%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWC167+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 : n018.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 08:52:33 AM UTC 2026
% Result : Theorem 174.68s 44.10s
% Output : Refutation 166.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 123
% Syntax : Number of formulae : 1220 ( 115 unt; 0 typ; 27 def)
% Number of atoms : 5074 (1285 equ; 0 cnn)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 11611 (2031 ~;2066 |; 232 &;6581 @)
% ( 26 <=>; 675 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 51 usr; 14 con; 0-2 aty)
% Number of variables : 1192 ( 17 ^;1082 !; 66 ?;1192 :)
% ( 0 !>; 0 ?*; 0 @-; 27 @+)
% Comments :
%------------------------------------------------------------------------------
thf(ssList_decl,type,
ssList: $i > $o ).
thf(app_decl,type,
app: $i > $i > $i ).
thf(strictorderedP_decl,type,
strictorderedP: $i > $o ).
thf(ssItem_decl,type,
ssItem: $i > $o ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(nil_decl,type,
nil: $i ).
thf(lt_decl,type,
lt: $i > $i > $o ).
thf(neq_decl,type,
neq: $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(hd_decl,type,
hd: $i > $i ).
thf(segmentP_decl,type,
segmentP: $i > $i > $o ).
thf(cyclefreeP_decl,type,
cyclefreeP: $i > $o ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(strictorderP_decl,type,
strictorderP: $i > $o ).
thf(duplicatefreeP_decl,type,
duplicatefreeP: $i > $o ).
thf(singletonP_decl,type,
singletonP: $i > $o ).
thf(memberP_decl,type,
memberP: $i > $i > $o ).
thf(tl_decl,type,
tl: $i > $i ).
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 ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk9_decl,type,
sk9: $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 ).
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 > $i ).
thf(sk42_decl,type,
sk42: $i ).
thf(sk43_decl,type,
sk43: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( nil = C )
& ( nil != D ) )
| ! [E: $i] :
( ( E @ ssItem )
=> ! [F: $i] :
( ( F @ ssItem )
=> ! [G: $i] :
( ( G @ ssList )
=> ! [H: $i] :
( ( H @ ssList )
=> ( ( F @ ( E @ neq ) )
| ( ( H @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ ( G @ app ) @ app ) @ app ) )
!= A ) ) ) ) ) )
| ! [E: $i] :
( ( E @ ssList )
=> ( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ( F @ ( H @ lt ) )
& ( ( nil @ ( H @ cons ) @ ( I @ app ) )
= C )
& ( I @ ssList ) )
& ( H @ ssItem ) )
& ( ( G @ ( nil @ ( F @ cons ) @ app ) )
= E )
& ( G @ ssList ) )
& ( F @ ssItem ) )
| ~ ( C @ strictorderedP )
| ( ( E @ ( C @ app ) )
!= D ) ) )
| ( A != C )
| ( B != D ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( nil = B )
& ( nil != C ) )
| ! [D: $i] :
( ( D @ ssItem )
=> ! [E: $i] :
( ( E @ ssItem )
=> ! [F: $i] :
( ( F @ ssList )
=> ! [G: $i] :
( ( G @ ssList )
=> ( ( E @ ( D @ neq ) )
| ( ( G @ ( nil @ ( E @ cons ) @ ( nil @ ( D @ cons ) @ ( F @ app ) @ app ) @ app ) )
!= sk1 ) ) ) ) ) )
| ! [D: $i] :
( ( D @ ssList )
=> ( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( E @ ( G @ lt ) )
& ( ( nil @ ( G @ cons ) @ ( H @ app ) )
= B )
& ( H @ ssList ) )
& ( G @ ssItem ) )
& ( ( F @ ( nil @ ( E @ cons ) @ app ) )
= D )
& ( F @ ssList ) )
& ( E @ ssItem ) )
| ~ ( B @ strictorderedP )
| ( ( D @ ( B @ app ) )
!= C ) ) )
| ( sk1 != B )
| ( A != C ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( nil = A )
& ( nil != B ) )
| ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssItem )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( D @ ( C @ neq ) )
| ( ( F @ ( nil @ ( D @ cons ) @ ( nil @ ( C @ cons ) @ ( E @ app ) @ app ) @ app ) )
!= sk1 ) ) ) ) ) )
| ! [C: $i] :
( ( C @ ssList )
=> ( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( D @ ( F @ lt ) )
& ( ( nil @ ( F @ cons ) @ ( G @ app ) )
= A )
& ( G @ ssList ) )
& ( F @ ssItem ) )
& ( ( E @ ( nil @ ( D @ cons ) @ app ) )
= C )
& ( E @ ssList ) )
& ( D @ ssItem ) )
| ~ ( A @ strictorderedP )
| ( ( C @ ( A @ app ) )
!= B ) ) )
| ( sk1 != A )
| ( sk2 != B ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ( ( ( nil = sk3 )
& ( nil != A ) )
| ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ( ( C @ ( B @ neq ) )
| ( ( E @ ( nil @ ( C @ cons ) @ ( nil @ ( B @ cons ) @ ( D @ app ) @ app ) @ app ) )
!= sk1 ) ) ) ) ) )
| ! [B: $i] :
( ( B @ ssList )
=> ( ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ( C @ ( E @ lt ) )
& ( ( nil @ ( E @ cons ) @ ( F @ app ) )
= sk3 )
& ( F @ ssList ) )
& ( E @ ssItem ) )
& ( ( D @ ( nil @ ( C @ cons ) @ app ) )
= B )
& ( D @ ssList ) )
& ( C @ ssItem ) )
| ~ ( sk3 @ strictorderedP )
| ( ( B @ ( sk3 @ app ) )
!= A ) ) )
| ( sk1 != sk3 )
| ( sk2 != A ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ( ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ( B @ ( D @ lt ) )
& ( ( nil @ ( D @ cons ) @ ( E @ app ) )
= sk3 )
& ( E @ ssList ) )
& ( D @ ssItem ) )
& ( ( C @ ( nil @ ( B @ cons ) @ app ) )
= A )
& ( C @ ssList ) )
& ( B @ ssItem ) )
| ~ ( sk3 @ strictorderedP )
| ( ( A @ ( sk3 @ app ) )
!= sk4 ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( B @ ( A @ neq ) )
| ( ( D @ ( nil @ ( B @ cons ) @ ( nil @ ( A @ cons ) @ ( C @ app ) @ app ) @ app ) )
!= sk1 ) ) ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( A @ ( sk6 @ neq ) )
| ( ( C @ ( nil @ ( A @ cons ) @ ( nil @ ( sk6 @ cons ) @ ( B @ app ) @ app ) @ app ) )
!= sk1 ) ) ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( sk7 @ ( sk6 @ neq ) )
| ( ( B @ ( nil @ ( sk7 @ cons ) @ ( nil @ ( sk6 @ cons ) @ ( A @ app ) @ app ) @ app ) )
!= sk1 ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ( ( sk7 @ ( sk6 @ neq ) )
| ( ( A @ ( nil @ ( sk7 @ cons ) @ ( nil @ ( sk6 @ cons ) @ ( sk8 @ app ) @ app ) @ app ) )
!= sk1 ) ) ) ) ) ).
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 @ leq ) )
& ( C @ ( B @ leq ) ) ) ) ) ) ) ) ) ) ) ).
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 @ leq ) )
& ( B @ ( A @ sk10 @ leq ) ) ) ) ) ) ) ) ) ) ).
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 @ leq ) )
& ( A @ sk11 @ ( A @ sk10 @ leq ) ) ) ) ) ) ) ) ) ).
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 @ leq ) )
& ( A @ sk11 @ ( A @ sk10 @ leq ) ) ) ) ) ) ) ) ).
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 @ leq ) )
& ( A @ sk11 @ ( A @ sk10 @ leq ) ) ) ) ) ) ) ).
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 )
=> ( ( B @ ( C @ lt ) )
| ( 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 )
=> ( ( A @ sk15 @ ( B @ lt ) )
| ( 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 @ sk15 @ ( A @ sk16 @ lt ) )
| ( 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 @ sk15 @ ( A @ sk16 @ lt ) )
| ( 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 @ sk15 @ ( A @ sk16 @ lt ) )
| ( A @ sk16 @ ( A @ sk15 @ lt ) ) ) ) ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( ^ [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(sk21_def,definition,
( sk21
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ( ( ( E @ ( B @ cons ) @ ( D @ ( A @ sk20 @ cons ) @ ( C @ app ) @ app ) )
= A )
=> ( B @ ( A @ sk20 @ lt ) ) ) ) ) ) ) ) ) ).
thf(sk22_def,definition,
( sk22
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( D @ ( A @ sk21 @ cons ) @ ( C @ ( A @ sk20 @ cons ) @ ( B @ app ) @ app ) )
= A )
=> ( A @ sk21 @ ( A @ sk20 @ lt ) ) ) ) ) ) ) ) ).
thf(sk23_def,definition,
( sk23
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( A @ sk21 @ cons ) @ ( B @ ( A @ sk20 @ cons ) @ ( A @ sk22 @ app ) @ app ) )
= A )
=> ( A @ sk21 @ ( A @ sk20 @ lt ) ) ) ) ) ) ) ).
thf(sk24_def,definition,
( sk24
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ( ( ( B @ ( A @ sk21 @ cons ) @ ( A @ sk23 @ ( A @ sk20 @ cons ) @ ( A @ sk22 @ app ) @ app ) )
= A )
=> ( A @ sk21 @ ( A @ sk20 @ lt ) ) ) ) ) ) ).
thf(sk25_def,definition,
( sk25
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( ( C @ ( A @ app ) )
= B )
& ( C @ ssList ) ) ) ) ).
thf(sk42_def,definition,
( sk42
= ( @+[A: $i] :
( ? [B: $i] :
( ( A != B )
& ( B @ ssItem ) )
& ( A @ ssItem ) ) ) ) ).
thf(sk43_def,definition,
( sk43
= ( @+[A: $i] :
( ( sk42 != A )
& ( A @ ssItem ) ) ) ) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( nil = C )
& ( nil != D ) )
| ! [E: $i] :
( ( E @ ssItem )
=> ! [F: $i] :
( ( F @ ssItem )
=> ! [G: $i] :
( ( G @ ssList )
=> ! [H: $i] :
( ( H @ ssList )
=> ( ( F @ ( E @ neq ) )
| ( ( H @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ ( G @ app ) @ app ) @ app ) )
!= A ) ) ) ) ) )
| ! [E: $i] :
( ( E @ ssList )
=> ( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ( F @ ( H @ lt ) )
& ( ( nil @ ( H @ cons ) @ ( I @ app ) )
= C )
& ( I @ ssList ) )
& ( H @ ssItem ) )
& ( ( G @ ( nil @ ( F @ cons ) @ app ) )
= E )
& ( G @ ssList ) )
& ( F @ ssItem ) )
| ~ ( C @ strictorderedP )
| ( ( E @ ( C @ app ) )
!= D ) ) )
| ( A != C )
| ( B != D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( nil = C )
& ( nil != D ) )
| ! [E: $i] :
( ( E @ ssItem )
=> ! [F: $i] :
( ( F @ ssItem )
=> ! [G: $i] :
( ( G @ ssList )
=> ! [H: $i] :
( ( H @ ssList )
=> ( ( F @ ( E @ neq ) )
| ( ( H @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ ( G @ app ) @ app ) @ app ) )
!= A ) ) ) ) ) )
| ! [E: $i] :
( ( E @ ssList )
=> ( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ( F @ ( H @ lt ) )
& ( ( nil @ ( H @ cons ) @ ( I @ app ) )
= C )
& ( I @ ssList ) )
& ( H @ ssItem ) )
& ( ( G @ ( nil @ ( F @ cons ) @ app ) )
= E )
& ( G @ ssList ) )
& ( F @ ssItem ) )
| ~ ( C @ strictorderedP )
| ( ( E @ ( C @ app ) )
!= D ) ) )
| ( A != C )
| ( B != D ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(98,plain,
~ ! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( nil = C )
& ( nil != D ) )
| ! [E: $i] :
( ( E @ ssItem )
=> ! [F: $i] :
( ( F @ ssItem )
=> ! [G: $i] :
( ( G @ ssList )
=> ! [H: $i] :
( ( H @ ssList )
=> ( ( F @ ( E @ neq ) )
| ( ( H @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ ( G @ app ) @ app ) @ app ) )
!= A ) ) ) ) ) )
| ! [E: $i] :
( ( E @ ssList )
=> ( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ( F @ ( H @ lt ) )
& ( ( nil @ ( H @ cons ) @ ( I @ app ) )
= C )
& ( I @ ssList ) )
& ( H @ ssItem ) )
& ( ( G @ ( nil @ ( F @ cons ) @ app ) )
= E )
& ( G @ ssList ) )
& ( F @ ssItem ) )
| ~ ( C @ strictorderedP )
| ( ( E @ ( C @ app ) )
!= D ) ) )
| ( A != C )
| ( B != D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(99,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( nil != sk3 )
| ( nil = sk4 ) )
& ~ ( sk7 @ ( sk6 @ neq ) )
& ( ( sk9 @ ( nil @ ( sk7 @ cons ) @ ( nil @ ( sk6 @ cons ) @ ( sk8 @ app ) @ app ) @ app ) )
= sk1 )
& ( sk9 @ ssList )
& ( sk8 @ ssList )
& ( sk7 @ ssItem )
& ( sk6 @ ssItem )
& ( ~ ( A @ ( C @ lt ) )
| ( ( nil @ ( C @ cons ) @ ( D @ app ) )
!= sk3 )
| ~ ( D @ ssList )
| ~ ( C @ ssItem )
| ( ( B @ ( nil @ ( A @ cons ) @ app ) )
!= sk5 )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) )
& ( sk3 @ strictorderedP )
& ( ( sk5 @ ( sk3 @ app ) )
= sk4 )
& ( sk5 @ ssList )
& ( sk1 = sk3 )
& ( sk2 = sk4 )
& ( sk4 @ ssList )
& ( sk3 @ ssList )
& ( sk2 @ ssList )
& ( sk1 @ ssList ) ),
inference(cnf,[status(esa)],[98]) ).
thf(115,plain,
sk5 @ ssList,
inference(cnfConj,[status(thm)],[99]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ frontsegP ) )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax46) ).
thf(128,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(129,plain,
! [A: $i] :
( ( ( A @ ( nil @ frontsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) )
& ( ( nil = A )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[128]) ).
thf(130,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[129]) ).
thf(132,plain,
! [A: $i] :
( ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[130]) ).
thf(919,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[115,132]) ).
thf(920,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[919]) ).
thf(921,plain,
( ~ ( sk5 @ ( nil @ frontsegP ) )
| ( sk5 = nil ) ),
inference(pattern_uni,[status(thm)],[920:[bind(A,$thf( sk5 ))]]) ).
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(333,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(334,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ neq ) )
| ( A = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) )
& ( ( A != B )
| ~ ( B @ ( A @ neq ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[333]) ).
thf(335,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ ( A @ neq ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[334]) ).
thf(337,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ neq ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( A != B ) ),
inference(lifteq,[status(thm)],[335]) ).
thf(338,plain,
! [A: $i] :
( ~ ( A @ ( A @ neq ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[337]) ).
thf(813,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[115,338]) ).
thf(814,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[813]) ).
thf(815,plain,
~ ( sk5 @ ( sk5 @ neq ) ),
inference(pattern_uni,[status(thm)],[814:[bind(A,$thf( sk5 ))]]) ).
thf(1336,plain,
( ( sk5 != sk5 )
| ~ ( sk5 @ ( nil @ neq ) )
| ~ ( sk5 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[921,815]) ).
thf(1337,plain,
( ~ ( sk5 @ ( nil @ neq ) )
| ~ ( sk5 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1336:[]]) ).
thf(106,plain,
sk1 @ ssList,
inference(cnfConj,[status(thm)],[99]) ).
thf(948,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[106,132]) ).
thf(949,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[948]) ).
thf(950,plain,
( ~ ( sk1 @ ( nil @ frontsegP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[949:[bind(A,$thf( sk1 ))]]) ).
thf(110,plain,
( ( nil != sk3 )
| ( nil = sk4 ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(118,plain,
( ( sk3 != nil )
| ( sk4 = nil ) ),
inference(lifteq,[status(thm)],[110]) ).
thf(109,plain,
sk2 = sk4,
inference(cnfConj,[status(thm)],[99]) ).
thf(120,plain,
sk4 = sk2,
inference(lifteq,[status(thm)],[109]) ).
thf(107,plain,
sk1 = sk3,
inference(cnfConj,[status(thm)],[99]) ).
thf(121,plain,
sk3 = sk1,
inference(lifteq,[status(thm)],[107]) ).
thf(563,plain,
( ( sk1 != nil )
| ( sk2 = nil ) ),
inference(rewrite,[status(thm)],[118,120,121]) ).
thf(1409,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ( sk2 = nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[950,563]) ).
thf(1410,plain,
( ( sk1 != sk1 )
| ( sk2 = nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1409]) ).
thf(1411,plain,
( ( sk2 = nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1410:[]]) ).
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(138,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(131,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[129]) ).
thf(133,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[131]) ).
thf(134,plain,
( ( nil @ ( nil @ frontsegP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[133]) ).
thf(53,axiom,
nil @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
thf(354,plain,
nil @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(735,plain,
( ( nil @ ( nil @ frontsegP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[134,354]) ).
thf(736,plain,
nil @ ( nil @ frontsegP ),
inference(simp,[status(thm)],[735]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil @ ( A @ app ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax84) ).
thf(192,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil @ ( A @ app ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(193,plain,
! [A: $i] :
( ( ( nil @ ( A @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[192]) ).
thf(194,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[193]) ).
thf(20261,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[106,194]) ).
thf(20262,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[20261]) ).
thf(20263,plain,
( ( nil @ ( sk1 @ app ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[20262:[bind(A,$thf( sk1 ))]]) ).
thf(108,plain,
( ( sk5 @ ( sk3 @ app ) )
= sk4 ),
inference(cnfConj,[status(thm)],[99]) ).
thf(122,plain,
( ( sk5 @ ( sk3 @ app ) )
= sk4 ),
inference(lifteq,[status(thm)],[108]) ).
thf(660,plain,
( ( sk5 @ ( sk1 @ app ) )
= sk2 ),
inference(rewrite,[status(thm)],[122,120,121]) ).
thf(20625,plain,
( ( ( sk5 @ ( sk1 @ app ) )
!= ( nil @ ( sk1 @ app ) ) )
| ( sk2 = sk1 ) ),
inference(paramod_ordered,[status(thm)],[20263,660]) ).
thf(20677,plain,
( ( sk5 != nil )
| ( sk1 != sk1 )
| ( sk2 = sk1 ) ),
inference(simp,[status(thm)],[20625]) ).
thf(20692,plain,
( ( sk5 != nil )
| ( sk2 = sk1 ) ),
inference(simp,[status(thm)],[20677]) ).
thf(21175,plain,
( ( sk5 != sk5 )
| ( nil != nil )
| ( sk2 = sk1 )
| ~ ( sk5 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[921,20692]) ).
thf(21176,plain,
( ( sk5 != sk5 )
| ( sk2 = sk1 )
| ~ ( sk5 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[21175]) ).
thf(21177,plain,
( ( sk2 = sk1 )
| ~ ( sk5 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[21176:[]]) ).
thf(105,plain,
sk2 @ ssList,
inference(cnfConj,[status(thm)],[99]) ).
thf(822,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,338]) ).
thf(823,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[822]) ).
thf(824,plain,
~ ( sk2 @ ( sk2 @ neq ) ),
inference(pattern_uni,[status(thm)],[823:[bind(A,$thf( sk2 ))]]) ).
thf(21960,plain,
( ( sk2 != sk2 )
| ~ ( sk1 @ ( sk2 @ neq ) )
| ~ ( sk5 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[21177,824]) ).
thf(21961,plain,
( ~ ( sk1 @ ( sk2 @ neq ) )
| ~ ( sk5 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[21960:[]]) ).
thf(23113,plain,
( ( ( sk5 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk1 @ ( sk2 @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[736,21961]) ).
thf(23114,plain,
( ( ( sk5 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk1 @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[23113]) ).
thf(23134,plain,
( ( sk5 != nil )
| ( nil != nil )
| ~ ( sk1 @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[23114]) ).
thf(23137,plain,
( ( sk5 != nil )
| ~ ( sk1 @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[23134]) ).
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(162,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(163,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ cyclefreeP )
| ( A @ sk10 @ ( A @ sk11 @ leq ) )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk11 @ ( A @ sk10 @ leq ) )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( ( A @ sk14 @ ( A @ sk11 @ cons ) @ ( A @ sk13 @ ( A @ sk10 @ cons ) @ ( A @ sk12 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk14 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk13 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk12 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk11 @ ssItem )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk10 @ 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)],[162]) ).
thf(169,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk10 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[163]) ).
thf(7491,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[115,169]) ).
thf(7492,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ssItem ) ),
inference(simp,[status(thm)],[7491]) ).
thf(7493,plain,
( ( sk5 @ cyclefreeP )
| ( sk5 @ sk10 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[7492:[bind(A,$thf( sk5 ))]]) ).
thf(34,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( nil @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
thf(241,plain,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( nil @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(242,plain,
! [A: $i] :
( ~ ( A @ ( nil @ memberP ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[241]) ).
thf(7671,plain,
! [A: $i] :
( ( ( sk5 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk5 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7493,242]) ).
thf(7672,plain,
! [A: $i] :
( ( ( sk5 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk5 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7671]) ).
thf(7673,plain,
( ~ ( sk5 @ sk10 @ ( nil @ memberP ) )
| ( sk5 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7672:[bind(A,$thf( sk5 @ sk10 ))]]) ).
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(228,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(229,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ strictorderedP )
| ~ ( A @ sk21 @ ( A @ sk20 @ lt ) )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( ( A @ sk24 @ ( A @ sk21 @ cons ) @ ( A @ sk23 @ ( A @ sk20 @ cons ) @ ( A @ sk22 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( A @ sk24 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( A @ sk23 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( A @ sk22 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( A @ sk21 @ ssItem )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( A @ sk20 @ 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)],[228]) ).
thf(234,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk22 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[229]) ).
thf(113,plain,
sk8 @ ssList,
inference(cnfConj,[status(thm)],[99]) ).
thf(171,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk11 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[163]) ).
thf(8846,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[113,171]) ).
thf(8847,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssItem ) ),
inference(simp,[status(thm)],[8846]) ).
thf(8848,plain,
( ( sk8 @ cyclefreeP )
| ( sk8 @ sk11 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[8847:[bind(A,$thf( sk8 ))]]) ).
thf(9220,plain,
! [A: $i] :
( ( ( sk8 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk8 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[8848,242]) ).
thf(9221,plain,
! [A: $i] :
( ( ( sk8 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk8 @ cyclefreeP ) ),
inference(simp,[status(thm)],[9220]) ).
thf(9222,plain,
( ~ ( sk8 @ sk11 @ ( nil @ memberP ) )
| ( sk8 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[9221:[bind(A,$thf( sk8 @ sk11 ))]]) ).
thf(111,plain,
sk9 @ ssList,
inference(cnfConj,[status(thm)],[99]) ).
thf(1105,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[111,132]) ).
thf(1106,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[1105]) ).
thf(1107,plain,
( ~ ( sk9 @ ( nil @ frontsegP ) )
| ( sk9 = nil ) ),
inference(pattern_uni,[status(thm)],[1106:[bind(A,$thf( sk9 ))]]) ).
thf(828,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,338]) ).
thf(829,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[828]) ).
thf(830,plain,
~ ( sk9 @ ( sk9 @ neq ) ),
inference(pattern_uni,[status(thm)],[829:[bind(A,$thf( sk9 ))]]) ).
thf(1685,plain,
( ( sk9 != sk9 )
| ~ ( nil @ ( sk9 @ neq ) )
| ~ ( sk9 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1107,830]) ).
thf(1686,plain,
( ~ ( nil @ ( sk9 @ neq ) )
| ~ ( sk9 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1685:[]]) ).
thf(170,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk14 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[163]) ).
thf(8152,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk14 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,170]) ).
thf(8153,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk14 @ ssList ) ),
inference(simp,[status(thm)],[8152]) ).
thf(8154,plain,
( ( sk9 @ cyclefreeP )
| ( sk9 @ sk14 @ ssList ) ),
inference(pattern_uni,[status(thm)],[8153:[bind(A,$thf( sk9 ))]]) ).
thf(232,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk24 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[229]) ).
thf(42733,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk24 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,232]) ).
thf(42734,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk24 @ ssList ) ),
inference(simp,[status(thm)],[42733]) ).
thf(42735,plain,
( ( sk9 @ strictorderedP )
| ( sk9 @ sk24 @ ssList ) ),
inference(pattern_uni,[status(thm)],[42734:[bind(A,$thf( sk9 ))]]) ).
thf(237,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk23 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[229]) ).
thf(48657,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk23 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[113,237]) ).
thf(48658,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk23 @ ssList ) ),
inference(simp,[status(thm)],[48657]) ).
thf(48659,plain,
( ( sk8 @ strictorderedP )
| ( sk8 @ sk23 @ ssList ) ),
inference(pattern_uni,[status(thm)],[48658:[bind(A,$thf( sk8 ))]]) ).
thf(1029,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[113,132]) ).
thf(1030,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[1029]) ).
thf(1031,plain,
( ~ ( sk8 @ ( nil @ frontsegP ) )
| ( sk8 = nil ) ),
inference(pattern_uni,[status(thm)],[1030:[bind(A,$thf( sk8 ))]]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ segmentP ) )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax58) ).
thf(143,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(144,plain,
! [A: $i] :
( ( ( A @ ( nil @ segmentP ) )
| ( nil != A )
| ~ ( A @ ssList ) )
& ( ( nil = A )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[143]) ).
thf(145,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[144]) ).
thf(147,plain,
! [A: $i] :
( ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[145]) ).
thf(2361,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[105,147]) ).
thf(2362,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[2361]) ).
thf(2363,plain,
( ~ ( sk2 @ ( nil @ segmentP ) )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[2362:[bind(A,$thf( sk2 ))]]) ).
thf(2136,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[115,147]) ).
thf(2137,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[2136]) ).
thf(2138,plain,
( ~ ( sk5 @ ( nil @ segmentP ) )
| ( sk5 = nil ) ),
inference(pattern_uni,[status(thm)],[2137:[bind(A,$thf( sk5 ))]]) ).
thf(2658,plain,
( ( sk5 != sk5 )
| ~ ( sk5 @ ( nil @ neq ) )
| ~ ( sk5 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2138,815]) ).
thf(2659,plain,
( ~ ( sk5 @ ( nil @ neq ) )
| ~ ( sk5 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[2658:[]]) ).
thf(164,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk11 @ ( A @ sk10 @ leq ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[163]) ).
thf(6617,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ( A @ sk10 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[115,164]) ).
thf(6618,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ( A @ sk10 @ leq ) ) ),
inference(simp,[status(thm)],[6617]) ).
thf(6619,plain,
( ( sk5 @ cyclefreeP )
| ( sk5 @ sk11 @ ( sk5 @ sk10 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[6618:[bind(A,$thf( sk5 ))]]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ equalelemsP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax73) ).
thf(308,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ equalelemsP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(73,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax63) ).
thf(440,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(992,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[105,132]) ).
thf(993,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[992]) ).
thf(994,plain,
( ~ ( sk2 @ ( nil @ frontsegP ) )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[993:[bind(A,$thf( sk2 ))]]) ).
thf(2597,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[111,147]) ).
thf(2598,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[2597]) ).
thf(2599,plain,
( ~ ( sk9 @ ( nil @ segmentP ) )
| ( sk9 = nil ) ),
inference(pattern_uni,[status(thm)],[2598:[bind(A,$thf( sk9 ))]]) ).
thf(3039,plain,
( ( sk9 != sk9 )
| ~ ( nil @ ( sk9 @ neq ) )
| ~ ( sk9 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2599,830]) ).
thf(3040,plain,
( ~ ( nil @ ( sk9 @ neq ) )
| ~ ( sk9 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[3039:[]]) ).
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(245,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(246,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ frontsegP ) )
| ( ( C @ ( B @ app ) )
!= A )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) )
& ( ( ( A @ ( B @ sk25 ) @ ( B @ app ) )
= A )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ ( B @ sk25 ) @ ssList )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[245]) ).
thf(247,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk25 ) @ ssList )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[246]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax65) ).
thf(202,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(172,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk13 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[163]) ).
thf(9362,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk13 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,172]) ).
thf(9363,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk13 @ ssList ) ),
inference(simp,[status(thm)],[9362]) ).
thf(9364,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk13 @ ssList ) ),
inference(pattern_uni,[status(thm)],[9363:[bind(A,$thf( sk1 ))]]) ).
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(178,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(179,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ strictorderP )
| ~ ( A @ sk15 @ ( A @ sk16 @ lt ) )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ~ ( A @ sk16 @ ( A @ sk15 @ lt ) )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( ( A @ sk19 @ ( A @ sk16 @ cons ) @ ( A @ sk18 @ ( A @ sk15 @ cons ) @ ( A @ sk17 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( A @ sk19 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( A @ sk18 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( A @ sk17 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( A @ sk16 @ ssItem )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( A @ sk15 @ 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)],[178]) ).
thf(183,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk17 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[179]) ).
thf(13185,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk17 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,183]) ).
thf(13186,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk17 @ ssList ) ),
inference(simp,[status(thm)],[13185]) ).
thf(13187,plain,
( ( sk9 @ strictorderP )
| ( sk9 @ sk17 @ ssList ) ),
inference(pattern_uni,[status(thm)],[13186:[bind(A,$thf( sk9 ))]]) ).
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(385,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(165,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk12 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[163]) ).
thf(768,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,165]) ).
thf(769,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssList ) ),
inference(simp,[status(thm)],[768]) ).
thf(770,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk12 @ ssList ) ),
inference(pattern_uni,[status(thm)],[769:[bind(A,$thf( sk1 ))]]) ).
thf(1208,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssList )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[770,165]) ).
thf(1209,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssList )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1208]) ).
thf(1210,plain,
( ( sk1 @ sk12 @ cyclefreeP )
| ( sk1 @ sk12 @ sk12 @ ssList )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1209:[bind(A,$thf( sk1 @ sk12 ))]]) ).
thf(1754,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssList )
| ~ $true
| ( sk1 @ sk12 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[1210,165]) ).
thf(1755,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssList )
| ( sk1 @ sk12 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1754]) ).
thf(1756,plain,
( ( sk1 @ sk12 @ sk12 @ cyclefreeP )
| ( sk1 @ sk12 @ sk12 @ sk12 @ ssList )
| ( sk1 @ sk12 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1755:[bind(A,$thf( sk1 @ sk12 @ sk12 ))]]) ).
thf(114,plain,
sk7 @ ssItem,
inference(cnfConj,[status(thm)],[99]) ).
thf(548,plain,
! [A: $i] :
( ( ( sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[114,242]) ).
thf(549,plain,
! [A: $i] :
( ( ( sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[548]) ).
thf(550,plain,
~ ( sk7 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[549:[bind(A,$thf( sk7 ))]]) ).
thf(7522,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,169]) ).
thf(7523,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ssItem ) ),
inference(simp,[status(thm)],[7522]) ).
thf(7524,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk10 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[7523:[bind(A,$thf( sk1 ))]]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ app ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
thf(223,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ app ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(224,plain,
! [A: $i] :
( ( ( A @ ( nil @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[223]) ).
thf(225,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[224]) ).
thf(39548,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[115,225]) ).
thf(39549,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[39548]) ).
thf(39550,plain,
( ( sk5 @ ( nil @ app ) )
= sk5 ),
inference(pattern_uni,[status(thm)],[39549:[bind(A,$thf( sk5 ))]]) ).
thf(39924,plain,
( ( ( sk5 @ ( sk1 @ app ) )
!= ( sk5 @ ( nil @ app ) ) )
| ( sk5 = sk2 ) ),
inference(paramod_ordered,[status(thm)],[660,39550]) ).
thf(40021,plain,
( ( sk5 != sk5 )
| ( sk1 != nil )
| ( sk5 = sk2 ) ),
inference(simp,[status(thm)],[39924]) ).
thf(40053,plain,
( ( sk1 != nil )
| ( sk5 = sk2 ) ),
inference(simp,[status(thm)],[40021]) ).
thf(41000,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ( sk5 = sk2 )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[950,40053]) ).
thf(41001,plain,
( ( sk1 != sk1 )
| ( sk5 = sk2 )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[41000]) ).
thf(41002,plain,
( ( sk5 = sk2 )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[41001:[]]) ).
thf(2224,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[106,147]) ).
thf(2225,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[2224]) ).
thf(2226,plain,
( ~ ( sk1 @ ( nil @ segmentP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[2225:[bind(A,$thf( sk1 ))]]) ).
thf(2738,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ( sk2 = nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2226,563]) ).
thf(2739,plain,
( ( sk1 != sk1 )
| ( sk2 = nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[2738]) ).
thf(2740,plain,
( ( sk2 = nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[2739:[]]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax55) ).
thf(200,plain,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(201,plain,
! [A: $i] :
( ( A @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[200]) ).
thf(23528,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,201]) ).
thf(23529,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[23528]) ).
thf(23530,plain,
sk2 @ ( sk2 @ segmentP ),
inference(pattern_uni,[status(thm)],[23529:[bind(A,$thf( sk2 ))]]) ).
thf(23928,plain,
( ( sk2 != sk2 )
| ( nil @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2740,23530]) ).
thf(23929,plain,
( ( nil @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[23928:[]]) ).
thf(103,plain,
sk6 @ ssItem,
inference(cnfConj,[status(thm)],[99]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax90) ).
thf(226,plain,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(227,plain,
! [A: $i] :
( ~ ( A @ ( A @ lt ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[226]) ).
thf(745,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,227]) ).
thf(746,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[745]) ).
thf(747,plain,
~ ( sk6 @ ( sk6 @ lt ) ),
inference(pattern_uni,[status(thm)],[746:[bind(A,$thf( sk6 ))]]) ).
thf(187,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk15 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[179]) ).
thf(16454,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk15 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,187]) ).
thf(16455,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk15 @ ssItem ) ),
inference(simp,[status(thm)],[16454]) ).
thf(16456,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk15 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[16455:[bind(A,$thf( sk1 ))]]) ).
thf(16782,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[16456,242]) ).
thf(16783,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[16782]) ).
thf(16784,plain,
( ~ ( sk1 @ sk15 @ ( nil @ memberP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[16783:[bind(A,$thf( sk1 @ sk15 ))]]) ).
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(151,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(152,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[151]) ).
thf(153,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( A = B ) ),
inference(lifteq,[status(thm)],[152]) ).
thf(23433,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[115,201]) ).
thf(23434,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[23433]) ).
thf(23435,plain,
sk5 @ ( sk5 @ segmentP ),
inference(pattern_uni,[status(thm)],[23434:[bind(A,$thf( sk5 ))]]) ).
thf(40940,plain,
( ( sk5 != sk5 )
| ( sk5 @ ( sk2 @ segmentP ) )
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[40053,23435]) ).
thf(40941,plain,
( ( sk5 @ ( sk2 @ segmentP ) )
| ( sk1 != nil ) ),
inference(pattern_uni,[status(thm)],[40940:[]]) ).
thf(41548,plain,
( ( sk2 != sk2 )
| ( sk5 @ ( nil @ segmentP ) )
| ( sk1 != nil )
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[563,40941]) ).
thf(41549,plain,
( ( sk2 != sk2 )
| ( sk5 @ ( nil @ segmentP ) )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[41548]) ).
thf(41550,plain,
( ( sk5 @ ( nil @ segmentP ) )
| ( sk1 != nil ) ),
inference(pattern_uni,[status(thm)],[41549:[]]) ).
thf(21178,plain,
( ( sk5 != sk5 )
| ( nil != nil )
| ( sk2 = sk1 )
| ~ ( sk5 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2138,20692]) ).
thf(21179,plain,
( ( sk5 != sk5 )
| ( sk2 = sk1 )
| ~ ( sk5 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[21178]) ).
thf(21180,plain,
( ( sk2 = sk1 )
| ~ ( sk5 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[21179:[]]) ).
thf(43905,plain,
( ( ( sk5 @ ( nil @ segmentP ) )
!= ( sk5 @ ( nil @ segmentP ) ) )
| ( sk2 = sk1 )
| ~ $true
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[41550,21180]) ).
thf(43906,plain,
( ( ( sk5 @ ( nil @ segmentP ) )
!= ( sk5 @ ( nil @ segmentP ) ) )
| ( sk2 = sk1 )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[43905]) ).
thf(43907,plain,
( ( sk2 = sk1 )
| ( sk1 != nil ) ),
inference(pattern_uni,[status(thm)],[43906:[]]) ).
thf(44163,plain,
( ( sk2 != sk2 )
| ( sk2 @ ( sk1 @ segmentP ) )
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[43907,23530]) ).
thf(44164,plain,
( ( sk2 @ ( sk1 @ segmentP ) )
| ( sk1 != nil ) ),
inference(pattern_uni,[status(thm)],[44163:[]]) ).
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(140,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) @ hd )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(141,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ cons ) @ hd )
= B )
| ~ ( B @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[140]) ).
thf(142,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( ( A @ ( B @ cons ) @ hd )
= B ) ),
inference(lifteq,[status(thm)],[141]) ).
thf(6663,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ( A @ sk10 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,164]) ).
thf(6664,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ( A @ sk10 @ leq ) ) ),
inference(simp,[status(thm)],[6663]) ).
thf(6665,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk11 @ ( sk2 @ sk10 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[6664:[bind(A,$thf( sk2 ))]]) ).
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(340,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(8879,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,171]) ).
thf(8880,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssItem ) ),
inference(simp,[status(thm)],[8879]) ).
thf(8881,plain,
( ( sk9 @ cyclefreeP )
| ( sk9 @ sk11 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[8880:[bind(A,$thf( sk9 ))]]) ).
thf(185,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk18 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[179]) ).
thf(23960,plain,
( ( sk2 != sk2 )
| ( sk2 @ ( nil @ segmentP ) )
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[563,23530]) ).
thf(23961,plain,
( ( sk2 @ ( nil @ segmentP ) )
| ( sk1 != nil ) ),
inference(pattern_uni,[status(thm)],[23960:[]]) ).
thf(61,axiom,
? [A: $i] :
( ? [B: $i] :
( ( A != B )
& ( B @ ssItem ) )
& ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
thf(399,plain,
? [A: $i] :
( ? [B: $i] :
( ( A != B )
& ( B @ ssItem ) )
& ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(400,plain,
( ( sk42 != sk43 )
& ( sk43 @ ssItem )
& ( sk42 @ ssItem ) ),
inference(cnf,[status(esa)],[399]) ).
thf(403,plain,
sk42 != sk43,
inference(cnfConj,[status(thm)],[400]) ).
thf(404,plain,
sk43 != sk42,
inference(lifteq,[status(thm)],[403]) ).
thf(2164,plain,
! [A: $i] :
( ( A != sk43 )
| ( sk42 != nil )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[147,404]) ).
thf(2165,plain,
( ( sk42 != nil )
| ~ ( sk43 @ ( nil @ segmentP ) )
| ~ ( sk43 @ ssList ) ),
inference(pattern_uni,[status(thm)],[2164:[bind(A,$thf( sk43 ))]]) ).
thf(13937,plain,
( ( ( sk43 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk42 != nil )
| ~ ( sk43 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,2165]) ).
thf(13938,plain,
( ( ( sk43 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk42 != nil )
| ~ ( sk43 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[13937]) ).
thf(13977,plain,
( ( sk43 != sk2 )
| ( sk42 != nil )
| ~ ( sk43 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[13938]) ).
thf(33209,plain,
( ( ( sk43 @ ( nil @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) )
| ( sk43 != sk2 )
| ( sk42 != nil )
| ~ $true
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[23961,13977]) ).
thf(33210,plain,
( ( ( sk43 @ ( nil @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) )
| ( sk43 != sk2 )
| ( sk42 != nil )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[33209]) ).
thf(33307,plain,
( ( sk43 != sk2 )
| ( nil != nil )
| ( sk43 != sk2 )
| ( sk42 != nil )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[33210]) ).
thf(33326,plain,
( ( sk43 != sk2 )
| ( sk42 != nil )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[33307]) ).
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(417,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(71,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( B @ ( A @ app ) @ ssList ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
thf(436,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( B @ ( A @ app ) @ ssList ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(186,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk19 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[179]) ).
thf(15340,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk19 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,186]) ).
thf(15341,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk19 @ ssList ) ),
inference(simp,[status(thm)],[15340]) ).
thf(15342,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk19 @ ssList ) ),
inference(pattern_uni,[status(thm)],[15341:[bind(A,$thf( sk1 ))]]) ).
thf(839,plain,
! [A: $i] :
( ( A != sk43 )
| ( sk42 != nil )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[132,404]) ).
thf(840,plain,
( ( sk42 != nil )
| ~ ( sk43 @ ( nil @ frontsegP ) )
| ~ ( sk43 @ ssList ) ),
inference(pattern_uni,[status(thm)],[839:[bind(A,$thf( sk43 ))]]) ).
thf(11892,plain,
( ( ( sk43 @ ssList )
!= ( sk5 @ ssList ) )
| ( sk42 != nil )
| ~ ( sk43 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[115,840]) ).
thf(11893,plain,
( ( ( sk43 @ ssList )
!= ( sk5 @ ssList ) )
| ( sk42 != nil )
| ~ ( sk43 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[11892]) ).
thf(12026,plain,
( ( sk43 != sk5 )
| ( sk42 != nil )
| ~ ( sk43 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[11893]) ).
thf(166,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)],[163]) ).
thf(173,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)],[166]) ).
thf(174,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)],[173]) ).
thf(780,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,165]) ).
thf(781,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssList ) ),
inference(simp,[status(thm)],[780]) ).
thf(782,plain,
( ( sk9 @ cyclefreeP )
| ( sk9 @ sk12 @ ssList ) ),
inference(pattern_uni,[status(thm)],[781:[bind(A,$thf( sk9 ))]]) ).
thf(1440,plain,
( ( sk2 != sk2 )
| ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[994,824]) ).
thf(1441,plain,
( ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1440:[]]) ).
thf(188,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk16 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[179]) ).
thf(17306,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[113,188]) ).
thf(17307,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssItem ) ),
inference(simp,[status(thm)],[17306]) ).
thf(17308,plain,
( ( sk8 @ strictorderP )
| ( sk8 @ sk16 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[17307:[bind(A,$thf( sk8 ))]]) ).
thf(17822,plain,
! [A: $i] :
( ( ( sk8 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk8 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[17308,242]) ).
thf(17823,plain,
! [A: $i] :
( ( ( sk8 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk8 @ strictorderP ) ),
inference(simp,[status(thm)],[17822]) ).
thf(17824,plain,
( ~ ( sk8 @ sk16 @ ( nil @ memberP ) )
| ( sk8 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[17823:[bind(A,$thf( sk8 @ sk16 ))]]) ).
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(504,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(837,plain,
( ( sk2 != sk2 )
| ~ ( nil @ ( sk2 @ neq ) )
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[563,824]) ).
thf(838,plain,
( ~ ( nil @ ( sk2 @ neq ) )
| ( sk1 != nil ) ),
inference(pattern_uni,[status(thm)],[837:[]]) ).
thf(21958,plain,
( ( sk2 != sk2 )
| ~ ( sk2 @ ( sk1 @ neq ) )
| ~ ( sk5 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[21177,824]) ).
thf(21959,plain,
( ~ ( sk2 @ ( sk1 @ neq ) )
| ~ ( sk5 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[21958:[]]) ).
thf(22264,plain,
( ( ( sk5 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk2 @ ( sk1 @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[736,21959]) ).
thf(22265,plain,
( ( ( sk5 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[22264]) ).
thf(22284,plain,
( ( sk5 != nil )
| ( nil != nil )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[22265]) ).
thf(22287,plain,
( ( sk5 != nil )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[22284]) ).
thf(44232,plain,
( ( sk1 != sk1 )
| ( sk2 = sk1 )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2226,43907]) ).
thf(44233,plain,
( ( sk1 != sk1 )
| ( sk2 = sk1 )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[44232]) ).
thf(44234,plain,
( ( sk2 = sk1 )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[44233:[]]) ).
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(195,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(196,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)],[195]) ).
thf(23540,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[113,201]) ).
thf(23541,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[23540]) ).
thf(23542,plain,
sk8 @ ( sk8 @ segmentP ),
inference(pattern_uni,[status(thm)],[23541:[bind(A,$thf( sk8 ))]]) ).
thf(777,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[113,165]) ).
thf(778,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssList ) ),
inference(simp,[status(thm)],[777]) ).
thf(779,plain,
( ( sk8 @ cyclefreeP )
| ( sk8 @ sk12 @ ssList ) ),
inference(pattern_uni,[status(thm)],[778:[bind(A,$thf( sk8 ))]]) ).
thf(1296,plain,
! [A: $i] :
( ( ( sk8 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk8 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[779,338]) ).
thf(1297,plain,
! [A: $i] :
( ( ( sk8 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ( sk8 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1296]) ).
thf(1298,plain,
( ~ ( sk8 @ sk12 @ ( sk8 @ sk12 @ neq ) )
| ( sk8 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1297:[bind(A,$thf( sk8 @ sk12 ))]]) ).
thf(816,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,338]) ).
thf(817,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[816]) ).
thf(818,plain,
~ ( sk1 @ ( sk1 @ neq ) ),
inference(pattern_uni,[status(thm)],[817:[bind(A,$thf( sk1 ))]]) ).
thf(2754,plain,
( ( sk1 != sk1 )
| ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2226,818]) ).
thf(2755,plain,
( ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[2754:[]]) ).
thf(23486,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,201]) ).
thf(23487,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[23486]) ).
thf(23488,plain,
sk1 @ ( sk1 @ segmentP ),
inference(pattern_uni,[status(thm)],[23487:[bind(A,$thf( sk1 ))]]) ).
thf(23856,plain,
( ( sk1 != sk1 )
| ( sk1 @ ( nil @ segmentP ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[950,23488]) ).
thf(23857,plain,
( ( sk1 @ ( nil @ segmentP ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[23856:[]]) ).
thf(31287,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk1 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[736,23857]) ).
thf(31288,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[31287]) ).
thf(31342,plain,
( ( sk1 != nil )
| ( nil != nil )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[31288]) ).
thf(31372,plain,
( ( sk1 != nil )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[31342]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax68) ).
thf(126,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(127,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[126]) ).
thf(800,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,127]) ).
thf(801,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[800]) ).
thf(802,plain,
nil @ ( sk6 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[801:[bind(A,$thf( sk6 ))]]) ).
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(124,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(125,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)],[124]) ).
thf(17184,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[115,188]) ).
thf(17185,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssItem ) ),
inference(simp,[status(thm)],[17184]) ).
thf(17186,plain,
( ( sk5 @ strictorderP )
| ( sk5 @ sk16 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[17185:[bind(A,$thf( sk5 ))]]) ).
thf(17479,plain,
! [A: $i] :
( ( ( sk5 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk5 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[17186,242]) ).
thf(17480,plain,
! [A: $i] :
( ( ( sk5 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk5 @ strictorderP ) ),
inference(simp,[status(thm)],[17479]) ).
thf(17481,plain,
( ~ ( sk5 @ sk16 @ ( nil @ memberP ) )
| ( sk5 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[17480:[bind(A,$thf( sk5 @ sk16 ))]]) ).
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(460,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(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(157,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(17294,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,188]) ).
thf(17295,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssItem ) ),
inference(simp,[status(thm)],[17294]) ).
thf(17296,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk16 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[17295:[bind(A,$thf( sk2 ))]]) ).
thf(17675,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[17296,242]) ).
thf(17676,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[17675]) ).
thf(17677,plain,
( ~ ( sk2 @ sk16 @ ( nil @ memberP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[17676:[bind(A,$thf( sk2 @ sk16 ))]]) ).
thf(184,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( ( A @ sk19 @ ( A @ sk16 @ cons ) @ ( A @ sk18 @ ( A @ sk15 @ cons ) @ ( A @ sk17 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[179]) ).
thf(189,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ( ( A @ sk19 @ ( A @ sk16 @ cons ) @ ( A @ sk18 @ ( A @ sk15 @ cons ) @ ( A @ sk17 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[184]) ).
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(316,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ( A @ hd )
= B )
& ( B @ ssItem ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
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(261,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(774,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,165]) ).
thf(775,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssList ) ),
inference(simp,[status(thm)],[774]) ).
thf(776,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk12 @ ssList ) ),
inference(pattern_uni,[status(thm)],[775:[bind(A,$thf( sk2 ))]]) ).
thf(1230,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssList )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[776,165]) ).
thf(1231,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssList )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1230]) ).
thf(1232,plain,
( ( sk2 @ sk12 @ cyclefreeP )
| ( sk2 @ sk12 @ sk12 @ ssList )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1231:[bind(A,$thf( sk2 @ sk12 ))]]) ).
thf(7586,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,169]) ).
thf(7587,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ssItem ) ),
inference(simp,[status(thm)],[7586]) ).
thf(7588,plain,
( ( sk9 @ cyclefreeP )
| ( sk9 @ sk10 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[7587:[bind(A,$thf( sk9 ))]]) ).
thf(9423,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk13 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[113,172]) ).
thf(9424,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk13 @ ssList ) ),
inference(simp,[status(thm)],[9423]) ).
thf(9425,plain,
( ( sk8 @ cyclefreeP )
| ( sk8 @ sk13 @ ssList ) ),
inference(pattern_uni,[status(thm)],[9424:[bind(A,$thf( sk8 ))]]) ).
thf(40989,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ( sk5 = sk2 )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2226,40053]) ).
thf(40990,plain,
( ( sk1 != sk1 )
| ( sk5 = sk2 )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[40989]) ).
thf(40991,plain,
( ( sk5 = sk2 )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[40990:[]]) ).
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(216,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(217,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)],[216]) ).
thf(218,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ ( A @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[217]) ).
thf(220,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A != B ) ),
inference(lifteq,[status(thm)],[218]) ).
thf(221,plain,
! [A: $i] :
( ~ ( A @ ( A @ neq ) )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[220]) ).
thf(557,plain,
! [A: $i] :
( ( ( sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[114,221]) ).
thf(558,plain,
! [A: $i] :
( ( ( sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[557]) ).
thf(559,plain,
~ ( sk7 @ ( sk7 @ neq ) ),
inference(pattern_uni,[status(thm)],[558:[bind(A,$thf( sk7 ))]]) ).
thf(22146,plain,
( ( sk2 != sk2 )
| ~ ( sk2 @ ( sk1 @ neq ) )
| ~ ( sk5 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[21180,824]) ).
thf(22147,plain,
( ~ ( sk2 @ ( sk1 @ neq ) )
| ~ ( sk5 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[22146:[]]) ).
thf(43922,plain,
( ( ( sk5 @ ( nil @ segmentP ) )
!= ( sk5 @ ( nil @ segmentP ) ) )
| ~ ( sk2 @ ( sk1 @ neq ) )
| ~ $true
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[41550,22147]) ).
thf(43923,plain,
( ( ( sk5 @ ( nil @ segmentP ) )
!= ( sk5 @ ( nil @ segmentP ) ) )
| ~ ( sk2 @ ( sk1 @ neq ) )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[43922]) ).
thf(43924,plain,
( ~ ( sk2 @ ( sk1 @ neq ) )
| ( sk1 != nil ) ),
inference(pattern_uni,[status(thm)],[43923:[]]) ).
thf(11928,plain,
( ( ( sk43 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk42 != nil )
| ~ ( sk43 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,840]) ).
thf(11929,plain,
( ( ( sk43 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk42 != nil )
| ~ ( sk43 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[11928]) ).
thf(12018,plain,
( ( sk43 != sk1 )
| ( sk42 != nil )
| ~ ( sk43 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[11929]) ).
thf(8027,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk14 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[115,170]) ).
thf(8028,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk14 @ ssList ) ),
inference(simp,[status(thm)],[8027]) ).
thf(8029,plain,
( ( sk5 @ cyclefreeP )
| ( sk5 @ sk14 @ ssList ) ),
inference(pattern_uni,[status(thm)],[8028:[bind(A,$thf( sk5 ))]]) ).
thf(20342,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[113,194]) ).
thf(20343,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[20342]) ).
thf(20344,plain,
( ( nil @ ( sk8 @ app ) )
= sk8 ),
inference(pattern_uni,[status(thm)],[20343:[bind(A,$thf( sk8 ))]]) ).
thf(9328,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk13 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[115,172]) ).
thf(9329,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk13 @ ssList ) ),
inference(simp,[status(thm)],[9328]) ).
thf(9330,plain,
( ( sk5 @ cyclefreeP )
| ( sk5 @ sk13 @ ssList ) ),
inference(pattern_uni,[status(thm)],[9329:[bind(A,$thf( sk5 ))]]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax61) ).
thf(376,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(1417,plain,
( ( sk1 != sk1 )
| ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[950,818]) ).
thf(1418,plain,
( ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1417:[]]) ).
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(485,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(39694,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[113,225]) ).
thf(39695,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[39694]) ).
thf(39696,plain,
( ( sk8 @ ( nil @ app ) )
= sk8 ),
inference(pattern_uni,[status(thm)],[39695:[bind(A,$thf( sk8 ))]]) ).
thf(45493,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk22 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[113,234]) ).
thf(45494,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk22 @ ssList ) ),
inference(simp,[status(thm)],[45493]) ).
thf(45495,plain,
( ( sk8 @ strictorderedP )
| ( sk8 @ sk22 @ ssList ) ),
inference(pattern_uni,[status(thm)],[45494:[bind(A,$thf( sk8 ))]]) ).
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(480,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) @ tl )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(28,axiom,
~ ( nil @ singletonP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).
thf(210,plain,
~ ( nil @ singletonP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(211,plain,
~ ( nil @ singletonP ),
inference(polarity_switch,[status(thm)],[210]) ).
thf(40900,plain,
( ( sk5 != sk5 )
| ~ ( sk5 @ ( sk2 @ neq ) )
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[40053,815]) ).
thf(40901,plain,
( ~ ( sk5 @ ( sk2 @ neq ) )
| ( sk1 != nil ) ),
inference(pattern_uni,[status(thm)],[40900:[]]) ).
thf(41328,plain,
( ( sk2 != sk2 )
| ~ ( sk5 @ ( nil @ neq ) )
| ( sk1 != nil )
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[563,40901]) ).
thf(41329,plain,
( ( sk2 != sk2 )
| ~ ( sk5 @ ( nil @ neq ) )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[41328]) ).
thf(41330,plain,
( ~ ( sk5 @ ( nil @ neq ) )
| ( sk1 != nil ) ),
inference(pattern_uni,[status(thm)],[41329:[]]) ).
thf(41702,plain,
( ( sk1 != sk1 )
| ~ ( sk5 @ ( nil @ neq ) )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2226,41330]) ).
thf(41703,plain,
( ( sk1 != sk1 )
| ~ ( sk5 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[41702]) ).
thf(41704,plain,
( ~ ( sk5 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[41703:[]]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax57) ).
thf(253,plain,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(14406,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk18 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,185]) ).
thf(14407,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk18 @ ssList ) ),
inference(simp,[status(thm)],[14406]) ).
thf(14408,plain,
( ( sk9 @ strictorderP )
| ( sk9 @ sk18 @ ssList ) ),
inference(pattern_uni,[status(thm)],[14407:[bind(A,$thf( sk9 ))]]) ).
thf(43929,plain,
( ( ( sk5 @ ( nil @ segmentP ) )
!= ( sk5 @ ( nil @ segmentP ) ) )
| ~ $true
| ( sk5 = nil )
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[41550,2138]) ).
thf(43930,plain,
( ( ( sk5 @ ( nil @ segmentP ) )
!= ( sk5 @ ( nil @ segmentP ) ) )
| ( sk5 = nil )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[43929]) ).
thf(43931,plain,
( ( sk5 = nil )
| ( sk1 != nil ) ),
inference(pattern_uni,[status(thm)],[43930:[]]) ).
thf(44809,plain,
( ( sk1 != sk1 )
| ( sk5 = nil )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2226,43931]) ).
thf(44810,plain,
( ( sk1 != sk1 )
| ( sk5 = nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[44809]) ).
thf(44811,plain,
( ( sk5 = nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[44810:[]]) ).
thf(7556,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[113,169]) ).
thf(7557,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ssItem ) ),
inference(simp,[status(thm)],[7556]) ).
thf(7558,plain,
( ( sk8 @ cyclefreeP )
| ( sk8 @ sk10 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[7557:[bind(A,$thf( sk8 ))]]) ).
thf(7924,plain,
! [A: $i] :
( ( ( sk8 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk8 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7558,242]) ).
thf(7925,plain,
! [A: $i] :
( ( ( sk8 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk8 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7924]) ).
thf(7926,plain,
( ~ ( sk8 @ sk10 @ ( nil @ memberP ) )
| ( sk8 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7925:[bind(A,$thf( sk8 @ sk10 ))]]) ).
thf(91,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49) ).
thf(514,plain,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(23910,plain,
( ( sk2 != sk2 )
| ( sk2 @ ( nil @ segmentP ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[994,23530]) ).
thf(23911,plain,
( ( sk2 @ ( nil @ segmentP ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[23910:[]]) ).
thf(38267,plain,
( ( ( sk2 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk2 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[736,23911]) ).
thf(38268,plain,
( ( ( sk2 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk2 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[38267]) ).
thf(38352,plain,
( ( sk2 != nil )
| ( nil != nil )
| ( sk2 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[38268]) ).
thf(38387,plain,
( ( sk2 != nil )
| ( sk2 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[38352]) ).
thf(146,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ( nil != A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[144]) ).
thf(148,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[146]) ).
thf(149,plain,
( ( nil @ ( nil @ segmentP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[148]) ).
thf(737,plain,
( ( nil @ ( nil @ segmentP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[149,354]) ).
thf(738,plain,
nil @ ( nil @ segmentP ),
inference(simp,[status(thm)],[737]) ).
thf(23906,plain,
( ( sk2 != sk2 )
| ( nil @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2363,23530]) ).
thf(23907,plain,
( ( nil @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[23906:[]]) ).
thf(32853,plain,
( ( ( sk2 @ ( nil @ segmentP ) )
!= ( nil @ ( nil @ segmentP ) ) )
| ( nil @ ( sk2 @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[738,23907]) ).
thf(32854,plain,
( ( ( sk2 @ ( nil @ segmentP ) )
!= ( nil @ ( nil @ segmentP ) ) )
| ( nil @ ( sk2 @ segmentP ) ) ),
inference(simp,[status(thm)],[32853]) ).
thf(32930,plain,
( ( sk2 != nil )
| ( nil != nil )
| ( nil @ ( sk2 @ segmentP ) ) ),
inference(simp,[status(thm)],[32854]) ).
thf(32976,plain,
( ( sk2 != nil )
| ( nil @ ( sk2 @ segmentP ) ) ),
inference(simp,[status(thm)],[32930]) ).
thf(40902,plain,
( ( sk5 != sk5 )
| ~ ( sk2 @ ( sk5 @ neq ) )
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[40053,815]) ).
thf(40903,plain,
( ~ ( sk2 @ ( sk5 @ neq ) )
| ( sk1 != nil ) ),
inference(pattern_uni,[status(thm)],[40902:[]]) ).
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(243,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(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(428,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(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(507,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(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(204,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(205,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ lt ) )
| ( A = B )
| ~ ( B @ ( A @ leq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[204]) ).
thf(206,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ lt ) )
| ~ ( B @ ( A @ leq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A = B ) ),
inference(lifteq,[status(thm)],[205]) ).
thf(402,plain,
sk43 @ ssItem,
inference(cnfConj,[status(thm)],[400]) ).
thf(203,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[202]) ).
thf(24587,plain,
! [A: $i] :
( ( ( sk43 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[402,203]) ).
thf(24588,plain,
! [A: $i] :
( ( ( sk43 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[24587]) ).
thf(24589,plain,
nil @ ( sk43 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[24588:[bind(A,$thf( sk43 ))]]) ).
thf(40942,plain,
( ( sk5 != sk5 )
| ( sk2 @ ( sk5 @ segmentP ) )
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[40053,23435]) ).
thf(40943,plain,
( ( sk2 @ ( sk5 @ segmentP ) )
| ( sk1 != nil ) ),
inference(pattern_uni,[status(thm)],[40942:[]]) ).
thf(8772,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[115,171]) ).
thf(8773,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssItem ) ),
inference(simp,[status(thm)],[8772]) ).
thf(8774,plain,
( ( sk5 @ cyclefreeP )
| ( sk5 @ sk11 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[8773:[bind(A,$thf( sk5 ))]]) ).
thf(235,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk20 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[229]) ).
thf(46619,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk20 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[115,235]) ).
thf(46620,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk20 @ ssItem ) ),
inference(simp,[status(thm)],[46619]) ).
thf(46621,plain,
( ( sk5 @ strictorderedP )
| ( sk5 @ sk20 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[46620:[bind(A,$thf( sk5 ))]]) ).
thf(401,plain,
sk42 @ ssItem,
inference(cnfConj,[status(thm)],[400]) ).
thf(632,plain,
! [A: $i] :
( ( ( sk42 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[401,221]) ).
thf(633,plain,
! [A: $i] :
( ( ( sk42 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[632]) ).
thf(634,plain,
~ ( sk42 @ ( sk42 @ neq ) ),
inference(pattern_uni,[status(thm)],[633:[bind(A,$thf( sk42 ))]]) ).
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(527,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(14251,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk18 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,185]) ).
thf(14252,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk18 @ ssList ) ),
inference(simp,[status(thm)],[14251]) ).
thf(14253,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk18 @ ssList ) ),
inference(pattern_uni,[status(thm)],[14252:[bind(A,$thf( sk1 ))]]) ).
thf(233,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk21 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[229]) ).
thf(101,plain,
( ( sk9 @ ( nil @ ( sk7 @ cons ) @ ( nil @ ( sk6 @ cons ) @ ( sk8 @ app ) @ app ) @ app ) )
= sk1 ),
inference(cnfConj,[status(thm)],[99]) ).
thf(117,plain,
( ( sk9 @ ( nil @ ( sk7 @ cons ) @ ( nil @ ( sk6 @ cons ) @ ( sk8 @ app ) @ app ) @ app ) )
= sk1 ),
inference(lifteq,[status(thm)],[101]) ).
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(512,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(7743,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7524,127]) ).
thf(7744,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7743]) ).
thf(7745,plain,
( ( nil @ ( sk1 @ sk10 @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7744:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(15422,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk19 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[113,186]) ).
thf(15423,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk19 @ ssList ) ),
inference(simp,[status(thm)],[15422]) ).
thf(15424,plain,
( ( sk8 @ strictorderP )
| ( sk8 @ sk19 @ ssList ) ),
inference(pattern_uni,[status(thm)],[15423:[bind(A,$thf( sk8 ))]]) ).
thf(13047,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk17 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,183]) ).
thf(13048,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk17 @ ssList ) ),
inference(simp,[status(thm)],[13047]) ).
thf(13049,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk17 @ ssList ) ),
inference(pattern_uni,[status(thm)],[13048:[bind(A,$thf( sk1 ))]]) ).
thf(168,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk10 @ ( A @ sk11 @ leq ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[163]) ).
thf(7267,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ( A @ sk11 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,168]) ).
thf(7268,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ( A @ sk11 @ leq ) ) ),
inference(simp,[status(thm)],[7267]) ).
thf(7269,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk10 @ ( sk1 @ sk11 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[7268:[bind(A,$thf( sk1 ))]]) ).
thf(1309,plain,
! [A: $i] :
( ( ( sk9 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssList )
| ~ $true
| ( sk9 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[782,165]) ).
thf(1310,plain,
! [A: $i] :
( ( ( sk9 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssList )
| ( sk9 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1309]) ).
thf(1311,plain,
( ( sk9 @ sk12 @ cyclefreeP )
| ( sk9 @ sk12 @ sk12 @ ssList )
| ( sk9 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1310:[bind(A,$thf( sk9 @ sk12 ))]]) ).
thf(8840,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,171]) ).
thf(8841,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssItem ) ),
inference(simp,[status(thm)],[8840]) ).
thf(8842,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk11 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[8841:[bind(A,$thf( sk2 ))]]) ).
thf(7997,plain,
! [A: $i] :
( ( ( sk9 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk9 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7588,127]) ).
thf(7998,plain,
! [A: $i] :
( ( ( sk9 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk9 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7997]) ).
thf(7999,plain,
( ( nil @ ( sk9 @ sk10 @ cons ) @ strictorderedP )
| ( sk9 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7998:[bind(A,$thf( sk9 @ sk10 ))]]) ).
thf(1385,plain,
( ( sk1 != sk1 )
| ~ ( nil @ ( sk2 @ neq ) )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[950,838]) ).
thf(1386,plain,
( ( sk1 != sk1 )
| ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1385]) ).
thf(1387,plain,
( ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1386:[]]) ).
thf(22148,plain,
( ( sk2 != sk2 )
| ~ ( sk1 @ ( sk2 @ neq ) )
| ~ ( sk5 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[21180,824]) ).
thf(22149,plain,
( ~ ( sk1 @ ( sk2 @ neq ) )
| ~ ( sk5 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[22148:[]]) ).
thf(43874,plain,
( ( ( sk5 @ ( nil @ segmentP ) )
!= ( sk5 @ ( nil @ segmentP ) ) )
| ~ ( sk1 @ ( sk2 @ neq ) )
| ~ $true
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[41550,22149]) ).
thf(43875,plain,
( ( ( sk5 @ ( nil @ segmentP ) )
!= ( sk5 @ ( nil @ segmentP ) ) )
| ~ ( sk1 @ ( sk2 @ neq ) )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[43874]) ).
thf(43876,plain,
( ~ ( sk1 @ ( sk2 @ neq ) )
| ( sk1 != nil ) ),
inference(pattern_uni,[status(thm)],[43875:[]]) ).
thf(23912,plain,
( ( sk2 != sk2 )
| ( nil @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[994,23530]) ).
thf(23913,plain,
( ( nil @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[23912:[]]) ).
thf(23622,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,201]) ).
thf(23623,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[23622]) ).
thf(23624,plain,
sk9 @ ( sk9 @ segmentP ),
inference(pattern_uni,[status(thm)],[23623:[bind(A,$thf( sk9 ))]]) ).
thf(23724,plain,
( ( sk5 != sk5 )
| ( nil @ ( sk5 @ segmentP ) )
| ~ ( sk5 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[921,23435]) ).
thf(23725,plain,
( ( nil @ ( sk5 @ segmentP ) )
| ~ ( sk5 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[23724:[]]) ).
thf(29334,plain,
( ( ( sk5 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( nil @ ( sk5 @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[736,23725]) ).
thf(29335,plain,
( ( ( sk5 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( nil @ ( sk5 @ segmentP ) ) ),
inference(simp,[status(thm)],[29334]) ).
thf(29396,plain,
( ( sk5 != nil )
| ( nil != nil )
| ( nil @ ( sk5 @ segmentP ) ) ),
inference(simp,[status(thm)],[29335]) ).
thf(29413,plain,
( ( sk5 != nil )
| ( nil @ ( sk5 @ segmentP ) ) ),
inference(simp,[status(thm)],[29396]) ).
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(275,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(8,axiom,
nil @ totalorderedP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax66) ).
thf(137,plain,
nil @ totalorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
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(467,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(249,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ frontsegP ) )
| ( ( C @ ( B @ app ) )
!= A )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[246]) ).
thf(251,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ frontsegP ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( C @ ( B @ app ) )
!= A ) ),
inference(lifteq,[status(thm)],[249]) ).
thf(252,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ app ) @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ( A @ app ) @ ssList ) ),
inference(simp,[status(thm)],[251]) ).
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(197,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(4978,plain,
( ( ( sk2 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( sk2 @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[736,1441]) ).
thf(4979,plain,
( ( ( sk2 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[4978]) ).
thf(4987,plain,
( ( sk2 != nil )
| ( nil != nil )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[4979]) ).
thf(4994,plain,
( ( sk2 != nil )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[4987]) ).
thf(48783,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk23 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,237]) ).
thf(48784,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk23 @ ssList ) ),
inference(simp,[status(thm)],[48783]) ).
thf(48785,plain,
( ( sk9 @ strictorderedP )
| ( sk9 @ sk23 @ ssList ) ),
inference(pattern_uni,[status(thm)],[48784:[bind(A,$thf( sk9 ))]]) ).
thf(9299,plain,
! [A: $i] :
( ( ( sk9 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk9 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[8881,242]) ).
thf(9300,plain,
! [A: $i] :
( ( ( sk9 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk9 @ cyclefreeP ) ),
inference(simp,[status(thm)],[9299]) ).
thf(9301,plain,
( ~ ( sk9 @ sk11 @ ( nil @ memberP ) )
| ( sk9 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[9300:[bind(A,$thf( sk9 @ sk11 ))]]) ).
thf(23696,plain,
( ( ( sk5 @ ( sk5 @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ( sk2 = nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23435,2740]) ).
thf(23697,plain,
( ( ( sk5 @ ( sk5 @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ( sk2 = nil ) ),
inference(simp,[status(thm)],[23696]) ).
thf(23763,plain,
( ( sk5 != sk1 )
| ( sk5 != nil )
| ( sk2 = nil ) ),
inference(simp,[status(thm)],[23697]) ).
thf(44292,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk21 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[115,233]) ).
thf(44293,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk21 @ ssItem ) ),
inference(simp,[status(thm)],[44292]) ).
thf(44294,plain,
( ( sk5 @ strictorderedP )
| ( sk5 @ sk21 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[44293:[bind(A,$thf( sk5 ))]]) ).
thf(42421,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk24 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[115,232]) ).
thf(42422,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk24 @ ssList ) ),
inference(simp,[status(thm)],[42421]) ).
thf(42423,plain,
( ( sk5 @ strictorderedP )
| ( sk5 @ sk24 @ ssList ) ),
inference(pattern_uni,[status(thm)],[42422:[bind(A,$thf( sk5 ))]]) ).
thf(44181,plain,
( ( sk2 != sk2 )
| ( sk5 @ ( sk1 @ segmentP ) )
| ( sk1 != nil )
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[43907,40941]) ).
thf(44182,plain,
( ( sk2 != sk2 )
| ( sk5 @ ( sk1 @ segmentP ) )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[44181]) ).
thf(44183,plain,
( ( sk5 @ ( sk1 @ segmentP ) )
| ( sk1 != nil ) ),
inference(pattern_uni,[status(thm)],[44182:[]]) ).
thf(102,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ lt ) )
| ( ( nil @ ( C @ cons ) @ ( D @ app ) )
!= sk3 )
| ~ ( D @ ssList )
| ~ ( C @ ssItem )
| ( ( B @ ( nil @ ( A @ cons ) @ app ) )
!= sk5 )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ lt ) )
| ~ ( D @ ssList )
| ~ ( C @ ssItem )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( nil @ ( C @ cons ) @ ( D @ app ) )
!= sk3 )
| ( ( B @ ( nil @ ( A @ cons ) @ app ) )
!= sk5 ) ),
inference(lifteq,[status(thm)],[102]) ).
thf(566,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ lt ) )
| ~ ( D @ ssList )
| ~ ( C @ ssItem )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( nil @ ( C @ cons ) @ ( D @ app ) )
!= sk1 )
| ( ( B @ ( nil @ ( A @ cons ) @ app ) )
!= sk5 ) ),
inference(rewrite,[status(thm)],[119,121]) ).
thf(2420,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[113,147]) ).
thf(2421,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[2420]) ).
thf(2422,plain,
( ~ ( sk8 @ ( nil @ segmentP ) )
| ( sk8 = nil ) ),
inference(pattern_uni,[status(thm)],[2421:[bind(A,$thf( sk8 ))]]) ).
thf(825,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[113,338]) ).
thf(826,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[825]) ).
thf(827,plain,
~ ( sk8 @ ( sk8 @ neq ) ),
inference(pattern_uni,[status(thm)],[826:[bind(A,$thf( sk8 ))]]) ).
thf(2872,plain,
( ( sk8 != sk8 )
| ~ ( sk8 @ ( nil @ neq ) )
| ~ ( sk8 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2422,827]) ).
thf(2873,plain,
( ~ ( sk8 @ ( nil @ neq ) )
| ~ ( sk8 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[2872:[]]) ).
thf(7553,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,169]) ).
thf(7554,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ssItem ) ),
inference(simp,[status(thm)],[7553]) ).
thf(7555,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk10 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[7554:[bind(A,$thf( sk2 ))]]) ).
thf(11995,plain,
( ( ( sk43 @ ssList )
!= ( sk9 @ ssList ) )
| ( sk42 != nil )
| ~ ( sk43 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,840]) ).
thf(11996,plain,
( ( ( sk43 @ ssList )
!= ( sk9 @ ssList ) )
| ( sk42 != nil )
| ~ ( sk43 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[11995]) ).
thf(12025,plain,
( ( sk43 != sk9 )
| ( sk42 != nil )
| ~ ( sk43 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[11996]) ).
thf(7921,plain,
! [A: $i] :
( ( ( sk8 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk8 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7558,127]) ).
thf(7922,plain,
! [A: $i] :
( ( ( sk8 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk8 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7921]) ).
thf(7923,plain,
( ( nil @ ( sk8 @ sk10 @ cons ) @ strictorderedP )
| ( sk8 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7922:[bind(A,$thf( sk8 @ sk10 ))]]) ).
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(519,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(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(154,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(155,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ cons ) )
= ( A @ ( nil @ ( B @ cons ) @ app ) ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[154]) ).
thf(156,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( ( A @ ( B @ cons ) )
= ( A @ ( nil @ ( B @ cons ) @ app ) ) ) ),
inference(lifteq,[status(thm)],[155]) ).
thf(14300,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk18 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,185]) ).
thf(14301,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk18 @ ssList ) ),
inference(simp,[status(thm)],[14300]) ).
thf(14302,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk18 @ ssList ) ),
inference(pattern_uni,[status(thm)],[14301:[bind(A,$thf( sk2 ))]]) ).
thf(44820,plain,
( ( sk1 != sk1 )
| ( sk5 = nil )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[950,43931]) ).
thf(44821,plain,
( ( sk1 != sk1 )
| ( sk5 = nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[44820]) ).
thf(44822,plain,
( ( sk5 = nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[44821:[]]) ).
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(420,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(85,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ geq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax89) ).
thf(499,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(1338,plain,
( ( sk5 != sk5 )
| ~ ( nil @ ( sk5 @ neq ) )
| ~ ( sk5 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[921,815]) ).
thf(1339,plain,
( ~ ( nil @ ( sk5 @ neq ) )
| ~ ( sk5 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1338:[]]) ).
thf(1928,plain,
( ( ( sk5 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( sk5 @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[736,1339]) ).
thf(1929,plain,
( ( ( sk5 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( sk5 @ neq ) ) ),
inference(simp,[status(thm)],[1928]) ).
thf(1933,plain,
( ( sk5 != nil )
| ( nil != nil )
| ~ ( nil @ ( sk5 @ neq ) ) ),
inference(simp,[status(thm)],[1929]) ).
thf(1936,plain,
( ( sk5 != nil )
| ~ ( nil @ ( sk5 @ neq ) ) ),
inference(simp,[status(thm)],[1933]) ).
thf(20405,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[111,194]) ).
thf(20406,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[20405]) ).
thf(20407,plain,
( ( nil @ ( sk9 @ app ) )
= sk9 ),
inference(pattern_uni,[status(thm)],[20406:[bind(A,$thf( sk9 ))]]) ).
thf(21066,plain,
( ( ( nil @ ( sk9 @ app ) )
!= ( sk5 @ ( sk1 @ app ) ) )
| ( sk9 = sk2 ) ),
inference(paramod_ordered,[status(thm)],[20407,660]) ).
thf(21123,plain,
( ( sk5 != nil )
| ( sk9 != sk1 )
| ( sk9 = sk2 ) ),
inference(simp,[status(thm)],[21066]) ).
thf(13114,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk17 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[113,183]) ).
thf(13115,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk17 @ ssList ) ),
inference(simp,[status(thm)],[13114]) ).
thf(13116,plain,
( ( sk8 @ strictorderP )
| ( sk8 @ sk17 @ ssList ) ),
inference(pattern_uni,[status(thm)],[13115:[bind(A,$thf( sk8 ))]]) ).
thf(41336,plain,
( ( sk1 != sk1 )
| ~ ( sk5 @ ( sk2 @ neq ) )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[950,40901]) ).
thf(41337,plain,
( ( sk1 != sk1 )
| ~ ( sk5 @ ( sk2 @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[41336]) ).
thf(41338,plain,
( ~ ( sk5 @ ( sk2 @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[41337:[]]) ).
thf(23852,plain,
( ( sk1 != sk1 )
| ( nil @ ( sk1 @ segmentP ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2226,23488]) ).
thf(23853,plain,
( ( nil @ ( sk1 @ segmentP ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[23852:[]]) ).
thf(44520,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk21 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,233]) ).
thf(44521,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk21 @ ssItem ) ),
inference(simp,[status(thm)],[44520]) ).
thf(44522,plain,
( ( sk9 @ strictorderedP )
| ( sk9 @ sk21 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[44521:[bind(A,$thf( sk9 ))]]) ).
thf(751,plain,
! [A: $i] :
( ( ( sk42 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[401,227]) ).
thf(752,plain,
! [A: $i] :
( ( ( sk42 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[751]) ).
thf(753,plain,
~ ( sk42 @ ( sk42 @ lt ) ),
inference(pattern_uni,[status(thm)],[752:[bind(A,$thf( sk42 ))]]) ).
thf(6640,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ( A @ sk10 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,164]) ).
thf(6641,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ( A @ sk10 @ leq ) ) ),
inference(simp,[status(thm)],[6640]) ).
thf(6642,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk11 @ ( sk1 @ sk10 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[6641:[bind(A,$thf( sk1 ))]]) ).
thf(835,plain,
( ( sk2 != sk2 )
| ~ ( sk2 @ ( nil @ neq ) )
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[563,824]) ).
thf(836,plain,
( ~ ( sk2 @ ( nil @ neq ) )
| ( sk1 != nil ) ),
inference(pattern_uni,[status(thm)],[835:[]]) ).
thf(1412,plain,
( ( sk1 != sk1 )
| ~ ( sk2 @ ( nil @ neq ) )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[950,836]) ).
thf(1413,plain,
( ( sk1 != sk1 )
| ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1412]) ).
thf(1414,plain,
( ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1413:[]]) ).
thf(8966,plain,
! [A: $i] :
( ( ( sk5 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk5 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[8774,242]) ).
thf(8967,plain,
! [A: $i] :
( ( ( sk5 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk5 @ cyclefreeP ) ),
inference(simp,[status(thm)],[8966]) ).
thf(8968,plain,
( ~ ( sk5 @ sk11 @ ( nil @ memberP ) )
| ( sk5 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[8967:[bind(A,$thf( sk5 @ sk11 ))]]) ).
thf(11970,plain,
( ( ( sk43 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk42 != nil )
| ~ $true
| ~ ( sk43 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[736,840]) ).
thf(11971,plain,
( ( ( sk43 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk42 != nil )
| ~ ( sk43 @ ssList ) ),
inference(simp,[status(thm)],[11970]) ).
thf(12016,plain,
( ( sk43 != nil )
| ( nil != nil )
| ( sk42 != nil )
| ~ ( sk43 @ ssList ) ),
inference(simp,[status(thm)],[11971]) ).
thf(12044,plain,
( ( sk43 != nil )
| ( sk42 != nil )
| ~ ( sk43 @ ssList ) ),
inference(simp,[status(thm)],[12016]) ).
thf(12142,plain,
( ( ( sk43 @ ssList )
!= ( nil @ ssList ) )
| ( sk43 != nil )
| ( sk42 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[354,12044]) ).
thf(12143,plain,
( ( ( sk43 @ ssList )
!= ( nil @ ssList ) )
| ( sk43 != nil )
| ( sk42 != nil ) ),
inference(simp,[status(thm)],[12142]) ).
thf(12148,plain,
( ( sk43 != nil )
| ( sk43 != nil )
| ( sk42 != nil ) ),
inference(simp,[status(thm)],[12143]) ).
thf(12183,plain,
( ( sk43 != nil )
| ( sk42 != nil ) ),
inference(simp,[status(thm)],[12148]) ).
thf(12452,plain,
! [A: $i] :
( ( A != sk42 )
| ( sk43 != nil )
| ( nil != nil )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[132,12183]) ).
thf(12453,plain,
! [A: $i] :
( ( A != sk42 )
| ( sk43 != nil )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[12452]) ).
thf(12454,plain,
( ( sk43 != nil )
| ~ ( sk42 @ ( nil @ frontsegP ) )
| ~ ( sk42 @ ssList ) ),
inference(pattern_uni,[status(thm)],[12453:[bind(A,$thf( sk42 ))]]) ).
thf(7311,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ( A @ sk11 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,168]) ).
thf(7312,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ( A @ sk11 @ leq ) ) ),
inference(simp,[status(thm)],[7311]) ).
thf(7313,plain,
( ( sk9 @ cyclefreeP )
| ( sk9 @ sk10 @ ( sk9 @ sk11 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[7312:[bind(A,$thf( sk9 ))]]) ).
thf(545,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,242]) ).
thf(546,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[545]) ).
thf(547,plain,
~ ( sk6 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[546:[bind(A,$thf( sk6 ))]]) ).
thf(1658,plain,
( ( sk8 != sk8 )
| ~ ( sk8 @ ( nil @ neq ) )
| ~ ( sk8 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1031,827]) ).
thf(1659,plain,
( ~ ( sk8 @ ( nil @ neq ) )
| ~ ( sk8 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1658:[]]) ).
thf(1438,plain,
( ( sk2 != sk2 )
| ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[994,824]) ).
thf(1439,plain,
( ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1438:[]]) ).
thf(4845,plain,
( ( ( sk2 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk2 @ ( nil @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[736,1439]) ).
thf(4846,plain,
( ( ( sk2 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk2 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[4845]) ).
thf(4854,plain,
( ( sk2 != nil )
| ( nil != nil )
| ~ ( sk2 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[4846]) ).
thf(4861,plain,
( ( sk2 != nil )
| ~ ( sk2 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[4854]) ).
thf(16515,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk15 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[113,187]) ).
thf(16516,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk15 @ ssItem ) ),
inference(simp,[status(thm)],[16515]) ).
thf(16517,plain,
( ( sk8 @ strictorderP )
| ( sk8 @ sk15 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[16516:[bind(A,$thf( sk8 ))]]) ).
thf(17031,plain,
! [A: $i] :
( ( ( sk8 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk8 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[16517,242]) ).
thf(17032,plain,
! [A: $i] :
( ( ( sk8 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk8 @ strictorderP ) ),
inference(simp,[status(thm)],[17031]) ).
thf(17033,plain,
( ~ ( sk8 @ sk15 @ ( nil @ memberP ) )
| ( sk8 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[17032:[bind(A,$thf( sk8 @ sk15 ))]]) ).
thf(8098,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk14 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,170]) ).
thf(8099,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk14 @ ssList ) ),
inference(simp,[status(thm)],[8098]) ).
thf(8100,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk14 @ ssList ) ),
inference(pattern_uni,[status(thm)],[8099:[bind(A,$thf( sk2 ))]]) ).
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(212,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(23722,plain,
( ( sk5 != sk5 )
| ( sk5 @ ( nil @ segmentP ) )
| ~ ( sk5 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[921,23435]) ).
thf(23723,plain,
( ( sk5 @ ( nil @ segmentP ) )
| ~ ( sk5 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[23722:[]]) ).
thf(29007,plain,
( ( ( sk5 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk5 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[736,23723]) ).
thf(29008,plain,
( ( ( sk5 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk5 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[29007]) ).
thf(29062,plain,
( ( sk5 != nil )
| ( nil != nil )
| ( sk5 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[29008]) ).
thf(29077,plain,
( ( sk5 != nil )
| ( sk5 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[29062]) ).
thf(23974,plain,
( ( sk2 != sk2 )
| ( sk2 @ ( sk1 @ segmentP ) )
| ~ ( sk5 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[21180,23530]) ).
thf(23975,plain,
( ( sk2 @ ( sk1 @ segmentP ) )
| ~ ( sk5 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[23974:[]]) ).
thf(61263,plain,
( ( ( sk5 @ ( nil @ segmentP ) )
!= ( sk5 @ ( nil @ segmentP ) ) )
| ( sk2 @ ( sk1 @ segmentP ) )
| ~ $true
| ( sk5 != nil ) ),
inference(paramod_ordered,[status(thm)],[29077,23975]) ).
thf(61264,plain,
( ( ( sk5 @ ( nil @ segmentP ) )
!= ( sk5 @ ( nil @ segmentP ) ) )
| ( sk2 @ ( sk1 @ segmentP ) )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[61263]) ).
thf(61265,plain,
( ( sk2 @ ( sk1 @ segmentP ) )
| ( sk5 != nil ) ),
inference(pattern_uni,[status(thm)],[61264:[]]) ).
thf(5224,plain,
( ( ( sk8 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk8 @ ( nil @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[736,1659]) ).
thf(5225,plain,
( ( ( sk8 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk8 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[5224]) ).
thf(5229,plain,
( ( sk8 != nil )
| ( nil != nil )
| ~ ( sk8 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[5225]) ).
thf(5234,plain,
( ( sk8 != nil )
| ~ ( sk8 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[5229]) ).
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(457,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(2812,plain,
( ( sk2 != sk2 )
| ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2363,824]) ).
thf(2813,plain,
( ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[2812:[]]) ).
thf(41426,plain,
( ( sk1 != sk1 )
| ~ ( sk2 @ ( sk5 @ neq ) )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2226,40903]) ).
thf(41427,plain,
( ( sk1 != sk1 )
| ~ ( sk2 @ ( sk5 @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[41426]) ).
thf(41428,plain,
( ~ ( sk2 @ ( sk5 @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[41427:[]]) ).
thf(17375,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,188]) ).
thf(17376,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssItem ) ),
inference(simp,[status(thm)],[17375]) ).
thf(17377,plain,
( ( sk9 @ strictorderP )
| ( sk9 @ sk16 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[17376:[bind(A,$thf( sk9 ))]]) ).
thf(16393,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk15 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[115,187]) ).
thf(16394,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk15 @ ssItem ) ),
inference(simp,[status(thm)],[16393]) ).
thf(16395,plain,
( ( sk5 @ strictorderP )
| ( sk5 @ sk15 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[16394:[bind(A,$thf( sk5 ))]]) ).
thf(16688,plain,
! [A: $i] :
( ( ( sk5 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk5 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[16395,242]) ).
thf(16689,plain,
! [A: $i] :
( ( ( sk5 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk5 @ strictorderP ) ),
inference(simp,[status(thm)],[16688]) ).
thf(16690,plain,
( ~ ( sk5 @ sk15 @ ( nil @ memberP ) )
| ( sk5 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[16689:[bind(A,$thf( sk5 @ sk15 ))]]) ).
thf(46760,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk20 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[113,235]) ).
thf(46761,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk20 @ ssItem ) ),
inference(simp,[status(thm)],[46760]) ).
thf(46762,plain,
( ( sk8 @ strictorderedP )
| ( sk8 @ sk20 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[46761:[bind(A,$thf( sk8 ))]]) ).
thf(803,plain,
! [A: $i] :
( ( ( sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[114,127]) ).
thf(804,plain,
! [A: $i] :
( ( ( sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[803]) ).
thf(805,plain,
nil @ ( sk7 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[804:[bind(A,$thf( sk7 ))]]) ).
thf(655,plain,
! [A: $i] :
( ( ( sk43 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[402,242]) ).
thf(656,plain,
! [A: $i] :
( ( ( sk43 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[655]) ).
thf(657,plain,
~ ( sk43 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[656:[bind(A,$thf( sk43 ))]]) ).
thf(23962,plain,
( ( sk2 != sk2 )
| ( nil @ ( sk2 @ segmentP ) )
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[563,23530]) ).
thf(23963,plain,
( ( nil @ ( sk2 @ segmentP ) )
| ( sk1 != nil ) ),
inference(pattern_uni,[status(thm)],[23962:[]]) ).
thf(16503,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk15 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,187]) ).
thf(16504,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk15 @ ssItem ) ),
inference(simp,[status(thm)],[16503]) ).
thf(16505,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk15 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[16504:[bind(A,$thf( sk2 ))]]) ).
thf(16884,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[16505,242]) ).
thf(16885,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[16884]) ).
thf(16886,plain,
( ~ ( sk2 @ sk15 @ ( nil @ memberP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[16885:[bind(A,$thf( sk2 @ sk15 ))]]) ).
thf(95,axiom,
nil @ totalorderP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax62) ).
thf(530,plain,
nil @ totalorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(44415,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk21 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,233]) ).
thf(44416,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk21 @ ssItem ) ),
inference(simp,[status(thm)],[44415]) ).
thf(44417,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk21 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[44416:[bind(A,$thf( sk2 ))]]) ).
thf(244,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)],[243]) ).
thf(46853,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk20 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,235]) ).
thf(46854,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk20 @ ssItem ) ),
inference(simp,[status(thm)],[46853]) ).
thf(46855,plain,
( ( sk9 @ strictorderedP )
| ( sk9 @ sk20 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[46854:[bind(A,$thf( sk9 ))]]) ).
thf(748,plain,
! [A: $i] :
( ( ( sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[114,227]) ).
thf(749,plain,
! [A: $i] :
( ( ( sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[748]) ).
thf(750,plain,
~ ( sk7 @ ( sk7 @ lt ) ),
inference(pattern_uni,[status(thm)],[749:[bind(A,$thf( sk7 ))]]) ).
thf(8806,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,171]) ).
thf(8807,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssItem ) ),
inference(simp,[status(thm)],[8806]) ).
thf(8808,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk11 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[8807:[bind(A,$thf( sk1 ))]]) ).
thf(9038,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[8808,127]) ).
thf(9039,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[9038]) ).
thf(9040,plain,
( ( nil @ ( sk1 @ sk11 @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[9039:[bind(A,$thf( sk1 @ sk11 ))]]) ).
thf(20879,plain,
( ( ( nil @ ( sk8 @ app ) )
!= ( sk5 @ ( sk1 @ app ) ) )
| ( sk8 = sk2 ) ),
inference(paramod_ordered,[status(thm)],[660,20344]) ).
thf(20935,plain,
( ( sk5 != nil )
| ( sk8 != sk1 )
| ( sk8 = sk2 ) ),
inference(simp,[status(thm)],[20879]) ).
thf(1217,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[770,338]) ).
thf(1218,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1217]) ).
thf(1219,plain,
( ~ ( sk1 @ sk12 @ ( sk1 @ sk12 @ neq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1218:[bind(A,$thf( sk1 @ sk12 ))]]) ).
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(159,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(160,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)],[159]) ).
thf(161,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)],[160]) ).
thf(8110,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk14 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[113,170]) ).
thf(8111,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk14 @ ssList ) ),
inference(simp,[status(thm)],[8110]) ).
thf(8112,plain,
( ( sk8 @ cyclefreeP )
| ( sk8 @ sk14 @ ssList ) ),
inference(pattern_uni,[status(thm)],[8111:[bind(A,$thf( sk8 ))]]) ).
thf(11968,plain,
( ( ( sk43 @ ssList )
!= ( sk8 @ ssList ) )
| ( sk42 != nil )
| ~ ( sk43 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[113,840]) ).
thf(11969,plain,
( ( ( sk43 @ ssList )
!= ( sk8 @ ssList ) )
| ( sk42 != nil )
| ~ ( sk43 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[11968]) ).
thf(12028,plain,
( ( sk43 != sk8 )
| ( sk42 != nil )
| ~ ( sk43 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[11969]) ).
thf(560,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,221]) ).
thf(561,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[560]) ).
thf(562,plain,
~ ( sk6 @ ( sk6 @ neq ) ),
inference(pattern_uni,[status(thm)],[561:[bind(A,$thf( sk6 ))]]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( A @ ( B @ cons ) @ ssList ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
thf(176,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( A @ ( B @ cons ) @ ssList ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(68,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( ( A @ tl @ ( A @ hd @ cons ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax78) ).
thf(423,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( ( A @ tl @ ( A @ hd @ cons ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(24617,plain,
! [A: $i] :
( ( ( sk42 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[401,203]) ).
thf(24618,plain,
! [A: $i] :
( ( ( sk42 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[24617]) ).
thf(24619,plain,
nil @ ( sk42 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[24618:[bind(A,$thf( sk42 ))]]) ).
thf(9140,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[8842,242]) ).
thf(9141,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[9140]) ).
thf(9142,plain,
( ~ ( sk2 @ sk11 @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[9141:[bind(A,$thf( sk2 @ sk11 ))]]) ).
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(286,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(5860,plain,
( ( ( sk9 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( sk9 @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[736,1686]) ).
thf(5861,plain,
( ( ( sk9 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( sk9 @ neq ) ) ),
inference(simp,[status(thm)],[5860]) ).
thf(5872,plain,
( ( sk9 != nil )
| ( nil != nil )
| ~ ( nil @ ( sk9 @ neq ) ) ),
inference(simp,[status(thm)],[5861]) ).
thf(5876,plain,
( ( sk9 != nil )
| ~ ( nil @ ( sk9 @ neq ) ) ),
inference(simp,[status(thm)],[5872]) ).
thf(14324,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk18 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[113,185]) ).
thf(14325,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk18 @ ssList ) ),
inference(simp,[status(thm)],[14324]) ).
thf(14326,plain,
( ( sk8 @ strictorderP )
| ( sk8 @ sk18 @ ssList ) ),
inference(pattern_uni,[status(thm)],[14325:[bind(A,$thf( sk8 ))]]) ).
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(413,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(180,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)],[179]) ).
thf(190,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)],[180]) ).
thf(191,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)],[190]) ).
thf(45452,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk22 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,234]) ).
thf(45453,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk22 @ ssList ) ),
inference(simp,[status(thm)],[45452]) ).
thf(45454,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk22 @ ssList ) ),
inference(pattern_uni,[status(thm)],[45453:[bind(A,$thf( sk2 ))]]) ).
thf(84,axiom,
nil @ equalelemsP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax74) ).
thf(498,plain,
nil @ equalelemsP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(181,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ sk15 @ ( A @ sk16 @ lt ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[179]) ).
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(540,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(42616,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk24 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[113,232]) ).
thf(42617,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk24 @ ssList ) ),
inference(simp,[status(thm)],[42616]) ).
thf(42618,plain,
( ( sk8 @ strictorderedP )
| ( sk8 @ sk24 @ ssList ) ),
inference(pattern_uni,[status(thm)],[42617:[bind(A,$thf( sk8 ))]]) ).
thf(14191,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk18 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[115,185]) ).
thf(14192,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk18 @ ssList ) ),
inference(simp,[status(thm)],[14191]) ).
thf(14193,plain,
( ( sk5 @ strictorderP )
| ( sk5 @ sk18 @ ssList ) ),
inference(pattern_uni,[status(thm)],[14192:[bind(A,$thf( sk5 ))]]) ).
thf(230,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ sk21 @ ( A @ sk20 @ lt ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[229]) ).
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(207,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(208,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)],[207]) ).
thf(3037,plain,
( ( sk9 != sk9 )
| ~ ( sk9 @ ( nil @ neq ) )
| ~ ( sk9 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2599,830]) ).
thf(3038,plain,
( ~ ( sk9 @ ( nil @ neq ) )
| ~ ( sk9 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[3037:[]]) ).
thf(75,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ rearsegP ) )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax52) ).
thf(450,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(451,plain,
! [A: $i] :
( ( ( A @ ( nil @ rearsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) )
& ( ( nil = A )
| ~ ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[450]) ).
thf(453,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[451]) ).
thf(455,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[453]) ).
thf(456,plain,
( ( nil @ ( nil @ rearsegP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[455]) ).
thf(1143,plain,
( ( nil @ ( nil @ rearsegP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[456,354]) ).
thf(1144,plain,
nil @ ( nil @ rearsegP ),
inference(simp,[status(thm)],[1143]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ tl @ ssList ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
thf(303,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ tl @ ssList ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(41429,plain,
( ( sk1 != sk1 )
| ~ ( sk2 @ ( sk5 @ neq ) )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[950,40903]) ).
thf(41430,plain,
( ( sk1 != sk1 )
| ~ ( sk2 @ ( sk5 @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[41429]) ).
thf(41431,plain,
( ~ ( sk2 @ ( sk5 @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[41430:[]]) ).
thf(7290,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ( A @ sk11 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,168]) ).
thf(7291,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ( A @ sk11 @ leq ) ) ),
inference(simp,[status(thm)],[7290]) ).
thf(7292,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk10 @ ( sk2 @ sk11 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[7291:[bind(A,$thf( sk2 ))]]) ).
thf(2756,plain,
( ( sk1 != sk1 )
| ~ ( nil @ ( sk1 @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2226,818]) ).
thf(2757,plain,
( ~ ( nil @ ( sk1 @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[2756:[]]) ).
thf(231,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( ( A @ sk24 @ ( A @ sk21 @ cons ) @ ( A @ sk23 @ ( A @ sk20 @ cons ) @ ( A @ sk22 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[229]) ).
thf(240,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ( ( A @ sk24 @ ( A @ sk21 @ cons ) @ ( A @ sk23 @ ( A @ sk20 @ cons ) @ ( A @ sk22 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[231]) ).
thf(1660,plain,
( ( sk8 != sk8 )
| ~ ( nil @ ( sk8 @ neq ) )
| ~ ( sk8 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1031,827]) ).
thf(1661,plain,
( ~ ( nil @ ( sk8 @ neq ) )
| ~ ( sk8 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1660:[]]) ).
thf(5644,plain,
( ( ( sk8 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( sk8 @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[736,1661]) ).
thf(5645,plain,
( ( ( sk8 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( sk8 @ neq ) ) ),
inference(simp,[status(thm)],[5644]) ).
thf(5652,plain,
( ( sk8 != nil )
| ( nil != nil )
| ~ ( nil @ ( sk8 @ neq ) ) ),
inference(simp,[status(thm)],[5645]) ).
thf(5656,plain,
( ( sk8 != nil )
| ~ ( nil @ ( sk8 @ neq ) ) ),
inference(simp,[status(thm)],[5652]) ).
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(367,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(368,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)],[367]) ).
thf(371,plain,
! [B: $i,A: $i] :
( ( nil
= ( B @ ( A @ app ) ) )
| ( nil != A )
| ( nil != B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[368]) ).
thf(374,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
= nil )
| ( nil != A )
| ( nil != B ) ),
inference(lifteq,[status(thm)],[371]) ).
thf(375,plain,
( ~ ( nil @ ssList )
| ( ( nil @ ( nil @ app ) )
= nil ) ),
inference(simp,[status(thm)],[374]) ).
thf(4725,plain,
( ~ $true
| ( ( nil @ ( nil @ app ) )
= nil ) ),
inference(rewrite,[status(thm)],[375,354]) ).
thf(4726,plain,
( ( nil @ ( nil @ app ) )
= nil ),
inference(simp,[status(thm)],[4725]) ).
thf(78,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax42) ).
thf(462,plain,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(45292,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk22 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[115,234]) ).
thf(45293,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk22 @ ssList ) ),
inference(simp,[status(thm)],[45292]) ).
thf(45294,plain,
( ( sk5 @ strictorderedP )
| ( sk5 @ sk22 @ ssList ) ),
inference(pattern_uni,[status(thm)],[45293:[bind(A,$thf( sk5 ))]]) ).
thf(9405,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk13 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,172]) ).
thf(9406,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk13 @ ssList ) ),
inference(simp,[status(thm)],[9405]) ).
thf(9407,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk13 @ ssList ) ),
inference(pattern_uni,[status(thm)],[9406:[bind(A,$thf( sk2 ))]]) ).
thf(23682,plain,
( ( ( sk5 @ ( sk5 @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) )
| ~ $true
| ( sk2 = nil ) ),
inference(paramod_ordered,[status(thm)],[23435,2363]) ).
thf(23683,plain,
( ( ( sk5 @ ( sk5 @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) )
| ( sk2 = nil ) ),
inference(simp,[status(thm)],[23682]) ).
thf(23762,plain,
( ( sk5 != sk2 )
| ( sk5 != nil )
| ( sk2 = nil ) ),
inference(simp,[status(thm)],[23683]) ).
thf(100,plain,
sk3 @ strictorderedP,
inference(cnfConj,[status(thm)],[99]) ).
thf(552,plain,
sk1 @ strictorderedP,
inference(rewrite,[status(thm)],[100,121]) ).
thf(797,plain,
! [A: $i] :
( ( ( sk43 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[402,127]) ).
thf(798,plain,
! [A: $i] :
( ( ( sk43 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[797]) ).
thf(799,plain,
nil @ ( sk43 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[798:[bind(A,$thf( sk43 ))]]) ).
thf(23898,plain,
( ( sk2 != sk2 )
| ( sk2 @ ( nil @ segmentP ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1411,23530]) ).
thf(23899,plain,
( ( sk2 @ ( nil @ segmentP ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[23898:[]]) ).
thf(17912,plain,
! [A: $i] :
( ( ( sk9 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk9 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[17377,242]) ).
thf(17913,plain,
! [A: $i] :
( ( ( sk9 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk9 @ strictorderP ) ),
inference(simp,[status(thm)],[17912]) ).
thf(17914,plain,
( ~ ( sk9 @ sk16 @ ( nil @ memberP ) )
| ( sk9 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[17913:[bind(A,$thf( sk9 @ sk16 ))]]) ).
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(483,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(45610,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk22 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,234]) ).
thf(45611,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk22 @ ssList ) ),
inference(simp,[status(thm)],[45610]) ).
thf(45612,plain,
( ( sk9 @ strictorderedP )
| ( sk9 @ sk22 @ ssList ) ),
inference(pattern_uni,[status(thm)],[45611:[bind(A,$thf( sk9 ))]]) ).
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(330,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(1243,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[776,338]) ).
thf(1244,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1243]) ).
thf(1245,plain,
( ~ ( sk2 @ sk12 @ ( sk2 @ sk12 @ neq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1244:[bind(A,$thf( sk2 @ sk12 ))]]) ).
thf(41705,plain,
( ( sk1 != sk1 )
| ~ ( sk5 @ ( nil @ neq ) )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[950,41330]) ).
thf(41706,plain,
( ( sk1 != sk1 )
| ~ ( sk5 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[41705]) ).
thf(41707,plain,
( ~ ( sk5 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[41706:[]]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax51) ).
thf(306,plain,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(72,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax31) ).
thf(438,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(48453,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk23 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[115,237]) ).
thf(48454,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk23 @ ssList ) ),
inference(simp,[status(thm)],[48453]) ).
thf(48455,plain,
( ( sk5 @ strictorderedP )
| ( sk5 @ sk23 @ ssList ) ),
inference(pattern_uni,[status(thm)],[48454:[bind(A,$thf( sk5 ))]]) ).
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(135,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(1718,plain,
( ( ( sk5 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk5 @ ( nil @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[736,1337]) ).
thf(1719,plain,
( ( ( sk5 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk5 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[1718]) ).
thf(1723,plain,
( ( sk5 != nil )
| ( nil != nil )
| ~ ( sk5 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[1719]) ).
thf(1726,plain,
( ( sk5 != nil )
| ~ ( sk5 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[1723]) ).
thf(20206,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[115,194]) ).
thf(20207,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[20206]) ).
thf(20208,plain,
( ( nil @ ( sk5 @ app ) )
= sk5 ),
inference(pattern_uni,[status(thm)],[20207:[bind(A,$thf( sk5 ))]]) ).
thf(23744,plain,
( ( ( sk5 @ ( sk5 @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[23435,2226]) ).
thf(23745,plain,
( ( ( sk5 @ ( sk5 @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[23744]) ).
thf(23766,plain,
( ( sk5 != sk1 )
| ( sk5 != nil )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[23745]) ).
thf(8963,plain,
! [A: $i] :
( ( ( sk5 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk5 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[8774,127]) ).
thf(8964,plain,
! [A: $i] :
( ( ( sk5 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk5 @ cyclefreeP ) ),
inference(simp,[status(thm)],[8963]) ).
thf(8965,plain,
( ( nil @ ( sk5 @ sk11 @ cons ) @ strictorderedP )
| ( sk5 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[8964:[bind(A,$thf( sk5 @ sk11 ))]]) ).
thf(69,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ cyclefreeP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax59) ).
thf(426,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ cyclefreeP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(15274,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk19 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[115,186]) ).
thf(15275,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk19 @ ssList ) ),
inference(simp,[status(thm)],[15274]) ).
thf(15276,plain,
( ( sk5 @ strictorderP )
| ( sk5 @ sk19 @ ssList ) ),
inference(pattern_uni,[status(thm)],[15275:[bind(A,$thf( sk5 ))]]) ).
thf(44165,plain,
( ( sk2 != sk2 )
| ( sk1 @ ( sk2 @ segmentP ) )
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[43907,23530]) ).
thf(44166,plain,
( ( sk1 @ ( sk2 @ segmentP ) )
| ( sk1 != nil ) ),
inference(pattern_uni,[status(thm)],[44165:[]]) ).
thf(1419,plain,
( ( sk1 != sk1 )
| ~ ( nil @ ( sk1 @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[950,818]) ).
thf(1420,plain,
( ~ ( nil @ ( sk1 @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1419:[]]) ).
thf(112,plain,
~ ( sk7 @ ( sk6 @ neq ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(2627,plain,
( ( sk5 != sk5 )
| ( nil != nil )
| ~ ( nil @ ( sk5 @ neq ) )
| ~ ( sk5 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2138,1936]) ).
thf(2628,plain,
( ( sk5 != sk5 )
| ~ ( nil @ ( sk5 @ neq ) )
| ~ ( sk5 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[2627]) ).
thf(2629,plain,
( ~ ( nil @ ( sk5 @ neq ) )
| ~ ( sk5 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[2628:[]]) ).
thf(92,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( nil
!= ( A @ ( B @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
thf(516,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( nil
!= ( A @ ( B @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(3,axiom,
nil @ strictorderedP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax69) ).
thf(123,plain,
nil @ strictorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
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(355,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(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(531,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(38,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ( A @ tl )
= B )
& ( B @ ssList ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax76) ).
thf(255,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ( A @ tl )
= B )
& ( B @ ssList ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(1683,plain,
( ( sk9 != sk9 )
| ~ ( sk9 @ ( nil @ neq ) )
| ~ ( sk9 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1107,830]) ).
thf(1684,plain,
( ~ ( sk9 @ ( nil @ neq ) )
| ~ ( sk9 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1683:[]]) ).
thf(646,plain,
! [A: $i] :
( ( ( sk43 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[402,221]) ).
thf(647,plain,
! [A: $i] :
( ( ( sk43 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[646]) ).
thf(648,plain,
~ ( sk43 @ ( sk43 @ neq ) ),
inference(pattern_uni,[status(thm)],[647:[bind(A,$thf( sk43 ))]]) ).
thf(27,axiom,
nil @ duplicatefreeP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax72) ).
thf(209,plain,
nil @ duplicatefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(12,axiom,
nil @ cyclefreeP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax60) ).
thf(150,plain,
nil @ cyclefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(39671,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[105,225]) ).
thf(39672,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[39671]) ).
thf(39673,plain,
( ( sk2 @ ( nil @ app ) )
= sk2 ),
inference(pattern_uni,[status(thm)],[39672:[bind(A,$thf( sk2 ))]]) ).
thf(7754,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7524,242]) ).
thf(7755,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7754]) ).
thf(7756,plain,
( ~ ( sk1 @ sk10 @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7755:[bind(A,$thf( sk1 @ sk10 ))]]) ).
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(310,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(9471,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk13 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,172]) ).
thf(9472,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk13 @ ssList ) ),
inference(simp,[status(thm)],[9471]) ).
thf(9473,plain,
( ( sk9 @ cyclefreeP )
| ( sk9 @ sk13 @ ssList ) ),
inference(pattern_uni,[status(thm)],[9472:[bind(A,$thf( sk9 ))]]) ).
thf(8058,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk14 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,170]) ).
thf(8059,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk14 @ ssList ) ),
inference(simp,[status(thm)],[8058]) ).
thf(8060,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk14 @ ssList ) ),
inference(pattern_uni,[status(thm)],[8059:[bind(A,$thf( sk1 ))]]) ).
thf(198,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)],[197]) ).
thf(199,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)],[198]) ).
thf(12993,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk17 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[115,183]) ).
thf(12994,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk17 @ ssList ) ),
inference(simp,[status(thm)],[12993]) ).
thf(12995,plain,
( ( sk5 @ strictorderP )
| ( sk5 @ sk17 @ ssList ) ),
inference(pattern_uni,[status(thm)],[12994:[bind(A,$thf( sk5 ))]]) ).
thf(7845,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7555,242]) ).
thf(7846,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7845]) ).
thf(7847,plain,
( ~ ( sk2 @ sk10 @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7846:[bind(A,$thf( sk2 @ sk10 ))]]) ).
thf(641,plain,
! [A: $i] :
( ( ( sk42 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[401,242]) ).
thf(642,plain,
! [A: $i] :
( ( ( sk42 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[641]) ).
thf(643,plain,
~ ( sk42 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[642:[bind(A,$thf( sk42 ))]]) ).
thf(177,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[176]) ).
thf(182,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ sk16 @ ( A @ sk15 @ lt ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[179]) ).
thf(765,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[115,165]) ).
thf(766,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssList ) ),
inference(simp,[status(thm)],[765]) ).
thf(767,plain,
( ( sk5 @ cyclefreeP )
| ( sk5 @ sk12 @ ssList ) ),
inference(pattern_uni,[status(thm)],[766:[bind(A,$thf( sk5 ))]]) ).
thf(1186,plain,
! [A: $i] :
( ( ( sk5 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssList )
| ~ $true
| ( sk5 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[767,165]) ).
thf(1187,plain,
! [A: $i] :
( ( ( sk5 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssList )
| ( sk5 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1186]) ).
thf(1188,plain,
( ( sk5 @ sk12 @ cyclefreeP )
| ( sk5 @ sk12 @ sk12 @ ssList )
| ( sk5 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1187:[bind(A,$thf( sk5 @ sk12 ))]]) ).
thf(39607,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[106,225]) ).
thf(39608,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[39607]) ).
thf(39609,plain,
( ( sk1 @ ( nil @ app ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[39608:[bind(A,$thf( sk1 ))]]) ).
thf(44433,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk21 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[113,233]) ).
thf(44434,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk21 @ ssItem ) ),
inference(simp,[status(thm)],[44433]) ).
thf(44435,plain,
( ( sk8 @ strictorderedP )
| ( sk8 @ sk21 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[44434:[bind(A,$thf( sk8 ))]]) ).
thf(806,plain,
! [A: $i] :
( ( ( sk42 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[401,127]) ).
thf(807,plain,
! [A: $i] :
( ( ( sk42 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[806]) ).
thf(808,plain,
nil @ ( sk42 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[807:[bind(A,$thf( sk42 ))]]) ).
thf(742,plain,
! [A: $i] :
( ( ( sk43 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[402,227]) ).
thf(743,plain,
! [A: $i] :
( ( ( sk43 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[742]) ).
thf(744,plain,
~ ( sk43 @ ( sk43 @ lt ) ),
inference(pattern_uni,[status(thm)],[743:[bind(A,$thf( sk43 ))]]) ).
thf(41333,plain,
( ( sk1 != sk1 )
| ~ ( sk5 @ ( sk2 @ neq ) )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2226,40901]) ).
thf(41334,plain,
( ( sk1 != sk1 )
| ~ ( sk5 @ ( sk2 @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[41333]) ).
thf(41335,plain,
( ~ ( sk5 @ ( sk2 @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[41334:[]]) ).
thf(167,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( ( A @ sk14 @ ( A @ sk11 @ cons ) @ ( A @ sk13 @ ( A @ sk10 @ cons ) @ ( A @ sk12 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[163]) ).
thf(175,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ~ ( A @ ssList )
| ( ( A @ sk14 @ ( A @ sk11 @ cons ) @ ( A @ sk13 @ ( A @ sk10 @ cons ) @ ( A @ sk12 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[167]) ).
thf(15395,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk19 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,186]) ).
thf(15396,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk19 @ ssList ) ),
inference(simp,[status(thm)],[15395]) ).
thf(15397,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk19 @ ssList ) ),
inference(pattern_uni,[status(thm)],[15396:[bind(A,$thf( sk2 ))]]) ).
thf(4393,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( sk1 @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[736,1420]) ).
thf(4394,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[4393]) ).
thf(4407,plain,
( ( sk1 != nil )
| ( nil != nil )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[4394]) ).
thf(4414,plain,
( ( sk1 != nil )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[4407]) ).
thf(24614,plain,
! [A: $i] :
( ( ( sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[114,203]) ).
thf(24615,plain,
! [A: $i] :
( ( ( sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[24614]) ).
thf(24616,plain,
nil @ ( sk7 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[24615:[bind(A,$thf( sk7 ))]]) ).
thf(48613,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk23 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,237]) ).
thf(48614,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk23 @ ssList ) ),
inference(simp,[status(thm)],[48613]) ).
thf(48615,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk23 @ ssList ) ),
inference(pattern_uni,[status(thm)],[48614:[bind(A,$thf( sk2 ))]]) ).
thf(2874,plain,
( ( sk8 != sk8 )
| ~ ( nil @ ( sk8 @ neq ) )
| ~ ( sk8 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2422,827]) ).
thf(2875,plain,
( ~ ( nil @ ( sk8 @ neq ) )
| ~ ( sk8 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[2874:[]]) ).
thf(44093,plain,
( ( sk2 != sk2 )
| ( sk1 @ ( sk5 @ segmentP ) )
| ( sk1 != nil )
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[43907,40943]) ).
thf(44094,plain,
( ( sk2 != sk2 )
| ( sk1 @ ( sk5 @ segmentP ) )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[44093]) ).
thf(44095,plain,
( ( sk1 @ ( sk5 @ segmentP ) )
| ( sk1 != nil ) ),
inference(pattern_uni,[status(thm)],[44094:[]]) ).
thf(248,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk25 ) @ ( B @ app ) )
= A )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[246]) ).
thf(250,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( A @ ( B @ sk25 ) @ ( B @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[248]) ).
thf(17245,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,188]) ).
thf(17246,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssItem ) ),
inference(simp,[status(thm)],[17245]) ).
thf(17247,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk16 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[17246:[bind(A,$thf( sk1 ))]]) ).
thf(20319,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[105,194]) ).
thf(20320,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[20319]) ).
thf(20321,plain,
( ( nil @ ( sk2 @ app ) )
= sk2 ),
inference(pattern_uni,[status(thm)],[20320:[bind(A,$thf( sk2 ))]]) ).
thf(2741,plain,
( ( sk1 != sk1 )
| ~ ( sk2 @ ( nil @ neq ) )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2226,836]) ).
thf(2742,plain,
( ( sk1 != sk1 )
| ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[2741]) ).
thf(2743,plain,
( ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[2742:[]]) ).
thf(7842,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7555,127]) ).
thf(7843,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7842]) ).
thf(7844,plain,
( ( nil @ ( sk2 @ sk10 @ cons ) @ strictorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7843:[bind(A,$thf( sk2 @ sk10 ))]]) ).
thf(1287,plain,
! [A: $i] :
( ( ( sk8 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssList )
| ~ $true
| ( sk8 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[779,165]) ).
thf(1288,plain,
! [A: $i] :
( ( ( sk8 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssList )
| ( sk8 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1287]) ).
thf(1289,plain,
( ( sk8 @ sk12 @ cyclefreeP )
| ( sk8 @ sk12 @ sk12 @ ssList )
| ( sk8 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1288:[bind(A,$thf( sk8 @ sk12 ))]]) ).
thf(41421,plain,
( ( sk2 != sk2 )
| ~ ( nil @ ( sk5 @ neq ) )
| ( sk1 != nil )
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[563,40903]) ).
thf(41422,plain,
( ( sk2 != sk2 )
| ~ ( nil @ ( sk5 @ neq ) )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[41421]) ).
thf(41423,plain,
( ~ ( nil @ ( sk5 @ neq ) )
| ( sk1 != nil ) ),
inference(pattern_uni,[status(thm)],[41422:[]]) ).
thf(42575,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk24 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,232]) ).
thf(42576,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk24 @ ssList ) ),
inference(simp,[status(thm)],[42575]) ).
thf(42577,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk24 @ ssList ) ),
inference(pattern_uni,[status(thm)],[42576:[bind(A,$thf( sk2 ))]]) ).
thf(7668,plain,
! [A: $i] :
( ( ( sk5 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk5 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7493,127]) ).
thf(7669,plain,
! [A: $i] :
( ( ( sk5 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk5 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7668]) ).
thf(7670,plain,
( ( nil @ ( sk5 @ sk10 @ cons ) @ strictorderedP )
| ( sk5 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7669:[bind(A,$thf( sk5 @ sk10 ))]]) ).
thf(16584,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk15 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,187]) ).
thf(16585,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk15 @ ssItem ) ),
inference(simp,[status(thm)],[16584]) ).
thf(16586,plain,
( ( sk9 @ strictorderP )
| ( sk9 @ sk15 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[16585:[bind(A,$thf( sk9 ))]]) ).
thf(30572,plain,
( ( ( sk1 @ ( nil @ segmentP ) )
!= ( nil @ ( nil @ segmentP ) ) )
| ( nil @ ( sk1 @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[738,23853]) ).
thf(30573,plain,
( ( ( sk1 @ ( nil @ segmentP ) )
!= ( nil @ ( nil @ segmentP ) ) )
| ( nil @ ( sk1 @ segmentP ) ) ),
inference(simp,[status(thm)],[30572]) ).
thf(30661,plain,
( ( sk1 != nil )
| ( nil != nil )
| ( nil @ ( sk1 @ segmentP ) ) ),
inference(simp,[status(thm)],[30573]) ).
thf(30689,plain,
( ( sk1 != nil )
| ( nil @ ( sk1 @ segmentP ) ) ),
inference(simp,[status(thm)],[30661]) ).
thf(33280,plain,
( ( ( sk2 @ ( sk2 @ segmentP ) )
!= ( sk43 @ ( nil @ segmentP ) ) )
| ( sk43 != sk2 )
| ( sk42 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23530,13977]) ).
thf(33281,plain,
( ( ( sk2 @ ( sk2 @ segmentP ) )
!= ( sk43 @ ( nil @ segmentP ) ) )
| ( sk43 != sk2 )
| ( sk42 != nil ) ),
inference(simp,[status(thm)],[33280]) ).
thf(33301,plain,
( ( sk43 != sk2 )
| ( sk2 != nil )
| ( sk43 != sk2 )
| ( sk42 != nil ) ),
inference(simp,[status(thm)],[33281]) ).
thf(33321,plain,
( ( sk2 != nil )
| ( sk43 != sk2 )
| ( sk42 != nil ) ),
inference(simp,[status(thm)],[33301]) ).
thf(139,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)],[138]) ).
thf(158,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)],[157]) ).
thf(23900,plain,
( ( sk2 != sk2 )
| ( nil @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1411,23530]) ).
thf(23901,plain,
( ( nil @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[23900:[]]) ).
thf(43154,plain,
( ( sk1 != sk1 )
| ~ ( nil @ ( sk5 @ neq ) )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2226,41423]) ).
thf(43155,plain,
( ( sk1 != sk1 )
| ~ ( nil @ ( sk5 @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[43154]) ).
thf(43156,plain,
( ~ ( nil @ ( sk5 @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[43155:[]]) ).
thf(46742,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk20 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,235]) ).
thf(46743,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk20 @ ssItem ) ),
inference(simp,[status(thm)],[46742]) ).
thf(46744,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk20 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[46743:[bind(A,$thf( sk2 ))]]) ).
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(510,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(59,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax45) ).
thf(383,plain,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(2906,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk1 @ ( nil @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[736,1418]) ).
thf(2907,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk1 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[2906]) ).
thf(2916,plain,
( ( sk1 != nil )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[2907]) ).
thf(2917,plain,
( ( sk1 != nil )
| ~ ( sk1 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[2916]) ).
thf(39771,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[111,225]) ).
thf(39772,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[39771]) ).
thf(39773,plain,
( ( sk9 @ ( nil @ app ) )
= sk9 ),
inference(pattern_uni,[status(thm)],[39772:[bind(A,$thf( sk9 ))]]) ).
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(378,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(12446,plain,
! [A: $i] :
( ( A != sk42 )
| ( sk43 != nil )
| ( nil != nil )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[147,12183]) ).
thf(12447,plain,
! [A: $i] :
( ( A != sk42 )
| ( sk43 != nil )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[12446]) ).
thf(12448,plain,
( ( sk43 != nil )
| ~ ( sk42 @ ( nil @ segmentP ) )
| ~ ( sk42 @ ssList ) ),
inference(pattern_uni,[status(thm)],[12447:[bind(A,$thf( sk42 ))]]) ).
thf(44082,plain,
( ( sk2 != sk2 )
| ~ ( sk1 @ ( sk5 @ neq ) )
| ( sk1 != nil )
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[43907,40903]) ).
thf(44083,plain,
( ( sk2 != sk2 )
| ~ ( sk1 @ ( sk5 @ neq ) )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[44082]) ).
thf(44084,plain,
( ~ ( sk1 @ ( sk5 @ neq ) )
| ( sk1 != nil ) ),
inference(pattern_uni,[status(thm)],[44083:[]]) ).
thf(213,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)],[212]) ).
thf(214,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[213]) ).
thf(43157,plain,
( ( sk1 != sk1 )
| ~ ( nil @ ( sk5 @ neq ) )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[950,41423]) ).
thf(43158,plain,
( ( sk1 != sk1 )
| ~ ( nil @ ( sk5 @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[43157]) ).
thf(43159,plain,
( ~ ( nil @ ( sk5 @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[43158:[]]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ hd @ ssItem ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
thf(300,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ hd @ ssItem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(831,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[354,338]) ).
thf(832,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[831]) ).
thf(833,plain,
~ ( nil @ ( nil @ neq ) ),
inference(pattern_uni,[status(thm)],[832:[bind(A,$thf( nil ))]]) ).
thf(2814,plain,
( ( sk2 != sk2 )
| ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2363,824]) ).
thf(2815,plain,
( ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[2814:[]]) ).
thf(67,axiom,
nil @ strictorderP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax64) ).
thf(422,plain,
nil @ strictorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(9049,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[8808,242]) ).
thf(9050,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[9049]) ).
thf(9051,plain,
( ~ ( sk1 @ sk11 @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[9050:[bind(A,$thf( sk1 @ sk11 ))]]) ).
thf(24593,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,203]) ).
thf(24594,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[24593]) ).
thf(24595,plain,
nil @ ( sk6 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[24594:[bind(A,$thf( sk6 ))]]) ).
thf(5750,plain,
( ( ( sk9 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk9 @ ( nil @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[736,1684]) ).
thf(5751,plain,
( ( ( sk9 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk9 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[5750]) ).
thf(5761,plain,
( ( sk9 != nil )
| ( nil != nil )
| ~ ( sk9 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[5751]) ).
thf(5764,plain,
( ( sk9 != nil )
| ~ ( sk9 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[5761]) ).
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(405,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(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(358,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(1195,plain,
! [A: $i] :
( ( ( sk5 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk5 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[767,338]) ).
thf(1196,plain,
! [A: $i] :
( ( ( sk5 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ( sk5 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1195]) ).
thf(1197,plain,
( ~ ( sk5 @ sk12 @ ( sk5 @ sk12 @ neq ) )
| ( sk5 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1196:[bind(A,$thf( sk5 @ sk12 ))]]) ).
thf(23926,plain,
( ( sk2 != sk2 )
| ( sk2 @ ( nil @ segmentP ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2740,23530]) ).
thf(23927,plain,
( ( sk2 @ ( nil @ segmentP ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[23926:[]]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) )
!= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
thf(283,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) )
!= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(64,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ duplicatefreeP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax71) ).
thf(415,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ duplicatefreeP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(236,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)],[229]) ).
thf(238,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)],[236]) ).
thf(239,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)],[238]) ).
thf(136,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[135]) ).
thf(15510,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk19 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,186]) ).
thf(15511,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk19 @ ssList ) ),
inference(simp,[status(thm)],[15510]) ).
thf(15512,plain,
( ( sk9 @ strictorderP )
| ( sk9 @ sk19 @ ssList ) ),
inference(pattern_uni,[status(thm)],[15511:[bind(A,$thf( sk9 ))]]) ).
thf(17573,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[17247,242]) ).
thf(17574,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[17573]) ).
thf(17575,plain,
( ~ ( sk1 @ sk16 @ ( nil @ memberP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[17574:[bind(A,$thf( sk1 @ sk16 ))]]) ).
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(464,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(23858,plain,
( ( sk1 != sk1 )
| ( nil @ ( sk1 @ segmentP ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[950,23488]) ).
thf(23859,plain,
( ( nil @ ( sk1 @ segmentP ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[23858:[]]) ).
thf(7244,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ( A @ sk11 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[115,168]) ).
thf(7245,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ( A @ sk11 @ leq ) ) ),
inference(simp,[status(thm)],[7244]) ).
thf(7246,plain,
( ( sk5 @ cyclefreeP )
| ( sk5 @ sk10 @ ( sk5 @ sk11 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[7245:[bind(A,$thf( sk5 ))]]) ).
thf(11962,plain,
( ( ( sk43 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk42 != nil )
| ~ ( sk43 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,840]) ).
thf(11963,plain,
( ( ( sk43 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk42 != nil )
| ~ ( sk43 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[11962]) ).
thf(12007,plain,
( ( sk43 != sk2 )
| ( sk42 != nil )
| ~ ( sk43 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[11963]) ).
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(501,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(44205,plain,
( ( sk2 != sk2 )
| ~ ( sk5 @ ( sk1 @ neq ) )
| ( sk1 != nil )
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[43907,40901]) ).
thf(44206,plain,
( ( sk2 != sk2 )
| ~ ( sk5 @ ( sk1 @ neq ) )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[44205]) ).
thf(44207,plain,
( ~ ( sk5 @ ( sk1 @ neq ) )
| ( sk1 != nil ) ),
inference(pattern_uni,[status(thm)],[44206:[]]) ).
thf(1975,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssList )
| ~ $true
| ( sk2 @ sk12 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[1232,165]) ).
thf(1976,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssList )
| ( sk2 @ sk12 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1975]) ).
thf(1977,plain,
( ( sk2 @ sk12 @ sk12 @ cyclefreeP )
| ( sk2 @ sk12 @ sk12 @ sk12 @ ssList )
| ( sk2 @ sk12 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1976:[bind(A,$thf( sk2 @ sk12 @ sk12 ))]]) ).
thf(20513,plain,
( ( ( nil @ ( sk5 @ app ) )
!= ( sk5 @ ( sk1 @ app ) ) )
| ( sk5 = sk2 ) ),
inference(paramod_ordered,[status(thm)],[660,20208]) ).
thf(20548,plain,
( ( sk5 != nil )
| ( sk5 != sk1 )
| ( sk5 = sk2 ) ),
inference(simp,[status(thm)],[20513]) ).
thf(2697,plain,
( ( sk1 != sk1 )
| ~ ( nil @ ( sk2 @ neq ) )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2226,838]) ).
thf(2698,plain,
( ( sk1 != sk1 )
| ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[2697]) ).
thf(2699,plain,
( ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[2698:[]]) ).
thf(13090,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk17 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,183]) ).
thf(13091,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk17 @ ssList ) ),
inference(simp,[status(thm)],[13090]) ).
thf(13092,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk17 @ ssList ) ),
inference(pattern_uni,[status(thm)],[13091:[bind(A,$thf( sk2 ))]]) ).
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(442,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(44244,plain,
( ( sk1 != sk1 )
| ( sk2 = sk1 )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[950,43907]) ).
thf(44245,plain,
( ( sk1 != sk1 )
| ( sk2 = sk1 )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[44244]) ).
thf(44246,plain,
( ( sk2 = sk1 )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[44245:[]]) ).
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(322,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(41937,plain,
( ( sk2 != sk2 )
| ( nil @ ( sk5 @ segmentP ) )
| ( sk1 != nil )
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[563,40943]) ).
thf(41938,plain,
( ( sk2 != sk2 )
| ( nil @ ( sk5 @ segmentP ) )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[41937]) ).
thf(41939,plain,
( ( nil @ ( sk5 @ segmentP ) )
| ( sk1 != nil ) ),
inference(pattern_uni,[status(thm)],[41938:[]]) ).
thf(1318,plain,
! [A: $i] :
( ( ( sk9 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk9 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[782,338]) ).
thf(1319,plain,
! [A: $i] :
( ( ( sk9 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ( sk9 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1318]) ).
thf(1320,plain,
( ~ ( sk9 @ sk12 @ ( sk9 @ sk12 @ neq ) )
| ( sk9 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1319:[bind(A,$thf( sk9 @ sk12 ))]]) ).
thf(1365,plain,
! [A: $i] :
( ( ( sk5 @ sk12 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssList )
| ~ $true
| ( sk5 @ sk12 @ cyclefreeP )
| ( sk5 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[1188,165]) ).
thf(1366,plain,
! [A: $i] :
( ( ( sk5 @ sk12 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssList )
| ( sk5 @ sk12 @ cyclefreeP )
| ( sk5 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1365]) ).
thf(1367,plain,
( ( sk5 @ sk12 @ sk12 @ cyclefreeP )
| ( sk5 @ sk12 @ sk12 @ sk12 @ ssList )
| ( sk5 @ sk12 @ cyclefreeP )
| ( sk5 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1366:[bind(A,$thf( sk5 @ sk12 @ sk12 ))]]) ).
thf(17121,plain,
! [A: $i] :
( ( ( sk9 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk9 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[16586,242]) ).
thf(17122,plain,
! [A: $i] :
( ( ( sk9 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk9 @ strictorderP ) ),
inference(simp,[status(thm)],[17121]) ).
thf(17123,plain,
( ~ ( sk9 @ sk15 @ ( nil @ memberP ) )
| ( sk9 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[17122:[bind(A,$thf( sk9 @ sk15 ))]]) ).
thf(6666,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ( A @ sk10 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[113,164]) ).
thf(6667,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ( A @ sk10 @ leq ) ) ),
inference(simp,[status(thm)],[6666]) ).
thf(6668,plain,
( ( sk8 @ cyclefreeP )
| ( sk8 @ sk11 @ ( sk8 @ sk10 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[6667:[bind(A,$thf( sk8 ))]]) ).
thf(8004,plain,
! [A: $i] :
( ( ( sk9 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk9 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7588,242]) ).
thf(8005,plain,
! [A: $i] :
( ( ( sk9 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk9 @ cyclefreeP ) ),
inference(simp,[status(thm)],[8004]) ).
thf(8006,plain,
( ~ ( sk9 @ sk10 @ ( nil @ memberP ) )
| ( sk9 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[8005:[bind(A,$thf( sk9 @ sk10 ))]]) ).
thf(215,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ gt ) )
| ~ ( A @ ( B @ lt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[213]) ).
thf(23754,plain,
( ( sk5 != sk5 )
| ( nil @ ( sk5 @ segmentP ) )
| ~ ( sk5 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2138,23435]) ).
thf(23755,plain,
( ( nil @ ( sk5 @ segmentP ) )
| ~ ( sk5 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[23754:[]]) ).
thf(6684,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ( A @ sk10 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,164]) ).
thf(6685,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ( A @ sk10 @ leq ) ) ),
inference(simp,[status(thm)],[6684]) ).
thf(6686,plain,
( ( sk9 @ cyclefreeP )
| ( sk9 @ sk11 @ ( sk9 @ sk10 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[6685:[bind(A,$thf( sk9 ))]]) ).
thf(219,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ neq ) )
| ( A = B )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[217]) ).
thf(222,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A = B ) ),
inference(lifteq,[status(thm)],[219]) ).
thf(7293,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ( A @ sk11 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[113,168]) ).
thf(7294,plain,
! [A: $i] :
( ( ( sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ( A @ sk11 @ leq ) ) ),
inference(simp,[status(thm)],[7293]) ).
thf(7295,plain,
( ( sk8 @ cyclefreeP )
| ( sk8 @ sk10 @ ( sk8 @ sk11 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[7294:[bind(A,$thf( sk8 ))]]) ).
thf(90310,plain,
$false,
inference(e,[status(thm)],[1337,1411,138,23137,7673,234,9222,1686,8154,42735,48659,333,1031,2363,170,115,2659,6619,308,21961,440,994,3040,120,247,202,9364,13187,385,1756,550,7524,41002,23929,747,16784,153,44164,142,2740,6665,340,8881,185,8848,33326,16456,417,23961,436,15342,404,12026,174,782,1441,17824,504,838,22287,44234,196,23542,1298,2755,31372,802,125,17481,460,157,17677,189,770,228,316,261,1232,7588,9425,40991,559,43924,216,164,12018,8029,20344,9330,376,1418,485,39696,45495,480,211,41704,253,14408,44811,7926,106,121,514,147,221,38387,132,32976,660,40903,243,428,507,206,24589,40943,8774,46621,634,527,14253,233,117,512,7745,201,15424,13049,7269,1311,8842,7999,1387,43876,23913,23624,192,29413,275,137,165,815,467,252,197,4994,48785,9301,1210,23763,17296,44294,42423,44183,566,2873,22149,7555,12025,830,7923,519,156,14302,44822,188,169,420,499,1936,21123,13116,41338,23853,44522,753,6642,1414,8968,12454,7313,547,124,225,1659,4861,17033,8100,212,61265,23857,5234,457,2813,41428,779,738,17377,39550,16690,46762,17186,805,657,23963,16886,530,23725,237,128,12183,105,44417,244,46855,921,750,9040,16395,23435,16505,20935,29077,43931,1219,824,161,8112,12028,562,176,423,24619,9142,43907,286,5876,14326,204,413,191,402,45454,23907,498,1107,181,540,159,187,172,113,42618,14193,736,40053,230,245,208,3038,2422,20407,1144,98,303,23530,1439,41431,1339,103,7292,140,2757,240,5656,4726,462,45294,9407,23762,367,552,799,23899,17914,483,45612,330,40941,399,827,1245,41707,223,306,438,48455,135,563,226,1726,7558,241,20208,23766,23975,20692,8965,426,15276,44166,1420,112,2629,516,123,355,836,194,162,531,255,1684,648,209,776,150,23911,40901,39673,7756,310,9473,8060,199,2165,8808,840,127,12995,7847,643,177,182,1188,39609,44435,338,2599,808,744,16517,17308,41335,154,175,15397,143,4414,24616,23488,41330,48615,2875,44095,250,17247,20321,203,21180,2743,7844,450,1289,41423,2226,42577,7670,16586,30689,186,33321,114,401,171,139,158,23901,43156,46744,235,510,207,23723,383,1661,2917,39773,378,12448,44084,214,43159,300,833,818,2815,183,422,9051,24595,151,950,168,5764,405,21959,358,195,21177,767,1197,23927,283,415,22147,210,239,242,126,136,15512,17575,13977,464,23859,7493,200,7246,12007,501,44207,1977,20548,178,2699,13092,442,44246,2138,111,227,322,41939,1320,1367,354,17123,6668,41550,232,20263,8006,215,23755,6686,222,7295]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC167+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.38 % Computer : n018.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 26 12:25:52 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.58/0.68 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.02/0.84 % [INFO] Parsing done (156ms).
% 1.02/0.85 % [INFO] Running in sequential loop mode.
% 1.88/1.05 % [INFO] eprover registered as external prover.
% 1.88/1.05 % [INFO] Scanning for conjecture ...
% 2.19/1.13 % [INFO] Found a conjecture (or negated_conjecture) and 95 axioms. Running axiom selection ...
% 2.39/1.20 % [INFO] Axiom selection finished. Selected 95 axioms (removed 0 axioms).
% 2.39/1.28 % [INFO] Problem is first-order (TPTP FOF).
% 2.39/1.29 % [INFO] Type checking passed.
% 2.75/1.30 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 174.68/44.09 % External prover 'e' found a proof!
% 174.68/44.09 % [INFO] Killing All external provers ...
% 174.68/44.10 % Time passed: 43617ms (effective reasoning time: 43245ms)
% 174.68/44.10 % 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)>
% 174.68/44.10 % 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
% 174.68/44.10 % No. of inferences in proof: 1193
% 174.68/44.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 43617 ms resp. 43245 ms w/o parsing
% 166.69/44.46 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 166.69/44.46 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------