TSTP Solution File: SWC117-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWC117-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:09:45 EDT 2023
% Result : Unsatisfiable 12.56s 3.35s
% Output : Refutation 12.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 268
% Syntax : Number of formulae : 465 ( 125 unt; 72 typ; 0 def)
% Number of atoms : 1243 ( 204 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 3768 ( 814 ~; 850 |; 0 &;2104 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 82 ( 82 >; 0 *; 0 +; 0 <<)
% Number of symbols : 74 ( 72 usr; 8 con; 0-2 aty)
% Number of variables : 654 ( 0 ^; 654 !; 0 ?; 654 :)
% Comments :
%------------------------------------------------------------------------------
thf(ssList_type,type,
ssList: $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(segmentP_type,type,
segmentP: $i > $i > $o ).
thf(equalelemsP_type,type,
equalelemsP: $i > $o ).
thf(neq_type,type,
neq: $i > $i > $o ).
thf(nil_type,type,
nil: $i ).
thf(skac3_type,type,
skac3: $i ).
thf(skac2_type,type,
skac2: $i ).
thf(leq_type,type,
leq: $i > $i > $o ).
thf(ssItem_type,type,
ssItem: $i > $o ).
thf(geq_type,type,
geq: $i > $i > $o ).
thf(lt_type,type,
lt: $i > $i > $o ).
thf(gt_type,type,
gt: $i > $i > $o ).
thf(skaf79_type,type,
skaf79: $i > $i ).
thf(skaf64_type,type,
skaf64: $i > $i ).
thf(skaf44_type,type,
skaf44: $i > $i ).
thf(skaf69_type,type,
skaf69: $i > $i ).
thf(skaf55_type,type,
skaf55: $i > $i ).
thf(skaf70_type,type,
skaf70: $i > $i ).
thf(skaf60_type,type,
skaf60: $i > $i ).
thf(skaf49_type,type,
skaf49: $i > $i ).
thf(skaf83_type,type,
skaf83: $i > $i ).
thf(skaf74_type,type,
skaf74: $i > $i ).
thf(skaf54_type,type,
skaf54: $i > $i ).
thf(skaf65_type,type,
skaf65: $i > $i ).
thf(skaf50_type,type,
skaf50: $i > $i ).
thf(skaf78_type,type,
skaf78: $i > $i ).
thf(skaf59_type,type,
skaf59: $i > $i ).
thf(skaf43_type,type,
skaf43: $i > $i > $i ).
thf(totalorderedP_type,type,
totalorderedP: $i > $o ).
thf(cons_type,type,
cons: $i > $i > $i ).
thf(skaf62_type,type,
skaf62: $i > $i ).
thf(memberP_type,type,
memberP: $i > $i > $o ).
thf(app_type,type,
app: $i > $i > $i ).
thf(strictorderedP_type,type,
strictorderedP: $i > $o ).
thf(cyclefreeP_type,type,
cyclefreeP: $i > $o ).
thf(singletonP_type,type,
singletonP: $i > $o ).
thf(duplicatefreeP_type,type,
duplicatefreeP: $i > $o ).
thf(skaf75_type,type,
skaf75: $i > $i ).
thf(skaf76_type,type,
skaf76: $i > $i ).
thf(skaf77_type,type,
skaf77: $i > $i ).
thf(skaf72_type,type,
skaf72: $i > $i ).
thf(hd_type,type,
hd: $i > $i ).
thf(frontsegP_type,type,
frontsegP: $i > $i > $o ).
thf(skaf71_type,type,
skaf71: $i > $i ).
thf(skaf73_type,type,
skaf73: $i > $i ).
thf(skaf46_type,type,
skaf46: $i > $i > $i ).
thf(tl_type,type,
tl: $i > $i ).
thf(skaf66_type,type,
skaf66: $i > $i ).
thf(skaf67_type,type,
skaf67: $i > $i ).
thf(skaf68_type,type,
skaf68: $i > $i ).
thf(skaf45_type,type,
skaf45: $i > $i > $i ).
thf(rearsegP_type,type,
rearsegP: $i > $i > $o ).
thf(strictorderP_type,type,
strictorderP: $i > $o ).
thf(skaf61_type,type,
skaf61: $i > $i ).
thf(skaf63_type,type,
skaf63: $i > $i ).
thf(skaf51_type,type,
skaf51: $i > $i ).
thf(skaf52_type,type,
skaf52: $i > $i ).
thf(skaf53_type,type,
skaf53: $i > $i ).
thf(skaf57_type,type,
skaf57: $i > $i ).
thf(totalorderP_type,type,
totalorderP: $i > $o ).
thf(skaf56_type,type,
skaf56: $i > $i ).
thf(skaf58_type,type,
skaf58: $i > $i ).
thf(skaf48_type,type,
skaf48: $i > $i > $i ).
thf(skaf80_type,type,
skaf80: $i > $i ).
thf(skaf47_type,type,
skaf47: $i > $i > $i ).
thf(skaf81_type,type,
skaf81: $i > $i ).
thf(skaf82_type,type,
skaf82: $i > $i ).
thf(skaf42_type,type,
skaf42: $i > $i > $i ).
thf(193,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( segmentP @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause57) ).
thf(628,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( segmentP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(150,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ A @ B ) @ C )
!= D )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ D )
| ( segmentP @ D @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause173) ).
thf(518,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ A @ B ) @ C )
!= D )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ D )
| ( segmentP @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( gt @ B @ C )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( gt @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause146) ).
thf(234,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( gt @ B @ C )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( gt @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(163,axiom,
! [A: $i] : ( ssList @ ( skaf66 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause29) ).
thf(555,plain,
! [A: $i] : ( ssList @ ( skaf66 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(79,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause67) ).
thf(352,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(62,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ~ ( frontsegP @ B @ C )
| ~ ( ssList @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( frontsegP @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause154) ).
thf(308,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ~ ( frontsegP @ B @ C )
| ~ ( ssList @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( frontsegP @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(30,axiom,
! [A: $i] : ( ssItem @ ( skaf60 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause35) ).
thf(247,plain,
! [A: $i] : ( ssItem @ ( skaf60 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(146,axiom,
! [A: $i] : ( ssList @ ( skaf67 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause28) ).
thf(511,plain,
! [A: $i] : ( ssList @ ( skaf67 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(2,negated_conjecture,
ssList @ sk2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
thf(202,plain,
ssList @ sk2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( geq @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause108) ).
thf(217,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( geq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(47,axiom,
! [A: $i] :
( ~ ( lt @ A @ A )
| ~ ( ssItem @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause63) ).
thf(276,plain,
! [A: $i] :
( ~ ( lt @ A @ A )
| ~ ( ssItem @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(94,axiom,
! [B: $i,A: $i] :
( ~ ( rearsegP @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( ( app @ ( skaf46 @ A @ B ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause131) ).
thf(385,plain,
! [B: $i,A: $i] :
( ~ ( rearsegP @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( ( app @ ( skaf46 @ A @ B ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(93,axiom,
! [A: $i] : ( ssList @ ( skaf58 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause37) ).
thf(384,plain,
! [A: $i] : ( ssList @ ( skaf58 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(129,axiom,
! [A: $i] : ( ssList @ ( skaf75 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause20) ).
thf(472,plain,
! [A: $i] : ( ssList @ ( skaf75 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(74,axiom,
strictorderP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause5) ).
thf(340,plain,
strictorderP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(99,axiom,
! [A: $i] :
( ~ ( leq @ ( skaf55 @ A ) @ ( skaf54 @ A ) )
| ~ ( ssList @ A )
| ( totalorderP @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause94) ).
thf(404,plain,
! [A: $i] :
( ~ ( leq @ ( skaf55 @ A ) @ ( skaf54 @ A ) )
| ~ ( ssList @ A )
| ( totalorderP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(104,axiom,
! [A: $i] : ( ssList @ ( skaf73 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause22) ).
thf(417,plain,
! [A: $i] : ( ssList @ ( skaf73 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(169,axiom,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ( tl @ ( cons @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause96) ).
thf(570,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ( tl @ ( cons @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(143,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf47 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause49) ).
thf(504,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf47 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(176,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( cons @ A @ B )
!= ( cons @ C @ D ) )
| ~ ( ssItem @ C )
| ~ ( ssItem @ A )
| ~ ( ssList @ D )
| ~ ( ssList @ B )
| ( D = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause171) ).
thf(587,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( cons @ A @ B )
!= ( cons @ C @ D ) )
| ~ ( ssItem @ C )
| ~ ( ssItem @ A )
| ~ ( ssList @ D )
| ~ ( ssList @ B )
| ( D = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(165,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( cons @ A @ B )
!= ( cons @ C @ D ) )
| ~ ( ssItem @ C )
| ~ ( ssItem @ A )
| ~ ( ssList @ D )
| ~ ( ssList @ B )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause170) ).
thf(559,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( cons @ A @ B )
!= ( cons @ C @ D ) )
| ~ ( ssItem @ C )
| ~ ( ssItem @ A )
| ~ ( ssList @ D )
| ~ ( ssList @ B )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(106,axiom,
! [B: $i,A: $i] :
( ( ( cons @ A @ B )
!= nil )
| ~ ( ssItem @ A )
| ~ ( ssList @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause98) ).
thf(421,plain,
! [B: $i,A: $i] :
( ( ( cons @ A @ B )
!= nil )
| ~ ( ssItem @ A )
| ~ ( ssList @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(53,axiom,
! [A: $i] : ( ssList @ ( skaf62 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause33) ).
thf(289,plain,
! [A: $i] : ( ssList @ ( skaf62 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(118,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( segmentP @ A @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause56) ).
thf(448,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( segmentP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(38,axiom,
! [A: $i] : ( ssItem @ ( skaf54 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause41) ).
thf(261,plain,
! [A: $i] : ( ssItem @ ( skaf54 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(136,axiom,
! [A: $i] : ( ssList @ ( skaf68 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause27) ).
thf(492,plain,
! [A: $i] : ( ssList @ ( skaf68 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(178,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( frontsegP @ ( cons @ A @ B ) @ ( cons @ C @ D ) )
| ~ ( ssList @ D )
| ~ ( ssList @ B )
| ~ ( ssItem @ C )
| ~ ( ssItem @ A )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause176) ).
thf(591,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( frontsegP @ ( cons @ A @ B ) @ ( cons @ C @ D ) )
| ~ ( ssList @ D )
| ~ ( ssList @ B )
| ~ ( ssItem @ C )
| ~ ( ssItem @ A )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(115,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( memberP @ A @ B )
| ~ ( ssList @ A )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ( memberP @ ( cons @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause139) ).
thf(443,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( memberP @ A @ B )
| ~ ( ssList @ A )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ( memberP @ ( cons @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(67,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( totalorderedP @ A )
| ( ( app @ ( app @ ( skaf66 @ A ) @ ( cons @ ( skaf64 @ A ) @ ( skaf67 @ A ) ) ) @ ( cons @ ( skaf65 @ A ) @ ( skaf68 @ A ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause164) ).
thf(321,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( totalorderedP @ A )
| ( ( app @ ( app @ ( skaf66 @ A ) @ ( cons @ ( skaf64 @ A ) @ ( skaf67 @ A ) ) ) @ ( cons @ ( skaf65 @ A ) @ ( skaf68 @ A ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(148,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( equalelemsP @ A )
| ( ( app @ ( skaf80 @ A ) @ ( cons @ ( skaf78 @ A ) @ ( cons @ ( skaf79 @ A ) @ ( skaf81 @ A ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause142) ).
thf(514,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( equalelemsP @ A )
| ( ( app @ ( skaf80 @ A ) @ ( cons @ ( skaf78 @ A ) @ ( cons @ ( skaf79 @ A ) @ ( skaf81 @ A ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(132,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ A @ ( cons @ B @ C ) ) @ ( cons @ B @ D ) )
!= E )
| ~ ( ssList @ D )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ~ ( duplicatefreeP @ E )
| ~ ( ssList @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause179) ).
thf(480,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ A @ ( cons @ B @ C ) ) @ ( cons @ B @ D ) )
!= E )
| ~ ( ssList @ D )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ~ ( duplicatefreeP @ E )
| ~ ( ssList @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(184,axiom,
! [A: $i] :
( ~ ( frontsegP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause84) ).
thf(602,plain,
! [A: $i] :
( ~ ( frontsegP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(50,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf43 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause52) ).
thf(280,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf43 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(196,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( frontsegP @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause61) ).
thf(634,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( frontsegP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(15,axiom,
! [A: $i] : ( ssItem @ ( skaf79 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause16) ).
thf(221,plain,
! [A: $i] : ( ssItem @ ( skaf79 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(120,axiom,
! [B: $i,A: $i] :
( ~ ( totalorderedP @ ( cons @ A @ B ) )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( leq @ A @ ( hd @ B ) )
| ( nil = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause135) ).
thf(453,plain,
! [B: $i,A: $i] :
( ~ ( totalorderedP @ ( cons @ A @ B ) )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( leq @ A @ ( hd @ B ) )
| ( nil = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(97,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ A @ ( cons @ B @ ( cons @ C @ D ) ) )
!= E )
| ~ ( ssList @ D )
| ~ ( ssList @ A )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( equalelemsP @ E )
| ~ ( ssList @ E )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause180) ).
thf(396,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ A @ ( cons @ B @ ( cons @ C @ D ) ) )
!= E )
| ~ ( ssList @ D )
| ~ ( ssList @ A )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( equalelemsP @ E )
| ~ ( ssList @ E )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(102,axiom,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( neq @ B @ A )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause102) ).
thf(411,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( neq @ B @ A )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( leq @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause130) ).
thf(243,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( leq @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(41,axiom,
! [A: $i] : ( ssItem @ ( skaf50 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause45) ).
thf(265,plain,
! [A: $i] : ( ssItem @ ( skaf50 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(8,negated_conjecture,
equalelemsP @ sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
thf(206,plain,
equalelemsP @ sk3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(55,axiom,
! [A: $i] :
( ~ ( lt @ ( skaf69 @ A ) @ ( skaf70 @ A ) )
| ~ ( ssList @ A )
| ( strictorderedP @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause90) ).
thf(292,plain,
! [A: $i] :
( ~ ( lt @ ( skaf69 @ A ) @ ( skaf70 @ A ) )
| ~ ( ssList @ A )
| ( strictorderedP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( gt @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause110) ).
thf(248,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( gt @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(147,axiom,
! [A: $i] :
( ~ ( lt @ ( skaf59 @ A ) @ ( skaf60 @ A ) )
| ~ ( ssList @ A )
| ( strictorderP @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause93) ).
thf(512,plain,
! [A: $i] :
( ~ ( lt @ ( skaf59 @ A ) @ ( skaf60 @ A ) )
| ~ ( ssList @ A )
| ( strictorderP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( lt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause111) ).
thf(270,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( lt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(9,negated_conjecture,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( neq @ sk3 @ A )
| ~ ( segmentP @ sk4 @ A )
| ~ ( segmentP @ A @ sk3 )
| ~ ( equalelemsP @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
thf(201,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( neq @ sk3 @ A )
| ~ ( segmentP @ sk4 @ A )
| ~ ( segmentP @ A @ sk3 )
| ~ ( equalelemsP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(92,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ nil @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause74) ).
thf(381,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ nil @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ( ( app @ A @ B )
!= nil )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause118) ).
thf(334,plain,
! [B: $i,A: $i] :
( ( ( app @ A @ B )
!= nil )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(59,axiom,
! [A: $i] : ( ssList @ ( skaf72 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause23) ).
thf(302,plain,
! [A: $i] : ( ssList @ ( skaf72 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(78,axiom,
! [A: $i] :
( ~ ( rearsegP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause82) ).
thf(349,plain,
! [A: $i] :
( ~ ( rearsegP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(181,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( segmentP @ A @ B )
| ~ ( ssList @ C )
| ~ ( ssList @ D )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( segmentP @ ( app @ ( app @ D @ A ) @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause172) ).
thf(598,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( segmentP @ A @ B )
| ~ ( ssList @ C )
| ~ ( ssList @ D )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( segmentP @ ( app @ ( app @ D @ A ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(96,axiom,
! [B: $i,A: $i] :
( ( nil != A )
| ( nil != B )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( ( app @ A @ B )
= nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause145) ).
thf(392,plain,
! [B: $i,A: $i] :
( ( nil != A )
| ( nil != B )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( ( app @ A @ B )
= nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(107,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( rearsegP @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause59) ).
thf(424,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( rearsegP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(194,axiom,
totalorderedP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause4) ).
thf(630,plain,
totalorderedP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(46,axiom,
ssItem @ skac3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause9) ).
thf(275,plain,
ssItem @ skac3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(133,axiom,
! [A: $i] :
( ~ ( leq @ ( skaf64 @ A ) @ ( skaf65 @ A ) )
| ~ ( ssList @ A )
| ( totalorderedP @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause91) ).
thf(484,plain,
! [A: $i] :
( ~ ( leq @ ( skaf64 @ A ) @ ( skaf65 @ A ) )
| ~ ( ssList @ A )
| ( totalorderedP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
thf(197,plain,
sk2 = sk4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(192,axiom,
! [B: $i,A: $i] :
( ~ ( segmentP @ A @ B )
| ~ ( segmentP @ B @ A )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause127) ).
thf(625,plain,
! [B: $i,A: $i] :
( ~ ( segmentP @ A @ B )
| ~ ( segmentP @ B @ A )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(112,axiom,
! [B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ~ ( frontsegP @ B @ A )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause129) ).
thf(435,plain,
! [B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ~ ( frontsegP @ B @ A )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(70,axiom,
! [B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( ( app @ B @ ( skaf45 @ A @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause132) ).
thf(329,plain,
! [B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( ( app @ B @ ( skaf45 @ A @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( segmentP @ A @ B )
| ~ ( segmentP @ B @ C )
| ~ ( ssList @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( segmentP @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause152) ).
thf(461,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( segmentP @ A @ B )
| ~ ( segmentP @ B @ C )
| ~ ( ssList @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( segmentP @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(137,axiom,
totalorderP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause6) ).
thf(493,plain,
totalorderP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(161,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( hd @ A ) )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause78) ).
thf(551,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( hd @ A ) )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(121,axiom,
! [A: $i] : ( ssList @ ( skaf80 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause15) ).
thf(456,plain,
! [A: $i] : ( ssList @ ( skaf80 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(68,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause117) ).
thf(324,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(174,axiom,
! [A: $i] : ( ssList @ ( skaf82 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause13) ).
thf(583,plain,
! [A: $i] : ( ssList @ ( skaf82 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(151,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( duplicatefreeP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause65) ).
thf(522,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( duplicatefreeP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(52,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause115) ).
thf(285,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(17,axiom,
! [A: $i] : ( ssItem @ ( skaf64 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause31) ).
thf(224,plain,
! [A: $i] : ( ssItem @ ( skaf64 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(172,axiom,
! [A: $i] :
( ~ ( segmentP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause80) ).
thf(578,plain,
! [A: $i] :
( ~ ( segmentP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(65,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf46 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause50) ).
thf(317,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf46 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(95,axiom,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( rearsegP @ nil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause81) ).
thf(388,plain,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( rearsegP @ nil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(81,axiom,
! [A: $i] :
( ~ ( lt @ ( skaf60 @ A ) @ ( skaf59 @ A ) )
| ~ ( ssList @ A )
| ( strictorderP @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause92) ).
thf(356,plain,
! [A: $i] :
( ~ ( lt @ ( skaf60 @ A ) @ ( skaf59 @ A ) )
| ~ ( ssList @ A )
| ( strictorderP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(187,axiom,
! [B: $i,A: $i] :
( ~ ( segmentP @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( ( app @ ( app @ ( skaf47 @ A @ B ) @ B ) @ ( skaf48 @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause168) ).
thf(610,plain,
! [B: $i,A: $i] :
( ~ ( segmentP @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( ( app @ ( app @ ( skaf47 @ A @ B ) @ B ) @ ( skaf48 @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(141,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ A @ ( cons @ B @ C ) ) @ ( cons @ D @ E ) )
!= F )
| ~ ( ssList @ E )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ D )
| ~ ( ssItem @ B )
| ~ ( totalorderP @ F )
| ~ ( ssList @ F )
| ( leq @ B @ D )
| ( leq @ D @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause184) ).
thf(499,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ A @ ( cons @ B @ C ) ) @ ( cons @ D @ E ) )
!= F )
| ~ ( ssList @ E )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ D )
| ~ ( ssItem @ B )
| ~ ( totalorderP @ F )
| ~ ( ssList @ F )
| ( leq @ B @ D )
| ( leq @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( lt @ B @ C )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause155) ).
thf(225,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( lt @ B @ C )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(162,axiom,
! [A: $i] : ( ssList @ ( skaf63 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause32) ).
thf(554,plain,
! [A: $i] : ( ssList @ ( skaf63 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(135,axiom,
! [B: $i,A: $i] :
( ( ( cons @ A @ B )
!= B )
| ~ ( ssItem @ A )
| ~ ( ssList @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause99) ).
thf(489,plain,
! [B: $i,A: $i] :
( ( ( cons @ A @ B )
!= B )
| ~ ( ssItem @ A )
| ~ ( ssList @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(177,axiom,
! [A: $i] : ( ssList @ ( skaf56 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause39) ).
thf(590,plain,
! [A: $i] : ( ssList @ ( skaf56 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(69,axiom,
ssList @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
thf(328,plain,
ssList @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(128,axiom,
! [A: $i] : ( ssList @ ( skaf53 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause42) ).
thf(471,plain,
! [A: $i] : ( ssList @ ( skaf53 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(191,axiom,
! [B: $i,A: $i] :
( ( ( tl @ A )
!= ( tl @ B ) )
| ( ( hd @ A )
!= ( hd @ B ) )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( nil = B )
| ( A = B )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause177) ).
thf(622,plain,
! [B: $i,A: $i] :
( ( ( tl @ A )
!= ( tl @ B ) )
| ( ( hd @ A )
!= ( hd @ B ) )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( nil = B )
| ( A = B )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(122,axiom,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ~ ( ssItem @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause71) ).
thf(457,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ~ ( ssItem @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(88,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( totalorderP @ A )
| ( ( app @ ( app @ ( skaf56 @ A ) @ ( cons @ ( skaf54 @ A ) @ ( skaf57 @ A ) ) ) @ ( cons @ ( skaf55 @ A ) @ ( skaf58 @ A ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause166) ).
thf(371,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( totalorderP @ A )
| ( ( app @ ( app @ ( skaf56 @ A ) @ ( cons @ ( skaf54 @ A ) @ ( skaf57 @ A ) ) ) @ ( cons @ ( skaf55 @ A ) @ ( skaf58 @ A ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(142,axiom,
! [A: $i] : ( ssList @ ( skaf52 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause43) ).
thf(503,plain,
! [A: $i] : ( ssList @ ( skaf52 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(185,axiom,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ssList @ ( cons @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause86) ).
thf(605,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ssList @ ( cons @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(24,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( geq @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause55) ).
thf(237,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( geq @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( lt @ B @ C )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause147) ).
thf(266,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( lt @ B @ C )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(84,axiom,
! [B: $i,A: $i] :
( ( ( cons @ A @ nil )
!= B )
| ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( singletonP @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause116) ).
thf(360,plain,
! [B: $i,A: $i] :
( ( ( cons @ A @ nil )
!= B )
| ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( singletonP @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(11,negated_conjecture,
( ~ ( neq @ sk1 @ nil )
| ~ ( segmentP @ sk2 @ sk1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
thf(205,plain,
( ~ ( neq @ sk1 @ nil )
| ~ ( segmentP @ sk2 @ sk1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(190,axiom,
! [B: $i,A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( strictorderedP @ ( cons @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause112) ).
thf(618,plain,
! [B: $i,A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( strictorderedP @ ( cons @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(110,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ~ ( ssList @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( frontsegP @ ( app @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause137) ).
thf(430,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ~ ( ssList @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( frontsegP @ ( app @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(49,axiom,
! [A: $i] : ( ssItem @ ( skaf59 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause36) ).
thf(279,plain,
! [A: $i] : ( ssItem @ ( skaf59 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(170,axiom,
! [B: $i,A: $i] :
( ~ ( totalorderedP @ ( cons @ A @ B ) )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( totalorderedP @ B )
| ( nil = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause125) ).
thf(573,plain,
! [B: $i,A: $i] :
( ~ ( totalorderedP @ ( cons @ A @ B ) )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( totalorderedP @ B )
| ( nil = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(57,axiom,
! [A: $i] :
( ~ ( singletonP @ A )
| ~ ( ssList @ A )
| ( ( cons @ ( skaf44 @ A ) @ nil )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause101) ).
thf(296,plain,
! [A: $i] :
( ~ ( singletonP @ A )
| ~ ( ssList @ A )
| ( ( cons @ ( skaf44 @ A ) @ nil )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(90,axiom,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ( hd @ ( cons @ A @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause97) ).
thf(375,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ( hd @ ( cons @ A @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(183,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf42 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause53) ).
thf(601,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf42 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(175,axiom,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( nil = B )
| ( ( hd @ ( app @ B @ A ) )
= ( hd @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause123) ).
thf(584,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( nil = B )
| ( ( hd @ ( app @ B @ A ) )
= ( hd @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(166,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( memberP @ A @ B )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( memberP @ ( app @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause140) ).
thf(562,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( memberP @ A @ B )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( memberP @ ( app @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(158,axiom,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( nil = B )
| ( ( tl @ ( app @ B @ A ) )
= ( app @ ( tl @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause133) ).
thf(545,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( nil = B )
| ( ( tl @ ( app @ B @ A ) )
= ( app @ ( tl @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(37,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( leq @ B @ C )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( leq @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause156) ).
thf(259,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( leq @ B @ C )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( leq @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( totalorderedP @ ( cons @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause113) ).
thf(281,plain,
! [B: $i,A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( totalorderedP @ ( cons @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(3,negated_conjecture,
ssList @ sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
thf(204,plain,
ssList @ sk3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(116,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( frontsegP @ ( cons @ A @ B ) @ ( cons @ C @ D ) )
| ~ ( ssList @ D )
| ~ ( ssList @ B )
| ~ ( ssItem @ C )
| ~ ( ssItem @ A )
| ( frontsegP @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause174) ).
thf(445,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( frontsegP @ ( cons @ A @ B ) @ ( cons @ C @ D ) )
| ~ ( ssList @ D )
| ~ ( ssList @ B )
| ~ ( ssItem @ C )
| ~ ( ssItem @ A )
| ( frontsegP @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(64,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ A @ ( cons @ B @ C ) ) @ ( cons @ D @ E ) )
!= F )
| ~ ( ssList @ E )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ D )
| ~ ( ssItem @ B )
| ~ ( strictorderedP @ F )
| ~ ( ssList @ F )
| ( lt @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause181) ).
thf(313,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ A @ ( cons @ B @ C ) ) @ ( cons @ D @ E ) )
!= F )
| ~ ( ssList @ E )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ D )
| ~ ( ssItem @ B )
| ~ ( strictorderedP @ F )
| ~ ( ssList @ F )
| ( lt @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(140,axiom,
cyclefreeP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause7) ).
thf(498,plain,
cyclefreeP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(126,axiom,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( neq @ B @ A )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause100) ).
thf(466,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( neq @ B @ A )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(23,axiom,
! [A: $i] : ( ssItem @ ( skaf44 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause47) ).
thf(236,plain,
! [A: $i] : ( ssItem @ ( skaf44 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( ( app @ ( app @ C @ B ) @ A )
= ( app @ C @ ( app @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause149) ).
thf(406,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( ( app @ ( app @ C @ B ) @ A )
= ( app @ C @ ( app @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( gt @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause106) ).
thf(219,plain,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( gt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(45,axiom,
ssItem @ skac2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause10) ).
thf(274,plain,
ssItem @ skac2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause105) ).
thf(230,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(168,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( cons @ ( skaf83 @ A ) @ ( skaf82 @ A ) )
= A )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause109) ).
thf(567,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( cons @ ( skaf83 @ A ) @ ( skaf82 @ A ) )
= A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(66,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( tl @ A ) )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause75) ).
thf(318,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( tl @ A ) )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(145,axiom,
~ ( singletonP @ nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause11) ).
thf(509,plain,
~ ( singletonP @ nil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(60,axiom,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( ssList @ ( app @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause85) ).
thf(303,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( ssList @ ( app @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(131,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( memberP @ ( cons @ A @ B ) @ C )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ C )
| ( memberP @ B @ C )
| ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause161) ).
thf(477,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( memberP @ ( cons @ A @ B ) @ C )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ C )
| ( memberP @ B @ C )
| ( C = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(138,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( frontsegP @ A @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause60) ).
thf(494,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( frontsegP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(195,axiom,
! [B: $i,A: $i] :
( ~ ( strictorderedP @ ( cons @ A @ B ) )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( strictorderedP @ B )
| ( nil = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause124) ).
thf(631,plain,
! [B: $i,A: $i] :
( ~ ( strictorderedP @ ( cons @ A @ B ) )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( strictorderedP @ B )
| ( nil = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(76,axiom,
! [A: $i] : ( ssList @ ( skaf77 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause18) ).
thf(345,plain,
! [A: $i] : ( ssList @ ( skaf77 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( app @ A @ B )
!= C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ~ ( ssList @ C )
| ( frontsegP @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause144) ).
thf(535,plain,
! [C: $i,B: $i,A: $i] :
( ( ( app @ A @ B )
!= C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ~ ( ssList @ C )
| ( frontsegP @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(179,axiom,
! [A: $i] : ( ssList @ ( skaf71 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause24) ).
thf(594,plain,
! [A: $i] : ( ssList @ ( skaf71 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause122) ).
thf(251,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(10,negated_conjecture,
( ( nil != sk2 )
| ( nil != sk1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
thf(198,plain,
( ( nil != sk2 )
| ( nil != sk1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(48,axiom,
! [A: $i] : ( ssItem @ ( skaf78 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause17) ).
thf(278,plain,
! [A: $i] : ( ssItem @ ( skaf78 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(58,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( duplicatefreeP @ A )
| ( ( app @ ( app @ ( skaf75 @ A ) @ ( cons @ ( skaf74 @ A ) @ ( skaf76 @ A ) ) ) @ ( cons @ ( skaf74 @ A ) @ ( skaf77 @ A ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause162) ).
thf(299,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( duplicatefreeP @ A )
| ( ( app @ ( app @ ( skaf75 @ A ) @ ( cons @ ( skaf74 @ A ) @ ( skaf76 @ A ) ) ) @ ( cons @ ( skaf74 @ A ) @ ( skaf77 @ A ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(26,axiom,
! [A: $i] : ( ssItem @ ( skaf69 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause26) ).
thf(241,plain,
! [A: $i] : ( ssItem @ ( skaf69 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(144,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ A @ ( cons @ B @ C ) ) @ ( cons @ D @ E ) )
!= F )
| ~ ( ssList @ E )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ D )
| ~ ( ssItem @ B )
| ~ ( strictorderP @ F )
| ~ ( ssList @ F )
| ( lt @ B @ D )
| ( lt @ D @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause183) ).
thf(505,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ A @ ( cons @ B @ C ) ) @ ( cons @ D @ E ) )
!= F )
| ~ ( ssList @ E )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ D )
| ~ ( ssItem @ B )
| ~ ( strictorderP @ F )
| ~ ( ssList @ F )
| ( lt @ B @ D )
| ( lt @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(113,axiom,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ( app @ ( cons @ A @ nil ) @ B )
= ( cons @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause120) ).
thf(438,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ( app @ ( cons @ A @ nil ) @ B )
= ( cons @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(130,axiom,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( segmentP @ nil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause79) ).
thf(473,plain,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( segmentP @ nil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(108,axiom,
! [A: $i] : ( ssList @ ( skaf61 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause34) ).
thf(426,plain,
! [A: $i] : ( ssList @ ( skaf61 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(159,axiom,
! [A: $i] : ( ssList @ ( skaf51 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause44) ).
thf(548,plain,
! [A: $i] : ( ssList @ ( skaf51 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(89,axiom,
duplicatefreeP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause2) ).
thf(374,plain,
duplicatefreeP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(35,axiom,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause121) ).
thf(255,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(189,axiom,
strictorderedP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause3) ).
thf(617,plain,
strictorderedP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(103,axiom,
! [B: $i,A: $i] :
( ( ( app @ A @ B )
!= nil )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( nil = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause119) ).
thf(414,plain,
! [B: $i,A: $i] :
( ( ( app @ A @ B )
!= nil )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( nil = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( rearsegP @ A @ B )
| ~ ( ssList @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( rearsegP @ ( app @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause136) ).
thf(409,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rearsegP @ A @ B )
| ~ ( ssList @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( rearsegP @ ( app @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( lt @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause114) ).
thf(263,plain,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( lt @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(63,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( strictorderedP @ A )
| ( ( app @ ( app @ ( skaf71 @ A ) @ ( cons @ ( skaf69 @ A ) @ ( skaf72 @ A ) ) ) @ ( cons @ ( skaf70 @ A ) @ ( skaf73 @ A ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause163) ).
thf(310,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( strictorderedP @ A )
| ( ( app @ ( app @ ( skaf71 @ A ) @ ( cons @ ( skaf69 @ A ) @ ( skaf72 @ A ) ) ) @ ( cons @ ( skaf70 @ A ) @ ( skaf73 @ A ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(1,negated_conjecture,
ssList @ sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
thf(199,plain,
ssList @ sk1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(114,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( cyclefreeP @ A )
| ( leq @ ( skaf50 @ A ) @ ( skaf49 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause87) ).
thf(441,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( cyclefreeP @ A )
| ( leq @ ( skaf50 @ A ) @ ( skaf49 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(87,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf45 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause51) ).
thf(370,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf45 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(125,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ A @ nil )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause73) ).
thf(463,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ A @ nil )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(171,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( totalorderP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause69) ).
thf(576,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( totalorderP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(83,axiom,
equalelemsP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause1) ).
thf(359,plain,
equalelemsP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(188,axiom,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( frontsegP @ nil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause83) ).
thf(613,plain,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( frontsegP @ nil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(182,axiom,
! [A: $i] : ( ssList @ ( skaf76 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause19) ).
thf(600,plain,
! [A: $i] : ( ssList @ ( skaf76 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(180,axiom,
! [B: $i,A: $i] :
( ~ ( memberP @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssList @ A )
| ( ( app @ ( skaf42 @ A @ B ) @ ( cons @ B @ ( skaf43 @ B @ A ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause169) ).
thf(595,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssList @ A )
| ( ( app @ ( skaf42 @ A @ B ) @ ( cons @ B @ ( skaf43 @ B @ A ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(32,axiom,
! [A: $i] : ( ssItem @ ( skaf49 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause46) ).
thf(250,plain,
! [A: $i] : ( ssItem @ ( skaf49 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(119,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( hd @ A ) )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause76) ).
thf(450,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( hd @ A ) )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(164,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( app @ A @ B )
!= ( app @ A @ C ) )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ~ ( ssList @ C )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause150) ).
thf(556,plain,
! [C: $i,B: $i,A: $i] :
( ( ( app @ A @ B )
!= ( app @ A @ C ) )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ~ ( ssList @ C )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(156,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ A @ ( cons @ B @ C ) ) @ ( cons @ D @ E ) )
!= F )
| ~ ( ssList @ E )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ D )
| ~ ( ssItem @ B )
| ~ ( totalorderedP @ F )
| ~ ( ssList @ F )
| ( leq @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause182) ).
thf(539,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ A @ ( cons @ B @ C ) ) @ ( cons @ D @ E ) )
!= F )
| ~ ( ssList @ E )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ D )
| ~ ( ssItem @ B )
| ~ ( totalorderedP @ F )
| ~ ( ssList @ F )
| ( leq @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(7,negated_conjecture,
segmentP @ sk4 @ sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
thf(203,plain,
segmentP @ sk4 @ sk3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(86,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( strictorderedP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause66) ).
thf(368,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( strictorderedP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(152,axiom,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ~ ( ssList @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( memberP @ ( cons @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause138) ).
thf(524,plain,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ~ ( ssList @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( memberP @ ( cons @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(173,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( rearsegP @ A @ B )
| ~ ( rearsegP @ B @ C )
| ~ ( ssList @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( rearsegP @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause153) ).
thf(581,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rearsegP @ A @ B )
| ~ ( rearsegP @ B @ C )
| ~ ( ssList @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( rearsegP @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(149,axiom,
! [A: $i] : ( ssList @ ( skaf81 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause14) ).
thf(517,plain,
! [A: $i] : ( ssList @ ( skaf81 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(36,axiom,
! [A: $i] : ( ssItem @ ( skaf74 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause21) ).
thf(258,plain,
! [A: $i] : ( ssItem @ ( skaf74 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(105,axiom,
! [B: $i,A: $i] :
( ~ ( rearsegP @ A @ B )
| ~ ( rearsegP @ B @ A )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause128) ).
thf(418,plain,
! [B: $i,A: $i] :
( ~ ( rearsegP @ A @ B )
| ~ ( rearsegP @ B @ A )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(29,axiom,
! [A: $i] : ( ssItem @ ( skaf70 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause25) ).
thf(246,plain,
! [A: $i] : ( ssItem @ ( skaf70 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(4,negated_conjecture,
ssList @ sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
thf(207,plain,
ssList @ sk4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(77,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( cyclefreeP @ A )
| ( ( app @ ( app @ ( skaf51 @ A ) @ ( cons @ ( skaf49 @ A ) @ ( skaf52 @ A ) ) ) @ ( cons @ ( skaf50 @ A ) @ ( skaf53 @ A ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause167) ).
thf(346,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( cyclefreeP @ A )
| ( ( app @ ( app @ ( skaf51 @ A ) @ ( cons @ ( skaf49 @ A ) @ ( skaf52 @ A ) ) ) @ ( cons @ ( skaf50 @ A ) @ ( skaf53 @ A ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(160,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( strictorderP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause68) ).
thf(549,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( strictorderP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(12,axiom,
skac3 != skac2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause54) ).
thf(214,plain,
skac3 != skac2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(54,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( memberP @ ( app @ A @ B ) @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ~ ( ssItem @ C )
| ( memberP @ B @ C )
| ( memberP @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause158) ).
thf(290,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( memberP @ ( app @ A @ B ) @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ~ ( ssItem @ C )
| ( memberP @ B @ C )
| ( memberP @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(91,axiom,
! [B: $i,A: $i] :
( ~ ( leq @ A @ ( hd @ B ) )
| ~ ( totalorderedP @ B )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ B ) )
| ( nil = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause159) ).
thf(378,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ ( hd @ B ) )
| ~ ( totalorderedP @ B )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ B ) )
| ( nil = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(117,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf48 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause48) ).
thf(447,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf48 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(111,axiom,
! [B: $i,A: $i] :
( ~ ( lt @ A @ ( hd @ B ) )
| ~ ( strictorderedP @ B )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( strictorderedP @ ( cons @ A @ B ) )
| ( nil = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause160) ).
thf(432,plain,
! [B: $i,A: $i] :
( ~ ( lt @ A @ ( hd @ B ) )
| ~ ( strictorderedP @ B )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( strictorderedP @ ( cons @ A @ B ) )
| ( nil = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(39,axiom,
! [A: $i] : ( ssItem @ ( skaf65 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause30) ).
thf(262,plain,
! [A: $i] : ( ssItem @ ( skaf65 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(167,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( tl @ A ) )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause77) ).
thf(564,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( tl @ A ) )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(61,axiom,
! [B: $i,A: $i] :
( ~ ( strictorderedP @ ( cons @ A @ B ) )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ ( hd @ B ) )
| ( nil = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause134) ).
thf(305,plain,
! [B: $i,A: $i] :
( ~ ( strictorderedP @ ( cons @ A @ B ) )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ ( hd @ B ) )
| ( nil = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(56,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( cyclefreeP @ A )
| ( leq @ ( skaf49 @ A ) @ ( skaf50 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause88) ).
thf(294,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( cyclefreeP @ A )
| ( leq @ ( skaf49 @ A ) @ ( skaf50 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(75,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( leq @ B @ A )
| ( ( app @ ( app @ C @ ( cons @ A @ D ) ) @ ( cons @ B @ E ) )
!= F )
| ~ ( ssList @ E )
| ~ ( ssList @ D )
| ~ ( ssList @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ~ ( cyclefreeP @ F )
| ~ ( ssList @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause185) ).
thf(341,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( leq @ B @ A )
| ( ( app @ ( app @ C @ ( cons @ A @ D ) ) @ ( cons @ B @ E ) )
!= F )
| ~ ( ssList @ E )
| ~ ( ssList @ D )
| ~ ( ssList @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ~ ( cyclefreeP @ F )
| ~ ( ssList @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(43,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( leq @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause62) ).
thf(268,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( leq @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(82,axiom,
! [A: $i] : ( ssList @ ( skaf57 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause38) ).
thf(358,plain,
! [A: $i] : ( ssList @ ( skaf57 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(98,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ( C != D )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ~ ( ssItem @ D )
| ~ ( ssItem @ C )
| ( frontsegP @ ( cons @ C @ A ) @ ( cons @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause178) ).
thf(400,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ( C != D )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ~ ( ssItem @ D )
| ~ ( ssItem @ C )
| ( frontsegP @ ( cons @ C @ A ) @ ( cons @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( ( cons @ A @ ( app @ B @ C ) )
= ( app @ ( cons @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause157) ).
thf(532,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( ( cons @ A @ ( app @ B @ C ) )
= ( app @ ( cons @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(25,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ~ ( geq @ B @ C )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( geq @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause148) ).
thf(239,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ~ ( geq @ B @ C )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( geq @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(27,axiom,
! [A: $i] : ( ssItem @ ( skaf55 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause40) ).
thf(242,plain,
! [A: $i] : ( ssItem @ ( skaf55 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(71,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( rearsegP @ A @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause58) ).
thf(332,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( rearsegP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(109,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( app @ A @ B )
!= ( app @ C @ B ) )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause151) ).
thf(427,plain,
! [C: $i,B: $i,A: $i] :
( ( ( app @ A @ B )
!= ( app @ C @ B ) )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(153,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ A @ ( cons @ B @ C ) )
!= D )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ~ ( ssList @ D )
| ( memberP @ D @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause175) ).
thf(528,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ A @ ( cons @ B @ C ) )
!= D )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ~ ( ssList @ D )
| ( memberP @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(123,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( equalelemsP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause64) ).
thf(459,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( equalelemsP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
thf(200,plain,
sk1 = sk3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(186,axiom,
! [A: $i] :
( ( ( skaf79 @ A )
!= ( skaf78 @ A ) )
| ~ ( ssList @ A )
| ( equalelemsP @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause89) ).
thf(607,plain,
! [A: $i] :
( ( ( skaf79 @ A )
!= ( skaf78 @ A ) )
| ~ ( ssList @ A )
| ( equalelemsP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(134,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( cons @ ( hd @ A ) @ ( tl @ A ) )
= A )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause104) ).
thf(486,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( cons @ ( hd @ A ) @ ( tl @ A ) )
= A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(73,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( strictorderP @ A )
| ( ( app @ ( app @ ( skaf61 @ A ) @ ( cons @ ( skaf59 @ A ) @ ( skaf62 @ A ) ) ) @ ( cons @ ( skaf60 @ A ) @ ( skaf63 @ A ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause165) ).
thf(337,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( strictorderP @ A )
| ( ( app @ ( app @ ( skaf61 @ A ) @ ( cons @ ( skaf59 @ A ) @ ( skaf62 @ A ) ) ) @ ( cons @ ( skaf60 @ A ) @ ( skaf63 @ A ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(127,axiom,
! [A: $i] :
( ~ ( leq @ ( skaf54 @ A ) @ ( skaf55 @ A ) )
| ~ ( ssList @ A )
| ( totalorderP @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause95) ).
thf(469,plain,
! [A: $i] :
( ~ ( leq @ ( skaf54 @ A ) @ ( skaf55 @ A ) )
| ~ ( ssList @ A )
| ( totalorderP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(80,axiom,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ( duplicatefreeP @ A )
| ( ssItem @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause72) ).
thf(354,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ( duplicatefreeP @ A )
| ( ssItem @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(157,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( memberP @ A @ B )
| ~ ( ssList @ A )
| ~ ( ssList @ C )
| ~ ( ssItem @ B )
| ( memberP @ ( app @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause141) ).
thf(543,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( memberP @ A @ B )
| ~ ( ssList @ A )
| ~ ( ssList @ C )
| ~ ( ssItem @ B )
| ( memberP @ ( app @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( leq @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause107) ).
thf(222,plain,
! [B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( leq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(139,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( cyclefreeP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause70) ).
thf(496,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( cyclefreeP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( app @ A @ B )
!= C )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( rearsegP @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause143) ).
thf(364,plain,
! [C: $i,B: $i,A: $i] :
( ( ( app @ A @ B )
!= C )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( rearsegP @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( leq @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause103) ).
thf(232,plain,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( leq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(34,axiom,
! [A: $i] : ( ssItem @ ( skaf83 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause12) ).
thf(254,plain,
! [A: $i] : ( ssItem @ ( skaf83 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ~ ( geq @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause126) ).
thf(227,plain,
! [B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ~ ( geq @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1934,plain,
$false,
inference(e,[status(thm)],[628,518,234,555,352,308,247,511,202,217,276,385,384,472,340,404,417,570,504,587,559,421,289,448,261,492,591,443,321,514,480,602,280,634,221,453,396,411,243,265,206,292,248,512,270,201,381,334,302,349,598,392,424,630,275,484,197,625,435,329,461,493,551,456,324,583,522,285,224,578,317,388,356,610,499,225,554,489,590,328,471,622,457,371,503,605,237,266,360,205,618,430,279,573,296,375,601,584,562,545,259,281,204,445,313,498,466,236,406,219,274,230,567,318,509,303,477,494,631,345,535,594,251,198,278,299,241,505,438,473,426,548,374,255,617,414,409,263,310,199,441,370,463,576,359,613,600,595,250,450,556,539,203,368,524,581,517,258,418,246,207,346,549,214,290,378,447,432,262,564,305,294,341,268,358,400,532,239,242,332,427,528,459,200,607,486,337,469,354,543,222,496,364,232,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC117-1 : TPTP v8.1.2. Released v2.4.0.
% 0.03/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n022.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 19 01:11:18 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.97/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.53/1.06 % [INFO] Parsing done (182ms).
% 1.53/1.07 % [INFO] Running in sequential loop mode.
% 1.97/1.27 % [INFO] eprover registered as external prover.
% 1.97/1.28 % [INFO] cvc4 registered as external prover.
% 1.97/1.28 % [INFO] Scanning for conjecture ...
% 2.19/1.36 % [INFO] Found a conjecture and 185 axioms. Running axiom selection ...
% 2.56/1.44 % [INFO] Axiom selection finished. Selected 185 axioms (removed 0 axioms).
% 2.93/1.53 % [INFO] Problem is propositional (TPTP CNF).
% 2.93/1.54 % [INFO] Type checking passed.
% 2.93/1.54 % [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 ...
% 12.56/3.35 % External prover 'e' found a proof!
% 12.56/3.35 % [INFO] Killing All external provers ...
% 12.56/3.35 % Time passed: 2832ms (effective reasoning time: 2271ms)
% 12.56/3.35 % Solved by 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)>
% 12.56/3.35 % 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
% 12.56/3.35 % No. of inferences in proof: 393
% 12.56/3.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2832 ms resp. 2271 ms w/o parsing
% 12.56/3.43 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.56/3.43 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------