TSTP Solution File: SWC410+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWC410+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.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 12:12:06 EDT 2023
% Result : Theorem 141.55s 26.25s
% Output : Refutation 141.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 128
% Syntax : Number of formulae : 351 ( 58 unt; 32 typ; 0 def)
% Number of atoms : 1335 ( 285 equ; 0 cnn)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 3190 ( 279 ~; 215 |; 153 &;1955 @)
% ( 26 <=>; 562 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 32 usr; 10 con; 0-2 aty)
% Number of variables : 543 ( 0 ^; 498 !; 45 ?; 543 :)
% Comments :
%------------------------------------------------------------------------------
thf(ssList_type,type,
ssList: $i > $o ).
thf(ssItem_type,type,
ssItem: $i > $o ).
thf(memberP_type,type,
memberP: $i > $i > $o ).
thf(nil_type,type,
nil: $i ).
thf(neq_type,type,
neq: $i > $i > $o ).
thf(tl_type,type,
tl: $i > $i ).
thf(app_type,type,
app: $i > $i > $i ).
thf(cons_type,type,
cons: $i > $i > $i ).
thf(hd_type,type,
hd: $i > $i ).
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(segmentP_type,type,
segmentP: $i > $i > $o ).
thf(cyclefreeP_type,type,
cyclefreeP: $i > $o ).
thf(leq_type,type,
leq: $i > $i > $o ).
thf(strictorderP_type,type,
strictorderP: $i > $o ).
thf(duplicatefreeP_type,type,
duplicatefreeP: $i > $o ).
thf(singletonP_type,type,
singletonP: $i > $o ).
thf(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(sk9_type,type,
sk9: $i > $i ).
thf(sk38_type,type,
sk38: $i ).
thf(sk39_type,type,
sk39: $i ).
thf(1,conjecture,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ( ( B != D )
| ( A != C )
| ! [E: $i] :
( ( ssItem @ E )
=> ( ~ ( memberP @ B @ E )
| ( memberP @ A @ E ) ) )
| ( ( nil != C )
& ( nil = D ) )
| ( ( neq @ D @ nil )
& ( ~ ( neq @ C @ nil )
| ? [E: $i] :
( ( ssList @ E )
& ( D != E )
& ? [F: $i] :
( ( ssList @ F )
& ? [G: $i] :
( ( ssList @ G )
& ( ( tl @ C )
= F )
& ( ( app @ F @ G )
= E )
& ? [H: $i] :
( ( ssItem @ H )
& ( ( cons @ H @ nil )
= G )
& ( ( hd @ C )
= H )
& ( neq @ nil @ C ) )
& ( neq @ nil @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ( ( B != D )
| ( A != C )
| ! [E: $i] :
( ( ssItem @ E )
=> ( ~ ( memberP @ B @ E )
| ( memberP @ A @ E ) ) )
| ( ( nil != C )
& ( nil = D ) )
| ( ( neq @ D @ nil )
& ( ~ ( neq @ C @ nil )
| ? [E: $i] :
( ( ssList @ E )
& ( D != E )
& ? [F: $i] :
( ( ssList @ F )
& ? [G: $i] :
( ( ssList @ G )
& ( ( tl @ C )
= F )
& ( ( app @ F @ G )
= E )
& ? [H: $i] :
( ( ssItem @ H )
& ( ( cons @ H @ nil )
= G )
& ( ( hd @ C )
= H )
& ( neq @ nil @ C ) )
& ( neq @ nil @ C ) ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(98,plain,
~ ! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ! [D: $i] :
( ( ssList @ D )
=> ( ( B != D )
| ( A != C )
| ! [E: $i] :
( ( ssItem @ E )
=> ( ~ ( memberP @ B @ E )
| ( memberP @ A @ E ) ) )
| ( ( nil != C )
& ( nil = D ) )
| ( ( neq @ D @ nil )
& ( ~ ( neq @ C @ nil )
| ? [E: $i] :
( ( ssList @ E )
& ( D != E )
& ? [F: $i] :
( ( ssList @ F )
& ? [G: $i] :
( ( ssList @ G )
& ( ( tl @ C )
= F )
& ( ( app @ F @ G )
= E )
& ? [H: $i] :
( ( ssItem @ H )
& ( ( cons @ H @ nil )
= G )
& ( ( hd @ C )
= H )
& ( neq @ nil @ C ) )
& ( neq @ nil @ C ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(100,plain,
ssItem @ sk5,
inference(cnf,[status(esa)],[98]) ).
thf(32,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ~ ( lt @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax90) ).
thf(213,plain,
! [A: $i] :
( ( ssItem @ A )
=> ~ ( lt @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(214,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ~ ( lt @ A @ A ) ),
inference(cnf,[status(esa)],[213]) ).
thf(644,plain,
! [A: $i] :
( ~ ( lt @ A @ A )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[100,214]) ).
thf(645,plain,
~ ( lt @ sk5 @ sk5 ),
inference(pattern_uni,[status(thm)],[644:[bind(A,$thf( sk5 ))]]) ).
thf(11,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( segmentP @ nil @ A )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).
thf(135,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(137,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( nil != A )
| ( segmentP @ nil @ A ) ),
inference(cnf,[status(esa)],[135]) ).
thf(139,plain,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( segmentP @ nil @ A ) ),
inference(lifteq,[status(thm)],[137]) ).
thf(140,plain,
( ~ ( ssList @ nil )
| ( segmentP @ nil @ nil ) ),
inference(simp,[status(thm)],[139]) ).
thf(53,axiom,
ssList @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
thf(330,plain,
ssList @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(628,plain,
( ~ $true
| ( segmentP @ nil @ nil ) ),
inference(rewrite,[status(thm)],[140,330]) ).
thf(629,plain,
segmentP @ nil @ nil,
inference(simp,[status(thm)],[628]) ).
thf(91,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( rearsegP @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax49) ).
thf(479,plain,
! [A: $i] :
( ( ssList @ A )
=> ( rearsegP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(109,plain,
memberP @ sk2 @ sk5,
inference(cnf,[status(esa)],[98]) ).
thf(99,plain,
~ ( memberP @ sk1 @ sk5 ),
inference(cnf,[status(esa)],[98]) ).
thf(512,plain,
( ( memberP @ sk2 @ sk5 )
!= ( memberP @ sk1 @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[109,99]) ).
thf(515,plain,
( ( sk2 != sk1 )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[512]) ).
thf(518,plain,
sk2 != sk1,
inference(simp,[status(thm)],[515]) ).
thf(92,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( nil
!= ( cons @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).
thf(481,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( nil
!= ( cons @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
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(352,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(61,axiom,
? [A: $i] :
( ( ssItem @ A )
& ? [B: $i] :
( ( ssItem @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(371,plain,
? [A: $i] :
( ( ssItem @ A )
& ? [B: $i] :
( ( ssItem @ B )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(374,plain,
ssItem @ sk38,
inference(cnf,[status(esa)],[371]) ).
thf(34,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ~ ( memberP @ nil @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
thf(227,plain,
! [A: $i] :
( ( ssItem @ A )
=> ~ ( memberP @ nil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(228,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ~ ( memberP @ nil @ A ) ),
inference(cnf,[status(esa)],[227]) ).
thf(522,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ( ( ssItem @ sk38 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[374,228]) ).
thf(523,plain,
~ ( memberP @ nil @ sk38 ),
inference(pattern_uni,[status(thm)],[522:[bind(A,$thf( sk38 ))]]) ).
thf(108,plain,
sk2 = sk4,
inference(cnf,[status(esa)],[98]) ).
thf(115,plain,
sk4 = sk2,
inference(lifteq,[status(thm)],[108]) ).
thf(105,plain,
ssList @ sk2,
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(153,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(154,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( ssList @ ( sk9 @ A ) )
| ( cyclefreeP @ A ) ),
inference(cnf,[status(esa)],[153]) ).
thf(577,plain,
! [A: $i] :
( ( ssList @ ( sk9 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,154]) ).
thf(578,plain,
( ( ssList @ ( sk9 @ sk2 ) )
| ( cyclefreeP @ sk2 ) ),
inference(pattern_uni,[status(thm)],[577:[bind(A,$thf( sk2 ))]]) ).
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(311,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(313,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( neq @ A @ B )
| ( A != B ) ),
inference(cnf,[status(esa)],[311]) ).
thf(315,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( neq @ A @ B ) ),
inference(lifteq,[status(thm)],[313]) ).
thf(316,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( neq @ A @ A ) ),
inference(simp,[status(thm)],[315]) ).
thf(682,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ~ ( neq @ A @ A )
| ( ( ssList @ ( sk9 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[578,316]) ).
thf(683,plain,
( ( cyclefreeP @ sk2 )
| ~ ( neq @ ( sk9 @ sk2 ) @ ( sk9 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[682:[bind(A,$thf( sk9 @ sk2 ))]]) ).
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(308,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(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(449,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(5,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( strictorderedP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax68) ).
thf(119,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( strictorderedP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(120,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ( strictorderedP @ ( cons @ A @ nil ) ) ),
inference(cnf,[status(esa)],[119]) ).
thf(676,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,316]) ).
thf(677,plain,
~ ( neq @ sk2 @ sk2 ),
inference(pattern_uni,[status(thm)],[676:[bind(A,$thf( 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(342,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(343,plain,
! [B: $i,A: $i] :
( ~ ( ssList @ A )
| ~ ( ssList @ B )
| ( nil != B )
| ( nil != A )
| ( nil
= ( app @ A @ B ) ) ),
inference(cnf,[status(esa)],[342]) ).
thf(346,plain,
! [B: $i,A: $i] :
( ( nil != B )
| ( nil != A )
| ( ( app @ A @ B )
= nil )
| ~ ( ssList @ A )
| ~ ( ssList @ B ) ),
inference(lifteq,[status(thm)],[343]) ).
thf(347,plain,
( ( ( app @ nil @ nil )
= nil )
| ~ ( ssList @ nil ) ),
inference(simp,[status(thm)],[346]) ).
thf(1172,plain,
( ( ( app @ nil @ nil )
= nil )
| ~ $true ),
inference(rewrite,[status(thm)],[347,330]) ).
thf(1173,plain,
( ( app @ nil @ nil )
= nil ),
inference(simp,[status(thm)],[1172]) ).
thf(64,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( duplicatefreeP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax71) ).
thf(385,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( duplicatefreeP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
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(142,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(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(472,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(669,plain,
! [A: $i] :
( ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[100,120]) ).
thf(670,plain,
strictorderedP @ ( cons @ sk5 @ nil ),
inference(pattern_uni,[status(thm)],[669:[bind(A,$thf( sk5 ))]]) ).
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(301,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(6,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( frontsegP @ nil @ A )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax46) ).
thf(121,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(123,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( nil != A )
| ( frontsegP @ nil @ A ) ),
inference(cnf,[status(esa)],[121]) ).
thf(125,plain,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( frontsegP @ nil @ A ) ),
inference(lifteq,[status(thm)],[123]) ).
thf(126,plain,
( ~ ( ssList @ nil )
| ( frontsegP @ nil @ nil ) ),
inference(simp,[status(thm)],[125]) ).
thf(564,plain,
( ~ $true
| ( frontsegP @ nil @ nil ) ),
inference(rewrite,[status(thm)],[126,330]) ).
thf(565,plain,
frontsegP @ nil @ nil,
inference(simp,[status(thm)],[564]) ).
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(184,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(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(196,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(23,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( segmentP @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).
thf(189,plain,
! [A: $i] :
( ( ssList @ A )
=> ( segmentP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(44,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ssList @ ( tl @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).
thf(284,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ssList @ ( tl @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(46,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( equalelemsP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax73) ).
thf(289,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( equalelemsP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
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(475,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(106,plain,
ssList @ sk1,
inference(cnf,[status(esa)],[98]) ).
thf(572,plain,
! [A: $i] :
( ( ssList @ ( sk9 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,154]) ).
thf(573,plain,
( ( ssList @ ( sk9 @ sk1 ) )
| ( cyclefreeP @ sk1 ) ),
inference(pattern_uni,[status(thm)],[572:[bind(A,$thf( sk1 ))]]) ).
thf(590,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( ssList @ ( sk9 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ ( sk9 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[573,154]) ).
thf(591,plain,
( ( cyclefreeP @ sk1 )
| ( ssList @ ( sk9 @ ( sk9 @ sk1 ) ) )
| ( cyclefreeP @ ( sk9 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[590:[bind(A,$thf( sk9 @ sk1 ))]]) ).
thf(62,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ! [C: $i] :
( ( ssList @ C )
=> ( ( memberP @ ( cons @ B @ C ) @ A )
<=> ( ( A = B )
| ( memberP @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax37) ).
thf(376,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(37,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( segmentP @ A @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax57) ).
thf(238,plain,
! [A: $i] :
( ( ssList @ A )
=> ( segmentP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(686,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssList @ nil )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[330,316]) ).
thf(687,plain,
~ ( neq @ nil @ nil ),
inference(pattern_uni,[status(thm)],[686:[bind(A,$thf( nil ))]]) ).
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(132,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( hd @ ( cons @ B @ A ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(69,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( cyclefreeP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax59) ).
thf(396,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( cyclefreeP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(659,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ( cyclefreeP @ ( sk9 @ sk1 ) )
| ( ssList @ ( sk9 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ ( sk9 @ ( sk9 @ sk1 ) ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[591,154]) ).
thf(660,plain,
( ( cyclefreeP @ sk1 )
| ( cyclefreeP @ ( sk9 @ sk1 ) )
| ( ssList @ ( sk9 @ ( sk9 @ ( sk9 @ sk1 ) ) ) )
| ( cyclefreeP @ ( sk9 @ ( sk9 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[659:[bind(A,$thf( sk9 @ ( sk9 @ sk1 ) ))]]) ).
thf(74,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ( rearsegP @ A @ B )
<=> ? [C: $i] :
( ( ssList @ C )
& ( ( app @ C @ B )
= A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
thf(411,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(3,axiom,
strictorderedP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax69) ).
thf(116,plain,
strictorderedP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(122,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A )
| ( nil = A ) ),
inference(cnf,[status(esa)],[121]) ).
thf(124,plain,
! [A: $i] :
( ( nil = A )
| ~ ( ssList @ A )
| ~ ( frontsegP @ nil @ A ) ),
inference(lifteq,[status(thm)],[122]) ).
thf(874,plain,
! [A: $i] :
( ( nil = A )
| ~ ( frontsegP @ nil @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,124]) ).
thf(875,plain,
( ( sk1 = nil )
| ~ ( frontsegP @ nil @ sk1 ) ),
inference(pattern_uni,[status(thm)],[874:[bind(A,$thf( sk1 ))]]) ).
thf(680,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,316]) ).
thf(681,plain,
~ ( neq @ sk1 @ sk1 ),
inference(pattern_uni,[status(thm)],[680:[bind(A,$thf( sk1 ))]]) ).
thf(1076,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ~ ( neq @ nil @ sk1 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[875,681]) ).
thf(1077,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ~ ( neq @ nil @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1076:[]]) ).
thf(1085,plain,
( ~ ( neq @ nil @ sk1 )
| ( ( frontsegP @ nil @ sk1 )
!= ( frontsegP @ nil @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[565,1077]) ).
thf(1102,plain,
( ~ ( neq @ nil @ sk1 )
| ( nil != nil )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[1085]) ).
thf(1104,plain,
( ~ ( neq @ nil @ sk1 )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[1102]) ).
thf(41,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( cons @ B @ A )
!= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
thf(265,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( cons @ B @ A )
!= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
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(117,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(101,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( neq @ sk4 @ nil )
| ~ ( ssList @ A )
| ( sk4 = A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ( ( tl @ sk3 )
!= B )
| ( ( app @ B @ C )
!= A )
| ~ ( ssItem @ D )
| ( ( cons @ D @ nil )
!= C )
| ( ( hd @ sk3 )
!= D )
| ~ ( neq @ nil @ sk3 )
| ~ ( neq @ nil @ sk3 ) ),
inference(cnf,[status(esa)],[98]) ).
thf(111,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( sk4 = A )
| ( ( tl @ sk3 )
!= B )
| ( ( app @ B @ C )
!= A )
| ( ( cons @ D @ nil )
!= C )
| ( ( hd @ sk3 )
!= D )
| ~ ( neq @ sk4 @ nil )
| ~ ( ssList @ A )
| ~ ( ssList @ B )
| ~ ( ssList @ C )
| ~ ( ssItem @ D )
| ~ ( neq @ nil @ sk3 )
| ~ ( neq @ nil @ sk3 ) ),
inference(lifteq,[status(thm)],[101]) ).
thf(112,plain,
( ( ( app @ ( tl @ sk3 ) @ ( cons @ ( hd @ sk3 ) @ nil ) )
= sk4 )
| ~ ( neq @ sk4 @ nil )
| ~ ( ssList @ ( app @ ( tl @ sk3 ) @ ( cons @ ( hd @ sk3 ) @ nil ) ) )
| ~ ( ssList @ ( tl @ sk3 ) )
| ~ ( ssList @ ( cons @ ( hd @ sk3 ) @ nil ) )
| ~ ( ssItem @ ( hd @ sk3 ) )
| ~ ( neq @ nil @ sk3 ) ),
inference(simp,[status(thm)],[111]) ).
thf(107,plain,
sk1 = sk3,
inference(cnf,[status(esa)],[98]) ).
thf(114,plain,
sk3 = sk1,
inference(lifteq,[status(thm)],[107]) ).
thf(529,plain,
( ( ( app @ ( tl @ sk1 ) @ ( cons @ ( hd @ sk1 ) @ nil ) )
= sk2 )
| ~ ( neq @ sk2 @ nil )
| ~ ( ssList @ ( app @ ( tl @ sk1 ) @ ( cons @ ( hd @ sk1 ) @ nil ) ) )
| ~ ( ssList @ ( tl @ sk1 ) )
| ~ ( ssList @ ( cons @ ( hd @ sk1 ) @ nil ) )
| ~ ( ssItem @ ( hd @ sk1 ) )
| ~ ( neq @ nil @ sk1 ) ),
inference(rewrite,[status(thm)],[112,114,115]) ).
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(201,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(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(334,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(67,axiom,
strictorderP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax64) ).
thf(392,plain,
strictorderP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
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(424,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(72,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( leq @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax31) ).
thf(407,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( leq @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(78,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( frontsegP @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax42) ).
thf(429,plain,
! [A: $i] :
( ( ssList @ A )
=> ( frontsegP @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
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(229,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(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(484,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(1078,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ~ ( neq @ sk1 @ nil )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[875,681]) ).
thf(1079,plain,
( ~ ( frontsegP @ nil @ sk1 )
| ~ ( neq @ sk1 @ nil ) ),
inference(pattern_uni,[status(thm)],[1078:[]]) ).
thf(794,plain,
! [A: $i] :
( ( nil = A )
| ~ ( frontsegP @ nil @ A )
| ( ( ssList @ sk2 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[105,124]) ).
thf(795,plain,
( ( sk2 = nil )
| ~ ( frontsegP @ nil @ sk2 ) ),
inference(pattern_uni,[status(thm)],[794:[bind(A,$thf( sk2 ))]]) ).
thf(508,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[100,228]) ).
thf(509,plain,
~ ( memberP @ nil @ sk5 ),
inference(pattern_uni,[status(thm)],[508:[bind(A,$thf( sk5 ))]]) ).
thf(511,plain,
( ( memberP @ sk2 @ sk5 )
!= ( memberP @ nil @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[109,509]) ).
thf(514,plain,
( ( sk2 != nil )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[511]) ).
thf(517,plain,
sk2 != nil,
inference(simp,[status(thm)],[514]) ).
thf(1027,plain,
~ ( frontsegP @ nil @ sk2 ),
inference(simplifyReflect,[status(thm)],[795,517]) ).
thf(635,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( ssList @ ( sk9 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ ( sk9 @ sk2 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[578,154]) ).
thf(636,plain,
( ( cyclefreeP @ sk2 )
| ( ssList @ ( sk9 @ ( sk9 @ sk2 ) ) )
| ( cyclefreeP @ ( sk9 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[635:[bind(A,$thf( sk9 @ sk2 ))]]) ).
thf(696,plain,
! [A: $i] :
( ( cyclefreeP @ sk2 )
| ( cyclefreeP @ ( sk9 @ sk2 ) )
| ( ssList @ ( sk9 @ A ) )
| ( cyclefreeP @ A )
| ( ( ssList @ ( sk9 @ ( sk9 @ sk2 ) ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[636,154]) ).
thf(697,plain,
( ( cyclefreeP @ sk2 )
| ( cyclefreeP @ ( sk9 @ sk2 ) )
| ( ssList @ ( sk9 @ ( sk9 @ ( sk9 @ sk2 ) ) ) )
| ( cyclefreeP @ ( sk9 @ ( sk9 @ sk2 ) ) ) ),
inference(pattern_uni,[status(thm)],[696:[bind(A,$thf( sk9 @ ( sk9 @ sk2 ) ))]]) ).
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(317,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(59,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( frontsegP @ A @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax45) ).
thf(356,plain,
! [A: $i] :
( ( ssList @ A )
=> ( frontsegP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(12,axiom,
cyclefreeP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax60) ).
thf(141,plain,
cyclefreeP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(104,plain,
( ~ ( neq @ sk4 @ nil )
| ( neq @ sk3 @ nil ) ),
inference(cnf,[status(esa)],[98]) ).
thf(519,plain,
( ~ ( neq @ sk2 @ nil )
| ( neq @ sk1 @ nil ) ),
inference(rewrite,[status(thm)],[104,114,115]) ).
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(193,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(68,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ( cons @ ( hd @ A ) @ ( tl @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax78) ).
thf(393,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ( cons @ ( hd @ A ) @ ( tl @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(646,plain,
! [A: $i] :
( ~ ( lt @ A @ A )
| ( ( ssItem @ sk38 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[374,214]) ).
thf(647,plain,
~ ( lt @ sk38 @ sk38 ),
inference(pattern_uni,[status(thm)],[646:[bind(A,$thf( sk38 ))]]) ).
thf(8,axiom,
totalorderedP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax66) ).
thf(129,plain,
totalorderedP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
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(204,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(206,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( neq @ A @ B )
| ( A != B ) ),
inference(cnf,[status(esa)],[204]) ).
thf(208,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( neq @ A @ B ) ),
inference(lifteq,[status(thm)],[206]) ).
thf(209,plain,
! [A: $i] :
( ~ ( ssItem @ A )
| ~ ( neq @ A @ A ) ),
inference(simp,[status(thm)],[208]) ).
thf(568,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssItem @ sk5 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[100,209]) ).
thf(569,plain,
~ ( neq @ sk5 @ sk5 ),
inference(pattern_uni,[status(thm)],[568:[bind(A,$thf( sk5 ))]]) ).
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(503,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(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(127,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(128,plain,
! [B: $i,A: $i] :
( ~ ( ssItem @ A )
| ~ ( ssItem @ B )
| ~ ( gt @ A @ B )
| ~ ( gt @ B @ A ) ),
inference(cnf,[status(esa)],[127]) ).
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(398,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(18,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ssList @ ( cons @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
thf(166,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ssList @ ( cons @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
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(148,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(48,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ssItem @ B )
& ( ( hd @ A )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax75) ).
thf(296,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ssItem @ B )
& ( ( hd @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(372,plain,
sk38 != sk39,
inference(cnf,[status(esa)],[371]) ).
thf(375,plain,
sk39 != sk38,
inference(lifteq,[status(thm)],[372]) ).
thf(24,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( totalorderedP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax65) ).
thf(191,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( totalorderedP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
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(291,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(118,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)],[117]) ).
thf(43,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ssItem @ ( hd @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
thf(281,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ( ssItem @ ( hd @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
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(466,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(20,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( app @ A @ nil )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).
thf(181,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( app @ A @ nil )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(57,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( totalorderP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax61) ).
thf(350,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( totalorderP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(671,plain,
! [A: $i] :
( ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk38 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[374,120]) ).
thf(672,plain,
strictorderedP @ ( cons @ sk38 @ nil ),
inference(pattern_uni,[status(thm)],[671:[bind(A,$thf( sk38 ))]]) ).
thf(1190,plain,
( ~ ( neq @ sk1 @ nil )
| ( ( frontsegP @ nil @ sk1 )
!= ( frontsegP @ nil @ nil ) ) ),
inference(paramod_ordered,[status(thm)],[565,1079]) ).
thf(1207,plain,
( ~ ( neq @ sk1 @ nil )
| ( nil != nil )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[1190]) ).
thf(1209,plain,
( ~ ( neq @ sk1 @ nil )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[1207]) ).
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(245,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(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(451,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(373,plain,
ssItem @ sk39,
inference(cnf,[status(esa)],[371]) ).
thf(566,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssItem @ sk39 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[373,209]) ).
thf(567,plain,
~ ( neq @ sk39 @ sk39 ),
inference(pattern_uni,[status(thm)],[566:[bind(A,$thf( sk39 ))]]) ).
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(434,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(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(477,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(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(387,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(95,axiom,
totalorderP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax62) ).
thf(494,plain,
totalorderP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(75,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( rearsegP @ nil @ A )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52) ).
thf(418,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(420,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( nil != A )
| ( rearsegP @ nil @ A ) ),
inference(cnf,[status(esa)],[418]) ).
thf(422,plain,
! [A: $i] :
( ( nil != A )
| ~ ( ssList @ A )
| ( rearsegP @ nil @ A ) ),
inference(lifteq,[status(thm)],[420]) ).
thf(423,plain,
( ~ ( ssList @ nil )
| ( rearsegP @ nil @ nil ) ),
inference(simp,[status(thm)],[422]) ).
thf(630,plain,
( ~ $true
| ( rearsegP @ nil @ nil ) ),
inference(rewrite,[status(thm)],[423,330]) ).
thf(631,plain,
rearsegP @ nil @ nil,
inference(simp,[status(thm)],[630]) ).
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(240,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ssList @ B )
& ( ( tl @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(667,plain,
! [A: $i] :
( ( strictorderedP @ ( cons @ A @ nil ) )
| ( ( ssItem @ sk39 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[373,120]) ).
thf(668,plain,
strictorderedP @ ( cons @ sk39 @ nil ),
inference(pattern_uni,[status(thm)],[667:[bind(A,$thf( sk39 ))]]) ).
thf(27,axiom,
duplicatefreeP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax72) ).
thf(198,plain,
duplicatefreeP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
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(130,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(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(431,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(684,plain,
! [A: $i] :
( ( cyclefreeP @ sk1 )
| ~ ( neq @ A @ A )
| ( ( ssList @ ( sk9 @ sk1 ) )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[573,316]) ).
thf(685,plain,
( ( cyclefreeP @ sk1 )
| ~ ( neq @ ( sk9 @ sk1 ) @ ( sk9 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[684:[bind(A,$thf( sk9 @ sk1 ))]]) ).
thf(520,plain,
! [A: $i] :
( ~ ( memberP @ nil @ A )
| ( ( ssItem @ sk39 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[373,228]) ).
thf(521,plain,
~ ( memberP @ nil @ sk39 ),
inference(pattern_uni,[status(thm)],[520:[bind(A,$thf( sk39 ))]]) ).
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(145,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(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(150,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(73,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( strictorderP @ ( cons @ A @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax63) ).
thf(409,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( strictorderP @ ( cons @ A @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(28,axiom,
~ ( singletonP @ nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).
thf(199,plain,
~ ( singletonP @ nil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
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(331,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(84,axiom,
equalelemsP @ nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax74) ).
thf(463,plain,
equalelemsP @ nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(642,plain,
! [A: $i] :
( ~ ( lt @ A @ A )
| ( ( ssItem @ sk39 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[373,214]) ).
thf(643,plain,
~ ( lt @ sk39 @ sk39 ),
inference(pattern_uni,[status(thm)],[642:[bind(A,$thf( sk39 ))]]) ).
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(446,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssItem @ B )
=> ( ( tl @ ( cons @ B @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(570,plain,
! [A: $i] :
( ~ ( neq @ A @ A )
| ( ( ssItem @ sk38 )
!= ( ssItem @ A ) ) ),
inference(paramod_ordered,[status(thm)],[374,209]) ).
thf(571,plain,
~ ( neq @ sk38 @ sk38 ),
inference(pattern_uni,[status(thm)],[570:[bind(A,$thf( sk38 ))]]) ).
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(231,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(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(495,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(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(258,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(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(390,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(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(186,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(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(383,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(45,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( rearsegP @ A @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax51) ).
thf(287,plain,
! [A: $i] :
( ( ssList @ A )
=> ( rearsegP @ A @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
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(168,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(71,axiom,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ssList @ ( app @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
thf(405,plain,
! [A: $i] :
( ( ssList @ A )
=> ! [B: $i] :
( ( ssList @ B )
=> ( ssList @ ( app @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(31,axiom,
! [A: $i] :
( ( ssList @ A )
=> ( ( app @ nil @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
thf(210,plain,
! [A: $i] :
( ( ssList @ A )
=> ( ( app @ nil @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(239,plain,
! [A: $i] :
( ~ ( ssList @ A )
| ( segmentP @ A @ nil ) ),
inference(cnf,[status(esa)],[238]) ).
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(268,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(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(358,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(85,axiom,
! [A: $i] :
( ( ssItem @ A )
=> ( geq @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax89) ).
thf(464,plain,
! [A: $i] :
( ( ssItem @ A )
=> ( geq @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
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(427,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(1383,plain,
! [A: $i] :
( ( segmentP @ A @ nil )
| ( ( ssList @ sk1 )
!= ( ssList @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,239]) ).
thf(1384,plain,
segmentP @ sk1 @ nil,
inference(pattern_uni,[status(thm)],[1383:[bind(A,$thf( sk1 ))]]) ).
thf(131,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)],[130]) ).
thf(200,plain,
~ ( singletonP @ nil ),
inference(polarity_switch,[status(thm)],[199]) ).
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(469,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(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(215,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(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(491,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(98529,plain,
$false,
inference(cvc4,[status(thm)],[645,629,479,518,481,352,523,115,683,308,449,120,677,1173,385,142,472,153,670,301,565,184,196,189,284,228,289,316,475,591,376,106,238,121,687,132,396,660,411,116,1104,265,117,529,201,334,392,424,407,429,229,484,1079,1027,697,317,356,141,519,578,109,124,193,393,647,129,569,371,503,128,105,311,398,166,148,573,296,375,191,875,291,118,281,204,466,181,350,672,1209,681,245,98,451,567,509,434,477,387,494,631,213,240,668,198,330,130,636,135,431,685,521,374,209,342,145,150,409,199,331,463,127,643,154,446,571,231,99,495,517,258,390,186,114,418,119,1077,383,214,287,168,405,373,210,239,268,358,464,427,1384,131,200,227,469,215,491,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWC410+1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n012.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 19 02:17:02 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.96/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.47/1.01 % [INFO] Parsing done (160ms).
% 1.47/1.02 % [INFO] Running in sequential loop mode.
% 1.80/1.21 % [INFO] eprover registered as external prover.
% 1.80/1.21 % [INFO] cvc4 registered as external prover.
% 1.80/1.21 % [INFO] Scanning for conjecture ...
% 2.12/1.30 % [INFO] Found a conjecture and 95 axioms. Running axiom selection ...
% 2.43/1.37 % [INFO] Axiom selection finished. Selected 95 axioms (removed 0 axioms).
% 2.70/1.45 % [INFO] Problem is first-order (TPTP FOF).
% 2.70/1.47 % [INFO] Type checking passed.
% 2.70/1.47 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 141.55/26.25 % External prover 'cvc4' found a proof!
% 141.55/26.25 % [INFO] Killing All external provers ...
% 141.55/26.25 % Time passed: 25732ms (effective reasoning time: 25233ms)
% 141.55/26.25 % 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)>
% 141.55/26.25 % 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
% 141.55/26.25 % No. of inferences in proof: 319
% 141.55/26.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 25732 ms resp. 25233 ms w/o parsing
% 141.81/26.33 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 141.81/26.33 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------