%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWC172-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n014.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 08:52:35 AM UTC 2026
% Result : Unsatisfiable 212.32s 59.04s
% Output : Refutation 214.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 205
% Syntax : Number of formulae : 1733 ( 489 unt; 0 typ; 0 def)
% Number of atoms : 5212 (1217 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 12882 (2614 ~;2557 |; 0 &;7711 @)
% ( 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 : 80 ( 77 usr; 14 con; 0-2 aty)
% Number of variables : 1990 ( 0 ^;1990 !; 0 ?;1990 :)
% 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(ssItem_decl,type,
ssItem: $i > $o ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(app_decl,type,
app: $i > $i > $i ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(nil_decl,type,
nil: $i ).
thf(neq_decl,type,
neq: $i > $i > $o ).
thf(sk9_decl,type,
sk9: $i ).
thf(memberP_decl,type,
memberP: $i > $i > $o ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(skac3_decl,type,
skac3: $i ).
thf(skac2_decl,type,
skac2: $i ).
thf(skaf43_decl,type,
skaf43: $i > $i > $i ).
thf(geq_decl,type,
geq: $i > $i > $o ).
thf(totalorderedP_decl,type,
totalorderedP: $i > $o ).
thf(lt_decl,type,
lt: $i > $i > $o ).
thf(gt_decl,type,
gt: $i > $i > $o ).
thf(skaf62_decl,type,
skaf62: $i > $i ).
thf(skaf69_decl,type,
skaf69: $i > $i ).
thf(skaf70_decl,type,
skaf70: $i > $i ).
thf(strictorderedP_decl,type,
strictorderedP: $i > $o ).
thf(cyclefreeP_decl,type,
cyclefreeP: $i > $o ).
thf(skaf49_decl,type,
skaf49: $i > $i ).
thf(skaf50_decl,type,
skaf50: $i > $i ).
thf(singletonP_decl,type,
singletonP: $i > $o ).
thf(skaf44_decl,type,
skaf44: $i > $i ).
thf(duplicatefreeP_decl,type,
duplicatefreeP: $i > $o ).
thf(skaf75_decl,type,
skaf75: $i > $i ).
thf(skaf74_decl,type,
skaf74: $i > $i ).
thf(skaf76_decl,type,
skaf76: $i > $i ).
thf(skaf77_decl,type,
skaf77: $i > $i ).
thf(skaf72_decl,type,
skaf72: $i > $i ).
thf(skaf79_decl,type,
skaf79: $i > $i ).
thf(hd_decl,type,
hd: $i > $i ).
thf(frontsegP_decl,type,
frontsegP: $i > $i > $o ).
thf(skaf71_decl,type,
skaf71: $i > $i ).
thf(skaf73_decl,type,
skaf73: $i > $i ).
thf(skaf46_decl,type,
skaf46: $i > $i > $i ).
thf(skaf64_decl,type,
skaf64: $i > $i ).
thf(tl_decl,type,
tl: $i > $i ).
thf(skaf66_decl,type,
skaf66: $i > $i ).
thf(skaf67_decl,type,
skaf67: $i > $i ).
thf(skaf65_decl,type,
skaf65: $i > $i ).
thf(skaf68_decl,type,
skaf68: $i > $i ).
thf(skaf45_decl,type,
skaf45: $i > $i > $i ).
thf(rearsegP_decl,type,
rearsegP: $i > $i > $o ).
thf(strictorderP_decl,type,
strictorderP: $i > $o ).
thf(skaf61_decl,type,
skaf61: $i > $i ).
thf(skaf59_decl,type,
skaf59: $i > $i ).
thf(skaf60_decl,type,
skaf60: $i > $i ).
thf(skaf63_decl,type,
skaf63: $i > $i ).
thf(skaf51_decl,type,
skaf51: $i > $i ).
thf(skaf52_decl,type,
skaf52: $i > $i ).
thf(skaf53_decl,type,
skaf53: $i > $i ).
thf(skaf57_decl,type,
skaf57: $i > $i ).
thf(equalelemsP_decl,type,
equalelemsP: $i > $o ).
thf(totalorderP_decl,type,
totalorderP: $i > $o ).
thf(skaf56_decl,type,
skaf56: $i > $i ).
thf(skaf54_decl,type,
skaf54: $i > $i ).
thf(skaf55_decl,type,
skaf55: $i > $i ).
thf(skaf58_decl,type,
skaf58: $i > $i ).
thf(skaf48_decl,type,
skaf48: $i > $i > $i ).
thf(segmentP_decl,type,
segmentP: $i > $i > $o ).
thf(skaf80_decl,type,
skaf80: $i > $i ).
thf(skaf47_decl,type,
skaf47: $i > $i > $i ).
thf(skaf78_decl,type,
skaf78: $i > $i ).
thf(skaf81_decl,type,
skaf81: $i > $i ).
thf(skaf83_decl,type,
skaf83: $i > $i ).
thf(skaf82_decl,type,
skaf82: $i > $i ).
thf(skaf42_decl,type,
skaf42: $i > $i > $i ).
thf(178,axiom,
! [A: $i] : ( A @ skaf65 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause30) ).
thf(608,plain,
! [A: $i] : ( A @ skaf65 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(115,axiom,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( nil @ memberP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause71) ).
thf(462,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(463,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(cnf,[status(esa)],[462]) ).
thf(2159,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[608,463]) ).
thf(2160,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2159]) ).
thf(2161,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2160:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(2163,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2161]) ).
thf(157,axiom,
skac3 @ ssItem,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause9) ).
thf(563,plain,
skac3 @ ssItem,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(84,axiom,
! [A: $i] :
( ( A @ ( A @ geq ) )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause55) ).
thf(397,plain,
! [A: $i] :
( ( A @ ( A @ geq ) )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(398,plain,
! [A: $i] :
( ( A @ ( A @ geq ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[397]) ).
thf(64597,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[563,398]) ).
thf(64598,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) ) ),
inference(simp,[status(thm)],[64597]) ).
thf(64599,plain,
skac3 @ ( skac3 @ geq ),
inference(pattern_uni,[status(thm)],[64598:[bind(A,$thf( skac3 ))]]) ).
thf(13,negated_conjecture,
( ( nil = sk4 )
| ( sk9 @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
thf(213,plain,
( ( nil = sk4 )
| ( sk9 @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(228,plain,
( ( nil = sk4 )
| ( sk9 @ ssItem ) ),
inference(cnf,[status(esa)],[213]) ).
thf(229,plain,
( ( sk9 @ ssItem )
| ( nil = sk4 ) ),
inference(lifteq,[status(thm)],[228]) ).
thf(5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
thf(206,plain,
sk2 = sk4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(237,plain,
sk4 = sk2,
inference(lifteq,[status(thm)],[206]) ).
thf(733,plain,
( ( sk9 @ ssItem )
| ( nil = sk2 ) ),
inference(rewrite,[status(thm)],[229,237]) ).
thf(746,plain,
! [A: $i] :
( ( ( sk9 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( nil @ memberP ) )
| ( nil = sk2 ) ),
inference(paramod_ordered,[status(thm)],[733,463]) ).
thf(747,plain,
! [A: $i] :
( ( ( sk9 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( nil = sk2 ) ),
inference(simp,[status(thm)],[746]) ).
thf(748,plain,
( ~ ( sk9 @ ( nil @ memberP ) )
| ( nil = sk2 ) ),
inference(pattern_uni,[status(thm)],[747:[bind(A,$thf( sk9 ))]]) ).
thf(730,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[563,463]) ).
thf(731,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[730]) ).
thf(732,plain,
~ ( skac3 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[731:[bind(A,$thf( skac3 ))]]) ).
thf(4907,plain,
( ( nil != nil )
| ~ ( skac3 @ ( sk2 @ memberP ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[748,732]) ).
thf(4908,plain,
( ~ ( skac3 @ ( sk2 @ memberP ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[4907:[]]) ).
thf(6070,plain,
( ~ $true
| ( ( sk9 @ ( nil @ memberP ) )
!= ( skac3 @ ( sk2 @ memberP ) ) )
| ~ ( skac3 @ ( sk2 @ memberP ) ) ),
inference(eqfactor_ordered,[status(thm)],[4908]) ).
thf(6085,plain,
( ( skac3 != sk9 )
| ( nil != sk2 )
| ~ ( skac3 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[6070]) ).
thf(189,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf42 ) @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause53) ).
thf(629,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf42 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(110,axiom,
! [A: $i] : ( A @ skaf49 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause46) ).
thf(452,plain,
! [A: $i] : ( A @ skaf49 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause113) ).
thf(252,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(253,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(cnf,[status(esa)],[252]) ).
thf(254,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[253]) ).
thf(255,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[254]) ).
thf(49,axiom,
nil @ ssList,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
thf(312,plain,
nil @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(2250,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ $true ),
inference(rewrite,[status(thm)],[255,312]) ).
thf(2251,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[2250]) ).
thf(2261,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[452,2251]) ).
thf(2262,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[2261]) ).
thf(2263,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[2262:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(2336,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[2263]) ).
thf(96,axiom,
! [A: $i] : ( A @ skaf70 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause25) ).
thf(424,plain,
! [A: $i] : ( A @ skaf70 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(64555,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[424,398]) ).
thf(64556,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[64555]) ).
thf(64557,plain,
! [A: $i] : ( A @ skaf70 @ ( A @ skaf70 @ geq ) ),
inference(pattern_uni,[status(thm)],[64556:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(64631,plain,
! [A: $i] : ( A @ skaf70 @ ( A @ skaf70 @ geq ) ),
inference(simp,[status(thm)],[64557]) ).
thf(48,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause117) ).
thf(308,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(309,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[308]) ).
thf(310,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[309]) ).
thf(311,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[310]) ).
thf(20012,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[563,311]) ).
thf(20013,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[20012]) ).
thf(20014,plain,
~ ( skac3 @ ( skac3 @ neq ) ),
inference(pattern_uni,[status(thm)],[20013:[bind(A,$thf( skac3 ))]]) ).
thf(140,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause111) ).
thf(518,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(118,axiom,
! [A: $i] :
( ( ( nil @ ( A @ app ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause73) ).
thf(468,plain,
! [A: $i] :
( ( ( nil @ ( A @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(12,negated_conjecture,
~ ( sk6 @ ( sk5 @ neq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
thf(216,plain,
~ ( sk6 @ ( sk5 @ neq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(234,plain,
~ ( sk6 @ ( sk5 @ neq ) ),
inference(polarity_switch,[status(thm)],[216]) ).
thf(80,axiom,
! [A: $i] : ( A @ skaf44 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause47) ).
thf(386,plain,
! [A: $i] : ( A @ skaf44 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(66,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause66) ).
thf(352,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(353,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[352]) ).
thf(32591,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[386,353]) ).
thf(32592,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[32591]) ).
thf(32593,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[32592:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(32643,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[32593]) ).
thf(153,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ app ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause141) ).
thf(555,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)],[153]) ).
thf(205,axiom,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( A @ lt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause63) ).
thf(666,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ~ ( A @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause103) ).
thf(364,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(365,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
inference(cnf,[status(esa)],[364]) ).
thf(130,axiom,
! [A: $i] : ( A @ skaf68 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause27) ).
thf(499,plain,
! [A: $i] : ( A @ skaf68 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(71,axiom,
! [A: $i] :
( ( ( A @ ( nil @ app ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause74) ).
thf(361,plain,
! [A: $i] :
( ( ( A @ ( nil @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(362,plain,
! [A: $i] :
( ( ( A @ ( nil @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[361]) ).
thf(363,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[362]) ).
thf(35870,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[499,363]) ).
thf(35871,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[35870]) ).
thf(35872,plain,
! [A: $i] :
( ( A @ skaf68 @ ( nil @ app ) )
= ( A @ skaf68 ) ),
inference(pattern_uni,[status(thm)],[35871:[bind(A,$thf( C )),bind(B,$thf( C @ skaf68 ))]]) ).
thf(36066,plain,
! [A: $i] :
( ( A @ skaf68 @ ( nil @ app ) )
= ( A @ skaf68 ) ),
inference(simp,[status(thm)],[35872]) ).
thf(56,axiom,
! [A: $i] : ( A @ skaf77 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause18) ).
thf(329,plain,
! [A: $i] : ( A @ skaf77 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(51,axiom,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause58) ).
thf(316,plain,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(317,plain,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[316]) ).
thf(20913,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[329,317]) ).
thf(20914,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[20913]) ).
thf(20915,plain,
! [A: $i] : ( nil @ ( A @ skaf77 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[20914:[bind(A,$thf( C )),bind(B,$thf( C @ skaf77 ))]]) ).
thf(21040,plain,
! [A: $i] : ( nil @ ( A @ skaf77 @ rearsegP ) ),
inference(simp,[status(thm)],[20915]) ).
thf(151,axiom,
skac2 @ ssItem,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause10) ).
thf(550,plain,
skac2 @ ssItem,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(32499,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[550,353]) ).
thf(32500,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[32499]) ).
thf(32501,plain,
nil @ ( skac2 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[32500:[bind(A,$thf( skac2 ))]]) ).
thf(93,axiom,
! [A: $i] : ( A @ skaf69 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause26) ).
thf(419,plain,
! [A: $i] : ( A @ skaf69 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(2286,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[419,2251]) ).
thf(2287,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[2286]) ).
thf(2288,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[2287:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(2341,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[2288]) ).
thf(64,axiom,
! [B: $i,A: $i] :
( ( B @ singletonP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( nil @ ( A @ cons ) )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause116) ).
thf(344,plain,
! [B: $i,A: $i] :
( ( B @ singletonP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( nil @ ( A @ cons ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(345,plain,
! [B: $i,A: $i] :
( ( B @ singletonP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( nil @ ( A @ cons ) )
!= B ) ),
inference(cnf,[status(esa)],[344]) ).
thf(346,plain,
! [B: $i,A: $i] :
( ( B @ singletonP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( nil @ ( A @ cons ) )
!= B ) ),
inference(lifteq,[status(thm)],[345]) ).
thf(347,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ singletonP )
| ~ ( nil @ ( A @ cons ) @ ssList )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[346]) ).
thf(159,axiom,
! [A: $i] : ( A @ skaf63 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause32) ).
thf(567,plain,
! [A: $i] : ( A @ skaf63 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(20949,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[567,317]) ).
thf(20950,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[20949]) ).
thf(20951,plain,
! [A: $i] : ( nil @ ( A @ skaf63 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[20950:[bind(A,$thf( C )),bind(B,$thf( C @ skaf63 ))]]) ).
thf(21025,plain,
! [A: $i] : ( nil @ ( A @ skaf63 @ rearsegP ) ),
inference(simp,[status(thm)],[20951]) ).
thf(22,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf43 ) @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause52) ).
thf(249,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf43 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(58,axiom,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause82) ).
thf(333,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(188,axiom,
! [A: $i] : ( A @ skaf76 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause19) ).
thf(628,plain,
! [A: $i] : ( A @ skaf76 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(142,axiom,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf60 @ ( A @ skaf59 @ lt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause93) ).
thf(523,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf60 @ ( A @ skaf59 @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(1,negated_conjecture,
sk1 @ ssList,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
thf(210,plain,
sk1 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(35994,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[210,363]) ).
thf(35995,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[35994]) ).
thf(35996,plain,
( ( sk1 @ ( nil @ app ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[35995:[bind(A,$thf( sk1 ))]]) ).
thf(19,negated_conjecture,
( ( nil = sk3 )
| ( sk9 @ ( sk4 @ memberP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_19) ).
thf(223,plain,
( ( nil = sk3 )
| ( sk9 @ ( sk4 @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(230,plain,
( ( nil = sk3 )
| ( sk9 @ ( sk4 @ memberP ) ) ),
inference(cnf,[status(esa)],[223]) ).
thf(231,plain,
( ( sk9 @ ( sk4 @ memberP ) )
| ( nil = sk3 ) ),
inference(lifteq,[status(thm)],[230]) ).
thf(6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
thf(211,plain,
sk1 = sk3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(235,plain,
sk3 = sk1,
inference(lifteq,[status(thm)],[211]) ).
thf(835,plain,
( ( sk9 @ ( sk2 @ memberP ) )
| ( nil = sk1 ) ),
inference(rewrite,[status(thm)],[231,235,237]) ).
thf(54,axiom,
nil @ strictorderP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause5) ).
thf(324,plain,
nil @ strictorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(844,plain,
( ( nil != nil )
| ( sk1 @ strictorderP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[835,324]) ).
thf(845,plain,
( ( sk1 @ strictorderP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[844:[]]) ).
thf(14,negated_conjecture,
( ( nil = sk3 )
| ( sk9 @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
thf(208,plain,
( ( nil = sk3 )
| ( sk9 @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(242,plain,
( ( nil = sk3 )
| ( sk9 @ ssItem ) ),
inference(cnf,[status(esa)],[208]) ).
thf(243,plain,
( ( sk9 @ ssItem )
| ( nil = sk3 ) ),
inference(lifteq,[status(thm)],[242]) ).
thf(788,plain,
( ( sk9 @ ssItem )
| ( nil = sk1 ) ),
inference(rewrite,[status(thm)],[243,235]) ).
thf(825,plain,
! [A: $i] :
( ( ( sk9 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( nil @ memberP ) )
| ( nil = sk1 ) ),
inference(paramod_ordered,[status(thm)],[788,463]) ).
thf(826,plain,
! [A: $i] :
( ( ( sk9 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( nil = sk1 ) ),
inference(simp,[status(thm)],[825]) ).
thf(827,plain,
( ~ ( sk9 @ ( nil @ memberP ) )
| ( nil = sk1 ) ),
inference(pattern_uni,[status(thm)],[826:[bind(A,$thf( sk9 ))]]) ).
thf(9110,plain,
( ( nil != nil )
| ( sk1 @ strictorderP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[827,324]) ).
thf(9111,plain,
( ( sk1 @ strictorderP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[9110:[]]) ).
thf(22008,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( sk1 @ strictorderP )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[845,9111]) ).
thf(22009,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[22008]) ).
thf(22048,plain,
( ( sk9 != sk9 )
| ( nil != sk2 )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[22009]) ).
thf(22069,plain,
( ( nil != sk2 )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[22048]) ).
thf(122,axiom,
! [A: $i] : ( A @ skaf75 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause20) ).
thf(477,plain,
! [A: $i] : ( A @ skaf75 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(26,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause115) ).
thf(258,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(259,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[258]) ).
thf(260,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[259]) ).
thf(261,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[260]) ).
thf(1438,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[477,261]) ).
thf(1439,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1438]) ).
thf(1440,plain,
! [A: $i] :
~ ( A @ skaf75 @ ( A @ skaf75 @ neq ) ),
inference(pattern_uni,[status(thm)],[1439:[bind(A,$thf( C )),bind(B,$thf( C @ skaf75 ))]]) ).
thf(1443,plain,
! [A: $i] :
~ ( A @ skaf75 @ ( A @ skaf75 @ neq ) ),
inference(simp,[status(thm)],[1440]) ).
thf(10,negated_conjecture,
sk8 @ ssList,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
thf(207,plain,
sk8 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(46,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause75) ).
thf(302,plain,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(303,plain,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[302]) ).
thf(304,plain,
! [A: $i] :
( ( A @ tl @ ssList )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[303]) ).
thf(18738,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[207,304]) ).
thf(18739,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[18738]) ).
thf(18740,plain,
( ( sk8 @ tl @ ssList )
| ( nil = sk8 ) ),
inference(pattern_uni,[status(thm)],[18739:[bind(A,$thf( sk8 ))]]) ).
thf(134,axiom,
nil @ cyclefreeP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause7) ).
thf(505,plain,
nil @ cyclefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(30492,plain,
( ( nil != nil )
| ( sk8 @ cyclefreeP )
| ( sk8 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[18740,505]) ).
thf(30493,plain,
( ( sk8 @ cyclefreeP )
| ( sk8 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[30492:[]]) ).
thf(7,negated_conjecture,
sk5 @ ssItem,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
thf(217,plain,
sk5 @ ssItem,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(670,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[217,463]) ).
thf(671,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[670]) ).
thf(672,plain,
~ ( sk5 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[671:[bind(A,$thf( sk5 ))]]) ).
thf(740,plain,
( ( nil != nil )
| ~ ( sk5 @ ( sk2 @ memberP ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,672]) ).
thf(741,plain,
( ~ ( sk5 @ ( sk2 @ memberP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[740:[]]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause88) ).
thf(269,plain,
! [A: $i] :
( ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(171,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ rearsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ rearsegP ) )
| ~ ( B @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause153) ).
thf(597,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ rearsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ rearsegP ) )
| ~ ( B @ ( A @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(9,negated_conjecture,
sk7 @ ssList,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
thf(212,plain,
sk7 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(18148,plain,
! [A: $i] :
( ( ( sk7 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[212,304]) ).
thf(18149,plain,
! [A: $i] :
( ( ( sk7 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[18148]) ).
thf(18150,plain,
( ( sk7 @ tl @ ssList )
| ( nil = sk7 ) ),
inference(pattern_uni,[status(thm)],[18149:[bind(A,$thf( sk7 ))]]) ).
thf(29794,plain,
( ( nil != nil )
| ( sk7 @ strictorderP )
| ( sk7 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[18150,324]) ).
thf(29795,plain,
( ( sk7 @ strictorderP )
| ( sk7 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[29794:[]]) ).
thf(17,negated_conjecture,
! [A: $i] :
( ( nil = sk4 )
| ~ ( sk9 @ ( A @ leq ) )
| ~ ( A @ ( sk4 @ memberP ) )
| ( sk9 = A )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
thf(215,plain,
! [A: $i] :
( ( nil = sk4 )
| ~ ( sk9 @ ( A @ leq ) )
| ~ ( A @ ( sk4 @ memberP ) )
| ( sk9 = A )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(244,plain,
! [A: $i] :
( ( nil = sk4 )
| ~ ( sk9 @ ( A @ leq ) )
| ~ ( A @ ( sk4 @ memberP ) )
| ( sk9 = A )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[215]) ).
thf(245,plain,
! [A: $i] :
( ~ ( sk9 @ ( A @ leq ) )
| ~ ( A @ ( sk4 @ memberP ) )
| ~ ( A @ ssItem )
| ( nil = sk4 )
| ( sk9 = A ) ),
inference(lifteq,[status(thm)],[244]) ).
thf(1486,plain,
! [A: $i] :
( ~ ( sk9 @ ( A @ leq ) )
| ~ ( A @ ( sk2 @ memberP ) )
| ~ ( A @ ssItem )
| ( nil = sk2 )
| ( sk9 = A ) ),
inference(rewrite,[status(thm)],[245,237]) ).
thf(33,axiom,
! [A: $i] :
( ( ( A @ skaf77 @ ( A @ skaf74 @ cons ) @ ( A @ skaf76 @ ( A @ skaf74 @ cons ) @ ( A @ skaf75 @ app ) @ app ) )
= A )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause162) ).
thf(274,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)],[33]) ).
thf(275,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)],[274]) ).
thf(276,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)],[275]) ).
thf(64537,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[550,398]) ).
thf(64538,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) ) ),
inference(simp,[status(thm)],[64537]) ).
thf(64539,plain,
skac2 @ ( skac2 @ geq ),
inference(pattern_uni,[status(thm)],[64538:[bind(A,$thf( skac2 ))]]) ).
thf(16,negated_conjecture,
( ( nil = sk4 )
| ( sk9 @ ( sk4 @ memberP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
thf(220,plain,
( ( nil = sk4 )
| ( sk9 @ ( sk4 @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(226,plain,
( ( nil = sk4 )
| ( sk9 @ ( sk4 @ memberP ) ) ),
inference(cnf,[status(esa)],[220]) ).
thf(227,plain,
( ( sk9 @ ( sk4 @ memberP ) )
| ( nil = sk4 ) ),
inference(lifteq,[status(thm)],[226]) ).
thf(676,plain,
( ( sk9 @ ( sk2 @ memberP ) )
| ( nil = sk2 ) ),
inference(rewrite,[status(thm)],[227,237]) ).
thf(201,axiom,
nil @ totalorderedP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause4) ).
thf(659,plain,
nil @ totalorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(771,plain,
( ( nil != nil )
| ( sk2 @ totalorderedP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[676,659]) ).
thf(772,plain,
( ( sk2 @ totalorderedP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[771:[]]) ).
thf(5002,plain,
( ( nil != nil )
| ( sk2 @ totalorderedP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[748,659]) ).
thf(5003,plain,
( ( sk2 @ totalorderedP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[5002:[]]) ).
thf(19389,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( sk2 @ totalorderedP )
| ~ $true
| ( sk2 @ totalorderedP ) ),
inference(paramod_ordered,[status(thm)],[772,5003]) ).
thf(19390,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( sk2 @ totalorderedP ) ),
inference(simp,[status(thm)],[19389]) ).
thf(19441,plain,
( ( sk9 != sk9 )
| ( nil != sk2 )
| ( sk2 @ totalorderedP ) ),
inference(simp,[status(thm)],[19390]) ).
thf(19462,plain,
( ( nil != sk2 )
| ( sk2 @ totalorderedP ) ),
inference(simp,[status(thm)],[19441]) ).
thf(183,axiom,
! [A: $i] : ( A @ skaf50 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause45) ).
thf(618,plain,
! [A: $i] : ( A @ skaf50 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(32533,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[618,353]) ).
thf(32534,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[32533]) ).
thf(32535,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[32534:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(32631,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[32535]) ).
thf(35819,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf43 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ( ( C @ ( nil @ app ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[249,363]) ).
thf(35820,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf43 ) @ ssList )
!= ( C @ ssList ) )
| ( ( C @ ( nil @ app ) )
= C ) ),
inference(simp,[status(thm)],[35819]) ).
thf(35821,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ skaf43 ) @ ( nil @ app ) )
= ( B @ ( A @ skaf43 ) ) ),
inference(pattern_uni,[status(thm)],[35820:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf43 ) ))]]) ).
thf(36128,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ skaf43 ) @ ( nil @ app ) )
= ( B @ ( A @ skaf43 ) ) ),
inference(simp,[status(thm)],[35821]) ).
thf(70,axiom,
nil @ duplicatefreeP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause2) ).
thf(360,plain,
nil @ duplicatefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(872,plain,
( ( nil != nil )
| ( sk1 @ duplicatefreeP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[835,360]) ).
thf(873,plain,
( ( sk1 @ duplicatefreeP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[872:[]]) ).
thf(94,axiom,
! [A: $i] : ( A @ skaf55 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause40) ).
thf(420,plain,
! [A: $i] : ( A @ skaf55 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(1201,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[420,463]) ).
thf(1202,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1201]) ).
thf(1203,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1202:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(1205,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1203]) ).
thf(108,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf48 ) @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause48) ).
thf(449,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf48 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( nil @ ( A @ cons ) @ app ) )
= ( B @ ( A @ cons ) ) )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause120) ).
thf(440,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)],[104]) ).
thf(137,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf47 ) @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause49) ).
thf(511,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf47 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(9183,plain,
( ( nil != nil )
| ( sk1 @ cyclefreeP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[827,505]) ).
thf(9184,plain,
( ( sk1 @ cyclefreeP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[9183:[]]) ).
thf(123,axiom,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause79) ).
thf(478,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(479,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(cnf,[status(esa)],[478]) ).
thf(480,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[479]) ).
thf(481,plain,
( ( nil @ ( nil @ segmentP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[480]) ).
thf(11904,plain,
( ( nil @ ( nil @ segmentP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[481,312]) ).
thf(11905,plain,
nil @ ( nil @ segmentP ),
inference(simp,[status(thm)],[11904]) ).
thf(11908,plain,
( ( nil != nil )
| ( nil @ ( sk1 @ segmentP ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[788,11905]) ).
thf(11909,plain,
( ( nil @ ( sk1 @ segmentP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[11908:[]]) ).
thf(20143,plain,
( ( nil != nil )
| ( sk1 @ ( sk1 @ segmentP ) )
| ( sk9 @ ssItem )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[788,11909]) ).
thf(20144,plain,
( ( nil != nil )
| ( sk1 @ ( sk1 @ segmentP ) )
| ( sk9 @ ssItem ) ),
inference(simp,[status(thm)],[20143]) ).
thf(20145,plain,
( ( sk1 @ ( sk1 @ segmentP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[20144:[]]) ).
thf(797,plain,
( ( nil != nil )
| ( sk9 @ ssItem )
| ( sk2 = sk1 )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[788,733]) ).
thf(798,plain,
( ( nil != nil )
| ( sk2 = sk1 )
| ( sk9 @ ssItem ) ),
inference(simp,[status(thm)],[797]) ).
thf(799,plain,
( ( sk2 = sk1 )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[798:[]]) ).
thf(20003,plain,
! [A: $i] :
( ( ( sk9 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( A @ neq ) )
| ( sk2 = sk1 ) ),
inference(paramod_ordered,[status(thm)],[799,311]) ).
thf(20004,plain,
! [A: $i] :
( ( ( sk9 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ( sk2 = sk1 ) ),
inference(simp,[status(thm)],[20003]) ).
thf(20005,plain,
( ~ ( sk9 @ ( sk9 @ neq ) )
| ( sk2 = sk1 ) ),
inference(pattern_uni,[status(thm)],[20004:[bind(A,$thf( sk9 ))]]) ).
thf(2,negated_conjecture,
sk2 @ ssList,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).
thf(214,plain,
sk2 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(727,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[214,261]) ).
thf(728,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[727]) ).
thf(729,plain,
~ ( sk2 @ ( sk2 @ neq ) ),
inference(pattern_uni,[status(thm)],[728:[bind(A,$thf( sk2 ))]]) ).
thf(34933,plain,
( ( sk2 != sk2 )
| ~ ( sk1 @ ( sk2 @ neq ) )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[20005,729]) ).
thf(34934,plain,
( ~ ( sk1 @ ( sk2 @ neq ) )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[34933:[]]) ).
thf(146,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause65) ).
thf(533,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(131,axiom,
nil @ totalorderP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause6) ).
thf(500,plain,
nil @ totalorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(703,plain,
( ( nil != nil )
| ( sk2 @ totalorderP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[676,500]) ).
thf(704,plain,
( ( sk2 @ totalorderP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[703:[]]) ).
thf(4837,plain,
( ( nil != nil )
| ( sk2 @ totalorderP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[748,500]) ).
thf(4838,plain,
( ( sk2 @ totalorderP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[4837:[]]) ).
thf(14014,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( sk2 @ totalorderP )
| ~ $true
| ( sk2 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[704,4838]) ).
thf(14015,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( sk2 @ totalorderP ) ),
inference(simp,[status(thm)],[14014]) ).
thf(14065,plain,
( ( sk9 != sk9 )
| ( nil != sk2 )
| ( sk2 @ totalorderP ) ),
inference(simp,[status(thm)],[14015]) ).
thf(14084,plain,
( ( nil != sk2 )
| ( sk2 @ totalorderP ) ),
inference(simp,[status(thm)],[14065]) ).
thf(813,plain,
( ( nil != nil )
| ( sk1 @ duplicatefreeP )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[788,360]) ).
thf(814,plain,
( ( sk1 @ duplicatefreeP )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[813:[]]) ).
thf(185,axiom,
! [A: $i] : ( A @ skaf71 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause24) ).
thf(622,plain,
! [A: $i] : ( A @ skaf71 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(20934,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[622,317]) ).
thf(20935,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[20934]) ).
thf(20936,plain,
! [A: $i] : ( nil @ ( A @ skaf71 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[20935:[bind(A,$thf( C )),bind(B,$thf( C @ skaf71 ))]]) ).
thf(21016,plain,
! [A: $i] : ( nil @ ( A @ skaf71 @ rearsegP ) ),
inference(simp,[status(thm)],[20936]) ).
thf(61,axiom,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf59 @ ( A @ skaf60 @ lt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause92) ).
thf(340,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf59 @ ( A @ skaf60 @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(136,axiom,
! [A: $i] : ( A @ skaf52 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause43) ).
thf(510,plain,
! [A: $i] : ( A @ skaf52 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(1452,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[510,261]) ).
thf(1453,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1452]) ).
thf(1454,plain,
! [A: $i] :
~ ( A @ skaf52 @ ( A @ skaf52 @ neq ) ),
inference(pattern_uni,[status(thm)],[1453:[bind(A,$thf( C )),bind(B,$thf( C @ skaf52 ))]]) ).
thf(1458,plain,
! [A: $i] :
~ ( A @ skaf52 @ ( A @ skaf52 @ neq ) ),
inference(simp,[status(thm)],[1454]) ).
thf(30208,plain,
( ( nil != nil )
| ( sk8 @ totalorderP )
| ( sk8 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[18740,500]) ).
thf(30209,plain,
( ( sk8 @ totalorderP )
| ( sk8 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[30208:[]]) ).
thf(35888,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[622,363]) ).
thf(35889,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[35888]) ).
thf(35890,plain,
! [A: $i] :
( ( A @ skaf71 @ ( nil @ app ) )
= ( A @ skaf71 ) ),
inference(pattern_uni,[status(thm)],[35889:[bind(A,$thf( C )),bind(B,$thf( C @ skaf71 ))]]) ).
thf(36070,plain,
! [A: $i] :
( ( A @ skaf71 @ ( nil @ app ) )
= ( A @ skaf71 ) ),
inference(simp,[status(thm)],[35890]) ).
thf(19976,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[452,311]) ).
thf(19977,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[19976]) ).
thf(19978,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( A @ skaf49 @ neq ) ),
inference(pattern_uni,[status(thm)],[19977:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(20034,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( A @ skaf49 @ neq ) ),
inference(simp,[status(thm)],[19978]) ).
thf(196,axiom,
nil @ strictorderedP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause3) ).
thf(646,plain,
nil @ strictorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(767,plain,
( ( nil != nil )
| ( sk2 @ strictorderedP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[676,646]) ).
thf(768,plain,
( ( sk2 @ strictorderedP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[767:[]]) ).
thf(4848,plain,
( ( nil != nil )
| ( sk2 @ strictorderedP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[748,646]) ).
thf(4849,plain,
( ( sk2 @ strictorderedP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[4848:[]]) ).
thf(14155,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( sk2 @ strictorderedP )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[768,4849]) ).
thf(14156,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[14155]) ).
thf(14184,plain,
( ( sk9 != sk9 )
| ( nil != sk2 )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[14156]) ).
thf(14203,plain,
( ( nil != sk2 )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[14184]) ).
thf(781,plain,
( ( nil != nil )
| ~ ( skac3 @ ( sk2 @ memberP ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,732]) ).
thf(782,plain,
( ~ ( skac3 @ ( sk2 @ memberP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[781:[]]) ).
thf(707,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[550,463]) ).
thf(708,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[707]) ).
thf(709,plain,
~ ( skac2 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[708:[bind(A,$thf( skac2 ))]]) ).
thf(840,plain,
( ( nil != nil )
| ( sk1 @ strictorderedP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[835,646]) ).
thf(841,plain,
( ( sk1 @ strictorderedP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[840:[]]) ).
thf(40,axiom,
! [A: $i] :
( ( ( A @ skaf73 @ ( A @ skaf70 @ cons ) @ ( A @ skaf72 @ ( A @ skaf69 @ cons ) @ ( A @ skaf71 @ app ) @ app ) )
= A )
| ( A @ strictorderedP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause163) ).
thf(288,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)],[40]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause126) ).
thf(299,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)],[45]) ).
thf(300,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
inference(cnf,[status(esa)],[299]) ).
thf(301,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[300]) ).
thf(139,axiom,
~ ( nil @ singletonP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause11) ).
thf(516,plain,
~ ( nil @ singletonP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(517,plain,
~ ( nil @ singletonP ),
inference(polarity_switch,[status(thm)],[516]) ).
thf(30037,plain,
( ( nil != nil )
| ~ ( sk7 @ singletonP )
| ( sk7 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[18150,517]) ).
thf(30038,plain,
( ~ ( sk7 @ singletonP )
| ( sk7 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[30037:[]]) ).
thf(8,negated_conjecture,
sk6 @ ssItem,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
thf(222,plain,
sk6 @ ssItem,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(673,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[222,463]) ).
thf(674,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[673]) ).
thf(675,plain,
~ ( sk6 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[674:[bind(A,$thf( sk6 ))]]) ).
thf(4940,plain,
( ( nil != nil )
| ~ ( sk6 @ ( sk2 @ memberP ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[748,675]) ).
thf(4941,plain,
( ~ ( sk6 @ ( sk2 @ memberP ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[4940:[]]) ).
thf(828,plain,
( ( nil != nil )
| ( sk1 @ totalorderedP )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[788,659]) ).
thf(829,plain,
( ( sk1 @ totalorderedP )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[828:[]]) ).
thf(193,axiom,
! [A: $i] : ( A @ skaf78 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause17) ).
thf(638,plain,
! [A: $i] : ( A @ skaf78 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(19970,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[638,311]) ).
thf(19971,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[19970]) ).
thf(19972,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( A @ skaf78 @ neq ) ),
inference(pattern_uni,[status(thm)],[19971:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(20031,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( A @ skaf78 @ neq ) ),
inference(simp,[status(thm)],[19972]) ).
thf(62,axiom,
! [A: $i] : ( A @ skaf57 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause38) ).
thf(342,plain,
! [A: $i] : ( A @ skaf57 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(1090,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[342,261]) ).
thf(1091,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1090]) ).
thf(1092,plain,
! [A: $i] :
~ ( A @ skaf57 @ ( A @ skaf57 @ neq ) ),
inference(pattern_uni,[status(thm)],[1091:[bind(A,$thf( C )),bind(B,$thf( C @ skaf57 ))]]) ).
thf(1095,plain,
! [A: $i] :
~ ( A @ skaf57 @ ( A @ skaf57 @ neq ) ),
inference(simp,[status(thm)],[1092]) ).
thf(87,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause102) ).
thf(404,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(52,axiom,
! [B: $i,A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause118) ).
thf(318,plain,
! [B: $i,A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(319,plain,
! [B: $i,A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
inference(cnf,[status(esa)],[318]) ).
thf(320,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( nil = A )
| ( ( B @ ( A @ app ) )
!= nil ) ),
inference(lifteq,[status(thm)],[319]) ).
thf(160,axiom,
! [A: $i] : ( A @ skaf66 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause29) ).
thf(568,plain,
! [A: $i] : ( A @ skaf66 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(35970,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[568,363]) ).
thf(35971,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[35970]) ).
thf(35972,plain,
! [A: $i] :
( ( A @ skaf66 @ ( nil @ app ) )
= ( A @ skaf66 ) ),
inference(pattern_uni,[status(thm)],[35971:[bind(A,$thf( C )),bind(B,$thf( C @ skaf66 ))]]) ).
thf(36087,plain,
! [A: $i] :
( ( A @ skaf66 @ ( nil @ app ) )
= ( A @ skaf66 ) ),
inference(simp,[status(thm)],[35972]) ).
thf(198,axiom,
! [B: $i,A: $i] :
( ( nil = A )
| ( A = B )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( A @ hd )
!= ( B @ hd ) )
| ( ( A @ tl )
!= ( B @ tl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause177) ).
thf(651,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)],[198]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause106) ).
thf(256,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(257,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ lt ) ) ),
inference(cnf,[status(esa)],[256]) ).
thf(144,axiom,
! [A: $i] : ( A @ skaf81 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause14) ).
thf(528,plain,
! [A: $i] : ( A @ skaf81 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(20999,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[528,317]) ).
thf(21000,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[20999]) ).
thf(21001,plain,
! [A: $i] : ( nil @ ( A @ skaf81 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[21000:[bind(A,$thf( C )),bind(B,$thf( C @ skaf81 ))]]) ).
thf(21017,plain,
! [A: $i] : ( nil @ ( A @ skaf81 @ rearsegP ) ),
inference(simp,[status(thm)],[21001]) ).
thf(9066,plain,
( ( nil != nil )
| ( sk1 @ totalorderP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[827,500]) ).
thf(9067,plain,
( ( sk1 @ totalorderP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[9066:[]]) ).
thf(34,axiom,
! [A: $i] : ( A @ skaf72 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause23) ).
thf(277,plain,
! [A: $i] : ( A @ skaf72 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(36023,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[277,363]) ).
thf(36024,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[36023]) ).
thf(36025,plain,
! [A: $i] :
( ( A @ skaf72 @ ( nil @ app ) )
= ( A @ skaf72 ) ),
inference(pattern_uni,[status(thm)],[36024:[bind(A,$thf( C )),bind(B,$thf( C @ skaf72 ))]]) ).
thf(36097,plain,
! [A: $i] :
( ( A @ skaf72 @ ( nil @ app ) )
= ( A @ skaf72 ) ),
inference(simp,[status(thm)],[36025]) ).
thf(11912,plain,
( ( nil != nil )
| ( nil @ ( sk2 @ segmentP ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,11905]) ).
thf(11913,plain,
( ( nil @ ( sk2 @ segmentP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[11912:[]]) ).
thf(75,axiom,
! [A: $i] : ( A @ skaf58 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause37) ).
thf(372,plain,
! [A: $i] : ( A @ skaf58 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(19994,plain,
! [A: $i] :
( ( ( sk9 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( A @ neq ) )
| ( nil = sk2 ) ),
inference(paramod_ordered,[status(thm)],[733,311]) ).
thf(19995,plain,
! [A: $i] :
( ( ( sk9 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ( nil = sk2 ) ),
inference(simp,[status(thm)],[19994]) ).
thf(19996,plain,
( ~ ( sk9 @ ( sk9 @ neq ) )
| ( nil = sk2 ) ),
inference(pattern_uni,[status(thm)],[19995:[bind(A,$thf( sk9 ))]]) ).
thf(33831,plain,
( ( nil != nil )
| ~ ( sk2 @ singletonP )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[19996,517]) ).
thf(33832,plain,
( ~ ( sk2 @ singletonP )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[33831:[]]) ).
thf(184,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( D @ ( C @ cons ) @ ( B @ ( A @ cons ) @ frontsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause176) ).
thf(619,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)],[184]) ).
thf(701,plain,
( ( nil != nil )
| ( sk2 @ duplicatefreeP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[676,360]) ).
thf(702,plain,
( ( sk2 @ duplicatefreeP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[701:[]]) ).
thf(181,axiom,
! [A: $i] : ( A @ skaf56 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause39) ).
thf(615,plain,
! [A: $i] : ( A @ skaf56 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(20922,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[615,317]) ).
thf(20923,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[20922]) ).
thf(20924,plain,
! [A: $i] : ( nil @ ( A @ skaf56 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[20923:[bind(A,$thf( C )),bind(B,$thf( C @ skaf56 ))]]) ).
thf(21043,plain,
! [A: $i] : ( nil @ ( A @ skaf56 @ rearsegP ) ),
inference(simp,[status(thm)],[20924]) ).
thf(2275,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[618,2251]) ).
thf(2276,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[2275]) ).
thf(2277,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[2276:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(2339,plain,
! [A: $i] : ( nil @ ( A @ skaf50 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[2277]) ).
thf(68,axiom,
! [A: $i] :
( ( ( A @ skaf58 @ ( A @ skaf55 @ cons ) @ ( A @ skaf57 @ ( A @ skaf54 @ cons ) @ ( A @ skaf56 @ app ) @ app ) )
= A )
| ( A @ totalorderP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause166) ).
thf(355,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)],[68]) ).
thf(356,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)],[355]) ).
thf(357,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)],[356]) ).
thf(334,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
inference(cnf,[status(esa)],[333]) ).
thf(335,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[334]) ).
thf(26487,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( nil @ rearsegP ) )
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[207,335]) ).
thf(26488,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ rearsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[26487]) ).
thf(26489,plain,
( ~ ( sk8 @ ( nil @ rearsegP ) )
| ( nil = sk8 ) ),
inference(pattern_uni,[status(thm)],[26488:[bind(A,$thf( sk8 ))]]) ).
thf(35885,plain,
! [A: $i] :
( ( ( sk7 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[212,363]) ).
thf(35886,plain,
! [A: $i] :
( ( ( sk7 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[35885]) ).
thf(35887,plain,
( ( sk7 @ ( nil @ app ) )
= sk7 ),
inference(pattern_uni,[status(thm)],[35886:[bind(A,$thf( sk7 ))]]) ).
thf(11910,plain,
( ( nil != nil )
| ( sk1 @ ( nil @ segmentP ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[788,11905]) ).
thf(11911,plain,
( ( sk1 @ ( nil @ segmentP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[11910:[]]) ).
thf(95,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause130) ).
thf(421,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)],[95]) ).
thf(19985,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[420,311]) ).
thf(19986,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[19985]) ).
thf(19987,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( A @ skaf55 @ neq ) ),
inference(pattern_uni,[status(thm)],[19986:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(20038,plain,
! [A: $i] :
~ ( A @ skaf55 @ ( A @ skaf55 @ neq ) ),
inference(simp,[status(thm)],[19987]) ).
thf(92,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause98) ).
thf(416,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(55,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ssList )
| ~ ( F @ cyclefreeP )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) )
!= F )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause185) ).
thf(325,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)],[55]) ).
thf(4966,plain,
( ( nil != nil )
| ~ ( sk2 @ singletonP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[748,517]) ).
thf(4967,plain,
( ~ ( sk2 @ singletonP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[4966:[]]) ).
thf(20979,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[207,317]) ).
thf(20980,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[20979]) ).
thf(20981,plain,
nil @ ( sk8 @ rearsegP ),
inference(pattern_uni,[status(thm)],[20980:[bind(A,$thf( sk8 ))]]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ frontsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause154) ).
thf(284,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)],[38]) ).
thf(769,plain,
( ( nil != nil )
| ( sk2 @ totalorderedP )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,659]) ).
thf(770,plain,
( ( sk2 @ totalorderedP )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[769:[]]) ).
thf(35822,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf47 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ( ( C @ ( nil @ app ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[511,363]) ).
thf(35823,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf47 ) @ ssList )
!= ( C @ ssList ) )
| ( ( C @ ( nil @ app ) )
= C ) ),
inference(simp,[status(thm)],[35822]) ).
thf(35824,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ skaf47 ) @ ( nil @ app ) )
= ( B @ ( A @ skaf47 ) ) ),
inference(pattern_uni,[status(thm)],[35823:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf47 ) ))]]) ).
thf(36129,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ skaf47 ) @ ( nil @ app ) )
= ( B @ ( A @ skaf47 ) ) ),
inference(simp,[status(thm)],[35824]) ).
thf(43,axiom,
! [A: $i] : ( A @ skaf64 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause31) ).
thf(296,plain,
! [A: $i] : ( A @ skaf64 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(19991,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[296,311]) ).
thf(19992,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[19991]) ).
thf(19993,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( A @ skaf64 @ neq ) ),
inference(pattern_uni,[status(thm)],[19992:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(20042,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( A @ skaf64 @ neq ) ),
inference(simp,[status(thm)],[19993]) ).
thf(1445,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[499,261]) ).
thf(1446,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1445]) ).
thf(1447,plain,
! [A: $i] :
~ ( A @ skaf68 @ ( A @ skaf68 @ neq ) ),
inference(pattern_uni,[status(thm)],[1446:[bind(A,$thf( C )),bind(B,$thf( C @ skaf68 ))]]) ).
thf(1450,plain,
! [A: $i] :
~ ( A @ skaf68 @ ( A @ skaf68 @ neq ) ),
inference(simp,[status(thm)],[1447]) ).
thf(105,axiom,
! [A: $i] :
( ( A @ skaf49 @ ( A @ skaf50 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause87) ).
thf(443,plain,
! [A: $i] :
( ( A @ skaf49 @ ( A @ skaf50 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(53,axiom,
! [A: $i] :
( ( ( A @ skaf63 @ ( A @ skaf60 @ cons ) @ ( A @ skaf62 @ ( A @ skaf59 @ cons ) @ ( A @ skaf61 @ app ) @ app ) )
= A )
| ( A @ strictorderP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause165) ).
thf(321,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)],[53]) ).
thf(64546,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[638,398]) ).
thf(64547,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[64546]) ).
thf(64548,plain,
! [A: $i] : ( A @ skaf78 @ ( A @ skaf78 @ geq ) ),
inference(pattern_uni,[status(thm)],[64547:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(64627,plain,
! [A: $i] : ( A @ skaf78 @ ( A @ skaf78 @ geq ) ),
inference(simp,[status(thm)],[64548]) ).
thf(186,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ skaf43 ) @ ( B @ cons ) @ ( B @ ( A @ skaf42 ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ memberP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause169) ).
thf(623,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)],[186]) ).
thf(125,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ssList )
| ~ ( E @ duplicatefreeP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ( ( D @ ( B @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause179) ).
thf(485,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ssList )
| ~ ( E @ duplicatefreeP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( D @ ssList )
| ( ( D @ ( B @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(805,plain,
( ( nil != nil )
| ~ ( sk5 @ ( sk1 @ memberP ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[788,672]) ).
thf(806,plain,
( ~ ( sk5 @ ( sk1 @ memberP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[805:[]]) ).
thf(90,axiom,
! [A: $i] : ( A @ skaf73 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause22) ).
thf(412,plain,
! [A: $i] : ( A @ skaf73 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(1178,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[412,261]) ).
thf(1179,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1178]) ).
thf(1180,plain,
! [A: $i] :
~ ( A @ skaf73 @ ( A @ skaf73 @ neq ) ),
inference(pattern_uni,[status(thm)],[1179:[bind(A,$thf( C )),bind(B,$thf( C @ skaf73 ))]]) ).
thf(1183,plain,
! [A: $i] :
~ ( A @ skaf73 @ ( A @ skaf73 @ neq ) ),
inference(simp,[status(thm)],[1180]) ).
thf(63,axiom,
nil @ equalelemsP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause1) ).
thf(343,plain,
nil @ equalelemsP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(755,plain,
( ( nil != nil )
| ( sk2 @ equalelemsP )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,343]) ).
thf(756,plain,
( ( sk2 @ equalelemsP )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[755:[]]) ).
thf(195,axiom,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause83) ).
thf(642,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(643,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(cnf,[status(esa)],[642]) ).
thf(644,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[643]) ).
thf(645,plain,
( ( nil @ ( nil @ frontsegP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[644]) ).
thf(13131,plain,
( ( nil @ ( nil @ frontsegP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[645,312]) ).
thf(13132,plain,
nil @ ( nil @ frontsegP ),
inference(simp,[status(thm)],[13131]) ).
thf(13137,plain,
( ( nil != nil )
| ( sk1 @ ( nil @ frontsegP ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[788,13132]) ).
thf(13138,plain,
( ( sk1 @ ( nil @ frontsegP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[13137:[]]) ).
thf(30143,plain,
( ( nil != nil )
| ( sk7 @ totalorderedP )
| ( sk7 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[18150,659]) ).
thf(30144,plain,
( ( sk7 @ totalorderedP )
| ( sk7 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[30143:[]]) ).
thf(20894,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf47 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[511,317]) ).
thf(20895,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf47 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[20894]) ).
thf(20896,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf47 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[20895:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf47 ) ))]]) ).
thf(21029,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf47 ) @ rearsegP ) ),
inference(simp,[status(thm)],[20896]) ).
thf(20885,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf42 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[629,317]) ).
thf(20886,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf42 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[20885]) ).
thf(20887,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf42 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[20886:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf42 ) ))]]) ).
thf(21024,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf42 ) @ rearsegP ) ),
inference(simp,[status(thm)],[20887]) ).
thf(876,plain,
( ( nil != nil )
| ( sk1 @ cyclefreeP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[835,505]) ).
thf(877,plain,
( ( sk1 @ cyclefreeP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[876:[]]) ).
thf(25056,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( sk1 @ cyclefreeP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[877,9184]) ).
thf(25057,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[25056]) ).
thf(25132,plain,
( ( sk9 != sk9 )
| ( nil != sk2 )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[25057]) ).
thf(25153,plain,
( ( nil != sk2 )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[25132]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ rearsegP ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
!= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause143) ).
thf(348,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)],[65]) ).
thf(2252,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[217,2251]) ).
thf(2253,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[2252]) ).
thf(2254,plain,
nil @ ( sk5 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[2253:[bind(A,$thf( sk5 ))]]) ).
thf(177,axiom,
! [A: $i] : ( A @ skaf54 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause41) ).
thf(607,plain,
! [A: $i] : ( A @ skaf54 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(2322,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[607,2251]) ).
thf(2323,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[2322]) ).
thf(2324,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[2323:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(2335,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[2324]) ).
thf(765,plain,
( ( nil != nil )
| ( sk2 @ strictorderedP )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,646]) ).
thf(766,plain,
( ( sk2 @ strictorderedP )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[765:[]]) ).
thf(35927,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[477,363]) ).
thf(35928,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[35927]) ).
thf(35929,plain,
! [A: $i] :
( ( A @ skaf75 @ ( nil @ app ) )
= ( A @ skaf75 ) ),
inference(pattern_uni,[status(thm)],[35928:[bind(A,$thf( C )),bind(B,$thf( C @ skaf75 ))]]) ).
thf(36078,plain,
! [A: $i] :
( ( A @ skaf75 @ ( nil @ app ) )
= ( A @ skaf75 ) ),
inference(simp,[status(thm)],[35929]) ).
thf(26510,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( nil @ rearsegP ) )
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[214,335]) ).
thf(26511,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ rearsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[26510]) ).
thf(26512,plain,
( ~ ( sk2 @ ( nil @ rearsegP ) )
| ( nil = sk2 ) ),
inference(pattern_uni,[status(thm)],[26511:[bind(A,$thf( sk2 ))]]) ).
thf(862,plain,
( ( nil != nil )
| ~ ( sk1 @ singletonP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[835,517]) ).
thf(863,plain,
( ~ ( sk1 @ singletonP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[862:[]]) ).
thf(9222,plain,
( ( nil != nil )
| ~ ( sk1 @ singletonP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[827,517]) ).
thf(9223,plain,
( ~ ( sk1 @ singletonP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[9222:[]]) ).
thf(10304,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ~ ( sk1 @ singletonP )
| ~ $true
| ~ ( sk1 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[863,9223]) ).
thf(10305,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ~ ( sk1 @ singletonP ) ),
inference(simp,[status(thm)],[10304]) ).
thf(10329,plain,
( ( sk9 != sk9 )
| ( nil != sk2 )
| ~ ( sk1 @ singletonP ) ),
inference(simp,[status(thm)],[10305]) ).
thf(10376,plain,
( ( nil != sk2 )
| ~ ( sk1 @ singletonP ) ),
inference(simp,[status(thm)],[10329]) ).
thf(59033,plain,
( ( nil != nil )
| ( sk2 != sk2 )
| ~ ( sk1 @ singletonP )
| ~ ( sk2 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[26512,10376]) ).
thf(59034,plain,
( ( nil != nil )
| ~ ( sk1 @ singletonP )
| ~ ( sk2 @ ( nil @ rearsegP ) ) ),
inference(simp,[status(thm)],[59033]) ).
thf(59035,plain,
( ~ ( sk1 @ singletonP )
| ~ ( sk2 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[59034:[]]) ).
thf(11,negated_conjecture,
( ( sk8 @ ( nil @ ( sk6 @ cons ) @ ( nil @ ( sk5 @ cons ) @ ( sk7 @ app ) @ app ) @ app ) )
= sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
thf(221,plain,
( ( sk8 @ ( nil @ ( sk6 @ cons ) @ ( nil @ ( sk5 @ cons ) @ ( sk7 @ app ) @ app ) @ app ) )
= sk1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(111,axiom,
! [A: $i] :
( ( nil @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause56) ).
thf(453,plain,
! [A: $i] :
( ( nil @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(715,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[312,261]) ).
thf(716,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[715]) ).
thf(717,plain,
~ ( nil @ ( nil @ neq ) ),
inference(pattern_uni,[status(thm)],[716:[bind(A,$thf( nil ))]]) ).
thf(773,plain,
( ( nil != nil )
| ~ ( nil @ ( sk2 @ neq ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,717]) ).
thf(774,plain,
( ~ ( nil @ ( sk2 @ neq ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[773:[]]) ).
thf(83,axiom,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf54 @ ( A @ skaf55 @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause94) ).
thf(395,plain,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf54 @ ( A @ skaf55 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(396,plain,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf54 @ ( A @ skaf55 @ leq ) ) ),
inference(cnf,[status(esa)],[395]) ).
thf(202,axiom,
! [A: $i] : ( A @ skaf59 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause36) ).
thf(660,plain,
! [A: $i] : ( A @ skaf59 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ geq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause148) ).
thf(410,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)],[89]) ).
thf(411,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)],[410]) ).
thf(29864,plain,
( ( nil != nil )
| ( sk7 @ duplicatefreeP )
| ( sk7 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[18150,360]) ).
thf(29865,plain,
( ( sk7 @ duplicatefreeP )
| ( sk7 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[29864:[]]) ).
thf(99,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
!= ( B @ ( C @ app ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause151) ).
thf(428,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)],[99]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ memberP ) )
| ( C @ ( B @ memberP ) )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ( B @ ( A @ app ) @ memberP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause158) ).
thf(265,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)],[29]) ).
thf(4954,plain,
( ( nil != nil )
| ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[748,717]) ).
thf(4955,plain,
( ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[4954:[]]) ).
thf(9270,plain,
( ( nil != nil )
| ~ ( sk2 @ ( sk1 @ neq ) )
| ~ ( sk9 @ ( nil @ memberP ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[827,4955]) ).
thf(9271,plain,
( ( nil != nil )
| ~ ( sk2 @ ( sk1 @ neq ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[9270]) ).
thf(9272,plain,
( ~ ( sk2 @ ( sk1 @ neq ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[9271:[]]) ).
thf(1890,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[568,261]) ).
thf(1891,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1890]) ).
thf(1892,plain,
! [A: $i] :
~ ( A @ skaf66 @ ( A @ skaf66 @ neq ) ),
inference(pattern_uni,[status(thm)],[1891:[bind(A,$thf( C )),bind(B,$thf( C @ skaf66 ))]]) ).
thf(1896,plain,
! [A: $i] :
~ ( A @ skaf66 @ ( A @ skaf66 @ neq ) ),
inference(simp,[status(thm)],[1892]) ).
thf(1880,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf43 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ~ ( C @ ( C @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[249,261]) ).
thf(1881,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf43 ) @ ssList )
!= ( C @ ssList ) )
| ~ ( C @ ( C @ neq ) ) ),
inference(simp,[status(thm)],[1880]) ).
thf(1882,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf43 ) @ ( B @ ( A @ skaf43 ) @ neq ) ),
inference(pattern_uni,[status(thm)],[1881:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf43 ) ))]]) ).
thf(1886,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf43 ) @ ( B @ ( A @ skaf43 ) @ neq ) ),
inference(simp,[status(thm)],[1882]) ).
thf(35979,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[207,363]) ).
thf(35980,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[35979]) ).
thf(35981,plain,
( ( sk8 @ ( nil @ app ) )
= sk8 ),
inference(pattern_uni,[status(thm)],[35980:[bind(A,$thf( sk8 ))]]) ).
thf(4842,plain,
( ( nil != nil )
| ~ ( skac2 @ ( sk2 @ memberP ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[748,709]) ).
thf(4843,plain,
( ~ ( skac2 @ ( sk2 @ memberP ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[4842:[]]) ).
thf(5951,plain,
( ~ $true
| ( ( sk9 @ ( nil @ memberP ) )
!= ( skac2 @ ( sk2 @ memberP ) ) )
| ~ ( skac2 @ ( sk2 @ memberP ) ) ),
inference(eqfactor_ordered,[status(thm)],[4843]) ).
thf(5970,plain,
( ( skac2 != sk9 )
| ( nil != sk2 )
| ~ ( skac2 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[5951]) ).
thf(47,axiom,
! [A: $i] :
( ( ( A @ skaf68 @ ( A @ skaf65 @ cons ) @ ( A @ skaf67 @ ( A @ skaf64 @ cons ) @ ( A @ skaf66 @ app ) @ app ) )
= A )
| ( A @ totalorderedP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause164) ).
thf(305,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)],[47]) ).
thf(306,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)],[305]) ).
thf(307,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)],[306]) ).
thf(203,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ strictorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause124) ).
thf(661,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)],[203]) ).
thf(18761,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[214,304]) ).
thf(18762,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[18761]) ).
thf(18763,plain,
( ( sk2 @ tl @ ssList )
| ( nil = sk2 ) ),
inference(pattern_uni,[status(thm)],[18762:[bind(A,$thf( sk2 ))]]) ).
thf(31336,plain,
( ( nil != nil )
| ( sk2 != sk2 )
| ( sk2 @ totalorderedP )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[18763,19462]) ).
thf(31337,plain,
( ( nil != nil )
| ( sk2 @ totalorderedP )
| ( sk2 @ tl @ ssList ) ),
inference(simp,[status(thm)],[31336]) ).
thf(31338,plain,
( ( sk2 @ totalorderedP )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[31337:[]]) ).
thf(809,plain,
( ( nil != nil )
| ~ ( sk1 @ singletonP )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[788,517]) ).
thf(810,plain,
( ~ ( sk1 @ singletonP )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[809:[]]) ).
thf(35850,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[312,363]) ).
thf(35851,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[35850]) ).
thf(35852,plain,
( ( nil @ ( nil @ app ) )
= nil ),
inference(pattern_uni,[status(thm)],[35851:[bind(A,$thf( nil ))]]) ).
thf(21,axiom,
skac3 != skac2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause54) ).
thf(246,plain,
skac3 != skac2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(247,plain,
skac3 != skac2,
inference(polarity_switch,[status(thm)],[246]) ).
thf(248,plain,
skac2 != skac3,
inference(lifteq,[status(thm)],[247]) ).
thf(35816,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[628,363]) ).
thf(35817,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[35816]) ).
thf(35818,plain,
! [A: $i] :
( ( A @ skaf76 @ ( nil @ app ) )
= ( A @ skaf76 ) ),
inference(pattern_uni,[status(thm)],[35817:[bind(A,$thf( C )),bind(B,$thf( C @ skaf76 ))]]) ).
thf(36127,plain,
! [A: $i] :
( ( A @ skaf76 @ ( nil @ app ) )
= ( A @ skaf76 ) ),
inference(simp,[status(thm)],[35818]) ).
thf(138,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ lt ) )
| ( D @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( F @ strictorderP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause183) ).
thf(512,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ lt ) )
| ( D @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( F @ strictorderP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(67,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf45 ) @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause51) ).
thf(354,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf45 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(5761,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ~ ( C @ ( C @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[354,261]) ).
thf(5762,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ssList )
!= ( C @ ssList ) )
| ~ ( C @ ( C @ neq ) ) ),
inference(simp,[status(thm)],[5761]) ).
thf(5763,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf45 ) @ ( B @ ( A @ skaf45 ) @ neq ) ),
inference(pattern_uni,[status(thm)],[5762:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf45 ) ))]]) ).
thf(5783,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf45 ) @ ( B @ ( A @ skaf45 ) @ neq ) ),
inference(simp,[status(thm)],[5763]) ).
thf(49734,plain,
( ( nil != nil )
| ~ ( sk8 @ singletonP )
| ~ ( sk8 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[26489,517]) ).
thf(49735,plain,
( ~ ( sk8 @ singletonP )
| ~ ( sk8 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[49734:[]]) ).
thf(61352,plain,
( ( ( sk8 @ ( nil @ rearsegP ) )
!= ( nil @ ( sk8 @ rearsegP ) ) )
| ~ ( sk8 @ singletonP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20981,49735]) ).
thf(61353,plain,
( ( ( sk8 @ ( nil @ rearsegP ) )
!= ( nil @ ( sk8 @ rearsegP ) ) )
| ~ ( sk8 @ singletonP ) ),
inference(simp,[status(thm)],[61352]) ).
thf(61499,plain,
( ( nil != sk8 )
| ( nil != sk8 )
| ~ ( sk8 @ singletonP ) ),
inference(simp,[status(thm)],[61353]) ).
thf(61551,plain,
( ( nil != sk8 )
| ~ ( sk8 @ singletonP ) ),
inference(simp,[status(thm)],[61499]) ).
thf(270,plain,
! [A: $i] :
( ( A @ skaf50 @ ( A @ skaf49 @ leq ) )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[269]) ).
thf(145,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ segmentP ) )
| ~ ( D @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ( ( C @ ( B @ ( A @ app ) @ app ) )
!= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause173) ).
thf(529,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)],[145]) ).
thf(150,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ frontsegP ) )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause144) ).
thf(546,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)],[150]) ).
thf(13147,plain,
( ( nil != nil )
| ( sk2 @ ( nil @ frontsegP ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,13132]) ).
thf(13148,plain,
( ( sk2 @ ( nil @ frontsegP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[13147:[]]) ).
thf(9208,plain,
( ( nil != nil )
| ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[827,717]) ).
thf(9209,plain,
( ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[9208:[]]) ).
thf(13135,plain,
( ( nil != nil )
| ( nil @ ( sk1 @ frontsegP ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[788,13132]) ).
thf(13136,plain,
( ( nil @ ( sk1 @ frontsegP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[13135:[]]) ).
thf(22643,plain,
( ( nil != nil )
| ( sk1 @ ( sk1 @ frontsegP ) )
| ( sk9 @ ssItem )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[788,13136]) ).
thf(22644,plain,
( ( nil != nil )
| ( sk1 @ ( sk1 @ frontsegP ) )
| ( sk9 @ ssItem ) ),
inference(simp,[status(thm)],[22643]) ).
thf(22645,plain,
( ( sk1 @ ( sk1 @ frontsegP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[22644:[]]) ).
thf(9125,plain,
( ( nil != nil )
| ( sk1 @ duplicatefreeP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[827,360]) ).
thf(9126,plain,
( ( sk1 @ duplicatefreeP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[9125:[]]) ).
thf(22728,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( sk1 @ duplicatefreeP )
| ~ $true
| ( sk1 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[873,9126]) ).
thf(22729,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[22728]) ).
thf(22821,plain,
( ( sk9 != sk9 )
| ( nil != sk2 )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[22729]) ).
thf(22842,plain,
( ( nil != sk2 )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[22821]) ).
thf(73,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ hd )
= A )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause97) ).
thf(366,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ hd )
= A )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(64534,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[217,398]) ).
thf(64535,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) ) ),
inference(simp,[status(thm)],[64534]) ).
thf(64536,plain,
sk5 @ ( sk5 @ geq ),
inference(pattern_uni,[status(thm)],[64535:[bind(A,$thf( sk5 ))]]) ).
thf(155,axiom,
! [A: $i] : ( A @ skaf51 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause44) ).
thf(560,plain,
! [A: $i] : ( A @ skaf51 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(36029,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[560,363]) ).
thf(36030,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[36029]) ).
thf(36031,plain,
! [A: $i] :
( ( A @ skaf51 @ ( nil @ app ) )
= ( A @ skaf51 ) ),
inference(pattern_uni,[status(thm)],[36030:[bind(A,$thf( C )),bind(B,$thf( C @ skaf51 ))]]) ).
thf(36099,plain,
! [A: $i] :
( ( A @ skaf51 @ ( nil @ app ) )
= ( A @ skaf51 ) ),
inference(simp,[status(thm)],[36031]) ).
thf(1212,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[424,463]) ).
thf(1213,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1212]) ).
thf(1214,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1213:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(1217,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1214]) ).
thf(819,plain,
( ( nil != nil )
| ~ ( nil @ ( sk1 @ neq ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[788,717]) ).
thf(820,plain,
( ~ ( nil @ ( sk1 @ neq ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[819:[]]) ).
thf(156,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause68) ).
thf(561,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(64564,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[420,398]) ).
thf(64565,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[64564]) ).
thf(64566,plain,
! [A: $i] : ( A @ skaf55 @ ( A @ skaf55 @ geq ) ),
inference(pattern_uni,[status(thm)],[64565:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(64632,plain,
! [A: $i] : ( A @ skaf55 @ ( A @ skaf55 @ geq ) ),
inference(simp,[status(thm)],[64566]) ).
thf(20958,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[342,317]) ).
thf(20959,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[20958]) ).
thf(20960,plain,
! [A: $i] : ( nil @ ( A @ skaf57 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[20959:[bind(A,$thf( C )),bind(B,$thf( C @ skaf57 ))]]) ).
thf(21030,plain,
! [A: $i] : ( nil @ ( A @ skaf57 @ rearsegP ) ),
inference(simp,[status(thm)],[20960]) ).
thf(33807,plain,
( ( nil != nil )
| ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[19996,717]) ).
thf(33808,plain,
( ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[33807:[]]) ).
thf(35831,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf48 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ( ( C @ ( nil @ app ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[449,363]) ).
thf(35832,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf48 ) @ ssList )
!= ( C @ ssList ) )
| ( ( C @ ( nil @ app ) )
= C ) ),
inference(simp,[status(thm)],[35831]) ).
thf(35833,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ skaf48 ) @ ( nil @ app ) )
= ( B @ ( A @ skaf48 ) ) ),
inference(pattern_uni,[status(thm)],[35832:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf48 ) ))]]) ).
thf(36131,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ skaf48 ) @ ( nil @ app ) )
= ( B @ ( A @ skaf48 ) ) ),
inference(simp,[status(thm)],[35833]) ).
thf(78,axiom,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause81) ).
thf(378,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(379,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(cnf,[status(esa)],[378]) ).
thf(380,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[379]) ).
thf(381,plain,
( ( nil @ ( nil @ rearsegP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[380]) ).
thf(11866,plain,
( ( nil @ ( nil @ rearsegP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[381,312]) ).
thf(11867,plain,
nil @ ( nil @ rearsegP ),
inference(simp,[status(thm)],[11866]) ).
thf(11872,plain,
( ( nil != nil )
| ( sk1 @ ( nil @ rearsegP ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[788,11867]) ).
thf(11873,plain,
( ( sk1 @ ( nil @ rearsegP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[11872:[]]) ).
thf(17572,plain,
( ( nil != nil )
| ( sk1 @ ( sk2 @ rearsegP ) )
| ( sk9 @ ssItem )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,11873]) ).
thf(17573,plain,
( ( nil != nil )
| ( sk1 @ ( sk2 @ rearsegP ) )
| ( sk9 @ ssItem ) ),
inference(simp,[status(thm)],[17572]) ).
thf(17574,plain,
( ( sk1 @ ( sk2 @ rearsegP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[17573:[]]) ).
thf(9206,plain,
( ( nil != nil )
| ~ ( nil @ ( sk1 @ neq ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[827,717]) ).
thf(9207,plain,
( ~ ( nil @ ( sk1 @ neq ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[9206:[]]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause155) ).
thf(297,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)],[44]) ).
thf(88,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause119) ).
thf(407,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(30566,plain,
( ( nil != nil )
| ~ ( sk8 @ singletonP )
| ( sk8 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[18740,517]) ).
thf(30567,plain,
( ~ ( sk8 @ singletonP )
| ( sk8 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[30566:[]]) ).
thf(190,axiom,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ frontsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause84) ).
thf(630,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(2312,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[386,2251]) ).
thf(2313,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[2312]) ).
thf(2314,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[2313:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(2332,plain,
! [A: $i] : ( nil @ ( A @ skaf44 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[2314]) ).
thf(25726,plain,
! [A: $i] :
( ( ( sk7 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( nil @ rearsegP ) )
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[212,335]) ).
thf(25727,plain,
! [A: $i] :
( ( ( sk7 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ rearsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[25726]) ).
thf(25728,plain,
( ~ ( sk7 @ ( nil @ rearsegP ) )
| ( nil = sk7 ) ),
inference(pattern_uni,[status(thm)],[25727:[bind(A,$thf( sk7 ))]]) ).
thf(21094,plain,
( ( nil != nil )
| ( sk2 @ ( sk8 @ rearsegP ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,20981]) ).
thf(21095,plain,
( ( sk2 @ ( sk8 @ rearsegP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[21094:[]]) ).
thf(100,axiom,
! [A: $i] : ( A @ skaf60 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause35) ).
thf(431,plain,
! [A: $i] : ( A @ skaf60 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(1291,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[431,463]) ).
thf(1292,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1291]) ).
thf(1293,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1292:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(1296,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1293]) ).
thf(114,axiom,
! [A: $i] : ( A @ skaf80 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause15) ).
thf(461,plain,
! [A: $i] : ( A @ skaf80 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(128,axiom,
! [A: $i] :
( ( nil = A )
| ( ( A @ tl @ ( A @ hd @ cons ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause104) ).
thf(493,plain,
! [A: $i] :
( ( nil = A )
| ( ( A @ tl @ ( A @ hd @ cons ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(60,axiom,
! [B: $i,A: $i] :
( ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause72) ).
thf(338,plain,
! [B: $i,A: $i] :
( ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(339,plain,
! [B: $i,A: $i] :
( ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[338]) ).
thf(28034,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[210,339]) ).
thf(28035,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP ) ),
inference(simp,[status(thm)],[28034]) ).
thf(28036,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk1 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[28035:[bind(A,$thf( sk1 ))]]) ).
thf(28063,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk1 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[28036]) ).
thf(1190,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[419,463]) ).
thf(1191,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1190]) ).
thf(1192,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1191:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(1195,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1192]) ).
thf(64594,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[608,398]) ).
thf(64595,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[64594]) ).
thf(64596,plain,
! [A: $i] : ( A @ skaf65 @ ( A @ skaf65 @ geq ) ),
inference(pattern_uni,[status(thm)],[64595:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(64622,plain,
! [A: $i] : ( A @ skaf65 @ ( A @ skaf65 @ geq ) ),
inference(simp,[status(thm)],[64596]) ).
thf(174,axiom,
! [A: $i] : ( A @ skaf74 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause21) ).
thf(603,plain,
! [A: $i] : ( A @ skaf74 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(32606,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[603,353]) ).
thf(32607,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[32606]) ).
thf(32608,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[32607:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(32647,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[32608]) ).
thf(1364,plain,
( ( sk2 != sk2 )
| ~ ( sk2 @ ( sk1 @ neq ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[799,729]) ).
thf(1365,plain,
( ~ ( sk2 @ ( sk1 @ neq ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[1364:[]]) ).
thf(35976,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[510,363]) ).
thf(35977,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[35976]) ).
thf(35978,plain,
! [A: $i] :
( ( A @ skaf52 @ ( nil @ app ) )
= ( A @ skaf52 ) ),
inference(pattern_uni,[status(thm)],[35977:[bind(A,$thf( C )),bind(B,$thf( C @ skaf52 ))]]) ).
thf(36088,plain,
! [A: $i] :
( ( A @ skaf52 @ ( nil @ app ) )
= ( A @ skaf52 ) ),
inference(simp,[status(thm)],[35978]) ).
thf(9189,plain,
( ( nil != nil )
| ~ ( sk6 @ ( sk1 @ memberP ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[827,675]) ).
thf(9190,plain,
( ~ ( sk6 @ ( sk1 @ memberP ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[9189:[]]) ).
thf(166,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ tl )
= B )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause96) ).
thf(583,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ tl )
= B )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(141,axiom,
! [A: $i] : ( A @ skaf67 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause28) ).
thf(522,plain,
! [A: $i] : ( A @ skaf67 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(1830,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[560,261]) ).
thf(1831,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1830]) ).
thf(1832,plain,
! [A: $i] :
~ ( A @ skaf51 @ ( A @ skaf51 @ neq ) ),
inference(pattern_uni,[status(thm)],[1831:[bind(A,$thf( C )),bind(B,$thf( C @ skaf51 ))]]) ).
thf(1836,plain,
! [A: $i] :
~ ( A @ skaf51 @ ( A @ skaf51 @ neq ) ),
inference(simp,[status(thm)],[1832]) ).
thf(9131,plain,
( ( nil != nil )
| ( sk1 @ equalelemsP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[827,343]) ).
thf(9132,plain,
( ( sk1 @ equalelemsP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[9131:[]]) ).
thf(2298,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[608,2251]) ).
thf(2299,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[2298]) ).
thf(2300,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[2299:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(2344,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[2300]) ).
thf(152,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ leq ) )
| ~ ( F @ ssList )
| ~ ( F @ totalorderedP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause182) ).
thf(551,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)],[152]) ).
thf(285,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)],[284]) ).
thf(4,negated_conjecture,
sk4 @ ssList,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).
thf(224,plain,
sk4 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11870,plain,
( ( nil != nil )
| ( nil @ ( sk1 @ rearsegP ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[788,11867]) ).
thf(11871,plain,
( ( nil @ ( sk1 @ rearsegP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[11870:[]]) ).
thf(14378,plain,
( ( nil != nil )
| ( sk1 @ ( sk1 @ rearsegP ) )
| ( sk9 @ ssItem )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[788,11871]) ).
thf(14379,plain,
( ( nil != nil )
| ( sk1 @ ( sk1 @ rearsegP ) )
| ( sk9 @ ssItem ) ),
inference(simp,[status(thm)],[14378]) ).
thf(14380,plain,
( ( sk1 @ ( sk1 @ rearsegP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[14379:[]]) ).
thf(86,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ app ) @ rearsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause136) ).
thf(402,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)],[86]) ).
thf(403,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)],[402]) ).
thf(19973,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[660,311]) ).
thf(19974,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[19973]) ).
thf(19975,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( A @ skaf59 @ neq ) ),
inference(pattern_uni,[status(thm)],[19974:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(20032,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( A @ skaf59 @ neq ) ),
inference(simp,[status(thm)],[19975]) ).
thf(5791,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf48 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ~ ( C @ ( C @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[449,261]) ).
thf(5792,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf48 ) @ ssList )
!= ( C @ ssList ) )
| ~ ( C @ ( C @ neq ) ) ),
inference(simp,[status(thm)],[5791]) ).
thf(5793,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf48 ) @ ( B @ ( A @ skaf48 ) @ neq ) ),
inference(pattern_uni,[status(thm)],[5792:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf48 ) ))]]) ).
thf(5811,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf48 ) @ ( B @ ( A @ skaf48 ) @ neq ) ),
inference(simp,[status(thm)],[5793]) ).
thf(32578,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[563,353]) ).
thf(32579,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[32578]) ).
thf(32580,plain,
nil @ ( skac3 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[32579:[bind(A,$thf( skac3 ))]]) ).
thf(11876,plain,
( ( nil != nil )
| ( sk2 @ ( nil @ rearsegP ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,11867]) ).
thf(11877,plain,
( ( sk2 @ ( nil @ rearsegP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[11876:[]]) ).
thf(32536,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[296,353]) ).
thf(32537,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[32536]) ).
thf(32538,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[32537:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(32632,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[32538]) ).
thf(20146,plain,
( ( nil != nil )
| ( sk2 @ ( sk1 @ segmentP ) )
| ( sk9 @ ssItem )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,11909]) ).
thf(20147,plain,
( ( nil != nil )
| ( sk2 @ ( sk1 @ segmentP ) )
| ( sk9 @ ssItem ) ),
inference(simp,[status(thm)],[20146]) ).
thf(20148,plain,
( ( sk2 @ ( sk1 @ segmentP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[20147:[]]) ).
thf(30397,plain,
( ( nil != nil )
| ( sk8 @ equalelemsP )
| ( sk8 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[18740,343]) ).
thf(30398,plain,
( ( sk8 @ equalelemsP )
| ( sk8 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[30397:[]]) ).
thf(19982,plain,
! [A: $i] :
( ( ( sk9 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( A @ neq ) )
| ( nil = sk1 ) ),
inference(paramod_ordered,[status(thm)],[788,311]) ).
thf(19983,plain,
! [A: $i] :
( ( ( sk9 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ( nil = sk1 ) ),
inference(simp,[status(thm)],[19982]) ).
thf(19984,plain,
( ~ ( sk9 @ ( sk9 @ neq ) )
| ( nil = sk1 ) ),
inference(pattern_uni,[status(thm)],[19983:[bind(A,$thf( sk9 ))]]) ).
thf(33177,plain,
( ( nil != nil )
| ~ ( skac3 @ ( sk1 @ memberP ) )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[19984,732]) ).
thf(33178,plain,
( ~ ( skac3 @ ( sk1 @ memberP ) )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[33177:[]]) ).
thf(20888,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[628,317]) ).
thf(20889,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[20888]) ).
thf(20890,plain,
! [A: $i] : ( nil @ ( A @ skaf76 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[20889:[bind(A,$thf( C )),bind(B,$thf( C @ skaf76 ))]]) ).
thf(21026,plain,
! [A: $i] : ( nil @ ( A @ skaf76 @ rearsegP ) ),
inference(simp,[status(thm)],[20890]) ).
thf(15,negated_conjecture,
( ( nil = sk4 )
| ( ( nil @ ( sk9 @ cons ) )
= sk3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
thf(225,plain,
( ( nil = sk4 )
| ( ( nil @ ( sk9 @ cons ) )
= sk3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(21005,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[354,317]) ).
thf(21006,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[21005]) ).
thf(21007,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf45 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[21006:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf45 ) ))]]) ).
thf(21020,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf45 ) @ rearsegP ) ),
inference(simp,[status(thm)],[21007]) ).
thf(121,axiom,
! [A: $i] : ( A @ skaf53 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause42) ).
thf(476,plain,
! [A: $i] : ( A @ skaf53 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(35,axiom,
! [A: $i] : ( A @ skaf79 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause16) ).
thf(278,plain,
! [A: $i] : ( A @ skaf79 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(20006,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[278,311]) ).
thf(20007,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[20006]) ).
thf(20008,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( A @ skaf79 @ neq ) ),
inference(pattern_uni,[status(thm)],[20007:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(20033,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( A @ skaf79 @ neq ) ),
inference(simp,[status(thm)],[20008]) ).
thf(126,axiom,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause62) ).
thf(489,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(64576,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[296,398]) ).
thf(64577,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[64576]) ).
thf(64578,plain,
! [A: $i] : ( A @ skaf64 @ ( A @ skaf64 @ geq ) ),
inference(pattern_uni,[status(thm)],[64577:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(64618,plain,
! [A: $i] : ( A @ skaf64 @ ( A @ skaf64 @ geq ) ),
inference(simp,[status(thm)],[64578]) ).
thf(20024,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[607,311]) ).
thf(20025,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[20024]) ).
thf(20026,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( A @ skaf54 @ neq ) ),
inference(pattern_uni,[status(thm)],[20025:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(20043,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( A @ skaf54 @ neq ) ),
inference(simp,[status(thm)],[20026]) ).
thf(886,plain,
( ( nil != nil )
| ( sk1 @ totalorderedP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[835,659]) ).
thf(887,plain,
( ( sk1 @ totalorderedP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[886:[]]) ).
thf(9275,plain,
( ( nil != nil )
| ( sk1 @ totalorderedP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[827,659]) ).
thf(9276,plain,
( ( sk1 @ totalorderedP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[9275:[]]) ).
thf(27820,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( sk1 @ totalorderedP )
| ~ $true
| ( sk1 @ totalorderedP ) ),
inference(paramod_ordered,[status(thm)],[887,9276]) ).
thf(27821,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[27820]) ).
thf(27845,plain,
( ( sk9 != sk9 )
| ( nil != sk2 )
| ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[27821]) ).
thf(27864,plain,
( ( nil != sk2 )
| ( sk1 @ totalorderedP ) ),
inference(simp,[status(thm)],[27845]) ).
thf(326,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)],[325]) ).
thf(327,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)],[326]) ).
thf(328,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)],[327]) ).
thf(119,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause100) ).
thf(471,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(36026,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ( ( C @ ( nil @ app ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[354,363]) ).
thf(36027,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ssList )
!= ( C @ ssList ) )
| ( ( C @ ( nil @ app ) )
= C ) ),
inference(simp,[status(thm)],[36026]) ).
thf(36028,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ skaf45 ) @ ( nil @ app ) )
= ( B @ ( A @ skaf45 ) ) ),
inference(pattern_uni,[status(thm)],[36027:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf45 ) ))]]) ).
thf(36098,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ skaf45 ) @ ( nil @ app ) )
= ( B @ ( A @ skaf45 ) ) ),
inference(simp,[status(thm)],[36028]) ).
thf(28022,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[214,339]) ).
thf(28023,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP ) ),
inference(simp,[status(thm)],[28022]) ).
thf(28024,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk2 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[28023:[bind(A,$thf( sk2 ))]]) ).
thf(28105,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[28024]) ).
thf(20919,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[461,317]) ).
thf(20920,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[20919]) ).
thf(20921,plain,
! [A: $i] : ( nil @ ( A @ skaf80 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[20920:[bind(A,$thf( C )),bind(B,$thf( C @ skaf80 ))]]) ).
thf(21042,plain,
! [A: $i] : ( nil @ ( A @ skaf80 @ rearsegP ) ),
inference(simp,[status(thm)],[20921]) ).
thf(705,plain,
( ( nil != nil )
| ( sk2 @ cyclefreeP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[676,505]) ).
thf(706,plain,
( ( sk2 @ cyclefreeP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[705:[]]) ).
thf(197,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause112) ).
thf(647,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(32516,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[452,353]) ).
thf(32517,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[32516]) ).
thf(32518,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[32517:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(32628,plain,
! [A: $i] : ( nil @ ( A @ skaf49 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[32518]) ).
thf(22652,plain,
( ( nil != nil )
| ( sk2 @ ( sk1 @ frontsegP ) )
| ( sk9 @ ssItem )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,13136]) ).
thf(22653,plain,
( ( nil != nil )
| ( sk2 @ ( sk1 @ frontsegP ) )
| ( sk9 @ ssItem ) ),
inference(simp,[status(thm)],[22652]) ).
thf(22654,plain,
( ( sk2 @ ( sk1 @ frontsegP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[22653:[]]) ).
thf(20931,plain,
! [A: $i] :
( ( ( sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[212,317]) ).
thf(20932,plain,
! [A: $i] :
( ( ( sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[20931]) ).
thf(20933,plain,
nil @ ( sk7 @ rearsegP ),
inference(pattern_uni,[status(thm)],[20932:[bind(A,$thf( sk7 ))]]) ).
thf(21058,plain,
( ( nil != nil )
| ( sk2 @ ( sk7 @ rearsegP ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,20933]) ).
thf(21059,plain,
( ( sk2 @ ( sk7 @ rearsegP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[21058:[]]) ).
thf(20973,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[568,317]) ).
thf(20974,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf66 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[20973]) ).
thf(20975,plain,
! [A: $i] : ( nil @ ( A @ skaf66 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[20974:[bind(A,$thf( C )),bind(B,$thf( C @ skaf66 ))]]) ).
thf(21038,plain,
! [A: $i] : ( nil @ ( A @ skaf66 @ rearsegP ) ),
inference(simp,[status(thm)],[20975]) ).
thf(199,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ segmentP ) )
| ~ ( B @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause127) ).
thf(654,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)],[199]) ).
thf(1926,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[603,463]) ).
thf(1927,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1926]) ).
thf(1928,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1927:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(1932,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1928]) ).
thf(908,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[278,463]) ).
thf(909,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[908]) ).
thf(910,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[909:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(911,plain,
! [A: $i] :
~ ( A @ skaf79 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[910]) ).
thf(32572,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[278,353]) ).
thf(32573,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[32572]) ).
thf(32574,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[32573:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(32639,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[32574]) ).
thf(9143,plain,
( ( nil != nil )
| ~ ( skac3 @ ( sk1 @ memberP ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[827,732]) ).
thf(9144,plain,
( ~ ( skac3 @ ( sk1 @ memberP ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[9143:[]]) ).
thf(161,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( C @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= ( C @ ( A @ app ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause150) ).
thf(569,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)],[161]) ).
thf(4952,plain,
( ( nil != nil )
| ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[748,717]) ).
thf(4953,plain,
( ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[4952:[]]) ).
thf(74,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ totalorderedP )
| ~ ( B @ hd @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause159) ).
thf(369,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)],[74]) ).
thf(370,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)],[369]) ).
thf(371,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)],[370]) ).
thf(27944,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[212,339]) ).
thf(27945,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP ) ),
inference(simp,[status(thm)],[27944]) ).
thf(27946,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk7 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[27945:[bind(A,$thf( sk7 ))]]) ).
thf(28083,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk7 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[27946]) ).
thf(1109,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[386,463]) ).
thf(1110,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1109]) ).
thf(1111,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1110:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(1114,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1111]) ).
thf(133,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause70) ).
thf(503,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(176,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause156) ).
thf(605,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)],[176]) ).
thf(32620,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[222,353]) ).
thf(32621,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[32620]) ).
thf(32622,plain,
nil @ ( sk6 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[32621:[bind(A,$thf( sk6 ))]]) ).
thf(9080,plain,
( ( nil != nil )
| ( sk1 @ strictorderedP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[827,646]) ).
thf(9081,plain,
( ( sk1 @ strictorderedP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[9080:[]]) ).
thf(791,plain,
( ( nil != nil )
| ( sk1 @ strictorderedP )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[788,646]) ).
thf(792,plain,
( ( sk1 @ strictorderedP )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[791:[]]) ).
thf(20928,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[476,317]) ).
thf(20929,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[20928]) ).
thf(20930,plain,
! [A: $i] : ( nil @ ( A @ skaf53 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[20929:[bind(A,$thf( C )),bind(B,$thf( C @ skaf53 ))]]) ).
thf(21013,plain,
! [A: $i] : ( nil @ ( A @ skaf53 @ rearsegP ) ),
inference(simp,[status(thm)],[20930]) ).
thf(266,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)],[265]) ).
thf(35864,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[461,363]) ).
thf(35865,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[35864]) ).
thf(35866,plain,
! [A: $i] :
( ( A @ skaf80 @ ( nil @ app ) )
= ( A @ skaf80 ) ),
inference(pattern_uni,[status(thm)],[35865:[bind(A,$thf( C )),bind(B,$thf( C @ skaf80 ))]]) ).
thf(36064,plain,
! [A: $i] :
( ( A @ skaf80 @ ( nil @ app ) )
= ( A @ skaf80 ) ),
inference(simp,[status(thm)],[35866]) ).
thf(200,axiom,
! [A: $i] :
( ( A @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause57) ).
thf(657,plain,
! [A: $i] :
( ( A @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(35919,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[567,363]) ).
thf(35920,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[35919]) ).
thf(35921,plain,
! [A: $i] :
( ( A @ skaf63 @ ( nil @ app ) )
= ( A @ skaf63 ) ),
inference(pattern_uni,[status(thm)],[35920:[bind(A,$thf( C )),bind(B,$thf( C @ skaf63 ))]]) ).
thf(36077,plain,
! [A: $i] :
( ( A @ skaf63 @ ( nil @ app ) )
= ( A @ skaf63 ) ),
inference(simp,[status(thm)],[35921]) ).
thf(2781,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[660,2251]) ).
thf(2782,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[2781]) ).
thf(2783,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[2782:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(2793,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[2783]) ).
thf(33273,plain,
( ( nil != nil )
| ~ ( sk6 @ ( sk1 @ memberP ) )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[19984,675]) ).
thf(33274,plain,
( ~ ( sk6 @ ( sk1 @ memberP ) )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[33273:[]]) ).
thf(175,axiom,
! [A: $i] : ( A @ skaf82 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause13) ).
thf(604,plain,
! [A: $i] : ( A @ skaf82 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(20946,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[604,317]) ).
thf(20947,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[20946]) ).
thf(20948,plain,
! [A: $i] : ( nil @ ( A @ skaf82 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[20947:[bind(A,$thf( C )),bind(B,$thf( C @ skaf82 ))]]) ).
thf(21023,plain,
! [A: $i] : ( nil @ ( A @ skaf82 @ rearsegP ) ),
inference(simp,[status(thm)],[20948]) ).
thf(191,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause86) ).
thf(633,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(20015,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[431,311]) ).
thf(20016,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[20015]) ).
thf(20017,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( A @ skaf60 @ neq ) ),
inference(pattern_uni,[status(thm)],[20016:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(20037,plain,
! [A: $i] :
~ ( A @ skaf60 @ ( A @ skaf60 @ neq ) ),
inference(simp,[status(thm)],[20017]) ).
thf(36020,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[528,363]) ).
thf(36021,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[36020]) ).
thf(36022,plain,
! [A: $i] :
( ( A @ skaf81 @ ( nil @ app ) )
= ( A @ skaf81 ) ),
inference(pattern_uni,[status(thm)],[36021:[bind(A,$thf( C )),bind(B,$thf( C @ skaf81 ))]]) ).
thf(36096,plain,
! [A: $i] :
( ( A @ skaf81 @ ( nil @ app ) )
= ( A @ skaf81 ) ),
inference(simp,[status(thm)],[36022]) ).
thf(167,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause122) ).
thf(586,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)],[167]) ).
thf(2272,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[420,2251]) ).
thf(2273,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[2272]) ).
thf(2274,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[2273:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(2338,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[2274]) ).
thf(298,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)],[297]) ).
thf(749,plain,
( ( nil != nil )
| ~ ( sk2 @ singletonP )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,517]) ).
thf(750,plain,
( ~ ( sk2 @ singletonP )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[749:[]]) ).
thf(97,axiom,
! [A: $i] :
( ( A @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause59) ).
thf(425,plain,
! [A: $i] :
( ( A @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(4873,plain,
( ( nil != nil )
| ( sk2 @ strictorderP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[748,324]) ).
thf(4874,plain,
( ( sk2 @ strictorderP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[4873:[]]) ).
thf(33322,plain,
( ( nil != nil )
| ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[19984,717]) ).
thf(33323,plain,
( ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[33322:[]]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ lt ) )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause147) ).
thf(263,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)],[28]) ).
thf(264,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)],[263]) ).
thf(695,plain,
( ( nil != nil )
| ( sk2 @ equalelemsP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[676,343]) ).
thf(696,plain,
( ( sk2 @ equalelemsP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[695:[]]) ).
thf(4893,plain,
( ( nil != nil )
| ( sk2 @ equalelemsP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[748,343]) ).
thf(4894,plain,
( ( sk2 @ equalelemsP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[4893:[]]) ).
thf(17513,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( sk2 @ equalelemsP )
| ~ $true
| ( sk2 @ equalelemsP ) ),
inference(paramod_ordered,[status(thm)],[696,4894]) ).
thf(17514,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( sk2 @ equalelemsP ) ),
inference(simp,[status(thm)],[17513]) ).
thf(17521,plain,
( ( sk9 != sk9 )
| ( nil != sk2 )
| ( sk2 @ equalelemsP ) ),
inference(simp,[status(thm)],[17514]) ).
thf(17542,plain,
( ( nil != sk2 )
| ( sk2 @ equalelemsP ) ),
inference(simp,[status(thm)],[17521]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause134) ).
thf(279,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)],[36]) ).
thf(2258,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[550,2251]) ).
thf(2259,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[2258]) ).
thf(2260,plain,
nil @ ( skac2 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[2259:[bind(A,$thf( skac2 ))]]) ).
thf(64612,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[607,398]) ).
thf(64613,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[64612]) ).
thf(64614,plain,
! [A: $i] : ( A @ skaf54 @ ( A @ skaf54 @ geq ) ),
inference(pattern_uni,[status(thm)],[64613:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(64628,plain,
! [A: $i] : ( A @ skaf54 @ ( A @ skaf54 @ geq ) ),
inference(simp,[status(thm)],[64614]) ).
thf(77,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ skaf46 ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause131) ).
thf(375,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)],[77]) ).
thf(35914,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[604,363]) ).
thf(35915,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[35914]) ).
thf(35916,plain,
! [A: $i] :
( ( A @ skaf82 @ ( nil @ app ) )
= ( A @ skaf82 ) ),
inference(pattern_uni,[status(thm)],[35915:[bind(A,$thf( C )),bind(B,$thf( C @ skaf82 ))]]) ).
thf(36076,plain,
! [A: $i] :
( ( A @ skaf82 @ ( nil @ app ) )
= ( A @ skaf82 ) ),
inference(simp,[status(thm)],[35916]) ).
thf(27,axiom,
! [A: $i] : ( A @ skaf62 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause33) ).
thf(262,plain,
! [A: $i] : ( A @ skaf62 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(35991,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[262,363]) ).
thf(35992,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[35991]) ).
thf(35993,plain,
! [A: $i] :
( ( A @ skaf62 @ ( nil @ app ) )
= ( A @ skaf62 ) ),
inference(pattern_uni,[status(thm)],[35992:[bind(A,$thf( C )),bind(B,$thf( C @ skaf62 ))]]) ).
thf(36091,plain,
! [A: $i] :
( ( A @ skaf62 @ ( nil @ app ) )
= ( A @ skaf62 ) ),
inference(simp,[status(thm)],[35993]) ).
thf(693,plain,
( ( nil != nil )
| ~ ( sk2 @ singletonP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[676,517]) ).
thf(694,plain,
( ~ ( sk2 @ singletonP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[693:[]]) ).
thf(1387,plain,
! [A: $i] :
( ( ( sk9 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 = sk1 ) ),
inference(paramod_ordered,[status(thm)],[799,463]) ).
thf(1388,plain,
! [A: $i] :
( ( ( sk9 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 = sk1 ) ),
inference(simp,[status(thm)],[1387]) ).
thf(1389,plain,
( ~ ( sk9 @ ( nil @ memberP ) )
| ( sk2 = sk1 ) ),
inference(pattern_uni,[status(thm)],[1388:[bind(A,$thf( sk9 ))]]) ).
thf(39,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ geq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause107) ).
thf(286,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(742,plain,
( ( nil != nil )
| ~ ( sk6 @ ( sk2 @ memberP ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,675]) ).
thf(743,plain,
( ~ ( sk6 @ ( sk2 @ memberP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[742:[]]) ).
thf(35813,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf42 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ( ( C @ ( nil @ app ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[629,363]) ).
thf(35814,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf42 ) @ ssList )
!= ( C @ ssList ) )
| ( ( C @ ( nil @ app ) )
= C ) ),
inference(simp,[status(thm)],[35813]) ).
thf(35815,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ skaf42 ) @ ( nil @ app ) )
= ( B @ ( A @ skaf42 ) ) ),
inference(pattern_uni,[status(thm)],[35814:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf42 ) ))]]) ).
thf(36126,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ skaf42 ) @ ( nil @ app ) )
= ( B @ ( A @ skaf42 ) ) ),
inference(simp,[status(thm)],[35815]) ).
thf(2710,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[628,261]) ).
thf(2711,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf76 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[2710]) ).
thf(2712,plain,
! [A: $i] :
~ ( A @ skaf76 @ ( A @ skaf76 @ neq ) ),
inference(pattern_uni,[status(thm)],[2711:[bind(A,$thf( C )),bind(B,$thf( C @ skaf76 ))]]) ).
thf(2716,plain,
! [A: $i] :
~ ( A @ skaf76 @ ( A @ skaf76 @ neq ) ),
inference(simp,[status(thm)],[2712]) ).
thf(280,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP ) ),
inference(cnf,[status(esa)],[279]) ).
thf(281,plain,
! [B: $i,A: $i] :
( ( B @ hd @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ strictorderedP )
| ( nil = B ) ),
inference(lifteq,[status(thm)],[280]) ).
thf(91,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ rearsegP ) )
| ~ ( B @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause128) ).
thf(413,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)],[91]) ).
thf(32510,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[638,353]) ).
thf(32511,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[32510]) ).
thf(32512,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[32511:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(32626,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[32512]) ).
thf(32617,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[607,353]) ).
thf(32618,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[32617]) ).
thf(32619,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[32618:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(32648,plain,
! [A: $i] : ( nil @ ( A @ skaf54 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[32619]) ).
thf(2778,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[660,463]) ).
thf(2779,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2778]) ).
thf(2780,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2779:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(2791,plain,
! [A: $i] :
~ ( A @ skaf59 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2780]) ).
thf(874,plain,
( ( nil != nil )
| ( sk1 @ equalelemsP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[835,343]) ).
thf(875,plain,
( ( sk1 @ equalelemsP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[874:[]]) ).
thf(164,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause77) ).
thf(577,plain,
! [A: $i] :
( ( nil = A )
| ( A @ tl @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(42,axiom,
! [B: $i,A: $i] : ( B @ ( A @ skaf46 ) @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause50) ).
thf(295,plain,
! [B: $i,A: $i] : ( B @ ( A @ skaf46 ) @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(35946,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf46 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ( ( C @ ( nil @ app ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[295,363]) ).
thf(35947,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf46 ) @ ssList )
!= ( C @ ssList ) )
| ( ( C @ ( nil @ app ) )
= C ) ),
inference(simp,[status(thm)],[35946]) ).
thf(35948,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ skaf46 ) @ ( nil @ app ) )
= ( B @ ( A @ skaf46 ) ) ),
inference(pattern_uni,[status(thm)],[35947:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf46 ) ))]]) ).
thf(36081,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ skaf46 ) @ ( nil @ app ) )
= ( B @ ( A @ skaf46 ) ) ),
inference(simp,[status(thm)],[35948]) ).
thf(30389,plain,
( ( nil != nil )
| ( sk8 @ duplicatefreeP )
| ( sk8 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[18740,360]) ).
thf(30390,plain,
( ( sk8 @ duplicatefreeP )
| ( sk8 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[30389:[]]) ).
thf(4938,plain,
( ( nil != nil )
| ( sk2 @ cyclefreeP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[748,505]) ).
thf(4939,plain,
( ( sk2 @ cyclefreeP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[4938:[]]) ).
thf(17657,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( sk2 @ cyclefreeP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[706,4939]) ).
thf(17658,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17657]) ).
thf(17716,plain,
( ( sk9 != sk9 )
| ( nil != sk2 )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17658]) ).
thf(17737,plain,
( ( nil != sk2 )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17716]) ).
thf(41,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( F @ strictorderedP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause181) ).
thf(291,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)],[41]) ).
thf(19964,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[217,311]) ).
thf(19965,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[19964]) ).
thf(19966,plain,
~ ( sk5 @ ( sk5 @ neq ) ),
inference(pattern_uni,[status(thm)],[19965:[bind(A,$thf( sk5 ))]]) ).
thf(35982,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[214,363]) ).
thf(35983,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[35982]) ).
thf(35984,plain,
( ( sk2 @ ( nil @ app ) )
= sk2 ),
inference(pattern_uni,[status(thm)],[35983:[bind(A,$thf( sk2 ))]]) ).
thf(82,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ cons ) @ ( A @ ( C @ cons ) @ frontsegP ) )
| ~ ( C @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( C != D )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause178) ).
thf(391,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)],[82]) ).
thf(106,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ cons ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause139) ).
thf(445,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)],[106]) ).
thf(79,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ app ) )
= nil )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( nil != B )
| ( nil != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause145) ).
thf(382,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)],[79]) ).
thf(162,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ( ( B @ ( A @ cons ) )
!= ( D @ ( C @ cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause170) ).
thf(572,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)],[162]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ( B @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause132) ).
thf(313,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)],[50]) ).
thf(2743,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[638,2251]) ).
thf(2744,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[2743]) ).
thf(2745,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[2744:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(2753,plain,
! [A: $i] : ( nil @ ( A @ skaf78 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[2745]) ).
thf(236,plain,
( ( sk8 @ ( nil @ ( sk6 @ cons ) @ ( nil @ ( sk5 @ cons ) @ ( sk7 @ app ) @ app ) @ app ) )
= sk1 ),
inference(lifteq,[status(thm)],[221]) ).
thf(803,plain,
( ( nil != nil )
| ~ ( skac3 @ ( sk1 @ memberP ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[788,732]) ).
thf(804,plain,
( ~ ( skac3 @ ( sk1 @ memberP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[803:[]]) ).
thf(20021,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[603,311]) ).
thf(20022,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[20021]) ).
thf(20023,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( A @ skaf74 @ neq ) ),
inference(pattern_uni,[status(thm)],[20022:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(20041,plain,
! [A: $i] :
~ ( A @ skaf74 @ ( A @ skaf74 @ neq ) ),
inference(simp,[status(thm)],[20023]) ).
thf(4889,plain,
( ( nil != nil )
| ( sk2 @ duplicatefreeP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[748,360]) ).
thf(4890,plain,
( ( sk2 @ duplicatefreeP )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[4889:[]]) ).
thf(17306,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( sk2 @ duplicatefreeP )
| ~ $true
| ( sk2 @ duplicatefreeP ) ),
inference(paramod_ordered,[status(thm)],[702,4890]) ).
thf(17307,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[17306]) ).
thf(17371,plain,
( ( sk9 != sk9 )
| ( nil != sk2 )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[17307]) ).
thf(17392,plain,
( ( nil != sk2 )
| ( sk2 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[17371]) ).
thf(20925,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[499,317]) ).
thf(20926,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf68 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[20925]) ).
thf(20927,plain,
! [A: $i] : ( nil @ ( A @ skaf68 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[20926:[bind(A,$thf( C )),bind(B,$thf( C @ skaf68 ))]]) ).
thf(21045,plain,
! [A: $i] : ( nil @ ( A @ skaf68 @ rearsegP ) ),
inference(simp,[status(thm)],[20927]) ).
thf(4922,plain,
( ( nil != nil )
| ~ ( sk5 @ ( sk2 @ memberP ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[748,672]) ).
thf(4923,plain,
( ~ ( sk5 @ ( sk2 @ memberP ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[4922:[]]) ).
thf(6518,plain,
( ~ $true
| ( ( sk9 @ ( nil @ memberP ) )
!= ( sk5 @ ( sk2 @ memberP ) ) )
| ~ ( sk5 @ ( sk2 @ memberP ) ) ),
inference(eqfactor_ordered,[status(thm)],[4923]) ).
thf(6532,plain,
( ( sk9 != sk5 )
| ( nil != sk2 )
| ~ ( sk5 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[6518]) ).
thf(35858,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[329,363]) ).
thf(35859,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[35858]) ).
thf(35860,plain,
! [A: $i] :
( ( A @ skaf77 @ ( nil @ app ) )
= ( A @ skaf77 ) ),
inference(pattern_uni,[status(thm)],[35859:[bind(A,$thf( C )),bind(B,$thf( C @ skaf77 ))]]) ).
thf(36062,plain,
! [A: $i] :
( ( A @ skaf77 @ ( nil @ app ) )
= ( A @ skaf77 ) ),
inference(simp,[status(thm)],[35860]) ).
thf(117,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ segmentP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ segmentP ) )
| ~ ( B @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause152) ).
thf(466,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ segmentP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( C @ ( B @ segmentP ) )
| ~ ( B @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(21249,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( sk1 @ strictorderedP )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[841,9081]) ).
thf(21250,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[21249]) ).
thf(21339,plain,
( ( sk9 != sk9 )
| ( nil != sk2 )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[21250]) ).
thf(21360,plain,
( ( nil != sk2 )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[21339]) ).
thf(679,plain,
( ( nil != nil )
| ( sk2 @ strictorderP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[676,324]) ).
thf(680,plain,
( ( sk2 @ strictorderP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[679:[]]) ).
thf(14446,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( sk2 @ strictorderP )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[680,4874]) ).
thf(14447,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[14446]) ).
thf(14483,plain,
( ( sk9 != sk9 )
| ( nil != sk2 )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[14447]) ).
thf(14502,plain,
( ( nil != sk2 )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[14483]) ).
thf(20027,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[222,311]) ).
thf(20028,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[20027]) ).
thf(20029,plain,
~ ( sk6 @ ( sk6 @ neq ) ),
inference(pattern_uni,[status(thm)],[20028:[bind(A,$thf( sk6 ))]]) ).
thf(19979,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[424,311]) ).
thf(19980,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[19979]) ).
thf(19981,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( A @ skaf70 @ neq ) ),
inference(pattern_uni,[status(thm)],[19980:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(20036,plain,
! [A: $i] :
~ ( A @ skaf70 @ ( A @ skaf70 @ neq ) ),
inference(simp,[status(thm)],[19981]) ).
thf(405,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[404]) ).
thf(406,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( B = A ) ),
inference(lifteq,[status(thm)],[405]) ).
thf(18,negated_conjecture,
( ( nil = sk3 )
| ( ( nil @ ( sk9 @ cons ) )
= sk3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
thf(219,plain,
( ( nil = sk3 )
| ( ( nil @ ( sk9 @ cons ) )
= sk3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(30319,plain,
( ( nil != nil )
| ( sk8 @ strictorderP )
| ( sk8 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[18740,324]) ).
thf(30320,plain,
( ( sk8 @ strictorderP )
| ( sk8 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[30319:[]]) ).
thf(376,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ skaf46 ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ rearsegP ) ) ),
inference(cnf,[status(esa)],[375]) ).
thf(377,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ rearsegP ) )
| ( ( B @ ( B @ ( A @ skaf46 ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[376]) ).
thf(32519,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[424,353]) ).
thf(32520,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[32519]) ).
thf(32521,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[32520:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(32629,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[32521]) ).
thf(102,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ strictorderedP )
| ~ ( B @ hd @ ( A @ lt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause160) ).
thf(434,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)],[102]) ).
thf(182,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ ( D @ app ) @ app ) @ segmentP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause172) ).
thf(616,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ ( D @ app ) @ app ) @ segmentP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(172,axiom,
! [A: $i] : ( A @ skaf83 @ ssItem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause12) ).
thf(599,plain,
! [A: $i] : ( A @ skaf83 @ ssItem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(5821,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf47 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ~ ( C @ ( C @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[511,261]) ).
thf(5822,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf47 ) @ ssList )
!= ( C @ ssList ) )
| ~ ( C @ ( C @ neq ) ) ),
inference(simp,[status(thm)],[5821]) ).
thf(5823,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf47 ) @ ( B @ ( A @ skaf47 ) @ neq ) ),
inference(pattern_uni,[status(thm)],[5822:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf47 ) ))]]) ).
thf(5848,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf47 ) @ ( B @ ( A @ skaf47 ) @ neq ) ),
inference(simp,[status(thm)],[5823]) ).
thf(32,axiom,
! [A: $i] :
( ( ( nil @ ( A @ skaf44 @ cons ) )
= A )
| ~ ( A @ ssList )
| ~ ( A @ singletonP ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause101) ).
thf(271,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf44 @ cons ) )
= A )
| ~ ( A @ ssList )
| ~ ( A @ singletonP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(33761,plain,
( ( nil != nil )
| ~ ( sk6 @ ( sk2 @ memberP ) )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[19996,675]) ).
thf(33762,plain,
( ~ ( sk6 @ ( sk2 @ memberP ) )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[33761:[]]) ).
thf(1302,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[452,463]) ).
thf(1303,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1302]) ).
thf(1304,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1303:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(1307,plain,
! [A: $i] :
~ ( A @ skaf49 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1304]) ).
thf(26598,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( nil @ rearsegP ) )
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[210,335]) ).
thf(26599,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ rearsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[26598]) ).
thf(26600,plain,
( ~ ( sk1 @ ( nil @ rearsegP ) )
| ( nil = sk1 ) ),
inference(pattern_uni,[status(thm)],[26599:[bind(A,$thf( sk1 ))]]) ).
thf(888,plain,
( ( nil != nil )
| ( sk9 @ ( sk2 @ memberP ) )
| ( sk2 = sk1 )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[835,676]) ).
thf(889,plain,
( ( nil != nil )
| ( sk2 = sk1 )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(simp,[status(thm)],[888]) ).
thf(890,plain,
( ( sk2 = sk1 )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[889:[]]) ).
thf(81,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( E @ ssList )
| ~ ( E @ equalelemsP )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( A @ ssList )
| ~ ( D @ ssList )
| ( ( D @ ( C @ cons ) @ ( B @ cons ) @ ( A @ app ) )
!= E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause180) ).
thf(387,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)],[81]) ).
thf(49015,plain,
( ( nil != nil )
| ~ ( sk7 @ singletonP )
| ~ ( sk7 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[25728,517]) ).
thf(49016,plain,
( ~ ( sk7 @ singletonP )
| ~ ( sk7 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[49015:[]]) ).
thf(179,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ app ) @ hd )
= ( B @ hd ) )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause123) ).
thf(609,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)],[179]) ).
thf(322,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)],[321]) ).
thf(323,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)],[322]) ).
thf(20952,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[477,317]) ).
thf(20953,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf75 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[20952]) ).
thf(20954,plain,
! [A: $i] : ( nil @ ( A @ skaf75 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[20953:[bind(A,$thf( C )),bind(B,$thf( C @ skaf75 ))]]) ).
thf(21027,plain,
! [A: $i] : ( nil @ ( A @ skaf75 @ rearsegP ) ),
inference(simp,[status(thm)],[20954]) ).
thf(64585,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[419,398]) ).
thf(64586,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[64585]) ).
thf(64587,plain,
! [A: $i] : ( A @ skaf69 @ ( A @ skaf69 @ geq ) ),
inference(pattern_uni,[status(thm)],[64586:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(64620,plain,
! [A: $i] : ( A @ skaf69 @ ( A @ skaf69 @ geq ) ),
inference(simp,[status(thm)],[64587]) ).
thf(28019,plain,
! [B: $i,A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[207,339]) ).
thf(28020,plain,
! [B: $i,A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( B @ ssItem )
| ( A @ duplicatefreeP ) ),
inference(simp,[status(thm)],[28019]) ).
thf(28021,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk8 @ duplicatefreeP ) ),
inference(pattern_uni,[status(thm)],[28020:[bind(A,$thf( sk8 ))]]) ).
thf(28103,plain,
! [A: $i] :
( ( A @ ssItem )
| ( sk8 @ duplicatefreeP ) ),
inference(simp,[status(thm)],[28021]) ).
thf(32583,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[431,353]) ).
thf(32584,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[32583]) ).
thf(32585,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[32584:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(32641,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[32585]) ).
thf(57,axiom,
! [A: $i] :
( ( ( A @ skaf53 @ ( A @ skaf50 @ cons ) @ ( A @ skaf52 @ ( A @ skaf49 @ cons ) @ ( A @ skaf51 @ app ) @ app ) )
= A )
| ( A @ cyclefreeP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause167) ).
thf(330,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)],[57]) ).
thf(20990,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[210,317]) ).
thf(20991,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[20990]) ).
thf(20992,plain,
nil @ ( sk1 @ rearsegP ),
inference(pattern_uni,[status(thm)],[20991:[bind(A,$thf( sk1 ))]]) ).
thf(13145,plain,
( ( nil != nil )
| ( nil @ ( sk2 @ frontsegP ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,13132]) ).
thf(13146,plain,
( ( nil @ ( sk2 @ frontsegP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[13145:[]]) ).
thf(24959,plain,
( ( nil != nil )
| ( sk2 @ ( sk2 @ frontsegP ) )
| ( sk9 @ ssItem )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,13146]) ).
thf(24960,plain,
( ( nil != nil )
| ( sk2 @ ( sk2 @ frontsegP ) )
| ( sk9 @ ssItem ) ),
inference(simp,[status(thm)],[24959]) ).
thf(24961,plain,
( ( sk2 @ ( sk2 @ frontsegP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[24960:[]]) ).
thf(757,plain,
( ( nil != nil )
| ( sk2 @ cyclefreeP )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,505]) ).
thf(758,plain,
( ( sk2 @ cyclefreeP )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[757:[]]) ).
thf(147,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ cons ) @ memberP ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssList )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause138) ).
thf(535,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)],[147]) ).
thf(2295,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[278,2251]) ).
thf(2296,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[2295]) ).
thf(2297,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[2296:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(2343,plain,
! [A: $i] : ( nil @ ( A @ skaf79 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[2297]) ).
thf(815,plain,
( ( nil != nil )
| ( sk1 @ equalelemsP )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[788,343]) ).
thf(816,plain,
( ( sk1 @ equalelemsP )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[815:[]]) ).
thf(64591,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[278,398]) ).
thf(64592,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf79 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[64591]) ).
thf(64593,plain,
! [A: $i] : ( A @ skaf79 @ ( A @ skaf79 @ geq ) ),
inference(pattern_uni,[status(thm)],[64592:[bind(A,$thf( C )),bind(B,$thf( C @ skaf79 ))]]) ).
thf(64621,plain,
! [A: $i] : ( A @ skaf79 @ ( A @ skaf79 @ geq ) ),
inference(simp,[status(thm)],[64593]) ).
thf(33231,plain,
( ( nil != nil )
| ~ ( sk5 @ ( sk1 @ memberP ) )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[19984,672]) ).
thf(33232,plain,
( ~ ( sk5 @ ( sk1 @ memberP ) )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[33231:[]]) ).
thf(170,axiom,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ segmentP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause80) ).
thf(594,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(724,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[207,261]) ).
thf(725,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[724]) ).
thf(726,plain,
~ ( sk8 @ ( sk8 @ neq ) ),
inference(pattern_uni,[status(thm)],[725:[bind(A,$thf( sk8 ))]]) ).
thf(33495,plain,
( ( nil != nil )
| ~ ( skac2 @ ( sk2 @ memberP ) )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[19996,709]) ).
thf(33496,plain,
( ~ ( skac2 @ ( sk2 @ memberP ) )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[33495:[]]) ).
thf(19967,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[550,311]) ).
thf(19968,plain,
! [A: $i] :
( ( ( skac2 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[19967]) ).
thf(19969,plain,
~ ( skac2 @ ( skac2 @ neq ) ),
inference(pattern_uni,[status(thm)],[19968:[bind(A,$thf( skac2 ))]]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause108) ).
thf(250,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(251,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[250]) ).
thf(187,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause114) ).
thf(626,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(912,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[296,463]) ).
thf(913,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[912]) ).
thf(914,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[913:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(915,plain,
! [A: $i] :
~ ( A @ skaf64 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[914]) ).
thf(2327,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[222,2251]) ).
thf(2328,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[2327]) ).
thf(2329,plain,
nil @ ( sk6 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[2328:[bind(A,$thf( sk6 ))]]) ).
thf(30672,plain,
( ( nil != nil )
| ( sk8 @ totalorderedP )
| ( sk8 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[18740,659]) ).
thf(30673,plain,
( ( sk8 @ totalorderedP )
| ( sk8 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[30672:[]]) ).
thf(59036,plain,
( ( nil != nil )
| ~ ( sk2 @ singletonP )
| ~ ( sk2 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[26512,517]) ).
thf(59037,plain,
( ~ ( sk2 @ singletonP )
| ~ ( sk2 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[59036:[]]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ app ) @ app ) )
= ( A @ ( B @ app ) @ ( C @ app ) ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause149) ).
thf(399,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)],[85]) ).
thf(392,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)],[391]) ).
thf(393,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)],[392]) ).
thf(394,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)],[393]) ).
thf(11874,plain,
( ( nil != nil )
| ( nil @ ( sk2 @ rearsegP ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,11867]) ).
thf(11875,plain,
( ( nil @ ( sk2 @ rearsegP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[11874:[]]) ).
thf(19533,plain,
( ( nil != nil )
| ( sk2 @ ( sk2 @ rearsegP ) )
| ( sk9 @ ssItem )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,11875]) ).
thf(19534,plain,
( ( nil != nil )
| ( sk2 @ ( sk2 @ rearsegP ) )
| ( sk9 @ ssItem ) ),
inference(simp,[status(thm)],[19533]) ).
thf(19535,plain,
( ( sk2 @ ( sk2 @ rearsegP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[19534:[]]) ).
thf(2301,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[563,2251]) ).
thf(2302,plain,
! [A: $i] :
( ( ( skac3 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[2301]) ).
thf(2303,plain,
nil @ ( skac3 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[2302:[bind(A,$thf( skac3 ))]]) ).
thf(21002,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[277,317]) ).
thf(21003,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[21002]) ).
thf(21004,plain,
! [A: $i] : ( nil @ ( A @ skaf72 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[21003:[bind(A,$thf( C )),bind(B,$thf( C @ skaf72 ))]]) ).
thf(21019,plain,
! [A: $i] : ( nil @ ( A @ skaf72 @ rearsegP ) ),
inference(simp,[status(thm)],[21004]) ).
thf(2133,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[607,463]) ).
thf(2134,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf54 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2133]) ).
thf(2135,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2134:[bind(A,$thf( C )),bind(B,$thf( C @ skaf54 ))]]) ).
thf(2139,plain,
! [A: $i] :
~ ( A @ skaf54 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2135]) ).
thf(112,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause76) ).
thf(455,plain,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(32575,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[608,353]) ).
thf(32576,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[32575]) ).
thf(32577,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[32576:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(32640,plain,
! [A: $i] : ( nil @ ( A @ skaf65 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[32577]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause90) ).
thf(267,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1097,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[372,261]) ).
thf(1098,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1097]) ).
thf(1099,plain,
! [A: $i] :
~ ( A @ skaf58 @ ( A @ skaf58 @ neq ) ),
inference(pattern_uni,[status(thm)],[1098:[bind(A,$thf( C )),bind(B,$thf( C @ skaf58 ))]]) ).
thf(1102,plain,
! [A: $i] :
~ ( A @ skaf58 @ ( A @ skaf58 @ neq ) ),
inference(simp,[status(thm)],[1099]) ).
thf(64615,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[222,398]) ).
thf(64616,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) ) ),
inference(simp,[status(thm)],[64615]) ).
thf(64617,plain,
sk6 @ ( sk6 @ geq ),
inference(pattern_uni,[status(thm)],[64616:[bind(A,$thf( sk6 ))]]) ).
thf(168,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ totalorderedP )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ totalorderedP ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause125) ).
thf(589,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)],[168]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ gt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( C @ ssItem )
| ~ ( C @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause146) ).
thf(373,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)],[76]) ).
thf(374,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)],[373]) ).
thf(20,negated_conjecture,
! [A: $i] :
( ( nil = sk3 )
| ~ ( sk9 @ ( A @ leq ) )
| ~ ( A @ ( sk4 @ memberP ) )
| ( sk9 = A )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_20) ).
thf(209,plain,
! [A: $i] :
( ( nil = sk3 )
| ~ ( sk9 @ ( A @ leq ) )
| ~ ( A @ ( sk4 @ memberP ) )
| ( sk9 = A )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(811,plain,
( ( nil != nil )
| ( sk1 @ totalorderP )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[788,500]) ).
thf(812,plain,
( ( sk1 @ totalorderP )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[811:[]]) ).
thf(2315,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[603,2251]) ).
thf(2316,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[2315]) ).
thf(2317,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[2316:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(2333,plain,
! [A: $i] : ( nil @ ( A @ skaf74 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[2317]) ).
thf(113,axiom,
! [B: $i,A: $i] :
( ( nil = B )
| ( B @ hd @ ( A @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ cons ) @ totalorderedP ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause135) ).
thf(458,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)],[113]) ).
thf(24114,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( sk1 @ equalelemsP )
| ~ $true
| ( sk1 @ equalelemsP ) ),
inference(paramod_ordered,[status(thm)],[875,9132]) ).
thf(24115,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( sk1 @ equalelemsP ) ),
inference(simp,[status(thm)],[24114]) ).
thf(24169,plain,
( ( sk9 != sk9 )
| ( nil != sk2 )
| ( sk1 @ equalelemsP ) ),
inference(simp,[status(thm)],[24115]) ).
thf(24190,plain,
( ( nil != sk2 )
| ( sk1 @ equalelemsP ) ),
inference(simp,[status(thm)],[24169]) ).
thf(9169,plain,
( ( nil != nil )
| ~ ( sk5 @ ( sk1 @ memberP ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[827,672]) ).
thf(9170,plain,
( ~ ( sk5 @ ( sk1 @ memberP ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[9169:[]]) ).
thf(30259,plain,
( ( nil != nil )
| ( sk8 @ strictorderedP )
| ( sk8 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[18740,646]) ).
thf(30260,plain,
( ( sk8 @ strictorderedP )
| ( sk8 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[30259:[]]) ).
thf(232,plain,
! [A: $i] :
( ( nil = sk3 )
| ~ ( sk9 @ ( A @ leq ) )
| ~ ( A @ ( sk4 @ memberP ) )
| ( sk9 = A )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[209]) ).
thf(233,plain,
! [A: $i] :
( ~ ( sk9 @ ( A @ leq ) )
| ~ ( A @ ( sk4 @ memberP ) )
| ~ ( A @ ssItem )
| ( nil = sk3 )
| ( sk9 = A ) ),
inference(lifteq,[status(thm)],[232]) ).
thf(944,plain,
! [A: $i] :
( ~ ( sk9 @ ( A @ leq ) )
| ~ ( A @ ( sk2 @ memberP ) )
| ~ ( A @ ssItem )
| ( nil = sk1 )
| ( sk9 = A ) ),
inference(rewrite,[status(thm)],[233,235,237]) ).
thf(20961,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf46 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[295,317]) ).
thf(20962,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf46 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[20961]) ).
thf(20963,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf46 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[20962:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf46 ) ))]]) ).
thf(21031,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf46 ) @ rearsegP ) ),
inference(simp,[status(thm)],[20963]) ).
thf(9068,plain,
( ( nil != nil )
| ~ ( skac2 @ ( sk1 @ memberP ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[827,709]) ).
thf(9069,plain,
( ~ ( skac2 @ ( sk1 @ memberP ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[9068:[]]) ).
thf(21008,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[560,317]) ).
thf(21009,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf51 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[21008]) ).
thf(21010,plain,
! [A: $i] : ( nil @ ( A @ skaf51 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[21009:[bind(A,$thf( C )),bind(B,$thf( C @ skaf51 ))]]) ).
thf(21022,plain,
! [A: $i] : ( nil @ ( A @ skaf51 @ rearsegP ) ),
inference(simp,[status(thm)],[21010]) ).
thf(753,plain,
( ( nil != nil )
| ( sk2 @ duplicatefreeP )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,360]) ).
thf(754,plain,
( ( sk2 @ duplicatefreeP )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[753:[]]) ).
thf(64603,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[386,398]) ).
thf(64604,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[64603]) ).
thf(64605,plain,
! [A: $i] : ( A @ skaf44 @ ( A @ skaf44 @ geq ) ),
inference(pattern_uni,[status(thm)],[64604:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(64624,plain,
! [A: $i] : ( A @ skaf44 @ ( A @ skaf44 @ geq ) ),
inference(simp,[status(thm)],[64605]) ).
thf(1840,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[567,261]) ).
thf(1841,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf63 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1840]) ).
thf(1842,plain,
! [A: $i] :
~ ( A @ skaf63 @ ( A @ skaf63 @ neq ) ),
inference(pattern_uni,[status(thm)],[1841:[bind(A,$thf( C )),bind(B,$thf( C @ skaf63 ))]]) ).
thf(1845,plain,
! [A: $i] :
~ ( A @ skaf63 @ ( A @ skaf63 @ neq ) ),
inference(simp,[status(thm)],[1842]) ).
thf(775,plain,
( ( nil != nil )
| ~ ( sk2 @ ( nil @ neq ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,717]) ).
thf(776,plain,
( ~ ( sk2 @ ( nil @ neq ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[775:[]]) ).
thf(143,axiom,
! [A: $i] :
( ( ( A @ skaf81 @ ( A @ skaf79 @ cons ) @ ( A @ skaf78 @ cons ) @ ( A @ skaf80 @ app ) )
= A )
| ( A @ equalelemsP )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause142) ).
thf(525,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)],[143]) ).
thf(165,axiom,
! [A: $i] :
( ( nil = A )
| ( ( A @ skaf82 @ ( A @ skaf83 @ cons ) )
= A )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause109) ).
thf(580,plain,
! [A: $i] :
( ( nil = A )
| ( ( A @ skaf82 @ ( A @ skaf83 @ cons ) )
= A )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ app ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause85) ).
thf(282,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ app ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(1936,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[604,261]) ).
thf(1937,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf82 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1936]) ).
thf(1938,plain,
! [A: $i] :
~ ( A @ skaf82 @ ( A @ skaf82 @ neq ) ),
inference(pattern_uni,[status(thm)],[1937:[bind(A,$thf( C )),bind(B,$thf( C @ skaf82 ))]]) ).
thf(1941,plain,
! [A: $i] :
~ ( A @ skaf82 @ ( A @ skaf82 @ neq ) ),
inference(simp,[status(thm)],[1938]) ).
thf(738,plain,
( ( nil != nil )
| ( sk2 @ strictorderP )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,324]) ).
thf(739,plain,
( ( sk2 @ strictorderP )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[738:[]]) ).
thf(20976,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[510,317]) ).
thf(20977,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf52 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[20976]) ).
thf(20978,plain,
! [A: $i] : ( nil @ ( A @ skaf52 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[20977:[bind(A,$thf( C )),bind(B,$thf( C @ skaf52 ))]]) ).
thf(21039,plain,
! [A: $i] : ( nil @ ( A @ skaf52 @ rearsegP ) ),
inference(simp,[status(thm)],[20978]) ).
thf(408,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( ( B @ ( A @ app ) )
!= nil ) ),
inference(cnf,[status(esa)],[407]) ).
thf(409,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ( nil = B )
| ( ( B @ ( A @ app ) )
!= nil ) ),
inference(lifteq,[status(thm)],[408]) ).
thf(98,axiom,
! [A: $i] : ( A @ skaf61 @ ssList ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause34) ).
thf(427,plain,
! [A: $i] : ( A @ skaf61 @ ssList ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(36017,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[427,363]) ).
thf(36018,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[36017]) ).
thf(36019,plain,
! [A: $i] :
( ( A @ skaf61 @ ( nil @ app ) )
= ( A @ skaf61 ) ),
inference(pattern_uni,[status(thm)],[36018:[bind(A,$thf( C )),bind(B,$thf( C @ skaf61 ))]]) ).
thf(36095,plain,
! [A: $i] :
( ( A @ skaf61 @ ( nil @ app ) )
= ( A @ skaf61 ) ),
inference(simp,[status(thm)],[36019]) ).
thf(154,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ app ) @ tl )
= ( A @ ( B @ tl @ app ) ) )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause133) ).
thf(557,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)],[154]) ).
thf(32564,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[419,353]) ).
thf(32565,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[32564]) ).
thf(32566,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[32565:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(32638,plain,
! [A: $i] : ( nil @ ( A @ skaf69 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[32566]) ).
thf(64549,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[660,398]) ).
thf(64550,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[64549]) ).
thf(64551,plain,
! [A: $i] : ( A @ skaf59 @ ( A @ skaf59 @ geq ) ),
inference(pattern_uni,[status(thm)],[64550:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(64629,plain,
! [A: $i] : ( A @ skaf59 @ ( A @ skaf59 @ geq ) ),
inference(simp,[status(thm)],[64551]) ).
thf(19997,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[599,311]) ).
thf(19998,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[19997]) ).
thf(19999,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( A @ skaf83 @ neq ) ),
inference(pattern_uni,[status(thm)],[19998:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(20044,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( A @ skaf83 @ neq ) ),
inference(simp,[status(thm)],[19999]) ).
thf(20916,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[522,317]) ).
thf(20917,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[20916]) ).
thf(20918,plain,
! [A: $i] : ( nil @ ( A @ skaf67 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[20917:[bind(A,$thf( C )),bind(B,$thf( C @ skaf67 ))]]) ).
thf(21041,plain,
! [A: $i] : ( nil @ ( A @ skaf67 @ rearsegP ) ),
inference(simp,[status(thm)],[20918]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ gt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause105) ).
thf(358,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(359,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ gt ) ) ),
inference(cnf,[status(esa)],[358]) ).
thf(62232,plain,
( ( nil != nil )
| ~ ( sk1 @ singletonP )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[26600,517]) ).
thf(62233,plain,
( ~ ( sk1 @ singletonP )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[62232:[]]) ).
thf(35861,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[522,363]) ).
thf(35862,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[35861]) ).
thf(35863,plain,
! [A: $i] :
( ( A @ skaf67 @ ( nil @ app ) )
= ( A @ skaf67 ) ),
inference(pattern_uni,[status(thm)],[35862:[bind(A,$thf( C )),bind(B,$thf( C @ skaf67 ))]]) ).
thf(36063,plain,
! [A: $i] :
( ( A @ skaf67 @ ( nil @ app ) )
= ( A @ skaf67 ) ),
inference(simp,[status(thm)],[35863]) ).
thf(904,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[277,261]) ).
thf(905,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf72 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[904]) ).
thf(906,plain,
! [A: $i] :
~ ( A @ skaf72 @ ( A @ skaf72 @ neq ) ),
inference(pattern_uni,[status(thm)],[905:[bind(A,$thf( C )),bind(B,$thf( C @ skaf72 ))]]) ).
thf(907,plain,
! [A: $i] :
~ ( A @ skaf72 @ ( A @ skaf72 @ neq ) ),
inference(simp,[status(thm)],[906]) ).
thf(11914,plain,
( ( nil != nil )
| ( sk2 @ ( nil @ segmentP ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,11905]) ).
thf(11915,plain,
( ( sk2 @ ( nil @ segmentP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[11914:[]]) ).
thf(2264,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[424,2251]) ).
thf(2265,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf70 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[2264]) ).
thf(2266,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[2265:[bind(A,$thf( C )),bind(B,$thf( C @ skaf70 ))]]) ).
thf(2337,plain,
! [A: $i] : ( nil @ ( A @ skaf70 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[2266]) ).
thf(9252,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ~ $true
| ( nil = sk1 )
| ( nil = sk1 ) ),
inference(paramod_ordered,[status(thm)],[835,827]) ).
thf(9253,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( nil = sk1 ) ),
inference(simp,[status(thm)],[9252]) ).
thf(9299,plain,
( ( sk9 != sk9 )
| ( nil != sk2 )
| ( nil = sk1 ) ),
inference(simp,[status(thm)],[9253]) ).
thf(9313,plain,
( ( nil != sk2 )
| ( nil = sk1 ) ),
inference(simp,[status(thm)],[9299]) ).
thf(807,plain,
( ( nil != nil )
| ~ ( sk6 @ ( sk1 @ memberP ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[788,675]) ).
thf(808,plain,
( ~ ( sk6 @ ( sk1 @ memberP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[807:[]]) ).
thf(35844,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[372,363]) ).
thf(35845,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[35844]) ).
thf(35846,plain,
! [A: $i] :
( ( A @ skaf58 @ ( nil @ app ) )
= ( A @ skaf58 ) ),
inference(pattern_uni,[status(thm)],[35845:[bind(A,$thf( C )),bind(B,$thf( C @ skaf58 ))]]) ).
thf(36061,plain,
! [A: $i] :
( ( A @ skaf58 @ ( nil @ app ) )
= ( A @ skaf58 ) ),
inference(simp,[status(thm)],[35846]) ).
thf(59,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause67) ).
thf(336,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(238,plain,
( ( nil = sk4 )
| ( ( nil @ ( sk9 @ cons ) )
= sk3 ) ),
inference(cnf,[status(esa)],[225]) ).
thf(239,plain,
( ( nil = sk4 )
| ( ( nil @ ( sk9 @ cons ) )
= sk3 ) ),
inference(lifteq,[status(thm)],[238]) ).
thf(1257,plain,
( ( nil = sk2 )
| ( ( nil @ ( sk9 @ cons ) )
= sk1 ) ),
inference(rewrite,[status(thm)],[239,235,237]) ).
thf(1279,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[427,261]) ).
thf(1280,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1279]) ).
thf(1281,plain,
! [A: $i] :
~ ( A @ skaf61 @ ( A @ skaf61 @ neq ) ),
inference(pattern_uni,[status(thm)],[1280:[bind(A,$thf( C )),bind(B,$thf( C @ skaf61 ))]]) ).
thf(1284,plain,
! [A: $i] :
~ ( A @ skaf61 @ ( A @ skaf61 @ neq ) ),
inference(simp,[status(thm)],[1281]) ).
thf(173,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ lt ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause121) ).
thf(600,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)],[173]) ).
thf(20000,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[419,311]) ).
thf(20001,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf69 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[20000]) ).
thf(20002,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( A @ skaf69 @ neq ) ),
inference(pattern_uni,[status(thm)],[20001:[bind(A,$thf( C )),bind(B,$thf( C @ skaf69 ))]]) ).
thf(20030,plain,
! [A: $i] :
~ ( A @ skaf69 @ ( A @ skaf69 @ neq ) ),
inference(simp,[status(thm)],[20002]) ).
thf(14381,plain,
( ( nil != nil )
| ( sk2 @ ( sk1 @ rearsegP ) )
| ( sk9 @ ssItem )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,11871]) ).
thf(14382,plain,
( ( nil != nil )
| ( sk2 @ ( sk1 @ rearsegP ) )
| ( sk9 @ ssItem ) ),
inference(simp,[status(thm)],[14381]) ).
thf(14383,plain,
( ( sk2 @ ( sk1 @ rearsegP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[14382:[]]) ).
thf(180,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D = B )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ( ( B @ ( A @ cons ) )
!= ( D @ ( C @ cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause171) ).
thf(612,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)],[180]) ).
thf(20891,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf43 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[249,317]) ).
thf(20892,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf43 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[20891]) ).
thf(20893,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf43 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[20892:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf43 ) ))]]) ).
thf(21028,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf43 ) @ rearsegP ) ),
inference(simp,[status(thm)],[20893]) ).
thf(33805,plain,
( ( nil != nil )
| ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[19996,717]) ).
thf(33806,plain,
( ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[33805:[]]) ).
thf(33719,plain,
( ( nil != nil )
| ~ ( sk5 @ ( sk2 @ memberP ) )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[19996,672]) ).
thf(33720,plain,
( ~ ( sk5 @ ( sk2 @ memberP ) )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[33719:[]]) ).
thf(31352,plain,
( ( nil != nil )
| ( sk2 @ totalorderP )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[18763,500]) ).
thf(31353,plain,
( ( sk2 @ totalorderP )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[31352:[]]) ).
thf(64609,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[603,398]) ).
thf(64610,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf74 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[64609]) ).
thf(64611,plain,
! [A: $i] : ( A @ skaf74 @ ( A @ skaf74 @ geq ) ),
inference(pattern_uni,[status(thm)],[64610:[bind(A,$thf( C )),bind(B,$thf( C @ skaf74 ))]]) ).
thf(64626,plain,
! [A: $i] : ( A @ skaf74 @ ( A @ skaf74 @ geq ) ),
inference(simp,[status(thm)],[64611]) ).
thf(109,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause110) ).
thf(450,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(29734,plain,
( ( nil != nil )
| ( sk7 @ strictorderedP )
| ( sk7 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[18150,646]) ).
thf(29735,plain,
( ( sk7 @ strictorderedP )
| ( sk7 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[29734:[]]) ).
thf(21210,plain,
( ( nil != nil )
| ( sk2 @ ( sk2 @ segmentP ) )
| ( sk9 @ ssItem )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,11913]) ).
thf(21211,plain,
( ( nil != nil )
| ( sk2 @ ( sk2 @ segmentP ) )
| ( sk9 @ ssItem ) ),
inference(simp,[status(thm)],[21210]) ).
thf(21212,plain,
( ( sk2 @ ( sk2 @ segmentP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[21211:[]]) ).
thf(148,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ memberP ) )
| ~ ( D @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ( ( C @ ( B @ cons ) @ ( A @ app ) )
!= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause175) ).
thf(539,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)],[148]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = A )
| ( C @ ( B @ memberP ) )
| ~ ( C @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( C @ ( B @ ( A @ cons ) @ memberP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause161) ).
thf(482,plain,
! [C: $i,B: $i,A: $i] :
( ( C = A )
| ( C @ ( B @ memberP ) )
| ~ ( C @ ssItem )
| ~ ( A @ ssItem )
| ~ ( B @ ssList )
| ~ ( C @ ( B @ ( A @ cons ) @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(1908,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[599,463]) ).
thf(1909,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[1908]) ).
thf(1910,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[1909:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(1913,plain,
! [A: $i] :
~ ( A @ skaf83 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[1910]) ).
thf(900,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[262,261]) ).
thf(901,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[900]) ).
thf(902,plain,
! [A: $i] :
~ ( A @ skaf62 @ ( A @ skaf62 @ neq ) ),
inference(pattern_uni,[status(thm)],[901:[bind(A,$thf( C )),bind(B,$thf( C @ skaf62 ))]]) ).
thf(903,plain,
! [A: $i] :
~ ( A @ skaf62 @ ( A @ skaf62 @ neq ) ),
inference(simp,[status(thm)],[902]) ).
thf(20009,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[608,311]) ).
thf(20010,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf65 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[20009]) ).
thf(20011,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( A @ skaf65 @ neq ) ),
inference(pattern_uni,[status(thm)],[20010:[bind(A,$thf( C )),bind(B,$thf( C @ skaf65 ))]]) ).
thf(20035,plain,
! [A: $i] :
~ ( A @ skaf65 @ ( A @ skaf65 @ neq ) ),
inference(simp,[status(thm)],[20011]) ).
thf(3,negated_conjecture,
sk3 @ ssList,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
thf(218,plain,
sk3 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2289,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[599,2251]) ).
thf(2290,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[2289]) ).
thf(2291,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[2290:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(2342,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[2291]) ).
thf(367,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ hd )
= A )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[366]) ).
thf(368,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) @ hd )
= A ) ),
inference(lifteq,[status(thm)],[367]) ).
thf(19988,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[618,311]) ).
thf(19989,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[19988]) ).
thf(19990,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( A @ skaf50 @ neq ) ),
inference(pattern_uni,[status(thm)],[19989:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(20040,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( A @ skaf50 @ neq ) ),
inference(simp,[status(thm)],[19990]) ).
thf(35867,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[615,363]) ).
thf(35868,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[35867]) ).
thf(35869,plain,
! [A: $i] :
( ( A @ skaf56 @ ( nil @ app ) )
= ( A @ skaf56 ) ),
inference(pattern_uni,[status(thm)],[35868:[bind(A,$thf( C )),bind(B,$thf( C @ skaf56 ))]]) ).
thf(36065,plain,
! [A: $i] :
( ( A @ skaf56 @ ( nil @ app ) )
= ( A @ skaf56 ) ),
inference(simp,[status(thm)],[35869]) ).
thf(2700,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[622,261]) ).
thf(2701,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf71 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[2700]) ).
thf(2702,plain,
! [A: $i] :
~ ( A @ skaf71 @ ( A @ skaf71 @ neq ) ),
inference(pattern_uni,[status(thm)],[2701:[bind(A,$thf( C )),bind(B,$thf( C @ skaf71 ))]]) ).
thf(2707,plain,
! [A: $i] :
~ ( A @ skaf71 @ ( A @ skaf71 @ neq ) ),
inference(simp,[status(thm)],[2702]) ).
thf(64582,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[599,398]) ).
thf(64583,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[64582]) ).
thf(64584,plain,
! [A: $i] : ( A @ skaf83 @ ( A @ skaf83 @ geq ) ),
inference(pattern_uni,[status(thm)],[64583:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(64619,plain,
! [A: $i] : ( A @ skaf83 @ ( A @ skaf83 @ geq ) ),
inference(simp,[status(thm)],[64584]) ).
thf(18838,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[210,304]) ).
thf(18839,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ tl @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[18838]) ).
thf(18840,plain,
( ( sk1 @ tl @ ssList )
| ( nil = sk1 ) ),
inference(pattern_uni,[status(thm)],[18839:[bind(A,$thf( sk1 ))]]) ).
thf(20905,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[372,317]) ).
thf(20906,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf58 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[20905]) ).
thf(20907,plain,
! [A: $i] : ( nil @ ( A @ skaf58 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[20906:[bind(A,$thf( C )),bind(B,$thf( C @ skaf58 ))]]) ).
thf(21036,plain,
! [A: $i] : ( nil @ ( A @ skaf58 @ rearsegP ) ),
inference(simp,[status(thm)],[20907]) ).
thf(349,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ rearsegP ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
!= C ) ),
inference(cnf,[status(esa)],[348]) ).
thf(350,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ rearsegP ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
!= C ) ),
inference(lifteq,[status(thm)],[349]) ).
thf(351,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ app ) @ rearsegP ) )
| ~ ( B @ ( A @ app ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[350]) ).
thf(388,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)],[387]) ).
thf(389,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)],[388]) ).
thf(390,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)],[389]) ).
thf(400,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)],[399]) ).
thf(401,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)],[400]) ).
thf(20898,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf48 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[449,317]) ).
thf(20899,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf48 ) @ ssList )
!= ( C @ ssList ) )
| ( nil @ ( C @ rearsegP ) ) ),
inference(simp,[status(thm)],[20898]) ).
thf(20900,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf48 ) @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[20899:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf48 ) ))]]) ).
thf(21032,plain,
! [B: $i,A: $i] : ( nil @ ( B @ ( A @ skaf48 ) @ rearsegP ) ),
inference(simp,[status(thm)],[20900]) ).
thf(58300,plain,
( ( ( sk7 @ ( nil @ rearsegP ) )
!= ( nil @ ( sk7 @ rearsegP ) ) )
| ~ ( sk7 @ singletonP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20933,49016]) ).
thf(58301,plain,
( ( ( sk7 @ ( nil @ rearsegP ) )
!= ( nil @ ( sk7 @ rearsegP ) ) )
| ~ ( sk7 @ singletonP ) ),
inference(simp,[status(thm)],[58300]) ).
thf(58318,plain,
( ( nil != sk7 )
| ( nil != sk7 )
| ~ ( sk7 @ singletonP ) ),
inference(simp,[status(thm)],[58301]) ).
thf(58366,plain,
( ( nil != sk7 )
| ~ ( sk7 @ singletonP ) ),
inference(simp,[status(thm)],[58318]) ).
thf(32527,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[420,353]) ).
thf(32528,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf55 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[32527]) ).
thf(32529,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[32528:[bind(A,$thf( C )),bind(B,$thf( C @ skaf55 ))]]) ).
thf(32630,plain,
! [A: $i] : ( nil @ ( A @ skaf55 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[32529]) ).
thf(33320,plain,
( ( nil != nil )
| ~ ( nil @ ( sk1 @ neq ) )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[19984,717]) ).
thf(33321,plain,
( ~ ( nil @ ( sk1 @ neq ) )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[33320:[]]) ).
thf(34931,plain,
( ( sk2 != sk2 )
| ~ ( sk2 @ ( sk1 @ neq ) )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[20005,729]) ).
thf(34932,plain,
( ~ ( sk2 @ ( sk1 @ neq ) )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[34931:[]]) ).
thf(29872,plain,
( ( nil != nil )
| ( sk7 @ equalelemsP )
| ( sk7 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[18150,343]) ).
thf(29873,plain,
( ( sk7 @ equalelemsP )
| ( sk7 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[29872:[]]) ).
thf(2304,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[431,2251]) ).
thf(2305,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[2304]) ).
thf(2306,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[2305:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(2330,plain,
! [A: $i] : ( nil @ ( A @ skaf60 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[2306]) ).
thf(21092,plain,
( ( nil != nil )
| ( sk1 @ ( sk8 @ rearsegP ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[788,20981]) ).
thf(21093,plain,
( ( sk1 @ ( sk8 @ rearsegP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[21092:[]]) ).
thf(32513,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[660,353]) ).
thf(32514,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf59 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[32513]) ).
thf(32515,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[32514:[bind(A,$thf( C )),bind(B,$thf( C @ skaf59 ))]]) ).
thf(32627,plain,
! [A: $i] : ( nil @ ( A @ skaf59 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[32515]) ).
thf(13272,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ~ $true
| ( sk2 = sk1 )
| ( sk2 = sk1 ) ),
inference(paramod_ordered,[status(thm)],[890,1389]) ).
thf(13273,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( sk2 = sk1 ) ),
inference(simp,[status(thm)],[13272]) ).
thf(13370,plain,
( ( sk9 != sk9 )
| ( nil != sk2 )
| ( sk2 = sk1 ) ),
inference(simp,[status(thm)],[13273]) ).
thf(13389,plain,
( ( nil != sk2 )
| ( sk2 = sk1 ) ),
inference(simp,[status(thm)],[13370]) ).
thf(289,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)],[288]) ).
thf(290,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)],[289]) ).
thf(35882,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[476,363]) ).
thf(35883,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[35882]) ).
thf(35884,plain,
! [A: $i] :
( ( A @ skaf53 @ ( nil @ app ) )
= ( A @ skaf53 ) ),
inference(pattern_uni,[status(thm)],[35883:[bind(A,$thf( C )),bind(B,$thf( C @ skaf53 ))]]) ).
thf(36069,plain,
! [A: $i] :
( ( A @ skaf53 @ ( nil @ app ) )
= ( A @ skaf53 ) ),
inference(simp,[status(thm)],[35884]) ).
thf(35893,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[412,363]) ).
thf(35894,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[35893]) ).
thf(35895,plain,
! [A: $i] :
( ( A @ skaf73 @ ( nil @ app ) )
= ( A @ skaf73 ) ),
inference(pattern_uni,[status(thm)],[35894:[bind(A,$thf( C )),bind(B,$thf( C @ skaf73 ))]]) ).
thf(36071,plain,
! [A: $i] :
( ( A @ skaf73 @ ( nil @ app ) )
= ( A @ skaf73 ) ),
inference(simp,[status(thm)],[35895]) ).
thf(287,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( A @ ssItem )
| ~ ( B @ ssItem )
| ~ ( B @ ( A @ geq ) ) ),
inference(cnf,[status(esa)],[286]) ).
thf(751,plain,
( ( nil != nil )
| ( sk2 @ totalorderP )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,500]) ).
thf(752,plain,
( ( sk2 @ totalorderP )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[751:[]]) ).
thf(107,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ frontsegP ) )
| ~ ( A @ ssItem )
| ~ ( C @ ssItem )
| ~ ( B @ ssList )
| ~ ( D @ ssList )
| ~ ( D @ ( C @ cons ) @ ( B @ ( A @ cons ) @ frontsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause174) ).
thf(447,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)],[107]) ).
thf(314,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ skaf45 ) @ ( B @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ frontsegP ) ) ),
inference(cnf,[status(esa)],[313]) ).
thf(315,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ frontsegP ) )
| ( ( B @ ( A @ skaf45 ) @ ( B @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[314]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ app ) @ frontsegP ) )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause137) ).
thf(432,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)],[101]) ).
thf(864,plain,
( ( nil != nil )
| ( sk1 @ totalorderP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[835,500]) ).
thf(865,plain,
( ( sk1 @ totalorderP )
| ( sk9 @ ( sk2 @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[864:[]]) ).
thf(20791,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( sk1 @ totalorderP )
| ~ $true
| ( sk1 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[865,9067]) ).
thf(20792,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ( sk1 @ totalorderP ) ),
inference(simp,[status(thm)],[20791]) ).
thf(20810,plain,
( ( sk9 != sk9 )
| ( nil != sk2 )
| ( sk1 @ totalorderP ) ),
inference(simp,[status(thm)],[20792]) ).
thf(20831,plain,
( ( nil != sk2 )
| ( sk1 @ totalorderP ) ),
inference(simp,[status(thm)],[20810]) ).
thf(817,plain,
( ( nil != nil )
| ( sk1 @ cyclefreeP )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[788,505]) ).
thf(818,plain,
( ( sk1 @ cyclefreeP )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[817:[]]) ).
thf(789,plain,
( ( nil != nil )
| ~ ( skac2 @ ( sk1 @ memberP ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[788,709]) ).
thf(790,plain,
( ~ ( skac2 @ ( sk1 @ memberP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[789:[]]) ).
thf(272,plain,
! [A: $i] :
( ( ( nil @ ( A @ skaf44 @ cons ) )
= A )
| ~ ( A @ ssList )
| ~ ( A @ singletonP ) ),
inference(cnf,[status(esa)],[271]) ).
thf(273,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ~ ( A @ singletonP )
| ( ( nil @ ( A @ skaf44 @ cons ) )
= A ) ),
inference(lifteq,[status(thm)],[272]) ).
thf(734,plain,
( ( nil != nil )
| ~ ( skac2 @ ( sk2 @ memberP ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,709]) ).
thf(735,plain,
( ~ ( skac2 @ ( sk2 @ memberP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[734:[]]) ).
thf(64600,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[431,398]) ).
thf(64601,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf60 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[64600]) ).
thf(64602,plain,
! [A: $i] : ( A @ skaf60 @ ( A @ skaf60 @ geq ) ),
inference(pattern_uni,[status(thm)],[64601:[bind(A,$thf( C )),bind(B,$thf( C @ skaf60 ))]]) ).
thf(64623,plain,
! [A: $i] : ( A @ skaf60 @ ( A @ skaf60 @ geq ) ),
inference(simp,[status(thm)],[64602]) ).
thf(2740,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[638,463]) ).
thf(2741,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf78 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2740]) ).
thf(2742,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2741:[bind(A,$thf( C )),bind(B,$thf( C @ skaf78 ))]]) ).
thf(2751,plain,
! [A: $i] :
~ ( A @ skaf78 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2742]) ).
thf(20996,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[427,317]) ).
thf(20997,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf61 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[20996]) ).
thf(20998,plain,
! [A: $i] : ( nil @ ( A @ skaf61 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[20997:[bind(A,$thf( C )),bind(B,$thf( C @ skaf61 ))]]) ).
thf(21015,plain,
! [A: $i] : ( nil @ ( A @ skaf61 @ rearsegP ) ),
inference(simp,[status(thm)],[20998]) ).
thf(1308,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[461,261]) ).
thf(1309,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf80 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1308]) ).
thf(1310,plain,
! [A: $i] :
~ ( A @ skaf80 @ ( A @ skaf80 @ neq ) ),
inference(pattern_uni,[status(thm)],[1309:[bind(A,$thf( C )),bind(B,$thf( C @ skaf80 ))]]) ).
thf(1314,plain,
! [A: $i] :
~ ( A @ skaf80 @ ( A @ skaf80 @ neq ) ),
inference(simp,[status(thm)],[1310]) ).
thf(64573,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[618,398]) ).
thf(64574,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[64573]) ).
thf(64575,plain,
! [A: $i] : ( A @ skaf50 @ ( A @ skaf50 @ geq ) ),
inference(pattern_uni,[status(thm)],[64574:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(64633,plain,
! [A: $i] : ( A @ skaf50 @ ( A @ skaf50 @ geq ) ),
inference(simp,[status(thm)],[64575]) ).
thf(103,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( A @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause129) ).
thf(437,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)],[103]) ).
thf(120,axiom,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf55 @ ( A @ skaf54 @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause95) ).
thf(474,plain,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf55 @ ( A @ skaf54 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(204,axiom,
! [A: $i] :
( ( A @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause61) ).
thf(664,plain,
! [A: $i] :
( ( A @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(192,axiom,
! [A: $i] :
( ( A @ equalelemsP )
| ~ ( A @ ssList )
| ( ( A @ skaf79 )
!= ( A @ skaf78 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause89) ).
thf(635,plain,
! [A: $i] :
( ( A @ equalelemsP )
| ~ ( A @ ssList )
| ( ( A @ skaf79 )
!= ( A @ skaf78 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(31333,plain,
( ( nil != nil )
| ( sk2 != sk2 )
| ( sk1 @ strictorderP )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[18763,22069]) ).
thf(31334,plain,
( ( nil != nil )
| ( sk1 @ strictorderP )
| ( sk2 @ tl @ ssList ) ),
inference(simp,[status(thm)],[31333]) ).
thf(31335,plain,
( ( sk1 @ strictorderP )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[31334:[]]) ).
thf(158,axiom,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause78) ).
thf(564,plain,
! [A: $i] :
( ( nil = A )
| ( A @ hd @ ssItem )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(29683,plain,
( ( nil != nil )
| ( sk7 @ totalorderP )
| ( sk7 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[18150,500]) ).
thf(29684,plain,
( ( sk7 @ totalorderP )
| ( sk7 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[29683:[]]) ).
thf(1431,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[476,261]) ).
thf(1432,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf53 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1431]) ).
thf(1433,plain,
! [A: $i] :
~ ( A @ skaf53 @ ( A @ skaf53 @ neq ) ),
inference(pattern_uni,[status(thm)],[1432:[bind(A,$thf( C )),bind(B,$thf( C @ skaf53 ))]]) ).
thf(1436,plain,
! [A: $i] :
~ ( A @ skaf53 @ ( A @ skaf53 @ neq ) ),
inference(simp,[status(thm)],[1433]) ).
thf(33660,plain,
( ( nil != nil )
| ~ ( skac3 @ ( sk2 @ memberP ) )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[19996,732]) ).
thf(33661,plain,
( ~ ( skac3 @ ( sk2 @ memberP ) )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[33660:[]]) ).
thf(292,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)],[291]) ).
thf(293,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)],[292]) ).
thf(294,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)],[293]) ).
thf(2195,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[618,463]) ).
thf(2196,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf50 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[2195]) ).
thf(2197,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[2196:[bind(A,$thf( C )),bind(B,$thf( C @ skaf50 ))]]) ).
thf(2201,plain,
! [A: $i] :
~ ( A @ skaf50 @ ( nil @ memberP ) ),
inference(simp,[status(thm)],[2197]) ).
thf(341,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ~ ( A @ skaf59 @ ( A @ skaf60 @ lt ) ) ),
inference(cnf,[status(esa)],[340]) ).
thf(1810,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[522,261]) ).
thf(1811,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf67 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1810]) ).
thf(1812,plain,
! [A: $i] :
~ ( A @ skaf67 @ ( A @ skaf67 @ neq ) ),
inference(pattern_uni,[status(thm)],[1811:[bind(A,$thf( C )),bind(B,$thf( C @ skaf67 ))]]) ).
thf(1816,plain,
! [A: $i] :
~ ( A @ skaf67 @ ( A @ skaf67 @ neq ) ),
inference(simp,[status(thm)],[1812]) ).
thf(33344,plain,
( ( nil != nil )
| ~ ( sk1 @ singletonP )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[19984,517]) ).
thf(33345,plain,
( ~ ( sk1 @ singletonP )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[33344:[]]) ).
thf(135,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ leq ) )
| ( D @ ( B @ leq ) )
| ~ ( F @ ssList )
| ~ ( F @ totalorderP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause184) ).
thf(506,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ leq ) )
| ( D @ ( B @ leq ) )
| ~ ( F @ ssList )
| ~ ( F @ totalorderP )
| ~ ( B @ ssItem )
| ~ ( D @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( E @ ssList )
| ( ( E @ ( D @ cons ) @ ( C @ ( B @ cons ) @ ( A @ app ) @ app ) )
!= F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(268,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf70 @ ( A @ skaf69 @ lt ) ) ),
inference(cnf,[status(esa)],[267]) ).
thf(5269,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf46 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ~ ( C @ ( C @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[295,261]) ).
thf(5270,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf46 ) @ ssList )
!= ( C @ ssList ) )
| ~ ( C @ ( C @ neq ) ) ),
inference(simp,[status(thm)],[5269]) ).
thf(5271,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf46 ) @ ( B @ ( A @ skaf46 ) @ neq ) ),
inference(pattern_uni,[status(thm)],[5270:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf46 ) ))]]) ).
thf(5290,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf46 ) @ ( B @ ( A @ skaf46 ) @ neq ) ),
inference(simp,[status(thm)],[5271]) ).
thf(718,plain,
! [A: $i] :
( ( ( sk7 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[212,261]) ).
thf(719,plain,
! [A: $i] :
( ( ( sk7 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[718]) ).
thf(720,plain,
~ ( sk7 @ ( sk7 @ neq ) ),
inference(pattern_uni,[status(thm)],[719:[bind(A,$thf( sk7 ))]]) ).
thf(2278,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[296,2251]) ).
thf(2279,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf64 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[2278]) ).
thf(2280,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ totalorderedP ),
inference(pattern_uni,[status(thm)],[2279:[bind(A,$thf( C )),bind(B,$thf( C @ skaf64 ))]]) ).
thf(2340,plain,
! [A: $i] : ( nil @ ( A @ skaf64 @ cons ) @ totalorderedP ),
inference(simp,[status(thm)],[2280]) ).
thf(795,plain,
( ( nil != nil )
| ( sk1 @ strictorderP )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[788,324]) ).
thf(796,plain,
( ( sk1 @ strictorderP )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[795:[]]) ).
thf(283,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ app ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[282]) ).
thf(331,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)],[330]) ).
thf(332,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)],[331]) ).
thf(1820,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[528,261]) ).
thf(1821,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf81 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1820]) ).
thf(1822,plain,
! [A: $i] :
~ ( A @ skaf81 @ ( A @ skaf81 @ neq ) ),
inference(pattern_uni,[status(thm)],[1821:[bind(A,$thf( C )),bind(B,$thf( C @ skaf81 ))]]) ).
thf(1827,plain,
! [A: $i] :
~ ( A @ skaf81 @ ( A @ skaf81 @ neq ) ),
inference(simp,[status(thm)],[1822]) ).
thf(163,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ app ) @ memberP ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ( A @ memberP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause140) ).
thf(575,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)],[163]) ).
thf(821,plain,
( ( nil != nil )
| ~ ( sk1 @ ( nil @ neq ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[788,717]) ).
thf(822,plain,
( ~ ( sk1 @ ( nil @ neq ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[821:[]]) ).
thf(5307,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ~ ( sk2 @ singletonP )
| ~ $true
| ~ ( sk2 @ singletonP ) ),
inference(paramod_ordered,[status(thm)],[694,4967]) ).
thf(5308,plain,
( ( ( sk9 @ ( nil @ memberP ) )
!= ( sk9 @ ( sk2 @ memberP ) ) )
| ~ ( sk2 @ singletonP ) ),
inference(simp,[status(thm)],[5307]) ).
thf(5341,plain,
( ( sk9 != sk9 )
| ( nil != sk2 )
| ~ ( sk2 @ singletonP ) ),
inference(simp,[status(thm)],[5308]) ).
thf(5354,plain,
( ( nil != sk2 )
| ~ ( sk2 @ singletonP ) ),
inference(simp,[status(thm)],[5341]) ).
thf(132,axiom,
! [A: $i] :
( ( nil @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause60) ).
thf(501,plain,
! [A: $i] :
( ( nil @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(64981,plain,
( ( ( nil @ ( nil @ rearsegP ) )
!= ( sk1 @ ( nil @ rearsegP ) ) )
| ~ ( sk1 @ singletonP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11867,62233]) ).
thf(64982,plain,
( ( ( nil @ ( nil @ rearsegP ) )
!= ( sk1 @ ( nil @ rearsegP ) ) )
| ~ ( sk1 @ singletonP ) ),
inference(simp,[status(thm)],[64981]) ).
thf(65032,plain,
( ( nil != sk1 )
| ( nil != nil )
| ~ ( sk1 @ singletonP ) ),
inference(simp,[status(thm)],[64982]) ).
thf(65050,plain,
( ( nil != sk1 )
| ~ ( sk1 @ singletonP ) ),
inference(simp,[status(thm)],[65032]) ).
thf(24014,plain,
( ( nil != nil )
| ( sk1 @ ( sk2 @ frontsegP ) )
| ( sk9 @ ssItem )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,13138]) ).
thf(24015,plain,
( ( nil != nil )
| ( sk1 @ ( sk2 @ frontsegP ) )
| ( sk9 @ ssItem ) ),
inference(simp,[status(thm)],[24014]) ).
thf(24016,plain,
( ( sk1 @ ( sk2 @ frontsegP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[24015:[]]) ).
thf(116,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ equalelemsP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause64) ).
thf(464,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ equalelemsP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(9122,plain,
( ( nil != nil )
| ~ ( sk1 @ ( sk2 @ neq ) )
| ~ ( sk9 @ ( nil @ memberP ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(paramod_ordered,[status(thm)],[827,4953]) ).
thf(9123,plain,
( ( nil != nil )
| ~ ( sk1 @ ( sk2 @ neq ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[9122]) ).
thf(9124,plain,
( ~ ( sk1 @ ( sk2 @ neq ) )
| ~ ( sk9 @ ( nil @ memberP ) ) ),
inference(pattern_uni,[status(thm)],[9123:[]]) ).
thf(721,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[210,261]) ).
thf(722,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[721]) ).
thf(723,plain,
~ ( sk1 @ ( sk1 @ neq ) ),
inference(pattern_uni,[status(thm)],[722:[bind(A,$thf( sk1 ))]]) ).
thf(64552,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[452,398]) ).
thf(64553,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf49 @ ssItem )
!= ( B @ ssItem ) )
| ( B @ ( B @ geq ) ) ),
inference(simp,[status(thm)],[64552]) ).
thf(64554,plain,
! [A: $i] : ( A @ skaf49 @ ( A @ skaf49 @ geq ) ),
inference(pattern_uni,[status(thm)],[64553:[bind(A,$thf( C )),bind(B,$thf( C @ skaf49 ))]]) ).
thf(64630,plain,
! [A: $i] : ( A @ skaf49 @ ( A @ skaf49 @ geq ) ),
inference(simp,[status(thm)],[64554]) ).
thf(32496,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[217,353]) ).
thf(32497,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[32496]) ).
thf(32498,plain,
nil @ ( sk5 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[32497:[bind(A,$thf( sk5 ))]]) ).
thf(20698,plain,
( ( nil != nil )
| ( sk1 @ ( sk2 @ segmentP ) )
| ( sk9 @ ssItem )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[733,11911]) ).
thf(20699,plain,
( ( nil != nil )
| ( sk1 @ ( sk2 @ segmentP ) )
| ( sk9 @ ssItem ) ),
inference(simp,[status(thm)],[20698]) ).
thf(20700,plain,
( ( sk1 @ ( sk2 @ segmentP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[20699:[]]) ).
thf(240,plain,
( ( nil = sk3 )
| ( ( nil @ ( sk9 @ cons ) )
= sk3 ) ),
inference(cnf,[status(esa)],[219]) ).
thf(241,plain,
( ( nil = sk3 )
| ( ( nil @ ( sk9 @ cons ) )
= sk3 ) ),
inference(lifteq,[status(thm)],[240]) ).
thf(1399,plain,
( ( nil = sk1 )
| ( ( nil @ ( sk9 @ cons ) )
= sk1 ) ),
inference(rewrite,[status(thm)],[241,235]) ).
thf(32561,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[599,353]) ).
thf(32562,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf83 @ ssItem )
!= ( B @ ssItem ) )
| ( nil @ ( B @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[32561]) ).
thf(32563,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ strictorderedP ),
inference(pattern_uni,[status(thm)],[32562:[bind(A,$thf( C )),bind(B,$thf( C @ skaf83 ))]]) ).
thf(32637,plain,
! [A: $i] : ( nil @ ( A @ skaf83 @ cons ) @ strictorderedP ),
inference(simp,[status(thm)],[32563]) ).
thf(5851,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf42 ) @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ~ ( C @ ( C @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[629,261]) ).
thf(5852,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ skaf42 ) @ ssList )
!= ( C @ ssList ) )
| ~ ( C @ ( C @ neq ) ) ),
inference(simp,[status(thm)],[5851]) ).
thf(5853,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf42 ) @ ( B @ ( A @ skaf42 ) @ neq ) ),
inference(pattern_uni,[status(thm)],[5852:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ skaf42 ) ))]]) ).
thf(5877,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ skaf42 ) @ ( B @ ( A @ skaf42 ) @ neq ) ),
inference(simp,[status(thm)],[5853]) ).
thf(1366,plain,
( ( sk2 != sk2 )
| ~ ( sk1 @ ( sk2 @ neq ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[799,729]) ).
thf(1367,plain,
( ~ ( sk1 @ ( sk2 @ neq ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[1366:[]]) ).
thf(29963,plain,
( ( nil != nil )
| ( sk7 @ cyclefreeP )
| ( sk7 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[18150,505]) ).
thf(29964,plain,
( ( sk7 @ cyclefreeP )
| ( sk7 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[29963:[]]) ).
thf(149,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ app ) @ ( A @ cons ) )
= ( C @ ( B @ ( A @ cons ) @ app ) ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause157) ).
thf(543,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)],[149]) ).
thf(20937,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[412,317]) ).
thf(20938,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf73 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[20937]) ).
thf(20939,plain,
! [A: $i] : ( nil @ ( A @ skaf73 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[20938:[bind(A,$thf( C )),bind(B,$thf( C @ skaf73 ))]]) ).
thf(21018,plain,
! [A: $i] : ( nil @ ( A @ skaf73 @ rearsegP ) ),
inference(simp,[status(thm)],[20939]) ).
thf(194,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ skaf48 ) @ ( B @ ( B @ ( A @ skaf47 ) @ app ) @ app ) )
= A )
| ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause168) ).
thf(639,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)],[194]) ).
thf(21056,plain,
( ( nil != nil )
| ( sk1 @ ( sk7 @ rearsegP ) )
| ( sk9 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[788,20933]) ).
thf(21057,plain,
( ( sk1 @ ( sk7 @ rearsegP ) )
| ( sk9 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[21056:[]]) ).
thf(2171,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[615,261]) ).
thf(2172,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf56 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[2171]) ).
thf(2173,plain,
! [A: $i] :
~ ( A @ skaf56 @ ( A @ skaf56 @ neq ) ),
inference(pattern_uni,[status(thm)],[2172:[bind(A,$thf( C )),bind(B,$thf( C @ skaf56 ))]]) ).
thf(2177,plain,
! [A: $i] :
~ ( A @ skaf56 @ ( A @ skaf56 @ neq ) ),
inference(simp,[status(thm)],[2173]) ).
thf(33023,plain,
( ( nil != nil )
| ~ ( skac2 @ ( sk1 @ memberP ) )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[19984,709]) ).
thf(33024,plain,
( ~ ( skac2 @ ( sk1 @ memberP ) )
| ~ ( sk9 @ ( sk9 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[33023:[]]) ).
thf(35940,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[342,363]) ).
thf(35941,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf57 @ ssList )
!= ( B @ ssList ) )
| ( ( B @ ( nil @ app ) )
= B ) ),
inference(simp,[status(thm)],[35940]) ).
thf(35942,plain,
! [A: $i] :
( ( A @ skaf57 @ ( nil @ app ) )
= ( A @ skaf57 ) ),
inference(pattern_uni,[status(thm)],[35941:[bind(A,$thf( C )),bind(B,$thf( C @ skaf57 ))]]) ).
thf(36079,plain,
! [A: $i] :
( ( A @ skaf57 @ ( nil @ app ) )
= ( A @ skaf57 ) ),
inference(simp,[status(thm)],[35942]) ).
thf(20982,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[214,317]) ).
thf(20983,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[20982]) ).
thf(20984,plain,
nil @ ( sk2 @ rearsegP ),
inference(pattern_uni,[status(thm)],[20983:[bind(A,$thf( sk2 ))]]) ).
thf(127,axiom,
! [A: $i] :
( ( A @ totalorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf65 @ ( A @ skaf64 @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause91) ).
thf(491,plain,
! [A: $i] :
( ( A @ totalorderedP )
| ~ ( A @ ssList )
| ~ ( A @ skaf65 @ ( A @ skaf64 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(1083,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[329,261]) ).
thf(1084,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf77 @ ssList )
!= ( B @ ssList ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[1083]) ).
thf(1085,plain,
! [A: $i] :
~ ( A @ skaf77 @ ( A @ skaf77 @ neq ) ),
inference(pattern_uni,[status(thm)],[1084:[bind(A,$thf( C )),bind(B,$thf( C @ skaf77 ))]]) ).
thf(1088,plain,
! [A: $i] :
~ ( A @ skaf77 @ ( A @ skaf77 @ neq ) ),
inference(simp,[status(thm)],[1085]) ).
thf(169,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderP )
| ~ ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause69) ).
thf(592,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderP )
| ~ ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(20018,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( B @ ( B @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[386,311]) ).
thf(20019,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf44 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( B @ ( B @ neq ) ) ),
inference(simp,[status(thm)],[20018]) ).
thf(20020,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( A @ skaf44 @ neq ) ),
inference(pattern_uni,[status(thm)],[20019:[bind(A,$thf( C )),bind(B,$thf( C @ skaf44 ))]]) ).
thf(20039,plain,
! [A: $i] :
~ ( A @ skaf44 @ ( A @ skaf44 @ neq ) ),
inference(simp,[status(thm)],[20020]) ).
thf(20987,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[262,317]) ).
thf(20988,plain,
! [B: $i,A: $i] :
( ( ( A @ skaf62 @ ssList )
!= ( B @ ssList ) )
| ( nil @ ( B @ rearsegP ) ) ),
inference(simp,[status(thm)],[20987]) ).
thf(20989,plain,
! [A: $i] : ( nil @ ( A @ skaf62 @ rearsegP ) ),
inference(pattern_uni,[status(thm)],[20988:[bind(A,$thf( C )),bind(B,$thf( C @ skaf62 ))]]) ).
thf(21044,plain,
! [A: $i] : ( nil @ ( A @ skaf62 @ rearsegP ) ),
inference(simp,[status(thm)],[20989]) ).
thf(129,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause99) ).
thf(496,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( A @ cons ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(95120,plain,
$false,
inference(e,[status(thm)],[2163,64599,6085,629,2336,64631,20014,518,468,234,32643,555,666,352,365,36066,21040,32501,2341,347,21025,249,333,628,523,35996,22069,1443,30493,741,269,597,29795,1486,217,276,64539,19462,32631,308,36128,873,1205,449,440,511,9184,20145,34934,533,550,500,14084,814,21016,340,1458,30209,36070,20034,14203,782,709,841,288,301,30038,4941,829,20031,1095,404,320,36087,651,257,21017,9067,36097,11913,372,33832,619,702,344,21043,2339,357,26489,35887,11911,421,20038,416,325,316,261,4967,20981,638,284,770,216,36129,20042,1450,443,321,64627,623,485,806,1183,756,13138,30144,21029,21024,25153,211,646,348,2254,353,2335,766,397,36078,59035,221,453,774,396,660,411,29865,428,265,9272,206,1896,877,1886,35981,312,5970,307,452,661,31338,810,35852,248,36127,512,5783,61551,270,529,546,13148,9209,22645,22842,220,366,64536,36099,302,1217,820,561,424,64632,788,21030,729,33808,36131,17574,9207,297,407,30567,630,9126,252,2332,25728,329,21095,1296,461,493,28063,1195,64622,32647,324,4849,361,1365,36088,9190,583,522,1836,9132,2344,551,285,224,14380,615,403,20032,5811,32580,420,11877,32632,317,20148,30398,33178,499,21026,19984,225,339,21020,476,642,20033,489,64618,20043,27864,328,471,256,36098,28105,21042,212,706,622,647,32628,22654,21059,21038,654,1932,911,32639,9144,569,4953,371,28083,1114,11873,503,605,32622,9081,792,21013,266,311,36064,657,398,36077,2793,33274,21023,343,237,633,360,20037,36096,586,2338,298,412,750,618,425,4874,33323,264,17542,279,2260,64628,296,375,733,36076,36091,694,732,1389,286,743,36126,2716,281,13132,413,32626,402,32648,2791,11905,772,875,577,36081,30390,17737,291,19966,35984,391,26512,445,382,572,313,20005,2753,236,804,704,20041,17392,21045,6532,36062,466,335,21360,14502,672,604,20029,20036,406,219,274,19996,30320,377,567,32629,318,434,616,18150,599,5848,419,271,208,33762,1307,26600,863,890,477,387,49016,609,323,21027,64620,28103,32641,330,20992,24961,758,535,2343,816,64621,33232,594,799,213,726,33496,19969,18763,251,626,915,2329,462,30673,59037,399,278,394,563,299,19535,2303,505,21019,768,827,2139,455,32640,223,608,267,1102,431,4890,9111,675,64617,589,374,209,812,516,342,2333,355,458,24190,9170,30260,944,21031,680,9069,21022,754,9276,64624,5003,1845,776,525,580,282,887,1941,739,4894,21039,409,263,13136,36095,557,11909,295,32638,4939,64629,20044,21041,338,359,62233,36063,907,11915,717,463,2337,9313,808,36061,336,1257,1284,600,20030,14383,612,21028,33806,33720,386,31353,4838,64626,845,450,29735,21212,539,482,1913,903,20035,218,2342,368,13146,250,20040,363,36065,10376,2707,64619,517,18840,2251,304,21036,258,351,390,401,21032,58366,32630,748,11867,33321,34932,568,510,29873,207,2330,9223,478,21093,32627,13389,290,378,235,246,36069,36071,214,287,752,447,315,432,410,20831,49735,818,4843,790,273,865,735,835,262,64623,373,603,305,2751,21015,1314,64633,358,437,474,664,635,31335,564,29684,1436,210,33661,294,2201,341,1816,33345,506,268,5290,696,18740,720,2340,796,283,395,332,1827,575,427,528,822,20933,5354,4955,501,65050,4923,24016,464,9124,723,277,64630,32498,20700,1399,32637,369,607,5877,1367,354,29964,659,543,215,560,21018,639,21057,222,364,2177,33024,36079,20984,4908,676,491,1088,592,20039,21044,496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC172-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.13 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.24/0.49 % Computer : n014.cluster.edu
% 0.24/0.49 % Model : x86_64 x86_64
% 0.24/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.49 % Memory : 8046.5625MB
% 0.24/0.49 % OS : Linux 6.8.0-71-generic
% 0.13/0.49 % CPULimit : 300
% 0.13/0.49 % WCLimit : 300
% 0.13/0.49 % DateTime : Sat Sep 26 12:25:48 UTC 2026
% 0.13/0.50 % CPUTime :
% 0.13/0.50 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.35/1.21 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.38/1.65 % [INFO] Parsing done (429ms).
% 2.38/1.67 % [INFO] Running in sequential loop mode.
% 4.06/2.25 % [INFO] eprover registered as external prover.
% 4.06/2.27 % [INFO] Scanning for conjecture ...
% 4.62/2.49 % [INFO] Found a conjecture (or negated_conjecture) and 185 axioms. Running axiom selection ...
% 5.04/2.70 % [INFO] Axiom selection finished. Selected 185 axioms (removed 0 axioms).
% 6.08/2.90 % [INFO] Problem is propositional (TPTP CNF).
% 6.08/2.93 % [INFO] Type checking passed.
% 6.08/2.93 % [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 ...
% 212.32/59.03 % External prover 'e' found a proof!
% 212.32/59.03 % [INFO] Killing All external provers ...
% 212.32/59.03 % Time passed: 58331ms (effective reasoning time: 57358ms)
% 212.32/59.04 % 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
% 212.32/59.04 % No. of inferences in proof: 1733
% 212.32/59.04 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 58331 ms resp. 57358 ms w/o parsing
% 214.07/59.33 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 214.07/59.34 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------