TSTP Solution File: SWC374-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWC374-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n010.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 12:11:45 EDT 2023
% Result : Unsatisfiable 223.13s 40.81s
% Output : Refutation 223.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 271
% Syntax : Number of formulae : 736 ( 208 unt; 73 typ; 0 def)
% Number of atoms : 1876 ( 359 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 5250 (1089 ~;1119 |; 0 &;3042 @)
% ( 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 : 845 ( 0 ^; 845 !; 0 ?; 845 :)
% 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(skac3_type,type,
skac3: $i ).
thf(skac2_type,type,
skac2: $i ).
thf(skaf43_type,type,
skaf43: $i > $i > $i ).
thf(leq_type,type,
leq: $i > $i > $o ).
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(150,axiom,
ssItem @ skac3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause9) ).
thf(544,plain,
ssItem @ skac3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( totalorderedP @ ( cons @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause113) ).
thf(233,plain,
! [B: $i,A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( totalorderedP @ ( cons @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(234,plain,
! [B: $i,A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( totalorderedP @ ( cons @ B @ A ) ) ),
inference(cnf,[status(esa)],[233]) ).
thf(235,plain,
! [B: $i,A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( totalorderedP @ ( cons @ B @ A ) ) ),
inference(lifteq,[status(thm)],[234]) ).
thf(236,plain,
! [A: $i] :
( ~ ( ssList @ nil )
| ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ nil ) ) ),
inference(simp,[status(thm)],[235]) ).
thf(42,axiom,
ssList @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
thf(293,plain,
ssList @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(1031,plain,
! [A: $i] :
( ~ $true
| ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ nil ) ) ),
inference(rewrite,[status(thm)],[236,293]) ).
thf(1032,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ nil ) ) ),
inference(simp,[status(thm)],[1031]) ).
thf(1035,plain,
! [A: $i] :
( ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ skac3 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[544,1032]) ).
thf(1036,plain,
totalorderedP @ ( cons @ skac3 @ nil ),
inference(pattern_uni,[status(thm)],[1035:[bind(A,$thf( skac3 ))]]) ).
thf(66,axiom,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ( hd @ ( cons @ A @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause97) ).
thf(347,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ( hd @ ( cons @ A @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(124,axiom,
totalorderP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause6) ).
thf(481,plain,
totalorderP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(197,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( frontsegP @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause61) ).
thf(645,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( frontsegP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(73,axiom,
! [A: $i] : ( ssItem @ ( skaf44 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause47) ).
thf(367,plain,
! [A: $i] : ( ssItem @ ( skaf44 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(108,axiom,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ~ ( ssItem @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause71) ).
thf(443,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ~ ( ssItem @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(444,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ~ ( ssItem @ A ) ),
inference(cnf,[status(esa)],[443]) ).
thf(890,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf44 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[367,444]) ).
thf(891,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf44 @ A ) ),
inference(pattern_uni,[status(thm)],[890:[bind(A,$thf( C )),bind(B,$thf( skaf44 @ C ))]]) ).
thf(892,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf44 @ A ) ),
inference(simp,[status(thm)],[891]) ).
thf(23,axiom,
! [A: $i] :
( ~ ( lt @ ( skaf69 @ A ) @ ( skaf70 @ A ) )
| ~ ( ssList @ A )
| ( strictorderedP @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause90) ).
thf(248,plain,
! [A: $i] :
( ~ ( lt @ ( skaf69 @ A ) @ ( skaf70 @ A ) )
| ~ ( ssList @ A )
| ( strictorderedP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(249,plain,
! [A: $i] :
( ~ ( lt @ ( skaf69 @ A ) @ ( skaf70 @ A ) )
| ~ ( ssList @ A )
| ( strictorderedP @ A ) ),
inference(cnf,[status(esa)],[248]) ).
thf(59,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( strictorderedP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause66) ).
thf(333,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( strictorderedP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(190,axiom,
! [B: $i,A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( strictorderedP @ ( cons @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause112) ).
thf(628,plain,
! [B: $i,A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( strictorderedP @ ( cons @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(91,axiom,
! [A: $i] : ( ssList @ ( skaf61 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause34) ).
thf(408,plain,
! [A: $i] : ( ssList @ ( skaf61 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(186,axiom,
! [A: $i] : ( ssItem @ ( skaf78 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause17) ).
thf(619,plain,
! [A: $i] : ( ssItem @ ( skaf78 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(2100,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf78 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[619,1032]) ).
thf(2101,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf78 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[2100:[bind(A,$thf( C )),bind(B,$thf( skaf78 @ C ))]]) ).
thf(2117,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf78 @ A ) @ nil ) ),
inference(simp,[status(thm)],[2101]) ).
thf(682,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ( ( ssItem @ skac3 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[544,444]) ).
thf(683,plain,
~ ( memberP @ nil @ skac3 ),
inference(pattern_uni,[status(thm)],[682:[bind(A,$thf( skac3 ))]]) ).
thf(111,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ A @ nil )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause73) ).
thf(449,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ A @ nil )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(22,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/sandbox2/benchmark/theBenchmark.p',clause158) ).
thf(246,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)],[22]) ).
thf(247,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)],[246]) ).
thf(1,negated_conjecture,
ssList @ sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
thf(201,plain,
ssList @ sk1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause115) ).
thf(239,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(240,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A ) ),
inference(cnf,[status(esa)],[239]) ).
thf(241,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A ) ),
inference(lifteq,[status(thm)],[240]) ).
thf(242,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ~ ( ssList @ A ) ),
inference(simp,[status(thm)],[241]) ).
thf(654,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[201,242]) ).
thf(655,plain,
~ ( neq @ sk1 @ sk1 ),
inference(pattern_uni,[status(thm)],[654:[bind(A,$thf( sk1 ))]]) ).
thf(9,negated_conjecture,
( ( ssItem @ sk5 )
| ( nil = sk3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
thf(203,plain,
( ( ssItem @ sk5 )
| ( nil = sk3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(220,plain,
( ( ssItem @ sk5 )
| ( nil = sk3 ) ),
inference(cnf,[status(esa)],[203]) ).
thf(221,plain,
( ( nil = sk3 )
| ( ssItem @ sk5 ) ),
inference(lifteq,[status(thm)],[220]) ).
thf(6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
thf(202,plain,
sk1 = sk3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(212,plain,
sk3 = sk1,
inference(lifteq,[status(thm)],[202]) ).
thf(696,plain,
( ( nil = sk1 )
| ( ssItem @ sk5 ) ),
inference(rewrite,[status(thm)],[221,212]) ).
thf(127,axiom,
cyclefreeP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause7) ).
thf(486,plain,
cyclefreeP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(729,plain,
( ( ssItem @ sk5 )
| ( cyclefreeP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[696,486]) ).
thf(730,plain,
( ( ssItem @ sk5 )
| ( cyclefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[729:[]]) ).
thf(35,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf46 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause50) ).
thf(276,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf46 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(8,negated_conjecture,
( ( ssItem @ sk5 )
| ( nil = sk4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
thf(210,plain,
( ( ssItem @ sk5 )
| ( nil = sk4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(223,plain,
( ( ssItem @ sk5 )
| ( nil = sk4 ) ),
inference(cnf,[status(esa)],[210]) ).
thf(224,plain,
( ( nil = sk4 )
| ( ssItem @ sk5 ) ),
inference(lifteq,[status(thm)],[223]) ).
thf(5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
thf(199,plain,
sk2 = sk4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(219,plain,
sk4 = sk2,
inference(lifteq,[status(thm)],[199]) ).
thf(731,plain,
( ( nil = sk2 )
| ( ssItem @ sk5 ) ),
inference(rewrite,[status(thm)],[224,219]) ).
thf(740,plain,
! [A: $i] :
( ( nil = sk2 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[731,444]) ).
thf(741,plain,
( ( nil = sk2 )
| ~ ( memberP @ nil @ sk5 ) ),
inference(pattern_uni,[status(thm)],[740:[bind(A,$thf( sk5 ))]]) ).
thf(93,axiom,
! [A: $i] : ( ssItem @ ( skaf60 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause35) ).
thf(412,plain,
! [A: $i] : ( ssItem @ ( skaf60 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(1041,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf60 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[412,1032]) ).
thf(1042,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf60 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1041:[bind(A,$thf( C )),bind(B,$thf( skaf60 @ C ))]]) ).
thf(1073,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf60 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1042]) ).
thf(184,axiom,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ssList @ ( cons @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause86) ).
thf(614,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ssList @ ( cons @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(33,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/sandbox2/benchmark/theBenchmark.p',clause163) ).
thf(269,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)],[33]) ).
thf(175,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/sandbox2/benchmark/theBenchmark.p',clause172) ).
thf(597,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)],[175]) ).
thf(80,axiom,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( neq @ B @ A )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause102) ).
thf(385,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( neq @ B @ A )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( app @ A @ B )
!= ( app @ A @ C ) )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ~ ( ssList @ C )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause150) ).
thf(550,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)],[154]) ).
thf(120,axiom,
! [A: $i] :
( ~ ( leq @ ( skaf64 @ A ) @ ( skaf65 @ A ) )
| ~ ( ssList @ A )
| ( totalorderedP @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause91) ).
thf(472,plain,
! [A: $i] :
( ~ ( leq @ ( skaf64 @ A ) @ ( skaf65 @ A ) )
| ~ ( ssList @ A )
| ( totalorderedP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(697,plain,
( ( ssItem @ sk5 )
| ( totalorderP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[696,481]) ).
thf(698,plain,
( ( ssItem @ sk5 )
| ( totalorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[697:[]]) ).
thf(189,axiom,
strictorderedP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause3) ).
thf(627,plain,
strictorderedP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(746,plain,
( ( ssItem @ sk5 )
| ( strictorderedP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[731,627]) ).
thf(747,plain,
( ( ssItem @ sk5 )
| ( strictorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[746:[]]) ).
thf(147,axiom,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( nil = B )
| ( ( tl @ ( app @ B @ A ) )
= ( app @ ( tl @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause133) ).
thf(538,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)],[147]) ).
thf(195,axiom,
! [A: $i] : ( ssItem @ ( skaf59 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause36) ).
thf(641,plain,
! [A: $i] : ( ssItem @ ( skaf59 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(2132,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf59 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[641,444]) ).
thf(2133,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf59 @ A ) ),
inference(pattern_uni,[status(thm)],[2132:[bind(A,$thf( C )),bind(B,$thf( skaf59 @ C ))]]) ).
thf(2146,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf59 @ A ) ),
inference(simp,[status(thm)],[2133]) ).
thf(86,axiom,
! [A: $i] : ( ssItem @ ( skaf69 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause26) ).
thf(400,plain,
! [A: $i] : ( ssItem @ ( skaf69 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(896,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf69 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[400,444]) ).
thf(897,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf69 @ A ) ),
inference(pattern_uni,[status(thm)],[896:[bind(A,$thf( C )),bind(B,$thf( skaf69 @ C ))]]) ).
thf(898,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf69 @ A ) ),
inference(simp,[status(thm)],[897]) ).
thf(105,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( hd @ A ) )
| ( nil = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause76) ).
thf(436,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( hd @ A ) )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(12,negated_conjecture,
( ( ( cons @ sk5 @ nil )
= sk3 )
| ( nil = sk3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
thf(206,plain,
( ( ( cons @ sk5 @ nil )
= sk3 )
| ( nil = sk3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(213,plain,
( ( ( cons @ sk5 @ nil )
= sk3 )
| ( nil = sk3 ) ),
inference(cnf,[status(esa)],[206]) ).
thf(214,plain,
( ( ( cons @ sk5 @ nil )
= sk3 )
| ( nil = sk3 ) ),
inference(lifteq,[status(thm)],[213]) ).
thf(651,plain,
( ( ( cons @ sk5 @ nil )
= sk1 )
| ( nil = sk1 ) ),
inference(rewrite,[status(thm)],[214,212]) ).
thf(26,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/sandbox2/benchmark/theBenchmark.p',clause162) ).
thf(255,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)],[26]) ).
thf(256,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( duplicatefreeP @ A )
| ( ( app @ ( app @ ( skaf75 @ A ) @ ( cons @ ( skaf74 @ A ) @ ( skaf76 @ A ) ) ) @ ( cons @ ( skaf74 @ A ) @ ( skaf77 @ A ) ) )
= A ) ),
inference(cnf,[status(esa)],[255]) ).
thf(257,plain,
! [A: $i] :
( ( ( app @ ( app @ ( skaf75 @ A ) @ ( cons @ ( skaf74 @ A ) @ ( skaf76 @ A ) ) ) @ ( cons @ ( skaf74 @ A ) @ ( skaf77 @ A ) ) )
= A )
| ~ ( ssList @ A )
| ( duplicatefreeP @ A ) ),
inference(lifteq,[status(thm)],[256]) ).
thf(161,axiom,
! [B: $i,A: $i] :
( ~ ( totalorderedP @ ( cons @ A @ B ) )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( totalorderedP @ B )
| ( nil = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause125) ).
thf(570,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)],[161]) ).
thf(11,negated_conjecture,
( ( memberP @ sk4 @ sk5 )
| ( nil = sk4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
thf(209,plain,
( ( memberP @ sk4 @ sk5 )
| ( nil = sk4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(217,plain,
( ( memberP @ sk4 @ sk5 )
| ( nil = sk4 ) ),
inference(cnf,[status(esa)],[209]) ).
thf(218,plain,
( ( nil = sk4 )
| ( memberP @ sk4 @ sk5 ) ),
inference(lifteq,[status(thm)],[217]) ).
thf(770,plain,
( ( nil = sk2 )
| ( memberP @ sk2 @ sk5 ) ),
inference(rewrite,[status(thm)],[218,219]) ).
thf(784,plain,
( ( memberP @ sk2 @ sk5 )
| ( strictorderedP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[770,627]) ).
thf(785,plain,
( ( memberP @ sk2 @ sk5 )
| ( strictorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[784:[]]) ).
thf(75,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/sandbox2/benchmark/theBenchmark.p',clause178) ).
thf(372,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)],[75]) ).
thf(144,axiom,
ssItem @ skac2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause10) ).
thf(531,plain,
ssItem @ skac2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(680,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ( ( ssItem @ skac2 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[531,444]) ).
thf(681,plain,
~ ( memberP @ nil @ skac2 ),
inference(pattern_uni,[status(thm)],[680:[bind(A,$thf( skac2 ))]]) ).
thf(750,plain,
( ( ssItem @ sk5 )
| ~ ( memberP @ sk2 @ skac2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[731,681]) ).
thf(751,plain,
( ( ssItem @ sk5 )
| ~ ( memberP @ sk2 @ skac2 ) ),
inference(pattern_uni,[status(thm)],[750:[]]) ).
thf(13,negated_conjecture,
( ( memberP @ sk4 @ sk5 )
| ( nil = sk3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
thf(204,plain,
( ( memberP @ sk4 @ sk5 )
| ( nil = sk3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(215,plain,
( ( memberP @ sk4 @ sk5 )
| ( nil = sk3 ) ),
inference(cnf,[status(esa)],[204]) ).
thf(216,plain,
( ( nil = sk3 )
| ( memberP @ sk4 @ sk5 ) ),
inference(lifteq,[status(thm)],[215]) ).
thf(658,plain,
( ( nil = sk1 )
| ( memberP @ sk2 @ sk5 ) ),
inference(rewrite,[status(thm)],[216,212,219]) ).
thf(705,plain,
! [A: $i] :
( ( nil = sk1 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[696,444]) ).
thf(706,plain,
( ( nil = sk1 )
| ~ ( memberP @ nil @ sk5 ) ),
inference(pattern_uni,[status(thm)],[705:[bind(A,$thf( sk5 ))]]) ).
thf(2687,plain,
( ( nil = sk1 )
| ( ( memberP @ nil @ sk5 )
!= ( memberP @ sk2 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[658,706]) ).
thf(2734,plain,
( ( nil = sk1 )
| ( nil != sk2 )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[2687]) ).
thf(2745,plain,
( ( nil = sk1 )
| ( nil != sk2 ) ),
inference(simp,[status(thm)],[2734]) ).
thf(149,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( strictorderP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause68) ).
thf(542,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( strictorderP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(135,axiom,
! [A: $i] :
( ~ ( lt @ ( skaf59 @ A ) @ ( skaf60 @ A ) )
| ~ ( ssList @ A )
| ( strictorderP @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause93) ).
thf(504,plain,
! [A: $i] :
( ~ ( lt @ ( skaf59 @ A ) @ ( skaf60 @ A ) )
| ~ ( ssList @ A )
| ( strictorderP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(176,axiom,
! [A: $i] : ( ssItem @ ( skaf50 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause45) ).
thf(599,plain,
! [A: $i] : ( ssItem @ ( skaf50 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(1858,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf50 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[599,444]) ).
thf(1859,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf50 @ A ) ),
inference(pattern_uni,[status(thm)],[1858:[bind(A,$thf( C )),bind(B,$thf( skaf50 @ C ))]]) ).
thf(1871,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf50 @ A ) ),
inference(simp,[status(thm)],[1859]) ).
thf(193,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( segmentP @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause57) ).
thf(638,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( segmentP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(97,axiom,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ( app @ ( cons @ A @ nil ) @ B )
= ( cons @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause120) ).
thf(421,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)],[97]) ).
thf(167,axiom,
! [A: $i] : ( ssItem @ ( skaf74 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause21) ).
thf(584,plain,
! [A: $i] : ( ssItem @ ( skaf74 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(1590,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf74 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[584,1032]) ).
thf(1591,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf74 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1590:[bind(A,$thf( C )),bind(B,$thf( skaf74 @ C ))]]) ).
thf(1609,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf74 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1591]) ).
thf(57,axiom,
! [B: $i,A: $i] :
( ( ( cons @ A @ nil )
!= B )
| ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( singletonP @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause116) ).
thf(325,plain,
! [B: $i,A: $i] :
( ( ( cons @ A @ nil )
!= B )
| ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( singletonP @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause117) ).
thf(289,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( neq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(130,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf47 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause49) ).
thf(492,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf47 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(54,axiom,
! [A: $i] :
( ~ ( lt @ ( skaf60 @ A ) @ ( skaf59 @ A ) )
| ~ ( ssList @ A )
| ( strictorderP @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause92) ).
thf(321,plain,
! [A: $i] :
( ~ ( lt @ ( skaf60 @ A ) @ ( skaf59 @ A ) )
| ~ ( ssList @ A )
| ( strictorderP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(76,axiom,
! [A: $i] :
( ~ ( leq @ ( skaf55 @ A ) @ ( skaf54 @ A ) )
| ~ ( ssList @ A )
| ( totalorderP @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause94) ).
thf(376,plain,
! [A: $i] :
( ~ ( leq @ ( skaf55 @ A ) @ ( skaf54 @ A ) )
| ~ ( ssList @ A )
| ( totalorderP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(188,axiom,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( frontsegP @ nil @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause83) ).
thf(623,plain,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( frontsegP @ nil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(4,negated_conjecture,
ssList @ sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).
thf(211,plain,
ssList @ sk4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( gt @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause106) ).
thf(237,plain,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( gt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(238,plain,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( gt @ B @ A ) ),
inference(cnf,[status(esa)],[237]) ).
thf(139,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( duplicatefreeP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause65) ).
thf(514,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( duplicatefreeP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(123,axiom,
! [A: $i] : ( ssList @ ( skaf68 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause27) ).
thf(480,plain,
! [A: $i] : ( ssList @ ( skaf68 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(165,axiom,
! [A: $i] : ( ssItem @ ( skaf83 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause12) ).
thf(580,plain,
! [A: $i] : ( ssItem @ ( skaf83 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(1562,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf83 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[580,444]) ).
thf(1563,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf83 @ A ) ),
inference(pattern_uni,[status(thm)],[1562:[bind(A,$thf( C )),bind(B,$thf( skaf83 @ C ))]]) ).
thf(1581,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf83 @ A ) ),
inference(simp,[status(thm)],[1563]) ).
thf(68,axiom,
! [A: $i] : ( ssList @ ( skaf58 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause37) ).
thf(353,plain,
! [A: $i] : ( ssList @ ( skaf58 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(85,axiom,
! [B: $i,A: $i] :
( ( ( cons @ A @ B )
!= nil )
| ~ ( ssItem @ A )
| ~ ( ssList @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause98) ).
thf(397,plain,
! [B: $i,A: $i] :
( ( ( cons @ A @ B )
!= nil )
| ~ ( ssItem @ A )
| ~ ( ssList @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(38,axiom,
! [B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ~ ( geq @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause126) ).
thf(280,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)],[38]) ).
thf(103,axiom,
! [A: $i] : ( ssItem @ ( skaf49 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause46) ).
thf(433,plain,
! [A: $i] : ( ssItem @ ( skaf49 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(1037,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf49 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[433,1032]) ).
thf(1038,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf49 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1037:[bind(A,$thf( C )),bind(B,$thf( skaf49 @ C ))]]) ).
thf(1072,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf49 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1038]) ).
thf(659,plain,
( ( memberP @ sk2 @ sk5 )
| ( totalorderP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[658,481]) ).
thf(660,plain,
( ( memberP @ sk2 @ sk5 )
| ( totalorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[659:[]]) ).
thf(20,axiom,
! [A: $i] : ( ssList @ ( skaf62 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause33) ).
thf(243,plain,
! [A: $i] : ( ssList @ ( skaf62 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(100,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/sandbox2/benchmark/theBenchmark.p',clause174) ).
thf(428,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)],[100]) ).
thf(31,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/sandbox2/benchmark/theBenchmark.p',clause154) ).
thf(265,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)],[31]) ).
thf(143,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( app @ A @ B )
!= C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ~ ( ssList @ C )
| ( frontsegP @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause144) ).
thf(527,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)],[143]) ).
thf(28,axiom,
! [A: $i] : ( ssItem @ ( skaf79 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause16) ).
thf(259,plain,
! [A: $i] : ( ssItem @ ( skaf79 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(1043,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf79 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[259,1032]) ).
thf(1044,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf79 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1043:[bind(A,$thf( C )),bind(B,$thf( skaf79 @ C ))]]) ).
thf(1074,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf79 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1044]) ).
thf(78,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/sandbox2/benchmark/theBenchmark.p',clause149) ).
thf(380,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)],[78]) ).
thf(106,axiom,
! [B: $i,A: $i] :
( ~ ( totalorderedP @ ( cons @ A @ B ) )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( leq @ A @ ( hd @ B ) )
| ( nil = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause135) ).
thf(439,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)],[106]) ).
thf(47,axiom,
strictorderP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause5) ).
thf(305,plain,
strictorderP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(760,plain,
( ( ssItem @ sk5 )
| ( strictorderP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[731,305]) ).
thf(761,plain,
( ( ssItem @ sk5 )
| ( strictorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[760:[]]) ).
thf(2102,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf78 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[619,444]) ).
thf(2103,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf78 @ A ) ),
inference(pattern_uni,[status(thm)],[2102:[bind(A,$thf( C )),bind(B,$thf( skaf78 @ C ))]]) ).
thf(2118,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf78 @ A ) ),
inference(simp,[status(thm)],[2103]) ).
thf(2620,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( memberP @ sk1 @ skac3 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[706,683]) ).
thf(2621,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( memberP @ sk1 @ skac3 ) ),
inference(pattern_uni,[status(thm)],[2620:[]]) ).
thf(56,axiom,
equalelemsP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause1) ).
thf(324,plain,
equalelemsP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(713,plain,
( ( ssItem @ sk5 )
| ( equalelemsP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[696,324]) ).
thf(714,plain,
( ( ssItem @ sk5 )
| ( equalelemsP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[713:[]]) ).
thf(112,axiom,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( neq @ B @ A )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause100) ).
thf(452,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( neq @ B @ A )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(1560,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf83 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[580,1032]) ).
thf(1561,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf83 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1560:[bind(A,$thf( C )),bind(B,$thf( skaf83 @ C ))]]) ).
thf(1580,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf83 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1561]) ).
thf(46,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/sandbox2/benchmark/theBenchmark.p',clause165) ).
thf(302,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)],[46]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ~ ( strictorderedP @ ( cons @ A @ B ) )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ ( hd @ B ) )
| ( nil = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause134) ).
thf(260,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)],[29]) ).
thf(158,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( cons @ ( skaf83 @ A ) @ ( skaf82 @ A ) )
= A )
| ( nil = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause109) ).
thf(561,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( cons @ ( skaf83 @ A ) @ ( skaf82 @ A ) )
= A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(44,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( rearsegP @ A @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause58) ).
thf(297,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( rearsegP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(98,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( cyclefreeP @ A )
| ( leq @ ( skaf50 @ A ) @ ( skaf49 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause87) ).
thf(424,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( cyclefreeP @ A )
| ( leq @ ( skaf50 @ A ) @ ( skaf49 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( app @ A @ B )
!= C )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( rearsegP @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause143) ).
thf(329,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)],[58]) ).
thf(828,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf62 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[243,242]) ).
thf(829,plain,
! [A: $i] :
~ ( neq @ ( skaf62 @ A ) @ ( skaf62 @ A ) ),
inference(pattern_uni,[status(thm)],[828:[bind(A,$thf( C )),bind(B,$thf( skaf62 @ C ))]]) ).
thf(830,plain,
! [A: $i] :
~ ( neq @ ( skaf62 @ A ) @ ( skaf62 @ A ) ),
inference(simp,[status(thm)],[829]) ).
thf(131,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/sandbox2/benchmark/theBenchmark.p',clause183) ).
thf(493,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)],[131]) ).
thf(194,axiom,
totalorderedP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause4) ).
thf(640,plain,
totalorderedP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(709,plain,
( ( ssItem @ sk5 )
| ( totalorderedP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[696,640]) ).
thf(710,plain,
( ( ssItem @ sk5 )
| ( totalorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[709:[]]) ).
thf(14,axiom,
skac3 != skac2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause54) ).
thf(227,plain,
skac3 != skac2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(228,plain,
skac3 != skac2,
inference(polarity_switch,[status(thm)],[227]) ).
thf(229,plain,
skac2 != skac3,
inference(lifteq,[status(thm)],[228]) ).
thf(126,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( cyclefreeP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause70) ).
thf(484,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( cyclefreeP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(25,axiom,
! [A: $i] :
( ~ ( singletonP @ A )
| ~ ( ssList @ A )
| ( ( cons @ ( skaf44 @ A ) @ nil )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause101) ).
thf(252,plain,
! [A: $i] :
( ~ ( singletonP @ A )
| ~ ( ssList @ A )
| ( ( cons @ ( skaf44 @ A ) @ nil )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(164,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/sandbox2/benchmark/theBenchmark.p',clause153) ).
thf(578,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)],[164]) ).
thf(872,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf58 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[353,242]) ).
thf(873,plain,
! [A: $i] :
~ ( neq @ ( skaf58 @ A ) @ ( skaf58 @ A ) ),
inference(pattern_uni,[status(thm)],[872:[bind(A,$thf( C )),bind(B,$thf( skaf58 @ C ))]]) ).
thf(874,plain,
! [A: $i] :
~ ( neq @ ( skaf58 @ A ) @ ( skaf58 @ A ) ),
inference(simp,[status(thm)],[873]) ).
thf(52,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause67) ).
thf(317,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ( ( app @ A @ B )
!= nil )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( nil = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause119) ).
thf(388,plain,
! [B: $i,A: $i] :
( ( ( app @ A @ B )
!= nil )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( nil = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(70,axiom,
! [B: $i,A: $i] :
( ~ ( rearsegP @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( ( app @ ( skaf46 @ A @ B ) @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause131) ).
thf(356,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)],[70]) ).
thf(173,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/sandbox2/benchmark/theBenchmark.p',clause171) ).
thf(593,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)],[173]) ).
thf(182,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf42 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause53) ).
thf(610,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf42 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(782,plain,
( ( memberP @ sk2 @ sk5 )
| ( totalorderedP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[770,640]) ).
thf(783,plain,
( ( memberP @ sk2 @ sk5 )
| ( totalorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[782:[]]) ).
thf(133,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( lt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause111) ).
thf(499,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( lt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause105) ).
thf(339,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(652,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssList @ nil )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[293,242]) ).
thf(653,plain,
~ ( neq @ nil @ nil ),
inference(pattern_uni,[status(thm)],[652:[bind(A,$thf( nil ))]]) ).
thf(752,plain,
( ( ssItem @ sk5 )
| ~ ( neq @ sk2 @ nil )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[731,653]) ).
thf(753,plain,
( ( ssItem @ sk5 )
| ~ ( neq @ sk2 @ nil ) ),
inference(pattern_uni,[status(thm)],[752:[]]) ).
thf(132,axiom,
~ ( singletonP @ nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause11) ).
thf(497,plain,
~ ( singletonP @ nil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(498,plain,
~ ( singletonP @ nil ),
inference(polarity_switch,[status(thm)],[497]) ).
thf(668,plain,
( ( memberP @ sk2 @ sk5 )
| ~ ( singletonP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[658,498]) ).
thf(669,plain,
( ( memberP @ sk2 @ sk5 )
| ~ ( singletonP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[668:[]]) ).
thf(196,axiom,
! [B: $i,A: $i] :
( ~ ( strictorderedP @ ( cons @ A @ B ) )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( strictorderedP @ B )
| ( nil = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause124) ).
thf(642,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)],[196]) ).
thf(4190,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( singletonP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[741,498]) ).
thf(4191,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( singletonP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[4190:[]]) ).
thf(172,axiom,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( nil = B )
| ( ( hd @ ( app @ B @ A ) )
= ( hd @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause123) ).
thf(590,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)],[172]) ).
thf(678,plain,
( ( memberP @ sk2 @ sk5 )
| ( cyclefreeP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[658,486]) ).
thf(679,plain,
( ( memberP @ sk2 @ sk5 )
| ( cyclefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[678:[]]) ).
thf(87,axiom,
! [A: $i] : ( ssItem @ ( skaf55 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause40) ).
thf(401,plain,
! [A: $i] : ( ssItem @ ( skaf55 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(899,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf55 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[401,444]) ).
thf(900,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf55 @ A ) ),
inference(pattern_uni,[status(thm)],[899:[bind(A,$thf( C )),bind(B,$thf( skaf55 @ C ))]]) ).
thf(901,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf55 @ A ) ),
inference(simp,[status(thm)],[900]) ).
thf(1045,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf44 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[367,1032]) ).
thf(1046,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf44 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1045:[bind(A,$thf( C )),bind(B,$thf( skaf44 @ C ))]]) ).
thf(1075,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf44 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1046]) ).
thf(198,axiom,
! [A: $i] :
( ~ ( lt @ A @ A )
| ~ ( ssItem @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause63) ).
thf(647,plain,
! [A: $i] :
( ~ ( lt @ A @ A )
| ~ ( ssItem @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(134,axiom,
! [A: $i] : ( ssList @ ( skaf67 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause28) ).
thf(503,plain,
! [A: $i] : ( ssList @ ( skaf67 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(2667,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( singletonP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[706,498]) ).
thf(2668,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( singletonP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[2667:[]]) ).
thf(2934,plain,
( ~ ( singletonP @ sk1 )
| ( ( memberP @ nil @ sk5 )
!= ( memberP @ sk2 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[669,2668]) ).
thf(2957,plain,
( ~ ( singletonP @ sk1 )
| ( nil != sk2 )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[2934]) ).
thf(2968,plain,
( ~ ( singletonP @ sk1 )
| ( nil != sk2 ) ),
inference(simp,[status(thm)],[2957]) ).
thf(83,axiom,
! [A: $i] : ( ssList @ ( skaf73 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause22) ).
thf(393,plain,
! [A: $i] : ( ssList @ ( skaf73 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(1049,plain,
! [A: $i] :
( ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ skac2 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[531,1032]) ).
thf(1050,plain,
totalorderedP @ ( cons @ skac2 @ nil ),
inference(pattern_uni,[status(thm)],[1049:[bind(A,$thf( skac2 ))]]) ).
thf(114,axiom,
! [A: $i] : ( ssList @ ( skaf53 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause42) ).
thf(457,plain,
! [A: $i] : ( ssList @ ( skaf53 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(21,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/sandbox2/benchmark/theBenchmark.p',clause147) ).
thf(244,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)],[21]) ).
thf(266,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ~ ( frontsegP @ B @ C )
| ~ ( ssList @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( frontsegP @ A @ C ) ),
inference(cnf,[status(esa)],[265]) ).
thf(2,negated_conjecture,
ssList @ sk2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).
thf(205,plain,
ssList @ sk2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(50,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/sandbox2/benchmark/theBenchmark.p',clause167) ).
thf(311,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)],[50]) ).
thf(148,axiom,
! [A: $i] : ( ssList @ ( skaf51 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause44) ).
thf(541,plain,
! [A: $i] : ( ssList @ ( skaf51 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(656,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[205,242]) ).
thf(657,plain,
~ ( neq @ sk2 @ sk2 ),
inference(pattern_uni,[status(thm)],[656:[bind(A,$thf( sk2 ))]]) ).
thf(764,plain,
( ( ssItem @ sk5 )
| ( sk2 = sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[731,696]) ).
thf(765,plain,
( ( ssItem @ sk5 )
| ( sk2 = sk1 ) ),
inference(pattern_uni,[status(thm)],[764:[]]) ).
thf(169,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/sandbox2/benchmark/theBenchmark.p',clause156) ).
thf(586,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)],[169]) ).
thf(717,plain,
( ( ssItem @ sk5 )
| ~ ( neq @ sk1 @ nil )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[696,653]) ).
thf(718,plain,
( ( ssItem @ sk5 )
| ~ ( neq @ sk1 @ nil ) ),
inference(pattern_uni,[status(thm)],[717:[]]) ).
thf(157,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( tl @ A ) )
| ( nil = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause77) ).
thf(558,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( tl @ A ) )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(36,axiom,
! [A: $i] : ( ssItem @ ( skaf64 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause31) ).
thf(277,plain,
! [A: $i] : ( ssItem @ ( skaf64 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(1067,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf64 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[277,1032]) ).
thf(1068,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf64 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1067:[bind(A,$thf( C )),bind(B,$thf( skaf64 @ C ))]]) ).
thf(1071,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf64 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1068]) ).
thf(101,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf48 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause48) ).
thf(430,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf48 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( ssList @ ( app @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause85) ).
thf(263,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( ssList @ ( app @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(264,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( ssList @ ( app @ B @ A ) ) ),
inference(cnf,[status(esa)],[263]) ).
thf(744,plain,
( ( ssItem @ sk5 )
| ( totalorderedP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[731,640]) ).
thf(745,plain,
( ( ssItem @ sk5 )
| ( totalorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[744:[]]) ).
thf(162,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( totalorderP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause69) ).
thf(573,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( totalorderP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(732,plain,
( ( ssItem @ sk5 )
| ( totalorderP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[731,481]) ).
thf(733,plain,
( ( ssItem @ sk5 )
| ( totalorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[732:[]]) ).
thf(171,axiom,
! [A: $i] : ( ssItem @ ( skaf65 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause30) ).
thf(589,plain,
! [A: $i] : ( ssItem @ ( skaf65 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(1814,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf65 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[589,1032]) ).
thf(1815,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf65 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1814:[bind(A,$thf( C )),bind(B,$thf( skaf65 @ C ))]]) ).
thf(1833,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf65 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1815]) ).
thf(88,axiom,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( leq @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause130) ).
thf(402,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)],[88]) ).
thf(771,plain,
( ( memberP @ sk2 @ sk5 )
| ( totalorderP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[770,481]) ).
thf(772,plain,
( ( memberP @ sk2 @ sk5 )
| ( totalorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[771:[]]) ).
thf(40,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/sandbox2/benchmark/theBenchmark.p',clause164) ).
thf(286,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)],[40]) ).
thf(170,axiom,
! [A: $i] : ( ssItem @ ( skaf54 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause41) ).
thf(588,plain,
! [A: $i] : ( ssItem @ ( skaf54 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(1629,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf54 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[588,1032]) ).
thf(1630,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf54 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1629:[bind(A,$thf( C )),bind(B,$thf( skaf54 @ C ))]]) ).
thf(1652,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf54 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1630]) ).
thf(742,plain,
( ( ssItem @ sk5 )
| ~ ( singletonP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[731,498]) ).
thf(743,plain,
( ( ssItem @ sk5 )
| ~ ( singletonP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[742:[]]) ).
thf(151,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( hd @ A ) )
| ( nil = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause78) ).
thf(545,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( hd @ A ) )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ~ ( ssList @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( frontsegP @ ( app @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause137) ).
thf(413,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)],[94]) ).
thf(82,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/sandbox2/benchmark/theBenchmark.p',clause148) ).
thf(391,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)],[82]) ).
thf(109,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( equalelemsP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause64) ).
thf(445,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( equalelemsP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(183,axiom,
! [A: $i] :
( ~ ( frontsegP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause84) ).
thf(611,plain,
! [A: $i] :
( ~ ( frontsegP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(118,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/sandbox2/benchmark/theBenchmark.p',clause179) ).
thf(466,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)],[118]) ).
thf(60,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf45 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause51) ).
thf(335,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf45 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(67,axiom,
! [B: $i,A: $i] :
( ~ ( leq @ A @ ( hd @ B ) )
| ~ ( totalorderedP @ B )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ B ) )
| ( nil = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause159) ).
thf(350,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)],[67]) ).
thf(179,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/sandbox2/benchmark/theBenchmark.p',clause169) ).
thf(604,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)],[179]) ).
thf(90,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( rearsegP @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause59) ).
thf(406,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( rearsegP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(15,axiom,
! [B: $i,A: $i] : ( ssList @ ( skaf43 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause52) ).
thf(230,plain,
! [B: $i,A: $i] : ( ssList @ ( skaf43 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(160,axiom,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause122) ).
thf(567,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)],[160]) ).
thf(245,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)],[244]) ).
thf(185,axiom,
! [A: $i] :
( ( ( skaf79 @ A )
!= ( skaf78 @ A ) )
| ~ ( ssList @ A )
| ( equalelemsP @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause89) ).
thf(616,plain,
! [A: $i] :
( ( ( skaf79 @ A )
!= ( skaf78 @ A ) )
| ~ ( ssList @ A )
| ( equalelemsP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(3,negated_conjecture,
ssList @ sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
thf(208,plain,
ssList @ sk3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(137,axiom,
! [A: $i] : ( ssList @ ( skaf81 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause14) ).
thf(509,plain,
! [A: $i] : ( ssList @ ( skaf81 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(104,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( segmentP @ A @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause56) ).
thf(434,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( segmentP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(122,axiom,
! [B: $i,A: $i] :
( ( ( cons @ A @ B )
!= B )
| ~ ( ssItem @ A )
| ~ ( ssList @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause99) ).
thf(477,plain,
! [B: $i,A: $i] :
( ( ( cons @ A @ B )
!= B )
| ~ ( ssItem @ A )
| ~ ( ssList @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(181,axiom,
! [A: $i] : ( ssList @ ( skaf76 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause19) ).
thf(609,plain,
! [A: $i] : ( ssList @ ( skaf76 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(55,axiom,
! [A: $i] : ( ssList @ ( skaf57 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause38) ).
thf(323,plain,
! [A: $i] : ( ssList @ ( skaf57 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(725,plain,
( ( ssItem @ sk5 )
| ( strictorderP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[696,305]) ).
thf(726,plain,
( ( ssItem @ sk5 )
| ( strictorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[725:[]]) ).
thf(141,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/sandbox2/benchmark/theBenchmark.p',clause175) ).
thf(520,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)],[141]) ).
thf(24,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( cyclefreeP @ A )
| ( leq @ ( skaf49 @ A ) @ ( skaf50 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause88) ).
thf(250,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( cyclefreeP @ A )
| ( leq @ ( skaf49 @ A ) @ ( skaf50 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(251,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( cyclefreeP @ A )
| ( leq @ ( skaf49 @ A ) @ ( skaf50 @ A ) ) ),
inference(cnf,[status(esa)],[250]) ).
thf(893,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf73 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[393,242]) ).
thf(894,plain,
! [A: $i] :
~ ( neq @ ( skaf73 @ A ) @ ( skaf73 @ A ) ),
inference(pattern_uni,[status(thm)],[893:[bind(A,$thf( C )),bind(B,$thf( skaf73 @ C ))]]) ).
thf(895,plain,
! [A: $i] :
~ ( neq @ ( skaf73 @ A ) @ ( skaf73 @ A ) ),
inference(simp,[status(thm)],[894]) ).
thf(768,plain,
( ( ssItem @ sk5 )
| ( cyclefreeP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[731,486]) ).
thf(769,plain,
( ( ssItem @ sk5 )
| ( cyclefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[768:[]]) ).
thf(65,axiom,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( leq @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause103) ).
thf(345,plain,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( leq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(684,plain,
( ( memberP @ sk2 @ sk5 )
| ( strictorderedP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[658,627]) ).
thf(685,plain,
( ( memberP @ sk2 @ sk5 )
| ( strictorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[684:[]]) ).
thf(694,plain,
( ( memberP @ sk2 @ sk5 )
| ( totalorderedP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[658,640]) ).
thf(695,plain,
( ( memberP @ sk2 @ sk5 )
| ( totalorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[694:[]]) ).
thf(1631,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf54 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[588,444]) ).
thf(1632,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf54 @ A ) ),
inference(pattern_uni,[status(thm)],[1631:[bind(A,$thf( C )),bind(B,$thf( skaf54 @ C ))]]) ).
thf(1643,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf54 @ A ) ),
inference(simp,[status(thm)],[1632]) ).
thf(113,axiom,
! [A: $i] :
( ~ ( leq @ ( skaf54 @ A ) @ ( skaf55 @ A ) )
| ~ ( ssList @ A )
| ( totalorderP @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause95) ).
thf(455,plain,
! [A: $i] :
( ~ ( leq @ ( skaf54 @ A ) @ ( skaf55 @ A ) )
| ~ ( ssList @ A )
| ( totalorderP @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ( ( app @ A @ B )
!= nil )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( nil = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause118) ).
thf(299,plain,
! [B: $i,A: $i] :
( ( ( app @ A @ B )
!= nil )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( leq @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause107) ).
thf(267,plain,
! [B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( leq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(102,axiom,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( gt @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause110) ).
thf(431,plain,
! [B: $i,A: $i] :
( ~ ( gt @ A @ B )
| ~ ( gt @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(37,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/sandbox2/benchmark/theBenchmark.p',clause155) ).
thf(278,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)],[37]) ).
thf(49,axiom,
! [A: $i] : ( ssList @ ( skaf77 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause18) ).
thf(310,plain,
! [A: $i] : ( ssList @ ( skaf77 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(866,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf77 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[310,242]) ).
thf(867,plain,
! [A: $i] :
~ ( neq @ ( skaf77 @ A ) @ ( skaf77 @ A ) ),
inference(pattern_uni,[status(thm)],[866:[bind(A,$thf( C )),bind(B,$thf( skaf77 @ C ))]]) ).
thf(868,plain,
! [A: $i] :
~ ( neq @ ( skaf77 @ A ) @ ( skaf77 @ A ) ),
inference(simp,[status(thm)],[867]) ).
thf(84,axiom,
! [B: $i,A: $i] :
( ~ ( rearsegP @ A @ B )
| ~ ( rearsegP @ B @ A )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause128) ).
thf(394,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)],[84]) ).
thf(48,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/sandbox2/benchmark/theBenchmark.p',clause185) ).
thf(306,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)],[48]) ).
thf(1051,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf55 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[401,1032]) ).
thf(1052,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf55 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1051:[bind(A,$thf( C )),bind(B,$thf( skaf55 @ C ))]]) ).
thf(1076,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf55 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1052]) ).
thf(63,axiom,
duplicatefreeP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause2) ).
thf(341,plain,
duplicatefreeP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(674,plain,
( ( memberP @ sk2 @ sk5 )
| ( duplicatefreeP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[658,341]) ).
thf(675,plain,
( ( memberP @ sk2 @ sk5 )
| ( duplicatefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[674:[]]) ).
thf(99,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( memberP @ A @ B )
| ~ ( ssList @ A )
| ~ ( ssItem @ C )
| ~ ( ssItem @ B )
| ( memberP @ ( cons @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause139) ).
thf(426,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)],[99]) ).
thf(152,axiom,
! [A: $i] : ( ssList @ ( skaf63 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause32) ).
thf(548,plain,
! [A: $i] : ( ssList @ ( skaf63 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(748,plain,
( ( ssItem @ sk5 )
| ( equalelemsP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[731,324]) ).
thf(749,plain,
( ( ssItem @ sk5 )
| ( equalelemsP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[748:[]]) ).
thf(140,axiom,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ~ ( ssList @ C )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( memberP @ ( cons @ B @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause138) ).
thf(516,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)],[140]) ).
thf(64,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ nil @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause74) ).
thf(342,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ nil @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(155,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/sandbox2/benchmark/theBenchmark.p',clause170) ).
thf(553,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)],[155]) ).
thf(115,axiom,
! [A: $i] : ( ssList @ ( skaf75 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause20) ).
thf(458,plain,
! [A: $i] : ( ssList @ ( skaf75 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(834,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf79 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[259,444]) ).
thf(835,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf79 @ A ) ),
inference(pattern_uni,[status(thm)],[834:[bind(A,$thf( C )),bind(B,$thf( skaf79 @ C ))]]) ).
thf(836,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf79 @ A ) ),
inference(simp,[status(thm)],[835]) ).
thf(128,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/sandbox2/benchmark/theBenchmark.p',clause184) ).
thf(487,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)],[128]) ).
thf(1059,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf69 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[400,1032]) ).
thf(1060,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf69 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1059:[bind(A,$thf( C )),bind(B,$thf( skaf69 @ C ))]]) ).
thf(1070,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf69 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1060]) ).
thf(2677,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( neq @ sk1 @ nil )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[706,653]) ).
thf(2678,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( neq @ sk1 @ nil ) ),
inference(pattern_uni,[status(thm)],[2677:[]]) ).
thf(92,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( app @ A @ B )
!= ( app @ C @ B ) )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause151) ).
thf(409,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)],[92]) ).
thf(711,plain,
( ( ssItem @ sk5 )
| ( strictorderedP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[696,627]) ).
thf(712,plain,
( ( ssItem @ sk5 )
| ( strictorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[711:[]]) ).
thf(997,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf49 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[433,444]) ).
thf(998,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf49 @ A ) ),
inference(pattern_uni,[status(thm)],[997:[bind(A,$thf( C )),bind(B,$thf( skaf49 @ C ))]]) ).
thf(1003,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf49 @ A ) ),
inference(simp,[status(thm)],[998]) ).
thf(790,plain,
( ( memberP @ sk2 @ sk5 )
| ( equalelemsP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[770,324]) ).
thf(791,plain,
( ( memberP @ sk2 @ sk5 )
| ( equalelemsP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[790:[]]) ).
thf(168,axiom,
! [A: $i] : ( ssList @ ( skaf82 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause13) ).
thf(585,plain,
! [A: $i] : ( ssList @ ( skaf82 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(117,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/sandbox2/benchmark/theBenchmark.p',clause161) ).
thf(463,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)],[117]) ).
thf(71,axiom,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( rearsegP @ nil @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause81) ).
thf(359,plain,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( rearsegP @ nil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(672,plain,
( ( memberP @ sk2 @ sk5 )
| ( strictorderP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[658,305]) ).
thf(673,plain,
( ( memberP @ sk2 @ sk5 )
| ( strictorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[672:[]]) ).
thf(119,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( leq @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause62) ).
thf(470,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( leq @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(4131,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( memberP @ sk2 @ skac3 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[741,683]) ).
thf(4132,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( memberP @ sk2 @ skac3 ) ),
inference(pattern_uni,[status(thm)],[4131:[]]) ).
thf(61,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/sandbox2/benchmark/theBenchmark.p',clause166) ).
thf(336,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)],[61]) ).
thf(51,axiom,
! [A: $i] :
( ~ ( rearsegP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause82) ).
thf(314,plain,
! [A: $i] :
( ~ ( rearsegP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(177,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/sandbox2/benchmark/theBenchmark.p',clause176) ).
thf(600,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)],[177]) ).
thf(2130,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf59 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[641,1032]) ).
thf(2131,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf59 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[2130:[bind(A,$thf( C )),bind(B,$thf( skaf59 @ C ))]]) ).
thf(2145,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf59 @ A ) @ nil ) ),
inference(simp,[status(thm)],[2131]) ).
thf(670,plain,
( ( memberP @ sk2 @ sk5 )
| ( equalelemsP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[658,324]) ).
thf(671,plain,
( ( memberP @ sk2 @ sk5 )
| ( equalelemsP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[670:[]]) ).
thf(1816,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf65 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[589,444]) ).
thf(1817,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf65 @ A ) ),
inference(pattern_uni,[status(thm)],[1816:[bind(A,$thf( C )),bind(B,$thf( skaf65 @ C ))]]) ).
thf(1834,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf65 @ A ) ),
inference(simp,[status(thm)],[1817]) ).
thf(74,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/sandbox2/benchmark/theBenchmark.p',clause180) ).
thf(368,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)],[74]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( geq @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause108) ).
thf(231,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( geq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ( nil != A )
| ( nil != B )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( ( app @ A @ B )
= nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause145) ).
thf(363,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)],[72]) ).
thf(156,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( memberP @ A @ B )
| ~ ( ssList @ C )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( memberP @ ( app @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause140) ).
thf(556,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)],[156]) ).
thf(125,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( frontsegP @ A @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause60) ).
thf(482,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( frontsegP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(142,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/sandbox2/benchmark/theBenchmark.p',clause157) ).
thf(524,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)],[142]) ).
thf(166,axiom,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause121) ).
thf(581,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)],[166]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ( duplicatefreeP @ A )
| ( ssItem @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause72) ).
thf(319,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ( duplicatefreeP @ A )
| ( ssItem @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(27,axiom,
! [A: $i] : ( ssList @ ( skaf72 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause23) ).
thf(258,plain,
! [A: $i] : ( ssList @ ( skaf72 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(191,axiom,
! [B: $i,A: $i] :
( ( ( tl @ A )
!= ( tl @ B ) )
| ( ( hd @ A )
!= ( hd @ B ) )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( nil = B )
| ( A = B )
| ( nil = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause177) ).
thf(632,plain,
! [B: $i,A: $i] :
( ( ( tl @ A )
!= ( tl @ B ) )
| ( ( hd @ A )
!= ( hd @ B ) )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( nil = B )
| ( A = B )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(780,plain,
( ( memberP @ sk2 @ sk5 )
| ~ ( singletonP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[770,498]) ).
thf(781,plain,
( ( memberP @ sk2 @ sk5 )
| ~ ( singletonP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[780:[]]) ).
thf(988,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf60 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[412,444]) ).
thf(989,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf60 @ A ) ),
inference(pattern_uni,[status(thm)],[988:[bind(A,$thf( C )),bind(B,$thf( skaf60 @ C ))]]) ).
thf(995,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf60 @ A ) ),
inference(simp,[status(thm)],[989]) ).
thf(96,axiom,
! [B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ~ ( frontsegP @ B @ A )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause129) ).
thf(418,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)],[96]) ).
thf(77,axiom,
! [A: $i] :
( ~ ( ssItem @ A )
| ( geq @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause55) ).
thf(378,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( geq @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(7,negated_conjecture,
~ ( segmentP @ sk2 @ sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
thf(207,plain,
~ ( segmentP @ sk2 @ sk1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2679,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( neq @ nil @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[706,653]) ).
thf(2680,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( neq @ nil @ sk1 ) ),
inference(pattern_uni,[status(thm)],[2679:[]]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( rearsegP @ A @ B )
| ~ ( ssList @ C )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( rearsegP @ ( app @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause136) ).
thf(383,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)],[79]) ).
thf(153,axiom,
! [A: $i] : ( ssList @ ( skaf66 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause29) ).
thf(549,plain,
! [A: $i] : ( ssList @ ( skaf66 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(146,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( memberP @ A @ B )
| ~ ( ssList @ A )
| ~ ( ssList @ C )
| ~ ( ssItem @ B )
| ( memberP @ ( app @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause141) ).
thf(536,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)],[146]) ).
thf(715,plain,
( ( ssItem @ sk5 )
| ~ ( memberP @ sk1 @ skac2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[696,681]) ).
thf(716,plain,
( ( ssItem @ sk5 )
| ~ ( memberP @ sk1 @ skac2 ) ),
inference(pattern_uni,[status(thm)],[715:[]]) ).
thf(138,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/sandbox2/benchmark/theBenchmark.p',clause173) ).
thf(510,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)],[138]) ).
thf(762,plain,
( ( ssItem @ sk5 )
| ( duplicatefreeP @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[731,341]) ).
thf(763,plain,
( ( ssItem @ sk5 )
| ( duplicatefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[762:[]]) ).
thf(34,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/sandbox2/benchmark/theBenchmark.p',clause181) ).
thf(272,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)],[34]) ).
thf(187,axiom,
! [B: $i,A: $i] :
( ~ ( segmentP @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( ( app @ ( app @ ( skaf47 @ A @ B ) @ B ) @ ( skaf48 @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause168) ).
thf(620,plain,
! [B: $i,A: $i] :
( ~ ( segmentP @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( ( app @ ( app @ ( skaf47 @ A @ B ) @ B ) @ ( skaf48 @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(110,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/sandbox2/benchmark/theBenchmark.p',clause152) ).
thf(447,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)],[110]) ).
thf(831,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf72 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[258,242]) ).
thf(832,plain,
! [A: $i] :
~ ( neq @ ( skaf72 @ A ) @ ( skaf72 @ A ) ),
inference(pattern_uni,[status(thm)],[831:[bind(A,$thf( C )),bind(B,$thf( skaf72 @ C ))]]) ).
thf(833,plain,
! [A: $i] :
~ ( neq @ ( skaf72 @ A ) @ ( skaf72 @ A ) ),
inference(simp,[status(thm)],[832]) ).
thf(261,plain,
! [B: $i,A: $i] :
( ~ ( strictorderedP @ ( cons @ A @ B ) )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ ( hd @ B ) )
| ( nil = B ) ),
inference(cnf,[status(esa)],[260]) ).
thf(262,plain,
! [B: $i,A: $i] :
( ( nil = B )
| ~ ( strictorderedP @ ( cons @ A @ B ) )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( lt @ A @ ( hd @ B ) ) ),
inference(lifteq,[status(thm)],[261]) ).
thf(89,axiom,
! [A: $i] : ( ssItem @ ( skaf70 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause25) ).
thf(405,plain,
! [A: $i] : ( ssItem @ ( skaf70 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(863,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf64 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[277,444]) ).
thf(864,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf64 @ A ) ),
inference(pattern_uni,[status(thm)],[863:[bind(A,$thf( C )),bind(B,$thf( skaf64 @ C ))]]) ).
thf(865,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf64 @ A ) ),
inference(simp,[status(thm)],[864]) ).
thf(178,axiom,
! [A: $i] : ( ssList @ ( skaf71 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause24) ).
thf(603,plain,
! [A: $i] : ( ssList @ ( skaf71 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(159,axiom,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ( tl @ ( cons @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause96) ).
thf(564,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssList @ B )
| ( ( tl @ ( cons @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(43,axiom,
! [B: $i,A: $i] :
( ~ ( frontsegP @ A @ B )
| ~ ( ssList @ B )
| ~ ( ssList @ A )
| ( ( app @ B @ ( skaf45 @ A @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause132) ).
thf(294,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)],[43]) ).
thf(121,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( cons @ ( hd @ A ) @ ( tl @ A ) )
= A )
| ( nil = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause104) ).
thf(474,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( cons @ ( hd @ A ) @ ( tl @ A ) )
= A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(192,axiom,
! [B: $i,A: $i] :
( ~ ( segmentP @ A @ B )
| ~ ( segmentP @ B @ A )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause127) ).
thf(635,plain,
! [B: $i,A: $i] :
( ~ ( segmentP @ A @ B )
| ~ ( segmentP @ B @ A )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(145,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/sandbox2/benchmark/theBenchmark.p',clause182) ).
thf(532,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)],[145]) ).
thf(1592,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf74 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[584,444]) ).
thf(1593,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf74 @ A ) ),
inference(pattern_uni,[status(thm)],[1592:[bind(A,$thf( C )),bind(B,$thf( skaf74 @ C ))]]) ).
thf(1610,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf74 @ A ) ),
inference(simp,[status(thm)],[1593]) ).
thf(39,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( tl @ A ) )
| ( nil = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause75) ).
thf(283,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( tl @ A ) )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(95,axiom,
! [B: $i,A: $i] :
( ~ ( lt @ A @ ( hd @ B ) )
| ~ ( strictorderedP @ B )
| ~ ( ssList @ B )
| ~ ( ssItem @ A )
| ( strictorderedP @ ( cons @ A @ B ) )
| ( nil = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause160) ).
thf(415,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)],[95]) ).
thf(136,axiom,
! [A: $i] :
( ~ ( ssList @ A )
| ( equalelemsP @ A )
| ( ( app @ ( skaf80 @ A ) @ ( cons @ ( skaf78 @ A ) @ ( cons @ ( skaf79 @ A ) @ ( skaf81 @ A ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause142) ).
thf(506,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)],[136]) ).
thf(268,plain,
! [B: $i,A: $i] :
( ~ ( geq @ A @ B )
| ~ ( ssItem @ B )
| ~ ( ssItem @ A )
| ( leq @ B @ A ) ),
inference(cnf,[status(esa)],[267]) ).
thf(719,plain,
( ( ssItem @ sk5 )
| ~ ( neq @ nil @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[696,653]) ).
thf(720,plain,
( ( ssItem @ sk5 )
| ~ ( neq @ nil @ sk1 ) ),
inference(pattern_uni,[status(thm)],[719:[]]) ).
thf(727,plain,
( ( ssItem @ sk5 )
| ( duplicatefreeP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[696,341]) ).
thf(728,plain,
( ( ssItem @ sk5 )
| ( duplicatefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[727:[]]) ).
thf(163,axiom,
! [A: $i] :
( ~ ( segmentP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause80) ).
thf(575,plain,
! [A: $i] :
( ~ ( segmentP @ nil @ A )
| ~ ( ssList @ A )
| ( nil = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(174,axiom,
! [A: $i] : ( ssList @ ( skaf56 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause39) ).
thf(596,plain,
! [A: $i] : ( ssList @ ( skaf56 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(116,axiom,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( segmentP @ nil @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause79) ).
thf(459,plain,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( segmentP @ nil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(10,negated_conjecture,
( ( ( cons @ sk5 @ nil )
= sk3 )
| ( nil = sk4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
thf(200,plain,
( ( ( cons @ sk5 @ nil )
= sk3 )
| ( nil = sk4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(225,plain,
( ( ( cons @ sk5 @ nil )
= sk3 )
| ( nil = sk4 ) ),
inference(cnf,[status(esa)],[200]) ).
thf(226,plain,
( ( ( cons @ sk5 @ nil )
= sk3 )
| ( nil = sk4 ) ),
inference(lifteq,[status(thm)],[225]) ).
thf(850,plain,
( ( ( cons @ sk5 @ nil )
= sk1 )
| ( nil = sk2 ) ),
inference(rewrite,[status(thm)],[226,212,219]) ).
thf(976,plain,
! [B: $i,A: $i] :
( ~ ( memberP @ nil @ B )
| ( ( ssItem @ ( skaf70 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[405,444]) ).
thf(977,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf70 @ A ) ),
inference(pattern_uni,[status(thm)],[976:[bind(A,$thf( C )),bind(B,$thf( skaf70 @ C ))]]) ).
thf(982,plain,
! [A: $i] :
~ ( memberP @ nil @ ( skaf70 @ A ) ),
inference(simp,[status(thm)],[977]) ).
thf(107,axiom,
! [A: $i] : ( ssList @ ( skaf80 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause15) ).
thf(442,plain,
! [A: $i] : ( ssList @ ( skaf80 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(869,plain,
! [B: $i,A: $i] :
( ~ ( neq @ B @ B )
| ( ( ssList @ ( skaf57 @ A ) )
!= ( ssList @ B ) ) ),
inference(paramod_ordered,[status(thm)],[323,242]) ).
thf(870,plain,
! [A: $i] :
~ ( neq @ ( skaf57 @ A ) @ ( skaf57 @ A ) ),
inference(pattern_uni,[status(thm)],[869:[bind(A,$thf( C )),bind(B,$thf( skaf57 @ C ))]]) ).
thf(871,plain,
! [A: $i] :
~ ( neq @ ( skaf57 @ A ) @ ( skaf57 @ A ) ),
inference(simp,[status(thm)],[870]) ).
thf(180,axiom,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( lt @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause114) ).
thf(607,plain,
! [B: $i,A: $i] :
( ~ ( lt @ A @ B )
| ~ ( lt @ B @ A )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(69,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/sandbox2/benchmark/theBenchmark.p',clause146) ).
thf(354,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)],[69]) ).
thf(754,plain,
( ( ssItem @ sk5 )
| ~ ( neq @ nil @ sk2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[731,653]) ).
thf(755,plain,
( ( ssItem @ sk5 )
| ~ ( neq @ nil @ sk2 ) ),
inference(pattern_uni,[status(thm)],[754:[]]) ).
thf(129,axiom,
! [A: $i] : ( ssList @ ( skaf52 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause43) ).
thf(491,plain,
! [A: $i] : ( ssList @ ( skaf52 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(222,plain,
~ ( segmentP @ sk2 @ sk1 ),
inference(polarity_switch,[status(thm)],[207]) ).
thf(1057,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf70 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[405,1032]) ).
thf(1058,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf70 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1057:[bind(A,$thf( C )),bind(B,$thf( skaf70 @ C ))]]) ).
thf(1069,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf70 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1058]) ).
thf(1856,plain,
! [B: $i,A: $i] :
( ( totalorderedP @ ( cons @ B @ nil ) )
| ( ( ssItem @ ( skaf50 @ A ) )
!= ( ssItem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[599,1032]) ).
thf(1857,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf50 @ A ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1856:[bind(A,$thf( C )),bind(B,$thf( skaf50 @ C ))]]) ).
thf(1870,plain,
! [A: $i] : ( totalorderedP @ ( cons @ ( skaf50 @ A ) @ nil ) ),
inference(simp,[status(thm)],[1857]) ).
thf(253,plain,
! [A: $i] :
( ~ ( singletonP @ A )
| ~ ( ssList @ A )
| ( ( cons @ ( skaf44 @ A ) @ nil )
= A ) ),
inference(cnf,[status(esa)],[252]) ).
thf(254,plain,
! [A: $i] :
( ( ( cons @ ( skaf44 @ A ) @ nil )
= A )
| ~ ( singletonP @ A )
| ~ ( ssList @ A ) ),
inference(lifteq,[status(thm)],[253]) ).
thf(2671,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( memberP @ sk1 @ skac2 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[706,681]) ).
thf(2672,plain,
( ~ ( memberP @ nil @ sk5 )
| ~ ( memberP @ sk1 @ skac2 ) ),
inference(pattern_uni,[status(thm)],[2671:[]]) ).
thf(707,plain,
( ( ssItem @ sk5 )
| ~ ( singletonP @ sk1 )
| ( nil != nil ) ),
inference(paramod_ordered,[status(thm)],[696,498]) ).
thf(708,plain,
( ( ssItem @ sk5 )
| ~ ( singletonP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[707:[]]) ).
thf(232,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( geq @ B @ A ) ),
inference(cnf,[status(esa)],[231]) ).
thf(140342,plain,
$false,
inference(cvc4,[status(thm)],[1036,347,481,645,892,249,333,628,408,2117,683,449,247,655,730,276,741,1073,614,269,202,597,385,550,472,698,747,538,2146,898,436,651,257,570,785,372,619,751,2745,542,504,1871,638,421,1609,770,325,289,492,443,321,376,623,211,238,514,480,1581,353,397,280,293,1072,660,243,428,265,527,206,1074,248,380,439,201,761,2118,2621,714,233,452,1580,302,260,561,297,424,329,830,493,710,324,229,484,1032,252,578,874,317,388,356,593,610,783,499,339,753,669,642,4191,590,679,901,1075,212,706,647,503,2968,393,1050,457,237,244,266,205,311,541,657,765,586,718,558,1071,412,430,264,745,573,444,733,584,1833,402,772,286,1652,743,204,545,259,413,641,391,445,611,498,466,335,350,604,406,681,219,230,567,245,616,208,599,509,434,477,609,323,726,520,251,895,769,345,367,685,695,1643,455,299,267,431,653,658,278,868,394,306,1076,675,426,589,531,548,255,749,516,342,553,458,836,209,487,580,640,1070,2678,409,712,1003,263,310,791,585,463,359,544,199,673,470,4132,336,314,497,600,2145,627,671,1834,368,250,231,363,556,482,203,524,581,588,319,258,632,401,781,995,731,418,378,246,207,2680,383,549,536,716,433,510,763,272,620,447,833,262,405,865,603,564,305,210,294,341,474,400,635,532,696,1610,283,415,239,242,506,268,720,2668,728,575,596,459,200,850,982,277,442,871,607,354,755,491,222,1069,1870,254,227,486,2672,708,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC374-1 : TPTP v8.1.2. Released v2.4.0.
% 0.15/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n010.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.37 % DateTime : Fri May 19 00:49:58 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.95/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.33/1.03 % [INFO] Parsing done (184ms).
% 1.65/1.04 % [INFO] Running in sequential loop mode.
% 2.02/1.25 % [INFO] eprover registered as external prover.
% 2.02/1.25 % [INFO] cvc4 registered as external prover.
% 2.07/1.26 % [INFO] Scanning for conjecture ...
% 2.22/1.34 % [INFO] Found a conjecture and 185 axioms. Running axiom selection ...
% 2.35/1.42 % [INFO] Axiom selection finished. Selected 185 axioms (removed 0 axioms).
% 2.79/1.52 % [INFO] Problem is propositional (TPTP CNF).
% 2.93/1.53 % [INFO] Type checking passed.
% 2.93/1.53 % [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 ...
% 223.13/40.80 % External prover 'cvc4' found a proof!
% 223.13/40.80 % [INFO] Killing All external provers ...
% 223.13/40.80 % Time passed: 40280ms (effective reasoning time: 39758ms)
% 223.13/40.80 % 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)>
% 223.13/40.80 % 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
% 223.13/40.80 % No. of inferences in proof: 663
% 223.13/40.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 40280 ms resp. 39758 ms w/o parsing
% 223.38/40.91 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 223.38/40.91 % [INFO] Killing All external provers ...
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