TSTP Solution File: SWC368-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWC368-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.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 12:11:42 EDT 2023
% Result : Unsatisfiable 213.31s 39.37s
% Output : Refutation 213.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 273
% Syntax : Number of formulae : 678 ( 182 unt; 73 typ; 0 def)
% Number of atoms : 1761 ( 348 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 4929 (1062 ~;1090 |; 0 &;2777 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 82 ( 82 >; 0 *; 0 +; 0 <<)
% Number of symbols : 76 ( 73 usr; 10 con; 0-2 aty)
% Number of variables : 787 ( 0 ^; 787 !; 0 ?; 787 :)
% 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(ssItem_type,type,
ssItem: $i > $o ).
thf(sk5_type,type,
sk5: $i ).
thf(nil_type,type,
nil: $i ).
thf(cons_type,type,
cons: $i > $i > $i ).
thf(memberP_type,type,
memberP: $i > $i > $o ).
thf(leq_type,type,
leq: $i > $i > $o ).
thf(skac3_type,type,
skac3: $i ).
thf(skac2_type,type,
skac2: $i ).
thf(skaf43_type,type,
skaf43: $i > $i > $i ).
thf(geq_type,type,
geq: $i > $i > $o ).
thf(totalorderedP_type,type,
totalorderedP: $i > $o ).
thf(lt_type,type,
lt: $i > $i > $o ).
thf(gt_type,type,
gt: $i > $i > $o ).
thf(neq_type,type,
neq: $i > $i > $o ).
thf(skaf62_type,type,
skaf62: $i > $i ).
thf(app_type,type,
app: $i > $i > $i ).
thf(skaf69_type,type,
skaf69: $i > $i ).
thf(skaf70_type,type,
skaf70: $i > $i ).
thf(strictorderedP_type,type,
strictorderedP: $i > $o ).
thf(cyclefreeP_type,type,
cyclefreeP: $i > $o ).
thf(skaf49_type,type,
skaf49: $i > $i ).
thf(skaf50_type,type,
skaf50: $i > $i ).
thf(singletonP_type,type,
singletonP: $i > $o ).
thf(skaf44_type,type,
skaf44: $i > $i ).
thf(duplicatefreeP_type,type,
duplicatefreeP: $i > $o ).
thf(skaf75_type,type,
skaf75: $i > $i ).
thf(skaf74_type,type,
skaf74: $i > $i ).
thf(skaf76_type,type,
skaf76: $i > $i ).
thf(skaf77_type,type,
skaf77: $i > $i ).
thf(skaf72_type,type,
skaf72: $i > $i ).
thf(skaf79_type,type,
skaf79: $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(skaf64_type,type,
skaf64: $i > $i ).
thf(tl_type,type,
tl: $i > $i ).
thf(skaf66_type,type,
skaf66: $i > $i ).
thf(skaf67_type,type,
skaf67: $i > $i ).
thf(skaf65_type,type,
skaf65: $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(skaf59_type,type,
skaf59: $i > $i ).
thf(skaf60_type,type,
skaf60: $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(equalelemsP_type,type,
equalelemsP: $i > $o ).
thf(totalorderP_type,type,
totalorderP: $i > $o ).
thf(skaf56_type,type,
skaf56: $i > $i ).
thf(skaf54_type,type,
skaf54: $i > $i ).
thf(skaf55_type,type,
skaf55: $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(skaf78_type,type,
skaf78: $i > $i ).
thf(skaf81_type,type,
skaf81: $i > $i ).
thf(skaf83_type,type,
skaf83: $i > $i ).
thf(skaf82_type,type,
skaf82: $i > $i ).
thf(skaf42_type,type,
skaf42: $i > $i > $i ).
thf(64,axiom,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause105) ).
thf(347,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(140,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)],[140]) ).
thf(9,negated_conjecture,
( ( ssItem @ sk5 )
| ( nil = sk3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
thf(206,plain,
( ( ssItem @ sk5 )
| ( nil = sk3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(218,plain,
( ( ssItem @ sk5 )
| ( nil = sk3 ) ),
inference(cnf,[status(esa)],[206]) ).
thf(219,plain,
( ( nil = sk3 )
| ( ssItem @ sk5 ) ),
inference(lifteq,[status(thm)],[218]) ).
thf(6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
thf(205,plain,
sk1 = sk3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(223,plain,
sk3 = sk1,
inference(lifteq,[status(thm)],[205]) ).
thf(666,plain,
( ( nil = sk1 )
| ( ssItem @ sk5 ) ),
inference(rewrite,[status(thm)],[219,223]) ).
thf(88,axiom,
! [A: $i] : ( ssItem @ ( skaf69 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause26) ).
thf(408,plain,
! [A: $i] : ( ssItem @ ( skaf69 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(110,axiom,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ~ ( ssItem @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause71) ).
thf(451,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ~ ( ssItem @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(452,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ~ ( ssItem @ A ) ),
inference(cnf,[status(esa)],[451]) ).
thf(1102,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf69 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[408,452]) ).
thf(1103,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf69 @ A ) ),
inference(pattern_uni,[status(thm)],[1102:[bind(A,$thf( C )),bind(B,$thf( skaf69 @ C ))]]) ).
thf(1110,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf69 @ A ) ),
inference(simp,[status(thm)],[1103]) ).
thf(59,axiom,
! [B: $i,A: $i] :
( ( ( cons @ A @ nil )
!= B )
| ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( singletonP @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause116) ).
thf(333,plain,
! [B: $i,A: $i] :
( ( ( cons @ A @ nil )
!= B )
| ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( singletonP @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(189,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(628,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)],[189]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause115) ).
thf(247,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(200,axiom,
! [A: $i] :
( ~ ( lt @ A @ A )
| ~ ( ssItem @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause63) ).
thf(655,plain,
! [A: $i] :
( ~ ( lt @ A @ A )
| ~ ( ssItem @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(136,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)],[136]) ).
thf(10,negated_conjecture,
( ( ( cons @ sk5 @ nil )
= sk3 )
| ( nil = sk4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
thf(202,plain,
( ( ( cons @ sk5 @ nil )
= sk3 )
| ( nil = sk4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(173,axiom,
! [A: $i] : ( ssItem @ ( skaf65 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause30) ).
thf(597,plain,
! [A: $i] : ( ssItem @ ( skaf65 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(95,axiom,
! [A: $i] : ( ssItem @ ( skaf60 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause35) ).
thf(420,plain,
! [A: $i] : ( ssItem @ ( skaf60 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(1484,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf60 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[420,452]) ).
thf(1485,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf60 @ A ) ),
inference(pattern_uni,[status(thm)],[1484:[bind(A,$thf( C )),bind(B,$thf( skaf60 @ C ))]]) ).
thf(1497,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf60 @ A ) ),
inference(simp,[status(thm)],[1485]) ).
thf(78,axiom,
! [A: $i] :
( ~ ( leq @ ( skaf55 @ A ) @ ( skaf54 @ A ) )
| ~ ( ssList @ A )
| ( totalorderP @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause94) ).
thf(384,plain,
! [A: $i] :
( ~ ( leq @ ( skaf55 @ A ) @ ( skaf54 @ A ) )
| ~ ( ssList @ A )
| ( totalorderP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(151,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( strictorderP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause68) ).
thf(550,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( strictorderP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(132,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf47 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause49) ).
thf(500,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf47 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(8,negated_conjecture,
( ( ssItem @ sk5 )
| ( nil = sk4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
thf(213,plain,
( ( ssItem @ sk5 )
| ( nil = sk4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(224,plain,
( ( ssItem @ sk5 )
| ( nil = sk4 ) ),
inference(cnf,[status(esa)],[213]) ).
thf(225,plain,
( ( nil = sk4 )
| ( ssItem @ sk5 ) ),
inference(lifteq,[status(thm)],[224]) ).
thf(5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
thf(201,plain,
sk2 = sk4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(220,plain,
sk4 = sk2,
inference(lifteq,[status(thm)],[201]) ).
thf(701,plain,
( ( nil = sk2 )
| ( ssItem @ sk5 ) ),
inference(rewrite,[status(thm)],[225,220]) ).
thf(58,axiom,
equalelemsP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause1) ).
thf(332,plain,
equalelemsP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(714,plain,
( ( ssItem @ sk5 )
| ( equalelemsP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[701,332]) ).
thf(715,plain,
( ( ssItem @ sk5 )
| ( equalelemsP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[714:[]]) ).
thf(146,axiom,
ssItem @ skac2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause10) ).
thf(539,plain,
ssItem @ skac2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(687,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ( ( ssItem @ skac2 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[539,452]) ).
thf(688,plain,
~ ( memberP @ nil @ skac2 ),
inference(pattern_uni,[status(thm)],[687:[bind(A,$thf( skac2 ))]]) ).
thf(697,plain,
( ( ssItem @ sk5 )
| ~ ( memberP @ sk1 @ skac2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[666,688]) ).
thf(698,plain,
( ( ssItem @ sk5 )
| ~ ( memberP @ sk1 @ skac2 ) ),
inference(pattern_uni,[status(thm)],[697:[]]) ).
thf(11,negated_conjecture,
( ( memberP @ sk4 @ sk5 )
| ( nil = sk4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
thf(212,plain,
( ( memberP @ sk4 @ sk5 )
| ( nil = sk4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(221,plain,
( ( memberP @ sk4 @ sk5 )
| ( nil = sk4 ) ),
inference(cnf,[status(esa)],[212]) ).
thf(222,plain,
( ( nil = sk4 )
| ( memberP @ sk4 @ sk5 ) ),
inference(lifteq,[status(thm)],[221]) ).
thf(737,plain,
( ( nil = sk2 )
| ( memberP @ sk2 @ sk5 ) ),
inference(rewrite,[status(thm)],[222,220]) ).
thf(126,axiom,
totalorderP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause6) ).
thf(489,plain,
totalorderP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(746,plain,
( ( memberP @ sk2 @ sk5 )
| ( totalorderP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[737,489]) ).
thf(747,plain,
( ( memberP @ sk2 @ sk5 )
| ( totalorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[746:[]]) ).
thf(65,axiom,
duplicatefreeP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause2) ).
thf(349,plain,
duplicatefreeP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(669,plain,
( ( ssItem @ sk5 )
| ( duplicatefreeP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[666,349]) ).
thf(670,plain,
( ( ssItem @ sk5 )
| ( duplicatefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[669:[]]) ).
thf(708,plain,
( ( ssItem @ sk5 )
| ( duplicatefreeP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[701,349]) ).
thf(709,plain,
( ( ssItem @ sk5 )
| ( duplicatefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[708:[]]) ).
thf(94,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(417,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)],[94]) ).
thf(40,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(288,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)],[40]) ).
thf(44,axiom,
ssList @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
thf(301,plain,
ssList @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(683,plain,
! [A: $i] :
( ( nil = sk1 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[666,452]) ).
thf(684,plain,
( ( nil = sk1 )
| ~ ( memberP @ nil @ sk5 ) ),
inference(pattern_uni,[status(thm)],[683:[bind(A,$thf( sk5 ))]]) ).
thf(134,axiom,
~ ( singletonP @ nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause11) ).
thf(505,plain,
~ ( singletonP @ nil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(506,plain,
~ ( singletonP @ nil ),
inference(polarity_switch,[status(thm)],[505]) ).
thf(2066,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( singletonP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[684,506]) ).
thf(2067,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( singletonP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[2066:[]]) ).
thf(102,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(436,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)],[102]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( totalorderedP @ ( cons @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause113) ).
thf(241,plain,
! [B: $i,A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( totalorderedP @ ( cons @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(242,plain,
! [B: $i,A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( totalorderedP @ ( cons @ B @ A ) ) ),
inference(cnf,[status(esa)],[241]) ).
thf(243,plain,
! [B: $i,A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( totalorderedP @ ( cons @ B @ A ) ) ),
inference(lifteq,[status(thm)],[242]) ).
thf(244,plain,
! [A: $i] :
( ~ ( ssList @ nil )
| ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ nil ) ) ),
inference(simp,[status(thm)],[243]) ).
thf(2095,plain,
! [A: $i] :
( ~ $true
| ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ nil ) ) ),
inference(rewrite,[status(thm)],[244,301]) ).
thf(2096,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ nil ) ) ),
inference(simp,[status(thm)],[2095]) ).
thf(2135,plain,
! [A: $i] :
( ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ skac2 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[539,2096]) ).
thf(2136,plain,
totalorderedP @ ( cons @ skac2 @ nil ),
inference(pattern_uni,[status(thm)],[2135:[bind(A,$thf( skac2 ))]]) ).
thf(25,axiom,
! [A: $i] :
( ~ ( lt @ ( skaf69 @ A ) @ ( skaf70 @ A ) )
| ~ ( ssList @ A )
| ( strictorderedP @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause90) ).
thf(256,plain,
! [A: $i] :
( ~ ( lt @ ( skaf69 @ A ) @ ( skaf70 @ A ) )
| ~ ( ssList @ A )
| ( strictorderedP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(257,plain,
! [A: $i] :
( ~ ( lt @ ( skaf69 @ A ) @ ( skaf70 @ A ) )
| ~ ( ssList @ A )
| ( strictorderedP @ A ) ),
inference(cnf,[status(esa)],[256]) ).
thf(185,axiom,
! [A: $i] :
( ~ ( frontsegP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause84) ).
thf(619,plain,
! [A: $i] :
( ~ ( frontsegP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(63,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(344,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)],[63]) ).
thf(152,axiom,
ssItem @ skac3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause9) ).
thf(552,plain,
ssItem @ skac3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(2125,plain,
! [A: $i] :
( ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ skac3 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[552,2096]) ).
thf(2126,plain,
totalorderedP @ ( cons @ skac3 @ nil ),
inference(pattern_uni,[status(thm)],[2125:[bind(A,$thf( skac3 ))]]) ).
thf(114,axiom,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( neq @ B @ A )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause100) ).
thf(460,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( neq @ B @ A )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(96,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(421,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)],[96]) ).
thf(37,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf46 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause50) ).
thf(284,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf46 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(93,axiom,
! [A: $i] : ( ssList @ ( skaf61 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause34) ).
thf(416,plain,
! [A: $i] : ( ssList @ ( skaf61 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(54,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause67) ).
thf(325,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(89,axiom,
! [A: $i] : ( ssItem @ ( skaf55 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause40) ).
thf(409,plain,
! [A: $i] : ( ssItem @ ( skaf55 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(2129,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf55 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[409,2096]) ).
thf(2130,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf55 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[2129:[bind(A,$thf( C )),bind(B,$thf( skaf55 @ C ))]]) ).
thf(2158,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf55 @ A ) @ nil ) ),
inference(simp,[status(thm)],[2130]) ).
thf(128,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( cyclefreeP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause70) ).
thf(492,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( cyclefreeP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(22,axiom,
! [A: $i] : ( ssList @ ( skaf62 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause33) ).
thf(251,plain,
! [A: $i] : ( ssList @ ( skaf62 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(248,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A ) ),
inference(cnf,[status(esa)],[247]) ).
thf(249,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A ) ),
inference(lifteq,[status(thm)],[248]) ).
thf(250,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ~ ( ssList @ A ) ),
inference(simp,[status(thm)],[249]) ).
thf(787,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf62 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[251,250]) ).
thf(788,plain,
! [A: $i] :
~ ( neq @ ( skaf62 @ A ) @ ( skaf62 @ A ) ),
inference(pattern_uni,[status(thm)],[787:[bind(A,$thf( C )),bind(B,$thf( skaf62 @ C ))]]) ).
thf(789,plain,
! [A: $i] :
~ ( neq @ ( skaf62 @ A ) @ ( skaf62 @ A ) ),
inference(simp,[status(thm)],[788]) ).
thf(76,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(376,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)],[76]) ).
thf(124,axiom,
! [B: $i,A: $i] :
( ( ( cons @ A @ B )
!= B )
| ~ ( ssItem @ A )
| ~ ( ssList @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause99) ).
thf(485,plain,
! [B: $i,A: $i] :
( ( ( cons @ A @ B )
!= B )
| ~ ( ssItem @ A )
| ~ ( ssList @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(17,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf43 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause52) ).
thf(238,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf43 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(138,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)],[138]) ).
thf(67,axiom,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( leq @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause103) ).
thf(353,plain,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( leq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(122,axiom,
! [A: $i] :
( ~ ( leq @ ( skaf64 @ A ) @ ( skaf65 @ A ) )
| ~ ( ssList @ A )
| ( totalorderedP @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause91) ).
thf(480,plain,
! [A: $i] :
( ~ ( leq @ ( skaf64 @ A ) @ ( skaf65 @ A ) )
| ~ ( ssList @ A )
| ( totalorderedP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(3,negated_conjecture,
ssList @ sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
thf(211,plain,
ssList @ sk3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(195,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( segmentP @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause57) ).
thf(646,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( segmentP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(23,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(252,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)],[23]) ).
thf(253,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( lt @ B @ C )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ C ) ),
inference(cnf,[status(esa)],[252]) ).
thf(36,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(280,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)],[36]) ).
thf(191,axiom,
strictorderedP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause3) ).
thf(635,plain,
strictorderedP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(691,plain,
( ( ssItem @ sk5 )
| ( strictorderedP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[666,635]) ).
thf(692,plain,
( ( ssItem @ sk5 )
| ( strictorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[691:[]]) ).
thf(111,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( equalelemsP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause64) ).
thf(453,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( equalelemsP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(720,plain,
! [A: $i] :
( ( nil = sk2 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[701,452]) ).
thf(721,plain,
( ( nil = sk2 )
| ~ ( memberP @ nil @ sk5 ) ),
inference(pattern_uni,[status(thm)],[720:[bind(A,$thf( sk5 ))]]) ).
thf(660,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssList @ nil )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[301,250]) ).
thf(661,plain,
~ ( neq @ nil @ nil ),
inference(pattern_uni,[status(thm)],[660:[bind(A,$thf( nil ))]]) ).
thf(2001,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( neq @ nil @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[684,661]) ).
thf(2002,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( neq @ nil @ sk1 ) ),
inference(pattern_uni,[status(thm)],[2001:[]]) ).
thf(3156,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( neq @ sk2 @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[721,2002]) ).
thf(3157,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( neq @ sk2 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[3156:[]]) ).
thf(83,axiom,
! [B: $i,A: $i] :
( ( ( app @ A @ B )
!= nil )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( nil = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause119) ).
thf(396,plain,
! [B: $i,A: $i] :
( ( ( app @ A @ B )
!= nil )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( nil = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(91,axiom,
! [A: $i] : ( ssItem @ ( skaf70 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause25) ).
thf(413,plain,
! [A: $i] : ( ssItem @ ( skaf70 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(2115,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf70 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[413,2096]) ).
thf(2116,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf70 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[2115:[bind(A,$thf( C )),bind(B,$thf( skaf70 @ C ))]]) ).
thf(2154,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf70 @ A ) @ nil ) ),
inference(simp,[status(thm)],[2116]) ).
thf(135,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( lt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause111) ).
thf(507,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( lt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ( ( app @ A @ B )
!= nil )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause118) ).
thf(307,plain,
! [B: $i,A: $i] :
( ( ( app @ A @ B )
!= nil )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(77,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(380,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)],[77]) ).
thf(677,plain,
( ( ssItem @ sk5 )
| ( equalelemsP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[666,332]) ).
thf(678,plain,
( ( ssItem @ sk5 )
| ( equalelemsP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[677:[]]) ).
thf(149,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(546,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)],[149]) ).
thf(1999,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( neq @ sk1 @ nil )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[684,661]) ).
thf(2000,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( neq @ sk1 @ nil ) ),
inference(pattern_uni,[status(thm)],[1999:[]]) ).
thf(137,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)],[137]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( gt @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause110) ).
thf(439,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( gt @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(1460,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf70 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[413,452]) ).
thf(1461,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf70 @ A ) ),
inference(pattern_uni,[status(thm)],[1460:[bind(A,$thf( C )),bind(B,$thf( skaf70 @ C ))]]) ).
thf(1470,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf70 @ A ) ),
inference(simp,[status(thm)],[1461]) ).
thf(14,negated_conjecture,
( ( memberP @ sk4 @ sk5 )
| ( nil = sk3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
thf(203,plain,
( ( memberP @ sk4 @ sk5 )
| ( nil = sk3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(228,plain,
( ( memberP @ sk4 @ sk5 )
| ( nil = sk3 ) ),
inference(cnf,[status(esa)],[203]) ).
thf(229,plain,
( ( nil = sk3 )
| ( memberP @ sk4 @ sk5 ) ),
inference(lifteq,[status(thm)],[228]) ).
thf(1017,plain,
( ( nil = sk1 )
| ( memberP @ sk2 @ sk5 ) ),
inference(rewrite,[status(thm)],[229,220,223]) ).
thf(2015,plain,
( ( nil = sk1 )
| ( ( memberP @ nil @ sk5 )
!= ( memberP @ sk2 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[1017,684]) ).
thf(2091,plain,
( ( nil = sk1 )
| ( nil != sk2 )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[2015]) ).
thf(2093,plain,
( ( nil = sk1 )
| ( nil != sk2 ) ),
inference(simp,[status(thm)],[2091]) ).
thf(167,axiom,
! [A: $i] : ( ssItem @ ( skaf83 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause12) ).
thf(588,plain,
! [A: $i] : ( ssItem @ ( skaf83 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(1882,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf83 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[588,452]) ).
thf(1883,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf83 @ A ) ),
inference(pattern_uni,[status(thm)],[1882:[bind(A,$thf( C )),bind(B,$thf( skaf83 @ C ))]]) ).
thf(1900,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf83 @ A ) ),
inference(simp,[status(thm)],[1883]) ).
thf(45,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(302,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)],[45]) ).
thf(174,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(598,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)],[174]) ).
thf(157,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(561,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)],[157]) ).
thf(43,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause117) ).
thf(297,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(188,axiom,
! [A: $i] : ( ssItem @ ( skaf78 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause17) ).
thf(627,plain,
! [A: $i] : ( ssItem @ ( skaf78 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(2915,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf78 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[627,452]) ).
thf(2916,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf78 @ A ) ),
inference(pattern_uni,[status(thm)],[2915:[bind(A,$thf( C )),bind(B,$thf( skaf78 @ C ))]]) ).
thf(2937,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf78 @ A ) ),
inference(simp,[status(thm)],[2916]) ).
thf(99,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(429,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)],[99]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( leq @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause107) ).
thf(275,plain,
! [B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( leq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(196,axiom,
totalorderedP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause4) ).
thf(648,plain,
totalorderedP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(728,plain,
( ( ssItem @ sk5 )
| ( totalorderedP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[701,648]) ).
thf(729,plain,
( ( ssItem @ sk5 )
| ( totalorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[728:[]]) ).
thf(27,axiom,
! [A: $i] :
( ~ ( singletonP @ A )
| ~ ( ssList @ A )
| ( ( cons @ ( skaf44 @ A ) @ nil )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause101) ).
thf(260,plain,
! [A: $i] :
( ~ ( singletonP @ A )
| ~ ( ssList @ A )
| ( ( cons @ ( skaf44 @ A ) @ nil )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(118,axiom,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( segmentP @ nil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause79) ).
thf(467,plain,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( segmentP @ nil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(159,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( tl @ A ) )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause77) ).
thf(566,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( tl @ A ) )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(70,axiom,
! [A: $i] : ( ssList @ ( skaf58 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause37) ).
thf(361,plain,
! [A: $i] : ( ssList @ ( skaf58 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(56,axiom,
! [A: $i] :
( ~ ( lt @ ( skaf60 @ A ) @ ( skaf59 @ A ) )
| ~ ( ssList @ A )
| ( strictorderP @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause92) ).
thf(329,plain,
! [A: $i] :
( ~ ( lt @ ( skaf60 @ A ) @ ( skaf59 @ A ) )
| ~ ( ssList @ A )
| ( strictorderP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(2,negated_conjecture,
ssList @ sk2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
thf(208,plain,
ssList @ sk2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(664,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[208,250]) ).
thf(665,plain,
~ ( neq @ sk2 @ sk2 ),
inference(pattern_uni,[status(thm)],[664:[bind(A,$thf( sk2 ))]]) ).
thf(38,axiom,
! [A: $i] : ( ssItem @ ( skaf64 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause31) ).
thf(285,plain,
! [A: $i] : ( ssItem @ ( skaf64 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(165,axiom,
! [A: $i] :
( ~ ( segmentP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause80) ).
thf(583,plain,
! [A: $i] :
( ~ ( segmentP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(141,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)],[141]) ).
thf(163,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(578,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)],[163]) ).
thf(30,axiom,
! [A: $i] : ( ssItem @ ( skaf79 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause16) ).
thf(267,plain,
! [A: $i] : ( ssItem @ ( skaf79 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(2127,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf79 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[267,2096]) ).
thf(2128,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf79 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[2127:[bind(A,$thf( C )),bind(B,$thf( skaf79 @ C ))]]) ).
thf(2157,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf79 @ A ) @ nil ) ),
inference(simp,[status(thm)],[2128]) ).
thf(198,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(650,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)],[198]) ).
thf(182,axiom,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( lt @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause114) ).
thf(615,plain,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( lt @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(724,plain,
( ( ssItem @ sk5 )
| ~ ( neq @ nil @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[701,661]) ).
thf(725,plain,
( ( ssItem @ sk5 )
| ~ ( neq @ nil @ sk2 ) ),
inference(pattern_uni,[status(thm)],[724:[]]) ).
thf(80,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(388,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)],[80]) ).
thf(178,axiom,
! [A: $i] : ( ssItem @ ( skaf50 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause45) ).
thf(607,plain,
! [A: $i] : ( ssItem @ ( skaf50 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(2515,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf50 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[607,452]) ).
thf(2516,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf50 @ A ) ),
inference(pattern_uni,[status(thm)],[2515:[bind(A,$thf( C )),bind(B,$thf( skaf50 @ C ))]]) ).
thf(2537,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf50 @ A ) ),
inference(simp,[status(thm)],[2516]) ).
thf(170,axiom,
! [A: $i] : ( ssList @ ( skaf82 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause13) ).
thf(593,plain,
! [A: $i] : ( ssList @ ( skaf82 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(131,axiom,
! [A: $i] : ( ssList @ ( skaf52 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause43) ).
thf(499,plain,
! [A: $i] : ( ssList @ ( skaf52 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(125,axiom,
! [A: $i] : ( ssList @ ( skaf68 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause27) ).
thf(488,plain,
! [A: $i] : ( ssList @ ( skaf68 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(49,axiom,
strictorderP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause5) ).
thf(313,plain,
strictorderP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(752,plain,
( ( memberP @ sk2 @ sk5 )
| ( strictorderP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[737,313]) ).
thf(753,plain,
( ( memberP @ sk2 @ sk5 )
| ( strictorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[752:[]]) ).
thf(129,axiom,
cyclefreeP @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause7) ).
thf(494,plain,
cyclefreeP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(685,plain,
( ( ssItem @ sk5 )
| ( cyclefreeP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[666,494]) ).
thf(686,plain,
( ( ssItem @ sk5 )
| ( cyclefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[685:[]]) ).
thf(119,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(471,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)],[119]) ).
thf(186,axiom,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ssList @ ( cons @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause86) ).
thf(622,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ssList @ ( cons @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(82,axiom,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( neq @ B @ A )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause102) ).
thf(393,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( neq @ B @ A )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(57,axiom,
! [A: $i] : ( ssList @ ( skaf57 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause38) ).
thf(331,plain,
! [A: $i] : ( ssList @ ( skaf57 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(982,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf57 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[331,250]) ).
thf(983,plain,
! [A: $i] :
~ ( neq @ ( skaf57 @ A ) @ ( skaf57 @ A ) ),
inference(pattern_uni,[status(thm)],[982:[bind(A,$thf( C )),bind(B,$thf( skaf57 @ C ))]]) ).
thf(985,plain,
! [A: $i] :
~ ( neq @ ( skaf57 @ A ) @ ( skaf57 @ A ) ),
inference(simp,[status(thm)],[983]) ).
thf(75,axiom,
! [A: $i] : ( ssItem @ ( skaf44 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause47) ).
thf(375,plain,
! [A: $i] : ( ssItem @ ( skaf44 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(2113,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf44 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[375,2096]) ).
thf(2114,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf44 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[2113:[bind(A,$thf( C )),bind(B,$thf( skaf44 @ C ))]]) ).
thf(2153,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf44 @ A ) @ nil ) ),
inference(simp,[status(thm)],[2114]) ).
thf(113,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ A @ nil )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause73) ).
thf(457,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ A @ nil )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(160,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( cons @ ( skaf83 @ A ) @ ( skaf82 @ A ) )
= A )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause109) ).
thf(569,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( cons @ ( skaf83 @ A ) @ ( skaf82 @ A ) )
= A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(74,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(371,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)],[74]) ).
thf(177,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(605,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)],[177]) ).
thf(29,axiom,
! [A: $i] : ( ssList @ ( skaf72 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause23) ).
thf(266,plain,
! [A: $i] : ( ssList @ ( skaf72 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(790,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf72 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[266,250]) ).
thf(791,plain,
! [A: $i] :
~ ( neq @ ( skaf72 @ A ) @ ( skaf72 @ A ) ),
inference(pattern_uni,[status(thm)],[790:[bind(A,$thf( C )),bind(B,$thf( skaf72 @ C ))]]) ).
thf(792,plain,
! [A: $i] :
~ ( neq @ ( skaf72 @ A ) @ ( skaf72 @ A ) ),
inference(simp,[status(thm)],[791]) ).
thf(156,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(558,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)],[156]) ).
thf(673,plain,
( ( ssItem @ sk5 )
| ( strictorderP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[666,313]) ).
thf(674,plain,
( ( ssItem @ sk5 )
| ( strictorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[673:[]]) ).
thf(166,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(586,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)],[166]) ).
thf(62,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf45 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause51) ).
thf(343,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf45 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(16,axiom,
skac3 != skac2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause54) ).
thf(235,plain,
skac3 != skac2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(236,plain,
skac3 != skac2,
inference(polarity_switch,[status(thm)],[235]) ).
thf(237,plain,
skac2 != skac3,
inference(lifteq,[status(thm)],[236]) ).
thf(184,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf42 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause53) ).
thf(618,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf42 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(744,plain,
( ( memberP @ sk2 @ sk5 )
| ( duplicatefreeP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[737,349]) ).
thf(745,plain,
( ( memberP @ sk2 @ sk5 )
| ( duplicatefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[744:[]]) ).
thf(107,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( hd @ A ) )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause76) ).
thf(444,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( hd @ A ) )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(175,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(601,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)],[175]) ).
thf(732,plain,
( ( ssItem @ sk5 )
| ~ ( singletonP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[701,506]) ).
thf(733,plain,
( ( ssItem @ sk5 )
| ~ ( singletonP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[732:[]]) ).
thf(97,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(423,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)],[97]) ).
thf(693,plain,
( ( ssItem @ sk5 )
| ~ ( neq @ sk1 @ nil )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[666,661]) ).
thf(694,plain,
( ( ssItem @ sk5 )
| ~ ( neq @ sk1 @ nil ) ),
inference(pattern_uni,[status(thm)],[693:[]]) ).
thf(86,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(402,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)],[86]) ).
thf(39,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(286,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)],[39]) ).
thf(710,plain,
( ( ssItem @ sk5 )
| ( totalorderP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[701,489]) ).
thf(711,plain,
( ( ssItem @ sk5 )
| ( totalorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[710:[]]) ).
thf(41,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( tl @ A ) )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause75) ).
thf(291,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( tl @ A ) )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(1,negated_conjecture,
ssList @ sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
thf(204,plain,
ssList @ sk1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(81,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(391,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)],[81]) ).
thf(161,axiom,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ( tl @ ( cons @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause96) ).
thf(572,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ( tl @ ( cons @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(180,axiom,
! [A: $i] : ( ssList @ ( skaf71 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause24) ).
thf(611,plain,
! [A: $i] : ( ssList @ ( skaf71 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(712,plain,
( ( ssItem @ sk5 )
| ( strictorderP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[701,313]) ).
thf(713,plain,
( ( ssItem @ sk5 )
| ( strictorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[712:[]]) ).
thf(12,negated_conjecture,
! [A: $i] :
( ~ ( ssItem @ A )
| ( sk5 = A )
| ~ ( memberP @ sk4 @ A )
| ~ ( leq @ A @ sk5 )
| ( nil = sk4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
thf(209,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( sk5 = A )
| ~ ( memberP @ sk4 @ A )
| ~ ( leq @ A @ sk5 )
| ( nil = sk4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(226,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( sk5 = A )
| ~ ( memberP @ sk4 @ A )
| ~ ( leq @ A @ sk5 )
| ( nil = sk4 ) ),
inference(cnf,[status(esa)],[209]) ).
thf(227,plain,
! [A: $i] :
( ( sk5 = A )
| ( nil = sk4 )
| ~ ( ssItem @ A )
| ~ ( memberP @ sk4 @ A )
| ~ ( leq @ A @ sk5 ) ),
inference(lifteq,[status(thm)],[226]) ).
thf(804,plain,
! [A: $i] :
( ( sk5 = A )
| ( nil = sk2 )
| ~ ( ssItem @ A )
| ~ ( memberP @ sk2 @ A )
| ~ ( leq @ A @ sk5 ) ),
inference(rewrite,[status(thm)],[227,220]) ).
thf(66,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ nil @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause74) ).
thf(350,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ nil @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(147,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(540,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)],[147]) ).
thf(671,plain,
( ( ssItem @ sk5 )
| ( totalorderP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[666,489]) ).
thf(672,plain,
( ( ssItem @ sk5 )
| ( totalorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[671:[]]) ).
thf(117,axiom,
! [A: $i] : ( ssList @ ( skaf75 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause20) ).
thf(466,plain,
! [A: $i] : ( ssList @ ( skaf75 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(689,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ( ( ssItem @ skac3 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[552,452]) ).
thf(690,plain,
~ ( memberP @ nil @ skac3 ),
inference(pattern_uni,[status(thm)],[689:[bind(A,$thf( skac3 ))]]) ).
thf(2054,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( memberP @ sk1 @ skac3 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[684,690]) ).
thf(2055,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( memberP @ sk1 @ skac3 ) ),
inference(pattern_uni,[status(thm)],[2054:[]]) ).
thf(176,axiom,
! [A: $i] : ( ssList @ ( skaf56 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause39) ).
thf(604,plain,
! [A: $i] : ( ssList @ ( skaf56 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(3250,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( singletonP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[721,506]) ).
thf(3251,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( singletonP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3250:[]]) ).
thf(1111,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf55 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[409,452]) ).
thf(1112,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf55 @ A ) ),
inference(pattern_uni,[status(thm)],[1111:[bind(A,$thf( C )),bind(B,$thf( skaf55 @ C ))]]) ).
thf(1117,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf55 @ A ) ),
inference(simp,[status(thm)],[1112]) ).
thf(7,negated_conjecture,
~ ( segmentP @ sk2 @ sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
thf(210,plain,
~ ( segmentP @ sk2 @ sk1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(230,plain,
~ ( segmentP @ sk2 @ sk1 ),
inference(polarity_switch,[status(thm)],[210]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( gt @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause106) ).
thf(245,plain,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( gt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(71,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(362,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)],[71]) ).
thf(51,axiom,
! [A: $i] : ( ssList @ ( skaf77 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause18) ).
thf(318,plain,
! [A: $i] : ( ssList @ ( skaf77 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(197,axiom,
! [A: $i] : ( ssItem @ ( skaf59 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause36) ).
thf(649,plain,
! [A: $i] : ( ssItem @ ( skaf59 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(101,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(434,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)],[101]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( ssList @ ( app @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause85) ).
thf(271,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( ssList @ ( app @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(190,axiom,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( frontsegP @ nil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause83) ).
thf(631,plain,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( frontsegP @ nil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(145,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)],[145]) ).
thf(171,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(594,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)],[171]) ).
thf(699,plain,
( ( ssItem @ sk5 )
| ( totalorderedP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[666,648]) ).
thf(700,plain,
( ( ssItem @ sk5 )
| ( totalorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[699:[]]) ).
thf(73,axiom,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( rearsegP @ nil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause81) ).
thf(367,plain,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( rearsegP @ nil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( geq @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause108) ).
thf(239,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( geq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(240,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( geq @ B @ A ) ),
inference(cnf,[status(esa)],[239]) ).
thf(84,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(399,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)],[84]) ).
thf(192,axiom,
! [B: $i,A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( strictorderedP @ ( cons @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause112) ).
thf(636,plain,
! [B: $i,A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( strictorderedP @ ( cons @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(112,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(455,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)],[112]) ).
thf(179,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(608,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)],[179]) ).
thf(103,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf48 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause48) ).
thf(438,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf48 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(199,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( frontsegP @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause61) ).
thf(653,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( frontsegP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(127,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( frontsegP @ A @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause60) ).
thf(490,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( frontsegP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(98,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(426,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)],[98]) ).
thf(168,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(589,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)],[168]) ).
thf(793,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf79 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[267,452]) ).
thf(794,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf79 @ A ) ),
inference(pattern_uni,[status(thm)],[793:[bind(A,$thf( C )),bind(B,$thf( skaf79 @ C ))]]) ).
thf(795,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf79 @ A ) ),
inference(simp,[status(thm)],[794]) ).
thf(662,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[204,250]) ).
thf(663,plain,
~ ( neq @ sk1 @ sk1 ),
inference(pattern_uni,[status(thm)],[662:[bind(A,$thf( sk1 ))]]) ).
thf(3160,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( neq @ sk2 @ nil )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[721,661]) ).
thf(3161,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( neq @ sk2 @ nil ) ),
inference(pattern_uni,[status(thm)],[3160:[]]) ).
thf(24,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(254,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)],[24]) ).
thf(255,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(cnf,[status(esa)],[254]) ).
thf(183,axiom,
! [A: $i] : ( ssList @ ( skaf76 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause19) ).
thf(617,plain,
! [A: $i] : ( ssList @ ( skaf76 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(172,axiom,
! [A: $i] : ( ssItem @ ( skaf54 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause41) ).
thf(596,plain,
! [A: $i] : ( ssItem @ ( skaf54 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(2240,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf54 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[596,452]) ).
thf(2241,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf54 @ A ) ),
inference(pattern_uni,[status(thm)],[2240:[bind(A,$thf( C )),bind(B,$thf( skaf54 @ C ))]]) ).
thf(2256,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf54 @ A ) ),
inference(simp,[status(thm)],[2241]) ).
thf(68,axiom,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ( hd @ ( cons @ A @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause97) ).
thf(355,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ( hd @ ( cons @ A @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(153,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( hd @ A ) )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause78) ).
thf(553,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( hd @ A ) )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(155,axiom,
! [A: $i] : ( ssList @ ( skaf66 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause29) ).
thf(557,plain,
! [A: $i] : ( ssList @ ( skaf66 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(193,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(640,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)],[193]) ).
thf(2954,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf59 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[649,452]) ).
thf(2955,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf59 @ A ) ),
inference(pattern_uni,[status(thm)],[2954:[bind(A,$thf( C )),bind(B,$thf( skaf59 @ C ))]]) ).
thf(2977,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf59 @ A ) ),
inference(simp,[status(thm)],[2955]) ).
thf(55,axiom,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ( duplicatefreeP @ A )
| ( ssItem @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause72) ).
thf(327,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ( duplicatefreeP @ A )
| ( ssItem @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(92,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( rearsegP @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause59) ).
thf(414,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( rearsegP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(965,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf64 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[285,452]) ).
thf(966,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf64 @ A ) ),
inference(pattern_uni,[status(thm)],[965:[bind(A,$thf( C )),bind(B,$thf( skaf64 @ C ))]]) ).
thf(971,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf64 @ A ) ),
inference(simp,[status(thm)],[966]) ).
thf(28,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(263,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)],[28]) ).
thf(48,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(310,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)],[48]) ).
thf(105,axiom,
! [A: $i] : ( ssItem @ ( skaf49 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause46) ).
thf(441,plain,
! [A: $i] : ( ssItem @ ( skaf49 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(115,axiom,
! [A: $i] :
( ~ ( leq @ ( skaf54 @ A ) @ ( skaf55 @ A ) )
| ~ ( ssList @ A )
| ( totalorderP @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause95) ).
thf(463,plain,
! [A: $i] :
( ~ ( leq @ ( skaf54 @ A ) @ ( skaf55 @ A ) )
| ~ ( ssList @ A )
| ( totalorderP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(194,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(643,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)],[194]) ).
thf(148,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(544,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)],[148]) ).
thf(702,plain,
( ( ssItem @ sk5 )
| ( sk2 = sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[701,666]) ).
thf(703,plain,
( ( ssItem @ sk5 )
| ( sk2 = sk1 ) ),
inference(pattern_uni,[status(thm)],[702:[]]) ).
thf(726,plain,
( ( ssItem @ sk5 )
| ( cyclefreeP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[701,494]) ).
thf(727,plain,
( ( ssItem @ sk5 )
| ( cyclefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[726:[]]) ).
thf(50,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(314,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)],[50]) ).
thf(181,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(612,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)],[181]) ).
thf(976,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf77 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[318,250]) ).
thf(977,plain,
! [A: $i] :
~ ( neq @ ( skaf77 @ A ) @ ( skaf77 @ A ) ),
inference(pattern_uni,[status(thm)],[976:[bind(A,$thf( C )),bind(B,$thf( skaf77 @ C ))]]) ).
thf(978,plain,
! [A: $i] :
~ ( neq @ ( skaf77 @ A ) @ ( skaf77 @ A ) ),
inference(simp,[status(thm)],[977]) ).
thf(79,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( geq @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause55) ).
thf(386,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( geq @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(109,axiom,
! [A: $i] : ( ssList @ ( skaf80 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause15) ).
thf(450,plain,
! [A: $i] : ( ssList @ ( skaf80 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(154,axiom,
! [A: $i] : ( ssList @ ( skaf63 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause32) ).
thf(556,plain,
! [A: $i] : ( ssList @ ( skaf63 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(130,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(495,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)],[130]) ).
thf(13,negated_conjecture,
( ( ( cons @ sk5 @ nil )
= sk3 )
| ( nil = sk3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
thf(207,plain,
( ( ( cons @ sk5 @ nil )
= sk3 )
| ( nil = sk3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(233,plain,
( ( ( cons @ sk5 @ nil )
= sk3 )
| ( nil = sk3 ) ),
inference(cnf,[status(esa)],[207]) ).
thf(234,plain,
( ( ( cons @ sk5 @ nil )
= sk3 )
| ( nil = sk3 ) ),
inference(lifteq,[status(thm)],[233]) ).
thf(1575,plain,
( ( ( cons @ sk5 @ nil )
= sk1 )
| ( nil = sk1 ) ),
inference(rewrite,[status(thm)],[234,223]) ).
thf(116,axiom,
! [A: $i] : ( ssList @ ( skaf53 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause42) ).
thf(465,plain,
! [A: $i] : ( ssList @ ( skaf53 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(123,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( cons @ ( hd @ A ) @ ( tl @ A ) )
= A )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause104) ).
thf(482,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( cons @ ( hd @ A ) @ ( tl @ A ) )
= A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(142,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)],[142]) ).
thf(164,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( totalorderP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause69) ).
thf(581,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( totalorderP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(139,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)],[139]) ).
thf(52,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(319,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)],[52]) ).
thf(26,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( cyclefreeP @ A )
| ( leq @ ( skaf49 @ A ) @ ( skaf50 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause88) ).
thf(258,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( cyclefreeP @ A )
| ( leq @ ( skaf49 @ A ) @ ( skaf50 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(85,axiom,
! [A: $i] : ( ssList @ ( skaf73 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause22) ).
thf(401,plain,
! [A: $i] : ( ssList @ ( skaf73 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(730,plain,
( ( ssItem @ sk5 )
| ~ ( memberP @ sk2 @ skac2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[701,688]) ).
thf(731,plain,
( ( ssItem @ sk5 )
| ~ ( memberP @ sk2 @ skac2 ) ),
inference(pattern_uni,[status(thm)],[730:[]]) ).
thf(121,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( leq @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause62) ).
thf(478,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( leq @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(150,axiom,
! [A: $i] : ( ssList @ ( skaf51 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause44) ).
thf(549,plain,
! [A: $i] : ( ssList @ ( skaf51 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(4,negated_conjecture,
ssList @ sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
thf(214,plain,
ssList @ sk4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(246,plain,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( gt @ B @ A ) ),
inference(cnf,[status(esa)],[245]) ).
thf(1499,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf49 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[441,452]) ).
thf(1500,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf49 @ A ) ),
inference(pattern_uni,[status(thm)],[1499:[bind(A,$thf( C )),bind(B,$thf( skaf49 @ C ))]]) ).
thf(1512,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf49 @ A ) ),
inference(simp,[status(thm)],[1500]) ).
thf(108,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(447,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)],[108]) ).
thf(100,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( cyclefreeP @ A )
| ( leq @ ( skaf50 @ A ) @ ( skaf49 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause87) ).
thf(432,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( cyclefreeP @ A )
| ( leq @ ( skaf50 @ A ) @ ( skaf49 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(90,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(410,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)],[90]) ).
thf(87,axiom,
! [B: $i,A: $i] :
( ( ( cons @ A @ B )
!= nil )
| ~ ( ssItem @ A )
| ~ ( ssList @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause98) ).
thf(405,plain,
! [B: $i,A: $i] :
( ( ( cons @ A @ B )
!= nil )
| ~ ( ssItem @ A )
| ~ ( ssList @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(33,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(273,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)],[33]) ).
thf(734,plain,
( ( ssItem @ sk5 )
| ( strictorderedP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[701,635]) ).
thf(735,plain,
( ( ssItem @ sk5 )
| ( strictorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[734:[]]) ).
thf(158,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(564,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)],[158]) ).
thf(46,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( rearsegP @ A @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause58) ).
thf(305,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( rearsegP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(42,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(294,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)],[42]) ).
thf(61,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( strictorderedP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause66) ).
thf(341,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( strictorderedP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(69,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(358,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)],[69]) ).
thf(120,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(474,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)],[120]) ).
thf(144,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)],[144]) ).
thf(695,plain,
( ( ssItem @ sk5 )
| ~ ( neq @ nil @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[666,661]) ).
thf(696,plain,
( ( ssItem @ sk5 )
| ~ ( neq @ nil @ sk1 ) ),
inference(pattern_uni,[status(thm)],[695:[]]) ).
thf(31,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(268,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)],[31]) ).
thf(2476,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf65 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[597,452]) ).
thf(2477,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf65 @ A ) ),
inference(pattern_uni,[status(thm)],[2476:[bind(A,$thf( C )),bind(B,$thf( skaf65 @ C ))]]) ).
thf(2502,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf65 @ A ) ),
inference(simp,[status(thm)],[2477]) ).
thf(162,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(575,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)],[162]) ).
thf(143,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)],[143]) ).
thf(722,plain,
( ( ssItem @ sk5 )
| ~ ( neq @ sk2 @ nil )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[701,661]) ).
thf(723,plain,
( ( ssItem @ sk5 )
| ~ ( neq @ sk2 @ nil ) ),
inference(pattern_uni,[status(thm)],[722:[]]) ).
thf(35,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(277,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)],[35]) ).
thf(106,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( segmentP @ A @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause56) ).
thf(442,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( segmentP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(133,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(501,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)],[133]) ).
thf(1087,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf44 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[375,452]) ).
thf(1088,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf44 @ A ) ),
inference(pattern_uni,[status(thm)],[1087:[bind(A,$thf( C )),bind(B,$thf( skaf44 @ C ))]]) ).
thf(1093,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf44 @ A ) ),
inference(simp,[status(thm)],[1088]) ).
thf(187,axiom,
! [A: $i] :
( ( ( skaf79 @ A )
!= ( skaf78 @ A ) )
| ~ ( ssList @ A )
| ( equalelemsP @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause89) ).
thf(624,plain,
! [A: $i] :
( ( ( skaf79 @ A )
!= ( skaf78 @ A ) )
| ~ ( ssList @ A )
| ( equalelemsP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(53,axiom,
! [A: $i] :
( ~ ( rearsegP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause82) ).
thf(322,plain,
! [A: $i] :
( ~ ( rearsegP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(60,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(337,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)],[60]) ).
thf(15,negated_conjecture,
! [A: $i] :
( ~ ( ssItem @ A )
| ( sk5 = A )
| ~ ( memberP @ sk4 @ A )
| ~ ( leq @ A @ sk5 )
| ( nil = sk3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
thf(215,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( sk5 = A )
| ~ ( memberP @ sk4 @ A )
| ~ ( leq @ A @ sk5 )
| ( nil = sk3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(231,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( sk5 = A )
| ~ ( memberP @ sk4 @ A )
| ~ ( leq @ A @ sk5 )
| ( nil = sk3 ) ),
inference(cnf,[status(esa)],[215]) ).
thf(232,plain,
! [A: $i] :
( ( sk5 = A )
| ( nil = sk3 )
| ~ ( ssItem @ A )
| ~ ( memberP @ sk4 @ A )
| ~ ( leq @ A @ sk5 ) ),
inference(lifteq,[status(thm)],[231]) ).
thf(1184,plain,
! [A: $i] :
( ( sk5 = A )
| ( nil = sk1 )
| ~ ( ssItem @ A )
| ~ ( memberP @ sk2 @ A )
| ~ ( leq @ A @ sk5 ) ),
inference(rewrite,[status(thm)],[232,220,223]) ).
thf(216,plain,
( ( ( cons @ sk5 @ nil )
= sk3 )
| ( nil = sk4 ) ),
inference(cnf,[status(esa)],[202]) ).
thf(217,plain,
( ( ( cons @ sk5 @ nil )
= sk3 )
| ( nil = sk4 ) ),
inference(lifteq,[status(thm)],[216]) ).
thf(659,plain,
( ( ( cons @ sk5 @ nil )
= sk1 )
| ( nil = sk2 ) ),
inference(rewrite,[status(thm)],[217,220,223]) ).
thf(169,axiom,
! [A: $i] : ( ssItem @ ( skaf74 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause21) ).
thf(592,plain,
! [A: $i] : ( ssItem @ ( skaf74 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(72,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(364,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)],[72]) ).
thf(2058,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( memberP @ sk1 @ skac2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[684,688]) ).
thf(2059,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( memberP @ sk1 @ skac2 ) ),
inference(pattern_uni,[status(thm)],[2058:[]]) ).
thf(1903,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf74 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[592,452]) ).
thf(1904,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf74 @ A ) ),
inference(pattern_uni,[status(thm)],[1903:[bind(A,$thf( C )),bind(B,$thf( skaf74 @ C ))]]) ).
thf(1917,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf74 @ A ) ),
inference(simp,[status(thm)],[1904]) ).
thf(754,plain,
( ( memberP @ sk2 @ sk5 )
| ( equalelemsP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[737,332]) ).
thf(755,plain,
( ( memberP @ sk2 @ sk5 )
| ( equalelemsP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[754:[]]) ).
thf(675,plain,
( ( ssItem @ sk5 )
| ~ ( singletonP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[666,506]) ).
thf(676,plain,
( ( ssItem @ sk5 )
| ~ ( singletonP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[675:[]]) ).
thf(127470,plain,
$false,
inference(cvc4,[status(thm)],[347,518,666,1110,333,628,408,247,655,511,202,597,1497,384,550,500,715,698,747,670,709,417,288,301,2067,436,2136,257,619,344,2126,460,421,284,416,325,2158,492,789,376,485,238,514,353,480,211,646,253,280,692,453,3157,396,2002,2154,507,206,307,452,380,678,661,546,201,220,2000,512,439,1470,2093,1900,302,598,561,297,2937,429,275,729,260,349,467,566,252,361,329,665,285,583,522,578,2157,650,1017,615,725,388,2537,593,420,499,488,753,686,489,212,471,256,622,393,985,701,2153,457,721,569,371,605,792,266,205,558,674,586,343,237,618,745,444,601,375,733,423,694,402,286,711,291,204,413,391,572,313,611,713,804,350,540,672,466,2055,604,3251,1117,230,245,362,451,737,318,649,434,271,208,494,631,535,594,213,700,367,552,240,251,399,636,455,267,223,608,505,438,241,653,490,2096,426,589,795,663,3161,255,617,2256,355,553,648,209,557,690,640,2977,327,409,414,971,263,310,331,441,463,643,544,703,727,314,612,978,386,627,450,556,539,688,495,1575,250,465,482,203,524,581,588,517,319,258,401,731,207,478,684,549,214,235,246,1512,447,432,410,405,273,735,564,305,210,239,294,341,358,474,635,532,696,506,268,2502,332,575,596,528,723,277,442,501,607,1093,624,254,322,337,1184,659,592,364,2059,215,1917,755,676]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC368-1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n009.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 19 00:50:34 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.81/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.51/1.01 % [INFO] Parsing done (166ms).
% 1.51/1.02 % [INFO] Running in sequential loop mode.
% 1.94/1.21 % [INFO] eprover registered as external prover.
% 1.94/1.21 % [INFO] cvc4 registered as external prover.
% 1.94/1.21 % [INFO] Scanning for conjecture ...
% 2.02/1.29 % [INFO] Found a conjecture and 185 axioms. Running axiom selection ...
% 2.29/1.37 % [INFO] Axiom selection finished. Selected 185 axioms (removed 0 axioms).
% 2.58/1.46 % [INFO] Problem is propositional (TPTP CNF).
% 2.80/1.47 % [INFO] Type checking passed.
% 2.80/1.47 % [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 ...
% 213.31/39.36 % External prover 'cvc4' found a proof!
% 213.31/39.36 % [INFO] Killing All external provers ...
% 213.31/39.36 % Time passed: 38840ms (effective reasoning time: 38335ms)
% 213.31/39.36 % 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)>
% 213.31/39.37 % 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
% 213.31/39.37 % No. of inferences in proof: 605
% 213.31/39.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 38840 ms resp. 38335 ms w/o parsing
% 213.77/39.51 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 213.86/39.52 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------