%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWC066-1 : 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 : n026.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 08:52:03 AM UTC 2026
% Result : Unsatisfiable 207.62s 61.85s
% Output : Refutation 210.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 198
% Syntax : Number of formulae : 1726 ( 523 unt; 0 typ; 0 def)
% Number of atoms : 5365 (1283 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 13578 (2909 ~;2595 |; 0 &;8074 @)
% ( 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 : 2141 ( 0 ^;2141 !; 0 ?;2141 :)
% Comments :
%------------------------------------------------------------------------------
thf(ssList_decl,type,
ssList: $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(segmentP_decl,type,
segmentP: $i > $i > $o ).
thf(totalorderedP_decl,type,
totalorderedP: $i > $o ).
thf(neq_decl,type,
neq: $i > $i > $o ).
thf(nil_decl,type,
nil: $i ).
thf(skac3_decl,type,
skac3: $i ).
thf(skac2_decl,type,
skac2: $i ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(ssItem_decl,type,
ssItem: $i > $o ).
thf(geq_decl,type,
geq: $i > $i > $o ).
thf(lt_decl,type,
lt: $i > $i > $o ).
thf(gt_decl,type,
gt: $i > $i > $o ).
thf(skaf79_decl,type,
skaf79: $i > $i ).
thf(skaf64_decl,type,
skaf64: $i > $i ).
thf(skaf44_decl,type,
skaf44: $i > $i ).
thf(skaf69_decl,type,
skaf69: $i > $i ).
thf(skaf55_decl,type,
skaf55: $i > $i ).
thf(skaf70_decl,type,
skaf70: $i > $i ).
thf(skaf60_decl,type,
skaf60: $i > $i ).
thf(skaf49_decl,type,
skaf49: $i > $i ).
thf(skaf83_decl,type,
skaf83: $i > $i ).
thf(skaf74_decl,type,
skaf74: $i > $i ).
thf(skaf54_decl,type,
skaf54: $i > $i ).
thf(skaf65_decl,type,
skaf65: $i > $i ).
thf(skaf50_decl,type,
skaf50: $i > $i ).
thf(skaf78_decl,type,
skaf78: $i > $i ).
thf(skaf59_decl,type,
skaf59: $i > $i ).
thf(skaf43_decl,type,
skaf43: $i > $i > $i ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(skaf62_decl,type,
skaf62: $i > $i ).
thf(memberP_decl,type,
memberP: $i > $i > $o ).
thf(app_decl,type,
app: $i > $i > $i ).
thf(strictorderedP_decl,type,
strictorderedP: $i > $o ).
thf(cyclefreeP_decl,type,
cyclefreeP: $i > $o ).
thf(singletonP_decl,type,
singletonP: $i > $o ).
thf(duplicatefreeP_decl,type,
duplicatefreeP: $i > $o ).
thf(skaf75_decl,type,
skaf75: $i > $i ).
thf(skaf76_decl,type,
skaf76: $i > $i ).
thf(skaf77_decl,type,
skaf77: $i > $i ).
thf(skaf72_decl,type,
skaf72: $i > $i ).
thf(hd_decl,type,
hd: $i > $i ).
thf(frontsegP_decl,type,
frontsegP: $i > $i > $o ).
thf(skaf71_decl,type,
skaf71: $i > $i ).
thf(skaf73_decl,type,
skaf73: $i > $i ).
thf(skaf46_decl,type,
skaf46: $i > $i > $i ).
thf(tl_decl,type,
tl: $i > $i ).
thf(skaf66_decl,type,
skaf66: $i > $i ).
thf(skaf67_decl,type,
skaf67: $i > $i ).
thf(skaf68_decl,type,
skaf68: $i > $i ).
thf(skaf45_decl,type,
skaf45: $i > $i > $i ).
thf(rearsegP_decl,type,
rearsegP: $i > $i > $o ).
thf(strictorderP_decl,type,
strictorderP: $i > $o ).
thf(skaf61_decl,type,
skaf61: $i > $i ).
thf(skaf63_decl,type,
skaf63: $i > $i ).
thf(skaf51_decl,type,
skaf51: $i > $i ).
thf(skaf52_decl,type,
skaf52: $i > $i ).
thf(skaf53_decl,type,
skaf53: $i > $i ).
thf(skaf57_decl,type,
skaf57: $i > $i ).
thf(equalelemsP_decl,type,
equalelemsP: $i > $o ).
thf(totalorderP_decl,type,
totalorderP: $i > $o ).
thf(skaf56_decl,type,
skaf56: $i > $i ).
thf(skaf58_decl,type,
skaf58: $i > $i ).
thf(skaf48_decl,type,
skaf48: $i > $i > $i ).
thf(skaf80_decl,type,
skaf80: $i > $i ).
thf(skaf47_decl,type,
skaf47: $i > $i > $i ).
thf(skaf81_decl,type,
skaf81: $i > $i ).
thf(skaf82_decl,type,
skaf82: $i > $i ).
thf(skaf42_decl,type,
skaf42: $i > $i > $i ).
thf(19,axiom,
! [A: $i] : ( A @ skaf64 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause31) ).
thf(233,plain,
! [A: $i] : ( A @ skaf64 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause113) ).
thf(290,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(291,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(cnf,[status(esa)],[290]) ).
thf(292,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[291]) ).
thf(293,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[292]) ).
thf(71,axiom,
nil @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
thf(337,plain,
nil @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(10171,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ $true ),
inference(rewrite,[status(thm)],[293,337]) ).
thf(10172,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[10171]) ).
thf(10189,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[233,10172]) ).
thf(10190,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[10189]) ).
thf(10191,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[10190:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(10267,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[10191]) ).
thf(1,negated_conjecture,
sk1 @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
thf(201,plain,
sk1 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(94,axiom,
! [A: $i] :
( ( ( A @ ( nil @ app ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause74) ).
thf(390,plain,
! [A: $i] :
( ( ( A @ ( nil @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(391,plain,
! [A: $i] :
( ( ( A @ ( nil @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[390]) ).
thf(392,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[391]) ).
thf(49464,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[201,392]) ).
thf(49465,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[49464]) ).
thf(49466,plain,
( ( sk1 @ ( nil @ app ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[49465:[bind(A,$thf( sk1 ))]]) ).
thf(125,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ equalelemsP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause64) ).
thf(468,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ equalelemsP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(131,axiom,
! [A: $i] : ( A @ skaf75 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause20) ).
thf(481,plain,
! [A: $i] : ( A @ skaf75 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(83,axiom,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf59 @ ( A @ skaf60 @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause92) ).
thf(365,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf59 @ ( A @ skaf60 @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(10,negated_conjecture,
( ( nil @ ( sk2 @ neq ) )
| ( nil = sk2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
thf(200,plain,
( ( nil @ ( sk2 @ neq ) )
| ( nil = sk2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(221,plain,
( ( nil @ ( sk2 @ neq ) )
| ( nil = sk2 ) ),
inference(cnf,[status(esa)],[200]) ).
thf(222,plain,
( ( nil @ ( sk2 @ neq ) )
| ( nil = sk2 ) ),
inference(lifteq,[status(thm)],[221]) ).
thf(47,axiom,
skac2 @ ssItem,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause10) ).
thf(283,plain,
skac2 @ ssItem,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(10244,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[283,10172]) ).
thf(10245,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[10244]) ).
thf(10246,plain,
nil @ ( skac2 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[10245:[bind(A,$thf( skac2 ))]]) ).
thf(10372,plain,
( ( nil != nil )
| ( sk2 @ ( skac2 @ cons ) @ totalorderedP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,10246]) ).
thf(10373,plain,
( ( sk2 @ ( skac2 @ cons ) @ totalorderedP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[10372:[]]) ).
thf(119,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf48 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause48) ).
thf(456,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf48 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(73,axiom,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause58) ).
thf(341,plain,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(342,plain,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[341]) ).
thf(26319,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf48 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[456,342]) ).
thf(26320,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf48 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[26319]) ).
thf(26321,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf48 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[26320:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf48 ) ))]]) ).
thf(26456,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf48 ) @ rearsegP ) ),
inference(simp,[status(thm)],[26321]) ).
thf(106,axiom,
! [A: $i] : ( A @ skaf73 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause22) ).
thf(426,plain,
! [A: $i] : ( A @ skaf73 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(49552,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[426,392]) ).
thf(49553,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[49552]) ).
thf(49554,plain,
! [A: $i] :
( ( A @ skaf73 @ ( nil @ app ) )
= ( A @ skaf73 ) ),
inference(pattern_uni,[status(thm)],[49553:[bind(A,$thf( C )),bind(B,$thf( C @ skaf73 ))]]) ).
thf(49705,plain,
! [A: $i] :
( ( A @ skaf73 @ ( nil @ app ) )
= ( A @ skaf73 ) ),
inference(simp,[status(thm)],[49554]) ).
thf(52,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf43 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause52) ).
thf(289,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf43 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(49420,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf43 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ( ( C @ ( nil @ app ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[289,392]) ).
thf(49421,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf43 ) @ ssList )
!= ( C @ ssList ) )
| ( ( C @ ( nil @ app ) )
= C ) ),
inference(simp,[status(thm)],[49420]) ).
thf(49422,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ skaf43 ) @ ( nil @ app ) )
= ( B @ ( A @ skaf43 ) ) ),
inference(pattern_uni,[status(thm)],[49421:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf43 ) ))]]) ).
thf(49673,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ skaf43 ) @ ( nil @ app ) )
= ( B @ ( A @ skaf43 ) ) ),
inference(simp,[status(thm)],[49422]) ).
thf(70,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause117) ).
thf(333,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ geq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause148) ).
thf(248,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ geq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(249,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ geq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
inference(cnf,[status(esa)],[248]) ).
thf(161,axiom,
! [A: $i] : ( A @ skaf51 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause44) ).
thf(557,plain,
! [A: $i] : ( A @ skaf51 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause115) ).
thf(294,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(295,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[294]) ).
thf(296,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[295]) ).
thf(297,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[296]) ).
thf(10730,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[557,297]) ).
thf(10731,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[10730]) ).
thf(10732,plain,
! [A: $i] :
~ ( A @ skaf51 @ ( A @ skaf51 @ neq ) ),
inference(pattern_uni,[status(thm)],[10731:[bind(A,$thf( C )),bind(B,$thf( C @ skaf51 ))]]) ).
thf(10812,plain,
! [A: $i] :
~ ( A @ skaf51 @ ( A @ skaf51 @ neq ) ),
inference(simp,[status(thm)],[10732]) ).
thf(147,axiom,
~ ( nil @ singletonP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause11) ).
thf(518,plain,
~ ( nil @ singletonP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(25,axiom,
! [A: $i] : ( A @ skaf44 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause47) ).
thf(245,plain,
! [A: $i] : ( A @ skaf44 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(334,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[333]) ).
thf(335,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[334]) ).
thf(336,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[335]) ).
thf(24456,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[245,336]) ).
thf(24457,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[24456]) ).
thf(24458,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( A @ skaf44 @ neq ) ),
inference(pattern_uni,[status(thm)],[24457:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(24518,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( A @ skaf44 @ neq ) ),
inference(simp,[status(thm)],[24458]) ).
thf(58,axiom,
! [A: $i] :
( ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause88) ).
thf(303,plain,
! [A: $i] :
( ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(304,plain,
! [A: $i] :
( ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[303]) ).
thf(12729,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[201,304]) ).
thf(12730,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP ) ),
inference(simp,[status(thm)],[12729]) ).
thf(12731,plain,
( ( sk1 @ skaf50 @ ( sk1 @ skaf49 @ leq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12730:[bind(A,$thf( sk1 ))]]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause155) ).
thf(234,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(61,axiom,
! [A: $i] : ( A @ skaf72 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause23) ).
thf(311,plain,
! [A: $i] : ( A @ skaf72 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(26337,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[311,342]) ).
thf(26338,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[26337]) ).
thf(26339,plain,
! [A: $i] : ( nil @ ( A @ skaf72 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[26338:[bind(A,$thf( C )),bind(B,$thf( C @ skaf72 ))]]) ).
thf(26461,plain,
! [A: $i] : ( nil @ ( A @ skaf72 @ rearsegP ) ),
inference(simp,[status(thm)],[26339]) ).
thf(84,axiom,
! [A: $i] : ( A @ skaf57 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause38) ).
thf(367,plain,
! [A: $i] : ( A @ skaf57 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(26360,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[367,342]) ).
thf(26361,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[26360]) ).
thf(26362,plain,
! [A: $i] : ( nil @ ( A @ skaf57 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[26361:[bind(A,$thf( C )),bind(B,$thf( C @ skaf57 ))]]) ).
thf(26466,plain,
! [A: $i] : ( nil @ ( A @ skaf57 @ rearsegP ) ),
inference(simp,[status(thm)],[26362]) ).
thf(190,axiom,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause83) ).
thf(622,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(623,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(cnf,[status(esa)],[622]) ).
thf(624,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[623]) ).
thf(625,plain,
( ( nil @ ( nil @ frontsegP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[624]) ).
thf(7386,plain,
( ( nil @ ( nil @ frontsegP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[625,337]) ).
thf(7387,plain,
nil @ ( nil @ frontsegP ),
inference(simp,[status(thm)],[7386]) ).
thf(7408,plain,
( ( nil != nil )
| ( nil @ ( sk2 @ frontsegP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,7387]) ).
thf(7409,plain,
( ( nil @ ( sk2 @ frontsegP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[7408:[]]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ lt ) )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause147) ).
thf(275,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ lt ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(276,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ lt ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[275]) ).
thf(60,axiom,
! [A: $i] :
( ( ( A @ skaf77 @ ( A @ skaf74 @ cons ) @ ( A @ skaf76 @ ( A @ skaf74 @ cons ) @ ( A @ skaf75 @ app ) @ app ) )
= A )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause162) ).
thf(308,plain,
! [A: $i] :
( ( ( A @ skaf77 @ ( A @ skaf74 @ cons ) @ ( A @ skaf76 @ ( A @ skaf74 @ cons ) @ ( A @ skaf75 @ app ) @ app ) )
= A )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ ( A @ geq ) )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause55) ).
thf(246,plain,
! [A: $i] :
( ( A @ ( A @ geq ) )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(247,plain,
! [A: $i] :
( ( A @ ( A @ geq ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[246]) ).
thf(50,axiom,
! [A: $i] : ( A @ skaf78 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause17) ).
thf(287,plain,
! [A: $i] : ( A @ skaf78 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause62) ).
thf(277,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(278,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[277]) ).
thf(9128,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[287,278]) ).
thf(9129,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[9128]) ).
thf(9130,plain,
! [A: $i] : ( A @ skaf78 @ ( A @ skaf78 @ leq ) ),
inference(pattern_uni,[status(thm)],[9129:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(9152,plain,
! [A: $i] : ( A @ skaf78 @ ( A @ skaf78 @ leq ) ),
inference(simp,[status(thm)],[9130]) ).
thf(40,axiom,
! [A: $i] : ( A @ skaf54 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause41) ).
thf(270,plain,
! [A: $i] : ( A @ skaf54 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(24426,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[270,336]) ).
thf(24427,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[24426]) ).
thf(24428,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( A @ skaf54 @ neq ) ),
inference(pattern_uni,[status(thm)],[24427:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(24529,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( A @ skaf54 @ neq ) ),
inference(simp,[status(thm)],[24428]) ).
thf(68,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause75) ).
thf(327,plain,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(328,plain,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[327]) ).
thf(329,plain,
! [A: $i] :
( ( A @ tl @ ssList )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[328]) ).
thf(20582,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[201,329]) ).
thf(20583,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[20582]) ).
thf(20584,plain,
( ( sk1 @ tl @ ssList )
| ( nil = sk1 ) ),
inference(pattern_uni,[status(thm)],[20583:[bind(A,$thf( sk1 ))]]) ).
thf(12,negated_conjecture,
( ( nil @ ( sk2 @ neq ) )
| ( nil != sk1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
thf(206,plain,
( ( nil @ ( sk2 @ neq ) )
| ( nil != sk1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(213,plain,
( ( nil @ ( sk2 @ neq ) )
| ( nil != sk1 ) ),
inference(cnf,[status(esa)],[206]) ).
thf(214,plain,
( ( nil @ ( sk2 @ neq ) )
| ( nil != sk1 ) ),
inference(lifteq,[status(thm)],[213]) ).
thf(22541,plain,
( ( nil != nil )
| ( nil @ ( sk2 @ neq ) )
| ( sk1 != sk1 )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[20584,214]) ).
thf(22542,plain,
( ( nil != nil )
| ( nil @ ( sk2 @ neq ) )
| ( sk1 @ tl @ ssList ) ),
inference(simp,[status(thm)],[22541]) ).
thf(22543,plain,
( ( nil @ ( sk2 @ neq ) )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[22542:[]]) ).
thf(99,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( E @ ssList )
| ~ ( E @ equalelemsP )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( D @ ssList )
| ( ( D @ ( C @ cons ) @ ( B @ cons ) @ ( A @ app ) )
!= E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause180) ).
thf(405,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( E @ ssList )
| ~ ( E @ equalelemsP )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( D @ ssList )
| ( ( D @ ( C @ cons ) @ ( B @ cons ) @ ( A @ app ) )
!= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(406,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(cnf,[status(esa)],[405]) ).
thf(407,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ssList )
| ~ ( E @ equalelemsP )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( D @ ssList )
| ( B = C )
| ( ( D @ ( C @ cons ) @ ( B @ cons ) @ ( A @ app ) )
!= E ) ),
inference(lifteq,[status(thm)],[406]) ).
thf(408,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ cons ) @ ( B @ cons ) @ ( A @ app ) @ ssList )
| ~ ( D @ ( C @ cons ) @ ( B @ cons ) @ ( A @ app ) @ equalelemsP )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( D @ ssList )
| ( B = C ) ),
inference(simp,[status(thm)],[407]) ).
thf(150,axiom,
! [A: $i] :
( ( ( A @ skaf81 @ ( A @ skaf79 @ cons ) @ ( A @ skaf78 @ cons ) @ ( A @ skaf80 @ app ) )
= A )
| ( A @ equalelemsP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause142) ).
thf(523,plain,
! [A: $i] :
( ( ( A @ skaf81 @ ( A @ skaf79 @ cons ) @ ( A @ skaf78 @ cons ) @ ( A @ skaf80 @ app ) )
= A )
| ( A @ equalelemsP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(172,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ totalorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause125) ).
thf(582,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ totalorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(29,axiom,
! [A: $i] : ( A @ skaf55 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause40) ).
thf(251,plain,
! [A: $i] : ( A @ skaf55 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(10216,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[251,10172]) ).
thf(10217,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[10216]) ).
thf(10218,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[10217:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(10277,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[10218]) ).
thf(151,axiom,
! [A: $i] : ( A @ skaf81 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause14) ).
thf(526,plain,
! [A: $i] : ( A @ skaf81 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(10688,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[526,297]) ).
thf(10689,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[10688]) ).
thf(10690,plain,
! [A: $i] :
~ ( A @ skaf81 @ ( A @ skaf81 @ neq ) ),
inference(pattern_uni,[status(thm)],[10689:[bind(A,$thf( C )),bind(B,$thf( C @ skaf81 ))]]) ).
thf(10780,plain,
! [A: $i] :
~ ( A @ skaf81 @ ( A @ skaf81 @ neq ) ),
inference(simp,[status(thm)],[10690]) ).
thf(2,negated_conjecture,
sk2 @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
thf(205,plain,
sk2 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20821,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[205,329]) ).
thf(20822,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[20821]) ).
thf(20823,plain,
( ( sk2 @ tl @ ssList )
| ( nil = sk2 ) ),
inference(pattern_uni,[status(thm)],[20822:[bind(A,$thf( sk2 ))]]) ).
thf(139,axiom,
nil @ totalorderP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause6) ).
thf(502,plain,
nil @ totalorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(698,plain,
( ( nil != nil )
| ( sk2 @ totalorderP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,502]) ).
thf(699,plain,
( ( sk2 @ totalorderP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[698:[]]) ).
thf(10696,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[205,297]) ).
thf(10697,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[10696]) ).
thf(10698,plain,
~ ( sk2 @ ( sk2 @ neq ) ),
inference(pattern_uni,[status(thm)],[10697:[bind(A,$thf( sk2 ))]]) ).
thf(10922,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ~ $true
| ( sk2 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[699,10698]) ).
thf(10923,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ( sk2 @ totalorderP ) ),
inference(simp,[status(thm)],[10922]) ).
thf(10947,plain,
( ( nil != sk2 )
| ( sk2 != sk2 )
| ( sk2 @ totalorderP ) ),
inference(simp,[status(thm)],[10923]) ).
thf(10962,plain,
( ( nil != sk2 )
| ( sk2 @ totalorderP ) ),
inference(simp,[status(thm)],[10947]) ).
thf(22786,plain,
( ( nil != nil )
| ( sk2 != sk2 )
| ( sk2 @ totalorderP )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[20823,10962]) ).
thf(22787,plain,
( ( nil != nil )
| ( sk2 @ totalorderP )
| ( sk2 @ tl @ ssList ) ),
inference(simp,[status(thm)],[22786]) ).
thf(22788,plain,
( ( sk2 @ totalorderP )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[22787:[]]) ).
thf(91,axiom,
nil @ duplicatefreeP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause2) ).
thf(383,plain,
nil @ duplicatefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(22909,plain,
( ( nil != nil )
| ( sk2 @ duplicatefreeP )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[20823,383]) ).
thf(22910,plain,
( ( sk2 @ duplicatefreeP )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[22909:[]]) ).
thf(89,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf45 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause51) ).
thf(379,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf45 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(187,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause86) ).
thf(614,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(184,axiom,
! [A: $i] : ( A @ skaf76 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause19) ).
thf(609,plain,
! [A: $i] : ( A @ skaf76 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(10718,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[609,297]) ).
thf(10719,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[10718]) ).
thf(10720,plain,
! [A: $i] :
~ ( A @ skaf76 @ ( A @ skaf76 @ neq ) ),
inference(pattern_uni,[status(thm)],[10719:[bind(A,$thf( C )),bind(B,$thf( C @ skaf76 ))]]) ).
thf(10805,plain,
! [A: $i] :
~ ( A @ skaf76 @ ( A @ skaf76 @ neq ) ),
inference(simp,[status(thm)],[10720]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause156) ).
thf(268,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(269,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[268]) ).
thf(6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
thf(202,plain,
sk1 = sk3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(22505,plain,
( ( nil != nil )
| ( sk1 @ totalorderP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[20584,502]) ).
thf(22506,plain,
( ( sk1 @ totalorderP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[22505:[]]) ).
thf(10233,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[287,10172]) ).
thf(10234,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[10233]) ).
thf(10235,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[10234:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(10282,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[10235]) ).
thf(92,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ hd )
= A )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause97) ).
thf(384,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ hd )
= A )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(132,axiom,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause79) ).
thf(482,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(483,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(cnf,[status(esa)],[482]) ).
thf(484,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[483]) ).
thf(485,plain,
( ( nil @ ( nil @ segmentP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[484]) ).
thf(7302,plain,
( ( nil @ ( nil @ segmentP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[485,337]) ).
thf(7303,plain,
nil @ ( nil @ segmentP ),
inference(simp,[status(thm)],[7302]) ).
thf(13,negated_conjecture,
! [A: $i] :
( ~ ( A @ ( sk1 @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( A @ neq ) )
| ~ ( A @ ssList )
| ( nil != sk1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
thf(204,plain,
! [A: $i] :
( ~ ( A @ ( sk1 @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( A @ neq ) )
| ~ ( A @ ssList )
| ( nil != sk1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(215,plain,
! [A: $i] :
( ~ ( A @ ( sk1 @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( A @ neq ) )
| ~ ( A @ ssList )
| ( nil != sk1 ) ),
inference(cnf,[status(esa)],[204]) ).
thf(216,plain,
! [A: $i] :
( ~ ( A @ ( sk1 @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( A @ neq ) )
| ~ ( A @ ssList )
| ( nil != sk1 ) ),
inference(lifteq,[status(thm)],[215]) ).
thf(666,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( A @ neq ) ) )
| ~ ( A @ ( sk1 @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ $true
| ~ ( A @ ssList )
| ( nil != sk1 )
| ( nil != sk1 ) ),
inference(paramod_ordered,[status(thm)],[214,216]) ).
thf(667,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( A @ neq ) ) )
| ~ ( A @ ( sk1 @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[666]) ).
thf(668,plain,
( ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ssList )
| ( nil != sk1 ) ),
inference(pattern_uni,[status(thm)],[667:[bind(A,$thf( sk2 ))]]) ).
thf(3195,plain,
( ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ $true
| ( nil != sk1 ) ),
inference(rewrite,[status(thm)],[668,205]) ).
thf(3196,plain,
( ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[3195]) ).
thf(7342,plain,
( ( ( nil @ ( nil @ segmentP ) )
!= ( sk2 @ ( sk2 @ segmentP ) ) )
| ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ $true
| ( nil != sk1 ) ),
inference(paramod_ordered,[status(thm)],[7303,3196]) ).
thf(7343,plain,
( ( ( nil @ ( nil @ segmentP ) )
!= ( sk2 @ ( sk2 @ segmentP ) ) )
| ~ ( sk2 @ ( sk1 @ segmentP ) )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[7342]) ).
thf(7365,plain,
( ( nil != sk2 )
| ( nil != sk2 )
| ~ ( sk2 @ ( sk1 @ segmentP ) )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[7343]) ).
thf(7374,plain,
( ( nil != sk2 )
| ~ ( sk2 @ ( sk1 @ segmentP ) )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[7365]) ).
thf(8509,plain,
( ( ( nil @ ( nil @ segmentP ) )
!= ( sk2 @ ( sk1 @ segmentP ) ) )
| ( nil != sk2 )
| ~ $true
| ( nil != sk1 ) ),
inference(paramod_ordered,[status(thm)],[7303,7374]) ).
thf(8510,plain,
( ( ( nil @ ( nil @ segmentP ) )
!= ( sk2 @ ( sk1 @ segmentP ) ) )
| ( nil != sk2 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[8509]) ).
thf(8554,plain,
( ( nil != sk2 )
| ( nil != sk1 )
| ( nil != sk2 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[8510]) ).
thf(8568,plain,
( ( nil != sk2 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[8554]) ).
thf(88,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause66) ).
thf(377,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(378,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[377]) ).
thf(42145,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[251,378]) ).
thf(42146,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[42145]) ).
thf(42147,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[42146:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(42207,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[42147]) ).
thf(127,axiom,
! [A: $i] :
( ( ( nil @ ( A @ app ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause73) ).
thf(472,plain,
! [A: $i] :
( ( ( nil @ ( A @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ( B @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause132) ).
thf(338,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ( B @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(339,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ( B @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ frontsegP ) ) ),
inference(cnf,[status(esa)],[338]) ).
thf(340,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ frontsegP ) )
| ( ( B @ ( A @ skaf45 ) @ ( B @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[339]) ).
thf(32,axiom,
! [A: $i] : ( A @ skaf60 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause35) ).
thf(256,plain,
! [A: $i] : ( A @ skaf60 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(3678,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[256,247]) ).
thf(3679,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3678]) ).
thf(3680,plain,
! [A: $i] : ( A @ skaf60 @ ( A @ skaf60 @ geq ) ),
inference(pattern_uni,[status(thm)],[3679:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(3717,plain,
! [A: $i] : ( A @ skaf60 @ ( A @ skaf60 @ geq ) ),
inference(simp,[status(thm)],[3680]) ).
thf(17,axiom,
! [A: $i] : ( A @ skaf79 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause16) ).
thf(230,plain,
! [A: $i] : ( A @ skaf79 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause111) ).
thf(279,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(280,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[279]) ).
thf(281,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[280]) ).
thf(282,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[281]) ).
thf(9622,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[230,282]) ).
thf(9623,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[9622]) ).
thf(9624,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( A @ skaf79 @ lt ) ),
inference(pattern_uni,[status(thm)],[9623:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(9672,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( A @ skaf79 @ lt ) ),
inference(simp,[status(thm)],[9624]) ).
thf(179,axiom,
! [A: $i] : ( A @ skaf56 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause39) ).
thf(599,plain,
! [A: $i] : ( A @ skaf56 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(49531,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[599,392]) ).
thf(49532,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[49531]) ).
thf(49533,plain,
! [A: $i] :
( ( A @ skaf56 @ ( nil @ app ) )
= ( A @ skaf56 ) ),
inference(pattern_uni,[status(thm)],[49532:[bind(A,$thf( C )),bind(B,$thf( C @ skaf56 ))]]) ).
thf(49700,plain,
! [A: $i] :
( ( A @ skaf56 @ ( nil @ app ) )
= ( A @ skaf56 ) ),
inference(simp,[status(thm)],[49533]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ cons ) @ memberP ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause138) ).
thf(533,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ cons ) @ memberP ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(80,axiom,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause82) ).
thf(358,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(359,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
inference(cnf,[status(esa)],[358]) ).
thf(360,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[359]) ).
thf(32806,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( nil @ rearsegP ) )
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[201,360]) ).
thf(32807,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ rearsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[32806]) ).
thf(32808,plain,
( ~ ( sk1 @ ( nil @ rearsegP ) )
| ( nil = sk1 ) ),
inference(pattern_uni,[status(thm)],[32807:[bind(A,$thf( sk1 ))]]) ).
thf(191,axiom,
nil @ strictorderedP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause3) ).
thf(626,plain,
nil @ strictorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(38134,plain,
( ( nil != nil )
| ( sk1 @ strictorderedP )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[32808,626]) ).
thf(38135,plain,
( ( sk1 @ strictorderedP )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[38134:[]]) ).
thf(26309,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[201,342]) ).
thf(26310,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[26309]) ).
thf(26311,plain,
nil @ ( sk1 @ rearsegP ),
inference(pattern_uni,[status(thm)],[26310:[bind(A,$thf( sk1 ))]]) ).
thf(142,axiom,
nil @ cyclefreeP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause7) ).
thf(507,plain,
nil @ cyclefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(37980,plain,
( ( nil != nil )
| ( sk1 @ cyclefreeP )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[32808,507]) ).
thf(37981,plain,
( ( sk1 @ cyclefreeP )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[37980:[]]) ).
thf(43101,plain,
( ( ( sk1 @ ( nil @ rearsegP ) )
!= ( nil @ ( sk1 @ rearsegP ) ) )
| ( sk1 @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26311,37981]) ).
thf(43102,plain,
( ( ( sk1 @ ( nil @ rearsegP ) )
!= ( nil @ ( sk1 @ rearsegP ) ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[43101]) ).
thf(43220,plain,
( ( nil != sk1 )
| ( nil != sk1 )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[43102]) ).
thf(43250,plain,
( ( nil != sk1 )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[43220]) ).
thf(49534,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[609,392]) ).
thf(49535,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[49534]) ).
thf(49536,plain,
! [A: $i] :
( ( A @ skaf76 @ ( nil @ app ) )
= ( A @ skaf76 ) ),
inference(pattern_uni,[status(thm)],[49535:[bind(A,$thf( C )),bind(B,$thf( C @ skaf76 ))]]) ).
thf(49701,plain,
! [A: $i] :
( ( A @ skaf76 @ ( nil @ app ) )
= ( A @ skaf76 ) ),
inference(simp,[status(thm)],[49536]) ).
thf(38,axiom,
! [A: $i] : ( A @ skaf74 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause21) ).
thf(267,plain,
! [A: $i] : ( A @ skaf74 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(24468,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[267,336]) ).
thf(24469,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[24468]) ).
thf(24470,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( A @ skaf74 @ neq ) ),
inference(pattern_uni,[status(thm)],[24469:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(24522,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( A @ skaf74 @ neq ) ),
inference(simp,[status(thm)],[24470]) ).
thf(28,axiom,
! [A: $i] : ( A @ skaf69 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause26) ).
thf(250,plain,
! [A: $i] : ( A @ skaf69 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(124,axiom,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( nil @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause71) ).
thf(466,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(467,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(cnf,[status(esa)],[466]) ).
thf(826,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[250,467]) ).
thf(827,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[826]) ).
thf(828,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[827:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(829,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[828]) ).
thf(33108,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( nil @ rearsegP ) )
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[205,360]) ).
thf(33109,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ rearsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[33108]) ).
thf(33110,plain,
( ~ ( sk2 @ ( nil @ rearsegP ) )
| ( nil = sk2 ) ),
inference(pattern_uni,[status(thm)],[33109:[bind(A,$thf( sk2 ))]]) ).
thf(38376,plain,
( ( nil != nil )
| ( sk2 != sk2 )
| ( nil != sk1 )
| ~ ( sk2 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[33110,8568]) ).
thf(38377,plain,
( ( nil != nil )
| ( nil != sk1 )
| ~ ( sk2 @ ( nil @ rearsegP ) ) ),
inference(simp,[status(thm)],[38376]) ).
thf(38378,plain,
( ( nil != sk1 )
| ~ ( sk2 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[38377:[]]) ).
thf(102,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ app ) @ app ) )
= ( A @ ( B @ app ) @ ( C @ app ) ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause149) ).
thf(415,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ app ) @ app ) )
= ( A @ ( B @ app ) @ ( C @ app ) ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(416,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ app ) @ app ) )
= ( A @ ( B @ app ) @ ( C @ app ) ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[415]) ).
thf(417,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( A @ ( B @ ( C @ app ) @ app ) )
= ( A @ ( B @ app ) @ ( C @ app ) ) ) ),
inference(lifteq,[status(thm)],[416]) ).
thf(3705,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[250,247]) ).
thf(3706,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3705]) ).
thf(3707,plain,
! [A: $i] : ( A @ skaf69 @ ( A @ skaf69 @ geq ) ),
inference(pattern_uni,[status(thm)],[3706:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(3730,plain,
! [A: $i] : ( A @ skaf69 @ ( A @ skaf69 @ geq ) ),
inference(simp,[status(thm)],[3707]) ).
thf(26375,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[557,342]) ).
thf(26376,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[26375]) ).
thf(26377,plain,
! [A: $i] : ( nil @ ( A @ skaf51 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[26376:[bind(A,$thf( C )),bind(B,$thf( C @ skaf51 ))]]) ).
thf(26434,plain,
! [A: $i] : ( nil @ ( A @ skaf51 @ rearsegP ) ),
inference(simp,[status(thm)],[26377]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
!= ( B @ ( C @ app ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause151) ).
thf(436,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
!= ( B @ ( C @ app ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(9113,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[251,278]) ).
thf(9114,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[9113]) ).
thf(9115,plain,
! [A: $i] : ( A @ skaf55 @ ( A @ skaf55 @ leq ) ),
inference(pattern_uni,[status(thm)],[9114:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(9159,plain,
! [A: $i] : ( A @ skaf55 @ ( A @ skaf55 @ leq ) ),
inference(simp,[status(thm)],[9115]) ).
thf(51,axiom,
! [A: $i] : ( A @ skaf59 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause36) ).
thf(288,plain,
! [A: $i] : ( A @ skaf59 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(22511,plain,
( ( nil != nil )
| ( sk1 @ ( nil @ segmentP ) )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[20584,7303]) ).
thf(22512,plain,
( ( sk1 @ ( nil @ segmentP ) )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[22511:[]]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause90) ).
thf(301,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(166,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= ( C @ ( A @ app ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause150) ).
thf(565,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= ( C @ ( A @ app ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(36,axiom,
! [A: $i] : ( A @ skaf83 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause12) ).
thf(263,plain,
! [A: $i] : ( A @ skaf83 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(9122,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[263,278]) ).
thf(9123,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[9122]) ).
thf(9124,plain,
! [A: $i] : ( A @ skaf83 @ ( A @ skaf83 @ leq ) ),
inference(pattern_uni,[status(thm)],[9123:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(9148,plain,
! [A: $i] : ( A @ skaf83 @ ( A @ skaf83 @ leq ) ),
inference(simp,[status(thm)],[9124]) ).
thf(148,axiom,
! [A: $i] : ( A @ skaf67 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause28) ).
thf(520,plain,
! [A: $i] : ( A @ skaf67 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(10721,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[520,297]) ).
thf(10722,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[10721]) ).
thf(10723,plain,
! [A: $i] :
~ ( A @ skaf67 @ ( A @ skaf67 @ neq ) ),
inference(pattern_uni,[status(thm)],[10722:[bind(A,$thf( C )),bind(B,$thf( C @ skaf67 ))]]) ).
thf(10807,plain,
! [A: $i] :
~ ( A @ skaf67 @ ( A @ skaf67 @ neq ) ),
inference(simp,[status(thm)],[10723]) ).
thf(9655,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( A @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[283,282]) ).
thf(9656,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[9655]) ).
thf(9657,plain,
~ ( skac2 @ ( skac2 @ lt ) ),
inference(pattern_uni,[status(thm)],[9656:[bind(A,$thf( skac2 ))]]) ).
thf(48,axiom,
skac3 @ ssItem,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause9) ).
thf(284,plain,
skac3 @ ssItem,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(649,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[284,467]) ).
thf(650,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[649]) ).
thf(651,plain,
~ ( skac3 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[650:[bind(A,$thf( skac3 ))]]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause110) ).
thf(257,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(138,axiom,
! [A: $i] : ( A @ skaf68 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause27) ).
thf(501,plain,
! [A: $i] : ( A @ skaf68 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(26413,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[501,342]) ).
thf(26414,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[26413]) ).
thf(26415,plain,
! [A: $i] : ( nil @ ( A @ skaf68 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[26414:[bind(A,$thf( C )),bind(B,$thf( C @ skaf68 ))]]) ).
thf(26442,plain,
! [A: $i] : ( nil @ ( A @ skaf68 @ rearsegP ) ),
inference(simp,[status(thm)],[26415]) ).
thf(717,plain,
( ( nil != nil )
| ( nil @ ( sk2 @ neq ) )
| ( sk2 != sk1 )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,214]) ).
thf(718,plain,
( ( nil != nil )
| ( sk2 != sk1 )
| ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[717]) ).
thf(719,plain,
( ( sk2 != sk1 )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[718:[]]) ).
thf(38472,plain,
( ( nil != nil )
| ( sk2 @ cyclefreeP )
| ~ ( sk2 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[33110,507]) ).
thf(38473,plain,
( ( sk2 @ cyclefreeP )
| ~ ( sk2 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[38472:[]]) ).
thf(42133,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[230,378]) ).
thf(42134,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[42133]) ).
thf(42135,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[42134:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(42203,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[42135]) ).
thf(86,axiom,
! [B: $i,A: $i] :
( ( B @ singletonP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( nil @ ( A @ cons ) )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause116) ).
thf(369,plain,
! [B: $i,A: $i] :
( ( B @ singletonP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( nil @ ( A @ cons ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(370,plain,
! [B: $i,A: $i] :
( ( B @ singletonP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( nil @ ( A @ cons ) )
!= B ) ),
inference(cnf,[status(esa)],[369]) ).
thf(371,plain,
! [B: $i,A: $i] :
( ( B @ singletonP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( nil @ ( A @ cons ) )
!= B ) ),
inference(lifteq,[status(thm)],[370]) ).
thf(372,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ singletonP )
| ~ ( nil @ ( A @ cons ) @ ssList )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[371]) ).
thf(7348,plain,
( ( nil != nil )
| ( sk2 @ ( nil @ segmentP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,7303]) ).
thf(7349,plain,
( ( sk2 @ ( nil @ segmentP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[7348:[]]) ).
thf(79,axiom,
! [A: $i] :
( ( ( A @ skaf53 @ ( A @ skaf50 @ cons ) @ ( A @ skaf52 @ ( A @ skaf49 @ cons ) @ ( A @ skaf51 @ app ) @ app ) )
= A )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause167) ).
thf(355,plain,
! [A: $i] :
( ( ( A @ skaf53 @ ( A @ skaf50 @ cons ) @ ( A @ skaf52 @ ( A @ skaf49 @ cons ) @ ( A @ skaf51 @ app ) @ app ) )
= A )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(356,plain,
! [A: $i] :
( ( ( A @ skaf53 @ ( A @ skaf50 @ cons ) @ ( A @ skaf52 @ ( A @ skaf49 @ cons ) @ ( A @ skaf51 @ app ) @ app ) )
= A )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[355]) ).
thf(357,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ~ ( A @ ssList )
| ( ( A @ skaf53 @ ( A @ skaf50 @ cons ) @ ( A @ skaf52 @ ( A @ skaf49 @ cons ) @ ( A @ skaf51 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[356]) ).
thf(98,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ app ) )
= nil )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( nil != B )
| ( nil != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause145) ).
thf(401,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ app ) )
= nil )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( nil != B )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(402,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ app ) )
= nil )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( nil != B )
| ( nil != A ) ),
inference(cnf,[status(esa)],[401]) ).
thf(403,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
= nil )
| ( nil != B )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[402]) ).
thf(404,plain,
( ~ ( nil @ ssList )
| ( ( nil @ ( nil @ app ) )
= nil ) ),
inference(simp,[status(thm)],[403]) ).
thf(8021,plain,
( ~ $true
| ( ( nil @ ( nil @ app ) )
= nil ) ),
inference(rewrite,[status(thm)],[404,337]) ).
thf(8022,plain,
( ( nil @ ( nil @ app ) )
= nil ),
inference(simp,[status(thm)],[8021]) ).
thf(93,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ totalorderedP )
| ~ ( B @ hd @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause159) ).
thf(387,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ totalorderedP )
| ~ ( B @ hd @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(388,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ totalorderedP )
| ~ ( B @ hd @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[387]) ).
thf(389,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ totalorderedP )
| ~ ( B @ hd @ ( A @ leq ) )
| ( nil = B ) ),
inference(lifteq,[status(thm)],[388]) ).
thf(174,axiom,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause80) ).
thf(587,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(189,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ skaf48 ) @ ( B @ ( B @ ( A @ skaf47 ) @ app ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause168) ).
thf(619,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ skaf48 ) @ ( B @ ( B @ ( A @ skaf47 ) @ app ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(24477,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[250,336]) ).
thf(24478,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[24477]) ).
thf(24479,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( A @ skaf69 @ neq ) ),
inference(pattern_uni,[status(thm)],[24478:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(24526,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( A @ skaf69 @ neq ) ),
inference(simp,[status(thm)],[24479]) ).
thf(144,axiom,
! [A: $i] : ( A @ skaf52 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause43) ).
thf(512,plain,
! [A: $i] : ( A @ skaf52 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(26306,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[512,342]) ).
thf(26307,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[26306]) ).
thf(26308,plain,
! [A: $i] : ( nil @ ( A @ skaf52 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[26307:[bind(A,$thf( C )),bind(B,$thf( C @ skaf52 ))]]) ).
thf(26453,plain,
! [A: $i] : ( nil @ ( A @ skaf52 @ rearsegP ) ),
inference(simp,[status(thm)],[26308]) ).
thf(164,axiom,
! [A: $i] : ( A @ skaf63 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause32) ).
thf(563,plain,
! [A: $i] : ( A @ skaf63 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(49547,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[563,392]) ).
thf(49548,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[49547]) ).
thf(49549,plain,
! [A: $i] :
( ( A @ skaf63 @ ( nil @ app ) )
= ( A @ skaf63 ) ),
inference(pattern_uni,[status(thm)],[49548:[bind(A,$thf( C )),bind(B,$thf( C @ skaf63 ))]]) ).
thf(49704,plain,
! [A: $i] :
( ( A @ skaf63 @ ( nil @ app ) )
= ( A @ skaf63 ) ),
inference(simp,[status(thm)],[49549]) ).
thf(946,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[251,467]) ).
thf(947,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[946]) ).
thf(948,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[947:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(949,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[948]) ).
thf(3711,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[283,247]) ).
thf(3712,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) ) ),
inference(simp,[status(thm)],[3711]) ).
thf(3713,plain,
skac2 @ ( skac2 @ geq ),
inference(pattern_uni,[status(thm)],[3712:[bind(A,$thf( skac2 ))]]) ).
thf(814,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[230,467]) ).
thf(815,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[814]) ).
thf(816,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[815:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(817,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[816]) ).
thf(9104,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[230,278]) ).
thf(9105,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[9104]) ).
thf(9106,plain,
! [A: $i] : ( A @ skaf79 @ ( A @ skaf79 @ leq ) ),
inference(pattern_uni,[status(thm)],[9105:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(9155,plain,
! [A: $i] : ( A @ skaf79 @ ( A @ skaf79 @ leq ) ),
inference(simp,[status(thm)],[9106]) ).
thf(66,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( F @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause181) ).
thf(322,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( F @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(323,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( F @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
inference(cnf,[status(esa)],[322]) ).
thf(324,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( F @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
inference(lifteq,[status(thm)],[323]) ).
thf(325,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ lt ) )
| ~ ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) @ ssList )
| ~ ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList ) ),
inference(simp,[status(thm)],[324]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause106) ).
thf(228,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(181,axiom,
! [A: $i] : ( A @ skaf71 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause24) ).
thf(603,plain,
! [A: $i] : ( A @ skaf71 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(26404,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[603,342]) ).
thf(26405,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[26404]) ).
thf(26406,plain,
! [A: $i] : ( nil @ ( A @ skaf71 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[26405:[bind(A,$thf( C )),bind(B,$thf( C @ skaf71 ))]]) ).
thf(26438,plain,
! [A: $i] : ( nil @ ( A @ skaf71 @ rearsegP ) ),
inference(simp,[status(thm)],[26406]) ).
thf(63,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause134) ).
thf(314,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(315,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP ) ),
inference(cnf,[status(esa)],[314]) ).
thf(316,plain,
! [B: $i,A: $i] :
( ( B @ hd @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP )
| ( nil = B ) ),
inference(lifteq,[status(thm)],[315]) ).
thf(519,plain,
~ ( nil @ singletonP ),
inference(polarity_switch,[status(thm)],[518]) ).
thf(38033,plain,
( ( nil != nil )
| ~ ( sk1 @ singletonP )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[32808,519]) ).
thf(38034,plain,
( ~ ( sk1 @ singletonP )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[38033:[]]) ).
thf(39850,plain,
( ( ( sk1 @ ( nil @ rearsegP ) )
!= ( nil @ ( sk1 @ rearsegP ) ) )
| ~ ( sk1 @ singletonP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26311,38034]) ).
thf(39851,plain,
( ( ( sk1 @ ( nil @ rearsegP ) )
!= ( nil @ ( sk1 @ rearsegP ) ) )
| ~ ( sk1 @ singletonP ) ),
inference(simp,[status(thm)],[39850]) ).
thf(40003,plain,
( ( nil != sk1 )
| ( nil != sk1 )
| ~ ( sk1 @ singletonP ) ),
inference(simp,[status(thm)],[39851]) ).
thf(40019,plain,
( ( nil != sk1 )
| ~ ( sk1 @ singletonP ) ),
inference(simp,[status(thm)],[40003]) ).
thf(9634,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[267,282]) ).
thf(9635,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[9634]) ).
thf(9636,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( A @ skaf74 @ lt ) ),
inference(pattern_uni,[status(thm)],[9635:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(9661,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( A @ skaf74 @ lt ) ),
inference(simp,[status(thm)],[9636]) ).
thf(128,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause100) ).
thf(475,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(49461,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[512,392]) ).
thf(49462,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[49461]) ).
thf(49463,plain,
! [A: $i] :
( ( A @ skaf52 @ ( nil @ app ) )
= ( A @ skaf52 ) ),
inference(pattern_uni,[status(thm)],[49462:[bind(A,$thf( C )),bind(B,$thf( C @ skaf52 ))]]) ).
thf(49685,plain,
! [A: $i] :
( ( A @ skaf52 @ ( nil @ app ) )
= ( A @ skaf52 ) ),
inference(simp,[status(thm)],[49463]) ).
thf(3660,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[288,247]) ).
thf(3661,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3660]) ).
thf(3662,plain,
! [A: $i] : ( A @ skaf59 @ ( A @ skaf59 @ geq ) ),
inference(pattern_uni,[status(thm)],[3661:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(3724,plain,
! [A: $i] : ( A @ skaf59 @ ( A @ skaf59 @ geq ) ),
inference(simp,[status(thm)],[3662]) ).
thf(65,axiom,
! [A: $i] :
( ( ( A @ skaf73 @ ( A @ skaf70 @ cons ) @ ( A @ skaf72 @ ( A @ skaf69 @ cons ) @ ( A @ skaf71 @ app ) @ app ) )
= A )
| ( A @ strictorderedP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause163) ).
thf(319,plain,
! [A: $i] :
( ( ( A @ skaf73 @ ( A @ skaf70 @ cons ) @ ( A @ skaf72 @ ( A @ skaf69 @ cons ) @ ( A @ skaf71 @ app ) @ app ) )
= A )
| ( A @ strictorderedP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(320,plain,
! [A: $i] :
( ( ( A @ skaf73 @ ( A @ skaf70 @ cons ) @ ( A @ skaf72 @ ( A @ skaf69 @ cons ) @ ( A @ skaf71 @ app ) @ app ) )
= A )
| ( A @ strictorderedP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[319]) ).
thf(321,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ( ( A @ skaf73 @ ( A @ skaf70 @ cons ) @ ( A @ skaf72 @ ( A @ skaf69 @ cons ) @ ( A @ skaf71 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[320]) ).
thf(34,axiom,
! [A: $i] : ( A @ skaf49 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause46) ).
thf(259,plain,
! [A: $i] : ( A @ skaf49 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(10198,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[259,10172]) ).
thf(10199,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[10198]) ).
thf(10200,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[10199:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(10271,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[10200]) ).
thf(24488,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[287,336]) ).
thf(24489,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[24488]) ).
thf(24490,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( A @ skaf78 @ neq ) ),
inference(pattern_uni,[status(thm)],[24489:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(24528,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( A @ skaf78 @ neq ) ),
inference(simp,[status(thm)],[24490]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause126) ).
thf(236,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(237,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
inference(cnf,[status(esa)],[236]) ).
thf(238,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[237]) ).
thf(110,axiom,
! [A: $i] : ( A @ skaf61 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause34) ).
thf(435,plain,
! [A: $i] : ( A @ skaf61 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(49479,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[435,392]) ).
thf(49480,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[49479]) ).
thf(49481,plain,
! [A: $i] :
( ( A @ skaf61 @ ( nil @ app ) )
= ( A @ skaf61 ) ),
inference(pattern_uni,[status(thm)],[49480:[bind(A,$thf( C )),bind(B,$thf( C @ skaf61 ))]]) ).
thf(49690,plain,
! [A: $i] :
( ( A @ skaf61 @ ( nil @ app ) )
= ( A @ skaf61 ) ),
inference(simp,[status(thm)],[49481]) ).
thf(77,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ssList )
| ~ ( F @ cyclefreeP )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) )
!= F )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause185) ).
thf(350,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ssList )
| ~ ( F @ cyclefreeP )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) )
!= F )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(351,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ssList )
| ~ ( F @ cyclefreeP )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) )
!= F )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[350]) ).
thf(352,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ssList )
| ~ ( F @ cyclefreeP )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ~ ( E @ ssList )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ( ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) )
!= F ) ),
inference(lifteq,[status(thm)],[351]) ).
thf(353,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) @ ssList )
| ~ ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) @ cyclefreeP )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ~ ( E @ ssList )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[352]) ).
thf(818,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[233,467]) ).
thf(819,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[818]) ).
thf(820,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[819:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(821,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[820]) ).
thf(130,axiom,
! [A: $i] : ( A @ skaf53 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause42) ).
thf(480,plain,
! [A: $i] : ( A @ skaf53 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(22415,plain,
( ( nil != nil )
| ~ ( sk1 @ singletonP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[20584,519]) ).
thf(22416,plain,
( ~ ( sk1 @ singletonP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[22415:[]]) ).
thf(67,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf46 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause50) ).
thf(326,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf46 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(10748,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf46 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ~ ( C @ ( C @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[326,297]) ).
thf(10749,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf46 ) @ ssList )
!= ( C @ ssList ) )
| ~ ( C @ ( C @ neq ) ) ),
inference(simp,[status(thm)],[10748]) ).
thf(10750,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf46 ) @ ( B @ ( A @ skaf46 ) @ neq ) ),
inference(pattern_uni,[status(thm)],[10749:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf46 ) ))]]) ).
thf(10818,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf46 ) @ ( B @ ( A @ skaf46 ) @ neq ) ),
inference(simp,[status(thm)],[10750]) ).
thf(87,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ rearsegP ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
!= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause143) ).
thf(373,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ rearsegP ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
!= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(374,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ rearsegP ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
!= C ) ),
inference(cnf,[status(esa)],[373]) ).
thf(375,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ rearsegP ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
!= C ) ),
inference(lifteq,[status(thm)],[374]) ).
thf(376,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ app ) @ rearsegP ) )
| ~ ( B @ ( A @ app ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[375]) ).
thf(8,negated_conjecture,
sk3 @ totalorderedP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
thf(210,plain,
sk3 @ totalorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(212,plain,
sk3 = sk1,
inference(lifteq,[status(thm)],[202]) ).
thf(646,plain,
sk1 @ totalorderedP,
inference(rewrite,[status(thm)],[210,212]) ).
thf(7,negated_conjecture,
sk3 @ ( sk4 @ segmentP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
thf(207,plain,
sk3 @ ( sk4 @ segmentP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
thf(199,plain,
sk2 = sk4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(219,plain,
sk4 = sk2,
inference(lifteq,[status(thm)],[199]) ).
thf(648,plain,
sk1 @ ( sk2 @ segmentP ),
inference(rewrite,[status(thm)],[207,212,219]) ).
thf(9,negated_conjecture,
! [A: $i] :
( ~ ( A @ totalorderedP )
| ~ ( sk3 @ ( A @ segmentP ) )
| ~ ( A @ ( sk4 @ segmentP ) )
| ~ ( A @ ( sk3 @ neq ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
thf(203,plain,
! [A: $i] :
( ~ ( A @ totalorderedP )
| ~ ( sk3 @ ( A @ segmentP ) )
| ~ ( A @ ( sk4 @ segmentP ) )
| ~ ( A @ ( sk3 @ neq ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(220,plain,
! [A: $i] :
( ~ ( A @ totalorderedP )
| ~ ( sk3 @ ( A @ segmentP ) )
| ~ ( A @ ( sk4 @ segmentP ) )
| ~ ( A @ ( sk3 @ neq ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[203]) ).
thf(900,plain,
! [A: $i] :
( ~ ( A @ totalorderedP )
| ~ ( sk1 @ ( A @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( A @ ( sk1 @ neq ) )
| ~ ( A @ ssList ) ),
inference(rewrite,[status(thm)],[220,212,219]) ).
thf(921,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ segmentP ) )
!= ( sk1 @ ( A @ segmentP ) ) )
| ~ ( A @ totalorderedP )
| ~ $true
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( A @ ( sk1 @ neq ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[648,900]) ).
thf(922,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ segmentP ) )
!= ( sk1 @ ( A @ segmentP ) ) )
| ~ ( A @ totalorderedP )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( A @ ( sk1 @ neq ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[921]) ).
thf(923,plain,
( ~ ( sk2 @ totalorderedP )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) )
| ~ ( sk2 @ ssList ) ),
inference(pattern_uni,[status(thm)],[922:[bind(A,$thf( sk2 ))]]) ).
thf(5359,plain,
( ~ ( sk2 @ totalorderedP )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) )
| ~ $true ),
inference(rewrite,[status(thm)],[923,205]) ).
thf(5360,plain,
( ~ ( sk2 @ totalorderedP )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[5359]) ).
thf(5397,plain,
( ( ( sk2 @ ( sk2 @ segmentP ) )
!= ( sk1 @ ( sk2 @ segmentP ) ) )
| ~ ( sk2 @ totalorderedP )
| ~ $true
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[648,5360]) ).
thf(5398,plain,
( ( ( sk2 @ ( sk2 @ segmentP ) )
!= ( sk1 @ ( sk2 @ segmentP ) ) )
| ~ ( sk2 @ totalorderedP )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[5397]) ).
thf(5435,plain,
( ( sk2 != sk1 )
| ( sk2 != sk2 )
| ~ ( sk2 @ totalorderedP )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[5398]) ).
thf(5452,plain,
( ( sk2 != sk1 )
| ~ ( sk2 @ totalorderedP )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[5435]) ).
thf(5456,plain,
( ( ( sk2 @ totalorderedP )
!= ( sk1 @ totalorderedP ) )
| ( sk2 != sk1 )
| ~ $true
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[646,5452]) ).
thf(5457,plain,
( ( ( sk2 @ totalorderedP )
!= ( sk1 @ totalorderedP ) )
| ( sk2 != sk1 )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[5456]) ).
thf(5513,plain,
( ( sk2 != sk1 )
| ( sk2 != sk1 )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[5457]) ).
thf(5528,plain,
( ( sk2 != sk1 )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[5513]) ).
thf(5545,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk1 @ neq ) ) )
| ( sk2 != sk1 )
| ~ $true
| ( sk2 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[719,5528]) ).
thf(5546,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk1 @ neq ) ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[5545]) ).
thf(5598,plain,
( ( nil != sk2 )
| ( sk2 != sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[5546]) ).
thf(5619,plain,
( ( nil != sk2 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[5598]) ).
thf(22493,plain,
( ( nil != nil )
| ( sk2 != sk1 )
| ( sk2 != sk1 )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[20584,5619]) ).
thf(22494,plain,
( ( nil != nil )
| ( sk2 != sk1 )
| ( sk1 @ tl @ ssList ) ),
inference(simp,[status(thm)],[22493]) ).
thf(22495,plain,
( ( sk2 != sk1 )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[22494:[]]) ).
thf(25112,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) )
| ( sk2 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[22495,297]) ).
thf(25113,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[25112]) ).
thf(25114,plain,
( ~ ( sk1 @ tl @ ( sk1 @ tl @ neq ) )
| ( sk2 != sk1 ) ),
inference(pattern_uni,[status(thm)],[25113:[bind(A,$thf( sk1 @ tl ))]]) ).
thf(30504,plain,
( ( ( sk1 @ tl @ ( sk1 @ tl @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true
| ( sk2 != sk1 )
| ( sk2 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[719,25114]) ).
thf(30505,plain,
( ( ( sk1 @ tl @ ( sk1 @ tl @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[30504]) ).
thf(30626,plain,
( ( ( sk1 @ tl )
!= nil )
| ( ( sk1 @ tl )
!= sk2 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[30505]) ).
thf(661,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ segmentP ) )
!= ( A @ ( sk2 @ segmentP ) ) )
| ~ ( A @ ( sk1 @ segmentP ) )
| ~ $true
| ~ ( nil @ ( A @ neq ) )
| ~ ( A @ ssList )
| ( nil != sk1 ) ),
inference(paramod_ordered,[status(thm)],[648,216]) ).
thf(662,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ segmentP ) )
!= ( A @ ( sk2 @ segmentP ) ) )
| ~ ( A @ ( sk1 @ segmentP ) )
| ~ ( nil @ ( A @ neq ) )
| ~ ( A @ ssList )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[661]) ).
thf(663,plain,
( ~ ( sk1 @ ( sk1 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) )
| ~ ( sk1 @ ssList )
| ( nil != sk1 ) ),
inference(pattern_uni,[status(thm)],[662:[bind(A,$thf( sk1 ))]]) ).
thf(674,plain,
( ~ ( sk1 @ ( sk1 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) )
| ~ $true
| ( nil != sk1 ) ),
inference(rewrite,[status(thm)],[663,201]) ).
thf(675,plain,
( ~ ( sk1 @ ( sk1 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[674]) ).
thf(7324,plain,
( ( ( nil @ ( nil @ segmentP ) )
!= ( sk1 @ ( sk1 @ segmentP ) ) )
| ~ $true
| ~ ( nil @ ( sk1 @ neq ) )
| ( nil != sk1 ) ),
inference(paramod_ordered,[status(thm)],[7303,675]) ).
thf(7325,plain,
( ( ( nil @ ( nil @ segmentP ) )
!= ( sk1 @ ( sk1 @ segmentP ) ) )
| ~ ( nil @ ( sk1 @ neq ) )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[7324]) ).
thf(7360,plain,
( ( nil != sk1 )
| ( nil != sk1 )
| ~ ( nil @ ( sk1 @ neq ) )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[7325]) ).
thf(7369,plain,
( ~ ( nil @ ( sk1 @ neq ) )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[7360]) ).
thf(4,negated_conjecture,
sk4 @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
thf(211,plain,
sk4 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10742,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[603,297]) ).
thf(10743,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[10742]) ).
thf(10744,plain,
! [A: $i] :
~ ( A @ skaf71 @ ( A @ skaf71 @ neq ) ),
inference(pattern_uni,[status(thm)],[10743:[bind(A,$thf( C )),bind(B,$thf( C @ skaf71 ))]]) ).
thf(10816,plain,
! [A: $i] :
~ ( A @ skaf71 @ ( A @ skaf71 @ neq ) ),
inference(simp,[status(thm)],[10744]) ).
thf(26322,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[435,342]) ).
thf(26323,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[26322]) ).
thf(26324,plain,
! [A: $i] : ( nil @ ( A @ skaf61 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[26323:[bind(A,$thf( C )),bind(B,$thf( C @ skaf61 ))]]) ).
thf(26457,plain,
! [A: $i] : ( nil @ ( A @ skaf61 @ rearsegP ) ),
inference(simp,[status(thm)],[26324]) ).
thf(146,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ lt ) )
| ( D @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( F @ strictorderP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause183) ).
thf(514,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ lt ) )
| ( D @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( F @ strictorderP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(10896,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ~ $true
| ( sk2 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[7349,10698]) ).
thf(10897,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ( sk2 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[10896]) ).
thf(10957,plain,
( ( nil != sk2 )
| ( sk2 != sk2 )
| ( sk2 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[10897]) ).
thf(10972,plain,
( ( nil != sk2 )
| ( sk2 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[10957]) ).
thf(75,axiom,
! [A: $i] :
( ( ( A @ skaf63 @ ( A @ skaf60 @ cons ) @ ( A @ skaf62 @ ( A @ skaf59 @ cons ) @ ( A @ skaf61 @ app ) @ app ) )
= A )
| ( A @ strictorderP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause165) ).
thf(346,plain,
! [A: $i] :
( ( ( A @ skaf63 @ ( A @ skaf60 @ cons ) @ ( A @ skaf62 @ ( A @ skaf59 @ cons ) @ ( A @ skaf61 @ app ) @ app ) )
= A )
| ( A @ strictorderP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(347,plain,
! [A: $i] :
( ( ( A @ skaf63 @ ( A @ skaf60 @ cons ) @ ( A @ skaf62 @ ( A @ skaf59 @ cons ) @ ( A @ skaf61 @ app ) @ app ) )
= A )
| ( A @ strictorderP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[346]) ).
thf(348,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ( ( A @ skaf63 @ ( A @ skaf60 @ cons ) @ ( A @ skaf62 @ ( A @ skaf59 @ cons ) @ ( A @ skaf61 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[347]) ).
thf(24446,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[259,336]) ).
thf(24447,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[24446]) ).
thf(24448,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( A @ skaf49 @ neq ) ),
inference(pattern_uni,[status(thm)],[24447:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(24514,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( A @ skaf49 @ neq ) ),
inference(simp,[status(thm)],[24448]) ).
thf(10668,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[201,297]) ).
thf(10669,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[10668]) ).
thf(10670,plain,
~ ( sk1 @ ( sk1 @ neq ) ),
inference(pattern_uni,[status(thm)],[10669:[bind(A,$thf( sk1 ))]]) ).
thf(194,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ segmentP ) )
| ~ ( B @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause127) ).
thf(634,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ segmentP ) )
| ~ ( B @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(24418,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[284,336]) ).
thf(24419,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[24418]) ).
thf(24420,plain,
~ ( skac3 @ ( skac3 @ neq ) ),
inference(pattern_uni,[status(thm)],[24419:[bind(A,$thf( skac3 ))]]) ).
thf(24595,plain,
( ( ( skac3 @ ( skac3 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true
| ( nil != sk1 ) ),
inference(paramod_ordered,[status(thm)],[214,24420]) ).
thf(24596,plain,
( ( ( skac3 @ ( skac3 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[24595]) ).
thf(24621,plain,
( ( skac3 != nil )
| ( skac3 != sk2 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[24596]) ).
thf(76,axiom,
nil @ strictorderP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause5) ).
thf(349,plain,
nil @ strictorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(22384,plain,
( ( nil != nil )
| ( sk1 @ strictorderP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[20584,349]) ).
thf(22385,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[22384:[]]) ).
thf(1110,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[267,467]) ).
thf(1111,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1110]) ).
thf(1112,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1111:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(1119,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1112]) ).
thf(7346,plain,
( ( nil != nil )
| ( nil @ ( sk2 @ segmentP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,7303]) ).
thf(7347,plain,
( ( nil @ ( sk2 @ segmentP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[7346:[]]) ).
thf(10920,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ~ $true
| ( nil @ ( sk2 @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[7347,10698]) ).
thf(10921,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ( nil @ ( sk2 @ segmentP ) ) ),
inference(simp,[status(thm)],[10920]) ).
thf(10950,plain,
( ( nil != sk2 )
| ( sk2 != sk2 )
| ( nil @ ( sk2 @ segmentP ) ) ),
inference(simp,[status(thm)],[10921]) ).
thf(10965,plain,
( ( nil != sk2 )
| ( nil @ ( sk2 @ segmentP ) ) ),
inference(simp,[status(thm)],[10950]) ).
thf(10712,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[599,297]) ).
thf(10713,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[10712]) ).
thf(10714,plain,
! [A: $i] :
~ ( A @ skaf56 @ ( A @ skaf56 @ neq ) ),
inference(pattern_uni,[status(thm)],[10713:[bind(A,$thf( C )),bind(B,$thf( C @ skaf56 ))]]) ).
thf(10801,plain,
! [A: $i] :
~ ( A @ skaf56 @ ( A @ skaf56 @ neq ) ),
inference(simp,[status(thm)],[10714]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ gt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause146) ).
thf(243,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ gt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(10647,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[481,297]) ).
thf(10648,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[10647]) ).
thf(10649,plain,
! [A: $i] :
~ ( A @ skaf75 @ ( A @ skaf75 @ neq ) ),
inference(pattern_uni,[status(thm)],[10648:[bind(A,$thf( C )),bind(B,$thf( C @ skaf75 ))]]) ).
thf(10799,plain,
! [A: $i] :
~ ( A @ skaf75 @ ( A @ skaf75 @ neq ) ),
inference(simp,[status(thm)],[10649]) ).
thf(97,axiom,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause81) ).
thf(397,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(686,plain,
( ( nil != nil )
| ( sk2 @ cyclefreeP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,507]) ).
thf(687,plain,
( ( sk2 @ cyclefreeP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[686:[]]) ).
thf(96,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ skaf46 ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause131) ).
thf(394,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ skaf46 ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(395,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ skaf46 ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ rearsegP ) ) ),
inference(cnf,[status(esa)],[394]) ).
thf(396,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ rearsegP ) )
| ( ( B @ ( B @ ( A @ skaf46 ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[395]) ).
thf(43,axiom,
! [A: $i] : ( A @ skaf50 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause45) ).
thf(274,plain,
! [A: $i] : ( A @ skaf50 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(10204,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[274,10172]) ).
thf(10205,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[10204]) ).
thf(10206,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[10205:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(10273,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[10206]) ).
thf(10699,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[311,297]) ).
thf(10700,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[10699]) ).
thf(10701,plain,
! [A: $i] :
~ ( A @ skaf72 @ ( A @ skaf72 @ neq ) ),
inference(pattern_uni,[status(thm)],[10700:[bind(A,$thf( C )),bind(B,$thf( C @ skaf72 ))]]) ).
thf(10784,plain,
! [A: $i] :
~ ( A @ skaf72 @ ( A @ skaf72 @ neq ) ),
inference(simp,[status(thm)],[10701]) ).
thf(152,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ segmentP ) )
| ~ ( D @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ( ( C @ ( B @ ( A @ app ) @ app ) )
!= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause173) ).
thf(527,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ segmentP ) )
| ~ ( D @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ( ( C @ ( B @ ( A @ app ) @ app ) )
!= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ app ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause85) ).
thf(312,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ app ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(165,axiom,
! [A: $i] : ( A @ skaf66 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause29) ).
thf(564,plain,
! [A: $i] : ( A @ skaf66 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(49611,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[564,392]) ).
thf(49612,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[49611]) ).
thf(49613,plain,
! [A: $i] :
( ( A @ skaf66 @ ( nil @ app ) )
= ( A @ skaf66 ) ),
inference(pattern_uni,[status(thm)],[49612:[bind(A,$thf( C )),bind(B,$thf( C @ skaf66 ))]]) ).
thf(49714,plain,
! [A: $i] :
( ( A @ skaf66 @ ( nil @ app ) )
= ( A @ skaf66 ) ),
inference(simp,[status(thm)],[49613]) ).
thf(3684,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[230,247]) ).
thf(3685,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3684]) ).
thf(3686,plain,
! [A: $i] : ( A @ skaf79 @ ( A @ skaf79 @ geq ) ),
inference(pattern_uni,[status(thm)],[3685:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(3720,plain,
! [A: $i] : ( A @ skaf79 @ ( A @ skaf79 @ geq ) ),
inference(simp,[status(thm)],[3686]) ).
thf(42130,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[259,378]) ).
thf(42131,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[42130]) ).
thf(42132,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[42131:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(42202,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[42132]) ).
thf(24491,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[283,336]) ).
thf(24492,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[24491]) ).
thf(24493,plain,
~ ( skac2 @ ( skac2 @ neq ) ),
inference(pattern_uni,[status(thm)],[24492:[bind(A,$thf( skac2 ))]]) ).
thf(49599,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[603,392]) ).
thf(49600,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[49599]) ).
thf(49601,plain,
! [A: $i] :
( ( A @ skaf71 @ ( nil @ app ) )
= ( A @ skaf71 ) ),
inference(pattern_uni,[status(thm)],[49600:[bind(A,$thf( C )),bind(B,$thf( C @ skaf71 ))]]) ).
thf(49712,plain,
! [A: $i] :
( ( A @ skaf71 @ ( nil @ app ) )
= ( A @ skaf71 ) ),
inference(simp,[status(thm)],[49601]) ).
thf(10751,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[501,297]) ).
thf(10752,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[10751]) ).
thf(10753,plain,
! [A: $i] :
~ ( A @ skaf68 @ ( A @ skaf68 @ neq ) ),
inference(pattern_uni,[status(thm)],[10752:[bind(A,$thf( C )),bind(B,$thf( C @ skaf68 ))]]) ).
thf(10779,plain,
! [A: $i] :
~ ( A @ skaf68 @ ( A @ skaf68 @ neq ) ),
inference(simp,[status(thm)],[10753]) ).
thf(59,axiom,
! [A: $i] :
( ( ( nil @ ( A @ skaf44 @ cons ) )
= A )
| ~ ( A @ ssList )
| ~ ( A @ singletonP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause101) ).
thf(305,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf44 @ cons ) )
= A )
| ~ ( A @ ssList )
| ~ ( A @ singletonP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(306,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf44 @ cons ) )
= A )
| ~ ( A @ ssList )
| ~ ( A @ singletonP ) ),
inference(cnf,[status(esa)],[305]) ).
thf(307,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(lifteq,[status(thm)],[306]) ).
thf(26334,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[205,342]) ).
thf(26335,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[26334]) ).
thf(26336,plain,
nil @ ( sk2 @ rearsegP ),
inference(pattern_uni,[status(thm)],[26335:[bind(A,$thf( sk2 ))]]) ).
thf(38385,plain,
( ( nil != nil )
| ~ ( skac3 @ ( sk2 @ memberP ) )
| ~ ( sk2 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[33110,651]) ).
thf(38386,plain,
( ~ ( skac3 @ ( sk2 @ memberP ) )
| ~ ( sk2 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[38385:[]]) ).
thf(68052,plain,
( ( ( sk2 @ ( nil @ rearsegP ) )
!= ( nil @ ( sk2 @ rearsegP ) ) )
| ~ ( skac3 @ ( sk2 @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26336,38386]) ).
thf(68053,plain,
( ( ( sk2 @ ( nil @ rearsegP ) )
!= ( nil @ ( sk2 @ rearsegP ) ) )
| ~ ( skac3 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[68052]) ).
thf(68125,plain,
( ( nil != sk2 )
| ( nil != sk2 )
| ~ ( skac3 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[68053]) ).
thf(68137,plain,
( ( nil != sk2 )
| ~ ( skac3 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[68125]) ).
thf(117,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ cons ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause139) ).
thf(452,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ cons ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(49381,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[481,392]) ).
thf(49382,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[49381]) ).
thf(49383,plain,
! [A: $i] :
( ( A @ skaf75 @ ( nil @ app ) )
= ( A @ skaf75 ) ),
inference(pattern_uni,[status(thm)],[49382:[bind(A,$thf( C )),bind(B,$thf( C @ skaf75 ))]]) ).
thf(49721,plain,
! [A: $i] :
( ( A @ skaf75 @ ( nil @ app ) )
= ( A @ skaf75 ) ),
inference(simp,[status(thm)],[49383]) ).
thf(652,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[283,467]) ).
thf(653,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[652]) ).
thf(654,plain,
~ ( skac2 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[653:[bind(A,$thf( skac2 ))]]) ).
thf(38060,plain,
( ( nil != nil )
| ~ ( skac2 @ ( sk1 @ memberP ) )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[32808,654]) ).
thf(38061,plain,
( ~ ( skac2 @ ( sk1 @ memberP ) )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[38060:[]]) ).
thf(90,axiom,
! [A: $i] :
( ( ( A @ skaf58 @ ( A @ skaf55 @ cons ) @ ( A @ skaf57 @ ( A @ skaf54 @ cons ) @ ( A @ skaf56 @ app ) @ app ) )
= A )
| ( A @ totalorderP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause166) ).
thf(380,plain,
! [A: $i] :
( ( ( A @ skaf58 @ ( A @ skaf55 @ cons ) @ ( A @ skaf57 @ ( A @ skaf54 @ cons ) @ ( A @ skaf56 @ app ) @ app ) )
= A )
| ( A @ totalorderP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(10665,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[512,297]) ).
thf(10666,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[10665]) ).
thf(10667,plain,
! [A: $i] :
~ ( A @ skaf52 @ ( A @ skaf52 @ neq ) ),
inference(pattern_uni,[status(thm)],[10666:[bind(A,$thf( C )),bind(B,$thf( C @ skaf52 ))]]) ).
thf(10811,plain,
! [A: $i] :
~ ( A @ skaf52 @ ( A @ skaf52 @ neq ) ),
inference(simp,[status(thm)],[10667]) ).
thf(49476,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf48 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ( ( C @ ( nil @ app ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[456,392]) ).
thf(49477,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf48 ) @ ssList )
!= ( C @ ssList ) )
| ( ( C @ ( nil @ app ) )
= C ) ),
inference(simp,[status(thm)],[49476]) ).
thf(49478,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ skaf48 ) @ ( nil @ app ) )
= ( B @ ( A @ skaf48 ) ) ),
inference(pattern_uni,[status(thm)],[49477:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf48 ) ))]]) ).
thf(49689,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ skaf48 ) @ ( nil @ app ) )
= ( B @ ( A @ skaf48 ) ) ),
inference(simp,[status(thm)],[49478]) ).
thf(112,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ app ) @ frontsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause137) ).
thf(439,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ app ) @ frontsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(85,axiom,
nil @ equalelemsP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause1) ).
thf(368,plain,
nil @ equalelemsP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(38187,plain,
( ( nil != nil )
| ( sk1 @ equalelemsP )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[32808,368]) ).
thf(38188,plain,
( ( sk1 @ equalelemsP )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[38187:[]]) ).
thf(123,axiom,
! [A: $i] : ( A @ skaf80 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause15) ).
thf(465,plain,
! [A: $i] : ( A @ skaf80 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(26387,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[465,342]) ).
thf(26388,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[26387]) ).
thf(26389,plain,
! [A: $i] : ( nil @ ( A @ skaf80 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[26388:[bind(A,$thf( C )),bind(B,$thf( C @ skaf80 ))]]) ).
thf(26435,plain,
! [A: $i] : ( nil @ ( A @ skaf80 @ rearsegP ) ),
inference(simp,[status(thm)],[26389]) ).
thf(10754,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[337,297]) ).
thf(10755,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[10754]) ).
thf(10756,plain,
~ ( nil @ ( nil @ neq ) ),
inference(pattern_uni,[status(thm)],[10755:[bind(A,$thf( nil ))]]) ).
thf(38018,plain,
( ( nil != nil )
| ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[32808,10756]) ).
thf(38019,plain,
( ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[38018:[]]) ).
thf(398,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(cnf,[status(esa)],[397]) ).
thf(399,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[398]) ).
thf(400,plain,
( ( nil @ ( nil @ rearsegP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[399]) ).
thf(7262,plain,
( ( nil @ ( nil @ rearsegP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[400,337]) ).
thf(7263,plain,
nil @ ( nil @ rearsegP ),
inference(simp,[status(thm)],[7262]) ).
thf(7284,plain,
( ( nil != nil )
| ( nil @ ( sk2 @ rearsegP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,7263]) ).
thf(7285,plain,
( ( nil @ ( sk2 @ rearsegP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[7284:[]]) ).
thf(7640,plain,
( ( nil != nil )
| ( sk2 @ ( sk2 @ rearsegP ) )
| ( nil @ ( sk2 @ neq ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,7285]) ).
thf(7641,plain,
( ( nil != nil )
| ( sk2 @ ( sk2 @ rearsegP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[7640]) ).
thf(7642,plain,
( ( sk2 @ ( sk2 @ rearsegP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[7641:[]]) ).
thf(366,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf59 @ ( A @ skaf60 @ lt ) ) ),
inference(cnf,[status(esa)],[365]) ).
thf(22858,plain,
( ( nil != nil )
| ( sk2 != sk2 )
| ( sk2 != sk1 )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[20823,5619]) ).
thf(22859,plain,
( ( nil != nil )
| ( sk2 != sk1 )
| ( sk2 @ tl @ ssList ) ),
inference(simp,[status(thm)],[22858]) ).
thf(22860,plain,
( ( sk2 != sk1 )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[22859:[]]) ).
thf(32181,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) )
| ( sk2 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[22860,297]) ).
thf(32182,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[32181]) ).
thf(32183,plain,
( ~ ( sk2 @ tl @ ( sk2 @ tl @ neq ) )
| ( sk2 != sk1 ) ),
inference(pattern_uni,[status(thm)],[32182:[bind(A,$thf( sk2 @ tl ))]]) ).
thf(954,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[256,467]) ).
thf(955,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[954]) ).
thf(956,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[955:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(957,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[956]) ).
thf(822,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[245,467]) ).
thf(823,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[822]) ).
thf(824,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[823:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(825,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[824]) ).
thf(302,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(cnf,[status(esa)],[301]) ).
thf(26363,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[609,342]) ).
thf(26364,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[26363]) ).
thf(26365,plain,
! [A: $i] : ( nil @ ( A @ skaf76 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[26364:[bind(A,$thf( C )),bind(B,$thf( C @ skaf76 ))]]) ).
thf(26467,plain,
! [A: $i] : ( nil @ ( A @ skaf76 @ rearsegP ) ),
inference(simp,[status(thm)],[26365]) ).
thf(692,plain,
( ( nil != nil )
| ~ ( sk2 @ singletonP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,519]) ).
thf(693,plain,
( ~ ( sk2 @ singletonP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[692:[]]) ).
thf(10195,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[256,10172]) ).
thf(10196,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[10195]) ).
thf(10197,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[10196:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(10270,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[10197]) ).
thf(11105,plain,
! [A: $i] :
( ( nil != nil )
| ( sk2 @ ( A @ skaf60 @ cons ) @ totalorderedP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,10270]) ).
thf(11106,plain,
! [A: $i] :
( ( sk2 @ ( A @ skaf60 @ cons ) @ totalorderedP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[11105:[]]) ).
thf(10219,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[267,10172]) ).
thf(10220,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[10219]) ).
thf(10221,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[10220:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(10278,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[10221]) ).
thf(35,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause122) ).
thf(260,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(42180,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[283,378]) ).
thf(42181,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[42180]) ).
thf(42182,plain,
nil @ ( skac2 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[42181:[bind(A,$thf( skac2 ))]]) ).
thf(38148,plain,
( ( nil != nil )
| ( sk2 != sk1 )
| ( sk2 != sk1 )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[32808,5619]) ).
thf(38149,plain,
( ( nil != nil )
| ( sk2 != sk1 )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(simp,[status(thm)],[38148]) ).
thf(38150,plain,
( ( sk2 != sk1 )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[38149:[]]) ).
thf(78,axiom,
! [A: $i] : ( A @ skaf77 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause18) ).
thf(354,plain,
! [A: $i] : ( A @ skaf77 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(26419,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[354,342]) ).
thf(26420,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[26419]) ).
thf(26421,plain,
! [A: $i] : ( nil @ ( A @ skaf77 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[26420:[bind(A,$thf( C )),bind(B,$thf( C @ skaf77 ))]]) ).
thf(26445,plain,
! [A: $i] : ( nil @ ( A @ skaf77 @ rearsegP ) ),
inference(simp,[status(thm)],[26421]) ).
thf(229,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
inference(cnf,[status(esa)],[228]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause130) ).
thf(252,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(81,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause67) ).
thf(361,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(10660,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[480,297]) ).
thf(10661,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[10660]) ).
thf(10662,plain,
! [A: $i] :
~ ( A @ skaf53 @ ( A @ skaf53 @ neq ) ),
inference(pattern_uni,[status(thm)],[10661:[bind(A,$thf( C )),bind(B,$thf( C @ skaf53 ))]]) ).
thf(10808,plain,
! [A: $i] :
~ ( A @ skaf53 @ ( A @ skaf53 @ neq ) ),
inference(simp,[status(thm)],[10662]) ).
thf(3681,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[274,247]) ).
thf(3682,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3681]) ).
thf(3683,plain,
! [A: $i] : ( A @ skaf50 @ ( A @ skaf50 @ geq ) ),
inference(pattern_uni,[status(thm)],[3682:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(3718,plain,
! [A: $i] : ( A @ skaf50 @ ( A @ skaf50 @ geq ) ),
inference(simp,[status(thm)],[3683]) ).
thf(135,axiom,
! [A: $i] :
( ( A @ totalorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf65 @ ( A @ skaf64 @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause91) ).
thf(493,plain,
! [A: $i] :
( ( A @ totalorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf65 @ ( A @ skaf64 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(24567,plain,
( ( ( skac3 @ ( skac3 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true
| ~ ( sk2 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[693,24420]) ).
thf(24568,plain,
( ( ( skac3 @ ( skac3 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ ( sk2 @ singletonP ) ),
inference(simp,[status(thm)],[24567]) ).
thf(24620,plain,
( ( skac3 != nil )
| ( skac3 != sk2 )
| ~ ( sk2 @ singletonP ) ),
inference(simp,[status(thm)],[24568]) ).
thf(31,axiom,
! [A: $i] : ( A @ skaf70 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause25) ).
thf(255,plain,
! [A: $i] : ( A @ skaf70 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(3699,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[255,247]) ).
thf(3700,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3699]) ).
thf(3701,plain,
! [A: $i] : ( A @ skaf70 @ ( A @ skaf70 @ geq ) ),
inference(pattern_uni,[status(thm)],[3700:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(3727,plain,
! [A: $i] : ( A @ skaf70 @ ( A @ skaf70 @ geq ) ),
inference(simp,[status(thm)],[3701]) ).
thf(49447,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[480,392]) ).
thf(49448,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[49447]) ).
thf(49449,plain,
! [A: $i] :
( ( A @ skaf53 @ ( nil @ app ) )
= ( A @ skaf53 ) ),
inference(pattern_uni,[status(thm)],[49448:[bind(A,$thf( C )),bind(B,$thf( C @ skaf53 ))]]) ).
thf(49682,plain,
! [A: $i] :
( ( A @ skaf53 @ ( nil @ app ) )
= ( A @ skaf53 ) ),
inference(simp,[status(thm)],[49449]) ).
thf(9619,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[274,282]) ).
thf(9620,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[9619]) ).
thf(9621,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( A @ skaf50 @ lt ) ),
inference(pattern_uni,[status(thm)],[9620:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(9671,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( A @ skaf50 @ lt ) ),
inference(simp,[status(thm)],[9621]) ).
thf(95,axiom,
! [A: $i] : ( A @ skaf58 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause37) ).
thf(393,plain,
! [A: $i] : ( A @ skaf58 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(49494,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[393,392]) ).
thf(49495,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[49494]) ).
thf(49496,plain,
! [A: $i] :
( ( A @ skaf58 @ ( nil @ app ) )
= ( A @ skaf58 ) ),
inference(pattern_uni,[status(thm)],[49495:[bind(A,$thf( C )),bind(B,$thf( C @ skaf58 ))]]) ).
thf(49693,plain,
! [A: $i] :
( ( A @ skaf58 @ ( nil @ app ) )
= ( A @ skaf58 ) ),
inference(simp,[status(thm)],[49496]) ).
thf(14,axiom,
skac3 != skac2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause54) ).
thf(223,plain,
skac3 != skac2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(224,plain,
skac3 != skac2,
inference(polarity_switch,[status(thm)],[223]) ).
thf(225,plain,
skac2 != skac3,
inference(lifteq,[status(thm)],[224]) ).
thf(33014,plain,
! [A: $i] :
( ( A != skac2 )
| ( skac3 != nil )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[360,225]) ).
thf(33015,plain,
( ( skac3 != nil )
| ~ ( skac2 @ ssList )
| ~ ( skac2 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[33014:[bind(A,$thf( skac2 ))]]) ).
thf(35848,plain,
( ( ( skac2 @ ( nil @ rearsegP ) )
!= ( nil @ ( nil @ rearsegP ) ) )
| ( skac3 != nil )
| ~ ( skac2 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7263,33015]) ).
thf(35849,plain,
( ( ( skac2 @ ( nil @ rearsegP ) )
!= ( nil @ ( nil @ rearsegP ) ) )
| ( skac3 != nil )
| ~ ( skac2 @ ssList ) ),
inference(simp,[status(thm)],[35848]) ).
thf(35948,plain,
( ( skac2 != nil )
| ( nil != nil )
| ( skac3 != nil )
| ~ ( skac2 @ ssList ) ),
inference(simp,[status(thm)],[35849]) ).
thf(35965,plain,
( ( skac2 != nil )
| ( skac3 != nil )
| ~ ( skac2 @ ssList ) ),
inference(simp,[status(thm)],[35948]) ).
thf(36110,plain,
( ( ( skac2 @ ssList )
!= ( nil @ ssList ) )
| ( skac2 != nil )
| ( skac3 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[337,35965]) ).
thf(36111,plain,
( ( ( skac2 @ ssList )
!= ( nil @ ssList ) )
| ( skac2 != nil )
| ( skac3 != nil ) ),
inference(simp,[status(thm)],[36110]) ).
thf(36149,plain,
( ( skac2 != nil )
| ( skac2 != nil )
| ( skac3 != nil ) ),
inference(simp,[status(thm)],[36111]) ).
thf(36188,plain,
( ( skac2 != nil )
| ( skac3 != nil ) ),
inference(simp,[status(thm)],[36149]) ).
thf(22725,plain,
( ( nil != nil )
| ( sk2 @ cyclefreeP )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[20823,507]) ).
thf(22726,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[22725:[]]) ).
thf(42142,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[274,378]) ).
thf(42143,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[42142]) ).
thf(42144,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[42143:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(42206,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[42144]) ).
thf(49,axiom,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause63) ).
thf(285,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(3675,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[270,247]) ).
thf(3676,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3675]) ).
thf(3677,plain,
! [A: $i] : ( A @ skaf54 @ ( A @ skaf54 @ geq ) ),
inference(pattern_uni,[status(thm)],[3676:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(3731,plain,
! [A: $i] : ( A @ skaf54 @ ( A @ skaf54 @ geq ) ),
inference(simp,[status(thm)],[3677]) ).
thf(1341,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[288,467]) ).
thf(1342,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1341]) ).
thf(1343,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1342:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(1360,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1343]) ).
thf(41,axiom,
! [A: $i] : ( A @ skaf65 @ ssItem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause30) ).
thf(271,plain,
! [A: $i] : ( A @ skaf65 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(1134,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[271,467]) ).
thf(1135,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1134]) ).
thf(1136,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1135:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(1143,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1136]) ).
thf(64,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ frontsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause154) ).
thf(317,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ frontsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(196,axiom,
nil @ totalorderedP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause4) ).
thf(639,plain,
nil @ totalorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(724,plain,
( ( nil != nil )
| ( sk2 @ totalorderedP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,639]) ).
thf(725,plain,
( ( sk2 @ totalorderedP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[724:[]]) ).
thf(700,plain,
( ( nil != nil )
| ( sk2 @ equalelemsP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,368]) ).
thf(701,plain,
( ( sk2 @ equalelemsP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[700:[]]) ).
thf(10916,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ~ $true
| ( sk2 @ equalelemsP ) ),
inference(paramod_ordered,[status(thm)],[701,10698]) ).
thf(10917,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ( sk2 @ equalelemsP ) ),
inference(simp,[status(thm)],[10916]) ).
thf(10953,plain,
( ( nil != sk2 )
| ( sk2 != sk2 )
| ( sk2 @ equalelemsP ) ),
inference(simp,[status(thm)],[10917]) ).
thf(10968,plain,
( ( nil != sk2 )
| ( sk2 @ equalelemsP ) ),
inference(simp,[status(thm)],[10953]) ).
thf(22793,plain,
( ( nil != nil )
| ( sk2 != sk2 )
| ( sk2 @ equalelemsP )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[20823,10968]) ).
thf(22794,plain,
( ( nil != nil )
| ( sk2 @ equalelemsP )
| ( sk2 @ tl @ ssList ) ),
inference(simp,[status(thm)],[22793]) ).
thf(22795,plain,
( ( sk2 @ equalelemsP )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[22794:[]]) ).
thf(177,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ app ) @ hd )
= ( B @ hd ) )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause123) ).
thf(593,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ app ) @ hd )
= ( B @ hd ) )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause102) ).
thf(420,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(696,plain,
( ( nil != nil )
| ( sk2 @ strictorderedP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,626]) ).
thf(697,plain,
( ( sk2 @ strictorderedP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[696:[]]) ).
thf(24459,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[271,336]) ).
thf(24460,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[24459]) ).
thf(24461,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( A @ skaf65 @ neq ) ),
inference(pattern_uni,[status(thm)],[24460:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(24519,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( A @ skaf65 @ neq ) ),
inference(simp,[status(thm)],[24461]) ).
thf(10228,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[250,10172]) ).
thf(10229,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[10228]) ).
thf(10230,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[10229:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(10281,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[10230]) ).
thf(42075,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[288,378]) ).
thf(42076,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[42075]) ).
thf(42077,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[42076:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(42221,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[42077]) ).
thf(10176,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[284,10172]) ).
thf(10177,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[10176]) ).
thf(10178,plain,
nil @ ( skac3 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[10177:[bind(A,$thf( skac3 ))]]) ).
thf(10317,plain,
( ( nil != nil )
| ( sk2 @ ( skac3 @ cons ) @ totalorderedP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,10178]) ).
thf(10318,plain,
( ( sk2 @ ( skac3 @ cons ) @ totalorderedP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[10317:[]]) ).
thf(37998,plain,
( ( nil != nil )
| ( sk1 @ strictorderP )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[32808,349]) ).
thf(37999,plain,
( ( sk1 @ strictorderP )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[37998:[]]) ).
thf(44462,plain,
( ( ( nil @ ( nil @ rearsegP ) )
!= ( sk1 @ ( nil @ rearsegP ) ) )
| ( sk1 @ strictorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7263,37999]) ).
thf(44463,plain,
( ( ( nil @ ( nil @ rearsegP ) )
!= ( sk1 @ ( nil @ rearsegP ) ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[44462]) ).
thf(44494,plain,
( ( nil != sk1 )
| ( nil != nil )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[44463]) ).
thf(44517,plain,
( ( nil != sk1 )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[44494]) ).
thf(185,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf42 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause53) ).
thf(610,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf42 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(37958,plain,
( ( nil != nil )
| ~ ( nil @ ( sk1 @ neq ) )
| ( sk1 != sk1 )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[32808,7369]) ).
thf(37959,plain,
( ( nil != nil )
| ~ ( nil @ ( sk1 @ neq ) )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(simp,[status(thm)],[37958]) ).
thf(37960,plain,
( ~ ( nil @ ( sk1 @ neq ) )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[37959:[]]) ).
thf(38508,plain,
( ( nil != nil )
| ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk2 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[33110,10756]) ).
thf(38509,plain,
( ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk2 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[38508:[]]) ).
thf(24641,plain,
( ( ( skac2 @ ( skac2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true
| ( sk2 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[719,24493]) ).
thf(24642,plain,
( ( ( skac2 @ ( skac2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[24641]) ).
thf(24722,plain,
( ( skac2 != nil )
| ( skac2 != sk2 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[24642]) ).
thf(9613,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[256,282]) ).
thf(9614,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[9613]) ).
thf(9615,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( A @ skaf60 @ lt ) ),
inference(pattern_uni,[status(thm)],[9614:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(9667,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( A @ skaf60 @ lt ) ),
inference(simp,[status(thm)],[9615]) ).
thf(155,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ memberP ) )
| ~ ( D @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ( ( C @ ( B @ cons ) @ ( A @ app ) )
!= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause175) ).
thf(537,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ memberP ) )
| ~ ( D @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ( ( C @ ( B @ cons ) @ ( A @ app ) )
!= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(3702,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[263,247]) ).
thf(3703,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3702]) ).
thf(3704,plain,
! [A: $i] : ( A @ skaf83 @ ( A @ skaf83 @ geq ) ),
inference(pattern_uni,[status(thm)],[3703:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(3728,plain,
! [A: $i] : ( A @ skaf83 @ ( A @ skaf83 @ geq ) ),
inference(simp,[status(thm)],[3704]) ).
thf(195,axiom,
! [A: $i] :
( ( A @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause57) ).
thf(637,plain,
! [A: $i] :
( ( A @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(134,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ssList )
| ~ ( E @ duplicatefreeP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ( ( D @ ( B @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause179) ).
thf(489,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ssList )
| ~ ( E @ duplicatefreeP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ( ( D @ ( B @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(175,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ rearsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ rearsegP ) )
| ~ ( B @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause153) ).
thf(590,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ rearsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ rearsegP ) )
| ~ ( B @ ( A @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(3690,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[271,247]) ).
thf(3691,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3690]) ).
thf(3692,plain,
! [A: $i] : ( A @ skaf65 @ ( A @ skaf65 @ geq ) ),
inference(pattern_uni,[status(thm)],[3691:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(3723,plain,
! [A: $i] : ( A @ skaf65 @ ( A @ skaf65 @ geq ) ),
inference(simp,[status(thm)],[3692]) ).
thf(9637,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[255,282]) ).
thf(9638,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[9637]) ).
thf(9639,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( A @ skaf70 @ lt ) ),
inference(pattern_uni,[status(thm)],[9638:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(9662,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( A @ skaf70 @ lt ) ),
inference(simp,[status(thm)],[9639]) ).
thf(160,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ app ) @ tl )
= ( A @ ( B @ tl @ app ) ) )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause133) ).
thf(554,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ app ) @ tl )
= ( A @ ( B @ tl @ app ) ) )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(22278,plain,
( ( nil != nil )
| ( nil != sk2 )
| ( sk1 != sk1 )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[20584,8568]) ).
thf(22279,plain,
( ( nil != nil )
| ( nil != sk2 )
| ( sk1 @ tl @ ssList ) ),
inference(simp,[status(thm)],[22278]) ).
thf(22280,plain,
( ( nil != sk2 )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[22279:[]]) ).
thf(23044,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) )
| ( nil != sk2 ) ),
inference(paramod_ordered,[status(thm)],[22280,297]) ).
thf(23045,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ( nil != sk2 ) ),
inference(simp,[status(thm)],[23044]) ).
thf(23046,plain,
( ~ ( sk1 @ tl @ ( sk1 @ tl @ neq ) )
| ( nil != sk2 ) ),
inference(pattern_uni,[status(thm)],[23045:[bind(A,$thf( sk1 @ tl ))]]) ).
thf(9092,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[270,278]) ).
thf(9093,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[9092]) ).
thf(9094,plain,
! [A: $i] : ( A @ skaf54 @ ( A @ skaf54 @ leq ) ),
inference(pattern_uni,[status(thm)],[9093:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(9149,plain,
! [A: $i] : ( A @ skaf54 @ ( A @ skaf54 @ leq ) ),
inference(simp,[status(thm)],[9094]) ).
thf(22639,plain,
( ( nil != nil )
| ( sk2 != sk2 )
| ( nil != sk1 )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[20823,8568]) ).
thf(22640,plain,
( ( nil != nil )
| ( nil != sk1 )
| ( sk2 @ tl @ ssList ) ),
inference(simp,[status(thm)],[22639]) ).
thf(22641,plain,
( ( nil != sk1 )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[22640:[]]) ).
thf(120,axiom,
! [A: $i] :
( ( nil @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause56) ).
thf(457,plain,
! [A: $i] :
( ( nil @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(82,axiom,
! [B: $i,A: $i] :
( ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause72) ).
thf(363,plain,
! [B: $i,A: $i] :
( ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(364,plain,
! [B: $i,A: $i] :
( ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[363]) ).
thf(36267,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[201,364]) ).
thf(36268,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP ) ),
inference(simp,[status(thm)],[36267]) ).
thf(36269,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk1 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[36268:[bind(A,$thf( sk1 ))]]) ).
thf(36501,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[36269]) ).
thf(42153,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[255,378]) ).
thf(42154,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[42153]) ).
thf(42155,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[42154:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(42209,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[42155]) ).
thf(140,axiom,
! [A: $i] :
( ( nil @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause60) ).
thf(503,plain,
! [A: $i] :
( ( nil @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(1122,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[270,467]) ).
thf(1123,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1122]) ).
thf(1124,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1123:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(1131,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1124]) ).
thf(24411,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[288,336]) ).
thf(24412,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[24411]) ).
thf(24413,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( A @ skaf59 @ neq ) ),
inference(pattern_uni,[status(thm)],[24412:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(24525,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( A @ skaf59 @ neq ) ),
inference(simp,[status(thm)],[24413]) ).
thf(49245,plain,
( ( ( nil @ ( nil @ rearsegP ) )
!= ( sk1 @ ( nil @ rearsegP ) ) )
| ( sk1 @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7263,38135]) ).
thf(49246,plain,
( ( ( nil @ ( nil @ rearsegP ) )
!= ( sk1 @ ( nil @ rearsegP ) ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[49245]) ).
thf(49283,plain,
( ( nil != sk1 )
| ( nil != nil )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[49246]) ).
thf(49294,plain,
( ( nil != sk1 )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[49283]) ).
thf(244,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ gt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
inference(cnf,[status(esa)],[243]) ).
thf(10676,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf48 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ~ ( C @ ( C @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[456,297]) ).
thf(10677,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf48 ) @ ssList )
!= ( C @ ssList ) )
| ~ ( C @ ( C @ neq ) ) ),
inference(simp,[status(thm)],[10676]) ).
thf(10678,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf48 ) @ ( B @ ( A @ skaf48 ) @ neq ) ),
inference(pattern_uni,[status(thm)],[10677:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf48 ) ))]]) ).
thf(10815,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf48 ) @ ( B @ ( A @ skaf48 ) @ neq ) ),
inference(simp,[status(thm)],[10678]) ).
thf(22571,plain,
( ( nil != nil )
| ( nil @ ( sk1 @ frontsegP ) )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[20584,7387]) ).
thf(22572,plain,
( ( nil @ ( sk1 @ frontsegP ) )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[22571:[]]) ).
thf(143,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ leq ) )
| ( D @ ( B @ leq ) )
| ~ ( F @ ssList )
| ~ ( F @ totalorderP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause184) ).
thf(508,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ leq ) )
| ( D @ ( B @ leq ) )
| ~ ( F @ ssList )
| ~ ( F @ totalorderP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(42116,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[256,378]) ).
thf(42117,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[42116]) ).
thf(42118,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[42117:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(42199,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[42118]) ).
thf(156,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ app ) @ ( A @ cons ) )
= ( C @ ( B @ ( A @ cons ) @ app ) ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause157) ).
thf(541,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ app ) @ ( A @ cons ) )
= ( C @ ( B @ ( A @ cons ) @ app ) ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(162,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause68) ).
thf(558,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(950,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[255,467]) ).
thf(951,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[950]) ).
thf(952,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[951:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(953,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[952]) ).
thf(74,axiom,
! [B: $i,A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause118) ).
thf(343,plain,
! [B: $i,A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(26331,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[393,342]) ).
thf(26332,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[26331]) ).
thf(26333,plain,
! [A: $i] : ( nil @ ( A @ skaf58 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[26332:[bind(A,$thf( C )),bind(B,$thf( C @ skaf58 ))]]) ).
thf(26460,plain,
! [A: $i] : ( nil @ ( A @ skaf58 @ rearsegP ) ),
inference(simp,[status(thm)],[26333]) ).
thf(1301,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[274,467]) ).
thf(1302,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1301]) ).
thf(1303,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1302:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(1318,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1303]) ).
thf(26407,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[564,342]) ).
thf(26408,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[26407]) ).
thf(26409,plain,
! [A: $i] : ( nil @ ( A @ skaf66 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[26408:[bind(A,$thf( C )),bind(B,$thf( C @ skaf66 ))]]) ).
thf(26439,plain,
! [A: $i] : ( nil @ ( A @ skaf66 @ rearsegP ) ),
inference(simp,[status(thm)],[26409]) ).
thf(10685,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf42 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ~ ( C @ ( C @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[610,297]) ).
thf(10686,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf42 ) @ ssList )
!= ( C @ ssList ) )
| ~ ( C @ ( C @ neq ) ) ),
inference(simp,[status(thm)],[10685]) ).
thf(10687,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf42 ) @ ( B @ ( A @ skaf42 ) @ neq ) ),
inference(pattern_uni,[status(thm)],[10686:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf42 ) ))]]) ).
thf(10819,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf42 ) @ ( B @ ( A @ skaf42 ) @ neq ) ),
inference(simp,[status(thm)],[10687]) ).
thf(176,axiom,
! [A: $i] : ( A @ skaf82 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause13) ).
thf(592,plain,
! [A: $i] : ( A @ skaf82 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(10762,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[592,297]) ).
thf(10763,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[10762]) ).
thf(10764,plain,
! [A: $i] :
~ ( A @ skaf82 @ ( A @ skaf82 @ neq ) ),
inference(pattern_uni,[status(thm)],[10763:[bind(A,$thf( C )),bind(B,$thf( C @ skaf82 ))]]) ).
thf(10783,plain,
! [A: $i] :
~ ( A @ skaf82 @ ( A @ skaf82 @ neq ) ),
inference(simp,[status(thm)],[10764]) ).
thf(26369,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[563,342]) ).
thf(26370,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[26369]) ).
thf(26371,plain,
! [A: $i] : ( nil @ ( A @ skaf63 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[26370:[bind(A,$thf( C )),bind(B,$thf( C @ skaf63 ))]]) ).
thf(26432,plain,
! [A: $i] : ( nil @ ( A @ skaf63 @ rearsegP ) ),
inference(simp,[status(thm)],[26371]) ).
thf(55,axiom,
! [A: $i] : ( A @ skaf62 @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause33) ).
thf(298,plain,
! [A: $i] : ( A @ skaf62 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(100,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ cons ) @ ( A @ ( C @ cons ) @ frontsegP ) )
| ~ ( C @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( C != D )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause178) ).
thf(409,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ cons ) @ ( A @ ( C @ cons ) @ frontsegP ) )
| ~ ( C @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( C != D )
| ~ ( B @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(410,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(cnf,[status(esa)],[409]) ).
thf(411,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ cons ) @ ( A @ ( C @ cons ) @ frontsegP ) )
| ~ ( C @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ frontsegP ) )
| ( C != D ) ),
inference(lifteq,[status(thm)],[410]) ).
thf(412,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ cons ) @ ( A @ ( C @ cons ) @ frontsegP ) )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ frontsegP ) ) ),
inference(simp,[status(thm)],[411]) ).
thf(964,plain,
! [A: $i] :
( ( nil != nil )
| ~ ( A @ skaf79 @ ( sk2 @ memberP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,817]) ).
thf(965,plain,
! [A: $i] :
( ~ ( A @ skaf79 @ ( sk2 @ memberP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[964:[]]) ).
thf(10906,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[687,10698]) ).
thf(10907,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[10906]) ).
thf(10956,plain,
( ( nil != sk2 )
| ( sk2 != sk2 )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[10907]) ).
thf(10971,plain,
( ( nil != sk2 )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[10956]) ).
thf(38169,plain,
( ( nil != nil )
| ( sk1 @ totalorderP )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[32808,502]) ).
thf(38170,plain,
( ( sk1 @ totalorderP )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[38169:[]]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause121) ).
thf(264,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(688,plain,
( ( nil != nil )
| ( sk2 @ strictorderP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,349]) ).
thf(689,plain,
( ( sk2 @ strictorderP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[688:[]]) ).
thf(26283,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[481,342]) ).
thf(26284,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[26283]) ).
thf(26285,plain,
! [A: $i] : ( nil @ ( A @ skaf75 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[26284:[bind(A,$thf( C )),bind(B,$thf( C @ skaf75 ))]]) ).
thf(26441,plain,
! [A: $i] : ( nil @ ( A @ skaf75 @ rearsegP ) ),
inference(simp,[status(thm)],[26285]) ).
thf(114,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause129) ).
thf(444,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(50664,plain,
( ( ( sk1 @ ( nil @ rearsegP ) )
!= ( nil @ ( sk1 @ rearsegP ) ) )
| ( sk1 @ totalorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26311,38170]) ).
thf(50665,plain,
( ( ( sk1 @ ( nil @ rearsegP ) )
!= ( nil @ ( sk1 @ rearsegP ) ) )
| ( sk1 @ totalorderP ) ),
inference(simp,[status(thm)],[50664]) ).
thf(50776,plain,
( ( nil != sk1 )
| ( nil != sk1 )
| ( sk1 @ totalorderP ) ),
inference(simp,[status(thm)],[50665]) ).
thf(50810,plain,
( ( nil != sk1 )
| ( sk1 @ totalorderP ) ),
inference(simp,[status(thm)],[50776]) ).
thf(42080,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[284,378]) ).
thf(42081,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[42080]) ).
thf(42082,plain,
nil @ ( skac3 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[42081:[bind(A,$thf( skac3 ))]]) ).
thf(145,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf47 ) @ ssList ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause49) ).
thf(513,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf47 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(108,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause98) ).
thf(430,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(169,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause77) ).
thf(573,plain,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(9101,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[274,278]) ).
thf(9102,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[9101]) ).
thf(9103,plain,
! [A: $i] : ( A @ skaf50 @ ( A @ skaf50 @ leq ) ),
inference(pattern_uni,[status(thm)],[9102:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(9154,plain,
! [A: $i] : ( A @ skaf50 @ ( A @ skaf50 @ leq ) ),
inference(simp,[status(thm)],[9103]) ).
thf(10207,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[230,10172]) ).
thf(10208,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[10207]) ).
thf(10209,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[10208:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(10274,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[10209]) ).
thf(105,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause119) ).
thf(423,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(22944,plain,
( ( nil != nil )
| ( sk2 @ ( nil @ frontsegP ) )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[20823,7387]) ).
thf(22945,plain,
( ( sk2 @ ( nil @ frontsegP ) )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[22944:[]]) ).
thf(24549,plain,
( ( ( skac3 @ ( skac3 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true
| ( sk2 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[719,24420]) ).
thf(24550,plain,
( ( ( skac3 @ ( skac3 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[24549]) ).
thf(24619,plain,
( ( skac3 != nil )
| ( skac3 != sk2 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[24550]) ).
thf(10912,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ~ $true
| ( sk2 @ totalorderedP ) ),
inference(paramod_ordered,[status(thm)],[725,10698]) ).
thf(10913,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ( sk2 @ totalorderedP ) ),
inference(simp,[status(thm)],[10912]) ).
thf(10948,plain,
( ( nil != sk2 )
| ( sk2 != sk2 )
| ( sk2 @ totalorderedP ) ),
inference(simp,[status(thm)],[10913]) ).
thf(10963,plain,
( ( nil != sk2 )
| ( sk2 @ totalorderedP ) ),
inference(simp,[status(thm)],[10948]) ).
thf(9110,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[271,278]) ).
thf(9111,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[9110]) ).
thf(9112,plain,
! [A: $i] : ( A @ skaf65 @ ( A @ skaf65 @ leq ) ),
inference(pattern_uni,[status(thm)],[9111:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(9157,plain,
! [A: $i] : ( A @ skaf65 @ ( A @ skaf65 @ leq ) ),
inference(simp,[status(thm)],[9112]) ).
thf(42159,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[250,378]) ).
thf(42160,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[42159]) ).
thf(42161,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[42160:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(42211,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[42161]) ).
thf(171,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ tl )
= B )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause96) ).
thf(579,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ tl )
= B )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(9607,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[233,282]) ).
thf(9608,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[9607]) ).
thf(9609,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( A @ skaf64 @ lt ) ),
inference(pattern_uni,[status(thm)],[9608:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(9663,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( A @ skaf64 @ lt ) ),
inference(simp,[status(thm)],[9609]) ).
thf(37894,plain,
( ( nil != nil )
| ~ ( skac3 @ ( sk1 @ memberP ) )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[32808,651]) ).
thf(37895,plain,
( ~ ( skac3 @ ( sk1 @ memberP ) )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[37894:[]]) ).
thf(101,axiom,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf54 @ ( A @ skaf55 @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause94) ).
thf(413,plain,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf54 @ ( A @ skaf55 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(22743,plain,
( ( nil != nil )
| ( sk2 @ strictorderP )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[20823,349]) ).
thf(22744,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[22743:[]]) ).
thf(7410,plain,
( ( nil != nil )
| ( sk2 @ ( nil @ frontsegP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,7387]) ).
thf(7411,plain,
( ( sk2 @ ( nil @ frontsegP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[7410:[]]) ).
thf(7286,plain,
( ( nil != nil )
| ( sk2 @ ( nil @ rearsegP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,7263]) ).
thf(7287,plain,
( ( sk2 @ ( nil @ rearsegP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[7286:[]]) ).
thf(24439,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[256,336]) ).
thf(24440,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[24439]) ).
thf(24441,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( A @ skaf60 @ neq ) ),
inference(pattern_uni,[status(thm)],[24440:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(24539,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( A @ skaf60 @ neq ) ),
inference(simp,[status(thm)],[24441]) ).
thf(22509,plain,
( ( nil != nil )
| ( nil @ ( sk1 @ segmentP ) )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[20584,7303]) ).
thf(22510,plain,
( ( nil @ ( sk1 @ segmentP ) )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[22509:[]]) ).
thf(10173,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[288,10172]) ).
thf(10174,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[10173]) ).
thf(10175,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[10174:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(10284,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[10175]) ).
thf(381,plain,
! [A: $i] :
( ( ( A @ skaf58 @ ( A @ skaf55 @ cons ) @ ( A @ skaf57 @ ( A @ skaf54 @ cons ) @ ( A @ skaf56 @ app ) @ app ) )
= A )
| ( A @ totalorderP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[380]) ).
thf(382,plain,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ( ( A @ skaf58 @ ( A @ skaf55 @ cons ) @ ( A @ skaf57 @ ( A @ skaf54 @ cons ) @ ( A @ skaf56 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[381]) ).
thf(3696,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[267,247]) ).
thf(3697,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3696]) ).
thf(3698,plain,
! [A: $i] : ( A @ skaf74 @ ( A @ skaf74 @ geq ) ),
inference(pattern_uni,[status(thm)],[3697:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(3726,plain,
! [A: $i] : ( A @ skaf74 @ ( A @ skaf74 @ geq ) ),
inference(simp,[status(thm)],[3698]) ).
thf(186,axiom,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause84) ).
thf(611,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(137,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause99) ).
thf(498,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(10192,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[270,10172]) ).
thf(10193,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[10192]) ).
thf(10194,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[10193:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(10269,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[10194]) ).
thf(10492,plain,
! [A: $i] :
( ( nil != nil )
| ( sk2 @ ( A @ skaf54 @ cons ) @ totalorderedP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,10269]) ).
thf(10493,plain,
! [A: $i] :
( ( sk2 @ ( A @ skaf54 @ cons ) @ totalorderedP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[10492:[]]) ).
thf(3663,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[284,247]) ).
thf(3664,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) ) ),
inference(simp,[status(thm)],[3663]) ).
thf(3665,plain,
skac3 @ ( skac3 @ geq ),
inference(pattern_uni,[status(thm)],[3664:[bind(A,$thf( skac3 ))]]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ geq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause107) ).
thf(231,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(232,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ geq ) ) ),
inference(cnf,[status(esa)],[231]) ).
thf(3747,plain,
! [B: $i,A: $i] :
( ( ( skac3 @ ( skac3 @ geq ) )
!= ( B @ ( A @ geq ) ) )
| ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3665,232]) ).
thf(3748,plain,
! [B: $i,A: $i] :
( ( ( skac3 @ ( skac3 @ geq ) )
!= ( B @ ( A @ geq ) ) )
| ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem ) ),
inference(simp,[status(thm)],[3747]) ).
thf(3749,plain,
( ( skac3 @ ( skac3 @ leq ) )
| ~ ( skac3 @ ssItem )
| ~ ( skac3 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[3748:[bind(A,$thf( skac3 )),bind(B,$thf( skac3 ))]]) ).
thf(3750,plain,
( ( skac3 @ ( skac3 @ leq ) )
| ~ ( skac3 @ ssItem ) ),
inference(simp,[status(thm)],[3749]) ).
thf(7657,plain,
( ( skac3 @ ( skac3 @ leq ) )
| ~ $true ),
inference(rewrite,[status(thm)],[3750,284]) ).
thf(7658,plain,
skac3 @ ( skac3 @ leq ),
inference(simp,[status(thm)],[7657]) ).
thf(10908,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ~ $true
| ~ ( sk2 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[693,10698]) ).
thf(10909,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ~ ( sk2 @ singletonP ) ),
inference(simp,[status(thm)],[10908]) ).
thf(10959,plain,
( ( nil != sk2 )
| ( sk2 != sk2 )
| ~ ( sk2 @ singletonP ) ),
inference(simp,[status(thm)],[10909]) ).
thf(10974,plain,
( ( nil != sk2 )
| ~ ( sk2 @ singletonP ) ),
inference(simp,[status(thm)],[10959]) ).
thf(9649,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[287,282]) ).
thf(9650,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[9649]) ).
thf(9651,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( A @ skaf78 @ lt ) ),
inference(pattern_uni,[status(thm)],[9650:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(9670,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( A @ skaf78 @ lt ) ),
inference(simp,[status(thm)],[9651]) ).
thf(313,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ app ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[312]) ).
thf(9631,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[251,282]) ).
thf(9632,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[9631]) ).
thf(9633,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( A @ skaf55 @ lt ) ),
inference(pattern_uni,[status(thm)],[9632:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(9659,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( A @ skaf55 @ lt ) ),
inference(simp,[status(thm)],[9633]) ).
thf(24474,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[263,336]) ).
thf(24475,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[24474]) ).
thf(24476,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( A @ skaf83 @ neq ) ),
inference(pattern_uni,[status(thm)],[24475:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(24524,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( A @ skaf83 @ neq ) ),
inference(simp,[status(thm)],[24476]) ).
thf(22366,plain,
( ( nil != nil )
| ( sk1 @ cyclefreeP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[20584,507]) ).
thf(22367,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[22366:[]]) ).
thf(182,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ skaf43 ) @ ( B @ cons ) @ ( B @ ( A @ skaf42 ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause169) ).
thf(604,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ skaf43 ) @ ( B @ cons ) @ ( B @ ( A @ skaf42 ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(318,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ frontsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) ) ),
inference(cnf,[status(esa)],[317]) ).
thf(9116,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[267,278]) ).
thf(9117,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[9116]) ).
thf(9118,plain,
! [A: $i] : ( A @ skaf74 @ ( A @ skaf74 @ leq ) ),
inference(pattern_uni,[status(thm)],[9117:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(9161,plain,
! [A: $i] : ( A @ skaf74 @ ( A @ skaf74 @ leq ) ),
inference(simp,[status(thm)],[9118]) ).
thf(10222,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[255,10172]) ).
thf(10223,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[10222]) ).
thf(10224,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[10223:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(10279,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[10224]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ app ) @ rearsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause136) ).
thf(418,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ app ) @ rearsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(419,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ app ) @ rearsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ rearsegP ) ) ),
inference(cnf,[status(esa)],[418]) ).
thf(3708,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[287,247]) ).
thf(3709,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3708]) ).
thf(3710,plain,
! [A: $i] : ( A @ skaf78 @ ( A @ skaf78 @ geq ) ),
inference(pattern_uni,[status(thm)],[3709:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(3732,plain,
! [A: $i] : ( A @ skaf78 @ ( A @ skaf78 @ geq ) ),
inference(simp,[status(thm)],[3710]) ).
thf(22774,plain,
( ( nil != nil )
| ~ ( sk2 @ singletonP )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[20823,519]) ).
thf(22775,plain,
( ~ ( sk2 @ singletonP )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[22774:[]]) ).
thf(27955,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) )
| ~ ( sk2 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[22775,297]) ).
thf(27956,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ ( sk2 @ singletonP ) ),
inference(simp,[status(thm)],[27955]) ).
thf(27957,plain,
( ~ ( sk2 @ tl @ ( sk2 @ tl @ neq ) )
| ~ ( sk2 @ singletonP ) ),
inference(pattern_uni,[status(thm)],[27956:[bind(A,$thf( sk2 @ tl ))]]) ).
thf(9119,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[255,278]) ).
thf(9120,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[9119]) ).
thf(9121,plain,
! [A: $i] : ( A @ skaf70 @ ( A @ skaf70 @ leq ) ),
inference(pattern_uni,[status(thm)],[9120:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(9146,plain,
! [A: $i] : ( A @ skaf70 @ ( A @ skaf70 @ leq ) ),
inference(simp,[status(thm)],[9121]) ).
thf(188,axiom,
! [A: $i] :
( ( A @ equalelemsP )
| ~ ( A @ ssList )
| ( ( A @ skaf79 )
!= ( A @ skaf78 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause89) ).
thf(616,plain,
! [A: $i] :
( ( A @ equalelemsP )
| ~ ( A @ ssList )
| ( ( A @ skaf79 )
!= ( A @ skaf78 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(3,negated_conjecture,
sk3 @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
thf(208,plain,
sk3 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(193,axiom,
! [B: $i,A: $i] :
( ( nil = A )
| ( A = B )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( A @ hd )
!= ( B @ hd ) )
| ( ( A @ tl )
!= ( B @ tl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause177) ).
thf(631,plain,
! [B: $i,A: $i] :
( ( nil = A )
| ( A = B )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( A @ hd )
!= ( B @ hd ) )
| ( ( A @ tl )
!= ( B @ tl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(1321,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[287,467]) ).
thf(1322,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1321]) ).
thf(1323,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1322:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(1339,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1323]) ).
thf(10727,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[426,297]) ).
thf(10728,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[10727]) ).
thf(10729,plain,
! [A: $i] :
~ ( A @ skaf73 @ ( A @ skaf73 @ neq ) ),
inference(pattern_uni,[status(thm)],[10728:[bind(A,$thf( C )),bind(B,$thf( C @ skaf73 ))]]) ).
thf(10810,plain,
! [A: $i] :
~ ( A @ skaf73 @ ( A @ skaf73 @ neq ) ),
inference(simp,[status(thm)],[10729]) ).
thf(42139,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[271,378]) ).
thf(42140,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[42139]) ).
thf(42141,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[42140:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(42205,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[42141]) ).
thf(24462,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[274,336]) ).
thf(24463,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[24462]) ).
thf(24464,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( A @ skaf50 @ neq ) ),
inference(pattern_uni,[status(thm)],[24463:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(24520,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( A @ skaf50 @ neq ) ),
inference(simp,[status(thm)],[24464]) ).
thf(26343,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf47 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[513,342]) ).
thf(26344,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf47 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[26343]) ).
thf(26345,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf47 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[26344:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf47 ) ))]]) ).
thf(26463,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf47 ) @ rearsegP ) ),
inference(simp,[status(thm)],[26345]) ).
thf(9628,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[271,282]) ).
thf(9629,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[9628]) ).
thf(9630,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( A @ skaf65 @ lt ) ),
inference(pattern_uni,[status(thm)],[9629:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(9674,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( A @ skaf65 @ lt ) ),
inference(simp,[status(thm)],[9630]) ).
thf(122,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ totalorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause135) ).
thf(462,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ totalorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(10910,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[697,10698]) ).
thf(10911,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[10910]) ).
thf(10955,plain,
( ( nil != sk2 )
| ( sk2 != sk2 )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[10911]) ).
thf(10970,plain,
( ( nil != sk2 )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[10955]) ).
thf(24687,plain,
( ( ( skac2 @ ( skac2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true
| ( nil != sk1 ) ),
inference(paramod_ordered,[status(thm)],[214,24493]) ).
thf(24688,plain,
( ( ( skac2 @ ( skac2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[24687]) ).
thf(24713,plain,
( ( skac2 != nil )
| ( skac2 != sk2 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[24688]) ).
thf(60615,plain,
( ( ( sk1 @ ( nil @ rearsegP ) )
!= ( nil @ ( sk1 @ rearsegP ) ) )
| ~ ( sk1 @ ( nil @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26311,38019]) ).
thf(60616,plain,
( ( ( sk1 @ ( nil @ rearsegP ) )
!= ( nil @ ( sk1 @ rearsegP ) ) )
| ~ ( sk1 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[60615]) ).
thf(60805,plain,
( ( nil != sk1 )
| ( nil != sk1 )
| ~ ( sk1 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[60616]) ).
thf(60864,plain,
( ( nil != sk1 )
| ~ ( sk1 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[60805]) ).
thf(48836,plain,
( ( ( sk1 @ ( nil @ rearsegP ) )
!= ( nil @ ( sk1 @ rearsegP ) ) )
| ~ ( skac3 @ ( sk1 @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26311,37895]) ).
thf(48837,plain,
( ( ( sk1 @ ( nil @ rearsegP ) )
!= ( nil @ ( sk1 @ rearsegP ) ) )
| ~ ( skac3 @ ( sk1 @ memberP ) ) ),
inference(simp,[status(thm)],[48836]) ).
thf(48981,plain,
( ( nil != sk1 )
| ( nil != sk1 )
| ~ ( skac3 @ ( sk1 @ memberP ) ) ),
inference(simp,[status(thm)],[48837]) ).
thf(49016,plain,
( ( nil != sk1 )
| ~ ( skac3 @ ( sk1 @ memberP ) ) ),
inference(simp,[status(thm)],[48981]) ).
thf(344,plain,
! [B: $i,A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
inference(cnf,[status(esa)],[343]) ).
thf(345,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( nil = A )
| ( ( B @ ( A @ app ) )
!= nil ) ),
inference(lifteq,[status(thm)],[344]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ app ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause141) ).
thf(552,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ app ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause105) ).
thf(239,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(240,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ gt ) ) ),
inference(cnf,[status(esa)],[239]) ).
thf(42102,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[233,378]) ).
thf(42103,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[42102]) ).
thf(42104,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[42103:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(42228,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[42104]) ).
thf(49619,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[501,392]) ).
thf(49620,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[49619]) ).
thf(49621,plain,
! [A: $i] :
( ( A @ skaf68 @ ( nil @ app ) )
= ( A @ skaf68 ) ),
inference(pattern_uni,[status(thm)],[49620:[bind(A,$thf( C )),bind(B,$thf( C @ skaf68 ))]]) ).
thf(49715,plain,
! [A: $i] :
( ( A @ skaf68 @ ( nil @ app ) )
= ( A @ skaf68 ) ),
inference(simp,[status(thm)],[49621]) ).
thf(49506,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[311,392]) ).
thf(49507,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[49506]) ).
thf(49508,plain,
! [A: $i] :
( ( A @ skaf72 @ ( nil @ app ) )
= ( A @ skaf72 ) ),
inference(pattern_uni,[status(thm)],[49507:[bind(A,$thf( C )),bind(B,$thf( C @ skaf72 ))]]) ).
thf(49696,plain,
! [A: $i] :
( ( A @ skaf72 @ ( nil @ app ) )
= ( A @ skaf72 ) ),
inference(simp,[status(thm)],[49508]) ).
thf(69,axiom,
! [A: $i] :
( ( ( A @ skaf68 @ ( A @ skaf65 @ cons ) @ ( A @ skaf67 @ ( A @ skaf64 @ cons ) @ ( A @ skaf66 @ app ) @ app ) )
= A )
| ( A @ totalorderedP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause164) ).
thf(330,plain,
! [A: $i] :
( ( ( A @ skaf68 @ ( A @ skaf65 @ cons ) @ ( A @ skaf67 @ ( A @ skaf64 @ cons ) @ ( A @ skaf66 @ app ) @ app ) )
= A )
| ( A @ totalorderedP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(10705,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf47 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ~ ( C @ ( C @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[513,297]) ).
thf(10706,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf47 ) @ ssList )
!= ( C @ ssList ) )
| ~ ( C @ ( C @ neq ) ) ),
inference(simp,[status(thm)],[10705]) ).
thf(10707,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf47 ) @ ( B @ ( A @ skaf47 ) @ neq ) ),
inference(pattern_uni,[status(thm)],[10706:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf47 ) ))]]) ).
thf(10792,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf47 ) @ ( B @ ( A @ skaf47 ) @ neq ) ),
inference(simp,[status(thm)],[10707]) ).
thf(8051,plain,
( ( nil != nil )
| ( ( nil @ ( sk2 @ app ) )
= nil )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,8022]) ).
thf(8052,plain,
( ( ( nil @ ( sk2 @ app ) )
= nil )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[8051:[]]) ).
thf(22713,plain,
( ( nil != nil )
| ( sk2 != sk2 )
| ( sk2 @ ( nil @ segmentP ) )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[20823,10972]) ).
thf(22714,plain,
( ( nil != nil )
| ( sk2 @ ( nil @ segmentP ) )
| ( sk2 @ tl @ ssList ) ),
inference(simp,[status(thm)],[22713]) ).
thf(22715,plain,
( ( sk2 @ ( nil @ segmentP ) )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[22714:[]]) ).
thf(24465,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[251,336]) ).
thf(24466,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[24465]) ).
thf(24467,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( A @ skaf55 @ neq ) ),
inference(pattern_uni,[status(thm)],[24466:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(24521,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( A @ skaf55 @ neq ) ),
inference(simp,[status(thm)],[24467]) ).
thf(26366,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[520,342]) ).
thf(26367,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[26366]) ).
thf(26368,plain,
! [A: $i] : ( nil @ ( A @ skaf67 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[26367:[bind(A,$thf( C )),bind(B,$thf( C @ skaf67 ))]]) ).
thf(26431,plain,
! [A: $i] : ( nil @ ( A @ skaf67 @ rearsegP ) ),
inference(simp,[status(thm)],[26368]) ).
thf(10757,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[354,297]) ).
thf(10758,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[10757]) ).
thf(10759,plain,
! [A: $i] :
~ ( A @ skaf77 @ ( A @ skaf77 @ neq ) ),
inference(pattern_uni,[status(thm)],[10758:[bind(A,$thf( C )),bind(B,$thf( C @ skaf77 ))]]) ).
thf(10782,plain,
! [A: $i] :
~ ( A @ skaf77 @ ( A @ skaf77 @ neq ) ),
inference(simp,[status(thm)],[10759]) ).
thf(56,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ memberP ) )
| ( C @ ( B @ memberP ) )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ( B @ ( A @ app ) @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause158) ).
thf(299,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ memberP ) )
| ( C @ ( B @ memberP ) )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ( B @ ( A @ app ) @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(10650,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ~ ( C @ ( C @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[379,297]) ).
thf(10651,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ssList )
!= ( C @ ssList ) )
| ~ ( C @ ( C @ neq ) ) ),
inference(simp,[status(thm)],[10650]) ).
thf(10652,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf45 ) @ ( B @ ( A @ skaf45 ) @ neq ) ),
inference(pattern_uni,[status(thm)],[10651:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf45 ) ))]]) ).
thf(10803,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf45 ) @ ( B @ ( A @ skaf45 ) @ neq ) ),
inference(simp,[status(thm)],[10652]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause108) ).
thf(226,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(141,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause70) ).
thf(505,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(684,plain,
( ( nil != nil )
| ~ ( skac3 @ ( sk2 @ memberP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,651]) ).
thf(685,plain,
( ~ ( skac3 @ ( sk2 @ memberP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[684:[]]) ).
thf(149,axiom,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf60 @ ( A @ skaf59 @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause93) ).
thf(521,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf60 @ ( A @ skaf59 @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(694,plain,
( ( nil != nil )
| ~ ( skac2 @ ( sk2 @ memberP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,654]) ).
thf(695,plain,
( ~ ( skac2 @ ( sk2 @ memberP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[694:[]]) ).
thf(10210,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[245,10172]) ).
thf(10211,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[10210]) ).
thf(10212,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[10211:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(10275,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[10212]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause103) ).
thf(241,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(9125,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[250,278]) ).
thf(9126,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[9125]) ).
thf(9127,plain,
! [A: $i] : ( A @ skaf69 @ ( A @ skaf69 @ leq ) ),
inference(pattern_uni,[status(thm)],[9126:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(9150,plain,
! [A: $i] : ( A @ skaf69 @ ( A @ skaf69 @ leq ) ),
inference(simp,[status(thm)],[9127]) ).
thf(42156,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[263,378]) ).
thf(42157,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[42156]) ).
thf(42158,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[42157:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(42210,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[42158]) ).
thf(153,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause65) ).
thf(531,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(158,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ leq ) )
| ~ ( F @ ssList )
| ~ ( F @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause182) ).
thf(548,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ leq ) )
| ~ ( F @ ssList )
| ~ ( F @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(2123,plain,
! [B: $i,A: $i] :
( ( B != skac2 )
| ( A != skac3 )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
inference(paramod_ordered,[status(thm)],[238,225]) ).
thf(2124,plain,
! [A: $i] :
( ( A != skac3 )
| ~ ( skac2 @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( A @ geq ) ) ),
inference(pattern_uni,[status(thm)],[2123:[bind(A,$thf( A )),bind(B,$thf( skac2 ))]]) ).
thf(2474,plain,
( ~ ( skac2 @ ssItem )
| ~ ( skac3 @ ssItem )
| ~ ( skac3 @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( skac3 @ geq ) ) ),
inference(simp,[status(thm)],[2124]) ).
thf(14723,plain,
( ~ $true
| ~ $true
| ~ ( skac3 @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( skac3 @ geq ) ) ),
inference(rewrite,[status(thm)],[2474,283,284]) ).
thf(14724,plain,
( ~ ( skac3 @ ( skac2 @ geq ) )
| ~ ( skac2 @ ( skac3 @ geq ) ) ),
inference(simp,[status(thm)],[14723]) ).
thf(49488,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[526,392]) ).
thf(49489,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[49488]) ).
thf(49490,plain,
! [A: $i] :
( ( A @ skaf81 @ ( nil @ app ) )
= ( A @ skaf81 ) ),
inference(pattern_uni,[status(thm)],[49489:[bind(A,$thf( C )),bind(B,$thf( C @ skaf81 ))]]) ).
thf(49692,plain,
! [A: $i] :
( ( A @ skaf81 @ ( nil @ app ) )
= ( A @ skaf81 ) ),
inference(simp,[status(thm)],[49490]) ).
thf(9625,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[245,282]) ).
thf(9626,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[9625]) ).
thf(9627,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( A @ skaf44 @ lt ) ),
inference(pattern_uni,[status(thm)],[9626:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(9673,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( A @ skaf44 @ lt ) ),
inference(simp,[status(thm)],[9627]) ).
thf(49625,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[354,392]) ).
thf(49626,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[49625]) ).
thf(49627,plain,
! [A: $i] :
( ( A @ skaf77 @ ( nil @ app ) )
= ( A @ skaf77 ) ),
inference(pattern_uni,[status(thm)],[49626:[bind(A,$thf( C )),bind(B,$thf( C @ skaf77 ))]]) ).
thf(49716,plain,
! [A: $i] :
( ( A @ skaf77 @ ( nil @ app ) )
= ( A @ skaf77 ) ),
inference(simp,[status(thm)],[49627]) ).
thf(11,negated_conjecture,
! [A: $i] :
( ~ ( A @ ( sk1 @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( A @ neq ) )
| ~ ( A @ ssList )
| ( nil = sk2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
thf(209,plain,
! [A: $i] :
( ~ ( A @ ( sk1 @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( A @ neq ) )
| ~ ( A @ ssList )
| ( nil = sk2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(26328,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[526,342]) ).
thf(26329,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[26328]) ).
thf(26330,plain,
! [A: $i] : ( nil @ ( A @ skaf81 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[26329:[bind(A,$thf( C )),bind(B,$thf( C @ skaf81 ))]]) ).
thf(26459,plain,
! [A: $i] : ( nil @ ( A @ skaf81 @ rearsegP ) ),
inference(simp,[status(thm)],[26330]) ).
thf(10673,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[435,297]) ).
thf(10674,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[10673]) ).
thf(10675,plain,
! [A: $i] :
~ ( A @ skaf61 @ ( A @ skaf61 @ neq ) ),
inference(pattern_uni,[status(thm)],[10674:[bind(A,$thf( C )),bind(B,$thf( C @ skaf61 ))]]) ).
thf(10814,plain,
! [A: $i] :
~ ( A @ skaf61 @ ( A @ skaf61 @ neq ) ),
inference(simp,[status(thm)],[10675]) ).
thf(10702,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[298,297]) ).
thf(10703,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[10702]) ).
thf(10704,plain,
! [A: $i] :
~ ( A @ skaf62 @ ( A @ skaf62 @ neq ) ),
inference(pattern_uni,[status(thm)],[10703:[bind(A,$thf( C )),bind(B,$thf( C @ skaf62 ))]]) ).
thf(10788,plain,
! [A: $i] :
~ ( A @ skaf62 @ ( A @ skaf62 @ neq ) ),
inference(simp,[status(thm)],[10704]) ).
thf(38490,plain,
( ( nil != nil )
| ( sk2 @ strictorderP )
| ~ ( sk2 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[33110,349]) ).
thf(38491,plain,
( ( sk2 @ strictorderP )
| ~ ( sk2 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[38490:[]]) ).
thf(197,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ strictorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause124) ).
thf(640,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ strictorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(9098,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[259,278]) ).
thf(9099,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[9098]) ).
thf(9100,plain,
! [A: $i] : ( A @ skaf49 @ ( A @ skaf49 @ leq ) ),
inference(pattern_uni,[status(thm)],[9099:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(9153,plain,
! [A: $i] : ( A @ skaf49 @ ( A @ skaf49 @ leq ) ),
inference(simp,[status(thm)],[9100]) ).
thf(414,plain,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf54 @ ( A @ skaf55 @ leq ) ) ),
inference(cnf,[status(esa)],[413]) ).
thf(63197,plain,
( ( ( sk1 @ ( nil @ rearsegP ) )
!= ( nil @ ( sk1 @ rearsegP ) ) )
| ~ ( skac2 @ ( sk1 @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26311,38061]) ).
thf(63198,plain,
( ( ( sk1 @ ( nil @ rearsegP ) )
!= ( nil @ ( sk1 @ rearsegP ) ) )
| ~ ( skac2 @ ( sk1 @ memberP ) ) ),
inference(simp,[status(thm)],[63197]) ).
thf(63368,plain,
( ( nil != sk1 )
| ( nil != sk1 )
| ~ ( skac2 @ ( sk1 @ memberP ) ) ),
inference(simp,[status(thm)],[63198]) ).
thf(63375,plain,
( ( nil != sk1 )
| ~ ( skac2 @ ( sk1 @ memberP ) ) ),
inference(simp,[status(thm)],[63368]) ).
thf(22573,plain,
( ( nil != nil )
| ( sk1 @ ( nil @ frontsegP ) )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[20584,7387]) ).
thf(22574,plain,
( ( sk1 @ ( nil @ frontsegP ) )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[22573:[]]) ).
thf(9604,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( A @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[284,282]) ).
thf(9605,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[9604]) ).
thf(9606,plain,
~ ( skac3 @ ( skac3 @ lt ) ),
inference(pattern_uni,[status(thm)],[9605:[bind(A,$thf( skac3 ))]]) ).
thf(309,plain,
! [A: $i] :
( ( ( A @ skaf77 @ ( A @ skaf74 @ cons ) @ ( A @ skaf76 @ ( A @ skaf74 @ cons ) @ ( A @ skaf75 @ app ) @ app ) )
= A )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[308]) ).
thf(310,plain,
! [A: $i] :
( ( A @ duplicatefreeP )
| ~ ( A @ ssList )
| ( ( A @ skaf77 @ ( A @ skaf74 @ cons ) @ ( A @ skaf76 @ ( A @ skaf74 @ cons ) @ ( A @ skaf75 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[309]) ).
thf(26289,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf43 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[289,342]) ).
thf(26290,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf43 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[26289]) ).
thf(26291,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf43 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[26290:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf43 ) ))]]) ).
thf(26444,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf43 ) @ rearsegP ) ),
inference(simp,[status(thm)],[26291]) ).
thf(173,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause69) ).
thf(585,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(49570,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[465,392]) ).
thf(49571,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[49570]) ).
thf(49572,plain,
! [A: $i] :
( ( A @ skaf80 @ ( nil @ app ) )
= ( A @ skaf80 ) ),
inference(pattern_uni,[status(thm)],[49571:[bind(A,$thf( C )),bind(B,$thf( C @ skaf80 ))]]) ).
thf(49707,plain,
! [A: $i] :
( ( A @ skaf80 @ ( nil @ app ) )
= ( A @ skaf80 ) ),
inference(simp,[status(thm)],[49572]) ).
thf(22485,plain,
( ( nil != nil )
| ( sk1 @ strictorderedP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[20584,626]) ).
thf(22486,plain,
( ( sk1 @ strictorderedP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[22485:[]]) ).
thf(198,axiom,
! [A: $i] :
( ( A @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause61) ).
thf(643,plain,
! [A: $i] :
( ( A @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(157,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ frontsegP ) )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause144) ).
thf(544,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ frontsegP ) )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(113,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ strictorderedP )
| ~ ( B @ hd @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause160) ).
thf(441,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ strictorderedP )
| ~ ( B @ hd @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(3657,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[259,247]) ).
thf(3658,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3657]) ).
thf(3659,plain,
! [A: $i] : ( A @ skaf49 @ ( A @ skaf49 @ geq ) ),
inference(pattern_uni,[status(thm)],[3658:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(3722,plain,
! [A: $i] : ( A @ skaf49 @ ( A @ skaf49 @ geq ) ),
inference(simp,[status(thm)],[3659]) ).
thf(38228,plain,
( ( nil != nil )
| ( sk1 @ duplicatefreeP )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[32808,383]) ).
thf(38229,plain,
( ( sk1 @ duplicatefreeP )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[38228:[]]) ).
thf(126,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ segmentP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ segmentP ) )
| ~ ( B @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause152) ).
thf(470,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ segmentP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ segmentP ) )
| ~ ( B @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(170,axiom,
! [A: $i] :
( ( nil = A )
| ( ( A @ skaf82 @ ( A @ skaf83 @ cons ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause109) ).
thf(576,plain,
! [A: $i] :
( ( nil = A )
| ( ( A @ skaf82 @ ( A @ skaf83 @ cons ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(9643,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[250,282]) ).
thf(9644,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[9643]) ).
thf(9645,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( A @ skaf69 @ lt ) ),
inference(pattern_uni,[status(thm)],[9644:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(9666,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( A @ skaf69 @ lt ) ),
inference(simp,[status(thm)],[9645]) ).
thf(38654,plain,
( ( nil != nil )
| ( sk2 != sk2 )
| ( sk2 != sk1 )
| ~ ( sk2 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[33110,5619]) ).
thf(38655,plain,
( ( nil != nil )
| ( sk2 != sk1 )
| ~ ( sk2 @ ( nil @ rearsegP ) ) ),
inference(simp,[status(thm)],[38654]) ).
thf(38656,plain,
( ( sk2 != sk1 )
| ~ ( sk2 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[38655:[]]) ).
thf(49509,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[298,392]) ).
thf(49510,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[49509]) ).
thf(49511,plain,
! [A: $i] :
( ( A @ skaf62 @ ( nil @ app ) )
= ( A @ skaf62 ) ),
inference(pattern_uni,[status(thm)],[49510:[bind(A,$thf( C )),bind(B,$thf( C @ skaf62 ))]]) ).
thf(49697,plain,
! [A: $i] :
( ( A @ skaf62 @ ( nil @ app ) )
= ( A @ skaf62 ) ),
inference(simp,[status(thm)],[49511]) ).
thf(49537,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[520,392]) ).
thf(49538,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[49537]) ).
thf(49539,plain,
! [A: $i] :
( ( A @ skaf67 @ ( nil @ app ) )
= ( A @ skaf67 ) ),
inference(pattern_uni,[status(thm)],[49538:[bind(A,$thf( C )),bind(B,$thf( C @ skaf67 ))]]) ).
thf(49702,plain,
! [A: $i] :
( ( A @ skaf67 @ ( nil @ app ) )
= ( A @ skaf67 ) ),
inference(simp,[status(thm)],[49539]) ).
thf(10918,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[689,10698]) ).
thf(10919,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[10918]) ).
thf(10949,plain,
( ( nil != sk2 )
| ( sk2 != sk2 )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[10919]) ).
thf(10964,plain,
( ( nil != sk2 )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[10949]) ).
thf(9095,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[256,278]) ).
thf(9096,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[9095]) ).
thf(9097,plain,
! [A: $i] : ( A @ skaf60 @ ( A @ skaf60 @ leq ) ),
inference(pattern_uni,[status(thm)],[9096:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(9151,plain,
! [A: $i] : ( A @ skaf60 @ ( A @ skaf60 @ leq ) ),
inference(simp,[status(thm)],[9097]) ).
thf(385,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ hd )
= A )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[384]) ).
thf(386,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) @ hd )
= A ) ),
inference(lifteq,[status(thm)],[385]) ).
thf(26410,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf46 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[326,342]) ).
thf(26411,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf46 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[26410]) ).
thf(26412,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf46 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[26411:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf46 ) ))]]) ).
thf(26440,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf46 ) @ rearsegP ) ),
inference(simp,[status(thm)],[26412]) ).
thf(168,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ app ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause140) ).
thf(571,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ app ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(61117,plain,
( ( ( sk1 @ ( nil @ rearsegP ) )
!= ( nil @ ( sk1 @ rearsegP ) ) )
| ( sk1 @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26311,38188]) ).
thf(61118,plain,
( ( ( sk1 @ ( nil @ rearsegP ) )
!= ( nil @ ( sk1 @ rearsegP ) ) )
| ( sk1 @ equalelemsP ) ),
inference(simp,[status(thm)],[61117]) ).
thf(61230,plain,
( ( nil != sk1 )
| ( nil != sk1 )
| ( sk1 @ equalelemsP ) ),
inference(simp,[status(thm)],[61118]) ).
thf(61267,plain,
( ( nil != sk1 )
| ( sk1 @ equalelemsP ) ),
inference(simp,[status(thm)],[61230]) ).
thf(33283,plain,
! [A: $i] :
( ( nil != nil )
| ( A != sk2 )
| ~ ( sk2 @ singletonP )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[360,10974]) ).
thf(33284,plain,
! [A: $i] :
( ( A != sk2 )
| ~ ( sk2 @ singletonP )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[33283:[]]) ).
thf(34205,plain,
( ~ ( sk2 @ singletonP )
| ~ ( sk2 @ ssList )
| ~ ( sk2 @ ( nil @ rearsegP ) ) ),
inference(simp,[status(thm)],[33284]) ).
thf(37612,plain,
( ~ ( sk2 @ singletonP )
| ~ $true
| ~ ( sk2 @ ( nil @ rearsegP ) ) ),
inference(rewrite,[status(thm)],[34205,205]) ).
thf(37613,plain,
( ~ ( sk2 @ singletonP )
| ~ ( sk2 @ ( nil @ rearsegP ) ) ),
inference(simp,[status(thm)],[37612]) ).
thf(24322,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) )
| ~ ( sk1 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[22416,297]) ).
thf(24323,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ ( sk1 @ singletonP ) ),
inference(simp,[status(thm)],[24322]) ).
thf(24324,plain,
( ~ ( sk1 @ tl @ ( sk1 @ tl @ neq ) )
| ~ ( sk1 @ singletonP ) ),
inference(pattern_uni,[status(thm)],[24323:[bind(A,$thf( sk1 @ tl ))]]) ).
thf(180,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( D @ ( C @ cons ) @ ( B @ ( A @ cons ) @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause176) ).
thf(600,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( D @ ( C @ cons ) @ ( B @ ( A @ cons ) @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(192,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause112) ).
thf(627,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(116,axiom,
! [A: $i] :
( ( A @ skaf49 @ ( A @ skaf50 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause87) ).
thf(450,plain,
! [A: $i] :
( ( A @ skaf49 @ ( A @ skaf50 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(24471,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[255,336]) ).
thf(24472,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[24471]) ).
thf(24473,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( A @ skaf70 @ neq ) ),
inference(pattern_uni,[status(thm)],[24472:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(24523,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( A @ skaf70 @ neq ) ),
inference(simp,[status(thm)],[24473]) ).
thf(10657,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf43 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ~ ( C @ ( C @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[289,297]) ).
thf(10658,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf43 ) @ ssList )
!= ( C @ ssList ) )
| ~ ( C @ ( C @ neq ) ) ),
inference(simp,[status(thm)],[10657]) ).
thf(10659,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf43 ) @ ( B @ ( A @ skaf43 ) @ neq ) ),
inference(pattern_uni,[status(thm)],[10658:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf43 ) ))]]) ).
thf(10806,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf43 ) @ ( B @ ( A @ skaf43 ) @ neq ) ),
inference(simp,[status(thm)],[10659]) ).
thf(136,axiom,
! [A: $i] :
( ( nil = A )
| ( ( A @ tl @ ( A @ hd @ cons ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause104) ).
thf(495,plain,
! [A: $i] :
( ( nil = A )
| ( ( A @ tl @ ( A @ hd @ cons ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(8226,plain,
( ( nil != nil )
| ( sk2 @ ( sk2 @ frontsegP ) )
| ( nil @ ( sk2 @ neq ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,7409]) ).
thf(8227,plain,
( ( nil != nil )
| ( sk2 @ ( sk2 @ frontsegP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[8226]) ).
thf(8228,plain,
( ( sk2 @ ( sk2 @ frontsegP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[8227:[]]) ).
thf(24659,plain,
( ( ( skac2 @ ( skac2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true
| ~ ( sk2 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[693,24493]) ).
thf(24660,plain,
( ( ( skac2 @ ( skac2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ ( sk2 @ singletonP ) ),
inference(simp,[status(thm)],[24659]) ).
thf(24717,plain,
( ( skac2 != nil )
| ( skac2 != sk2 )
| ~ ( sk2 @ singletonP ) ),
inference(simp,[status(thm)],[24660]) ).
thf(9640,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[263,282]) ).
thf(9641,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[9640]) ).
thf(9642,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( A @ skaf83 @ lt ) ),
inference(pattern_uni,[status(thm)],[9641:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(9664,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( A @ skaf83 @ lt ) ),
inference(simp,[status(thm)],[9642]) ).
thf(9610,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[270,282]) ).
thf(9611,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[9610]) ).
thf(9612,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( A @ skaf54 @ lt ) ),
inference(pattern_uni,[status(thm)],[9611:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(9665,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( A @ skaf54 @ lt ) ),
inference(simp,[status(thm)],[9612]) ).
thf(217,plain,
! [A: $i] :
( ~ ( A @ ( sk1 @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( A @ neq ) )
| ~ ( A @ ssList )
| ( nil = sk2 ) ),
inference(cnf,[status(esa)],[209]) ).
thf(218,plain,
! [A: $i] :
( ~ ( A @ ( sk1 @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( A @ neq ) )
| ~ ( A @ ssList )
| ( nil = sk2 ) ),
inference(lifteq,[status(thm)],[217]) ).
thf(3693,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[251,247]) ).
thf(3694,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3693]) ).
thf(3695,plain,
! [A: $i] : ( A @ skaf55 @ ( A @ skaf55 @ geq ) ),
inference(pattern_uni,[status(thm)],[3694:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(3725,plain,
! [A: $i] : ( A @ skaf55 @ ( A @ skaf55 @ geq ) ),
inference(simp,[status(thm)],[3695]) ).
thf(1098,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[263,467]) ).
thf(1099,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1098]) ).
thf(1100,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1099:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(1108,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1100]) ).
thf(958,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[259,467]) ).
thf(959,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[958]) ).
thf(960,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[959:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(961,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[960]) ).
thf(22815,plain,
( ( nil != nil )
| ( sk2 != sk2 )
| ( sk2 @ totalorderedP )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[20823,10963]) ).
thf(22816,plain,
( ( nil != nil )
| ( sk2 @ totalorderedP )
| ( sk2 @ tl @ ssList ) ),
inference(simp,[status(thm)],[22815]) ).
thf(22817,plain,
( ( sk2 @ totalorderedP )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[22816:[]]) ).
thf(9089,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[233,278]) ).
thf(9090,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[9089]) ).
thf(9091,plain,
! [A: $i] : ( A @ skaf64 @ ( A @ skaf64 @ leq ) ),
inference(pattern_uni,[status(thm)],[9090:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(9147,plain,
! [A: $i] : ( A @ skaf64 @ ( A @ skaf64 @ leq ) ),
inference(simp,[status(thm)],[9091]) ).
thf(258,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
inference(cnf,[status(esa)],[257]) ).
thf(26883,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) )
| ( nil != sk1 ) ),
inference(paramod_ordered,[status(thm)],[22641,297]) ).
thf(26884,plain,
! [A: $i] :
( ( ( sk2 @ tl @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[26883]) ).
thf(26885,plain,
( ~ ( sk2 @ tl @ ( sk2 @ tl @ neq ) )
| ( nil != sk1 ) ),
inference(pattern_uni,[status(thm)],[26884:[bind(A,$thf( sk2 @ tl ))]]) ).
thf(10427,plain,
! [A: $i] :
( ( nil != nil )
| ( sk2 @ ( A @ skaf64 @ cons ) @ totalorderedP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,10267]) ).
thf(10428,plain,
! [A: $i] :
( ( sk2 @ ( A @ skaf64 @ cons ) @ totalorderedP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[10427:[]]) ).
thf(3765,plain,
! [B: $i,A: $i] :
( ( ( skac2 @ ( skac2 @ geq ) )
!= ( B @ ( A @ geq ) ) )
| ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3713,232]) ).
thf(3766,plain,
! [B: $i,A: $i] :
( ( ( skac2 @ ( skac2 @ geq ) )
!= ( B @ ( A @ geq ) ) )
| ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem ) ),
inference(simp,[status(thm)],[3765]) ).
thf(3767,plain,
( ( skac2 @ ( skac2 @ leq ) )
| ~ ( skac2 @ ssItem )
| ~ ( skac2 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[3766:[bind(A,$thf( skac2 )),bind(B,$thf( skac2 ))]]) ).
thf(3768,plain,
( ( skac2 @ ( skac2 @ leq ) )
| ~ ( skac2 @ ssItem ) ),
inference(simp,[status(thm)],[3767]) ).
thf(7699,plain,
( ( skac2 @ ( skac2 @ leq ) )
| ~ $true ),
inference(rewrite,[status(thm)],[3768,283]) ).
thf(7700,plain,
skac2 @ ( skac2 @ leq ),
inference(simp,[status(thm)],[7699]) ).
thf(26424,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[592,342]) ).
thf(26425,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[26424]) ).
thf(26426,plain,
! [A: $i] : ( nil @ ( A @ skaf82 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[26425:[bind(A,$thf( C )),bind(B,$thf( C @ skaf82 ))]]) ).
thf(26447,plain,
! [A: $i] : ( nil @ ( A @ skaf82 @ rearsegP ) ),
inference(simp,[status(thm)],[26426]) ).
thf(9083,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[288,278]) ).
thf(9084,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[9083]) ).
thf(9085,plain,
! [A: $i] : ( A @ skaf59 @ ( A @ skaf59 @ leq ) ),
inference(pattern_uni,[status(thm)],[9084:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(9160,plain,
! [A: $i] : ( A @ skaf59 @ ( A @ skaf59 @ leq ) ),
inference(simp,[status(thm)],[9085]) ).
thf(42169,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[287,378]) ).
thf(42170,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[42169]) ).
thf(42171,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[42170:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(42212,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[42171]) ).
thf(3672,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[233,247]) ).
thf(3673,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3672]) ).
thf(3674,plain,
! [A: $i] : ( A @ skaf64 @ ( A @ skaf64 @ geq ) ),
inference(pattern_uni,[status(thm)],[3673:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(3729,plain,
! [A: $i] : ( A @ skaf64 @ ( A @ skaf64 @ geq ) ),
inference(simp,[status(thm)],[3674]) ).
thf(24453,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[230,336]) ).
thf(24454,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[24453]) ).
thf(24455,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( A @ skaf79 @ neq ) ),
inference(pattern_uni,[status(thm)],[24454:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(24517,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( A @ skaf79 @ neq ) ),
inference(simp,[status(thm)],[24455]) ).
thf(49630,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[592,392]) ).
thf(49631,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[49630]) ).
thf(49632,plain,
! [A: $i] :
( ( A @ skaf82 @ ( nil @ app ) )
= ( A @ skaf82 ) ),
inference(pattern_uni,[status(thm)],[49631:[bind(A,$thf( C )),bind(B,$thf( C @ skaf82 ))]]) ).
thf(49717,plain,
! [A: $i] :
( ( A @ skaf82 @ ( nil @ app ) )
= ( A @ skaf82 ) ),
inference(simp,[status(thm)],[49632]) ).
thf(26303,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[480,342]) ).
thf(26304,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[26303]) ).
thf(26305,plain,
! [A: $i] : ( nil @ ( A @ skaf53 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[26304:[bind(A,$thf( C )),bind(B,$thf( C @ skaf53 ))]]) ).
thf(26452,plain,
! [A: $i] : ( nil @ ( A @ skaf53 @ rearsegP ) ),
inference(simp,[status(thm)],[26305]) ).
thf(63424,plain,
( ( ( sk1 @ ( nil @ rearsegP ) )
!= ( nil @ ( sk1 @ rearsegP ) ) )
| ( sk1 @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26311,38229]) ).
thf(63425,plain,
( ( ( sk1 @ ( nil @ rearsegP ) )
!= ( nil @ ( sk1 @ rearsegP ) ) )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[63424]) ).
thf(63547,plain,
( ( nil != sk1 )
| ( nil != sk1 )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[63425]) ).
thf(63576,plain,
( ( nil != sk1 )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[63547]) ).
thf(167,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ( ( B @ ( A @ cons ) )
!= ( D @ ( C @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause170) ).
thf(568,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ( ( B @ ( A @ cons ) )
!= ( D @ ( C @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(109,axiom,
! [A: $i] :
( ( A @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause59) ).
thf(433,plain,
! [A: $i] :
( ( A @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(26357,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[599,342]) ).
thf(26358,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[26357]) ).
thf(26359,plain,
! [A: $i] : ( nil @ ( A @ skaf56 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[26358:[bind(A,$thf( C )),bind(B,$thf( C @ skaf56 ))]]) ).
thf(26465,plain,
! [A: $i] : ( nil @ ( A @ skaf56 @ rearsegP ) ),
inference(simp,[status(thm)],[26359]) ).
thf(22537,plain,
( ( nil != nil )
| ( sk1 @ duplicatefreeP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[20584,383]) ).
thf(22538,plain,
( ( sk1 @ duplicatefreeP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[22537:[]]) ).
thf(129,axiom,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf55 @ ( A @ skaf54 @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause95) ).
thf(478,plain,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf55 @ ( A @ skaf54 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(42,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause114) ).
thf(272,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(36312,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[205,364]) ).
thf(36313,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP ) ),
inference(simp,[status(thm)],[36312]) ).
thf(36314,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk2 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[36313:[bind(A,$thf( sk2 ))]]) ).
thf(36523,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[36314]) ).
thf(22579,plain,
( ( nil != nil )
| ( sk1 @ ( nil @ rearsegP ) )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[20584,7263]) ).
thf(22580,plain,
( ( sk1 @ ( nil @ rearsegP ) )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[22579:[]]) ).
thf(49503,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[205,392]) ).
thf(49504,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[49503]) ).
thf(49505,plain,
( ( sk2 @ ( nil @ app ) )
= sk2 ),
inference(pattern_uni,[status(thm)],[49504:[bind(A,$thf( sk2 ))]]) ).
thf(235,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
inference(cnf,[status(esa)],[234]) ).
thf(26372,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[426,342]) ).
thf(26373,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[26372]) ).
thf(26374,plain,
! [A: $i] : ( nil @ ( A @ skaf73 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[26373:[bind(A,$thf( C )),bind(B,$thf( C @ skaf73 ))]]) ).
thf(26433,plain,
! [A: $i] : ( nil @ ( A @ skaf73 @ rearsegP ) ),
inference(simp,[status(thm)],[26374]) ).
thf(9616,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[259,282]) ).
thf(9617,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[9616]) ).
thf(9618,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( A @ skaf49 @ lt ) ),
inference(pattern_uni,[status(thm)],[9617:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(9669,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( A @ skaf49 @ lt ) ),
inference(simp,[status(thm)],[9618]) ).
thf(22722,plain,
( ( nil != nil )
| ( sk2 != sk2 )
| ( nil @ ( sk2 @ segmentP ) )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[20823,10965]) ).
thf(22723,plain,
( ( nil != nil )
| ( nil @ ( sk2 @ segmentP ) )
| ( sk2 @ tl @ ssList ) ),
inference(simp,[status(thm)],[22722]) ).
thf(22724,plain,
( ( nil @ ( sk2 @ segmentP ) )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[22723:[]]) ).
thf(9601,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[288,282]) ).
thf(9602,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[9601]) ).
thf(9603,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( A @ skaf59 @ lt ) ),
inference(pattern_uni,[status(thm)],[9602:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(9660,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( A @ skaf59 @ lt ) ),
inference(simp,[status(thm)],[9603]) ).
thf(715,plain,
( ( nil != nil )
| ( sk2 @ duplicatefreeP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,383]) ).
thf(716,plain,
( ( sk2 @ duplicatefreeP )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[715:[]]) ).
thf(42150,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[267,378]) ).
thf(42151,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[42150]) ).
thf(42152,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[42151:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(42208,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[42152]) ).
thf(300,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ memberP ) )
| ( C @ ( B @ memberP ) )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ( B @ ( A @ app ) @ memberP ) ) ),
inference(cnf,[status(esa)],[299]) ).
thf(115,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( nil @ ( A @ cons ) @ app ) )
= ( B @ ( A @ cons ) ) )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause120) ).
thf(447,plain,
! [B: $i,A: $i] :
( ( ( B @ ( nil @ ( A @ cons ) @ app ) )
= ( B @ ( A @ cons ) ) )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(261,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[260]) ).
thf(262,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ leq ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[261]) ).
thf(26286,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[379,342]) ).
thf(26287,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[26286]) ).
thf(26288,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf45 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[26287:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf45 ) ))]]) ).
thf(26443,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf45 ) @ rearsegP ) ),
inference(simp,[status(thm)],[26288]) ).
thf(10225,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[263,10172]) ).
thf(10226,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[10225]) ).
thf(10227,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[10226:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(10280,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[10227]) ).
thf(273,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
inference(cnf,[status(esa)],[272]) ).
thf(9107,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[245,278]) ).
thf(9108,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[9107]) ).
thf(9109,plain,
! [A: $i] : ( A @ skaf44 @ ( A @ skaf44 @ leq ) ),
inference(pattern_uni,[status(thm)],[9108:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(9156,plain,
! [A: $i] : ( A @ skaf44 @ ( A @ skaf44 @ leq ) ),
inference(simp,[status(thm)],[9109]) ).
thf(49485,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf42 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ( ( C @ ( nil @ app ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[610,392]) ).
thf(49486,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf42 ) @ ssList )
!= ( C @ ssList ) )
| ( ( C @ ( nil @ app ) )
= C ) ),
inference(simp,[status(thm)],[49485]) ).
thf(49487,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ skaf42 ) @ ( nil @ app ) )
= ( B @ ( A @ skaf42 ) ) ),
inference(pattern_uni,[status(thm)],[49486:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf42 ) ))]]) ).
thf(49691,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ skaf42 ) @ ( nil @ app ) )
= ( B @ ( A @ skaf42 ) ) ),
inference(simp,[status(thm)],[49487]) ).
thf(22515,plain,
( ( nil != nil )
| ( sk1 @ equalelemsP )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[20584,368]) ).
thf(22516,plain,
( ( sk1 @ equalelemsP )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[22515:[]]) ).
thf(49555,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[557,392]) ).
thf(49556,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[49555]) ).
thf(49557,plain,
! [A: $i] :
( ( A @ skaf51 @ ( nil @ app ) )
= ( A @ skaf51 ) ),
inference(pattern_uni,[status(thm)],[49556:[bind(A,$thf( C )),bind(B,$thf( C @ skaf51 ))]]) ).
thf(49706,plain,
! [A: $i] :
( ( A @ skaf51 @ ( nil @ app ) )
= ( A @ skaf51 ) ),
inference(simp,[status(thm)],[49557]) ).
thf(42136,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[245,378]) ).
thf(42137,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[42136]) ).
thf(42138,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[42137:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(42204,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[42138]) ).
thf(37883,plain,
( ( nil != nil )
| ( nil != sk2 )
| ( sk1 != sk1 )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[32808,8568]) ).
thf(37884,plain,
( ( nil != nil )
| ( nil != sk2 )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(simp,[status(thm)],[37883]) ).
thf(37885,plain,
( ( nil != sk2 )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[37884:[]]) ).
thf(26325,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf42 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[610,342]) ).
thf(26326,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf42 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[26325]) ).
thf(26327,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf42 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[26326:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf42 ) ))]]) ).
thf(26458,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf42 ) @ rearsegP ) ),
inference(simp,[status(thm)],[26327]) ).
thf(242,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
inference(cnf,[status(esa)],[241]) ).
thf(10724,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[563,297]) ).
thf(10725,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[10724]) ).
thf(10726,plain,
! [A: $i] :
~ ( A @ skaf63 @ ( A @ skaf63 @ neq ) ),
inference(pattern_uni,[status(thm)],[10725:[bind(A,$thf( C )),bind(B,$thf( C @ skaf63 ))]]) ).
thf(10809,plain,
! [A: $i] :
~ ( A @ skaf63 @ ( A @ skaf63 @ neq ) ),
inference(simp,[status(thm)],[10726]) ).
thf(8651,plain,
( ( nil != nil )
| ( ( sk2 @ ( sk2 @ app ) )
= nil )
| ( nil @ ( sk2 @ neq ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,8052]) ).
thf(8652,plain,
( ( nil != nil )
| ( ( sk2 @ ( sk2 @ app ) )
= nil )
| ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[8651]) ).
thf(8653,plain,
( ( ( sk2 @ ( sk2 @ app ) )
= nil )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[8652:[]]) ).
thf(10715,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[367,297]) ).
thf(10716,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[10715]) ).
thf(10717,plain,
! [A: $i] :
~ ( A @ skaf57 @ ( A @ skaf57 @ neq ) ),
inference(pattern_uni,[status(thm)],[10716:[bind(A,$thf( C )),bind(B,$thf( C @ skaf57 ))]]) ).
thf(10804,plain,
! [A: $i] :
~ ( A @ skaf57 @ ( A @ skaf57 @ neq ) ),
inference(simp,[status(thm)],[10717]) ).
thf(49542,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[367,392]) ).
thf(49543,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[49542]) ).
thf(49544,plain,
! [A: $i] :
( ( A @ skaf57 @ ( nil @ app ) )
= ( A @ skaf57 ) ),
inference(pattern_uni,[status(thm)],[49543:[bind(A,$thf( C )),bind(B,$thf( C @ skaf57 ))]]) ).
thf(49703,plain,
! [A: $i] :
( ( A @ skaf57 @ ( nil @ app ) )
= ( A @ skaf57 ) ),
inference(simp,[status(thm)],[49544]) ).
thf(10691,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[393,297]) ).
thf(10692,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[10691]) ).
thf(10693,plain,
! [A: $i] :
~ ( A @ skaf58 @ ( A @ skaf58 @ neq ) ),
inference(pattern_uni,[status(thm)],[10692:[bind(A,$thf( C )),bind(B,$thf( C @ skaf58 ))]]) ).
thf(10781,plain,
! [A: $i] :
~ ( A @ skaf58 @ ( A @ skaf58 @ neq ) ),
inference(simp,[status(thm)],[10693]) ).
thf(22849,plain,
( ( nil != nil )
| ( sk2 @ strictorderedP )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[20823,626]) ).
thf(22850,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[22849:[]]) ).
thf(10924,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ~ $true
| ( sk2 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[716,10698]) ).
thf(10925,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( sk2 @ neq ) ) )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[10924]) ).
thf(10951,plain,
( ( nil != sk2 )
| ( sk2 != sk2 )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[10925]) ).
thf(10966,plain,
( ( nil != sk2 )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[10951]) ).
thf(331,plain,
! [A: $i] :
( ( ( A @ skaf68 @ ( A @ skaf65 @ cons ) @ ( A @ skaf67 @ ( A @ skaf64 @ cons ) @ ( A @ skaf66 @ app ) @ app ) )
= A )
| ( A @ totalorderedP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[330]) ).
thf(332,plain,
! [A: $i] :
( ( A @ totalorderedP )
| ~ ( A @ ssList )
| ( ( A @ skaf68 @ ( A @ skaf65 @ cons ) @ ( A @ skaf67 @ ( A @ skaf64 @ cons ) @ ( A @ skaf66 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[331]) ).
thf(107,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ rearsegP ) )
| ~ ( B @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause128) ).
thf(427,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ rearsegP ) )
| ~ ( B @ ( A @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(121,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause76) ).
thf(459,plain,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(22942,plain,
( ( nil != nil )
| ( nil @ ( sk2 @ frontsegP ) )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[20823,7387]) ).
thf(22943,plain,
( ( nil @ ( sk2 @ frontsegP ) )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[22942:[]]) ).
thf(42105,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[270,378]) ).
thf(42106,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[42105]) ).
thf(42107,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[42106:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(42229,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[42107]) ).
thf(178,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D = B )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ( ( B @ ( A @ cons ) )
!= ( D @ ( C @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause171) ).
thf(596,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D = B )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ( ( B @ ( A @ cons ) )
!= ( D @ ( C @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(676,plain,
( ( ( sk1 @ ( sk2 @ segmentP ) )
!= ( sk1 @ ( sk1 @ segmentP ) ) )
| ~ $true
| ~ ( nil @ ( sk1 @ neq ) )
| ( nil != sk1 ) ),
inference(paramod_ordered,[status(thm)],[648,675]) ).
thf(677,plain,
( ( ( sk1 @ ( sk2 @ segmentP ) )
!= ( sk1 @ ( sk1 @ segmentP ) ) )
| ~ ( nil @ ( sk1 @ neq ) )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[676]) ).
thf(680,plain,
( ( sk1 != sk1 )
| ( sk2 != sk1 )
| ~ ( nil @ ( sk1 @ neq ) )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[677]) ).
thf(682,plain,
( ( sk2 != sk1 )
| ~ ( nil @ ( sk1 @ neq ) )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[680]) ).
thf(837,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ( sk2 != sk1 )
| ~ $true
| ( nil != sk1 )
| ( nil != sk1 ) ),
inference(paramod_ordered,[status(thm)],[214,682]) ).
thf(838,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ( sk2 != sk1 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[837]) ).
thf(846,plain,
( ( nil != nil )
| ( sk2 != sk1 )
| ( sk2 != sk1 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[838]) ).
thf(850,plain,
( ( sk2 != sk1 )
| ( nil != sk1 ) ),
inference(simp,[status(thm)],[846]) ).
thf(7316,plain,
( ( ( nil @ ( nil @ segmentP ) )
!= ( sk2 @ ( sk2 @ segmentP ) ) )
| ~ ( sk2 @ totalorderedP )
| ~ $true
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[7303,5360]) ).
thf(7317,plain,
( ( ( nil @ ( nil @ segmentP ) )
!= ( sk2 @ ( sk2 @ segmentP ) ) )
| ~ ( sk2 @ totalorderedP )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[7316]) ).
thf(7359,plain,
( ( nil != sk2 )
| ( nil != sk2 )
| ~ ( sk2 @ totalorderedP )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[7317]) ).
thf(7385,plain,
( ( nil != sk2 )
| ~ ( sk2 @ totalorderedP )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[7359]) ).
thf(9431,plain,
( ( ( nil @ totalorderedP )
!= ( sk2 @ totalorderedP ) )
| ( nil != sk2 )
| ~ $true
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[639,7385]) ).
thf(9432,plain,
( ( ( nil @ totalorderedP )
!= ( sk2 @ totalorderedP ) )
| ( nil != sk2 )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[9431]) ).
thf(9461,plain,
( ( nil != sk2 )
| ( nil != sk2 )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[9432]) ).
thf(9489,plain,
( ( nil != sk2 )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[9461]) ).
thf(10213,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[271,10172]) ).
thf(10214,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[10213]) ).
thf(10215,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[10214:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(10276,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[10215]) ).
thf(183,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ ( D @ app ) @ app ) @ segmentP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause172) ).
thf(607,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ ( D @ app ) @ app ) @ segmentP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(12747,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[205,304]) ).
thf(12748,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP ) ),
inference(simp,[status(thm)],[12747]) ).
thf(12749,plain,
( ( sk2 @ skaf50 @ ( sk2 @ skaf49 @ leq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12748:[bind(A,$thf( sk2 ))]]) ).
thf(133,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = A )
| ( C @ ( B @ memberP ) )
| ~ ( C @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( C @ ( B @ ( A @ cons ) @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause161) ).
thf(486,plain,
! [C: $i,B: $i,A: $i] :
( ( C = A )
| ( C @ ( B @ memberP ) )
| ~ ( C @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( C @ ( B @ ( A @ cons ) @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(10733,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[465,297]) ).
thf(10734,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[10733]) ).
thf(10735,plain,
! [A: $i] :
~ ( A @ skaf80 @ ( A @ skaf80 @ neq ) ),
inference(pattern_uni,[status(thm)],[10734:[bind(A,$thf( C )),bind(B,$thf( C @ skaf80 ))]]) ).
thf(10813,plain,
! [A: $i] :
~ ( A @ skaf80 @ ( A @ skaf80 @ neq ) ),
inference(simp,[status(thm)],[10735]) ).
thf(163,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause78) ).
thf(560,plain,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(10745,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[564,297]) ).
thf(10746,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[10745]) ).
thf(10747,plain,
! [A: $i] :
~ ( A @ skaf66 @ ( A @ skaf66 @ neq ) ),
inference(pattern_uni,[status(thm)],[10746:[bind(A,$thf( C )),bind(B,$thf( C @ skaf66 ))]]) ).
thf(10817,plain,
! [A: $i] :
~ ( A @ skaf66 @ ( A @ skaf66 @ neq ) ),
inference(simp,[status(thm)],[10747]) ).
thf(253,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[252]) ).
thf(254,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[253]) ).
thf(227,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[226]) ).
thf(24423,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[233,336]) ).
thf(24424,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[24423]) ).
thf(24425,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( A @ skaf64 @ neq ) ),
inference(pattern_uni,[status(thm)],[24424:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(24527,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( A @ skaf64 @ neq ) ),
inference(simp,[status(thm)],[24425]) ).
thf(26340,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[298,342]) ).
thf(26341,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[26340]) ).
thf(26342,plain,
! [A: $i] : ( nil @ ( A @ skaf62 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[26341:[bind(A,$thf( C )),bind(B,$thf( C @ skaf62 ))]]) ).
thf(26462,plain,
! [A: $i] : ( nil @ ( A @ skaf62 @ rearsegP ) ),
inference(simp,[status(thm)],[26342]) ).
thf(3687,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[245,247]) ).
thf(3688,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[3687]) ).
thf(3689,plain,
! [A: $i] : ( A @ skaf44 @ ( A @ skaf44 @ geq ) ),
inference(pattern_uni,[status(thm)],[3688:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(3721,plain,
! [A: $i] : ( A @ skaf44 @ ( A @ skaf44 @ geq ) ),
inference(simp,[status(thm)],[3689]) ).
thf(118,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ frontsegP ) )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( D @ ( C @ cons ) @ ( B @ ( A @ cons ) @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause174) ).
thf(454,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ frontsegP ) )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( D @ ( C @ cons ) @ ( B @ ( A @ cons ) @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(91730,plain,
$false,
inference(e,[status(thm)],[10267,49466,468,481,365,10373,26456,49705,49673,333,249,10812,518,24518,12731,234,26461,26466,7409,276,308,247,9152,24529,22543,408,523,582,10277,10780,22788,22910,379,614,10805,269,202,22506,10282,384,8568,42207,472,340,3717,9672,49700,533,38135,43250,49701,24522,829,38378,417,3730,10698,26434,436,9159,288,22512,301,565,9148,10807,9657,651,257,33110,26442,719,38473,42203,372,7349,357,8022,389,26311,587,619,24526,26453,49704,949,3713,817,9155,284,325,228,26438,289,316,40019,9661,216,475,49685,3724,321,10271,24528,238,49690,353,821,480,22416,10818,376,30626,7369,211,646,10816,26457,514,10972,348,5360,24514,10670,634,24621,22385,1119,10965,10801,243,507,206,10799,397,687,396,10273,10784,527,312,49714,3720,201,42202,24493,49712,10779,307,68137,233,452,248,49721,38061,380,10811,49689,512,439,38188,26435,270,38019,7642,366,32183,957,825,302,26467,392,297,693,11106,275,10278,260,349,42182,38150,26445,467,229,252,10756,361,10808,3718,493,24620,3727,49682,456,9671,435,49693,329,36188,22726,42206,285,3731,1360,519,1143,317,725,22795,593,420,697,10962,24519,10281,42221,10318,44517,610,37960,256,38509,225,24722,9667,537,3728,526,637,489,590,3723,212,9662,554,622,701,23046,9149,22641,457,36501,42209,10270,503,10968,393,1131,654,24525,49294,244,10815,22572,360,205,508,311,42199,541,558,953,343,26460,1318,26439,10819,38386,10783,26432,298,412,965,10971,38170,264,279,689,26441,444,50810,42082,513,430,573,9154,10274,423,22945,24619,20823,10963,9157,42211,579,9663,37895,259,413,22744,7411,7287,24539,22510,204,10284,382,3726,611,498,10493,236,7658,10974,9670,313,9659,466,7347,24524,24420,350,22367,604,900,219,33015,230,245,318,599,274,9161,10279,419,377,3732,27957,9146,616,303,271,208,387,631,1339,10810,609,42205,520,24520,26463,10172,9674,462,10970,24713,60864,49016,345,367,552,240,251,626,42228,49715,49696,330,10792,8052,22715,24521,278,26431,10782,223,394,563,299,10803,32808,226,267,505,5619,685,521,695,10275,241,9150,42210,426,531,548,14724,255,342,49692,5528,9673,10269,49716,648,209,26459,10814,10788,355,38491,557,640,9153,282,414,327,63375,22574,9606,10246,409,263,310,22495,199,26444,585,49707,22486,338,643,544,441,3722,38229,502,470,576,9666,38656,49697,49702,10964,336,9151,7303,386,37999,26440,314,571,10178,61267,37613,24324,600,22280,627,450,24523,10806,25114,495,8228,368,24717,250,465,231,9664,9665,363,482,203,218,3725,1108,3665,961,22817,319,9147,258,390,26885,10428,7700,418,26447,20584,9160,42212,3729,24517,49717,699,22775,304,26452,401,63576,568,433,26465,22538,478,272,383,36523,22580,346,49505,290,378,235,246,26433,9669,207,22724,9660,26336,716,214,287,42208,300,447,262,405,26443,10280,273,9156,373,603,305,326,341,358,49691,3196,22516,49706,42204,564,37885,210,26458,239,242,294,22860,10809,8653,10804,268,49703,10781,283,22850,415,10966,332,427,459,22943,7387,200,42229,596,7263,850,9489,277,10276,501,38034,369,607,12749,486,337,10813,354,560,639,10817,222,592,364,232,254,227,322,24527,37981,26462,3721,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC066-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.12 % 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
% 0.24/5.72 % Computer : n026.cluster.edu
% 0.24/5.72 % Model : x86_64 x86_64
% 0.24/5.72 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/5.72 % Memory : 8046.5625MB
% 0.24/5.72 % OS : Linux 6.8.0-71-generic
% 0.24/5.72 % CPULimit : 300
% 0.24/5.72 % WCLimit : 300
% 0.24/5.72 % DateTime : Sat Sep 26 12:13:16 UTC 2026
% 0.24/5.73 % CPUTime :
% 0.24/5.73 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
% 1.01/6.28 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.78/6.54 % [INFO] Parsing done (252ms).
% 1.78/6.55 % [INFO] Running in sequential loop mode.
% 3.04/6.89 % [INFO] eprover registered as external prover.
% 3.38/6.90 % [INFO] Scanning for conjecture ...
% 3.38/7.04 % [INFO] Found a conjecture (or negated_conjecture) and 185 axioms. Running axiom selection ...
% 4.18/7.17 % [INFO] Axiom selection finished. Selected 185 axioms (removed 0 axioms).
% 4.78/7.33 % [INFO] Problem is propositional (TPTP CNF).
% 4.78/7.35 % [INFO] Type checking passed.
% 4.78/7.35 % [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 ...
% 207.62/61.84 % External prover 'e' found a proof!
% 207.62/61.84 % [INFO] Killing All external provers ...
% 207.62/61.85 % Time passed: 55936ms (effective reasoning time: 55291ms)
% 207.62/61.85 % 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
% 207.62/61.85 % No. of inferences in proof: 1726
% 207.62/61.85 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 55936 ms resp. 55291 ms w/o parsing
% 210.03/62.16 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 210.03/62.18 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------