3 != nil ) ),
inference(simp,[status(thm)],[33383]) ).
thf(33450,plain,
( ( skac2 != nil )
| ( skac3 != nil ) ),
inference(simp,[status(thm)],[33434]) ).
thf(133,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/sandbox/benchmark/theBenchmark.p',clause161) ).
thf(486,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)],[133]) ).
thf(24420,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[480,342]) ).
thf(24421,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[24420]) ).
thf(24422,plain,
! [A: $i] : ( nil @ ( A @ skaf53 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[24421:[bind(A,$thf( C )),bind(B,$thf( C @ skaf53 ))]]) ).
thf(24574,plain,
! [A: $i] : ( nil @ ( A @ skaf53 @ rearsegP ) ),
inference(simp,[status(thm)],[24422]) ).
thf(22754,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[230,336]) ).
thf(22755,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[22754]) ).
thf(22756,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( A @ skaf79 @ neq ) ),
inference(pattern_uni,[status(thm)],[22755:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(22826,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( A @ skaf79 @ neq ) ),
inference(simp,[status(thm)],[22756]) ).
thf(21056,plain,
( ( nil != nil )
| ( sk1 @ strictorderedP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[19190,626]) ).
thf(21057,plain,
( ( sk1 @ strictorderedP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[21056:[]]) ).
thf(21214,plain,
( ( nil != nil )
| ( sk2 != sk2 )
| ( sk2 @ equalelemsP )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[19485,10221]) ).
thf(21215,plain,
( ( nil != nil )
| ( sk2 @ equalelemsP )
| ( sk2 @ tl @ ssList ) ),
inference(simp,[status(thm)],[21214]) ).
thf(21216,plain,
( ( sk2 @ equalelemsP )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[21215:[]]) ).
thf(118,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/sandbox/benchmark/theBenchmark.p',clause174) ).
thf(454,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)],[118]) ).
thf(8403,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[256,278]) ).
thf(8404,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[8403]) ).
thf(8405,plain,
! [A: $i] : ( A @ skaf60 @ ( A @ skaf60 @ leq ) ),
inference(pattern_uni,[status(thm)],[8404:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(8465,plain,
! [A: $i] : ( A @ skaf60 @ ( A @ skaf60 @ leq ) ),
inference(simp,[status(thm)],[8405]) ).
thf(10001,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[426,297]) ).
thf(10002,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[10001]) ).
thf(10003,plain,
! [A: $i] :
~ ( A @ skaf73 @ ( A @ skaf73 @ neq ) ),
inference(pattern_uni,[status(thm)],[10002:[bind(A,$thf( C )),bind(B,$thf( C @ skaf73 ))]]) ).
thf(10060,plain,
! [A: $i] :
~ ( A @ skaf73 @ ( A @ skaf73 @ neq ) ),
inference(simp,[status(thm)],[10003]) ).
thf(253,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[252]) ).
thf(254,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[253]) ).
thf(227,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[226]) ).
thf(7964,plain,
( ( nil != nil )
| ( nil @ ( sk2 @ rearsegP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,7943]) ).
thf(7965,plain,
( ( nil @ ( sk2 @ rearsegP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[7964:[]]) ).
thf(8243,plain,
( ( nil != nil )
| ( sk2 @ ( sk2 @ rearsegP ) )
| ( nil @ ( sk2 @ neq ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,7965]) ).
thf(8244,plain,
( ( nil != nil )
| ( sk2 @ ( sk2 @ rearsegP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[8243]) ).
thf(8245,plain,
( ( sk2 @ ( sk2 @ rearsegP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[8244:[]]) ).
thf(36619,plain,
( ( ( sk1 @ ( nil @ rearsegP ) )
!= ( nil @ ( sk1 @ rearsegP ) ) )
| ( sk1 @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24432,33685]) ).
thf(36620,plain,
( ( ( sk1 @ ( nil @ rearsegP ) )
!= ( nil @ ( sk1 @ rearsegP ) ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[36619]) ).
thf(36745,plain,
( ( nil != sk1 )
| ( nil != sk1 )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[36620]) ).
thf(36752,plain,
( ( nil != sk1 )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[36745]) ).
thf(163,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause78) ).
thf(560,plain,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(364,plain,
! [B: $i,A: $i] :
( ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[363]) ).
thf(3279,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[287,247]) ).
thf(3280,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3279]) ).
thf(3281,plain,
! [A: $i] : ( A @ skaf78 @ ( A @ skaf78 @ geq ) ),
inference(pattern_uni,[status(thm)],[3280:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(3296,plain,
! [A: $i] : ( A @ skaf78 @ ( A @ skaf78 @ geq ) ),
inference(simp,[status(thm)],[3281]) ).
thf(62510,plain,
$false,
inference(e,[status(thm)],[518,468,234,27055,21299,24432,481,365,21040,333,249,24550,22807,24462,276,10061,247,379,202,24569,49668,523,582,308,8463,614,39510,269,384,533,22824,8915,472,22987,24554,340,9540,9644,46425,8911,22829,10230,46966,34943,21363,9735,10071,301,565,436,24565,257,288,10078,389,10221,24558,357,22834,21086,372,587,619,802,8919,22827,24577,284,1398,325,228,289,316,30575,10074,8468,22902,30321,9636,475,3295,321,514,9680,480,33898,24568,376,19485,211,646,8065,238,20917,348,3290,806,3300,24546,353,39538,10070,397,396,39414,10057,8459,1345,243,35495,507,8454,634,527,312,24573,206,33739,8924,39551,307,10062,248,380,678,270,9968,201,761,21098,714,798,233,452,512,439,3301,3303,39526,366,22806,21384,39553,22832,392,297,8910,275,10229,302,260,1123,349,3233,693,24544,46965,33916,467,229,252,8920,361,435,3297,329,19190,493,25888,710,456,9641,285,8462,519,697,317,650,24566,39546,21325,8282,9608,725,1006,46922,593,869,420,8916,10052,26043,21421,610,256,24547,9640,225,8017,554,1182,537,22828,41532,637,489,590,21042,970,526,24578,8467,3294,9645,212,706,622,8458,701,39550,457,9620,8455,24562,39554,39335,10222,393,984,9630,503,10252,9534,343,244,360,205,311,10069,558,21102,24298,10058,508,39529,8923,541,33703,794,662,718,298,42760,10227,264,573,689,22787,11837,21406,513,24557,430,745,3289,279,9635,444,21211,39558,22502,21465,22831,8015,423,8909,579,24567,204,30696,259,413,11819,313,1371,7983,611,498,10051,466,3302,350,10056,9638,382,21154,236,604,219,274,10066,377,8461,230,1144,245,318,616,303,271,208,20943,599,8926,387,33685,631,39527,609,9642,46829,520,626,668,330,345,367,552,10219,240,251,6319,3298,22818,462,24556,521,8456,46695,695,278,223,394,563,226,267,505,10226,10063,299,241,653,33734,22984,531,10223,9646,255,342,754,3292,426,24553,1166,3293,548,648,209,9639,8067,46782,355,22825,640,46964,39555,8466,10059,327,24563,22908,7967,21126,409,712,557,282,21292,263,310,199,8858,441,585,502,338,39532,643,544,8917,24548,470,576,8464,336,656,600,24555,10028,9632,386,9637,571,46967,8043,314,3288,8914,3284,627,450,24545,363,495,368,8469,250,465,231,482,203,40111,319,304,10225,401,8083,39540,33906,10072,699,10220,22808,258,22830,390,8912,418,10254,995,9940,10050,35233,568,9908,207,22720,478,383,21528,346,21100,33977,9643,290,378,235,246,433,24549,8925,10065,272,716,214,287,33860,447,24564,8038,3291,262,39552,405,273,10054,33848,300,21157,39556,10073,373,603,564,305,210,326,294,341,268,358,33892,664,7943,24552,415,239,242,22833,8921,10224,283,21121,8460,332,596,24559,459,723,20965,200,8918,21272,501,8444,427,277,691,369,607,33450,322,486,337,24574,22826,639,21057,21216,222,592,454,232,8465,10060,254,227,354,8245,36752,560,364,3296]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC111-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/5.62 % Computer : n018.cluster.edu
% 0.10/5.62 % Model : x86_64 x86_64
% 0.10/5.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.62 % Memory : 8046.5625MB
% 0.10/5.62 % OS : Linux 6.8.0-71-generic
% 0.10/5.63 % CPULimit : 300
% 0.10/5.63 % WCLimit : 300
% 0.10/5.63 % DateTime : Sat Sep 26 12:18:57 UTC 2026
% 0.10/5.63 % CPUTime :
% 0.10/5.63 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.96/6.22 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.74/6.52 % [INFO] Parsing done (299ms).
% 1.74/6.54 % [INFO] Running in sequential loop mode.
% 2.81/6.94 % [INFO] eprover registered as external prover.
% 2.81/6.95 % [INFO] Scanning for conjecture ...
% 3.10/7.09 % [INFO] Found a conjecture (or negated_conjecture) and 185 axioms. Running axiom selection ...
% 3.49/7.23 % [INFO] Axiom selection finished. Selected 185 axioms (removed 0 axioms).
% 3.92/7.39 % [INFO] Problem is propositional (TPTP CNF).
% 4.20/7.41 % [INFO] Type checking passed.
% 4.20/7.41 % [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 ...
% 146.55/41.77 % External prover 'e' found a proof!
% 146.55/41.77 % [INFO] Killing All external provers ...
% 146.55/41.78 % Time passed: 36003ms (effective reasoning time: 35234ms)
% 146.55/41.78 % 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
% 146.55/41.78 % No. of inferences in proof: 1534
% 146.55/41.78 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 36003 ms resp. 35234 ms w/o parsing
% 149.38/42.25 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 149.38/42.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------