%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWC073+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 : n013.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 08:52:05 AM UTC 2026
% Result : Theorem 241.11s 70.55s
% Output : Refutation 230.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 126
% Syntax : Number of formulae : 1532 ( 137 unt; 0 typ; 30 def)
% Number of atoms : 6696 (1589 equ; 0 cnn)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 15030 (2433 ~;2824 |; 301 &;8797 @)
% ( 26 <=>; 649 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 54 usr; 9 con; 0-2 aty)
% Number of variables : 1479 ( 25 ^;1354 !; 70 ?;1479 :)
% ( 0 !>; 0 ?*; 0 @-; 30 @+)
% Comments :
%------------------------------------------------------------------------------
thf(ssList_decl,type,
ssList: $i > $o ).
thf(neq_decl,type,
neq: $i > $i > $o ).
thf(nil_decl,type,
nil: $i ).
thf(segmentP_decl,type,
segmentP: $i > $i > $o ).
thf(tl_decl,type,
tl: $i > $i ).
thf(app_decl,type,
app: $i > $i > $i ).
thf(ssItem_decl,type,
ssItem: $i > $o ).
thf(cons_decl,type,
cons: $i > $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(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(sk10_decl,type,
sk10: $i > $i ).
thf(sk11_decl,type,
sk11: $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i ).
thf(sk13_decl,type,
sk13: $i > $i ).
thf(sk14_decl,type,
sk14: $i > $i ).
thf(sk15_decl,type,
sk15: $i > $i ).
thf(sk16_decl,type,
sk16: $i > $i ).
thf(sk17_decl,type,
sk17: $i > $i ).
thf(sk18_decl,type,
sk18: $i > $i ).
thf(sk19_decl,type,
sk19: $i > $i ).
thf(sk20_decl,type,
sk20: $i > $i > $i ).
thf(sk21_decl,type,
sk21: $i > $i ).
thf(sk22_decl,type,
sk22: $i > $i ).
thf(sk23_decl,type,
sk23: $i > $i ).
thf(sk24_decl,type,
sk24: $i > $i ).
thf(sk25_decl,type,
sk25: $i > $i ).
thf(sk26_decl,type,
sk26: $i > $i ).
thf(sk27_decl,type,
sk27: $i > $i ).
thf(sk28_decl,type,
sk28: $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 )
=> ( ( ( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( C @ ( nil @ neq ) )
& ? [H: $i] :
( ( C @ ( nil @ neq ) )
& ( ( C @ hd )
= H )
& ( ( nil @ ( H @ cons ) )
= G )
& ( H @ ssItem ) )
& ( ( G @ ( F @ app ) )
= E )
& ( ( C @ tl )
= F )
& ( G @ ssList ) )
& ( F @ ssList ) )
& ( D != E )
& ( E @ ssList ) )
| ~ ( nil @ ( C @ neq ) ) )
& ( nil @ ( D @ neq ) ) )
| ( ( nil = A )
& ( nil = B ) )
| ( ( nil = D )
& ( nil != C ) )
| ? [E: $i] :
( ( E @ ( A @ segmentP ) )
& ( E @ ( B @ segmentP ) )
& ( nil @ ( E @ neq ) )
& ( E @ ssList ) )
| ( A != C )
| ( B != D ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ( B @ ( nil @ neq ) )
& ? [G: $i] :
( ( B @ ( nil @ neq ) )
& ( ( B @ hd )
= G )
& ( ( nil @ ( G @ cons ) )
= F )
& ( G @ ssItem ) )
& ( ( F @ ( E @ app ) )
= D )
& ( ( B @ tl )
= E )
& ( F @ ssList ) )
& ( E @ ssList ) )
& ( C != D )
& ( D @ ssList ) )
| ~ ( nil @ ( B @ neq ) ) )
& ( nil @ ( C @ neq ) ) )
| ( ( nil = sk1 )
& ( nil = A ) )
| ( ( nil = C )
& ( nil != B ) )
| ? [D: $i] :
( ( D @ ( sk1 @ segmentP ) )
& ( D @ ( A @ segmentP ) )
& ( nil @ ( D @ neq ) )
& ( D @ ssList ) )
| ( sk1 != B )
| ( A != C ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ( A @ ( nil @ neq ) )
& ? [F: $i] :
( ( A @ ( nil @ neq ) )
& ( ( A @ hd )
= F )
& ( ( nil @ ( F @ cons ) )
= E )
& ( F @ ssItem ) )
& ( ( E @ ( D @ app ) )
= C )
& ( ( A @ tl )
= D )
& ( E @ ssList ) )
& ( D @ ssList ) )
& ( B != C )
& ( C @ ssList ) )
| ~ ( nil @ ( A @ neq ) ) )
& ( nil @ ( B @ neq ) ) )
| ( ( nil = sk1 )
& ( nil = sk2 ) )
| ( ( nil = B )
& ( nil != A ) )
| ? [C: $i] :
( ( C @ ( sk1 @ segmentP ) )
& ( C @ ( sk2 @ segmentP ) )
& ( nil @ ( C @ neq ) )
& ( C @ ssList ) )
| ( sk1 != A )
| ( sk2 != B ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ( ( ( ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ( sk3 @ ( nil @ neq ) )
& ? [E: $i] :
( ( sk3 @ ( nil @ neq ) )
& ( ( sk3 @ hd )
= E )
& ( ( nil @ ( E @ cons ) )
= D )
& ( E @ ssItem ) )
& ( ( D @ ( C @ app ) )
= B )
& ( ( sk3 @ tl )
= C )
& ( D @ ssList ) )
& ( C @ ssList ) )
& ( A != B )
& ( B @ ssList ) )
| ~ ( nil @ ( sk3 @ neq ) ) )
& ( nil @ ( A @ neq ) ) )
| ( ( nil = sk1 )
& ( nil = sk2 ) )
| ( ( nil = A )
& ( nil != sk3 ) )
| ? [B: $i] :
( ( B @ ( sk1 @ segmentP ) )
& ( B @ ( sk2 @ segmentP ) )
& ( nil @ ( B @ neq ) )
& ( B @ ssList ) )
| ( 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(sk10_def,definition,
( sk10
= ( ^ [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 @ lt ) )
| ( C @ ( B @ lt ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ( ( ( E @ ( B @ cons ) @ ( D @ ( A @ sk10 @ cons ) @ ( C @ app ) @ app ) )
= A )
=> ( ( A @ sk10 @ ( B @ lt ) )
| ( B @ ( A @ sk10 @ lt ) ) ) ) ) ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( D @ ( A @ sk11 @ cons ) @ ( C @ ( A @ sk10 @ cons ) @ ( B @ app ) @ app ) )
= A )
=> ( ( A @ sk10 @ ( A @ sk11 @ lt ) )
| ( A @ sk11 @ ( A @ sk10 @ lt ) ) ) ) ) ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( A @ sk11 @ cons ) @ ( B @ ( A @ sk10 @ cons ) @ ( A @ sk12 @ app ) @ app ) )
= A )
=> ( ( A @ sk10 @ ( A @ sk11 @ lt ) )
| ( A @ sk11 @ ( A @ sk10 @ lt ) ) ) ) ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ( ( ( B @ ( A @ sk11 @ cons ) @ ( A @ sk13 @ ( A @ sk10 @ cons ) @ ( A @ sk12 @ app ) @ app ) )
= A )
=> ( ( A @ sk10 @ ( A @ sk11 @ lt ) )
| ( A @ sk11 @ ( A @ sk10 @ lt ) ) ) ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [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 )
=> ( C @ ( B @ lt ) ) ) ) ) ) ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ( ( ( E @ ( B @ cons ) @ ( D @ ( A @ sk15 @ cons ) @ ( C @ app ) @ app ) )
= A )
=> ( B @ ( A @ sk15 @ lt ) ) ) ) ) ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( D @ ( A @ sk16 @ cons ) @ ( C @ ( A @ sk15 @ cons ) @ ( B @ app ) @ app ) )
= A )
=> ( A @ sk16 @ ( A @ sk15 @ lt ) ) ) ) ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( A @ sk16 @ cons ) @ ( B @ ( A @ sk15 @ cons ) @ ( A @ sk17 @ app ) @ app ) )
= A )
=> ( A @ sk16 @ ( A @ sk15 @ lt ) ) ) ) ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ( ( ( B @ ( A @ sk16 @ cons ) @ ( A @ sk18 @ ( A @ sk15 @ cons ) @ ( A @ sk17 @ app ) @ app ) )
= A )
=> ( A @ sk16 @ ( A @ sk15 @ lt ) ) ) ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( ( C @ ( A @ app ) )
= B )
& ( C @ ssList ) ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( ^ [A: $i] :
@+[B: $i] :
( ( ( A @ tl )
= B )
& ( B @ ssList ) ) ) ) ).
thf(sk22_def,definition,
( sk22
= ( ^ [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(sk23_def,definition,
( sk23
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ( ( ( E @ ( B @ cons ) @ ( D @ ( A @ sk22 @ cons ) @ ( C @ app ) @ app ) )
= A )
=> ( ( A @ sk22 @ ( B @ leq ) )
| ( B @ ( A @ sk22 @ leq ) ) ) ) ) ) ) ) ) ) ).
thf(sk24_def,definition,
( sk24
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( D @ ( A @ sk23 @ cons ) @ ( C @ ( A @ sk22 @ cons ) @ ( B @ app ) @ app ) )
= A )
=> ( ( A @ sk22 @ ( A @ sk23 @ leq ) )
| ( A @ sk23 @ ( A @ sk22 @ leq ) ) ) ) ) ) ) ) ) ).
thf(sk25_def,definition,
( sk25
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( A @ sk23 @ cons ) @ ( B @ ( A @ sk22 @ cons ) @ ( A @ sk24 @ app ) @ app ) )
= A )
=> ( ( A @ sk22 @ ( A @ sk23 @ leq ) )
| ( A @ sk23 @ ( A @ sk22 @ leq ) ) ) ) ) ) ) ) ).
thf(sk26_def,definition,
( sk26
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ( ( ( B @ ( A @ sk23 @ cons ) @ ( A @ sk25 @ ( A @ sk22 @ cons ) @ ( A @ sk24 @ app ) @ app ) )
= A )
=> ( ( A @ sk22 @ ( A @ sk23 @ leq ) )
| ( A @ sk23 @ ( A @ sk22 @ leq ) ) ) ) ) ) ) ).
thf(sk27_def,definition,
( sk27
= ( ^ [A: $i] :
@+[B: $i] :
( ? [C: $i] :
( ( ( B @ ( C @ cons ) )
= A )
& ( C @ ssItem ) )
& ( B @ ssList ) ) ) ) ).
thf(sk28_def,definition,
( sk28
= ( ^ [A: $i] :
@+[B: $i] :
( ( ( A @ sk27 @ ( B @ cons ) )
= A )
& ( B @ ssItem ) ) ) ) ).
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(1,conjecture,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( C @ ( nil @ neq ) )
& ? [H: $i] :
( ( C @ ( nil @ neq ) )
& ( ( C @ hd )
= H )
& ( ( nil @ ( H @ cons ) )
= G )
& ( H @ ssItem ) )
& ( ( G @ ( F @ app ) )
= E )
& ( ( C @ tl )
= F )
& ( G @ ssList ) )
& ( F @ ssList ) )
& ( D != E )
& ( E @ ssList ) )
| ~ ( nil @ ( C @ neq ) ) )
& ( nil @ ( D @ neq ) ) )
| ( ( nil = A )
& ( nil = B ) )
| ( ( nil = D )
& ( nil != C ) )
| ? [E: $i] :
( ( E @ ( A @ segmentP ) )
& ( E @ ( B @ segmentP ) )
& ( nil @ ( E @ neq ) )
& ( E @ ssList ) )
| ( 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 )
=> ( ( ( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( C @ ( nil @ neq ) )
& ? [H: $i] :
( ( C @ ( nil @ neq ) )
& ( ( C @ hd )
= H )
& ( ( nil @ ( H @ cons ) )
= G )
& ( H @ ssItem ) )
& ( ( G @ ( F @ app ) )
= E )
& ( ( C @ tl )
= F )
& ( G @ ssList ) )
& ( F @ ssList ) )
& ( D != E )
& ( E @ ssList ) )
| ~ ( nil @ ( C @ neq ) ) )
& ( nil @ ( D @ neq ) ) )
| ( ( nil = A )
& ( nil = B ) )
| ( ( nil = D )
& ( nil != C ) )
| ? [E: $i] :
( ( E @ ( A @ segmentP ) )
& ( E @ ( B @ segmentP ) )
& ( nil @ ( E @ neq ) )
& ( E @ ssList ) )
| ( 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 )
=> ( ( ( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( C @ ( nil @ neq ) )
& ? [H: $i] :
( ( C @ ( nil @ neq ) )
& ( ( C @ hd )
= H )
& ( ( nil @ ( H @ cons ) )
= G )
& ( H @ ssItem ) )
& ( ( G @ ( F @ app ) )
= E )
& ( ( C @ tl )
= F )
& ( G @ ssList ) )
& ( F @ ssList ) )
& ( D != E )
& ( E @ ssList ) )
| ~ ( nil @ ( C @ neq ) ) )
& ( nil @ ( D @ neq ) ) )
| ( ( nil = A )
& ( nil = B ) )
| ( ( nil = D )
& ( nil != C ) )
| ? [E: $i] :
( ( E @ ( A @ segmentP ) )
& ( E @ ( B @ segmentP ) )
& ( nil @ ( E @ neq ) )
& ( E @ ssList ) )
| ( A != C )
| ( B != D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(99,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ~ ( sk3 @ ( nil @ neq ) )
| ~ ( sk3 @ ( nil @ neq ) )
| ( ( sk3 @ hd )
!= E )
| ( ( nil @ ( E @ cons ) )
!= D )
| ~ ( E @ ssItem )
| ( ( D @ ( C @ app ) )
!= B )
| ( ( sk3 @ tl )
!= C )
| ~ ( D @ ssList )
| ~ ( C @ ssList )
| ( sk4 = B )
| ~ ( B @ ssList )
| ~ ( nil @ ( sk4 @ neq ) ) )
& ( ( nil @ ( sk3 @ neq ) )
| ~ ( nil @ ( sk4 @ neq ) ) )
& ( ( nil != sk1 )
| ( nil != sk2 ) )
& ( ( nil != sk4 )
| ( nil = sk3 ) )
& ( ~ ( A @ ( sk1 @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( A @ neq ) )
| ~ ( A @ ssList ) )
& ( 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(20,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil @ ( A @ app ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax84) ).
thf(186,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil @ ( A @ app ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(187,plain,
! [A: $i] :
( ( ( nil @ ( A @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[186]) ).
thf(188,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[187]) ).
thf(16338,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[105,188]) ).
thf(16339,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[16338]) ).
thf(16340,plain,
( ( nil @ ( sk2 @ app ) )
= sk2 ),
inference(pattern_uni,[status(thm)],[16339:[bind(A,$thf( sk2 ))]]) ).
thf(106,plain,
sk1 @ ssList,
inference(cnfConj,[status(thm)],[99]) ).
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(249,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ( A @ tl )
= B )
& ( B @ ssList ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(250,plain,
! [A: $i] :
( ( ( ( A @ tl )
= ( A @ sk21 ) )
| ( nil = A )
| ~ ( A @ ssList ) )
& ( ( A @ sk21 @ ssList )
| ( nil = A )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[249]) ).
thf(251,plain,
! [A: $i] :
( ( A @ sk21 @ ssList )
| ( nil = A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[250]) ).
thf(253,plain,
! [A: $i] :
( ( A @ sk21 @ ssList )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[251]) ).
thf(49344,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk21 @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[106,253]) ).
thf(49345,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk21 @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[49344]) ).
thf(49346,plain,
( ( sk1 @ sk21 @ ssList )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[49345:[bind(A,$thf( sk1 ))]]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ frontsegP ) )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax46) ).
thf(122,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(123,plain,
! [A: $i] :
( ( ( A @ ( nil @ frontsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) )
& ( ( nil = A )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[122]) ).
thf(125,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[123]) ).
thf(127,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[125]) ).
thf(128,plain,
( ( nil @ ( nil @ frontsegP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[127]) ).
thf(53,axiom,
nil @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
thf(348,plain,
nil @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(643,plain,
( ( nil @ ( nil @ frontsegP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[128,348]) ).
thf(644,plain,
nil @ ( nil @ frontsegP ),
inference(simp,[status(thm)],[643]) ).
thf(124,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[123]) ).
thf(126,plain,
! [A: $i] :
( ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[124]) ).
thf(1046,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[105,126]) ).
thf(1047,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[1046]) ).
thf(1048,plain,
( ~ ( sk2 @ ( nil @ frontsegP ) )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[1047:[bind(A,$thf( sk2 ))]]) ).
thf(981,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[106,126]) ).
thf(982,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[981]) ).
thf(983,plain,
( ~ ( sk1 @ ( nil @ frontsegP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[982:[bind(A,$thf( sk1 ))]]) ).
thf(103,plain,
( ( nil != sk1 )
| ( nil != sk2 ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(114,plain,
( ( sk1 != nil )
| ( sk2 != nil ) ),
inference(lifteq,[status(thm)],[103]) ).
thf(1209,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ( sk2 != nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[983,114]) ).
thf(1210,plain,
( ( sk1 != sk1 )
| ( sk2 != nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1209]) ).
thf(1211,plain,
( ( sk2 != nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1210:[]]) ).
thf(1345,plain,
( ( sk2 != sk2 )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ frontsegP ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1048,1211]) ).
thf(1346,plain,
( ( sk2 != sk2 )
| ~ ( sk1 @ ( nil @ frontsegP ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1345]) ).
thf(1347,plain,
( ~ ( sk1 @ ( nil @ frontsegP ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1346:[]]) ).
thf(1393,plain,
( ~ $true
| ( ( sk2 @ ( nil @ frontsegP ) )
!= ( sk1 @ ( nil @ frontsegP ) ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(eqfactor_ordered,[status(thm)],[1347]) ).
thf(1397,plain,
( ( sk2 != sk1 )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1393]) ).
thf(1400,plain,
( ( sk2 != sk1 )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1397]) ).
thf(1571,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk2 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[644,1400]) ).
thf(1572,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[1571]) ).
thf(1573,plain,
( ( sk1 != nil )
| ( nil != nil )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[1572]) ).
thf(1574,plain,
( ( sk1 != nil )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[1573]) ).
thf(52464,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ( sk2 != sk1 )
| ( sk1 @ sk21 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[49346,1574]) ).
thf(52465,plain,
( ( sk1 != sk1 )
| ( sk2 != sk1 )
| ( sk1 @ sk21 @ ssList ) ),
inference(simp,[status(thm)],[52464]) ).
thf(52466,plain,
( ( sk2 != sk1 )
| ( sk1 @ sk21 @ ssList ) ),
inference(pattern_uni,[status(thm)],[52465:[]]) ).
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(479,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(252,plain,
! [A: $i] :
( ( ( A @ tl )
= ( A @ sk21 ) )
| ( nil = A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[250]) ).
thf(254,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ( ( A @ sk21 )
= ( A @ tl ) )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[252]) ).
thf(53496,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ sk21 )
= ( A @ tl ) )
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[106,254]) ).
thf(53497,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ sk21 )
= ( A @ tl ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[53496]) ).
thf(53498,plain,
( ( ( sk1 @ sk21 )
= ( sk1 @ tl ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[53497:[bind(A,$thf( sk1 ))]]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax57) ).
thf(247,plain,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(248,plain,
! [A: $i] :
( ( nil @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[247]) ).
thf(52267,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[49346,248]) ).
thf(52268,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[52267]) ).
thf(52269,plain,
( ( nil @ ( sk1 @ sk21 @ segmentP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[52268:[bind(A,$thf( sk1 @ sk21 ))]]) ).
thf(58053,plain,
( ( ( sk1 @ sk21 )
!= ( sk1 @ sk21 ) )
| ( nil @ ( sk1 @ tl @ segmentP ) )
| ( sk1 = nil )
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[53498,52269]) ).
thf(58054,plain,
( ( ( sk1 @ sk21 )
!= ( sk1 @ sk21 ) )
| ( nil @ ( sk1 @ tl @ segmentP ) )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[58053]) ).
thf(58055,plain,
( ( nil @ ( sk1 @ tl @ segmentP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[58054:[]]) ).
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(222,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(223,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ strictorderedP )
| ~ ( A @ sk16 @ ( A @ sk15 @ lt ) )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( ( A @ sk19 @ ( A @ sk16 @ cons ) @ ( A @ sk18 @ ( A @ sk15 @ cons ) @ ( A @ sk17 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( A @ sk19 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( A @ sk18 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( A @ sk17 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( A @ sk16 @ ssItem )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( A @ sk15 @ ssItem )
| ~ ( A @ ssList ) )
& ( ( C @ ( B @ lt ) )
| ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
!= A )
| ~ ( F @ ssList )
| ~ ( E @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssItem )
| ~ ( B @ ssItem )
| ~ ( A @ strictorderedP )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[222]) ).
thf(226,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk17 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[223]) ).
thf(33109,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk17 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,226]) ).
thf(33110,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk17 @ ssList ) ),
inference(simp,[status(thm)],[33109]) ).
thf(33111,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk17 @ ssList ) ),
inference(pattern_uni,[status(thm)],[33110:[bind(A,$thf( sk2 ))]]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax55) ).
thf(194,plain,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(195,plain,
! [A: $i] :
( ( A @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[194]) ).
thf(33788,plain,
! [A: $i] :
( ( ( sk2 @ sk17 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[33111,195]) ).
thf(33789,plain,
! [A: $i] :
( ( ( sk2 @ sk17 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[33788]) ).
thf(33790,plain,
( ( sk2 @ sk17 @ ( sk2 @ sk17 @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[33789:[bind(A,$thf( sk2 @ sk17 ))]]) ).
thf(224,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( ( A @ sk19 @ ( A @ sk16 @ cons ) @ ( A @ sk18 @ ( A @ sk15 @ cons ) @ ( A @ sk17 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[223]) ).
thf(234,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ( ( A @ sk19 @ ( A @ sk16 @ cons ) @ ( A @ sk18 @ ( A @ sk15 @ cons ) @ ( A @ sk17 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[224]) ).
thf(227,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk16 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[223]) ).
thf(34520,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk16 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,227]) ).
thf(34521,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk16 @ ssItem ) ),
inference(simp,[status(thm)],[34520]) ).
thf(34522,plain,
( ( sk1 @ strictorderedP )
| ( sk1 @ sk16 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[34521:[bind(A,$thf( sk1 ))]]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax61) ).
thf(370,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(371,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[370]) ).
thf(34795,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[34522,371]) ).
thf(34796,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[34795]) ).
thf(34797,plain,
( ( nil @ ( sk1 @ sk16 @ cons ) @ totalorderP )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[34796:[bind(A,$thf( sk1 @ sk16 ))]]) ).
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(172,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(173,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ strictorderP )
| ~ ( A @ sk10 @ ( A @ sk11 @ lt ) )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ~ ( A @ sk11 @ ( A @ sk10 @ lt ) )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( ( A @ sk14 @ ( A @ sk11 @ cons ) @ ( A @ sk13 @ ( A @ sk10 @ cons ) @ ( A @ sk12 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( A @ sk14 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( A @ sk13 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( A @ sk12 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( A @ sk11 @ ssItem )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( A @ sk10 @ ssItem )
| ~ ( A @ ssList ) )
& ( ( B @ ( C @ lt ) )
| ( C @ ( B @ lt ) )
| ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
!= A )
| ~ ( F @ ssList )
| ~ ( E @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssItem )
| ~ ( B @ ssItem )
| ~ ( A @ strictorderP )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[172]) ).
thf(177,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk10 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[173]) ).
thf(10768,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk10 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,177]) ).
thf(10769,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk10 @ ssItem ) ),
inference(simp,[status(thm)],[10768]) ).
thf(10770,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk10 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[10769:[bind(A,$thf( sk2 ))]]) ).
thf(34,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( nil @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
thf(235,plain,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( nil @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(236,plain,
! [A: $i] :
( ~ ( A @ ( nil @ memberP ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[235]) ).
thf(10985,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10770,236]) ).
thf(10986,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[10985]) ).
thf(10987,plain,
( ~ ( sk2 @ sk10 @ ( nil @ memberP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10986:[bind(A,$thf( sk2 @ sk10 ))]]) ).
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(352,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(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(156,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(157,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)],[156]) ).
thf(165,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk5 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[157]) ).
thf(7468,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk5 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,165]) ).
thf(7469,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk5 @ ssItem ) ),
inference(simp,[status(thm)],[7468]) ).
thf(7470,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk5 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[7469:[bind(A,$thf( sk1 ))]]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax90) ).
thf(220,plain,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(221,plain,
! [A: $i] :
( ~ ( A @ ( A @ lt ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[220]) ).
thf(31254,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7470,221]) ).
thf(31255,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[31254]) ).
thf(31256,plain,
( ~ ( sk1 @ sk5 @ ( sk1 @ sk5 @ lt ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[31255:[bind(A,$thf( sk1 @ sk5 ))]]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ segmentP ) )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax58) ).
thf(137,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(138,plain,
! [A: $i] :
( ( ( A @ ( nil @ segmentP ) )
| ( nil != A )
| ~ ( A @ ssList ) )
& ( ( nil = A )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[137]) ).
thf(139,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[138]) ).
thf(141,plain,
! [A: $i] :
( ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[139]) ).
thf(2276,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[106,141]) ).
thf(2277,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[2276]) ).
thf(2278,plain,
( ~ ( sk1 @ ( nil @ segmentP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[2277:[bind(A,$thf( sk1 ))]]) ).
thf(18592,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,195]) ).
thf(18593,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[18592]) ).
thf(18594,plain,
sk1 @ ( sk1 @ segmentP ),
inference(pattern_uni,[status(thm)],[18593:[bind(A,$thf( sk1 ))]]) ).
thf(61,axiom,
? [A: $i] :
( ? [B: $i] :
( ( A != B )
& ( B @ ssItem ) )
& ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
thf(393,plain,
? [A: $i] :
( ? [B: $i] :
( ( A != B )
& ( B @ ssItem ) )
& ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(394,plain,
( ( sk37 != sk38 )
& ( sk38 @ ssItem )
& ( sk37 @ ssItem ) ),
inference(cnf,[status(esa)],[393]) ).
thf(397,plain,
sk37 != sk38,
inference(cnfConj,[status(thm)],[394]) ).
thf(398,plain,
sk38 != sk37,
inference(lifteq,[status(thm)],[397]) ).
thf(2363,plain,
! [A: $i] :
( ( A != sk38 )
| ( sk37 != nil )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[141,398]) ).
thf(2364,plain,
( ( sk37 != nil )
| ~ ( sk38 @ ( nil @ segmentP ) )
| ~ ( sk38 @ ssList ) ),
inference(pattern_uni,[status(thm)],[2363:[bind(A,$thf( sk38 ))]]) ).
thf(6718,plain,
( ( ( sk38 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk37 != nil )
| ~ ( sk38 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,2364]) ).
thf(6719,plain,
( ( ( sk38 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk37 != nil )
| ~ ( sk38 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[6718]) ).
thf(6804,plain,
( ( sk38 != sk1 )
| ( sk37 != nil )
| ~ ( sk38 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[6719]) ).
thf(18743,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk38 @ ( nil @ segmentP ) ) )
| ( sk38 != sk1 )
| ( sk37 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18594,6804]) ).
thf(18744,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk38 @ ( nil @ segmentP ) ) )
| ( sk38 != sk1 )
| ( sk37 != nil ) ),
inference(simp,[status(thm)],[18743]) ).
thf(18811,plain,
( ( sk38 != sk1 )
| ( sk1 != nil )
| ( sk38 != sk1 )
| ( sk37 != nil ) ),
inference(simp,[status(thm)],[18744]) ).
thf(18828,plain,
( ( sk1 != nil )
| ( sk38 != sk1 )
| ( sk37 != nil ) ),
inference(simp,[status(thm)],[18811]) ).
thf(23295,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ( sk38 != sk1 )
| ( sk37 != nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2278,18828]) ).
thf(23296,plain,
( ( sk1 != sk1 )
| ( sk38 != sk1 )
| ( sk37 != nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[23295]) ).
thf(23297,plain,
( ( sk38 != sk1 )
| ( sk37 != nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[23296:[]]) ).
thf(10741,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk10 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,177]) ).
thf(10742,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk10 @ ssItem ) ),
inference(simp,[status(thm)],[10741]) ).
thf(10743,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk10 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[10742:[bind(A,$thf( sk1 ))]]) ).
thf(163,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk8 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[157]) ).
thf(6315,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,163]) ).
thf(6316,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ssList ) ),
inference(simp,[status(thm)],[6315]) ).
thf(6317,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk8 @ ssList ) ),
inference(pattern_uni,[status(thm)],[6316:[bind(A,$thf( sk2 ))]]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( A @ ( B @ cons ) @ ssList ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
thf(170,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( A @ ( B @ cons ) @ ssList ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(58044,plain,
( ( ( sk1 @ sk21 )
!= ( sk1 @ sk21 ) )
| ( sk1 @ tl @ ssList )
| ( sk1 = nil )
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[53498,49346]) ).
thf(58045,plain,
( ( ( sk1 @ sk21 )
!= ( sk1 @ sk21 ) )
| ( sk1 @ tl @ ssList )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[58044]) ).
thf(58046,plain,
( ( sk1 @ tl @ ssList )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[58045:[]]) ).
thf(18781,plain,
( ( sk1 != sk1 )
| ( sk1 @ ( nil @ segmentP ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[983,18594]) ).
thf(18782,plain,
( ( sk1 @ ( nil @ segmentP ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[18781:[]]) ).
thf(23059,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk1 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[644,18782]) ).
thf(23060,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[23059]) ).
thf(23076,plain,
( ( sk1 != nil )
| ( nil != nil )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[23060]) ).
thf(23091,plain,
( ( sk1 != nil )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[23076]) ).
thf(58380,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ( sk1 @ ( nil @ segmentP ) )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[58046,23091]) ).
thf(58381,plain,
( ( sk1 != sk1 )
| ( sk1 @ ( nil @ segmentP ) )
| ( sk1 @ tl @ ssList ) ),
inference(simp,[status(thm)],[58380]) ).
thf(58382,plain,
( ( sk1 @ ( nil @ segmentP ) )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[58381:[]]) ).
thf(1053,plain,
! [A: $i] :
( ( A != sk38 )
| ( sk37 != nil )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[126,398]) ).
thf(1054,plain,
( ( sk37 != nil )
| ~ ( sk38 @ ( nil @ frontsegP ) )
| ~ ( sk38 @ ssList ) ),
inference(pattern_uni,[status(thm)],[1053:[bind(A,$thf( sk38 ))]]) ).
thf(4697,plain,
( ( ( sk38 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk37 != nil )
| ~ $true
| ~ ( sk38 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[644,1054]) ).
thf(4698,plain,
( ( ( sk38 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk37 != nil )
| ~ ( sk38 @ ssList ) ),
inference(simp,[status(thm)],[4697]) ).
thf(4713,plain,
( ( sk38 != nil )
| ( nil != nil )
| ( sk37 != nil )
| ~ ( sk38 @ ssList ) ),
inference(simp,[status(thm)],[4698]) ).
thf(4723,plain,
( ( sk38 != nil )
| ( sk37 != nil )
| ~ ( sk38 @ ssList ) ),
inference(simp,[status(thm)],[4713]) ).
thf(5072,plain,
( ( ( sk38 @ ssList )
!= ( nil @ ssList ) )
| ( sk38 != nil )
| ( sk37 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[348,4723]) ).
thf(5073,plain,
( ( ( sk38 @ ssList )
!= ( nil @ ssList ) )
| ( sk38 != nil )
| ( sk37 != nil ) ),
inference(simp,[status(thm)],[5072]) ).
thf(5111,plain,
( ( sk38 != nil )
| ( sk38 != nil )
| ( sk37 != nil ) ),
inference(simp,[status(thm)],[5073]) ).
thf(5121,plain,
( ( sk38 != nil )
| ( sk37 != nil ) ),
inference(simp,[status(thm)],[5111]) ).
thf(5139,plain,
! [A: $i] :
( ( A != sk37 )
| ( sk38 != nil )
| ( nil != nil )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[126,5121]) ).
thf(5140,plain,
! [A: $i] :
( ( A != sk37 )
| ( sk38 != nil )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[5139]) ).
thf(5141,plain,
( ( sk38 != nil )
| ~ ( sk37 @ ( nil @ frontsegP ) )
| ~ ( sk37 @ ssList ) ),
inference(pattern_uni,[status(thm)],[5140:[bind(A,$thf( sk37 ))]]) ).
thf(5125,plain,
! [A: $i] :
( ( A != sk37 )
| ( sk38 != nil )
| ( nil != nil )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[141,5121]) ).
thf(5126,plain,
! [A: $i] :
( ( A != sk37 )
| ( sk38 != nil )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[5125]) ).
thf(5127,plain,
( ( sk38 != nil )
| ~ ( sk37 @ ( nil @ segmentP ) )
| ~ ( sk37 @ ssList ) ),
inference(pattern_uni,[status(thm)],[5126:[bind(A,$thf( sk37 ))]]) ).
thf(9727,plain,
( ( ( sk37 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk38 != nil )
| ~ ( sk37 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,5127]) ).
thf(9728,plain,
( ( ( sk37 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk38 != nil )
| ~ ( sk37 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[9727]) ).
thf(9836,plain,
( ( sk37 != sk1 )
| ( sk38 != nil )
| ~ ( sk37 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[9728]) ).
thf(18761,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk37 @ ( nil @ segmentP ) ) )
| ( sk37 != sk1 )
| ( sk38 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18594,9836]) ).
thf(18762,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk37 @ ( nil @ segmentP ) ) )
| ( sk37 != sk1 )
| ( sk38 != nil ) ),
inference(simp,[status(thm)],[18761]) ).
thf(18810,plain,
( ( sk37 != sk1 )
| ( sk1 != nil )
| ( sk37 != sk1 )
| ( sk38 != nil ) ),
inference(simp,[status(thm)],[18762]) ).
thf(18827,plain,
( ( sk1 != nil )
| ( sk37 != sk1 )
| ( sk38 != nil ) ),
inference(simp,[status(thm)],[18810]) ).
thf(23238,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ( sk37 != sk1 )
| ( sk38 != nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[983,18827]) ).
thf(23239,plain,
( ( sk1 != sk1 )
| ( sk37 != sk1 )
| ( sk38 != nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[23238]) ).
thf(23240,plain,
( ( sk37 != sk1 )
| ( sk38 != nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[23239:[]]) ).
thf(395,plain,
sk37 @ ssItem,
inference(cnfConj,[status(thm)],[394]) ).
thf(396,plain,
sk38 @ ssItem,
inference(cnfConj,[status(thm)],[394]) ).
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(210,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(211,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)],[210]) ).
thf(213,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ neq ) )
| ( A = B )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[211]) ).
thf(216,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A = B ) ),
inference(lifteq,[status(thm)],[213]) ).
thf(102,plain,
( ( nil != sk4 )
| ( nil = sk3 ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(112,plain,
( ( sk4 != nil )
| ( sk3 = nil ) ),
inference(lifteq,[status(thm)],[102]) ).
thf(107,plain,
sk2 = sk4,
inference(cnfConj,[status(thm)],[99]) ).
thf(113,plain,
sk4 = sk2,
inference(lifteq,[status(thm)],[107]) ).
thf(110,plain,
sk1 = sk3,
inference(cnfConj,[status(thm)],[99]) ).
thf(111,plain,
sk3 = sk1,
inference(lifteq,[status(thm)],[110]) ).
thf(540,plain,
( ( sk2 != nil )
| ( sk1 = nil ) ),
inference(rewrite,[status(thm)],[112,113,111]) ).
thf(1314,plain,
( ( sk2 != sk2 )
| ( nil != nil )
| ( sk1 = nil )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1048,540]) ).
thf(1315,plain,
( ( sk2 != sk2 )
| ( sk1 = nil )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1314]) ).
thf(1316,plain,
( ( sk1 = nil )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1315:[]]) ).
thf(1286,plain,
( ( sk2 != sk2 )
| ( sk1 != nil )
| ( nil != nil )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1048,114]) ).
thf(1287,plain,
( ( sk2 != sk2 )
| ( sk1 != nil )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1286]) ).
thf(1288,plain,
( ( sk1 != nil )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1287:[]]) ).
thf(1514,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ~ ( sk2 @ ( nil @ frontsegP ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1316,1288]) ).
thf(1515,plain,
( ( sk1 != sk1 )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1514]) ).
thf(1516,plain,
~ ( sk2 @ ( nil @ frontsegP ) ),
inference(pattern_uni,[status(thm)],[1515:[]]) ).
thf(1554,plain,
( ( ( sk2 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[644,1516]) ).
thf(1555,plain,
( ( sk2 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1554]) ).
thf(1556,plain,
( ( sk2 != nil )
| ( nil != nil ) ),
inference(simp,[status(thm)],[1555]) ).
thf(1557,plain,
sk2 != nil,
inference(simp,[status(thm)],[1556]) ).
thf(27591,plain,
! [B: $i,A: $i] :
( ( A != sk2 )
| ( B != nil )
| ( B @ ( A @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[216,1557]) ).
thf(27592,plain,
! [A: $i] :
( ( A != nil )
| ( A @ ( sk2 @ neq ) )
| ~ ( A @ ssItem )
| ~ ( sk2 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[27591:[bind(A,$thf( sk2 ))]]) ).
thf(29477,plain,
( ( nil @ ( sk2 @ neq ) )
| ~ ( nil @ ssItem )
| ~ ( sk2 @ ssItem ) ),
inference(simp,[status(thm)],[27592]) ).
thf(100,plain,
! [A: $i] :
( ~ ( A @ ( sk1 @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( A @ neq ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(544,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( sk1 @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,100]) ).
thf(545,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( sk1 @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[544]) ).
thf(546,plain,
( ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[545:[bind(A,$thf( sk2 ))]]) ).
thf(18637,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,195]) ).
thf(18638,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[18637]) ).
thf(18639,plain,
sk2 @ ( sk2 @ segmentP ),
inference(pattern_uni,[status(thm)],[18638:[bind(A,$thf( sk2 ))]]) ).
thf(18833,plain,
( ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ $true
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(rewrite,[status(thm)],[546,18639]) ).
thf(18834,plain,
( ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[18833]) ).
thf(42054,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ $true
| ~ ( nil @ ssItem )
| ~ ( sk2 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[29477,18834]) ).
thf(42055,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ ( nil @ ssItem )
| ~ ( sk2 @ ssItem ) ),
inference(simp,[status(thm)],[42054]) ).
thf(42056,plain,
( ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ ( nil @ ssItem )
| ~ ( sk2 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[42055:[]]) ).
thf(56683,plain,
( ( ( sk38 @ ssItem )
!= ( sk2 @ ssItem ) )
| ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ ( nil @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[396,42056]) ).
thf(56684,plain,
( ( ( sk38 @ ssItem )
!= ( sk2 @ ssItem ) )
| ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[56683]) ).
thf(56936,plain,
( ( sk38 != sk2 )
| ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[56684]) ).
thf(65188,plain,
( ( ( sk37 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk38 != sk2 )
| ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[395,56936]) ).
thf(65189,plain,
( ( ( sk37 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk38 != sk2 )
| ~ ( sk2 @ ( sk1 @ segmentP ) ) ),
inference(simp,[status(thm)],[65188]) ).
thf(65250,plain,
( ( sk37 != nil )
| ( sk38 != sk2 )
| ~ ( sk2 @ ( sk1 @ segmentP ) ) ),
inference(simp,[status(thm)],[65189]) ).
thf(176,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk11 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[173]) ).
thf(10155,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk11 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,176]) ).
thf(10156,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk11 @ ssItem ) ),
inference(simp,[status(thm)],[10155]) ).
thf(10157,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk11 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[10156:[bind(A,$thf( sk1 ))]]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax68) ).
thf(120,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(121,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[120]) ).
thf(10312,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10157,121]) ).
thf(10313,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[10312]) ).
thf(10314,plain,
( ( nil @ ( sk1 @ sk11 @ cons ) @ strictorderedP )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10313:[bind(A,$thf( sk1 @ sk11 ))]]) ).
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(379,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(159,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk7 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[157]) ).
thf(704,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,159]) ).
thf(705,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssList ) ),
inference(simp,[status(thm)],[704]) ).
thf(706,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk7 @ ssList ) ),
inference(pattern_uni,[status(thm)],[705:[bind(A,$thf( sk1 ))]]) ).
thf(1791,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[706,248]) ).
thf(1792,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1791]) ).
thf(1793,plain,
( ( nil @ ( sk1 @ sk7 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1792:[bind(A,$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(269,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(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(201,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(202,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ gt ) )
| ~ ( C @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) )
| ~ ( C @ ssItem )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[201]) ).
thf(58555,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ( sk2 != sk1 )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[58046,1574]) ).
thf(58556,plain,
( ( sk1 != sk1 )
| ( sk2 != sk1 )
| ( sk1 @ tl @ ssList ) ),
inference(simp,[status(thm)],[58555]) ).
thf(58557,plain,
( ( sk2 != sk1 )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[58556:[]]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax51) ).
thf(300,plain,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(301,plain,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[300]) ).
thf(58931,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[58557,301]) ).
thf(58932,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[58931]) ).
thf(58933,plain,
( ( nil @ ( sk1 @ tl @ rearsegP ) )
| ( sk2 != sk1 ) ),
inference(pattern_uni,[status(thm)],[58932:[bind(A,$thf( sk1 @ tl ))]]) ).
thf(179,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk13 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[173]) ).
thf(11313,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk13 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,179]) ).
thf(11314,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk13 @ ssList ) ),
inference(simp,[status(thm)],[11313]) ).
thf(11315,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk13 @ ssList ) ),
inference(pattern_uni,[status(thm)],[11314:[bind(A,$thf( sk2 ))]]) ).
thf(11633,plain,
! [A: $i] :
( ( ( sk2 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[11315,301]) ).
thf(11634,plain,
! [A: $i] :
( ( ( sk2 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[11633]) ).
thf(11635,plain,
( ( nil @ ( sk2 @ sk13 @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[11634:[bind(A,$thf( sk2 @ sk13 ))]]) ).
thf(270,plain,
! [A: $i] :
( ( ( ( A @ sk27 @ ( A @ sk28 @ cons ) )
= A )
| ( nil = A )
| ~ ( A @ ssList ) )
& ( ( A @ sk28 @ ssItem )
| ( nil = A )
| ~ ( A @ ssList ) )
& ( ( A @ sk27 @ ssList )
| ( nil = A )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[269]) ).
thf(272,plain,
! [A: $i] :
( ( A @ sk28 @ ssItem )
| ( nil = A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[270]) ).
thf(275,plain,
! [A: $i] :
( ( A @ sk28 @ ssItem )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[272]) ).
thf(79672,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk28 @ ssItem )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[105,275]) ).
thf(79673,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk28 @ ssItem )
| ( nil = A ) ),
inference(simp,[status(thm)],[79672]) ).
thf(79674,plain,
( ( sk2 @ sk28 @ ssItem )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[79673:[bind(A,$thf( sk2 ))]]) ).
thf(83839,plain,
sk2 @ sk28 @ ssItem,
inference(simplifyReflect,[status(thm)],[79674,1557]) ).
thf(83926,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83839,371]) ).
thf(83927,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP ) ),
inference(simp,[status(thm)],[83926]) ).
thf(83928,plain,
nil @ ( sk2 @ sk28 @ cons ) @ totalorderP,
inference(pattern_uni,[status(thm)],[83927:[bind(A,$thf( sk2 @ sk28 ))]]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ app ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
thf(217,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ app ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(273,plain,
! [A: $i] :
( ( ( A @ sk27 @ ( A @ sk28 @ cons ) )
= A )
| ( nil = A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[270]) ).
thf(276,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ( ( A @ sk27 @ ( A @ sk28 @ cons ) )
= A )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[273]) ).
thf(52313,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ( sk1 @ ( nil @ segmentP ) )
| ( sk1 @ sk21 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[49346,23091]) ).
thf(52314,plain,
( ( sk1 != sk1 )
| ( sk1 @ ( nil @ segmentP ) )
| ( sk1 @ sk21 @ ssList ) ),
inference(simp,[status(thm)],[52313]) ).
thf(52315,plain,
( ( sk1 @ ( nil @ segmentP ) )
| ( sk1 @ sk21 @ ssList ) ),
inference(pattern_uni,[status(thm)],[52314:[]]) ).
thf(602,plain,
( ~ $true
| ( ( sk2 @ ( sk2 @ segmentP ) )
!= ( sk2 @ ( sk1 @ segmentP ) ) )
| ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(eqfactor_ordered,[status(thm)],[546]) ).
thf(604,plain,
( ( sk2 != sk2 )
| ( sk2 != sk1 )
| ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[602]) ).
thf(605,plain,
( ( sk2 != sk1 )
| ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[604]) ).
thf(18773,plain,
( ( ( sk2 @ ( sk1 @ segmentP ) )
!= ( sk1 @ ( sk1 @ segmentP ) ) )
| ( sk2 != sk1 )
| ~ $true
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[18594,605]) ).
thf(18774,plain,
( ( ( sk2 @ ( sk1 @ segmentP ) )
!= ( sk1 @ ( sk1 @ segmentP ) ) )
| ( sk2 != sk1 )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[18773]) ).
thf(18815,plain,
( ( sk2 != sk1 )
| ( sk1 != sk1 )
| ( sk2 != sk1 )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[18774]) ).
thf(18832,plain,
( ( sk2 != sk1 )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[18815]) ).
thf(42147,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( sk2 != sk1 )
| ~ $true
| ~ ( nil @ ssItem )
| ~ ( sk2 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[29477,18832]) ).
thf(42148,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( sk2 != sk1 )
| ~ ( nil @ ssItem )
| ~ ( sk2 @ ssItem ) ),
inference(simp,[status(thm)],[42147]) ).
thf(42149,plain,
( ( sk2 != sk1 )
| ~ ( nil @ ssItem )
| ~ ( sk2 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[42148:[]]) ).
thf(42388,plain,
( ( ( sk38 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk2 != sk1 )
| ~ $true
| ~ ( sk2 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[396,42149]) ).
thf(42389,plain,
( ( ( sk38 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk2 != sk1 )
| ~ ( sk2 @ ssItem ) ),
inference(simp,[status(thm)],[42388]) ).
thf(42490,plain,
( ( sk38 != nil )
| ( sk2 != sk1 )
| ~ ( sk2 @ ssItem ) ),
inference(simp,[status(thm)],[42389]) ).
thf(44002,plain,
( ( ( sk37 @ ssItem )
!= ( sk2 @ ssItem ) )
| ( sk38 != nil )
| ( sk2 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[395,42490]) ).
thf(44003,plain,
( ( ( sk37 @ ssItem )
!= ( sk2 @ ssItem ) )
| ( sk38 != nil )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[44002]) ).
thf(44022,plain,
( ( sk37 != sk2 )
| ( sk38 != nil )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[44003]) ).
thf(218,plain,
! [A: $i] :
( ( ( A @ ( nil @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[217]) ).
thf(219,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[218]) ).
thf(30373,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[105,219]) ).
thf(30374,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[30373]) ).
thf(30375,plain,
( ( sk2 @ ( nil @ app ) )
= sk2 ),
inference(pattern_uni,[status(thm)],[30374:[bind(A,$thf( sk2 ))]]) ).
thf(229,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk15 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[223]) ).
thf(35946,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk15 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,229]) ).
thf(35947,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk15 @ ssItem ) ),
inference(simp,[status(thm)],[35946]) ).
thf(35948,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk15 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[35947:[bind(A,$thf( sk2 ))]]) ).
thf(36349,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[35948,236]) ).
thf(36350,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[36349]) ).
thf(36351,plain,
( ~ ( sk2 @ sk15 @ ( nil @ memberP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[36350:[bind(A,$thf( sk2 @ sk15 ))]]) ).
thf(271,plain,
! [A: $i] :
( ( A @ sk27 @ ssList )
| ( nil = A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[270]) ).
thf(274,plain,
! [A: $i] :
( ( A @ sk27 @ ssList )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[271]) ).
thf(73733,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk27 @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[105,274]) ).
thf(73734,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk27 @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[73733]) ).
thf(73735,plain,
( ( sk2 @ sk27 @ ssList )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[73734:[bind(A,$thf( sk2 ))]]) ).
thf(76903,plain,
sk2 @ sk27 @ ssList,
inference(simplifyReflect,[status(thm)],[73735,1557]) ).
thf(77089,plain,
! [A: $i] :
( ( ( sk2 @ sk27 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[76903,219]) ).
thf(77090,plain,
! [A: $i] :
( ( ( sk2 @ sk27 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[77089]) ).
thf(77091,plain,
( ( sk2 @ sk27 @ ( nil @ app ) )
= ( sk2 @ sk27 ) ),
inference(pattern_uni,[status(thm)],[77090:[bind(A,$thf( sk2 @ sk27 ))]]) ).
thf(64,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ duplicatefreeP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax71) ).
thf(409,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ duplicatefreeP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(410,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[409]) ).
thf(11012,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10770,410]) ).
thf(11013,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[11012]) ).
thf(11014,plain,
( ( nil @ ( sk2 @ sk10 @ cons ) @ duplicatefreeP )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[11013:[bind(A,$thf( sk2 @ sk10 ))]]) ).
thf(230,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk18 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[223]) ).
thf(37087,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk18 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,230]) ).
thf(37088,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk18 @ ssList ) ),
inference(simp,[status(thm)],[37087]) ).
thf(37089,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk18 @ ssList ) ),
inference(pattern_uni,[status(thm)],[37088:[bind(A,$thf( sk2 ))]]) ).
thf(37683,plain,
! [A: $i] :
( ( ( sk2 @ sk18 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[37089,248]) ).
thf(37684,plain,
! [A: $i] :
( ( ( sk2 @ sk18 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[37683]) ).
thf(37685,plain,
( ( nil @ ( sk2 @ sk18 @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[37684:[bind(A,$thf( sk2 @ sk18 ))]]) ).
thf(31269,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[395,221]) ).
thf(31270,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[31269]) ).
thf(31271,plain,
~ ( sk37 @ ( sk37 @ lt ) ),
inference(pattern_uni,[status(thm)],[31270:[bind(A,$thf( sk37 ))]]) ).
thf(710,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,159]) ).
thf(711,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssList ) ),
inference(simp,[status(thm)],[710]) ).
thf(712,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk7 @ ssList ) ),
inference(pattern_uni,[status(thm)],[711:[bind(A,$thf( sk2 ))]]) ).
thf(745,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssList )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[712,159]) ).
thf(746,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssList )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[745]) ).
thf(747,plain,
( ( sk2 @ sk7 @ cyclefreeP )
| ( sk2 @ sk7 @ sk7 @ ssList )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[746:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(50100,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk21 @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[105,253]) ).
thf(50101,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk21 @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[50100]) ).
thf(50102,plain,
( ( sk2 @ sk21 @ ssList )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[50101:[bind(A,$thf( sk2 ))]]) ).
thf(52804,plain,
sk2 @ sk21 @ ssList,
inference(simplifyReflect,[status(thm)],[50102,1557]) ).
thf(59,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax45) ).
thf(377,plain,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(378,plain,
! [A: $i] :
( ( nil @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[377]) ).
thf(53028,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[52804,378]) ).
thf(53029,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) ) ),
inference(simp,[status(thm)],[53028]) ).
thf(53030,plain,
nil @ ( sk2 @ sk21 @ frontsegP ),
inference(pattern_uni,[status(thm)],[53029:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(53537,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ sk21 )
= ( A @ tl ) )
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[105,254]) ).
thf(53538,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ sk21 )
= ( A @ tl ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[53537]) ).
thf(53539,plain,
( ( ( sk2 @ sk21 )
= ( sk2 @ tl ) )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[53538:[bind(A,$thf( sk2 ))]]) ).
thf(60517,plain,
( ( sk2 @ sk21 )
= ( sk2 @ tl ) ),
inference(simplifyReflect,[status(thm)],[53539,1557]) ).
thf(60522,plain,
nil @ ( sk2 @ tl @ frontsegP ),
inference(rewrite,[status(thm)],[53030,60517]) ).
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(153,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(10182,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk11 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,176]) ).
thf(10183,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk11 @ ssItem ) ),
inference(simp,[status(thm)],[10182]) ).
thf(10184,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk11 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[10183:[bind(A,$thf( sk2 ))]]) ).
thf(10431,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10184,236]) ).
thf(10432,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[10431]) ).
thf(10433,plain,
( ~ ( sk2 @ sk11 @ ( nil @ memberP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10432:[bind(A,$thf( sk2 @ sk11 ))]]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax65) ).
thf(196,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(197,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[196]) ).
thf(83919,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83839,197]) ).
thf(83920,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[83919]) ).
thf(83921,plain,
nil @ ( sk2 @ sk28 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[83920:[bind(A,$thf( sk2 @ sk28 ))]]) ).
thf(4573,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[396,197]) ).
thf(4574,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[4573]) ).
thf(4575,plain,
nil @ ( sk38 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[4574:[bind(A,$thf( sk38 ))]]) ).
thf(225,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk19 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[223]) ).
thf(31875,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk19 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,225]) ).
thf(31876,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk19 @ ssList ) ),
inference(simp,[status(thm)],[31875]) ).
thf(31877,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk19 @ ssList ) ),
inference(pattern_uni,[status(thm)],[31876:[bind(A,$thf( sk2 ))]]) ).
thf(32537,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[31877,195]) ).
thf(32538,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[32537]) ).
thf(32539,plain,
( ( sk2 @ sk19 @ ( sk2 @ sk19 @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[32538:[bind(A,$thf( sk2 @ sk19 ))]]) ).
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(239,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(240,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ frontsegP ) )
| ( ( C @ ( B @ app ) )
!= A )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) )
& ( ( ( A @ ( B @ sk20 ) @ ( B @ app ) )
= A )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ ( B @ sk20 ) @ ssList )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[239]) ).
thf(241,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk20 ) @ ssList )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[240]) ).
thf(44664,plain,
! [B: $i,A: $i] :
( ( ( nil @ ( nil @ frontsegP ) )
!= ( B @ ( A @ frontsegP ) ) )
| ( A @ ( B @ sk20 ) @ ssList )
| ~ $true
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[644,241]) ).
thf(44665,plain,
! [B: $i,A: $i] :
( ( ( nil @ ( nil @ frontsegP ) )
!= ( B @ ( A @ frontsegP ) ) )
| ( A @ ( B @ sk20 ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[44664]) ).
thf(44666,plain,
( ( nil @ ( nil @ sk20 ) @ ssList )
| ~ ( nil @ ssList )
| ~ ( nil @ ssList ) ),
inference(pattern_uni,[status(thm)],[44665:[bind(A,$thf( nil )),bind(B,$thf( nil ))]]) ).
thf(44768,plain,
( ( nil @ ( nil @ sk20 ) @ ssList )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[44666]) ).
thf(44833,plain,
( ( nil @ ( nil @ sk20 ) @ ssList )
| ~ $true ),
inference(rewrite,[status(thm)],[44768,348]) ).
thf(44834,plain,
nil @ ( nil @ sk20 ) @ ssList,
inference(simp,[status(thm)],[44833]) ).
thf(44846,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk20 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44834,301]) ).
thf(44847,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk20 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[44846]) ).
thf(44848,plain,
nil @ ( nil @ ( nil @ sk20 ) @ rearsegP ),
inference(pattern_uni,[status(thm)],[44847:[bind(A,$thf( nil @ ( nil @ sk20 ) ))]]) ).
thf(212,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ ( A @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[211]) ).
thf(214,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A != B ) ),
inference(lifteq,[status(thm)],[212]) ).
thf(215,plain,
! [A: $i] :
( ~ ( A @ ( A @ neq ) )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[214]) ).
thf(25076,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10157,215]) ).
thf(25077,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[25076]) ).
thf(25078,plain,
( ~ ( sk1 @ sk11 @ ( sk1 @ sk11 @ neq ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25077:[bind(A,$thf( sk1 @ sk11 ))]]) ).
thf(10339,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10157,236]) ).
thf(10340,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[10339]) ).
thf(10341,plain,
( ~ ( sk1 @ sk11 @ ( nil @ memberP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10340:[bind(A,$thf( sk1 @ sk11 ))]]) ).
thf(164,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk6 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[157]) ).
thf(7032,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk6 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,164]) ).
thf(7033,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk6 @ ssItem ) ),
inference(simp,[status(thm)],[7032]) ).
thf(7034,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk6 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[7033:[bind(A,$thf( sk2 ))]]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ equalelemsP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax73) ).
thf(302,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ equalelemsP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(303,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ equalelemsP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[302]) ).
thf(7218,plain,
! [A: $i] :
( ( ( sk2 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7034,303]) ).
thf(7219,plain,
! [A: $i] :
( ( ( sk2 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7218]) ).
thf(7220,plain,
( ( nil @ ( sk2 @ sk6 @ cons ) @ equalelemsP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7219:[bind(A,$thf( sk2 @ sk6 ))]]) ).
thf(178,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( ( A @ sk14 @ ( A @ sk11 @ cons ) @ ( A @ sk13 @ ( A @ sk10 @ cons ) @ ( A @ sk12 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[173]) ).
thf(185,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ( ( A @ sk14 @ ( A @ sk11 @ cons ) @ ( A @ sk13 @ ( A @ sk10 @ cons ) @ ( A @ sk12 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[178]) ).
thf(78819,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk28 @ ssItem )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[106,275]) ).
thf(78820,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk28 @ ssItem )
| ( nil = A ) ),
inference(simp,[status(thm)],[78819]) ).
thf(78821,plain,
( ( sk1 @ sk28 @ ssItem )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[78820:[bind(A,$thf( sk1 ))]]) ).
thf(83489,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ( sk2 != sk1 )
| ( sk1 @ sk28 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[78821,1574]) ).
thf(83490,plain,
( ( sk1 != sk1 )
| ( sk2 != sk1 )
| ( sk1 @ sk28 @ ssItem ) ),
inference(simp,[status(thm)],[83489]) ).
thf(83491,plain,
( ( sk2 != sk1 )
| ( sk1 @ sk28 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[83490:[]]) ).
thf(52646,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[49346,378]) ).
thf(52647,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[52646]) ).
thf(52648,plain,
( ( nil @ ( sk1 @ sk21 @ frontsegP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[52647:[bind(A,$thf( sk1 @ sk21 ))]]) ).
thf(34568,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk16 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,227]) ).
thf(34569,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk16 @ ssItem ) ),
inference(simp,[status(thm)],[34568]) ).
thf(34570,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk16 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[34569:[bind(A,$thf( sk2 ))]]) ).
thf(34941,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[34570,121]) ).
thf(34942,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[34941]) ).
thf(34943,plain,
( ( nil @ ( sk2 @ sk16 @ cons ) @ strictorderedP )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[34942:[bind(A,$thf( sk2 @ sk16 ))]]) ).
thf(180,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk12 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[173]) ).
thf(12203,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk12 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,180]) ).
thf(12204,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk12 @ ssList ) ),
inference(simp,[status(thm)],[12203]) ).
thf(12205,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk12 @ ssList ) ),
inference(pattern_uni,[status(thm)],[12204:[bind(A,$thf( sk2 ))]]) ).
thf(16317,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A )
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[12205,188]) ).
thf(16318,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[16317]) ).
thf(16319,plain,
( ( ( nil @ ( sk2 @ sk12 @ app ) )
= ( sk2 @ sk12 ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[16318:[bind(A,$thf( sk2 @ sk12 ))]]) ).
thf(3807,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[706,301]) ).
thf(3808,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[3807]) ).
thf(3809,plain,
( ( nil @ ( sk1 @ sk7 @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[3808:[bind(A,$thf( sk1 @ sk7 ))]]) ).
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(436,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(42462,plain,
( ( ( sk37 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk2 != sk1 )
| ~ $true
| ~ ( sk2 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[395,42149]) ).
thf(42463,plain,
( ( ( sk37 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk2 != sk1 )
| ~ ( sk2 @ ssItem ) ),
inference(simp,[status(thm)],[42462]) ).
thf(42501,plain,
( ( sk37 != nil )
| ( sk2 != sk1 )
| ~ ( sk2 @ ssItem ) ),
inference(simp,[status(thm)],[42463]) ).
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(255,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(256,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ totalorderP )
| ~ ( A @ sk22 @ ( A @ sk23 @ leq ) )
| ~ ( A @ ssList ) )
& ( ( A @ totalorderP )
| ~ ( A @ sk23 @ ( A @ sk22 @ leq ) )
| ~ ( A @ ssList ) )
& ( ( A @ totalorderP )
| ( ( A @ sk26 @ ( A @ sk23 @ cons ) @ ( A @ sk25 @ ( A @ sk22 @ cons ) @ ( A @ sk24 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) )
& ( ( A @ totalorderP )
| ( A @ sk26 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ totalorderP )
| ( A @ sk25 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ totalorderP )
| ( A @ sk24 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ totalorderP )
| ( A @ sk23 @ ssItem )
| ~ ( A @ ssList ) )
& ( ( A @ totalorderP )
| ( A @ sk22 @ 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 @ totalorderP )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[255]) ).
thf(257,plain,
! [A: $i] :
( ( A @ totalorderP )
| ( A @ sk22 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[256]) ).
thf(7603,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7470,303]) ).
thf(7604,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7603]) ).
thf(7605,plain,
( ( nil @ ( sk1 @ sk5 @ cons ) @ equalelemsP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7604:[bind(A,$thf( sk1 @ sk5 ))]]) ).
thf(174,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ sk11 @ ( A @ sk10 @ lt ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[173]) ).
thf(68,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( ( A @ tl @ ( A @ hd @ cons ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax78) ).
thf(417,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( ( A @ tl @ ( A @ hd @ cons ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(7007,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk6 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,164]) ).
thf(7008,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk6 @ ssItem ) ),
inference(simp,[status(thm)],[7007]) ).
thf(7009,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk6 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[7008:[bind(A,$thf( sk1 ))]]) ).
thf(7134,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7009,371]) ).
thf(7135,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7134]) ).
thf(7136,plain,
( ( nil @ ( sk1 @ sk6 @ cons ) @ totalorderP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7135:[bind(A,$thf( sk1 @ sk6 ))]]) ).
thf(161,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[157]) ).
thf(5422,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,161]) ).
thf(5423,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList ) ),
inference(simp,[status(thm)],[5422]) ).
thf(5424,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk9 @ ssList ) ),
inference(pattern_uni,[status(thm)],[5423:[bind(A,$thf( sk1 ))]]) ).
thf(5619,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5424,378]) ).
thf(5620,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5619]) ).
thf(5621,plain,
( ( nil @ ( sk1 @ sk9 @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5620:[bind(A,$thf( sk1 @ sk9 ))]]) ).
thf(175,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ lt ) )
| ( C @ ( B @ lt ) )
| ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
!= A )
| ~ ( F @ ssList )
| ~ ( E @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssItem )
| ~ ( B @ ssItem )
| ~ ( A @ strictorderP )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[173]) ).
thf(183,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ lt ) )
| ( C @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( E @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssItem )
| ~ ( B @ ssItem )
| ~ ( A @ strictorderP )
| ~ ( A @ ssList )
| ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
!= A ) ),
inference(lifteq,[status(thm)],[175]) ).
thf(184,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ( B @ ( A @ lt ) )
| ~ ( E @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) @ strictorderP )
| ~ ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) @ ssList ) ),
inference(simp,[status(thm)],[183]) ).
thf(32514,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[31877,378]) ).
thf(32515,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[32514]) ).
thf(32516,plain,
( ( nil @ ( sk2 @ sk19 @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[32515:[bind(A,$thf( sk2 @ sk19 ))]]) ).
thf(77163,plain,
! [A: $i] :
( ( ( sk2 @ sk27 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76903,378]) ).
thf(77164,plain,
! [A: $i] :
( ( ( sk2 @ sk27 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) ) ),
inference(simp,[status(thm)],[77163]) ).
thf(77165,plain,
nil @ ( sk2 @ sk27 @ frontsegP ),
inference(pattern_uni,[status(thm)],[77164:[bind(A,$thf( sk2 @ sk27 ))]]) ).
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(504,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(5453,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,161]) ).
thf(5454,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList ) ),
inference(simp,[status(thm)],[5453]) ).
thf(5455,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk9 @ ssList ) ),
inference(pattern_uni,[status(thm)],[5454:[bind(A,$thf( sk2 ))]]) ).
thf(5710,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5455,248]) ).
thf(5711,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5710]) ).
thf(5712,plain,
( ( nil @ ( sk2 @ sk9 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5711:[bind(A,$thf( sk2 @ sk9 ))]]) ).
thf(25088,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10184,215]) ).
thf(25089,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[25088]) ).
thf(25090,plain,
( ~ ( sk2 @ sk11 @ ( sk2 @ sk11 @ neq ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25089:[bind(A,$thf( sk2 @ sk11 ))]]) ).
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(372,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(7495,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk5 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,165]) ).
thf(7496,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk5 @ ssItem ) ),
inference(simp,[status(thm)],[7495]) ).
thf(7497,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk5 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[7496:[bind(A,$thf( sk2 ))]]) ).
thf(7681,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7497,303]) ).
thf(7682,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7681]) ).
thf(7683,plain,
( ( nil @ ( sk2 @ sk5 @ cons ) @ equalelemsP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7682:[bind(A,$thf( sk2 @ sk5 ))]]) ).
thf(77011,plain,
! [A: $i] :
( ( ( sk2 @ sk27 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76903,248]) ).
thf(77012,plain,
! [A: $i] :
( ( ( sk2 @ sk27 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[77011]) ).
thf(77013,plain,
nil @ ( sk2 @ sk27 @ segmentP ),
inference(pattern_uni,[status(thm)],[77012:[bind(A,$thf( sk2 @ sk27 ))]]) ).
thf(31260,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7009,221]) ).
thf(31261,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[31260]) ).
thf(31262,plain,
( ~ ( sk1 @ sk6 @ ( sk1 @ sk6 @ lt ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[31261:[bind(A,$thf( sk1 @ sk6 ))]]) ).
thf(3819,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[712,301]) ).
thf(3820,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[3819]) ).
thf(3821,plain,
( ( nil @ ( sk2 @ sk7 @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[3820:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(12587,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[12205,248]) ).
thf(12588,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[12587]) ).
thf(12589,plain,
( ( nil @ ( sk2 @ sk12 @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[12588:[bind(A,$thf( sk2 @ sk12 ))]]) ).
thf(108,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( sk3 @ ( nil @ neq ) )
| ~ ( sk3 @ ( nil @ neq ) )
| ( ( sk3 @ hd )
!= D )
| ( ( nil @ ( D @ cons ) )
!= C )
| ~ ( D @ ssItem )
| ( ( C @ ( B @ app ) )
!= A )
| ( ( sk3 @ tl )
!= B )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ( sk4 = A )
| ~ ( A @ ssList )
| ~ ( nil @ ( sk4 @ neq ) ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(115,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( sk3 @ ( nil @ neq ) )
| ~ ( sk3 @ ( nil @ neq ) )
| ~ ( D @ ssItem )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( nil @ ( sk4 @ neq ) )
| ( ( sk3 @ hd )
!= D )
| ( ( nil @ ( D @ cons ) )
!= C )
| ( ( C @ ( B @ app ) )
!= A )
| ( ( sk3 @ tl )
!= B )
| ( sk4 = A ) ),
inference(lifteq,[status(thm)],[108]) ).
thf(116,plain,
( ~ ( sk3 @ ( nil @ neq ) )
| ~ ( sk3 @ hd @ ssItem )
| ~ ( nil @ ( sk3 @ hd @ cons ) @ ssList )
| ~ ( sk3 @ tl @ ssList )
| ~ ( nil @ ( sk3 @ hd @ cons ) @ ( sk3 @ tl @ app ) @ ssList )
| ~ ( nil @ ( sk4 @ neq ) )
| ( ( nil @ ( sk3 @ hd @ cons ) @ ( sk3 @ tl @ app ) )
= sk4 ) ),
inference(simp,[status(thm)],[115]) ).
thf(559,plain,
( ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ hd @ ssItem )
| ~ ( nil @ ( sk1 @ hd @ cons ) @ ssList )
| ~ ( sk1 @ tl @ ssList )
| ~ ( nil @ ( sk1 @ hd @ cons ) @ ( sk1 @ tl @ app ) @ ssList )
| ~ ( nil @ ( sk2 @ neq ) )
| ( ( nil @ ( sk1 @ hd @ cons ) @ ( sk1 @ tl @ app ) )
= sk2 ) ),
inference(rewrite,[status(thm)],[116,113,111]) ).
thf(18615,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[12205,195]) ).
thf(18616,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[18615]) ).
thf(18617,plain,
( ( sk2 @ sk12 @ ( sk2 @ sk12 @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[18616:[bind(A,$thf( sk2 @ sk12 ))]]) ).
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(189,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(67,axiom,
nil @ strictorderP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax64) ).
thf(416,plain,
nil @ strictorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
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(151,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(152,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)],[151]) ).
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(316,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(261,plain,
! [A: $i] :
( ( A @ totalorderP )
| ( A @ sk23 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[256]) ).
thf(61355,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk23 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,261]) ).
thf(61356,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk23 @ ssItem ) ),
inference(simp,[status(thm)],[61355]) ).
thf(61357,plain,
( ( sk2 @ totalorderP )
| ( sk2 @ sk23 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[61356:[bind(A,$thf( sk2 ))]]) ).
thf(18657,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5424,195]) ).
thf(18658,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18657]) ).
thf(18659,plain,
( ( sk1 @ sk9 @ ( sk1 @ sk9 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18658:[bind(A,$thf( sk1 @ sk9 ))]]) ).
thf(4950,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[395,303]) ).
thf(4951,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP ) ),
inference(simp,[status(thm)],[4950]) ).
thf(4952,plain,
nil @ ( sk37 @ cons ) @ equalelemsP,
inference(pattern_uni,[status(thm)],[4951:[bind(A,$thf( sk37 ))]]) ).
thf(56844,plain,
( ( ( sk37 @ ssItem )
!= ( sk2 @ ssItem ) )
| ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ ( nil @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[395,42056]) ).
thf(56845,plain,
( ( ( sk37 @ ssItem )
!= ( sk2 @ ssItem ) )
| ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[56844]) ).
thf(56913,plain,
( ( sk37 != sk2 )
| ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[56845]) ).
thf(25100,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7470,215]) ).
thf(25101,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[25100]) ).
thf(25102,plain,
( ~ ( sk1 @ sk5 @ ( sk1 @ sk5 @ neq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[25101:[bind(A,$thf( sk1 @ sk5 ))]]) ).
thf(754,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[396,121]) ).
thf(755,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[754]) ).
thf(756,plain,
nil @ ( sk38 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[755:[bind(A,$thf( sk38 ))]]) ).
thf(34881,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[34522,215]) ).
thf(34882,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[34881]) ).
thf(34883,plain,
( ~ ( sk1 @ sk16 @ ( sk1 @ sk16 @ neq ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[34882:[bind(A,$thf( sk1 @ sk16 ))]]) ).
thf(181,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk14 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[173]) ).
thf(13104,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk14 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,181]) ).
thf(13105,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk14 @ ssList ) ),
inference(simp,[status(thm)],[13104]) ).
thf(13106,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk14 @ ssList ) ),
inference(pattern_uni,[status(thm)],[13105:[bind(A,$thf( sk1 ))]]) ).
thf(13323,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[13106,301]) ).
thf(13324,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[13323]) ).
thf(13325,plain,
( ( nil @ ( sk1 @ sk14 @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[13324:[bind(A,$thf( sk1 @ sk14 ))]]) ).
thf(260,plain,
! [A: $i] :
( ( A @ totalorderP )
| ( A @ sk25 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[256]) ).
thf(59476,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk25 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,260]) ).
thf(59477,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk25 @ ssList ) ),
inference(simp,[status(thm)],[59476]) ).
thf(59478,plain,
( ( sk2 @ totalorderP )
| ( sk2 @ sk25 @ ssList ) ),
inference(pattern_uni,[status(thm)],[59477:[bind(A,$thf( sk2 ))]]) ).
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(237,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(238,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( A @ ( C @ app ) @ app ) @ segmentP ) )
| ~ ( B @ ( A @ segmentP ) )
| ~ ( D @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[237]) ).
thf(56685,plain,
( ( ( sk38 @ ssItem )
!= ( nil @ ssItem ) )
| ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ $true
| ~ ( sk2 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[396,42056]) ).
thf(56686,plain,
( ( ( sk38 @ ssItem )
!= ( nil @ ssItem ) )
| ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ ( sk2 @ ssItem ) ),
inference(simp,[status(thm)],[56685]) ).
thf(56958,plain,
( ( sk38 != nil )
| ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ ( sk2 @ ssItem ) ),
inference(simp,[status(thm)],[56686]) ).
thf(7137,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7009,236]) ).
thf(7138,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7137]) ).
thf(7139,plain,
( ~ ( sk1 @ sk6 @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7138:[bind(A,$thf( sk1 @ sk6 ))]]) ).
thf(84,axiom,
nil @ equalelemsP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax74) ).
thf(492,plain,
nil @ equalelemsP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(63105,plain,
( ( ( sk37 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk37 != sk2 )
| ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[395,56913]) ).
thf(63106,plain,
( ( ( sk37 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk37 != sk2 )
| ~ ( sk2 @ ( sk1 @ segmentP ) ) ),
inference(simp,[status(thm)],[63105]) ).
thf(63152,plain,
( ( sk37 != nil )
| ( sk37 != sk2 )
| ~ ( sk2 @ ( sk1 @ segmentP ) ) ),
inference(simp,[status(thm)],[63106]) ).
thf(140,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ( nil != A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[138]) ).
thf(142,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[140]) ).
thf(143,plain,
( ( nil @ ( nil @ segmentP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[142]) ).
thf(645,plain,
( ( nil @ ( nil @ segmentP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[143,348]) ).
thf(646,plain,
nil @ ( nil @ segmentP ),
inference(simp,[status(thm)],[645]) ).
thf(34959,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[34570,197]) ).
thf(34960,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[34959]) ).
thf(34961,plain,
( ( nil @ ( sk2 @ sk16 @ cons ) @ totalorderedP )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[34960:[bind(A,$thf( sk2 @ sk16 ))]]) ).
thf(11689,plain,
! [A: $i] :
( ( ( sk2 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[11315,248]) ).
thf(11690,plain,
! [A: $i] :
( ( ( sk2 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[11689]) ).
thf(11691,plain,
( ( nil @ ( sk2 @ sk13 @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[11690:[bind(A,$thf( sk2 @ sk13 ))]]) ).
thf(58017,plain,
( ( ( sk1 @ sk21 )
!= ( sk1 @ sk21 ) )
| ( nil @ ( sk1 @ tl @ frontsegP ) )
| ( sk1 = nil )
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[53498,52648]) ).
thf(58018,plain,
( ( ( sk1 @ sk21 )
!= ( sk1 @ sk21 ) )
| ( nil @ ( sk1 @ tl @ frontsegP ) )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[58017]) ).
thf(58019,plain,
( ( nil @ ( sk1 @ tl @ frontsegP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[58018:[]]) ).
thf(7675,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7497,371]) ).
thf(7676,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7675]) ).
thf(7677,plain,
( ( nil @ ( sk2 @ sk5 @ cons ) @ totalorderP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7676:[bind(A,$thf( sk2 @ sk5 ))]]) ).
thf(10539,plain,
( ( ( sk37 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk38 != nil )
| ~ ( sk37 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,5141]) ).
thf(10540,plain,
( ( ( sk37 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk38 != nil )
| ~ ( sk37 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[10539]) ).
thf(10602,plain,
( ( sk37 != sk2 )
| ( sk38 != nil )
| ~ ( sk37 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[10540]) ).
thf(764,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[395,236]) ).
thf(765,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[764]) ).
thf(766,plain,
~ ( sk37 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[765:[bind(A,$thf( sk37 ))]]) ).
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(145,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(146,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[145]) ).
thf(147,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( A = B ) ),
inference(lifteq,[status(thm)],[146]) ).
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(280,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(2182,plain,
! [A: $i] :
( ( A != sk2 )
| ( nil != nil )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[141,1557]) ).
thf(2183,plain,
! [A: $i] :
( ( A != sk2 )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[2182]) ).
thf(2184,plain,
( ~ ( sk2 @ ( nil @ segmentP ) )
| ~ ( sk2 @ ssList ) ),
inference(pattern_uni,[status(thm)],[2183:[bind(A,$thf( sk2 ))]]) ).
thf(2617,plain,
( ~ ( sk2 @ ( nil @ segmentP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[2184,105]) ).
thf(2618,plain,
~ ( sk2 @ ( nil @ segmentP ) ),
inference(simp,[status(thm)],[2617]) ).
thf(11263,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk13 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,179]) ).
thf(11264,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk13 @ ssList ) ),
inference(simp,[status(thm)],[11263]) ).
thf(11265,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk13 @ ssList ) ),
inference(pattern_uni,[status(thm)],[11264:[bind(A,$thf( sk1 ))]]) ).
thf(45074,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk20 ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44834,195]) ).
thf(45075,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk20 ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[45074]) ).
thf(45076,plain,
nil @ ( nil @ sk20 ) @ ( nil @ ( nil @ sk20 ) @ segmentP ),
inference(pattern_uni,[status(thm)],[45075:[bind(A,$thf( nil @ ( nil @ sk20 ) ))]]) ).
thf(59374,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk25 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,260]) ).
thf(59375,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk25 @ ssList ) ),
inference(simp,[status(thm)],[59374]) ).
thf(59376,plain,
( ( sk1 @ totalorderP )
| ( sk1 @ sk25 @ ssList ) ),
inference(pattern_uni,[status(thm)],[59375:[bind(A,$thf( sk1 ))]]) ).
thf(1794,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,248]) ).
thf(1795,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[1794]) ).
thf(1796,plain,
nil @ ( sk2 @ segmentP ),
inference(pattern_uni,[status(thm)],[1795:[bind(A,$thf( sk2 ))]]) ).
thf(10893,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10743,236]) ).
thf(10894,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[10893]) ).
thf(10895,plain,
( ~ ( sk1 @ sk10 @ ( nil @ memberP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10894:[bind(A,$thf( sk1 @ sk10 ))]]) ).
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(411,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(265,plain,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ sk23 @ ( A @ sk22 @ leq ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[256]) ).
thf(9921,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ~ ( A @ sk11 @ ( A @ sk10 @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,174]) ).
thf(9922,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ~ ( A @ sk11 @ ( A @ sk10 @ lt ) ) ),
inference(simp,[status(thm)],[9921]) ).
thf(9923,plain,
( ( sk2 @ strictorderP )
| ~ ( sk2 @ sk11 @ ( sk2 @ sk10 @ lt ) ) ),
inference(pattern_uni,[status(thm)],[9922:[bind(A,$thf( sk2 ))]]) ).
thf(16274,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[6317,188]) ).
thf(16275,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[16274]) ).
thf(16276,plain,
( ( ( nil @ ( sk2 @ sk8 @ app ) )
= ( sk2 @ sk8 ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[16275:[bind(A,$thf( sk2 @ sk8 ))]]) ).
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(206,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(4080,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,378]) ).
thf(4081,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) ) ),
inference(simp,[status(thm)],[4080]) ).
thf(4082,plain,
nil @ ( sk1 @ frontsegP ),
inference(pattern_uni,[status(thm)],[4081:[bind(A,$thf( sk1 ))]]) ).
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(132,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(33029,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk17 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,226]) ).
thf(33030,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk17 @ ssList ) ),
inference(simp,[status(thm)],[33029]) ).
thf(33031,plain,
( ( sk1 @ strictorderedP )
| ( sk1 @ sk17 @ ssList ) ),
inference(pattern_uni,[status(thm)],[33030:[bind(A,$thf( sk1 ))]]) ).
thf(33332,plain,
! [A: $i] :
( ( ( sk1 @ sk17 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[33031,301]) ).
thf(33333,plain,
! [A: $i] :
( ( ( sk1 @ sk17 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[33332]) ).
thf(33334,plain,
( ( nil @ ( sk1 @ sk17 @ rearsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[33333:[bind(A,$thf( sk1 @ sk17 ))]]) ).
thf(133,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)],[132]) ).
thf(264,plain,
! [A: $i] :
( ( A @ totalorderP )
| ( A @ sk24 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[256]) ).
thf(63896,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk24 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,264]) ).
thf(63897,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk24 @ ssList ) ),
inference(simp,[status(thm)],[63896]) ).
thf(63898,plain,
( ( sk2 @ totalorderP )
| ( sk2 @ sk24 @ ssList ) ),
inference(pattern_uni,[status(thm)],[63897:[bind(A,$thf( sk2 ))]]) ).
thf(10060,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7009,410]) ).
thf(10061,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[10060]) ).
thf(10062,plain,
( ( nil @ ( sk1 @ sk6 @ cons ) @ duplicatefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[10061:[bind(A,$thf( sk1 @ sk6 ))]]) ).
thf(3,axiom,
nil @ strictorderedP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax69) ).
thf(117,plain,
nil @ strictorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7215,plain,
! [A: $i] :
( ( ( sk2 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7034,236]) ).
thf(7216,plain,
! [A: $i] :
( ( ( sk2 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7215]) ).
thf(7217,plain,
( ~ ( sk2 @ sk6 @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7216:[bind(A,$thf( sk2 @ sk6 ))]]) ).
thf(5543,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5424,301]) ).
thf(5544,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5543]) ).
thf(5545,plain,
( ( nil @ ( sk1 @ sk9 @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5544:[bind(A,$thf( sk1 @ sk9 ))]]) ).
thf(83891,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83839,121]) ).
thf(83892,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[83891]) ).
thf(83893,plain,
nil @ ( sk2 @ sk28 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[83892:[bind(A,$thf( sk2 @ sk28 ))]]) ).
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(534,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(228,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ lt ) )
| ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
!= A )
| ~ ( F @ ssList )
| ~ ( E @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssItem )
| ~ ( B @ ssItem )
| ~ ( A @ strictorderedP )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[223]) ).
thf(232,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( E @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssItem )
| ~ ( B @ ssItem )
| ~ ( A @ strictorderedP )
| ~ ( A @ ssList )
| ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
!= A ) ),
inference(lifteq,[status(thm)],[228]) ).
thf(233,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ lt ) )
| ~ ( E @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) @ strictorderedP )
| ~ ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) @ ssList ) ),
inference(simp,[status(thm)],[232]) ).
thf(541,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( sk1 @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,100]) ).
thf(542,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( sk1 @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[541]) ).
thf(543,plain,
( ~ ( sk1 @ ( sk1 @ segmentP ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[542:[bind(A,$thf( sk1 ))]]) ).
thf(18741,plain,
( ~ $true
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(rewrite,[status(thm)],[543,18594]) ).
thf(18742,plain,
( ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[18741]) ).
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(334,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(4672,plain,
( ( ( sk38 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk37 != nil )
| ~ ( sk38 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,1054]) ).
thf(4673,plain,
( ( ( sk38 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk37 != nil )
| ~ ( sk38 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[4672]) ).
thf(4712,plain,
( ( sk38 != sk2 )
| ( sk37 != nil )
| ~ ( sk38 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[4673]) ).
thf(59029,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[58557,248]) ).
thf(59030,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[59029]) ).
thf(59031,plain,
( ( nil @ ( sk1 @ tl @ segmentP ) )
| ( sk2 != sk1 ) ),
inference(pattern_uni,[status(thm)],[59030:[bind(A,$thf( sk1 @ tl ))]]) ).
thf(31798,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk19 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,225]) ).
thf(31799,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk19 @ ssList ) ),
inference(simp,[status(thm)],[31798]) ).
thf(31800,plain,
( ( sk1 @ strictorderedP )
| ( sk1 @ sk19 @ ssList ) ),
inference(pattern_uni,[status(thm)],[31799:[bind(A,$thf( sk1 ))]]) ).
thf(32256,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[31800,378]) ).
thf(32257,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[32256]) ).
thf(32258,plain,
( ( nil @ ( sk1 @ sk19 @ frontsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[32257:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(6548,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[6317,301]) ).
thf(6549,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[6548]) ).
thf(6550,plain,
( ( nil @ ( sk2 @ sk8 @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[6549:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(60525,plain,
sk2 @ tl @ ssList,
inference(rewrite,[status(thm)],[52804,60517]) ).
thf(10973,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10770,197]) ).
thf(10974,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[10973]) ).
thf(10975,plain,
( ( nil @ ( sk2 @ sk10 @ cons ) @ totalorderedP )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10974:[bind(A,$thf( sk2 @ sk10 ))]]) ).
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(407,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(55906,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk22 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,257]) ).
thf(55907,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk22 @ ssItem ) ),
inference(simp,[status(thm)],[55906]) ).
thf(55908,plain,
( ( sk1 @ totalorderP )
| ( sk1 @ sk22 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[55907:[bind(A,$thf( sk1 ))]]) ).
thf(56260,plain,
! [A: $i] :
( ( ( sk1 @ sk22 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[55908,236]) ).
thf(56261,plain,
! [A: $i] :
( ( ( sk1 @ sk22 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ totalorderP ) ),
inference(simp,[status(thm)],[56260]) ).
thf(56262,plain,
( ~ ( sk1 @ sk22 @ ( nil @ memberP ) )
| ( sk1 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[56261:[bind(A,$thf( sk1 @ sk22 ))]]) ).
thf(45006,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk20 ) @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[44834,219]) ).
thf(45007,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk20 ) @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[45006]) ).
thf(45008,plain,
( ( nil @ ( nil @ sk20 ) @ ( nil @ app ) )
= ( nil @ ( nil @ sk20 ) ) ),
inference(pattern_uni,[status(thm)],[45007:[bind(A,$thf( nil @ ( nil @ sk20 ) ))]]) ).
thf(10988,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10770,303]) ).
thf(10989,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[10988]) ).
thf(10990,plain,
( ( nil @ ( sk2 @ sk10 @ cons ) @ equalelemsP )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10989:[bind(A,$thf( sk2 @ sk10 ))]]) ).
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(349,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(44,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ tl @ ssList ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
thf(297,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ tl @ ssList ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(33601,plain,
! [A: $i] :
( ( ( sk2 @ sk17 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[33111,301]) ).
thf(33602,plain,
! [A: $i] :
( ( ( sk2 @ sk17 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[33601]) ).
thf(33603,plain,
( ( nil @ ( sk2 @ sk17 @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[33602:[bind(A,$thf( sk2 @ sk17 ))]]) ).
thf(62974,plain,
( ( ( sk38 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk37 != sk2 )
| ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[396,56913]) ).
thf(62975,plain,
( ( ( sk38 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk37 != sk2 )
| ~ ( sk2 @ ( sk1 @ segmentP ) ) ),
inference(simp,[status(thm)],[62974]) ).
thf(63208,plain,
( ( sk38 != nil )
| ( sk37 != sk2 )
| ~ ( sk2 @ ( sk1 @ segmentP ) ) ),
inference(simp,[status(thm)],[62975]) ).
thf(35898,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk15 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,229]) ).
thf(35899,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk15 @ ssItem ) ),
inference(simp,[status(thm)],[35898]) ).
thf(35900,plain,
( ( sk1 @ strictorderedP )
| ( sk1 @ sk15 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[35899:[bind(A,$thf( sk1 ))]]) ).
thf(36176,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[35900,236]) ).
thf(36177,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[36176]) ).
thf(36178,plain,
( ~ ( sk1 @ sk15 @ ( nil @ memberP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[36177:[bind(A,$thf( sk1 @ sk15 ))]]) ).
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(361,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(4583,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[395,197]) ).
thf(4584,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[4583]) ).
thf(4585,plain,
nil @ ( sk37 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[4584:[bind(A,$thf( sk37 ))]]) ).
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(461,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(4940,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[396,303]) ).
thf(4941,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP ) ),
inference(simp,[status(thm)],[4940]) ).
thf(4942,plain,
nil @ ( sk38 @ cons ) @ equalelemsP,
inference(pattern_uni,[status(thm)],[4941:[bind(A,$thf( sk38 ))]]) ).
thf(85,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ geq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax89) ).
thf(493,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(4102,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[706,378]) ).
thf(4103,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[4102]) ).
thf(4104,plain,
( ( nil @ ( sk1 @ sk7 @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[4103:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(37001,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk18 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,230]) ).
thf(37002,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk18 @ ssList ) ),
inference(simp,[status(thm)],[37001]) ).
thf(37003,plain,
( ( sk1 @ strictorderedP )
| ( sk1 @ sk18 @ ssList ) ),
inference(pattern_uni,[status(thm)],[37002:[bind(A,$thf( sk1 ))]]) ).
thf(37504,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[37003,378]) ).
thf(37505,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[37504]) ).
thf(37506,plain,
( ( nil @ ( sk1 @ sk18 @ frontsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[37505:[bind(A,$thf( sk1 @ sk18 ))]]) ).
thf(45628,plain,
( ( ( sk37 @ ssItem )
!= ( sk2 @ ssItem ) )
| ( sk37 != nil )
| ( sk2 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[395,42501]) ).
thf(45629,plain,
( ( ( sk37 @ ssItem )
!= ( sk2 @ ssItem ) )
| ( sk37 != nil )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[45628]) ).
thf(45661,plain,
( ( sk37 != sk2 )
| ( sk37 != nil )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[45629]) ).
thf(78,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax42) ).
thf(456,plain,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
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(324,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(54548,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[52466,378]) ).
thf(54549,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[54548]) ).
thf(54550,plain,
( ( nil @ ( sk1 @ sk21 @ frontsegP ) )
| ( sk2 != sk1 ) ),
inference(pattern_uni,[status(thm)],[54549:[bind(A,$thf( sk1 @ sk21 ))]]) ).
thf(3797,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,301]) ).
thf(3798,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[3797]) ).
thf(3799,plain,
nil @ ( sk1 @ rearsegP ),
inference(pattern_uni,[status(thm)],[3798:[bind(A,$thf( sk1 ))]]) ).
thf(7140,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7009,303]) ).
thf(7141,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7140]) ).
thf(7142,plain,
( ( nil @ ( sk1 @ sk6 @ cons ) @ equalelemsP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7141:[bind(A,$thf( sk1 @ sk6 ))]]) ).
thf(6746,plain,
( ( ( sk38 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk37 != nil )
| ~ ( sk38 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,2364]) ).
thf(6747,plain,
( ( ( sk38 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk37 != nil )
| ~ ( sk38 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[6746]) ).
thf(6801,plain,
( ( sk38 != sk2 )
| ( sk37 != nil )
| ~ ( sk38 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[6747]) ).
thf(37604,plain,
! [A: $i] :
( ( ( sk2 @ sk18 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[37089,301]) ).
thf(37605,plain,
! [A: $i] :
( ( ( sk2 @ sk18 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[37604]) ).
thf(37606,plain,
( ( nil @ ( sk2 @ sk18 @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[37605:[bind(A,$thf( sk2 @ sk18 ))]]) ).
thf(52816,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[52804,301]) ).
thf(52817,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[52816]) ).
thf(52818,plain,
nil @ ( sk2 @ sk21 @ rearsegP ),
inference(pattern_uni,[status(thm)],[52817:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(60521,plain,
nil @ ( sk2 @ tl @ rearsegP ),
inference(rewrite,[status(thm)],[52818,60517]) ).
thf(69,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ cyclefreeP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax59) ).
thf(420,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ cyclefreeP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(166,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( ( A @ sk9 @ ( A @ sk6 @ cons ) @ ( A @ sk8 @ ( A @ sk5 @ cons ) @ ( A @ sk7 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[157]) ).
thf(169,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ~ ( A @ ssList )
| ( ( A @ sk9 @ ( A @ sk6 @ cons ) @ ( A @ sk8 @ ( A @ sk5 @ cons ) @ ( A @ sk7 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[166]) ).
thf(10428,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10184,371]) ).
thf(10429,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[10428]) ).
thf(10430,plain,
( ( nil @ ( sk2 @ sk11 @ cons ) @ totalorderP )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10429:[bind(A,$thf( sk2 @ sk11 ))]]) ).
thf(6622,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[6317,378]) ).
thf(6623,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[6622]) ).
thf(6624,plain,
( ( nil @ ( sk2 @ sk8 @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[6623:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(34968,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[34570,371]) ).
thf(34969,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[34968]) ).
thf(34970,plain,
( ( nil @ ( sk2 @ sk16 @ cons ) @ totalorderP )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[34969:[bind(A,$thf( sk2 @ sk16 ))]]) ).
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(191,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(192,plain,
! [C: $i,B: $i,A: $i] :
( ( C = A )
| ( ( B @ ( C @ app ) )
!= ( B @ ( A @ app ) ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[191]) ).
thf(193,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( C = A )
| ( ( B @ ( C @ app ) )
!= ( B @ ( A @ app ) ) ) ),
inference(lifteq,[status(thm)],[192]) ).
thf(54415,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[52466,248]) ).
thf(54416,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[54415]) ).
thf(54417,plain,
( ( nil @ ( sk1 @ sk21 @ segmentP ) )
| ( sk2 != sk1 ) ),
inference(pattern_uni,[status(thm)],[54416:[bind(A,$thf( sk1 @ sk21 ))]]) ).
thf(52903,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[52804,248]) ).
thf(52904,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[52903]) ).
thf(52905,plain,
nil @ ( sk2 @ sk21 @ segmentP ),
inference(pattern_uni,[status(thm)],[52904:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(60518,plain,
nil @ ( sk2 @ tl @ segmentP ),
inference(rewrite,[status(thm)],[52905,60517]) ).
thf(262,plain,
! [A: $i] :
( ( A @ totalorderP )
| ( A @ sk26 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[256]) ).
thf(61949,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk26 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,262]) ).
thf(61950,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk26 @ ssList ) ),
inference(simp,[status(thm)],[61949]) ).
thf(61951,plain,
( ( sk1 @ totalorderP )
| ( sk1 @ sk26 @ ssList ) ),
inference(pattern_uni,[status(thm)],[61950:[bind(A,$thf( sk1 ))]]) ).
thf(7666,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7497,197]) ).
thf(7667,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7666]) ).
thf(7668,plain,
( ( nil @ ( sk2 @ sk5 @ cons ) @ totalorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7667:[bind(A,$thf( sk2 @ sk5 ))]]) ).
thf(12147,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk12 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,180]) ).
thf(12148,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk12 @ ssList ) ),
inference(simp,[status(thm)],[12147]) ).
thf(12149,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk12 @ ssList ) ),
inference(pattern_uni,[status(thm)],[12148:[bind(A,$thf( sk1 ))]]) ).
thf(12408,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[12149,248]) ).
thf(12409,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[12408]) ).
thf(12410,plain,
( ( nil @ ( sk1 @ sk12 @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[12409:[bind(A,$thf( sk1 @ sk12 ))]]) ).
thf(16314,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A )
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[13106,188]) ).
thf(16315,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[16314]) ).
thf(16316,plain,
( ( ( nil @ ( sk1 @ sk14 @ app ) )
= ( sk1 @ sk14 ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[16315:[bind(A,$thf( sk1 @ sk14 ))]]) ).
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(129,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(1001,plain,
! [A: $i] :
( ( A != sk37 )
| ~ ( nil @ ( nil @ memberP ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[126,766]) ).
thf(1002,plain,
( ~ ( nil @ ( nil @ memberP ) )
| ~ ( sk37 @ ( nil @ frontsegP ) )
| ~ ( sk37 @ ssList ) ),
inference(pattern_uni,[status(thm)],[1001:[bind(A,$thf( sk37 ))]]) ).
thf(12531,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[12205,301]) ).
thf(12532,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[12531]) ).
thf(12533,plain,
( ( nil @ ( sk2 @ sk12 @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[12532:[bind(A,$thf( sk2 @ sk12 ))]]) ).
thf(18579,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[6317,195]) ).
thf(18580,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18579]) ).
thf(18581,plain,
( ( sk2 @ sk8 @ ( sk2 @ sk8 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18580:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(10336,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10157,371]) ).
thf(10337,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[10336]) ).
thf(10338,plain,
( ( nil @ ( sk1 @ sk11 @ cons ) @ totalorderP )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10337:[bind(A,$thf( sk1 @ sk11 ))]]) ).
thf(91,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49) ).
thf(508,plain,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(23298,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ( sk38 != sk1 )
| ( sk37 != nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[983,18828]) ).
thf(23299,plain,
( ( sk1 != sk1 )
| ( sk38 != sk1 )
| ( sk37 != nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[23298]) ).
thf(23300,plain,
( ( sk38 != sk1 )
| ( sk37 != nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[23299:[]]) ).
thf(25073,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10743,215]) ).
thf(25074,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[25073]) ).
thf(25075,plain,
( ~ ( sk1 @ sk10 @ ( sk1 @ sk10 @ neq ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25074:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(34807,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[34522,303]) ).
thf(34808,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[34807]) ).
thf(34809,plain,
( ( nil @ ( sk1 @ sk16 @ cons ) @ equalelemsP )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[34808:[bind(A,$thf( sk1 @ sk16 ))]]) ).
thf(7131,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7009,197]) ).
thf(7132,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7131]) ).
thf(7133,plain,
( ( nil @ ( sk1 @ sk6 @ cons ) @ totalorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7132:[bind(A,$thf( sk1 @ sk6 ))]]) ).
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(134,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) @ hd )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(10404,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10184,121]) ).
thf(10405,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[10404]) ).
thf(10406,plain,
( ( nil @ ( sk2 @ sk11 @ cons ) @ strictorderedP )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10405:[bind(A,$thf( sk2 @ sk11 ))]]) ).
thf(13163,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk14 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,181]) ).
thf(13164,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk14 @ ssList ) ),
inference(simp,[status(thm)],[13163]) ).
thf(13165,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk14 @ ssList ) ),
inference(pattern_uni,[status(thm)],[13164:[bind(A,$thf( sk2 ))]]) ).
thf(13505,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[13165,301]) ).
thf(13506,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[13505]) ).
thf(13507,plain,
( ( nil @ ( sk2 @ sk14 @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[13506:[bind(A,$thf( sk2 @ sk14 ))]]) ).
thf(242,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk20 ) @ ( B @ app ) )
= A )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[240]) ).
thf(244,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( A @ ( B @ sk20 ) @ ( B @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[242]) ).
thf(31251,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10770,221]) ).
thf(31252,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[31251]) ).
thf(31253,plain,
( ~ ( sk2 @ sk10 @ ( sk2 @ sk10 @ lt ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[31252:[bind(A,$thf( sk2 @ sk10 ))]]) ).
thf(28,axiom,
~ ( nil @ singletonP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).
thf(204,plain,
~ ( nil @ singletonP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(205,plain,
~ ( nil @ singletonP ),
inference(polarity_switch,[status(thm)],[204]) ).
thf(663,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( nil @ ( nil @ segmentP ) ) )
| ~ $true
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[646,543]) ).
thf(664,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( nil @ ( nil @ segmentP ) ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[663]) ).
thf(679,plain,
( ( sk1 != nil )
| ( sk1 != nil )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[664]) ).
thf(686,plain,
( ( sk1 != nil )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[679]) ).
thf(17627,plain,
( ( ( sk1 @ ( sk2 @ segmentP ) )
!= ( nil @ ( sk2 @ segmentP ) ) )
| ( sk1 != nil )
| ~ $true
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[1796,686]) ).
thf(17628,plain,
( ( ( sk1 @ ( sk2 @ segmentP ) )
!= ( nil @ ( sk2 @ segmentP ) ) )
| ( sk1 != nil )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[17627]) ).
thf(17706,plain,
( ( sk1 != nil )
| ( sk2 != sk2 )
| ( sk1 != nil )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[17628]) ).
thf(17731,plain,
( ( sk1 != nil )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[17706]) ).
thf(32353,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[31877,301]) ).
thf(32354,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[32353]) ).
thf(32355,plain,
( ( nil @ ( sk2 @ sk19 @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[32354:[bind(A,$thf( sk2 @ sk19 ))]]) ).
thf(109,plain,
( ( nil @ ( sk3 @ neq ) )
| ~ ( nil @ ( sk4 @ neq ) ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(558,plain,
( ( nil @ ( sk1 @ neq ) )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(rewrite,[status(thm)],[109,113,111]) ).
thf(33680,plain,
! [A: $i] :
( ( ( sk2 @ sk17 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[33111,248]) ).
thf(33681,plain,
! [A: $i] :
( ( ( sk2 @ sk17 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[33680]) ).
thf(33682,plain,
( ( nil @ ( sk2 @ sk17 @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[33681:[bind(A,$thf( sk2 @ sk17 ))]]) ).
thf(11576,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[11265,378]) ).
thf(11577,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[11576]) ).
thf(11578,plain,
( ( nil @ ( sk1 @ sk13 @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[11577:[bind(A,$thf( sk1 @ sk13 ))]]) ).
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(148,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(41,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) )
!= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
thf(277,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) )
!= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(278,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ cons ) )
!= A )
| ~ ( B @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[277]) ).
thf(279,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( ( A @ ( B @ cons ) )
!= A ) ),
inference(lifteq,[status(thm)],[278]) ).
thf(3790,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ sk7 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[747,301]) ).
thf(3791,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ sk7 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[3790]) ).
thf(3792,plain,
( ( nil @ ( sk2 @ sk7 @ sk7 @ rearsegP ) )
| ( sk2 @ sk7 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[3791:[bind(A,$thf( sk2 @ sk7 @ sk7 ))]]) ).
thf(6284,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,163]) ).
thf(6285,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ssList ) ),
inference(simp,[status(thm)],[6284]) ).
thf(6286,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk8 @ ssList ) ),
inference(pattern_uni,[status(thm)],[6285:[bind(A,$thf( sk1 ))]]) ).
thf(6420,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[6286,301]) ).
thf(6421,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[6420]) ).
thf(6422,plain,
( ( nil @ ( sk1 @ sk8 @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[6421:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(83906,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83839,221]) ).
thf(83907,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[83906]) ).
thf(83908,plain,
~ ( sk2 @ sk28 @ ( sk2 @ sk28 @ lt ) ),
inference(pattern_uni,[status(thm)],[83907:[bind(A,$thf( sk2 @ sk28 ))]]) ).
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(513,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(71,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( B @ ( A @ app ) @ ssList ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
thf(430,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( B @ ( A @ app ) @ ssList ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(182,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ sk10 @ ( A @ sk11 @ lt ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[173]) ).
thf(13987,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ~ ( A @ sk10 @ ( A @ sk11 @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,182]) ).
thf(13988,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ~ ( A @ sk10 @ ( A @ sk11 @ lt ) ) ),
inference(simp,[status(thm)],[13987]) ).
thf(13989,plain,
( ( sk2 @ strictorderP )
| ~ ( sk2 @ sk10 @ ( sk2 @ sk11 @ lt ) ) ),
inference(pattern_uni,[status(thm)],[13988:[bind(A,$thf( sk2 ))]]) ).
thf(45051,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk20 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44834,378]) ).
thf(45052,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk20 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) ) ),
inference(simp,[status(thm)],[45051]) ).
thf(45053,plain,
nil @ ( nil @ ( nil @ sk20 ) @ frontsegP ),
inference(pattern_uni,[status(thm)],[45052:[bind(A,$thf( nil @ ( nil @ sk20 ) ))]]) ).
thf(33765,plain,
! [A: $i] :
( ( ( sk2 @ sk17 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[33111,378]) ).
thf(33766,plain,
! [A: $i] :
( ( ( sk2 @ sk17 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[33765]) ).
thf(33767,plain,
( ( nil @ ( sk2 @ sk17 @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[33766:[bind(A,$thf( sk2 @ sk17 ))]]) ).
thf(7597,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7470,371]) ).
thf(7598,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7597]) ).
thf(7599,plain,
( ( nil @ ( sk1 @ sk5 @ cons ) @ totalorderP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7598:[bind(A,$thf( sk1 @ sk5 ))]]) ).
thf(75,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ rearsegP ) )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax52) ).
thf(444,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(445,plain,
! [A: $i] :
( ( ( A @ ( nil @ rearsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) )
& ( ( nil = A )
| ~ ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[444]) ).
thf(447,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[445]) ).
thf(449,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[447]) ).
thf(450,plain,
( ( nil @ ( nil @ rearsegP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[449]) ).
thf(688,plain,
( ( nil @ ( nil @ rearsegP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[450,348]) ).
thf(689,plain,
nil @ ( nil @ rearsegP ),
inference(simp,[status(thm)],[688]) ).
thf(7116,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7009,121]) ).
thf(7117,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7116]) ).
thf(7118,plain,
( ( nil @ ( sk1 @ sk6 @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7117:[bind(A,$thf( sk1 @ sk6 ))]]) ).
thf(37774,plain,
! [A: $i] :
( ( ( sk2 @ sk18 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[37089,378]) ).
thf(37775,plain,
! [A: $i] :
( ( ( sk2 @ sk18 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[37774]) ).
thf(37776,plain,
( ( nil @ ( sk2 @ sk18 @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[37775:[bind(A,$thf( sk2 @ sk18 ))]]) ).
thf(11457,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[11265,301]) ).
thf(11458,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[11457]) ).
thf(11459,plain,
( ( nil @ ( sk1 @ sk13 @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[11458:[bind(A,$thf( sk1 @ sk13 ))]]) ).
thf(18687,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[12149,195]) ).
thf(18688,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[18687]) ).
thf(18689,plain,
( ( sk1 @ sk12 @ ( sk1 @ sk12 @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[18688:[bind(A,$thf( sk1 @ sk12 ))]]) ).
thf(7588,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7470,197]) ).
thf(7589,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7588]) ).
thf(7590,plain,
( ( nil @ ( sk1 @ sk5 @ cons ) @ totalorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7589:[bind(A,$thf( sk1 @ sk5 ))]]) ).
thf(730,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssList )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[706,159]) ).
thf(731,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssList )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[730]) ).
thf(732,plain,
( ( sk1 @ sk7 @ cyclefreeP )
| ( sk1 @ sk7 @ sk7 @ ssList )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[731:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(34971,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[34570,236]) ).
thf(34972,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[34971]) ).
thf(34973,plain,
( ~ ( sk2 @ sk16 @ ( nil @ memberP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[34972:[bind(A,$thf( sk2 @ sk16 ))]]) ).
thf(43960,plain,
( ( ( sk38 @ ssItem )
!= ( sk2 @ ssItem ) )
| ( sk38 != nil )
| ( sk2 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[396,42490]) ).
thf(43961,plain,
( ( ( sk38 @ ssItem )
!= ( sk2 @ ssItem ) )
| ( sk38 != nil )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[43960]) ).
thf(44024,plain,
( ( sk38 != sk2 )
| ( sk38 != nil )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[43961]) ).
thf(55967,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk22 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,257]) ).
thf(55968,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk22 @ ssItem ) ),
inference(simp,[status(thm)],[55967]) ).
thf(55969,plain,
( ( sk2 @ totalorderP )
| ( sk2 @ sk22 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[55968:[bind(A,$thf( sk2 ))]]) ).
thf(10327,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10157,197]) ).
thf(10328,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[10327]) ).
thf(10329,plain,
( ( nil @ ( sk1 @ sk11 @ cons ) @ totalorderedP )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10328:[bind(A,$thf( sk1 @ sk11 ))]]) ).
thf(13561,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[13165,248]) ).
thf(13562,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[13561]) ).
thf(13563,plain,
( ( nil @ ( sk2 @ sk14 @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[13562:[bind(A,$thf( sk2 @ sk14 ))]]) ).
thf(61285,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk23 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,261]) ).
thf(61286,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk23 @ ssItem ) ),
inference(simp,[status(thm)],[61285]) ).
thf(61287,plain,
( ( sk1 @ totalorderP )
| ( sk1 @ sk23 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[61286:[bind(A,$thf( sk1 ))]]) ).
thf(34786,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[34522,197]) ).
thf(34787,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[34786]) ).
thf(34788,plain,
( ( nil @ ( sk1 @ sk16 @ cons ) @ totalorderedP )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[34787:[bind(A,$thf( sk1 @ sk16 ))]]) ).
thf(555,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( sk1 @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[348,100]) ).
thf(556,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( sk1 @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[555]) ).
thf(557,plain,
( ~ ( nil @ ( sk1 @ segmentP ) )
| ~ ( nil @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( nil @ neq ) ) ),
inference(pattern_uni,[status(thm)],[556:[bind(A,$thf( nil ))]]) ).
thf(1779,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,248]) ).
thf(1780,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[1779]) ).
thf(1781,plain,
nil @ ( sk1 @ segmentP ),
inference(pattern_uni,[status(thm)],[1780:[bind(A,$thf( sk1 ))]]) ).
thf(1841,plain,
( ~ $true
| ~ ( nil @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( nil @ neq ) ) ),
inference(rewrite,[status(thm)],[557,1781]) ).
thf(1842,plain,
( ~ ( nil @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[1841]) ).
thf(1915,plain,
( ~ $true
| ~ ( nil @ ( nil @ neq ) ) ),
inference(rewrite,[status(thm)],[1842,1796]) ).
thf(1916,plain,
~ ( nil @ ( nil @ neq ) ),
inference(simp,[status(thm)],[1915]) ).
thf(16311,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A )
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[11265,188]) ).
thf(16312,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[16311]) ).
thf(16313,plain,
( ( ( nil @ ( sk1 @ sk13 @ app ) )
= ( sk1 @ sk13 ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[16312:[bind(A,$thf( sk1 @ sk13 ))]]) ).
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(118,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(10881,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10743,197]) ).
thf(10882,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[10881]) ).
thf(10883,plain,
( ( nil @ ( sk1 @ sk10 @ cons ) @ totalorderedP )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10882:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(13951,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ~ ( A @ sk10 @ ( A @ sk11 @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,182]) ).
thf(13952,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ~ ( A @ sk10 @ ( A @ sk11 @ lt ) ) ),
inference(simp,[status(thm)],[13951]) ).
thf(13953,plain,
( ( sk1 @ strictorderP )
| ~ ( sk1 @ sk10 @ ( sk1 @ sk11 @ lt ) ) ),
inference(pattern_uni,[status(thm)],[13952:[bind(A,$thf( sk1 ))]]) ).
thf(25094,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7497,215]) ).
thf(25095,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[25094]) ).
thf(25096,plain,
( ~ ( sk2 @ sk5 @ ( sk2 @ sk5 @ neq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[25095:[bind(A,$thf( sk2 @ sk5 ))]]) ).
thf(12,axiom,
nil @ cyclefreeP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax60) ).
thf(144,plain,
nil @ cyclefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(37326,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[37003,301]) ).
thf(37327,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[37326]) ).
thf(37328,plain,
( ( nil @ ( sk1 @ sk18 @ rearsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[37327:[bind(A,$thf( sk1 @ sk18 ))]]) ).
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(498,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(31263,plain,
! [A: $i] :
( ( ( sk2 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7034,221]) ).
thf(31264,plain,
! [A: $i] :
( ( ( sk2 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[31263]) ).
thf(31265,plain,
( ~ ( sk2 @ sk6 @ ( sk2 @ sk6 @ lt ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[31264:[bind(A,$thf( sk2 @ sk6 ))]]) ).
thf(11513,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[11265,248]) ).
thf(11514,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[11513]) ).
thf(11515,plain,
( ( nil @ ( sk1 @ sk13 @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[11514:[bind(A,$thf( sk1 @ sk13 ))]]) ).
thf(158,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk6 @ ( A @ sk5 @ leq ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[157]) ).
thf(5188,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk6 @ ( A @ sk5 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,158]) ).
thf(5189,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk6 @ ( A @ sk5 @ leq ) ) ),
inference(simp,[status(thm)],[5188]) ).
thf(5190,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk6 @ ( sk1 @ sk5 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[5189:[bind(A,$thf( sk1 ))]]) ).
thf(5205,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk6 @ ( A @ sk5 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,158]) ).
thf(5206,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk6 @ ( A @ sk5 @ leq ) ) ),
inference(simp,[status(thm)],[5205]) ).
thf(5207,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk6 @ ( sk2 @ sk5 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[5206:[bind(A,$thf( sk2 ))]]) ).
thf(5733,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5455,378]) ).
thf(5734,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5733]) ).
thf(5735,plain,
( ( nil @ ( sk2 @ sk9 @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5734:[bind(A,$thf( sk2 @ sk9 ))]]) ).
thf(4641,plain,
( ( ( sk38 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk37 != nil )
| ~ ( sk38 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,1054]) ).
thf(4642,plain,
( ( ( sk38 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk37 != nil )
| ~ ( sk38 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[4641]) ).
thf(4716,plain,
( ( sk38 != sk1 )
| ( sk37 != nil )
| ~ ( sk38 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[4642]) ).
thf(10086,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7497,410]) ).
thf(10087,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[10086]) ).
thf(10088,plain,
( ( nil @ ( sk2 @ sk5 @ cons ) @ duplicatefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[10087:[bind(A,$thf( sk2 @ sk5 ))]]) ).
thf(10896,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10743,303]) ).
thf(10897,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[10896]) ).
thf(10898,plain,
( ( nil @ ( sk1 @ sk10 @ cons ) @ equalelemsP )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10897:[bind(A,$thf( sk1 @ sk10 ))]]) ).
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(451,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(73,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax63) ).
thf(434,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(42460,plain,
( ( ( sk37 @ ssItem )
!= ( sk2 @ ssItem ) )
| ( sk2 != sk1 )
| ~ ( nil @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[395,42149]) ).
thf(42461,plain,
( ( ( sk37 @ ssItem )
!= ( sk2 @ ssItem ) )
| ( sk2 != sk1 )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[42460]) ).
thf(42514,plain,
( ( sk37 != sk2 )
| ( sk2 != sk1 )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[42461]) ).
thf(207,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ gt ) )
| ~ ( A @ ( B @ lt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) )
& ( ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ) ),
inference(cnf,[status(esa)],[206]) ).
thf(208,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[207]) ).
thf(34956,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[34570,221]) ).
thf(34957,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[34956]) ).
thf(34958,plain,
( ~ ( sk2 @ sk16 @ ( sk2 @ sk16 @ lt ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[34957:[bind(A,$thf( sk2 @ sk16 ))]]) ).
thf(4105,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,378]) ).
thf(4106,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) ) ),
inference(simp,[status(thm)],[4105]) ).
thf(4107,plain,
nil @ ( sk2 @ frontsegP ),
inference(pattern_uni,[status(thm)],[4106:[bind(A,$thf( sk2 ))]]) ).
thf(52925,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[52804,188]) ).
thf(52926,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[52925]) ).
thf(52927,plain,
( ( nil @ ( sk2 @ sk21 @ app ) )
= ( sk2 @ sk21 ) ),
inference(pattern_uni,[status(thm)],[52926:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(60519,plain,
( ( nil @ ( sk2 @ tl @ app ) )
= ( sk2 @ tl ) ),
inference(rewrite,[status(thm)],[52927,60517]) ).
thf(12352,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[12149,301]) ).
thf(12353,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[12352]) ).
thf(12354,plain,
( ( nil @ ( sk1 @ sk12 @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[12353:[bind(A,$thf( sk1 @ sk12 ))]]) ).
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(477,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(25109,plain,
! [A: $i] :
( ( ( sk2 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7034,215]) ).
thf(25110,plain,
! [A: $i] :
( ( ( sk2 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[25109]) ).
thf(25111,plain,
( ~ ( sk2 @ sk6 @ ( sk2 @ sk6 @ neq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[25110:[bind(A,$thf( sk2 @ sk6 ))]]) ).
thf(77192,plain,
! [A: $i] :
( ( ( sk2 @ sk27 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76903,195]) ).
thf(77193,plain,
! [A: $i] :
( ( ( sk2 @ sk27 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[77192]) ).
thf(77194,plain,
sk2 @ sk27 @ ( sk2 @ sk27 @ segmentP ),
inference(pattern_uni,[status(thm)],[77193:[bind(A,$thf( sk2 @ sk27 ))]]) ).
thf(81899,plain,
( ( ( sk2 @ sk27 @ ( sk2 @ sk27 @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[77194,2618]) ).
thf(81900,plain,
( ( sk2 @ sk27 @ ( sk2 @ sk27 @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[81899]) ).
thf(81983,plain,
( ( ( sk2 @ sk27 )
!= sk2 )
| ( ( sk2 @ sk27 )
!= nil ) ),
inference(simp,[status(thm)],[81900]) ).
thf(11744,plain,
! [A: $i] :
( ( ( sk2 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[11315,378]) ).
thf(11745,plain,
! [A: $i] :
( ( ( sk2 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[11744]) ).
thf(11746,plain,
( ( nil @ ( sk2 @ sk13 @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[11745:[bind(A,$thf( sk2 @ sk13 ))]]) ).
thf(7573,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7470,121]) ).
thf(7574,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7573]) ).
thf(7575,plain,
( ( nil @ ( sk1 @ sk5 @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7574:[bind(A,$thf( sk1 @ sk5 ))]]) ).
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(198,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(25082,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[396,215]) ).
thf(25083,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[25082]) ).
thf(25084,plain,
~ ( sk38 @ ( sk38 @ neq ) ),
inference(pattern_uni,[status(thm)],[25083:[bind(A,$thf( sk38 ))]]) ).
thf(85436,plain,
! [A: $i] :
( ( ( sk1 @ sk28 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[83491,236]) ).
thf(85437,plain,
! [A: $i] :
( ( ( sk1 @ sk28 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[85436]) ).
thf(85438,plain,
( ~ ( sk1 @ sk28 @ ( nil @ memberP ) )
| ( sk2 != sk1 ) ),
inference(pattern_uni,[status(thm)],[85437:[bind(A,$thf( sk1 @ sk28 ))]]) ).
thf(63785,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk24 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,264]) ).
thf(63786,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk24 @ ssList ) ),
inference(simp,[status(thm)],[63785]) ).
thf(63787,plain,
( ( sk1 @ totalorderP )
| ( sk1 @ sk24 @ ssList ) ),
inference(pattern_uni,[status(thm)],[63786:[bind(A,$thf( sk1 ))]]) ).
thf(31248,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7497,221]) ).
thf(31249,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[31248]) ).
thf(31250,plain,
( ~ ( sk2 @ sk5 @ ( sk2 @ sk5 @ lt ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[31249:[bind(A,$thf( sk2 @ sk5 ))]]) ).
thf(77036,plain,
! [A: $i] :
( ( ( sk2 @ sk27 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[76903,188]) ).
thf(77037,plain,
! [A: $i] :
( ( ( sk2 @ sk27 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[77036]) ).
thf(77038,plain,
( ( nil @ ( sk2 @ sk27 @ app ) )
= ( sk2 @ sk27 ) ),
inference(pattern_uni,[status(thm)],[77037:[bind(A,$thf( sk2 @ sk27 ))]]) ).
thf(18629,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[706,195]) ).
thf(18630,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18629]) ).
thf(18631,plain,
( ( sk1 @ sk7 @ ( sk1 @ sk7 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18630:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(154,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)],[153]) ).
thf(155,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)],[154]) ).
thf(130,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[129]) ).
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(399,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(18600,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[11265,195]) ).
thf(18601,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[18600]) ).
thf(18602,plain,
( ( sk1 @ sk13 @ ( sk1 @ sk13 @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[18601:[bind(A,$thf( sk1 @ sk13 ))]]) ).
thf(9897,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ~ ( A @ sk11 @ ( A @ sk10 @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,174]) ).
thf(9898,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ~ ( A @ sk11 @ ( A @ sk10 @ lt ) ) ),
inference(simp,[status(thm)],[9897]) ).
thf(9899,plain,
( ( sk1 @ strictorderP )
| ~ ( sk1 @ sk11 @ ( sk1 @ sk10 @ lt ) ) ),
inference(pattern_uni,[status(thm)],[9898:[bind(A,$thf( sk1 ))]]) ).
thf(10074,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[396,410]) ).
thf(10075,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP ) ),
inference(simp,[status(thm)],[10074]) ).
thf(10076,plain,
nil @ ( sk38 @ cons ) @ duplicatefreeP,
inference(pattern_uni,[status(thm)],[10075:[bind(A,$thf( sk38 ))]]) ).
thf(10982,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10770,371]) ).
thf(10983,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[10982]) ).
thf(10984,plain,
( ( nil @ ( sk2 @ sk10 @ cons ) @ totalorderP )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10983:[bind(A,$thf( sk2 @ sk10 ))]]) ).
thf(6502,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[6286,378]) ).
thf(6503,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[6502]) ).
thf(6504,plain,
( ( nil @ ( sk1 @ sk8 @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[6503:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(59900,plain,
! [A: $i] :
( ( ( sk1 @ sk25 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[59376,248]) ).
thf(59901,plain,
! [A: $i] :
( ( ( sk1 @ sk25 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ totalorderP ) ),
inference(simp,[status(thm)],[59900]) ).
thf(59902,plain,
( ( nil @ ( sk1 @ sk25 @ segmentP ) )
| ( sk1 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[59901:[bind(A,$thf( sk1 @ sk25 ))]]) ).
thf(32087,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[31800,301]) ).
thf(32088,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[32087]) ).
thf(32089,plain,
( ( nil @ ( sk1 @ sk19 @ rearsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[32088:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(10928,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10743,410]) ).
thf(10929,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[10928]) ).
thf(10930,plain,
( ( nil @ ( sk1 @ sk10 @ cons ) @ duplicatefreeP )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10929:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(5665,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5455,301]) ).
thf(5666,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5665]) ).
thf(5667,plain,
( ( nil @ ( sk2 @ sk9 @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5666:[bind(A,$thf( sk2 @ sk9 ))]]) ).
thf(259,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( 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 @ totalorderP )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[256]) ).
thf(266,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ leq ) )
| ( C @ ( B @ leq ) )
| ~ ( F @ ssList )
| ~ ( E @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssItem )
| ~ ( B @ ssItem )
| ~ ( A @ totalorderP )
| ~ ( A @ ssList )
| ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
!= A ) ),
inference(lifteq,[status(thm)],[259]) ).
thf(267,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) )
| ~ ( E @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) @ totalorderP )
| ~ ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) @ ssList ) ),
inference(simp,[status(thm)],[266]) ).
thf(42386,plain,
( ( ( sk38 @ ssItem )
!= ( sk2 @ ssItem ) )
| ( sk2 != sk1 )
| ~ ( nil @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[396,42149]) ).
thf(42387,plain,
( ( ( sk38 @ ssItem )
!= ( sk2 @ ssItem ) )
| ( sk2 != sk1 )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[42386]) ).
thf(42493,plain,
( ( sk38 != sk2 )
| ( sk2 != sk1 )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[42387]) ).
thf(44133,plain,
( ( ( sk37 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk38 != sk2 )
| ( sk2 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[395,42493]) ).
thf(44134,plain,
( ( ( sk37 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk38 != sk2 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[44133]) ).
thf(44152,plain,
( ( sk37 != nil )
| ( sk38 != sk2 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[44134]) ).
thf(1803,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[712,248]) ).
thf(1804,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1803]) ).
thf(1805,plain,
( ( nil @ ( sk2 @ sk7 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1804:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(34768,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[34522,121]) ).
thf(34769,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[34768]) ).
thf(34770,plain,
( ( nil @ ( sk1 @ sk16 @ cons ) @ strictorderedP )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[34769:[bind(A,$thf( sk1 @ sk16 ))]]) ).
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(521,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(162,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk5 @ ( A @ sk6 @ leq ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[157]) ).
thf(10089,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7470,410]) ).
thf(10090,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[10089]) ).
thf(10091,plain,
( ( nil @ ( sk1 @ sk5 @ cons ) @ duplicatefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[10090:[bind(A,$thf( sk1 @ sk5 ))]]) ).
thf(209,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ gt ) )
| ~ ( A @ ( B @ lt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[207]) ).
thf(83929,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83839,236]) ).
thf(83930,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[83929]) ).
thf(83931,plain,
~ ( sk2 @ sk28 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[83930:[bind(A,$thf( sk2 @ sk28 ))]]) ).
thf(33527,plain,
! [A: $i] :
( ( ( sk1 @ sk17 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[33031,195]) ).
thf(33528,plain,
! [A: $i] :
( ( ( sk1 @ sk17 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[33527]) ).
thf(33529,plain,
( ( sk1 @ sk17 @ ( sk1 @ sk17 @ segmentP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[33528:[bind(A,$thf( sk1 @ sk17 ))]]) ).
thf(32279,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[31800,195]) ).
thf(32280,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[32279]) ).
thf(32281,plain,
( ( sk1 @ sk19 @ ( sk1 @ sk19 @ segmentP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[32280:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(72838,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk27 @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[106,274]) ).
thf(72839,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk27 @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[72838]) ).
thf(72840,plain,
( ( sk1 @ sk27 @ ssList )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[72839:[bind(A,$thf( sk1 ))]]) ).
thf(76504,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ( sk2 != sk1 )
| ( sk1 @ sk27 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[72840,1574]) ).
thf(76505,plain,
( ( sk1 != sk1 )
| ( sk2 != sk1 )
| ( sk1 @ sk27 @ ssList ) ),
inference(simp,[status(thm)],[76504]) ).
thf(76506,plain,
( ( sk2 != sk1 )
| ( sk1 @ sk27 @ ssList ) ),
inference(pattern_uni,[status(thm)],[76505:[]]) ).
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(458,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(53051,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[52804,195]) ).
thf(53052,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[53051]) ).
thf(53053,plain,
sk2 @ sk21 @ ( sk2 @ sk21 @ segmentP ),
inference(pattern_uni,[status(thm)],[53052:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(53689,plain,
( ( ( sk2 @ sk21 @ ( sk2 @ sk21 @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[53053,2618]) ).
thf(53690,plain,
( ( sk2 @ sk21 @ ( sk2 @ sk21 @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[53689]) ).
thf(53766,plain,
( ( ( sk2 @ sk21 )
!= sk2 )
| ( ( sk2 @ sk21 )
!= nil ) ),
inference(simp,[status(thm)],[53690]) ).
thf(60524,plain,
( ( ( sk2 @ tl )
!= sk2 )
| ( ( sk2 @ tl )
!= nil ) ),
inference(rewrite,[status(thm)],[53766,60517]) ).
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(525,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(2713,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ( sk2 != sk1 )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2278,1574]) ).
thf(2714,plain,
( ( sk1 != sk1 )
| ( sk2 != sk1 )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[2713]) ).
thf(2715,plain,
( ( sk2 != sk1 )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[2714:[]]) ).
thf(37405,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[37003,248]) ).
thf(37406,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[37405]) ).
thf(37407,plain,
( ( nil @ ( sk1 @ sk18 @ segmentP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[37406:[bind(A,$thf( sk1 @ sk18 ))]]) ).
thf(7209,plain,
! [A: $i] :
( ( ( sk2 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7034,197]) ).
thf(7210,plain,
! [A: $i] :
( ( ( sk2 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7209]) ).
thf(7211,plain,
( ( nil @ ( sk2 @ sk6 @ cons ) @ totalorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7210:[bind(A,$thf( sk2 @ sk6 ))]]) ).
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(414,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(83944,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83839,303]) ).
thf(83945,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP ) ),
inference(simp,[status(thm)],[83944]) ).
thf(83946,plain,
nil @ ( sk2 @ sk28 @ cons ) @ equalelemsP,
inference(pattern_uni,[status(thm)],[83945:[bind(A,$thf( sk2 @ sk28 ))]]) ).
thf(17803,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ~ ( nil @ ( sk1 @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2278,17731]) ).
thf(17804,plain,
( ( sk1 != sk1 )
| ~ ( nil @ ( sk1 @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[17803]) ).
thf(17805,plain,
( ~ ( nil @ ( sk1 @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[17804:[]]) ).
thf(54318,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[52466,301]) ).
thf(54319,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[54318]) ).
thf(54320,plain,
( ( nil @ ( sk1 @ sk21 @ rearsegP ) )
| ( sk2 != sk1 ) ),
inference(pattern_uni,[status(thm)],[54319:[bind(A,$thf( sk1 @ sk21 ))]]) ).
thf(31230,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10157,221]) ).
thf(31231,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[31230]) ).
thf(31232,plain,
( ~ ( sk1 @ sk11 @ ( sk1 @ sk11 @ lt ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[31231:[bind(A,$thf( sk1 @ sk11 ))]]) ).
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(310,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ( A @ hd )
= B )
& ( B @ ssItem ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(13448,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[13106,378]) ).
thf(13449,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[13448]) ).
thf(13450,plain,
( ( nil @ ( sk1 @ sk14 @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[13449:[bind(A,$thf( sk1 @ sk14 ))]]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ cons ) )
= ( A @ ( nil @ ( B @ cons ) @ app ) ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[148]) ).
thf(150,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( ( A @ ( B @ cons ) )
= ( A @ ( nil @ ( B @ cons ) @ app ) ) ) ),
inference(lifteq,[status(thm)],[149]) ).
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(327,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(7194,plain,
! [A: $i] :
( ( ( sk2 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7034,121]) ).
thf(7195,plain,
! [A: $i] :
( ( ( sk2 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7194]) ).
thf(7196,plain,
( ( nil @ ( sk2 @ sk6 @ cons ) @ strictorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7195:[bind(A,$thf( sk2 @ sk6 ))]]) ).
thf(52107,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[49346,301]) ).
thf(52108,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[52107]) ).
thf(52109,plain,
( ( nil @ ( sk1 @ sk21 @ rearsegP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[52108:[bind(A,$thf( sk1 @ sk21 ))]]) ).
thf(58066,plain,
( ( ( sk1 @ sk21 )
!= ( sk1 @ sk21 ) )
| ( nil @ ( sk1 @ tl @ rearsegP ) )
| ( sk1 = nil )
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[53498,52109]) ).
thf(58067,plain,
( ( ( sk1 @ sk21 )
!= ( sk1 @ sk21 ) )
| ( nil @ ( sk1 @ tl @ rearsegP ) )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[58066]) ).
thf(58068,plain,
( ( nil @ ( sk1 @ tl @ rearsegP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[58067:[]]) ).
thf(18603,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[13106,195]) ).
thf(18604,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[18603]) ).
thf(18605,plain,
( ( sk1 @ sk14 @ ( sk1 @ sk14 @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[18604:[bind(A,$thf( sk1 @ sk14 ))]]) ).
thf(60057,plain,
! [A: $i] :
( ( ( sk1 @ sk25 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[59376,378]) ).
thf(60058,plain,
! [A: $i] :
( ( ( sk1 @ sk25 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ totalorderP ) ),
inference(simp,[status(thm)],[60057]) ).
thf(60059,plain,
( ( nil @ ( sk1 @ sk25 @ frontsegP ) )
| ( sk1 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[60058:[bind(A,$thf( sk1 @ sk25 ))]]) ).
thf(18667,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[6286,195]) ).
thf(18668,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18667]) ).
thf(18669,plain,
( ( sk1 @ sk8 @ ( sk1 @ sk8 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18668:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(10493,plain,
( ( ( sk37 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk38 != nil )
| ~ ( sk37 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,5141]) ).
thf(10494,plain,
( ( ( sk37 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk38 != nil )
| ~ ( sk37 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[10493]) ).
thf(10585,plain,
( ( sk37 != sk1 )
| ( sk38 != nil )
| ~ ( sk37 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[10494]) ).
thf(10093,plain,
! [A: $i] :
( ( ( sk2 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7034,410]) ).
thf(10094,plain,
! [A: $i] :
( ( ( sk2 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[10093]) ).
thf(10095,plain,
( ( nil @ ( sk2 @ sk6 @ cons ) @ duplicatefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[10094:[bind(A,$thf( sk2 @ sk6 ))]]) ).
thf(33411,plain,
! [A: $i] :
( ( ( sk1 @ sk17 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[33031,248]) ).
thf(33412,plain,
! [A: $i] :
( ( ( sk1 @ sk17 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[33411]) ).
thf(33413,plain,
( ( nil @ ( sk1 @ sk17 @ segmentP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[33412:[bind(A,$thf( sk1 @ sk17 ))]]) ).
thf(18664,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[712,195]) ).
thf(18665,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18664]) ).
thf(18666,plain,
( ( sk2 @ sk7 @ ( sk2 @ sk7 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18665:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(32166,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[31800,248]) ).
thf(32167,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[32166]) ).
thf(32168,plain,
( ( nil @ ( sk1 @ sk19 @ segmentP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[32167:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(12645,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[12205,378]) ).
thf(12646,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[12645]) ).
thf(12647,plain,
( ( nil @ ( sk2 @ sk12 @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[12646:[bind(A,$thf( sk2 @ sk12 ))]]) ).
thf(59803,plain,
! [A: $i] :
( ( ( sk1 @ sk25 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[59376,301]) ).
thf(59804,plain,
! [A: $i] :
( ( ( sk1 @ sk25 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ totalorderP ) ),
inference(simp,[status(thm)],[59803]) ).
thf(59805,plain,
( ( nil @ ( sk1 @ sk25 @ rearsegP ) )
| ( sk1 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[59804:[bind(A,$thf( sk1 @ sk25 ))]]) ).
thf(10434,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10184,303]) ).
thf(10435,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[10434]) ).
thf(10436,plain,
( ( nil @ ( sk2 @ sk11 @ cons ) @ equalelemsP )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10435:[bind(A,$thf( sk2 @ sk11 ))]]) ).
thf(6465,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[6286,248]) ).
thf(6466,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[6465]) ).
thf(6467,plain,
( ( nil @ ( sk1 @ sk8 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[6466:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(56474,plain,
! [A: $i] :
( ( ( sk2 @ sk22 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[55969,236]) ).
thf(56475,plain,
! [A: $i] :
( ( ( sk2 @ sk22 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ totalorderP ) ),
inference(simp,[status(thm)],[56474]) ).
thf(56476,plain,
( ~ ( sk2 @ sk22 @ ( nil @ memberP ) )
| ( sk2 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[56475:[bind(A,$thf( sk2 @ sk22 ))]]) ).
thf(32432,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[31877,248]) ).
thf(32433,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[32432]) ).
thf(32434,plain,
( ( nil @ ( sk2 @ sk19 @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[32433:[bind(A,$thf( sk2 @ sk19 ))]]) ).
thf(31221,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10743,221]) ).
thf(31222,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[31221]) ).
thf(31223,plain,
( ~ ( sk1 @ sk10 @ ( sk1 @ sk10 @ lt ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[31222:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(27,axiom,
nil @ duplicatefreeP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax72) ).
thf(203,plain,
nil @ duplicatefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(52381,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ~ ( nil @ ( sk1 @ neq ) )
| ( sk1 @ sk21 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[49346,17731]) ).
thf(52382,plain,
( ( sk1 != sk1 )
| ~ ( nil @ ( sk1 @ neq ) )
| ( sk1 @ sk21 @ ssList ) ),
inference(simp,[status(thm)],[52381]) ).
thf(52383,plain,
( ~ ( nil @ ( sk1 @ neq ) )
| ( sk1 @ sk21 @ ssList ) ),
inference(pattern_uni,[status(thm)],[52382:[]]) ).
thf(25112,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[395,215]) ).
thf(25113,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[25112]) ).
thf(25114,plain,
~ ( sk37 @ ( sk37 @ neq ) ),
inference(pattern_uni,[status(thm)],[25113:[bind(A,$thf( sk37 ))]]) ).
thf(95,axiom,
nil @ totalorderP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax62) ).
thf(524,plain,
nil @ totalorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
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(495,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(757,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[395,121]) ).
thf(758,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[757]) ).
thf(759,plain,
nil @ ( sk37 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[758:[bind(A,$thf( sk37 ))]]) ).
thf(10374,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10157,410]) ).
thf(10375,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[10374]) ).
thf(10376,plain,
( ( nil @ ( sk1 @ sk11 @ cons ) @ duplicatefreeP )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10375:[bind(A,$thf( sk1 @ sk11 ))]]) ).
thf(31236,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[396,221]) ).
thf(31237,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[31236]) ).
thf(31238,plain,
~ ( sk38 @ ( sk38 @ lt ) ),
inference(pattern_uni,[status(thm)],[31237:[bind(A,$thf( sk38 ))]]) ).
thf(231,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ sk16 @ ( A @ sk15 @ lt ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[223]) ).
thf(56846,plain,
( ( ( sk37 @ ssItem )
!= ( nil @ ssItem ) )
| ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ $true
| ~ ( sk2 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[395,42056]) ).
thf(56847,plain,
( ( ( sk37 @ ssItem )
!= ( nil @ ssItem ) )
| ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ ( sk2 @ ssItem ) ),
inference(simp,[status(thm)],[56846]) ).
thf(56977,plain,
( ( sk37 != nil )
| ~ ( sk2 @ ( sk1 @ segmentP ) )
| ~ ( sk2 @ ssItem ) ),
inference(simp,[status(thm)],[56847]) ).
thf(76918,plain,
! [A: $i] :
( ( ( sk2 @ sk27 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76903,301]) ).
thf(76919,plain,
! [A: $i] :
( ( ( sk2 @ sk27 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[76918]) ).
thf(76920,plain,
nil @ ( sk2 @ sk27 @ rearsegP ),
inference(pattern_uni,[status(thm)],[76919:[bind(A,$thf( sk2 @ sk27 ))]]) ).
thf(7651,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7497,121]) ).
thf(7652,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7651]) ).
thf(7653,plain,
( ( nil @ ( sk2 @ sk5 @ cons ) @ strictorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7652:[bind(A,$thf( sk2 @ sk5 ))]]) ).
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(304,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(258,plain,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ sk22 @ ( A @ sk23 @ leq ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[256]) ).
thf(6001,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk5 @ ( A @ sk6 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,162]) ).
thf(6002,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk5 @ ( A @ sk6 @ leq ) ) ),
inference(simp,[status(thm)],[6001]) ).
thf(6003,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk5 @ ( sk2 @ sk6 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[6002:[bind(A,$thf( sk2 ))]]) ).
thf(60179,plain,
! [A: $i] :
( ( ( sk2 @ sk25 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[59478,301]) ).
thf(60180,plain,
! [A: $i] :
( ( ( sk2 @ sk25 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ totalorderP ) ),
inference(simp,[status(thm)],[60179]) ).
thf(60181,plain,
( ( nil @ ( sk2 @ sk25 @ rearsegP ) )
| ( sk2 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[60180:[bind(A,$thf( sk2 @ sk25 ))]]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[170]) ).
thf(10102,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[395,410]) ).
thf(10103,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP ) ),
inference(simp,[status(thm)],[10102]) ).
thf(10104,plain,
nil @ ( sk37 @ cons ) @ duplicatefreeP,
inference(pattern_uni,[status(thm)],[10103:[bind(A,$thf( sk37 ))]]) ).
thf(31242,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10184,221]) ).
thf(31243,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[31242]) ).
thf(31244,plain,
( ~ ( sk2 @ sk11 @ ( sk2 @ sk11 @ lt ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[31243:[bind(A,$thf( sk2 @ sk11 ))]]) ).
thf(34798,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[34522,236]) ).
thf(34799,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[34798]) ).
thf(34800,plain,
( ~ ( sk1 @ sk16 @ ( nil @ memberP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[34799:[bind(A,$thf( sk1 @ sk16 ))]]) ).
thf(58470,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ~ ( nil @ ( sk1 @ neq ) )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[58046,17731]) ).
thf(58471,plain,
( ( sk1 != sk1 )
| ~ ( nil @ ( sk1 @ neq ) )
| ( sk1 @ tl @ ssList ) ),
inference(simp,[status(thm)],[58470]) ).
thf(58472,plain,
( ~ ( nil @ ( sk1 @ neq ) )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[58471:[]]) ).
thf(16320,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5455,188]) ).
thf(16321,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[16320]) ).
thf(16322,plain,
( ( ( nil @ ( sk2 @ sk9 @ app ) )
= ( sk2 @ sk9 ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[16321:[bind(A,$thf( sk2 @ sk9 ))]]) ).
thf(7678,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7497,236]) ).
thf(7679,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7678]) ).
thf(7680,plain,
( ~ ( sk2 @ sk5 @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7679:[bind(A,$thf( sk2 @ sk5 ))]]) ).
thf(92,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( nil
!= ( A @ ( B @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
thf(510,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( nil
!= ( A @ ( B @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(34783,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[34522,221]) ).
thf(34784,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[34783]) ).
thf(34785,plain,
( ~ ( sk1 @ sk16 @ ( sk1 @ sk16 @ lt ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[34784:[bind(A,$thf( sk1 @ sk16 ))]]) ).
thf(25097,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10770,215]) ).
thf(25098,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[25097]) ).
thf(25099,plain,
( ~ ( sk2 @ sk10 @ ( sk2 @ sk10 @ neq ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25098:[bind(A,$thf( sk2 @ sk10 ))]]) ).
thf(761,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[396,236]) ).
thf(762,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[761]) ).
thf(763,plain,
~ ( sk38 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[762:[bind(A,$thf( sk38 ))]]) ).
thf(10958,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10770,121]) ).
thf(10959,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[10958]) ).
thf(10960,plain,
( ( nil @ ( sk2 @ sk10 @ cons ) @ strictorderedP )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10959:[bind(A,$thf( sk2 @ sk10 ))]]) ).
thf(5588,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5424,248]) ).
thf(5589,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5588]) ).
thf(5590,plain,
( ( nil @ ( sk1 @ sk9 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5589:[bind(A,$thf( sk1 @ sk9 ))]]) ).
thf(52975,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[52804,219]) ).
thf(52976,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[52975]) ).
thf(52977,plain,
( ( sk2 @ sk21 @ ( nil @ app ) )
= ( sk2 @ sk21 ) ),
inference(pattern_uni,[status(thm)],[52976:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(60520,plain,
( ( sk2 @ tl @ ( nil @ app ) )
= ( sk2 @ tl ) ),
inference(rewrite,[status(thm)],[52977,60517]) ).
thf(119,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)],[118]) ).
thf(18632,plain,
! [A: $i] :
( ( ( sk2 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[11315,195]) ).
thf(18633,plain,
! [A: $i] :
( ( ( sk2 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[18632]) ).
thf(18634,plain,
( ( sk2 @ sk13 @ ( sk2 @ sk13 @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[18633:[bind(A,$thf( sk2 @ sk13 ))]]) ).
thf(243,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ frontsegP ) )
| ( ( C @ ( B @ app ) )
!= A )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[240]) ).
thf(245,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ frontsegP ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( C @ ( B @ app ) )
!= A ) ),
inference(lifteq,[status(thm)],[243]) ).
thf(246,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ app ) @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ( A @ app ) @ ssList ) ),
inference(simp,[status(thm)],[245]) ).
thf(30320,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[106,219]) ).
thf(30321,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[30320]) ).
thf(30322,plain,
( ( sk1 @ ( nil @ app ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[30321:[bind(A,$thf( sk1 ))]]) ).
thf(281,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( B @ hd @ ( A @ lt ) )
| ~ ( B @ strictorderedP )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) )
& ( ( B @ ( A @ cons ) @ strictorderedP )
| ( nil != B )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) )
& ( ( B @ hd @ ( A @ lt ) )
| ( nil = B )
| ~ ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) )
& ( ( B @ strictorderedP )
| ( nil = B )
| ~ ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) )
& ( ( nil != B )
| ( nil = B )
| ~ ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ) ),
inference(cnf,[status(esa)],[280]) ).
thf(284,plain,
! [B: $i,A: $i] :
( ( B @ strictorderedP )
| ( nil = B )
| ~ ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[281]) ).
thf(287,plain,
! [B: $i,A: $i] :
( ( B @ strictorderedP )
| ~ ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( nil = B ) ),
inference(lifteq,[status(thm)],[284]) ).
thf(34845,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[34522,410]) ).
thf(34846,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[34845]) ).
thf(34847,plain,
( ( nil @ ( sk1 @ sk16 @ cons ) @ duplicatefreeP )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[34846:[bind(A,$thf( sk1 @ sk16 ))]]) ).
thf(1772,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ sk7 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[732,248]) ).
thf(1773,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ sk7 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1772]) ).
thf(1774,plain,
( ( nil @ ( sk1 @ sk7 @ sk7 @ segmentP ) )
| ( sk1 @ sk7 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1773:[bind(A,$thf( sk1 @ sk7 @ sk7 ))]]) ).
thf(60523,plain,
sk2 @ tl @ ( sk2 @ tl @ segmentP ),
inference(rewrite,[status(thm)],[53053,60517]) ).
thf(190,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ segmentP ) )
| ~ ( C @ ( B @ segmentP ) )
| ~ ( B @ ( A @ segmentP ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[189]) ).
thf(13622,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[13165,378]) ).
thf(13623,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[13622]) ).
thf(13624,plain,
( ( nil @ ( sk2 @ sk14 @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[13623:[bind(A,$thf( sk2 @ sk14 ))]]) ).
thf(10890,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10743,371]) ).
thf(10891,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[10890]) ).
thf(10892,plain,
( ( nil @ ( sk1 @ sk10 @ cons ) @ totalorderP )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10891:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(10866,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10743,121]) ).
thf(10867,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[10866]) ).
thf(10868,plain,
( ( nil @ ( sk1 @ sk10 @ cons ) @ strictorderedP )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10867:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(23235,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ( sk37 != sk1 )
| ( sk38 != nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2278,18827]) ).
thf(23236,plain,
( ( sk1 != sk1 )
| ( sk37 != sk1 )
| ( sk38 != nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[23235]) ).
thf(23237,plain,
( ( sk37 != sk1 )
| ( sk38 != nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[23236:[]]) ).
thf(5039,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[396,371]) ).
thf(5040,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP ) ),
inference(simp,[status(thm)],[5039]) ).
thf(5041,plain,
nil @ ( sk38 @ cons ) @ totalorderP,
inference(pattern_uni,[status(thm)],[5040:[bind(A,$thf( sk38 ))]]) ).
thf(5049,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[395,371]) ).
thf(5050,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP ) ),
inference(simp,[status(thm)],[5049]) ).
thf(5051,plain,
nil @ ( sk37 @ cons ) @ totalorderP,
inference(pattern_uni,[status(thm)],[5050:[bind(A,$thf( sk37 ))]]) ).
thf(72,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax31) ).
thf(432,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(40503,plain,
( ( ( sk37 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( nil @ memberP ) )
| ~ $true
| ~ ( sk37 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[644,1002]) ).
thf(40504,plain,
( ( ( sk37 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( nil @ memberP ) )
| ~ ( sk37 @ ssList ) ),
inference(simp,[status(thm)],[40503]) ).
thf(40584,plain,
( ( sk37 != nil )
| ( nil != nil )
| ~ ( nil @ ( nil @ memberP ) )
| ~ ( sk37 @ ssList ) ),
inference(simp,[status(thm)],[40504]) ).
thf(40599,plain,
( ( sk37 != nil )
| ~ ( nil @ ( nil @ memberP ) )
| ~ ( sk37 @ ssList ) ),
inference(simp,[status(thm)],[40584]) ).
thf(41670,plain,
( ( ( sk37 @ ssList )
!= ( nil @ ssList ) )
| ( sk37 != nil )
| ~ ( nil @ ( nil @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[348,40599]) ).
thf(41671,plain,
( ( ( sk37 @ ssList )
!= ( nil @ ssList ) )
| ( sk37 != nil )
| ~ ( nil @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[41670]) ).
thf(41820,plain,
( ( sk37 != nil )
| ( sk37 != nil )
| ~ ( nil @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[41671]) ).
thf(41840,plain,
( ( sk37 != nil )
| ~ ( nil @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[41820]) ).
thf(160,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( 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(cnfConj,[status(thm)],[157]) ).
thf(167,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( B @ leq ) )
| ~ ( F @ ssList )
| ~ ( E @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssItem )
| ~ ( B @ ssItem )
| ~ ( A @ cyclefreeP )
| ~ ( A @ ssList )
| ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
!= A ) ),
inference(lifteq,[status(thm)],[160]) ).
thf(168,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ~ ( E @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) @ cyclefreeP )
| ~ ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) @ ssList ) ),
inference(simp,[status(thm)],[167]) ).
thf(44934,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk20 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44834,248]) ).
thf(44935,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk20 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[44934]) ).
thf(44936,plain,
nil @ ( nil @ ( nil @ sk20 ) @ segmentP ),
inference(pattern_uni,[status(thm)],[44935:[bind(A,$thf( nil @ ( nil @ sk20 ) ))]]) ).
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(422,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(17808,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ~ ( nil @ ( sk1 @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[983,17731]) ).
thf(17809,plain,
( ( sk1 != sk1 )
| ~ ( nil @ ( sk1 @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[17808]) ).
thf(17810,plain,
( ~ ( nil @ ( sk1 @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[17809:[]]) ).
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(474,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) @ tl )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(12474,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[12149,378]) ).
thf(12475,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[12474]) ).
thf(12476,plain,
( ( nil @ ( sk1 @ sk12 @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[12475:[bind(A,$thf( sk1 @ sk12 ))]]) ).
thf(16297,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[106,188]) ).
thf(16298,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[16297]) ).
thf(16299,plain,
( ( nil @ ( sk1 @ app ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[16298:[bind(A,$thf( sk1 ))]]) ).
thf(551,plain,
( ~ $true
| ( ( sk1 @ ( sk2 @ segmentP ) )
!= ( sk1 @ ( sk1 @ segmentP ) ) )
| ~ ( sk1 @ ( sk1 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(eqfactor_ordered,[status(thm)],[543]) ).
thf(553,plain,
( ( sk1 != sk1 )
| ( sk2 != sk1 )
| ~ ( sk1 @ ( sk1 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[551]) ).
thf(554,plain,
( ( sk2 != sk1 )
| ~ ( sk1 @ ( sk1 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[553]) ).
thf(18739,plain,
( ( sk2 != sk1 )
| ~ $true
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(rewrite,[status(thm)],[554,18594]) ).
thf(18740,plain,
( ( sk2 != sk1 )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[18739]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ hd @ ssItem ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
thf(294,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ hd @ ssItem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(135,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ cons ) @ hd )
= B )
| ~ ( B @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[134]) ).
thf(136,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( ( A @ ( B @ cons ) @ hd )
= B ) ),
inference(lifteq,[status(thm)],[135]) ).
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(506,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(263,plain,
! [A: $i] :
( ( A @ totalorderP )
| ( ( A @ sk26 @ ( A @ sk23 @ cons ) @ ( A @ sk25 @ ( A @ sk22 @ cons ) @ ( A @ sk24 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[256]) ).
thf(268,plain,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ( ( A @ sk26 @ ( A @ sk23 @ cons ) @ ( A @ sk25 @ ( A @ sk22 @ cons ) @ ( A @ sk24 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[263]) ).
thf(9768,plain,
( ( ( sk37 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk38 != nil )
| ~ ( sk37 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,5127]) ).
thf(9769,plain,
( ( ( sk37 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk38 != nil )
| ~ ( sk37 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[9768]) ).
thf(9816,plain,
( ( sk37 != sk2 )
| ( sk38 != nil )
| ~ ( sk37 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[9769]) ).
thf(10419,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10184,197]) ).
thf(10420,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[10419]) ).
thf(10421,plain,
( ( nil @ ( sk2 @ sk11 @ cons ) @ totalorderedP )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10420:[bind(A,$thf( sk2 @ sk11 ))]]) ).
thf(83984,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83839,410]) ).
thf(83985,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP ) ),
inference(simp,[status(thm)],[83984]) ).
thf(83986,plain,
nil @ ( sk2 @ sk28 @ cons ) @ duplicatefreeP,
inference(pattern_uni,[status(thm)],[83985:[bind(A,$thf( sk2 @ sk28 ))]]) ).
thf(4116,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[712,378]) ).
thf(4117,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[4116]) ).
thf(4118,plain,
( ( nil @ ( sk2 @ sk7 @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[4117:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(25106,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7009,215]) ).
thf(25107,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[25106]) ).
thf(25108,plain,
( ~ ( sk1 @ sk6 @ ( sk1 @ sk6 @ neq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[25107:[bind(A,$thf( sk1 @ sk6 ))]]) ).
thf(8,axiom,
nil @ totalorderedP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax66) ).
thf(131,plain,
nil @ totalorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6593,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[6317,248]) ).
thf(6594,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[6593]) ).
thf(6595,plain,
( ( nil @ ( sk2 @ sk8 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[6594:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(33504,plain,
! [A: $i] :
( ( ( sk1 @ sk17 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[33031,378]) ).
thf(33505,plain,
! [A: $i] :
( ( ( sk1 @ sk17 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[33504]) ).
thf(33506,plain,
( ( nil @ ( sk1 @ sk17 @ frontsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[33505:[bind(A,$thf( sk1 @ sk17 ))]]) ).
thf(3810,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,301]) ).
thf(3811,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[3810]) ).
thf(3812,plain,
nil @ ( sk2 @ rearsegP ),
inference(pattern_uni,[status(thm)],[3811:[bind(A,$thf( sk2 ))]]) ).
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(501,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(84016,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83839,215]) ).
thf(84017,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[84016]) ).
thf(84018,plain,
~ ( sk2 @ sk28 @ ( sk2 @ sk28 @ neq ) ),
inference(pattern_uni,[status(thm)],[84017:[bind(A,$thf( sk2 @ sk28 ))]]) ).
thf(44956,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk20 ) @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[44834,188]) ).
thf(44957,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk20 ) @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[44956]) ).
thf(44958,plain,
( ( nil @ ( nil @ ( nil @ sk20 ) @ app ) )
= ( nil @ ( nil @ sk20 ) ) ),
inference(pattern_uni,[status(thm)],[44957:[bind(A,$thf( nil @ ( nil @ sk20 ) ))]]) ).
thf(7212,plain,
! [A: $i] :
( ( ( sk2 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7034,371]) ).
thf(7213,plain,
! [A: $i] :
( ( ( sk2 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7212]) ).
thf(7214,plain,
( ( nil @ ( sk2 @ sk6 @ cons ) @ totalorderP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7213:[bind(A,$thf( sk2 @ sk6 ))]]) ).
thf(62060,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk26 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,262]) ).
thf(62061,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk26 @ ssList ) ),
inference(simp,[status(thm)],[62060]) ).
thf(62062,plain,
( ( sk2 @ totalorderP )
| ( sk2 @ sk26 @ ssList ) ),
inference(pattern_uni,[status(thm)],[62061:[bind(A,$thf( sk2 ))]]) ).
thf(199,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ lt ) )
| ( A = B )
| ~ ( B @ ( A @ leq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[198]) ).
thf(200,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ lt ) )
| ~ ( B @ ( A @ leq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A = B ) ),
inference(lifteq,[status(thm)],[199]) ).
thf(362,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)],[361]) ).
thf(365,plain,
! [B: $i,A: $i] :
( ( nil
= ( B @ ( A @ app ) ) )
| ( nil != A )
| ( nil != B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[362]) ).
thf(368,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
= nil )
| ( nil != A )
| ( nil != B ) ),
inference(lifteq,[status(thm)],[365]) ).
thf(369,plain,
( ~ ( nil @ ssList )
| ( ( nil @ ( nil @ app ) )
= nil ) ),
inference(simp,[status(thm)],[368]) ).
thf(690,plain,
( ~ $true
| ( ( nil @ ( nil @ app ) )
= nil ) ),
inference(rewrite,[status(thm)],[369,348]) ).
thf(691,plain,
( ( nil @ ( nil @ app ) )
= nil ),
inference(simp,[status(thm)],[690]) ).
thf(10458,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10184,410]) ).
thf(10459,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[10458]) ).
thf(10460,plain,
( ( nil @ ( sk2 @ sk11 @ cons ) @ duplicatefreeP )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10459:[bind(A,$thf( sk2 @ sk11 ))]]) ).
thf(10342,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10157,303]) ).
thf(10343,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[10342]) ).
thf(10344,plain,
( ( nil @ ( sk1 @ sk11 @ cons ) @ equalelemsP )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10343:[bind(A,$thf( sk1 @ sk11 ))]]) ).
thf(18673,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[13165,195]) ).
thf(18674,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[18673]) ).
thf(18675,plain,
( ( sk2 @ sk14 @ ( sk2 @ sk14 @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[18674:[bind(A,$thf( sk2 @ sk14 ))]]) ).
thf(773,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssList )
| ~ $true
| ( sk1 @ sk7 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[732,159]) ).
thf(774,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssList )
| ( sk1 @ sk7 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[773]) ).
thf(775,plain,
( ( sk1 @ sk7 @ sk7 @ cyclefreeP )
| ( sk1 @ sk7 @ sk7 @ sk7 @ ssList )
| ( sk1 @ sk7 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[774:[bind(A,$thf( sk1 @ sk7 @ sk7 ))]]) ).
thf(1767,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ sk7 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[747,248]) ).
thf(1768,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ sk7 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1767]) ).
thf(1769,plain,
( ( nil @ ( sk2 @ sk7 @ sk7 @ segmentP ) )
| ( sk2 @ sk7 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1768:[bind(A,$thf( sk2 @ sk7 @ sk7 ))]]) ).
thf(18618,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5455,195]) ).
thf(18619,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18618]) ).
thf(18620,plain,
( ( sk2 @ sk9 @ ( sk2 @ sk9 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18619:[bind(A,$thf( sk2 @ sk9 ))]]) ).
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(454,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(59171,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[58557,378]) ).
thf(59172,plain,
! [A: $i] :
( ( ( sk1 @ tl @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[59171]) ).
thf(59173,plain,
( ( nil @ ( sk1 @ tl @ frontsegP ) )
| ( sk2 != sk1 ) ),
inference(pattern_uni,[status(thm)],[59172:[bind(A,$thf( sk1 @ tl ))]]) ).
thf(5984,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk5 @ ( A @ sk6 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,162]) ).
thf(5985,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk5 @ ( A @ sk6 @ leq ) ) ),
inference(simp,[status(thm)],[5984]) ).
thf(5986,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk5 @ ( sk1 @ sk6 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[5985:[bind(A,$thf( sk1 ))]]) ).
thf(7600,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7470,236]) ).
thf(7601,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7600]) ).
thf(7602,plain,
( ~ ( sk1 @ sk5 @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7601:[bind(A,$thf( sk1 @ sk5 ))]]) ).
thf(13379,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[13106,248]) ).
thf(13380,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[13379]) ).
thf(13381,plain,
( ( nil @ ( sk1 @ sk14 @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[13380:[bind(A,$thf( sk1 @ sk14 ))]]) ).
thf(142380,plain,
$false,
inference(e,[status(thm)],[16340,52466,479,58055,33790,234,34797,10987,352,31256,23297,249,10743,6317,170,58382,5141,23240,65250,10314,379,1793,269,202,42056,58933,11635,83928,217,276,52315,44022,120,247,30375,36351,77091,11014,37685,31271,747,60522,153,10433,83921,4575,32539,44848,25078,6804,10341,7220,185,83491,52648,34943,18834,16319,3809,436,42501,257,7605,174,417,7136,44834,301,5621,42149,184,32516,77165,504,18782,5712,25090,196,372,7683,77013,31262,3821,12589,42490,559,18617,189,5127,60517,416,152,316,83839,261,10157,61357,18659,34570,4952,216,56913,25102,756,34883,13325,59478,238,56958,348,7139,492,164,63152,179,646,253,34961,106,11691,58019,7677,121,29477,10602,766,147,280,2618,11265,45076,221,59376,1796,10895,411,265,9923,16276,206,4082,132,33334,396,13106,133,18639,63898,10062,248,117,2364,7217,5545,83893,220,534,233,18742,9836,201,37089,12205,334,4712,59031,32258,6550,60525,10975,302,5455,407,165,56262,33031,45008,260,10990,349,297,33603,63208,36178,275,137,229,197,361,4585,461,4942,493,4104,37506,45661,456,324,54550,3799,7142,23091,6801,37606,156,60521,188,18828,420,169,10430,10184,55908,49346,6624,141,34970,225,52269,193,54417,60518,61951,706,7668,393,12410,16316,129,11315,1002,12533,18581,371,10338,508,23300,398,25075,34809,7133,134,10406,237,13507,105,244,18832,31253,205,17731,32355,1054,558,33682,11578,37003,18594,148,279,3792,6422,83908,513,430,13989,45053,33767,264,161,7599,180,689,7118,37776,11459,444,18689,176,7590,732,34973,7497,44024,5121,55969,10329,13563,61287,204,34788,58046,191,1916,16313,118,10883,13953,25096,10770,144,236,37328,498,31265,11515,5190,5207,181,5735,35900,159,4716,10088,172,219,274,10898,377,451,434,42514,208,34958,4107,113,18827,1574,60519,230,12354,98,7470,303,477,25111,1557,81983,11746,7575,198,25084,85438,63787,31250,77038,18631,2278,155,983,130,399,18602,9899,10076,10984,6504,59902,32089,10930,78821,226,5667,267,44152,241,1805,34770,521,5424,162,10091,255,209,83931,33529,32281,76506,458,60524,194,145,525,2715,1516,37407,35948,7211,414,83946,17805,54320,31232,409,310,712,13450,150,1400,327,7196,58068,18605,60059,18669,10585,370,42493,31877,177,182,10095,33413,18666,7009,32168,12647,59805,52109,10436,6467,56476,77194,32434,31223,203,52383,25114,524,495,759,1781,10376,31238,6286,231,56977,76920,7034,7653,72840,304,258,158,6003,60181,171,10104,31244,34800,76903,58472,186,16322,7680,510,34785,25099,763,10960,5590,31800,60520,119,378,18634,235,246,30322,287,300,34847,1774,410,60523,190,13624,10892,10868,23237,5041,151,5051,432,41840,168,262,34522,13165,44936,422,56936,210,239,195,17810,474,53498,33111,12476,16299,18740,294,126,136,506,268,9816,10421,83986,4118,644,25108,131,6595,33506,3812,501,84018,395,44958,7214,62062,163,200,277,691,111,12149,122,10460,10344,18675,775,1769,18620,58557,222,454,254,227,59173,5986,7602,215,13381,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC073+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.08 % 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
% 0.15/5.43 % Computer : n013.cluster.edu
% 0.15/5.43 % Model : x86_64 x86_64
% 0.15/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.43 % Memory : 8046.5625MB
% 0.15/5.43 % OS : Linux 6.8.0-71-generic
% 0.15/5.43 % CPULimit : 300
% 0.15/5.43 % WCLimit : 300
% 0.15/5.43 % DateTime : Sat Sep 26 12:10:26 UTC 2026
% 0.15/5.43 % CPUTime :
% 0.15/5.43 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
% 1.29/6.16 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.40/6.64 % [INFO] Parsing done (469ms).
% 2.40/6.66 % [INFO] Running in sequential loop mode.
% 3.47/7.33 % [INFO] eprover registered as external prover.
% 3.47/7.34 % [INFO] Scanning for conjecture ...
% 3.88/7.58 % [INFO] Found a conjecture (or negated_conjecture) and 95 axioms. Running axiom selection ...
% 4.30/7.77 % [INFO] Axiom selection finished. Selected 95 axioms (removed 0 axioms).
% 4.79/7.97 % [INFO] Problem is first-order (TPTP FOF).
% 4.79/8.01 % [INFO] Type checking passed.
% 4.79/8.02 % [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 ...
% 241.11/70.54 % External prover 'e' found a proof!
% 241.11/70.54 % [INFO] Killing All external provers ...
% 241.11/70.54 % Time passed: 64973ms (effective reasoning time: 63873ms)
% 241.11/70.54 % 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)>
% 241.11/70.55 % 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
% 241.11/70.55 % No. of inferences in proof: 1502
% 241.11/70.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 64973 ms resp. 63873 ms w/o parsing
% 230.63/70.98 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 230.63/70.99 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------