%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWC418+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:53:44 AM UTC 2026
% Result : Theorem 187.30s 52.28s
% Output : Refutation 185.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 107
% Syntax : Number of formulae : 550 ( 70 unt; 0 typ; 11 def)
% Number of atoms : 2473 ( 596 equ; 0 cnn)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 5771 ( 800 ~; 746 |; 263 &;3347 @)
% ( 26 <=>; 589 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 35 usr; 9 con; 0-2 aty)
% Number of variables : 774 ( 5 ^; 675 !; 83 ?; 774 :)
% ( 0 !>; 0 ?*; 0 @-; 11 @+)
% Comments :
%------------------------------------------------------------------------------
thf(ssList_decl,type,
ssList: $i > $o ).
thf(neq_decl,type,
neq: $i > $i > $o ).
thf(nil_decl,type,
nil: $i ).
thf(ssItem_decl,type,
ssItem: $i > $o ).
thf(app_decl,type,
app: $i > $i > $i ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(tl_decl,type,
tl: $i > $i ).
thf(hd_decl,type,
hd: $i > $i ).
thf(strictorderedP_decl,type,
strictorderedP: $i > $o ).
thf(lt_decl,type,
lt: $i > $i > $o ).
thf(frontsegP_decl,type,
frontsegP: $i > $i > $o ).
thf(gt_decl,type,
gt: $i > $i > $o ).
thf(totalorderedP_decl,type,
totalorderedP: $i > $o ).
thf(segmentP_decl,type,
segmentP: $i > $i > $o ).
thf(cyclefreeP_decl,type,
cyclefreeP: $i > $o ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(strictorderP_decl,type,
strictorderP: $i > $o ).
thf(duplicatefreeP_decl,type,
duplicatefreeP: $i > $o ).
thf(singletonP_decl,type,
singletonP: $i > $o ).
thf(memberP_decl,type,
memberP: $i > $i > $o ).
thf(totalorderP_decl,type,
totalorderP: $i > $o ).
thf(rearsegP_decl,type,
rearsegP: $i > $i > $o ).
thf(equalelemsP_decl,type,
equalelemsP: $i > $o ).
thf(geq_decl,type,
geq: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i ).
thf(sk9_decl,type,
sk9: $i > $i ).
thf(sk37_decl,type,
sk37: $i ).
thf(sk38_decl,type,
sk38: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( nil @ ( D @ neq ) )
& ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( D @ ( nil @ neq ) )
& ? [H: $i] :
( ( D @ ( nil @ neq ) )
& ( ( D @ hd )
= H )
& ( ( nil @ ( H @ cons ) )
= G )
& ( H @ ssItem ) )
& ( ( G @ ( F @ app ) )
= E )
& ( ( D @ tl )
= F )
& ( G @ ssList ) )
& ( F @ ssList ) )
& ( C != E )
& ( E @ ssList ) ) )
| ( ( nil = D )
& ( nil != C ) )
| ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( ( F @ ( nil @ ( E @ cons ) @ ( G @ app ) @ app ) )
= A )
& ( ( G @ ( nil @ ( E @ cons ) @ ( F @ app ) @ app ) )
= B )
& ( G @ ssList ) )
& ( F @ ssList ) )
& ( E @ ssItem ) )
| ~ ( nil @ ( B @ neq ) )
| ( A != C )
| ( B != D ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( nil @ ( C @ neq ) )
& ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ( C @ ( nil @ neq ) )
& ? [G: $i] :
( ( C @ ( nil @ neq ) )
& ( ( C @ hd )
= G )
& ( ( nil @ ( G @ cons ) )
= F )
& ( G @ ssItem ) )
& ( ( F @ ( E @ app ) )
= D )
& ( ( C @ tl )
= E )
& ( F @ ssList ) )
& ( E @ ssList ) )
& ( B != D )
& ( D @ ssList ) ) )
| ( ( nil = C )
& ( nil != B ) )
| ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ( ( E @ ( nil @ ( D @ cons ) @ ( F @ app ) @ app ) )
= sk1 )
& ( ( F @ ( nil @ ( D @ cons ) @ ( E @ app ) @ app ) )
= A )
& ( F @ ssList ) )
& ( E @ ssList ) )
& ( D @ ssItem ) )
| ~ ( nil @ ( A @ neq ) )
| ( sk1 != B )
| ( A != C ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( nil @ ( B @ neq ) )
& ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ( B @ ( nil @ neq ) )
& ? [F: $i] :
( ( B @ ( nil @ neq ) )
& ( ( B @ hd )
= F )
& ( ( nil @ ( F @ cons ) )
= E )
& ( F @ ssItem ) )
& ( ( E @ ( D @ app ) )
= C )
& ( ( B @ tl )
= D )
& ( E @ ssList ) )
& ( D @ ssList ) )
& ( A != C )
& ( C @ ssList ) ) )
| ( ( nil = B )
& ( nil != A ) )
| ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ( ( D @ ( nil @ ( C @ cons ) @ ( E @ app ) @ app ) )
= sk1 )
& ( ( E @ ( nil @ ( C @ cons ) @ ( D @ app ) @ app ) )
= sk2 )
& ( E @ ssList ) )
& ( D @ ssList ) )
& ( C @ ssItem ) )
| ~ ( nil @ ( sk2 @ neq ) )
| ( sk1 != A )
| ( sk2 != B ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ( ( ( nil @ ( A @ neq ) )
& ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ( A @ ( nil @ neq ) )
& ? [E: $i] :
( ( A @ ( nil @ neq ) )
& ( ( A @ hd )
= E )
& ( ( nil @ ( E @ cons ) )
= D )
& ( E @ ssItem ) )
& ( ( D @ ( C @ app ) )
= B )
& ( ( A @ tl )
= C )
& ( D @ ssList ) )
& ( C @ ssList ) )
& ( sk3 != B )
& ( B @ ssList ) ) )
| ( ( nil = A )
& ( nil != sk3 ) )
| ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ( ( C @ ( nil @ ( B @ cons ) @ ( D @ app ) @ app ) )
= sk1 )
& ( ( D @ ( nil @ ( B @ cons ) @ ( C @ app ) @ app ) )
= sk2 )
& ( D @ ssList ) )
& ( C @ ssList ) )
& ( B @ ssItem ) )
| ~ ( nil @ ( sk2 @ neq ) )
| ( sk1 != sk3 )
| ( sk2 != A ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ~ ( ( B @ ( C @ leq ) )
& ( C @ ( B @ leq ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ( ( ( E @ ( B @ cons ) @ ( D @ ( A @ sk5 @ cons ) @ ( C @ app ) @ app ) )
= A )
=> ~ ( ( A @ sk5 @ ( B @ leq ) )
& ( B @ ( A @ sk5 @ leq ) ) ) ) ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( D @ ( A @ sk6 @ cons ) @ ( C @ ( A @ sk5 @ cons ) @ ( B @ app ) @ app ) )
= A )
=> ~ ( ( A @ sk5 @ ( A @ sk6 @ leq ) )
& ( A @ sk6 @ ( A @ sk5 @ leq ) ) ) ) ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( A @ sk6 @ cons ) @ ( B @ ( A @ sk5 @ cons ) @ ( A @ sk7 @ app ) @ app ) )
= A )
=> ~ ( ( A @ sk5 @ ( A @ sk6 @ leq ) )
& ( A @ sk6 @ ( A @ sk5 @ leq ) ) ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ( ( ( B @ ( A @ sk6 @ cons ) @ ( A @ sk8 @ ( A @ sk5 @ cons ) @ ( A @ sk7 @ app ) @ app ) )
= A )
=> ~ ( ( A @ sk5 @ ( A @ sk6 @ leq ) )
& ( A @ sk6 @ ( A @ sk5 @ leq ) ) ) ) ) ) ) ).
thf(sk37_def,definition,
( sk37
= ( @+[A: $i] :
( ? [B: $i] :
( ( A != B )
& ( B @ ssItem ) )
& ( A @ ssItem ) ) ) ) ).
thf(sk38_def,definition,
( sk38
= ( @+[A: $i] :
( ( sk37 != A )
& ( A @ ssItem ) ) ) ) ).
thf(61,axiom,
? [A: $i] :
( ? [B: $i] :
( ( A != B )
& ( B @ ssItem ) )
& ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
thf(392,plain,
? [A: $i] :
( ? [B: $i] :
( ( A != B )
& ( B @ ssItem ) )
& ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(393,plain,
( ( sk37 != sk38 )
& ( sk38 @ ssItem )
& ( sk37 @ ssItem ) ),
inference(cnf,[status(esa)],[392]) ).
thf(395,plain,
sk38 @ ssItem,
inference(cnfConj,[status(thm)],[393]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ neq ) )
<=> ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(209,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( ( A != B )
=> ( B @ ( A @ neq ) ) )
& ( ( B @ ( A @ neq ) )
=> ( A != B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(210,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ neq ) )
| ( A = B )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) )
& ( ( A != B )
| ~ ( B @ ( A @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ) ),
inference(cnf,[status(esa)],[209]) ).
thf(211,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ ( A @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[210]) ).
thf(213,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A != B ) ),
inference(lifteq,[status(thm)],[211]) ).
thf(214,plain,
! [A: $i] :
( ~ ( A @ ( A @ neq ) )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[213]) ).
thf(643,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[395,214]) ).
thf(644,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[643]) ).
thf(645,plain,
~ ( sk38 @ ( sk38 @ neq ) ),
inference(pattern_uni,[status(thm)],[644:[bind(A,$thf( sk38 ))]]) ).
thf(394,plain,
sk37 @ ssItem,
inference(cnfConj,[status(thm)],[393]) ).
thf(627,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[394,214]) ).
thf(628,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[627]) ).
thf(629,plain,
~ ( sk37 @ ( sk37 @ neq ) ),
inference(pattern_uni,[status(thm)],[628:[bind(A,$thf( sk37 ))]]) ).
thf(53,axiom,
nil @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
thf(347,plain,
nil @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(52,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( B @ ( A @ cons ) @ totalorderedP )
<=> ( ( ( B @ hd @ ( A @ leq ) )
& ( B @ totalorderedP )
& ( nil != B ) )
| ( nil = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax67) ).
thf(333,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( ( ( B @ hd @ ( A @ leq ) )
& ( B @ totalorderedP )
& ( nil != B ) )
| ( nil = B ) )
=> ( B @ ( A @ cons ) @ totalorderedP ) )
& ( ( B @ ( A @ cons ) @ totalorderedP )
=> ( ( ( B @ hd @ ( A @ leq ) )
& ( B @ totalorderedP )
& ( nil != B ) )
| ( nil = B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( nil @ ( D @ neq ) )
& ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( D @ ( nil @ neq ) )
& ? [H: $i] :
( ( D @ ( nil @ neq ) )
& ( ( D @ hd )
= H )
& ( ( nil @ ( H @ cons ) )
= G )
& ( H @ ssItem ) )
& ( ( G @ ( F @ app ) )
= E )
& ( ( D @ tl )
= F )
& ( G @ ssList ) )
& ( F @ ssList ) )
& ( C != E )
& ( E @ ssList ) ) )
| ( ( nil = D )
& ( nil != C ) )
| ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( ( F @ ( nil @ ( E @ cons ) @ ( G @ app ) @ app ) )
= A )
& ( ( G @ ( nil @ ( E @ cons ) @ ( F @ app ) @ app ) )
= B )
& ( G @ ssList ) )
& ( F @ ssList ) )
& ( E @ ssItem ) )
| ~ ( nil @ ( B @ neq ) )
| ( A != C )
| ( B != D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( nil @ ( D @ neq ) )
& ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( D @ ( nil @ neq ) )
& ? [H: $i] :
( ( D @ ( nil @ neq ) )
& ( ( D @ hd )
= H )
& ( ( nil @ ( H @ cons ) )
= G )
& ( H @ ssItem ) )
& ( ( G @ ( F @ app ) )
= E )
& ( ( D @ tl )
= F )
& ( G @ ssList ) )
& ( F @ ssList ) )
& ( C != E )
& ( E @ ssList ) ) )
| ( ( nil = D )
& ( nil != C ) )
| ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( ( F @ ( nil @ ( E @ cons ) @ ( G @ app ) @ app ) )
= A )
& ( ( G @ ( nil @ ( E @ cons ) @ ( F @ app ) @ app ) )
= B )
& ( G @ ssList ) )
& ( F @ ssList ) )
& ( E @ ssItem ) )
| ~ ( nil @ ( B @ neq ) )
| ( A != C )
| ( B != D ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(98,plain,
~ ! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( nil @ ( D @ neq ) )
& ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( D @ ( nil @ neq ) )
& ? [H: $i] :
( ( D @ ( nil @ neq ) )
& ( ( D @ hd )
= H )
& ( ( nil @ ( H @ cons ) )
= G )
& ( H @ ssItem ) )
& ( ( G @ ( F @ app ) )
= E )
& ( ( D @ tl )
= F )
& ( G @ ssList ) )
& ( F @ ssList ) )
& ( C != E )
& ( E @ ssList ) ) )
| ( ( nil = D )
& ( nil != C ) )
| ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( ( F @ ( nil @ ( E @ cons ) @ ( G @ app ) @ app ) )
= A )
& ( ( G @ ( nil @ ( E @ cons ) @ ( F @ app ) @ app ) )
= B )
& ( G @ ssList ) )
& ( F @ ssList ) )
& ( E @ ssItem ) )
| ~ ( nil @ ( B @ neq ) )
| ( A != C )
| ( B != D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(99,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ~ ( nil @ ( sk4 @ neq ) )
| ~ ( sk4 @ ( nil @ neq ) )
| ~ ( sk4 @ ( nil @ neq ) )
| ( ( sk4 @ hd )
!= G )
| ( ( nil @ ( G @ cons ) )
!= F )
| ~ ( G @ ssItem )
| ( ( F @ ( E @ app ) )
!= D )
| ( ( sk4 @ tl )
!= E )
| ~ ( F @ ssList )
| ~ ( E @ ssList )
| ( sk3 = D )
| ~ ( D @ ssList ) )
& ( ( nil != sk4 )
| ( nil = sk3 ) )
& ( ( ( B @ ( nil @ ( A @ cons ) @ ( C @ app ) @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) )
& ( nil @ ( sk2 @ neq ) )
& ( sk1 = sk3 )
& ( sk2 = sk4 )
& ( sk4 @ ssList )
& ( sk3 @ ssList )
& ( sk2 @ ssList )
& ( sk1 @ ssList ) ),
inference(cnf,[status(esa)],[98]) ).
thf(105,plain,
sk2 @ ssList,
inference(cnfConj,[status(thm)],[99]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax57) ).
thf(246,plain,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(247,plain,
! [A: $i] :
( ( nil @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[246]) ).
thf(3828,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,247]) ).
thf(3829,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[3828]) ).
thf(3830,plain,
nil @ ( sk2 @ segmentP ),
inference(pattern_uni,[status(thm)],[3829:[bind(A,$thf( sk2 ))]]) ).
thf(34,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( nil @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
thf(234,plain,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( nil @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(106,plain,
sk1 @ ssList,
inference(cnfConj,[status(thm)],[99]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ cyclefreeP )
<=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ~ ( ( B @ ( C @ leq ) )
& ( C @ ( B @ leq ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8) ).
thf(155,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ~ ( ( B @ ( C @ leq ) )
& ( C @ ( B @ leq ) ) ) ) ) ) ) ) )
=> ( A @ cyclefreeP ) )
& ( ( A @ cyclefreeP )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ~ ( ( B @ ( C @ leq ) )
& ( C @ ( B @ leq ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(156,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ cyclefreeP )
| ( A @ sk5 @ ( A @ sk6 @ leq ) )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk6 @ ( A @ sk5 @ leq ) )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( ( A @ sk9 @ ( A @ sk6 @ cons ) @ ( A @ sk8 @ ( A @ sk5 @ cons ) @ ( A @ sk7 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk8 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk7 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk6 @ ssItem )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk5 @ ssItem )
| ~ ( A @ ssList ) )
& ( ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( B @ leq ) )
| ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
!= A )
| ~ ( F @ ssList )
| ~ ( E @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssItem )
| ~ ( B @ ssItem )
| ~ ( A @ cyclefreeP )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[155]) ).
thf(159,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk7 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[156]) ).
thf(4729,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,159]) ).
thf(4730,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssList ) ),
inference(simp,[status(thm)],[4729]) ).
thf(4731,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk7 @ ssList ) ),
inference(pattern_uni,[status(thm)],[4730:[bind(A,$thf( sk1 ))]]) ).
thf(59,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax45) ).
thf(376,plain,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(377,plain,
! [A: $i] :
( ( nil @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[376]) ).
thf(4875,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[4731,377]) ).
thf(4876,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[4875]) ).
thf(4877,plain,
( ( nil @ ( sk1 @ sk7 @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[4876:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(64,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ duplicatefreeP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax71) ).
thf(408,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ duplicatefreeP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(95,axiom,
nil @ totalorderP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax62) ).
thf(523,plain,
nil @ totalorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(108,plain,
sk2 = sk4,
inference(cnfConj,[status(thm)],[99]) ).
thf(115,plain,
sk4 = sk2,
inference(lifteq,[status(thm)],[108]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) )
!= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
thf(276,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) )
!= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(164,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk8 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[156]) ).
thf(6887,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,164]) ).
thf(6888,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ssList ) ),
inference(simp,[status(thm)],[6887]) ).
thf(6889,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk8 @ ssList ) ),
inference(pattern_uni,[status(thm)],[6888:[bind(A,$thf( sk1 ))]]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax51) ).
thf(299,plain,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(300,plain,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[299]) ).
thf(7130,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[6889,300]) ).
thf(7131,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7130]) ).
thf(7132,plain,
( ( nil @ ( sk1 @ sk8 @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7131:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(27,axiom,
nil @ duplicatefreeP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax72) ).
thf(202,plain,
nil @ duplicatefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax68) ).
thf(119,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(120,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[119]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ frontsegP ) )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax46) ).
thf(121,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( ( nil = A )
=> ( A @ ( nil @ frontsegP ) ) )
& ( ( A @ ( nil @ frontsegP ) )
=> ( nil = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(122,plain,
! [A: $i] :
( ( ( A @ ( nil @ frontsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) )
& ( ( nil = A )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[121]) ).
thf(124,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[122]) ).
thf(126,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[124]) ).
thf(127,plain,
( ( nil @ ( nil @ frontsegP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[126]) ).
thf(830,plain,
( ( nil @ ( nil @ frontsegP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[127,347]) ).
thf(831,plain,
nil @ ( nil @ frontsegP ),
inference(simp,[status(thm)],[830]) ).
thf(123,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[122]) ).
thf(125,plain,
! [A: $i] :
( ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[123]) ).
thf(1031,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[106,125]) ).
thf(1032,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[1031]) ).
thf(1033,plain,
( ~ ( sk1 @ ( nil @ frontsegP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[1032:[bind(A,$thf( sk1 ))]]) ).
thf(157,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk5 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[156]) ).
thf(707,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk5 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,157]) ).
thf(708,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk5 @ ssItem ) ),
inference(simp,[status(thm)],[707]) ).
thf(709,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk5 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[708:[bind(A,$thf( sk1 ))]]) ).
thf(1206,plain,
( ( sk1 != sk1 )
| ( sk1 @ cyclefreeP )
| ( nil @ sk5 @ ssItem )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1033,709]) ).
thf(1207,plain,
( ( sk1 @ cyclefreeP )
| ( nil @ sk5 @ ssItem )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1206:[]]) ).
thf(1551,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk1 @ cyclefreeP )
| ( nil @ sk5 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[831,1207]) ).
thf(1552,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk1 @ cyclefreeP )
| ( nil @ sk5 @ ssItem ) ),
inference(simp,[status(thm)],[1551]) ).
thf(1564,plain,
( ( sk1 != nil )
| ( nil != nil )
| ( sk1 @ cyclefreeP )
| ( nil @ sk5 @ ssItem ) ),
inference(simp,[status(thm)],[1552]) ).
thf(1566,plain,
( ( sk1 != nil )
| ( sk1 @ cyclefreeP )
| ( nil @ sk5 @ ssItem ) ),
inference(simp,[status(thm)],[1564]) ).
thf(1703,plain,
! [A: $i] :
( ( ( nil @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk1 != nil )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[1566,120]) ).
thf(1704,plain,
! [A: $i] :
( ( ( nil @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk1 != nil )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1703]) ).
thf(1705,plain,
( ( nil @ ( nil @ sk5 @ cons ) @ strictorderedP )
| ( sk1 != nil )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1704:[bind(A,$thf( nil @ sk5 ))]]) ).
thf(97,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ geq ) )
<=> ( A @ ( B @ leq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax32) ).
thf(533,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( ( A @ ( B @ leq ) )
=> ( B @ ( A @ geq ) ) )
& ( ( B @ ( A @ geq ) )
=> ( A @ ( B @ leq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(4837,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[4731,247]) ).
thf(4838,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[4837]) ).
thf(4839,plain,
( ( nil @ ( sk1 @ sk7 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[4838:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(88,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax29) ).
thf(500,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(713,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk5 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,157]) ).
thf(714,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk5 @ ssItem ) ),
inference(simp,[status(thm)],[713]) ).
thf(715,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk5 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[714:[bind(A,$thf( sk2 ))]]) ).
thf(4741,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,159]) ).
thf(4742,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssList ) ),
inference(simp,[status(thm)],[4741]) ).
thf(4743,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk7 @ ssList ) ),
inference(pattern_uni,[status(thm)],[4742:[bind(A,$thf( sk2 ))]]) ).
thf(5003,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[4743,377]) ).
thf(5004,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5003]) ).
thf(5005,plain,
( ( nil @ ( sk2 @ sk7 @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5004:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(51,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( B @ ( A @ neq ) )
<=> ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
thf(326,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( A != B )
=> ( B @ ( A @ neq ) ) )
& ( ( B @ ( A @ neq ) )
=> ( A != B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(327,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ neq ) )
| ( A = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) )
& ( ( A != B )
| ~ ( B @ ( A @ neq ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[326]) ).
thf(328,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ ( A @ neq ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[327]) ).
thf(330,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ neq ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( A != B ) ),
inference(lifteq,[status(thm)],[328]) ).
thf(331,plain,
! [A: $i] :
( ~ ( A @ ( A @ neq ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[330]) ).
thf(832,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,331]) ).
thf(833,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[832]) ).
thf(834,plain,
~ ( sk1 @ ( sk1 @ neq ) ),
inference(pattern_uni,[status(thm)],[833:[bind(A,$thf( sk1 ))]]) ).
thf(1221,plain,
( ( sk1 != sk1 )
| ~ ( nil @ ( sk1 @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1033,834]) ).
thf(1222,plain,
( ~ ( nil @ ( sk1 @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1221:[]]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil @ ( A @ app ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax84) ).
thf(185,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil @ ( A @ app ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax90) ).
thf(219,plain,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(220,plain,
! [A: $i] :
( ~ ( A @ ( A @ lt ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[219]) ).
thf(780,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[715,220]) ).
thf(781,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[780]) ).
thf(782,plain,
( ~ ( sk2 @ sk5 @ ( sk2 @ sk5 @ lt ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[781:[bind(A,$thf( sk2 @ sk5 ))]]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ equalelemsP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax73) ).
thf(301,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ equalelemsP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(100,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( nil @ ( sk4 @ neq ) )
| ~ ( sk4 @ ( nil @ neq ) )
| ~ ( sk4 @ ( nil @ neq ) )
| ( ( sk4 @ hd )
!= D )
| ( ( nil @ ( D @ cons ) )
!= C )
| ~ ( D @ ssItem )
| ( ( C @ ( B @ app ) )
!= A )
| ( ( sk4 @ tl )
!= B )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ( sk3 = A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(113,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( nil @ ( sk4 @ neq ) )
| ~ ( sk4 @ ( nil @ neq ) )
| ~ ( sk4 @ ( nil @ neq ) )
| ~ ( D @ ssItem )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( sk4 @ hd )
!= D )
| ( ( nil @ ( D @ cons ) )
!= C )
| ( ( C @ ( B @ app ) )
!= A )
| ( ( sk4 @ tl )
!= B )
| ( sk3 = A ) ),
inference(lifteq,[status(thm)],[100]) ).
thf(114,plain,
( ~ ( nil @ ( sk4 @ neq ) )
| ~ ( sk4 @ ( nil @ neq ) )
| ~ ( sk4 @ hd @ ssItem )
| ~ ( nil @ ( sk4 @ hd @ cons ) @ ssList )
| ~ ( sk4 @ tl @ ssList )
| ~ ( nil @ ( sk4 @ hd @ cons ) @ ( sk4 @ tl @ app ) @ ssList )
| ( ( nil @ ( sk4 @ hd @ cons ) @ ( sk4 @ tl @ app ) )
= sk3 ) ),
inference(simp,[status(thm)],[113]) ).
thf(107,plain,
sk1 = sk3,
inference(cnfConj,[status(thm)],[99]) ).
thf(112,plain,
sk3 = sk1,
inference(lifteq,[status(thm)],[107]) ).
thf(565,plain,
( ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk2 @ hd @ ssItem )
| ~ ( nil @ ( sk2 @ hd @ cons ) @ ssList )
| ~ ( sk2 @ tl @ ssList )
| ~ ( nil @ ( sk2 @ hd @ cons ) @ ( sk2 @ tl @ app ) @ ssList )
| ( ( nil @ ( sk2 @ hd @ cons ) @ ( sk2 @ tl @ app ) )
= sk1 ) ),
inference(rewrite,[status(thm)],[114,112,115]) ).
thf(161,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[156]) ).
thf(5748,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,161]) ).
thf(5749,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList ) ),
inference(simp,[status(thm)],[5748]) ).
thf(5750,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk9 @ ssList ) ),
inference(pattern_uni,[status(thm)],[5749:[bind(A,$thf( sk1 ))]]) ).
thf(4894,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[4731,331]) ).
thf(4895,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[4894]) ).
thf(4896,plain,
( ~ ( sk1 @ sk7 @ ( sk1 @ sk7 @ neq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[4895:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(104,plain,
nil @ ( sk2 @ neq ),
inference(cnfConj,[status(thm)],[99]) ).
thf(654,plain,
( ( ( sk37 @ ( sk37 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,629]) ).
thf(655,plain,
( ( sk37 @ ( sk37 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[654]) ).
thf(656,plain,
( ( sk37 != nil )
| ( sk37 != sk2 ) ),
inference(simp,[status(thm)],[655]) ).
thf(1069,plain,
! [A: $i] :
( ( A != sk37 )
| ( nil != nil )
| ( sk37 != sk2 )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[125,656]) ).
thf(1070,plain,
! [A: $i] :
( ( A != sk37 )
| ( sk37 != sk2 )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[1069]) ).
thf(1071,plain,
( ( sk37 != sk2 )
| ~ ( sk37 @ ( nil @ frontsegP ) )
| ~ ( sk37 @ ssList ) ),
inference(pattern_uni,[status(thm)],[1070:[bind(A,$thf( sk37 ))]]) ).
thf(3573,plain,
( ( ( sk37 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk37 != sk2 )
| ~ ( sk37 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,1071]) ).
thf(3574,plain,
( ( ( sk37 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk37 != sk2 )
| ~ ( sk37 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[3573]) ).
thf(3603,plain,
( ( sk37 != sk2 )
| ( sk37 != sk2 )
| ~ ( sk37 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[3574]) ).
thf(3617,plain,
( ( sk37 != sk2 )
| ~ ( sk37 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[3603]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ segmentP ) )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax58) ).
thf(136,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( ( nil = A )
=> ( A @ ( nil @ segmentP ) ) )
& ( ( A @ ( nil @ segmentP ) )
=> ( nil = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(137,plain,
! [A: $i] :
( ( ( A @ ( nil @ segmentP ) )
| ( nil != A )
| ~ ( A @ ssList ) )
& ( ( nil = A )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[136]) ).
thf(138,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[137]) ).
thf(140,plain,
! [A: $i] :
( ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[138]) ).
thf(835,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,331]) ).
thf(836,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[835]) ).
thf(837,plain,
~ ( sk2 @ ( sk2 @ neq ) ),
inference(pattern_uni,[status(thm)],[836:[bind(A,$thf( sk2 ))]]) ).
thf(849,plain,
( ( ( sk2 @ ( sk2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,837]) ).
thf(850,plain,
( ( sk2 @ ( sk2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[849]) ).
thf(851,plain,
( ( sk2 != nil )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[850]) ).
thf(852,plain,
sk2 != nil,
inference(simp,[status(thm)],[851]) ).
thf(1976,plain,
! [A: $i] :
( ( A != sk2 )
| ( nil != nil )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[140,852]) ).
thf(1977,plain,
! [A: $i] :
( ( A != sk2 )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[1976]) ).
thf(1978,plain,
( ~ ( sk2 @ ( nil @ segmentP ) )
| ~ ( sk2 @ ssList ) ),
inference(pattern_uni,[status(thm)],[1977:[bind(A,$thf( sk2 ))]]) ).
thf(2355,plain,
( ~ ( sk2 @ ( nil @ segmentP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[1978,105]) ).
thf(2356,plain,
~ ( sk2 @ ( nil @ segmentP ) ),
inference(simp,[status(thm)],[2355]) ).
thf(80,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ equalelemsP )
<=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ( ( ( E @ ( C @ cons ) @ ( B @ cons ) @ ( D @ app ) )
= A )
=> ( B = C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax14) ).
thf(460,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ( ( ( E @ ( C @ cons ) @ ( B @ cons ) @ ( D @ app ) )
= A )
=> ( B = C ) ) ) ) ) )
=> ( A @ equalelemsP ) )
& ( ( A @ equalelemsP )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ( ( ( E @ ( C @ cons ) @ ( B @ cons ) @ ( D @ app ) )
= A )
=> ( B = C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(70,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ singletonP )
<=> ? [B: $i] :
( ( ( nil @ ( B @ cons ) )
= A )
& ( B @ ssItem ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
thf(421,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( ? [B: $i] :
( ( ( nil @ ( B @ cons ) )
= A )
& ( B @ ssItem ) )
=> ( A @ singletonP ) )
& ( ( A @ singletonP )
=> ? [B: $i] :
( ( ( nil @ ( B @ cons ) )
= A )
& ( B @ ssItem ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(160,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk6 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[156]) ).
thf(5325,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk6 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,160]) ).
thf(5326,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk6 @ ssItem ) ),
inference(simp,[status(thm)],[5325]) ).
thf(5327,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk6 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[5326:[bind(A,$thf( sk1 ))]]) ).
thf(5395,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5327,120]) ).
thf(5396,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5395]) ).
thf(5397,plain,
( ( nil @ ( sk1 @ sk6 @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5396:[bind(A,$thf( sk1 @ sk6 ))]]) ).
thf(68,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( ( A @ tl @ ( A @ hd @ cons ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax78) ).
thf(416,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( ( A @ tl @ ( A @ hd @ cons ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( C @ ( B @ ( A @ app ) @ app ) )
= ( C @ ( B @ app ) @ ( A @ app ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax82) ).
thf(152,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( C @ ( B @ ( A @ app ) @ app ) )
= ( C @ ( B @ app ) @ ( A @ app ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(5018,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[4743,331]) ).
thf(5019,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5018]) ).
thf(5020,plain,
( ~ ( sk2 @ sk7 @ ( sk2 @ sk7 @ neq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5019:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(4965,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[4743,247]) ).
thf(4966,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[4965]) ).
thf(4967,plain,
( ( nil @ ( sk2 @ sk7 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[4966:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ app ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
thf(216,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ app ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(75,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ rearsegP ) )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax52) ).
thf(443,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( ( nil = A )
=> ( A @ ( nil @ rearsegP ) ) )
& ( ( A @ ( nil @ rearsegP ) )
=> ( nil = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( B @ ( A @ frontsegP ) )
<=> ? [C: $i] :
( ( ( C @ ( B @ app ) )
= A )
& ( C @ ssList ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
thf(238,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ? [C: $i] :
( ( ( C @ ( B @ app ) )
= A )
& ( C @ ssList ) )
=> ( B @ ( A @ frontsegP ) ) )
& ( ( B @ ( A @ frontsegP ) )
=> ? [C: $i] :
( ( ( C @ ( B @ app ) )
= A )
& ( C @ ssList ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( ( B @ tl )
= ( A @ tl ) )
& ( ( B @ hd )
= ( A @ hd ) )
& ( nil != A )
& ( nil != B ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax77) ).
thf(348,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( ( B @ tl )
= ( A @ tl ) )
& ( ( B @ hd )
= ( A @ hd ) )
& ( nil != A )
& ( nil != B ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(819,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[709,120]) ).
thf(820,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[819]) ).
thf(821,plain,
( ( nil @ ( sk1 @ sk5 @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[820:[bind(A,$thf( sk1 @ sk5 ))]]) ).
thf(85,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ geq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax89) ).
thf(492,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(5912,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5750,377]) ).
thf(5913,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5912]) ).
thf(5914,plain,
( ( nil @ ( sk1 @ sk9 @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5913:[bind(A,$thf( sk1 @ sk9 ))]]) ).
thf(235,plain,
! [A: $i] :
( ~ ( A @ ( nil @ memberP ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[234]) ).
thf(764,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[709,235]) ).
thf(765,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[764]) ).
thf(766,plain,
( ~ ( sk1 @ sk5 @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[765:[bind(A,$thf( sk1 @ sk5 ))]]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) )
= ( A @ ( nil @ ( B @ cons ) @ app ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax81) ).
thf(147,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) )
= ( A @ ( nil @ ( B @ cons ) @ app ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(396,plain,
sk37 != sk38,
inference(cnfConj,[status(thm)],[393]) ).
thf(397,plain,
sk38 != sk37,
inference(lifteq,[status(thm)],[396]) ).
thf(690,plain,
( ( ( sk38 @ ( sk38 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,645]) ).
thf(691,plain,
( ( sk38 @ ( sk38 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[690]) ).
thf(692,plain,
( ( sk38 != nil )
| ( sk38 != sk2 ) ),
inference(simp,[status(thm)],[691]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ strictorderedP )
<=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( C @ ( B @ lt ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax12) ).
thf(221,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( C @ ( B @ lt ) ) ) ) ) ) ) )
=> ( A @ strictorderedP ) )
& ( ( A @ strictorderedP )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( C @ ( B @ lt ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ hd @ ssItem ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
thf(293,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ hd @ ssItem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(77,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ( ( ( C @ ( B @ lt ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ lt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax91) ).
thf(453,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ( ( ( C @ ( B @ lt ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ lt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( B @ frontsegP ) )
& ( B @ ( A @ frontsegP ) ) )
=> ( C @ ( A @ frontsegP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax40) ).
thf(131,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( B @ frontsegP ) )
& ( B @ ( A @ frontsegP ) ) )
=> ( C @ ( A @ frontsegP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(132,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ frontsegP ) )
| ~ ( C @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[131]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) @ hd )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).
thf(133,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) @ hd )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1034,plain,
! [A: $i] :
( ( A != sk38 )
| ( sk37 != nil )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[125,397]) ).
thf(1035,plain,
( ( sk37 != nil )
| ~ ( sk38 @ ( nil @ frontsegP ) )
| ~ ( sk38 @ ssList ) ),
inference(pattern_uni,[status(thm)],[1034:[bind(A,$thf( sk38 ))]]) ).
thf(1164,plain,
( ( ( sk38 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk37 != nil )
| ~ $true
| ~ ( sk38 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[831,1035]) ).
thf(1165,plain,
( ( ( sk38 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk37 != nil )
| ~ ( sk38 @ ssList ) ),
inference(simp,[status(thm)],[1164]) ).
thf(1186,plain,
( ( sk38 != nil )
| ( nil != nil )
| ( sk37 != nil )
| ~ ( sk38 @ ssList ) ),
inference(simp,[status(thm)],[1165]) ).
thf(1187,plain,
( ( sk38 != nil )
| ( sk37 != nil )
| ~ ( sk38 @ ssList ) ),
inference(simp,[status(thm)],[1186]) ).
thf(1327,plain,
( ( ( sk38 @ ssList )
!= ( nil @ ssList ) )
| ( sk38 != nil )
| ( sk37 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[347,1187]) ).
thf(1328,plain,
( ( ( sk38 @ ssList )
!= ( nil @ ssList ) )
| ( sk38 != nil )
| ( sk37 != nil ) ),
inference(simp,[status(thm)],[1327]) ).
thf(1342,plain,
( ( sk38 != nil )
| ( sk38 != nil )
| ( sk37 != nil ) ),
inference(simp,[status(thm)],[1328]) ).
thf(1345,plain,
( ( sk38 != nil )
| ( sk37 != nil ) ),
inference(simp,[status(thm)],[1342]) ).
thf(3,axiom,
nil @ strictorderedP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax69) ).
thf(116,plain,
nil @ strictorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(91,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49) ).
thf(507,plain,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ( A @ tl )
= B )
& ( B @ ssList ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax76) ).
thf(248,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ( A @ tl )
= B )
& ( B @ ssList ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ( ( ( C @ ( B @ lt ) )
& ( B @ ( A @ lt ) ) )
=> ( C @ ( A @ lt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax34) ).
thf(117,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ( ( ( C @ ( B @ lt ) )
& ( B @ ( A @ lt ) ) )
=> ( C @ ( A @ lt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(93,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ lt ) )
<=> ( ( B @ ( A @ leq ) )
& ( A != B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax93) ).
thf(512,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( ( ( B @ ( A @ leq ) )
& ( A != B ) )
=> ( B @ ( A @ lt ) ) )
& ( ( B @ ( A @ lt ) )
=> ( ( B @ ( A @ leq ) )
& ( A != B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(859,plain,
! [A: $i] :
( ( A != sk2 )
| ( nil != nil )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[125,852]) ).
thf(860,plain,
! [A: $i] :
( ( A != sk2 )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[859]) ).
thf(861,plain,
( ~ ( sk2 @ ( nil @ frontsegP ) )
| ~ ( sk2 @ ssList ) ),
inference(pattern_uni,[status(thm)],[860:[bind(A,$thf( sk2 ))]]) ).
thf(1152,plain,
( ~ ( sk2 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[861,105]) ).
thf(1153,plain,
~ ( sk2 @ ( nil @ frontsegP ) ),
inference(simp,[status(thm)],[1152]) ).
thf(71,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( B @ ( A @ app ) @ ssList ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
thf(429,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( B @ ( A @ app ) @ ssList ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(845,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk1 @ ( sk1 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,834]) ).
thf(846,plain,
( ( nil @ ( sk2 @ neq ) )
!= ( sk1 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[845]) ).
thf(847,plain,
( ( sk1 != nil )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[846]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ leq ) )
=> ( ( B @ ( A @ lt ) )
| ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax92) ).
thf(197,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ leq ) )
=> ( ( B @ ( A @ lt ) )
| ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(74,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( B @ ( A @ rearsegP ) )
<=> ? [C: $i] :
( ( ( B @ ( C @ app ) )
= A )
& ( C @ ssList ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).
thf(435,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ? [C: $i] :
( ( ( B @ ( C @ app ) )
= A )
& ( C @ ssList ) )
=> ( B @ ( A @ rearsegP ) ) )
& ( ( B @ ( A @ rearsegP ) )
=> ? [C: $i] :
( ( ( B @ ( C @ app ) )
= A )
& ( C @ ssList ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(139,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ( nil != A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[137]) ).
thf(141,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[139]) ).
thf(142,plain,
( ( nil @ ( nil @ segmentP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[141]) ).
thf(1142,plain,
( ( nil @ ( nil @ segmentP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[142,347]) ).
thf(1143,plain,
nil @ ( nil @ segmentP ),
inference(simp,[status(thm)],[1142]) ).
thf(1225,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ( sk2 != sk1 )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1033,847]) ).
thf(1226,plain,
( ( sk1 != sk1 )
| ( sk2 != sk1 )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1225]) ).
thf(1227,plain,
( ( sk2 != sk1 )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1226:[]]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( B @ segmentP ) )
& ( B @ ( A @ segmentP ) ) )
=> ( C @ ( A @ segmentP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax53) ).
thf(188,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( B @ segmentP ) )
& ( B @ ( A @ segmentP ) ) )
=> ( C @ ( A @ segmentP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( A @ ( B @ cons ) @ ssList ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
thf(169,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( A @ ( B @ cons ) @ ssList ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax55) ).
thf(193,plain,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(82,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( B @ rearsegP ) )
& ( B @ ( A @ rearsegP ) ) )
=> ( C @ ( A @ rearsegP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax47) ).
thf(476,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( B @ rearsegP ) )
& ( B @ ( A @ rearsegP ) ) )
=> ( C @ ( A @ rearsegP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(640,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[395,235]) ).
thf(641,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[640]) ).
thf(642,plain,
~ ( sk38 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[641:[bind(A,$thf( sk38 ))]]) ).
thf(1924,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[106,140]) ).
thf(1925,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[1924]) ).
thf(1926,plain,
( ~ ( sk1 @ ( nil @ segmentP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[1925:[bind(A,$thf( sk1 ))]]) ).
thf(2284,plain,
( ( sk1 != sk1 )
| ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[1926,834]) ).
thf(2285,plain,
( ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[2284:[]]) ).
thf(699,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[394,220]) ).
thf(700,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[699]) ).
thf(701,plain,
~ ( sk37 @ ( sk37 @ lt ) ),
inference(pattern_uni,[status(thm)],[700:[bind(A,$thf( sk37 ))]]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( nil
= ( B @ ( A @ app ) ) )
<=> ( ( nil = A )
& ( nil = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax83) ).
thf(360,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( ( nil = A )
& ( nil = B ) )
=> ( nil
= ( B @ ( A @ app ) ) ) )
& ( ( nil
= ( B @ ( A @ app ) ) )
=> ( ( nil = A )
& ( nil = B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(361,plain,
! [B: $i,A: $i] :
( ( ( nil
= ( B @ ( A @ app ) ) )
| ( nil != A )
| ( nil != B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) )
& ( ( nil = A )
| ( nil
!= ( B @ ( A @ app ) ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) )
& ( ( nil = B )
| ( nil
!= ( B @ ( A @ app ) ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[360]) ).
thf(364,plain,
! [B: $i,A: $i] :
( ( nil
= ( B @ ( A @ app ) ) )
| ( nil != A )
| ( nil != B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[361]) ).
thf(367,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
= nil )
| ( nil != A )
| ( nil != B ) ),
inference(lifteq,[status(thm)],[364]) ).
thf(368,plain,
( ~ ( nil @ ssList )
| ( ( nil @ ( nil @ app ) )
= nil ) ),
inference(simp,[status(thm)],[367]) ).
thf(1296,plain,
( ~ $true
| ( ( nil @ ( nil @ app ) )
= nil ) ),
inference(rewrite,[status(thm)],[368,347]) ).
thf(1297,plain,
( ( nil @ ( nil @ app ) )
= nil ),
inference(simp,[status(thm)],[1296]) ).
thf(79,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( nil != A )
=> ( ( B @ ( A @ app ) @ tl )
= ( B @ ( A @ tl @ app ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax86) ).
thf(457,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( nil != A )
=> ( ( B @ ( A @ app ) @ tl )
= ( B @ ( A @ tl @ app ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(2271,plain,
( ( sk1 != sk1 )
| ( sk1 @ cyclefreeP )
| ( nil @ sk5 @ ssItem )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[1926,709]) ).
thf(2272,plain,
( ( sk1 @ cyclefreeP )
| ( nil @ sk5 @ ssItem )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[2271:[]]) ).
thf(58,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( A @ ( C @ ( B @ app ) @ memberP ) )
<=> ( ( A @ ( C @ memberP ) )
| ( A @ ( B @ memberP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax36) ).
thf(371,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( ( A @ ( C @ memberP ) )
| ( A @ ( B @ memberP ) ) )
=> ( A @ ( C @ ( B @ app ) @ memberP ) ) )
& ( ( A @ ( C @ ( B @ app ) @ memberP ) )
=> ( ( A @ ( C @ memberP ) )
| ( A @ ( B @ memberP ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(89,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ lt ) )
=> ~ ( A @ ( B @ lt ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax33) ).
thf(503,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ lt ) )
=> ~ ( A @ ( B @ lt ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ gt ) )
=> ~ ( A @ ( B @ gt ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax94) ).
thf(128,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ gt ) )
=> ~ ( A @ ( B @ gt ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(129,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[128]) ).
thf(7025,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[6889,247]) ).
thf(7026,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7025]) ).
thf(7027,plain,
( ( nil @ ( sk1 @ sk8 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7026:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(4286,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,377]) ).
thf(4287,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) ) ),
inference(simp,[status(thm)],[4286]) ).
thf(4288,plain,
nil @ ( sk1 @ frontsegP ),
inference(pattern_uni,[status(thm)],[4287:[bind(A,$thf( sk1 ))]]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ gt ) )
<=> ( A @ ( B @ lt ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax35) ).
thf(205,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( ( A @ ( B @ lt ) )
=> ( B @ ( A @ gt ) ) )
& ( ( B @ ( A @ gt ) )
=> ( A @ ( B @ lt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(1179,plain,
( ( ( sk38 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk37 != nil )
| ~ ( sk38 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,1035]) ).
thf(1180,plain,
( ( ( sk38 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk37 != nil )
| ~ ( sk38 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1179]) ).
thf(1185,plain,
( ( sk38 != sk1 )
| ( sk37 != nil )
| ~ ( sk38 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1180]) ).
thf(62,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( A @ ( C @ ( B @ cons ) @ memberP ) )
<=> ( ( A @ ( C @ memberP ) )
| ( A = B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax37) ).
thf(398,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( ( A @ ( C @ memberP ) )
| ( A = B ) )
=> ( A @ ( C @ ( B @ cons ) @ memberP ) ) )
& ( ( A @ ( C @ ( B @ cons ) @ memberP ) )
=> ( ( A @ ( C @ memberP ) )
| ( A = B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(6899,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,164]) ).
thf(6900,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ssList ) ),
inference(simp,[status(thm)],[6899]) ).
thf(6901,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk8 @ ssList ) ),
inference(pattern_uni,[status(thm)],[6900:[bind(A,$thf( sk2 ))]]) ).
thf(5760,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,161]) ).
thf(5761,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList ) ),
inference(simp,[status(thm)],[5760]) ).
thf(5762,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk9 @ ssList ) ),
inference(pattern_uni,[status(thm)],[5761:[bind(A,$thf( sk2 ))]]) ).
thf(822,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[394,120]) ).
thf(823,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[822]) ).
thf(824,plain,
nil @ ( sk37 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[823:[bind(A,$thf( sk37 ))]]) ).
thf(1219,plain,
( ( sk1 != sk1 )
| ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1033,834]) ).
thf(1220,plain,
( ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1219:[]]) ).
thf(1456,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk1 @ ( nil @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[831,1220]) ).
thf(1457,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk1 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[1456]) ).
thf(1480,plain,
( ( sk1 != nil )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[1457]) ).
thf(1483,plain,
( ( sk1 != nil )
| ~ ( sk1 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[1480]) ).
thf(6082,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5762,300]) ).
thf(6083,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[6082]) ).
thf(6084,plain,
( ( nil @ ( sk2 @ sk9 @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[6083:[bind(A,$thf( sk2 @ sk9 ))]]) ).
thf(42,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( B @ ( A @ cons ) @ strictorderedP )
<=> ( ( ( B @ hd @ ( A @ lt ) )
& ( B @ strictorderedP )
& ( nil != B ) )
| ( nil = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax70) ).
thf(279,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( ( ( B @ hd @ ( A @ lt ) )
& ( B @ strictorderedP )
& ( nil != B ) )
| ( nil = B ) )
=> ( B @ ( A @ cons ) @ strictorderedP ) )
& ( ( B @ ( A @ cons ) @ strictorderedP )
=> ( ( ( B @ hd @ ( A @ lt ) )
& ( B @ strictorderedP )
& ( nil != B ) )
| ( nil = B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ tl @ ssList ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
thf(296,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ tl @ ssList ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(158,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk6 @ ( A @ sk5 @ leq ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[156]) ).
thf(4597,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk6 @ ( A @ sk5 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,158]) ).
thf(4598,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk6 @ ( A @ sk5 @ leq ) ) ),
inference(simp,[status(thm)],[4597]) ).
thf(4599,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk6 @ ( sk1 @ sk5 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[4598:[bind(A,$thf( sk1 ))]]) ).
thf(148,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ cons ) )
= ( A @ ( nil @ ( B @ cons ) @ app ) ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[147]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( ( A @ ( B @ cons ) )
= ( A @ ( nil @ ( B @ cons ) @ app ) ) ) ),
inference(lifteq,[status(thm)],[148]) ).
thf(118,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ lt ) )
| ~ ( C @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) )
| ~ ( C @ ssItem )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[117]) ).
thf(28,axiom,
~ ( nil @ singletonP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).
thf(203,plain,
~ ( nil @ singletonP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(204,plain,
~ ( nil @ singletonP ),
inference(polarity_switch,[status(thm)],[203]) ).
thf(66,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax30) ).
thf(413,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( B @ ( A @ segmentP ) )
=> ( B @ ( D @ ( A @ ( C @ app ) @ app ) @ segmentP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax56) ).
thf(236,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( B @ ( A @ segmentP ) )
=> ( B @ ( D @ ( A @ ( C @ app ) @ app ) @ segmentP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(4097,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,300]) ).
thf(4098,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[4097]) ).
thf(4099,plain,
nil @ ( sk1 @ rearsegP ),
inference(pattern_uni,[status(thm)],[4098:[bind(A,$thf( sk1 ))]]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( A @ ( B @ frontsegP ) )
& ( B @ ( A @ frontsegP ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax41) ).
thf(144,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( A @ ( B @ frontsegP ) )
& ( B @ ( A @ frontsegP ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6046,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5762,377]) ).
thf(6047,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[6046]) ).
thf(6048,plain,
( ( nil @ ( sk2 @ sk9 @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[6047:[bind(A,$thf( sk2 @ sk9 ))]]) ).
thf(63,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ( ( ( C @ ( B @ geq ) )
& ( B @ ( A @ geq ) ) )
=> ( C @ ( A @ geq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax88) ).
thf(406,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ( ( ( C @ ( B @ geq ) )
& ( B @ ( A @ geq ) ) )
=> ( C @ ( A @ geq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(69,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ cyclefreeP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax59) ).
thf(419,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ cyclefreeP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(92,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( nil
!= ( A @ ( B @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
thf(509,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( nil
!= ( A @ ( B @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(47,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssItem )
=> ( ( ( A @ ( C @ cons ) )
= ( B @ ( D @ cons ) ) )
=> ( ( B = A )
& ( C = D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax19) ).
thf(303,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssItem )
=> ( ( ( A @ ( C @ cons ) )
= ( B @ ( D @ cons ) ) )
=> ( ( B = A )
& ( C = D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(86,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( A @ ( B @ segmentP ) )
& ( B @ ( A @ segmentP ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax54) ).
thf(494,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( A @ ( B @ segmentP ) )
& ( B @ ( A @ segmentP ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( ( A @ ( B @ geq ) )
& ( B @ ( A @ geq ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax87) ).
thf(323,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( ( A @ ( B @ geq ) )
& ( B @ ( A @ geq ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(797,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[715,214]) ).
thf(798,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[797]) ).
thf(799,plain,
( ~ ( sk2 @ sk5 @ ( sk2 @ sk5 @ neq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[798:[bind(A,$thf( sk2 @ sk5 ))]]) ).
thf(94,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( A @ ( B @ rearsegP ) )
& ( B @ ( A @ rearsegP ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax48) ).
thf(520,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( A @ ( B @ rearsegP ) )
& ( B @ ( A @ rearsegP ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(624,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[394,235]) ).
thf(625,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[624]) ).
thf(626,plain,
~ ( sk37 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[625:[bind(A,$thf( sk37 ))]]) ).
thf(767,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[709,214]) ).
thf(768,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[767]) ).
thf(769,plain,
( ~ ( sk1 @ sk5 @ ( sk1 @ sk5 @ neq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[768:[bind(A,$thf( sk1 @ sk5 ))]]) ).
thf(8,axiom,
nil @ totalorderedP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax66) ).
thf(130,plain,
nil @ totalorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5440,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5327,235]) ).
thf(5441,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5440]) ).
thf(5442,plain,
( ~ ( sk1 @ sk6 @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5441:[bind(A,$thf( sk1 @ sk6 ))]]) ).
thf(693,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[395,220]) ).
thf(694,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[693]) ).
thf(695,plain,
~ ( sk38 @ ( sk38 @ lt ) ),
inference(pattern_uni,[status(thm)],[694:[bind(A,$thf( sk38 ))]]) ).
thf(5337,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk6 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,160]) ).
thf(5338,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk6 @ ssItem ) ),
inference(simp,[status(thm)],[5337]) ).
thf(5339,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk6 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[5338:[bind(A,$thf( sk2 ))]]) ).
thf(5514,plain,
! [A: $i] :
( ( ( sk2 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5339,235]) ).
thf(5515,plain,
! [A: $i] :
( ( ( sk2 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5514]) ).
thf(5516,plain,
( ~ ( sk2 @ sk6 @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5515:[bind(A,$thf( sk2 @ sk6 ))]]) ).
thf(78,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax42) ).
thf(455,plain,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(134,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ cons ) @ hd )
= B )
| ~ ( B @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[133]) ).
thf(135,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( ( A @ ( B @ cons ) @ hd )
= B ) ),
inference(lifteq,[status(thm)],[134]) ).
thf(90,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( B @ ( A @ rearsegP ) )
=> ( B @ ( A @ ( C @ app ) @ rearsegP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax50) ).
thf(505,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( B @ ( A @ rearsegP ) )
=> ( B @ ( A @ ( C @ app ) @ rearsegP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(72,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax31) ).
thf(431,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(81,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) @ tl )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax25) ).
thf(473,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) @ tl )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(162,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk5 @ ( A @ sk6 @ leq ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[156]) ).
thf(1038,plain,
! [A: $i] :
( ( A != sk38 )
| ( nil != nil )
| ( sk38 != sk2 )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[125,692]) ).
thf(1039,plain,
! [A: $i] :
( ( A != sk38 )
| ( sk38 != sk2 )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[1038]) ).
thf(1040,plain,
( ( sk38 != sk2 )
| ~ ( sk38 @ ( nil @ frontsegP ) )
| ~ ( sk38 @ ssList ) ),
inference(pattern_uni,[status(thm)],[1039:[bind(A,$thf( sk38 ))]]) ).
thf(1674,plain,
( ( ( sk38 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk38 != sk2 )
| ~ ( sk38 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,1040]) ).
thf(1675,plain,
( ( ( sk38 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk38 != sk2 )
| ~ ( sk38 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1674]) ).
thf(1677,plain,
( ( sk38 != sk2 )
| ( sk38 != sk2 )
| ~ ( sk38 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1675]) ).
thf(1684,plain,
( ( sk38 != sk2 )
| ~ ( sk38 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1677]) ).
thf(810,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[715,120]) ).
thf(811,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[810]) ).
thf(812,plain,
( ( nil @ ( sk2 @ sk5 @ cons ) @ strictorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[811:[bind(A,$thf( sk2 @ sk5 ))]]) ).
thf(2296,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ( sk2 != sk1 )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[1926,847]) ).
thf(2297,plain,
( ( sk1 != sk1 )
| ( sk2 != sk1 )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[2296]) ).
thf(2298,plain,
( ( sk2 != sk1 )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[2297:[]]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( B @ ( A @ frontsegP ) )
=> ( B @ ( C @ ( A @ app ) @ frontsegP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax43) ).
thf(150,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( B @ ( A @ frontsegP ) )
=> ( B @ ( C @ ( A @ app ) @ frontsegP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1503,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( sk1 @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[831,1222]) ).
thf(1504,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[1503]) ).
thf(1528,plain,
( ( sk1 != nil )
| ( nil != nil )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[1504]) ).
thf(1531,plain,
( ( sk1 != nil )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[1528]) ).
thf(838,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[347,331]) ).
thf(839,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[838]) ).
thf(840,plain,
~ ( nil @ ( nil @ neq ) ),
inference(pattern_uni,[status(thm)],[839:[bind(A,$thf( nil ))]]) ).
thf(3821,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,247]) ).
thf(3822,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[3821]) ).
thf(3823,plain,
nil @ ( sk1 @ segmentP ),
inference(pattern_uni,[status(thm)],[3822:[bind(A,$thf( sk1 ))]]) ).
thf(153,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ app ) @ app ) )
= ( C @ ( B @ app ) @ ( A @ app ) ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[152]) ).
thf(154,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( C @ ( B @ ( A @ app ) @ app ) )
= ( C @ ( B @ app ) @ ( A @ app ) ) ) ),
inference(lifteq,[status(thm)],[153]) ).
thf(444,plain,
! [A: $i] :
( ( ( A @ ( nil @ rearsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) )
& ( ( nil = A )
| ~ ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[443]) ).
thf(446,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[444]) ).
thf(448,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[446]) ).
thf(449,plain,
( ( nil @ ( nil @ rearsegP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[448]) ).
thf(1271,plain,
( ( nil @ ( nil @ rearsegP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[449,347]) ).
thf(1272,plain,
nil @ ( nil @ rearsegP ),
inference(simp,[status(thm)],[1271]) ).
thf(12,axiom,
nil @ cyclefreeP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax60) ).
thf(143,plain,
nil @ cyclefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(87,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssItem )
=> ( ( A @ ( B @ app ) @ ( C @ cons ) )
= ( A @ ( B @ ( C @ cons ) @ app ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax27) ).
thf(497,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssItem )
=> ( ( A @ ( B @ app ) @ ( C @ cons ) )
= ( A @ ( B @ ( C @ cons ) @ app ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(5871,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5750,247]) ).
thf(5872,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5871]) ).
thf(5873,plain,
( ( nil @ ( sk1 @ sk9 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5872:[bind(A,$thf( sk1 @ sk9 ))]]) ).
thf(76,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( nil != A )
=> ( ( B @ ( A @ app ) @ hd )
= ( A @ hd ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax85) ).
thf(450,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( nil != A )
=> ( ( B @ ( A @ app ) @ hd )
= ( A @ hd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(96,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ memberP ) )
<=> ? [C: $i] :
( ? [D: $i] :
( ( ( D @ ( B @ cons ) @ ( C @ app ) )
= A )
& ( D @ ssList ) )
& ( C @ ssList ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
thf(524,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( ? [C: $i] :
( ? [D: $i] :
( ( ( D @ ( B @ cons ) @ ( C @ app ) )
= A )
& ( D @ ssList ) )
& ( C @ ssList ) )
=> ( B @ ( A @ memberP ) ) )
& ( ( B @ ( A @ memberP ) )
=> ? [C: $i] :
( ? [D: $i] :
( ( ( D @ ( B @ cons ) @ ( C @ app ) )
= A )
& ( D @ ssList ) )
& ( C @ ssList ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(4100,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,300]) ).
thf(4101,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[4100]) ).
thf(4102,plain,
nil @ ( sk2 @ rearsegP ),
inference(pattern_uni,[status(thm)],[4101:[bind(A,$thf( sk2 ))]]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ strictorderP )
<=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( ( B @ ( C @ lt ) )
| ( C @ ( B @ lt ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10) ).
thf(171,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( ( B @ ( C @ lt ) )
| ( C @ ( B @ lt ) ) ) ) ) ) ) ) )
=> ( A @ strictorderP ) )
& ( ( A @ strictorderP )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( ( B @ ( C @ lt ) )
| ( C @ ( B @ lt ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(55,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( B @ ( A @ segmentP ) )
<=> ? [C: $i] :
( ? [D: $i] :
( ( ( D @ ( B @ ( C @ app ) @ app ) )
= A )
& ( D @ ssList ) )
& ( C @ ssList ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7) ).
thf(351,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ? [C: $i] :
( ? [D: $i] :
( ( ( D @ ( B @ ( C @ app ) @ app ) )
= A )
& ( D @ ssList ) )
& ( C @ ssList ) )
=> ( B @ ( A @ segmentP ) ) )
& ( ( B @ ( A @ segmentP ) )
=> ? [C: $i] :
( ? [D: $i] :
( ( ( D @ ( B @ ( C @ app ) @ app ) )
= A )
& ( D @ ssList ) )
& ( C @ ssList ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(4600,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk6 @ ( A @ sk5 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,158]) ).
thf(4601,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk6 @ ( A @ sk5 @ leq ) ) ),
inference(simp,[status(thm)],[4600]) ).
thf(4602,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk6 @ ( sk2 @ sk5 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[4601:[bind(A,$thf( sk2 ))]]) ).
thf(73,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax63) ).
thf(433,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(83,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ totalorderedP )
<=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( C @ ( B @ leq ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11) ).
thf(478,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( C @ ( B @ leq ) ) ) ) ) ) ) )
=> ( A @ totalorderedP ) )
& ( ( A @ totalorderedP )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( C @ ( B @ leq ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(60,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ duplicatefreeP )
<=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( B != C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax13) ).
thf(378,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( B != C ) ) ) ) ) ) )
=> ( A @ duplicatefreeP ) )
& ( ( A @ duplicatefreeP )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( B != C ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(151,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ app ) @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[150]) ).
thf(2286,plain,
( ( sk1 != sk1 )
| ~ ( nil @ ( sk1 @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[1926,834]) ).
thf(2287,plain,
( ~ ( nil @ ( sk1 @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[2286:[]]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( D @ ( B @ cons ) @ ( C @ ( A @ cons ) @ frontsegP ) )
<=> ( ( D @ ( C @ frontsegP ) )
& ( A = B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax44) ).
thf(315,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( ( D @ ( C @ frontsegP ) )
& ( A = B ) )
=> ( D @ ( B @ cons ) @ ( C @ ( A @ cons ) @ frontsegP ) ) )
& ( ( D @ ( B @ cons ) @ ( C @ ( A @ cons ) @ frontsegP ) )
=> ( ( D @ ( C @ frontsegP ) )
& ( A = B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(6005,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5762,247]) ).
thf(6006,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[6005]) ).
thf(6007,plain,
( ( nil @ ( sk2 @ sk9 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[6006:[bind(A,$thf( sk2 @ sk9 ))]]) ).
thf(65,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( B @ app ) )
= ( A @ ( B @ app ) ) )
=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax80) ).
thf(410,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( B @ app ) )
= ( A @ ( B @ app ) ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(145,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[144]) ).
thf(146,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( A = B ) ),
inference(lifteq,[status(thm)],[145]) ).
thf(5952,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5750,300]) ).
thf(5953,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5952]) ).
thf(5954,plain,
( ( nil @ ( sk1 @ sk9 @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5953:[bind(A,$thf( sk1 @ sk9 ))]]) ).
thf(816,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[395,120]) ).
thf(817,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[816]) ).
thf(818,plain,
nil @ ( sk38 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[817:[bind(A,$thf( sk38 ))]]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( B @ ( C @ app ) )
= ( B @ ( A @ app ) ) )
=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax79) ).
thf(190,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( B @ ( C @ app ) )
= ( B @ ( A @ app ) ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(5039,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[4743,300]) ).
thf(5040,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5039]) ).
thf(5041,plain,
( ( nil @ ( sk2 @ sk7 @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5040:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(1346,plain,
! [A: $i] :
( ( A != sk37 )
| ( sk38 != nil )
| ( nil != nil )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[125,1345]) ).
thf(1347,plain,
! [A: $i] :
( ( A != sk37 )
| ( sk38 != nil )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[1346]) ).
thf(1348,plain,
( ( sk38 != nil )
| ~ ( sk37 @ ( nil @ frontsegP ) )
| ~ ( sk37 @ ssList ) ),
inference(pattern_uni,[status(thm)],[1347:[bind(A,$thf( sk37 ))]]) ).
thf(750,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[709,220]) ).
thf(751,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[750]) ).
thf(752,plain,
( ~ ( sk1 @ sk5 @ ( sk1 @ sk5 @ lt ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[751:[bind(A,$thf( sk1 @ sk5 ))]]) ).
thf(4915,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[4731,300]) ).
thf(4916,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[4915]) ).
thf(4917,plain,
( ( nil @ ( sk1 @ sk7 @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[4916:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ? [B: $i] :
( ? [C: $i] :
( ( ( B @ ( C @ cons ) )
= A )
& ( C @ ssItem ) )
& ( B @ ssList ) )
| ( nil = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).
thf(268,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ? [B: $i] :
( ? [C: $i] :
( ( ( B @ ( C @ cons ) )
= A )
& ( C @ ssItem ) )
& ( B @ ssList ) )
| ( nil = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax65) ).
thf(195,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(794,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[715,235]) ).
thf(795,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[794]) ).
thf(796,plain,
( ~ ( sk2 @ sk5 @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[795:[bind(A,$thf( sk2 @ sk5 ))]]) ).
thf(67,axiom,
nil @ strictorderP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax64) ).
thf(415,plain,
nil @ strictorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(4301,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,377]) ).
thf(4302,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) ) ),
inference(simp,[status(thm)],[4301]) ).
thf(4303,plain,
nil @ ( sk2 @ frontsegP ),
inference(pattern_uni,[status(thm)],[4302:[bind(A,$thf( sk2 ))]]) ).
thf(7069,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[6889,377]) ).
thf(7070,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7069]) ).
thf(7071,plain,
( ( nil @ ( sk1 @ sk8 @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7070:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ( ( ( C @ ( B @ gt ) )
& ( B @ ( A @ gt ) ) )
=> ( C @ ( A @ gt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax95) ).
thf(200,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ( ( ( C @ ( B @ gt ) )
& ( B @ ( A @ gt ) ) )
=> ( C @ ( A @ gt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax61) ).
thf(369,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(109,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( nil @ ( A @ cons ) @ ( C @ app ) @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(111,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( B @ ( nil @ ( A @ cons ) @ ( C @ app ) @ app ) )
!= sk1 )
| ( ( C @ ( nil @ ( A @ cons ) @ ( B @ app ) @ app ) )
!= sk2 ) ),
inference(lifteq,[status(thm)],[109]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ totalorderP )
<=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( ( B @ ( C @ leq ) )
| ( C @ ( B @ leq ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax9) ).
thf(254,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( ( B @ ( C @ leq ) )
| ( C @ ( B @ leq ) ) ) ) ) ) ) ) )
=> ( A @ totalorderP ) )
& ( ( A @ totalorderP )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( ( B @ ( C @ leq ) )
| ( C @ ( B @ leq ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ( A @ hd )
= B )
& ( B @ ssItem ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax75) ).
thf(309,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ( A @ hd )
= B )
& ( B @ ssItem ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(84,axiom,
nil @ equalelemsP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax74) ).
thf(491,plain,
nil @ equalelemsP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(95194,plain,
$false,
inference(e,[status(thm)],[645,629,347,333,3830,234,4877,408,523,115,276,7132,202,120,247,1705,533,4839,500,715,5005,1222,185,782,709,301,565,5750,4743,4896,3617,125,2356,460,157,421,5397,416,152,5020,4967,216,443,376,834,106,238,348,821,492,164,5914,121,766,147,397,692,221,293,453,132,133,1345,116,507,248,117,512,1153,220,160,392,429,847,197,852,435,1143,1227,188,169,193,476,642,1207,837,2285,701,1297,457,2272,371,503,129,7027,128,105,4288,360,205,1185,398,1035,6901,5327,5762,824,1483,6084,161,279,296,4599,149,118,204,413,236,4099,144,159,6048,406,831,219,419,377,509,98,303,494,323,4731,140,799,520,626,769,155,130,1926,5442,695,5516,455,394,135,299,505,431,473,162,1684,209,112,812,2298,150,1566,1531,331,840,3823,1220,656,154,1272,143,497,5873,450,203,524,104,4102,171,158,351,4602,433,478,214,119,378,235,246,151,2287,315,6007,410,146,5954,818,190,5041,300,1348,752,4917,326,268,195,5339,1033,6889,796,415,4303,136,395,7071,131,200,369,111,254,309,491]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC418+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.40 % Computer : n016.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 13:06:03 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.70/0.70 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.96/0.86 % [INFO] Parsing done (159ms).
% 0.96/0.87 % [INFO] Running in sequential loop mode.
% 1.81/1.07 % [INFO] eprover registered as external prover.
% 1.81/1.07 % [INFO] Scanning for conjecture ...
% 2.12/1.15 % [INFO] Found a conjecture (or negated_conjecture) and 95 axioms. Running axiom selection ...
% 2.35/1.21 % [INFO] Axiom selection finished. Selected 95 axioms (removed 0 axioms).
% 2.35/1.29 % [INFO] Problem is first-order (TPTP FOF).
% 2.68/1.30 % [INFO] Type checking passed.
% 2.68/1.30 % [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 ...
% 187.30/52.27 % External prover 'e' found a proof!
% 187.30/52.27 % [INFO] Killing All external provers ...
% 187.30/52.27 % Time passed: 51771ms (effective reasoning time: 51399ms)
% 187.30/52.27 % 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)>
% 187.30/52.27 % 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
% 187.30/52.27 % No. of inferences in proof: 539
% 187.30/52.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 51771 ms resp. 51399 ms w/o parsing
% 185.60/52.52 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 185.60/52.52 % [INFO] Killing All external provers ...
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