TSTP Solution File: SWC390+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWC390+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:11:54 EDT 2023
% Result : Theorem 139.03s 26.14s
% Output : Refutation 139.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 151
% Syntax : Number of formulae : 1125 ( 83 unt; 55 typ; 0 def)
% Number of atoms : 3809 ( 921 equ; 0 cnn)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 8798 (1239 ~;1467 |; 126 &;5378 @)
% ( 26 <=>; 562 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% Number of symbols : 58 ( 55 usr; 10 con; 0-2 aty)
% Number of variables : 933 ( 0 ^; 900 !; 33 ?; 933 :)
% Comments :
%------------------------------------------------------------------------------
thf(ssList_type,type,
ssList: $i > $o ).
thf(nil_type,type,
nil: $i ).
thf(ssItem_type,type,
ssItem: $i > $o ).
thf(cons_type,type,
cons: $i > $i > $i ).
thf(memberP_type,type,
memberP: $i > $i > $o ).
thf(neq_type,type,
neq: $i > $i > $o ).
thf(segmentP_type,type,
segmentP: $i > $i > $o ).
thf(singletonP_type,type,
singletonP: $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(leq_type,type,
leq: $i > $i > $o ).
thf(strictorderP_type,type,
strictorderP: $i > $o ).
thf(duplicatefreeP_type,type,
duplicatefreeP: $i > $o ).
thf(tl_type,type,
tl: $i > $i ).
thf(totalorderP_type,type,
totalorderP: $i > $o ).
thf(rearsegP_type,type,
rearsegP: $i > $i > $o ).
thf(equalelemsP_type,type,
equalelemsP: $i > $o ).
thf(geq_type,type,
geq: $i > $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i > $i ).
thf(sk7_type,type,
sk7: $i > $i ).
thf(sk8_type,type,
sk8: $i > $i ).
thf(sk9_type,type,
sk9: $i > $i ).
thf(sk10_type,type,
sk10: $i > $i ).
thf(sk11_type,type,
sk11: $i > $i ).
thf(sk12_type,type,
sk12: $i > $i ).
thf(sk13_type,type,
sk13: $i > $i ).
thf(sk14_type,type,
sk14: $i > $i ).
thf(sk15_type,type,
sk15: $i > $i ).
thf(sk16_type,type,
sk16: $i > $i ).
thf(sk17_type,type,
sk17: $i > $i ).
thf(sk18_type,type,
sk18: $i > $i ).
thf(sk19_type,type,
sk19: $i > $i ).
thf(sk20_type,type,
sk20: $i > $i ).
thf(sk21_type,type,
sk21: $i > $i > $i ).
thf(sk22_type,type,
sk22: $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(sk29_type,type,
sk29: $i > $i ).
thf(sk38_type,type,
sk38: $i ).
thf(sk39_type,type,
sk39: $i ).
thf(1,conjecture,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ( ( B != D )
| ( A != C )
| ( ( nil != C )
& ( nil = D ) )
| ( ! [E: $i] :
( ( ssItem @ E )
=> ( ( ( cons @ E @ nil )
!= C )
| ~ ( memberP @ D @ E ) ) )
& ( neq @ D @ nil ) )
| ( ( segmentP @ B @ A )
& ( ~ ( neq @ B @ nil )
| ( singletonP @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ( ( B != D )
| ( A != C )
| ( ( nil != C )
& ( nil = D ) )
| ( ! [E: $i] :
( ( ssItem @ E )
=> ( ( ( cons @ E @ nil )
!= C )
| ~ ( memberP @ D @ E ) ) )
& ( neq @ D @ nil ) )
| ( ( segmentP @ B @ A )
& ( ~ ( neq @ B @ nil )
| ( singletonP @ A ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(98,plain,
~ ! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ( ( B != D )
| ( A != C )
| ( ( nil != C )
& ( nil = D ) )
| ( ! [E: $i] :
( ( ssItem @ E )
=> ( ( ( cons @ E @ nil )
!= C )
| ~ ( memberP @ D @ E ) ) )
& ( neq @ D @ nil ) )
| ( ( segmentP @ B @ A )
& ( ~ ( neq @ B @ nil )
| ( singletonP @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(107,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(152,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(159,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( sk6 @ A ) )
| ( cyclefreeP @ A ) ),
inference(cnf,[status(esa)],[152]) ).
thf(5538,plain,
! [A: $i] :
( ( ssItem @ ( sk6 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,159]) ).
thf(5539,plain,
( ( ssItem @ ( sk6 @ sk1 ) )
| ( cyclefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[5538:[bind(A,$thf( sk1 ))]]) ).
thf(34,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ~ ( memberP @ nil @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
thf(226,plain,
! [A: $i] :
( ( ssItem @ A )
=> ~ ( memberP @ nil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(227,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ~ ( memberP @ nil @ A ) ),
inference(cnf,[status(esa)],[226]) ).
thf(5658,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk6 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5539,227]) ).
thf(5659,plain,
( ( cyclefreeP @ sk1 )
| ~ ( memberP @ nil @ ( sk6 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[5658:[bind(A,$thf( sk6 @ sk1 ))]]) ).
thf(153,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk8 @ A ) )
| ( cyclefreeP @ A ) ),
inference(cnf,[status(esa)],[152]) ).
thf(618,plain,
! [A: $i] :
( ( ssList @ ( sk8 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,153]) ).
thf(619,plain,
( ( ssList @ ( sk8 @ sk1 ) )
| ( cyclefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[618:[bind(A,$thf( sk1 ))]]) ).
thf(628,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( ssList @ ( sk8 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ ( sk8 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[619,153]) ).
thf(629,plain,
( ( cyclefreeP @ sk1 )
| ( ssList @ ( sk8 @ ( sk8 @ sk1 ) ) )
| ( cyclefreeP @ ( sk8 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[628:[bind(A,$thf( sk8 @ sk1 ))]]) ).
thf(106,plain,
ssList @ sk2,
inference(cnf,[status(esa)],[98]) ).
thf(155,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( sk7 @ A ) )
| ( cyclefreeP @ A ) ),
inference(cnf,[status(esa)],[152]) ).
thf(4361,plain,
! [A: $i] :
( ( ssItem @ ( sk7 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,155]) ).
thf(4362,plain,
( ( ssItem @ ( sk7 @ sk2 ) )
| ( cyclefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[4361:[bind(A,$thf( sk2 ))]]) ).
thf(30,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( neq @ A @ B )
<=> ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(203,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(205,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( neq @ A @ B )
| ( A != B ) ),
inference(cnf,[status(esa)],[203]) ).
thf(207,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( neq @ A @ B ) ),
inference(lifteq,[status(thm)],[205]) ).
thf(208,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ~ ( neq @ A @ A ) ),
inference(simp,[status(thm)],[207]) ).
thf(26015,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ~ ( neq @ A @ A )
| ( ( ssItem @ ( sk7 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4362,208]) ).
thf(26016,plain,
( ( cyclefreeP @ sk2 )
| ~ ( neq @ ( sk7 @ sk2 ) @ ( sk7 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[26015:[bind(A,$thf( sk7 @ sk2 ))]]) ).
thf(19,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( strictorderP @ A )
<=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssItem @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ! [E: $i] :
( ( ssList @ E )
=> ! [F: $i] :
( ( ssList @ F )
=> ( ( ( app @ ( app @ D @ ( cons @ B @ E ) ) @ ( cons @ C @ F ) )
= A )
=> ( ( lt @ B @ C )
| ( lt @ C @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax10) ).
thf(167,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 )
| ( ssList @ ( sk13 @ A ) )
| ( strictorderP @ A ) ),
inference(cnf,[status(esa)],[167]) ).
thf(10398,plain,
! [A: $i] :
( ( ssList @ ( sk13 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,174]) ).
thf(10399,plain,
( ( ssList @ ( sk13 @ sk1 ) )
| ( strictorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[10398:[bind(A,$thf( sk1 ))]]) ).
thf(6,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( frontsegP @ nil @ A )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax46) ).
thf(120,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(121,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A )
| ( nil = A ) ),
inference(cnf,[status(esa)],[120]) ).
thf(123,plain,
! [A: $i] :
( ( nil = A )
| ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A ) ),
inference(lifteq,[status(thm)],[121]) ).
thf(692,plain,
! [A: $i] :
( ( nil = A )
| ~ ( frontsegP @ nil @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,123]) ).
thf(693,plain,
( ( sk1 = nil )
| ~ ( frontsegP @ nil @ sk1 ) ),
inference(pattern_uni,[status(thm)],[692:[bind(A,$thf( sk1 ))]]) ).
thf(37,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( segmentP @ A @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax57) ).
thf(237,plain,
! [A: $i] :
( ( ssList @ A )
=> ( segmentP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(238,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( segmentP @ A @ nil ) ),
inference(cnf,[status(esa)],[237]) ).
thf(103,plain,
( ~ ( segmentP @ sk2 @ sk1 )
| ~ ( singletonP @ sk1 ) ),
inference(cnf,[status(esa)],[98]) ).
thf(559,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( singletonP @ sk1 )
| ( ( segmentP @ A @ nil )
!= ( segmentP @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[238,103]) ).
thf(560,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( singletonP @ sk1 )
| ( A != sk2 )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[559]) ).
thf(562,plain,
( ~ ( ssList @ sk2 )
| ~ ( singletonP @ sk1 )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[560]) ).
thf(568,plain,
( ~ $true
| ~ ( singletonP @ sk1 )
| ( sk1 != nil ) ),
inference(rewrite,[status(thm)],[562,106]) ).
thf(569,plain,
( ~ ( singletonP @ sk1 )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[568]) ).
thf(892,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ~ ( singletonP @ sk1 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[693,569]) ).
thf(893,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ~ ( singletonP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[892:[]]) ).
thf(11,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( segmentP @ nil @ A )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).
thf(134,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(136,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( nil != A )
| ( segmentP @ nil @ A ) ),
inference(cnf,[status(esa)],[134]) ).
thf(138,plain,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( segmentP @ nil @ A ) ),
inference(lifteq,[status(thm)],[136]) ).
thf(139,plain,
( ~ ( ssList @ nil )
| ( segmentP @ nil @ nil ) ),
inference(simp,[status(thm)],[138]) ).
thf(53,axiom,
ssList @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
thf(329,plain,
ssList @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(517,plain,
( ~ $true
| ( segmentP @ nil @ nil ) ),
inference(rewrite,[status(thm)],[139,329]) ).
thf(518,plain,
segmentP @ nil @ nil,
inference(simp,[status(thm)],[517]) ).
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(468,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(173,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk15 @ A ) )
| ( strictorderP @ A ) ),
inference(cnf,[status(esa)],[167]) ).
thf(9675,plain,
! [A: $i] :
( ( ssList @ ( sk15 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,173]) ).
thf(9676,plain,
( ( ssList @ ( sk15 @ sk2 ) )
| ( strictorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[9675:[bind(A,$thf( sk2 ))]]) ).
thf(10297,plain,
! [A: $i] :
( ( ssList @ ( sk13 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,174]) ).
thf(10298,plain,
( ( ssList @ ( sk13 @ sk2 ) )
| ( strictorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[10297:[bind(A,$thf( sk2 ))]]) ).
thf(23,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( segmentP @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).
thf(188,plain,
! [A: $i] :
( ( ssList @ A )
=> ( segmentP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(189,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( segmentP @ A @ A ) ),
inference(cnf,[status(esa)],[188]) ).
thf(15471,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk13 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10298,189]) ).
thf(15472,plain,
( ( strictorderP @ sk2 )
| ( segmentP @ ( sk13 @ sk2 ) @ ( sk13 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[15471:[bind(A,$thf( sk13 @ sk2 ))]]) ).
thf(15452,plain,
! [A: $i] :
( ( segmentP @ A @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,189]) ).
thf(15453,plain,
segmentP @ sk2 @ sk2,
inference(pattern_uni,[status(thm)],[15452:[bind(A,$thf( sk2 ))]]) ).
thf(110,plain,
( ~ ( segmentP @ sk2 @ sk1 )
| ( neq @ sk2 @ nil ) ),
inference(cnf,[status(esa)],[98]) ).
thf(15559,plain,
( ( neq @ sk2 @ nil )
| ( ( segmentP @ sk2 @ sk2 )
!= ( segmentP @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[15453,110]) ).
thf(15605,plain,
( ( neq @ sk2 @ nil )
| ( sk2 != sk2 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[15559]) ).
thf(15620,plain,
( ( neq @ sk2 @ nil )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[15605]) ).
thf(105,plain,
( ( ( cons @ sk5 @ nil )
= sk3 )
| ~ ( neq @ sk4 @ nil ) ),
inference(cnf,[status(esa)],[98]) ).
thf(113,plain,
( ( ( cons @ sk5 @ nil )
= sk3 )
| ~ ( neq @ sk4 @ nil ) ),
inference(lifteq,[status(thm)],[105]) ).
thf(109,plain,
sk2 = sk4,
inference(cnf,[status(esa)],[98]) ).
thf(112,plain,
sk4 = sk2,
inference(lifteq,[status(thm)],[109]) ).
thf(108,plain,
sk1 = sk3,
inference(cnf,[status(esa)],[98]) ).
thf(114,plain,
sk3 = sk1,
inference(lifteq,[status(thm)],[108]) ).
thf(510,plain,
( ( ( cons @ sk5 @ nil )
= sk1 )
| ~ ( neq @ sk2 @ nil ) ),
inference(rewrite,[status(thm)],[113,112,114]) ).
thf(15890,plain,
( ( sk2 != sk1 )
| ( ( cons @ sk5 @ nil )
= sk1 )
| ( ( neq @ sk2 @ nil )
!= ( neq @ sk2 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[15620,510]) ).
thf(15891,plain,
( ( sk2 != sk1 )
| ( ( cons @ sk5 @ nil )
= sk1 ) ),
inference(pattern_uni,[status(thm)],[15890:[]]) ).
thf(99,plain,
( ( ssItem @ sk5 )
| ~ ( neq @ sk4 @ nil ) ),
inference(cnf,[status(esa)],[98]) ).
thf(508,plain,
( ( ssItem @ sk5 )
| ~ ( neq @ sk2 @ nil ) ),
inference(rewrite,[status(thm)],[99,112]) ).
thf(15864,plain,
( ( sk2 != sk1 )
| ( ssItem @ sk5 )
| ( ( neq @ sk2 @ nil )
!= ( neq @ sk2 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[15620,508]) ).
thf(15865,plain,
( ( sk2 != sk1 )
| ( ssItem @ sk5 ) ),
inference(pattern_uni,[status(thm)],[15864:[]]) ).
thf(5,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( strictorderedP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax68) ).
thf(118,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( strictorderedP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(119,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( strictorderedP @ ( cons @ A @ nil ) ) ),
inference(cnf,[status(esa)],[118]) ).
thf(15938,plain,
! [A: $i] :
( ( sk2 != sk1 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[15865,119]) ).
thf(15939,plain,
( ( sk2 != sk1 )
| ( strictorderedP @ ( cons @ sk5 @ nil ) ) ),
inference(pattern_uni,[status(thm)],[15938:[bind(A,$thf( sk5 ))]]) ).
thf(20992,plain,
( ( sk2 != sk1 )
| ( strictorderedP @ sk1 )
| ( ( cons @ sk5 @ nil )
!= ( cons @ sk5 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[15891,15939]) ).
thf(20993,plain,
( ( sk2 != sk1 )
| ( strictorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[20992:[]]) ).
thf(555,plain,
! [A: $i] :
( ( segmentP @ A @ nil )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,238]) ).
thf(556,plain,
segmentP @ sk2 @ nil,
inference(pattern_uni,[status(thm)],[555:[bind(A,$thf( sk2 ))]]) ).
thf(570,plain,
( ( neq @ sk2 @ nil )
| ( ( segmentP @ sk2 @ sk1 )
!= ( segmentP @ sk2 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[556,110]) ).
thf(572,plain,
( ( neq @ sk2 @ nil )
| ( sk2 != sk2 )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[570]) ).
thf(574,plain,
( ( neq @ sk2 @ nil )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[572]) ).
thf(578,plain,
( ( sk1 != nil )
| ( ssItem @ sk5 )
| ( ( neq @ sk2 @ nil )
!= ( neq @ sk2 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[574,508]) ).
thf(579,plain,
( ( sk1 != nil )
| ( ssItem @ sk5 ) ),
inference(pattern_uni,[status(thm)],[578:[]]) ).
thf(908,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( ssItem @ sk5 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[693,579]) ).
thf(909,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( ssItem @ sk5 ) ),
inference(pattern_uni,[status(thm)],[908:[]]) ).
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(333,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(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(244,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 )
| ( ssList @ ( sk25 @ A ) )
| ( totalorderP @ A ) ),
inference(cnf,[status(esa)],[244]) ).
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(214,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(216,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( sk16 @ A ) )
| ( strictorderedP @ A ) ),
inference(cnf,[status(esa)],[214]) ).
thf(28698,plain,
! [A: $i] :
( ( ssItem @ ( sk16 @ A ) )
| ( strictorderedP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,216]) ).
thf(28699,plain,
( ( ssItem @ ( sk16 @ sk1 ) )
| ( strictorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[28698:[bind(A,$thf( sk1 ))]]) ).
thf(28980,plain,
! [A: $i] :
( ( strictorderedP @ sk1 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk16 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[28699,227]) ).
thf(28981,plain,
( ( strictorderedP @ sk1 )
| ~ ( memberP @ nil @ ( sk16 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[28980:[bind(A,$thf( sk16 @ sk1 ))]]) ).
thf(168,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk14 @ A ) )
| ( strictorderP @ A ) ),
inference(cnf,[status(esa)],[167]) ).
thf(8294,plain,
! [A: $i] :
( ( ssList @ ( sk14 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,168]) ).
thf(8295,plain,
( ( ssList @ ( sk14 @ sk1 ) )
| ( strictorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[8294:[bind(A,$thf( sk1 ))]]) ).
thf(59,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( frontsegP @ A @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax45) ).
thf(355,plain,
! [A: $i] :
( ( ssList @ A )
=> ( frontsegP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(356,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( frontsegP @ A @ nil ) ),
inference(cnf,[status(esa)],[355]) ).
thf(8474,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk14 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8295,356]) ).
thf(8475,plain,
( ( strictorderP @ sk1 )
| ( frontsegP @ ( sk14 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[8474:[bind(A,$thf( sk14 @ sk1 ))]]) ).
thf(156,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk9 @ A ) )
| ( cyclefreeP @ A ) ),
inference(cnf,[status(esa)],[152]) ).
thf(4704,plain,
! [A: $i] :
( ( ssList @ ( sk9 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,156]) ).
thf(4705,plain,
( ( ssList @ ( sk9 @ sk1 ) )
| ( cyclefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[4704:[bind(A,$thf( sk1 ))]]) ).
thf(45,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( rearsegP @ A @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax51) ).
thf(286,plain,
! [A: $i] :
( ( ssList @ A )
=> ( rearsegP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(287,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( rearsegP @ A @ nil ) ),
inference(cnf,[status(esa)],[286]) ).
thf(4876,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk9 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4705,287]) ).
thf(4877,plain,
( ( cyclefreeP @ sk1 )
| ( rearsegP @ ( sk9 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[4876:[bind(A,$thf( sk9 @ sk1 ))]]) ).
thf(580,plain,
( ( sk1 != nil )
| ( ( cons @ sk5 @ nil )
= sk1 )
| ( ( neq @ sk2 @ nil )
!= ( neq @ sk2 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[574,510]) ).
thf(581,plain,
( ( sk1 != nil )
| ( ( cons @ sk5 @ nil )
= sk1 ) ),
inference(pattern_uni,[status(thm)],[580:[]]) ).
thf(592,plain,
! [A: $i] :
( ( sk1 != nil )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[579,119]) ).
thf(593,plain,
( ( sk1 != nil )
| ( strictorderedP @ ( cons @ sk5 @ nil ) ) ),
inference(pattern_uni,[status(thm)],[592:[bind(A,$thf( sk5 ))]]) ).
thf(1259,plain,
( ( sk1 != nil )
| ( strictorderedP @ sk1 )
| ( ( cons @ sk5 @ nil )
!= ( cons @ sk5 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[581,593]) ).
thf(1260,plain,
( ( sk1 != nil )
| ( strictorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1259:[]]) ).
thf(1294,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( strictorderedP @ sk1 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[693,1260]) ).
thf(1295,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( strictorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1294:[]]) ).
thf(215,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( sk17 @ A ) )
| ( strictorderedP @ A ) ),
inference(cnf,[status(esa)],[214]) ).
thf(28044,plain,
! [A: $i] :
( ( ssItem @ ( sk17 @ A ) )
| ( strictorderedP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,215]) ).
thf(28045,plain,
( ( ssItem @ ( sk17 @ sk1 ) )
| ( strictorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[28044:[bind(A,$thf( sk1 ))]]) ).
thf(38,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ssList @ B )
& ( ( tl @ A )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax76) ).
thf(239,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ssList @ B )
& ( ( tl @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(241,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( nil = A )
| ( ssList @ ( sk22 @ A ) ) ),
inference(cnf,[status(esa)],[239]) ).
thf(243,plain,
! [A: $i] :
( ( nil = A )
| ~ ( ssList @ A )
| ( ssList @ ( sk22 @ A ) ) ),
inference(lifteq,[status(thm)],[241]) ).
thf(43500,plain,
! [A: $i] :
( ( nil = A )
| ( ssList @ ( sk22 @ A ) )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,243]) ).
thf(43501,plain,
( ( sk1 = nil )
| ( ssList @ ( sk22 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[43500:[bind(A,$thf( sk1 ))]]) ).
thf(24,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( totalorderedP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax65) ).
thf(190,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( totalorderedP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(191,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( totalorderedP @ ( cons @ A @ nil ) ) ),
inference(cnf,[status(esa)],[190]) ).
thf(7994,plain,
! [A: $i] :
( ( sk1 != nil )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[579,191]) ).
thf(7995,plain,
( ( sk1 != nil )
| ( totalorderedP @ ( cons @ sk5 @ nil ) ) ),
inference(pattern_uni,[status(thm)],[7994:[bind(A,$thf( sk5 ))]]) ).
thf(8601,plain,
( ( sk1 != nil )
| ( totalorderedP @ sk1 )
| ( ( cons @ sk5 @ nil )
!= ( cons @ sk5 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[581,7995]) ).
thf(8602,plain,
( ( sk1 != nil )
| ( totalorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[8601:[]]) ).
thf(44991,plain,
( ( ssList @ ( sk22 @ sk1 ) )
| ( totalorderedP @ sk1 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[43501,8602]) ).
thf(44992,plain,
( ( ssList @ ( sk22 @ sk1 ) )
| ( totalorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[44991:[]]) ).
thf(171,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( sk12 @ A ) )
| ( strictorderP @ A ) ),
inference(cnf,[status(esa)],[167]) ).
thf(9250,plain,
! [A: $i] :
( ( ssItem @ ( sk12 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,171]) ).
thf(9251,plain,
( ( ssItem @ ( sk12 @ sk1 ) )
| ( strictorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[9250:[bind(A,$thf( sk1 ))]]) ).
thf(122,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( nil != A )
| ( frontsegP @ nil @ A ) ),
inference(cnf,[status(esa)],[120]) ).
thf(124,plain,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( frontsegP @ nil @ A ) ),
inference(lifteq,[status(thm)],[122]) ).
thf(125,plain,
( ~ ( ssList @ nil )
| ( frontsegP @ nil @ nil ) ),
inference(simp,[status(thm)],[124]) ).
thf(515,plain,
( ~ $true
| ( frontsegP @ nil @ nil ) ),
inference(rewrite,[status(thm)],[125,329]) ).
thf(516,plain,
frontsegP @ nil @ nil,
inference(simp,[status(thm)],[515]) ).
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(230,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(232,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( frontsegP @ A @ B )
| ( ssList @ ( sk21 @ B @ A ) ) ),
inference(cnf,[status(esa)],[230]) ).
thf(36972,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( ssList @ ( sk21 @ B @ A ) )
| ( ( frontsegP @ nil @ nil )
!= ( frontsegP @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[516,232]) ).
thf(36973,plain,
( ~ ( ssList @ nil )
| ~ ( ssList @ nil )
| ( ssList @ ( sk21 @ nil @ nil ) ) ),
inference(pattern_uni,[status(thm)],[36972:[bind(A,$thf( nil )),bind(B,$thf( nil ))]]) ).
thf(37114,plain,
( ~ ( ssList @ nil )
| ( ssList @ ( sk21 @ nil @ nil ) ) ),
inference(simp,[status(thm)],[36973]) ).
thf(37191,plain,
( ~ $true
| ( ssList @ ( sk21 @ nil @ nil ) ) ),
inference(rewrite,[status(thm)],[37114,329]) ).
thf(37192,plain,
ssList @ ( sk21 @ nil @ nil ),
inference(simp,[status(thm)],[37191]) ).
thf(37272,plain,
! [A: $i] :
( ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk21 @ nil @ nil ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[37192,356]) ).
thf(37273,plain,
frontsegP @ ( sk21 @ nil @ nil ) @ nil,
inference(pattern_uni,[status(thm)],[37272:[bind(A,$thf( sk21 @ nil @ nil ))]]) ).
thf(9900,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk15 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9676,287]) ).
thf(9901,plain,
( ( strictorderP @ sk2 )
| ( rearsegP @ ( sk15 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[9900:[bind(A,$thf( sk15 @ sk2 ))]]) ).
thf(27957,plain,
! [A: $i] :
( ( ssItem @ ( sk17 @ A ) )
| ( strictorderedP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,215]) ).
thf(27958,plain,
( ( ssItem @ ( sk17 @ sk2 ) )
| ( strictorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[27957:[bind(A,$thf( sk2 ))]]) ).
thf(28191,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk17 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27958,227]) ).
thf(28192,plain,
( ( strictorderedP @ sk2 )
| ~ ( memberP @ nil @ ( sk17 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[28191:[bind(A,$thf( sk17 @ sk2 ))]]) ).
thf(44837,plain,
( ( ssList @ ( sk22 @ sk1 ) )
| ( ssItem @ sk5 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[43501,579]) ).
thf(44838,plain,
( ( ssList @ ( sk22 @ sk1 ) )
| ( ssItem @ sk5 ) ),
inference(pattern_uni,[status(thm)],[44837:[]]) ).
thf(169,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( sk11 @ A ) )
| ( strictorderP @ A ) ),
inference(cnf,[status(esa)],[167]) ).
thf(8768,plain,
! [A: $i] :
( ( ssItem @ ( sk11 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,169]) ).
thf(8769,plain,
( ( ssItem @ ( sk11 @ sk2 ) )
| ( strictorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[8768:[bind(A,$thf( sk2 ))]]) ).
thf(8927,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk11 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8769,191]) ).
thf(8928,plain,
( ( strictorderP @ sk2 )
| ( totalorderedP @ ( cons @ ( sk11 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[8927:[bind(A,$thf( sk11 @ sk2 ))]]) ).
thf(135,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( segmentP @ nil @ A )
| ( nil = A ) ),
inference(cnf,[status(esa)],[134]) ).
thf(137,plain,
! [A: $i] :
( ( nil = A )
| ~ ( ssList @ A )
| ~ ( segmentP @ nil @ A ) ),
inference(lifteq,[status(thm)],[135]) ).
thf(61,axiom,
? [A: $i] :
( ( ssItem @ A )
& ? [B: $i] :
( ( ssItem @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(370,plain,
? [A: $i] :
( ( ssItem @ A )
& ? [B: $i] :
( ( ssItem @ B )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(371,plain,
sk38 != sk39,
inference(cnf,[status(esa)],[370]) ).
thf(374,plain,
sk39 != sk38,
inference(lifteq,[status(thm)],[371]) ).
thf(1715,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( segmentP @ nil @ A )
| ( sk38 != nil )
| ( A != sk39 ) ),
inference(paramod_ordered,[status(thm)],[137,374]) ).
thf(1716,plain,
( ~ ( ssList @ sk39 )
| ~ ( segmentP @ nil @ sk39 )
| ( sk38 != nil ) ),
inference(pattern_uni,[status(thm)],[1715:[bind(A,$thf( sk39 ))]]) ).
thf(5363,plain,
( ~ ( segmentP @ nil @ sk39 )
| ( sk38 != nil )
| ( ( ssList @ sk39 )
!= ( ssList @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[107,1716]) ).
thf(5383,plain,
( ~ ( segmentP @ nil @ sk39 )
| ( sk38 != nil )
| ( sk39 != sk1 ) ),
inference(simp,[status(thm)],[5363]) ).
thf(1813,plain,
! [A: $i] :
( ( nil = A )
| ~ ( segmentP @ nil @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,137]) ).
thf(1814,plain,
( ( sk1 = nil )
| ~ ( segmentP @ nil @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1813:[bind(A,$thf( sk1 ))]]) ).
thf(26005,plain,
! [A: $i] :
( ( sk1 != nil )
| ~ ( neq @ A @ A )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[579,208]) ).
thf(26006,plain,
( ( sk1 != nil )
| ~ ( neq @ sk5 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[26005:[bind(A,$thf( sk5 ))]]) ).
thf(26151,plain,
( ~ ( segmentP @ nil @ sk1 )
| ~ ( neq @ sk5 @ sk5 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1814,26006]) ).
thf(26152,plain,
( ~ ( segmentP @ nil @ sk1 )
| ~ ( neq @ sk5 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[26151:[]]) ).
thf(73,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( strictorderP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax63) ).
thf(408,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( strictorderP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(8004,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk7 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4362,191]) ).
thf(8005,plain,
( ( cyclefreeP @ sk2 )
| ( totalorderedP @ ( cons @ ( sk7 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[8004:[bind(A,$thf( sk7 @ sk2 ))]]) ).
thf(37368,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk21 @ nil @ nil ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[37192,287]) ).
thf(37369,plain,
rearsegP @ ( sk21 @ nil @ nil ) @ nil,
inference(pattern_uni,[status(thm)],[37368:[bind(A,$thf( sk21 @ nil @ nil ))]]) ).
thf(15449,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk8 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[619,189]) ).
thf(15450,plain,
( ( cyclefreeP @ sk1 )
| ( segmentP @ ( sk8 @ sk1 ) @ ( sk8 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[15449:[bind(A,$thf( sk8 @ sk1 ))]]) ).
thf(176,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( lt @ ( sk12 @ A ) @ ( sk11 @ A ) )
| ( strictorderP @ A ) ),
inference(cnf,[status(esa)],[167]) ).
thf(11351,plain,
! [A: $i] :
( ~ ( lt @ ( sk12 @ A ) @ ( sk11 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,176]) ).
thf(11352,plain,
( ~ ( lt @ ( sk12 @ sk2 ) @ ( sk11 @ sk2 ) )
| ( strictorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[11351:[bind(A,$thf( sk2 ))]]) ).
thf(3,axiom,
strictorderedP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax69) ).
thf(115,plain,
strictorderedP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(28931,plain,
! [A: $i] :
( ( strictorderedP @ sk1 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk16 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[28699,191]) ).
thf(28932,plain,
( ( strictorderedP @ sk1 )
| ( totalorderedP @ ( cons @ ( sk16 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[28931:[bind(A,$thf( sk16 @ sk1 ))]]) ).
thf(247,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( sk24 @ A ) )
| ( totalorderP @ A ) ),
inference(cnf,[status(esa)],[244]) ).
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(200,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(202,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( gt @ A @ B )
| ( lt @ B @ A ) ),
inference(cnf,[status(esa)],[200]) ).
thf(372,plain,
ssItem @ sk39,
inference(cnf,[status(esa)],[370]) ).
thf(596,plain,
! [A: $i] :
( ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk39 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[372,119]) ).
thf(597,plain,
strictorderedP @ ( cons @ sk39 @ nil ),
inference(pattern_uni,[status(thm)],[596:[bind(A,$thf( sk39 ))]]) ).
thf(37205,plain,
! [A: $i] :
( ( segmentP @ A @ A )
| ( ( ssList @ ( sk21 @ nil @ nil ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[37192,189]) ).
thf(37206,plain,
segmentP @ ( sk21 @ nil @ nil ) @ ( sk21 @ nil @ nil ),
inference(pattern_uni,[status(thm)],[37205:[bind(A,$thf( sk21 @ nil @ nil ))]]) ).
thf(25996,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ~ ( neq @ A @ A )
| ( ( ssItem @ ( sk12 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9251,208]) ).
thf(25997,plain,
( ( strictorderP @ sk1 )
| ~ ( neq @ ( sk12 @ sk1 ) @ ( sk12 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[25996:[bind(A,$thf( sk12 @ sk1 ))]]) ).
thf(64,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( duplicatefreeP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax71) ).
thf(384,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( duplicatefreeP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(826,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A )
| ( sk38 != nil )
| ( A != sk39 ) ),
inference(paramod_ordered,[status(thm)],[123,374]) ).
thf(827,plain,
( ~ ( ssList @ sk39 )
| ~ ( frontsegP @ nil @ sk39 )
| ( sk38 != nil ) ),
inference(pattern_uni,[status(thm)],[826:[bind(A,$thf( sk39 ))]]) ).
thf(4108,plain,
( ~ ( ssList @ sk39 )
| ( sk38 != nil )
| ( ( frontsegP @ nil @ sk39 )
!= ( frontsegP @ nil @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[516,827]) ).
thf(4139,plain,
( ~ ( ssList @ sk39 )
| ( sk38 != nil )
| ( nil != nil )
| ( sk39 != nil ) ),
inference(simp,[status(thm)],[4108]) ).
thf(4158,plain,
( ~ ( ssList @ sk39 )
| ( sk38 != nil )
| ( sk39 != nil ) ),
inference(simp,[status(thm)],[4139]) ).
thf(4172,plain,
( ( sk38 != nil )
| ( sk39 != nil )
| ( ( ssList @ sk39 )
!= ( ssList @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[329,4158]) ).
thf(4194,plain,
( ( sk38 != nil )
| ( sk39 != nil )
| ( sk39 != nil ) ),
inference(simp,[status(thm)],[4172]) ).
thf(4205,plain,
( ( sk38 != nil )
| ( sk39 != nil ) ),
inference(simp,[status(thm)],[4194]) ).
thf(4294,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A )
| ( sk39 != nil )
| ( A != sk38 ) ),
inference(paramod_ordered,[status(thm)],[123,4205]) ).
thf(4295,plain,
( ~ ( ssList @ sk38 )
| ~ ( frontsegP @ nil @ sk38 )
| ( sk39 != nil ) ),
inference(pattern_uni,[status(thm)],[4294:[bind(A,$thf( sk38 ))]]) ).
thf(11032,plain,
( ~ ( frontsegP @ nil @ sk38 )
| ( sk39 != nil )
| ( ( ssList @ sk38 )
!= ( ssList @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[106,4295]) ).
thf(11112,plain,
( ~ ( frontsegP @ nil @ sk38 )
| ( sk39 != nil )
| ( sk38 != sk2 ) ),
inference(simp,[status(thm)],[11032]) ).
thf(15502,plain,
! [A: $i] :
( ( segmentP @ A @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,189]) ).
thf(15503,plain,
segmentP @ sk1 @ sk1,
inference(pattern_uni,[status(thm)],[15502:[bind(A,$thf( sk1 ))]]) ).
thf(15631,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( segmentP @ nil @ sk1 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[693,15503]) ).
thf(15632,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( segmentP @ nil @ sk1 ) ),
inference(pattern_uni,[status(thm)],[15631:[]]) ).
thf(220,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk20 @ A ) )
| ( strictorderedP @ A ) ),
inference(cnf,[status(esa)],[214]) ).
thf(30344,plain,
! [A: $i] :
( ( ssList @ ( sk20 @ A ) )
| ( strictorderedP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,220]) ).
thf(30345,plain,
( ( ssList @ ( sk20 @ sk2 ) )
| ( strictorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[30344:[bind(A,$thf( sk2 ))]]) ).
thf(30706,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk20 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30345,287]) ).
thf(30707,plain,
( ( strictorderedP @ sk2 )
| ( rearsegP @ ( sk20 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[30706:[bind(A,$thf( sk20 @ sk2 ))]]) ).
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(185,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(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(257,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(259,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( nil = A )
| ( ssItem @ ( sk29 @ A ) ) ),
inference(cnf,[status(esa)],[257]) ).
thf(262,plain,
! [A: $i] :
( ( nil = A )
| ~ ( ssList @ A )
| ( ssItem @ ( sk29 @ A ) ) ),
inference(lifteq,[status(thm)],[259]) ).
thf(65208,plain,
! [A: $i] :
( ( nil = A )
| ( ssItem @ ( sk29 @ A ) )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,262]) ).
thf(65209,plain,
( ( sk1 = nil )
| ( ssItem @ ( sk29 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[65208:[bind(A,$thf( sk1 ))]]) ).
thf(66832,plain,
( ( ssItem @ ( sk29 @ sk1 ) )
| ( ssItem @ sk5 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[65209,579]) ).
thf(66833,plain,
( ( ssItem @ ( sk29 @ sk1 ) )
| ( ssItem @ sk5 ) ),
inference(pattern_uni,[status(thm)],[66832:[]]) ).
thf(9844,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk15 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9676,356]) ).
thf(9845,plain,
( ( strictorderP @ sk2 )
| ( frontsegP @ ( sk15 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[9844:[bind(A,$thf( sk15 @ sk2 ))]]) ).
thf(9771,plain,
! [A: $i] :
( ( ssList @ ( sk15 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,173]) ).
thf(9772,plain,
( ( ssList @ ( sk15 @ sk1 ) )
| ( strictorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[9771:[bind(A,$thf( sk1 ))]]) ).
thf(10021,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk15 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9772,287]) ).
thf(10022,plain,
( ( strictorderP @ sk1 )
| ( rearsegP @ ( sk15 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[10021:[bind(A,$thf( sk15 @ sk1 ))]]) ).
thf(75,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( rearsegP @ nil @ A )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52) ).
thf(417,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(25998,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssItem @ sk39 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[372,208]) ).
thf(25999,plain,
~ ( neq @ sk39 @ sk39 ),
inference(pattern_uni,[status(thm)],[25998:[bind(A,$thf( sk39 ))]]) ).
thf(26042,plain,
( ( sk1 != nil )
| ( ( neq @ sk39 @ sk39 )
!= ( neq @ sk2 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[574,25999]) ).
thf(26079,plain,
( ( sk1 != nil )
| ( sk39 != sk2 )
| ( sk39 != nil ) ),
inference(simp,[status(thm)],[26042]) ).
thf(30057,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( sk39 != sk2 )
| ( sk39 != nil )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[693,26079]) ).
thf(30058,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( sk39 != sk2 )
| ( sk39 != nil ) ),
inference(pattern_uni,[status(thm)],[30057:[]]) ).
thf(1566,plain,
! [A: $i] :
( ( nil = A )
| ~ ( segmentP @ nil @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,137]) ).
thf(1567,plain,
( ( sk2 = nil )
| ~ ( segmentP @ nil @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1566:[bind(A,$thf( sk2 ))]]) ).
thf(726,plain,
! [A: $i] :
( ( nil = A )
| ~ ( frontsegP @ nil @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,123]) ).
thf(727,plain,
( ( sk2 = nil )
| ~ ( frontsegP @ nil @ sk2 ) ),
inference(pattern_uni,[status(thm)],[726:[bind(A,$thf( sk2 ))]]) ).
thf(101,plain,
( ( nil = sk3 )
| ( nil != sk4 ) ),
inference(cnf,[status(esa)],[98]) ).
thf(111,plain,
( ( sk3 = nil )
| ( sk4 != nil ) ),
inference(lifteq,[status(thm)],[101]) ).
thf(507,plain,
( ( sk1 = nil )
| ( sk2 != nil ) ),
inference(rewrite,[status(thm)],[111,112,114]) ).
thf(927,plain,
( ~ ( frontsegP @ nil @ sk2 )
| ( sk1 = nil )
| ( sk2 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[727,507]) ).
thf(928,plain,
( ~ ( frontsegP @ nil @ sk2 )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[927:[]]) ).
thf(100,plain,
( ( memberP @ sk4 @ sk5 )
| ~ ( neq @ sk4 @ nil ) ),
inference(cnf,[status(esa)],[98]) ).
thf(509,plain,
( ( memberP @ sk2 @ sk5 )
| ~ ( neq @ sk2 @ nil ) ),
inference(rewrite,[status(thm)],[100,112]) ).
thf(576,plain,
( ( sk1 != nil )
| ( memberP @ sk2 @ sk5 )
| ( ( neq @ sk2 @ nil )
!= ( neq @ sk2 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[574,509]) ).
thf(577,plain,
( ( sk1 != nil )
| ( memberP @ sk2 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[576:[]]) ).
thf(582,plain,
! [A: $i] :
( ( sk1 != nil )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[579,227]) ).
thf(583,plain,
( ( sk1 != nil )
| ~ ( memberP @ nil @ sk5 ) ),
inference(pattern_uni,[status(thm)],[582:[bind(A,$thf( sk5 ))]]) ).
thf(613,plain,
( ( sk1 != nil )
| ( ( memberP @ sk2 @ sk5 )
!= ( memberP @ nil @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[577,583]) ).
thf(614,plain,
( ( sk1 != nil )
| ( sk2 != nil )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[613]) ).
thf(615,plain,
( ( sk1 != nil )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[614]) ).
thf(929,plain,
( ~ ( frontsegP @ nil @ sk2 )
| ( sk1 != nil )
| ( sk2 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[727,615]) ).
thf(930,plain,
( ~ ( frontsegP @ nil @ sk2 )
| ( sk1 != nil ) ),
inference(pattern_uni,[status(thm)],[929:[]]) ).
thf(1074,plain,
( ~ ( frontsegP @ nil @ sk2 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[928,930]) ).
thf(1075,plain,
~ ( frontsegP @ nil @ sk2 ),
inference(pattern_uni,[status(thm)],[1074:[]]) ).
thf(1115,plain,
( ( frontsegP @ nil @ sk2 )
!= ( frontsegP @ nil @ nil ) ),
inference(paramod_ordered,[status(thm)],[516,1075]) ).
thf(1122,plain,
( ( nil != nil )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[1115]) ).
thf(1123,plain,
sk2 != nil,
inference(simp,[status(thm)],[1122]) ).
thf(1845,plain,
~ ( segmentP @ nil @ sk2 ),
inference(simplifyReflect,[status(thm)],[1567,1123]) ).
thf(15656,plain,
( ( segmentP @ sk1 @ sk1 )
!= ( segmentP @ nil @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[15503,1845]) ).
thf(15684,plain,
( ( sk1 != nil )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[15656]) ).
thf(44591,plain,
( ( ssList @ ( sk22 @ sk1 ) )
| ( sk2 != sk1 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[43501,15684]) ).
thf(44592,plain,
( ( ssList @ ( sk22 @ sk1 ) )
| ( sk2 != sk1 ) ),
inference(pattern_uni,[status(thm)],[44591:[]]) ).
thf(46603,plain,
! [A: $i] :
( ( sk2 != sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk22 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44592,287]) ).
thf(46604,plain,
( ( sk2 != sk1 )
| ( rearsegP @ ( sk22 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[46603:[bind(A,$thf( sk22 @ sk1 ))]]) ).
thf(9395,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk12 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9251,227]) ).
thf(9396,plain,
( ( strictorderP @ sk1 )
| ~ ( memberP @ nil @ ( sk12 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[9395:[bind(A,$thf( sk12 @ sk1 ))]]) ).
thf(26028,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ~ ( neq @ A @ A )
| ( ( ssItem @ ( sk11 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8769,208]) ).
thf(26029,plain,
( ( strictorderP @ sk2 )
| ~ ( neq @ ( sk11 @ sk2 ) @ ( sk11 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[26028:[bind(A,$thf( sk11 @ sk2 ))]]) ).
thf(71,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ssList @ ( app @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
thf(404,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ssList @ ( app @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(4647,plain,
! [A: $i] :
( ( ssList @ ( sk9 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,156]) ).
thf(4648,plain,
( ( ssList @ ( sk9 @ sk2 ) )
| ( cyclefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[4647:[bind(A,$thf( sk2 ))]]) ).
thf(6582,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk9 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4648,356]) ).
thf(6583,plain,
( ( cyclefreeP @ sk2 )
| ( frontsegP @ ( sk9 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[6582:[bind(A,$thf( sk9 @ sk2 ))]]) ).
thf(160,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk10 @ A ) )
| ( cyclefreeP @ A ) ),
inference(cnf,[status(esa)],[152]) ).
thf(5882,plain,
! [A: $i] :
( ( ssList @ ( sk10 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,160]) ).
thf(5883,plain,
( ( ssList @ ( sk10 @ sk1 ) )
| ( cyclefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[5882:[bind(A,$thf( sk1 ))]]) ).
thf(6008,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk10 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5883,238]) ).
thf(6009,plain,
( ( cyclefreeP @ sk1 )
| ( segmentP @ ( sk10 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[6008:[bind(A,$thf( sk10 @ sk1 ))]]) ).
thf(46,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( equalelemsP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax73) ).
thf(288,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( equalelemsP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(5814,plain,
! [A: $i] :
( ( ssList @ ( sk10 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,160]) ).
thf(5815,plain,
( ( ssList @ ( sk10 @ sk2 ) )
| ( cyclefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[5814:[bind(A,$thf( sk2 ))]]) ).
thf(5920,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk10 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5815,238]) ).
thf(5921,plain,
( ( cyclefreeP @ sk2 )
| ( segmentP @ ( sk10 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[5920:[bind(A,$thf( sk10 @ sk2 ))]]) ).
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(389,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(62861,plain,
! [A: $i] :
( ( nil = A )
| ( ssItem @ ( sk29 @ A ) )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,262]) ).
thf(62862,plain,
( ( sk2 = nil )
| ( ssItem @ ( sk29 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[62861:[bind(A,$thf( sk2 ))]]) ).
thf(65689,plain,
ssItem @ ( sk29 @ sk2 ),
inference(simplifyReflect,[status(thm)],[62862,1123]) ).
thf(41488,plain,
! [A: $i] :
( ( nil = A )
| ( ssList @ ( sk22 @ A ) )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,243]) ).
thf(41489,plain,
( ( sk2 = nil )
| ( ssList @ ( sk22 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[41488:[bind(A,$thf( sk2 ))]]) ).
thf(240,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( nil = A )
| ( ( tl @ A )
= ( sk22 @ A ) ) ),
inference(cnf,[status(esa)],[239]) ).
thf(242,plain,
! [A: $i] :
( ( nil = A )
| ( ( sk22 @ A )
= ( tl @ A ) )
| ~ ( ssList @ A ) ),
inference(lifteq,[status(thm)],[240]) ).
thf(40142,plain,
! [A: $i] :
( ( nil = A )
| ( ( sk22 @ A )
= ( tl @ A ) )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,242]) ).
thf(40143,plain,
( ( sk2 = nil )
| ( ( sk22 @ sk2 )
= ( tl @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[40142:[bind(A,$thf( sk2 ))]]) ).
thf(40233,plain,
( ( sk22 @ sk2 )
= ( tl @ sk2 ) ),
inference(simplifyReflect,[status(thm)],[40143,1123]) ).
thf(43927,plain,
( ( sk2 = nil )
| ( ssList @ ( tl @ sk2 ) ) ),
inference(rewrite,[status(thm)],[41489,40233]) ).
thf(43928,plain,
ssList @ ( tl @ sk2 ),
inference(simplifyReflect,[status(thm)],[43927,1123]) ).
thf(44004,plain,
! [A: $i] :
( ( frontsegP @ A @ nil )
| ( ( ssList @ ( tl @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[43928,356]) ).
thf(44005,plain,
frontsegP @ ( tl @ sk2 ) @ nil,
inference(pattern_uni,[status(thm)],[44004:[bind(A,$thf( tl @ sk2 ))]]) ).
thf(21,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( ( segmentP @ A @ B )
& ( segmentP @ B @ C ) )
=> ( segmentP @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax53) ).
thf(183,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(184,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)],[183]) ).
thf(219,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk19 @ A ) )
| ( strictorderedP @ A ) ),
inference(cnf,[status(esa)],[214]) ).
thf(29511,plain,
! [A: $i] :
( ( ssList @ ( sk19 @ A ) )
| ( strictorderedP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,219]) ).
thf(29512,plain,
( ( ssList @ ( sk19 @ sk1 ) )
| ( strictorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[29511:[bind(A,$thf( sk1 ))]]) ).
thf(1263,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( cyclefreeP @ ( sk8 @ sk1 ) )
| ( ssList @ ( sk8 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ ( sk8 @ ( sk8 @ sk1 ) ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[629,153]) ).
thf(1264,plain,
( ( cyclefreeP @ sk1 )
| ( cyclefreeP @ ( sk8 @ sk1 ) )
| ( ssList @ ( sk8 @ ( sk8 @ ( sk8 @ sk1 ) ) ) )
| ( cyclefreeP @ ( sk8 @ ( sk8 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[1263:[bind(A,$thf( sk8 @ ( sk8 @ sk1 ) ))]]) ).
thf(373,plain,
ssItem @ sk38,
inference(cnf,[status(esa)],[370]) ).
thf(32,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ~ ( lt @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax90) ).
thf(212,plain,
! [A: $i] :
( ( ssItem @ A )
=> ~ ( lt @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(213,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ~ ( lt @ A @ A ) ),
inference(cnf,[status(esa)],[212]) ).
thf(27486,plain,
! [A: $i] :
( ~ ( lt @ A @ A )
| ( ( ssItem @ sk38 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[373,213]) ).
thf(27487,plain,
~ ( lt @ sk38 @ sk38 ),
inference(pattern_uni,[status(thm)],[27486:[bind(A,$thf( sk38 ))]]) ).
thf(26030,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssItem @ sk38 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[373,208]) ).
thf(26031,plain,
~ ( neq @ sk38 @ sk38 ),
inference(pattern_uni,[status(thm)],[26030:[bind(A,$thf( sk38 ))]]) ).
thf(26100,plain,
( ( sk2 != sk1 )
| ( ( neq @ sk38 @ sk38 )
!= ( neq @ sk2 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[15620,26031]) ).
thf(26121,plain,
( ( sk2 != sk1 )
| ( sk38 != sk2 )
| ( sk38 != nil ) ),
inference(simp,[status(thm)],[26100]) ).
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(357,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(15942,plain,
! [A: $i] :
( ( sk2 != sk1 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[15865,227]) ).
thf(15943,plain,
( ( sk2 != sk1 )
| ~ ( memberP @ nil @ sk5 ) ),
inference(pattern_uni,[status(thm)],[15942:[bind(A,$thf( sk5 ))]]) ).
thf(157,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( leq @ ( sk7 @ A ) @ ( sk6 @ A ) )
| ( cyclefreeP @ A ) ),
inference(cnf,[status(esa)],[152]) ).
thf(26007,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ~ ( neq @ A @ A )
| ( ( ssItem @ ( sk6 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5539,208]) ).
thf(26008,plain,
( ( cyclefreeP @ sk1 )
| ~ ( neq @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[26007:[bind(A,$thf( sk6 @ 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(195,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(196,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)],[195]) ).
thf(30478,plain,
! [A: $i] :
( ( ssList @ ( sk20 @ A ) )
| ( strictorderedP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,220]) ).
thf(30479,plain,
( ( ssList @ ( sk20 @ sk1 ) )
| ( strictorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[30478:[bind(A,$thf( sk1 ))]]) ).
thf(30909,plain,
! [A: $i] :
( ( strictorderedP @ sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk20 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30479,287]) ).
thf(30910,plain,
( ( strictorderedP @ sk1 )
| ( rearsegP @ ( sk20 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[30909:[bind(A,$thf( sk20 @ sk1 ))]]) ).
thf(5126,plain,
! [A: $i] :
( ( leq @ ( sk7 @ A ) @ ( sk6 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,157]) ).
thf(5127,plain,
( ( leq @ ( sk7 @ sk1 ) @ ( sk6 @ sk1 ) )
| ( cyclefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[5126:[bind(A,$thf( sk1 ))]]) ).
thf(27450,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ~ ( lt @ A @ A )
| ( ( ssItem @ ( sk12 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9251,213]) ).
thf(27451,plain,
( ( strictorderP @ sk1 )
| ~ ( lt @ ( sk12 @ sk1 ) @ ( sk12 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[27450:[bind(A,$thf( sk12 @ sk1 ))]]) ).
thf(11096,plain,
( ~ ( frontsegP @ nil @ sk38 )
| ( sk39 != nil )
| ( ( ssList @ sk38 )
!= ( ssList @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[107,4295]) ).
thf(11115,plain,
( ~ ( frontsegP @ nil @ sk38 )
| ( sk39 != nil )
| ( sk38 != sk1 ) ),
inference(simp,[status(thm)],[11096]) ).
thf(44795,plain,
( ( ssList @ ( sk22 @ sk1 ) )
| ~ ( singletonP @ sk1 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[43501,569]) ).
thf(44796,plain,
( ( ssList @ ( sk22 @ sk1 ) )
| ~ ( singletonP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[44795:[]]) ).
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(228,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(15743,plain,
( ~ ( segmentP @ nil @ sk1 )
| ( sk2 != sk1 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1814,15684]) ).
thf(15744,plain,
( ~ ( segmentP @ nil @ sk1 )
| ( sk2 != sk1 ) ),
inference(pattern_uni,[status(thm)],[15743:[]]) ).
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(316,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(46974,plain,
! [A: $i] :
( ( ssItem @ sk5 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk22 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44838,238]) ).
thf(46975,plain,
( ( ssItem @ sk5 )
| ( segmentP @ ( sk22 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[46974:[bind(A,$thf( sk22 @ sk1 ))]]) ).
thf(11403,plain,
! [A: $i] :
( ~ ( lt @ ( sk12 @ A ) @ ( sk11 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,176]) ).
thf(11404,plain,
( ~ ( lt @ ( sk12 @ sk1 ) @ ( sk11 @ sk1 ) )
| ( strictorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[11403:[bind(A,$thf( sk1 ))]]) ).
thf(31,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( app @ nil @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
thf(209,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( app @ nil @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(210,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ nil @ A )
= A ) ),
inference(cnf,[status(esa)],[209]) ).
thf(211,plain,
! [A: $i] :
( ( ( app @ nil @ A )
= A )
| ~ ( ssList @ A ) ),
inference(lifteq,[status(thm)],[210]) ).
thf(37225,plain,
! [A: $i] :
( ( ( app @ nil @ A )
= A )
| ( ( ssList @ ( sk21 @ nil @ nil ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[37192,211]) ).
thf(37226,plain,
( ( app @ nil @ ( sk21 @ nil @ nil ) )
= ( sk21 @ nil @ nil ) ),
inference(pattern_uni,[status(thm)],[37225:[bind(A,$thf( sk21 @ nil @ nil ))]]) ).
thf(10533,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk13 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10298,287]) ).
thf(10534,plain,
( ( strictorderP @ sk2 )
| ( rearsegP @ ( sk13 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[10533:[bind(A,$thf( sk13 @ sk2 ))]]) ).
thf(222,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk18 @ A ) )
| ( strictorderedP @ A ) ),
inference(cnf,[status(esa)],[214]) ).
thf(32231,plain,
! [A: $i] :
( ( ssList @ ( sk18 @ A ) )
| ( strictorderedP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,222]) ).
thf(32232,plain,
( ( ssList @ ( sk18 @ sk1 ) )
| ( strictorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[32231:[bind(A,$thf( sk1 ))]]) ).
thf(32673,plain,
! [A: $i] :
( ( strictorderedP @ sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk18 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[32232,287]) ).
thf(32674,plain,
( ( strictorderedP @ sk1 )
| ( rearsegP @ ( sk18 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[32673:[bind(A,$thf( sk18 @ sk1 ))]]) ).
thf(1930,plain,
( ~ ( segmentP @ nil @ sk1 )
| ( strictorderedP @ sk1 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1814,1260]) ).
thf(1931,plain,
( ~ ( segmentP @ nil @ sk1 )
| ( strictorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1930:[]]) ).
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(448,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(26128,plain,
( ( sk1 != nil )
| ( ( neq @ sk5 @ sk5 )
!= ( neq @ sk2 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[574,26006]) ).
thf(26185,plain,
( ( sk1 != nil )
| ( sk5 != sk2 )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[26128]) ).
thf(31106,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( sk5 != sk2 )
| ( sk5 != nil )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[693,26185]) ).
thf(31107,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( sk5 != sk2 )
| ( sk5 != nil ) ),
inference(pattern_uni,[status(thm)],[31106:[]]) ).
thf(8557,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( totalorderedP @ ( cons @ sk5 @ nil ) )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[693,7995]) ).
thf(8558,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( totalorderedP @ ( cons @ sk5 @ nil ) ) ),
inference(pattern_uni,[status(thm)],[8557:[]]) ).
thf(258,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( nil = A )
| ( ( cons @ ( sk29 @ A ) @ ( sk28 @ A ) )
= A ) ),
inference(cnf,[status(esa)],[257]) ).
thf(261,plain,
! [A: $i] :
( ( nil = A )
| ( ( cons @ ( sk29 @ A ) @ ( sk28 @ A ) )
= A )
| ~ ( ssList @ A ) ),
inference(lifteq,[status(thm)],[258]) ).
thf(9193,plain,
! [A: $i] :
( ( ssItem @ ( sk12 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,171]) ).
thf(9194,plain,
( ( ssItem @ ( sk12 @ sk2 ) )
| ( strictorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[9193:[bind(A,$thf( sk2 ))]]) ).
thf(9297,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk12 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9194,191]) ).
thf(9298,plain,
( ( strictorderP @ sk2 )
| ( totalorderedP @ ( cons @ ( sk12 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[9297:[bind(A,$thf( sk12 @ sk2 ))]]) ).
thf(158,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)],[152]) ).
thf(163,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)],[158]) ).
thf(164,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)],[163]) ).
thf(8028,plain,
! [A: $i] :
( ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk38 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[373,191]) ).
thf(8029,plain,
totalorderedP @ ( cons @ sk38 @ nil ),
inference(pattern_uni,[status(thm)],[8028:[bind(A,$thf( sk38 ))]]) ).
thf(172,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)],[167]) ).
thf(178,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)],[172]) ).
thf(179,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)],[178]) ).
thf(27482,plain,
! [A: $i] :
( ( sk2 != sk1 )
| ~ ( lt @ A @ A )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[15865,213]) ).
thf(27483,plain,
( ( sk2 != sk1 )
| ~ ( lt @ sk5 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[27482:[bind(A,$thf( sk5 ))]]) ).
thf(3972,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk8 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[619,287]) ).
thf(3973,plain,
( ( cyclefreeP @ sk1 )
| ( rearsegP @ ( sk8 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[3972:[bind(A,$thf( sk8 @ sk1 ))]]) ).
thf(37223,plain,
! [A: $i] :
( ( segmentP @ A @ nil )
| ( ( ssList @ ( sk21 @ nil @ nil ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[37192,238]) ).
thf(37224,plain,
segmentP @ ( sk21 @ nil @ nil ) @ nil,
inference(pattern_uni,[status(thm)],[37223:[bind(A,$thf( sk21 @ nil @ nil ))]]) ).
thf(4290,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( segmentP @ nil @ A )
| ( sk39 != nil )
| ( A != sk38 ) ),
inference(paramod_ordered,[status(thm)],[137,4205]) ).
thf(4291,plain,
( ~ ( ssList @ sk38 )
| ~ ( segmentP @ nil @ sk38 )
| ( sk39 != nil ) ),
inference(pattern_uni,[status(thm)],[4290:[bind(A,$thf( sk38 ))]]) ).
thf(10154,plain,
( ~ ( segmentP @ nil @ sk38 )
| ( sk39 != nil )
| ( ( ssList @ sk38 )
!= ( ssList @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[107,4291]) ).
thf(10173,plain,
( ~ ( segmentP @ nil @ sk38 )
| ( sk39 != nil )
| ( sk38 != sk1 ) ),
inference(simp,[status(thm)],[10154]) ).
thf(15669,plain,
( ( sk39 != nil )
| ( sk38 != sk1 )
| ( ( segmentP @ sk1 @ sk1 )
!= ( segmentP @ nil @ sk38 ) ) ),
inference(paramod_ordered,[status(thm)],[15503,10173]) ).
thf(15688,plain,
( ( sk39 != nil )
| ( sk38 != sk1 )
| ( sk1 != nil )
| ( sk38 != sk1 ) ),
inference(simp,[status(thm)],[15669]) ).
thf(15699,plain,
( ( sk39 != nil )
| ( sk38 != sk1 )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[15688]) ).
thf(21302,plain,
( ~ ( segmentP @ nil @ sk1 )
| ( sk39 != nil )
| ( sk38 != sk1 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1814,15699]) ).
thf(21303,plain,
( ~ ( segmentP @ nil @ sk1 )
| ( sk39 != nil )
| ( sk38 != sk1 ) ),
inference(pattern_uni,[status(thm)],[21302:[]]) ).
thf(40206,plain,
! [A: $i] :
( ( nil = A )
| ( ( sk22 @ A )
= ( tl @ A ) )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,242]) ).
thf(40207,plain,
( ( sk1 = nil )
| ( ( sk22 @ sk1 )
= ( tl @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[40206:[bind(A,$thf( sk1 ))]]) ).
thf(44944,plain,
( ( sk1 = nil )
| ( ssList @ ( tl @ sk1 ) )
| ( ( sk22 @ sk1 )
!= ( sk22 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[40207,43501]) ).
thf(44945,plain,
( ( sk1 = nil )
| ( ssList @ ( tl @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[44944:[]]) ).
thf(48051,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( totalorderedP @ sk1 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[44945,8602]) ).
thf(48052,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( totalorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[48051:[]]) ).
thf(6561,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk8 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[619,356]) ).
thf(6562,plain,
( ( cyclefreeP @ sk1 )
| ( frontsegP @ ( sk8 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[6561:[bind(A,$thf( sk8 @ sk1 ))]]) ).
thf(620,plain,
! [A: $i] :
( ( ssList @ ( sk8 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,153]) ).
thf(621,plain,
( ( ssList @ ( sk8 @ sk2 ) )
| ( cyclefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[620:[bind(A,$thf( sk2 ))]]) ).
thf(632,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( ssList @ ( sk8 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ ( sk8 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[621,153]) ).
thf(633,plain,
( ( cyclefreeP @ sk2 )
| ( ssList @ ( sk8 @ ( sk8 @ sk2 ) ) )
| ( cyclefreeP @ ( sk8 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[632:[bind(A,$thf( sk8 @ sk2 ))]]) ).
thf(1414,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( cyclefreeP @ ( sk8 @ sk2 ) )
| ( ssList @ ( sk8 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ ( sk8 @ ( sk8 @ sk2 ) ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[633,153]) ).
thf(1415,plain,
( ( cyclefreeP @ sk2 )
| ( cyclefreeP @ ( sk8 @ sk2 ) )
| ( ssList @ ( sk8 @ ( sk8 @ ( sk8 @ sk2 ) ) ) )
| ( cyclefreeP @ ( sk8 @ ( sk8 @ sk2 ) ) ) ),
inference(pattern_uni,[status(thm)],[1414:[bind(A,$thf( sk8 @ ( sk8 @ sk2 ) ))]]) ).
thf(15444,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk10 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5883,189]) ).
thf(15445,plain,
( ( cyclefreeP @ sk1 )
| ( segmentP @ ( sk10 @ sk1 ) @ ( sk10 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[15444:[bind(A,$thf( sk10 @ sk1 ))]]) ).
thf(253,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( leq @ ( sk24 @ A ) @ ( sk23 @ A ) )
| ( totalorderP @ A ) ),
inference(cnf,[status(esa)],[244]) ).
thf(8825,plain,
! [A: $i] :
( ( ssItem @ ( sk11 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,169]) ).
thf(8826,plain,
( ( ssItem @ ( sk11 @ sk1 ) )
| ( strictorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[8825:[bind(A,$thf( sk1 ))]]) ).
thf(26011,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ~ ( neq @ A @ A )
| ( ( ssItem @ ( sk11 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8826,208]) ).
thf(26012,plain,
( ( strictorderP @ sk1 )
| ~ ( neq @ ( sk11 @ sk1 ) @ ( sk11 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[26011:[bind(A,$thf( sk11 @ sk1 ))]]) ).
thf(252,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk26 @ A ) )
| ( totalorderP @ A ) ),
inference(cnf,[status(esa)],[244]) ).
thf(53463,plain,
! [A: $i] :
( ( ssList @ ( sk26 @ A ) )
| ( totalorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,252]) ).
thf(53464,plain,
( ( ssList @ ( sk26 @ sk2 ) )
| ( totalorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[53463:[bind(A,$thf( sk2 ))]]) ).
thf(513,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ( ( ssItem @ sk38 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[373,227]) ).
thf(514,plain,
~ ( memberP @ nil @ sk38 ),
inference(pattern_uni,[status(thm)],[513:[bind(A,$thf( sk38 ))]]) ).
thf(904,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ~ ( memberP @ nil @ sk5 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[693,583]) ).
thf(905,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ~ ( memberP @ nil @ sk5 ) ),
inference(pattern_uni,[status(thm)],[904:[]]) ).
thf(92,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( nil
!= ( cons @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).
thf(480,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( nil
!= ( cons @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(594,plain,
! [A: $i] :
( ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk38 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[373,119]) ).
thf(595,plain,
strictorderedP @ ( cons @ sk38 @ nil ),
inference(pattern_uni,[status(thm)],[594:[bind(A,$thf( sk38 ))]]) ).
thf(600,plain,
( ~ ( neq @ sk2 @ nil )
| ( strictorderedP @ sk1 )
| ( ( cons @ sk38 @ nil )
!= ( cons @ sk5 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[510,595]) ).
thf(601,plain,
( ( strictorderedP @ sk1 )
| ~ ( neq @ sk2 @ nil )
| ( sk38 != sk5 )
| ( nil != nil ) ),
inference(simp,[status(thm)],[600]) ).
thf(602,plain,
( ( strictorderedP @ sk1 )
| ~ ( neq @ sk2 @ nil )
| ( sk38 != sk5 ) ),
inference(simp,[status(thm)],[601]) ).
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(397,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(43,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ssItem @ ( hd @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
thf(280,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ssItem @ ( hd @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(221,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( lt @ ( sk16 @ A ) @ ( sk17 @ A ) )
| ( strictorderedP @ A ) ),
inference(cnf,[status(esa)],[214]) ).
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(131,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( hd @ ( cons @ B @ A ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(132,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( ( hd @ ( cons @ B @ A ) )
= B ) ),
inference(cnf,[status(esa)],[131]) ).
thf(133,plain,
! [B: $i,A: $i] :
( ( ( hd @ ( cons @ B @ A ) )
= B )
| ~ ( ssList @ A )
| ~ ( ssItem @ B ) ),
inference(lifteq,[status(thm)],[132]) ).
thf(28187,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk17 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27958,119]) ).
thf(28188,plain,
( ( strictorderedP @ sk2 )
| ( strictorderedP @ ( cons @ ( sk17 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[28187:[bind(A,$thf( sk17 @ sk2 ))]]) ).
thf(6615,plain,
! [A: $i] :
( ( frontsegP @ A @ nil )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,356]) ).
thf(6616,plain,
frontsegP @ sk1 @ nil,
inference(pattern_uni,[status(thm)],[6615:[bind(A,$thf( sk1 ))]]) ).
thf(204,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( A = B )
| ( neq @ A @ B ) ),
inference(cnf,[status(esa)],[203]) ).
thf(206,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ( neq @ A @ B ) ),
inference(lifteq,[status(thm)],[204]) ).
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(147,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(15573,plain,
( ~ ( singletonP @ sk1 )
| ( ( segmentP @ sk2 @ sk2 )
!= ( segmentP @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[15453,103]) ).
thf(15595,plain,
( ~ ( singletonP @ sk1 )
| ( sk2 != sk2 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[15573]) ).
thf(15618,plain,
( ~ ( singletonP @ sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[15595]) ).
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(116,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(15737,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( sk2 != sk1 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[693,15684]) ).
thf(15738,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( sk2 != sk1 ) ),
inference(pattern_uni,[status(thm)],[15737:[]]) ).
thf(32586,plain,
! [A: $i] :
( ( strictorderedP @ sk1 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk18 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[32232,356]) ).
thf(32587,plain,
( ( strictorderedP @ sk1 )
| ( frontsegP @ ( sk18 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[32586:[bind(A,$thf( sk18 @ sk1 ))]]) ).
thf(78,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( frontsegP @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax42) ).
thf(428,plain,
! [A: $i] :
( ( ssList @ A )
=> ( frontsegP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(9025,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk11 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8826,227]) ).
thf(9026,plain,
( ( strictorderP @ sk1 )
| ~ ( memberP @ nil @ ( sk11 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[9025:[bind(A,$thf( sk11 @ sk1 ))]]) ).
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(307,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(248,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( leq @ ( sk23 @ A ) @ ( sk24 @ A ) )
| ( totalorderP @ A ) ),
inference(cnf,[status(esa)],[244]) ).
thf(117,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)],[116]) ).
thf(245,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk27 @ A ) )
| ( totalorderP @ A ) ),
inference(cnf,[status(esa)],[244]) ).
thf(45334,plain,
! [A: $i] :
( ( ssList @ ( sk27 @ A ) )
| ( totalorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,245]) ).
thf(45335,plain,
( ( ssList @ ( sk27 @ sk2 ) )
| ( totalorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[45334:[bind(A,$thf( sk2 ))]]) ).
thf(201,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( lt @ B @ A )
| ( gt @ A @ B ) ),
inference(cnf,[status(esa)],[200]) ).
thf(6570,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk10 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5815,356]) ).
thf(6571,plain,
( ( cyclefreeP @ sk2 )
| ( frontsegP @ ( sk10 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[6570:[bind(A,$thf( sk10 @ sk2 ))]]) ).
thf(7998,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk6 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5539,191]) ).
thf(7999,plain,
( ( cyclefreeP @ sk1 )
| ( totalorderedP @ ( cons @ ( sk6 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[7998:[bind(A,$thf( sk6 @ sk1 ))]]) ).
thf(9322,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk12 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9194,119]) ).
thf(9323,plain,
( ( strictorderP @ sk2 )
| ( strictorderedP @ ( cons @ ( sk12 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[9322:[bind(A,$thf( sk12 @ sk2 ))]]) ).
thf(511,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ( ( ssItem @ sk39 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[372,227]) ).
thf(512,plain,
~ ( memberP @ nil @ sk39 ),
inference(pattern_uni,[status(thm)],[511:[bind(A,$thf( sk39 ))]]) ).
thf(8210,plain,
! [A: $i] :
( ( ssList @ ( sk14 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,168]) ).
thf(8211,plain,
( ( ssList @ ( sk14 @ sk2 ) )
| ( strictorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[8210:[bind(A,$thf( sk2 ))]]) ).
thf(66786,plain,
( ( ssItem @ ( sk29 @ sk1 ) )
| ~ ( singletonP @ sk1 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[65209,569]) ).
thf(66787,plain,
( ( ssItem @ ( sk29 @ sk1 ) )
| ~ ( singletonP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[66786:[]]) ).
thf(31114,plain,
( ~ ( segmentP @ nil @ sk1 )
| ( sk5 != sk2 )
| ( sk5 != nil )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1814,26185]) ).
thf(31115,plain,
( ~ ( segmentP @ nil @ sk1 )
| ( sk5 != sk2 )
| ( sk5 != nil ) ),
inference(pattern_uni,[status(thm)],[31114:[]]) ).
thf(49591,plain,
! [A: $i] :
( ( ssItem @ ( sk24 @ A ) )
| ( totalorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,247]) ).
thf(49592,plain,
( ( ssItem @ ( sk24 @ sk1 ) )
| ( totalorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[49591:[bind(A,$thf( sk1 ))]]) ).
thf(68,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ( cons @ ( hd @ A ) @ ( tl @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax78) ).
thf(392,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ( cons @ ( hd @ A ) @ ( tl @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(30623,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk20 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30345,356]) ).
thf(30624,plain,
( ( strictorderedP @ sk2 )
| ( frontsegP @ ( sk20 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[30623:[bind(A,$thf( sk20 @ sk2 ))]]) ).
thf(29381,plain,
! [A: $i] :
( ( ssList @ ( sk19 @ A ) )
| ( strictorderedP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,219]) ).
thf(29382,plain,
( ( ssList @ ( sk19 @ sk2 ) )
| ( strictorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[29381:[bind(A,$thf( sk2 ))]]) ).
thf(29617,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk19 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29382,238]) ).
thf(29618,plain,
( ( strictorderedP @ sk2 )
| ( segmentP @ ( sk19 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[29617:[bind(A,$thf( sk19 @ sk2 ))]]) ).
thf(57,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( totalorderP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax61) ).
thf(349,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( totalorderP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(15433,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk15 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9676,189]) ).
thf(15434,plain,
( ( strictorderP @ sk2 )
| ( segmentP @ ( sk15 @ sk2 ) @ ( sk15 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[15433:[bind(A,$thf( sk15 @ sk2 ))]]) ).
thf(29810,plain,
! [A: $i] :
( ( strictorderedP @ sk1 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk19 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29512,238]) ).
thf(29811,plain,
( ( strictorderedP @ sk1 )
| ( segmentP @ ( sk19 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[29810:[bind(A,$thf( sk19 @ sk1 ))]]) ).
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(192,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(18,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ssList @ ( cons @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
thf(165,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ssList @ ( cons @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1967,plain,
( ~ ( segmentP @ nil @ sk1 )
| ( ssItem @ sk5 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1814,579]) ).
thf(1968,plain,
( ~ ( segmentP @ nil @ sk1 )
| ( ssItem @ sk5 ) ),
inference(pattern_uni,[status(thm)],[1967:[]]) ).
thf(27462,plain,
! [A: $i] :
( ( sk1 != nil )
| ~ ( lt @ A @ A )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[579,213]) ).
thf(27463,plain,
( ( sk1 != nil )
| ~ ( lt @ sk5 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[27462:[bind(A,$thf( sk5 ))]]) ).
thf(27607,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ~ ( lt @ sk5 @ sk5 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[693,27463]) ).
thf(27608,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ~ ( lt @ sk5 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[27607:[]]) ).
thf(95,axiom,
totalorderP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax62) ).
thf(493,plain,
totalorderP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(15497,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk9 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4705,189]) ).
thf(15498,plain,
( ( cyclefreeP @ sk1 )
| ( segmentP @ ( sk9 @ sk1 ) @ ( sk9 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[15497:[bind(A,$thf( sk9 @ sk1 ))]]) ).
thf(9828,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk15 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9676,238]) ).
thf(9829,plain,
( ( strictorderP @ sk2 )
| ( segmentP @ ( sk15 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[9828:[bind(A,$thf( sk15 @ sk2 ))]]) ).
thf(229,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)],[228]) ).
thf(154,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( leq @ ( sk6 @ A ) @ ( sk7 @ A ) )
| ( cyclefreeP @ A ) ),
inference(cnf,[status(esa)],[152]) ).
thf(4279,plain,
! [A: $i] :
( ( leq @ ( sk6 @ A ) @ ( sk7 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,154]) ).
thf(4280,plain,
( ( leq @ ( sk6 @ sk1 ) @ ( sk7 @ sk1 ) )
| ( cyclefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[4279:[bind(A,$thf( sk1 ))]]) ).
thf(20078,plain,
( ( segmentP @ nil @ sk1 )
| ( ( frontsegP @ nil @ sk1 )
!= ( frontsegP @ nil @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[516,15632]) ).
thf(20116,plain,
( ( segmentP @ nil @ sk1 )
| ( nil != nil )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[20078]) ).
thf(20128,plain,
( ( segmentP @ nil @ sk1 )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[20116]) ).
thf(5654,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk6 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5539,119]) ).
thf(5655,plain,
( ( cyclefreeP @ sk1 )
| ( strictorderedP @ ( cons @ ( sk6 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[5654:[bind(A,$thf( sk6 @ sk1 ))]]) ).
thf(27,axiom,
duplicatefreeP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax72) ).
thf(197,plain,
duplicatefreeP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(43961,plain,
! [A: $i] :
( ( ( app @ nil @ A )
= A )
| ( ( ssList @ ( tl @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[43928,211]) ).
thf(43962,plain,
( ( app @ nil @ ( tl @ sk2 ) )
= ( tl @ sk2 ) ),
inference(pattern_uni,[status(thm)],[43961:[bind(A,$thf( tl @ sk2 ))]]) ).
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(341,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(342,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( nil != B )
| ( nil != A )
| ( nil
= ( app @ A @ B ) ) ),
inference(cnf,[status(esa)],[341]) ).
thf(345,plain,
! [B: $i,A: $i] :
( ( nil != B )
| ( nil != A )
| ( ( app @ A @ B )
= nil )
| ~ ( ssList @ A )
| ~ ( ssList @ B ) ),
inference(lifteq,[status(thm)],[342]) ).
thf(346,plain,
( ( ( app @ nil @ nil )
= nil )
| ~ ( ssList @ nil ) ),
inference(simp,[status(thm)],[345]) ).
thf(550,plain,
( ( ( app @ nil @ nil )
= nil )
| ~ $true ),
inference(rewrite,[status(thm)],[346,329]) ).
thf(551,plain,
( ( app @ nil @ nil )
= nil ),
inference(simp,[status(thm)],[550]) ).
thf(47676,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( neq @ sk2 @ nil )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[44945,574]) ).
thf(47677,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( neq @ sk2 @ nil ) ),
inference(pattern_uni,[status(thm)],[47676:[]]) ).
thf(6074,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk10 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5883,287]) ).
thf(6075,plain,
( ( cyclefreeP @ sk1 )
| ( rearsegP @ ( sk10 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[6074:[bind(A,$thf( sk10 @ sk1 ))]]) ).
thf(28322,plain,
! [A: $i] :
( ( strictorderedP @ sk1 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk17 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[28045,119]) ).
thf(28323,plain,
( ( strictorderedP @ sk1 )
| ( strictorderedP @ ( cons @ ( sk17 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[28322:[bind(A,$thf( sk17 @ sk1 ))]]) ).
thf(44821,plain,
( ( ssList @ ( sk22 @ sk1 ) )
| ( memberP @ sk2 @ sk5 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[43501,577]) ).
thf(44822,plain,
( ( ssList @ ( sk22 @ sk1 ) )
| ( memberP @ sk2 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[44821:[]]) ).
thf(4788,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk9 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4648,287]) ).
thf(4789,plain,
( ( cyclefreeP @ sk2 )
| ( rearsegP @ ( sk9 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[4788:[bind(A,$thf( sk9 @ sk2 ))]]) ).
thf(13,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( ( frontsegP @ A @ B )
& ( frontsegP @ B @ A ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax41) ).
thf(141,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(15918,plain,
! [A: $i] :
( ( sk2 != sk1 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[15865,191]) ).
thf(15919,plain,
( ( sk2 != sk1 )
| ( totalorderedP @ ( cons @ sk5 @ nil ) ) ),
inference(pattern_uni,[status(thm)],[15918:[bind(A,$thf( sk5 ))]]) ).
thf(20677,plain,
( ( sk2 != sk1 )
| ( totalorderedP @ sk1 )
| ( ( cons @ sk5 @ nil )
!= ( cons @ sk5 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[15891,15919]) ).
thf(20678,plain,
( ( sk2 != sk1 )
| ( totalorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[20677:[]]) ).
thf(8413,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk14 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8211,287]) ).
thf(8414,plain,
( ( strictorderP @ sk2 )
| ( rearsegP @ ( sk14 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[8413:[bind(A,$thf( sk14 @ sk2 ))]]) ).
thf(47045,plain,
! [A: $i] :
( ( ssItem @ sk5 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk22 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44838,356]) ).
thf(47046,plain,
( ( ssItem @ sk5 )
| ( frontsegP @ ( sk22 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[47045:[bind(A,$thf( sk22 @ sk1 ))]]) ).
thf(32089,plain,
! [A: $i] :
( ( ssList @ ( sk18 @ A ) )
| ( strictorderedP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,222]) ).
thf(32090,plain,
( ( ssList @ ( sk18 @ sk2 ) )
| ( strictorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[32089:[bind(A,$thf( sk2 ))]]) ).
thf(20,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( app @ A @ nil )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).
thf(180,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( app @ A @ nil )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(181,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ A @ nil )
= A ) ),
inference(cnf,[status(esa)],[180]) ).
thf(182,plain,
! [A: $i] :
( ( ( app @ A @ nil )
= A )
| ~ ( ssList @ A ) ),
inference(lifteq,[status(thm)],[181]) ).
thf(13634,plain,
! [A: $i] :
( ( ( app @ A @ nil )
= A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,182]) ).
thf(13635,plain,
( ( app @ sk1 @ nil )
= sk1 ),
inference(pattern_uni,[status(thm)],[13634:[bind(A,$thf( sk1 ))]]) ).
thf(47895,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( ssItem @ sk5 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[44945,579]) ).
thf(47896,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( ssItem @ sk5 ) ),
inference(pattern_uni,[status(thm)],[47895:[]]) ).
thf(44070,plain,
! [A: $i] :
( ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( tl @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[43928,182]) ).
thf(44071,plain,
( ( app @ ( tl @ sk2 ) @ nil )
= ( tl @ sk2 ) ),
inference(pattern_uni,[status(thm)],[44070:[bind(A,$thf( tl @ sk2 ))]]) ).
thf(30588,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk20 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30345,238]) ).
thf(30589,plain,
( ( strictorderedP @ sk2 )
| ( segmentP @ ( sk20 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[30588:[bind(A,$thf( sk20 @ sk2 ))]]) ).
thf(9391,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk12 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9251,119]) ).
thf(9392,plain,
( ( strictorderP @ sk1 )
| ( strictorderedP @ ( cons @ ( sk12 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[9391:[bind(A,$thf( sk12 @ sk1 ))]]) ).
thf(4735,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk9 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4648,238]) ).
thf(4736,plain,
( ( cyclefreeP @ sk2 )
| ( segmentP @ ( sk9 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[4735:[bind(A,$thf( sk9 @ sk2 ))]]) ).
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(471,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(250,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ ( app @ ( sk25 @ A ) @ ( cons @ ( sk23 @ A ) @ ( sk26 @ A ) ) ) @ ( cons @ ( sk24 @ A ) @ ( sk27 @ A ) ) )
= A )
| ( totalorderP @ A ) ),
inference(cnf,[status(esa)],[244]) ).
thf(256,plain,
! [A: $i] :
( ( ( app @ ( app @ ( sk25 @ A ) @ ( cons @ ( sk23 @ A ) @ ( sk26 @ A ) ) ) @ ( cons @ ( sk24 @ A ) @ ( sk27 @ A ) ) )
= A )
| ~ ( ssList @ A )
| ( totalorderP @ A ) ),
inference(lifteq,[status(thm)],[250]) ).
thf(65751,plain,
! [A: $i] :
( ~ ( lt @ A @ A )
| ( ( ssItem @ ( sk29 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[65689,213]) ).
thf(65752,plain,
~ ( lt @ ( sk29 @ sk2 ) @ ( sk29 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[65751:[bind(A,$thf( sk29 @ sk2 ))]]) ).
thf(1941,plain,
( ~ ( segmentP @ nil @ sk1 )
| ( neq @ sk2 @ nil )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1814,574]) ).
thf(1942,plain,
( ~ ( segmentP @ nil @ sk1 )
| ( neq @ sk2 @ nil ) ),
inference(pattern_uni,[status(thm)],[1941:[]]) ).
thf(218,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)],[214]) ).
thf(224,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)],[218]) ).
thf(225,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)],[224]) ).
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(476,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(13538,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk15 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9676,182]) ).
thf(13539,plain,
( ( strictorderP @ sk2 )
| ( ( app @ ( sk15 @ sk2 ) @ nil )
= ( sk15 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[13538:[bind(A,$thf( sk15 @ sk2 ))]]) ).
thf(47672,plain,
! [A: $i] :
( ( sk1 = nil )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( tl @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44945,238]) ).
thf(47673,plain,
( ( sk1 = nil )
| ( segmentP @ ( tl @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[47672:[bind(A,$thf( tl @ sk1 ))]]) ).
thf(28326,plain,
! [A: $i] :
( ( strictorderedP @ sk1 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk17 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[28045,227]) ).
thf(28327,plain,
( ( strictorderedP @ sk1 )
| ~ ( memberP @ nil @ ( sk17 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[28326:[bind(A,$thf( sk17 @ sk1 ))]]) ).
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(129,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(175,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( lt @ ( sk11 @ A ) @ ( sk12 @ A ) )
| ( strictorderP @ A ) ),
inference(cnf,[status(esa)],[167]) ).
thf(10865,plain,
! [A: $i] :
( ~ ( lt @ ( sk11 @ A ) @ ( sk12 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,175]) ).
thf(10866,plain,
( ~ ( lt @ ( sk11 @ sk1 ) @ ( sk12 @ sk1 ) )
| ( strictorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[10865:[bind(A,$thf( sk1 ))]]) ).
thf(9941,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk15 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9772,238]) ).
thf(9942,plain,
( ( strictorderP @ sk1 )
| ( segmentP @ ( sk15 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[9941:[bind(A,$thf( sk15 @ sk1 ))]]) ).
thf(603,plain,
( ~ ( neq @ sk2 @ nil )
| ( strictorderedP @ sk1 )
| ( ( cons @ sk39 @ nil )
!= ( cons @ sk5 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[510,597]) ).
thf(604,plain,
( ( strictorderedP @ sk1 )
| ~ ( neq @ sk2 @ nil )
| ( sk39 != sk5 )
| ( nil != nil ) ),
inference(simp,[status(thm)],[603]) ).
thf(605,plain,
( ( strictorderedP @ sk1 )
| ~ ( neq @ sk2 @ nil )
| ( sk39 != sk5 ) ),
inference(simp,[status(thm)],[604]) ).
thf(15866,plain,
( ( sk2 != sk1 )
| ( memberP @ sk2 @ sk5 )
| ( ( neq @ sk2 @ nil )
!= ( neq @ sk2 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[15620,509]) ).
thf(15867,plain,
( ( sk2 != sk1 )
| ( memberP @ sk2 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[15866:[]]) ).
thf(8672,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( totalorderedP @ sk1 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[693,8602]) ).
thf(8673,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( totalorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[8672:[]]) ).
thf(8454,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk14 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8295,238]) ).
thf(8455,plain,
( ( strictorderP @ sk1 )
| ( segmentP @ ( sk14 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[8454:[bind(A,$thf( sk14 @ sk1 ))]]) ).
thf(4447,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk7 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4362,119]) ).
thf(4448,plain,
( ( cyclefreeP @ sk2 )
| ( strictorderedP @ ( cons @ ( sk7 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[4447:[bind(A,$thf( sk7 @ sk2 ))]]) ).
thf(45074,plain,
( ( ssList @ ( sk22 @ sk1 ) )
| ~ ( lt @ sk5 @ sk5 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[43501,27463]) ).
thf(45075,plain,
( ( ssList @ ( sk22 @ sk1 ) )
| ~ ( lt @ sk5 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[45074:[]]) ).
thf(1995,plain,
( ~ ( segmentP @ nil @ sk1 )
| ( ( cons @ sk5 @ nil )
= sk1 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1814,581]) ).
thf(1996,plain,
( ~ ( segmentP @ nil @ sk1 )
| ( ( cons @ sk5 @ nil )
= sk1 ) ),
inference(pattern_uni,[status(thm)],[1995:[]]) ).
thf(8,axiom,
totalorderedP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax66) ).
thf(128,plain,
totalorderedP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(44625,plain,
( ( ssList @ ( sk22 @ sk1 ) )
| ( neq @ sk2 @ nil )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[43501,574]) ).
thf(44626,plain,
( ( ssList @ ( sk22 @ sk1 ) )
| ( neq @ sk2 @ nil ) ),
inference(pattern_uni,[status(thm)],[44625:[]]) ).
thf(7984,plain,
! [A: $i] :
( ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk39 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[372,191]) ).
thf(7985,plain,
totalorderedP @ ( cons @ sk39 @ nil ),
inference(pattern_uni,[status(thm)],[7984:[bind(A,$thf( sk39 ))]]) ).
thf(51904,plain,
! [A: $i] :
( ( ssList @ ( sk25 @ A ) )
| ( totalorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,249]) ).
thf(51905,plain,
( ( ssList @ ( sk25 @ sk2 ) )
| ( totalorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[51904:[bind(A,$thf( sk2 ))]]) ).
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(430,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(166,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( ssList @ ( cons @ B @ A ) ) ),
inference(cnf,[status(esa)],[165]) ).
thf(148,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)],[147]) ).
thf(4255,plain,
! [A: $i] :
( ( leq @ ( sk6 @ A ) @ ( sk7 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,154]) ).
thf(4256,plain,
( ( leq @ ( sk6 @ sk2 ) @ ( sk7 @ sk2 ) )
| ( cyclefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[4255:[bind(A,$thf( sk2 ))]]) ).
thf(41,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( cons @ B @ A )
!= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
thf(264,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( cons @ B @ A )
!= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
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(149,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(5094,plain,
! [A: $i] :
( ( leq @ ( sk7 @ A ) @ ( sk6 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,157]) ).
thf(5095,plain,
( ( leq @ ( sk7 @ sk2 ) @ ( sk6 @ sk2 ) )
| ( cyclefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[5094:[bind(A,$thf( sk2 ))]]) ).
thf(5978,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk10 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5815,287]) ).
thf(5979,plain,
( ( cyclefreeP @ sk2 )
| ( rearsegP @ ( sk10 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[5978:[bind(A,$thf( sk10 @ 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(375,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(13558,plain,
! [A: $i] :
( ( ( app @ A @ nil )
= A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,182]) ).
thf(13559,plain,
( ( app @ sk2 @ nil )
= sk2 ),
inference(pattern_uni,[status(thm)],[13558:[bind(A,$thf( sk2 ))]]) ).
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(423,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(28277,plain,
! [A: $i] :
( ( strictorderedP @ sk1 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk17 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[28045,191]) ).
thf(28278,plain,
( ( strictorderedP @ sk1 )
| ( totalorderedP @ ( cons @ ( sk17 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[28277:[bind(A,$thf( sk17 @ sk1 ))]]) ).
thf(47642,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( sk2 != sk1 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[44945,15684]) ).
thf(47643,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( sk2 != sk1 ) ),
inference(pattern_uni,[status(thm)],[47642:[]]) ).
thf(10460,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk13 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10298,238]) ).
thf(10461,plain,
( ( strictorderP @ sk2 )
| ( segmentP @ ( sk13 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[10460:[bind(A,$thf( sk13 @ sk2 ))]]) ).
thf(44621,plain,
! [A: $i] :
( ( sk1 = nil )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk22 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[43501,238]) ).
thf(44622,plain,
( ( sk1 = nil )
| ( segmentP @ ( sk22 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[44621:[bind(A,$thf( sk22 @ sk1 ))]]) ).
thf(4393,plain,
! [A: $i] :
( ( ssItem @ ( sk7 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,155]) ).
thf(4394,plain,
( ( ssItem @ ( sk7 @ sk1 ) )
| ( cyclefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[4393:[bind(A,$thf( sk1 ))]]) ).
thf(26018,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ~ ( neq @ A @ A )
| ( ( ssItem @ ( sk7 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4394,208]) ).
thf(26019,plain,
( ( cyclefreeP @ sk1 )
| ~ ( neq @ ( sk7 @ sk1 ) @ ( sk7 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[26018:[bind(A,$thf( sk7 @ sk1 ))]]) ).
thf(1225,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( ( cons @ sk5 @ nil )
= sk1 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[693,581]) ).
thf(1226,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( ( cons @ sk5 @ nil )
= sk1 ) ),
inference(pattern_uni,[status(thm)],[1225:[]]) ).
thf(4504,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk7 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4394,119]) ).
thf(4505,plain,
( ( cyclefreeP @ sk1 )
| ( strictorderedP @ ( cons @ ( sk7 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[4504:[bind(A,$thf( sk7 @ sk1 ))]]) ).
thf(1915,plain,
( ~ ( segmentP @ nil @ sk1 )
| ~ ( singletonP @ sk1 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1814,569]) ).
thf(1916,plain,
( ~ ( segmentP @ nil @ sk1 )
| ~ ( singletonP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1915:[]]) ).
thf(246,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssItem @ ( sk23 @ A ) )
| ( totalorderP @ A ) ),
inference(cnf,[status(esa)],[244]) ).
thf(48244,plain,
! [A: $i] :
( ( ssItem @ ( sk23 @ A ) )
| ( totalorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,246]) ).
thf(48245,plain,
( ( ssItem @ ( sk23 @ sk2 ) )
| ( totalorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[48244:[bind(A,$thf( sk2 ))]]) ).
thf(13562,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk14 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8211,182]) ).
thf(13563,plain,
( ( strictorderP @ sk2 )
| ( ( app @ ( sk14 @ sk2 ) @ nil )
= ( sk14 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[13562:[bind(A,$thf( sk14 @ sk2 ))]]) ).
thf(67,axiom,
strictorderP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax64) ).
thf(391,plain,
strictorderP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
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(445,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( tl @ ( cons @ B @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(5499,plain,
! [A: $i] :
( ( ssItem @ ( sk6 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,159]) ).
thf(5500,plain,
( ( ssItem @ ( sk6 @ sk2 ) )
| ( cyclefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[5499:[bind(A,$thf( sk2 ))]]) ).
thf(7982,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk6 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5500,191]) ).
thf(7983,plain,
( ( cyclefreeP @ sk2 )
| ( totalorderedP @ ( cons @ ( sk6 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[7982:[bind(A,$thf( sk6 @ sk2 ))]]) ).
thf(15469,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk15 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9772,189]) ).
thf(15470,plain,
( ( strictorderP @ sk1 )
| ( segmentP @ ( sk15 @ sk1 ) @ ( sk15 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[15469:[bind(A,$thf( sk15 @ sk1 ))]]) ).
thf(29934,plain,
! [A: $i] :
( ( strictorderedP @ sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk19 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29512,287]) ).
thf(29935,plain,
( ( strictorderedP @ sk1 )
| ( rearsegP @ ( sk19 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[29934:[bind(A,$thf( sk19 @ sk1 ))]]) ).
thf(30783,plain,
! [A: $i] :
( ( strictorderedP @ sk1 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk20 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30479,238]) ).
thf(30784,plain,
( ( strictorderedP @ sk1 )
| ( segmentP @ ( sk20 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[30783:[bind(A,$thf( sk20 @ sk1 ))]]) ).
thf(10094,plain,
( ~ ( segmentP @ nil @ sk38 )
| ( sk39 != nil )
| ( ( ssList @ sk38 )
!= ( ssList @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[106,4291]) ).
thf(10176,plain,
( ~ ( segmentP @ nil @ sk38 )
| ( sk39 != nil )
| ( sk38 != sk2 ) ),
inference(simp,[status(thm)],[10094]) ).
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(382,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(26085,plain,
( ( sk1 != nil )
| ( ( neq @ sk38 @ sk38 )
!= ( neq @ sk2 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[574,26031]) ).
thf(26122,plain,
( ( sk1 != nil )
| ( sk38 != sk2 )
| ( sk38 != nil ) ),
inference(simp,[status(thm)],[26085]) ).
thf(31044,plain,
( ~ ( segmentP @ nil @ sk1 )
| ( sk38 != sk2 )
| ( sk38 != nil )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1814,26122]) ).
thf(31045,plain,
( ~ ( segmentP @ nil @ sk1 )
| ( sk38 != sk2 )
| ( sk38 != nil ) ),
inference(pattern_uni,[status(thm)],[31044:[]]) ).
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(144,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(233,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( frontsegP @ A @ B )
| ( ( app @ B @ ( sk21 @ B @ A ) )
= A ) ),
inference(cnf,[status(esa)],[230]) ).
thf(236,plain,
! [B: $i,A: $i] :
( ( ( app @ B @ ( sk21 @ B @ A ) )
= A )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( frontsegP @ A @ B ) ),
inference(lifteq,[status(thm)],[233]) ).
thf(186,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)],[185]) ).
thf(187,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)],[186]) ).
thf(45028,plain,
! [A: $i] :
( ( sk1 = nil )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk22 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[43501,287]) ).
thf(45029,plain,
( ( sk1 = nil )
| ( rearsegP @ ( sk22 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[45028:[bind(A,$thf( sk22 @ sk1 ))]]) ).
thf(72,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( leq @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax31) ).
thf(406,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( leq @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(15624,plain,
( ( sk38 != nil )
| ( sk39 != sk1 )
| ( ( segmentP @ sk1 @ sk1 )
!= ( segmentP @ nil @ sk39 ) ) ),
inference(paramod_ordered,[status(thm)],[15503,5383]) ).
thf(15689,plain,
( ( sk38 != nil )
| ( sk39 != sk1 )
| ( sk1 != nil )
| ( sk39 != sk1 ) ),
inference(simp,[status(thm)],[15624]) ).
thf(15700,plain,
( ( sk38 != nil )
| ( sk39 != sk1 )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[15689]) ).
thf(47350,plain,
! [A: $i] :
( ~ ( singletonP @ sk1 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk22 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44796,356]) ).
thf(47351,plain,
( ~ ( singletonP @ sk1 )
| ( frontsegP @ ( sk22 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[47350:[bind(A,$thf( sk22 @ sk1 ))]]) ).
thf(27452,plain,
! [A: $i] :
( ~ ( lt @ A @ A )
| ( ( ssItem @ sk39 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[372,213]) ).
thf(27453,plain,
~ ( lt @ sk39 @ sk39 ),
inference(pattern_uni,[status(thm)],[27452:[bind(A,$thf( sk39 ))]]) ).
thf(6612,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk9 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4705,356]) ).
thf(6613,plain,
( ( cyclefreeP @ sk1 )
| ( frontsegP @ ( sk9 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[6612:[bind(A,$thf( sk9 @ sk1 ))]]) ).
thf(29650,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk19 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29382,356]) ).
thf(29651,plain,
( ( strictorderedP @ sk2 )
| ( frontsegP @ ( sk19 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[29650:[bind(A,$thf( sk19 @ sk2 ))]]) ).
thf(598,plain,
! [A: $i] :
( ~ ( neq @ sk2 @ nil )
| ~ ( ssItem @ A )
| ( strictorderedP @ sk1 )
| ( ( cons @ sk5 @ nil )
!= ( cons @ A @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[510,119]) ).
thf(599,plain,
( ~ ( neq @ sk2 @ nil )
| ~ ( ssItem @ sk5 )
| ( strictorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[598:[bind(A,$thf( sk5 ))]]) ).
thf(4508,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk7 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4394,227]) ).
thf(4509,plain,
( ( cyclefreeP @ sk1 )
| ~ ( memberP @ nil @ ( sk7 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[4508:[bind(A,$thf( sk7 @ sk1 ))]]) ).
thf(48363,plain,
! [A: $i] :
( ( ssItem @ ( sk23 @ A ) )
| ( totalorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,246]) ).
thf(48364,plain,
( ( ssItem @ ( sk23 @ sk1 ) )
| ( totalorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[48363:[bind(A,$thf( sk1 ))]]) ).
thf(630,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk8 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[619,238]) ).
thf(631,plain,
( ( cyclefreeP @ sk1 )
| ( segmentP @ ( sk8 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[630:[bind(A,$thf( sk8 @ sk1 ))]]) ).
thf(12,axiom,
cyclefreeP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax60) ).
thf(140,plain,
cyclefreeP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
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(483,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(8528,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk14 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8295,287]) ).
thf(8529,plain,
( ( strictorderP @ sk1 )
| ( rearsegP @ ( sk14 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[8528:[bind(A,$thf( sk14 @ sk1 ))]]) ).
thf(29733,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk19 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29382,287]) ).
thf(29734,plain,
( ( strictorderedP @ sk2 )
| ( rearsegP @ ( sk19 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[29733:[bind(A,$thf( sk19 @ sk2 ))]]) ).
thf(44535,plain,
( ( ssList @ ( sk22 @ sk1 ) )
| ( strictorderedP @ sk1 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[43501,1260]) ).
thf(44536,plain,
( ( ssList @ ( sk22 @ sk1 ) )
| ( strictorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[44535:[]]) ).
thf(46224,plain,
! [A: $i] :
( ( strictorderedP @ sk1 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk22 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44536,356]) ).
thf(46225,plain,
( ( strictorderedP @ sk1 )
| ( frontsegP @ ( sk22 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[46224:[bind(A,$thf( sk22 @ sk1 ))]]) ).
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(330,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(9326,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk12 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9194,227]) ).
thf(9327,plain,
( ( strictorderP @ sk2 )
| ~ ( memberP @ nil @ ( sk12 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[9326:[bind(A,$thf( sk12 @ sk2 ))]]) ).
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(494,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(47464,plain,
! [A: $i] :
( ~ ( singletonP @ sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk22 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44796,287]) ).
thf(47465,plain,
( ~ ( singletonP @ sk1 )
| ( rearsegP @ ( sk22 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[47464:[bind(A,$thf( sk22 @ sk1 ))]]) ).
thf(4451,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk7 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4362,227]) ).
thf(4452,plain,
( ( cyclefreeP @ sk2 )
| ~ ( memberP @ nil @ ( sk7 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[4451:[bind(A,$thf( sk7 @ sk2 ))]]) ).
thf(28611,plain,
! [A: $i] :
( ( ssItem @ ( sk16 @ A ) )
| ( strictorderedP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,216]) ).
thf(28612,plain,
( ( ssItem @ ( sk16 @ sk2 ) )
| ( strictorderedP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[28611:[bind(A,$thf( sk2 ))]]) ).
thf(3976,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,287]) ).
thf(3977,plain,
rearsegP @ sk2 @ nil,
inference(pattern_uni,[status(thm)],[3976:[bind(A,$thf( sk2 ))]]) ).
thf(28,axiom,
~ ( singletonP @ nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).
thf(198,plain,
~ ( singletonP @ nil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(52114,plain,
! [A: $i] :
( ( ssList @ ( sk25 @ A ) )
| ( totalorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,249]) ).
thf(52115,plain,
( ( ssList @ ( sk25 @ sk1 ) )
| ( totalorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[52114:[bind(A,$thf( sk1 ))]]) ).
thf(84,axiom,
equalelemsP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax74) ).
thf(462,plain,
equalelemsP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(8006,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk7 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4394,191]) ).
thf(8007,plain,
( ( cyclefreeP @ sk1 )
| ( totalorderedP @ ( cons @ ( sk7 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[8006:[bind(A,$thf( sk7 @ sk1 ))]]) ).
thf(15431,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk13 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10399,189]) ).
thf(15432,plain,
( ( strictorderP @ sk1 )
| ( segmentP @ ( sk13 @ sk1 ) @ ( sk13 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[15431:[bind(A,$thf( sk13 @ sk1 ))]]) ).
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(267,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(130,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)],[129]) ).
thf(66514,plain,
( ( ssItem @ ( sk29 @ sk1 ) )
| ( strictorderedP @ sk1 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[65209,1260]) ).
thf(66515,plain,
( ( ssItem @ ( sk29 @ sk1 ) )
| ( strictorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[66514:[]]) ).
thf(65793,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk29 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[65689,227]) ).
thf(65794,plain,
~ ( memberP @ nil @ ( sk29 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[65793:[bind(A,$thf( sk29 @ sk2 ))]]) ).
thf(217,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ ( app @ ( sk18 @ A ) @ ( cons @ ( sk16 @ A ) @ ( sk19 @ A ) ) ) @ ( cons @ ( sk17 @ A ) @ ( sk20 @ A ) ) )
= A )
| ( strictorderedP @ A ) ),
inference(cnf,[status(esa)],[214]) ).
thf(223,plain,
! [A: $i] :
( ( ( app @ ( app @ ( sk18 @ A ) @ ( cons @ ( sk16 @ A ) @ ( sk19 @ A ) ) ) @ ( cons @ ( sk17 @ A ) @ ( sk20 @ A ) ) )
= A )
| ~ ( ssList @ A )
| ( strictorderedP @ A ) ),
inference(lifteq,[status(thm)],[217]) ).
thf(26026,plain,
! [A: $i] :
( ( sk2 != sk1 )
| ~ ( neq @ A @ A )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[15865,208]) ).
thf(26027,plain,
( ( sk2 != sk1 )
| ~ ( neq @ sk5 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[26026:[bind(A,$thf( sk5 ))]]) ).
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(490,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(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(426,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(161,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ ( app @ ( sk8 @ A ) @ ( cons @ ( sk6 @ A ) @ ( sk9 @ A ) ) ) @ ( cons @ ( sk7 @ A ) @ ( sk10 @ A ) ) )
= A )
| ( cyclefreeP @ A ) ),
inference(cnf,[status(esa)],[152]) ).
thf(162,plain,
! [A: $i] :
( ( ( app @ ( app @ ( sk8 @ A ) @ ( cons @ ( sk6 @ A ) @ ( sk9 @ A ) ) ) @ ( cons @ ( sk7 @ A ) @ ( sk10 @ A ) ) )
= A )
| ~ ( ssList @ A )
| ( cyclefreeP @ A ) ),
inference(lifteq,[status(thm)],[161]) ).
thf(10813,plain,
! [A: $i] :
( ~ ( lt @ ( sk11 @ A ) @ ( sk12 @ A ) )
| ( strictorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,175]) ).
thf(10814,plain,
( ~ ( lt @ ( sk11 @ sk2 ) @ ( sk12 @ sk2 ) )
| ( strictorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[10813:[bind(A,$thf( sk2 ))]]) ).
thf(44716,plain,
( ( ssList @ ( sk22 @ sk1 ) )
| ~ ( memberP @ nil @ sk5 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[43501,583]) ).
thf(44717,plain,
( ( ssList @ ( sk22 @ sk1 ) )
| ~ ( memberP @ nil @ sk5 ) ),
inference(pattern_uni,[status(thm)],[44716:[]]) ).
thf(6563,plain,
! [A: $i] :
( ( frontsegP @ A @ nil )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,356]) ).
thf(6564,plain,
frontsegP @ sk2 @ nil,
inference(pattern_uni,[status(thm)],[6563:[bind(A,$thf( sk2 ))]]) ).
thf(193,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( leq @ A @ B )
| ( A = B )
| ( lt @ A @ B ) ),
inference(cnf,[status(esa)],[192]) ).
thf(194,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( leq @ A @ B )
| ( lt @ A @ B ) ),
inference(lifteq,[status(thm)],[193]) ).
thf(26568,plain,
! [A: $i] :
( ( ( app @ nil @ A )
= A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,211]) ).
thf(26569,plain,
( ( app @ nil @ sk1 )
= sk1 ),
inference(pattern_uni,[status(thm)],[26568:[bind(A,$thf( sk1 ))]]) ).
thf(251,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( totalorderP @ 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)],[244]) ).
thf(254,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 )
| ~ ( totalorderP @ A )
| ~ ( ssItem @ B )
| ~ ( ssItem @ C )
| ~ ( ssList @ D )
| ~ ( ssList @ E )
| ~ ( ssList @ F )
| ( leq @ B @ C )
| ( leq @ C @ B ) ),
inference(lifteq,[status(thm)],[251]) ).
thf(255,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( ssList @ ( app @ ( app @ C @ ( cons @ A @ D ) ) @ ( cons @ B @ E ) ) )
| ~ ( totalorderP @ ( 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)],[254]) ).
thf(65748,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssItem @ ( sk29 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[65689,208]) ).
thf(65749,plain,
~ ( neq @ ( sk29 @ sk2 ) @ ( sk29 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[65748:[bind(A,$thf( sk29 @ sk2 ))]]) ).
thf(32466,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk18 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[32090,287]) ).
thf(32467,plain,
( ( strictorderedP @ sk2 )
| ( rearsegP @ ( sk18 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[32466:[bind(A,$thf( sk18 @ sk2 ))]]) ).
thf(552,plain,
! [A: $i] :
( ( segmentP @ A @ nil )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,238]) ).
thf(553,plain,
segmentP @ sk1 @ nil,
inference(pattern_uni,[status(thm)],[552:[bind(A,$thf( sk1 ))]]) ).
thf(47582,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( strictorderedP @ sk1 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[44945,1260]) ).
thf(47583,plain,
( ( ssList @ ( tl @ sk1 ) )
| ( strictorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[47582:[]]) ).
thf(9021,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk11 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8826,119]) ).
thf(9022,plain,
( ( strictorderP @ sk1 )
| ( strictorderedP @ ( cons @ ( sk11 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[9021:[bind(A,$thf( sk11 @ sk1 ))]]) ).
thf(28142,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk17 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27958,191]) ).
thf(28143,plain,
( ( strictorderedP @ sk2 )
| ( totalorderedP @ ( cons @ ( sk17 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[28142:[bind(A,$thf( sk17 @ sk2 ))]]) ).
thf(5312,plain,
( ~ ( segmentP @ nil @ sk39 )
| ( sk38 != nil )
| ( ( ssList @ sk39 )
!= ( ssList @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[106,1716]) ).
thf(5388,plain,
( ~ ( segmentP @ nil @ sk39 )
| ( sk38 != nil )
| ( sk39 != sk2 ) ),
inference(simp,[status(thm)],[5312]) ).
thf(26057,plain,
( ( sk2 != sk1 )
| ( ( neq @ sk39 @ sk39 )
!= ( neq @ sk2 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[15620,25999]) ).
thf(26078,plain,
( ( sk2 != sk1 )
| ( sk39 != sk2 )
| ( sk39 != nil ) ),
inference(simp,[status(thm)],[26057]) ).
thf(8363,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk14 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8211,356]) ).
thf(8364,plain,
( ( strictorderP @ sk2 )
| ( frontsegP @ ( sk14 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[8363:[bind(A,$thf( sk14 @ sk2 ))]]) ).
thf(4359,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( ssItem @ ( sk7 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ ( sk8 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[619,155]) ).
thf(4360,plain,
( ( cyclefreeP @ sk1 )
| ( ssItem @ ( sk7 @ ( sk8 @ sk1 ) ) )
| ( cyclefreeP @ ( sk8 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[4359:[bind(A,$thf( sk8 @ sk1 ))]]) ).
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(295,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ssItem @ B )
& ( ( hd @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(47177,plain,
! [A: $i] :
( ( ssItem @ sk5 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk22 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44838,287]) ).
thf(47178,plain,
( ( ssItem @ sk5 )
| ( rearsegP @ ( sk22 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[47177:[bind(A,$thf( sk22 @ sk1 ))]]) ).
thf(260,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( nil = A )
| ( ssList @ ( sk28 @ A ) ) ),
inference(cnf,[status(esa)],[257]) ).
thf(263,plain,
! [A: $i] :
( ( nil = A )
| ~ ( ssList @ A )
| ( ssList @ ( sk28 @ A ) ) ),
inference(lifteq,[status(thm)],[260]) ).
thf(30822,plain,
! [A: $i] :
( ( strictorderedP @ sk1 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk20 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30479,356]) ).
thf(30823,plain,
( ( strictorderedP @ sk1 )
| ( frontsegP @ ( sk20 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[30822:[bind(A,$thf( sk20 @ sk1 ))]]) ).
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(310,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(31036,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( sk38 != sk2 )
| ( sk38 != nil )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[693,26122]) ).
thf(31037,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( sk38 != sk2 )
| ( sk38 != nil ) ),
inference(pattern_uni,[status(thm)],[31036:[]]) ).
thf(45520,plain,
! [A: $i] :
( ( ssList @ ( sk27 @ A ) )
| ( totalorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,245]) ).
thf(45521,plain,
( ( ssList @ ( sk27 @ sk1 ) )
| ( totalorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[45520:[bind(A,$thf( sk1 ))]]) ).
thf(199,plain,
~ ( singletonP @ nil ),
inference(polarity_switch,[status(thm)],[198]) ).
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(502,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(32545,plain,
! [A: $i] :
( ( strictorderedP @ sk1 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk18 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[32232,238]) ).
thf(32546,plain,
( ( strictorderedP @ sk1 )
| ( segmentP @ ( sk18 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[32545:[bind(A,$thf( sk18 @ sk1 ))]]) ).
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(126,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(127,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( gt @ A @ B )
| ~ ( gt @ B @ A ) ),
inference(cnf,[status(esa)],[126]) ).
thf(66570,plain,
( ( ssItem @ ( sk29 @ sk1 ) )
| ( sk2 != sk1 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[65209,15684]) ).
thf(66571,plain,
( ( ssItem @ ( sk29 @ sk1 ) )
| ( sk2 != sk1 ) ),
inference(pattern_uni,[status(thm)],[66570:[]]) ).
thf(170,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ( app @ ( app @ ( sk13 @ A ) @ ( cons @ ( sk11 @ A ) @ ( sk14 @ A ) ) ) @ ( cons @ ( sk12 @ A ) @ ( sk15 @ A ) ) )
= A )
| ( strictorderP @ A ) ),
inference(cnf,[status(esa)],[167]) ).
thf(177,plain,
! [A: $i] :
( ( ( app @ ( app @ ( sk13 @ A ) @ ( cons @ ( sk11 @ A ) @ ( sk14 @ A ) ) ) @ ( cons @ ( sk12 @ A ) @ ( sk15 @ A ) ) )
= A )
| ~ ( ssList @ A )
| ( strictorderP @ A ) ),
inference(lifteq,[status(thm)],[170]) ).
thf(4092,plain,
( ~ ( frontsegP @ nil @ sk39 )
| ( sk38 != nil )
| ( ( ssList @ sk39 )
!= ( ssList @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[106,827]) ).
thf(4145,plain,
( ~ ( frontsegP @ nil @ sk39 )
| ( sk38 != nil )
| ( sk39 != sk2 ) ),
inference(simp,[status(thm)],[4092]) ).
thf(85,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( geq @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax89) ).
thf(463,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( geq @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(43959,plain,
! [A: $i] :
( ( segmentP @ A @ nil )
| ( ( ssList @ ( tl @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[43928,238]) ).
thf(43960,plain,
segmentP @ ( tl @ sk2 ) @ nil,
inference(pattern_uni,[status(thm)],[43959:[bind(A,$thf( tl @ sk2 ))]]) ).
thf(906,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( memberP @ sk2 @ sk5 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[693,577]) ).
thf(907,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( memberP @ sk2 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[906:[]]) ).
thf(30065,plain,
( ~ ( segmentP @ nil @ sk1 )
| ( sk39 != sk2 )
| ( sk39 != nil )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1814,26079]) ).
thf(30066,plain,
( ~ ( segmentP @ nil @ sk1 )
| ( sk39 != sk2 )
| ( sk39 != nil ) ),
inference(pattern_uni,[status(thm)],[30065:[]]) ).
thf(43941,plain,
! [A: $i] :
( ( segmentP @ A @ A )
| ( ( ssList @ ( tl @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[43928,189]) ).
thf(43942,plain,
segmentP @ ( tl @ sk2 ) @ ( tl @ sk2 ),
inference(pattern_uni,[status(thm)],[43941:[bind(A,$thf( tl @ sk2 ))]]) ).
thf(45222,plain,
( ( segmentP @ ( tl @ sk2 ) @ ( tl @ sk2 ) )
!= ( segmentP @ nil @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[43942,1845]) ).
thf(45268,plain,
( ( ( tl @ sk2 )
!= nil )
| ( ( tl @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[45222]) ).
thf(1271,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( cyclefreeP @ ( sk8 @ sk1 ) )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk8 @ ( sk8 @ sk1 ) ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[629,238]) ).
thf(1272,plain,
( ( cyclefreeP @ sk1 )
| ( cyclefreeP @ ( sk8 @ sk1 ) )
| ( segmentP @ ( sk8 @ ( sk8 @ sk1 ) ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1271:[bind(A,$thf( sk8 @ ( sk8 @ sk1 ) ))]]) ).
thf(5595,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk6 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5500,119]) ).
thf(5596,plain,
( ( cyclefreeP @ sk2 )
| ( strictorderedP @ ( cons @ ( sk6 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[5595:[bind(A,$thf( sk6 @ sk2 ))]]) ).
thf(142,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( frontsegP @ A @ B )
| ~ ( frontsegP @ B @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[141]) ).
thf(143,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( frontsegP @ A @ B )
| ~ ( frontsegP @ B @ A ) ),
inference(lifteq,[status(thm)],[142]) ).
thf(32383,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk18 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[32090,356]) ).
thf(32384,plain,
( ( strictorderedP @ sk2 )
| ( frontsegP @ ( sk18 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[32383:[bind(A,$thf( sk18 @ sk2 ))]]) ).
thf(46493,plain,
! [A: $i] :
( ( sk2 != sk1 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk22 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44592,356]) ).
thf(46494,plain,
( ( sk2 != sk1 )
| ( frontsegP @ ( sk22 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[46493:[bind(A,$thf( sk22 @ sk1 ))]]) ).
thf(21346,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( sk38 != nil )
| ( sk39 != sk1 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[693,15700]) ).
thf(21347,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( sk38 != nil )
| ( sk39 != sk1 ) ),
inference(pattern_uni,[status(thm)],[21346:[]]) ).
thf(13544,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk10 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5883,182]) ).
thf(13545,plain,
( ( cyclefreeP @ sk1 )
| ( ( app @ ( sk10 @ sk1 ) @ nil )
= ( sk10 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[13544:[bind(A,$thf( sk10 @ sk1 ))]]) ).
thf(4135,plain,
( ~ ( frontsegP @ nil @ sk39 )
| ( sk38 != nil )
| ( ( ssList @ sk39 )
!= ( ssList @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[107,827]) ).
thf(4143,plain,
( ~ ( frontsegP @ nil @ sk39 )
| ( sk38 != nil )
| ( sk39 != sk1 ) ),
inference(simp,[status(thm)],[4135]) ).
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(386,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(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(465,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(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(450,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(8956,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk11 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8769,227]) ).
thf(8957,plain,
( ( strictorderP @ sk2 )
| ~ ( memberP @ nil @ ( sk11 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[8956:[bind(A,$thf( sk11 @ sk2 ))]]) ).
thf(10577,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk13 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10399,238]) ).
thf(10578,plain,
( ( strictorderP @ sk1 )
| ( segmentP @ ( sk13 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[10577:[bind(A,$thf( sk13 @ sk1 ))]]) ).
thf(8680,plain,
( ~ ( segmentP @ nil @ sk1 )
| ( totalorderedP @ sk1 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1814,8602]) ).
thf(8681,plain,
( ~ ( segmentP @ nil @ sk1 )
| ( totalorderedP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[8680:[]]) ).
thf(26032,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ~ ( neq @ A @ A )
| ( ( ssItem @ ( sk6 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5500,208]) ).
thf(26033,plain,
( ( cyclefreeP @ sk2 )
| ~ ( neq @ ( sk6 @ sk2 ) @ ( sk6 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[26032:[bind(A,$thf( sk6 @ sk2 ))]]) ).
thf(1965,plain,
( ~ ( segmentP @ nil @ sk1 )
| ( memberP @ sk2 @ sk5 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1814,577]) ).
thf(1966,plain,
( ~ ( segmentP @ nil @ sk1 )
| ( memberP @ sk2 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[1965:[]]) ).
thf(902,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( neq @ sk2 @ nil )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[693,574]) ).
thf(903,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( neq @ sk2 @ nil ) ),
inference(pattern_uni,[status(thm)],[902:[]]) ).
thf(13548,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk8 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[619,182]) ).
thf(13549,plain,
( ( cyclefreeP @ sk1 )
| ( ( app @ ( sk8 @ sk1 ) @ nil )
= ( sk8 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[13548:[bind(A,$thf( sk8 @ sk1 ))]]) ).
thf(10478,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk13 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10298,356]) ).
thf(10479,plain,
( ( strictorderP @ sk2 )
| ( frontsegP @ ( sk13 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[10478:[bind(A,$thf( sk13 @ sk2 ))]]) ).
thf(47293,plain,
! [A: $i] :
( ~ ( singletonP @ sk1 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk22 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44796,238]) ).
thf(47294,plain,
( ~ ( singletonP @ sk1 )
| ( segmentP @ ( sk22 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[47293:[bind(A,$thf( sk22 @ sk1 ))]]) ).
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(351,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(10658,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk13 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10399,287]) ).
thf(10659,plain,
( ( strictorderP @ sk1 )
| ( rearsegP @ ( sk13 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[10658:[bind(A,$thf( sk13 @ sk1 ))]]) ).
thf(46339,plain,
! [A: $i] :
( ( strictorderedP @ sk1 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk22 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44536,287]) ).
thf(46340,plain,
( ( strictorderedP @ sk1 )
| ( rearsegP @ ( sk22 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[46339:[bind(A,$thf( sk22 @ sk1 ))]]) ).
thf(21294,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( sk39 != nil )
| ( sk38 != sk1 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[693,15699]) ).
thf(21295,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( sk39 != nil )
| ( sk38 != sk1 ) ),
inference(pattern_uni,[status(thm)],[21294:[]]) ).
thf(15475,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk9 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4648,189]) ).
thf(15476,plain,
( ( cyclefreeP @ sk2 )
| ( segmentP @ ( sk9 @ sk2 ) @ ( sk9 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[15475:[bind(A,$thf( sk9 @ sk2 ))]]) ).
thf(5599,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk6 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5500,227]) ).
thf(5600,plain,
( ( cyclefreeP @ sk2 )
| ~ ( memberP @ nil @ ( sk6 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[5599:[bind(A,$thf( sk6 @ sk2 ))]]) ).
thf(26022,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ~ ( neq @ A @ A )
| ( ( ssItem @ ( sk12 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9194,208]) ).
thf(26023,plain,
( ( strictorderP @ sk2 )
| ~ ( neq @ ( sk12 @ sk2 ) @ ( sk12 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[26022:[bind(A,$thf( sk12 @ sk2 ))]]) ).
thf(47853,plain,
( ( ssList @ ( tl @ sk1 ) )
| ~ ( singletonP @ sk1 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[44945,569]) ).
thf(47854,plain,
( ( ssList @ ( tl @ sk1 ) )
| ~ ( singletonP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[47853:[]]) ).
thf(26464,plain,
! [A: $i] :
( ( ( app @ nil @ A )
= A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,211]) ).
thf(26465,plain,
( ( app @ nil @ sk2 )
= sk2 ),
inference(pattern_uni,[status(thm)],[26464:[bind(A,$thf( sk2 ))]]) ).
thf(91,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( rearsegP @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax49) ).
thf(478,plain,
! [A: $i] :
( ( ssList @ A )
=> ( rearsegP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
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(290,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(8996,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk11 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8826,191]) ).
thf(8997,plain,
( ( strictorderP @ sk1 )
| ( totalorderedP @ ( cons @ ( sk11 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[8996:[bind(A,$thf( sk11 @ sk1 ))]]) ).
thf(231,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( ( app @ B @ C )
!= A )
| ( frontsegP @ A @ B ) ),
inference(cnf,[status(esa)],[230]) ).
thf(234,plain,
! [C: $i,B: $i,A: $i] :
( ( ( app @ B @ C )
!= A )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( frontsegP @ A @ B ) ),
inference(lifteq,[status(thm)],[231]) ).
thf(235,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ ( app @ A @ B ) )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( frontsegP @ ( app @ A @ B ) @ A ) ),
inference(simp,[status(thm)],[234]) ).
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(433,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(9961,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk15 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9772,356]) ).
thf(9962,plain,
( ( strictorderP @ sk1 )
| ( frontsegP @ ( sk15 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[9961:[bind(A,$thf( sk15 @ sk1 ))]]) ).
thf(32346,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk18 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[32090,238]) ).
thf(32347,plain,
( ( strictorderedP @ sk2 )
| ( segmentP @ ( sk18 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[32346:[bind(A,$thf( sk18 @ sk2 ))]]) ).
thf(29847,plain,
! [A: $i] :
( ( strictorderedP @ sk1 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk19 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29512,356]) ).
thf(29848,plain,
( ( strictorderedP @ sk1 )
| ( frontsegP @ ( sk19 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[29847:[bind(A,$thf( sk19 @ sk1 ))]]) ).
thf(10599,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk13 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10399,356]) ).
thf(10600,plain,
( ( strictorderP @ sk1 )
| ( frontsegP @ ( sk13 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[10599:[bind(A,$thf( sk13 @ sk1 ))]]) ).
thf(8952,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk11 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8769,119]) ).
thf(8953,plain,
( ( strictorderP @ sk2 )
| ( strictorderedP @ ( cons @ ( sk11 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[8952:[bind(A,$thf( sk11 @ sk2 ))]]) ).
thf(28796,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk16 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[28612,191]) ).
thf(28797,plain,
( ( strictorderedP @ sk2 )
| ( totalorderedP @ ( cons @ ( sk16 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[28796:[bind(A,$thf( sk16 @ sk2 ))]]) ).
thf(419,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( nil != A )
| ( rearsegP @ nil @ A ) ),
inference(cnf,[status(esa)],[417]) ).
thf(421,plain,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( rearsegP @ nil @ A ) ),
inference(lifteq,[status(thm)],[419]) ).
thf(422,plain,
( ~ ( ssList @ nil )
| ( rearsegP @ nil @ nil ) ),
inference(simp,[status(thm)],[421]) ).
thf(548,plain,
( ~ $true
| ( rearsegP @ nil @ nil ) ),
inference(rewrite,[status(thm)],[422,329]) ).
thf(549,plain,
rearsegP @ nil @ nil,
inference(simp,[status(thm)],[548]) ).
thf(150,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)],[149]) ).
thf(151,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)],[150]) ).
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(300,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(4815,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk9 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4705,238]) ).
thf(4816,plain,
( ( cyclefreeP @ sk1 )
| ( segmentP @ ( sk9 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[4815:[bind(A,$thf( sk9 @ sk1 ))]]) ).
thf(37344,plain,
! [A: $i] :
( ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk21 @ nil @ nil ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[37192,182]) ).
thf(37345,plain,
( ( app @ ( sk21 @ nil @ nil ) @ nil )
= ( sk21 @ nil @ nil ) ),
inference(pattern_uni,[status(thm)],[37344:[bind(A,$thf( sk21 @ nil @ nil ))]]) ).
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(410,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(145,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssItem @ B )
| ( ( cons @ B @ A )
= ( app @ ( cons @ B @ nil ) @ A ) ) ),
inference(cnf,[status(esa)],[144]) ).
thf(146,plain,
! [B: $i,A: $i] :
( ( ( app @ ( cons @ B @ nil ) @ A )
= ( cons @ B @ A ) )
| ~ ( ssList @ A )
| ~ ( ssItem @ B ) ),
inference(lifteq,[status(thm)],[145]) ).
thf(3986,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( rearsegP @ A @ nil )
| ( ( ssList @ ( sk8 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[621,287]) ).
thf(3987,plain,
( ( cyclefreeP @ sk2 )
| ( rearsegP @ ( sk8 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[3986:[bind(A,$thf( sk8 @ sk2 ))]]) ).
thf(15460,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk10 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5815,189]) ).
thf(15461,plain,
( ( cyclefreeP @ sk2 )
| ( segmentP @ ( sk10 @ sk2 ) @ ( sk10 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[15460:[bind(A,$thf( sk10 @ sk2 ))]]) ).
thf(3996,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,287]) ).
thf(3997,plain,
rearsegP @ sk1 @ nil,
inference(pattern_uni,[status(thm)],[3996:[bind(A,$thf( sk1 ))]]) ).
thf(1247,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( strictorderedP @ ( cons @ sk5 @ nil ) )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[693,593]) ).
thf(1248,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ( strictorderedP @ ( cons @ sk5 @ nil ) ) ),
inference(pattern_uni,[status(thm)],[1247:[]]) ).
thf(28845,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ~ ( memberP @ nil @ A )
| ( ( ssItem @ ( sk16 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[28612,227]) ).
thf(28846,plain,
( ( strictorderedP @ sk2 )
| ~ ( memberP @ nil @ ( sk16 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[28845:[bind(A,$thf( sk16 @ sk2 ))]]) ).
thf(46438,plain,
! [A: $i] :
( ( sk2 != sk1 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk22 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44592,238]) ).
thf(46439,plain,
( ( sk2 != sk1 )
| ( segmentP @ ( sk22 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[46438:[bind(A,$thf( sk22 @ sk1 ))]]) ).
thf(6557,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk10 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5883,356]) ).
thf(6558,plain,
( ( cyclefreeP @ sk1 )
| ( frontsegP @ ( sk10 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[6557:[bind(A,$thf( sk10 @ sk1 ))]]) ).
thf(15492,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk14 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8295,189]) ).
thf(15493,plain,
( ( strictorderP @ sk1 )
| ( segmentP @ ( sk14 @ sk1 ) @ ( sk14 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[15492:[bind(A,$thf( sk14 @ sk1 ))]]) ).
thf(634,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk8 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[621,238]) ).
thf(635,plain,
( ( cyclefreeP @ sk2 )
| ( segmentP @ ( sk8 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[634:[bind(A,$thf( sk8 @ sk2 ))]]) ).
thf(44963,plain,
( ( ssList @ ( sk22 @ sk1 ) )
| ~ ( neq @ sk5 @ sk5 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[43501,26006]) ).
thf(44964,plain,
( ( ssList @ ( sk22 @ sk1 ) )
| ~ ( neq @ sk5 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[44963:[]]) ).
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(474,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(6589,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk8 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[621,356]) ).
thf(6590,plain,
( ( cyclefreeP @ sk2 )
| ( frontsegP @ ( sk8 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[6589:[bind(A,$thf( sk8 @ sk2 ))]]) ).
thf(44758,plain,
! [A: $i] :
( ( sk1 = nil )
| ( frontsegP @ A @ nil )
| ( ( ssList @ ( sk22 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[43501,356]) ).
thf(44759,plain,
( ( sk1 = nil )
| ( frontsegP @ ( sk22 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[44758:[bind(A,$thf( sk22 @ sk1 ))]]) ).
thf(44,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ssList @ ( tl @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).
thf(283,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ssList @ ( tl @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(69,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( cyclefreeP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax59) ).
thf(395,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( cyclefreeP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(9366,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk12 @ sk1 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9251,191]) ).
thf(9367,plain,
( ( strictorderP @ sk1 )
| ( totalorderedP @ ( cons @ ( sk12 @ sk1 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[9366:[bind(A,$thf( sk12 @ sk1 ))]]) ).
thf(28841,plain,
! [A: $i] :
( ( strictorderedP @ sk2 )
| ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk16 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[28612,119]) ).
thf(28842,plain,
( ( strictorderedP @ sk2 )
| ( strictorderedP @ ( cons @ ( sk16 @ sk2 ) @ nil ) ) ),
inference(pattern_uni,[status(thm)],[28841:[bind(A,$thf( sk16 @ sk2 ))]]) ).
thf(44683,plain,
( ( ssList @ ( sk22 @ sk1 ) )
| ( segmentP @ nil @ sk1 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[43501,15503]) ).
thf(44684,plain,
( ( ssList @ ( sk22 @ sk1 ) )
| ( segmentP @ nil @ sk1 ) ),
inference(pattern_uni,[status(thm)],[44683:[]]) ).
thf(26143,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ~ ( neq @ sk5 @ sk5 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[693,26006]) ).
thf(26144,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ~ ( neq @ sk5 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[26143:[]]) ).
thf(8569,plain,
( ~ ( segmentP @ nil @ sk1 )
| ( totalorderedP @ ( cons @ sk5 @ nil ) )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1814,7995]) ).
thf(8570,plain,
( ~ ( segmentP @ nil @ sk1 )
| ( totalorderedP @ ( cons @ sk5 @ nil ) ) ),
inference(pattern_uni,[status(thm)],[8569:[]]) ).
thf(26218,plain,
( ( sk2 != sk1 )
| ( ( neq @ sk5 @ sk5 )
!= ( neq @ sk2 @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[15620,26027]) ).
thf(26249,plain,
( ( sk2 != sk1 )
| ( sk5 != sk2 )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[26218]) ).
thf(27615,plain,
( ~ ( segmentP @ nil @ sk1 )
| ~ ( lt @ sk5 @ sk5 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1814,27463]) ).
thf(27616,plain,
( ~ ( segmentP @ nil @ sk1 )
| ~ ( lt @ sk5 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[27615:[]]) ).
thf(15456,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk14 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8211,189]) ).
thf(15457,plain,
( ( strictorderP @ sk2 )
| ( segmentP @ ( sk14 @ sk2 ) @ ( sk14 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[15456:[bind(A,$thf( sk14 @ sk2 ))]]) ).
thf(21354,plain,
( ~ ( segmentP @ nil @ sk1 )
| ( sk38 != nil )
| ( sk39 != sk1 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1814,15700]) ).
thf(21355,plain,
( ~ ( segmentP @ nil @ sk1 )
| ( sk38 != nil )
| ( sk39 != sk1 ) ),
inference(pattern_uni,[status(thm)],[21354:[]]) ).
thf(65785,plain,
! [A: $i] :
( ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk29 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[65689,119]) ).
thf(65786,plain,
strictorderedP @ ( cons @ ( sk29 @ sk2 ) @ nil ),
inference(pattern_uni,[status(thm)],[65785:[bind(A,$thf( sk29 @ sk2 ))]]) ).
thf(1961,plain,
( ~ ( segmentP @ nil @ sk1 )
| ~ ( memberP @ nil @ sk5 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1814,583]) ).
thf(1962,plain,
( ~ ( segmentP @ nil @ sk1 )
| ~ ( memberP @ nil @ sk5 ) ),
inference(pattern_uni,[status(thm)],[1961:[]]) ).
thf(49468,plain,
! [A: $i] :
( ( ssItem @ ( sk24 @ A ) )
| ( totalorderP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,247]) ).
thf(49469,plain,
( ( ssItem @ ( sk24 @ sk2 ) )
| ( totalorderP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[49468:[bind(A,$thf( sk2 ))]]) ).
thf(65746,plain,
! [A: $i] :
( ( totalorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ ( sk29 @ sk2 ) )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[65689,191]) ).
thf(65747,plain,
totalorderedP @ ( cons @ ( sk29 @ sk2 ) @ nil ),
inference(pattern_uni,[status(thm)],[65746:[bind(A,$thf( sk29 @ sk2 ))]]) ).
thf(15488,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( segmentP @ A @ A )
| ( ( ssList @ ( sk8 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[621,189]) ).
thf(15489,plain,
( ( cyclefreeP @ sk2 )
| ( segmentP @ ( sk8 @ sk2 ) @ ( sk8 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[15488:[bind(A,$thf( sk8 @ sk2 ))]]) ).
thf(44095,plain,
! [A: $i] :
( ( rearsegP @ A @ nil )
| ( ( ssList @ ( tl @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[43928,287]) ).
thf(44096,plain,
rearsegP @ ( tl @ sk2 ) @ nil,
inference(pattern_uni,[status(thm)],[44095:[bind(A,$thf( tl @ sk2 ))]]) ).
thf(46167,plain,
! [A: $i] :
( ( strictorderedP @ sk1 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk22 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44536,238]) ).
thf(46168,plain,
( ( strictorderedP @ sk1 )
| ( segmentP @ ( sk22 @ sk1 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[46167:[bind(A,$thf( sk22 @ sk1 ))]]) ).
thf(13536,plain,
! [A: $i] :
( ( strictorderP @ sk1 )
| ( ( app @ A @ nil )
= A )
| ( ( ssList @ ( sk13 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10399,182]) ).
thf(13537,plain,
( ( strictorderP @ sk1 )
| ( ( app @ ( sk13 @ sk1 ) @ nil )
= ( sk13 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[13536:[bind(A,$thf( sk13 @ sk1 ))]]) ).
thf(53679,plain,
! [A: $i] :
( ( ssList @ ( sk26 @ A ) )
| ( totalorderP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[107,252]) ).
thf(53680,plain,
( ( ssList @ ( sk26 @ sk1 ) )
| ( totalorderP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[53679:[bind(A,$thf( sk1 ))]]) ).
thf(1911,plain,
( ~ ( segmentP @ nil @ sk1 )
| ( strictorderedP @ ( cons @ sk5 @ nil ) )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1814,593]) ).
thf(1912,plain,
( ~ ( segmentP @ nil @ sk1 )
| ( strictorderedP @ ( cons @ sk5 @ nil ) ) ),
inference(pattern_uni,[status(thm)],[1911:[]]) ).
thf(1416,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( cyclefreeP @ ( sk8 @ sk2 ) )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk8 @ ( sk8 @ sk2 ) ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[633,238]) ).
thf(1417,plain,
( ( cyclefreeP @ sk2 )
| ( cyclefreeP @ ( sk8 @ sk2 ) )
| ( segmentP @ ( sk8 @ ( sk8 @ sk2 ) ) @ nil ) ),
inference(pattern_uni,[status(thm)],[1416:[bind(A,$thf( sk8 @ ( sk8 @ sk2 ) ))]]) ).
thf(8347,plain,
! [A: $i] :
( ( strictorderP @ sk2 )
| ( segmentP @ A @ nil )
| ( ( ssList @ ( sk14 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8211,238]) ).
thf(8348,plain,
( ( strictorderP @ sk2 )
| ( segmentP @ ( sk14 @ sk2 ) @ nil ) ),
inference(pattern_uni,[status(thm)],[8347:[bind(A,$thf( sk14 @ sk2 ))]]) ).
thf(99127,plain,
$false,
inference(e,[status(thm)],[5659,629,26016,10399,893,518,468,9676,15472,20993,909,333,249,28981,8475,4877,1295,28045,44992,9251,37273,9901,28192,44838,8928,5383,26152,408,8005,37369,15450,11352,115,28932,120,247,202,597,37206,25997,384,11112,15632,30707,1260,153,185,66833,9845,10022,417,30058,46604,9396,26029,257,174,404,6583,6009,288,5921,389,65689,44005,184,5883,110,29512,1264,619,27487,26121,357,15943,157,372,26008,196,30910,189,5127,27451,11115,44796,228,15684,15744,316,46975,11404,37226,10534,32674,1931,152,448,31107,8558,261,216,9298,164,8029,179,65209,27483,106,238,3973,574,37224,21303,48052,6562,4205,1415,211,15445,15939,253,26012,53464,514,905,480,602,397,280,221,133,28188,6616,206,147,15618,116,243,15738,32587,428,9026,307,248,117,37192,45335,201,6571,220,7999,9323,15503,512,8211,66787,31115,160,49592,392,30624,137,29618,1123,349,15434,29811,5815,192,693,165,30479,4295,252,1968,27608,329,583,493,15498,9829,229,4280,20128,5655,197,43962,551,47677,6075,28323,27958,156,44822,4789,169,593,141,9772,20678,8414,47046,188,356,10298,32090,13635,47896,44071,30589,4648,9392,4736,471,256,4291,65752,1942,225,1075,44945,476,13539,212,47673,28327,173,129,40233,10866,9942,605,43501,15867,8673,8455,569,134,244,1814,633,4448,45075,1996,128,237,26079,508,44626,7985,51905,430,166,148,4256,264,149,5095,180,5979,375,13559,176,423,28278,47643,286,577,118,10461,44622,26019,1226,4505,191,1916,48245,579,13563,391,445,7983,15470,29935,30784,10176,159,382,15919,31045,144,5539,236,7995,187,45029,406,15700,47351,27453,230,245,509,6613,219,98,29651,15453,208,599,4509,48364,8826,631,103,140,621,483,8529,29734,46225,155,330,9327,494,47465,213,4452,28612,3977,198,52115,462,15891,8007,15432,4362,267,167,15620,130,66515,827,65794,223,226,26027,490,426,162,374,209,112,10814,44717,123,6564,355,194,4394,26569,255,65749,32467,516,553,47583,9022,28143,5388,26031,26078,8364,8295,1845,28699,4360,295,40207,47178,263,30823,310,31037,45521,199,1716,43928,502,32546,127,66571,177,182,26006,25999,370,4145,463,43960,907,9194,30066,154,45268,595,1272,5596,143,32384,46494,21347,13545,8602,4143,175,386,465,450,203,581,8957,10578,8681,26033,1966,556,32232,903,13549,10479,47294,351,10659,46340,21295,171,4705,44536,15476,114,5600,26023,47854,26185,26465,478,290,119,8997,235,246,433,9962,510,32347,29848,10600,15699,8953,28797,549,214,287,151,300,4816,15865,37345,410,146,8769,3987,190,183,15461,30345,373,10173,3997,168,262,1248,28846,43942,107,126,341,195,46439,6558,15493,635,239,44964,242,474,6590,44759,283,395,9367,28842,27463,44684,200,26144,8570,44592,5500,26249,131,27616,15457,227,21355,65786,26122,1962,49469,65747,15489,215,44096,46168,13537,222,29382,53680,232,1912,1417,8348]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC390+1 : TPTP v8.1.2. Released v2.4.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n022.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 19 00:56:47 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.96/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.54/1.02 % [INFO] Parsing done (178ms).
% 1.54/1.03 % [INFO] Running in sequential loop mode.
% 1.87/1.23 % [INFO] eprover registered as external prover.
% 1.87/1.23 % [INFO] cvc4 registered as external prover.
% 1.97/1.23 % [INFO] Scanning for conjecture ...
% 2.18/1.31 % [INFO] Found a conjecture and 95 axioms. Running axiom selection ...
% 2.39/1.38 % [INFO] Axiom selection finished. Selected 95 axioms (removed 0 axioms).
% 2.70/1.46 % [INFO] Problem is first-order (TPTP FOF).
% 2.70/1.48 % [INFO] Type checking passed.
% 2.70/1.48 % [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 ...
% 139.03/26.14 % External prover 'e' found a proof!
% 139.03/26.14 % [INFO] Killing All external provers ...
% 139.03/26.14 % Time passed: 25611ms (effective reasoning time: 25103ms)
% 139.03/26.14 % 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)>
% 139.03/26.14 % 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
% 139.03/26.14 % No. of inferences in proof: 1070
% 139.03/26.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 25611 ms resp. 25103 ms w/o parsing
% 139.73/26.34 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 139.73/26.35 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------