TSTP Solution File: SWC342+1 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SWC342+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.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 : Tue May 21 04:32:42 EDT 2024
% Result : Theorem 149.83s 27.59s
% Output : Refutation 150.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 142
% Syntax : Number of formulae : 923 ( 80 unt; 46 typ; 0 def)
% Number of atoms : 3189 ( 708 equ; 0 cnn)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 7418 (1026 ~;1133 |; 123 &;4548 @)
% ( 26 <=>; 562 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 49 ( 49 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 46 usr; 10 con; 0-2 aty)
% Number of variables : 853 ( 0 ^ 820 !; 33 ?; 853 :)
% Comments :
%------------------------------------------------------------------------------
thf(ssList_type,type,
ssList: $i > $o ).
thf(ssItem_type,type,
ssItem: $i > $o ).
thf(cons_type,type,
cons: $i > $i > $i ).
thf(nil_type,type,
nil: $i ).
thf(memberP_type,type,
memberP: $i > $i > $o ).
thf(segmentP_type,type,
segmentP: $i > $i > $o ).
thf(totalorderedP_type,type,
totalorderedP: $i > $o ).
thf(strictorderedP_type,type,
strictorderedP: $i > $o ).
thf(lt_type,type,
lt: $i > $i > $o ).
thf(frontsegP_type,type,
frontsegP: $i > $i > $o ).
thf(gt_type,type,
gt: $i > $i > $o ).
thf(hd_type,type,
hd: $i > $i ).
thf(cyclefreeP_type,type,
cyclefreeP: $i > $o ).
thf(app_type,type,
app: $i > $i > $i ).
thf(leq_type,type,
leq: $i > $i > $o ).
thf(strictorderP_type,type,
strictorderP: $i > $o ).
thf(duplicatefreeP_type,type,
duplicatefreeP: $i > $o ).
thf(singletonP_type,type,
singletonP: $i > $o ).
thf(neq_type,type,
neq: $i > $i > $o ).
thf(tl_type,type,
tl: $i > $i ).
thf(totalorderP_type,type,
totalorderP: $i > $o ).
thf(rearsegP_type,type,
rearsegP: $i > $i > $o ).
thf(equalelemsP_type,type,
equalelemsP: $i > $o ).
thf(geq_type,type,
geq: $i > $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(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i > $i ).
thf(sk7_type,type,
sk7: $i > $i ).
thf(sk8_type,type,
sk8: $i > $i ).
thf(sk9_type,type,
sk9: $i > $i ).
thf(sk10_type,type,
sk10: $i > $i ).
thf(sk11_type,type,
sk11: $i > $i ).
thf(sk12_type,type,
sk12: $i > $i ).
thf(sk13_type,type,
sk13: $i > $i ).
thf(sk14_type,type,
sk14: $i > $i ).
thf(sk15_type,type,
sk15: $i > $i ).
thf(sk16_type,type,
sk16: $i > $i ).
thf(sk17_type,type,
sk17: $i > $i ).
thf(sk18_type,type,
sk18: $i > $i ).
thf(sk19_type,type,
sk19: $i > $i ).
thf(sk20_type,type,
sk20: $i > $i ).
thf(sk38_type,type,
sk38: $i ).
thf(sk39_type,type,
sk39: $i ).
thf(1,conjecture,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ( ( B != D )
| ( A != C )
| ( ! [E: $i] :
( ( ssItem @ E )
=> ( ( ( cons @ E @ nil )
!= C )
| ~ ( memberP @ D @ E ) ) )
& ( ( nil != D )
| ( nil != C ) ) )
| ( ( segmentP @ B @ A )
& ( totalorderedP @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ( ( B != D )
| ( A != C )
| ( ! [E: $i] :
( ( ssItem @ E )
=> ( ( ( cons @ E @ nil )
!= C )
| ~ ( memberP @ D @ E ) ) )
& ( ( nil != D )
| ( nil != C ) ) )
| ( ( segmentP @ B @ A )
& ( totalorderedP @ A ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(98,plain,
~ ! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ( ( B != D )
| ( A != C )
| ( ! [E: $i] :
( ( ssItem @ E )
=> ( ( ( cons @ E @ nil )
!= C )
| ~ ( memberP @ D @ E ) ) )
& ( ( nil != D )
| ( nil != C ) ) )
| ( ( segmentP @ B @ A )
& ( totalorderedP @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(105,plain,
ssList @ sk2,
inference(cnf,[status(esa)],[98]) ).
thf(33,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( strictorderedP @ A )
<=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( lt @ B @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax12) ).
thf(219,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( ( strictorderedP @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( lt @ B @ C ) ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( lt @ B @ C ) ) ) ) ) ) )
=> ( strictorderedP @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(224,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk18 @ A ) )
| ( strictorderedP @ A ) ),
inference(cnf,[status(esa)],[219]) ).
thf(29627,plain,
! [A: $i] :
( ( ssList @ ( sk18 @ A ) )
| ( strictorderedP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,224]) ).
thf(29628,plain,
( ( ssList @ ( sk18 @ sk2 ) )
| ( strictorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[29627:[bind(A,$thf( sk2 ))]]) ).
thf(45,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( rearsegP @ A @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax51) ).
thf(291,plain,
! [A: $i] :
( ( ssList @ A )
=> ( rearsegP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(292,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( rearsegP @ A @ nil ) ),
inference(cnf,[status(esa)],[291]) ).
thf(29861,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk18 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29628,292]) ).
thf(29862,plain,
( ( strictorderedP @ sk2 )
| ( rearsegP @ ( sk18 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[29861:[bind(A,$thf( sk18 @ sk2 ))]]) ).
thf(106,plain,
ssList @ sk1,
inference(cnf,[status(esa)],[98]) ).
thf(17,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( cyclefreeP @ A )
<=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ~ ( ( leq @ B @ C )
& ( leq @ C @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax8) ).
thf(157,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( ( cyclefreeP @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ~ ( ( leq @ B @ C )
& ( leq @ C @ B ) ) ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ~ ( ( leq @ B @ C )
& ( leq @ C @ B ) ) ) ) ) ) ) )
=> ( cyclefreeP @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(164,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( sk6 @ A ) )
| ( cyclefreeP @ A ) ),
inference(cnf,[status(esa)],[157]) ).
thf(4096,plain,
! [A: $i] :
( ( ssItem @ ( sk6 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,164]) ).
thf(4097,plain,
( ( ssItem @ ( sk6 @ sk1 ) )
| ( cyclefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[4096:[bind(A,$thf( sk1 ))]]) ).
thf(34,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ~ ( memberP @ nil @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
thf(231,plain,
! [A: $i] :
( ( ssItem @ A )
=> ~ ( memberP @ nil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(232,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ~ ( memberP @ nil @ A ) ),
inference(cnf,[status(esa)],[231]) ).
thf(4200,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk6 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4097,232]) ).
thf(4201,plain,
( ( cyclefreeP @ sk1 )
| ~ ( memberP @ nil @ ( sk6 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[4200:[bind(A,$thf( sk6 @ sk1 ))]]) ).
thf(227,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( sk16 @ A ) )
| ( strictorderedP @ A ) ),
inference(cnf,[status(esa)],[219]) ).
thf(31503,plain,
! [A: $i] :
( ( ssItem @ ( sk16 @ A ) )
| ( strictorderedP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,227]) ).
thf(31504,plain,
( ( ssItem @ ( sk16 @ sk2 ) )
| ( strictorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[31503:[bind(A,$thf( sk2 ))]]) ).
thf(19,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( strictorderP @ A )
<=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( ( lt @ B @ C )
| ( lt @ C @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax10) ).
thf(172,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( ( strictorderP @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( ( lt @ B @ C )
| ( lt @ C @ B ) ) ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( ( lt @ B @ C )
| ( lt @ C @ B ) ) ) ) ) ) ) )
=> ( strictorderP @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(175,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( sk11 @ A ) )
| ( strictorderP @ A ) ),
inference(cnf,[status(esa)],[172]) ).
thf(7716,plain,
! [A: $i] :
( ( ssItem @ ( sk11 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,175]) ).
thf(7717,plain,
( ( ssItem @ ( sk11 @ sk1 ) )
| ( strictorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[7716:[bind(A,$thf( sk1 ))]]) ).
thf(5,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( strictorderedP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax68) ).
thf(123,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( strictorderedP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(124,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( strictorderedP @ ( cons @ A @ nil ) ) ),
inference(cnf,[status(esa)],[123]) ).
thf(7889,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk11 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7717,124]) ).
thf(7890,plain,
( ( strictorderP @ sk1 )
| ( strictorderedP @ ( cons @ ( sk11 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[7889:[bind(A,$thf( sk11 @ sk1 ))]]) ).
thf(4168,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk6 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4097,124]) ).
thf(4169,plain,
( ( cyclefreeP @ sk1 )
| ( strictorderedP @ ( cons @ ( sk6 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[4168:[bind(A,$thf( sk6 @ sk1 ))]]) ).
thf(61,axiom,
? [A: $i] :
( ( ssItem @ A )
& ? [B: $i] :
( ( ssItem @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(375,plain,
? [A: $i] :
( ( ssItem @ A )
& ? [B: $i] :
( ( ssItem @ B )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(377,plain,
ssItem @ sk39,
inference(cnf,[status(esa)],[375]) ).
thf(46,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( equalelemsP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax73) ).
thf(293,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( equalelemsP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(294,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( equalelemsP @ ( cons @ A @ nil ) ) ),
inference(cnf,[status(esa)],[293]) ).
thf(2411,plain,
! [A: $i] :
( ( equalelemsP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk39 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[377,294]) ).
thf(2412,plain,
equalelemsP @ ( cons @ sk39 @ nil ),
inference(pattern_uni,[status(thm)],[2411:[bind(A,$thf( sk39 ))]]) ).
thf(39,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( totalorderP @ A )
<=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( ( leq @ B @ C )
| ( leq @ C @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax9) ).
thf(249,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( ( totalorderP @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( ( leq @ B @ C )
| ( leq @ C @ B ) ) ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( ( leq @ B @ C )
| ( leq @ C @ B ) ) ) ) ) ) ) )
=> ( totalorderP @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(6,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( frontsegP @ nil @ A )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax46) ).
thf(125,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( ( frontsegP @ nil @ A )
=> ( nil = A ) )
& ( ( nil = A )
=> ( frontsegP @ nil @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(126,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A )
| ( nil = A ) ),
inference(cnf,[status(esa)],[125]) ).
thf(128,plain,
! [A: $i] :
( ( nil = A )
| ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A ) ),
inference(lifteq,[status(thm)],[126]) ).
thf(376,plain,
sk38 != sk39,
inference(cnf,[status(esa)],[375]) ).
thf(379,plain,
sk39 != sk38,
inference(lifteq,[status(thm)],[376]) ).
thf(786,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A )
| ( sk38 != nil )
| ( A != sk39 ) ),
inference(paramod_ordered,[status(thm)],[128,379]) ).
thf(787,plain,
( ~ ( ssList @ sk39 )
| ~ ( frontsegP @ nil @ sk39 )
| ( sk38 != nil ) ),
inference(pattern_uni,[status(thm)],[786:[bind(A,$thf( sk39 ))]]) ).
thf(2458,plain,
( ~ ( frontsegP @ nil @ sk39 )
| ( sk38 != nil )
| ( ( ssList @ sk39 )
!= ( ssList @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[106,787]) ).
thf(2499,plain,
( ~ ( frontsegP @ nil @ sk39 )
| ( sk38 != nil )
| ( sk39 != sk1 ) ),
inference(simp,[status(thm)],[2458]) ).
thf(85,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( geq @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax89) ).
thf(468,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( geq @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(35,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ( ( segmentP @ A @ B )
=> ( segmentP @ ( app @ ( app @ C @ A ) @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax56) ).
thf(233,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ( ( segmentP @ A @ B )
=> ( segmentP @ ( app @ ( app @ C @ A ) @ D ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(234,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ~ ( ssList @ D )
| ~ ( segmentP @ A @ B )
| ( segmentP @ ( app @ ( app @ C @ A ) @ D ) @ B ) ),
inference(cnf,[status(esa)],[233]) ).
thf(159,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk10 @ A ) )
| ( cyclefreeP @ A ) ),
inference(cnf,[status(esa)],[157]) ).
thf(2762,plain,
! [A: $i] :
( ( ssList @ ( sk10 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,159]) ).
thf(2763,plain,
( ( ssList @ ( sk10 @ sk2 ) )
| ( cyclefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[2762:[bind(A,$thf( sk2 ))]]) ).
thf(20,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( app @ A @ nil )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).
thf(185,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( app @ A @ nil )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(186,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ A @ nil )
= A ) ),
inference(cnf,[status(esa)],[185]) ).
thf(187,plain,
! [A: $i] :
( ( ( app @ A @ nil )
= A )
| ~ ( ssList @ A ) ),
inference(lifteq,[status(thm)],[186]) ).
thf(11997,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk10 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2763,187]) ).
thf(11998,plain,
( ( cyclefreeP @ sk2 )
| ( ( app @ ( sk10 @ sk2 ) @ nil )
= ( sk10 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[11997:[bind(A,$thf( sk10 @ sk2 ))]]) ).
thf(30,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( neq @ A @ B )
<=> ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(208,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( ( neq @ A @ B )
=> ( A != B ) )
& ( ( A != B )
=> ( neq @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(210,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( neq @ A @ B )
| ( A != B ) ),
inference(cnf,[status(esa)],[208]) ).
thf(212,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( neq @ A @ B ) ),
inference(lifteq,[status(thm)],[210]) ).
thf(213,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ~ ( neq @ A @ A ) ),
inference(simp,[status(thm)],[212]) ).
thf(643,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssItem @ sk39 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[377,213]) ).
thf(644,plain,
~ ( neq @ sk39 @ sk39 ),
inference(pattern_uni,[status(thm)],[643:[bind(A,$thf( sk39 ))]]) ).
thf(776,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A )
| ~ ( neq @ nil @ sk39 )
| ( A != sk39 ) ),
inference(paramod_ordered,[status(thm)],[128,644]) ).
thf(777,plain,
( ~ ( ssList @ sk39 )
| ~ ( frontsegP @ nil @ sk39 )
| ~ ( neq @ nil @ sk39 ) ),
inference(pattern_uni,[status(thm)],[776:[bind(A,$thf( sk39 ))]]) ).
thf(10,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( hd @ ( cons @ B @ A ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax23) ).
thf(136,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( hd @ ( cons @ B @ A ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(137,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( ( hd @ ( cons @ B @ A ) )
= B ) ),
inference(cnf,[status(esa)],[136]) ).
thf(138,plain,
! [B: $i,A: $i] :
( ( ( hd @ ( cons @ B @ A ) )
= B )
| ~ ( ssList @ A )
| ~ ( ssItem @ B ) ),
inference(lifteq,[status(thm)],[137]) ).
thf(1189,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,292]) ).
thf(1190,plain,
rearsegP @ sk1 @ nil,
inference(pattern_uni,[status(thm)],[1189:[bind(A,$thf( sk1 ))]]) ).
thf(89,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( lt @ A @ B )
=> ~ ( lt @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax33) ).
thf(479,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( lt @ A @ B )
=> ~ ( lt @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(181,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( sk12 @ A ) )
| ( strictorderP @ A ) ),
inference(cnf,[status(esa)],[172]) ).
thf(10109,plain,
! [A: $i] :
( ( ssItem @ ( sk12 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,181]) ).
thf(10110,plain,
( ( ssItem @ ( sk12 @ sk2 ) )
| ( strictorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[10109:[bind(A,$thf( sk2 ))]]) ).
thf(10266,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk12 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10110,124]) ).
thf(10267,plain,
( ( strictorderP @ sk2 )
| ( strictorderedP @ ( cons @ ( sk12 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[10266:[bind(A,$thf( sk12 @ sk2 ))]]) ).
thf(90,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( rearsegP @ A @ B )
=> ( rearsegP @ ( app @ C @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax50) ).
thf(481,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( rearsegP @ A @ B )
=> ( rearsegP @ ( app @ C @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(111,plain,
( ( ssItem @ sk5 )
| ( nil = sk4 ) ),
inference(cnf,[status(esa)],[98]) ).
thf(118,plain,
( ( sk4 = nil )
| ( ssItem @ sk5 ) ),
inference(lifteq,[status(thm)],[111]) ).
thf(108,plain,
sk2 = sk4,
inference(cnf,[status(esa)],[98]) ).
thf(115,plain,
sk4 = sk2,
inference(lifteq,[status(thm)],[108]) ).
thf(527,plain,
( ( sk2 = nil )
| ( ssItem @ sk5 ) ),
inference(rewrite,[status(thm)],[118,115]) ).
thf(110,plain,
( ( ssItem @ sk5 )
| ( nil = sk3 ) ),
inference(cnf,[status(esa)],[98]) ).
thf(113,plain,
( ( sk3 = nil )
| ( ssItem @ sk5 ) ),
inference(lifteq,[status(thm)],[110]) ).
thf(107,plain,
sk1 = sk3,
inference(cnf,[status(esa)],[98]) ).
thf(114,plain,
sk3 = sk1,
inference(lifteq,[status(thm)],[107]) ).
thf(512,plain,
( ( sk1 = nil )
| ( ssItem @ sk5 ) ),
inference(rewrite,[status(thm)],[113,114]) ).
thf(11,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( segmentP @ nil @ A )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).
thf(139,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( ( segmentP @ nil @ A )
=> ( nil = A ) )
& ( ( nil = A )
=> ( segmentP @ nil @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(141,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( nil != A )
| ( segmentP @ nil @ A ) ),
inference(cnf,[status(esa)],[139]) ).
thf(143,plain,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( segmentP @ nil @ A ) ),
inference(lifteq,[status(thm)],[141]) ).
thf(144,plain,
( ~ ( ssList @ nil )
| ( segmentP @ nil @ nil ) ),
inference(simp,[status(thm)],[143]) ).
thf(53,axiom,
ssList @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
thf(334,plain,
ssList @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(593,plain,
( ~ $true
| ( segmentP @ nil @ nil ) ),
inference(rewrite,[status(thm)],[144,334]) ).
thf(594,plain,
segmentP @ nil @ nil,
inference(simp,[status(thm)],[593]) ).
thf(8,axiom,
totalorderedP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax66) ).
thf(133,plain,
totalorderedP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(109,plain,
( ~ ( segmentP @ sk2 @ sk1 )
| ~ ( totalorderedP @ sk1 ) ),
inference(cnf,[status(esa)],[98]) ).
thf(519,plain,
( ~ ( segmentP @ sk2 @ sk1 )
| ( ( totalorderedP @ sk1 )
!= ( totalorderedP @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[133,109]) ).
thf(520,plain,
( ~ ( segmentP @ sk2 @ sk1 )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[519]) ).
thf(596,plain,
( ( sk1 != nil )
| ( ( segmentP @ sk2 @ sk1 )
!= ( segmentP @ nil @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[594,520]) ).
thf(598,plain,
( ( sk1 != nil )
| ( sk2 != nil )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[596]) ).
thf(599,plain,
( ( sk1 != nil )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[598]) ).
thf(602,plain,
( ( ssItem @ sk5 )
| ( sk2 != nil )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[512,599]) ).
thf(603,plain,
( ( ssItem @ sk5 )
| ( sk2 != nil ) ),
inference(pattern_uni,[status(thm)],[602:[]]) ).
thf(608,plain,
( ( ssItem @ sk5 )
| ( sk2 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[527,603]) ).
thf(609,plain,
ssItem @ sk5,
inference(pattern_uni,[status(thm)],[608:[]]) ).
thf(24,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( totalorderedP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax65) ).
thf(195,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( totalorderedP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(196,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ nil ) ) ),
inference(cnf,[status(esa)],[195]) ).
thf(2199,plain,
! [A: $i] :
( ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[609,196]) ).
thf(2200,plain,
totalorderedP @ ( cons @ sk5 @ nil ),
inference(pattern_uni,[status(thm)],[2199:[bind(A,$thf( sk5 ))]]) ).
thf(101,plain,
( ( ( cons @ sk5 @ nil )
= sk3 )
| ( nil = sk4 ) ),
inference(cnf,[status(esa)],[98]) ).
thf(112,plain,
( ( ( cons @ sk5 @ nil )
= sk3 )
| ( sk4 = nil ) ),
inference(lifteq,[status(thm)],[101]) ).
thf(537,plain,
( ( ( cons @ sk5 @ nil )
= sk1 )
| ( sk2 = nil ) ),
inference(rewrite,[status(thm)],[112,114,115]) ).
thf(104,plain,
( ( memberP @ sk4 @ sk5 )
| ( nil = sk3 ) ),
inference(cnf,[status(esa)],[98]) ).
thf(117,plain,
( ( sk3 = nil )
| ( memberP @ sk4 @ sk5 ) ),
inference(lifteq,[status(thm)],[104]) ).
thf(565,plain,
( ( sk1 = nil )
| ( memberP @ sk2 @ sk5 ) ),
inference(rewrite,[status(thm)],[117,114,115]) ).
thf(600,plain,
( ( memberP @ sk2 @ sk5 )
| ( sk2 != nil )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[565,599]) ).
thf(601,plain,
( ( memberP @ sk2 @ sk5 )
| ( sk2 != nil ) ),
inference(pattern_uni,[status(thm)],[600:[]]) ).
thf(622,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[609,232]) ).
thf(623,plain,
~ ( memberP @ nil @ sk5 ),
inference(pattern_uni,[status(thm)],[622:[bind(A,$thf( sk5 ))]]) ).
thf(685,plain,
( ( sk2 != nil )
| ( ( memberP @ sk2 @ sk5 )
!= ( memberP @ nil @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[601,623]) ).
thf(693,plain,
( ( sk2 != nil )
| ( sk2 != nil )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[685]) ).
thf(697,plain,
sk2 != nil,
inference(simp,[status(thm)],[693]) ).
thf(700,plain,
( ( cons @ sk5 @ nil )
= sk1 ),
inference(simplifyReflect,[status(thm)],[537,697]) ).
thf(2250,plain,
totalorderedP @ sk1,
inference(rewrite,[status(thm)],[2200,700]) ).
thf(18,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ssList @ ( cons @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
thf(170,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ssList @ ( cons @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(10091,plain,
! [A: $i] :
( ( ssItem @ ( sk12 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,181]) ).
thf(10092,plain,
( ( ssItem @ ( sk12 @ sk1 ) )
| ( strictorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[10091:[bind(A,$thf( sk1 ))]]) ).
thf(10233,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( equalelemsP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk12 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10092,294]) ).
thf(10234,plain,
( ( strictorderP @ sk1 )
| ( equalelemsP @ ( cons @ ( sk12 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[10233:[bind(A,$thf( sk12 @ sk1 ))]]) ).
thf(32,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ~ ( lt @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax90) ).
thf(217,plain,
! [A: $i] :
( ( ssItem @ A )
=> ~ ( lt @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(174,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk13 @ A ) )
| ( strictorderP @ A ) ),
inference(cnf,[status(esa)],[172]) ).
thf(7150,plain,
! [A: $i] :
( ( ssList @ ( sk13 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,174]) ).
thf(7151,plain,
( ( ssList @ ( sk13 @ sk2 ) )
| ( strictorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[7150:[bind(A,$thf( sk2 ))]]) ).
thf(37,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( segmentP @ A @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax57) ).
thf(242,plain,
! [A: $i] :
( ( ssList @ A )
=> ( segmentP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(243,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( segmentP @ A @ nil ) ),
inference(cnf,[status(esa)],[242]) ).
thf(7376,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk13 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7151,243]) ).
thf(7377,plain,
( ( strictorderP @ sk2 )
| ( segmentP @ ( sk13 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[7376:[bind(A,$thf( sk13 @ sk2 ))]]) ).
thf(160,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk9 @ A ) )
| ( cyclefreeP @ A ) ),
inference(cnf,[status(esa)],[157]) ).
thf(3142,plain,
! [A: $i] :
( ( ssList @ ( sk9 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,160]) ).
thf(3143,plain,
( ( ssList @ ( sk9 @ sk1 ) )
| ( cyclefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[3142:[bind(A,$thf( sk1 ))]]) ).
thf(3229,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk9 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3143,292]) ).
thf(3230,plain,
( ( cyclefreeP @ sk1 )
| ( rearsegP @ ( sk9 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[3229:[bind(A,$thf( sk9 @ sk1 ))]]) ).
thf(166,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( sk7 @ A ) )
| ( cyclefreeP @ A ) ),
inference(cnf,[status(esa)],[157]) ).
thf(5003,plain,
! [A: $i] :
( ( ssItem @ ( sk7 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,166]) ).
thf(5004,plain,
( ( ssItem @ ( sk7 @ sk1 ) )
| ( cyclefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[5003:[bind(A,$thf( sk1 ))]]) ).
thf(5068,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk7 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5004,196]) ).
thf(5069,plain,
( ( cyclefreeP @ sk1 )
| ( totalorderedP @ ( cons @ ( sk7 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[5068:[bind(A,$thf( sk7 @ sk1 ))]]) ).
thf(3,axiom,
strictorderedP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax69) ).
thf(120,plain,
strictorderedP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(177,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk14 @ A ) )
| ( strictorderP @ A ) ),
inference(cnf,[status(esa)],[172]) ).
thf(8523,plain,
! [A: $i] :
( ( ssList @ ( sk14 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,177]) ).
thf(8524,plain,
( ( ssList @ ( sk14 @ sk1 ) )
| ( strictorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[8523:[bind(A,$thf( sk1 ))]]) ).
thf(23,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( segmentP @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).
thf(193,plain,
! [A: $i] :
( ( ssList @ A )
=> ( segmentP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(194,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( segmentP @ A @ A ) ),
inference(cnf,[status(esa)],[193]) ).
thf(13810,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk14 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8524,194]) ).
thf(13811,plain,
( ( strictorderP @ sk1 )
| ( segmentP @ ( sk14 @ sk1 ) @ ( sk14 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[13810:[bind(A,$thf( sk14 @ sk1 ))]]) ).
thf(27,axiom,
duplicatefreeP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax72) ).
thf(202,plain,
duplicatefreeP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(165,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk8 @ A ) )
| ( cyclefreeP @ A ) ),
inference(cnf,[status(esa)],[157]) ).
thf(4492,plain,
! [A: $i] :
( ( ssList @ ( sk8 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,165]) ).
thf(4493,plain,
( ( ssList @ ( sk8 @ sk2 ) )
| ( cyclefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[4492:[bind(A,$thf( sk2 ))]]) ).
thf(31,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( app @ nil @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
thf(214,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( app @ nil @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(215,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ nil @ A )
= A ) ),
inference(cnf,[status(esa)],[214]) ).
thf(216,plain,
! [A: $i] :
( ( ( app @ nil @ A )
= A )
| ~ ( ssList @ A ) ),
inference(lifteq,[status(thm)],[215]) ).
thf(25259,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( ( app @ nil @ A )
= A )
| ( ( ssList @ ( sk8 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4493,216]) ).
thf(25260,plain,
( ( cyclefreeP @ sk2 )
| ( ( app @ nil @ ( sk8 @ sk2 ) )
= ( sk8 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[25259:[bind(A,$thf( sk8 @ sk2 ))]]) ).
thf(10197,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk12 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10092,196]) ).
thf(10198,plain,
( ( strictorderP @ sk1 )
| ( totalorderedP @ ( cons @ ( sk12 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[10197:[bind(A,$thf( sk12 @ sk1 ))]]) ).
thf(127,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( nil != A )
| ( frontsegP @ nil @ A ) ),
inference(cnf,[status(esa)],[125]) ).
thf(129,plain,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( frontsegP @ nil @ A ) ),
inference(lifteq,[status(thm)],[127]) ).
thf(130,plain,
( ~ ( ssList @ nil )
| ( frontsegP @ nil @ nil ) ),
inference(simp,[status(thm)],[129]) ).
thf(591,plain,
( ~ $true
| ( frontsegP @ nil @ nil ) ),
inference(rewrite,[status(thm)],[130,334]) ).
thf(592,plain,
frontsegP @ nil @ nil,
inference(simp,[status(thm)],[591]) ).
thf(778,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A )
| ~ ( neq @ sk39 @ nil )
| ( A != sk39 ) ),
inference(paramod_ordered,[status(thm)],[128,644]) ).
thf(779,plain,
( ~ ( ssList @ sk39 )
| ~ ( frontsegP @ nil @ sk39 )
| ~ ( neq @ sk39 @ nil ) ),
inference(pattern_uni,[status(thm)],[778:[bind(A,$thf( sk39 ))]]) ).
thf(19041,plain,
( ~ ( ssList @ sk39 )
| ~ ( neq @ sk39 @ nil )
| ( ( frontsegP @ nil @ sk39 )
!= ( frontsegP @ nil @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[592,779]) ).
thf(19070,plain,
( ~ ( ssList @ sk39 )
| ~ ( neq @ sk39 @ nil )
| ( nil != nil )
| ( sk39 != nil ) ),
inference(simp,[status(thm)],[19041]) ).
thf(19101,plain,
( ~ ( ssList @ sk39 )
| ~ ( neq @ sk39 @ nil )
| ( sk39 != nil ) ),
inference(simp,[status(thm)],[19070]) ).
thf(19115,plain,
( ~ ( neq @ sk39 @ nil )
| ( sk39 != nil )
| ( ( ssList @ sk39 )
!= ( ssList @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[334,19101]) ).
thf(19193,plain,
( ~ ( neq @ sk39 @ nil )
| ( sk39 != nil )
| ( sk39 != nil ) ),
inference(simp,[status(thm)],[19115]) ).
thf(19213,plain,
( ~ ( neq @ sk39 @ nil )
| ( sk39 != nil ) ),
inference(simp,[status(thm)],[19193]) ).
thf(41,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( cons @ B @ A )
!= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
thf(269,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( cons @ B @ A )
!= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(7118,plain,
! [A: $i] :
( ( ssList @ ( sk13 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,174]) ).
thf(7119,plain,
( ( ssList @ ( sk13 @ sk1 ) )
| ( strictorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[7118:[bind(A,$thf( sk1 ))]]) ).
thf(13814,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk13 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7119,194]) ).
thf(13815,plain,
( ( strictorderP @ sk1 )
| ( segmentP @ ( sk13 @ sk1 ) @ ( sk13 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[13814:[bind(A,$thf( sk13 @ sk1 ))]]) ).
thf(140,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( segmentP @ nil @ A )
| ( nil = A ) ),
inference(cnf,[status(esa)],[139]) ).
thf(142,plain,
! [A: $i] :
( ( nil = A )
| ~ ( ssList @ A )
| ~ ( segmentP @ nil @ A ) ),
inference(lifteq,[status(thm)],[140]) ).
thf(796,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A )
| ~ ( memberP @ nil @ nil )
| ( A != sk5 ) ),
inference(paramod_ordered,[status(thm)],[128,623]) ).
thf(797,plain,
( ~ ( ssList @ sk5 )
| ~ ( frontsegP @ nil @ sk5 )
| ~ ( memberP @ nil @ nil ) ),
inference(pattern_uni,[status(thm)],[796:[bind(A,$thf( sk5 ))]]) ).
thf(220,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk19 @ A ) )
| ( strictorderedP @ A ) ),
inference(cnf,[status(esa)],[219]) ).
thf(27500,plain,
! [A: $i] :
( ( ssList @ ( sk19 @ A ) )
| ( strictorderedP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,220]) ).
thf(27501,plain,
( ( ssList @ ( sk19 @ sk2 ) )
| ( strictorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[27500:[bind(A,$thf( sk2 ))]]) ).
thf(27720,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk19 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27501,243]) ).
thf(27721,plain,
( ( strictorderedP @ sk2 )
| ( segmentP @ ( sk19 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[27720:[bind(A,$thf( sk19 @ sk2 ))]]) ).
thf(31728,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk16 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[31504,232]) ).
thf(31729,plain,
( ( strictorderedP @ sk2 )
| ~ ( memberP @ nil @ ( sk16 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[31728:[bind(A,$thf( sk16 @ sk2 ))]]) ).
thf(15,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( frontsegP @ A @ B )
=> ( frontsegP @ ( app @ A @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax43) ).
thf(152,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( frontsegP @ A @ B )
=> ( frontsegP @ ( app @ A @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(153,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ~ ( frontsegP @ A @ B )
| ( frontsegP @ ( app @ A @ C ) @ B ) ),
inference(cnf,[status(esa)],[152]) ).
thf(4468,plain,
! [A: $i] :
( ( ssList @ ( sk8 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,165]) ).
thf(4469,plain,
( ( ssList @ ( sk8 @ sk1 ) )
| ( cyclefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[4468:[bind(A,$thf( sk1 ))]]) ).
thf(4574,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk8 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4469,243]) ).
thf(4575,plain,
( ( cyclefreeP @ sk1 )
| ( segmentP @ ( sk8 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[4574:[bind(A,$thf( sk8 @ sk1 ))]]) ).
thf(852,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A )
| ( ssItem @ nil )
| ( A != sk5 ) ),
inference(paramod_ordered,[status(thm)],[128,609]) ).
thf(853,plain,
( ~ ( ssList @ sk5 )
| ~ ( frontsegP @ nil @ sk5 )
| ( ssItem @ nil ) ),
inference(pattern_uni,[status(thm)],[852:[bind(A,$thf( sk5 ))]]) ).
thf(7061,plain,
( ~ ( ssList @ sk5 )
| ( ssItem @ nil )
| ( ( frontsegP @ nil @ sk5 )
!= ( frontsegP @ nil @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[592,853]) ).
thf(7080,plain,
( ( ssItem @ nil )
| ~ ( ssList @ sk5 )
| ( nil != nil )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[7061]) ).
thf(7093,plain,
( ( ssItem @ nil )
| ~ ( ssList @ sk5 )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[7080]) ).
thf(7565,plain,
( ( ssItem @ nil )
| ( sk5 != nil )
| ( ( ssList @ sk5 )
!= ( ssList @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[334,7093]) ).
thf(7621,plain,
( ( ssItem @ nil )
| ( sk5 != nil )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[7565]) ).
thf(7637,plain,
( ( ssItem @ nil )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[7621]) ).
thf(7696,plain,
! [A: $i] :
( ( sk5 != nil )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ nil )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7637,232]) ).
thf(7697,plain,
( ( sk5 != nil )
| ~ ( memberP @ nil @ nil ) ),
inference(pattern_uni,[status(thm)],[7696:[bind(A,$thf( nil ))]]) ).
thf(3160,plain,
! [A: $i] :
( ( ssList @ ( sk9 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,160]) ).
thf(3161,plain,
( ( ssList @ ( sk9 @ sk2 ) )
| ( cyclefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3160:[bind(A,$thf( sk2 ))]]) ).
thf(3307,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk9 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3161,292]) ).
thf(3308,plain,
( ( cyclefreeP @ sk2 )
| ( rearsegP @ ( sk9 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[3307:[bind(A,$thf( sk9 @ sk2 ))]]) ).
thf(12008,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk8 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4493,187]) ).
thf(12009,plain,
( ( cyclefreeP @ sk2 )
| ( ( app @ ( sk8 @ sk2 ) @ nil )
= ( sk8 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[12008:[bind(A,$thf( sk8 @ sk2 ))]]) ).
thf(222,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( sk17 @ A ) )
| ( strictorderedP @ A ) ),
inference(cnf,[status(esa)],[219]) ).
thf(29134,plain,
! [A: $i] :
( ( ssItem @ ( sk17 @ A ) )
| ( strictorderedP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,222]) ).
thf(29135,plain,
( ( ssItem @ ( sk17 @ sk2 ) )
| ( strictorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[29134:[bind(A,$thf( sk2 ))]]) ).
thf(29355,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk17 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29135,232]) ).
thf(29356,plain,
( ( strictorderedP @ sk2 )
| ~ ( memberP @ nil @ ( sk17 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[29355:[bind(A,$thf( sk17 @ sk2 ))]]) ).
thf(4664,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk8 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4493,292]) ).
thf(4665,plain,
( ( cyclefreeP @ sk2 )
| ( rearsegP @ ( sk8 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[4664:[bind(A,$thf( sk8 @ sk2 ))]]) ).
thf(13799,plain,
! [A: $i] :
( ( segmentP @ A @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,194]) ).
thf(13800,plain,
segmentP @ sk2 @ sk2,
inference(pattern_uni,[status(thm)],[13799:[bind(A,$thf( sk2 ))]]) ).
thf(804,plain,
! [A: $i] :
( ( nil = A )
| ~ ( frontsegP @ nil @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,128]) ).
thf(805,plain,
( ( sk1 = nil )
| ~ ( frontsegP @ nil @ sk1 ) ),
inference(pattern_uni,[status(thm)],[804:[bind(A,$thf( sk1 ))]]) ).
thf(954,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ~ ( segmentP @ sk2 @ sk1 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[805,520]) ).
thf(955,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ~ ( segmentP @ sk2 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[954:[]]) ).
thf(1005,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ~ ( segmentP @ sk2 @ nil )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[805,955]) ).
thf(1006,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ~ ( segmentP @ sk2 @ nil ) ),
inference(pattern_uni,[status(thm)],[1005:[]]) ).
thf(1028,plain,
( ~ ( segmentP @ sk2 @ nil )
| ( ( frontsegP @ nil @ sk1 )
!= ( frontsegP @ nil @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[592,1006]) ).
thf(1030,plain,
( ~ ( segmentP @ sk2 @ nil )
| ( nil != nil )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[1028]) ).
thf(1032,plain,
( ~ ( segmentP @ sk2 @ nil )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[1030]) ).
thf(1106,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( sk1 != nil )
| ( ( segmentP @ A @ nil )
!= ( segmentP @ sk2 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[243,1032]) ).
thf(1107,plain,
( ~ ( ssList @ sk2 )
| ( sk1 != nil ) ),
inference(pattern_uni,[status(thm)],[1106:[bind(A,$thf( sk2 ))]]) ).
thf(1126,plain,
( ~ $true
| ( sk1 != nil ) ),
inference(rewrite,[status(thm)],[1107,105]) ).
thf(1127,plain,
sk1 != nil,
inference(simp,[status(thm)],[1126]) ).
thf(645,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[609,213]) ).
thf(646,plain,
~ ( neq @ sk5 @ sk5 ),
inference(pattern_uni,[status(thm)],[645:[bind(A,$thf( sk5 ))]]) ).
thf(798,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A )
| ~ ( neq @ nil @ sk5 )
| ( A != sk5 ) ),
inference(paramod_ordered,[status(thm)],[128,646]) ).
thf(799,plain,
( ~ ( ssList @ sk5 )
| ~ ( frontsegP @ nil @ sk5 )
| ~ ( neq @ nil @ sk5 ) ),
inference(pattern_uni,[status(thm)],[798:[bind(A,$thf( sk5 ))]]) ).
thf(26427,plain,
( ~ ( ssList @ sk5 )
| ~ ( neq @ nil @ sk5 )
| ( ( frontsegP @ nil @ sk5 )
!= ( frontsegP @ nil @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[592,799]) ).
thf(26454,plain,
( ~ ( ssList @ sk5 )
| ~ ( neq @ nil @ sk5 )
| ( nil != nil )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[26427]) ).
thf(26488,plain,
( ~ ( ssList @ sk5 )
| ~ ( neq @ nil @ sk5 )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[26454]) ).
thf(27014,plain,
( ~ ( neq @ nil @ sk5 )
| ( sk5 != nil )
| ( ( ssList @ sk5 )
!= ( ssList @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[334,26488]) ).
thf(27095,plain,
( ~ ( neq @ nil @ sk5 )
| ( sk5 != nil )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[27014]) ).
thf(27111,plain,
( ~ ( neq @ nil @ sk5 )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[27095]) ).
thf(44,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ssList @ ( tl @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).
thf(288,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ssList @ ( tl @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(10304,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk12 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10110,232]) ).
thf(10305,plain,
( ( strictorderP @ sk2 )
| ~ ( memberP @ nil @ ( sk12 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[10304:[bind(A,$thf( sk12 @ sk2 ))]]) ).
thf(173,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ ( app @ ( sk13 @ A ) @ ( cons @ ( sk11 @ A ) @ ( sk14 @ A ) ) ) @ ( cons @ ( sk12 @ A ) @ ( sk15 @ A ) ) )
= A )
| ( strictorderP @ A ) ),
inference(cnf,[status(esa)],[172]) ).
thf(184,plain,
! [A: $i] :
( ( ( app @ ( app @ ( sk13 @ A ) @ ( cons @ ( sk11 @ A ) @ ( sk14 @ A ) ) ) @ ( cons @ ( sk12 @ A ) @ ( sk15 @ A ) ) )
= A )
| ~ ( ssList @ A )
| ( strictorderP @ A ) ),
inference(lifteq,[status(thm)],[173]) ).
thf(218,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ~ ( lt @ A @ A ) ),
inference(cnf,[status(esa)],[217]) ).
thf(29329,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ~ ( lt @ A @ A )
| ( ( ssItem @ ( sk17 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29135,218]) ).
thf(29330,plain,
( ( strictorderedP @ sk2 )
| ~ ( lt @ ( sk17 @ sk2 ) @ ( sk17 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[29329:[bind(A,$thf( sk17 @ sk2 ))]]) ).
thf(180,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk15 @ A ) )
| ( strictorderP @ A ) ),
inference(cnf,[status(esa)],[172]) ).
thf(9537,plain,
! [A: $i] :
( ( ssList @ ( sk15 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,180]) ).
thf(9538,plain,
( ( ssList @ ( sk15 @ sk2 ) )
| ( strictorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[9537:[bind(A,$thf( sk2 ))]]) ).
thf(9804,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk15 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9538,292]) ).
thf(9805,plain,
( ( strictorderP @ sk2 )
| ( rearsegP @ ( sk15 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[9804:[bind(A,$thf( sk15 @ sk2 ))]]) ).
thf(59,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( frontsegP @ A @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax45) ).
thf(360,plain,
! [A: $i] :
( ( ssList @ A )
=> ( frontsegP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(361,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( frontsegP @ A @ nil ) ),
inference(cnf,[status(esa)],[360]) ).
thf(7385,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk13 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7151,361]) ).
thf(7386,plain,
( ( strictorderP @ sk2 )
| ( frontsegP @ ( sk13 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[7385:[bind(A,$thf( sk13 @ sk2 ))]]) ).
thf(64,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( duplicatefreeP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax71) ).
thf(389,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( duplicatefreeP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(4110,plain,
! [A: $i] :
( ( ssItem @ ( sk6 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,164]) ).
thf(4111,plain,
( ( ssItem @ ( sk6 @ sk2 ) )
| ( cyclefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[4110:[bind(A,$thf( sk2 ))]]) ).
thf(4223,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk6 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4111,124]) ).
thf(4224,plain,
( ( cyclefreeP @ sk2 )
| ( strictorderedP @ ( cons @ ( sk6 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[4223:[bind(A,$thf( sk6 @ sk2 ))]]) ).
thf(8555,plain,
! [A: $i] :
( ( ssList @ ( sk14 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,177]) ).
thf(8556,plain,
( ( ssList @ ( sk14 @ sk2 ) )
| ( strictorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[8555:[bind(A,$thf( sk2 ))]]) ).
thf(8805,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk14 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8556,292]) ).
thf(8806,plain,
( ( strictorderP @ sk2 )
| ( rearsegP @ ( sk14 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[8805:[bind(A,$thf( sk14 @ sk2 ))]]) ).
thf(9505,plain,
! [A: $i] :
( ( ssList @ ( sk15 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,180]) ).
thf(9506,plain,
( ( ssList @ ( sk15 @ sk1 ) )
| ( strictorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[9505:[bind(A,$thf( sk1 ))]]) ).
thf(12045,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk15 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9506,187]) ).
thf(12046,plain,
( ( strictorderP @ sk1 )
| ( ( app @ ( sk15 @ sk1 ) @ nil )
= ( sk15 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[12045:[bind(A,$thf( sk15 @ sk1 ))]]) ).
thf(29291,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk17 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29135,124]) ).
thf(29292,plain,
( ( strictorderedP @ sk2 )
| ( strictorderedP @ ( cons @ ( sk17 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[29291:[bind(A,$thf( sk17 @ sk2 ))]]) ).
thf(13819,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk9 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3161,194]) ).
thf(13820,plain,
( ( cyclefreeP @ sk2 )
| ( segmentP @ ( sk9 @ sk2 ) @ ( sk9 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[13819:[bind(A,$thf( sk9 @ sk2 ))]]) ).
thf(12002,plain,
! [A: $i] :
( ( ( app @ A @ nil )
= A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,187]) ).
thf(12003,plain,
( ( app @ sk1 @ nil )
= sk1 ),
inference(pattern_uni,[status(thm)],[12002:[bind(A,$thf( sk1 ))]]) ).
thf(25274,plain,
! [A: $i] :
( ( ( app @ nil @ A )
= A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,216]) ).
thf(25275,plain,
( ( app @ nil @ sk2 )
= sk2 ),
inference(pattern_uni,[status(thm)],[25274:[bind(A,$thf( sk2 ))]]) ).
thf(21,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( ( segmentP @ A @ B )
& ( segmentP @ B @ C ) )
=> ( segmentP @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax53) ).
thf(188,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( ( segmentP @ A @ B )
& ( segmentP @ B @ C ) )
=> ( segmentP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(189,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ~ ( segmentP @ A @ B )
| ~ ( segmentP @ B @ C )
| ( segmentP @ A @ C ) ),
inference(cnf,[status(esa)],[188]) ).
thf(225,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk20 @ A ) )
| ( strictorderedP @ A ) ),
inference(cnf,[status(esa)],[219]) ).
thf(30719,plain,
! [A: $i] :
( ( ssList @ ( sk20 @ A ) )
| ( strictorderedP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,225]) ).
thf(30720,plain,
( ( ssList @ ( sk20 @ sk2 ) )
| ( strictorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[30719:[bind(A,$thf( sk2 ))]]) ).
thf(31106,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk20 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30720,194]) ).
thf(31107,plain,
( ( strictorderedP @ sk2 )
| ( segmentP @ ( sk20 @ sk2 ) @ ( sk20 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[31106:[bind(A,$thf( sk20 @ sk2 ))]]) ).
thf(3311,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk9 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3161,361]) ).
thf(3312,plain,
( ( cyclefreeP @ sk2 )
| ( frontsegP @ ( sk9 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[3311:[bind(A,$thf( sk9 @ sk2 ))]]) ).
thf(7272,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk13 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7119,361]) ).
thf(7273,plain,
( ( strictorderP @ sk1 )
| ( frontsegP @ ( sk13 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[7272:[bind(A,$thf( sk13 @ sk1 ))]]) ).
thf(4582,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk8 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4469,361]) ).
thf(4583,plain,
( ( cyclefreeP @ sk1 )
| ( frontsegP @ ( sk8 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[4582:[bind(A,$thf( sk8 @ sk1 ))]]) ).
thf(52,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( totalorderedP @ ( cons @ A @ B ) )
<=> ( ( nil = B )
| ( ( nil != B )
& ( totalorderedP @ B )
& ( leq @ A @ ( hd @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax67) ).
thf(321,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( totalorderedP @ ( cons @ A @ B ) )
=> ( ( nil = B )
| ( ( nil != B )
& ( totalorderedP @ B )
& ( leq @ A @ ( hd @ B ) ) ) ) )
& ( ( ( nil = B )
| ( ( nil != B )
& ( totalorderedP @ B )
& ( leq @ A @ ( hd @ B ) ) ) )
=> ( totalorderedP @ ( cons @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(92,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( nil
!= ( cons @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).
thf(485,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( nil
!= ( cons @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(9679,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk15 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9506,243]) ).
thf(9680,plain,
( ( strictorderP @ sk1 )
| ( segmentP @ ( sk15 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[9679:[bind(A,$thf( sk15 @ sk1 ))]]) ).
thf(209,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( A = B )
| ( neq @ A @ B ) ),
inference(cnf,[status(esa)],[208]) ).
thf(211,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( neq @ A @ B ) ),
inference(lifteq,[status(thm)],[209]) ).
thf(29259,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk17 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29135,196]) ).
thf(29260,plain,
( ( strictorderedP @ sk2 )
| ( totalorderedP @ ( cons @ ( sk17 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[29259:[bind(A,$thf( sk17 @ sk2 ))]]) ).
thf(4,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ( ( ( lt @ A @ B )
& ( lt @ B @ C ) )
=> ( lt @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax34) ).
thf(121,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ( ( ( lt @ A @ B )
& ( lt @ B @ C ) )
=> ( lt @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13817,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk13 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7151,194]) ).
thf(13818,plain,
( ( strictorderP @ sk2 )
| ( segmentP @ ( sk13 @ sk2 ) @ ( sk13 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[13817:[bind(A,$thf( sk13 @ sk2 ))]]) ).
thf(7734,plain,
! [A: $i] :
( ( ssItem @ ( sk11 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,175]) ).
thf(7735,plain,
( ( ssItem @ ( sk11 @ sk2 ) )
| ( strictorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[7734:[bind(A,$thf( sk2 ))]]) ).
thf(8049,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( equalelemsP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk11 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7735,294]) ).
thf(8050,plain,
( ( strictorderP @ sk2 )
| ( equalelemsP @ ( cons @ ( sk11 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[8049:[bind(A,$thf( sk11 @ sk2 ))]]) ).
thf(29939,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk18 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29628,194]) ).
thf(29940,plain,
( ( strictorderedP @ sk2 )
| ( segmentP @ ( sk18 @ sk2 ) @ ( sk18 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[29939:[bind(A,$thf( sk18 @ sk2 ))]]) ).
thf(68,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ( cons @ ( hd @ A ) @ ( tl @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax78) ).
thf(397,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ( cons @ ( hd @ A ) @ ( tl @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(221,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( lt @ ( sk16 @ A ) @ ( sk17 @ A ) )
| ( strictorderedP @ A ) ),
inference(cnf,[status(esa)],[219]) ).
thf(82,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( ( rearsegP @ A @ B )
& ( rearsegP @ B @ C ) )
=> ( rearsegP @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax47) ).
thf(453,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( ( rearsegP @ A @ B )
& ( rearsegP @ B @ C ) )
=> ( rearsegP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(7,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( gt @ A @ B )
=> ~ ( gt @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax94) ).
thf(131,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( gt @ A @ B )
=> ~ ( gt @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(132,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( gt @ A @ B )
| ~ ( gt @ B @ A ) ),
inference(cnf,[status(esa)],[131]) ).
thf(67,axiom,
strictorderP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax64) ).
thf(396,plain,
strictorderP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(72,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( leq @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax31) ).
thf(411,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( leq @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(76,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( nil != A )
=> ( ( hd @ ( app @ A @ B ) )
= ( hd @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax85) ).
thf(428,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( nil != A )
=> ( ( hd @ ( app @ A @ B ) )
= ( hd @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(97,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( geq @ A @ B )
<=> ( leq @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax32) ).
thf(507,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( ( geq @ A @ B )
=> ( leq @ B @ A ) )
& ( ( leq @ B @ A )
=> ( geq @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(50,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( ( geq @ A @ B )
& ( geq @ B @ A ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax87) ).
thf(312,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( ( geq @ A @ B )
& ( geq @ B @ A ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(26742,plain,
! [A: $i] :
( ~ ( lt @ A @ A )
| ( ( ssItem @ sk39 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[377,218]) ).
thf(26743,plain,
~ ( lt @ sk39 @ sk39 ),
inference(pattern_uni,[status(thm)],[26742:[bind(A,$thf( sk39 ))]]) ).
thf(2001,plain,
! [A: $i] :
( ( frontsegP @ A @ nil )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,361]) ).
thf(2002,plain,
frontsegP @ sk2 @ nil,
inference(pattern_uni,[status(thm)],[2001:[bind(A,$thf( sk2 ))]]) ).
thf(29,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( gt @ A @ B )
<=> ( lt @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax35) ).
thf(205,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( ( gt @ A @ B )
=> ( lt @ B @ A ) )
& ( ( lt @ B @ A )
=> ( gt @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(206,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( lt @ B @ A )
| ( gt @ A @ B ) ),
inference(cnf,[status(esa)],[205]) ).
thf(2433,plain,
! [A: $i] :
( ( equalelemsP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[609,294]) ).
thf(2434,plain,
equalelemsP @ ( cons @ sk5 @ nil ),
inference(pattern_uni,[status(thm)],[2433:[bind(A,$thf( sk5 ))]]) ).
thf(2586,plain,
equalelemsP @ sk1,
inference(rewrite,[status(thm)],[2434,700]) ).
thf(7656,plain,
! [A: $i] :
( ( sk5 != nil )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ nil )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7637,196]) ).
thf(7657,plain,
( ( sk5 != nil )
| ( totalorderedP @ ( cons @ nil @ nil ) ) ),
inference(pattern_uni,[status(thm)],[7656:[bind(A,$thf( nil ))]]) ).
thf(378,plain,
ssItem @ sk38,
inference(cnf,[status(esa)],[375]) ).
thf(2203,plain,
! [A: $i] :
( ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk38 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[378,196]) ).
thf(2204,plain,
totalorderedP @ ( cons @ sk38 @ nil ),
inference(pattern_uni,[status(thm)],[2203:[bind(A,$thf( sk38 ))]]) ).
thf(26,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ( ( ( gt @ A @ B )
& ( gt @ B @ C ) )
=> ( gt @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax95) ).
thf(200,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ( ( ( gt @ A @ B )
& ( gt @ B @ C ) )
=> ( gt @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(201,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( ssItem @ C )
| ~ ( gt @ A @ B )
| ~ ( gt @ B @ C )
| ( gt @ A @ C ) ),
inference(cnf,[status(esa)],[200]) ).
thf(26734,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ~ ( lt @ A @ A )
| ( ( ssItem @ ( sk11 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7717,218]) ).
thf(26735,plain,
( ( strictorderP @ sk1 )
| ~ ( lt @ ( sk11 @ sk1 ) @ ( sk11 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[26734:[bind(A,$thf( sk11 @ sk1 ))]]) ).
thf(713,plain,
! [A: $i] :
( ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk39 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[377,124]) ).
thf(714,plain,
strictorderedP @ ( cons @ sk39 @ nil ),
inference(pattern_uni,[status(thm)],[713:[bind(A,$thf( sk39 ))]]) ).
thf(1285,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( segmentP @ nil @ A )
| ( sk38 != nil )
| ( A != sk39 ) ),
inference(paramod_ordered,[status(thm)],[142,379]) ).
thf(1286,plain,
( ~ ( ssList @ sk39 )
| ~ ( segmentP @ nil @ sk39 )
| ( sk38 != nil ) ),
inference(pattern_uni,[status(thm)],[1285:[bind(A,$thf( sk39 ))]]) ).
thf(3417,plain,
( ~ ( segmentP @ nil @ sk39 )
| ( sk38 != nil )
| ( ( ssList @ sk39 )
!= ( ssList @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[105,1286]) ).
thf(3450,plain,
( ~ ( segmentP @ nil @ sk39 )
| ( sk38 != nil )
| ( sk39 != sk2 ) ),
inference(simp,[status(thm)],[3417]) ).
thf(9681,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk15 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9506,292]) ).
thf(9682,plain,
( ( strictorderP @ sk1 )
| ( rearsegP @ ( sk15 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[9681:[bind(A,$thf( sk15 @ sk1 ))]]) ).
thf(62,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( memberP @ ( cons @ B @ C ) @ A )
<=> ( ( A = B )
| ( memberP @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax37) ).
thf(380,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( ( memberP @ ( cons @ B @ C ) @ A )
=> ( ( A = B )
| ( memberP @ C @ A ) ) )
& ( ( ( A = B )
| ( memberP @ C @ A ) )
=> ( memberP @ ( cons @ B @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(2492,plain,
( ~ ( ssList @ sk39 )
| ( sk38 != nil )
| ( ( frontsegP @ nil @ sk39 )
!= ( frontsegP @ nil @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[592,787]) ).
thf(2497,plain,
( ~ ( ssList @ sk39 )
| ( sk38 != nil )
| ( nil != nil )
| ( sk39 != nil ) ),
inference(simp,[status(thm)],[2492]) ).
thf(2501,plain,
( ~ ( ssList @ sk39 )
| ( sk38 != nil )
| ( sk39 != nil ) ),
inference(simp,[status(thm)],[2497]) ).
thf(2521,plain,
( ( sk38 != nil )
| ( sk39 != nil )
| ( ( ssList @ sk39 )
!= ( ssList @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[334,2501]) ).
thf(2542,plain,
( ( sk38 != nil )
| ( sk39 != nil )
| ( sk39 != nil ) ),
inference(simp,[status(thm)],[2521]) ).
thf(2550,plain,
( ( sk38 != nil )
| ( sk39 != nil ) ),
inference(simp,[status(thm)],[2542]) ).
thf(2704,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( segmentP @ nil @ A )
| ( sk39 != nil )
| ( A != sk38 ) ),
inference(paramod_ordered,[status(thm)],[142,2550]) ).
thf(2705,plain,
( ~ ( ssList @ sk38 )
| ~ ( segmentP @ nil @ sk38 )
| ( sk39 != nil ) ),
inference(pattern_uni,[status(thm)],[2704:[bind(A,$thf( sk38 ))]]) ).
thf(161,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( leq @ ( sk6 @ A ) @ ( sk7 @ A ) )
| ( cyclefreeP @ A ) ),
inference(cnf,[status(esa)],[157]) ).
thf(3609,plain,
! [A: $i] :
( ( leq @ ( sk6 @ A ) @ ( sk7 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,161]) ).
thf(3610,plain,
( ( leq @ ( sk6 @ sk1 ) @ ( sk7 @ sk1 ) )
| ( cyclefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[3609:[bind(A,$thf( sk1 ))]]) ).
thf(22,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( ( app @ C @ B )
= ( app @ A @ B ) )
=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax79) ).
thf(190,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( ( app @ C @ B )
= ( app @ A @ B ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(191,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( ( app @ C @ B )
!= ( app @ A @ B ) )
| ( C = A ) ),
inference(cnf,[status(esa)],[190]) ).
thf(192,plain,
! [C: $i,B: $i,A: $i] :
( ( ( app @ C @ B )
!= ( app @ A @ B ) )
| ( C = A )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C ) ),
inference(lifteq,[status(thm)],[191]) ).
thf(12057,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk8 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4469,187]) ).
thf(12058,plain,
( ( cyclefreeP @ sk1 )
| ( ( app @ ( sk8 @ sk1 ) @ nil )
= ( sk8 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[12057:[bind(A,$thf( sk8 @ sk1 ))]]) ).
thf(26758,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ~ ( lt @ A @ A )
| ( ( ssItem @ ( sk12 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10092,218]) ).
thf(26759,plain,
( ( strictorderP @ sk1 )
| ~ ( lt @ ( sk12 @ sk1 ) @ ( sk12 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[26758:[bind(A,$thf( sk12 @ sk1 ))]]) ).
thf(719,plain,
! [A: $i] :
( ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[609,124]) ).
thf(720,plain,
strictorderedP @ ( cons @ sk5 @ nil ),
inference(pattern_uni,[status(thm)],[719:[bind(A,$thf( sk5 ))]]) ).
thf(729,plain,
strictorderedP @ sk1,
inference(rewrite,[status(thm)],[720,700]) ).
thf(29311,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ~ ( neq @ A @ A )
| ( ( ssItem @ ( sk17 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29135,213]) ).
thf(29312,plain,
( ( strictorderedP @ sk2 )
| ~ ( neq @ ( sk17 @ sk2 ) @ ( sk17 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[29311:[bind(A,$thf( sk17 @ sk2 ))]]) ).
thf(3617,plain,
! [A: $i] :
( ( leq @ ( sk6 @ A ) @ ( sk7 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,161]) ).
thf(3618,plain,
( ( leq @ ( sk6 @ sk2 ) @ ( sk7 @ sk2 ) )
| ( cyclefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3617:[bind(A,$thf( sk2 ))]]) ).
thf(1128,plain,
~ ( frontsegP @ nil @ sk1 ),
inference(simplifyReflect,[status(thm)],[805,1127]) ).
thf(1391,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( segmentP @ nil @ A )
| ( ssItem @ nil )
| ( A != sk5 ) ),
inference(paramod_ordered,[status(thm)],[142,609]) ).
thf(1392,plain,
( ~ ( ssList @ sk5 )
| ~ ( segmentP @ nil @ sk5 )
| ( ssItem @ nil ) ),
inference(pattern_uni,[status(thm)],[1391:[bind(A,$thf( sk5 ))]]) ).
thf(176,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( lt @ ( sk11 @ A ) @ ( sk12 @ A ) )
| ( strictorderP @ A ) ),
inference(cnf,[status(esa)],[172]) ).
thf(8135,plain,
! [A: $i] :
( ~ ( lt @ ( sk11 @ A ) @ ( sk12 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,176]) ).
thf(8136,plain,
( ~ ( lt @ ( sk11 @ sk1 ) @ ( sk12 @ sk1 ) )
| ( strictorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[8135:[bind(A,$thf( sk1 ))]]) ).
thf(84,axiom,
equalelemsP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax74) ).
thf(467,plain,
equalelemsP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(13777,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk10 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2763,194]) ).
thf(13778,plain,
( ( cyclefreeP @ sk2 )
| ( segmentP @ ( sk10 @ sk2 ) @ ( sk10 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[13777:[bind(A,$thf( sk10 @ sk2 ))]]) ).
thf(7662,plain,
! [A: $i] :
( ( sk5 != nil )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ nil )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7637,124]) ).
thf(7663,plain,
( ( sk5 != nil )
| ( strictorderedP @ ( cons @ nil @ nil ) ) ),
inference(pattern_uni,[status(thm)],[7662:[bind(A,$thf( nil ))]]) ).
thf(223,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( strictorderedP @ A )
| ~ ( ssItem @ B )
| ~ ( ssItem @ C )
| ~ ( ssList @ D )
| ~ ( ssList @ E )
| ~ ( ssList @ F )
| ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
!= A )
| ( lt @ B @ C ) ),
inference(cnf,[status(esa)],[219]) ).
thf(228,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
!= A )
| ~ ( ssList @ A )
| ~ ( strictorderedP @ A )
| ~ ( ssItem @ B )
| ~ ( ssItem @ C )
| ~ ( ssList @ D )
| ~ ( ssList @ E )
| ~ ( ssList @ F )
| ( lt @ B @ C ) ),
inference(lifteq,[status(thm)],[223]) ).
thf(229,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( ssList @ ( app @ ( app @ C @ ( cons @ A @ D ) ) @ ( cons @ B @ E ) ) )
| ~ ( strictorderedP @ ( app @ ( app @ C @ ( cons @ A @ D ) ) @ ( cons @ B @ E ) ) )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( ssList @ C )
| ~ ( ssList @ D )
| ~ ( ssList @ E )
| ( lt @ A @ B ) ),
inference(simp,[status(thm)],[228]) ).
thf(8057,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk11 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7735,232]) ).
thf(8058,plain,
( ( strictorderP @ sk2 )
| ~ ( memberP @ nil @ ( sk11 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[8057:[bind(A,$thf( sk11 @ sk2 ))]]) ).
thf(2708,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A )
| ( sk39 != nil )
| ( A != sk38 ) ),
inference(paramod_ordered,[status(thm)],[128,2550]) ).
thf(2709,plain,
( ~ ( ssList @ sk38 )
| ~ ( frontsegP @ nil @ sk38 )
| ( sk39 != nil ) ),
inference(pattern_uni,[status(thm)],[2708:[bind(A,$thf( sk38 ))]]) ).
thf(5938,plain,
( ~ ( frontsegP @ nil @ sk38 )
| ( sk39 != nil )
| ( ( ssList @ sk38 )
!= ( ssList @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[105,2709]) ).
thf(5983,plain,
( ~ ( frontsegP @ nil @ sk38 )
| ( sk39 != nil )
| ( sk38 != sk2 ) ),
inference(simp,[status(thm)],[5938]) ).
thf(25,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( leq @ A @ B )
=> ( ( A = B )
| ( lt @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax92) ).
thf(197,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( leq @ A @ B )
=> ( ( A = B )
| ( lt @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(2746,plain,
! [A: $i] :
( ( ssList @ ( sk10 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,159]) ).
thf(2747,plain,
( ( ssList @ ( sk10 @ sk1 ) )
| ( cyclefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[2746:[bind(A,$thf( sk1 ))]]) ).
thf(2825,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk10 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2747,243]) ).
thf(2826,plain,
( ( cyclefreeP @ sk1 )
| ( segmentP @ ( sk10 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[2825:[bind(A,$thf( sk10 @ sk1 ))]]) ).
thf(4154,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk6 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4097,196]) ).
thf(4155,plain,
( ( cyclefreeP @ sk1 )
| ( totalorderedP @ ( cons @ ( sk6 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[4154:[bind(A,$thf( sk6 @ sk1 ))]]) ).
thf(79,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( nil != A )
=> ( ( tl @ ( app @ A @ B ) )
= ( app @ ( tl @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax86) ).
thf(435,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( nil != A )
=> ( ( tl @ ( app @ A @ B ) )
= ( app @ ( tl @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(43,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ssItem @ ( hd @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
thf(285,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ssItem @ ( hd @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(8693,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk14 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8524,361]) ).
thf(8694,plain,
( ( strictorderP @ sk1 )
| ( frontsegP @ ( sk14 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[8693:[bind(A,$thf( sk14 @ sk1 ))]]) ).
thf(16,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( app @ ( app @ A @ B ) @ C )
= ( app @ A @ ( app @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax82) ).
thf(154,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( app @ ( app @ A @ B ) @ C )
= ( app @ A @ ( app @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(155,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( ( app @ ( app @ A @ B ) @ C )
= ( app @ A @ ( app @ B @ C ) ) ) ),
inference(cnf,[status(esa)],[154]) ).
thf(156,plain,
! [C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ A @ B ) @ C )
= ( app @ A @ ( app @ B @ C ) ) )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C ) ),
inference(lifteq,[status(thm)],[155]) ).
thf(4247,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( equalelemsP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk6 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4111,294]) ).
thf(4248,plain,
( ( cyclefreeP @ sk2 )
| ( equalelemsP @ ( cons @ ( sk6 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[4247:[bind(A,$thf( sk6 @ sk2 ))]]) ).
thf(13783,plain,
! [A: $i] :
( ( segmentP @ A @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,194]) ).
thf(13784,plain,
segmentP @ sk1 @ sk1,
inference(pattern_uni,[status(thm)],[13783:[bind(A,$thf( sk1 ))]]) ).
thf(2251,plain,
( ~ ( segmentP @ sk2 @ sk1 )
| ~ $true ),
inference(rewrite,[status(thm)],[109,2250]) ).
thf(2252,plain,
~ ( segmentP @ sk2 @ sk1 ),
inference(simp,[status(thm)],[2251]) ).
thf(13886,plain,
( ( segmentP @ sk2 @ sk1 )
!= ( segmentP @ sk1 @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[13784,2252]) ).
thf(13897,plain,
( ( sk2 != sk1 )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[13886]) ).
thf(13904,plain,
sk2 != sk1,
inference(simp,[status(thm)],[13897]) ).
thf(58,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( memberP @ ( app @ B @ C ) @ A )
<=> ( ( memberP @ B @ A )
| ( memberP @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax36) ).
thf(356,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( ( memberP @ ( app @ B @ C ) @ A )
=> ( ( memberP @ B @ A )
| ( memberP @ C @ A ) ) )
& ( ( ( memberP @ B @ A )
| ( memberP @ C @ A ) )
=> ( memberP @ ( app @ B @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(158,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ ( app @ ( sk8 @ A ) @ ( cons @ ( sk6 @ A ) @ ( sk9 @ A ) ) ) @ ( cons @ ( sk7 @ A ) @ ( sk10 @ A ) ) )
= A )
| ( cyclefreeP @ A ) ),
inference(cnf,[status(esa)],[157]) ).
thf(169,plain,
! [A: $i] :
( ( ( app @ ( app @ ( sk8 @ A ) @ ( cons @ ( sk6 @ A ) @ ( sk9 @ A ) ) ) @ ( cons @ ( sk7 @ A ) @ ( sk10 @ A ) ) )
= A )
| ~ ( ssList @ A )
| ( cyclefreeP @ A ) ),
inference(lifteq,[status(thm)],[158]) ).
thf(96,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( memberP @ A @ B )
<=> ? [C: $i] :
( ( ssList @ C )
& ? [D: $i] :
( ( ssList @ D )
& ( ( app @ C @ ( cons @ B @ D ) )
= A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(499,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( ( memberP @ A @ B )
=> ? [C: $i] :
( ( ssList @ C )
& ? [D: $i] :
( ( ssList @ D )
& ( ( app @ C @ ( cons @ B @ D ) )
= A ) ) ) )
& ( ? [C: $i] :
( ( ssList @ C )
& ? [D: $i] :
( ( ssList @ D )
& ( ( app @ C @ ( cons @ B @ D ) )
= A ) ) )
=> ( memberP @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(8013,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk11 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7735,196]) ).
thf(8014,plain,
( ( strictorderP @ sk2 )
| ( totalorderedP @ ( cons @ ( sk11 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[8013:[bind(A,$thf( sk11 @ sk2 ))]]) ).
thf(8686,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk14 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8524,292]) ).
thf(8687,plain,
( ( strictorderP @ sk1 )
| ( rearsegP @ ( sk14 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[8686:[bind(A,$thf( sk14 @ sk1 ))]]) ).
thf(88,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( ( leq @ A @ B )
& ( leq @ B @ A ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax29) ).
thf(476,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( ( leq @ A @ B )
& ( leq @ B @ A ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(641,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssItem @ sk38 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[378,213]) ).
thf(642,plain,
~ ( neq @ sk38 @ sk38 ),
inference(pattern_uni,[status(thm)],[641:[bind(A,$thf( sk38 ))]]) ).
thf(178,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( lt @ ( sk12 @ A ) @ ( sk11 @ A ) )
| ( strictorderP @ A ) ),
inference(cnf,[status(esa)],[172]) ).
thf(9084,plain,
! [A: $i] :
( ~ ( lt @ ( sk12 @ A ) @ ( sk11 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,178]) ).
thf(9085,plain,
( ~ ( lt @ ( sk12 @ sk1 ) @ ( sk11 @ sk1 ) )
| ( strictorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[9084:[bind(A,$thf( sk1 ))]]) ).
thf(93,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( lt @ A @ B )
<=> ( ( A != B )
& ( leq @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax93) ).
thf(488,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( ( lt @ A @ B )
=> ( ( A != B )
& ( leq @ A @ B ) ) )
& ( ( ( A != B )
& ( leq @ A @ B ) )
=> ( lt @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(25232,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( ( app @ nil @ A )
= A )
| ( ( ssList @ ( sk10 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2763,216]) ).
thf(25233,plain,
( ( cyclefreeP @ sk2 )
| ( ( app @ nil @ ( sk10 @ sk2 ) )
= ( sk10 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[25232:[bind(A,$thf( sk10 @ sk2 ))]]) ).
thf(5106,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( equalelemsP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk7 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5004,294]) ).
thf(5107,plain,
( ( cyclefreeP @ sk1 )
| ( equalelemsP @ ( cons @ ( sk7 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[5106:[bind(A,$thf( sk7 @ sk1 ))]]) ).
thf(2829,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk10 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2747,361]) ).
thf(2830,plain,
( ( cyclefreeP @ sk1 )
| ( frontsegP @ ( sk10 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[2829:[bind(A,$thf( sk10 @ sk1 ))]]) ).
thf(1219,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( segmentP @ nil @ A )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[142,1127]) ).
thf(1220,plain,
( ~ ( ssList @ sk1 )
| ~ ( segmentP @ nil @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1219:[bind(A,$thf( sk1 ))]]) ).
thf(1477,plain,
( ~ $true
| ~ ( segmentP @ nil @ sk1 ) ),
inference(rewrite,[status(thm)],[1220,106]) ).
thf(1478,plain,
~ ( segmentP @ nil @ sk1 ),
inference(simp,[status(thm)],[1477]) ).
thf(26726,plain,
! [A: $i] :
( ( sk5 != nil )
| ~ ( lt @ A @ A )
| ( ( ssItem @ nil )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7637,218]) ).
thf(26727,plain,
( ( sk5 != nil )
| ~ ( lt @ nil @ nil ) ),
inference(pattern_uni,[status(thm)],[26726:[bind(A,$thf( nil ))]]) ).
thf(13804,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk15 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9538,194]) ).
thf(13805,plain,
( ( strictorderP @ sk2 )
| ( segmentP @ ( sk15 @ sk2 ) @ ( sk15 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[13804:[bind(A,$thf( sk15 @ sk2 ))]]) ).
thf(4243,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ~ ( neq @ A @ A )
| ( ( ssItem @ ( sk6 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4111,213]) ).
thf(4244,plain,
( ( cyclefreeP @ sk2 )
| ~ ( neq @ ( sk6 @ sk2 ) @ ( sk6 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[4243:[bind(A,$thf( sk6 @ sk2 ))]]) ).
thf(836,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A )
| ~ ( neq @ sk38 @ nil )
| ( A != sk38 ) ),
inference(paramod_ordered,[status(thm)],[128,642]) ).
thf(837,plain,
( ~ ( ssList @ sk38 )
| ~ ( frontsegP @ nil @ sk38 )
| ~ ( neq @ sk38 @ nil ) ),
inference(pattern_uni,[status(thm)],[836:[bind(A,$thf( sk38 ))]]) ).
thf(12443,plain,
( ~ ( ssList @ sk39 )
| ~ ( neq @ nil @ sk39 )
| ( ( frontsegP @ nil @ sk39 )
!= ( frontsegP @ nil @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[592,777]) ).
thf(12444,plain,
( ~ ( ssList @ sk39 )
| ~ ( neq @ nil @ sk39 )
| ( nil != nil )
| ( sk39 != nil ) ),
inference(simp,[status(thm)],[12443]) ).
thf(12486,plain,
( ~ ( ssList @ sk39 )
| ~ ( neq @ nil @ sk39 )
| ( sk39 != nil ) ),
inference(simp,[status(thm)],[12444]) ).
thf(13004,plain,
( ~ ( neq @ nil @ sk39 )
| ( sk39 != nil )
| ( ( ssList @ sk39 )
!= ( ssList @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[334,12486]) ).
thf(13053,plain,
( ~ ( neq @ nil @ sk39 )
| ( sk39 != nil )
| ( sk39 != nil ) ),
inference(simp,[status(thm)],[13004]) ).
thf(13081,plain,
( ~ ( neq @ nil @ sk39 )
| ( sk39 != nil ) ),
inference(simp,[status(thm)],[13053]) ).
thf(13821,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk8 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4469,194]) ).
thf(13822,plain,
( ( cyclefreeP @ sk1 )
| ( segmentP @ ( sk8 @ sk1 ) @ ( sk8 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[13821:[bind(A,$thf( sk8 @ sk1 ))]]) ).
thf(5021,plain,
! [A: $i] :
( ( ssItem @ ( sk7 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,166]) ).
thf(5022,plain,
( ( ssItem @ ( sk7 @ sk2 ) )
| ( cyclefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[5021:[bind(A,$thf( sk2 ))]]) ).
thf(5169,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk7 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5022,232]) ).
thf(5170,plain,
( ( cyclefreeP @ sk2 )
| ~ ( memberP @ nil @ ( sk7 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[5169:[bind(A,$thf( sk7 @ sk2 ))]]) ).
thf(9,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( ( frontsegP @ A @ B )
& ( frontsegP @ B @ C ) )
=> ( frontsegP @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax40) ).
thf(134,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( ( frontsegP @ A @ B )
& ( frontsegP @ B @ C ) )
=> ( frontsegP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(9688,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk15 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9506,361]) ).
thf(9689,plain,
( ( strictorderP @ sk1 )
| ( frontsegP @ ( sk15 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[9688:[bind(A,$thf( sk15 @ sk1 ))]]) ).
thf(540,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ( ( ssItem @ sk38 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[378,232]) ).
thf(541,plain,
~ ( memberP @ nil @ sk38 ),
inference(pattern_uni,[status(thm)],[540:[bind(A,$thf( sk38 ))]]) ).
thf(538,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ( ( ssItem @ sk39 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[377,232]) ).
thf(539,plain,
~ ( memberP @ nil @ sk39 ),
inference(pattern_uni,[status(thm)],[538:[bind(A,$thf( sk39 ))]]) ).
thf(772,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A )
| ~ ( memberP @ nil @ nil )
| ( A != sk39 ) ),
inference(paramod_ordered,[status(thm)],[128,539]) ).
thf(773,plain,
( ~ ( ssList @ sk39 )
| ~ ( frontsegP @ nil @ sk39 )
| ~ ( memberP @ nil @ nil ) ),
inference(pattern_uni,[status(thm)],[772:[bind(A,$thf( sk39 ))]]) ).
thf(1990,plain,
! [A: $i] :
( ( frontsegP @ A @ nil )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,361]) ).
thf(1991,plain,
frontsegP @ sk1 @ nil,
inference(pattern_uni,[status(thm)],[1990:[bind(A,$thf( sk1 ))]]) ).
thf(38,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ssList @ B )
& ( ( tl @ A )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax76) ).
thf(244,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ssList @ B )
& ( ( tl @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(31024,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk20 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30720,243]) ).
thf(31025,plain,
( ( strictorderedP @ sk2 )
| ( segmentP @ ( sk20 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[31024:[bind(A,$thf( sk20 @ sk2 ))]]) ).
thf(31952,plain,
( ~ ( ssList @ sk38 )
| ~ ( neq @ sk38 @ nil )
| ( ( frontsegP @ nil @ sk38 )
!= ( frontsegP @ nil @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[592,837]) ).
thf(32000,plain,
( ~ ( ssList @ sk38 )
| ~ ( neq @ sk38 @ nil )
| ( nil != nil )
| ( sk38 != nil ) ),
inference(simp,[status(thm)],[31952]) ).
thf(32001,plain,
( ~ ( ssList @ sk38 )
| ~ ( neq @ sk38 @ nil )
| ( sk38 != nil ) ),
inference(simp,[status(thm)],[32000]) ).
thf(32059,plain,
( ~ ( neq @ sk38 @ nil )
| ( sk38 != nil )
| ( ( ssList @ sk38 )
!= ( ssList @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[334,32001]) ).
thf(32126,plain,
( ~ ( neq @ sk38 @ nil )
| ( sk38 != nil )
| ( sk38 != nil ) ),
inference(simp,[status(thm)],[32059]) ).
thf(32173,plain,
( ~ ( neq @ sk38 @ nil )
| ( sk38 != nil ) ),
inference(simp,[status(thm)],[32126]) ).
thf(3305,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk9 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3161,243]) ).
thf(3306,plain,
( ( cyclefreeP @ sk2 )
| ( segmentP @ ( sk9 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[3305:[bind(A,$thf( sk9 @ sk2 ))]]) ).
thf(2903,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk10 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2763,292]) ).
thf(2904,plain,
( ( cyclefreeP @ sk2 )
| ( rearsegP @ ( sk10 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[2903:[bind(A,$thf( sk10 @ sk2 ))]]) ).
thf(1102,plain,
! [A: $i] :
( ( segmentP @ A @ nil )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,243]) ).
thf(1103,plain,
segmentP @ sk1 @ nil,
inference(pattern_uni,[status(thm)],[1102:[bind(A,$thf( sk1 ))]]) ).
thf(8039,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ~ ( neq @ A @ A )
| ( ( ssItem @ ( sk11 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7735,213]) ).
thf(8040,plain,
( ( strictorderP @ sk2 )
| ~ ( neq @ ( sk11 @ sk2 ) @ ( sk11 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[8039:[bind(A,$thf( sk11 @ sk2 ))]]) ).
thf(13,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( frontsegP @ A @ B )
& ( frontsegP @ B @ A ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax41) ).
thf(146,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( frontsegP @ A @ B )
& ( frontsegP @ B @ A ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(147,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( frontsegP @ A @ B )
| ~ ( frontsegP @ B @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[146]) ).
thf(148,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( frontsegP @ A @ B )
| ~ ( frontsegP @ B @ A ) ),
inference(lifteq,[status(thm)],[147]) ).
thf(4576,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk8 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4469,292]) ).
thf(4577,plain,
( ( cyclefreeP @ sk1 )
| ( rearsegP @ ( sk8 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[4576:[bind(A,$thf( sk8 @ sk1 ))]]) ).
thf(7909,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ~ ( neq @ A @ A )
| ( ( ssItem @ ( sk11 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7717,213]) ).
thf(7910,plain,
( ( strictorderP @ sk1 )
| ~ ( neq @ ( sk11 @ sk1 ) @ ( sk11 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[7909:[bind(A,$thf( sk11 @ sk1 ))]]) ).
thf(163,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( leq @ ( sk7 @ A ) @ ( sk6 @ A ) )
| ( cyclefreeP @ A ) ),
inference(cnf,[status(esa)],[157]) ).
thf(3870,plain,
! [A: $i] :
( ( leq @ ( sk7 @ A ) @ ( sk6 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,163]) ).
thf(3871,plain,
( ( leq @ ( sk7 @ sk1 ) @ ( sk6 @ sk1 ) )
| ( cyclefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[3870:[bind(A,$thf( sk1 ))]]) ).
thf(5137,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk7 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5022,124]) ).
thf(5138,plain,
( ( cyclefreeP @ sk2 )
| ( strictorderedP @ ( cons @ ( sk7 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[5137:[bind(A,$thf( sk7 @ sk2 ))]]) ).
thf(4255,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk6 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4111,232]) ).
thf(4256,plain,
( ( cyclefreeP @ sk2 )
| ~ ( memberP @ nil @ ( sk6 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[4255:[bind(A,$thf( sk6 @ sk2 ))]]) ).
thf(29347,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( equalelemsP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk17 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29135,294]) ).
thf(29348,plain,
( ( strictorderedP @ sk2 )
| ( equalelemsP @ ( cons @ ( sk17 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[29347:[bind(A,$thf( sk17 @ sk2 ))]]) ).
thf(7919,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( equalelemsP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk11 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7717,294]) ).
thf(7920,plain,
( ( strictorderP @ sk1 )
| ( equalelemsP @ ( cons @ ( sk11 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[7919:[bind(A,$thf( sk11 @ sk1 ))]]) ).
thf(12051,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk13 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7119,187]) ).
thf(12052,plain,
( ( strictorderP @ sk1 )
| ( ( app @ ( sk13 @ sk1 ) @ nil )
= ( sk13 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[12051:[bind(A,$thf( sk13 @ sk1 ))]]) ).
thf(28161,plain,
! [A: $i] :
( ~ ( lt @ ( sk16 @ A ) @ ( sk17 @ A ) )
| ( strictorderedP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,221]) ).
thf(28162,plain,
( ~ ( lt @ ( sk16 @ sk2 ) @ ( sk17 @ sk2 ) )
| ( strictorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[28161:[bind(A,$thf( sk2 ))]]) ).
thf(14,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( cons @ B @ A )
= ( app @ ( cons @ B @ nil ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax81) ).
thf(149,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( cons @ B @ A )
= ( app @ ( cons @ B @ nil ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(70,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( singletonP @ A )
<=> ? [B: $i] :
( ( ssItem @ B )
& ( ( cons @ B @ nil )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
thf(402,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( ( singletonP @ A )
=> ? [B: $i] :
( ( ssItem @ B )
& ( ( cons @ B @ nil )
= A ) ) )
& ( ? [B: $i] :
( ( ssItem @ B )
& ( ( cons @ B @ nil )
= A ) )
=> ( singletonP @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(13808,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk15 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9506,194]) ).
thf(13809,plain,
( ( strictorderP @ sk1 )
| ( segmentP @ ( sk15 @ sk1 ) @ ( sk15 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[13808:[bind(A,$thf( sk15 @ sk1 ))]]) ).
thf(28,axiom,
~ ( singletonP @ nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).
thf(203,plain,
~ ( singletonP @ nil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(204,plain,
~ ( singletonP @ nil ),
inference(polarity_switch,[status(thm)],[203]) ).
thf(73,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( strictorderP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax63) ).
thf(413,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( strictorderP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(3233,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk9 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3143,361]) ).
thf(3234,plain,
( ( cyclefreeP @ sk1 )
| ( frontsegP @ ( sk9 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[3233:[bind(A,$thf( sk9 @ sk1 ))]]) ).
thf(26728,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ~ ( lt @ A @ A )
| ( ( ssItem @ ( sk12 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10110,218]) ).
thf(26729,plain,
( ( strictorderP @ sk2 )
| ~ ( lt @ ( sk12 @ sk2 ) @ ( sk12 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[26728:[bind(A,$thf( sk12 @ sk2 ))]]) ).
thf(10241,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk12 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10092,232]) ).
thf(10242,plain,
( ( strictorderP @ sk1 )
| ~ ( memberP @ nil @ ( sk12 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[10241:[bind(A,$thf( sk12 @ sk1 ))]]) ).
thf(65,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( ( app @ B @ C )
= ( app @ B @ A ) )
=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax80) ).
thf(391,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( ( app @ B @ C )
= ( app @ B @ A ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(29876,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk18 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29628,361]) ).
thf(29877,plain,
( ( strictorderedP @ sk2 )
| ( frontsegP @ ( sk18 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[29876:[bind(A,$thf( sk18 @ sk2 ))]]) ).
thf(95,axiom,
totalorderP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax62) ).
thf(498,plain,
totalorderP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(54,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( nil != B )
& ( nil != A )
& ( ( hd @ B )
= ( hd @ A ) )
& ( ( tl @ B )
= ( tl @ A ) ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax77) ).
thf(335,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( nil != B )
& ( nil != A )
& ( ( hd @ B )
= ( hd @ A ) )
& ( ( tl @ B )
= ( tl @ A ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(9802,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk15 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9538,243]) ).
thf(9803,plain,
( ( strictorderP @ sk2 )
| ( segmentP @ ( sk15 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[9802:[bind(A,$thf( sk15 @ sk2 ))]]) ).
thf(7688,plain,
! [A: $i] :
( ( sk5 != nil )
| ( equalelemsP @ ( cons @ A @ nil ) )
| ( ( ssItem @ nil )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7637,294]) ).
thf(7689,plain,
( ( sk5 != nil )
| ( equalelemsP @ ( cons @ nil @ nil ) ) ),
inference(pattern_uni,[status(thm)],[7688:[bind(A,$thf( nil ))]]) ).
thf(5157,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ~ ( neq @ A @ A )
| ( ( ssItem @ ( sk7 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5022,213]) ).
thf(5158,plain,
( ( cyclefreeP @ sk2 )
| ~ ( neq @ ( sk7 @ sk2 ) @ ( sk7 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[5157:[bind(A,$thf( sk7 @ sk2 ))]]) ).
thf(5102,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ~ ( neq @ A @ A )
| ( ( ssItem @ ( sk7 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5004,213]) ).
thf(5103,plain,
( ( cyclefreeP @ sk1 )
| ~ ( neq @ ( sk7 @ sk1 ) @ ( sk7 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[5102:[bind(A,$thf( sk7 @ sk1 ))]]) ).
thf(10203,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk12 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10092,124]) ).
thf(10204,plain,
( ( strictorderP @ sk1 )
| ( strictorderedP @ ( cons @ ( sk12 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[10203:[bind(A,$thf( sk12 @ sk1 ))]]) ).
thf(226,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ ( app @ ( sk18 @ A ) @ ( cons @ ( sk16 @ A ) @ ( sk19 @ A ) ) ) @ ( cons @ ( sk17 @ A ) @ ( sk20 @ A ) ) )
= A )
| ( strictorderedP @ A ) ),
inference(cnf,[status(esa)],[219]) ).
thf(230,plain,
! [A: $i] :
( ( ( app @ ( app @ ( sk18 @ A ) @ ( cons @ ( sk16 @ A ) @ ( sk19 @ A ) ) ) @ ( cons @ ( sk17 @ A ) @ ( sk20 @ A ) ) )
= A )
| ~ ( ssList @ A )
| ( strictorderedP @ A ) ),
inference(lifteq,[status(thm)],[226]) ).
thf(10296,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( equalelemsP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk12 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10110,294]) ).
thf(10297,plain,
( ( strictorderP @ sk2 )
| ( equalelemsP @ ( cons @ ( sk12 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[10296:[bind(A,$thf( sk12 @ sk2 ))]]) ).
thf(2905,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk10 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2763,361]) ).
thf(2906,plain,
( ( cyclefreeP @ sk2 )
| ( frontsegP @ ( sk10 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[2905:[bind(A,$thf( sk10 @ sk2 ))]]) ).
thf(7378,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk13 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7151,292]) ).
thf(7379,plain,
( ( strictorderP @ sk2 )
| ( rearsegP @ ( sk13 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[7378:[bind(A,$thf( sk13 @ sk2 ))]]) ).
thf(60,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( duplicatefreeP @ A )
<=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( B != C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax13) ).
thf(362,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( ( duplicatefreeP @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( B != C ) ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( B != C ) ) ) ) ) ) )
=> ( duplicatefreeP @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(27798,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk19 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27501,194]) ).
thf(27799,plain,
( ( strictorderedP @ sk2 )
| ( segmentP @ ( sk19 @ sk2 ) @ ( sk19 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[27798:[bind(A,$thf( sk19 @ sk2 ))]]) ).
thf(63,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ( ( ( geq @ A @ B )
& ( geq @ B @ C ) )
=> ( geq @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax88) ).
thf(387,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ( ( ( geq @ A @ B )
& ( geq @ B @ C ) )
=> ( geq @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(27722,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk19 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27501,292]) ).
thf(27723,plain,
( ( strictorderedP @ sk2 )
| ( rearsegP @ ( sk19 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[27722:[bind(A,$thf( sk19 @ sk2 ))]]) ).
thf(91,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( rearsegP @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax49) ).
thf(483,plain,
! [A: $i] :
( ( ssList @ A )
=> ( rearsegP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(27737,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk19 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27501,361]) ).
thf(27738,plain,
( ( strictorderedP @ sk2 )
| ( frontsegP @ ( sk19 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[27737:[bind(A,$thf( sk19 @ sk2 ))]]) ).
thf(26750,plain,
! [A: $i] :
( ~ ( lt @ A @ A )
| ( ( ssItem @ sk38 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[378,218]) ).
thf(26751,plain,
~ ( lt @ sk38 @ sk38 ),
inference(pattern_uni,[status(thm)],[26750:[bind(A,$thf( sk38 ))]]) ).
thf(7927,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk11 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7717,232]) ).
thf(7928,plain,
( ( strictorderP @ sk1 )
| ~ ( memberP @ nil @ ( sk11 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[7927:[bind(A,$thf( sk11 @ sk1 ))]]) ).
thf(1197,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,292]) ).
thf(1198,plain,
rearsegP @ sk2 @ nil,
inference(pattern_uni,[status(thm)],[1197:[bind(A,$thf( sk2 ))]]) ).
thf(83,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( totalorderedP @ A )
<=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( leq @ B @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax11) ).
thf(455,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( ( totalorderedP @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( leq @ B @ C ) ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( leq @ B @ C ) ) ) ) ) ) )
=> ( totalorderedP @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(66,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ( ( ( leq @ A @ B )
& ( leq @ B @ C ) )
=> ( leq @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax30) ).
thf(394,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ( ( ( leq @ A @ B )
& ( leq @ B @ C ) )
=> ( leq @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(135,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ~ ( frontsegP @ A @ B )
| ~ ( frontsegP @ B @ C )
| ( frontsegP @ A @ C ) ),
inference(cnf,[status(esa)],[134]) ).
thf(850,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A )
| ~ ( memberP @ nil @ nil )
| ( A != sk38 ) ),
inference(paramod_ordered,[status(thm)],[128,541]) ).
thf(851,plain,
( ~ ( ssList @ sk38 )
| ~ ( frontsegP @ nil @ sk38 )
| ~ ( memberP @ nil @ nil ) ),
inference(pattern_uni,[status(thm)],[850:[bind(A,$thf( sk38 ))]]) ).
thf(80,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( equalelemsP @ A )
<=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ( ( ( app @ D @ ( cons @ B @ ( cons @ C @ E ) ) )
= A )
=> ( B = C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax14) ).
thf(438,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( ( equalelemsP @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ( ( ( app @ D @ ( cons @ B @ ( cons @ C @ E ) ) )
= A )
=> ( B = C ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ( ( ( app @ D @ ( cons @ B @ ( cons @ C @ E ) ) )
= A )
=> ( B = C ) ) ) ) ) )
=> ( equalelemsP @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(7883,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk11 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7717,196]) ).
thf(7884,plain,
( ( strictorderP @ sk1 )
| ( totalorderedP @ ( cons @ ( sk11 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[7883:[bind(A,$thf( sk11 @ sk1 ))]]) ).
thf(12059,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk10 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2747,187]) ).
thf(12060,plain,
( ( cyclefreeP @ sk1 )
| ( ( app @ ( sk10 @ sk1 ) @ nil )
= ( sk10 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[12059:[bind(A,$thf( sk10 @ sk1 ))]]) ).
thf(1176,plain,
! [B: $i,A: $i] :
( ( ( hd @ sk1 )
= B )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( ( cons @ sk5 @ nil )
!= ( cons @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[700,138]) ).
thf(1177,plain,
( ( ( hd @ sk1 )
= sk5 )
| ~ ( ssList @ nil )
| ~ ( ssItem @ sk5 ) ),
inference(pattern_uni,[status(thm)],[1176:[bind(A,$thf( nil )),bind(B,$thf( sk5 ))]]) ).
thf(11506,plain,
( ( ( hd @ sk1 )
= sk5 )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[1177,609,334]) ).
thf(11507,plain,
( ( hd @ sk1 )
= sk5 ),
inference(simp,[status(thm)],[11506]) ).
thf(77,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ( ( ( leq @ A @ B )
& ( lt @ B @ C ) )
=> ( lt @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax91) ).
thf(431,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ( ( ( leq @ A @ B )
& ( lt @ B @ C ) )
=> ( lt @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(87,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ( ( cons @ C @ ( app @ B @ A ) )
= ( app @ ( cons @ C @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax27) ).
thf(473,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ( ( cons @ C @ ( app @ B @ A ) )
= ( app @ ( cons @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(9096,plain,
! [A: $i] :
( ~ ( lt @ ( sk12 @ A ) @ ( sk11 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,178]) ).
thf(9097,plain,
( ~ ( lt @ ( sk12 @ sk2 ) @ ( sk11 @ sk2 ) )
| ( strictorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[9096:[bind(A,$thf( sk2 ))]]) ).
thf(12047,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk14 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8524,187]) ).
thf(12048,plain,
( ( strictorderP @ sk1 )
| ( ( app @ ( sk14 @ sk1 ) @ nil )
= ( sk14 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[12047:[bind(A,$thf( sk14 @ sk1 ))]]) ).
thf(7678,plain,
! [A: $i] :
( ( sk5 != nil )
| ~ ( neq @ A @ A )
| ( ( ssItem @ nil )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7637,213]) ).
thf(7679,plain,
( ( sk5 != nil )
| ~ ( neq @ nil @ nil ) ),
inference(pattern_uni,[status(thm)],[7678:[bind(A,$thf( nil ))]]) ).
thf(26732,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ~ ( lt @ A @ A )
| ( ( ssItem @ ( sk11 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7735,218]) ).
thf(26733,plain,
( ( strictorderP @ sk2 )
| ~ ( lt @ ( sk11 @ sk2 ) @ ( sk11 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[26732:[bind(A,$thf( sk11 @ sk2 ))]]) ).
thf(8019,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk11 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7735,124]) ).
thf(8020,plain,
( ( strictorderP @ sk2 )
| ( strictorderedP @ ( cons @ ( sk11 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[8019:[bind(A,$thf( sk11 @ sk2 ))]]) ).
thf(8803,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk14 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8556,243]) ).
thf(8804,plain,
( ( strictorderP @ sk2 )
| ( segmentP @ ( sk14 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[8803:[bind(A,$thf( sk14 @ sk2 ))]]) ).
thf(12,axiom,
cyclefreeP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax60) ).
thf(145,plain,
cyclefreeP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(99,plain,
( ( memberP @ sk4 @ sk5 )
| ( nil = sk4 ) ),
inference(cnf,[status(esa)],[98]) ).
thf(116,plain,
( ( sk4 = nil )
| ( memberP @ sk4 @ sk5 ) ),
inference(lifteq,[status(thm)],[99]) ).
thf(543,plain,
( ( sk2 = nil )
| ( memberP @ sk2 @ sk5 ) ),
inference(rewrite,[status(thm)],[116,115]) ).
thf(689,plain,
( ( memberP @ sk2 @ sk5 )
| ( sk2 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[543,601]) ).
thf(690,plain,
memberP @ sk2 @ sk5,
inference(pattern_uni,[status(thm)],[689:[]]) ).
thf(11315,plain,
( ~ ( ssList @ sk39 )
| ~ ( memberP @ nil @ nil )
| ( ( frontsegP @ nil @ sk39 )
!= ( frontsegP @ nil @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[592,773]) ).
thf(11337,plain,
( ~ ( ssList @ sk39 )
| ~ ( memberP @ nil @ nil )
| ( nil != nil )
| ( sk39 != nil ) ),
inference(simp,[status(thm)],[11315]) ).
thf(11366,plain,
( ~ ( ssList @ sk39 )
| ~ ( memberP @ nil @ nil )
| ( sk39 != nil ) ),
inference(simp,[status(thm)],[11337]) ).
thf(11384,plain,
( ~ ( memberP @ nil @ nil )
| ( sk39 != nil )
| ( ( ssList @ sk39 )
!= ( ssList @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[334,11366]) ).
thf(11441,plain,
( ~ ( memberP @ nil @ nil )
| ( sk39 != nil )
| ( sk39 != nil ) ),
inference(simp,[status(thm)],[11384]) ).
thf(11461,plain,
( ~ ( memberP @ nil @ nil )
| ( sk39 != nil ) ),
inference(simp,[status(thm)],[11441]) ).
thf(47,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssItem @ D )
=> ( ( ( cons @ C @ A )
= ( cons @ D @ B ) )
=> ( ( C = D )
& ( B = A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax19) ).
thf(295,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssItem @ D )
=> ( ( ( cons @ C @ A )
= ( cons @ D @ B ) )
=> ( ( C = D )
& ( B = A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(12055,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk9 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3161,187]) ).
thf(12056,plain,
( ( cyclefreeP @ sk2 )
| ( ( app @ ( sk9 @ sk2 ) @ nil )
= ( sk9 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[12055:[bind(A,$thf( sk9 @ sk2 ))]]) ).
thf(26738,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ~ ( lt @ A @ A )
| ( ( ssItem @ ( sk7 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5022,218]) ).
thf(26739,plain,
( ( cyclefreeP @ sk2 )
| ~ ( lt @ ( sk7 @ sk2 ) @ ( sk7 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[26738:[bind(A,$thf( sk7 @ sk2 ))]]) ).
thf(3227,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk9 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3143,243]) ).
thf(3228,plain,
( ( cyclefreeP @ sk1 )
| ( segmentP @ ( sk9 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[3227:[bind(A,$thf( sk9 @ sk1 ))]]) ).
thf(13812,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk14 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8556,194]) ).
thf(13813,plain,
( ( strictorderP @ sk2 )
| ( segmentP @ ( sk14 @ sk2 ) @ ( sk14 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[13812:[bind(A,$thf( sk14 @ sk2 ))]]) ).
thf(71,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ssList @ ( app @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
thf(409,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ssList @ ( app @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(8812,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk14 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8556,361]) ).
thf(8813,plain,
( ( strictorderP @ sk2 )
| ( frontsegP @ ( sk14 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[8812:[bind(A,$thf( sk14 @ sk2 ))]]) ).
thf(198,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( leq @ A @ B )
| ( A = B )
| ( lt @ A @ B ) ),
inference(cnf,[status(esa)],[197]) ).
thf(199,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( leq @ A @ B )
| ( lt @ A @ B ) ),
inference(lifteq,[status(thm)],[198]) ).
thf(7263,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk13 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7119,243]) ).
thf(7264,plain,
( ( strictorderP @ sk1 )
| ( segmentP @ ( sk13 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[7263:[bind(A,$thf( sk13 @ sk1 ))]]) ).
thf(55,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( segmentP @ A @ B )
<=> ? [C: $i] :
( ( ssList @ C )
& ? [D: $i] :
( ( ssList @ D )
& ( ( app @ ( app @ C @ B ) @ D )
= A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
thf(338,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( segmentP @ A @ B )
=> ? [C: $i] :
( ( ssList @ C )
& ? [D: $i] :
( ( ssList @ D )
& ( ( app @ ( app @ C @ B ) @ D )
= A ) ) ) )
& ( ? [C: $i] :
( ( ssList @ C )
& ? [D: $i] :
( ( ssList @ D )
& ( ( app @ ( app @ C @ B ) @ D )
= A ) ) )
=> ( segmentP @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(25272,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( ( app @ nil @ A )
= A )
| ( ( ssList @ ( sk9 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3143,216]) ).
thf(25273,plain,
( ( cyclefreeP @ sk1 )
| ( ( app @ nil @ ( sk9 @ sk1 ) )
= ( sk9 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[25272:[bind(A,$thf( sk9 @ sk1 ))]]) ).
thf(834,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A )
| ~ ( neq @ nil @ sk38 )
| ( A != sk38 ) ),
inference(paramod_ordered,[status(thm)],[128,642]) ).
thf(835,plain,
( ~ ( ssList @ sk38 )
| ~ ( frontsegP @ nil @ sk38 )
| ~ ( neq @ nil @ sk38 ) ),
inference(pattern_uni,[status(thm)],[834:[bind(A,$thf( sk38 ))]]) ).
thf(30246,plain,
( ~ ( ssList @ sk38 )
| ~ ( neq @ nil @ sk38 )
| ( ( frontsegP @ nil @ sk38 )
!= ( frontsegP @ nil @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[592,835]) ).
thf(30264,plain,
( ~ ( ssList @ sk38 )
| ~ ( neq @ nil @ sk38 )
| ( nil != nil )
| ( sk38 != nil ) ),
inference(simp,[status(thm)],[30246]) ).
thf(30302,plain,
( ~ ( ssList @ sk38 )
| ~ ( neq @ nil @ sk38 )
| ( sk38 != nil ) ),
inference(simp,[status(thm)],[30264]) ).
thf(30349,plain,
( ~ ( neq @ nil @ sk38 )
| ( sk38 != nil )
| ( ( ssList @ sk38 )
!= ( ssList @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[334,30302]) ).
thf(30436,plain,
( ~ ( neq @ nil @ sk38 )
| ( sk38 != nil )
| ( sk38 != nil ) ),
inference(simp,[status(thm)],[30349]) ).
thf(30454,plain,
( ~ ( neq @ nil @ sk38 )
| ( sk38 != nil ) ),
inference(simp,[status(thm)],[30436]) ).
thf(29859,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk18 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29628,243]) ).
thf(29860,plain,
( ( strictorderedP @ sk2 )
| ( segmentP @ ( sk18 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[29859:[bind(A,$thf( sk18 @ sk2 ))]]) ).
thf(86,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( segmentP @ A @ B )
& ( segmentP @ B @ A ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax54) ).
thf(470,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( segmentP @ A @ B )
& ( segmentP @ B @ A ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(8147,plain,
! [A: $i] :
( ~ ( lt @ ( sk11 @ A ) @ ( sk12 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,176]) ).
thf(8148,plain,
( ~ ( lt @ ( sk11 @ sk2 ) @ ( sk12 @ sk2 ) )
| ( strictorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[8147:[bind(A,$thf( sk2 ))]]) ).
thf(2462,plain,
( ~ ( frontsegP @ nil @ sk39 )
| ( sk38 != nil )
| ( ( ssList @ sk39 )
!= ( ssList @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[105,787]) ).
thf(2500,plain,
( ~ ( frontsegP @ nil @ sk39 )
| ( sk38 != nil )
| ( sk39 != sk2 ) ),
inference(simp,[status(thm)],[2462]) ).
thf(26756,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ~ ( lt @ A @ A )
| ( ( ssItem @ ( sk7 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5004,218]) ).
thf(26757,plain,
( ( cyclefreeP @ sk1 )
| ~ ( lt @ ( sk7 @ sk1 ) @ ( sk7 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[26756:[bind(A,$thf( sk7 @ sk1 ))]]) ).
thf(4670,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk8 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4493,361]) ).
thf(4671,plain,
( ( cyclefreeP @ sk2 )
| ( frontsegP @ ( sk8 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[4670:[bind(A,$thf( sk8 @ sk2 ))]]) ).
thf(26744,plain,
! [A: $i] :
( ~ ( lt @ A @ A )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[609,218]) ).
thf(26745,plain,
~ ( lt @ sk5 @ sk5 ),
inference(pattern_uni,[status(thm)],[26744:[bind(A,$thf( sk5 ))]]) ).
thf(12053,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk13 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7151,187]) ).
thf(12054,plain,
( ( strictorderP @ sk2 )
| ( ( app @ ( sk13 @ sk2 ) @ nil )
= ( sk13 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[12053:[bind(A,$thf( sk13 @ sk2 ))]]) ).
thf(5082,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk7 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5004,124]) ).
thf(5083,plain,
( ( cyclefreeP @ sk1 )
| ( strictorderedP @ ( cons @ ( sk7 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[5082:[bind(A,$thf( sk7 @ sk1 ))]]) ).
thf(3411,plain,
( ~ ( segmentP @ nil @ sk39 )
| ( sk38 != nil )
| ( ( ssList @ sk39 )
!= ( ssList @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[106,1286]) ).
thf(3452,plain,
( ~ ( segmentP @ nil @ sk39 )
| ( sk38 != nil )
| ( sk39 != sk1 ) ),
inference(simp,[status(thm)],[3411]) ).
thf(81,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( tl @ ( cons @ B @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax25) ).
thf(450,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( tl @ ( cons @ B @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(13796,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk9 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3143,194]) ).
thf(13797,plain,
( ( cyclefreeP @ sk1 )
| ( segmentP @ ( sk9 @ sk1 ) @ ( sk9 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[13796:[bind(A,$thf( sk9 @ sk1 ))]]) ).
thf(94,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( rearsegP @ A @ B )
& ( rearsegP @ B @ A ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax48) ).
thf(495,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( rearsegP @ A @ B )
& ( rearsegP @ B @ A ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(5114,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk7 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5004,232]) ).
thf(5115,plain,
( ( cyclefreeP @ sk1 )
| ~ ( memberP @ nil @ ( sk7 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[5114:[bind(A,$thf( sk7 @ sk1 ))]]) ).
thf(5123,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk7 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5022,196]) ).
thf(5124,plain,
( ( cyclefreeP @ sk2 )
| ( totalorderedP @ ( cons @ ( sk7 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[5123:[bind(A,$thf( sk7 @ sk2 ))]]) ).
thf(10260,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk12 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10110,196]) ).
thf(10261,plain,
( ( strictorderP @ sk2 )
| ( totalorderedP @ ( cons @ ( sk12 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[10260:[bind(A,$thf( sk12 @ sk2 ))]]) ).
thf(2827,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk10 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2747,292]) ).
thf(2828,plain,
( ( cyclefreeP @ sk1 )
| ( rearsegP @ ( sk10 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[2827:[bind(A,$thf( sk10 @ sk1 ))]]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( ssList @ ( cons @ B @ A ) ) ),
inference(cnf,[status(esa)],[170]) ).
thf(12049,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk14 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8556,187]) ).
thf(12050,plain,
( ( strictorderP @ sk2 )
| ( ( app @ ( sk14 @ sk2 ) @ nil )
= ( sk14 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[12049:[bind(A,$thf( sk14 @ sk2 ))]]) ).
thf(25241,plain,
! [A: $i] :
( ( ( app @ nil @ A )
= A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,216]) ).
thf(25242,plain,
( ( app @ nil @ sk1 )
= sk1 ),
inference(pattern_uni,[status(thm)],[25241:[bind(A,$thf( sk1 ))]]) ).
thf(25294,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( ( app @ nil @ A )
= A )
| ( ( ssList @ ( sk15 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9538,216]) ).
thf(25295,plain,
( ( strictorderP @ sk2 )
| ( ( app @ nil @ ( sk15 @ sk2 ) )
= ( sk15 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[25294:[bind(A,$thf( sk15 @ sk2 ))]]) ).
thf(207,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( gt @ A @ B )
| ( lt @ B @ A ) ),
inference(cnf,[status(esa)],[205]) ).
thf(2182,plain,
! [A: $i] :
( ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk39 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[377,196]) ).
thf(2183,plain,
totalorderedP @ ( cons @ sk39 @ nil ),
inference(pattern_uni,[status(thm)],[2182:[bind(A,$thf( sk39 ))]]) ).
thf(42,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( strictorderedP @ ( cons @ A @ B ) )
<=> ( ( nil = B )
| ( ( nil != B )
& ( strictorderedP @ B )
& ( lt @ A @ ( hd @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax70) ).
thf(272,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( strictorderedP @ ( cons @ A @ B ) )
=> ( ( nil = B )
| ( ( nil != B )
& ( strictorderedP @ B )
& ( lt @ A @ ( hd @ B ) ) ) ) )
& ( ( ( nil = B )
| ( ( nil != B )
& ( strictorderedP @ B )
& ( lt @ A @ ( hd @ B ) ) ) )
=> ( strictorderedP @ ( cons @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(2901,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk10 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2763,243]) ).
thf(2902,plain,
( ( cyclefreeP @ sk2 )
| ( segmentP @ ( sk10 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[2901:[bind(A,$thf( sk10 @ sk2 ))]]) ).
thf(800,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A )
| ~ ( neq @ sk5 @ nil )
| ( A != sk5 ) ),
inference(paramod_ordered,[status(thm)],[128,646]) ).
thf(801,plain,
( ~ ( ssList @ sk5 )
| ~ ( frontsegP @ nil @ sk5 )
| ~ ( neq @ sk5 @ nil ) ),
inference(pattern_uni,[status(thm)],[800:[bind(A,$thf( sk5 ))]]) ).
thf(28709,plain,
( ~ ( ssList @ sk5 )
| ~ ( neq @ sk5 @ nil )
| ( ( frontsegP @ nil @ sk5 )
!= ( frontsegP @ nil @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[592,801]) ).
thf(28717,plain,
( ~ ( ssList @ sk5 )
| ~ ( neq @ sk5 @ nil )
| ( nil != nil )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[28709]) ).
thf(28762,plain,
( ~ ( ssList @ sk5 )
| ~ ( neq @ sk5 @ nil )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[28717]) ).
thf(28810,plain,
( ~ ( neq @ sk5 @ nil )
| ( sk5 != nil )
| ( ( ssList @ sk5 )
!= ( ssList @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[334,28762]) ).
thf(28891,plain,
( ~ ( neq @ sk5 @ nil )
| ( sk5 != nil )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[28810]) ).
thf(28910,plain,
( ~ ( neq @ sk5 @ nil )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[28891]) ).
thf(56,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( nil
= ( app @ A @ B ) )
<=> ( ( nil = B )
& ( nil = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax83) ).
thf(346,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( nil
= ( app @ A @ B ) )
=> ( ( nil = B )
& ( nil = A ) ) )
& ( ( ( nil = B )
& ( nil = A ) )
=> ( nil
= ( app @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(5161,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( equalelemsP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk7 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5022,294]) ).
thf(5162,plain,
( ( cyclefreeP @ sk2 )
| ( equalelemsP @ ( cons @ ( sk7 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[5161:[bind(A,$thf( sk7 @ sk2 ))]]) ).
thf(7265,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk13 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7119,292]) ).
thf(7266,plain,
( ( strictorderP @ sk1 )
| ( rearsegP @ ( sk13 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[7265:[bind(A,$thf( sk13 @ sk1 ))]]) ).
thf(36,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( frontsegP @ A @ B )
<=> ? [C: $i] :
( ( ssList @ C )
& ( ( app @ B @ C )
= A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
thf(235,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( frontsegP @ A @ B )
=> ? [C: $i] :
( ( ssList @ C )
& ( ( app @ B @ C )
= A ) ) )
& ( ? [C: $i] :
( ( ssList @ C )
& ( ( app @ B @ C )
= A ) )
=> ( frontsegP @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(78,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( frontsegP @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax42) ).
thf(433,plain,
! [A: $i] :
( ( ssList @ A )
=> ( frontsegP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(3878,plain,
! [A: $i] :
( ( leq @ ( sk7 @ A ) @ ( sk6 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,163]) ).
thf(3879,plain,
( ( leq @ ( sk7 @ sk2 ) @ ( sk6 @ sk2 ) )
| ( cyclefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3878:[bind(A,$thf( sk2 ))]]) ).
thf(715,plain,
! [A: $i] :
( ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk38 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[378,124]) ).
thf(716,plain,
strictorderedP @ ( cons @ sk38 @ nil ),
inference(pattern_uni,[status(thm)],[715:[bind(A,$thf( sk38 ))]]) ).
thf(1115,plain,
! [A: $i] :
( ( segmentP @ A @ nil )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,243]) ).
thf(1116,plain,
segmentP @ sk2 @ nil,
inference(pattern_uni,[status(thm)],[1115:[bind(A,$thf( sk2 ))]]) ).
thf(150,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( ( cons @ B @ A )
= ( app @ ( cons @ B @ nil ) @ A ) ) ),
inference(cnf,[status(esa)],[149]) ).
thf(151,plain,
! [B: $i,A: $i] :
( ( ( app @ ( cons @ B @ nil ) @ A )
= ( cons @ B @ A ) )
| ~ ( ssList @ A )
| ~ ( ssItem @ B ) ),
inference(lifteq,[status(thm)],[150]) ).
thf(51,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( neq @ A @ B )
<=> ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
thf(315,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( neq @ A @ B )
=> ( A != B ) )
& ( ( A != B )
=> ( neq @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(179,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( strictorderP @ A )
| ~ ( ssItem @ B )
| ~ ( ssItem @ C )
| ~ ( ssList @ D )
| ~ ( ssList @ E )
| ~ ( ssList @ F )
| ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
!= A )
| ( lt @ B @ C )
| ( lt @ C @ B ) ),
inference(cnf,[status(esa)],[172]) ).
thf(182,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
!= A )
| ~ ( ssList @ A )
| ~ ( strictorderP @ A )
| ~ ( ssItem @ B )
| ~ ( ssItem @ C )
| ~ ( ssList @ D )
| ~ ( ssList @ E )
| ~ ( ssList @ F )
| ( lt @ B @ C )
| ( lt @ C @ B ) ),
inference(lifteq,[status(thm)],[179]) ).
thf(183,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( ssList @ ( app @ ( app @ C @ ( cons @ A @ D ) ) @ ( cons @ B @ E ) ) )
| ~ ( strictorderP @ ( app @ ( app @ C @ ( cons @ A @ D ) ) @ ( cons @ B @ E ) ) )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( ssList @ C )
| ~ ( ssList @ D )
| ~ ( ssList @ E )
| ( lt @ A @ B )
| ( lt @ B @ A ) ),
inference(simp,[status(thm)],[182]) ).
thf(75,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( rearsegP @ nil @ A )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52) ).
thf(422,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( ( rearsegP @ nil @ A )
=> ( nil = A ) )
& ( ( nil = A )
=> ( rearsegP @ nil @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(4662,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk8 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4493,243]) ).
thf(4663,plain,
( ( cyclefreeP @ sk2 )
| ( segmentP @ ( sk8 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[4662:[bind(A,$thf( sk8 @ sk2 ))]]) ).
thf(9811,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk15 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9538,361]) ).
thf(9812,plain,
( ( strictorderP @ sk2 )
| ( frontsegP @ ( sk15 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[9811:[bind(A,$thf( sk15 @ sk2 ))]]) ).
thf(48,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ssItem @ B )
& ( ( hd @ A )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax75) ).
thf(300,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ssItem @ B )
& ( ( hd @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(40,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil = A )
| ? [B: $i] :
( ( ssList @ B )
& ? [C: $i] :
( ( ssItem @ C )
& ( ( cons @ C @ B )
= A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).
thf(262,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil = A )
| ? [B: $i] :
( ( ssList @ B )
& ? [C: $i] :
( ( ssItem @ C )
& ( ( cons @ C @ B )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(162,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( cyclefreeP @ A )
| ~ ( ssItem @ B )
| ~ ( ssItem @ C )
| ~ ( ssList @ D )
| ~ ( ssList @ E )
| ~ ( ssList @ F )
| ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
!= A )
| ~ ( leq @ B @ C )
| ~ ( leq @ C @ B ) ),
inference(cnf,[status(esa)],[157]) ).
thf(167,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
!= A )
| ~ ( ssList @ A )
| ~ ( cyclefreeP @ A )
| ~ ( ssItem @ B )
| ~ ( ssItem @ C )
| ~ ( ssList @ D )
| ~ ( ssList @ E )
| ~ ( ssList @ F )
| ~ ( leq @ B @ C )
| ~ ( leq @ C @ B ) ),
inference(lifteq,[status(thm)],[162]) ).
thf(168,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( ssList @ ( app @ ( app @ C @ ( cons @ A @ D ) ) @ ( cons @ B @ E ) ) )
| ~ ( cyclefreeP @ ( app @ ( app @ C @ ( cons @ A @ D ) ) @ ( cons @ B @ E ) ) )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( ssList @ C )
| ~ ( ssList @ D )
| ~ ( ssList @ E )
| ~ ( leq @ A @ B )
| ~ ( leq @ B @ A ) ),
inference(simp,[status(thm)],[167]) ).
thf(4786,plain,
( ~ ( segmentP @ nil @ sk38 )
| ( sk39 != nil )
| ( ( ssList @ sk38 )
!= ( ssList @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[106,2705]) ).
thf(4841,plain,
( ~ ( segmentP @ nil @ sk38 )
| ( sk39 != nil )
| ( sk38 != sk1 ) ),
inference(simp,[status(thm)],[4786]) ).
thf(49,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ( ( frontsegP @ ( cons @ A @ C ) @ ( cons @ B @ D ) )
<=> ( ( A = B )
& ( frontsegP @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax44) ).
thf(305,plain,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ( ( ( frontsegP @ ( cons @ A @ C ) @ ( cons @ B @ D ) )
=> ( ( A = B )
& ( frontsegP @ C @ D ) ) )
& ( ( ( A = B )
& ( frontsegP @ C @ D ) )
=> ( frontsegP @ ( cons @ A @ C ) @ ( cons @ B @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(4209,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk6 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4111,196]) ).
thf(4210,plain,
( ( cyclefreeP @ sk2 )
| ( totalorderedP @ ( cons @ ( sk6 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[4209:[bind(A,$thf( sk6 @ sk2 ))]]) ).
thf(69,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( cyclefreeP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax59) ).
thf(400,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( cyclefreeP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(12021,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk9 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3143,187]) ).
thf(12022,plain,
( ( cyclefreeP @ sk1 )
| ( ( app @ ( sk9 @ sk1 ) @ nil )
= ( sk9 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[12021:[bind(A,$thf( sk9 @ sk1 ))]]) ).
thf(10223,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ~ ( neq @ A @ A )
| ( ( ssItem @ ( sk12 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10092,213]) ).
thf(10224,plain,
( ( strictorderP @ sk1 )
| ~ ( neq @ ( sk12 @ sk1 ) @ ( sk12 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[10223:[bind(A,$thf( sk12 @ sk1 ))]]) ).
thf(31026,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk20 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30720,292]) ).
thf(31027,plain,
( ( strictorderedP @ sk2 )
| ( rearsegP @ ( sk20 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[31026:[bind(A,$thf( sk20 @ sk2 ))]]) ).
thf(748,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[128,697]) ).
thf(749,plain,
( ~ ( ssList @ sk2 )
| ~ ( frontsegP @ nil @ sk2 ) ),
inference(pattern_uni,[status(thm)],[748:[bind(A,$thf( sk2 ))]]) ).
thf(917,plain,
( ~ $true
| ~ ( frontsegP @ nil @ sk2 ) ),
inference(rewrite,[status(thm)],[749,105]) ).
thf(918,plain,
~ ( frontsegP @ nil @ sk2 ),
inference(simp,[status(thm)],[917]) ).
thf(12023,plain,
! [A: $i] :
( ( ( app @ A @ nil )
= A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,187]) ).
thf(12024,plain,
( ( app @ sk2 @ nil )
= sk2 ),
inference(pattern_uni,[status(thm)],[12023:[bind(A,$thf( sk2 ))]]) ).
thf(4192,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( equalelemsP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk6 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4097,294]) ).
thf(4193,plain,
( ( cyclefreeP @ sk1 )
| ( equalelemsP @ ( cons @ ( sk6 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[4192:[bind(A,$thf( sk6 @ sk1 ))]]) ).
thf(74,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( rearsegP @ A @ B )
<=> ? [C: $i] :
( ( ssList @ C )
& ( ( app @ C @ B )
= A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
thf(415,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( rearsegP @ A @ B )
=> ? [C: $i] :
( ( ssList @ C )
& ( ( app @ C @ B )
= A ) ) )
& ( ? [C: $i] :
( ( ssList @ C )
& ( ( app @ C @ B )
= A ) )
=> ( rearsegP @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(4794,plain,
( ~ ( segmentP @ nil @ sk38 )
| ( sk39 != nil )
| ( ( ssList @ sk38 )
!= ( ssList @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[105,2705]) ).
thf(4848,plain,
( ~ ( segmentP @ nil @ sk38 )
| ( sk39 != nil )
| ( sk38 != sk2 ) ),
inference(simp,[status(thm)],[4794]) ).
thf(26724,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ~ ( lt @ A @ A )
| ( ( ssItem @ ( sk6 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4097,218]) ).
thf(26725,plain,
( ( cyclefreeP @ sk1 )
| ~ ( lt @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[26724:[bind(A,$thf( sk6 @ sk1 ))]]) ).
thf(12041,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk15 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9538,187]) ).
thf(12042,plain,
( ( strictorderP @ sk2 )
| ( ( app @ ( sk15 @ sk2 ) @ nil )
= ( sk15 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[12041:[bind(A,$thf( sk15 @ sk2 ))]]) ).
thf(10286,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ~ ( neq @ A @ A )
| ( ( ssItem @ ( sk12 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10110,213]) ).
thf(10287,plain,
( ( strictorderP @ sk2 )
| ~ ( neq @ ( sk12 @ sk2 ) @ ( sk12 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[10286:[bind(A,$thf( sk12 @ sk2 ))]]) ).
thf(347,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( nil != B )
| ( nil != A )
| ( nil
= ( app @ A @ B ) ) ),
inference(cnf,[status(esa)],[346]) ).
thf(350,plain,
! [B: $i,A: $i] :
( ( nil != B )
| ( nil != A )
| ( ( app @ A @ B )
= nil )
| ~ ( ssList @ A )
| ~ ( ssList @ B ) ),
inference(lifteq,[status(thm)],[347]) ).
thf(351,plain,
( ( ( app @ nil @ nil )
= nil )
| ~ ( ssList @ nil ) ),
inference(simp,[status(thm)],[350]) ).
thf(981,plain,
( ( ( app @ nil @ nil )
= nil )
| ~ $true ),
inference(rewrite,[status(thm)],[351,334]) ).
thf(982,plain,
( ( app @ nil @ nil )
= nil ),
inference(simp,[status(thm)],[981]) ).
thf(31041,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk20 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30720,361]) ).
thf(31042,plain,
( ( strictorderedP @ sk2 )
| ( frontsegP @ ( sk20 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[31041:[bind(A,$thf( sk20 @ sk2 ))]]) ).
thf(1221,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( segmentP @ nil @ A )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[142,697]) ).
thf(1222,plain,
( ~ ( ssList @ sk2 )
| ~ ( segmentP @ nil @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1221:[bind(A,$thf( sk2 ))]]) ).
thf(1504,plain,
( ~ $true
| ~ ( segmentP @ nil @ sk2 ) ),
inference(rewrite,[status(thm)],[1222,105]) ).
thf(1505,plain,
~ ( segmentP @ nil @ sk2 ),
inference(simp,[status(thm)],[1504]) ).
thf(26748,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ~ ( lt @ A @ A )
| ( ( ssItem @ ( sk6 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4111,218]) ).
thf(26749,plain,
( ( cyclefreeP @ sk2 )
| ~ ( lt @ ( sk6 @ sk2 ) @ ( sk6 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[26748:[bind(A,$thf( sk6 @ sk2 ))]]) ).
thf(13823,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk10 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2747,194]) ).
thf(13824,plain,
( ( cyclefreeP @ sk1 )
| ( segmentP @ ( sk10 @ sk1 ) @ ( sk10 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[13823:[bind(A,$thf( sk10 @ sk1 ))]]) ).
thf(13791,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk8 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4493,194]) ).
thf(13792,plain,
( ( cyclefreeP @ sk2 )
| ( segmentP @ ( sk8 @ sk2 ) @ ( sk8 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[13791:[bind(A,$thf( sk8 @ sk2 ))]]) ).
thf(122,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( ssItem @ C )
| ~ ( lt @ A @ B )
| ~ ( lt @ B @ C )
| ( lt @ A @ C ) ),
inference(cnf,[status(esa)],[121]) ).
thf(5929,plain,
( ~ ( frontsegP @ nil @ sk38 )
| ( sk39 != nil )
| ( ( ssList @ sk38 )
!= ( ssList @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[106,2709]) ).
thf(5986,plain,
( ~ ( frontsegP @ nil @ sk38 )
| ( sk39 != nil )
| ( sk38 != sk1 ) ),
inference(simp,[status(thm)],[5929]) ).
thf(57,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( totalorderP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax61) ).
thf(354,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( totalorderP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(2437,plain,
! [A: $i] :
( ( equalelemsP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk38 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[378,294]) ).
thf(2438,plain,
equalelemsP @ ( cons @ sk38 @ nil ),
inference(pattern_uni,[status(thm)],[2437:[bind(A,$thf( sk38 ))]]) ).
thf(424,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( nil != A )
| ( rearsegP @ nil @ A ) ),
inference(cnf,[status(esa)],[422]) ).
thf(426,plain,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( rearsegP @ nil @ A ) ),
inference(lifteq,[status(thm)],[424]) ).
thf(427,plain,
( ~ ( ssList @ nil )
| ( rearsegP @ nil @ nil ) ),
inference(simp,[status(thm)],[426]) ).
thf(638,plain,
( ~ $true
| ( rearsegP @ nil @ nil ) ),
inference(rewrite,[status(thm)],[427,334]) ).
thf(639,plain,
rearsegP @ nil @ nil,
inference(simp,[status(thm)],[638]) ).
thf(4188,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ~ ( neq @ A @ A )
| ( ( ssItem @ ( sk6 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4097,213]) ).
thf(4189,plain,
( ( cyclefreeP @ sk1 )
| ~ ( neq @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[4188:[bind(A,$thf( sk6 @ sk1 ))]]) ).
thf(8684,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk14 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8524,243]) ).
thf(8685,plain,
( ( strictorderP @ sk1 )
| ( segmentP @ ( sk14 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[8684:[bind(A,$thf( sk14 @ sk1 ))]]) ).
thf(57893,plain,
$false,
inference(e,[status(thm)],[29862,4201,31504,7890,4169,2412,249,2499,468,234,11998,777,138,1190,479,10267,481,2250,170,10234,217,7377,3230,5069,120,379,13811,202,115,25260,10198,19213,269,13815,4097,142,797,27721,31729,153,4575,7697,174,185,3308,12009,29356,4665,13800,1127,7637,2763,27111,288,10305,184,29330,9805,7386,389,4224,8806,12046,29292,13820,125,196,12003,25275,157,853,189,10110,31107,3312,152,216,164,7273,4583,321,623,485,106,9680,211,646,29260,121,13818,8050,29940,397,221,293,453,132,396,133,411,243,428,29135,507,312,26743,2002,206,2586,7657,292,233,2204,201,220,26735,714,7735,3450,9682,380,2705,160,3610,192,4493,165,12058,334,26759,729,29312,3618,361,1128,1392,8136,467,13778,7663,229,8058,5983,197,2826,4155,435,285,224,8694,697,156,4248,13904,2709,356,169,499,188,8014,193,8687,476,642,9085,3143,488,124,225,7717,25233,5107,2830,1478,26727,13805,4244,837,13081,13822,779,5170,134,360,205,9689,541,1286,773,128,1991,105,244,31025,32173,3306,30720,2904,1103,166,8040,148,161,4577,7910,375,3871,5138,4256,29348,7920,180,12052,28162,149,176,402,13809,204,5022,413,3234,26729,10242,291,391,29877,498,9538,335,181,9803,159,9506,787,7689,8524,5158,187,219,5103,10204,377,230,98,208,8556,172,10297,2906,7379,362,27799,387,7119,609,27723,594,483,27738,2252,26751,799,213,7928,700,1198,2550,455,394,135,851,438,7884,12060,11507,431,473,9097,12048,7151,7679,123,26733,8020,3161,8804,194,145,690,11461,295,12056,26739,3228,4469,13813,409,8813,2747,199,7264,177,338,25273,30454,29860,470,8148,2500,26757,154,27501,4671,4111,175,26745,12054,5083,13784,3452,450,13797,539,495,5115,218,5124,29628,10261,231,203,2828,114,171,139,12050,25242,25295,207,2183,272,2902,28910,346,378,5162,7266,235,433,3879,716,214,1116,151,315,146,183,422,4663,9812,300,835,262,5004,168,190,4841,305,4210,195,400,12022,10224,31027,242,294,918,801,136,12024,4193,10092,415,4848,26725,12042,644,131,10287,982,178,31042,1505,163,200,26749,13824,13792,122,5986,354,2438,639,4189,222,592,232,8685,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SWC342+1 : TPTP v8.2.0. Released v2.4.0.
% 0.09/0.12 % Command : run_Leo-III %s %d
% 0.11/0.32 % Computer : n027.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun May 19 03:42:39 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.99/0.94 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.30/1.16 % [INFO] Parsing done (216ms).
% 1.30/1.17 % [INFO] Running in sequential loop mode.
% 2.21/1.53 % [INFO] eprover registered as external prover.
% 2.21/1.53 % [INFO] cvc4 registered as external prover.
% 2.21/1.54 % [INFO] Scanning for conjecture ...
% 2.38/1.67 % [INFO] Found a conjecture (or negated_conjecture) and 95 axioms. Running axiom selection ...
% 2.52/1.77 % [INFO] Axiom selection finished. Selected 95 axioms (removed 0 axioms).
% 2.95/1.90 % [INFO] Problem is first-order (TPTP FOF).
% 3.15/1.92 % [INFO] Type checking passed.
% 3.15/1.93 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 149.83/27.59 % External prover 'e' found a proof!
% 149.83/27.59 % [INFO] Killing All external provers ...
% 149.83/27.59 % Time passed: 27124ms (effective reasoning time: 26411ms)
% 149.83/27.59 % 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)>
% 149.83/27.59 % Axioms used in derivation (95): ax74, ax13, ax37, ax14, ax12, ax79, ax20, ax52, ax67, ax24, ax63, ax56, ax4, ax47, ax41, ax90, ax31, ax28, ax9, ax17, ax6, ax45, ax40, ax85, ax35, ax58, ax69, ax78, ax39, ax89, ax27, ax66, ax8, ax91, ax73, ax51, ax48, ax21, ax88, ax62, ax10, ax55, ax32, ax95, ax16, ax80, ax59, ax1, ax7, ax77, ax38, ax44, ax84, ax92, ax94, ax33, ax26, ax61, ax11, ax50, ax87, ax72, ax65, ax22, ax15, ax81, ax76, ax43, ax83, ax19, ax2, ax70, ax54, ax49, ax46, ax34, ax23, ax86, ax25, ax60, ax71, ax57, ax68, ax30, ax42, ax82, ax18, ax3, ax5, ax36, ax64, ax29, ax75, ax53, ax93
% 149.83/27.59 % No. of inferences in proof: 877
% 149.83/27.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 27124 ms resp. 26411 ms w/o parsing
% 150.72/27.94 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 150.72/27.95 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------