%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWC340-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n011.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 08:53:22 AM UTC 2026
% Result : Unsatisfiable 95.53s 22.73s
% Output : Refutation 97.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 194
% Syntax : Number of formulae : 1341 ( 473 unt; 0 typ; 0 def)
% Number of atoms : 4290 ( 823 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 10784 (2179 ~;2013 |; 0 &;6592 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 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 : 1872 ( 0 ^;1872 !; 0 ?;1872 :)
% 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(strictorderedP_decl,type,
strictorderedP: $i > $o ).
thf(totalorderedP_decl,type,
totalorderedP: $i > $o ).
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(duplicatefreeP_decl,type,
duplicatefreeP: $i > $o ).
thf(nil_decl,type,
nil: $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(memberP_decl,type,
memberP: $i > $i > $o ).
thf(equalelemsP_decl,type,
equalelemsP: $i > $o ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(totalorderP_decl,type,
totalorderP: $i > $o ).
thf(cyclefreeP_decl,type,
cyclefreeP: $i > $o ).
thf(singletonP_decl,type,
singletonP: $i > $o ).
thf(strictorderP_decl,type,
strictorderP: $i > $o ).
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(neq_decl,type,
neq: $i > $i > $o ).
thf(skaf78_decl,type,
skaf78: $i > $i ).
thf(skaf59_decl,type,
skaf59: $i > $i ).
thf(skaf43_decl,type,
skaf43: $i > $i > $i ).
thf(skaf62_decl,type,
skaf62: $i > $i ).
thf(app_decl,type,
app: $i > $i > $i ).
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(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(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(61,axiom,
! [A: $i] : ( A @ skaf59 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause36) ).
thf(298,plain,
! [A: $i] : ( A @ skaf59 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(39,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause68) ).
thf(259,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(260,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[259]) ).
thf(7307,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[298,260]) ).
thf(7308,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP ) ),
inference(simp,[status(thm)],[7307]) ).
thf(7309,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ strictorderP ),
inference(pattern_uni,[status(thm)],[7308:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(7375,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ strictorderP ),
inference(simp,[status(thm)],[7309]) ).
thf(29,axiom,
! [A: $i] : ( A @ skaf60 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause35) ).
thf(241,plain,
! [A: $i] : ( A @ skaf60 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(32,axiom,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( nil @ memberP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause71) ).
thf(245,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(246,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(cnf,[status(esa)],[245]) ).
thf(804,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[241,246]) ).
thf(805,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[804]) ).
thf(806,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[805:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(809,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[806]) ).
thf(8,negated_conjecture,
sk3 @ strictorderedP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
thf(202,plain,
sk3 @ strictorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
thf(197,plain,
sk1 = sk3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(204,plain,
sk3 = sk1,
inference(lifteq,[status(thm)],[197]) ).
thf(629,plain,
sk1 @ strictorderedP,
inference(rewrite,[status(thm)],[202,204]) ).
thf(58,axiom,
skac2 @ ssItem,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause10) ).
thf(294,plain,
skac2 @ ssItem,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause62) ).
thf(290,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(291,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[290]) ).
thf(15416,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[294,291]) ).
thf(15417,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[15416]) ).
thf(15418,plain,
skac2 @ ( skac2 @ leq ),
inference(pattern_uni,[status(thm)],[15417:[bind(A,$thf( skac2 ))]]) ).
thf(45,axiom,
! [A: $i] : ( A @ skaf74 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause21) ).
thf(271,plain,
! [A: $i] : ( A @ skaf74 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(57,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause65) ).
thf(292,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(293,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[292]) ).
thf(16523,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[271,293]) ).
thf(16524,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP ) ),
inference(simp,[status(thm)],[16523]) ).
thf(16525,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ duplicatefreeP ),
inference(pattern_uni,[status(thm)],[16524:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(16576,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ duplicatefreeP ),
inference(simp,[status(thm)],[16525]) ).
thf(82,axiom,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause58) ).
thf(347,plain,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(34,axiom,
nil @ totalorderP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause6) ).
thf(249,plain,
nil @ totalorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ ( A @ geq ) )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause55) ).
thf(231,plain,
! [A: $i] :
( ( A @ ( A @ geq ) )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(232,plain,
! [A: $i] :
( ( A @ ( A @ geq ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[231]) ).
thf(2973,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[294,232]) ).
thf(2974,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) ) ),
inference(simp,[status(thm)],[2973]) ).
thf(2975,plain,
skac2 @ ( skac2 @ geq ),
inference(pattern_uni,[status(thm)],[2974:[bind(A,$thf( skac2 ))]]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause126) ).
thf(220,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)],[17]) ).
thf(221,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
inference(cnf,[status(esa)],[220]) ).
thf(222,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[221]) ).
thf(192,axiom,
nil @ totalorderedP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause4) ).
thf(623,plain,
nil @ totalorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(9,negated_conjecture,
( ~ ( sk1 @ totalorderedP )
| ~ ( sk1 @ ( sk2 @ segmentP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
thf(198,plain,
( ~ ( sk1 @ totalorderedP )
| ~ ( sk1 @ ( sk2 @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(205,plain,
( ~ ( sk1 @ totalorderedP )
| ~ ( sk1 @ ( sk2 @ segmentP ) ) ),
inference(cnf,[status(esa)],[198]) ).
thf(7,negated_conjecture,
sk3 @ ( sk4 @ segmentP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
thf(200,plain,
sk3 @ ( sk4 @ segmentP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
thf(195,plain,
sk2 = sk4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(206,plain,
sk4 = sk2,
inference(lifteq,[status(thm)],[195]) ).
thf(632,plain,
sk1 @ ( sk2 @ segmentP ),
inference(rewrite,[status(thm)],[200,204,206]) ).
thf(633,plain,
( ~ ( sk1 @ totalorderedP )
| ~ $true ),
inference(rewrite,[status(thm)],[205,632]) ).
thf(634,plain,
~ ( sk1 @ totalorderedP ),
inference(simp,[status(thm)],[633]) ).
thf(655,plain,
( ( ( nil @ totalorderedP )
!= ( sk1 @ totalorderedP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[623,634]) ).
thf(656,plain,
( ( nil @ totalorderedP )
!= ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[655]) ).
thf(657,plain,
nil != sk1,
inference(simp,[status(thm)],[656]) ).
thf(1488,plain,
! [B: $i,A: $i] :
( ( B != nil )
| ( A != sk1 )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
inference(paramod_ordered,[status(thm)],[222,657]) ).
thf(1489,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( nil @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( nil @ geq ) )
| ~ ( nil @ ( A @ geq ) ) ),
inference(pattern_uni,[status(thm)],[1488:[bind(A,$thf( A )),bind(B,$thf( nil ))]]) ).
thf(1766,plain,
( ~ ( nil @ ssItem )
| ~ ( sk1 @ ssItem )
| ~ ( sk1 @ ( nil @ geq ) )
| ~ ( nil @ ( sk1 @ geq ) ) ),
inference(simp,[status(thm)],[1489]) ).
thf(1842,plain,
( ( ( nil @ ssItem )
!= ( skac2 @ ssItem ) )
| ~ $true
| ~ ( sk1 @ ssItem )
| ~ ( sk1 @ ( nil @ geq ) )
| ~ ( nil @ ( sk1 @ geq ) ) ),
inference(paramod_ordered,[status(thm)],[294,1766]) ).
thf(1843,plain,
( ( ( nil @ ssItem )
!= ( skac2 @ ssItem ) )
| ~ ( sk1 @ ssItem )
| ~ ( sk1 @ ( nil @ geq ) )
| ~ ( nil @ ( sk1 @ geq ) ) ),
inference(simp,[status(thm)],[1842]) ).
thf(1942,plain,
( ( nil != skac2 )
| ~ ( sk1 @ ssItem )
| ~ ( sk1 @ ( nil @ geq ) )
| ~ ( nil @ ( sk1 @ geq ) ) ),
inference(simp,[status(thm)],[1843]) ).
thf(3147,plain,
( ( ( sk1 @ ( nil @ geq ) )
!= ( skac2 @ ( skac2 @ geq ) ) )
| ( nil != skac2 )
| ~ ( sk1 @ ssItem )
| ~ $true
| ~ ( nil @ ( sk1 @ geq ) ) ),
inference(paramod_ordered,[status(thm)],[2975,1942]) ).
thf(3148,plain,
( ( ( sk1 @ ( nil @ geq ) )
!= ( skac2 @ ( skac2 @ geq ) ) )
| ( nil != skac2 )
| ~ ( sk1 @ ssItem )
| ~ ( nil @ ( sk1 @ geq ) ) ),
inference(simp,[status(thm)],[3147]) ).
thf(3175,plain,
( ( skac2 != sk1 )
| ( nil != skac2 )
| ( nil != skac2 )
| ~ ( sk1 @ ssItem )
| ~ ( nil @ ( sk1 @ geq ) ) ),
inference(simp,[status(thm)],[3148]) ).
thf(3185,plain,
( ( skac2 != sk1 )
| ( nil != skac2 )
| ~ ( sk1 @ ssItem )
| ~ ( nil @ ( sk1 @ geq ) ) ),
inference(simp,[status(thm)],[3175]) ).
thf(9841,plain,
( ( ( skac2 @ ( skac2 @ geq ) )
!= ( nil @ ( sk1 @ geq ) ) )
| ( skac2 != sk1 )
| ( nil != skac2 )
| ~ ( sk1 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2975,3185]) ).
thf(9842,plain,
( ( ( skac2 @ ( skac2 @ geq ) )
!= ( nil @ ( sk1 @ geq ) ) )
| ( skac2 != sk1 )
| ( nil != skac2 )
| ~ ( sk1 @ ssItem ) ),
inference(simp,[status(thm)],[9841]) ).
thf(9942,plain,
( ( nil != skac2 )
| ( skac2 != sk1 )
| ( skac2 != sk1 )
| ( nil != skac2 )
| ~ ( sk1 @ ssItem ) ),
inference(simp,[status(thm)],[9842]) ).
thf(9974,plain,
( ( skac2 != sk1 )
| ( nil != skac2 )
| ~ ( sk1 @ ssItem ) ),
inference(simp,[status(thm)],[9942]) ).
thf(10095,plain,
( ( ( skac2 @ ssItem )
!= ( sk1 @ ssItem ) )
| ( skac2 != sk1 )
| ( nil != skac2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[294,9974]) ).
thf(10096,plain,
( ( ( skac2 @ ssItem )
!= ( sk1 @ ssItem ) )
| ( skac2 != sk1 )
| ( nil != skac2 ) ),
inference(simp,[status(thm)],[10095]) ).
thf(10129,plain,
( ( skac2 != sk1 )
| ( skac2 != sk1 )
| ( nil != skac2 ) ),
inference(simp,[status(thm)],[10096]) ).
thf(10134,plain,
( ( skac2 != sk1 )
| ( nil != skac2 ) ),
inference(simp,[status(thm)],[10129]) ).
thf(55,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause102) ).
thf(287,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(288,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[287]) ).
thf(289,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( B = A ) ),
inference(lifteq,[status(thm)],[288]) ).
thf(13348,plain,
! [B: $i,A: $i] :
( ( B != nil )
| ( A != sk1 )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[289,657]) ).
thf(13349,plain,
! [A: $i] :
( ( A != sk1 )
| ( A @ ( nil @ neq ) )
| ~ ( nil @ ssItem )
| ~ ( A @ ssItem ) ),
inference(pattern_uni,[status(thm)],[13348:[bind(A,$thf( A )),bind(B,$thf( nil ))]]) ).
thf(14264,plain,
( ( sk1 @ ( nil @ neq ) )
| ~ ( nil @ ssItem )
| ~ ( sk1 @ ssItem ) ),
inference(simp,[status(thm)],[13349]) ).
thf(17357,plain,
( ( ( skac2 @ ssItem )
!= ( sk1 @ ssItem ) )
| ( sk1 @ ( nil @ neq ) )
| ~ ( nil @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[294,14264]) ).
thf(17358,plain,
( ( ( skac2 @ ssItem )
!= ( sk1 @ ssItem ) )
| ( sk1 @ ( nil @ neq ) )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[17357]) ).
thf(17385,plain,
( ( skac2 != sk1 )
| ~ ( nil @ ssItem )
| ( sk1 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[17358]) ).
thf(2,negated_conjecture,
sk2 @ ssList,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).
thf(199,plain,
sk2 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(64,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause115) ).
thf(304,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(305,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[304]) ).
thf(306,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[305]) ).
thf(307,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[306]) ).
thf(18734,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[199,307]) ).
thf(18735,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[18734]) ).
thf(18736,plain,
~ ( sk2 @ ( sk2 @ neq ) ),
inference(pattern_uni,[status(thm)],[18735:[bind(A,$thf( sk2 ))]]) ).
thf(19820,plain,
( ( ( sk1 @ ( nil @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ~ $true
| ( skac2 != sk1 )
| ~ ( nil @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[17385,18736]) ).
thf(19821,plain,
( ( ( sk1 @ ( nil @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ( skac2 != sk1 )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[19820]) ).
thf(19936,plain,
( ( sk2 != sk1 )
| ( nil != sk2 )
| ( skac2 != sk1 )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[19821]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ geq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause148) ).
thf(233,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)],[24]) ).
thf(234,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)],[233]) ).
thf(22,axiom,
! [A: $i] : ( A @ skaf44 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause47) ).
thf(230,plain,
! [A: $i] : ( A @ skaf44 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(63,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause113) ).
thf(300,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(301,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(cnf,[status(esa)],[300]) ).
thf(302,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[301]) ).
thf(303,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[302]) ).
thf(80,axiom,
nil @ ssList,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
thf(343,plain,
nil @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(18107,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ $true ),
inference(rewrite,[status(thm)],[303,343]) ).
thf(18108,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[18107]) ).
thf(18151,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[230,18108]) ).
thf(18152,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[18151]) ).
thf(18153,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[18152:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(18228,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[18153]) ).
thf(40,axiom,
skac3 @ ssItem,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause9) ).
thf(261,plain,
skac3 @ ssItem,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(1836,plain,
( ( ( skac3 @ ssItem )
!= ( sk1 @ ssItem ) )
| ~ ( nil @ ssItem )
| ~ $true
| ~ ( sk1 @ ( nil @ geq ) )
| ~ ( nil @ ( sk1 @ geq ) ) ),
inference(paramod_ordered,[status(thm)],[261,1766]) ).
thf(1837,plain,
( ( ( skac3 @ ssItem )
!= ( sk1 @ ssItem ) )
| ~ ( nil @ ssItem )
| ~ ( sk1 @ ( nil @ geq ) )
| ~ ( nil @ ( sk1 @ geq ) ) ),
inference(simp,[status(thm)],[1836]) ).
thf(1956,plain,
( ( skac3 != sk1 )
| ~ ( nil @ ssItem )
| ~ ( sk1 @ ( nil @ geq ) )
| ~ ( nil @ ( sk1 @ geq ) ) ),
inference(simp,[status(thm)],[1837]) ).
thf(84,axiom,
! [A: $i] :
( ( ( A @ skaf63 @ ( A @ skaf60 @ cons ) @ ( A @ skaf62 @ ( A @ skaf59 @ cons ) @ ( A @ skaf61 @ app ) @ app ) )
= A )
| ( A @ strictorderP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause165) ).
thf(352,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)],[84]) ).
thf(959,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[271,246]) ).
thf(960,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[959]) ).
thf(961,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[960:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(962,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[961]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause108) ).
thf(210,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(211,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[210]) ).
thf(1848,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ geq ) )
!= ( nil @ ( sk1 @ geq ) ) )
| ~ ( nil @ ssItem )
| ~ ( sk1 @ ssItem )
| ~ ( sk1 @ ( nil @ geq ) )
| ~ $true
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[211,1766]) ).
thf(1849,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ geq ) )
!= ( nil @ ( sk1 @ geq ) ) )
| ~ ( nil @ ssItem )
| ~ ( sk1 @ ssItem )
| ~ ( sk1 @ ( nil @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[1848]) ).
thf(1850,plain,
( ~ ( nil @ ssItem )
| ~ ( sk1 @ ssItem )
| ~ ( sk1 @ ( nil @ geq ) )
| ~ ( sk1 @ ssItem )
| ~ ( nil @ ssItem )
| ~ ( sk1 @ ( nil @ leq ) ) ),
inference(pattern_uni,[status(thm)],[1849:[bind(A,$thf( nil )),bind(B,$thf( sk1 ))]]) ).
thf(1982,plain,
( ~ ( sk1 @ ( nil @ geq ) )
| ~ ( sk1 @ ssItem )
| ~ ( nil @ ssItem )
| ~ ( sk1 @ ( nil @ leq ) ) ),
inference(simp,[status(thm)],[1850]) ).
thf(130,axiom,
! [A: $i] :
( ( ( nil @ ( A @ app ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause73) ).
thf(468,plain,
! [A: $i] :
( ( ( nil @ ( A @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(105,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( E @ ssList )
| ~ ( E @ equalelemsP )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( D @ ssList )
| ( ( D @ ( C @ cons ) @ ( B @ cons ) @ ( A @ app ) )
!= E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause180) ).
thf(408,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)],[105]) ).
thf(60,axiom,
! [A: $i] : ( A @ skaf78 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause17) ).
thf(297,plain,
! [A: $i] : ( A @ skaf78 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(2986,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[297,232]) ).
thf(2987,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[2986]) ).
thf(2988,plain,
! [A: $i] : ( A @ skaf78 @ ( A @ skaf78 @ geq ) ),
inference(pattern_uni,[status(thm)],[2987:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(3072,plain,
! [A: $i] : ( A @ skaf78 @ ( A @ skaf78 @ geq ) ),
inference(simp,[status(thm)],[2988]) ).
thf(47,axiom,
! [A: $i] : ( A @ skaf54 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause41) ).
thf(274,plain,
! [A: $i] : ( A @ skaf54 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(7313,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[274,260]) ).
thf(7314,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP ) ),
inference(simp,[status(thm)],[7313]) ).
thf(7315,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ strictorderP ),
inference(pattern_uni,[status(thm)],[7314:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(7377,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ strictorderP ),
inference(simp,[status(thm)],[7315]) ).
thf(13,axiom,
! [A: $i] : ( A @ skaf79 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause16) ).
thf(214,plain,
! [A: $i] : ( A @ skaf79 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(35,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause70) ).
thf(250,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(251,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[250]) ).
thf(6700,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[214,251]) ).
thf(6701,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP ) ),
inference(simp,[status(thm)],[6700]) ).
thf(6702,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ cyclefreeP ),
inference(pattern_uni,[status(thm)],[6701:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(6744,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ cyclefreeP ),
inference(simp,[status(thm)],[6702]) ).
thf(18166,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[241,18108]) ).
thf(18167,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[18166]) ).
thf(18168,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[18167:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(18233,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[18168]) ).
thf(65,axiom,
! [A: $i] : ( A @ skaf62 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause33) ).
thf(308,plain,
! [A: $i] : ( A @ skaf62 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(90,axiom,
! [B: $i,A: $i] :
( ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause72) ).
thf(368,plain,
! [B: $i,A: $i] :
( ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(369,plain,
! [B: $i,A: $i] :
( ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[368]) ).
thf(5814,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[199,369]) ).
thf(5815,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP ) ),
inference(simp,[status(thm)],[5814]) ).
thf(5816,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk2 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[5815:[bind(A,$thf( sk2 ))]]) ).
thf(5886,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[5816]) ).
thf(5980,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) )
| ( sk2 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[5886,246]) ).
thf(5981,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[5980]) ).
thf(5982,plain,
! [A: $i] :
( ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[5981:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(33,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ equalelemsP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause64) ).
thf(247,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ equalelemsP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(148,axiom,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf60 @ ( A @ skaf59 @ lt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause93) ).
thf(511,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf60 @ ( A @ skaf59 @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(15344,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[261,291]) ).
thf(15345,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[15344]) ).
thf(15346,plain,
skac3 @ ( skac3 @ leq ),
inference(pattern_uni,[status(thm)],[15345:[bind(A,$thf( skac3 ))]]) ).
thf(15,axiom,
! [A: $i] : ( A @ skaf64 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause31) ).
thf(217,plain,
! [A: $i] : ( A @ skaf64 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(16480,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[217,293]) ).
thf(16481,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP ) ),
inference(simp,[status(thm)],[16480]) ).
thf(16482,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ duplicatefreeP ),
inference(pattern_uni,[status(thm)],[16481:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(16581,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ duplicatefreeP ),
inference(simp,[status(thm)],[16482]) ).
thf(48,axiom,
! [A: $i] : ( A @ skaf65 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause30) ).
thf(275,plain,
! [A: $i] : ( A @ skaf65 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(6661,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[275,251]) ).
thf(6662,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP ) ),
inference(simp,[status(thm)],[6661]) ).
thf(6663,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ cyclefreeP ),
inference(pattern_uni,[status(thm)],[6662:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(6732,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ cyclefreeP ),
inference(simp,[status(thm)],[6663]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause114) ).
thf(276,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(25,axiom,
! [A: $i] : ( A @ skaf69 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause26) ).
thf(235,plain,
! [A: $i] : ( A @ skaf69 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(18175,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[235,18108]) ).
thf(18176,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[18175]) ).
thf(18177,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[18176:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(18205,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[18177]) ).
thf(21991,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf69 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18205,634]) ).
thf(21992,plain,
! [A: $i] :
( ( nil @ ( A @ skaf69 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[21991]) ).
thf(22030,plain,
! [A: $i] :
( ( nil @ ( A @ skaf69 @ cons ) )
!= sk1 ),
inference(simp,[status(thm)],[21992]) ).
thf(162,axiom,
! [A: $i] : ( A @ skaf66 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause29) ).
thf(550,plain,
! [A: $i] : ( A @ skaf66 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(143,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ leq ) )
| ( D @ ( B @ leq ) )
| ~ ( F @ ssList )
| ~ ( F @ totalorderP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause184) ).
thf(500,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(50,axiom,
! [A: $i] : ( A @ skaf50 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause45) ).
thf(278,plain,
! [A: $i] : ( A @ skaf50 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(248,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ equalelemsP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[247]) ).
thf(6182,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[278,248]) ).
thf(6183,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP ) ),
inference(simp,[status(thm)],[6182]) ).
thf(6184,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ equalelemsP ),
inference(pattern_uni,[status(thm)],[6183:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(6241,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ equalelemsP ),
inference(simp,[status(thm)],[6184]) ).
thf(79,axiom,
! [A: $i] :
( ( ( A @ skaf68 @ ( A @ skaf65 @ cons ) @ ( A @ skaf67 @ ( A @ skaf64 @ cons ) @ ( A @ skaf66 @ app ) @ app ) )
= A )
| ( A @ totalorderedP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause164) ).
thf(340,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)],[79]) ).
thf(17245,plain,
( ( ( nil @ ssItem )
!= ( skac3 @ ssItem ) )
| ( sk1 @ ( nil @ neq ) )
| ~ $true
| ~ ( sk1 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[261,14264]) ).
thf(17246,plain,
( ( ( nil @ ssItem )
!= ( skac3 @ ssItem ) )
| ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ssItem ) ),
inference(simp,[status(thm)],[17245]) ).
thf(17390,plain,
( ( nil != skac3 )
| ~ ( sk1 @ ssItem )
| ( sk1 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[17246]) ).
thf(42,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause69) ).
thf(265,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(266,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[265]) ).
thf(9495,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[241,266]) ).
thf(9496,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP ) ),
inference(simp,[status(thm)],[9495]) ).
thf(9497,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ totalorderP ),
inference(pattern_uni,[status(thm)],[9496:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(9540,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ totalorderP ),
inference(simp,[status(thm)],[9497]) ).
thf(97,axiom,
! [A: $i] :
( ( ( A @ skaf58 @ ( A @ skaf55 @ cons ) @ ( A @ skaf57 @ ( A @ skaf54 @ cons ) @ ( A @ skaf56 @ app ) @ app ) )
= A )
| ( A @ totalorderP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause166) ).
thf(384,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)],[97]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ app ) )
= nil )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( nil != B )
| ( nil != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause145) ).
thf(404,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)],[104]) ).
thf(26,axiom,
! [A: $i] : ( A @ skaf55 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause40) ).
thf(236,plain,
! [A: $i] : ( A @ skaf55 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(6167,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[236,248]) ).
thf(6168,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP ) ),
inference(simp,[status(thm)],[6167]) ).
thf(6169,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ equalelemsP ),
inference(pattern_uni,[status(thm)],[6168:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(6236,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ equalelemsP ),
inference(simp,[status(thm)],[6169]) ).
thf(2970,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[261,232]) ).
thf(2971,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) ) ),
inference(simp,[status(thm)],[2970]) ).
thf(2972,plain,
skac3 @ ( skac3 @ geq ),
inference(pattern_uni,[status(thm)],[2971:[bind(A,$thf( skac3 ))]]) ).
thf(38,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause111) ).
thf(255,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(256,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[255]) ).
thf(257,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[256]) ).
thf(258,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[257]) ).
thf(7002,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[298,258]) ).
thf(7003,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[7002]) ).
thf(7004,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( A @ skaf59 @ lt ) ),
inference(pattern_uni,[status(thm)],[7003:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(7064,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( A @ skaf59 @ lt ) ),
inference(simp,[status(thm)],[7004]) ).
thf(116,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
!= ( B @ ( C @ app ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause151) ).
thf(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)],[116]) ).
thf(18169,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true
| ( sk2 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[5886,18108]) ).
thf(18170,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[18169]) ).
thf(18171,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk2 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[18170:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(7292,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[217,260]) ).
thf(7293,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP ) ),
inference(simp,[status(thm)],[7292]) ).
thf(7294,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ strictorderP ),
inference(pattern_uni,[status(thm)],[7293:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(7390,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ strictorderP ),
inference(simp,[status(thm)],[7294]) ).
thf(70,axiom,
! [A: $i] :
( ( ( A @ skaf77 @ ( A @ skaf74 @ cons ) @ ( A @ skaf76 @ ( A @ skaf74 @ cons ) @ ( A @ skaf75 @ app ) @ app ) )
= A )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause162) ).
thf(318,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)],[70]) ).
thf(319,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)],[318]) ).
thf(320,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)],[319]) ).
thf(168,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ tl )
= B )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause96) ).
thf(565,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ tl )
= B )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(43,axiom,
! [A: $i] : ( A @ skaf83 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause12) ).
thf(267,plain,
! [A: $i] : ( A @ skaf83 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(6185,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[267,248]) ).
thf(6186,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP ) ),
inference(simp,[status(thm)],[6185]) ).
thf(6187,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ equalelemsP ),
inference(pattern_uni,[status(thm)],[6186:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(6242,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ equalelemsP ),
inference(simp,[status(thm)],[6187]) ).
thf(92,axiom,
! [A: $i] : ( A @ skaf57 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause38) ).
thf(372,plain,
! [A: $i] : ( A @ skaf57 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(144,axiom,
! [A: $i] : ( A @ skaf52 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause43) ).
thf(504,plain,
! [A: $i] : ( A @ skaf52 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(3011,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[271,232]) ).
thf(3012,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3011]) ).
thf(3013,plain,
! [A: $i] : ( A @ skaf74 @ ( A @ skaf74 @ geq ) ),
inference(pattern_uni,[status(thm)],[3012:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(3061,plain,
! [A: $i] : ( A @ skaf74 @ ( A @ skaf74 @ geq ) ),
inference(simp,[status(thm)],[3013]) ).
thf(177,axiom,
! [A: $i] : ( A @ skaf71 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause24) ).
thf(587,plain,
! [A: $i] : ( A @ skaf71 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ( B @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause132) ).
thf(344,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)],[81]) ).
thf(52,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause117) ).
thf(281,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(282,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[281]) ).
thf(283,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[282]) ).
thf(284,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[283]) ).
thf(12063,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[294,284]) ).
thf(12064,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[12063]) ).
thf(12065,plain,
~ ( skac2 @ ( skac2 @ neq ) ),
inference(pattern_uni,[status(thm)],[12064:[bind(A,$thf( skac2 ))]]) ).
thf(15392,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true
| ( sk2 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[5886,291]) ).
thf(15393,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[15392]) ).
thf(15394,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ( sk2 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[15393:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(1,negated_conjecture,
sk1 @ ssList,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
thf(196,plain,
sk1 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(158,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ app ) @ tl )
= ( A @ ( B @ tl @ app ) ) )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause133) ).
thf(542,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)],[158]) ).
thf(16538,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP )
| ~ $true
| ( sk2 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[5886,293]) ).
thf(16539,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[16538]) ).
thf(16540,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ duplicatefreeP )
| ( sk2 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[16539:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(16547,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[235,293]) ).
thf(16548,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP ) ),
inference(simp,[status(thm)],[16547]) ).
thf(16549,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ duplicatefreeP ),
inference(pattern_uni,[status(thm)],[16548:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(16584,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ duplicatefreeP ),
inference(simp,[status(thm)],[16549]) ).
thf(186,axiom,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause83) ).
thf(606,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ gt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause146) ).
thf(228,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)],[21]) ).
thf(18128,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[275,18108]) ).
thf(18129,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[18128]) ).
thf(18130,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[18129:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(18215,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[18130]) ).
thf(31,axiom,
! [A: $i] : ( A @ skaf49 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause46) ).
thf(244,plain,
! [A: $i] : ( A @ skaf49 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(6664,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[244,251]) ).
thf(6665,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP ) ),
inference(simp,[status(thm)],[6664]) ).
thf(6666,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ cyclefreeP ),
inference(pattern_uni,[status(thm)],[6665:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(6734,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ cyclefreeP ),
inference(simp,[status(thm)],[6666]) ).
thf(28,axiom,
! [A: $i] : ( A @ skaf70 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause25) ).
thf(240,plain,
! [A: $i] : ( A @ skaf70 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(6179,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[240,248]) ).
thf(6180,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP ) ),
inference(simp,[status(thm)],[6179]) ).
thf(6181,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ equalelemsP ),
inference(pattern_uni,[status(thm)],[6180:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(6240,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ equalelemsP ),
inference(simp,[status(thm)],[6181]) ).
thf(166,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause77) ).
thf(559,plain,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(109,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ app ) @ rearsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause136) ).
thf(421,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)],[109]) ).
thf(7026,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[267,258]) ).
thf(7027,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[7026]) ).
thf(7028,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( A @ skaf83 @ lt ) ),
inference(pattern_uni,[status(thm)],[7027:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(7060,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( A @ skaf83 @ lt ) ),
inference(simp,[status(thm)],[7028]) ).
thf(3002,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[236,232]) ).
thf(3003,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3002]) ).
thf(3004,plain,
! [A: $i] : ( A @ skaf55 @ ( A @ skaf55 @ geq ) ),
inference(pattern_uni,[status(thm)],[3003:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(3084,plain,
! [A: $i] : ( A @ skaf55 @ ( A @ skaf55 @ geq ) ),
inference(simp,[status(thm)],[3004]) ).
thf(107,axiom,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf54 @ ( A @ skaf55 @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause94) ).
thf(416,plain,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf54 @ ( A @ skaf55 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ geq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause107) ).
thf(215,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(216,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ geq ) ) ),
inference(cnf,[status(esa)],[215]) ).
thf(18163,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[267,18108]) ).
thf(18164,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[18163]) ).
thf(18165,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[18164:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(18232,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[18165]) ).
thf(12030,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[274,284]) ).
thf(12031,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[12030]) ).
thf(12032,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( A @ skaf54 @ neq ) ),
inference(pattern_uni,[status(thm)],[12031:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(12069,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( A @ skaf54 @ neq ) ),
inference(simp,[status(thm)],[12032]) ).
thf(179,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ ( D @ app ) @ app ) @ segmentP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause172) ).
thf(591,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)],[179]) ).
thf(2179,plain,
( ( ( skac3 @ ssItem )
!= ( sk1 @ ssItem ) )
| ( nil != skac2 )
| ~ $true
| ~ ( sk1 @ ( nil @ geq ) )
| ~ ( nil @ ( sk1 @ geq ) ) ),
inference(paramod_ordered,[status(thm)],[261,1942]) ).
thf(2180,plain,
( ( ( skac3 @ ssItem )
!= ( sk1 @ ssItem ) )
| ( nil != skac2 )
| ~ ( sk1 @ ( nil @ geq ) )
| ~ ( nil @ ( sk1 @ geq ) ) ),
inference(simp,[status(thm)],[2179]) ).
thf(2259,plain,
( ( skac3 != sk1 )
| ( nil != skac2 )
| ~ ( sk1 @ ( nil @ geq ) )
| ~ ( nil @ ( sk1 @ geq ) ) ),
inference(simp,[status(thm)],[2180]) ).
thf(18178,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[214,18108]) ).
thf(18179,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[18178]) ).
thf(18180,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[18179:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(18207,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[18180]) ).
thf(171,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ rearsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ rearsegP ) )
| ~ ( B @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause153) ).
thf(574,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)],[171]) ).
thf(9518,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[294,266]) ).
thf(9519,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP ) ),
inference(simp,[status(thm)],[9518]) ).
thf(9520,plain,
nil @ ( skac2 @ cons ) @ totalorderP,
inference(pattern_uni,[status(thm)],[9519:[bind(A,$thf( skac2 ))]]) ).
thf(6149,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[217,248]) ).
thf(6150,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP ) ),
inference(simp,[status(thm)],[6149]) ).
thf(6151,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ equalelemsP ),
inference(pattern_uni,[status(thm)],[6150:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(6227,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ equalelemsP ),
inference(simp,[status(thm)],[6151]) ).
thf(6655,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[261,251]) ).
thf(6656,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP ) ),
inference(simp,[status(thm)],[6655]) ).
thf(6657,plain,
nil @ ( skac3 @ cons ) @ cyclefreeP,
inference(pattern_uni,[status(thm)],[6656:[bind(A,$thf( skac3 ))]]) ).
thf(71,axiom,
! [A: $i] : ( A @ skaf72 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause23) ).
thf(321,plain,
! [A: $i] : ( A @ skaf72 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(18189,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[294,18108]) ).
thf(18190,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[18189]) ).
thf(18191,plain,
nil @ ( skac2 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[18190:[bind(A,$thf( skac2 ))]]) ).
thf(18310,plain,
( ( ( nil @ ( skac2 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18191,634]) ).
thf(18311,plain,
( ( nil @ ( skac2 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[18310]) ).
thf(18348,plain,
( ( nil @ ( skac2 @ cons ) )
!= sk1 ),
inference(simp,[status(thm)],[18311]) ).
thf(78,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause75) ).
thf(337,plain,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(338,plain,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[337]) ).
thf(339,plain,
! [A: $i] :
( ( A @ tl @ ssList )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[338]) ).
thf(31666,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[196,339]) ).
thf(31667,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[31666]) ).
thf(31668,plain,
( ( sk1 @ tl @ ssList )
| ( nil = sk1 ) ),
inference(pattern_uni,[status(thm)],[31667:[bind(A,$thf( sk1 ))]]) ).
thf(34232,plain,
sk1 @ tl @ ssList,
inference(simplifyReflect,[status(thm)],[31668,657]) ).
thf(9454,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[297,266]) ).
thf(9455,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP ) ),
inference(simp,[status(thm)],[9454]) ).
thf(9456,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ totalorderP ),
inference(pattern_uni,[status(thm)],[9455:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(9548,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ totalorderP ),
inference(simp,[status(thm)],[9456]) ).
thf(37,axiom,
~ ( nil @ singletonP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause11) ).
thf(253,plain,
~ ( nil @ singletonP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(6703,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[235,251]) ).
thf(6704,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP ) ),
inference(simp,[status(thm)],[6703]) ).
thf(6705,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ cyclefreeP ),
inference(pattern_uni,[status(thm)],[6704:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(6745,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ cyclefreeP ),
inference(simp,[status(thm)],[6705]) ).
thf(137,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ssList )
| ~ ( E @ duplicatefreeP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ( ( D @ ( B @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause179) ).
thf(485,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)],[137]) ).
thf(7310,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[236,260]) ).
thf(7311,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP ) ),
inference(simp,[status(thm)],[7310]) ).
thf(7312,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ strictorderP ),
inference(pattern_uni,[status(thm)],[7311:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(7376,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ strictorderP ),
inference(simp,[status(thm)],[7312]) ).
thf(18160,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[278,18108]) ).
thf(18161,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[18160]) ).
thf(18162,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[18161:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(18231,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[18162]) ).
thf(24043,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf50 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18231,634]) ).
thf(24044,plain,
! [A: $i] :
( ( nil @ ( A @ skaf50 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[24043]) ).
thf(24083,plain,
! [A: $i] :
( ( nil @ ( A @ skaf50 @ cons ) )
!= sk1 ),
inference(simp,[status(thm)],[24044]) ).
thf(102,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ skaf46 ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause131) ).
thf(397,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)],[102]) ).
thf(17359,plain,
( ( ( nil @ ssItem )
!= ( skac2 @ ssItem ) )
| ( sk1 @ ( nil @ neq ) )
| ~ $true
| ~ ( sk1 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[294,14264]) ).
thf(17360,plain,
( ( ( nil @ ssItem )
!= ( skac2 @ ssItem ) )
| ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ssItem ) ),
inference(simp,[status(thm)],[17359]) ).
thf(17403,plain,
( ( nil != skac2 )
| ~ ( sk1 @ ssItem )
| ( sk1 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[17360]) ).
thf(7334,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP )
| ~ $true
| ( sk2 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[5886,260]) ).
thf(7335,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[7334]) ).
thf(7336,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderP )
| ( sk2 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[7335:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(18708,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[343,307]) ).
thf(18709,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[18708]) ).
thf(18710,plain,
~ ( nil @ ( nil @ neq ) ),
inference(pattern_uni,[status(thm)],[18709:[bind(A,$thf( nil ))]]) ).
thf(101,axiom,
! [A: $i] : ( A @ skaf58 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause37) ).
thf(396,plain,
! [A: $i] : ( A @ skaf58 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(9474,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[236,266]) ).
thf(9475,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP ) ),
inference(simp,[status(thm)],[9474]) ).
thf(9476,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ totalorderP ),
inference(pattern_uni,[status(thm)],[9475:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(9533,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ totalorderP ),
inference(simp,[status(thm)],[9476]) ).
thf(16526,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[240,293]) ).
thf(16527,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP ) ),
inference(simp,[status(thm)],[16526]) ).
thf(16528,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ duplicatefreeP ),
inference(pattern_uni,[status(thm)],[16527:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(16577,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ duplicatefreeP ),
inference(simp,[status(thm)],[16528]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause110) ).
thf(242,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(243,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
inference(cnf,[status(esa)],[242]) ).
thf(67,axiom,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause90) ).
thf(311,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(312,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(cnf,[status(esa)],[311]) ).
thf(2980,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[217,232]) ).
thf(2981,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[2980]) ).
thf(2982,plain,
! [A: $i] : ( A @ skaf64 @ ( A @ skaf64 @ geq ) ),
inference(pattern_uni,[status(thm)],[2981:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(3068,plain,
! [A: $i] : ( A @ skaf64 @ ( A @ skaf64 @ geq ) ),
inference(simp,[status(thm)],[2982]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ lt ) )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause147) ).
thf(279,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)],[51]) ).
thf(280,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)],[279]) ).
thf(6682,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[240,251]) ).
thf(6683,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP ) ),
inference(simp,[status(thm)],[6682]) ).
thf(6684,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ cyclefreeP ),
inference(pattern_uni,[status(thm)],[6683:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(6740,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ cyclefreeP ),
inference(simp,[status(thm)],[6684]) ).
thf(7325,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[278,260]) ).
thf(7326,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP ) ),
inference(simp,[status(thm)],[7325]) ).
thf(7327,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ strictorderP ),
inference(pattern_uni,[status(thm)],[7326:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(7381,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ strictorderP ),
inference(simp,[status(thm)],[7327]) ).
thf(3088,plain,
( ( ( sk1 @ ( nil @ geq ) )
!= ( skac3 @ ( skac3 @ geq ) ) )
| ( skac3 != sk1 )
| ~ ( nil @ ssItem )
| ~ $true
| ~ ( nil @ ( sk1 @ geq ) ) ),
inference(paramod_ordered,[status(thm)],[2972,1956]) ).
thf(3089,plain,
( ( ( sk1 @ ( nil @ geq ) )
!= ( skac3 @ ( skac3 @ geq ) ) )
| ( skac3 != sk1 )
| ~ ( nil @ ssItem )
| ~ ( nil @ ( sk1 @ geq ) ) ),
inference(simp,[status(thm)],[3088]) ).
thf(3123,plain,
( ( skac3 != sk1 )
| ( nil != skac3 )
| ( skac3 != sk1 )
| ~ ( nil @ ssItem )
| ~ ( nil @ ( sk1 @ geq ) ) ),
inference(simp,[status(thm)],[3089]) ).
thf(3133,plain,
( ( nil != skac3 )
| ( skac3 != sk1 )
| ~ ( nil @ ssItem )
| ~ ( nil @ ( sk1 @ geq ) ) ),
inference(simp,[status(thm)],[3123]) ).
thf(3252,plain,
( ( ( skac3 @ ( skac3 @ geq ) )
!= ( nil @ ( sk1 @ geq ) ) )
| ( nil != skac3 )
| ( skac3 != sk1 )
| ~ ( nil @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2972,3133]) ).
thf(3253,plain,
( ( ( skac3 @ ( skac3 @ geq ) )
!= ( nil @ ( sk1 @ geq ) ) )
| ( nil != skac3 )
| ( skac3 != sk1 )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[3252]) ).
thf(3328,plain,
( ( nil != skac3 )
| ( skac3 != sk1 )
| ( nil != skac3 )
| ( skac3 != sk1 )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[3253]) ).
thf(3340,plain,
( ( nil != skac3 )
| ( skac3 != sk1 )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[3328]) ).
thf(3352,plain,
( ( ( nil @ ssItem )
!= ( skac3 @ ssItem ) )
| ( nil != skac3 )
| ( skac3 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[261,3340]) ).
thf(3353,plain,
( ( ( nil @ ssItem )
!= ( skac3 @ ssItem ) )
| ( nil != skac3 )
| ( skac3 != sk1 ) ),
inference(simp,[status(thm)],[3352]) ).
thf(3401,plain,
( ( nil != skac3 )
| ( nil != skac3 )
| ( skac3 != sk1 ) ),
inference(simp,[status(thm)],[3353]) ).
thf(3421,plain,
( ( nil != skac3 )
| ( skac3 != sk1 ) ),
inference(simp,[status(thm)],[3401]) ).
thf(1071,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[297,246]) ).
thf(1072,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1071]) ).
thf(1073,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1072:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(1074,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1073]) ).
thf(117,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ app ) @ frontsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause137) ).
thf(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)],[117]) ).
thf(16558,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[294,293]) ).
thf(16559,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP ) ),
inference(simp,[status(thm)],[16558]) ).
thf(16560,plain,
nil @ ( skac2 @ cons ) @ duplicatefreeP,
inference(pattern_uni,[status(thm)],[16559:[bind(A,$thf( skac2 ))]]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ app ) @ ( A @ cons ) )
= ( C @ ( B @ ( A @ cons ) @ app ) ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause157) ).
thf(529,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)],[154]) ).
thf(160,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause78) ).
thf(546,plain,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(95,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause66) ).
thf(381,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(6685,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[278,251]) ).
thf(6686,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP ) ),
inference(simp,[status(thm)],[6685]) ).
thf(6687,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ cyclefreeP ),
inference(pattern_uni,[status(thm)],[6686:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(6741,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ cyclefreeP ),
inference(simp,[status(thm)],[6687]) ).
thf(122,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ cons ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause139) ).
thf(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)],[122]) ).
thf(3,negated_conjecture,
sk3 @ ssList,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
thf(201,plain,
sk3 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5716,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[196,369]) ).
thf(5717,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP ) ),
inference(simp,[status(thm)],[5716]) ).
thf(5718,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk1 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[5717:[bind(A,$thf( sk1 ))]]) ).
thf(5902,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[5718]) ).
thf(7035,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) )
| ( sk1 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[5902,258]) ).
thf(7036,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[7035]) ).
thf(7037,plain,
! [A: $i] :
( ~ ( A @ ( A @ lt ) )
| ( sk1 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[7036:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(89,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause67) ).
thf(366,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(34247,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[34232,307]) ).
thf(34248,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[34247]) ).
thf(34249,plain,
~ ( sk1 @ tl @ ( sk1 @ tl @ neq ) ),
inference(pattern_uni,[status(thm)],[34248:[bind(A,$thf( sk1 @ tl ))]]) ).
thf(6122,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true
| ( sk1 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[5902,232]) ).
thf(6123,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[6122]) ).
thf(6124,plain,
! [A: $i] :
( ( A @ ( A @ geq ) )
| ( sk1 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[6123:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(183,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause86) ).
thf(598,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(16503,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[298,293]) ).
thf(16504,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP ) ),
inference(simp,[status(thm)],[16503]) ).
thf(16505,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ duplicatefreeP ),
inference(pattern_uni,[status(thm)],[16504:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(16597,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ duplicatefreeP ),
inference(simp,[status(thm)],[16505]) ).
thf(6158,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[275,248]) ).
thf(6159,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP ) ),
inference(simp,[status(thm)],[6158]) ).
thf(6160,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ equalelemsP ),
inference(pattern_uni,[status(thm)],[6159:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(6232,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ equalelemsP ),
inference(simp,[status(thm)],[6160]) ).
thf(7316,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[230,260]) ).
thf(7317,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP ) ),
inference(simp,[status(thm)],[7316]) ).
thf(7318,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ strictorderP ),
inference(pattern_uni,[status(thm)],[7317:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(7378,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ strictorderP ),
inference(simp,[status(thm)],[7318]) ).
thf(9457,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[275,266]) ).
thf(9458,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP ) ),
inference(simp,[status(thm)],[9457]) ).
thf(9459,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ totalorderP ),
inference(pattern_uni,[status(thm)],[9458:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(9549,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ totalorderP ),
inference(simp,[status(thm)],[9459]) ).
thf(16494,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[297,293]) ).
thf(16495,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP ) ),
inference(simp,[status(thm)],[16494]) ).
thf(16496,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ duplicatefreeP ),
inference(pattern_uni,[status(thm)],[16495:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(16592,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ duplicatefreeP ),
inference(simp,[status(thm)],[16496]) ).
thf(83,axiom,
! [B: $i,A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause118) ).
thf(349,plain,
! [B: $i,A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(6694,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP )
| ~ $true
| ( sk2 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[5886,251]) ).
thf(6695,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[6694]) ).
thf(6696,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ cyclefreeP )
| ( sk2 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[6695:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(724,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[230,246]) ).
thf(725,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[724]) ).
thf(726,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[725:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(729,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[726]) ).
thf(229,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)],[228]) ).
thf(36,axiom,
nil @ cyclefreeP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause7) ).
thf(252,plain,
nil @ cyclefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(6999,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[244,258]) ).
thf(7000,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[6999]) ).
thf(7001,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( A @ skaf49 @ lt ) ),
inference(pattern_uni,[status(thm)],[7000:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(7063,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( A @ skaf49 @ lt ) ),
inference(simp,[status(thm)],[7001]) ).
thf(115,axiom,
! [A: $i] : ( A @ skaf61 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause34) ).
thf(435,plain,
! [A: $i] : ( A @ skaf61 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(3027,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[241,232]) ).
thf(3028,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3027]) ).
thf(3029,plain,
! [A: $i] : ( A @ skaf60 @ ( A @ skaf60 @ geq ) ),
inference(pattern_uni,[status(thm)],[3028:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(3065,plain,
! [A: $i] : ( A @ skaf60 @ ( A @ skaf60 @ geq ) ),
inference(simp,[status(thm)],[3029]) ).
thf(75,axiom,
! [A: $i] :
( ( ( A @ skaf73 @ ( A @ skaf70 @ cons ) @ ( A @ skaf72 @ ( A @ skaf69 @ cons ) @ ( A @ skaf71 @ app ) @ app ) )
= A )
| ( A @ strictorderedP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause163) ).
thf(329,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)],[75]) ).
thf(9492,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[267,266]) ).
thf(9493,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP ) ),
inference(simp,[status(thm)],[9492]) ).
thf(9494,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ totalorderP ),
inference(pattern_uni,[status(thm)],[9493:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(9539,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ totalorderP ),
inference(simp,[status(thm)],[9494]) ).
thf(163,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= ( C @ ( A @ app ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause150) ).
thf(551,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)],[163]) ).
thf(124,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf48 ) @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause48) ).
thf(456,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf48 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(73,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause134) ).
thf(324,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)],[73]) ).
thf(175,axiom,
! [A: $i] : ( A @ skaf56 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause39) ).
thf(583,plain,
! [A: $i] : ( A @ skaf56 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(18125,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[297,18108]) ).
thf(18126,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[18125]) ).
thf(18127,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[18126:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(18214,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[18127]) ).
thf(22147,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf78 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18214,634]) ).
thf(22148,plain,
! [A: $i] :
( ( nil @ ( A @ skaf78 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[22147]) ).
thf(22186,plain,
! [A: $i] :
( ( nil @ ( A @ skaf78 @ cons ) )
!= sk1 ),
inference(simp,[status(thm)],[22148]) ).
thf(824,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[244,246]) ).
thf(825,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[824]) ).
thf(826,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[825:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(830,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[826]) ).
thf(53,axiom,
nil @ strictorderP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause5) ).
thf(285,plain,
nil @ strictorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ gt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause105) ).
thf(223,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(224,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ gt ) ) ),
inference(cnf,[status(esa)],[223]) ).
thf(1851,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ geq ) )
!= ( sk1 @ ( nil @ geq ) ) )
| ~ ( nil @ ssItem )
| ~ ( sk1 @ ssItem )
| ~ $true
| ~ ( nil @ ( sk1 @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[211,1766]) ).
thf(1852,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ geq ) )
!= ( sk1 @ ( nil @ geq ) ) )
| ~ ( nil @ ssItem )
| ~ ( sk1 @ ssItem )
| ~ ( nil @ ( sk1 @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[1851]) ).
thf(1853,plain,
( ~ ( nil @ ssItem )
| ~ ( sk1 @ ssItem )
| ~ ( nil @ ( sk1 @ geq ) )
| ~ ( nil @ ssItem )
| ~ ( sk1 @ ssItem )
| ~ ( nil @ ( sk1 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[1852:[bind(A,$thf( sk1 )),bind(B,$thf( nil ))]]) ).
thf(1983,plain,
( ~ ( nil @ ( sk1 @ geq ) )
| ~ ( nil @ ssItem )
| ~ ( sk1 @ ssItem )
| ~ ( nil @ ( sk1 @ leq ) ) ),
inference(simp,[status(thm)],[1853]) ).
thf(69,axiom,
! [A: $i] :
( ( ( nil @ ( A @ skaf44 @ cons ) )
= A )
| ~ ( A @ ssList )
| ~ ( A @ singletonP ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause101) ).
thf(315,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf44 @ cons ) )
= A )
| ~ ( A @ ssList )
| ~ ( A @ singletonP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(316,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf44 @ cons ) )
= A )
| ~ ( A @ ssList )
| ~ ( A @ singletonP ) ),
inference(cnf,[status(esa)],[315]) ).
thf(317,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(lifteq,[status(thm)],[316]) ).
thf(6164,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[298,248]) ).
thf(6165,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP ) ),
inference(simp,[status(thm)],[6164]) ).
thf(6166,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ equalelemsP ),
inference(pattern_uni,[status(thm)],[6165:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(6235,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ equalelemsP ),
inference(simp,[status(thm)],[6166]) ).
thf(180,axiom,
! [A: $i] : ( A @ skaf76 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause19) ).
thf(593,plain,
! [A: $i] : ( A @ skaf76 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(187,axiom,
nil @ strictorderedP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause3) ).
thf(610,plain,
nil @ strictorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(3008,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[230,232]) ).
thf(3009,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3008]) ).
thf(3010,plain,
! [A: $i] : ( A @ skaf44 @ ( A @ skaf44 @ geq ) ),
inference(pattern_uni,[status(thm)],[3009:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(3060,plain,
! [A: $i] : ( A @ skaf44 @ ( A @ skaf44 @ geq ) ),
inference(simp,[status(thm)],[3010]) ).
thf(7005,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[236,258]) ).
thf(7006,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[7005]) ).
thf(7007,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( A @ skaf55 @ lt ) ),
inference(pattern_uni,[status(thm)],[7006:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(7065,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( A @ skaf55 @ lt ) ),
inference(simp,[status(thm)],[7007]) ).
thf(22225,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf65 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18215,634]) ).
thf(22226,plain,
! [A: $i] :
( ( nil @ ( A @ skaf65 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[22225]) ).
thf(22264,plain,
! [A: $i] :
( ( nil @ ( A @ skaf65 @ cons ) )
!= sk1 ),
inference(simp,[status(thm)],[22226]) ).
thf(189,axiom,
! [B: $i,A: $i] :
( ( nil = A )
| ( A = B )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( A @ hd )
!= ( B @ hd ) )
| ( ( A @ tl )
!= ( B @ tl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause177) ).
thf(615,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)],[189]) ).
thf(7014,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[230,258]) ).
thf(7015,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[7014]) ).
thf(7016,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( A @ skaf44 @ lt ) ),
inference(pattern_uni,[status(thm)],[7015:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(7054,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( A @ skaf44 @ lt ) ),
inference(simp,[status(thm)],[7016]) ).
thf(164,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ( ( B @ ( A @ cons ) )
!= ( D @ ( C @ cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause170) ).
thf(554,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)],[164]) ).
thf(664,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[214,246]) ).
thf(665,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[664]) ).
thf(666,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[665:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(669,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[666]) ).
thf(635,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[261,246]) ).
thf(636,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[635]) ).
thf(637,plain,
~ ( skac3 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[636:[bind(A,$thf( skac3 ))]]) ).
thf(6993,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[297,258]) ).
thf(6994,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[6993]) ).
thf(6995,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( A @ skaf78 @ lt ) ),
inference(pattern_uni,[status(thm)],[6994:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(7059,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( A @ skaf78 @ lt ) ),
inference(simp,[status(thm)],[6995]) ).
thf(16514,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[236,293]) ).
thf(16515,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP ) ),
inference(simp,[status(thm)],[16514]) ).
thf(16516,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ duplicatefreeP ),
inference(pattern_uni,[status(thm)],[16515:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(16573,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ duplicatefreeP ),
inference(simp,[status(thm)],[16516]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause106) ).
thf(212,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ frontsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause154) ).
thf(327,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)],[74]) ).
thf(328,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)],[327]) ).
thf(131,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause100) ).
thf(471,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(19,axiom,
nil @ duplicatefreeP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause2) ).
thf(225,plain,
nil @ duplicatefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(23810,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf44 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18228,634]) ).
thf(23811,plain,
! [A: $i] :
( ( nil @ ( A @ skaf44 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[23810]) ).
thf(23850,plain,
! [A: $i] :
( ( nil @ ( A @ skaf44 @ cons ) )
!= sk1 ),
inference(simp,[status(thm)],[23811]) ).
thf(133,axiom,
! [A: $i] : ( A @ skaf53 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause42) ).
thf(476,plain,
! [A: $i] : ( A @ skaf53 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(138,axiom,
! [A: $i] :
( ( A @ totalorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf65 @ ( A @ skaf64 @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause91) ).
thf(489,plain,
! [A: $i] :
( ( A @ totalorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf65 @ ( A @ skaf64 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(32823,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[199,339]) ).
thf(32824,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[32823]) ).
thf(32825,plain,
( ( sk2 @ tl @ ssList )
| ( nil = sk2 ) ),
inference(pattern_uni,[status(thm)],[32824:[bind(A,$thf( sk2 ))]]) ).
thf(34353,plain,
( ( nil != nil )
| ( sk2 @ totalorderP )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[32825,249]) ).
thf(34354,plain,
( ( sk2 @ totalorderP )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[34353:[]]) ).
thf(100,axiom,
! [A: $i] :
( ( ( A @ ( nil @ app ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause74) ).
thf(393,plain,
! [A: $i] :
( ( ( A @ ( nil @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(18142,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[298,18108]) ).
thf(18143,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[18142]) ).
thf(18144,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[18143:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(18225,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[18144]) ).
thf(125,axiom,
! [A: $i] :
( ( nil @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause56) ).
thf(457,plain,
! [A: $i] :
( ( nil @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(6176,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[271,248]) ).
thf(6177,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP ) ),
inference(simp,[status(thm)],[6176]) ).
thf(6178,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ equalelemsP ),
inference(pattern_uni,[status(thm)],[6177:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(6239,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ equalelemsP ),
inference(simp,[status(thm)],[6178]) ).
thf(7343,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[235,260]) ).
thf(7344,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP ) ),
inference(simp,[status(thm)],[7343]) ).
thf(7345,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ strictorderP ),
inference(pattern_uni,[status(thm)],[7344:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(7385,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ strictorderP ),
inference(simp,[status(thm)],[7345]) ).
thf(3024,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[267,232]) ).
thf(3025,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3024]) ).
thf(3026,plain,
! [A: $i] : ( A @ skaf83 @ ( A @ skaf83 @ geq ) ),
inference(pattern_uni,[status(thm)],[3025:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(3064,plain,
! [A: $i] : ( A @ skaf83 @ ( A @ skaf83 @ geq ) ),
inference(simp,[status(thm)],[3026]) ).
thf(2999,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[298,232]) ).
thf(3000,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[2999]) ).
thf(3001,plain,
! [A: $i] : ( A @ skaf59 @ ( A @ skaf59 @ geq ) ),
inference(pattern_uni,[status(thm)],[3000:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(3083,plain,
! [A: $i] : ( A @ skaf59 @ ( A @ skaf59 @ geq ) ),
inference(simp,[status(thm)],[3001]) ).
thf(9477,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[274,266]) ).
thf(9478,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP ) ),
inference(simp,[status(thm)],[9477]) ).
thf(9479,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ totalorderP ),
inference(pattern_uni,[status(thm)],[9478:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(9534,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ totalorderP ),
inference(simp,[status(thm)],[9479]) ).
thf(22069,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf79 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18207,634]) ).
thf(22070,plain,
! [A: $i] :
( ( nil @ ( A @ skaf79 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[22069]) ).
thf(22109,plain,
! [A: $i] :
( ( nil @ ( A @ skaf79 @ cons ) )
!= sk1 ),
inference(simp,[status(thm)],[22070]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause130) ).
thf(237,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)],[27]) ).
thf(87,axiom,
! [A: $i] :
( ( ( A @ skaf53 @ ( A @ skaf50 @ cons ) @ ( A @ skaf52 @ ( A @ skaf49 @ cons ) @ ( A @ skaf51 @ app ) @ app ) )
= A )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause167) ).
thf(360,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)],[87]) ).
thf(7041,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[235,258]) ).
thf(7042,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[7041]) ).
thf(7043,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( A @ skaf69 @ lt ) ),
inference(pattern_uni,[status(thm)],[7042:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(7052,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( A @ skaf69 @ lt ) ),
inference(simp,[status(thm)],[7043]) ).
thf(6714,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[294,251]) ).
thf(6715,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP ) ),
inference(simp,[status(thm)],[6714]) ).
thf(6716,plain,
nil @ ( skac2 @ cons ) @ cyclefreeP,
inference(pattern_uni,[status(thm)],[6715:[bind(A,$thf( skac2 ))]]) ).
thf(106,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ cons ) @ ( A @ ( C @ cons ) @ frontsegP ) )
| ~ ( C @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( C != D )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause178) ).
thf(412,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)],[106]) ).
thf(744,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[235,246]) ).
thf(745,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[744]) ).
thf(746,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[745:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(750,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[746]) ).
thf(7044,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( A @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[294,258]) ).
thf(7045,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[7044]) ).
thf(7046,plain,
~ ( skac2 @ ( skac2 @ lt ) ),
inference(pattern_uni,[status(thm)],[7045:[bind(A,$thf( skac2 ))]]) ).
thf(6697,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP )
| ~ $true
| ( sk1 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[5902,251]) ).
thf(6698,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[6697]) ).
thf(6699,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ cyclefreeP )
| ( sk1 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[6698:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(18145,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[236,18108]) ).
thf(18146,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[18145]) ).
thf(18147,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[18146:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(18226,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[18147]) ).
thf(22956,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf55 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18226,634]) ).
thf(22957,plain,
! [A: $i] :
( ( nil @ ( A @ skaf55 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[22956]) ).
thf(22995,plain,
! [A: $i] :
( ( nil @ ( A @ skaf55 @ cons ) )
!= sk1 ),
inference(simp,[status(thm)],[22957]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause122) ).
thf(262,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)],[41]) ).
thf(263,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[262]) ).
thf(264,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ leq ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[263]) ).
thf(6188,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[241,248]) ).
thf(6189,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP ) ),
inference(simp,[status(thm)],[6188]) ).
thf(6190,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ equalelemsP ),
inference(pattern_uni,[status(thm)],[6189:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(6243,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ equalelemsP ),
inference(simp,[status(thm)],[6190]) ).
thf(7328,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[267,260]) ).
thf(7329,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP ) ),
inference(simp,[status(thm)],[7328]) ).
thf(7330,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ strictorderP ),
inference(pattern_uni,[status(thm)],[7329:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(7382,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ strictorderP ),
inference(simp,[status(thm)],[7330]) ).
thf(119,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause129) ).
thf(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)],[119]) ).
thf(7301,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[275,260]) ).
thf(7302,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP ) ),
inference(simp,[status(thm)],[7301]) ).
thf(7303,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ strictorderP ),
inference(pattern_uni,[status(thm)],[7302:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(7372,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ strictorderP ),
inference(simp,[status(thm)],[7303]) ).
thf(9448,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[217,266]) ).
thf(9449,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP ) ),
inference(simp,[status(thm)],[9448]) ).
thf(9450,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ totalorderP ),
inference(pattern_uni,[status(thm)],[9449:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(9545,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ totalorderP ),
inference(simp,[status(thm)],[9450]) ).
thf(190,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ segmentP ) )
| ~ ( B @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause127) ).
thf(618,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)],[190]) ).
thf(16535,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[241,293]) ).
thf(16536,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP ) ),
inference(simp,[status(thm)],[16535]) ).
thf(16537,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ duplicatefreeP ),
inference(pattern_uni,[status(thm)],[16536:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(16580,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ duplicatefreeP ),
inference(simp,[status(thm)],[16537]) ).
thf(149,axiom,
! [A: $i] :
( ( ( A @ skaf81 @ ( A @ skaf79 @ cons ) @ ( A @ skaf78 @ cons ) @ ( A @ skaf80 @ app ) )
= A )
| ( A @ equalelemsP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause142) ).
thf(513,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)],[149]) ).
thf(113,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= nil ) ),
file('/export/starexec/sandbox2/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)],[113]) ).
thf(18154,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[271,18108]) ).
thf(18155,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[18154]) ).
thf(18156,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[18155:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(18229,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[18156]) ).
thf(16497,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[275,293]) ).
thf(16498,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP ) ),
inference(simp,[status(thm)],[16497]) ).
thf(16499,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ duplicatefreeP ),
inference(pattern_uni,[status(thm)],[16498:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(16593,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ duplicatefreeP ),
inference(simp,[status(thm)],[16499]) ).
thf(176,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( D @ ( C @ cons ) @ ( B @ ( A @ cons ) @ frontsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause176) ).
thf(584,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)],[176]) ).
thf(6161,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[244,248]) ).
thf(6162,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP ) ),
inference(simp,[status(thm)],[6161]) ).
thf(6163,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ equalelemsP ),
inference(pattern_uni,[status(thm)],[6162:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(6234,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ equalelemsP ),
inference(simp,[status(thm)],[6163]) ).
thf(167,axiom,
! [A: $i] :
( ( nil = A )
| ( ( A @ skaf82 @ ( A @ skaf83 @ cons ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause109) ).
thf(562,plain,
! [A: $i] :
( ( nil = A )
| ( ( A @ skaf82 @ ( A @ skaf83 @ cons ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(110,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
file('/export/starexec/sandbox2/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)],[110]) ).
thf(10,axiom,
skac3 != skac2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause54) ).
thf(207,plain,
skac3 != skac2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(208,plain,
skac3 != skac2,
inference(polarity_switch,[status(thm)],[207]) ).
thf(209,plain,
skac2 != skac3,
inference(lifteq,[status(thm)],[208]) ).
thf(1626,plain,
! [B: $i,A: $i] :
( ( B != skac2 )
| ( A != skac3 )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
inference(paramod_ordered,[status(thm)],[222,209]) ).
thf(1627,plain,
! [A: $i] :
( ( A != skac3 )
| ~ ( skac2 @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( A @ geq ) ) ),
inference(pattern_uni,[status(thm)],[1626:[bind(A,$thf( A )),bind(B,$thf( skac2 ))]]) ).
thf(1709,plain,
( ~ ( skac2 @ ssItem )
| ~ ( skac3 @ ssItem )
| ~ ( skac3 @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( skac3 @ geq ) ) ),
inference(simp,[status(thm)],[1627]) ).
thf(2834,plain,
( ~ $true
| ~ $true
| ~ ( skac3 @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( skac3 @ geq ) ) ),
inference(rewrite,[status(thm)],[1709,261,294]) ).
thf(2835,plain,
( ~ ( skac3 @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( skac3 @ geq ) ) ),
inference(simp,[status(thm)],[2834]) ).
thf(2858,plain,
( ~ $true
| ( ( skac3 @ ( skac2 @ geq ) )
!= ( skac2 @ ( skac3 @ geq ) ) )
| ~ ( skac2 @ ( skac3 @ geq ) ) ),
inference(eqfactor_ordered,[status(thm)],[2835]) ).
thf(2859,plain,
( ( ( skac3 @ ( skac2 @ geq ) )
!= ( skac2 @ ( skac3 @ geq ) ) )
| ~ ( skac2 @ ( skac3 @ geq ) ) ),
inference(simp,[status(thm)],[2858]) ).
thf(54,axiom,
nil @ equalelemsP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause1) ).
thf(286,plain,
nil @ equalelemsP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(159,axiom,
! [A: $i] : ( A @ skaf51 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause44) ).
thf(545,plain,
! [A: $i] : ( A @ skaf51 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(173,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ app ) @ hd )
= ( B @ hd ) )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause123) ).
thf(577,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)],[173]) ).
thf(20544,plain,
( ( ( sk1 @ ( nil @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ~ $true
| ( nil != skac3 )
| ~ ( sk1 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[17390,18736]) ).
thf(20545,plain,
( ( ( sk1 @ ( nil @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ( nil != skac3 )
| ~ ( sk1 @ ssItem ) ),
inference(simp,[status(thm)],[20544]) ).
thf(20641,plain,
( ( sk2 != sk1 )
| ( nil != sk2 )
| ( nil != skac3 )
| ~ ( sk1 @ ssItem ) ),
inference(simp,[status(thm)],[20545]) ).
thf(68,axiom,
! [A: $i] :
( ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause88) ).
thf(313,plain,
! [A: $i] :
( ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(12051,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) )
| ( sk2 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[5886,284]) ).
thf(12052,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[12051]) ).
thf(12053,plain,
! [A: $i] :
( ~ ( A @ ( A @ neq ) )
| ( sk2 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[12052:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(142,axiom,
! [A: $i] :
( ( nil @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause60) ).
thf(498,plain,
! [A: $i] :
( ( nil @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(1099,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[298,246]) ).
thf(1100,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1099]) ).
thf(1101,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1100:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(1107,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1101]) ).
thf(9489,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[278,266]) ).
thf(9490,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP ) ),
inference(simp,[status(thm)],[9489]) ).
thf(9491,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ totalorderP ),
inference(pattern_uni,[status(thm)],[9490:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(9538,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ totalorderP ),
inference(simp,[status(thm)],[9491]) ).
thf(129,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ segmentP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ segmentP ) )
| ~ ( B @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause152) ).
thf(466,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)],[129]) ).
thf(76,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( F @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause181) ).
thf(332,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)],[76]) ).
thf(333,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)],[332]) ).
thf(334,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)],[333]) ).
thf(335,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)],[334]) ).
thf(7029,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[241,258]) ).
thf(7030,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[7029]) ).
thf(7031,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( A @ skaf60 @ lt ) ),
inference(pattern_uni,[status(thm)],[7030:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(7062,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( A @ skaf60 @ lt ) ),
inference(simp,[status(thm)],[7031]) ).
thf(157,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ app ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause141) ).
thf(540,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)],[157]) ).
thf(188,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause112) ).
thf(611,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(784,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[240,246]) ).
thf(785,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[784]) ).
thf(786,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[785:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(787,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[786]) ).
thf(6688,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[267,251]) ).
thf(6689,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP ) ),
inference(simp,[status(thm)],[6688]) ).
thf(6690,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ cyclefreeP ),
inference(pattern_uni,[status(thm)],[6689:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(6742,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ cyclefreeP ),
inference(simp,[status(thm)],[6690]) ).
thf(676,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[217,246]) ).
thf(677,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[676]) ).
thf(678,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[677:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(681,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[678]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause155) ).
thf(218,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)],[16]) ).
thf(219,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)],[218]) ).
thf(13350,plain,
! [B: $i,A: $i] :
( ( A != nil )
| ( B != sk1 )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[289,657]) ).
thf(13351,plain,
! [A: $i] :
( ( A != sk1 )
| ( nil @ ( A @ neq ) )
| ~ ( A @ ssItem )
| ~ ( nil @ ssItem ) ),
inference(pattern_uni,[status(thm)],[13350:[bind(A,$thf( nil ))]]) ).
thf(14265,plain,
( ( nil @ ( sk1 @ neq ) )
| ~ ( sk1 @ ssItem )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[13351]) ).
thf(17593,plain,
( ( ( nil @ ssItem )
!= ( skac2 @ ssItem ) )
| ( nil @ ( sk1 @ neq ) )
| ~ ( sk1 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[294,14265]) ).
thf(17594,plain,
( ( ( nil @ ssItem )
!= ( skac2 @ ssItem ) )
| ( nil @ ( sk1 @ neq ) )
| ~ ( sk1 @ ssItem ) ),
inference(simp,[status(thm)],[17593]) ).
thf(17622,plain,
( ( nil != skac2 )
| ~ ( sk1 @ ssItem )
| ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[17594]) ).
thf(6152,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[261,248]) ).
thf(6153,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP ) ),
inference(simp,[status(thm)],[6152]) ).
thf(6154,plain,
nil @ ( skac3 @ cons ) @ equalelemsP,
inference(pattern_uni,[status(thm)],[6153:[bind(A,$thf( skac3 ))]]) ).
thf(1838,plain,
( ( ( nil @ ssItem )
!= ( skac3 @ ssItem ) )
| ~ $true
| ~ ( sk1 @ ssItem )
| ~ ( sk1 @ ( nil @ geq ) )
| ~ ( nil @ ( sk1 @ geq ) ) ),
inference(paramod_ordered,[status(thm)],[261,1766]) ).
thf(1839,plain,
( ( ( nil @ ssItem )
!= ( skac3 @ ssItem ) )
| ~ ( sk1 @ ssItem )
| ~ ( sk1 @ ( nil @ geq ) )
| ~ ( nil @ ( sk1 @ geq ) ) ),
inference(simp,[status(thm)],[1838]) ).
thf(1969,plain,
( ( nil != skac3 )
| ~ ( sk1 @ ssItem )
| ~ ( sk1 @ ( nil @ geq ) )
| ~ ( nil @ ( sk1 @ geq ) ) ),
inference(simp,[status(thm)],[1839]) ).
thf(7319,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[271,260]) ).
thf(7320,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP ) ),
inference(simp,[status(thm)],[7319]) ).
thf(7321,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ strictorderP ),
inference(pattern_uni,[status(thm)],[7320:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(7379,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ strictorderP ),
inference(simp,[status(thm)],[7321]) ).
thf(1043,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[278,246]) ).
thf(1044,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1043]) ).
thf(1045,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1044:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(1048,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1045]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ rearsegP ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
!= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause143) ).
thf(377,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)],[94]) ).
thf(34517,plain,
( ( nil != nil )
| ( sk2 @ cyclefreeP )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[32825,252]) ).
thf(34518,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[34517:[]]) ).
thf(3034,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[214,232]) ).
thf(3035,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3034]) ).
thf(3036,plain,
! [A: $i] : ( A @ skaf79 @ ( A @ skaf79 @ geq ) ),
inference(pattern_uni,[status(thm)],[3035:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(3066,plain,
! [A: $i] : ( A @ skaf79 @ ( A @ skaf79 @ geq ) ),
inference(simp,[status(thm)],[3036]) ).
thf(6673,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[274,251]) ).
thf(6674,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP ) ),
inference(simp,[status(thm)],[6673]) ).
thf(6675,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ cyclefreeP ),
inference(pattern_uni,[status(thm)],[6674:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(6737,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ cyclefreeP ),
inference(simp,[status(thm)],[6675]) ).
thf(6194,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP )
| ~ $true
| ( sk1 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[5902,248]) ).
thf(6195,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[6194]) ).
thf(6196,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ equalelemsP )
| ( sk1 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[6195:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(7011,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[274,258]) ).
thf(7012,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[7011]) ).
thf(7013,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( A @ skaf54 @ lt ) ),
inference(pattern_uni,[status(thm)],[7012:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(7053,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( A @ skaf54 @ lt ) ),
inference(simp,[status(thm)],[7013]) ).
thf(18913,plain,
( ( ( sk2 @ ( sk2 @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ~ $true
| ~ ( sk1 @ ssItem )
| ~ ( nil @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[14265,18736]) ).
thf(18914,plain,
( ( ( sk2 @ ( sk2 @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ~ ( sk1 @ ssItem )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[18913]) ).
thf(18931,plain,
( ( nil != sk2 )
| ( sk2 != sk1 )
| ~ ( sk1 @ ssItem )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[18914]) ).
thf(134,axiom,
! [A: $i] : ( A @ skaf75 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause20) ).
thf(477,plain,
! [A: $i] : ( A @ skaf75 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(98,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ hd )
= A )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause97) ).
thf(387,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ hd )
= A )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(140,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause99) ).
thf(494,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ app ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause85) ).
thf(322,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ app ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(323,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ app ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[322]) ).
thf(181,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf42 ) @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause53) ).
thf(594,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf42 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(213,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
inference(cnf,[status(esa)],[212]) ).
thf(191,axiom,
! [A: $i] :
( ( A @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause57) ).
thf(621,plain,
! [A: $i] :
( ( A @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(27349,plain,
! [B: $i,A: $i] :
( ( ( nil @ ( A @ skaf44 @ cons ) )
!= ( nil @ ( B @ skaf44 @ cons ) ) )
| ( A != sk1 )
| ~ ( A @ ssList )
| ~ ( A @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[317,23850]) ).
thf(27350,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( A @ ssList )
| ~ ( A @ singletonP ) ),
inference(pattern_uni,[status(thm)],[27349:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(27403,plain,
( ~ ( sk1 @ ssList )
| ~ ( sk1 @ singletonP ) ),
inference(simp,[status(thm)],[27350]) ).
thf(27423,plain,
( ~ $true
| ~ ( sk1 @ singletonP ) ),
inference(rewrite,[status(thm)],[27403,196]) ).
thf(27424,plain,
~ ( sk1 @ singletonP ),
inference(simp,[status(thm)],[27423]) ).
thf(1015,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[275,246]) ).
thf(1016,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1015]) ).
thf(1017,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1016:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(1022,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1017]) ).
thf(7295,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[261,260]) ).
thf(7296,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP ) ),
inference(simp,[status(thm)],[7295]) ).
thf(7297,plain,
nil @ ( skac3 @ cons ) @ strictorderP,
inference(pattern_uni,[status(thm)],[7296:[bind(A,$thf( skac3 ))]]) ).
thf(127,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ totalorderedP ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause135) ).
thf(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)],[127]) ).
thf(9463,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[298,266]) ).
thf(9464,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP ) ),
inference(simp,[status(thm)],[9463]) ).
thf(9465,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ totalorderP ),
inference(pattern_uni,[status(thm)],[9464:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(9553,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ totalorderP ),
inference(simp,[status(thm)],[9465]) ).
thf(18109,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[217,18108]) ).
thf(18110,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[18109]) ).
thf(18111,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[18110:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(18234,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[18111]) ).
thf(26764,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf64 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18234,634]) ).
thf(26765,plain,
! [A: $i] :
( ( nil @ ( A @ skaf64 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[26764]) ).
thf(26812,plain,
! [A: $i] :
( ( nil @ ( A @ skaf64 @ cons ) )
!= sk1 ),
inference(simp,[status(thm)],[26765]) ).
thf(152,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ cons ) @ memberP ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause138) ).
thf(521,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)],[152]) ).
thf(7331,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[241,260]) ).
thf(7332,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP ) ),
inference(simp,[status(thm)],[7331]) ).
thf(7333,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ strictorderP ),
inference(pattern_uni,[status(thm)],[7332:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(7383,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ strictorderP ),
inference(simp,[status(thm)],[7333]) ).
thf(6676,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[230,251]) ).
thf(6677,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP ) ),
inference(simp,[status(thm)],[6676]) ).
thf(6678,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ cyclefreeP ),
inference(pattern_uni,[status(thm)],[6677:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(6738,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ cyclefreeP ),
inference(simp,[status(thm)],[6678]) ).
thf(23887,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf74 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18229,634]) ).
thf(23888,plain,
! [A: $i] :
( ( nil @ ( A @ skaf74 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[23887]) ).
thf(23926,plain,
! [A: $i] :
( ( nil @ ( A @ skaf74 @ cons ) )
!= sk1 ),
inference(simp,[status(thm)],[23888]) ).
thf(62,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf43 ) @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause52) ).
thf(299,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf43 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause103) ).
thf(226,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(7337,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP )
| ~ $true
| ( sk1 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[5902,260]) ).
thf(7338,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[7337]) ).
thf(7339,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderP )
| ( sk1 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[7338:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(145,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf47 ) @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause49) ).
thf(505,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf47 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(6658,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[297,251]) ).
thf(6659,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP ) ),
inference(simp,[status(thm)],[6658]) ).
thf(6660,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ cyclefreeP ),
inference(pattern_uni,[status(thm)],[6659:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(6730,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ cyclefreeP ),
inference(simp,[status(thm)],[6660]) ).
thf(16491,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[261,293]) ).
thf(16492,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP ) ),
inference(simp,[status(thm)],[16491]) ).
thf(16493,plain,
nil @ ( skac3 @ cons ) @ duplicatefreeP,
inference(pattern_uni,[status(thm)],[16492:[bind(A,$thf( skac3 ))]]) ).
thf(844,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[267,246]) ).
thf(845,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[844]) ).
thf(846,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[845:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(851,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[846]) ).
thf(7354,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[294,260]) ).
thf(7355,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP ) ),
inference(simp,[status(thm)],[7354]) ).
thf(7356,plain,
nil @ ( skac2 @ cons ) @ strictorderP,
inference(pattern_uni,[status(thm)],[7355:[bind(A,$thf( skac2 ))]]) ).
thf(651,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[294,246]) ).
thf(652,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[651]) ).
thf(653,plain,
~ ( skac2 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[652:[bind(A,$thf( skac2 ))]]) ).
thf(6670,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[236,251]) ).
thf(6671,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP ) ),
inference(simp,[status(thm)],[6670]) ).
thf(6672,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ cyclefreeP ),
inference(pattern_uni,[status(thm)],[6671:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(6736,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ cyclefreeP ),
inference(simp,[status(thm)],[6672]) ).
thf(9501,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP )
| ~ $true
| ( sk1 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[5902,266]) ).
thf(9502,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[9501]) ).
thf(9503,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderP )
| ( sk1 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[9502:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(17243,plain,
( ( ( skac3 @ ssItem )
!= ( sk1 @ ssItem ) )
| ( sk1 @ ( nil @ neq ) )
| ~ ( nil @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[261,14264]) ).
thf(17244,plain,
( ( ( skac3 @ ssItem )
!= ( sk1 @ ssItem ) )
| ( sk1 @ ( nil @ neq ) )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[17243]) ).
thf(17413,plain,
( ( skac3 != sk1 )
| ~ ( nil @ ssItem )
| ( sk1 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[17244]) ).
thf(16517,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[274,293]) ).
thf(16518,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP ) ),
inference(simp,[status(thm)],[16517]) ).
thf(16519,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ duplicatefreeP ),
inference(pattern_uni,[status(thm)],[16518:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(16574,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ duplicatefreeP ),
inference(simp,[status(thm)],[16519]) ).
thf(150,axiom,
! [A: $i] : ( A @ skaf81 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause14) ).
thf(516,plain,
! [A: $i] : ( A @ skaf81 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(341,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)],[340]) ).
thf(342,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)],[341]) ).
thf(85,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ssList )
| ~ ( F @ cyclefreeP )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) )
!= F )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause185) ).
thf(355,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)],[85]) ).
thf(18131,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[244,18108]) ).
thf(18132,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[18131]) ).
thf(18133,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[18132:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(18217,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[18133]) ).
thf(22800,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf49 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18217,634]) ).
thf(22801,plain,
! [A: $i] :
( ( nil @ ( A @ skaf49 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[22800]) ).
thf(22840,plain,
! [A: $i] :
( ( nil @ ( A @ skaf49 @ cons ) )
!= sk1 ),
inference(simp,[status(thm)],[22801]) ).
thf(24125,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf83 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18232,634]) ).
thf(24126,plain,
! [A: $i] :
( ( nil @ ( A @ skaf83 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[24125]) ).
thf(24164,plain,
! [A: $i] :
( ( nil @ ( A @ skaf83 @ cons ) )
!= sk1 ),
inference(simp,[status(thm)],[24126]) ).
thf(111,axiom,
! [A: $i] : ( A @ skaf73 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause22) ).
thf(426,plain,
! [A: $i] : ( A @ skaf73 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(153,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ memberP ) )
| ~ ( D @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ( ( C @ ( B @ cons ) @ ( A @ app ) )
!= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause175) ).
thf(525,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)],[153]) ).
thf(165,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ app ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause140) ).
thf(557,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)],[165]) ).
thf(174,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D = B )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ( ( B @ ( A @ cons ) )
!= ( D @ ( C @ cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause171) ).
thf(580,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)],[174]) ).
thf(6173,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[230,248]) ).
thf(6174,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP ) ),
inference(simp,[status(thm)],[6173]) ).
thf(6175,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ equalelemsP ),
inference(pattern_uni,[status(thm)],[6174:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(6238,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ equalelemsP ),
inference(simp,[status(thm)],[6175]) ).
thf(59,axiom,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( A @ lt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause63) ).
thf(295,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(7023,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[278,258]) ).
thf(7024,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[7023]) ).
thf(7025,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( A @ skaf50 @ lt ) ),
inference(pattern_uni,[status(thm)],[7024:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(7058,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( A @ skaf50 @ lt ) ),
inference(simp,[status(thm)],[7025]) ).
thf(5758,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ( C @ ssItem )
| ( B @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[583,369]) ).
thf(5759,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ( C @ ssItem )
| ( B @ duplicatefreeP ) ),
inference(simp,[status(thm)],[5758]) ).
thf(5760,plain,
! [B: $i,A: $i] :
( ( A @ ssItem )
| ( B @ skaf56 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[5759:[bind(A,$thf( D )),bind(B,$thf( D @ skaf56 ))]]) ).
thf(5871,plain,
! [B: $i,A: $i] :
( ( A @ ssItem )
| ( B @ skaf56 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[5760]) ).
thf(2996,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[244,232]) ).
thf(2997,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[2996]) ).
thf(2998,plain,
! [A: $i] : ( A @ skaf49 @ ( A @ skaf49 @ geq ) ),
inference(pattern_uni,[status(thm)],[2997:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(3082,plain,
! [A: $i] : ( A @ skaf49 @ ( A @ skaf49 @ geq ) ),
inference(simp,[status(thm)],[2998]) ).
thf(12054,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) )
| ( sk1 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[5902,284]) ).
thf(12055,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[12054]) ).
thf(12056,plain,
! [A: $i] :
( ~ ( A @ ( A @ neq ) )
| ( sk1 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[12055:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(9480,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[230,266]) ).
thf(9481,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP ) ),
inference(simp,[status(thm)],[9480]) ).
thf(9482,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ totalorderP ),
inference(pattern_uni,[status(thm)],[9481:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(9535,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ totalorderP ),
inference(simp,[status(thm)],[9482]) ).
thf(26675,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf60 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18233,634]) ).
thf(26676,plain,
! [A: $i] :
( ( nil @ ( A @ skaf60 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[26675]) ).
thf(26722,plain,
! [A: $i] :
( ( nil @ ( A @ skaf60 @ cons ) )
!= sk1 ),
inference(simp,[status(thm)],[26676]) ).
thf(16532,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[267,293]) ).
thf(16533,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP ) ),
inference(simp,[status(thm)],[16532]) ).
thf(16534,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ duplicatefreeP ),
inference(pattern_uni,[status(thm)],[16533:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(16579,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ duplicatefreeP ),
inference(simp,[status(thm)],[16534]) ).
thf(314,plain,
! [A: $i] :
( ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[313]) ).
thf(20712,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[196,314]) ).
thf(20713,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP ) ),
inference(simp,[status(thm)],[20712]) ).
thf(20714,plain,
( ( sk1 @ skaf50 @ ( sk1 @ skaf49 @ leq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[20713:[bind(A,$thf( sk1 ))]]) ).
thf(7017,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[271,258]) ).
thf(7018,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[7017]) ).
thf(7019,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( A @ skaf74 @ lt ) ),
inference(pattern_uni,[status(thm)],[7018:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(7055,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( A @ skaf74 @ lt ) ),
inference(simp,[status(thm)],[7019]) ).
thf(66,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ memberP ) )
| ( C @ ( B @ memberP ) )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ( B @ ( A @ app ) @ memberP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause158) ).
thf(309,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)],[66]) ).
thf(310,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)],[309]) ).
thf(6197,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[214,248]) ).
thf(6198,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP ) ),
inference(simp,[status(thm)],[6197]) ).
thf(6199,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ equalelemsP ),
inference(pattern_uni,[status(thm)],[6198:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(6244,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ equalelemsP ),
inference(simp,[status(thm)],[6199]) ).
thf(3021,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[278,232]) ).
thf(3022,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3021]) ).
thf(3023,plain,
! [A: $i] : ( A @ skaf50 @ ( A @ skaf50 @ geq ) ),
inference(pattern_uni,[status(thm)],[3022:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(3063,plain,
! [A: $i] : ( A @ skaf50 @ ( A @ skaf50 @ geq ) ),
inference(simp,[status(thm)],[3023]) ).
thf(330,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)],[329]) ).
thf(331,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)],[330]) ).
thf(118,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ strictorderedP )
| ~ ( B @ hd @ ( A @ lt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause160) ).
thf(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)],[118]) ).
thf(91,axiom,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf59 @ ( A @ skaf60 @ lt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause92) ).
thf(370,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf59 @ ( A @ skaf60 @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(172,axiom,
! [A: $i] : ( A @ skaf82 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause13) ).
thf(576,plain,
! [A: $i] : ( A @ skaf82 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(18157,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[240,18108]) ).
thf(18158,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[18157]) ).
thf(18159,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[18158:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(18230,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[18159]) ).
thf(86,axiom,
! [A: $i] : ( A @ skaf77 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause18) ).
thf(359,plain,
! [A: $i] : ( A @ skaf77 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(12036,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[271,284]) ).
thf(12037,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[12036]) ).
thf(12038,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( A @ skaf74 @ neq ) ),
inference(pattern_uni,[status(thm)],[12037:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(12071,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( A @ skaf74 @ neq ) ),
inference(simp,[status(thm)],[12038]) ).
thf(6191,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP )
| ~ $true
| ( sk2 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[5886,248]) ).
thf(6192,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[6191]) ).
thf(6193,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ equalelemsP )
| ( sk2 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[6192:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(6211,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[294,248]) ).
thf(6212,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP ) ),
inference(simp,[status(thm)],[6211]) ).
thf(6213,plain,
nil @ ( skac2 @ cons ) @ equalelemsP,
inference(pattern_uni,[status(thm)],[6212:[bind(A,$thf( skac2 ))]]) ).
thf(7304,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[244,260]) ).
thf(7305,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP ) ),
inference(simp,[status(thm)],[7304]) ).
thf(7306,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ strictorderP ),
inference(pattern_uni,[status(thm)],[7305:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(7374,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ strictorderP ),
inference(simp,[status(thm)],[7306]) ).
thf(170,axiom,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ segmentP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause80) ).
thf(571,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(141,axiom,
! [A: $i] : ( A @ skaf68 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause27) ).
thf(497,plain,
! [A: $i] : ( A @ skaf68 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(7322,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[240,260]) ).
thf(7323,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP ) ),
inference(simp,[status(thm)],[7322]) ).
thf(7324,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ strictorderP ),
inference(pattern_uni,[status(thm)],[7323:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(7380,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ strictorderP ),
inference(simp,[status(thm)],[7324]) ).
thf(77,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf46 ) @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause50) ).
thf(336,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf46 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(16544,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[214,293]) ).
thf(16545,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP ) ),
inference(simp,[status(thm)],[16544]) ).
thf(16546,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ duplicatefreeP ),
inference(pattern_uni,[status(thm)],[16545:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(16582,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ duplicatefreeP ),
inference(simp,[status(thm)],[16546]) ).
thf(9498,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP )
| ~ $true
| ( sk2 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[5886,266]) ).
thf(9499,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[9498]) ).
thf(9500,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderP )
| ( sk2 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[9499:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(12012,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[261,284]) ).
thf(12013,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[12012]) ).
thf(12014,plain,
~ ( skac3 @ ( skac3 @ neq ) ),
inference(pattern_uni,[status(thm)],[12013:[bind(A,$thf( skac3 ))]]) ).
thf(184,axiom,
! [A: $i] :
( ( A @ equalelemsP )
| ~ ( A @ ssList )
| ( ( A @ skaf79 )
!= ( A @ skaf78 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause89) ).
thf(600,plain,
! [A: $i] :
( ( A @ equalelemsP )
| ~ ( A @ ssList )
| ( ( A @ skaf79 )
!= ( A @ skaf78 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(15395,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true
| ( sk1 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[5902,291]) ).
thf(15396,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[15395]) ).
thf(15397,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ( sk1 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[15396:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(182,axiom,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ frontsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause84) ).
thf(595,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(6200,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[235,248]) ).
thf(6201,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP ) ),
inference(simp,[status(thm)],[6200]) ).
thf(6202,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ equalelemsP ),
inference(pattern_uni,[status(thm)],[6201:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(6245,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ equalelemsP ),
inference(simp,[status(thm)],[6202]) ).
thf(9451,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[261,266]) ).
thf(9452,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP ) ),
inference(simp,[status(thm)],[9451]) ).
thf(9453,plain,
nil @ ( skac3 @ cons ) @ totalorderP,
inference(pattern_uni,[status(thm)],[9452:[bind(A,$thf( skac3 ))]]) ).
thf(6990,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( A @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[261,258]) ).
thf(6991,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[6990]) ).
thf(6992,plain,
~ ( skac3 @ ( skac3 @ lt ) ),
inference(pattern_uni,[status(thm)],[6991:[bind(A,$thf( skac3 ))]]) ).
thf(5767,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ( C @ ssItem )
| ( B @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[593,369]) ).
thf(5768,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ( C @ ssItem )
| ( B @ duplicatefreeP ) ),
inference(simp,[status(thm)],[5767]) ).
thf(5769,plain,
! [B: $i,A: $i] :
( ( A @ ssItem )
| ( B @ skaf76 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[5768:[bind(A,$thf( D )),bind(B,$thf( D @ skaf76 ))]]) ).
thf(5873,plain,
! [B: $i,A: $i] :
( ( A @ ssItem )
| ( B @ skaf76 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[5769]) ).
thf(194,axiom,
! [A: $i] :
( ( A @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause61) ).
thf(627,plain,
! [A: $i] :
( ( A @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(3037,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[235,232]) ).
thf(3038,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3037]) ).
thf(3039,plain,
! [A: $i] : ( A @ skaf69 @ ( A @ skaf69 @ geq ) ),
inference(pattern_uni,[status(thm)],[3038:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(3067,plain,
! [A: $i] : ( A @ skaf69 @ ( A @ skaf69 @ geq ) ),
inference(simp,[status(thm)],[3039]) ).
thf(88,axiom,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause82) ).
thf(363,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(6691,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[241,251]) ).
thf(6692,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP ) ),
inference(simp,[status(thm)],[6691]) ).
thf(6693,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ cyclefreeP ),
inference(pattern_uni,[status(thm)],[6692:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(6743,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ cyclefreeP ),
inference(simp,[status(thm)],[6693]) ).
thf(764,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[236,246]) ).
thf(765,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[764]) ).
thf(766,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[765:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(771,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[766]) ).
thf(16520,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[230,293]) ).
thf(16521,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP ) ),
inference(simp,[status(thm)],[16520]) ).
thf(16522,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ duplicatefreeP ),
inference(pattern_uni,[status(thm)],[16521:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(16575,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ duplicatefreeP ),
inference(simp,[status(thm)],[16522]) ).
thf(128,axiom,
! [A: $i] : ( A @ skaf80 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause15) ).
thf(465,plain,
! [A: $i] : ( A @ skaf80 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(121,axiom,
! [A: $i] :
( ( A @ skaf49 @ ( A @ skaf50 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/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)],[121]) ).
thf(6996,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[275,258]) ).
thf(6997,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[6996]) ).
thf(6998,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( A @ skaf65 @ lt ) ),
inference(pattern_uni,[status(thm)],[6997:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(7061,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( A @ skaf65 @ lt ) ),
inference(simp,[status(thm)],[6998]) ).
thf(136,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = A )
| ( C @ ( B @ memberP ) )
| ~ ( C @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( C @ ( B @ ( A @ cons ) @ memberP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause161) ).
thf(482,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)],[136]) ).
thf(4,negated_conjecture,
sk4 @ ssList,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).
thf(203,plain,
sk4 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7032,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) )
| ( sk2 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[5886,258]) ).
thf(7033,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[7032]) ).
thf(7034,plain,
! [A: $i] :
( ~ ( A @ ( A @ lt ) )
| ( sk2 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[7033:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(178,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ skaf43 ) @ ( B @ cons ) @ ( B @ ( A @ skaf42 ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ memberP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause169) ).
thf(588,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)],[178]) ).
thf(6155,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[297,248]) ).
thf(6156,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP ) ),
inference(simp,[status(thm)],[6155]) ).
thf(6157,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ equalelemsP ),
inference(pattern_uni,[status(thm)],[6156:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(6230,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ equalelemsP ),
inference(simp,[status(thm)],[6157]) ).
thf(151,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ segmentP ) )
| ~ ( D @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ( ( C @ ( B @ ( A @ app ) @ app ) )
!= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause173) ).
thf(517,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)],[151]) ).
thf(99,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ totalorderedP )
| ~ ( B @ hd @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause159) ).
thf(390,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)],[99]) ).
thf(7340,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[214,260]) ).
thf(7341,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP ) ),
inference(simp,[status(thm)],[7340]) ).
thf(7342,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ strictorderP ),
inference(pattern_uni,[status(thm)],[7341:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(7384,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ strictorderP ),
inference(simp,[status(thm)],[7342]) ).
thf(108,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ app ) @ app ) )
= ( A @ ( B @ app ) @ ( C @ app ) ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause149) ).
thf(418,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)],[108]) ).
thf(987,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[274,246]) ).
thf(988,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[987]) ).
thf(989,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[988:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(995,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[989]) ).
thf(3005,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[274,232]) ).
thf(3006,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3005]) ).
thf(3007,plain,
! [A: $i] : ( A @ skaf54 @ ( A @ skaf54 @ geq ) ),
inference(pattern_uni,[status(thm)],[3006:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(3085,plain,
! [A: $i] : ( A @ skaf54 @ ( A @ skaf54 @ geq ) ),
inference(simp,[status(thm)],[3007]) ).
thf(34457,plain,
( ( nil != nil )
| ( sk2 @ totalorderedP )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[32825,623]) ).
thf(34458,plain,
( ( sk2 @ totalorderedP )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[34457:[]]) ).
thf(169,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ totalorderedP ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause125) ).
thf(568,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)],[169]) ).
thf(18681,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[196,307]) ).
thf(18682,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[18681]) ).
thf(18683,plain,
~ ( sk1 @ ( sk1 @ neq ) ),
inference(pattern_uni,[status(thm)],[18682:[bind(A,$thf( sk1 ))]]) ).
thf(9486,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[240,266]) ).
thf(9487,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP ) ),
inference(simp,[status(thm)],[9486]) ).
thf(9488,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ totalorderP ),
inference(pattern_uni,[status(thm)],[9487:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(9537,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ totalorderP ),
inference(simp,[status(thm)],[9488]) ).
thf(135,axiom,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause79) ).
thf(478,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause156) ).
thf(272,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)],[46]) ).
thf(96,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf45 ) @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause51) ).
thf(383,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf45 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(345,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ( B @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ frontsegP ) ) ),
inference(cnf,[status(esa)],[344]) ).
thf(346,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ frontsegP ) )
| ( ( B @ ( A @ skaf45 ) @ ( B @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[345]) ).
thf(161,axiom,
! [A: $i] : ( A @ skaf63 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause32) ).
thf(549,plain,
! [A: $i] : ( A @ skaf63 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(156,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ leq ) )
| ~ ( F @ ssList )
| ~ ( F @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause182) ).
thf(536,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)],[156]) ).
thf(114,axiom,
! [A: $i] :
( ( A @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause59) ).
thf(433,plain,
! [A: $i] :
( ( A @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(147,axiom,
! [A: $i] : ( A @ skaf67 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause28) ).
thf(510,plain,
! [A: $i] : ( A @ skaf67 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(9507,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[235,266]) ).
thf(9508,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP ) ),
inference(simp,[status(thm)],[9507]) ).
thf(9509,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ totalorderP ),
inference(pattern_uni,[status(thm)],[9508:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(9542,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ totalorderP ),
inference(simp,[status(thm)],[9509]) ).
thf(9460,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[244,266]) ).
thf(9461,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP ) ),
inference(simp,[status(thm)],[9460]) ).
thf(9462,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ totalorderP ),
inference(pattern_uni,[status(thm)],[9461:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(9551,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ totalorderP ),
inference(simp,[status(thm)],[9462]) ).
thf(120,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( nil @ ( A @ cons ) @ app ) )
= ( B @ ( A @ cons ) ) )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause120) ).
thf(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)],[120]) ).
thf(6005,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true
| ( sk2 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[5886,232]) ).
thf(6006,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[6005]) ).
thf(6007,plain,
! [A: $i] :
( ( A @ ( A @ geq ) )
| ( sk2 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[6006:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(20787,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[199,314]) ).
thf(20788,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP ) ),
inference(simp,[status(thm)],[20787]) ).
thf(20789,plain,
( ( sk2 @ skaf50 @ ( sk2 @ skaf49 @ leq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[20788:[bind(A,$thf( sk2 ))]]) ).
thf(18120,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[261,18108]) ).
thf(18121,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[18120]) ).
thf(18122,plain,
nil @ ( skac3 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[18121:[bind(A,$thf( skac3 ))]]) ).
thf(6170,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[274,248]) ).
thf(6171,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ equalelemsP ) ),
inference(simp,[status(thm)],[6170]) ).
thf(6172,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ equalelemsP ),
inference(pattern_uni,[status(thm)],[6171:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(6237,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ equalelemsP ),
inference(simp,[status(thm)],[6172]) ).
thf(273,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)],[272]) ).
thf(93,axiom,
! [B: $i,A: $i] :
( ( B @ singletonP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( nil @ ( A @ cons ) )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause116) ).
thf(373,plain,
! [B: $i,A: $i] :
( ( B @ singletonP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( nil @ ( A @ cons ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(185,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ skaf48 ) @ ( B @ ( B @ ( A @ skaf47 ) @ app ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause168) ).
thf(603,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)],[185]) ).
thf(3014,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[240,232]) ).
thf(3015,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3014]) ).
thf(3016,plain,
! [A: $i] : ( A @ skaf70 @ ( A @ skaf70 @ geq ) ),
inference(pattern_uni,[status(thm)],[3015:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(3062,plain,
! [A: $i] : ( A @ skaf70 @ ( A @ skaf70 @ geq ) ),
inference(simp,[status(thm)],[3016]) ).
thf(325,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP ) ),
inference(cnf,[status(esa)],[324]) ).
thf(326,plain,
! [B: $i,A: $i] :
( ( B @ hd @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP )
| ( nil = B ) ),
inference(lifteq,[status(thm)],[325]) ).
thf(6667,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[298,251]) ).
thf(6668,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP ) ),
inference(simp,[status(thm)],[6667]) ).
thf(6669,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ cyclefreeP ),
inference(pattern_uni,[status(thm)],[6668:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(6735,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ cyclefreeP ),
inference(simp,[status(thm)],[6669]) ).
thf(7038,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[214,258]) ).
thf(7039,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[7038]) ).
thf(7040,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( A @ skaf79 @ lt ) ),
inference(pattern_uni,[status(thm)],[7039:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(7050,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( A @ skaf79 @ lt ) ),
inference(simp,[status(thm)],[7040]) ).
thf(132,axiom,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf55 @ ( A @ skaf54 @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause95) ).
thf(474,plain,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf55 @ ( A @ skaf54 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(103,axiom,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause81) ).
thf(400,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ frontsegP ) )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause144) ).
thf(532,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)],[155]) ).
thf(23965,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf70 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18230,634]) ).
thf(23966,plain,
! [A: $i] :
( ( nil @ ( A @ skaf70 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[23965]) ).
thf(24004,plain,
! [A: $i] :
( ( nil @ ( A @ skaf70 @ cons ) )
!= sk1 ),
inference(simp,[status(thm)],[23966]) ).
thf(238,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[237]) ).
thf(239,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[238]) ).
thf(146,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ lt ) )
| ( D @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( F @ strictorderP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause183) ).
thf(506,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(44,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause121) ).
thf(268,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)],[44]) ).
thf(18148,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[274,18108]) ).
thf(18149,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[18148]) ).
thf(18150,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[18149:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(18227,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[18150]) ).
thf(23034,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf54 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18227,634]) ).
thf(23035,plain,
! [A: $i] :
( ( nil @ ( A @ skaf54 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[23034]) ).
thf(23073,plain,
! [A: $i] :
( ( nil @ ( A @ skaf54 @ cons ) )
!= sk1 ),
inference(simp,[status(thm)],[23035]) ).
thf(9504,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[214,266]) ).
thf(9505,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP ) ),
inference(simp,[status(thm)],[9504]) ).
thf(9506,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ totalorderP ),
inference(pattern_uni,[status(thm)],[9505:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(9541,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ totalorderP ),
inference(simp,[status(thm)],[9506]) ).
thf(193,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ strictorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause124) ).
thf(624,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)],[193]) ).
thf(112,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ rearsegP ) )
| ~ ( B @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause128) ).
thf(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)],[112]) ).
thf(18172,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true
| ( sk1 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[5902,18108]) ).
thf(18173,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[18172]) ).
thf(18174,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk1 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[18173:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(16500,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[244,293]) ).
thf(16501,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP ) ),
inference(simp,[status(thm)],[16500]) ).
thf(16502,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ duplicatefreeP ),
inference(pattern_uni,[status(thm)],[16501:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(16595,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ duplicatefreeP ),
inference(simp,[status(thm)],[16502]) ).
thf(7298,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[297,260]) ).
thf(7299,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderP ) ),
inference(simp,[status(thm)],[7298]) ).
thf(7300,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ strictorderP ),
inference(pattern_uni,[status(thm)],[7299:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(7370,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ strictorderP ),
inference(simp,[status(thm)],[7300]) ).
thf(16529,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[278,293]) ).
thf(16530,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP ) ),
inference(simp,[status(thm)],[16529]) ).
thf(16531,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ duplicatefreeP ),
inference(pattern_uni,[status(thm)],[16530:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(16578,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ duplicatefreeP ),
inference(simp,[status(thm)],[16531]) ).
thf(6652,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[217,251]) ).
thf(6653,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP ) ),
inference(simp,[status(thm)],[6652]) ).
thf(6654,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ cyclefreeP ),
inference(pattern_uni,[status(thm)],[6653:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(6750,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ cyclefreeP ),
inference(simp,[status(thm)],[6654]) ).
thf(6097,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) )
| ( sk1 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[5902,246]) ).
thf(6098,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[6097]) ).
thf(6099,plain,
! [A: $i] :
( ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[6098:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(126,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause76) ).
thf(459,plain,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(22878,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf59 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18225,634]) ).
thf(22879,plain,
! [A: $i] :
( ( nil @ ( A @ skaf59 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[22878]) ).
thf(22918,plain,
! [A: $i] :
( ( nil @ ( A @ skaf59 @ cons ) )
!= sk1 ),
inference(simp,[status(thm)],[22879]) ).
thf(2989,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[275,232]) ).
thf(2990,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[2989]) ).
thf(2991,plain,
! [A: $i] : ( A @ skaf65 @ ( A @ skaf65 @ geq ) ),
inference(pattern_uni,[status(thm)],[2990:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(3076,plain,
! [A: $i] : ( A @ skaf65 @ ( A @ skaf65 @ geq ) ),
inference(simp,[status(thm)],[2991]) ).
thf(277,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
inference(cnf,[status(esa)],[276]) ).
thf(1840,plain,
( ( ( skac2 @ ssItem )
!= ( sk1 @ ssItem ) )
| ~ ( nil @ ssItem )
| ~ $true
| ~ ( sk1 @ ( nil @ geq ) )
| ~ ( nil @ ( sk1 @ geq ) ) ),
inference(paramod_ordered,[status(thm)],[294,1766]) ).
thf(1841,plain,
( ( ( skac2 @ ssItem )
!= ( sk1 @ ssItem ) )
| ~ ( nil @ ssItem )
| ~ ( sk1 @ ( nil @ geq ) )
| ~ ( nil @ ( sk1 @ geq ) ) ),
inference(simp,[status(thm)],[1840]) ).
thf(1944,plain,
( ( skac2 != sk1 )
| ~ ( nil @ ssItem )
| ~ ( sk1 @ ( nil @ geq ) )
| ~ ( nil @ ( sk1 @ geq ) ) ),
inference(simp,[status(thm)],[1841]) ).
thf(9483,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[271,266]) ).
thf(9484,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderP ) ),
inference(simp,[status(thm)],[9483]) ).
thf(9485,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ totalorderP ),
inference(pattern_uni,[status(thm)],[9484:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(9536,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ totalorderP ),
inference(simp,[status(thm)],[9485]) ).
thf(6987,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[217,258]) ).
thf(6988,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[6987]) ).
thf(6989,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( A @ skaf64 @ lt ) ),
inference(pattern_uni,[status(thm)],[6988:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(7056,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( A @ skaf64 @ lt ) ),
inference(simp,[status(thm)],[6989]) ).
thf(16541,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP )
| ~ $true
| ( sk1 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[5902,293]) ).
thf(16542,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ duplicatefreeP )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[16541]) ).
thf(16543,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ duplicatefreeP )
| ( sk1 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[16542:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(139,axiom,
! [A: $i] :
( ( nil = A )
| ( ( A @ tl @ ( A @ hd @ cons ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause104) ).
thf(491,plain,
! [A: $i] :
( ( nil = A )
| ( ( A @ tl @ ( A @ hd @ cons ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(123,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ frontsegP ) )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( D @ ( C @ cons ) @ ( B @ ( A @ cons ) @ frontsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause174) ).
thf(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)],[123]) ).
thf(254,plain,
~ ( nil @ singletonP ),
inference(polarity_switch,[status(thm)],[253]) ).
thf(227,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
inference(cnf,[status(esa)],[226]) ).
thf(18247,plain,
( ( ( nil @ ( skac3 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18122,634]) ).
thf(18248,plain,
( ( nil @ ( skac3 @ cons ) @ totalorderedP )
!= ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[18247]) ).
thf(18285,plain,
( ( nil @ ( skac3 @ cons ) )
!= sk1 ),
inference(simp,[status(thm)],[18248]) ).
thf(12033,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[230,284]) ).
thf(12034,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[12033]) ).
thf(12035,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( A @ skaf44 @ neq ) ),
inference(pattern_uni,[status(thm)],[12034:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(12070,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( A @ skaf44 @ neq ) ),
inference(simp,[status(thm)],[12035]) ).
thf(6679,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[271,251]) ).
thf(6680,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ cyclefreeP ) ),
inference(simp,[status(thm)],[6679]) ).
thf(6681,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ cyclefreeP ),
inference(pattern_uni,[status(thm)],[6680:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(6739,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ cyclefreeP ),
inference(simp,[status(thm)],[6681]) ).
thf(7020,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[240,258]) ).
thf(7021,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[7020]) ).
thf(7022,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( A @ skaf70 @ lt ) ),
inference(pattern_uni,[status(thm)],[7021:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(7057,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( A @ skaf70 @ lt ) ),
inference(simp,[status(thm)],[7022]) ).
thf(42018,plain,
$false,
inference(e,[status(thm)],[7375,809,629,15418,16576,347,249,10134,19936,234,18228,1956,352,962,1982,468,408,3072,7377,6744,18233,308,5982,247,511,15346,16581,202,6732,217,276,22030,550,500,6241,340,17390,9540,384,14264,404,6236,2972,7064,436,18171,7390,320,565,6242,372,504,3061,587,344,12065,15394,196,542,16540,16584,606,284,228,18215,289,6734,261,6240,559,421,7060,3084,416,216,18232,12069,591,2259,18207,574,9520,6227,6657,321,18348,34232,9548,623,211,253,6745,485,7376,24083,397,17403,634,293,7336,18710,396,9533,16577,243,265,312,206,3068,280,6740,7381,3421,307,1074,292,248,439,16560,529,546,381,6741,233,452,201,7037,220,366,34249,6124,598,297,16597,275,6232,7378,9549,16592,260,349,6696,729,229,252,197,7063,435,3065,329,17385,9539,551,18108,456,324,583,22186,830,285,224,1983,317,18205,6235,593,610,3060,7065,22264,615,339,7054,554,669,637,7059,16573,212,328,471,1942,225,23850,476,489,34354,393,18225,457,6239,7385,3064,3083,9534,244,266,311,18191,22109,343,237,360,7052,6716,657,412,750,7046,6699,18736,22995,264,6243,279,7382,444,7372,9545,298,618,16580,513,430,18229,16593,584,6234,562,423,2859,286,291,545,259,577,20641,281,204,313,12053,498,1107,9538,466,335,236,7062,540,611,787,6742,681,219,274,230,245,318,17622,6154,1969,7379,1048,377,34518,271,3066,6737,6196,7053,18931,477,387,494,323,594,213,621,27424,1022,7297,462,9553,240,251,26812,198,521,2835,7383,6738,23926,223,299,226,7339,505,6730,16493,278,267,851,241,7356,653,6736,9503,17413,16574,209,516,342,355,18226,22840,24164,426,5886,255,14265,525,557,580,6238,295,7058,5871,3082,12056,327,9535,26722,16579,20714,7055,310,6244,3063,331,441,370,576,18230,359,199,12071,2975,6193,6213,7374,571,497,7380,1766,336,5902,16582,9500,12014,600,15397,314,595,6245,9453,6992,5873,627,3067,363,218,6743,368,18234,771,16575,250,465,231,450,7061,482,203,7034,588,6230,517,304,258,390,632,7384,418,18217,995,3085,34458,568,290,18683,207,9537,478,272,383,346,549,536,235,246,433,510,9542,214,287,300,9551,447,315,18231,6007,20789,262,18122,6237,273,373,603,3062,210,326,294,32825,6735,7050,474,400,532,24004,239,242,506,268,23073,195,9541,624,332,427,18174,16595,7370,200,369,16578,18227,6750,6099,459,22918,3076,277,322,337,1944,9536,18214,7056,215,16543,491,454,232,254,227,309,18285,12070,222,6739,7057]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC340-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.39 % Computer : n011.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sat Sep 26 12:49:45 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.89/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.44/1.28 % [INFO] Parsing done (293ms).
% 1.44/1.29 % [INFO] Running in sequential loop mode.
% 2.50/1.69 % [INFO] eprover registered as external prover.
% 2.70/1.70 % [INFO] Scanning for conjecture ...
% 2.96/1.84 % [INFO] Found a conjecture (or negated_conjecture) and 185 axioms. Running axiom selection ...
% 3.18/1.97 % [INFO] Axiom selection finished. Selected 185 axioms (removed 0 axioms).
% 3.98/2.13 % [INFO] Problem is propositional (TPTP CNF).
% 3.98/2.15 % [INFO] Type checking passed.
% 3.98/2.15 % [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 ...
% 95.53/22.72 % External prover 'e' found a proof!
% 95.53/22.72 % [INFO] Killing All external provers ...
% 95.53/22.72 % Time passed: 22182ms (effective reasoning time: 21419ms)
% 95.53/22.73 % 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
% 95.53/22.73 % No. of inferences in proof: 1341
% 95.53/22.73 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 22182 ms resp. 21419 ms w/o parsing
% 97.50/23.11 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 97.50/23.12 % [INFO] Killing All external provers ...
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