TSTP Solution File: SWC368+1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWC368+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:11:42 EDT 2023
% Result : Theorem 147.35s 27.13s
% Output : Refutation 148.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 150
% Syntax : Number of formulae : 1049 ( 110 unt; 54 typ; 0 def)
% Number of atoms : 3562 ( 757 equ; 0 cnn)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 8222 (1104 ~;1290 |; 129 &;5111 @)
% ( 26 <=>; 562 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 57 ( 57 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 54 usr; 11 con; 0-2 aty)
% Number of variables : 933 ( 0 ^; 897 !; 36 ?; 933 :)
% Comments :
%------------------------------------------------------------------------------
thf(ssList_type,type,
ssList: $i > $o ).
thf(segmentP_type,type,
segmentP: $i > $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(leq_type,type,
leq: $i > $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(totalorderedP_type,type,
totalorderedP: $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(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: $o ).
thf(sk6_type,type,
sk6: $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(sk21_type,type,
sk21: $i > $i ).
thf(sk22_type,type,
sk22: $i > $i > $i ).
thf(sk23_type,type,
sk23: $i > $i ).
thf(sk24_type,type,
sk24: $i > $i ).
thf(sk25_type,type,
sk25: $i > $i ).
thf(sk26_type,type,
sk26: $i > $i ).
thf(sk27_type,type,
sk27: $i > $i ).
thf(sk28_type,type,
sk28: $i > $i ).
thf(sk39_type,type,
sk39: $i ).
thf(sk40_type,type,
sk40: $i ).
thf(1,conjecture,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ( ( B != D )
| ( A != C )
| ( segmentP @ B @ A )
| ( ! [E: $i] :
( ( ssItem @ E )
=> ( ( ( cons @ E @ nil )
!= C )
| ~ ( memberP @ D @ E )
| ? [F: $i] :
( ( ssItem @ F )
& ( E != F )
& ( memberP @ D @ F )
& ( leq @ F @ E ) ) ) )
& ( ( nil != D )
| ( nil != C ) ) ) ) ) ) ) ),
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 )
| ( segmentP @ B @ A )
| ( ! [E: $i] :
( ( ssItem @ E )
=> ( ( ( cons @ E @ nil )
!= C )
| ~ ( memberP @ D @ E )
| ? [F: $i] :
( ( ssItem @ F )
& ( E != F )
& ( memberP @ D @ F )
& ( leq @ F @ E ) ) ) )
& ( ( nil != D )
| ( nil != C ) ) ) ) ) ) ) ),
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 )
| ( segmentP @ B @ A )
| ( ! [E: $i] :
( ( ssItem @ E )
=> ( ( ( cons @ E @ nil )
!= C )
| ~ ( memberP @ D @ E )
| ? [F: $i] :
( ( ssItem @ F )
& ( E != F )
& ( memberP @ D @ F )
& ( leq @ F @ E ) ) ) )
& ( ( nil != D )
| ( nil != C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(103,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(155,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(160,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( sk7 @ A ) )
| ( cyclefreeP @ A ) ),
inference(cnf,[status(esa)],[155]) ).
thf(3872,plain,
! [A: $i] :
( ( ssItem @ ( sk7 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,160]) ).
thf(3873,plain,
( ( ssItem @ ( sk7 @ sk1 ) )
| ( cyclefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[3872:[bind(A,$thf( sk1 ))]]) ).
thf(61,axiom,
? [A: $i] :
( ( ssItem @ A )
& ? [B: $i] :
( ( ssItem @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(373,plain,
? [A: $i] :
( ( ssItem @ A )
& ? [B: $i] :
( ( ssItem @ B )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(376,plain,
ssItem @ sk39,
inference(cnf,[status(esa)],[373]) ).
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(206,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(208,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( neq @ A @ B )
| ( A != B ) ),
inference(cnf,[status(esa)],[206]) ).
thf(210,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( neq @ A @ B ) ),
inference(lifteq,[status(thm)],[208]) ).
thf(211,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ~ ( neq @ A @ A ) ),
inference(simp,[status(thm)],[210]) ).
thf(24746,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssItem @ sk39 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[376,211]) ).
thf(24747,plain,
~ ( neq @ sk39 @ sk39 ),
inference(pattern_uni,[status(thm)],[24746:[bind(A,$thf( sk39 ))]]) ).
thf(11,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( segmentP @ nil @ A )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).
thf(137,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(138,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( segmentP @ nil @ A )
| ( nil = A ) ),
inference(cnf,[status(esa)],[137]) ).
thf(140,plain,
! [A: $i] :
( ( nil = A )
| ~ ( ssList @ A )
| ~ ( segmentP @ nil @ A ) ),
inference(lifteq,[status(thm)],[138]) ).
thf(53,axiom,
ssList @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
thf(332,plain,
ssList @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(6,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( frontsegP @ nil @ A )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax46) ).
thf(123,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(125,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( nil != A )
| ( frontsegP @ nil @ A ) ),
inference(cnf,[status(esa)],[123]) ).
thf(127,plain,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( frontsegP @ nil @ A ) ),
inference(lifteq,[status(thm)],[125]) ).
thf(128,plain,
( ~ ( ssList @ nil )
| ( frontsegP @ nil @ nil ) ),
inference(simp,[status(thm)],[127]) ).
thf(698,plain,
( ~ $true
| ( frontsegP @ nil @ nil ) ),
inference(rewrite,[status(thm)],[128,332]) ).
thf(699,plain,
frontsegP @ nil @ nil,
inference(simp,[status(thm)],[698]) ).
thf(124,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A )
| ( nil = A ) ),
inference(cnf,[status(esa)],[123]) ).
thf(126,plain,
! [A: $i] :
( ( nil = A )
| ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A ) ),
inference(lifteq,[status(thm)],[124]) ).
thf(374,plain,
sk39 != sk40,
inference(cnf,[status(esa)],[373]) ).
thf(377,plain,
sk40 != sk39,
inference(lifteq,[status(thm)],[374]) ).
thf(1029,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A )
| ( sk39 != nil )
| ( A != sk40 ) ),
inference(paramod_ordered,[status(thm)],[126,377]) ).
thf(1030,plain,
( ~ ( ssList @ sk40 )
| ~ ( frontsegP @ nil @ sk40 )
| ( sk39 != nil ) ),
inference(pattern_uni,[status(thm)],[1029:[bind(A,$thf( sk40 ))]]) ).
thf(1317,plain,
( ~ ( ssList @ sk40 )
| ( sk39 != nil )
| ( ( frontsegP @ nil @ sk40 )
!= ( frontsegP @ nil @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[699,1030]) ).
thf(1330,plain,
( ~ ( ssList @ sk40 )
| ( sk39 != nil )
| ( nil != nil )
| ( sk40 != nil ) ),
inference(simp,[status(thm)],[1317]) ).
thf(1333,plain,
( ~ ( ssList @ sk40 )
| ( sk39 != nil )
| ( sk40 != nil ) ),
inference(simp,[status(thm)],[1330]) ).
thf(1345,plain,
( ( sk39 != nil )
| ( sk40 != nil )
| ( ( ssList @ sk40 )
!= ( ssList @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[332,1333]) ).
thf(1347,plain,
( ( sk39 != nil )
| ( sk40 != nil )
| ( sk40 != nil ) ),
inference(simp,[status(thm)],[1345]) ).
thf(1350,plain,
( ( sk39 != nil )
| ( sk40 != nil ) ),
inference(simp,[status(thm)],[1347]) ).
thf(1601,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( segmentP @ nil @ A )
| ( sk40 != nil )
| ( A != sk39 ) ),
inference(paramod_ordered,[status(thm)],[140,1350]) ).
thf(1602,plain,
( ~ ( ssList @ sk39 )
| ~ ( segmentP @ nil @ sk39 )
| ( sk40 != nil ) ),
inference(pattern_uni,[status(thm)],[1601:[bind(A,$thf( sk39 ))]]) ).
thf(4516,plain,
( ~ ( segmentP @ nil @ sk39 )
| ( sk40 != nil )
| ( ( ssList @ sk39 )
!= ( ssList @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[103,1602]) ).
thf(4571,plain,
( ~ ( segmentP @ nil @ sk39 )
| ( sk40 != nil )
| ( sk39 != sk1 ) ),
inference(simp,[status(thm)],[4516]) ).
thf(156,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( sk8 @ A ) )
| ( cyclefreeP @ A ) ),
inference(cnf,[status(esa)],[155]) ).
thf(2833,plain,
! [A: $i] :
( ( ssItem @ ( sk8 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,156]) ).
thf(2834,plain,
( ( ssItem @ ( sk8 @ sk1 ) )
| ( cyclefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[2833:[bind(A,$thf( sk1 ))]]) ).
thf(34,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ~ ( memberP @ nil @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
thf(229,plain,
! [A: $i] :
( ( ssItem @ A )
=> ~ ( memberP @ nil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(230,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ~ ( memberP @ nil @ A ) ),
inference(cnf,[status(esa)],[229]) ).
thf(3007,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk8 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2834,230]) ).
thf(3008,plain,
( ( cyclefreeP @ sk1 )
| ~ ( memberP @ nil @ ( sk8 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[3007:[bind(A,$thf( sk8 @ sk1 ))]]) ).
thf(102,plain,
ssList @ sk2,
inference(cnf,[status(esa)],[98]) ).
thf(23,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( segmentP @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).
thf(191,plain,
! [A: $i] :
( ( ssList @ A )
=> ( segmentP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(192,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( segmentP @ A @ A ) ),
inference(cnf,[status(esa)],[191]) ).
thf(14921,plain,
! [A: $i] :
( ( segmentP @ A @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,192]) ).
thf(14922,plain,
segmentP @ sk2 @ sk2,
inference(pattern_uni,[status(thm)],[14921:[bind(A,$thf( 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(479,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(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(170,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(174,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( sk12 @ A ) )
| ( strictorderP @ A ) ),
inference(cnf,[status(esa)],[170]) ).
thf(8028,plain,
! [A: $i] :
( ( ssItem @ ( sk12 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,174]) ).
thf(8029,plain,
( ( ssItem @ ( sk12 @ sk2 ) )
| ( strictorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[8028:[bind(A,$thf( sk2 ))]]) ).
thf(8113,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk12 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8029,230]) ).
thf(8114,plain,
( ( strictorderP @ sk2 )
| ~ ( memberP @ nil @ ( sk12 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[8113:[bind(A,$thf( sk12 @ sk2 ))]]) ).
thf(159,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( leq @ ( sk7 @ A ) @ ( sk8 @ A ) )
| ( cyclefreeP @ A ) ),
inference(cnf,[status(esa)],[155]) ).
thf(3580,plain,
! [A: $i] :
( ( leq @ ( sk7 @ A ) @ ( sk8 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,159]) ).
thf(3581,plain,
( ( leq @ ( sk7 @ sk2 ) @ ( sk8 @ sk2 ) )
| ( cyclefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3580:[bind(A,$thf( 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(468,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(110,plain,
( ( memberP @ sk4 @ sk6 )
| ~ sk5 ),
inference(cnf,[status(esa)],[98]) ).
thf(105,plain,
sk2 = sk4,
inference(cnf,[status(esa)],[98]) ).
thf(114,plain,
sk4 = sk2,
inference(lifteq,[status(thm)],[105]) ).
thf(530,plain,
( ( memberP @ sk2 @ sk6 )
| ~ sk5 ),
inference(rewrite,[status(thm)],[110,114]) ).
thf(101,plain,
( ( ssItem @ sk6 )
| ~ sk5 ),
inference(cnf,[status(esa)],[98]) ).
thf(510,plain,
! [A: $i] :
( ~ sk5
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ sk6 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[101,230]) ).
thf(511,plain,
( ~ sk5
| ~ ( memberP @ nil @ sk6 ) ),
inference(pattern_uni,[status(thm)],[510:[bind(A,$thf( sk6 ))]]) ).
thf(533,plain,
( ~ sk5
| ( ( memberP @ sk2 @ sk6 )
!= ( memberP @ nil @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[530,511]) ).
thf(539,plain,
( ~ sk5
| ( sk2 != nil )
| ( sk6 != sk6 ) ),
inference(simp,[status(thm)],[533]) ).
thf(541,plain,
( ~ sk5
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[539]) ).
thf(111,plain,
( sk5
| ( nil = sk3 ) ),
inference(cnf,[status(esa)],[98]) ).
thf(117,plain,
( ( sk3 = nil )
| sk5 ),
inference(lifteq,[status(thm)],[111]) ).
thf(104,plain,
sk1 = sk3,
inference(cnf,[status(esa)],[98]) ).
thf(116,plain,
sk3 = sk1,
inference(lifteq,[status(thm)],[104]) ).
thf(521,plain,
( ( sk1 = nil )
| sk5 ),
inference(rewrite,[status(thm)],[117,116]) ).
thf(99,plain,
( sk5
| ( nil = sk4 ) ),
inference(cnf,[status(esa)],[98]) ).
thf(115,plain,
( ( sk4 = nil )
| sk5 ),
inference(lifteq,[status(thm)],[99]) ).
thf(512,plain,
( ( sk2 = nil )
| sk5 ),
inference(rewrite,[status(thm)],[115,114]) ).
thf(107,plain,
~ ( segmentP @ sk2 @ sk1 ),
inference(cnf,[status(esa)],[98]) ).
thf(515,plain,
( sk5
| ~ ( segmentP @ nil @ sk1 )
| ( sk2 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[512,107]) ).
thf(516,plain,
( sk5
| ~ ( segmentP @ nil @ sk1 ) ),
inference(pattern_uni,[status(thm)],[515:[]]) ).
thf(578,plain,
( sk5
| ~ ( segmentP @ nil @ nil )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[521,516]) ).
thf(579,plain,
( sk5
| ~ ( segmentP @ nil @ nil ) ),
inference(pattern_uni,[status(thm)],[578:[]]) ).
thf(139,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( nil != A )
| ( segmentP @ nil @ A ) ),
inference(cnf,[status(esa)],[137]) ).
thf(141,plain,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( segmentP @ nil @ A ) ),
inference(lifteq,[status(thm)],[139]) ).
thf(142,plain,
( ~ ( ssList @ nil )
| ( segmentP @ nil @ nil ) ),
inference(simp,[status(thm)],[141]) ).
thf(884,plain,
( ~ $true
| ( segmentP @ nil @ nil ) ),
inference(rewrite,[status(thm)],[142,332]) ).
thf(885,plain,
segmentP @ nil @ nil,
inference(simp,[status(thm)],[884]) ).
thf(886,plain,
( sk5
| ~ $true ),
inference(rewrite,[status(thm)],[579,885]) ).
thf(887,plain,
sk5,
inference(simp,[status(thm)],[886]) ).
thf(904,plain,
( ~ $true
| ( sk2 != nil ) ),
inference(rewrite,[status(thm)],[541,887]) ).
thf(905,plain,
sk2 != nil,
inference(simp,[status(thm)],[904]) ).
thf(1009,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[126,905]) ).
thf(1010,plain,
( ~ ( ssList @ sk2 )
| ~ ( frontsegP @ nil @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1009:[bind(A,$thf( sk2 ))]]) ).
thf(1109,plain,
( ~ $true
| ~ ( frontsegP @ nil @ sk2 ) ),
inference(rewrite,[status(thm)],[1010,102]) ).
thf(1110,plain,
~ ( frontsegP @ nil @ sk2 ),
inference(simp,[status(thm)],[1109]) ).
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(233,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(235,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( frontsegP @ A @ B )
| ( ssList @ ( sk22 @ B @ A ) ) ),
inference(cnf,[status(esa)],[233]) ).
thf(34835,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( ssList @ ( sk22 @ B @ A ) )
| ( ( frontsegP @ nil @ nil )
!= ( frontsegP @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[699,235]) ).
thf(34836,plain,
( ~ ( ssList @ nil )
| ~ ( ssList @ nil )
| ( ssList @ ( sk22 @ nil @ nil ) ) ),
inference(pattern_uni,[status(thm)],[34835:[bind(A,$thf( nil )),bind(B,$thf( nil ))]]) ).
thf(34952,plain,
( ~ ( ssList @ nil )
| ( ssList @ ( sk22 @ nil @ nil ) ) ),
inference(simp,[status(thm)],[34836]) ).
thf(35059,plain,
( ~ $true
| ( ssList @ ( sk22 @ nil @ nil ) ) ),
inference(rewrite,[status(thm)],[34952,332]) ).
thf(35060,plain,
ssList @ ( sk22 @ nil @ nil ),
inference(simp,[status(thm)],[35059]) ).
thf(45,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( rearsegP @ A @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax51) ).
thf(289,plain,
! [A: $i] :
( ( ssList @ A )
=> ( rearsegP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(290,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( rearsegP @ A @ nil ) ),
inference(cnf,[status(esa)],[289]) ).
thf(35192,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk22 @ nil @ nil ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[35060,290]) ).
thf(35193,plain,
rearsegP @ ( sk22 @ nil @ nil ) @ nil,
inference(pattern_uni,[status(thm)],[35192:[bind(A,$thf( sk22 @ nil @ nil ))]]) ).
thf(545,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ( ( ssItem @ sk39 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[376,230]) ).
thf(546,plain,
~ ( memberP @ nil @ sk39 ),
inference(pattern_uni,[status(thm)],[545:[bind(A,$thf( sk39 ))]]) ).
thf(1023,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A )
| ~ ( memberP @ nil @ nil )
| ( A != sk39 ) ),
inference(paramod_ordered,[status(thm)],[126,546]) ).
thf(1024,plain,
( ~ ( ssList @ sk39 )
| ~ ( frontsegP @ nil @ sk39 )
| ~ ( memberP @ nil @ nil ) ),
inference(pattern_uni,[status(thm)],[1023:[bind(A,$thf( sk39 ))]]) ).
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(333,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(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(247,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(249,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( sk25 @ A ) )
| ( totalorderP @ A ) ),
inference(cnf,[status(esa)],[247]) ).
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(242,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ssList @ B )
& ( ( tl @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(244,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( nil = A )
| ( ssList @ ( sk23 @ A ) ) ),
inference(cnf,[status(esa)],[242]) ).
thf(246,plain,
! [A: $i] :
( ( nil = A )
| ~ ( ssList @ A )
| ( ssList @ ( sk23 @ A ) ) ),
inference(lifteq,[status(thm)],[244]) ).
thf(977,plain,
! [A: $i] :
( ( nil = A )
| ~ ( frontsegP @ nil @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,126]) ).
thf(978,plain,
( ( sk1 = nil )
| ~ ( frontsegP @ nil @ sk1 ) ),
inference(pattern_uni,[status(thm)],[977:[bind(A,$thf( sk1 ))]]) ).
thf(1221,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ~ ( segmentP @ sk2 @ nil )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[978,107]) ).
thf(1222,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ~ ( segmentP @ sk2 @ nil ) ),
inference(pattern_uni,[status(thm)],[1221:[]]) ).
thf(1241,plain,
( ~ ( segmentP @ sk2 @ nil )
| ( ( frontsegP @ nil @ sk1 )
!= ( frontsegP @ nil @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[699,1222]) ).
thf(1254,plain,
( ~ ( segmentP @ sk2 @ nil )
| ( nil != nil )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[1241]) ).
thf(1257,plain,
( ~ ( segmentP @ sk2 @ nil )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[1254]) ).
thf(37,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( segmentP @ A @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax57) ).
thf(240,plain,
! [A: $i] :
( ( ssList @ A )
=> ( segmentP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(241,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( segmentP @ A @ nil ) ),
inference(cnf,[status(esa)],[240]) ).
thf(2540,plain,
! [A: $i] :
( ( segmentP @ A @ nil )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,241]) ).
thf(2541,plain,
segmentP @ sk2 @ nil,
inference(pattern_uni,[status(thm)],[2540:[bind(A,$thf( sk2 ))]]) ).
thf(2595,plain,
( ~ $true
| ( sk1 != nil ) ),
inference(rewrite,[status(thm)],[1257,2541]) ).
thf(2596,plain,
sk1 != nil,
inference(simp,[status(thm)],[2595]) ).
thf(38928,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk23 @ A ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[246,2596]) ).
thf(38929,plain,
( ~ ( ssList @ sk1 )
| ( ssList @ ( sk23 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[38928:[bind(A,$thf( sk1 ))]]) ).
thf(243,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( nil = A )
| ( ( tl @ A )
= ( sk23 @ A ) ) ),
inference(cnf,[status(esa)],[242]) ).
thf(245,plain,
! [A: $i] :
( ( nil = A )
| ( ( sk23 @ A )
= ( tl @ A ) )
| ~ ( ssList @ A ) ),
inference(lifteq,[status(thm)],[243]) ).
thf(37998,plain,
! [A: $i] :
( ( nil = A )
| ( ( sk23 @ A )
= ( tl @ A ) )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,245]) ).
thf(37999,plain,
( ( sk1 = nil )
| ( ( sk23 @ sk1 )
= ( tl @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[37998:[bind(A,$thf( sk1 ))]]) ).
thf(38098,plain,
( ( sk23 @ sk1 )
= ( tl @ sk1 ) ),
inference(simplifyReflect,[status(thm)],[37999,2596]) ).
thf(41761,plain,
( ~ $true
| ( ssList @ ( tl @ sk1 ) ) ),
inference(rewrite,[status(thm)],[38929,38098,103]) ).
thf(41762,plain,
ssList @ ( tl @ sk1 ),
inference(simp,[status(thm)],[41761]) ).
thf(59,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( frontsegP @ A @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax45) ).
thf(358,plain,
! [A: $i] :
( ( ssList @ A )
=> ( frontsegP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(359,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( frontsegP @ A @ nil ) ),
inference(cnf,[status(esa)],[358]) ).
thf(41868,plain,
! [A: $i] :
( ( frontsegP @ A @ nil )
| ( ( ssList @ ( tl @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41762,359]) ).
thf(41869,plain,
frontsegP @ ( tl @ sk1 ) @ nil,
inference(pattern_uni,[status(thm)],[41868:[bind(A,$thf( tl @ sk1 ))]]) ).
thf(248,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk27 @ A ) )
| ( totalorderP @ A ) ),
inference(cnf,[status(esa)],[247]) ).
thf(42157,plain,
! [A: $i] :
( ( ssList @ ( sk27 @ A ) )
| ( totalorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,248]) ).
thf(42158,plain,
( ( ssList @ ( sk27 @ sk2 ) )
| ( totalorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[42157:[bind(A,$thf( sk2 ))]]) ).
thf(44375,plain,
! [A: $i] :
( ( totalorderP @ sk2 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk27 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[42158,359]) ).
thf(44376,plain,
( ( totalorderP @ sk2 )
| ( frontsegP @ ( sk27 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[44375:[bind(A,$thf( sk27 @ sk2 ))]]) ).
thf(91,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( rearsegP @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax49) ).
thf(481,plain,
! [A: $i] :
( ( ssList @ A )
=> ( rearsegP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(57,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( totalorderP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax61) ).
thf(352,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( totalorderP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(38740,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk23 @ A ) )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[246,905]) ).
thf(38741,plain,
( ~ ( ssList @ sk2 )
| ( ssList @ ( sk23 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[38740:[bind(A,$thf( sk2 ))]]) ).
thf(37968,plain,
! [A: $i] :
( ( nil = A )
| ( ( sk23 @ A )
= ( tl @ A ) )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,245]) ).
thf(37969,plain,
( ( sk2 = nil )
| ( ( sk23 @ sk2 )
= ( tl @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[37968:[bind(A,$thf( sk2 ))]]) ).
thf(38055,plain,
( ( sk23 @ sk2 )
= ( tl @ sk2 ) ),
inference(simplifyReflect,[status(thm)],[37969,905]) ).
thf(41223,plain,
( ~ $true
| ( ssList @ ( tl @ sk2 ) ) ),
inference(rewrite,[status(thm)],[38741,102,38055]) ).
thf(41224,plain,
ssList @ ( tl @ sk2 ),
inference(simp,[status(thm)],[41223]) ).
thf(20,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( app @ A @ nil )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).
thf(183,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( app @ A @ nil )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(184,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ A @ nil )
= A ) ),
inference(cnf,[status(esa)],[183]) ).
thf(185,plain,
! [A: $i] :
( ( ( app @ A @ nil )
= A )
| ~ ( ssList @ A ) ),
inference(lifteq,[status(thm)],[184]) ).
thf(41228,plain,
! [A: $i] :
( ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( tl @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41224,185]) ).
thf(41229,plain,
( ( app @ ( tl @ sk2 ) @ nil )
= ( tl @ sk2 ) ),
inference(pattern_uni,[status(thm)],[41228:[bind(A,$thf( tl @ sk2 ))]]) ).
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(217,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(5,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( strictorderedP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax68) ).
thf(121,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( strictorderedP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(122,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( strictorderedP @ ( cons @ A @ nil ) ) ),
inference(cnf,[status(esa)],[121]) ).
thf(3039,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk8 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2834,122]) ).
thf(3040,plain,
( ( cyclefreeP @ sk1 )
| ( strictorderedP @ ( cons @ ( sk8 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[3039:[bind(A,$thf( sk8 @ sk1 ))]]) ).
thf(42927,plain,
! [A: $i] :
( ( ssItem @ ( sk25 @ A ) )
| ( totalorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,249]) ).
thf(42928,plain,
( ( ssItem @ ( sk25 @ sk2 ) )
| ( totalorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[42927:[bind(A,$thf( sk2 ))]]) ).
thf(45208,plain,
! [A: $i] :
( ( totalorderP @ sk2 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk25 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[42928,230]) ).
thf(45209,plain,
( ( totalorderP @ sk2 )
| ~ ( memberP @ nil @ ( sk25 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[45208:[bind(A,$thf( sk25 @ sk2 ))]]) ).
thf(13430,plain,
( ~ ( ssList @ sk39 )
| ~ ( memberP @ nil @ nil )
| ( ( frontsegP @ nil @ sk39 )
!= ( frontsegP @ nil @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[699,1024]) ).
thf(13501,plain,
( ~ ( ssList @ sk39 )
| ~ ( memberP @ nil @ nil )
| ( nil != nil )
| ( sk39 != nil ) ),
inference(simp,[status(thm)],[13430]) ).
thf(13527,plain,
( ~ ( ssList @ sk39 )
| ~ ( memberP @ nil @ nil )
| ( sk39 != nil ) ),
inference(simp,[status(thm)],[13501]) ).
thf(14752,plain,
( ~ ( memberP @ nil @ nil )
| ( sk39 != nil )
| ( ( ssList @ sk39 )
!= ( ssList @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[332,13527]) ).
thf(14771,plain,
( ~ ( memberP @ nil @ nil )
| ( sk39 != nil )
| ( sk39 != nil ) ),
inference(simp,[status(thm)],[14752]) ).
thf(14786,plain,
( ~ ( memberP @ nil @ nil )
| ( sk39 != nil ) ),
inference(simp,[status(thm)],[14771]) ).
thf(6440,plain,
! [A: $i] :
( ( frontsegP @ A @ nil )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,359]) ).
thf(6441,plain,
frontsegP @ sk2 @ nil,
inference(pattern_uni,[status(thm)],[6440:[bind(A,$thf( sk2 ))]]) ).
thf(254,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( sk24 @ A ) )
| ( totalorderP @ A ) ),
inference(cnf,[status(esa)],[247]) ).
thf(47013,plain,
! [A: $i] :
( ( ssItem @ ( sk24 @ A ) )
| ( totalorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,254]) ).
thf(47014,plain,
( ( ssItem @ ( sk24 @ sk2 ) )
| ( totalorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[47013:[bind(A,$thf( sk2 ))]]) ).
thf(47233,plain,
! [A: $i] :
( ( totalorderP @ sk2 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk24 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[47014,230]) ).
thf(47234,plain,
( ( totalorderP @ sk2 )
| ~ ( memberP @ nil @ ( sk24 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[47233:[bind(A,$thf( sk24 @ sk2 ))]]) ).
thf(28,axiom,
~ ( singletonP @ nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).
thf(201,plain,
~ ( singletonP @ nil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(202,plain,
~ ( singletonP @ nil ),
inference(polarity_switch,[status(thm)],[201]) ).
thf(172,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk16 @ A ) )
| ( strictorderP @ A ) ),
inference(cnf,[status(esa)],[170]) ).
thf(7090,plain,
! [A: $i] :
( ( ssList @ ( sk16 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,172]) ).
thf(7091,plain,
( ( ssList @ ( sk16 @ sk1 ) )
| ( strictorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[7090:[bind(A,$thf( sk1 ))]]) ).
thf(7367,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk16 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7091,290]) ).
thf(7368,plain,
( ( strictorderP @ sk1 )
| ( rearsegP @ ( sk16 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[7367:[bind(A,$thf( sk16 @ sk1 ))]]) ).
thf(179,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( sk13 @ A ) )
| ( strictorderP @ A ) ),
inference(cnf,[status(esa)],[170]) ).
thf(9736,plain,
! [A: $i] :
( ( ssItem @ ( sk13 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,179]) ).
thf(9737,plain,
( ( ssItem @ ( sk13 @ sk1 ) )
| ( strictorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[9736:[bind(A,$thf( sk1 ))]]) ).
thf(32,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ~ ( lt @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax90) ).
thf(215,plain,
! [A: $i] :
( ( ssItem @ A )
=> ~ ( lt @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(216,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ~ ( lt @ A @ A ) ),
inference(cnf,[status(esa)],[215]) ).
thf(26075,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ~ ( lt @ A @ A )
| ( ( ssItem @ ( sk13 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9737,216]) ).
thf(26076,plain,
( ( strictorderP @ sk1 )
| ~ ( lt @ ( sk13 @ sk1 ) @ ( sk13 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[26075:[bind(A,$thf( sk13 @ sk1 ))]]) ).
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(119,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(120,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)],[119]) ).
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(385,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(157,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk9 @ A ) )
| ( cyclefreeP @ A ) ),
inference(cnf,[status(esa)],[155]) ).
thf(2935,plain,
! [A: $i] :
( ( ssList @ ( sk9 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,157]) ).
thf(2936,plain,
( ( ssList @ ( sk9 @ sk2 ) )
| ( cyclefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[2935:[bind(A,$thf( sk2 ))]]) ).
thf(3048,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( ssList @ ( sk9 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ ( sk9 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2936,157]) ).
thf(3049,plain,
( ( cyclefreeP @ sk2 )
| ( ssList @ ( sk9 @ ( sk9 @ sk2 ) ) )
| ( cyclefreeP @ ( sk9 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[3048:[bind(A,$thf( sk9 @ sk2 ))]]) ).
thf(8149,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk12 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8029,122]) ).
thf(8150,plain,
( ( strictorderP @ sk2 )
| ( strictorderedP @ ( cons @ ( sk12 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[8149:[bind(A,$thf( sk12 @ sk2 ))]]) ).
thf(7344,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk16 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7091,241]) ).
thf(7345,plain,
( ( strictorderP @ sk1 )
| ( segmentP @ ( sk16 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[7344:[bind(A,$thf( sk16 @ sk1 ))]]) ).
thf(42979,plain,
! [A: $i] :
( ( ssItem @ ( sk25 @ A ) )
| ( totalorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,249]) ).
thf(42980,plain,
( ( ssItem @ ( sk25 @ sk1 ) )
| ( totalorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[42979:[bind(A,$thf( sk1 ))]]) ).
thf(45346,plain,
! [A: $i] :
( ( totalorderP @ sk1 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk25 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[42980,230]) ).
thf(45347,plain,
( ( totalorderP @ sk1 )
| ~ ( memberP @ nil @ ( sk25 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[45346:[bind(A,$thf( sk25 @ sk1 ))]]) ).
thf(2941,plain,
! [A: $i] :
( ( ssList @ ( sk9 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,157]) ).
thf(2942,plain,
( ( ssList @ ( sk9 @ sk1 ) )
| ( cyclefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[2941:[bind(A,$thf( sk1 ))]]) ).
thf(14958,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk9 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2942,192]) ).
thf(14959,plain,
( ( cyclefreeP @ sk1 )
| ( segmentP @ ( sk9 @ sk1 ) @ ( sk9 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[14958:[bind(A,$thf( sk9 @ sk1 ))]]) ).
thf(163,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk10 @ A ) )
| ( cyclefreeP @ A ) ),
inference(cnf,[status(esa)],[155]) ).
thf(4648,plain,
! [A: $i] :
( ( ssList @ ( sk10 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,163]) ).
thf(4649,plain,
( ( ssList @ ( sk10 @ sk1 ) )
| ( cyclefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[4648:[bind(A,$thf( sk1 ))]]) ).
thf(14963,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk10 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4649,192]) ).
thf(14964,plain,
( ( cyclefreeP @ sk1 )
| ( segmentP @ ( sk10 @ sk1 ) @ ( sk10 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[14963:[bind(A,$thf( sk10 @ sk1 ))]]) ).
thf(41792,plain,
! [A: $i] :
( ( segmentP @ A @ A )
| ( ( ssList @ ( tl @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41762,192]) ).
thf(41793,plain,
segmentP @ ( tl @ sk1 ) @ ( tl @ sk1 ),
inference(pattern_uni,[status(thm)],[41792:[bind(A,$thf( tl @ sk1 ))]]) ).
thf(1447,plain,
! [A: $i] :
( ( nil = A )
| ~ ( segmentP @ nil @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,140]) ).
thf(1448,plain,
( ( sk1 = nil )
| ~ ( segmentP @ nil @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1447:[bind(A,$thf( sk1 ))]]) ).
thf(1643,plain,
( ~ ( segmentP @ nil @ sk1 )
| ~ ( segmentP @ sk2 @ nil )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1448,1257]) ).
thf(1644,plain,
( ~ ( segmentP @ nil @ sk1 )
| ~ ( segmentP @ sk2 @ nil ) ),
inference(pattern_uni,[status(thm)],[1643:[]]) ).
thf(2593,plain,
( ~ ( segmentP @ nil @ sk1 )
| ~ $true ),
inference(rewrite,[status(thm)],[1644,2541]) ).
thf(2594,plain,
~ ( segmentP @ nil @ sk1 ),
inference(simp,[status(thm)],[2593]) ).
thf(42827,plain,
( ( segmentP @ ( tl @ sk1 ) @ ( tl @ sk1 ) )
!= ( segmentP @ nil @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[41793,2594]) ).
thf(42869,plain,
( ( ( tl @ sk1 )
!= nil )
| ( ( tl @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[42827]) ).
thf(11755,plain,
! [A: $i] :
( ( ( app @ A @ nil )
= A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,185]) ).
thf(11756,plain,
( ( app @ sk1 @ nil )
= sk1 ),
inference(pattern_uni,[status(thm)],[11755:[bind(A,$thf( sk1 ))]]) ).
thf(161,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk11 @ A ) )
| ( cyclefreeP @ A ) ),
inference(cnf,[status(esa)],[155]) ).
thf(4226,plain,
! [A: $i] :
( ( ssList @ ( sk11 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,161]) ).
thf(4227,plain,
( ( ssList @ ( sk11 @ sk1 ) )
| ( cyclefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[4226:[bind(A,$thf( sk1 ))]]) ).
thf(14926,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk11 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4227,192]) ).
thf(14927,plain,
( ( cyclefreeP @ sk1 )
| ( segmentP @ ( sk11 @ sk1 ) @ ( sk11 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[14926:[bind(A,$thf( sk11 @ sk1 ))]]) ).
thf(221,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk21 @ A ) )
| ( strictorderedP @ A ) ),
inference(cnf,[status(esa)],[217]) ).
thf(28430,plain,
! [A: $i] :
( ( ssList @ ( sk21 @ A ) )
| ( strictorderedP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,221]) ).
thf(28431,plain,
( ( ssList @ ( sk21 @ sk2 ) )
| ( strictorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[28430:[bind(A,$thf( sk2 ))]]) ).
thf(28785,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk21 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[28431,290]) ).
thf(28786,plain,
( ( strictorderedP @ sk2 )
| ( rearsegP @ ( sk21 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[28785:[bind(A,$thf( sk21 @ sk2 ))]]) ).
thf(219,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( sk17 @ A ) )
| ( strictorderedP @ A ) ),
inference(cnf,[status(esa)],[217]) ).
thf(27322,plain,
! [A: $i] :
( ( ssItem @ ( sk17 @ A ) )
| ( strictorderedP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,219]) ).
thf(27323,plain,
( ( ssItem @ ( sk17 @ sk2 ) )
| ( strictorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[27322:[bind(A,$thf( sk2 ))]]) ).
thf(46,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( equalelemsP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax73) ).
thf(291,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( equalelemsP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(292,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( equalelemsP @ ( cons @ A @ nil ) ) ),
inference(cnf,[status(esa)],[291]) ).
thf(27477,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( equalelemsP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk17 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27323,292]) ).
thf(27478,plain,
( ( strictorderedP @ sk2 )
| ( equalelemsP @ ( cons @ ( sk17 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[27477:[bind(A,$thf( sk17 @ sk2 ))]]) ).
thf(375,plain,
ssItem @ sk40,
inference(cnf,[status(esa)],[373]) ).
thf(543,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ( ( ssItem @ sk40 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[375,230]) ).
thf(544,plain,
~ ( memberP @ nil @ sk40 ),
inference(pattern_uni,[status(thm)],[543:[bind(A,$thf( sk40 ))]]) ).
thf(1039,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A )
| ~ ( memberP @ nil @ nil )
| ( A != sk40 ) ),
inference(paramod_ordered,[status(thm)],[126,544]) ).
thf(1040,plain,
( ~ ( ssList @ sk40 )
| ~ ( frontsegP @ nil @ sk40 )
| ~ ( memberP @ nil @ nil ) ),
inference(pattern_uni,[status(thm)],[1039:[bind(A,$thf( sk40 ))]]) ).
thf(20451,plain,
( ~ ( ssList @ sk40 )
| ~ ( memberP @ nil @ nil )
| ( ( frontsegP @ nil @ sk40 )
!= ( frontsegP @ nil @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[699,1040]) ).
thf(20515,plain,
( ~ ( ssList @ sk40 )
| ~ ( memberP @ nil @ nil )
| ( nil != nil )
| ( sk40 != nil ) ),
inference(simp,[status(thm)],[20451]) ).
thf(20542,plain,
( ~ ( ssList @ sk40 )
| ~ ( memberP @ nil @ nil )
| ( sk40 != nil ) ),
inference(simp,[status(thm)],[20515]) ).
thf(24536,plain,
( ~ ( memberP @ nil @ nil )
| ( sk40 != nil )
| ( ( ssList @ sk40 )
!= ( ssList @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[332,20542]) ).
thf(24547,plain,
( ~ ( memberP @ nil @ nil )
| ( sk40 != nil )
| ( sk40 != nil ) ),
inference(simp,[status(thm)],[24536]) ).
thf(24581,plain,
( ~ ( memberP @ nil @ nil )
| ( sk40 != nil ) ),
inference(simp,[status(thm)],[24547]) ).
thf(251,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk28 @ A ) )
| ( totalorderP @ A ) ),
inference(cnf,[status(esa)],[247]) ).
thf(44843,plain,
! [A: $i] :
( ( ssList @ ( sk28 @ A ) )
| ( totalorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,251]) ).
thf(44844,plain,
( ( ssList @ ( sk28 @ sk2 ) )
| ( totalorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[44843:[bind(A,$thf( sk2 ))]]) ).
thf(9708,plain,
! [A: $i] :
( ( ssItem @ ( sk13 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,179]) ).
thf(9709,plain,
( ( ssItem @ ( sk13 @ sk2 ) )
| ( strictorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[9708:[bind(A,$thf( sk2 ))]]) ).
thf(24,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( totalorderedP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax65) ).
thf(193,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( totalorderedP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(194,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ nil ) ) ),
inference(cnf,[status(esa)],[193]) ).
thf(15201,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk13 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9709,194]) ).
thf(15202,plain,
( ( strictorderP @ sk2 )
| ( totalorderedP @ ( cons @ ( sk13 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[15201:[bind(A,$thf( sk13 @ sk2 ))]]) ).
thf(900,plain,
( ( ssItem @ sk6 )
| ~ $true ),
inference(rewrite,[status(thm)],[101,887]) ).
thf(901,plain,
ssItem @ sk6,
inference(simp,[status(thm)],[900]) ).
thf(24754,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssItem @ sk6 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[901,211]) ).
thf(24755,plain,
~ ( neq @ sk6 @ sk6 ),
inference(pattern_uni,[status(thm)],[24754:[bind(A,$thf( sk6 ))]]) ).
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(436,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(3864,plain,
! [A: $i] :
( ( ssItem @ ( sk7 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,160]) ).
thf(3865,plain,
( ( ssItem @ ( sk7 @ sk2 ) )
| ( cyclefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3864:[bind(A,$thf( sk2 ))]]) ).
thf(26071,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ~ ( lt @ A @ A )
| ( ( ssItem @ ( sk7 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3865,216]) ).
thf(26072,plain,
( ( cyclefreeP @ sk2 )
| ~ ( lt @ ( sk7 @ sk2 ) @ ( sk7 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[26071:[bind(A,$thf( sk7 @ sk2 ))]]) ).
thf(106,plain,
( ( ( cons @ sk6 @ nil )
= sk3 )
| ~ sk5 ),
inference(cnf,[status(esa)],[98]) ).
thf(112,plain,
( ( ( cons @ sk6 @ nil )
= sk3 )
| ~ sk5 ),
inference(lifteq,[status(thm)],[106]) ).
thf(557,plain,
( ( ( cons @ sk6 @ nil )
= sk1 )
| ~ sk5 ),
inference(rewrite,[status(thm)],[112,116]) ).
thf(898,plain,
( ( ( cons @ sk6 @ nil )
= sk1 )
| ~ $true ),
inference(rewrite,[status(thm)],[557,887]) ).
thf(899,plain,
( ( cons @ sk6 @ nil )
= sk1 ),
inference(simp,[status(thm)],[898]) ).
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(134,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( hd @ ( cons @ B @ A ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(135,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( ( hd @ ( cons @ B @ A ) )
= B ) ),
inference(cnf,[status(esa)],[134]) ).
thf(136,plain,
! [B: $i,A: $i] :
( ( ( hd @ ( cons @ B @ A ) )
= B )
| ~ ( ssList @ A )
| ~ ( ssItem @ B ) ),
inference(lifteq,[status(thm)],[135]) ).
thf(1282,plain,
! [B: $i,A: $i] :
( ( ( hd @ sk1 )
= B )
| ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( ( cons @ sk6 @ nil )
!= ( cons @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[899,136]) ).
thf(1283,plain,
( ( ( hd @ sk1 )
= sk6 )
| ~ ( ssList @ nil )
| ~ ( ssItem @ sk6 ) ),
inference(pattern_uni,[status(thm)],[1282:[bind(A,$thf( nil )),bind(B,$thf( sk6 ))]]) ).
thf(7992,plain,
( ( ( hd @ sk1 )
= sk6 )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[1283,901,332]) ).
thf(7993,plain,
( ( hd @ sk1 )
= sk6 ),
inference(simp,[status(thm)],[7992]) ).
thf(1439,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( segmentP @ nil @ A )
| ( sk39 != nil )
| ( A != sk40 ) ),
inference(paramod_ordered,[status(thm)],[140,377]) ).
thf(1440,plain,
( ~ ( ssList @ sk40 )
| ~ ( segmentP @ nil @ sk40 )
| ( sk39 != nil ) ),
inference(pattern_uni,[status(thm)],[1439:[bind(A,$thf( sk40 ))]]) ).
thf(3733,plain,
( ~ ( segmentP @ nil @ sk40 )
| ( sk39 != nil )
| ( ( ssList @ sk40 )
!= ( ssList @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[103,1440]) ).
thf(3777,plain,
( ~ ( segmentP @ nil @ sk40 )
| ( sk39 != nil )
| ( sk40 != sk1 ) ),
inference(simp,[status(thm)],[3733]) ).
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(389,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(7061,plain,
! [A: $i] :
( ( ssList @ ( sk16 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,172]) ).
thf(7062,plain,
( ( ssList @ ( sk16 @ sk2 ) )
| ( strictorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[7061:[bind(A,$thf( sk2 ))]]) ).
thf(7240,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk16 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7062,359]) ).
thf(7241,plain,
( ( strictorderP @ sk2 )
| ( frontsegP @ ( sk16 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[7240:[bind(A,$thf( sk16 @ sk2 ))]]) ).
thf(2827,plain,
! [A: $i] :
( ( ssItem @ ( sk8 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,156]) ).
thf(2828,plain,
( ( ssItem @ ( sk8 @ sk2 ) )
| ( cyclefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[2827:[bind(A,$thf( sk2 ))]]) ).
thf(2915,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk8 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2828,122]) ).
thf(2916,plain,
( ( cyclefreeP @ sk2 )
| ( strictorderedP @ ( cons @ ( sk8 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[2915:[bind(A,$thf( sk8 @ sk2 ))]]) ).
thf(41254,plain,
! [A: $i] :
( ( segmentP @ A @ A )
| ( ( ssList @ ( tl @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41224,192]) ).
thf(41255,plain,
segmentP @ ( tl @ sk2 ) @ ( tl @ sk2 ),
inference(pattern_uni,[status(thm)],[41254:[bind(A,$thf( tl @ sk2 ))]]) ).
thf(42707,plain,
( ( segmentP @ ( tl @ sk2 ) @ ( tl @ sk2 ) )
!= ( segmentP @ nil @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[41255,2594]) ).
thf(42759,plain,
( ( ( tl @ sk2 )
!= nil )
| ( ( tl @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[42707]) ).
thf(218,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk19 @ A ) )
| ( strictorderedP @ A ) ),
inference(cnf,[status(esa)],[217]) ).
thf(26620,plain,
! [A: $i] :
( ( ssList @ ( sk19 @ A ) )
| ( strictorderedP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,218]) ).
thf(26621,plain,
( ( ssList @ ( sk19 @ sk2 ) )
| ( strictorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[26620:[bind(A,$thf( sk2 ))]]) ).
thf(220,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( sk18 @ A ) )
| ( strictorderedP @ A ) ),
inference(cnf,[status(esa)],[217]) ).
thf(27872,plain,
! [A: $i] :
( ( ssItem @ ( sk18 @ A ) )
| ( strictorderedP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,220]) ).
thf(27873,plain,
( ( ssItem @ ( sk18 @ sk2 ) )
| ( strictorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[27872:[bind(A,$thf( sk2 ))]]) ).
thf(28027,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( equalelemsP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk18 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27873,292]) ).
thf(28028,plain,
( ( strictorderedP @ sk2 )
| ( equalelemsP @ ( cons @ ( sk18 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[28027:[bind(A,$thf( sk18 @ sk2 ))]]) ).
thf(967,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A )
| ( ssItem @ nil )
| ( A != sk6 ) ),
inference(paramod_ordered,[status(thm)],[126,901]) ).
thf(968,plain,
( ~ ( ssList @ sk6 )
| ~ ( frontsegP @ nil @ sk6 )
| ( ssItem @ nil ) ),
inference(pattern_uni,[status(thm)],[967:[bind(A,$thf( sk6 ))]]) ).
thf(3805,plain,
( ~ ( frontsegP @ nil @ sk6 )
| ( ssItem @ nil )
| ( ( ssList @ sk6 )
!= ( ssList @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[103,968]) ).
thf(3845,plain,
( ( ssItem @ nil )
| ~ ( frontsegP @ nil @ sk6 )
| ( sk6 != sk1 ) ),
inference(simp,[status(thm)],[3805]) ).
thf(5988,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk11 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4227,290]) ).
thf(5989,plain,
( ( cyclefreeP @ sk1 )
| ( rearsegP @ ( sk11 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[5988:[bind(A,$thf( sk11 @ sk1 ))]]) ).
thf(178,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk14 @ A ) )
| ( strictorderP @ A ) ),
inference(cnf,[status(esa)],[170]) ).
thf(9056,plain,
! [A: $i] :
( ( ssList @ ( sk14 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,178]) ).
thf(9057,plain,
( ( ssList @ ( sk14 @ sk1 ) )
| ( strictorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[9056:[bind(A,$thf( sk1 ))]]) ).
thf(9359,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk14 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9057,290]) ).
thf(9360,plain,
( ( strictorderP @ sk1 )
| ( rearsegP @ ( sk14 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[9359:[bind(A,$thf( sk14 @ sk1 ))]]) ).
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(344,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(26057,plain,
! [A: $i] :
( ~ ( lt @ A @ A )
| ( ( ssItem @ sk6 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[901,216]) ).
thf(26058,plain,
~ ( lt @ sk6 @ sk6 ),
inference(pattern_uni,[status(thm)],[26057:[bind(A,$thf( sk6 ))]]) ).
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(152,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(222,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ ( app @ ( sk19 @ A ) @ ( cons @ ( sk17 @ A ) @ ( sk20 @ A ) ) ) @ ( cons @ ( sk18 @ A ) @ ( sk21 @ A ) ) )
= A )
| ( strictorderedP @ A ) ),
inference(cnf,[status(esa)],[217]) ).
thf(228,plain,
! [A: $i] :
( ( ( app @ ( app @ ( sk19 @ A ) @ ( cons @ ( sk17 @ A ) @ ( sk20 @ A ) ) ) @ ( cons @ ( sk18 @ A ) @ ( sk21 @ A ) ) )
= A )
| ~ ( ssList @ A )
| ( strictorderedP @ A ) ),
inference(lifteq,[status(thm)],[222]) ).
thf(24204,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( equalelemsP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk12 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8029,292]) ).
thf(24205,plain,
( ( strictorderP @ sk2 )
| ( equalelemsP @ ( cons @ ( sk12 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[24204:[bind(A,$thf( sk12 @ sk2 ))]]) ).
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(448,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( tl @ ( cons @ B @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(158,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( leq @ ( sk8 @ A ) @ ( sk7 @ A ) )
| ( cyclefreeP @ A ) ),
inference(cnf,[status(esa)],[155]) ).
thf(3267,plain,
! [A: $i] :
( ( leq @ ( sk8 @ A ) @ ( sk7 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,158]) ).
thf(3268,plain,
( ( leq @ ( sk8 @ sk2 ) @ ( sk7 @ sk2 ) )
| ( cyclefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3267:[bind(A,$thf( sk2 ))]]) ).
thf(26035,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ~ ( lt @ A @ A )
| ( ( ssItem @ ( sk7 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3873,216]) ).
thf(26036,plain,
( ( cyclefreeP @ sk1 )
| ~ ( lt @ ( sk7 @ sk1 ) @ ( sk7 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[26035:[bind(A,$thf( sk7 @ sk1 ))]]) ).
thf(345,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( nil != B )
| ( nil != A )
| ( nil
= ( app @ A @ B ) ) ),
inference(cnf,[status(esa)],[344]) ).
thf(348,plain,
! [B: $i,A: $i] :
( ( nil != B )
| ( nil != A )
| ( ( app @ A @ B )
= nil )
| ~ ( ssList @ A )
| ~ ( ssList @ B ) ),
inference(lifteq,[status(thm)],[345]) ).
thf(349,plain,
( ( ( app @ nil @ nil )
= nil )
| ~ ( ssList @ nil ) ),
inference(simp,[status(thm)],[348]) ).
thf(1301,plain,
( ( ( app @ nil @ nil )
= nil )
| ~ $true ),
inference(rewrite,[status(thm)],[349,332]) ).
thf(1302,plain,
( ( app @ nil @ nil )
= nil ),
inference(simp,[status(thm)],[1301]) ).
thf(4627,plain,
! [A: $i] :
( ( ssList @ ( sk10 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,163]) ).
thf(4628,plain,
( ( ssList @ ( sk10 @ sk2 ) )
| ( cyclefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[4627:[bind(A,$thf( sk2 ))]]) ).
thf(5984,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk10 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4628,290]) ).
thf(5985,plain,
( ( cyclefreeP @ sk2 )
| ( rearsegP @ ( sk10 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[5984:[bind(A,$thf( sk10 @ sk2 ))]]) ).
thf(9017,plain,
! [A: $i] :
( ( ssList @ ( sk14 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,178]) ).
thf(9018,plain,
( ( ssList @ ( sk14 @ sk2 ) )
| ( strictorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[9017:[bind(A,$thf( sk2 ))]]) ).
thf(9224,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk14 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9018,359]) ).
thf(9225,plain,
( ( strictorderP @ sk2 )
| ( frontsegP @ ( sk14 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[9224:[bind(A,$thf( sk14 @ sk2 ))]]) ).
thf(225,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk20 @ A ) )
| ( strictorderedP @ A ) ),
inference(cnf,[status(esa)],[217]) ).
thf(29940,plain,
! [A: $i] :
( ( ssList @ ( sk20 @ A ) )
| ( strictorderedP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,225]) ).
thf(29941,plain,
( ( ssList @ ( sk20 @ sk2 ) )
| ( strictorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[29940:[bind(A,$thf( sk2 ))]]) ).
thf(30311,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk20 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29941,290]) ).
thf(30312,plain,
( ( strictorderedP @ sk2 )
| ( rearsegP @ ( sk20 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[30311:[bind(A,$thf( sk20 @ sk2 ))]]) ).
thf(234,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( ( app @ B @ C )
!= A )
| ( frontsegP @ A @ B ) ),
inference(cnf,[status(esa)],[233]) ).
thf(237,plain,
! [C: $i,B: $i,A: $i] :
( ( ( app @ B @ C )
!= A )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( frontsegP @ A @ B ) ),
inference(lifteq,[status(thm)],[234]) ).
thf(238,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ ( app @ A @ B ) )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( frontsegP @ ( app @ A @ B ) @ A ) ),
inference(simp,[status(thm)],[237]) ).
thf(24232,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( equalelemsP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk13 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9709,292]) ).
thf(24233,plain,
( ( strictorderP @ sk2 )
| ( equalelemsP @ ( cons @ ( sk13 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[24232:[bind(A,$thf( sk13 @ 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(147,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(30292,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk20 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29941,359]) ).
thf(30293,plain,
( ( strictorderedP @ sk2 )
| ( frontsegP @ ( sk20 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[30292:[bind(A,$thf( sk20 @ sk2 ))]]) ).
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(293,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(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(453,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(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(132,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(133,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)],[132]) ).
thf(177,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk15 @ A ) )
| ( strictorderP @ A ) ),
inference(cnf,[status(esa)],[170]) ).
thf(8458,plain,
! [A: $i] :
( ( ssList @ ( sk15 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,177]) ).
thf(8459,plain,
( ( ssList @ ( sk15 @ sk1 ) )
| ( strictorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[8458:[bind(A,$thf( sk1 ))]]) ).
thf(73,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( strictorderP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax63) ).
thf(411,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( strictorderP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(24200,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( equalelemsP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk7 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3873,292]) ).
thf(24201,plain,
( ( cyclefreeP @ sk1 )
| ( equalelemsP @ ( cons @ ( sk7 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[24200:[bind(A,$thf( sk7 @ sk1 ))]]) ).
thf(9346,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk14 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9057,359]) ).
thf(9347,plain,
( ( strictorderP @ sk1 )
| ( frontsegP @ ( sk14 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[9346:[bind(A,$thf( sk14 @ sk1 ))]]) ).
thf(11727,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk11 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4227,185]) ).
thf(11728,plain,
( ( cyclefreeP @ sk1 )
| ( ( app @ ( sk11 @ sk1 ) @ nil )
= ( sk11 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[11727:[bind(A,$thf( sk11 @ sk1 ))]]) ).
thf(11782,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk10 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4649,185]) ).
thf(11783,plain,
( ( cyclefreeP @ sk1 )
| ( ( app @ ( sk10 @ sk1 ) @ nil )
= ( sk10 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[11782:[bind(A,$thf( sk10 @ sk1 ))]]) ).
thf(2883,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk8 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2828,230]) ).
thf(2884,plain,
( ( cyclefreeP @ sk2 )
| ~ ( memberP @ nil @ ( sk8 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[2883:[bind(A,$thf( sk8 @ sk2 ))]]) ).
thf(27473,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ~ ( lt @ A @ A )
| ( ( ssItem @ ( sk17 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27323,216]) ).
thf(27474,plain,
( ( strictorderedP @ sk2 )
| ~ ( lt @ ( sk17 @ sk2 ) @ ( sk17 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[27473:[bind(A,$thf( sk17 @ sk2 ))]]) ).
thf(24248,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( equalelemsP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk8 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2828,292]) ).
thf(24249,plain,
( ( cyclefreeP @ sk2 )
| ( equalelemsP @ ( cons @ ( sk8 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[24248:[bind(A,$thf( sk8 @ sk2 ))]]) ).
thf(941,plain,
! [A: $i] :
( ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk40 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[375,122]) ).
thf(942,plain,
strictorderedP @ ( cons @ sk40 @ nil ),
inference(pattern_uni,[status(thm)],[941:[bind(A,$thf( sk40 ))]]) ).
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(270,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(41850,plain,
! [A: $i] :
( ( segmentP @ A @ nil )
| ( ( ssList @ ( tl @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41762,241]) ).
thf(41851,plain,
segmentP @ ( tl @ sk1 ) @ nil,
inference(pattern_uni,[status(thm)],[41850:[bind(A,$thf( tl @ sk1 ))]]) ).
thf(7253,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk16 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7062,290]) ).
thf(7254,plain,
( ( strictorderP @ sk2 )
| ( rearsegP @ ( sk16 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[7253:[bind(A,$thf( sk16 @ sk2 ))]]) ).
thf(8052,plain,
! [A: $i] :
( ( ssItem @ ( sk12 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,174]) ).
thf(8053,plain,
( ( ssItem @ ( sk12 @ sk1 ) )
| ( strictorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[8052:[bind(A,$thf( sk1 ))]]) ).
thf(8169,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk12 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8053,230]) ).
thf(8170,plain,
( ( strictorderP @ sk1 )
| ~ ( memberP @ nil @ ( sk12 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[8169:[bind(A,$thf( sk12 @ sk1 ))]]) ).
thf(44919,plain,
! [A: $i] :
( ( ssList @ ( sk28 @ A ) )
| ( totalorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,251]) ).
thf(44920,plain,
( ( ssList @ ( sk28 @ sk1 ) )
| ( totalorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[44919:[bind(A,$thf( sk1 ))]]) ).
thf(35151,plain,
! [A: $i] :
( ( segmentP @ A @ nil )
| ( ( ssList @ ( sk22 @ nil @ nil ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[35060,241]) ).
thf(35152,plain,
segmentP @ ( sk22 @ nil @ nil ) @ nil,
inference(pattern_uni,[status(thm)],[35151:[bind(A,$thf( sk22 @ nil @ nil ))]]) ).
thf(255,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk26 @ A ) )
| ( totalorderP @ A ) ),
inference(cnf,[status(esa)],[247]) ).
thf(47887,plain,
! [A: $i] :
( ( ssList @ ( sk26 @ A ) )
| ( totalorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,255]) ).
thf(47888,plain,
( ( ssList @ ( sk26 @ sk2 ) )
| ( totalorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[47887:[bind(A,$thf( sk2 ))]]) ).
thf(24224,plain,
! [A: $i] :
( ( equalelemsP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk6 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[901,292]) ).
thf(24225,plain,
equalelemsP @ ( cons @ sk6 @ nil ),
inference(pattern_uni,[status(thm)],[24224:[bind(A,$thf( sk6 ))]]) ).
thf(24358,plain,
equalelemsP @ sk1,
inference(rewrite,[status(thm)],[24225,899]) ).
thf(14942,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk16 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7062,192]) ).
thf(14943,plain,
( ( strictorderP @ sk2 )
| ( segmentP @ ( sk16 @ sk2 ) @ ( sk16 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[14942:[bind(A,$thf( sk16 @ sk2 ))]]) ).
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(260,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(11718,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk10 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4628,185]) ).
thf(11719,plain,
( ( cyclefreeP @ sk2 )
| ( ( app @ ( sk10 @ sk2 ) @ nil )
= ( sk10 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[11718:[bind(A,$thf( sk10 @ sk2 ))]]) ).
thf(24774,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ~ ( neq @ A @ A )
| ( ( ssItem @ ( sk8 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2834,211]) ).
thf(24775,plain,
( ( cyclefreeP @ sk1 )
| ~ ( neq @ ( sk8 @ sk1 ) @ ( sk8 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[24774:[bind(A,$thf( sk8 @ sk1 ))]]) ).
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(392,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(3068,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk9 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2936,241]) ).
thf(3069,plain,
( ( cyclefreeP @ sk2 )
| ( segmentP @ ( sk9 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[3068:[bind(A,$thf( sk9 @ sk2 ))]]) ).
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(429,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(164,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ ( app @ ( sk9 @ A ) @ ( cons @ ( sk7 @ A ) @ ( sk10 @ A ) ) ) @ ( cons @ ( sk8 @ A ) @ ( sk11 @ A ) ) )
= A )
| ( cyclefreeP @ A ) ),
inference(cnf,[status(esa)],[155]) ).
thf(165,plain,
! [A: $i] :
( ( ( app @ ( app @ ( sk9 @ A ) @ ( cons @ ( sk7 @ A ) @ ( sk10 @ A ) ) ) @ ( cons @ ( sk8 @ A ) @ ( sk11 @ A ) ) )
= A )
| ~ ( ssList @ A )
| ( cyclefreeP @ A ) ),
inference(lifteq,[status(thm)],[164]) ).
thf(1417,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( segmentP @ nil @ A )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[140,905]) ).
thf(1418,plain,
( ~ ( ssList @ sk2 )
| ~ ( segmentP @ nil @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1417:[bind(A,$thf( sk2 ))]]) ).
thf(1609,plain,
( ~ $true
| ~ ( segmentP @ nil @ sk2 ) ),
inference(rewrite,[status(thm)],[1418,102]) ).
thf(1610,plain,
~ ( segmentP @ nil @ sk2 ),
inference(simp,[status(thm)],[1609]) ).
thf(42736,plain,
( ( segmentP @ ( tl @ sk2 ) @ ( tl @ sk2 ) )
!= ( segmentP @ nil @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[41255,1610]) ).
thf(42751,plain,
( ( ( tl @ sk2 )
!= nil )
| ( ( tl @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[42736]) ).
thf(173,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( lt @ ( sk12 @ A ) @ ( sk13 @ A ) )
| ( strictorderP @ A ) ),
inference(cnf,[status(esa)],[170]) ).
thf(7702,plain,
! [A: $i] :
( ~ ( lt @ ( sk12 @ A ) @ ( sk13 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,173]) ).
thf(7703,plain,
( ~ ( lt @ ( sk12 @ sk1 ) @ ( sk13 @ sk1 ) )
| ( strictorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[7702:[bind(A,$thf( sk1 ))]]) ).
thf(71,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ssList @ ( app @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
thf(407,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ssList @ ( app @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
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(195,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(196,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( leq @ A @ B )
| ( A = B )
| ( lt @ A @ B ) ),
inference(cnf,[status(esa)],[195]) ).
thf(197,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( leq @ A @ B )
| ( lt @ A @ B ) ),
inference(lifteq,[status(thm)],[196]) ).
thf(3815,plain,
( ~ ( ssList @ sk6 )
| ( ssItem @ nil )
| ( ( frontsegP @ nil @ sk6 )
!= ( frontsegP @ nil @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[699,968]) ).
thf(3838,plain,
( ( ssItem @ nil )
| ~ ( ssList @ sk6 )
| ( nil != nil )
| ( sk6 != nil ) ),
inference(simp,[status(thm)],[3815]) ).
thf(3855,plain,
( ( ssItem @ nil )
| ~ ( ssList @ sk6 )
| ( sk6 != nil ) ),
inference(simp,[status(thm)],[3838]) ).
thf(4139,plain,
( ( ssItem @ nil )
| ( sk6 != nil )
| ( ( ssList @ sk6 )
!= ( ssList @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[332,3855]) ).
thf(4147,plain,
( ( ssItem @ nil )
| ( sk6 != nil )
| ( sk6 != nil ) ),
inference(simp,[status(thm)],[4139]) ).
thf(4155,plain,
( ( ssItem @ nil )
| ( sk6 != nil ) ),
inference(simp,[status(thm)],[4147]) ).
thf(24252,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( equalelemsP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk7 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3865,292]) ).
thf(24253,plain,
( ( cyclefreeP @ sk2 )
| ( equalelemsP @ ( cons @ ( sk7 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[24252:[bind(A,$thf( sk7 @ sk2 ))]]) ).
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(493,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(28023,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ~ ( lt @ A @ A )
| ( ( ssItem @ ( sk18 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27873,216]) ).
thf(28024,plain,
( ( strictorderedP @ sk2 )
| ~ ( lt @ ( sk18 @ sk2 ) @ ( sk18 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[28023:[bind(A,$thf( sk18 @ sk2 ))]]) ).
thf(24750,plain,
! [A: $i] :
( ( sk6 != nil )
| ~ ( neq @ A @ A )
| ( ( ssItem @ nil )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4155,211]) ).
thf(24751,plain,
( ( sk6 != nil )
| ~ ( neq @ nil @ nil ) ),
inference(pattern_uni,[status(thm)],[24750:[bind(A,$thf( nil ))]]) ).
thf(24208,plain,
! [A: $i] :
( ( equalelemsP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk39 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[376,292]) ).
thf(24209,plain,
equalelemsP @ ( cons @ sk39 @ nil ),
inference(pattern_uni,[status(thm)],[24208:[bind(A,$thf( sk39 ))]]) ).
thf(252,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( leq @ ( sk25 @ A ) @ ( sk24 @ A ) )
| ( totalorderP @ A ) ),
inference(cnf,[status(esa)],[247]) ).
thf(8421,plain,
! [A: $i] :
( ( ssList @ ( sk15 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,177]) ).
thf(8422,plain,
( ( ssList @ ( sk15 @ sk2 ) )
| ( strictorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[8421:[bind(A,$thf( sk2 ))]]) ).
thf(11733,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk15 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8422,185]) ).
thf(11734,plain,
( ( strictorderP @ sk2 )
| ( ( app @ ( sk15 @ sk2 ) @ nil )
= ( sk15 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[11733:[bind(A,$thf( sk15 @ sk2 ))]]) ).
thf(3121,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( ssList @ ( sk9 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ ( sk9 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2942,157]) ).
thf(3122,plain,
( ( cyclefreeP @ sk1 )
| ( ssList @ ( sk9 @ ( sk9 @ sk1 ) ) )
| ( cyclefreeP @ ( sk9 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[3121:[bind(A,$thf( sk9 @ sk1 ))]]) ).
thf(14940,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk14 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9057,192]) ).
thf(14941,plain,
( ( strictorderP @ sk1 )
| ( segmentP @ ( sk14 @ sk1 ) @ ( sk14 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[14940:[bind(A,$thf( sk14 @ 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(188,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(75,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( rearsegP @ nil @ A )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52) ).
thf(420,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(42735,plain,
( ( segmentP @ ( tl @ sk2 ) @ ( tl @ sk2 ) )
!= ( segmentP @ sk2 @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[41255,107]) ).
thf(42747,plain,
( ( ( tl @ sk2 )
!= sk2 )
| ( ( tl @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[42735]) ).
thf(11735,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk9 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2936,185]) ).
thf(11736,plain,
( ( cyclefreeP @ sk2 )
| ( ( app @ ( sk9 @ sk2 ) @ nil )
= ( sk9 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[11735:[bind(A,$thf( sk9 @ sk2 ))]]) ).
thf(939,plain,
! [A: $i] :
( ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk6 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[901,122]) ).
thf(940,plain,
strictorderedP @ ( cons @ sk6 @ nil ),
inference(pattern_uni,[status(thm)],[939:[bind(A,$thf( sk6 ))]]) ).
thf(948,plain,
strictorderedP @ sk1,
inference(rewrite,[status(thm)],[940,899]) ).
thf(31,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( app @ nil @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
thf(212,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( app @ nil @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(213,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ nil @ A )
= A ) ),
inference(cnf,[status(esa)],[212]) ).
thf(214,plain,
! [A: $i] :
( ( ( app @ nil @ A )
= A )
| ~ ( ssList @ A ) ),
inference(lifteq,[status(thm)],[213]) ).
thf(25214,plain,
! [A: $i] :
( ( ( app @ nil @ A )
= A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,214]) ).
thf(25215,plain,
( ( app @ nil @ sk1 )
= sk1 ),
inference(pattern_uni,[status(thm)],[25214:[bind(A,$thf( sk1 ))]]) ).
thf(18,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ssList @ ( cons @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
thf(168,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ssList @ ( cons @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(169,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( ssList @ ( cons @ B @ A ) ) ),
inference(cnf,[status(esa)],[168]) ).
thf(14952,plain,
! [A: $i] :
( ( segmentP @ A @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,192]) ).
thf(14953,plain,
segmentP @ sk1 @ sk1,
inference(pattern_uni,[status(thm)],[14952:[bind(A,$thf( sk1 ))]]) ).
thf(24220,plain,
! [A: $i] :
( ( sk6 != nil )
| ( equalelemsP @ ( cons @ A @ nil ) )
| ( ( ssItem @ nil )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4155,292]) ).
thf(24221,plain,
( ( sk6 != nil )
| ( equalelemsP @ ( cons @ nil @ nil ) ) ),
inference(pattern_uni,[status(thm)],[24220:[bind(A,$thf( nil ))]]) ).
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(471,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(256,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( leq @ ( sk24 @ A ) @ ( sk25 @ A ) )
| ( totalorderP @ A ) ),
inference(cnf,[status(esa)],[247]) ).
thf(28766,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk21 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[28431,359]) ).
thf(28767,plain,
( ( strictorderedP @ sk2 )
| ( frontsegP @ ( sk21 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[28766:[bind(A,$thf( sk21 @ sk2 ))]]) ).
thf(4166,plain,
! [A: $i] :
( ( sk6 != nil )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ nil )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4155,230]) ).
thf(4167,plain,
( ( sk6 != nil )
| ~ ( memberP @ nil @ nil ) ),
inference(pattern_uni,[status(thm)],[4166:[bind(A,$thf( nil ))]]) ).
thf(25163,plain,
! [A: $i] :
( ( ( app @ nil @ A )
= A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,214]) ).
thf(25164,plain,
( ( app @ nil @ sk2 )
= sk2 ),
inference(pattern_uni,[status(thm)],[25163:[bind(A,$thf( sk2 ))]]) ).
thf(41352,plain,
! [A: $i] :
( ( ( app @ nil @ A )
= A )
| ( ( ssList @ ( tl @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41224,214]) ).
thf(41353,plain,
( ( app @ nil @ ( tl @ sk2 ) )
= ( tl @ sk2 ) ),
inference(pattern_uni,[status(thm)],[41352:[bind(A,$thf( tl @ sk2 ))]]) ).
thf(44353,plain,
! [A: $i] :
( ( totalorderP @ sk2 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk27 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[42158,241]) ).
thf(44354,plain,
( ( totalorderP @ sk2 )
| ( segmentP @ ( sk27 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[44353:[bind(A,$thf( sk27 @ sk2 ))]]) ).
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(129,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(6004,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk10 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4649,290]) ).
thf(6005,plain,
( ( cyclefreeP @ sk1 )
| ( rearsegP @ ( sk10 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[6004:[bind(A,$thf( sk10 @ sk1 ))]]) ).
thf(47965,plain,
! [A: $i] :
( ( ssList @ ( sk26 @ A ) )
| ( totalorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,255]) ).
thf(47966,plain,
( ( ssList @ ( sk26 @ sk1 ) )
| ( totalorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[47965:[bind(A,$thf( sk1 ))]]) ).
thf(27543,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk17 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27323,194]) ).
thf(27544,plain,
( ( strictorderedP @ sk2 )
| ( totalorderedP @ ( cons @ ( sk17 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[27543:[bind(A,$thf( sk17 @ sk2 ))]]) ).
thf(1477,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( segmentP @ nil @ A )
| ~ ( memberP @ nil @ nil )
| ( A != sk40 ) ),
inference(paramod_ordered,[status(thm)],[140,544]) ).
thf(1478,plain,
( ~ ( ssList @ sk40 )
| ~ ( segmentP @ nil @ sk40 )
| ~ ( memberP @ nil @ nil ) ),
inference(pattern_uni,[status(thm)],[1477:[bind(A,$thf( sk40 ))]]) ).
thf(42856,plain,
( ( segmentP @ ( tl @ sk1 ) @ ( tl @ sk1 ) )
!= ( segmentP @ nil @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[41793,1610]) ).
thf(42868,plain,
( ( ( tl @ sk1 )
!= nil )
| ( ( tl @ sk1 )
!= sk2 ) ),
inference(simp,[status(thm)],[42856]) ).
thf(109,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( sk6 = A )
| ~ ( memberP @ sk4 @ A )
| ~ ( leq @ A @ sk6 )
| ~ sk5 ),
inference(cnf,[status(esa)],[98]) ).
thf(113,plain,
! [A: $i] :
( ( sk6 = A )
| ~ ( ssItem @ A )
| ~ ( memberP @ sk4 @ A )
| ~ ( leq @ A @ sk6 )
| ~ sk5 ),
inference(lifteq,[status(thm)],[109]) ).
thf(601,plain,
! [A: $i] :
( ( sk6 = A )
| ~ ( ssItem @ A )
| ~ ( memberP @ sk2 @ A )
| ~ ( leq @ A @ sk6 )
| ~ sk5 ),
inference(rewrite,[status(thm)],[113,114]) ).
thf(682,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ~ ( memberP @ sk2 @ A )
| ~ ( leq @ A @ sk6 )
| ~ sk5
| ( sk39 != sk6 )
| ( A != sk40 ) ),
inference(paramod_ordered,[status(thm)],[601,377]) ).
thf(683,plain,
( ~ ( ssItem @ sk40 )
| ~ ( memberP @ sk2 @ sk40 )
| ~ ( leq @ sk40 @ sk6 )
| ~ sk5
| ( sk39 != sk6 ) ),
inference(pattern_uni,[status(thm)],[682:[bind(A,$thf( sk40 ))]]) ).
thf(702,plain,
( ~ $true
| ~ ( memberP @ sk2 @ sk40 )
| ~ ( leq @ sk40 @ sk6 )
| ~ sk5
| ( sk39 != sk6 ) ),
inference(rewrite,[status(thm)],[683,375]) ).
thf(703,plain,
( ~ ( memberP @ sk2 @ sk40 )
| ~ ( leq @ sk40 @ sk6 )
| ~ sk5
| ( sk39 != sk6 ) ),
inference(simp,[status(thm)],[702]) ).
thf(910,plain,
( ~ ( memberP @ sk2 @ sk40 )
| ~ ( leq @ sk40 @ sk6 )
| ~ $true
| ( sk39 != sk6 ) ),
inference(rewrite,[status(thm)],[703,887]) ).
thf(911,plain,
( ~ ( memberP @ sk2 @ sk40 )
| ~ ( leq @ sk40 @ sk6 )
| ( sk39 != sk6 ) ),
inference(simp,[status(thm)],[910]) ).
thf(24272,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( equalelemsP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk8 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2834,292]) ).
thf(24273,plain,
( ( cyclefreeP @ sk1 )
| ( equalelemsP @ ( cons @ ( sk8 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[24272:[bind(A,$thf( sk8 @ sk1 ))]]) ).
thf(15233,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk13 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9737,194]) ).
thf(15234,plain,
( ( strictorderP @ sk1 )
| ( totalorderedP @ ( cons @ ( sk13 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[15233:[bind(A,$thf( sk13 @ sk1 ))]]) ).
thf(24738,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ~ ( neq @ A @ A )
| ( ( ssItem @ ( sk7 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3873,211]) ).
thf(24739,plain,
( ( cyclefreeP @ sk1 )
| ~ ( neq @ ( sk7 @ sk1 ) @ ( sk7 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[24738:[bind(A,$thf( sk7 @ sk1 ))]]) ).
thf(6464,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk10 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4649,359]) ).
thf(6465,plain,
( ( cyclefreeP @ sk1 )
| ( frontsegP @ ( sk10 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[6464:[bind(A,$thf( sk10 @ sk1 ))]]) ).
thf(14917,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk15 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8459,192]) ).
thf(14918,plain,
( ( strictorderP @ sk1 )
| ( segmentP @ ( sk15 @ sk1 ) @ ( sk15 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[14917:[bind(A,$thf( sk15 @ sk1 ))]]) ).
thf(35173,plain,
! [A: $i] :
( ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk22 @ nil @ nil ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[35060,359]) ).
thf(35174,plain,
frontsegP @ ( sk22 @ nil @ nil ) @ nil,
inference(pattern_uni,[status(thm)],[35173:[bind(A,$thf( sk22 @ nil @ nil ))]]) ).
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(360,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(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(203,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(205,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( gt @ A @ B )
| ( lt @ B @ A ) ),
inference(cnf,[status(esa)],[203]) ).
thf(902,plain,
( ~ $true
| ~ ( memberP @ nil @ sk6 ) ),
inference(rewrite,[status(thm)],[511,887]) ).
thf(903,plain,
~ ( memberP @ nil @ sk6 ),
inference(simp,[status(thm)],[902]) ).
thf(1053,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A )
| ~ ( memberP @ nil @ nil )
| ( A != sk6 ) ),
inference(paramod_ordered,[status(thm)],[126,903]) ).
thf(1054,plain,
( ~ ( ssList @ sk6 )
| ~ ( frontsegP @ nil @ sk6 )
| ~ ( memberP @ nil @ nil ) ),
inference(pattern_uni,[status(thm)],[1053:[bind(A,$thf( sk6 ))]]) ).
thf(69,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( cyclefreeP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax59) ).
thf(398,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( cyclefreeP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(9212,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk14 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9018,241]) ).
thf(9213,plain,
( ( strictorderP @ sk2 )
| ( segmentP @ ( sk14 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[9212:[bind(A,$thf( sk14 @ sk2 ))]]) ).
thf(4447,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk11 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4227,241]) ).
thf(4448,plain,
( ( cyclefreeP @ sk1 )
| ( segmentP @ ( sk11 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[4447:[bind(A,$thf( sk11 @ sk1 ))]]) ).
thf(8608,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk15 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8422,241]) ).
thf(8609,plain,
( ( strictorderP @ sk2 )
| ( segmentP @ ( sk15 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[8608:[bind(A,$thf( sk15 @ sk2 ))]]) ).
thf(3803,plain,
( ~ ( frontsegP @ nil @ sk6 )
| ( ssItem @ nil )
| ( ( ssList @ sk6 )
!= ( ssList @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[102,968]) ).
thf(3841,plain,
( ( ssItem @ nil )
| ~ ( frontsegP @ nil @ sk6 )
| ( sk6 != sk2 ) ),
inference(simp,[status(thm)],[3803]) ).
thf(44394,plain,
! [A: $i] :
( ( totalorderP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk27 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[42158,290]) ).
thf(44395,plain,
( ( totalorderP @ sk2 )
| ( rearsegP @ ( sk27 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[44394:[bind(A,$thf( sk27 @ sk2 ))]]) ).
thf(1433,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( segmentP @ nil @ A )
| ~ ( memberP @ nil @ nil )
| ( A != sk39 ) ),
inference(paramod_ordered,[status(thm)],[140,546]) ).
thf(1434,plain,
( ~ ( ssList @ sk39 )
| ~ ( segmentP @ nil @ sk39 )
| ~ ( memberP @ nil @ nil ) ),
inference(pattern_uni,[status(thm)],[1433:[bind(A,$thf( sk39 ))]]) ).
thf(26063,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ~ ( lt @ A @ A )
| ( ( ssItem @ ( sk13 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9709,216]) ).
thf(26064,plain,
( ( strictorderP @ sk2 )
| ~ ( lt @ ( sk13 @ sk2 ) @ ( sk13 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[26063:[bind(A,$thf( sk13 @ sk2 ))]]) ).
thf(24742,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ~ ( neq @ A @ A )
| ( ( ssItem @ ( sk12 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8029,211]) ).
thf(24743,plain,
( ( strictorderP @ sk2 )
| ~ ( neq @ ( sk12 @ sk2 ) @ ( sk12 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[24742:[bind(A,$thf( sk12 @ sk2 ))]]) ).
thf(2545,plain,
! [A: $i] :
( ( segmentP @ A @ nil )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,241]) ).
thf(2546,plain,
segmentP @ sk1 @ nil,
inference(pattern_uni,[status(thm)],[2545:[bind(A,$thf( sk1 ))]]) ).
thf(4194,plain,
! [A: $i] :
( ( sk6 != nil )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ nil )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4155,122]) ).
thf(4195,plain,
( ( sk6 != nil )
| ( strictorderedP @ ( cons @ nil @ nil ) ) ),
inference(pattern_uni,[status(thm)],[4194:[bind(A,$thf( nil ))]]) ).
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(298,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ssItem @ B )
& ( ( hd @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(3129,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( ssItem @ ( sk8 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ ( sk9 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2942,156]) ).
thf(3130,plain,
( ( cyclefreeP @ sk1 )
| ( ssItem @ ( sk8 @ ( sk9 @ sk1 ) ) )
| ( cyclefreeP @ ( sk9 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[3129:[bind(A,$thf( sk9 @ sk1 ))]]) ).
thf(4509,plain,
( ~ ( segmentP @ nil @ sk39 )
| ( sk40 != nil )
| ( ( ssList @ sk39 )
!= ( ssList @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[102,1602]) ).
thf(4562,plain,
( ~ ( segmentP @ nil @ sk39 )
| ( sk40 != nil )
| ( sk39 != sk2 ) ),
inference(simp,[status(thm)],[4509]) ).
thf(6453,plain,
! [A: $i] :
( ( frontsegP @ A @ nil )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,359]) ).
thf(6454,plain,
frontsegP @ sk1 @ nil,
inference(pattern_uni,[status(thm)],[6453:[bind(A,$thf( sk1 ))]]) ).
thf(1605,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A )
| ( sk40 != nil )
| ( A != sk39 ) ),
inference(paramod_ordered,[status(thm)],[126,1350]) ).
thf(1606,plain,
( ~ ( ssList @ sk39 )
| ~ ( frontsegP @ nil @ sk39 )
| ( sk40 != nil ) ),
inference(pattern_uni,[status(thm)],[1605:[bind(A,$thf( sk39 ))]]) ).
thf(4955,plain,
( ~ ( frontsegP @ nil @ sk39 )
| ( sk40 != nil )
| ( ( ssList @ sk39 )
!= ( ssList @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[102,1606]) ).
thf(5016,plain,
( ~ ( frontsegP @ nil @ sk39 )
| ( sk40 != nil )
| ( sk39 != sk2 ) ),
inference(simp,[status(thm)],[4955]) ).
thf(24762,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ~ ( neq @ A @ A )
| ( ( ssItem @ ( sk13 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9709,211]) ).
thf(24763,plain,
( ( strictorderP @ sk2 )
| ~ ( neq @ ( sk13 @ sk2 ) @ ( sk13 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[24762:[bind(A,$thf( sk13 @ sk2 ))]]) ).
thf(14932,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk15 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8422,192]) ).
thf(14933,plain,
( ( strictorderP @ sk2 )
| ( segmentP @ ( sk15 @ sk2 ) @ ( sk15 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[14932:[bind(A,$thf( sk15 @ sk2 ))]]) ).
thf(148,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( ( cons @ B @ A )
= ( app @ ( cons @ B @ nil ) @ A ) ) ),
inference(cnf,[status(esa)],[147]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ( ( app @ ( cons @ B @ nil ) @ A )
= ( cons @ B @ A ) )
| ~ ( ssList @ A )
| ~ ( ssItem @ B ) ),
inference(lifteq,[status(thm)],[148]) ).
thf(47067,plain,
! [A: $i] :
( ( ssItem @ ( sk24 @ A ) )
| ( totalorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,254]) ).
thf(47068,plain,
( ( ssItem @ ( sk24 @ sk1 ) )
| ( totalorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[47067:[bind(A,$thf( sk1 ))]]) ).
thf(44,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ssList @ ( tl @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).
thf(286,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ssList @ ( tl @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(42231,plain,
! [A: $i] :
( ( ssList @ ( sk27 @ A ) )
| ( totalorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,248]) ).
thf(42232,plain,
( ( ssList @ ( sk27 @ sk1 ) )
| ( totalorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[42231:[bind(A,$thf( sk1 ))]]) ).
thf(44621,plain,
! [A: $i] :
( ( totalorderP @ sk1 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk27 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[42232,241]) ).
thf(44622,plain,
( ( totalorderP @ sk1 )
| ( segmentP @ ( sk27 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[44621:[bind(A,$thf( sk27 @ 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(413,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(15179,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk7 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3873,194]) ).
thf(15180,plain,
( ( cyclefreeP @ sk1 )
| ( totalorderedP @ ( cons @ ( sk7 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[15179:[bind(A,$thf( sk7 @ sk1 ))]]) ).
thf(26961,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk19 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[26621,290]) ).
thf(26962,plain,
( ( strictorderedP @ sk2 )
| ( rearsegP @ ( sk19 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[26961:[bind(A,$thf( sk19 @ sk2 ))]]) ).
thf(1387,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( segmentP @ nil @ A )
| ( ssItem @ nil )
| ( A != sk6 ) ),
inference(paramod_ordered,[status(thm)],[140,901]) ).
thf(1388,plain,
( ~ ( ssList @ sk6 )
| ~ ( segmentP @ nil @ sk6 )
| ( ssItem @ nil ) ),
inference(pattern_uni,[status(thm)],[1387:[bind(A,$thf( sk6 ))]]) ).
thf(3271,plain,
! [A: $i] :
( ( leq @ ( sk8 @ A ) @ ( sk7 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,158]) ).
thf(3272,plain,
( ( leq @ ( sk8 @ sk1 ) @ ( sk7 @ sk1 ) )
| ( cyclefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[3271:[bind(A,$thf( sk1 ))]]) ).
thf(3,axiom,
strictorderedP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax69) ).
thf(118,plain,
strictorderedP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(26866,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk19 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[26621,192]) ).
thf(26867,plain,
( ( strictorderedP @ sk2 )
| ( segmentP @ ( sk19 @ sk2 ) @ ( sk19 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[26866:[bind(A,$thf( sk19 @ sk2 ))]]) ).
thf(204,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( lt @ B @ A )
| ( gt @ A @ B ) ),
inference(cnf,[status(esa)],[203]) ).
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(313,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(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(144,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(1316,plain,
( ~ ( frontsegP @ nil @ sk40 )
| ( sk39 != nil )
| ( ( ssList @ sk40 )
!= ( ssList @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[102,1030]) ).
thf(1332,plain,
( ~ ( frontsegP @ nil @ sk40 )
| ( sk39 != nil )
| ( sk40 != sk2 ) ),
inference(simp,[status(thm)],[1316]) ).
thf(85,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( geq @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax89) ).
thf(466,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( geq @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(176,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)],[170]) ).
thf(180,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)],[176]) ).
thf(181,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)],[180]) ).
thf(11749,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk16 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7062,185]) ).
thf(11750,plain,
( ( strictorderP @ sk2 )
| ( ( app @ ( sk16 @ sk2 ) @ nil )
= ( sk16 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[11749:[bind(A,$thf( sk16 @ sk2 ))]]) ).
thf(41890,plain,
! [A: $i] :
( ( ( app @ nil @ A )
= A )
| ( ( ssList @ ( tl @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41762,214]) ).
thf(41891,plain,
( ( app @ nil @ ( tl @ sk1 ) )
= ( tl @ sk1 ) ),
inference(pattern_uni,[status(thm)],[41890:[bind(A,$thf( tl @ sk1 ))]]) ).
thf(14956,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk14 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9018,192]) ).
thf(14957,plain,
( ( strictorderP @ sk2 )
| ( segmentP @ ( sk14 @ sk2 ) @ ( sk14 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[14956:[bind(A,$thf( sk14 @ sk2 ))]]) ).
thf(5996,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,290]) ).
thf(5997,plain,
rearsegP @ sk1 @ nil,
inference(pattern_uni,[status(thm)],[5996:[bind(A,$thf( sk1 ))]]) ).
thf(15191,plain,
! [A: $i] :
( ( sk6 != nil )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ nil )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4155,194]) ).
thf(15192,plain,
( ( sk6 != nil )
| ( totalorderedP @ ( cons @ nil @ nil ) ) ),
inference(pattern_uni,[status(thm)],[15191:[bind(A,$thf( nil ))]]) ).
thf(41330,plain,
! [A: $i] :
( ( frontsegP @ A @ nil )
| ( ( ssList @ ( tl @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41224,359]) ).
thf(41331,plain,
frontsegP @ ( tl @ sk2 ) @ nil,
inference(pattern_uni,[status(thm)],[41330:[bind(A,$thf( tl @ sk2 ))]]) ).
thf(6442,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk11 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4227,359]) ).
thf(6443,plain,
( ( cyclefreeP @ sk1 )
| ( frontsegP @ ( sk11 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[6442:[bind(A,$thf( sk11 @ sk1 ))]]) ).
thf(6460,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk9 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2942,359]) ).
thf(6461,plain,
( ( cyclefreeP @ sk1 )
| ( frontsegP @ ( sk9 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[6460:[bind(A,$thf( sk9 @ sk1 ))]]) ).
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(451,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(4212,plain,
! [A: $i] :
( ( ssList @ ( sk11 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,161]) ).
thf(4213,plain,
( ( ssList @ ( sk11 @ sk2 ) )
| ( cyclefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[4212:[bind(A,$thf( sk2 ))]]) ).
thf(15211,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk8 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2828,194]) ).
thf(15212,plain,
( ( cyclefreeP @ sk2 )
| ( totalorderedP @ ( cons @ ( sk8 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[15211:[bind(A,$thf( sk8 @ sk2 ))]]) ).
thf(26069,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ~ ( lt @ A @ A )
| ( ( ssItem @ ( sk8 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2828,216]) ).
thf(26070,plain,
( ( cyclefreeP @ sk2 )
| ~ ( lt @ ( sk8 @ sk2 ) @ ( sk8 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[26069:[bind(A,$thf( sk8 @ sk2 ))]]) ).
thf(35064,plain,
! [A: $i] :
( ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk22 @ nil @ nil ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[35060,185]) ).
thf(35065,plain,
( ( app @ ( sk22 @ nil @ nil ) @ nil )
= ( sk22 @ nil @ nil ) ),
inference(pattern_uni,[status(thm)],[35064:[bind(A,$thf( sk22 @ nil @ nil ))]]) ).
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(186,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(187,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)],[186]) ).
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(303,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(64,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( duplicatefreeP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax71) ).
thf(387,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( duplicatefreeP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(92,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( nil
!= ( cons @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).
thf(483,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( nil
!= ( cons @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(9861,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk13 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9737,230]) ).
thf(9862,plain,
( ( strictorderP @ sk1 )
| ~ ( memberP @ nil @ ( sk13 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[9861:[bind(A,$thf( sk13 @ sk1 ))]]) ).
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(198,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(30270,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk20 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29941,241]) ).
thf(30271,plain,
( ( strictorderedP @ sk2 )
| ( segmentP @ ( sk20 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[30270:[bind(A,$thf( sk20 @ sk2 ))]]) ).
thf(5986,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,290]) ).
thf(5987,plain,
rearsegP @ sk2 @ nil,
inference(pattern_uni,[status(thm)],[5986:[bind(A,$thf( sk2 ))]]) ).
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(477,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(27511,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk17 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27323,230]) ).
thf(27512,plain,
( ( strictorderedP @ sk2 )
| ~ ( memberP @ nil @ ( sk17 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[27511:[bind(A,$thf( sk17 @ sk2 ))]]) ).
thf(7684,plain,
! [A: $i] :
( ~ ( lt @ ( sk12 @ A ) @ ( sk13 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,173]) ).
thf(7685,plain,
( ~ ( lt @ ( sk12 @ sk2 ) @ ( sk13 @ sk2 ) )
| ( strictorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[7684:[bind(A,$thf( sk2 ))]]) ).
thf(26041,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ~ ( lt @ A @ A )
| ( ( ssItem @ ( sk12 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8029,216]) ).
thf(26042,plain,
( ( strictorderP @ sk2 )
| ~ ( lt @ ( sk12 @ sk2 ) @ ( sk12 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[26041:[bind(A,$thf( sk12 @ sk2 ))]]) ).
thf(44662,plain,
! [A: $i] :
( ( totalorderP @ sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk27 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[42232,290]) ).
thf(44663,plain,
( ( totalorderP @ sk1 )
| ( rearsegP @ ( sk27 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[44662:[bind(A,$thf( sk27 @ sk1 ))]]) ).
thf(24270,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( equalelemsP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk13 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9737,292]) ).
thf(24271,plain,
( ( strictorderP @ sk1 )
| ( equalelemsP @ ( cons @ ( sk13 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[24270:[bind(A,$thf( sk13 @ sk1 ))]]) ).
thf(35085,plain,
! [A: $i] :
( ( segmentP @ A @ A )
| ( ( ssList @ ( sk22 @ nil @ nil ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[35060,192]) ).
thf(35086,plain,
segmentP @ ( sk22 @ nil @ nil ) @ ( sk22 @ nil @ nil ),
inference(pattern_uni,[status(thm)],[35085:[bind(A,$thf( sk22 @ nil @ nil ))]]) ).
thf(15187,plain,
! [A: $i] :
( ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk39 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[376,194]) ).
thf(15188,plain,
totalorderedP @ ( cons @ sk39 @ nil ),
inference(pattern_uni,[status(thm)],[15187:[bind(A,$thf( sk39 ))]]) ).
thf(15215,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk7 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3865,194]) ).
thf(15216,plain,
( ( cyclefreeP @ sk2 )
| ( totalorderedP @ ( cons @ ( sk7 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[15215:[bind(A,$thf( sk7 @ sk2 ))]]) ).
thf(223,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( lt @ ( sk17 @ A ) @ ( sk18 @ A ) )
| ( strictorderedP @ A ) ),
inference(cnf,[status(esa)],[217]) ).
thf(67,axiom,
strictorderP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax64) ).
thf(394,plain,
strictorderP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(3141,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk9 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2942,241]) ).
thf(3142,plain,
( ( cyclefreeP @ sk1 )
| ( segmentP @ ( sk9 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[3141:[bind(A,$thf( sk9 @ sk1 ))]]) ).
thf(41,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( cons @ B @ A )
!= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
thf(267,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( cons @ B @ A )
!= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
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(505,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(78,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( frontsegP @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax42) ).
thf(431,plain,
! [A: $i] :
( ( ssList @ A )
=> ( frontsegP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
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)],[155]) ).
thf(166,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(167,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)],[166]) ).
thf(130,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( gt @ A @ B )
| ~ ( gt @ B @ A ) ),
inference(cnf,[status(esa)],[129]) ).
thf(24756,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ~ ( neq @ A @ A )
| ( ( ssItem @ ( sk12 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8053,211]) ).
thf(24757,plain,
( ( strictorderP @ sk1 )
| ~ ( neq @ ( sk12 @ sk1 ) @ ( sk12 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[24756:[bind(A,$thf( sk12 @ sk1 ))]]) ).
thf(3916,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk7 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3865,230]) ).
thf(3917,plain,
( ( cyclefreeP @ sk2 )
| ~ ( memberP @ nil @ ( sk7 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[3916:[bind(A,$thf( sk7 @ sk2 ))]]) ).
thf(41766,plain,
! [A: $i] :
( ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( tl @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41762,185]) ).
thf(41767,plain,
( ( app @ ( tl @ sk1 ) @ nil )
= ( tl @ sk1 ) ),
inference(pattern_uni,[status(thm)],[41766:[bind(A,$thf( tl @ sk1 ))]]) ).
thf(11720,plain,
! [A: $i] :
( ( ( app @ A @ nil )
= A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,185]) ).
thf(11721,plain,
( ( app @ sk2 @ nil )
= sk2 ),
inference(pattern_uni,[status(thm)],[11720:[bind(A,$thf( sk2 ))]]) ).
thf(15027,plain,
( ( segmentP @ sk2 @ sk2 )
!= ( segmentP @ sk2 @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[14922,107]) ).
thf(15036,plain,
( ( sk2 != sk2 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[15027]) ).
thf(15048,plain,
sk2 != sk1,
inference(simp,[status(thm)],[15036]) ).
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(426,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(45990,plain,
! [A: $i] :
( ( totalorderP @ sk1 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk28 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44920,241]) ).
thf(45991,plain,
( ( totalorderP @ sk1 )
| ( segmentP @ ( sk28 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[45990:[bind(A,$thf( sk28 @ sk1 ))]]) ).
thf(24766,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ~ ( neq @ A @ A )
| ( ( ssItem @ ( sk8 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2828,211]) ).
thf(24767,plain,
( ( cyclefreeP @ sk2 )
| ~ ( neq @ ( sk8 @ sk2 ) @ ( sk8 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[24766:[bind(A,$thf( sk8 @ sk2 ))]]) ).
thf(943,plain,
! [A: $i] :
( ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk39 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[376,122]) ).
thf(944,plain,
strictorderedP @ ( cons @ sk39 @ nil ),
inference(pattern_uni,[status(thm)],[943:[bind(A,$thf( sk39 ))]]) ).
thf(45742,plain,
! [A: $i] :
( ( totalorderP @ sk2 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk28 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44844,359]) ).
thf(45743,plain,
( ( totalorderP @ sk2 )
| ( frontsegP @ ( sk28 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[45742:[bind(A,$thf( sk28 @ sk2 ))]]) ).
thf(26045,plain,
! [A: $i] :
( ~ ( lt @ A @ A )
| ( ( ssItem @ sk39 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[376,216]) ).
thf(26046,plain,
~ ( lt @ sk39 @ sk39 ),
inference(pattern_uni,[status(thm)],[26045:[bind(A,$thf( sk39 ))]]) ).
thf(207,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( A = B )
| ( neq @ A @ B ) ),
inference(cnf,[status(esa)],[206]) ).
thf(209,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( neq @ A @ B ) ),
inference(lifteq,[status(thm)],[207]) ).
thf(28025,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ~ ( neq @ A @ A )
| ( ( ssItem @ ( sk18 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27873,211]) ).
thf(28026,plain,
( ( strictorderedP @ sk2 )
| ~ ( neq @ ( sk18 @ sk2 ) @ ( sk18 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[28025:[bind(A,$thf( sk18 @ sk2 ))]]) ).
thf(422,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( nil != A )
| ( rearsegP @ nil @ A ) ),
inference(cnf,[status(esa)],[420]) ).
thf(424,plain,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( rearsegP @ nil @ A ) ),
inference(lifteq,[status(thm)],[422]) ).
thf(425,plain,
( ~ ( ssList @ nil )
| ( rearsegP @ nil @ nil ) ),
inference(simp,[status(thm)],[424]) ).
thf(1144,plain,
( ~ $true
| ( rearsegP @ nil @ nil ) ),
inference(rewrite,[status(thm)],[425,332]) ).
thf(1145,plain,
rearsegP @ nil @ nil,
inference(simp,[status(thm)],[1144]) ).
thf(5990,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk9 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2936,290]) ).
thf(5991,plain,
( ( cyclefreeP @ sk2 )
| ( rearsegP @ ( sk9 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[5990:[bind(A,$thf( sk9 @ sk2 ))]]) ).
thf(11769,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk9 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2942,185]) ).
thf(11770,plain,
( ( cyclefreeP @ sk1 )
| ( ( app @ ( sk9 @ sk1 ) @ nil )
= ( sk9 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[11769:[bind(A,$thf( sk9 @ sk1 ))]]) ).
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(150,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(28093,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk18 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27873,194]) ).
thf(28094,plain,
( ( strictorderedP @ sk2 )
| ( totalorderedP @ ( cons @ ( sk18 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[28093:[bind(A,$thf( sk18 @ sk2 ))]]) ).
thf(28744,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk21 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[28431,241]) ).
thf(28745,plain,
( ( strictorderedP @ sk2 )
| ( segmentP @ ( sk21 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[28744:[bind(A,$thf( sk21 @ sk2 ))]]) ).
thf(9237,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk14 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9018,290]) ).
thf(9238,plain,
( ( strictorderP @ sk2 )
| ( rearsegP @ ( sk14 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[9237:[bind(A,$thf( sk14 @ sk2 ))]]) ).
thf(14950,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk11 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4213,192]) ).
thf(14951,plain,
( ( cyclefreeP @ sk2 )
| ( segmentP @ ( sk11 @ sk2 ) @ ( sk11 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[14950:[bind(A,$thf( sk11 @ sk2 ))]]) ).
thf(72,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( leq @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax31) ).
thf(409,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( leq @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
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(310,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(44643,plain,
! [A: $i] :
( ( totalorderP @ sk1 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk27 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[42232,359]) ).
thf(44644,plain,
( ( totalorderP @ sk1 )
| ( frontsegP @ ( sk27 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[44643:[bind(A,$thf( sk27 @ sk1 ))]]) ).
thf(42855,plain,
( ( segmentP @ ( tl @ sk1 ) @ ( tl @ sk1 ) )
!= ( segmentP @ sk2 @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[41793,107]) ).
thf(42874,plain,
( ( ( tl @ sk1 )
!= sk2 )
| ( ( tl @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[42855]) ).
thf(41887,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ ( tl @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41762,290]) ).
thf(41888,plain,
rearsegP @ ( tl @ sk1 ) @ nil,
inference(pattern_uni,[status(thm)],[41887:[bind(A,$thf( tl @ sk1 ))]]) ).
thf(3948,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk7 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3865,122]) ).
thf(3949,plain,
( ( cyclefreeP @ sk2 )
| ( strictorderedP @ ( cons @ ( sk7 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[3948:[bind(A,$thf( sk7 @ sk2 ))]]) ).
thf(26077,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ~ ( lt @ A @ A )
| ( ( ssItem @ ( sk8 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2834,216]) ).
thf(26078,plain,
( ( cyclefreeP @ sk1 )
| ~ ( lt @ ( sk8 @ sk1 ) @ ( sk8 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[26077:[bind(A,$thf( sk8 @ sk1 ))]]) ).
thf(28688,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk21 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[28431,192]) ).
thf(28689,plain,
( ( strictorderedP @ sk2 )
| ( segmentP @ ( sk21 @ sk2 ) @ ( sk21 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[28688:[bind(A,$thf( sk21 @ sk2 ))]]) ).
thf(199,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)],[198]) ).
thf(5994,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk11 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4213,290]) ).
thf(5995,plain,
( ( cyclefreeP @ sk2 )
| ( rearsegP @ ( sk11 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[5994:[bind(A,$thf( sk11 @ sk2 ))]]) ).
thf(8205,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk12 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8053,122]) ).
thf(8206,plain,
( ( strictorderP @ sk1 )
| ( strictorderedP @ ( cons @ ( sk12 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[8205:[bind(A,$thf( sk12 @ sk1 ))]]) ).
thf(15183,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk12 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8029,194]) ).
thf(15184,plain,
( ( strictorderP @ sk2 )
| ( totalorderedP @ ( cons @ ( sk12 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[15183:[bind(A,$thf( sk12 @ sk2 ))]]) ).
thf(175,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ ( app @ ( sk14 @ A ) @ ( cons @ ( sk12 @ A ) @ ( sk15 @ A ) ) ) @ ( cons @ ( sk13 @ A ) @ ( sk16 @ A ) ) )
= A )
| ( strictorderP @ A ) ),
inference(cnf,[status(esa)],[170]) ).
thf(182,plain,
! [A: $i] :
( ( ( app @ ( app @ ( sk14 @ A ) @ ( cons @ ( sk12 @ A ) @ ( sk15 @ A ) ) ) @ ( cons @ ( sk13 @ A ) @ ( sk16 @ A ) ) )
= A )
| ~ ( ssList @ A )
| ( strictorderP @ A ) ),
inference(lifteq,[status(thm)],[175]) ).
thf(906,plain,
( ( memberP @ sk2 @ sk6 )
| ~ $true ),
inference(rewrite,[status(thm)],[530,887]) ).
thf(907,plain,
memberP @ sk2 @ sk6,
inference(simp,[status(thm)],[906]) ).
thf(8728,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk15 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8459,241]) ).
thf(8729,plain,
( ( strictorderP @ sk1 )
| ( segmentP @ ( sk15 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[8728:[bind(A,$thf( sk15 @ 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(336,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(46012,plain,
! [A: $i] :
( ( totalorderP @ sk1 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk28 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44920,359]) ).
thf(46013,plain,
( ( totalorderP @ sk1 )
| ( frontsegP @ ( sk28 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[46012:[bind(A,$thf( sk28 @ sk1 ))]]) ).
thf(153,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)],[152]) ).
thf(154,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)],[153]) ).
thf(14930,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk16 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7091,192]) ).
thf(14931,plain,
( ( strictorderP @ sk1 )
| ( segmentP @ ( sk16 @ sk1 ) @ ( sk16 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[14930:[bind(A,$thf( sk16 @ sk1 ))]]) ).
thf(41312,plain,
! [A: $i] :
( ( segmentP @ A @ nil )
| ( ( ssList @ ( tl @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41224,241]) ).
thf(41313,plain,
segmentP @ ( tl @ sk2 ) @ nil,
inference(pattern_uni,[status(thm)],[41312:[bind(A,$thf( tl @ sk2 ))]]) ).
thf(24230,plain,
! [A: $i] :
( ( equalelemsP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk40 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[375,292]) ).
thf(24231,plain,
equalelemsP @ ( cons @ sk40 @ nil ),
inference(pattern_uni,[status(thm)],[24230:[bind(A,$thf( sk40 ))]]) ).
thf(15195,plain,
! [A: $i] :
( ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk6 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[901,194]) ).
thf(15196,plain,
totalorderedP @ ( cons @ sk6 @ nil ),
inference(pattern_uni,[status(thm)],[15195:[bind(A,$thf( sk6 ))]]) ).
thf(15283,plain,
totalorderedP @ sk1,
inference(rewrite,[status(thm)],[15196,899]) ).
thf(12,axiom,
cyclefreeP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax60) ).
thf(143,plain,
cyclefreeP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
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(497,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(6446,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk9 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2936,359]) ).
thf(6447,plain,
( ( cyclefreeP @ sk2 )
| ( frontsegP @ ( sk9 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[6446:[bind(A,$thf( sk9 @ sk2 ))]]) ).
thf(26920,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk19 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[26621,241]) ).
thf(26921,plain,
( ( strictorderedP @ sk2 )
| ( segmentP @ ( sk19 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[26920:[bind(A,$thf( sk19 @ sk2 ))]]) ).
thf(84,axiom,
equalelemsP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax74) ).
thf(465,plain,
equalelemsP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
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(231,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(2590,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ~ $true ),
inference(rewrite,[status(thm)],[1222,2541]) ).
thf(2591,plain,
~ ( frontsegP @ nil @ sk1 ),
inference(simp,[status(thm)],[2590]) ).
thf(26055,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ~ ( lt @ A @ A )
| ( ( ssItem @ ( sk12 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8053,216]) ).
thf(26056,plain,
( ( strictorderP @ sk1 )
| ~ ( lt @ ( sk12 @ sk1 ) @ ( sk12 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[26055:[bind(A,$thf( sk12 @ 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(319,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(4960,plain,
( ~ ( frontsegP @ nil @ sk39 )
| ( sk40 != nil )
| ( ( ssList @ sk39 )
!= ( ssList @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[103,1606]) ).
thf(5008,plain,
( ~ ( frontsegP @ nil @ sk39 )
| ( sk40 != nil )
| ( sk39 != sk1 ) ),
inference(simp,[status(thm)],[4960]) ).
thf(6002,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk9 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2942,290]) ).
thf(6003,plain,
( ( cyclefreeP @ sk1 )
| ( rearsegP @ ( sk9 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[6002:[bind(A,$thf( sk9 @ sk1 ))]]) ).
thf(8633,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk15 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8422,290]) ).
thf(8634,plain,
( ( strictorderP @ sk2 )
| ( rearsegP @ ( sk15 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[8633:[bind(A,$thf( sk15 @ sk2 ))]]) ).
thf(41349,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ ( tl @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41224,290]) ).
thf(41350,plain,
rearsegP @ ( tl @ sk2 ) @ nil,
inference(pattern_uni,[status(thm)],[41349:[bind(A,$thf( tl @ sk2 ))]]) ).
thf(11731,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk16 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7091,185]) ).
thf(11732,plain,
( ( strictorderP @ sk1 )
| ( ( app @ ( sk16 @ sk1 ) @ nil )
= ( sk16 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[11731:[bind(A,$thf( sk16 @ sk1 ))]]) ).
thf(11716,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk15 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8459,185]) ).
thf(11717,plain,
( ( strictorderP @ sk1 )
| ( ( app @ ( sk15 @ sk1 ) @ nil )
= ( sk15 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[11716:[bind(A,$thf( sk15 @ sk1 ))]]) ).
thf(24768,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ~ ( neq @ A @ A )
| ( ( ssItem @ ( sk7 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3865,211]) ).
thf(24769,plain,
( ( cyclefreeP @ sk2 )
| ~ ( neq @ ( sk7 @ sk2 ) @ ( sk7 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[24768:[bind(A,$thf( sk7 @ sk2 ))]]) ).
thf(46031,plain,
! [A: $i] :
( ( totalorderP @ sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk28 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44920,290]) ).
thf(46032,plain,
( ( totalorderP @ sk1 )
| ( rearsegP @ ( sk28 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[46031:[bind(A,$thf( sk28 @ sk1 ))]]) ).
thf(45761,plain,
! [A: $i] :
( ( totalorderP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk28 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44844,290]) ).
thf(45762,plain,
( ( totalorderP @ sk2 )
| ( rearsegP @ ( sk28 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[45761:[bind(A,$thf( sk28 @ sk2 ))]]) ).
thf(171,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( lt @ ( sk13 @ A ) @ ( sk12 @ A ) )
| ( strictorderP @ A ) ),
inference(cnf,[status(esa)],[170]) ).
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(433,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(27571,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk17 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27323,122]) ).
thf(27572,plain,
( ( strictorderedP @ sk2 )
| ( strictorderedP @ ( cons @ ( sk17 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[27571:[bind(A,$thf( sk17 @ sk2 ))]]) ).
thf(27475,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ~ ( neq @ A @ A )
| ( ( ssItem @ ( sk17 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27323,211]) ).
thf(27476,plain,
( ( strictorderedP @ sk2 )
| ~ ( neq @ ( sk17 @ sk2 ) @ ( sk17 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[27475:[bind(A,$thf( sk17 @ sk2 ))]]) ).
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(378,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(3584,plain,
! [A: $i] :
( ( leq @ ( sk7 @ A ) @ ( sk8 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,159]) ).
thf(3585,plain,
( ( leq @ ( sk7 @ sk1 ) @ ( sk8 @ sk1 ) )
| ( cyclefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[3584:[bind(A,$thf( sk1 ))]]) ).
thf(11743,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk14 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9057,185]) ).
thf(11744,plain,
( ( strictorderP @ sk1 )
| ( ( app @ ( sk14 @ sk1 ) @ nil )
= ( sk14 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[11743:[bind(A,$thf( sk14 @ sk1 ))]]) ).
thf(151,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)],[150]) ).
thf(26051,plain,
! [A: $i] :
( ( sk6 != nil )
| ~ ( lt @ A @ A )
| ( ( ssItem @ nil )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4155,216]) ).
thf(26052,plain,
( ( sk6 != nil )
| ~ ( lt @ nil @ nil ) ),
inference(pattern_uni,[status(thm)],[26051:[bind(A,$thf( nil ))]]) ).
thf(1511,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( segmentP @ nil @ A )
| ~ ( memberP @ nil @ nil )
| ( A != sk6 ) ),
inference(paramod_ordered,[status(thm)],[140,903]) ).
thf(1512,plain,
( ~ ( ssList @ sk6 )
| ~ ( segmentP @ nil @ sk6 )
| ~ ( memberP @ nil @ nil ) ),
inference(pattern_uni,[status(thm)],[1511:[bind(A,$thf( sk6 ))]]) ).
thf(7354,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk16 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7091,359]) ).
thf(7355,plain,
( ( strictorderP @ sk1 )
| ( frontsegP @ ( sk16 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[7354:[bind(A,$thf( sk16 @ sk1 ))]]) ).
thf(3729,plain,
( ~ ( segmentP @ nil @ sk40 )
| ( sk39 != nil )
| ( ( ssList @ sk40 )
!= ( ssList @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[102,1440]) ).
thf(3785,plain,
( ~ ( segmentP @ nil @ sk40 )
| ( sk39 != nil )
| ( sk40 != sk2 ) ),
inference(simp,[status(thm)],[3729]) ).
thf(9805,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk13 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9709,230]) ).
thf(9806,plain,
( ( strictorderP @ sk2 )
| ~ ( memberP @ nil @ ( sk13 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[9805:[bind(A,$thf( sk13 @ sk2 ))]]) ).
thf(45720,plain,
! [A: $i] :
( ( totalorderP @ sk2 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk28 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44844,241]) ).
thf(45721,plain,
( ( totalorderP @ sk2 )
| ( segmentP @ ( sk28 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[45720:[bind(A,$thf( sk28 @ sk2 ))]]) ).
thf(8620,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk15 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8422,359]) ).
thf(8621,plain,
( ( strictorderP @ sk2 )
| ( frontsegP @ ( sk15 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[8620:[bind(A,$thf( sk15 @ sk2 ))]]) ).
thf(3996,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk7 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3873,122]) ).
thf(3997,plain,
( ( cyclefreeP @ sk1 )
| ( strictorderedP @ ( cons @ ( sk7 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[3996:[bind(A,$thf( sk7 @ sk1 ))]]) ).
thf(6438,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk10 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4628,359]) ).
thf(6439,plain,
( ( cyclefreeP @ sk2 )
| ( frontsegP @ ( sk10 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[6438:[bind(A,$thf( sk10 @ sk2 ))]]) ).
thf(710,plain,
( ~ sk5
| ~ ( leq @ sk40 @ sk6 )
| ( sk39 != sk6 )
| ( ( memberP @ sk2 @ sk40 )
!= ( memberP @ sk2 @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[530,703]) ).
thf(724,plain,
( ~ sk5
| ~ ( leq @ sk40 @ sk6 )
| ( sk39 != sk6 )
| ( sk2 != sk2 )
| ( sk40 != sk6 ) ),
inference(simp,[status(thm)],[710]) ).
thf(725,plain,
( ~ sk5
| ~ ( leq @ sk40 @ sk6 )
| ( sk39 != sk6 )
| ( sk40 != sk6 ) ),
inference(simp,[status(thm)],[724]) ).
thf(12266,plain,
( ~ $true
| ~ ( leq @ sk40 @ sk6 )
| ( sk39 != sk6 )
| ( sk40 != sk6 ) ),
inference(rewrite,[status(thm)],[725,887]) ).
thf(12267,plain,
( ~ ( leq @ sk40 @ sk6 )
| ( sk39 != sk6 )
| ( sk40 != sk6 ) ),
inference(simp,[status(thm)],[12266]) ).
thf(7230,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk16 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7062,241]) ).
thf(7231,plain,
( ( strictorderP @ sk2 )
| ( segmentP @ ( sk16 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[7230:[bind(A,$thf( sk16 @ sk2 ))]]) ).
thf(8753,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk15 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8459,290]) ).
thf(8754,plain,
( ( strictorderP @ sk1 )
| ( rearsegP @ ( sk15 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[8753:[bind(A,$thf( sk15 @ sk1 ))]]) ).
thf(24772,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ~ ( neq @ A @ A )
| ( ( ssItem @ ( sk13 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9737,211]) ).
thf(24773,plain,
( ( strictorderP @ sk1 )
| ~ ( neq @ ( sk13 @ sk1 ) @ ( sk13 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[24772:[bind(A,$thf( sk13 @ sk1 ))]]) ).
thf(145,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( frontsegP @ A @ B )
| ~ ( frontsegP @ B @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[144]) ).
thf(146,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( frontsegP @ A @ B )
| ~ ( frontsegP @ B @ A ) ),
inference(lifteq,[status(thm)],[145]) ).
thf(189,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)],[188]) ).
thf(190,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)],[189]) ).
thf(4840,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk10 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4649,241]) ).
thf(4841,plain,
( ( cyclefreeP @ sk1 )
| ( segmentP @ ( sk10 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[4840:[bind(A,$thf( sk10 @ sk1 ))]]) ).
thf(6643,plain,
! [A: $i] :
( ~ ( lt @ ( sk13 @ A ) @ ( sk12 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[103,171]) ).
thf(6644,plain,
( ~ ( lt @ ( sk13 @ sk1 ) @ ( sk12 @ sk1 ) )
| ( strictorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[6643:[bind(A,$thf( sk1 ))]]) ).
thf(15235,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk8 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2834,194]) ).
thf(15236,plain,
( ( cyclefreeP @ sk1 )
| ( totalorderedP @ ( cons @ ( sk8 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[15235:[bind(A,$thf( sk8 @ 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(474,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(28121,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk18 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27873,122]) ).
thf(28122,plain,
( ( strictorderedP @ sk2 )
| ( strictorderedP @ ( cons @ ( sk18 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[28121:[bind(A,$thf( sk18 @ sk2 ))]]) ).
thf(43,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ssItem @ ( hd @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
thf(283,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ssItem @ ( hd @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(26942,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk19 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[26621,359]) ).
thf(26943,plain,
( ( strictorderedP @ sk2 )
| ( frontsegP @ ( sk19 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[26942:[bind(A,$thf( sk19 @ sk2 ))]]) ).
thf(236,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( frontsegP @ A @ B )
| ( ( app @ B @ ( sk22 @ B @ A ) )
= A ) ),
inference(cnf,[status(esa)],[233]) ).
thf(239,plain,
! [B: $i,A: $i] :
( ( ( app @ B @ ( sk22 @ B @ A ) )
= A )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( frontsegP @ A @ B ) ),
inference(lifteq,[status(thm)],[236]) ).
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(400,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(68,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ( cons @ ( hd @ A ) @ ( tl @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax78) ).
thf(395,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ( cons @ ( hd @ A ) @ ( tl @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(15197,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk12 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8053,194]) ).
thf(15198,plain,
( ( strictorderP @ sk1 )
| ( totalorderedP @ ( cons @ ( sk12 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[15197:[bind(A,$thf( sk12 @ sk1 ))]]) ).
thf(3056,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( ssItem @ ( sk8 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ ( sk9 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2936,156]) ).
thf(3057,plain,
( ( cyclefreeP @ sk2 )
| ( ssItem @ ( sk8 @ ( sk9 @ sk2 ) ) )
| ( cyclefreeP @ ( sk9 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[3056:[bind(A,$thf( sk9 @ sk2 ))]]) ).
thf(11763,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk14 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9018,185]) ).
thf(11764,plain,
( ( strictorderP @ sk2 )
| ( ( app @ ( sk14 @ sk2 ) @ nil )
= ( sk14 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[11763:[bind(A,$thf( sk14 @ sk2 ))]]) ).
thf(35199,plain,
! [A: $i] :
( ( ( app @ nil @ A )
= A )
| ( ( ssList @ ( sk22 @ nil @ nil ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[35060,214]) ).
thf(35200,plain,
( ( app @ nil @ ( sk22 @ nil @ nil ) )
= ( sk22 @ nil @ nil ) ),
inference(pattern_uni,[status(thm)],[35199:[bind(A,$thf( sk22 @ nil @ nil ))]]) ).
thf(8,axiom,
totalorderedP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax66) ).
thf(131,plain,
totalorderedP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9897,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk13 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9737,122]) ).
thf(9898,plain,
( ( strictorderP @ sk1 )
| ( strictorderedP @ ( cons @ ( sk13 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[9897:[bind(A,$thf( sk13 @ sk1 ))]]) ).
thf(6451,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk11 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4213,359]) ).
thf(6452,plain,
( ( cyclefreeP @ sk2 )
| ( frontsegP @ ( sk11 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[6451:[bind(A,$thf( sk11 @ sk2 ))]]) ).
thf(4362,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk11 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4213,241]) ).
thf(4363,plain,
( ( cyclefreeP @ sk2 )
| ( segmentP @ ( sk11 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[4362:[bind(A,$thf( sk11 @ sk2 ))]]) ).
thf(15203,plain,
! [A: $i] :
( ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk40 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[375,194]) ).
thf(15204,plain,
totalorderedP @ ( cons @ sk40 @ nil ),
inference(pattern_uni,[status(thm)],[15203:[bind(A,$thf( sk40 ))]]) ).
thf(28061,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk18 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27873,230]) ).
thf(28062,plain,
( ( strictorderedP @ sk2 )
| ~ ( memberP @ nil @ ( sk18 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[28061:[bind(A,$thf( sk18 @ sk2 ))]]) ).
thf(24760,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssItem @ sk40 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[375,211]) ).
thf(24761,plain,
~ ( neq @ sk40 @ sk40 ),
inference(pattern_uni,[status(thm)],[24760:[bind(A,$thf( sk40 ))]]) ).
thf(14934,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk9 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2936,192]) ).
thf(14935,plain,
( ( cyclefreeP @ sk2 )
| ( segmentP @ ( sk9 @ sk2 ) @ ( sk9 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[14934:[bind(A,$thf( sk9 @ sk2 ))]]) ).
thf(3964,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk7 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3873,230]) ).
thf(3965,plain,
( ( cyclefreeP @ sk1 )
| ~ ( memberP @ nil @ ( sk7 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[3964:[bind(A,$thf( sk7 @ sk1 ))]]) ).
thf(27,axiom,
duplicatefreeP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax72) ).
thf(200,plain,
duplicatefreeP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(9334,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk14 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9057,241]) ).
thf(9335,plain,
( ( strictorderP @ sk1 )
| ( segmentP @ ( sk14 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[9334:[bind(A,$thf( sk14 @ sk1 ))]]) ).
thf(24226,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( equalelemsP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk12 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8053,292]) ).
thf(24227,plain,
( ( strictorderP @ sk1 )
| ( equalelemsP @ ( cons @ ( sk12 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[24226:[bind(A,$thf( sk12 @ sk1 ))]]) ).
thf(9841,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk13 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9709,122]) ).
thf(9842,plain,
( ( strictorderP @ sk2 )
| ( strictorderedP @ ( cons @ ( sk13 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[9841:[bind(A,$thf( sk13 @ sk2 ))]]) ).
thf(26061,plain,
! [A: $i] :
( ~ ( lt @ A @ A )
| ( ( ssItem @ sk40 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[375,216]) ).
thf(26062,plain,
~ ( lt @ sk40 @ sk40 ),
inference(pattern_uni,[status(thm)],[26061:[bind(A,$thf( sk40 ))]]) ).
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(486,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(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(354,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(14919,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk10 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4628,192]) ).
thf(14920,plain,
( ( cyclefreeP @ sk2 )
| ( segmentP @ ( sk10 @ sk2 ) @ ( sk10 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[14919:[bind(A,$thf( sk10 @ sk2 ))]]) ).
thf(8740,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk15 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8459,359]) ).
thf(8741,plain,
( ( strictorderP @ sk1 )
| ( frontsegP @ ( sk15 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[8740:[bind(A,$thf( sk15 @ sk1 ))]]) ).
thf(4751,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk10 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4628,241]) ).
thf(4752,plain,
( ( cyclefreeP @ sk2 )
| ( segmentP @ ( sk10 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[4751:[bind(A,$thf( sk10 @ sk2 ))]]) ).
thf(11753,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk11 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4213,185]) ).
thf(11754,plain,
( ( cyclefreeP @ sk2 )
| ( ( app @ ( sk11 @ sk2 ) @ nil )
= ( sk11 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[11753:[bind(A,$thf( sk11 @ sk2 ))]]) ).
thf(95,axiom,
totalorderP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax62) ).
thf(496,plain,
totalorderP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(232,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)],[231]) ).
thf(1313,plain,
( ~ ( frontsegP @ nil @ sk40 )
| ( sk39 != nil )
| ( ( ssList @ sk40 )
!= ( ssList @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[103,1030]) ).
thf(1331,plain,
( ~ ( frontsegP @ nil @ sk40 )
| ( sk39 != nil )
| ( sk40 != sk1 ) ),
inference(simp,[status(thm)],[1313]) ).
thf(224,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)],[217]) ).
thf(226,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)],[224]) ).
thf(227,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)],[226]) ).
thf(6631,plain,
! [A: $i] :
( ~ ( lt @ ( sk13 @ A ) @ ( sk12 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,171]) ).
thf(6632,plain,
( ~ ( lt @ ( sk13 @ sk2 ) @ ( sk12 @ sk2 ) )
| ( strictorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[6631:[bind(A,$thf( sk2 ))]]) ).
thf(100346,plain,
$false,
inference(e,[status(thm)],[3873,24747,4571,3008,14922,479,8114,3581,468,1110,35193,1024,333,249,41869,44376,481,352,41229,170,217,3040,45209,14786,6441,47234,202,7368,26076,120,247,385,3049,8150,7345,45347,14959,14964,42869,11756,14927,174,28786,185,27478,24581,44844,15202,24755,436,27323,26072,7993,885,3777,389,7241,2916,42759,26621,28028,3845,5989,157,9360,344,26058,152,228,24205,448,3268,289,26036,216,1302,8029,179,1040,211,121,5985,376,9225,30312,42158,238,905,24233,147,30293,221,293,453,132,133,8459,411,116,41224,24201,4628,9347,11728,11783,206,2884,27474,24249,292,248,942,270,201,41851,220,7254,8170,233,44920,546,35152,41762,102,47888,24358,2541,2596,14943,260,11719,160,24775,392,3069,429,137,165,42751,7703,192,407,197,4155,24253,493,28024,24751,229,24209,252,1602,1350,11734,3122,14941,188,4227,420,42747,11736,47014,948,25215,156,169,14953,225,24221,38055,8053,212,471,256,28767,7091,4167,193,901,25164,41353,44354,129,6005,47966,27544,41793,1478,42868,173,911,24273,15234,24739,6465,134,14918,35174,360,205,8422,1054,398,9213,4448,8609,3841,44395,1434,26064,24743,2546,4195,298,2936,3130,4562,161,6454,5016,24763,9709,14933,149,42928,47068,375,191,286,291,44622,413,15180,26962,1388,3272,9057,118,26867,204,313,144,1332,466,42232,159,181,11750,41891,14957,7062,5997,172,15192,219,41331,6443,6461,377,230,451,245,4213,15212,26070,35065,187,98,303,387,103,140,483,9862,198,30271,5987,477,27512,7685,26042,240,251,44663,24271,155,9018,35086,15188,15216,223,394,3142,267,505,431,241,167,130,24757,3917,41767,11721,15048,27873,426,45991,123,968,24767,944,45743,255,26046,209,28026,1145,5991,194,11770,150,887,28094,28745,9238,14951,409,310,44644,42874,41888,2942,3949,29941,26078,28431,28689,199,5995,8206,359,15184,177,182,544,907,8729,336,46013,154,14931,41313,24231,15283,143,497,6447,903,218,26921,465,231,203,2828,2591,26056,699,319,5008,186,6003,114,8634,35060,41350,11732,2594,158,11717,24769,46032,45762,171,1030,433,1440,27572,899,214,27476,4649,290,119,378,235,246,3585,38098,11744,151,26052,1512,7355,3785,9806,45721,183,373,8621,3997,6439,3865,12267,168,7231,8754,24773,146,190,4841,107,358,195,6644,15236,474,28122,1610,283,26943,239,242,126,136,42980,400,395,15198,332,3057,11764,41255,35200,131,9898,6452,4363,15204,28062,9737,24761,14935,3965,163,200,9335,178,24227,9842,26062,486,122,354,14920,8741,215,4752,11754,496,232,1331,254,227,1606,2834,6632]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC368+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n004.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri May 19 00:48:10 EDT 2023
% 0.15/0.37 % CPUTime :
% 1.03/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.42/1.07 % [INFO] Parsing done (164ms).
% 1.42/1.07 % [INFO] Running in sequential loop mode.
% 1.84/1.27 % [INFO] eprover registered as external prover.
% 1.84/1.27 % [INFO] cvc4 registered as external prover.
% 1.84/1.28 % [INFO] Scanning for conjecture ...
% 2.28/1.36 % [INFO] Found a conjecture and 95 axioms. Running axiom selection ...
% 2.28/1.43 % [INFO] Axiom selection finished. Selected 95 axioms (removed 0 axioms).
% 2.73/1.51 % [INFO] Problem is first-order (TPTP FOF).
% 2.73/1.53 % [INFO] Type checking passed.
% 2.73/1.53 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 147.35/27.12 % External prover 'e' found a proof!
% 147.35/27.12 % [INFO] Killing All external provers ...
% 147.35/27.13 % Time passed: 26580ms (effective reasoning time: 26048ms)
% 147.35/27.13 % 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)>
% 147.35/27.13 % 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
% 147.35/27.13 % No. of inferences in proof: 995
% 147.35/27.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 26580 ms resp. 26048 ms w/o parsing
% 148.02/27.33 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 148.02/27.33 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------