%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWC120-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:52:20 AM UTC 2026
% Result : Unsatisfiable 93.20s 19.23s
% Output : Refutation 95.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 197
% Syntax : Number of formulae : 1212 ( 393 unt; 0 typ; 0 def)
% Number of atoms : 3901 ( 722 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 10035 (2125 ~;1957 |; 0 &;5953 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 75 ( 72 usr; 9 con; 0-2 aty)
% Number of variables : 1745 ( 0 ^;1745 !; 0 ?;1745 :)
% Comments :
%------------------------------------------------------------------------------
thf(ssList_decl,type,
ssList: $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(neq_decl,type,
neq: $i > $i > $o ).
thf(nil_decl,type,
nil: $i ).
thf(tl_decl,type,
tl: $i > $i ).
thf(app_decl,type,
app: $i > $i > $i ).
thf(segmentP_decl,type,
segmentP: $i > $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(skaf44_decl,type,
skaf44: $i > $i ).
thf(skaf69_decl,type,
skaf69: $i > $i ).
thf(skaf55_decl,type,
skaf55: $i > $i ).
thf(skaf70_decl,type,
skaf70: $i > $i ).
thf(skaf60_decl,type,
skaf60: $i > $i ).
thf(skaf49_decl,type,
skaf49: $i > $i ).
thf(skaf83_decl,type,
skaf83: $i > $i ).
thf(skaf74_decl,type,
skaf74: $i > $i ).
thf(skaf54_decl,type,
skaf54: $i > $i ).
thf(skaf65_decl,type,
skaf65: $i > $i ).
thf(skaf50_decl,type,
skaf50: $i > $i ).
thf(skaf78_decl,type,
skaf78: $i > $i ).
thf(skaf59_decl,type,
skaf59: $i > $i ).
thf(skaf43_decl,type,
skaf43: $i > $i > $i ).
thf(totalorderedP_decl,type,
totalorderedP: $i > $o ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(skaf62_decl,type,
skaf62: $i > $i ).
thf(memberP_decl,type,
memberP: $i > $i > $o ).
thf(strictorderedP_decl,type,
strictorderedP: $i > $o ).
thf(cyclefreeP_decl,type,
cyclefreeP: $i > $o ).
thf(singletonP_decl,type,
singletonP: $i > $o ).
thf(duplicatefreeP_decl,type,
duplicatefreeP: $i > $o ).
thf(skaf75_decl,type,
skaf75: $i > $i ).
thf(skaf76_decl,type,
skaf76: $i > $i ).
thf(skaf77_decl,type,
skaf77: $i > $i ).
thf(skaf72_decl,type,
skaf72: $i > $i ).
thf(hd_decl,type,
hd: $i > $i ).
thf(frontsegP_decl,type,
frontsegP: $i > $i > $o ).
thf(skaf71_decl,type,
skaf71: $i > $i ).
thf(skaf73_decl,type,
skaf73: $i > $i ).
thf(skaf46_decl,type,
skaf46: $i > $i > $i ).
thf(skaf66_decl,type,
skaf66: $i > $i ).
thf(skaf67_decl,type,
skaf67: $i > $i ).
thf(skaf68_decl,type,
skaf68: $i > $i ).
thf(skaf45_decl,type,
skaf45: $i > $i > $i ).
thf(rearsegP_decl,type,
rearsegP: $i > $i > $o ).
thf(strictorderP_decl,type,
strictorderP: $i > $o ).
thf(skaf61_decl,type,
skaf61: $i > $i ).
thf(skaf63_decl,type,
skaf63: $i > $i ).
thf(skaf51_decl,type,
skaf51: $i > $i ).
thf(skaf52_decl,type,
skaf52: $i > $i ).
thf(skaf53_decl,type,
skaf53: $i > $i ).
thf(skaf57_decl,type,
skaf57: $i > $i ).
thf(equalelemsP_decl,type,
equalelemsP: $i > $o ).
thf(totalorderP_decl,type,
totalorderP: $i > $o ).
thf(skaf56_decl,type,
skaf56: $i > $i ).
thf(skaf58_decl,type,
skaf58: $i > $i ).
thf(skaf48_decl,type,
skaf48: $i > $i > $i ).
thf(skaf80_decl,type,
skaf80: $i > $i ).
thf(skaf47_decl,type,
skaf47: $i > $i > $i ).
thf(skaf81_decl,type,
skaf81: $i > $i ).
thf(skaf82_decl,type,
skaf82: $i > $i ).
thf(skaf42_decl,type,
skaf42: $i > $i > $i ).
thf(49,axiom,
! [A: $i] : ( A @ skaf78 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause17) ).
thf(285,plain,
! [A: $i] : ( A @ skaf78 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(123,axiom,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( nil @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause71) ).
thf(464,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(465,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(cnf,[status(esa)],[464]) ).
thf(1573,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[285,465]) ).
thf(1574,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1573]) ).
thf(1575,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1574:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(1586,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1575]) ).
thf(192,axiom,
! [B: $i,A: $i] :
( ( nil = A )
| ( A = B )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( A @ hd )
!= ( B @ hd ) )
| ( ( A @ tl )
!= ( B @ tl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause177) ).
thf(629,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)],[192]) ).
thf(37,axiom,
! [A: $i] : ( A @ skaf74 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause21) ).
thf(265,plain,
! [A: $i] : ( A @ skaf74 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(52,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause113) ).
thf(288,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(289,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(cnf,[status(esa)],[288]) ).
thf(290,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[289]) ).
thf(291,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[290]) ).
thf(70,axiom,
nil @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
thf(335,plain,
nil @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(13103,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ $true ),
inference(rewrite,[status(thm)],[291,335]) ).
thf(13104,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[13103]) ).
thf(13135,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[265,13104]) ).
thf(13136,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[13135]) ).
thf(13137,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[13136:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(13199,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[13137]) ).
thf(83,axiom,
! [A: $i] : ( A @ skaf57 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause38) ).
thf(365,plain,
! [A: $i] : ( A @ skaf57 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(66,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf46 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause50) ).
thf(324,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf46 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(72,axiom,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause58) ).
thf(339,plain,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(340,plain,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[339]) ).
thf(11288,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf46 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[324,340]) ).
thf(11289,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf46 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[11288]) ).
thf(11290,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf46 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[11289:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf46 ) ))]]) ).
thf(11372,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf46 ) @ rearsegP ) ),
inference(simp,[status(thm)],[11290]) ).
thf(75,axiom,
nil @ strictorderP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause5) ).
thf(347,plain,
nil @ strictorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(28,axiom,
! [A: $i] : ( A @ skaf55 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause40) ).
thf(249,plain,
! [A: $i] : ( A @ skaf55 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(147,axiom,
! [A: $i] : ( A @ skaf67 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause28) ).
thf(518,plain,
! [A: $i] : ( A @ skaf67 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ segmentP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ segmentP ) )
| ~ ( B @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause152) ).
thf(468,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ segmentP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ segmentP ) )
| ~ ( B @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause126) ).
thf(234,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)],[20]) ).
thf(77,axiom,
! [A: $i] : ( A @ skaf77 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause18) ).
thf(352,plain,
! [A: $i] : ( A @ skaf77 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(35,axiom,
! [A: $i] : ( A @ skaf83 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause12) ).
thf(261,plain,
! [A: $i] : ( A @ skaf83 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause111) ).
thf(277,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(278,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[277]) ).
thf(279,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[278]) ).
thf(280,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[279]) ).
thf(12510,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[261,280]) ).
thf(12511,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[12510]) ).
thf(12512,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( A @ skaf83 @ lt ) ),
inference(pattern_uni,[status(thm)],[12511:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(12564,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( A @ skaf83 @ lt ) ),
inference(simp,[status(thm)],[12512]) ).
thf(2,negated_conjecture,
sk2 @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
thf(203,plain,
sk2 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(67,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause75) ).
thf(325,plain,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(326,plain,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[325]) ).
thf(327,plain,
! [A: $i] :
( ( A @ tl @ ssList )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[326]) ).
thf(23889,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[203,327]) ).
thf(23890,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[23889]) ).
thf(23891,plain,
( ( sk2 @ tl @ ssList )
| ( nil = sk2 ) ),
inference(pattern_uni,[status(thm)],[23890:[bind(A,$thf( sk2 ))]]) ).
thf(7,negated_conjecture,
( ( nil @ ( sk2 @ neq ) )
| ( nil @ ( sk2 @ neq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
thf(205,plain,
nil @ ( sk2 @ neq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause115) ).
thf(292,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(293,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[292]) ).
thf(294,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[293]) ).
thf(295,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[294]) ).
thf(13527,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[335,295]) ).
thf(13528,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[13527]) ).
thf(13529,plain,
~ ( nil @ ( nil @ neq ) ),
inference(pattern_uni,[status(thm)],[13528:[bind(A,$thf( nil ))]]) ).
thf(13614,plain,
( ( ( nil @ ( nil @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[205,13529]) ).
thf(13615,plain,
( ( nil @ ( nil @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[13614]) ).
thf(13624,plain,
( ( nil != nil )
| ( nil != sk2 ) ),
inference(simp,[status(thm)],[13615]) ).
thf(13630,plain,
nil != sk2,
inference(simp,[status(thm)],[13624]) ).
thf(24804,plain,
sk2 @ tl @ ssList,
inference(simplifyReflect,[status(thm)],[23891,13630]) ).
thf(130,axiom,
! [A: $i] : ( A @ skaf75 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause20) ).
thf(479,plain,
! [A: $i] : ( A @ skaf75 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(42,axiom,
! [A: $i] : ( A @ skaf50 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause45) ).
thf(272,plain,
! [A: $i] : ( A @ skaf50 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(12555,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[272,280]) ).
thf(12556,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[12555]) ).
thf(12557,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( A @ skaf50 @ lt ) ),
inference(pattern_uni,[status(thm)],[12556:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(12570,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( A @ skaf50 @ lt ) ),
inference(simp,[status(thm)],[12557]) ).
thf(24,axiom,
! [A: $i] : ( A @ skaf44 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause47) ).
thf(243,plain,
! [A: $i] : ( A @ skaf44 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(772,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[243,465]) ).
thf(773,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[772]) ).
thf(774,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[773:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(777,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[774]) ).
thf(160,axiom,
! [A: $i] : ( A @ skaf51 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause44) ).
thf(555,plain,
! [A: $i] : ( A @ skaf51 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(11256,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[479,340]) ).
thf(11257,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[11256]) ).
thf(11258,plain,
! [A: $i] : ( nil @ ( A @ skaf75 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[11257:[bind(A,$thf( C )),bind(B,$thf( C @ skaf75 ))]]) ).
thf(11385,plain,
! [A: $i] : ( nil @ ( A @ skaf75 @ rearsegP ) ),
inference(simp,[status(thm)],[11258]) ).
thf(31,axiom,
! [A: $i] : ( A @ skaf60 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause35) ).
thf(254,plain,
! [A: $i] : ( A @ skaf60 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(12561,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[254,280]) ).
thf(12562,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[12561]) ).
thf(12563,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( A @ skaf60 @ lt ) ),
inference(pattern_uni,[status(thm)],[12562:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(12575,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( A @ skaf60 @ lt ) ),
inference(simp,[status(thm)],[12563]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause88) ).
thf(301,plain,
! [A: $i] :
( ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(302,plain,
! [A: $i] :
( ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[301]) ).
thf(15096,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[203,302]) ).
thf(15097,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP ) ),
inference(simp,[status(thm)],[15096]) ).
thf(15098,plain,
( ( sk2 @ skaf50 @ ( sk2 @ skaf49 @ leq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[15097:[bind(A,$thf( sk2 ))]]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause62) ).
thf(275,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(276,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[275]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause72) ).
thf(361,plain,
! [B: $i,A: $i] :
( ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(362,plain,
! [B: $i,A: $i] :
( ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[361]) ).
thf(9739,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ( C @ ssItem )
| ( B @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[352,362]) ).
thf(9740,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ( C @ ssItem )
| ( B @ duplicatefreeP ) ),
inference(simp,[status(thm)],[9739]) ).
thf(9741,plain,
! [B: $i,A: $i] :
( ( A @ ssItem )
| ( B @ skaf77 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[9740:[bind(A,$thf( D )),bind(B,$thf( D @ skaf77 ))]]) ).
thf(9924,plain,
! [B: $i,A: $i] :
( ( A @ ssItem )
| ( B @ skaf77 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[9741]) ).
thf(50,axiom,
! [A: $i] : ( A @ skaf59 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause36) ).
thf(286,plain,
! [A: $i] : ( A @ skaf59 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(12259,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[286,276]) ).
thf(12260,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[12259]) ).
thf(12261,plain,
! [A: $i] : ( A @ skaf59 @ ( A @ skaf59 @ leq ) ),
inference(pattern_uni,[status(thm)],[12260:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(12299,plain,
! [A: $i] : ( A @ skaf59 @ ( A @ skaf59 @ leq ) ),
inference(simp,[status(thm)],[12261]) ).
thf(59,axiom,
! [A: $i] :
( ( ( A @ skaf77 @ ( A @ skaf74 @ cons ) @ ( A @ skaf76 @ ( A @ skaf74 @ cons ) @ ( A @ skaf75 @ app ) @ app ) )
= A )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause162) ).
thf(306,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)],[59]) ).
thf(307,plain,
! [A: $i] :
( ( ( A @ skaf77 @ ( A @ skaf74 @ cons ) @ ( A @ skaf76 @ ( A @ skaf74 @ cons ) @ ( A @ skaf75 @ app ) @ app ) )
= A )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[306]) ).
thf(308,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)],[307]) ).
thf(9730,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ( C @ ssItem )
| ( B @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[365,362]) ).
thf(9731,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ( C @ ssItem )
| ( B @ duplicatefreeP ) ),
inference(simp,[status(thm)],[9730]) ).
thf(9732,plain,
! [B: $i,A: $i] :
( ( A @ ssItem )
| ( B @ skaf57 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[9731:[bind(A,$thf( D )),bind(B,$thf( D @ skaf57 ))]]) ).
thf(9918,plain,
! [B: $i,A: $i] :
( ( A @ ssItem )
| ( B @ skaf57 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[9732]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ geq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause148) ).
thf(246,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)],[26]) ).
thf(247,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)],[246]) ).
thf(13483,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[518,295]) ).
thf(13484,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[13483]) ).
thf(13485,plain,
! [A: $i] :
~ ( A @ skaf67 @ ( A @ skaf67 @ neq ) ),
inference(pattern_uni,[status(thm)],[13484:[bind(A,$thf( C )),bind(B,$thf( C @ skaf67 ))]]) ).
thf(13586,plain,
! [A: $i] :
~ ( A @ skaf67 @ ( A @ skaf67 @ neq ) ),
inference(simp,[status(thm)],[13485]) ).
thf(144,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf47 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause49) ).
thf(511,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf47 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(24861,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24804,362]) ).
thf(24862,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP ) ),
inference(simp,[status(thm)],[24861]) ).
thf(24863,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk2 @ tl @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[24862:[bind(A,$thf( sk2 @ tl )),bind(B,$thf( B ))]]) ).
thf(24907,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk2 @ tl @ duplicatefreeP ) ),
inference(simp,[status(thm)],[24863]) ).
thf(187,axiom,
! [A: $i] :
( ( A @ equalelemsP )
| ~ ( A @ ssList )
| ( ( A @ skaf79 )
!= ( A @ skaf78 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause89) ).
thf(614,plain,
! [A: $i] :
( ( A @ equalelemsP )
| ~ ( A @ ssList )
| ( ( A @ skaf79 )
!= ( A @ skaf78 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(40,axiom,
! [A: $i] : ( A @ skaf65 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause30) ).
thf(269,plain,
! [A: $i] : ( A @ skaf65 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(9,negated_conjecture,
! [B: $i,A: $i] :
( ( nil @ ( sk2 @ neq ) )
| ~ ( sk4 @ ( nil @ neq ) )
| ( ( B @ ( sk3 @ app ) )
!= A )
| ( ( sk4 @ tl )
!= B )
| ~ ( B @ ssList )
| ( sk4 = A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
thf(202,plain,
! [B: $i,A: $i] :
( ( nil @ ( sk2 @ neq ) )
| ~ ( sk4 @ ( nil @ neq ) )
| ( ( B @ ( sk3 @ app ) )
!= A )
| ( ( sk4 @ tl )
!= B )
| ~ ( B @ ssList )
| ( sk4 = A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(178,axiom,
! [A: $i] : ( A @ skaf56 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause39) ).
thf(597,plain,
! [A: $i] : ( A @ skaf56 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(39,axiom,
! [A: $i] : ( A @ skaf54 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause41) ).
thf(268,plain,
! [A: $i] : ( A @ skaf54 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ ( A @ geq ) )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause55) ).
thf(244,plain,
! [A: $i] :
( ( A @ ( A @ geq ) )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(245,plain,
! [A: $i] :
( ( A @ ( A @ geq ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[244]) ).
thf(4452,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[268,245]) ).
thf(4453,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[4452]) ).
thf(4454,plain,
! [A: $i] : ( A @ skaf54 @ ( A @ skaf54 @ geq ) ),
inference(pattern_uni,[status(thm)],[4453:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(4479,plain,
! [A: $i] : ( A @ skaf54 @ ( A @ skaf54 @ geq ) ),
inference(simp,[status(thm)],[4454]) ).
thf(1,negated_conjecture,
sk1 @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
thf(200,plain,
sk1 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(24119,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[200,327]) ).
thf(24120,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[24119]) ).
thf(24121,plain,
( ( sk1 @ tl @ ssList )
| ( nil = sk1 ) ),
inference(pattern_uni,[status(thm)],[24120:[bind(A,$thf( sk1 ))]]) ).
thf(84,axiom,
nil @ equalelemsP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause1) ).
thf(366,plain,
nil @ equalelemsP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(25038,plain,
( ( nil != nil )
| ( sk1 @ equalelemsP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[24121,366]) ).
thf(25039,plain,
( ( sk1 @ equalelemsP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[25038:[]]) ).
thf(92,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ totalorderedP )
| ~ ( B @ hd @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause159) ).
thf(385,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)],[92]) ).
thf(9895,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[200,362]) ).
thf(9896,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP ) ),
inference(simp,[status(thm)],[9895]) ).
thf(9897,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk1 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[9896:[bind(A,$thf( sk1 ))]]) ).
thf(9938,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[9897]) ).
thf(10179,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) )
| ( sk1 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[9938,465]) ).
thf(10180,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[10179]) ).
thf(10181,plain,
! [A: $i] :
( ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[10180:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(158,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ app ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause141) ).
thf(550,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)],[158]) ).
thf(138,axiom,
nil @ totalorderP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause6) ).
thf(500,plain,
nil @ totalorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(10168,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true
| ( sk1 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[9938,245]) ).
thf(10169,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[10168]) ).
thf(10170,plain,
! [A: $i] :
( ( A @ ( A @ geq ) )
| ( sk1 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[10169:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(18,axiom,
! [A: $i] : ( A @ skaf64 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause31) ).
thf(231,plain,
! [A: $i] : ( A @ skaf64 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(12552,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[231,280]) ).
thf(12553,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[12552]) ).
thf(12554,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( A @ skaf64 @ lt ) ),
inference(pattern_uni,[status(thm)],[12553:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(12568,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( A @ skaf64 @ lt ) ),
inference(simp,[status(thm)],[12554]) ).
thf(47,axiom,
skac3 @ ssItem,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause9) ).
thf(282,plain,
skac3 @ ssItem,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause117) ).
thf(331,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(332,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[331]) ).
thf(333,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[332]) ).
thf(334,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[333]) ).
thf(26147,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[282,334]) ).
thf(26148,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[26147]) ).
thf(26149,plain,
~ ( skac3 @ ( skac3 @ neq ) ),
inference(pattern_uni,[status(thm)],[26148:[bind(A,$thf( skac3 ))]]) ).
thf(26239,plain,
( ( ( skac3 @ ( skac3 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[205,26149]) ).
thf(26240,plain,
( ( skac3 @ ( skac3 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[26239]) ).
thf(26257,plain,
( ( skac3 != nil )
| ( skac3 != sk2 ) ),
inference(simp,[status(thm)],[26240]) ).
thf(235,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
inference(cnf,[status(esa)],[234]) ).
thf(236,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[235]) ).
thf(12,negated_conjecture,
( ~ ( nil @ ( sk4 @ neq ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
thf(204,plain,
( ~ ( nil @ ( sk4 @ neq ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(214,plain,
( ~ ( nil @ ( sk4 @ neq ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(cnf,[status(esa)],[204]) ).
thf(5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
thf(198,plain,
sk2 = sk4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(216,plain,
sk4 = sk2,
inference(lifteq,[status(thm)],[198]) ).
thf(646,plain,
( ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(rewrite,[status(thm)],[214,216]) ).
thf(649,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[205,646]) ).
thf(650,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[649]) ).
thf(651,plain,
( ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[650:[]]) ).
thf(654,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[205,651]) ).
thf(655,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) ) ),
inference(simp,[status(thm)],[654]) ).
thf(656,plain,
( ( nil != nil )
| ( sk2 != sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) ) ),
inference(simp,[status(thm)],[655]) ).
thf(657,plain,
( ( sk2 != sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) ) ),
inference(simp,[status(thm)],[656]) ).
thf(2133,plain,
! [B: $i,A: $i] :
( ( B != sk2 )
| ( A != sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
inference(paramod_ordered,[status(thm)],[236,657]) ).
thf(2134,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( sk2 @ geq ) )
| ~ ( sk2 @ ( A @ geq ) ) ),
inference(pattern_uni,[status(thm)],[2133:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(2470,plain,
( ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ssItem )
| ~ ( sk1 @ ssItem )
| ~ ( sk1 @ ( sk2 @ geq ) )
| ~ ( sk2 @ ( sk1 @ geq ) ) ),
inference(simp,[status(thm)],[2134]) ).
thf(2841,plain,
( ( ( skac3 @ ssItem )
!= ( sk1 @ ssItem ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ssItem )
| ~ $true
| ~ ( sk1 @ ( sk2 @ geq ) )
| ~ ( sk2 @ ( sk1 @ geq ) ) ),
inference(paramod_ordered,[status(thm)],[282,2470]) ).
thf(2842,plain,
( ( ( skac3 @ ssItem )
!= ( sk1 @ ssItem ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ssItem )
| ~ ( sk1 @ ( sk2 @ geq ) )
| ~ ( sk2 @ ( sk1 @ geq ) ) ),
inference(simp,[status(thm)],[2841]) ).
thf(2972,plain,
( ( skac3 != sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ssItem )
| ~ ( sk1 @ ( sk2 @ geq ) )
| ~ ( sk2 @ ( sk1 @ geq ) ) ),
inference(simp,[status(thm)],[2842]) ).
thf(13157,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[285,13104]) ).
thf(13158,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[13157]) ).
thf(13159,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[13158:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(13209,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[13159]) ).
thf(12232,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[243,276]) ).
thf(12233,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[12232]) ).
thf(12234,plain,
! [A: $i] : ( A @ skaf44 @ ( A @ skaf44 @ leq ) ),
inference(pattern_uni,[status(thm)],[12233:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(12303,plain,
! [A: $i] : ( A @ skaf44 @ ( A @ skaf44 @ leq ) ),
inference(simp,[status(thm)],[12234]) ).
thf(90,axiom,
nil @ duplicatefreeP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause2) ).
thf(381,plain,
nil @ duplicatefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(25034,plain,
( ( nil != nil )
| ( sk1 @ duplicatefreeP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[24121,381]) ).
thf(25035,plain,
( ( sk1 @ duplicatefreeP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[25034:[]]) ).
thf(65,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( F @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause181) ).
thf(320,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)],[65]) ).
thf(4410,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[243,245]) ).
thf(4411,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[4410]) ).
thf(4412,plain,
! [A: $i] : ( A @ skaf44 @ ( A @ skaf44 @ geq ) ),
inference(pattern_uni,[status(thm)],[4411:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(4496,plain,
! [A: $i] : ( A @ skaf44 @ ( A @ skaf44 @ geq ) ),
inference(simp,[status(thm)],[4412]) ).
thf(13177,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[282,13104]) ).
thf(13178,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[13177]) ).
thf(13179,plain,
nil @ ( skac3 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[13178:[bind(A,$thf( skac3 ))]]) ).
thf(88,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf45 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause51) ).
thf(377,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf45 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(11316,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[377,340]) ).
thf(11317,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[11316]) ).
thf(11318,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf45 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[11317:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf45 ) ))]]) ).
thf(11382,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf45 ) @ rearsegP ) ),
inference(simp,[status(thm)],[11318]) ).
thf(33,axiom,
! [A: $i] : ( A @ skaf49 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause46) ).
thf(257,plain,
! [A: $i] : ( A @ skaf49 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(74,axiom,
! [A: $i] :
( ( ( A @ skaf63 @ ( A @ skaf60 @ cons ) @ ( A @ skaf62 @ ( A @ skaf59 @ cons ) @ ( A @ skaf61 @ app ) @ app ) )
= A )
| ( A @ strictorderP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause165) ).
thf(344,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)],[74]) ).
thf(12534,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[285,280]) ).
thf(12535,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[12534]) ).
thf(12536,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( A @ skaf78 @ lt ) ),
inference(pattern_uni,[status(thm)],[12535:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(12578,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( A @ skaf78 @ lt ) ),
inference(simp,[status(thm)],[12536]) ).
thf(46,axiom,
skac2 @ ssItem,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause10) ).
thf(281,plain,
skac2 @ ssItem,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(4426,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[281,245]) ).
thf(4427,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) ) ),
inference(simp,[status(thm)],[4426]) ).
thf(4428,plain,
skac2 @ ( skac2 @ geq ),
inference(pattern_uni,[status(thm)],[4427:[bind(A,$thf( skac2 ))]]) ).
thf(156,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ frontsegP ) )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause144) ).
thf(542,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)],[156]) ).
thf(121,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ totalorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause135) ).
thf(460,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ totalorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(196,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ strictorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause124) ).
thf(638,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)],[196]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause130) ).
thf(250,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)],[29]) ).
thf(251,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[250]) ).
thf(252,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[251]) ).
thf(13,axiom,
skac3 != skac2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause54) ).
thf(221,plain,
skac3 != skac2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(222,plain,
skac3 != skac2,
inference(polarity_switch,[status(thm)],[221]) ).
thf(223,plain,
skac2 != skac3,
inference(lifteq,[status(thm)],[222]) ).
thf(6251,plain,
! [B: $i,A: $i] :
( ( B != skac2 )
| ( A != skac3 )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[252,223]) ).
thf(6252,plain,
! [A: $i] :
( ( A != skac3 )
| ~ ( skac2 @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( skac2 @ leq ) )
| ~ ( skac2 @ ( A @ leq ) ) ),
inference(pattern_uni,[status(thm)],[6251:[bind(A,$thf( A )),bind(B,$thf( skac2 ))]]) ).
thf(6544,plain,
( ~ ( skac2 @ ssItem )
| ~ ( skac3 @ ssItem )
| ~ ( skac3 @ ( skac2 @ leq ) )
| ~ ( skac2 @ ( skac3 @ leq ) ) ),
inference(simp,[status(thm)],[6252]) ).
thf(15392,plain,
( ~ $true
| ~ $true
| ~ ( skac3 @ ( skac2 @ leq ) )
| ~ ( skac2 @ ( skac3 @ leq ) ) ),
inference(rewrite,[status(thm)],[6544,281,282]) ).
thf(15393,plain,
( ~ ( skac3 @ ( skac2 @ leq ) )
| ~ ( skac2 @ ( skac3 @ leq ) ) ),
inference(simp,[status(thm)],[15392]) ).
thf(15472,plain,
( ~ $true
| ( ( skac3 @ ( skac2 @ leq ) )
!= ( skac2 @ ( skac3 @ leq ) ) )
| ~ ( skac2 @ ( skac3 @ leq ) ) ),
inference(eqfactor_ordered,[status(thm)],[15393]) ).
thf(15477,plain,
( ( ( skac3 @ ( skac2 @ leq ) )
!= ( skac2 @ ( skac3 @ leq ) ) )
| ~ ( skac2 @ ( skac3 @ leq ) ) ),
inference(simp,[status(thm)],[15472]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause119) ).
thf(421,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(102,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ app ) @ rearsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause136) ).
thf(416,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)],[102]) ).
thf(16,axiom,
! [A: $i] : ( A @ skaf79 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause16) ).
thf(228,plain,
! [A: $i] : ( A @ skaf79 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(115,axiom,
! [A: $i] :
( ( A @ skaf49 @ ( A @ skaf50 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause87) ).
thf(448,plain,
! [A: $i] :
( ( A @ skaf49 @ ( A @ skaf50 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(63,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ frontsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause154) ).
thf(315,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)],[63]) ).
thf(316,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)],[315]) ).
thf(109,axiom,
! [A: $i] : ( A @ skaf61 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause34) ).
thf(433,plain,
! [A: $i] : ( A @ skaf61 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(11337,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[433,340]) ).
thf(11338,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[11337]) ).
thf(11339,plain,
! [A: $i] : ( nil @ ( A @ skaf61 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[11338:[bind(A,$thf( C )),bind(B,$thf( C @ skaf61 ))]]) ).
thf(11363,plain,
! [A: $i] : ( nil @ ( A @ skaf61 @ rearsegP ) ),
inference(simp,[status(thm)],[11339]) ).
thf(4404,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[261,245]) ).
thf(4405,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[4404]) ).
thf(4406,plain,
! [A: $i] : ( A @ skaf83 @ ( A @ skaf83 @ geq ) ),
inference(pattern_uni,[status(thm)],[4405:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(4492,plain,
! [A: $i] : ( A @ skaf83 @ ( A @ skaf83 @ geq ) ),
inference(simp,[status(thm)],[4406]) ).
thf(164,axiom,
! [A: $i] : ( A @ skaf66 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause29) ).
thf(562,plain,
! [A: $i] : ( A @ skaf66 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(11303,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[562,340]) ).
thf(11304,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[11303]) ).
thf(11305,plain,
! [A: $i] : ( nil @ ( A @ skaf66 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[11304:[bind(A,$thf( C )),bind(B,$thf( C @ skaf66 ))]]) ).
thf(11378,plain,
! [A: $i] : ( nil @ ( A @ skaf66 @ rearsegP ) ),
inference(simp,[status(thm)],[11305]) ).
thf(9865,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[203,362]) ).
thf(9866,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP ) ),
inference(simp,[status(thm)],[9865]) ).
thf(9867,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk2 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[9866:[bind(A,$thf( sk2 ))]]) ).
thf(9923,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[9867]) ).
thf(13132,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true
| ( sk2 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[9923,13104]) ).
thf(13133,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[13132]) ).
thf(13134,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk2 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[13133:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(54,axiom,
! [A: $i] : ( A @ skaf62 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause33) ).
thf(296,plain,
! [A: $i] : ( A @ skaf62 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(13515,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[296,295]) ).
thf(13516,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[13515]) ).
thf(13517,plain,
! [A: $i] :
~ ( A @ skaf62 @ ( A @ skaf62 @ neq ) ),
inference(pattern_uni,[status(thm)],[13516:[bind(A,$thf( C )),bind(B,$thf( C @ skaf62 ))]]) ).
thf(13575,plain,
! [A: $i] :
~ ( A @ skaf62 @ ( A @ skaf62 @ neq ) ),
inference(simp,[status(thm)],[13517]) ).
thf(13123,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[261,13104]) ).
thf(13124,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[13123]) ).
thf(13125,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[13124:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(13195,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[13125]) ).
thf(30,axiom,
! [A: $i] : ( A @ skaf70 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause25) ).
thf(253,plain,
! [A: $i] : ( A @ skaf70 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause105) ).
thf(237,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(238,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ gt ) ) ),
inference(cnf,[status(esa)],[237]) ).
thf(12235,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true
| ( sk2 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[9923,276]) ).
thf(12236,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[12235]) ).
thf(12237,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ( sk2 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[12236:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(146,axiom,
~ ( nil @ singletonP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause11) ).
thf(516,plain,
~ ( nil @ singletonP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(517,plain,
~ ( nil @ singletonP ),
inference(polarity_switch,[status(thm)],[516]) ).
thf(25239,plain,
( ( nil != nil )
| ~ ( sk1 @ singletonP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[24121,517]) ).
thf(25240,plain,
( ~ ( sk1 @ singletonP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[25239:[]]) ).
thf(78,axiom,
! [A: $i] :
( ( ( A @ skaf53 @ ( A @ skaf50 @ cons ) @ ( A @ skaf52 @ ( A @ skaf49 @ cons ) @ ( A @ skaf51 @ app ) @ app ) )
= A )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause167) ).
thf(353,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)],[78]) ).
thf(131,axiom,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause79) ).
thf(480,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(176,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ app ) @ hd )
= ( B @ hd ) )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause123) ).
thf(591,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)],[176]) ).
thf(13489,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[555,295]) ).
thf(13490,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[13489]) ).
thf(13491,plain,
! [A: $i] :
~ ( A @ skaf51 @ ( A @ skaf51 @ neq ) ),
inference(pattern_uni,[status(thm)],[13490:[bind(A,$thf( C )),bind(B,$thf( C @ skaf51 ))]]) ).
thf(13590,plain,
! [A: $i] :
~ ( A @ skaf51 @ ( A @ skaf51 @ neq ) ),
inference(simp,[status(thm)],[13491]) ).
thf(76,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ssList )
| ~ ( F @ cyclefreeP )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) )
!= F )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause185) ).
thf(348,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)],[76]) ).
thf(169,axiom,
! [A: $i] :
( ( nil = A )
| ( ( A @ skaf82 @ ( A @ skaf83 @ cons ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause109) ).
thf(574,plain,
! [A: $i] :
( ( nil = A )
| ( ( A @ skaf82 @ ( A @ skaf83 @ cons ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(181,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ skaf43 ) @ ( B @ cons ) @ ( B @ ( A @ skaf42 ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause169) ).
thf(602,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)],[181]) ).
thf(12285,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[272,276]) ).
thf(12286,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[12285]) ).
thf(12287,plain,
! [A: $i] : ( A @ skaf50 @ ( A @ skaf50 @ leq ) ),
inference(pattern_uni,[status(thm)],[12286:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(12311,plain,
! [A: $i] : ( A @ skaf50 @ ( A @ skaf50 @ leq ) ),
inference(simp,[status(thm)],[12287]) ).
thf(184,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf42 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause53) ).
thf(608,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf42 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(11319,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf42 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[608,340]) ).
thf(11320,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf42 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[11319]) ).
thf(11321,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf42 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[11320:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf42 ) ))]]) ).
thf(11384,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf42 ) @ rearsegP ) ),
inference(simp,[status(thm)],[11321]) ).
thf(100,axiom,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf54 @ ( A @ skaf55 @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause94) ).
thf(411,plain,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf54 @ ( A @ skaf55 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(107,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause98) ).
thf(428,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(105,axiom,
! [A: $i] : ( A @ skaf73 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause22) ).
thf(424,plain,
! [A: $i] : ( A @ skaf73 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(11281,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[424,340]) ).
thf(11282,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[11281]) ).
thf(11283,plain,
! [A: $i] : ( nil @ ( A @ skaf73 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[11282:[bind(A,$thf( C )),bind(B,$thf( C @ skaf73 ))]]) ).
thf(11367,plain,
! [A: $i] : ( nil @ ( A @ skaf73 @ rearsegP ) ),
inference(simp,[status(thm)],[11283]) ).
thf(27,axiom,
! [A: $i] : ( A @ skaf69 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause26) ).
thf(248,plain,
! [A: $i] : ( A @ skaf69 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(12241,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[248,276]) ).
thf(12242,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[12241]) ).
thf(12243,plain,
! [A: $i] : ( A @ skaf69 @ ( A @ skaf69 @ leq ) ),
inference(pattern_uni,[status(thm)],[12242:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(12306,plain,
! [A: $i] : ( A @ skaf69 @ ( A @ skaf69 @ leq ) ),
inference(simp,[status(thm)],[12243]) ).
thf(1227,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[272,465]) ).
thf(1228,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1227]) ).
thf(1229,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1228:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(1242,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1229]) ).
thf(12220,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true
| ( sk1 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[9938,276]) ).
thf(12221,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[12220]) ).
thf(12222,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ( sk1 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[12221:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(13111,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[269,13104]) ).
thf(13112,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[13111]) ).
thf(13113,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[13112:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(13216,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[13113]) ).
thf(11265,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[555,340]) ).
thf(11266,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[11265]) ).
thf(11267,plain,
! [A: $i] : ( nil @ ( A @ skaf51 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[11266:[bind(A,$thf( C )),bind(B,$thf( C @ skaf51 ))]]) ).
thf(11357,plain,
! [A: $i] : ( nil @ ( A @ skaf51 @ rearsegP ) ),
inference(simp,[status(thm)],[11267]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause134) ).
thf(312,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(3,negated_conjecture,
sk3 @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
thf(206,plain,
sk3 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4382,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[285,245]) ).
thf(4383,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[4382]) ).
thf(4384,plain,
! [A: $i] : ( A @ skaf78 @ ( A @ skaf78 @ geq ) ),
inference(pattern_uni,[status(thm)],[4383:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(4475,plain,
! [A: $i] : ( A @ skaf78 @ ( A @ skaf78 @ geq ) ),
inference(simp,[status(thm)],[4384]) ).
thf(157,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ leq ) )
| ~ ( F @ ssList )
| ~ ( F @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause182) ).
thf(546,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)],[157]) ).
thf(6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
thf(201,plain,
sk1 = sk3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(13138,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[248,13104]) ).
thf(13139,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[13138]) ).
thf(13140,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[13139:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(13200,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[13140]) ).
thf(12291,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[254,276]) ).
thf(12292,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[12291]) ).
thf(12293,plain,
! [A: $i] : ( A @ skaf60 @ ( A @ skaf60 @ leq ) ),
inference(pattern_uni,[status(thm)],[12292:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(12300,plain,
! [A: $i] : ( A @ skaf60 @ ( A @ skaf60 @ leq ) ),
inference(simp,[status(thm)],[12293]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause90) ).
thf(299,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(300,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(cnf,[status(esa)],[299]) ).
thf(14535,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ~ $true
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[203,300]) ).
thf(14536,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(simp,[status(thm)],[14535]) ).
thf(14537,plain,
( ( sk2 @ strictorderedP )
| ~ ( sk2 @ skaf70 @ ( sk2 @ skaf69 @ lt ) ) ),
inference(pattern_uni,[status(thm)],[14536:[bind(A,$thf( sk2 ))]]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause155) ).
thf(232,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)],[19]) ).
thf(233,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)],[232]) ).
thf(117,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ frontsegP ) )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( D @ ( C @ cons ) @ ( B @ ( A @ cons ) @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause174) ).
thf(452,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)],[117]) ).
thf(145,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ lt ) )
| ( D @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( F @ strictorderP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause183) ).
thf(512,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)],[145]) ).
thf(112,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ strictorderedP )
| ~ ( B @ hd @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause160) ).
thf(439,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)],[112]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause114) ).
thf(270,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(152,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause65) ).
thf(529,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(4391,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[269,245]) ).
thf(4392,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[4391]) ).
thf(4393,plain,
! [A: $i] : ( A @ skaf65 @ ( A @ skaf65 @ geq ) ),
inference(pattern_uni,[status(thm)],[4392:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(4480,plain,
! [A: $i] : ( A @ skaf65 @ ( A @ skaf65 @ geq ) ),
inference(simp,[status(thm)],[4393]) ).
thf(919,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[253,465]) ).
thf(920,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[919]) ).
thf(921,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[920:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(925,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[921]) ).
thf(12540,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( A @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[281,280]) ).
thf(12541,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[12540]) ).
thf(12542,plain,
~ ( skac2 @ ( skac2 @ lt ) ),
inference(pattern_uni,[status(thm)],[12541:[bind(A,$thf( skac2 ))]]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause122) ).
thf(258,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)],[34]) ).
thf(259,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[258]) ).
thf(260,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ leq ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[259]) ).
thf(179,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( D @ ( C @ cons ) @ ( B @ ( A @ cons ) @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause176) ).
thf(598,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)],[179]) ).
thf(95,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ skaf46 ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause131) ).
thf(392,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)],[95]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ memberP ) )
| ( C @ ( B @ memberP ) )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ( B @ ( A @ app ) @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause158) ).
thf(297,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)],[55]) ).
thf(99,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ cons ) @ ( A @ ( C @ cons ) @ frontsegP ) )
| ~ ( C @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( C != D )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause178) ).
thf(407,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)],[99]) ).
thf(13180,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[231,13104]) ).
thf(13181,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[13180]) ).
thf(13182,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[13181:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(13218,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[13182]) ).
thf(24994,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( nil = sk1 ) ),
inference(paramod_ordered,[status(thm)],[24121,340]) ).
thf(24995,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( nil = sk1 ) ),
inference(simp,[status(thm)],[24994]) ).
thf(24996,plain,
( ( nil @ ( sk1 @ tl @ rearsegP ) )
| ( nil = sk1 ) ),
inference(pattern_uni,[status(thm)],[24995:[bind(A,$thf( sk1 @ tl ))]]) ).
thf(163,axiom,
! [A: $i] : ( A @ skaf63 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause32) ).
thf(561,plain,
! [A: $i] : ( A @ skaf63 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(12498,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[269,280]) ).
thf(12499,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[12498]) ).
thf(12500,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( A @ skaf65 @ lt ) ),
inference(pattern_uni,[status(thm)],[12499:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(12576,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( A @ skaf65 @ lt ) ),
inference(simp,[status(thm)],[12500]) ).
thf(2893,plain,
( ( ( skac2 @ ssItem )
!= ( sk2 @ ssItem ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ $true
| ~ ( sk1 @ ssItem )
| ~ ( sk1 @ ( sk2 @ geq ) )
| ~ ( sk2 @ ( sk1 @ geq ) ) ),
inference(paramod_ordered,[status(thm)],[281,2470]) ).
thf(2894,plain,
( ( ( skac2 @ ssItem )
!= ( sk2 @ ssItem ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ ssItem )
| ~ ( sk1 @ ( sk2 @ geq ) )
| ~ ( sk2 @ ( sk1 @ geq ) ) ),
inference(simp,[status(thm)],[2893]) ).
thf(2969,plain,
( ( skac2 != sk2 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ ssItem )
| ~ ( sk1 @ ( sk2 @ geq ) )
| ~ ( sk2 @ ( sk1 @ geq ) ) ),
inference(simp,[status(thm)],[2894]) ).
thf(15116,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[200,302]) ).
thf(15117,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP ) ),
inference(simp,[status(thm)],[15116]) ).
thf(15118,plain,
( ( sk1 @ skaf50 @ ( sk1 @ skaf49 @ leq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[15117:[bind(A,$thf( sk1 ))]]) ).
thf(60,axiom,
! [A: $i] : ( A @ skaf72 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause23) ).
thf(309,plain,
! [A: $i] : ( A @ skaf72 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(11349,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[309,340]) ).
thf(11350,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[11349]) ).
thf(11351,plain,
! [A: $i] : ( nil @ ( A @ skaf72 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[11350:[bind(A,$thf( C )),bind(B,$thf( C @ skaf72 ))]]) ).
thf(11371,plain,
! [A: $i] : ( nil @ ( A @ skaf72 @ rearsegP ) ),
inference(simp,[status(thm)],[11351]) ).
thf(150,axiom,
! [A: $i] : ( A @ skaf81 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause14) ).
thf(524,plain,
! [A: $i] : ( A @ skaf81 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(13542,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[524,295]) ).
thf(13543,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[13542]) ).
thf(13544,plain,
! [A: $i] :
~ ( A @ skaf81 @ ( A @ skaf81 @ neq ) ),
inference(pattern_uni,[status(thm)],[13543:[bind(A,$thf( C )),bind(B,$thf( C @ skaf81 ))]]) ).
thf(13583,plain,
! [A: $i] :
~ ( A @ skaf81 @ ( A @ skaf81 @ neq ) ),
inference(simp,[status(thm)],[13544]) ).
thf(191,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause112) ).
thf(625,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(11297,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[296,340]) ).
thf(11298,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[11297]) ).
thf(11299,plain,
! [A: $i] : ( nil @ ( A @ skaf62 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[11298:[bind(A,$thf( C )),bind(B,$thf( C @ skaf62 ))]]) ).
thf(11376,plain,
! [A: $i] : ( nil @ ( A @ skaf62 @ rearsegP ) ),
inference(simp,[status(thm)],[11299]) ).
thf(172,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause69) ).
thf(583,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(135,axiom,
! [A: $i] :
( ( nil = A )
| ( ( A @ tl @ ( A @ hd @ cons ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause104) ).
thf(493,plain,
! [A: $i] :
( ( nil = A )
| ( ( A @ tl @ ( A @ hd @ cons ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(12238,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[265,276]) ).
thf(12239,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[12238]) ).
thf(12240,plain,
! [A: $i] : ( A @ skaf74 @ ( A @ skaf74 @ leq ) ),
inference(pattern_uni,[status(thm)],[12239:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(12304,plain,
! [A: $i] : ( A @ skaf74 @ ( A @ skaf74 @ leq ) ),
inference(simp,[status(thm)],[12240]) ).
thf(97,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ app ) )
= nil )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( nil != B )
| ( nil != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause145) ).
thf(399,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)],[97]) ).
thf(400,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ app ) )
= nil )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( nil != B )
| ( nil != A ) ),
inference(cnf,[status(esa)],[399]) ).
thf(401,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
= nil )
| ( nil != B )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[400]) ).
thf(402,plain,
( ~ ( nil @ ssList )
| ( ( nil @ ( nil @ app ) )
= nil ) ),
inference(simp,[status(thm)],[401]) ).
thf(10709,plain,
( ~ $true
| ( ( nil @ ( nil @ app ) )
= nil ) ),
inference(rewrite,[status(thm)],[402,335]) ).
thf(10710,plain,
( ( nil @ ( nil @ app ) )
= nil ),
inference(simp,[status(thm)],[10709]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ geq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause107) ).
thf(229,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(166,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ( ( B @ ( A @ cons ) )
!= ( D @ ( C @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause170) ).
thf(566,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)],[166]) ).
thf(132,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = A )
| ( C @ ( B @ memberP ) )
| ~ ( C @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( C @ ( B @ ( A @ cons ) @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause161) ).
thf(484,plain,
! [C: $i,B: $i,A: $i] :
( ( C = A )
| ( C @ ( B @ memberP ) )
| ~ ( C @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( C @ ( B @ ( A @ cons ) @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(12492,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[249,280]) ).
thf(12493,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[12492]) ).
thf(12494,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( A @ skaf55 @ lt ) ),
inference(pattern_uni,[status(thm)],[12493:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(12571,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( A @ skaf55 @ lt ) ),
inference(simp,[status(thm)],[12494]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause108) ).
thf(224,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(11328,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[524,340]) ).
thf(11329,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[11328]) ).
thf(11330,plain,
! [A: $i] : ( nil @ ( A @ skaf81 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[11329:[bind(A,$thf( C )),bind(B,$thf( C @ skaf81 ))]]) ).
thf(11356,plain,
! [A: $i] : ( nil @ ( A @ skaf81 @ rearsegP ) ),
inference(simp,[status(thm)],[11330]) ).
thf(64,axiom,
! [A: $i] :
( ( ( A @ skaf73 @ ( A @ skaf70 @ cons ) @ ( A @ skaf72 @ ( A @ skaf69 @ cons ) @ ( A @ skaf71 @ app ) @ app ) )
= A )
| ( A @ strictorderedP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause163) ).
thf(317,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)],[64]) ).
thf(4385,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[282,245]) ).
thf(4386,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) ) ),
inference(simp,[status(thm)],[4385]) ).
thf(4387,plain,
skac3 @ ( skac3 @ geq ),
inference(pattern_uni,[status(thm)],[4386:[bind(A,$thf( skac3 ))]]) ).
thf(4500,plain,
( ( ( skac3 @ ( skac3 @ geq ) )
!= ( sk1 @ ( sk2 @ geq ) ) )
| ( skac3 != sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ssItem )
| ~ $true
| ~ ( sk2 @ ( sk1 @ geq ) ) ),
inference(paramod_ordered,[status(thm)],[4387,2972]) ).
thf(4501,plain,
( ( ( skac3 @ ( skac3 @ geq ) )
!= ( sk1 @ ( sk2 @ geq ) ) )
| ( skac3 != sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ssItem )
| ~ ( sk2 @ ( sk1 @ geq ) ) ),
inference(simp,[status(thm)],[4500]) ).
thf(4544,plain,
( ( skac3 != sk1 )
| ( skac3 != sk2 )
| ( skac3 != sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ssItem )
| ~ ( sk2 @ ( sk1 @ geq ) ) ),
inference(simp,[status(thm)],[4501]) ).
thf(4545,plain,
( ( skac3 != sk2 )
| ( skac3 != sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ssItem )
| ~ ( sk2 @ ( sk1 @ geq ) ) ),
inference(simp,[status(thm)],[4544]) ).
thf(4768,plain,
( ( ( skac3 @ ( skac3 @ geq ) )
!= ( sk2 @ ( sk1 @ geq ) ) )
| ( skac3 != sk2 )
| ( skac3 != sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4387,4545]) ).
thf(4769,plain,
( ( ( skac3 @ ( skac3 @ geq ) )
!= ( sk2 @ ( sk1 @ geq ) ) )
| ( skac3 != sk2 )
| ( skac3 != sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ssItem ) ),
inference(simp,[status(thm)],[4768]) ).
thf(4783,plain,
( ( skac3 != sk2 )
| ( skac3 != sk1 )
| ( skac3 != sk2 )
| ( skac3 != sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ssItem ) ),
inference(simp,[status(thm)],[4769]) ).
thf(4808,plain,
( ( skac3 != sk2 )
| ( skac3 != sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ssItem ) ),
inference(simp,[status(thm)],[4783]) ).
thf(5343,plain,
( ( ( skac3 @ ssItem )
!= ( sk2 @ ssItem ) )
| ( skac3 != sk2 )
| ( skac3 != sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[282,4808]) ).
thf(5344,plain,
( ( ( skac3 @ ssItem )
!= ( sk2 @ ssItem ) )
| ( skac3 != sk2 )
| ( skac3 != sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) ) ),
inference(simp,[status(thm)],[5343]) ).
thf(5415,plain,
( ( skac3 != sk2 )
| ( skac3 != sk2 )
| ( skac3 != sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) ) ),
inference(simp,[status(thm)],[5344]) ).
thf(5423,plain,
( ( skac3 != sk2 )
| ( skac3 != sk1 )
| ~ ( sk1 @ ( sk2 @ segmentP ) ) ),
inference(simp,[status(thm)],[5415]) ).
thf(180,axiom,
! [A: $i] : ( A @ skaf71 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause24) ).
thf(601,plain,
! [A: $i] : ( A @ skaf71 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(13518,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[601,295]) ).
thf(13519,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[13518]) ).
thf(13520,plain,
! [A: $i] :
~ ( A @ skaf71 @ ( A @ skaf71 @ neq ) ),
inference(pattern_uni,[status(thm)],[13519:[bind(A,$thf( C )),bind(B,$thf( C @ skaf71 ))]]) ).
thf(13576,plain,
! [A: $i] :
~ ( A @ skaf71 @ ( A @ skaf71 @ neq ) ),
inference(simp,[status(thm)],[13520]) ).
thf(12504,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) )
| ( sk1 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[9938,280]) ).
thf(12505,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[12504]) ).
thf(12506,plain,
! [A: $i] :
( ~ ( A @ ( A @ lt ) )
| ( sk1 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[12505:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(13557,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[200,295]) ).
thf(13558,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[13557]) ).
thf(13559,plain,
~ ( sk1 @ ( sk1 @ neq ) ),
inference(pattern_uni,[status(thm)],[13558:[bind(A,$thf( sk1 ))]]) ).
thf(13700,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk1 @ ( sk1 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[205,13559]) ).
thf(13701,plain,
( ( nil @ ( sk2 @ neq ) )
!= ( sk1 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[13700]) ).
thf(13710,plain,
( ( nil != sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[13701]) ).
thf(25119,plain,
( ( nil != nil )
| ( sk1 != sk1 )
| ( sk2 != sk1 )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[24121,13710]) ).
thf(25120,plain,
( ( nil != nil )
| ( sk2 != sk1 )
| ( sk1 @ tl @ ssList ) ),
inference(simp,[status(thm)],[25119]) ).
thf(25121,plain,
( ( sk2 != sk1 )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[25120:[]]) ).
thf(27188,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) )
| ( sk2 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[25121,295]) ).
thf(27189,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[27188]) ).
thf(27190,plain,
( ~ ( sk1 @ tl @ ( sk1 @ tl @ neq ) )
| ( sk2 != sk1 ) ),
inference(pattern_uni,[status(thm)],[27189:[bind(A,$thf( sk1 @ tl ))]]) ).
thf(27801,plain,
( ( ( sk1 @ tl @ ( sk1 @ tl @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true
| ( sk2 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[205,27190]) ).
thf(27802,plain,
( ( ( sk1 @ tl @ ( sk1 @ tl @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[27801]) ).
thf(27837,plain,
( ( ( sk1 @ tl )
!= nil )
| ( ( sk1 @ tl )
!= sk2 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[27802]) ).
thf(98,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( E @ ssList )
| ~ ( E @ equalelemsP )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( D @ ssList )
| ( ( D @ ( C @ cons ) @ ( B @ cons ) @ ( A @ app ) )
!= E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause180) ).
thf(403,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)],[98]) ).
thf(2289,plain,
! [B: $i,A: $i] :
( ( B != skac2 )
| ( A != skac3 )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
inference(paramod_ordered,[status(thm)],[236,223]) ).
thf(2290,plain,
! [A: $i] :
( ( A != skac3 )
| ~ ( skac2 @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( A @ geq ) ) ),
inference(pattern_uni,[status(thm)],[2289:[bind(A,$thf( A )),bind(B,$thf( skac2 ))]]) ).
thf(2526,plain,
( ~ ( skac2 @ ssItem )
| ~ ( skac3 @ ssItem )
| ~ ( skac3 @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( skac3 @ geq ) ) ),
inference(simp,[status(thm)],[2290]) ).
thf(4208,plain,
( ~ $true
| ~ $true
| ~ ( skac3 @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( skac3 @ geq ) ) ),
inference(rewrite,[status(thm)],[2526,281,282]) ).
thf(4209,plain,
( ~ ( skac3 @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( skac3 @ geq ) ) ),
inference(simp,[status(thm)],[4208]) ).
thf(4232,plain,
( ~ $true
| ( ( skac3 @ ( skac2 @ geq ) )
!= ( skac2 @ ( skac3 @ geq ) ) )
| ~ ( skac2 @ ( skac3 @ geq ) ) ),
inference(eqfactor_ordered,[status(thm)],[4209]) ).
thf(4233,plain,
( ( ( skac3 @ ( skac2 @ geq ) )
!= ( skac2 @ ( skac3 @ geq ) ) )
| ~ ( skac2 @ ( skac3 @ geq ) ) ),
inference(simp,[status(thm)],[4232]) ).
thf(93,axiom,
! [A: $i] :
( ( ( A @ ( nil @ app ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause74) ).
thf(388,plain,
! [A: $i] :
( ( ( A @ ( nil @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(79,axiom,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause82) ).
thf(356,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(137,axiom,
! [A: $i] : ( A @ skaf68 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause27) ).
thf(499,plain,
! [A: $i] : ( A @ skaf68 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(148,axiom,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf60 @ ( A @ skaf59 @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause93) ).
thf(519,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf60 @ ( A @ skaf59 @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(12519,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) )
| ( sk2 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[9923,280]) ).
thf(12520,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[12519]) ).
thf(12521,plain,
! [A: $i] :
( ~ ( A @ ( A @ lt ) )
| ( sk2 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[12520:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(225,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[224]) ).
thf(748,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[228,465]) ).
thf(749,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[748]) ).
thf(750,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[749:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(753,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[750]) ).
thf(128,axiom,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf55 @ ( A @ skaf54 @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause95) ).
thf(476,plain,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf55 @ ( A @ skaf54 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(195,axiom,
nil @ totalorderedP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause4) ).
thf(637,plain,
nil @ totalorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(175,axiom,
! [A: $i] : ( A @ skaf82 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause13) ).
thf(590,plain,
! [A: $i] : ( A @ skaf82 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(1143,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[265,465]) ).
thf(1144,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1143]) ).
thf(1145,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1144:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(1155,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1145]) ).
thf(68,axiom,
! [A: $i] :
( ( ( A @ skaf68 @ ( A @ skaf65 @ cons ) @ ( A @ skaf67 @ ( A @ skaf64 @ cons ) @ ( A @ skaf66 @ app ) @ app ) )
= A )
| ( A @ totalorderedP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause164) ).
thf(328,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)],[68]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause110) ).
thf(255,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(256,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
inference(cnf,[status(esa)],[255]) ).
thf(24810,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24804,340]) ).
thf(24811,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[24810]) ).
thf(24812,plain,
nil @ ( sk2 @ tl @ rearsegP ),
inference(pattern_uni,[status(thm)],[24811:[bind(A,$thf( sk2 @ tl ))]]) ).
thf(58,axiom,
! [A: $i] :
( ( ( nil @ ( A @ skaf44 @ cons ) )
= A )
| ~ ( A @ ssList )
| ~ ( A @ singletonP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause101) ).
thf(303,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf44 @ cons ) )
= A )
| ~ ( A @ ssList )
| ~ ( A @ singletonP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(304,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf44 @ cons ) )
= A )
| ~ ( A @ ssList )
| ~ ( A @ singletonP ) ),
inference(cnf,[status(esa)],[303]) ).
thf(305,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(lifteq,[status(thm)],[304]) ).
thf(15627,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[203,305]) ).
thf(15628,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(simp,[status(thm)],[15627]) ).
thf(15629,plain,
( ~ ( sk2 @ singletonP )
| ( ( nil @ ( sk2 @ skaf44 @ cons ) )
= sk2 ) ),
inference(pattern_uni,[status(thm)],[15628:[bind(A,$thf( sk2 ))]]) ).
thf(13129,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[243,13104]) ).
thf(13130,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[13129]) ).
thf(13131,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[13130:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(13198,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[13131]) ).
thf(21452,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ skaf44 @ cons ) )
!= ( nil @ ( A @ skaf44 @ cons ) ) )
| ( sk2 @ totalorderedP )
| ~ ( sk2 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[15629,13198]) ).
thf(21453,plain,
( ( sk2 @ totalorderedP )
| ~ ( sk2 @ singletonP ) ),
inference(pattern_uni,[status(thm)],[21452:[bind(A,$thf( sk2 ))]]) ).
thf(51,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf43 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause52) ).
thf(287,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf43 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(11334,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf43 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[287,340]) ).
thf(11335,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf43 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[11334]) ).
thf(11336,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf43 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[11335:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf43 ) ))]]) ).
thf(11360,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf43 ) @ rearsegP ) ),
inference(simp,[status(thm)],[11336]) ).
thf(120,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause76) ).
thf(457,plain,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(167,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ app ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause140) ).
thf(569,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)],[167]) ).
thf(12253,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[285,276]) ).
thf(12254,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[12253]) ).
thf(12255,plain,
! [A: $i] : ( A @ skaf78 @ ( A @ skaf78 @ leq ) ),
inference(pattern_uni,[status(thm)],[12254:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(12310,plain,
! [A: $i] : ( A @ skaf78 @ ( A @ skaf78 @ leq ) ),
inference(simp,[status(thm)],[12255]) ).
thf(143,axiom,
! [A: $i] : ( A @ skaf52 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause43) ).
thf(510,plain,
! [A: $i] : ( A @ skaf52 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(13554,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[510,295]) ).
thf(13555,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[13554]) ).
thf(13556,plain,
! [A: $i] :
~ ( A @ skaf52 @ ( A @ skaf52 @ neq ) ),
inference(pattern_uni,[status(thm)],[13555:[bind(A,$thf( C )),bind(B,$thf( C @ skaf52 ))]]) ).
thf(13591,plain,
! [A: $i] :
~ ( A @ skaf52 @ ( A @ skaf52 @ neq ) ),
inference(simp,[status(thm)],[13556]) ).
thf(86,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ rearsegP ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
!= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause143) ).
thf(371,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)],[86]) ).
thf(140,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause70) ).
thf(503,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(182,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ ( D @ app ) @ app ) @ segmentP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause172) ).
thf(605,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)],[182]) ).
thf(190,axiom,
nil @ strictorderedP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause3) ).
thf(624,plain,
nil @ strictorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(25270,plain,
( ( nil != nil )
| ( sk1 @ strictorderedP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[24121,624]) ).
thf(25271,plain,
( ( sk1 @ strictorderedP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[25270:[]]) ).
thf(61,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ app ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause85) ).
thf(310,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ app ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(311,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ app ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[310]) ).
thf(4446,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[231,245]) ).
thf(4447,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[4446]) ).
thf(4448,plain,
! [A: $i] : ( A @ skaf64 @ ( A @ skaf64 @ geq ) ),
inference(pattern_uni,[status(thm)],[4447:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(4476,plain,
! [A: $i] : ( A @ skaf64 @ ( A @ skaf64 @ geq ) ),
inference(simp,[status(thm)],[4448]) ).
thf(760,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[231,465]) ).
thf(761,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[760]) ).
thf(762,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[761:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(765,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[762]) ).
thf(9868,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ( C @ ssItem )
| ( B @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[524,362]) ).
thf(9869,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ( C @ ssItem )
| ( B @ duplicatefreeP ) ),
inference(simp,[status(thm)],[9868]) ).
thf(9870,plain,
! [B: $i,A: $i] :
( ( A @ ssItem )
| ( B @ skaf81 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[9869:[bind(A,$thf( D )),bind(B,$thf( D @ skaf81 ))]]) ).
thf(9925,plain,
! [B: $i,A: $i] :
( ( A @ ssItem )
| ( B @ skaf81 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[9870]) ).
thf(94,axiom,
! [A: $i] : ( A @ skaf58 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause37) ).
thf(391,plain,
! [A: $i] : ( A @ skaf58 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(11306,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[391,340]) ).
thf(11307,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[11306]) ).
thf(11308,plain,
! [A: $i] : ( nil @ ( A @ skaf58 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[11307:[bind(A,$thf( C )),bind(B,$thf( C @ skaf58 ))]]) ).
thf(11379,plain,
! [A: $i] : ( nil @ ( A @ skaf58 @ rearsegP ) ),
inference(simp,[status(thm)],[11308]) ).
thf(73,axiom,
! [B: $i,A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause118) ).
thf(341,plain,
! [B: $i,A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(342,plain,
! [B: $i,A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
inference(cnf,[status(esa)],[341]) ).
thf(343,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( nil = A )
| ( ( B @ ( A @ app ) )
!= nil ) ),
inference(lifteq,[status(thm)],[342]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause156) ).
thf(266,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)],[38]) ).
thf(13105,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[249,13104]) ).
thf(13106,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[13105]) ).
thf(13107,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[13106:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(13213,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[13107]) ).
thf(12501,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[257,280]) ).
thf(12502,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[12501]) ).
thf(12503,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( A @ skaf49 @ lt ) ),
inference(pattern_uni,[status(thm)],[12502:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(12577,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( A @ skaf49 @ lt ) ),
inference(simp,[status(thm)],[12503]) ).
thf(12208,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[249,276]) ).
thf(12209,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[12208]) ).
thf(12210,plain,
! [A: $i] : ( A @ skaf55 @ ( A @ skaf55 @ leq ) ),
inference(pattern_uni,[status(thm)],[12209:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(12305,plain,
! [A: $i] : ( A @ skaf55 @ ( A @ skaf55 @ leq ) ),
inference(simp,[status(thm)],[12210]) ).
thf(183,axiom,
! [A: $i] : ( A @ skaf76 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause19) ).
thf(607,plain,
! [A: $i] : ( A @ skaf76 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(11346,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[607,340]) ).
thf(11347,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[11346]) ).
thf(11348,plain,
! [A: $i] : ( nil @ ( A @ skaf76 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[11347:[bind(A,$thf( C )),bind(B,$thf( C @ skaf76 ))]]) ).
thf(11368,plain,
! [A: $i] : ( nil @ ( A @ skaf76 @ rearsegP ) ),
inference(simp,[status(thm)],[11348]) ).
thf(13189,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[254,13104]) ).
thf(13190,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[13189]) ).
thf(13191,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[13190:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(13196,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[13191]) ).
thf(162,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause78) ).
thf(558,plain,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(298,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ memberP ) )
| ( C @ ( B @ memberP ) )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ( B @ ( A @ app ) @ memberP ) ) ),
inference(cnf,[status(esa)],[297]) ).
thf(106,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ rearsegP ) )
| ~ ( B @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause128) ).
thf(425,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)],[106]) ).
thf(13480,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[479,295]) ).
thf(13481,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[13480]) ).
thf(13482,plain,
! [A: $i] :
~ ( A @ skaf75 @ ( A @ skaf75 @ neq ) ),
inference(pattern_uni,[status(thm)],[13481:[bind(A,$thf( C )),bind(B,$thf( C @ skaf75 ))]]) ).
thf(13584,plain,
! [A: $i] :
~ ( A @ skaf75 @ ( A @ skaf75 @ neq ) ),
inference(simp,[status(thm)],[13482]) ).
thf(953,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[257,465]) ).
thf(954,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[953]) ).
thf(955,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[954:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(965,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[955]) ).
thf(12223,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[228,276]) ).
thf(12224,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[12223]) ).
thf(12225,plain,
! [A: $i] : ( A @ skaf79 @ ( A @ skaf79 @ leq ) ),
inference(pattern_uni,[status(thm)],[12224:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(12295,plain,
! [A: $i] : ( A @ skaf79 @ ( A @ skaf79 @ leq ) ),
inference(simp,[status(thm)],[12225]) ).
thf(1613,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[286,465]) ).
thf(1614,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1613]) ).
thf(1615,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1614:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(1631,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1615]) ).
thf(87,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause66) ).
thf(375,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(170,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ tl )
= B )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause96) ).
thf(577,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ tl )
= B )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ app ) @ app ) )
= ( A @ ( B @ app ) @ ( C @ app ) ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause149) ).
thf(413,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)],[101]) ).
thf(197,axiom,
! [A: $i] :
( ( A @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause61) ).
thf(641,plain,
! [A: $i] :
( ( A @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(114,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( nil @ ( A @ cons ) @ app ) )
= ( B @ ( A @ cons ) ) )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause120) ).
thf(445,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)],[114]) ).
thf(91,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ hd )
= A )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause97) ).
thf(382,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ hd )
= A )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(13114,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[257,13104]) ).
thf(13115,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[13114]) ).
thf(13116,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[13115:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(13217,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[13116]) ).
thf(24979,plain,
( ( nil != nil )
| ( sk1 @ strictorderP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[24121,347]) ).
thf(24980,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[24979:[]]) ).
thf(12513,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[253,280]) ).
thf(12514,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[12513]) ).
thf(12515,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( A @ skaf70 @ lt ) ),
inference(pattern_uni,[status(thm)],[12514:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(12566,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( A @ skaf70 @ lt ) ),
inference(simp,[status(thm)],[12515]) ).
thf(10049,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) )
| ( sk2 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[9923,465]) ).
thf(10050,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[10049]) ).
thf(10051,plain,
! [A: $i] :
( ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[10050:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(124,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ equalelemsP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause64) ).
thf(466,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ equalelemsP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(13126,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[253,13104]) ).
thf(13127,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[13126]) ).
thf(13128,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[13127:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(13197,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[13128]) ).
thf(230,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ geq ) ) ),
inference(cnf,[status(esa)],[229]) ).
thf(4574,plain,
! [B: $i,A: $i] :
( ( ( skac2 @ ( skac2 @ geq ) )
!= ( B @ ( A @ geq ) ) )
| ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4428,230]) ).
thf(4575,plain,
! [B: $i,A: $i] :
( ( ( skac2 @ ( skac2 @ geq ) )
!= ( B @ ( A @ geq ) ) )
| ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem ) ),
inference(simp,[status(thm)],[4574]) ).
thf(4576,plain,
( ( skac2 @ ( skac2 @ leq ) )
| ~ ( skac2 @ ssItem )
| ~ ( skac2 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[4575:[bind(A,$thf( skac2 )),bind(B,$thf( skac2 ))]]) ).
thf(4599,plain,
( ( skac2 @ ( skac2 @ leq ) )
| ~ ( skac2 @ ssItem ) ),
inference(simp,[status(thm)],[4576]) ).
thf(10296,plain,
( ( skac2 @ ( skac2 @ leq ) )
| ~ $true ),
inference(rewrite,[status(thm)],[4599,281]) ).
thf(10297,plain,
skac2 @ ( skac2 @ leq ),
inference(simp,[status(thm)],[10296]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ lt ) )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause147) ).
thf(273,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)],[43]) ).
thf(274,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)],[273]) ).
thf(12288,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[268,276]) ).
thf(12289,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[12288]) ).
thf(12290,plain,
! [A: $i] : ( A @ skaf54 @ ( A @ skaf54 @ leq ) ),
inference(pattern_uni,[status(thm)],[12289:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(12297,plain,
! [A: $i] : ( A @ skaf54 @ ( A @ skaf54 @ leq ) ),
inference(simp,[status(thm)],[12290]) ).
thf(13477,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[365,295]) ).
thf(13478,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[13477]) ).
thf(13479,plain,
! [A: $i] :
~ ( A @ skaf57 @ ( A @ skaf57 @ neq ) ),
inference(pattern_uni,[status(thm)],[13478:[bind(A,$thf( C )),bind(B,$thf( C @ skaf57 ))]]) ).
thf(13582,plain,
! [A: $i] :
~ ( A @ skaf57 @ ( A @ skaf57 @ neq ) ),
inference(simp,[status(thm)],[13479]) ).
thf(13486,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[352,295]) ).
thf(13487,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[13486]) ).
thf(13488,plain,
! [A: $i] :
~ ( A @ skaf77 @ ( A @ skaf77 @ neq ) ),
inference(pattern_uni,[status(thm)],[13487:[bind(A,$thf( C )),bind(B,$thf( C @ skaf77 ))]]) ).
thf(13588,plain,
! [A: $i] :
~ ( A @ skaf77 @ ( A @ skaf77 @ neq ) ),
inference(simp,[status(thm)],[13488]) ).
thf(14553,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ~ $true
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[200,300]) ).
thf(14554,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(simp,[status(thm)],[14553]) ).
thf(14555,plain,
( ( sk1 @ strictorderedP )
| ~ ( sk1 @ skaf70 @ ( sk1 @ skaf69 @ lt ) ) ),
inference(pattern_uni,[status(thm)],[14554:[bind(A,$thf( sk1 ))]]) ).
thf(4449,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[272,245]) ).
thf(4450,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[4449]) ).
thf(4451,plain,
! [A: $i] : ( A @ skaf50 @ ( A @ skaf50 @ geq ) ),
inference(pattern_uni,[status(thm)],[4450:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(4477,plain,
! [A: $i] : ( A @ skaf50 @ ( A @ skaf50 @ geq ) ),
inference(simp,[status(thm)],[4451]) ).
thf(11262,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[352,340]) ).
thf(11263,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[11262]) ).
thf(11264,plain,
! [A: $i] : ( nil @ ( A @ skaf77 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[11263:[bind(A,$thf( C )),bind(B,$thf( C @ skaf77 ))]]) ).
thf(11355,plain,
! [A: $i] : ( nil @ ( A @ skaf77 @ rearsegP ) ),
inference(simp,[status(thm)],[11264]) ).
thf(9733,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ( C @ ssItem )
| ( B @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[479,362]) ).
thf(9734,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ( C @ ssItem )
| ( B @ duplicatefreeP ) ),
inference(simp,[status(thm)],[9733]) ).
thf(9735,plain,
! [B: $i,A: $i] :
( ( A @ ssItem )
| ( B @ skaf75 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[9734:[bind(A,$thf( D )),bind(B,$thf( D @ skaf75 ))]]) ).
thf(9920,plain,
! [B: $i,A: $i] :
( ( A @ ssItem )
| ( B @ skaf75 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[9735]) ).
thf(11340,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[510,340]) ).
thf(11341,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[11340]) ).
thf(11342,plain,
! [A: $i] : ( nil @ ( A @ skaf52 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[11341:[bind(A,$thf( C )),bind(B,$thf( C @ skaf52 ))]]) ).
thf(11365,plain,
! [A: $i] : ( nil @ ( A @ skaf52 @ rearsegP ) ),
inference(simp,[status(thm)],[11342]) ).
thf(110,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
!= ( B @ ( C @ app ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause151) ).
thf(434,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)],[110]) ).
thf(13160,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[286,13104]) ).
thf(13161,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[13160]) ).
thf(13162,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[13161:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(13210,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[13162]) ).
thf(271,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
inference(cnf,[status(esa)],[270]) ).
thf(8,negated_conjecture,
( ~ ( nil @ ( sk4 @ neq ) )
| ( nil @ ( sk2 @ neq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
thf(208,plain,
( ~ ( nil @ ( sk4 @ neq ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(154,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ memberP ) )
| ~ ( D @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ( ( C @ ( B @ cons ) @ ( A @ app ) )
!= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause175) ).
thf(535,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)],[154]) ).
thf(185,axiom,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause84) ).
thf(609,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(321,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)],[320]) ).
thf(322,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( F @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
inference(lifteq,[status(thm)],[321]) ).
thf(323,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)],[322]) ).
thf(177,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D = B )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ( ( B @ ( A @ cons ) )
!= ( D @ ( C @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause171) ).
thf(594,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)],[177]) ).
thf(213,plain,
sk3 = sk1,
inference(lifteq,[status(thm)],[201]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause103) ).
thf(239,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(240,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
inference(cnf,[status(esa)],[239]) ).
thf(11259,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[518,340]) ).
thf(11260,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[11259]) ).
thf(11261,plain,
! [A: $i] : ( nil @ ( A @ skaf67 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[11260:[bind(A,$thf( C )),bind(B,$thf( C @ skaf67 ))]]) ).
thf(11387,plain,
! [A: $i] : ( nil @ ( A @ skaf67 @ rearsegP ) ),
inference(simp,[status(thm)],[11261]) ).
thf(11294,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[590,340]) ).
thf(11295,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[11294]) ).
thf(11296,plain,
! [A: $i] : ( nil @ ( A @ skaf82 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[11295:[bind(A,$thf( C )),bind(B,$thf( C @ skaf82 ))]]) ).
thf(11375,plain,
! [A: $i] : ( nil @ ( A @ skaf82 @ rearsegP ) ),
inference(simp,[status(thm)],[11296]) ).
thf(85,axiom,
! [B: $i,A: $i] :
( ( B @ singletonP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( nil @ ( A @ cons ) )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause116) ).
thf(367,plain,
! [B: $i,A: $i] :
( ( B @ singletonP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( nil @ ( A @ cons ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(159,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ app ) @ tl )
= ( A @ ( B @ tl @ app ) ) )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause133) ).
thf(552,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)],[159]) ).
thf(25083,plain,
( ( nil != nil )
| ( sk1 @ totalorderedP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[24121,637]) ).
thf(25084,plain,
( ( sk1 @ totalorderedP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[25083:[]]) ).
thf(329,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)],[328]) ).
thf(330,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)],[329]) ).
thf(12549,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( A @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[282,280]) ).
thf(12550,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[12549]) ).
thf(12551,plain,
~ ( skac3 @ ( skac3 @ lt ) ),
inference(pattern_uni,[status(thm)],[12550:[bind(A,$thf( skac3 ))]]) ).
thf(12558,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[268,280]) ).
thf(12559,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[12558]) ).
thf(12560,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( A @ skaf54 @ lt ) ),
inference(pattern_uni,[status(thm)],[12559:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(12573,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( A @ skaf54 @ lt ) ),
inference(simp,[status(thm)],[12560]) ).
thf(149,axiom,
! [A: $i] :
( ( ( A @ skaf81 @ ( A @ skaf79 @ cons ) @ ( A @ skaf78 @ cons ) @ ( A @ skaf80 @ app ) )
= A )
| ( A @ equalelemsP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause142) ).
thf(521,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(13524,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[391,295]) ).
thf(13525,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[13524]) ).
thf(13526,plain,
! [A: $i] :
~ ( A @ skaf58 @ ( A @ skaf58 @ neq ) ),
inference(pattern_uni,[status(thm)],[13525:[bind(A,$thf( C )),bind(B,$thf( C @ skaf58 ))]]) ).
thf(13578,plain,
! [A: $i] :
~ ( A @ skaf58 @ ( A @ skaf58 @ neq ) ),
inference(simp,[status(thm)],[13526]) ).
thf(12282,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[231,276]) ).
thf(12283,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[12282]) ).
thf(12284,plain,
! [A: $i] : ( A @ skaf64 @ ( A @ skaf64 @ leq ) ),
inference(pattern_uni,[status(thm)],[12283:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(12309,plain,
! [A: $i] : ( A @ skaf64 @ ( A @ skaf64 @ leq ) ),
inference(simp,[status(thm)],[12284]) ).
thf(119,axiom,
! [A: $i] :
( ( nil @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause56) ).
thf(455,plain,
! [A: $i] :
( ( nil @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(165,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= ( C @ ( A @ app ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause150) ).
thf(563,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)],[165]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause106) ).
thf(226,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(141,axiom,
nil @ cyclefreeP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause7) ).
thf(505,plain,
nil @ cyclefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(108,axiom,
! [A: $i] :
( ( A @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause59) ).
thf(431,plain,
! [A: $i] :
( ( A @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ gt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause146) ).
thf(241,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)],[23]) ).
thf(11268,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf47 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[511,340]) ).
thf(11269,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf47 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[11268]) ).
thf(11270,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf47 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[11269:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf47 ) ))]]) ).
thf(11359,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf47 ) @ rearsegP ) ),
inference(simp,[status(thm)],[11270]) ).
thf(4423,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[286,245]) ).
thf(4424,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[4423]) ).
thf(4425,plain,
! [A: $i] : ( A @ skaf59 @ ( A @ skaf59 @ geq ) ),
inference(pattern_uni,[status(thm)],[4424:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(4473,plain,
! [A: $i] : ( A @ skaf59 @ ( A @ skaf59 @ geq ) ),
inference(simp,[status(thm)],[4425]) ).
thf(2843,plain,
( ( ( skac3 @ ssItem )
!= ( sk2 @ ssItem ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ $true
| ~ ( sk1 @ ssItem )
| ~ ( sk1 @ ( sk2 @ geq ) )
| ~ ( sk2 @ ( sk1 @ geq ) ) ),
inference(paramod_ordered,[status(thm)],[282,2470]) ).
thf(2844,plain,
( ( ( skac3 @ ssItem )
!= ( sk2 @ ssItem ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ ssItem )
| ~ ( sk1 @ ( sk2 @ geq ) )
| ~ ( sk2 @ ( sk1 @ geq ) ) ),
inference(simp,[status(thm)],[2843]) ).
thf(2962,plain,
( ( skac3 != sk2 )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ ssItem )
| ~ ( sk1 @ ( sk2 @ geq ) )
| ~ ( sk2 @ ( sk1 @ geq ) ) ),
inference(simp,[status(thm)],[2844]) ).
thf(267,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)],[266]) ).
thf(12217,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[257,276]) ).
thf(12218,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[12217]) ).
thf(12219,plain,
! [A: $i] : ( A @ skaf49 @ ( A @ skaf49 @ leq ) ),
inference(pattern_uni,[status(thm)],[12218:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(12308,plain,
! [A: $i] : ( A @ skaf49 @ ( A @ skaf49 @ leq ) ),
inference(simp,[status(thm)],[12219]) ).
thf(122,axiom,
! [A: $i] : ( A @ skaf80 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause15) ).
thf(463,plain,
! [A: $i] : ( A @ skaf80 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(9862,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ( C @ ssItem )
| ( B @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[463,362]) ).
thf(9863,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ( C @ ssItem )
| ( B @ duplicatefreeP ) ),
inference(simp,[status(thm)],[9862]) ).
thf(9864,plain,
! [B: $i,A: $i] :
( ( A @ ssItem )
| ( B @ skaf80 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[9863:[bind(A,$thf( D )),bind(B,$thf( D @ skaf80 ))]]) ).
thf(9921,plain,
! [B: $i,A: $i] :
( ( A @ ssItem )
| ( B @ skaf80 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[9864]) ).
thf(4413,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[265,245]) ).
thf(4414,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[4413]) ).
thf(4415,plain,
! [A: $i] : ( A @ skaf74 @ ( A @ skaf74 @ geq ) ),
inference(pattern_uni,[status(thm)],[4414:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(4497,plain,
! [A: $i] : ( A @ skaf74 @ ( A @ skaf74 @ geq ) ),
inference(simp,[status(thm)],[4415]) ).
thf(11271,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[597,340]) ).
thf(11272,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[11271]) ).
thf(11273,plain,
! [A: $i] : ( nil @ ( A @ skaf56 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[11272:[bind(A,$thf( C )),bind(B,$thf( C @ skaf56 ))]]) ).
thf(11361,plain,
! [A: $i] : ( nil @ ( A @ skaf56 @ rearsegP ) ),
inference(simp,[status(thm)],[11273]) ).
thf(4459,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[254,245]) ).
thf(4460,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[4459]) ).
thf(4461,plain,
! [A: $i] : ( A @ skaf60 @ ( A @ skaf60 @ geq ) ),
inference(pattern_uni,[status(thm)],[4460:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(4481,plain,
! [A: $i] : ( A @ skaf60 @ ( A @ skaf60 @ geq ) ),
inference(simp,[status(thm)],[4461]) ).
thf(127,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause100) ).
thf(473,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(1199,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[269,465]) ).
thf(1200,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1199]) ).
thf(1201,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1200:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(1208,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1201]) ).
thf(189,axiom,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause83) ).
thf(620,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(621,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(cnf,[status(esa)],[620]) ).
thf(622,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[621]) ).
thf(623,plain,
( ( nil @ ( nil @ frontsegP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[622]) ).
thf(10222,plain,
( ( nil @ ( nil @ frontsegP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[623,335]) ).
thf(10223,plain,
nil @ ( nil @ frontsegP ),
inference(simp,[status(thm)],[10222]) ).
thf(96,axiom,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause81) ).
thf(395,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(396,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(cnf,[status(esa)],[395]) ).
thf(397,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[396]) ).
thf(398,plain,
( ( nil @ ( nil @ rearsegP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[397]) ).
thf(9645,plain,
( ( nil @ ( nil @ rearsegP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[398,335]) ).
thf(9646,plain,
nil @ ( nil @ rearsegP ),
inference(simp,[status(thm)],[9645]) ).
thf(13539,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[203,295]) ).
thf(13540,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[13539]) ).
thf(13541,plain,
~ ( sk2 @ ( sk2 @ neq ) ),
inference(pattern_uni,[status(thm)],[13540:[bind(A,$thf( sk2 ))]]) ).
thf(1171,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[268,465]) ).
thf(1172,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1171]) ).
thf(1173,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1172:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(1181,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1173]) ).
thf(153,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ cons ) @ memberP ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause138) ).
thf(531,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)],[153]) ).
thf(933,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[254,465]) ).
thf(934,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[933]) ).
thf(935,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[934:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(944,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[935]) ).
thf(4,negated_conjecture,
sk4 @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
thf(209,plain,
sk4 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(133,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ssList )
| ~ ( E @ duplicatefreeP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ( ( D @ ( B @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause179) ).
thf(487,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ssList )
| ~ ( E @ duplicatefreeP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ( ( D @ ( B @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(481,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(cnf,[status(esa)],[480]) ).
thf(482,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[481]) ).
thf(483,plain,
( ( nil @ ( nil @ segmentP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[482]) ).
thf(9677,plain,
( ( nil @ ( nil @ segmentP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[483,335]) ).
thf(9678,plain,
nil @ ( nil @ segmentP ),
inference(simp,[status(thm)],[9677]) ).
thf(188,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ skaf48 ) @ ( B @ ( B @ ( A @ skaf47 ) @ app ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause168) ).
thf(617,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)],[188]) ).
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/sandbox/benchmark/theBenchmark.p',clause173) ).
thf(525,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(4213,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ geq ) )
!= ( skac3 @ ( skac2 @ geq ) ) )
| ~ $true
| ~ ( skac2 @ ( skac3 @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[225,4209]) ).
thf(4214,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ geq ) )
!= ( skac3 @ ( skac2 @ geq ) ) )
| ~ ( skac2 @ ( skac3 @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[4213]) ).
thf(4215,plain,
( ~ ( skac2 @ ( skac3 @ geq ) )
| ~ ( skac2 @ ssItem )
| ~ ( skac3 @ ssItem )
| ~ ( skac2 @ ( skac3 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[4214:[bind(A,$thf( skac3 )),bind(B,$thf( skac2 ))]]) ).
thf(12917,plain,
( ~ ( skac2 @ ( skac3 @ geq ) )
| ~ $true
| ~ $true
| ~ ( skac2 @ ( skac3 @ leq ) ) ),
inference(rewrite,[status(thm)],[4215,281,282]) ).
thf(12918,plain,
( ~ ( skac2 @ ( skac3 @ geq ) )
| ~ ( skac2 @ ( skac3 @ leq ) ) ),
inference(simp,[status(thm)],[12917]) ).
thf(171,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ totalorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause125) ).
thf(580,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)],[171]) ).
thf(11325,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[203,340]) ).
thf(11326,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[11325]) ).
thf(11327,plain,
nil @ ( sk2 @ rearsegP ),
inference(pattern_uni,[status(thm)],[11326:[bind(A,$thf( sk2 ))]]) ).
thf(13507,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[499,295]) ).
thf(13508,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[13507]) ).
thf(13509,plain,
! [A: $i] :
~ ( A @ skaf68 @ ( A @ skaf68 @ neq ) ),
inference(pattern_uni,[status(thm)],[13508:[bind(A,$thf( C )),bind(B,$thf( C @ skaf68 ))]]) ).
thf(13573,plain,
! [A: $i] :
~ ( A @ skaf68 @ ( A @ skaf68 @ neq ) ),
inference(simp,[status(thm)],[13509]) ).
thf(10,negated_conjecture,
( ( nil @ ( sk2 @ neq ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
thf(199,plain,
( ( nil @ ( sk2 @ neq ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(173,axiom,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause80) ).
thf(585,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(11291,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[499,340]) ).
thf(11292,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[11291]) ).
thf(11293,plain,
! [A: $i] : ( nil @ ( A @ skaf68 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[11292:[bind(A,$thf( C )),bind(B,$thf( C @ skaf68 ))]]) ).
thf(11374,plain,
! [A: $i] : ( nil @ ( A @ skaf68 @ rearsegP ) ),
inference(simp,[status(thm)],[11293]) ).
thf(71,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ( B @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause132) ).
thf(336,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)],[71]) ).
thf(337,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ( B @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ frontsegP ) ) ),
inference(cnf,[status(esa)],[336]) ).
thf(338,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ frontsegP ) )
| ( ( B @ ( A @ skaf45 ) @ ( B @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[337]) ).
thf(126,axiom,
! [A: $i] :
( ( ( nil @ ( A @ app ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause73) ).
thf(470,plain,
! [A: $i] :
( ( ( nil @ ( A @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(80,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause67) ).
thf(359,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(1115,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[261,465]) ).
thf(1116,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1115]) ).
thf(1117,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1116:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(1130,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1117]) ).
thf(12507,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[228,280]) ).
thf(12508,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[12507]) ).
thf(12509,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( A @ skaf79 @ lt ) ),
inference(pattern_uni,[status(thm)],[12508:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(12580,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( A @ skaf79 @ lt ) ),
inference(simp,[status(thm)],[12509]) ).
thf(129,axiom,
! [A: $i] : ( A @ skaf53 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause42) ).
thf(478,plain,
! [A: $i] : ( A @ skaf53 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(13545,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[478,295]) ).
thf(13546,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[13545]) ).
thf(13547,plain,
! [A: $i] :
~ ( A @ skaf53 @ ( A @ skaf53 @ neq ) ),
inference(pattern_uni,[status(thm)],[13546:[bind(A,$thf( C )),bind(B,$thf( C @ skaf53 ))]]) ).
thf(13585,plain,
! [A: $i] :
~ ( A @ skaf53 @ ( A @ skaf53 @ neq ) ),
inference(simp,[status(thm)],[13547]) ).
thf(11322,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[463,340]) ).
thf(11323,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[11322]) ).
thf(11324,plain,
! [A: $i] : ( nil @ ( A @ skaf80 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[11323:[bind(A,$thf( C )),bind(B,$thf( C @ skaf80 ))]]) ).
thf(11386,plain,
! [A: $i] : ( nil @ ( A @ skaf80 @ rearsegP ) ),
inference(simp,[status(thm)],[11324]) ).
thf(4401,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[228,245]) ).
thf(4402,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[4401]) ).
thf(4403,plain,
! [A: $i] : ( A @ skaf79 @ ( A @ skaf79 @ geq ) ),
inference(pattern_uni,[status(thm)],[4402:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(4488,plain,
! [A: $i] : ( A @ skaf79 @ ( A @ skaf79 @ geq ) ),
inference(simp,[status(thm)],[4403]) ).
thf(313,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP ) ),
inference(cnf,[status(esa)],[312]) ).
thf(314,plain,
! [B: $i,A: $i] :
( ( B @ hd @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP )
| ( nil = B ) ),
inference(lifteq,[status(thm)],[313]) ).
thf(168,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause77) ).
thf(571,plain,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(13117,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true
| ( sk1 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[9938,13104]) ).
thf(13118,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[13117]) ).
thf(13119,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk1 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[13118:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(186,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause86) ).
thf(612,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(116,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ cons ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause139) ).
thf(450,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)],[116]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ app ) @ ( A @ cons ) )
= ( C @ ( B @ ( A @ cons ) @ app ) ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause157) ).
thf(539,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)],[155]) ).
thf(4210,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ geq ) )
!= ( skac2 @ ( skac3 @ geq ) ) )
| ~ ( skac3 @ ( skac2 @ geq ) )
| ~ $true
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[225,4209]) ).
thf(4211,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ geq ) )
!= ( skac2 @ ( skac3 @ geq ) ) )
| ~ ( skac3 @ ( skac2 @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[4210]) ).
thf(4212,plain,
( ~ ( skac3 @ ( skac2 @ geq ) )
| ~ ( skac3 @ ssItem )
| ~ ( skac2 @ ssItem )
| ~ ( skac3 @ ( skac2 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[4211:[bind(A,$thf( skac2 )),bind(B,$thf( skac3 ))]]) ).
thf(12026,plain,
( ~ ( skac3 @ ( skac2 @ geq ) )
| ~ $true
| ~ $true
| ~ ( skac3 @ ( skac2 @ leq ) ) ),
inference(rewrite,[status(thm)],[4212,281,282]) ).
thf(12027,plain,
( ~ ( skac3 @ ( skac2 @ geq ) )
| ~ ( skac3 @ ( skac2 @ leq ) ) ),
inference(simp,[status(thm)],[12026]) ).
thf(899,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[249,465]) ).
thf(900,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[899]) ).
thf(901,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[900:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(903,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[901]) ).
thf(11253,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[365,340]) ).
thf(11254,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[11253]) ).
thf(11255,plain,
! [A: $i] : ( nil @ ( A @ skaf57 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[11254:[bind(A,$thf( C )),bind(B,$thf( C @ skaf57 ))]]) ).
thf(11383,plain,
! [A: $i] : ( nil @ ( A @ skaf57 @ rearsegP ) ),
inference(simp,[status(thm)],[11255]) ).
thf(12522,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[265,280]) ).
thf(12523,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[12522]) ).
thf(12524,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( A @ skaf74 @ lt ) ),
inference(pattern_uni,[status(thm)],[12523:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(12569,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( A @ skaf74 @ lt ) ),
inference(simp,[status(thm)],[12524]) ).
thf(12229,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[253,276]) ).
thf(12230,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[12229]) ).
thf(12231,plain,
! [A: $i] : ( A @ skaf70 @ ( A @ skaf70 @ leq ) ),
inference(pattern_uni,[status(thm)],[12230:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(12302,plain,
! [A: $i] : ( A @ skaf70 @ ( A @ skaf70 @ leq ) ),
inference(simp,[status(thm)],[12231]) ).
thf(82,axiom,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf59 @ ( A @ skaf60 @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause92) ).
thf(363,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf59 @ ( A @ skaf60 @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(161,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause68) ).
thf(556,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(174,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ rearsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ rearsegP ) )
| ~ ( B @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause153) ).
thf(588,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)],[174]) ).
thf(318,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)],[317]) ).
thf(319,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)],[318]) ).
thf(12528,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[248,280]) ).
thf(12529,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[12528]) ).
thf(12530,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( A @ skaf69 @ lt ) ),
inference(pattern_uni,[status(thm)],[12529:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(12574,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( A @ skaf69 @ lt ) ),
inference(simp,[status(thm)],[12530]) ).
thf(349,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ssList )
| ~ ( F @ cyclefreeP )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) )
!= F )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[348]) ).
thf(350,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ssList )
| ~ ( F @ cyclefreeP )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ~ ( E @ ssList )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ( ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) )
!= F ) ),
inference(lifteq,[status(thm)],[349]) ).
thf(351,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) @ ssList )
| ~ ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) @ cyclefreeP )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ~ ( E @ ssList )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[350]) ).
thf(24875,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[24804,295]) ).
thf(24876,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[24875]) ).
thf(24877,plain,
~ ( sk2 @ tl @ ( sk2 @ tl @ neq ) ),
inference(pattern_uni,[status(thm)],[24876:[bind(A,$thf( sk2 @ tl ))]]) ).
thf(4407,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[253,245]) ).
thf(4408,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[4407]) ).
thf(4409,plain,
! [A: $i] : ( A @ skaf70 @ ( A @ skaf70 @ geq ) ),
inference(pattern_uni,[status(thm)],[4408:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(4495,plain,
! [A: $i] : ( A @ skaf70 @ ( A @ skaf70 @ geq ) ),
inference(simp,[status(thm)],[4409]) ).
thf(103,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause102) ).
thf(418,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(13536,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[463,295]) ).
thf(13537,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[13536]) ).
thf(13538,plain,
! [A: $i] :
~ ( A @ skaf80 @ ( A @ skaf80 @ neq ) ),
inference(pattern_uni,[status(thm)],[13537:[bind(A,$thf( C )),bind(B,$thf( C @ skaf80 ))]]) ).
thf(13581,plain,
! [A: $i] :
~ ( A @ skaf80 @ ( A @ skaf80 @ neq ) ),
inference(simp,[status(thm)],[13538]) ).
thf(193,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ segmentP ) )
| ~ ( B @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause127) ).
thf(632,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)],[193]) ).
thf(13120,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[228,13104]) ).
thf(13121,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[13120]) ).
thf(13122,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[13121:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(13193,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[13122]) ).
thf(10038,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true
| ( sk2 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[9923,245]) ).
thf(10039,plain,
! [B: $i,A: $i] :
( ( ( A @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[10038]) ).
thf(10040,plain,
! [A: $i] :
( ( A @ ( A @ geq ) )
| ( sk2 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[10039:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(89,axiom,
! [A: $i] :
( ( ( A @ skaf58 @ ( A @ skaf55 @ cons ) @ ( A @ skaf57 @ ( A @ skaf54 @ cons ) @ ( A @ skaf56 @ app ) @ app ) )
= A )
| ( A @ totalorderP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause166) ).
thf(378,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)],[89]) ).
thf(11,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( nil @ ( sk4 @ neq ) )
| ~ ( sk4 @ ( nil @ neq ) )
| ( ( B @ ( sk3 @ app ) )
!= A )
| ( ( sk4 @ tl )
!= B )
| ~ ( B @ ssList )
| ( sk4 = A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
thf(207,plain,
! [B: $i,A: $i] :
( ~ ( nil @ ( sk4 @ neq ) )
| ~ ( sk4 @ ( nil @ neq ) )
| ( ( B @ ( sk3 @ app ) )
!= A )
| ( ( sk4 @ tl )
!= B )
| ~ ( B @ ssList )
| ( sk4 = A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(665,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[282,465]) ).
thf(666,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[665]) ).
thf(667,plain,
~ ( skac3 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[666:[bind(A,$thf( skac3 ))]]) ).
thf(11278,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[561,340]) ).
thf(11279,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[11278]) ).
thf(11280,plain,
! [A: $i] : ( nil @ ( A @ skaf63 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[11279:[bind(A,$thf( C )),bind(B,$thf( C @ skaf63 ))]]) ).
thf(11366,plain,
! [A: $i] : ( nil @ ( A @ skaf63 @ rearsegP ) ),
inference(simp,[status(thm)],[11280]) ).
thf(345,plain,
! [A: $i] :
( ( ( A @ skaf63 @ ( A @ skaf60 @ cons ) @ ( A @ skaf62 @ ( A @ skaf59 @ cons ) @ ( A @ skaf61 @ app ) @ app ) )
= A )
| ( A @ strictorderP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[344]) ).
thf(346,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ( ( A @ skaf63 @ ( A @ skaf60 @ cons ) @ ( A @ skaf62 @ ( A @ skaf59 @ cons ) @ ( A @ skaf61 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[345]) ).
thf(12516,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[243,280]) ).
thf(12517,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[12516]) ).
thf(12518,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( A @ skaf44 @ lt ) ),
inference(pattern_uni,[status(thm)],[12517:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(12567,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( A @ skaf44 @ lt ) ),
inference(simp,[status(thm)],[12518]) ).
thf(12226,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[261,276]) ).
thf(12227,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[12226]) ).
thf(12228,plain,
! [A: $i] : ( A @ skaf83 @ ( A @ skaf83 @ leq ) ),
inference(pattern_uni,[status(thm)],[12227:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(12298,plain,
! [A: $i] : ( A @ skaf83 @ ( A @ skaf83 @ leq ) ),
inference(simp,[status(thm)],[12228]) ).
thf(4388,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[249,245]) ).
thf(4389,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[4388]) ).
thf(4390,plain,
! [A: $i] : ( A @ skaf55 @ ( A @ skaf55 @ geq ) ),
inference(pattern_uni,[status(thm)],[4389:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(4478,plain,
! [A: $i] : ( A @ skaf55 @ ( A @ skaf55 @ geq ) ),
inference(simp,[status(thm)],[4390]) ).
thf(4416,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[248,245]) ).
thf(4417,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[4416]) ).
thf(4418,plain,
! [A: $i] : ( A @ skaf69 @ ( A @ skaf69 @ geq ) ),
inference(pattern_uni,[status(thm)],[4417:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(4472,plain,
! [A: $i] : ( A @ skaf69 @ ( A @ skaf69 @ geq ) ),
inference(simp,[status(thm)],[4418]) ).
thf(9736,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ( C @ ssItem )
| ( B @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[518,362]) ).
thf(9737,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ( C @ ssItem )
| ( B @ duplicatefreeP ) ),
inference(simp,[status(thm)],[9736]) ).
thf(9738,plain,
! [B: $i,A: $i] :
( ( A @ ssItem )
| ( B @ skaf67 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[9737:[bind(A,$thf( D )),bind(B,$thf( D @ skaf67 ))]]) ).
thf(9922,plain,
! [B: $i,A: $i] :
( ( A @ ssItem )
| ( B @ skaf67 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[9738]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause121) ).
thf(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)],[36]) ).
thf(13183,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[272,13104]) ).
thf(13184,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[13183]) ).
thf(13185,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[13184:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(13192,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[13185]) ).
thf(13521,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[562,295]) ).
thf(13522,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[13521]) ).
thf(13523,plain,
! [A: $i] :
~ ( A @ skaf66 @ ( A @ skaf66 @ neq ) ),
inference(pattern_uni,[status(thm)],[13522:[bind(A,$thf( C )),bind(B,$thf( C @ skaf66 ))]]) ).
thf(13577,plain,
! [A: $i] :
~ ( A @ skaf66 @ ( A @ skaf66 @ neq ) ),
inference(simp,[status(thm)],[13523]) ).
thf(13163,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[281,13104]) ).
thf(13164,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[13163]) ).
thf(13165,plain,
nil @ ( skac2 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[13164:[bind(A,$thf( skac2 ))]]) ).
thf(26135,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[281,334]) ).
thf(26136,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[26135]) ).
thf(26137,plain,
~ ( skac2 @ ( skac2 @ neq ) ),
inference(pattern_uni,[status(thm)],[26136:[bind(A,$thf( skac2 ))]]) ).
thf(26198,plain,
( ( ( skac2 @ ( skac2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[205,26137]) ).
thf(26199,plain,
( ( skac2 @ ( skac2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[26198]) ).
thf(26216,plain,
( ( skac2 != nil )
| ( skac2 != sk2 ) ),
inference(simp,[status(thm)],[26199]) ).
thf(12214,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[269,276]) ).
thf(12215,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[12214]) ).
thf(12216,plain,
! [A: $i] : ( A @ skaf65 @ ( A @ skaf65 @ leq ) ),
inference(pattern_uni,[status(thm)],[12215:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(12307,plain,
! [A: $i] : ( A @ skaf65 @ ( A @ skaf65 @ leq ) ),
inference(simp,[status(thm)],[12216]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ app ) @ frontsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause137) ).
thf(437,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)],[111]) ).
thf(662,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[281,465]) ).
thf(663,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[662]) ).
thf(664,plain,
~ ( skac2 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[663:[bind(A,$thf( skac2 ))]]) ).
thf(11300,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[601,340]) ).
thf(11301,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[11300]) ).
thf(11302,plain,
! [A: $i] : ( nil @ ( A @ skaf71 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[11301:[bind(A,$thf( C )),bind(B,$thf( C @ skaf71 ))]]) ).
thf(11377,plain,
! [A: $i] : ( nil @ ( A @ skaf71 @ rearsegP ) ),
inference(simp,[status(thm)],[11302]) ).
thf(48,axiom,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause63) ).
thf(283,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(242,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)],[241]) ).
thf(142,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ leq ) )
| ( D @ ( B @ leq ) )
| ~ ( F @ ssList )
| ~ ( F @ totalorderP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause184) ).
thf(506,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)],[142]) ).
thf(194,axiom,
! [A: $i] :
( ( A @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause57) ).
thf(635,plain,
! [A: $i] :
( ( A @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(13186,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[268,13104]) ).
thf(13187,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[13186]) ).
thf(13188,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[13187:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(13194,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[13188]) ).
thf(25729,plain,
( ( ( sk2 @ tl @ ( sk2 @ tl @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[205,24877]) ).
thf(25730,plain,
( ( sk2 @ tl @ ( sk2 @ tl @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[25729]) ).
thf(25759,plain,
( ( ( sk2 @ tl )
!= nil )
| ( ( sk2 @ tl )
!= sk2 ) ),
inference(simp,[status(thm)],[25730]) ).
thf(4520,plain,
! [B: $i,A: $i] :
( ( ( skac3 @ ( skac3 @ geq ) )
!= ( B @ ( A @ geq ) ) )
| ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4387,230]) ).
thf(4521,plain,
! [B: $i,A: $i] :
( ( ( skac3 @ ( skac3 @ geq ) )
!= ( B @ ( A @ geq ) ) )
| ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem ) ),
inference(simp,[status(thm)],[4520]) ).
thf(4522,plain,
( ( skac3 @ ( skac3 @ leq ) )
| ~ ( skac3 @ ssItem )
| ~ ( skac3 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[4521:[bind(A,$thf( skac3 )),bind(B,$thf( skac3 ))]]) ).
thf(4548,plain,
( ( skac3 @ ( skac3 @ leq ) )
| ~ ( skac3 @ ssItem ) ),
inference(simp,[status(thm)],[4522]) ).
thf(10254,plain,
( ( skac3 @ ( skac3 @ leq ) )
| ~ $true ),
inference(rewrite,[status(thm)],[4548,282]) ).
thf(10255,plain,
skac3 @ ( skac3 @ leq ),
inference(simp,[status(thm)],[10254]) ).
thf(11331,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[478,340]) ).
thf(11332,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[11331]) ).
thf(11333,plain,
! [A: $i] : ( nil @ ( A @ skaf53 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[11332:[bind(A,$thf( C )),bind(B,$thf( C @ skaf53 ))]]) ).
thf(11358,plain,
! [A: $i] : ( nil @ ( A @ skaf53 @ rearsegP ) ),
inference(simp,[status(thm)],[11333]) ).
thf(25172,plain,
( ( nil != nil )
| ( sk1 @ cyclefreeP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[24121,505]) ).
thf(25173,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[25172:[]]) ).
thf(4398,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[257,245]) ).
thf(4399,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[4398]) ).
thf(4400,plain,
! [A: $i] : ( A @ skaf49 @ ( A @ skaf49 @ geq ) ),
inference(pattern_uni,[status(thm)],[4399:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(4484,plain,
! [A: $i] : ( A @ skaf49 @ ( A @ skaf49 @ geq ) ),
inference(simp,[status(thm)],[4400]) ).
thf(13510,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[590,295]) ).
thf(13511,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[13510]) ).
thf(13512,plain,
! [A: $i] :
~ ( A @ skaf82 @ ( A @ skaf82 @ neq ) ),
inference(pattern_uni,[status(thm)],[13511:[bind(A,$thf( C )),bind(B,$thf( C @ skaf82 ))]]) ).
thf(13574,plain,
! [A: $i] :
~ ( A @ skaf82 @ ( A @ skaf82 @ neq ) ),
inference(simp,[status(thm)],[13512]) ).
thf(11343,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[200,340]) ).
thf(11344,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[11343]) ).
thf(11345,plain,
nil @ ( sk1 @ rearsegP ),
inference(pattern_uni,[status(thm)],[11344:[bind(A,$thf( sk1 ))]]) ).
thf(113,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause129) ).
thf(442,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)],[113]) ).
thf(13551,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[433,295]) ).
thf(13552,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[13551]) ).
thf(13553,plain,
! [A: $i] :
~ ( A @ skaf61 @ ( A @ skaf61 @ neq ) ),
inference(pattern_uni,[status(thm)],[13552:[bind(A,$thf( C )),bind(B,$thf( C @ skaf61 ))]]) ).
thf(13589,plain,
! [A: $i] :
~ ( A @ skaf61 @ ( A @ skaf61 @ neq ) ),
inference(simp,[status(thm)],[13553]) ).
thf(118,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf48 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause48) ).
thf(454,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf48 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(11352,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf48 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[454,340]) ).
thf(11353,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf48 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[11352]) ).
thf(11354,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf48 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[11353:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf48 ) ))]]) ).
thf(11373,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf48 ) @ rearsegP ) ),
inference(simp,[status(thm)],[11354]) ).
thf(139,axiom,
! [A: $i] :
( ( nil @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause60) ).
thf(501,plain,
! [A: $i] :
( ( nil @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(24990,plain,
( ( nil != nil )
| ( sk1 @ totalorderP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[24121,500]) ).
thf(24991,plain,
( ( sk1 @ totalorderP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[24990:[]]) ).
thf(12537,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[286,280]) ).
thf(12538,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[12537]) ).
thf(12539,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( A @ skaf59 @ lt ) ),
inference(pattern_uni,[status(thm)],[12538:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(12579,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( A @ skaf59 @ lt ) ),
inference(simp,[status(thm)],[12539]) ).
thf(134,axiom,
! [A: $i] :
( ( A @ totalorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf65 @ ( A @ skaf64 @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause91) ).
thf(491,plain,
! [A: $i] :
( ( A @ totalorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf65 @ ( A @ skaf64 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(879,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[248,465]) ).
thf(880,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[879]) ).
thf(881,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[880:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(882,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[881]) ).
thf(227,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
inference(cnf,[status(esa)],[226]) ).
thf(136,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause99) ).
thf(496,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(34578,plain,
$false,
inference(e,[status(thm)],[1586,629,13199,365,11372,347,249,518,468,234,352,12564,24804,479,12570,777,555,11385,12575,15098,276,9924,12299,308,9918,247,13586,511,24907,614,269,202,597,4479,25039,385,10181,550,500,10170,340,12568,26257,2972,13209,12303,288,25035,301,320,4496,13179,11382,651,257,344,12578,9938,4428,542,460,638,15477,421,416,325,228,448,316,11363,261,4492,11378,13134,13575,216,13195,253,238,12237,25240,353,480,591,13590,348,574,602,280,12311,221,11384,411,243,428,11367,12306,1242,265,12222,9923,13216,11357,312,206,4475,292,248,26149,546,201,13104,381,13200,366,12300,14537,233,452,512,439,270,529,4480,925,334,12542,260,598,392,297,424,407,13218,275,24996,302,561,12576,2969,15118,11371,13583,252,361,625,11376,583,493,12304,10710,229,566,484,12571,324,285,224,11356,317,5423,13576,12506,27837,403,4233,388,356,499,519,12521,225,339,753,476,637,590,1155,328,256,24812,21453,11360,457,569,12310,13591,371,503,605,25271,244,24121,205,311,4476,657,765,9925,11379,343,237,266,13213,12577,12305,11368,13196,558,298,425,13584,296,601,965,12295,1631,375,13559,13710,562,286,577,413,281,204,641,445,382,13217,24980,12566,10051,27190,466,335,236,391,13197,10297,274,12297,13582,377,362,13588,245,14555,4477,230,11355,9920,11365,434,303,13210,271,208,535,609,323,594,213,240,11387,198,11375,13529,367,552,25084,330,12551,12573,521,13578,13630,12309,455,306,563,299,226,505,431,241,11359,4473,399,2962,223,608,267,12308,9921,4497,4209,11361,4481,473,1208,10223,9646,255,13541,1181,531,944,209,487,9678,617,516,525,12918,580,11327,295,282,327,310,13573,199,331,585,11374,463,338,470,359,1130,12580,336,13585,11386,4488,314,571,13119,612,450,539,203,12027,903,524,11383,12569,12302,250,465,231,363,556,588,517,319,12574,258,351,24877,4495,418,13581,632,25121,13193,10040,378,246,207,667,11366,13198,478,272,346,12567,12298,287,433,510,4387,4478,300,620,4472,9922,262,13192,13577,13165,273,26216,315,305,26137,341,15393,12307,437,664,11377,283,239,242,506,268,635,13194,25759,464,10255,11358,200,277,25173,607,395,624,4484,13574,11345,442,13589,11373,501,24991,12579,309,15629,491,2470,232,882,254,227,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC120-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.16/0.40 % Computer : n019.cluster.edu
% 0.16/0.40 % Model : x86_64 x86_64
% 0.16/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.40 % Memory : 8046.5625MB
% 0.16/0.40 % OS : Linux 6.8.0-71-generic
% 0.16/0.40 % CPULimit : 300
% 0.16/0.40 % WCLimit : 300
% 0.16/0.40 % DateTime : Sat Sep 26 12:18:03 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.84/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.35/1.26 % [INFO] Parsing done (261ms).
% 1.35/1.28 % [INFO] Running in sequential loop mode.
% 2.24/1.67 % [INFO] eprover registered as external prover.
% 2.24/1.68 % [INFO] Scanning for conjecture ...
% 2.67/1.82 % [INFO] Found a conjecture (or negated_conjecture) and 185 axioms. Running axiom selection ...
% 2.86/1.96 % [INFO] Axiom selection finished. Selected 185 axioms (removed 0 axioms).
% 3.38/2.11 % [INFO] Problem is propositional (TPTP CNF).
% 3.38/2.12 % [INFO] Type checking passed.
% 3.38/2.13 % [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 ...
% 93.20/19.22 % External prover 'e' found a proof!
% 93.20/19.22 % [INFO] Killing All external provers ...
% 93.20/19.23 % Time passed: 18672ms (effective reasoning time: 17941ms)
% 93.20/19.23 % 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
% 93.20/19.23 % No. of inferences in proof: 1212
% 93.20/19.23 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 18672 ms resp. 17941 ms w/o parsing
% 95.19/19.59 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 95.66/19.60 % [INFO] Killing All external provers ...
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