%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWC176+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 : n003.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 08:52:36 AM UTC 2026
% Result : Theorem 120.62s 29.61s
% Output : Refutation 123.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 123
% Syntax : Number of formulae : 1238 ( 120 unt; 0 typ; 27 def)
% Number of atoms : 5329 (1316 equ; 0 cnn)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 12034 (2043 ~;2128 |; 291 &;6887 @)
% ( 26 <=>; 659 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 51 usr; 15 con; 0-2 aty)
% Number of variables : 1263 ( 15 ^;1115 !; 106 ?;1263 :)
% ( 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 ).
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 ).
thf(sk43_decl,type,
sk43: $i ).
thf(sk44_decl,type,
sk44: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( ( nil = C )
& ( nil != D ) )
| ! [E: $i] :
( ( E @ ssItem )
=> ! [F: $i] :
( ( F @ ( E @ neq ) )
| ! [G: $i] :
( ( G @ ssList )
=> ! [H: $i] :
( ( H @ ssList )
=> ( ( H @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ ( G @ app ) @ app ) @ app ) )
!= A ) ) )
| ~ ( F @ ssItem ) ) )
| ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( G @ ( I @ lt ) )
& ( ( nil @ ( I @ cons ) @ ( J @ app ) )
= C )
& ( J @ ssList ) )
& ( I @ ssItem ) )
& ( ( H @ ( nil @ ( G @ cons ) @ app ) )
= F )
& ( H @ ssList ) )
& ( G @ ssItem ) )
| ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( I @ ( G @ lt ) )
& ( ( J @ ( nil @ ( I @ cons ) @ app ) )
= C )
& ( J @ ssList ) )
& ( I @ ssItem ) )
& ( ( nil @ ( G @ cons ) @ ( H @ app ) )
= E )
& ( H @ ssList ) )
& ( G @ ssItem ) )
| ~ ( C @ strictorderedP )
| ( ( F @ ( C @ ( E @ app ) @ app ) )
!= D )
| ~ ( F @ ssList ) ) )
| ( A != C )
| ( B != D )
| ~ ( D @ ssList ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( ( nil = B )
& ( nil != C ) )
| ! [D: $i] :
( ( D @ ssItem )
=> ! [E: $i] :
( ( E @ ( D @ neq ) )
| ! [F: $i] :
( ( F @ ssList )
=> ! [G: $i] :
( ( G @ ssList )
=> ( ( G @ ( nil @ ( E @ cons ) @ ( nil @ ( D @ cons ) @ ( F @ app ) @ app ) @ app ) )
!= sk1 ) ) )
| ~ ( E @ ssItem ) ) )
| ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ( F @ ( H @ lt ) )
& ( ( nil @ ( H @ cons ) @ ( I @ app ) )
= B )
& ( I @ ssList ) )
& ( H @ ssItem ) )
& ( ( G @ ( nil @ ( F @ cons ) @ app ) )
= E )
& ( G @ ssList ) )
& ( F @ ssItem ) )
| ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ( H @ ( F @ lt ) )
& ( ( I @ ( nil @ ( H @ cons ) @ app ) )
= B )
& ( I @ ssList ) )
& ( H @ ssItem ) )
& ( ( nil @ ( F @ cons ) @ ( G @ app ) )
= D )
& ( G @ ssList ) )
& ( F @ ssItem ) )
| ~ ( B @ strictorderedP )
| ( ( E @ ( B @ ( D @ app ) @ app ) )
!= C )
| ~ ( E @ ssList ) ) )
| ( sk1 != B )
| ( A != C )
| ~ ( C @ ssList ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ! [B: $i] :
( ( ( nil = A )
& ( nil != B ) )
| ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ( C @ neq ) )
| ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( F @ ( nil @ ( D @ cons ) @ ( nil @ ( C @ cons ) @ ( E @ app ) @ app ) @ app ) )
!= sk1 ) ) )
| ~ ( D @ ssItem ) ) )
| ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( E @ ( G @ lt ) )
& ( ( nil @ ( G @ cons ) @ ( H @ app ) )
= A )
& ( H @ ssList ) )
& ( G @ ssItem ) )
& ( ( F @ ( nil @ ( E @ cons ) @ app ) )
= D )
& ( F @ ssList ) )
& ( E @ ssItem ) )
| ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( G @ ( E @ lt ) )
& ( ( H @ ( nil @ ( G @ cons ) @ app ) )
= A )
& ( H @ ssList ) )
& ( G @ ssItem ) )
& ( ( nil @ ( E @ cons ) @ ( F @ app ) )
= C )
& ( F @ ssList ) )
& ( E @ ssItem ) )
| ~ ( A @ strictorderedP )
| ( ( D @ ( A @ ( C @ app ) @ app ) )
!= B )
| ~ ( D @ ssList ) ) )
| ( sk1 != A )
| ( sk2 != B )
| ~ ( B @ ssList ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( ( nil = sk3 )
& ( nil != A ) )
| ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ( B @ neq ) )
| ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ( ( E @ ( nil @ ( C @ cons ) @ ( nil @ ( B @ cons ) @ ( D @ app ) @ app ) @ app ) )
!= sk1 ) ) )
| ~ ( C @ ssItem ) ) )
| ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( D @ ( F @ lt ) )
& ( ( nil @ ( F @ cons ) @ ( G @ app ) )
= sk3 )
& ( G @ ssList ) )
& ( F @ ssItem ) )
& ( ( E @ ( nil @ ( D @ cons ) @ app ) )
= C )
& ( E @ ssList ) )
& ( D @ ssItem ) )
| ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( F @ ( D @ lt ) )
& ( ( G @ ( nil @ ( F @ cons ) @ app ) )
= sk3 )
& ( G @ ssList ) )
& ( F @ ssItem ) )
& ( ( nil @ ( D @ cons ) @ ( E @ app ) )
= B )
& ( E @ ssList ) )
& ( D @ ssItem ) )
| ~ ( sk3 @ strictorderedP )
| ( ( C @ ( sk3 @ ( B @ app ) @ app ) )
!= A )
| ~ ( C @ ssList ) ) )
| ( sk1 != sk3 )
| ( sk2 != A )
| ~ ( A @ ssList ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ! [B: $i] :
( ? [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 ) )
| ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ( E @ ( C @ lt ) )
& ( ( F @ ( nil @ ( E @ cons ) @ app ) )
= sk3 )
& ( F @ ssList ) )
& ( E @ ssItem ) )
& ( ( nil @ ( C @ cons ) @ ( D @ app ) )
= A )
& ( D @ ssList ) )
& ( C @ ssItem ) )
| ~ ( sk3 @ strictorderedP )
| ( ( B @ ( sk3 @ ( A @ app ) @ app ) )
!= sk4 )
| ~ ( B @ ssList ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ( ? [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 ) )
| ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ( D @ ( B @ lt ) )
& ( ( E @ ( nil @ ( D @ cons ) @ app ) )
= sk3 )
& ( E @ ssList ) )
& ( D @ ssItem ) )
& ( ( nil @ ( B @ cons ) @ ( C @ app ) )
= sk5 )
& ( C @ ssList ) )
& ( B @ ssItem ) )
| ~ ( sk3 @ strictorderedP )
| ( ( A @ ( sk3 @ ( sk5 @ app ) @ app ) )
!= sk4 )
| ~ ( A @ ssList ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ( A @ neq ) )
| ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( D @ ( nil @ ( B @ cons ) @ ( nil @ ( A @ cons ) @ ( C @ app ) @ app ) @ app ) )
!= sk1 ) ) )
| ~ ( B @ ssItem ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
~ ( ( A @ ( sk7 @ neq ) )
| ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( C @ ( nil @ ( A @ cons ) @ ( nil @ ( sk7 @ cons ) @ ( B @ app ) @ app ) @ app ) )
!= sk1 ) ) )
| ~ ( A @ ssItem ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( B @ ( nil @ ( sk8 @ cons ) @ ( nil @ ( sk7 @ cons ) @ ( A @ app ) @ app ) @ app ) )
!= sk1 ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ( ( A @ ( nil @ ( sk8 @ cons ) @ ( nil @ ( sk7 @ cons ) @ ( sk9 @ app ) @ app ) @ app ) )
!= sk1 ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [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(sk12_def,definition,
( sk12
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ( ( ( E @ ( B @ cons ) @ ( D @ ( A @ sk11 @ cons ) @ ( C @ app ) @ app ) )
= A )
=> ~ ( ( A @ sk11 @ ( B @ leq ) )
& ( B @ ( A @ sk11 @ leq ) ) ) ) ) ) ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( D @ ( A @ sk12 @ cons ) @ ( C @ ( A @ sk11 @ cons ) @ ( B @ app ) @ app ) )
= A )
=> ~ ( ( A @ sk11 @ ( A @ sk12 @ leq ) )
& ( A @ sk12 @ ( A @ sk11 @ leq ) ) ) ) ) ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( A @ sk12 @ cons ) @ ( B @ ( A @ sk11 @ cons ) @ ( A @ sk13 @ app ) @ app ) )
= A )
=> ~ ( ( A @ sk11 @ ( A @ sk12 @ leq ) )
& ( A @ sk12 @ ( A @ sk11 @ leq ) ) ) ) ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ( ( ( B @ ( A @ sk12 @ cons ) @ ( A @ sk14 @ ( A @ sk11 @ cons ) @ ( A @ sk13 @ app ) @ app ) )
= A )
=> ~ ( ( A @ sk11 @ ( A @ sk12 @ leq ) )
& ( A @ sk12 @ ( A @ sk11 @ leq ) ) ) ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [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(sk17_def,definition,
( sk17
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ( ( ( E @ ( B @ cons ) @ ( D @ ( A @ sk16 @ cons ) @ ( C @ app ) @ app ) )
= A )
=> ( ( A @ sk16 @ ( B @ lt ) )
| ( B @ ( A @ sk16 @ lt ) ) ) ) ) ) ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( D @ ( A @ sk17 @ cons ) @ ( C @ ( A @ sk16 @ cons ) @ ( B @ app ) @ app ) )
= A )
=> ( ( A @ sk16 @ ( A @ sk17 @ lt ) )
| ( A @ sk17 @ ( A @ sk16 @ lt ) ) ) ) ) ) ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( A @ sk17 @ cons ) @ ( B @ ( A @ sk16 @ cons ) @ ( A @ sk18 @ app ) @ app ) )
= A )
=> ( ( A @ sk16 @ ( A @ sk17 @ lt ) )
| ( A @ sk17 @ ( A @ sk16 @ lt ) ) ) ) ) ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ( ( ( B @ ( A @ sk17 @ cons ) @ ( A @ sk19 @ ( A @ sk16 @ cons ) @ ( A @ sk18 @ app ) @ app ) )
= A )
=> ( ( A @ sk16 @ ( A @ sk17 @ lt ) )
| ( A @ sk17 @ ( A @ sk16 @ lt ) ) ) ) ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( ^ [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(sk22_def,definition,
( sk22
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ( ( ( E @ ( B @ cons ) @ ( D @ ( A @ sk21 @ cons ) @ ( C @ app ) @ app ) )
= A )
=> ( B @ ( A @ sk21 @ lt ) ) ) ) ) ) ) ) ) ).
thf(sk23_def,definition,
( sk23
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( D @ ( A @ sk22 @ cons ) @ ( C @ ( A @ sk21 @ cons ) @ ( B @ app ) @ app ) )
= A )
=> ( A @ sk22 @ ( A @ sk21 @ lt ) ) ) ) ) ) ) ) ).
thf(sk24_def,definition,
( sk24
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( A @ sk22 @ cons ) @ ( B @ ( A @ sk21 @ cons ) @ ( A @ sk23 @ app ) @ app ) )
= A )
=> ( A @ sk22 @ ( A @ sk21 @ lt ) ) ) ) ) ) ) ).
thf(sk25_def,definition,
( sk25
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ( ( ( B @ ( A @ sk22 @ cons ) @ ( A @ sk24 @ ( A @ sk21 @ cons ) @ ( A @ sk23 @ app ) @ app ) )
= A )
=> ( A @ sk22 @ ( A @ sk21 @ lt ) ) ) ) ) ) ).
thf(sk43_def,definition,
( sk43
= ( @+[A: $i] :
( ? [B: $i] :
( ( A != B )
& ( B @ ssItem ) )
& ( A @ ssItem ) ) ) ) ).
thf(sk44_def,definition,
( sk44
= ( @+[A: $i] :
( ( sk43 != A )
& ( A @ ssItem ) ) ) ) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( ( nil = C )
& ( nil != D ) )
| ! [E: $i] :
( ( E @ ssItem )
=> ! [F: $i] :
( ( F @ ( E @ neq ) )
| ! [G: $i] :
( ( G @ ssList )
=> ! [H: $i] :
( ( H @ ssList )
=> ( ( H @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ ( G @ app ) @ app ) @ app ) )
!= A ) ) )
| ~ ( F @ ssItem ) ) )
| ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( G @ ( I @ lt ) )
& ( ( nil @ ( I @ cons ) @ ( J @ app ) )
= C )
& ( J @ ssList ) )
& ( I @ ssItem ) )
& ( ( H @ ( nil @ ( G @ cons ) @ app ) )
= F )
& ( H @ ssList ) )
& ( G @ ssItem ) )
| ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( I @ ( G @ lt ) )
& ( ( J @ ( nil @ ( I @ cons ) @ app ) )
= C )
& ( J @ ssList ) )
& ( I @ ssItem ) )
& ( ( nil @ ( G @ cons ) @ ( H @ app ) )
= E )
& ( H @ ssList ) )
& ( G @ ssItem ) )
| ~ ( C @ strictorderedP )
| ( ( F @ ( C @ ( E @ app ) @ app ) )
!= D )
| ~ ( F @ ssList ) ) )
| ( A != C )
| ( B != D )
| ~ ( D @ ssList ) ) ) ) ),
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] :
( ( ( nil = C )
& ( nil != D ) )
| ! [E: $i] :
( ( E @ ssItem )
=> ! [F: $i] :
( ( F @ ( E @ neq ) )
| ! [G: $i] :
( ( G @ ssList )
=> ! [H: $i] :
( ( H @ ssList )
=> ( ( H @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ ( G @ app ) @ app ) @ app ) )
!= A ) ) )
| ~ ( F @ ssItem ) ) )
| ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( G @ ( I @ lt ) )
& ( ( nil @ ( I @ cons ) @ ( J @ app ) )
= C )
& ( J @ ssList ) )
& ( I @ ssItem ) )
& ( ( H @ ( nil @ ( G @ cons ) @ app ) )
= F )
& ( H @ ssList ) )
& ( G @ ssItem ) )
| ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( I @ ( G @ lt ) )
& ( ( J @ ( nil @ ( I @ cons ) @ app ) )
= C )
& ( J @ ssList ) )
& ( I @ ssItem ) )
& ( ( nil @ ( G @ cons ) @ ( H @ app ) )
= E )
& ( H @ ssList ) )
& ( G @ ssItem ) )
| ~ ( C @ strictorderedP )
| ( ( F @ ( C @ ( E @ app ) @ app ) )
!= D )
| ~ ( F @ ssList ) ) )
| ( A != C )
| ( B != D )
| ~ ( D @ ssList ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(98,plain,
~ ! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( ( nil = C )
& ( nil != D ) )
| ! [E: $i] :
( ( E @ ssItem )
=> ! [F: $i] :
( ( F @ ( E @ neq ) )
| ! [G: $i] :
( ( G @ ssList )
=> ! [H: $i] :
( ( H @ ssList )
=> ( ( H @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ ( G @ app ) @ app ) @ app ) )
!= A ) ) )
| ~ ( F @ ssItem ) ) )
| ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( G @ ( I @ lt ) )
& ( ( nil @ ( I @ cons ) @ ( J @ app ) )
= C )
& ( J @ ssList ) )
& ( I @ ssItem ) )
& ( ( H @ ( nil @ ( G @ cons ) @ app ) )
= F )
& ( H @ ssList ) )
& ( G @ ssItem ) )
| ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( I @ ( G @ lt ) )
& ( ( J @ ( nil @ ( I @ cons ) @ app ) )
= C )
& ( J @ ssList ) )
& ( I @ ssItem ) )
& ( ( nil @ ( G @ cons ) @ ( H @ app ) )
= E )
& ( H @ ssList ) )
& ( G @ ssItem ) )
| ~ ( C @ strictorderedP )
| ( ( F @ ( C @ ( E @ app ) @ app ) )
!= D )
| ~ ( F @ ssList ) ) )
| ( A != C )
| ( B != D )
| ~ ( D @ ssList ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(99,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( nil != sk3 )
| ( nil = sk4 ) )
& ~ ( sk8 @ ( sk7 @ neq ) )
& ( ( sk10 @ ( nil @ ( sk8 @ cons ) @ ( nil @ ( sk7 @ cons ) @ ( sk9 @ app ) @ app ) @ app ) )
= sk1 )
& ( sk10 @ ssList )
& ( sk9 @ ssList )
& ( sk8 @ ssItem )
& ( sk7 @ ssItem )
& ( ~ ( E @ ( G @ lt ) )
| ( ( nil @ ( G @ cons ) @ ( H @ app ) )
!= sk3 )
| ~ ( H @ ssList )
| ~ ( G @ ssItem )
| ( ( F @ ( nil @ ( E @ cons ) @ app ) )
!= sk6 )
| ~ ( F @ ssList )
| ~ ( E @ ssItem ) )
& ( ~ ( C @ ( A @ lt ) )
| ( ( D @ ( nil @ ( C @ cons ) @ app ) )
!= sk3 )
| ~ ( D @ ssList )
| ~ ( C @ ssItem )
| ( ( nil @ ( A @ cons ) @ ( B @ app ) )
!= sk5 )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) )
& ( sk3 @ strictorderedP )
& ( ( sk6 @ ( sk3 @ ( sk5 @ app ) @ app ) )
= sk4 )
& ( sk6 @ ssList )
& ( sk5 @ ssList )
& ( sk1 = sk3 )
& ( sk2 = sk4 )
& ( sk4 @ ssList )
& ( sk3 @ ssList )
& ( sk2 @ ssList )
& ( sk1 @ ssList ) ),
inference(cnf,[status(esa)],[98]) ).
thf(106,plain,
sk2 @ ssList,
inference(cnfConj,[status(thm)],[99]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ cyclefreeP )
<=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ~ ( ( B @ ( C @ leq ) )
& ( C @ ( B @ leq ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8) ).
thf(166,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(167,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ cyclefreeP )
| ( A @ sk11 @ ( A @ sk12 @ leq ) )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk12 @ ( A @ sk11 @ leq ) )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( ( A @ sk15 @ ( A @ sk12 @ cons ) @ ( A @ sk14 @ ( A @ sk11 @ cons ) @ ( A @ sk13 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk15 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk14 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk13 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk12 @ ssItem )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk11 @ 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)],[166]) ).
thf(170,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk15 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[167]) ).
thf(722,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,170]) ).
thf(723,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList ) ),
inference(simp,[status(thm)],[722]) ).
thf(724,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk15 @ ssList ) ),
inference(pattern_uni,[status(thm)],[723:[bind(A,$thf( sk2 ))]]) ).
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(337,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(338,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)],[337]) ).
thf(339,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ ( A @ neq ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[338]) ).
thf(341,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ neq ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( A != B ) ),
inference(lifteq,[status(thm)],[339]) ).
thf(342,plain,
! [A: $i] :
( ~ ( A @ ( A @ neq ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[341]) ).
thf(1022,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[724,342]) ).
thf(1023,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1022]) ).
thf(1024,plain,
( ~ ( sk2 @ sk15 @ ( sk2 @ sk15 @ neq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1023:[bind(A,$thf( sk2 @ sk15 ))]]) ).
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(249,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(108,plain,
sk9 @ ssList,
inference(cnfConj,[status(thm)],[99]) ).
thf(171,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk12 @ ( A @ sk11 @ leq ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[167]) ).
thf(8281,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ( A @ sk11 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[108,171]) ).
thf(8282,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ( A @ sk11 @ leq ) ) ),
inference(simp,[status(thm)],[8281]) ).
thf(8283,plain,
( ( sk9 @ cyclefreeP )
| ( sk9 @ sk12 @ ( sk9 @ sk11 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[8282:[bind(A,$thf( sk9 ))]]) ).
thf(100,plain,
sk10 @ ssList,
inference(cnfConj,[status(thm)],[99]) ).
thf(891,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[100,342]) ).
thf(892,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[891]) ).
thf(893,plain,
~ ( sk10 @ ( sk10 @ neq ) ),
inference(pattern_uni,[status(thm)],[892:[bind(A,$thf( sk10 ))]]) ).
thf(91,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49) ).
thf(518,plain,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
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(468,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(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(232,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(233,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ strictorderedP )
| ~ ( A @ sk22 @ ( A @ sk21 @ lt ) )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( ( A @ sk25 @ ( A @ sk22 @ cons ) @ ( A @ sk24 @ ( A @ sk21 @ cons ) @ ( A @ sk23 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( A @ sk25 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( A @ sk24 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( A @ sk23 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( A @ sk22 @ ssItem )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( A @ sk21 @ 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)],[232]) ).
thf(234,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk24 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[233]) ).
thf(110,plain,
sk5 @ ssList,
inference(cnfConj,[status(thm)],[99]) ).
thf(172,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk14 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[167]) ).
thf(8637,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk14 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[110,172]) ).
thf(8638,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk14 @ ssList ) ),
inference(simp,[status(thm)],[8637]) ).
thf(8639,plain,
( ( sk5 @ cyclefreeP )
| ( sk5 @ sk14 @ ssList ) ),
inference(pattern_uni,[status(thm)],[8638:[bind(A,$thf( sk5 ))]]) ).
thf(101,plain,
sk3 @ strictorderedP,
inference(cnfConj,[status(thm)],[99]) ).
thf(107,plain,
sk1 = sk3,
inference(cnfConj,[status(thm)],[99]) ).
thf(123,plain,
sk3 = sk1,
inference(lifteq,[status(thm)],[107]) ).
thf(555,plain,
sk1 @ strictorderedP,
inference(rewrite,[status(thm)],[101,123]) ).
thf(114,plain,
sk1 @ 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(132,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(133,plain,
! [A: $i] :
( ( ( A @ ( nil @ frontsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) )
& ( ( nil = A )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[132]) ).
thf(134,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[133]) ).
thf(136,plain,
! [A: $i] :
( ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[134]) ).
thf(1127,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[114,136]) ).
thf(1128,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[1127]) ).
thf(1129,plain,
( ~ ( sk1 @ ( nil @ frontsegP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[1128:[bind(A,$thf( sk1 ))]]) ).
thf(118,plain,
( ( nil != sk3 )
| ( nil = sk4 ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(121,plain,
( ( sk3 != nil )
| ( sk4 = nil ) ),
inference(lifteq,[status(thm)],[118]) ).
thf(115,plain,
sk2 = sk4,
inference(cnfConj,[status(thm)],[99]) ).
thf(119,plain,
sk4 = sk2,
inference(lifteq,[status(thm)],[115]) ).
thf(566,plain,
( ( sk1 != nil )
| ( sk2 = nil ) ),
inference(rewrite,[status(thm)],[121,119,123]) ).
thf(879,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,342]) ).
thf(880,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[879]) ).
thf(881,plain,
~ ( sk2 @ ( sk2 @ neq ) ),
inference(pattern_uni,[status(thm)],[880:[bind(A,$thf( sk2 ))]]) ).
thf(915,plain,
( ( sk2 != sk2 )
| ~ ( sk2 @ ( nil @ neq ) )
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[566,881]) ).
thf(916,plain,
( ~ ( sk2 @ ( nil @ neq ) )
| ( sk1 != nil ) ),
inference(pattern_uni,[status(thm)],[915:[]]) ).
thf(1552,plain,
( ( sk1 != sk1 )
| ~ ( sk2 @ ( nil @ neq ) )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1129,916]) ).
thf(1553,plain,
( ( sk1 != sk1 )
| ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1552]) ).
thf(1554,plain,
( ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1553:[]]) ).
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(523,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(1362,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[108,136]) ).
thf(1363,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[1362]) ).
thf(1364,plain,
( ~ ( sk9 @ ( nil @ frontsegP ) )
| ( sk9 = nil ) ),
inference(pattern_uni,[status(thm)],[1363:[bind(A,$thf( sk9 ))]]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax55) ).
thf(204,plain,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(205,plain,
! [A: $i] :
( ( A @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[204]) ).
thf(27265,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[108,205]) ).
thf(27266,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[27265]) ).
thf(27267,plain,
sk9 @ ( sk9 @ segmentP ),
inference(pattern_uni,[status(thm)],[27266:[bind(A,$thf( sk9 ))]]) ).
thf(27678,plain,
( ( sk9 != sk9 )
| ( sk9 @ ( nil @ segmentP ) )
| ~ ( sk9 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1364,27267]) ).
thf(27679,plain,
( ( sk9 @ ( nil @ segmentP ) )
| ~ ( sk9 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[27678:[]]) ).
thf(111,plain,
sk6 @ ssList,
inference(cnfConj,[status(thm)],[99]) ).
thf(174,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk12 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[167]) ).
thf(9766,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,174]) ).
thf(9767,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssItem ) ),
inference(simp,[status(thm)],[9766]) ).
thf(9768,plain,
( ( sk6 @ cyclefreeP )
| ( sk6 @ sk12 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[9767:[bind(A,$thf( sk6 ))]]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax68) ).
thf(130,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(131,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[130]) ).
thf(10232,plain,
! [A: $i] :
( ( ( sk6 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk6 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[9768,131]) ).
thf(10233,plain,
! [A: $i] :
( ( ( sk6 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk6 @ cyclefreeP ) ),
inference(simp,[status(thm)],[10232]) ).
thf(10234,plain,
( ( nil @ ( sk6 @ sk12 @ cons ) @ strictorderedP )
| ( sk6 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[10233:[bind(A,$thf( sk6 @ sk12 ))]]) ).
thf(8313,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ( A @ sk11 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,171]) ).
thf(8314,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ( A @ sk11 @ leq ) ) ),
inference(simp,[status(thm)],[8313]) ).
thf(8315,plain,
( ( sk6 @ cyclefreeP )
| ( sk6 @ sk12 @ ( sk6 @ sk11 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[8314:[bind(A,$thf( sk6 ))]]) ).
thf(169,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk11 @ ( A @ sk12 @ leq ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[167]) ).
thf(7848,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ( A @ sk12 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[114,169]) ).
thf(7849,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ( A @ sk12 @ leq ) ) ),
inference(simp,[status(thm)],[7848]) ).
thf(7850,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk11 @ ( sk1 @ sk12 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[7849:[bind(A,$thf( sk1 ))]]) ).
thf(1521,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[100,136]) ).
thf(1522,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[1521]) ).
thf(1523,plain,
( ~ ( sk10 @ ( nil @ frontsegP ) )
| ( sk10 = nil ) ),
inference(pattern_uni,[status(thm)],[1522:[bind(A,$thf( sk10 ))]]) ).
thf(1792,plain,
( ( sk10 != sk10 )
| ~ ( sk10 @ ( nil @ neq ) )
| ~ ( sk10 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1523,893]) ).
thf(1793,plain,
( ~ ( sk10 @ ( nil @ neq ) )
| ~ ( sk10 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1792:[]]) ).
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(182,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(183,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ strictorderP )
| ~ ( A @ sk16 @ ( A @ sk17 @ lt ) )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ~ ( A @ sk17 @ ( A @ sk16 @ lt ) )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( ( A @ sk20 @ ( A @ sk17 @ cons ) @ ( A @ sk19 @ ( A @ sk16 @ cons ) @ ( A @ sk18 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( A @ sk20 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( A @ sk19 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( A @ sk18 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( A @ sk17 @ ssItem )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( A @ sk16 @ 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)],[182]) ).
thf(192,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk16 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[183]) ).
thf(19991,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[110,192]) ).
thf(19992,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssItem ) ),
inference(simp,[status(thm)],[19991]) ).
thf(19993,plain,
( ( sk5 @ strictorderP )
| ( sk5 @ sk16 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[19992:[bind(A,$thf( sk5 ))]]) ).
thf(34,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( nil @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
thf(245,plain,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( nil @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(246,plain,
! [A: $i] :
( ~ ( A @ ( nil @ memberP ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[245]) ).
thf(20303,plain,
! [A: $i] :
( ( ( sk5 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk5 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[19993,246]) ).
thf(20304,plain,
! [A: $i] :
( ( ( sk5 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk5 @ strictorderP ) ),
inference(simp,[status(thm)],[20303]) ).
thf(20305,plain,
( ~ ( sk5 @ sk16 @ ( nil @ memberP ) )
| ( sk5 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[20304:[bind(A,$thf( sk5 @ sk16 ))]]) ).
thf(135,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[133]) ).
thf(137,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[135]) ).
thf(138,plain,
( ( nil @ ( nil @ frontsegP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[137]) ).
thf(53,axiom,
nil @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
thf(358,plain,
nil @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(696,plain,
( ( nil @ ( nil @ frontsegP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[138,358]) ).
thf(697,plain,
nil @ ( nil @ frontsegP ),
inference(simp,[status(thm)],[696]) ).
thf(27680,plain,
( ( sk9 != sk9 )
| ( nil @ ( sk9 @ segmentP ) )
| ~ ( sk9 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1364,27267]) ).
thf(27681,plain,
( ( nil @ ( sk9 @ segmentP ) )
| ~ ( sk9 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[27680:[]]) ).
thf(44343,plain,
( ( ( sk9 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( nil @ ( sk9 @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[697,27681]) ).
thf(44344,plain,
( ( ( sk9 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( nil @ ( sk9 @ segmentP ) ) ),
inference(simp,[status(thm)],[44343]) ).
thf(44484,plain,
( ( sk9 != nil )
| ( nil != nil )
| ( nil @ ( sk9 @ segmentP ) ) ),
inference(simp,[status(thm)],[44344]) ).
thf(44507,plain,
( ( sk9 != nil )
| ( nil @ ( sk9 @ segmentP ) ) ),
inference(simp,[status(thm)],[44484]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ segmentP ) )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax58) ).
thf(147,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(148,plain,
! [A: $i] :
( ( ( A @ ( nil @ segmentP ) )
| ( nil != A )
| ~ ( A @ ssList ) )
& ( ( nil = A )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[147]) ).
thf(149,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[148]) ).
thf(151,plain,
! [A: $i] :
( ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[149]) ).
thf(61,axiom,
? [A: $i] :
( ? [B: $i] :
( ( A != B )
& ( B @ ssItem ) )
& ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
thf(403,plain,
? [A: $i] :
( ? [B: $i] :
( ( A != B )
& ( B @ ssItem ) )
& ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(404,plain,
( ( sk43 != sk44 )
& ( sk44 @ ssItem )
& ( sk43 @ ssItem ) ),
inference(cnf,[status(esa)],[403]) ).
thf(407,plain,
sk43 != sk44,
inference(cnfConj,[status(thm)],[404]) ).
thf(408,plain,
sk44 != sk43,
inference(lifteq,[status(thm)],[407]) ).
thf(2799,plain,
! [A: $i] :
( ( A != sk44 )
| ( sk43 != nil )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[151,408]) ).
thf(2800,plain,
( ( sk43 != nil )
| ~ ( sk44 @ ( nil @ segmentP ) )
| ~ ( sk44 @ ssList ) ),
inference(pattern_uni,[status(thm)],[2799:[bind(A,$thf( sk44 ))]]) ).
thf(18939,plain,
( ( ( sk44 @ ssList )
!= ( sk5 @ ssList ) )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[110,2800]) ).
thf(18940,plain,
( ( ( sk44 @ ssList )
!= ( sk5 @ ssList ) )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[18939]) ).
thf(19127,plain,
( ( sk44 != sk5 )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[18940]) ).
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(247,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(1176,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[110,136]) ).
thf(1177,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[1176]) ).
thf(1178,plain,
( ~ ( sk5 @ ( nil @ frontsegP ) )
| ( sk5 = nil ) ),
inference(pattern_uni,[status(thm)],[1177:[bind(A,$thf( sk5 ))]]) ).
thf(867,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[110,342]) ).
thf(868,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[867]) ).
thf(869,plain,
~ ( sk5 @ ( sk5 @ neq ) ),
inference(pattern_uni,[status(thm)],[868:[bind(A,$thf( sk5 ))]]) ).
thf(1590,plain,
( ( sk5 != sk5 )
| ~ ( sk5 @ ( nil @ neq ) )
| ~ ( sk5 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1178,869]) ).
thf(1591,plain,
( ~ ( sk5 @ ( nil @ neq ) )
| ~ ( sk5 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1590:[]]) ).
thf(71,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( B @ ( A @ app ) @ ssList ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
thf(440,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( B @ ( A @ app ) @ ssList ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
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(511,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(734,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,170]) ).
thf(735,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList ) ),
inference(simp,[status(thm)],[734]) ).
thf(736,plain,
( ( sk6 @ cyclefreeP )
| ( sk6 @ sk15 @ ssList ) ),
inference(pattern_uni,[status(thm)],[735:[bind(A,$thf( sk6 ))]]) ).
thf(1076,plain,
! [A: $i] :
( ( ( sk6 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk6 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[736,342]) ).
thf(1077,plain,
! [A: $i] :
( ( ( sk6 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ( sk6 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1076]) ).
thf(1078,plain,
( ~ ( sk6 @ sk15 @ ( sk6 @ sk15 @ neq ) )
| ( sk6 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1077:[bind(A,$thf( sk6 @ sk15 ))]]) ).
thf(20115,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[108,192]) ).
thf(20116,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssItem ) ),
inference(simp,[status(thm)],[20115]) ).
thf(20117,plain,
( ( sk9 @ strictorderP )
| ( sk9 @ sk16 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[20116:[bind(A,$thf( sk9 ))]]) ).
thf(1555,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ( sk2 = nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1129,566]) ).
thf(1556,plain,
( ( sk1 != sk1 )
| ( sk2 = nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1555]) ).
thf(1557,plain,
( ( sk2 = nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1556:[]]) ).
thf(27182,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,205]) ).
thf(27183,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[27182]) ).
thf(27184,plain,
sk2 @ ( sk2 @ segmentP ),
inference(pattern_uni,[status(thm)],[27183:[bind(A,$thf( sk2 ))]]) ).
thf(27567,plain,
( ( sk2 != sk2 )
| ( nil @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1557,27184]) ).
thf(27568,plain,
( ( nil @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[27567:[]]) ).
thf(102,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)],[102,246]) ).
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(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(142,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(713,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[114,170]) ).
thf(714,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList ) ),
inference(simp,[status(thm)],[713]) ).
thf(715,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk15 @ ssList ) ),
inference(pattern_uni,[status(thm)],[714:[bind(A,$thf( sk1 ))]]) ).
thf(188,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk18 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[183]) ).
thf(16892,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk18 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[100,188]) ).
thf(16893,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk18 @ ssList ) ),
inference(simp,[status(thm)],[16892]) ).
thf(16894,plain,
( ( sk10 @ strictorderP )
| ( sk10 @ sk18 @ ssList ) ),
inference(pattern_uni,[status(thm)],[16893:[bind(A,$thf( sk10 ))]]) ).
thf(9772,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[100,174]) ).
thf(9773,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssItem ) ),
inference(simp,[status(thm)],[9772]) ).
thf(9774,plain,
( ( sk10 @ cyclefreeP )
| ( sk10 @ sk12 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[9773:[bind(A,$thf( sk10 ))]]) ).
thf(185,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk20 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[183]) ).
thf(882,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[108,342]) ).
thf(883,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[882]) ).
thf(884,plain,
~ ( sk9 @ ( sk9 @ neq ) ),
inference(pattern_uni,[status(thm)],[883:[bind(A,$thf( sk9 ))]]) ).
thf(1656,plain,
( ( sk9 != sk9 )
| ~ ( sk9 @ ( nil @ neq ) )
| ~ ( sk9 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1364,884]) ).
thf(1657,plain,
( ~ ( sk9 @ ( nil @ neq ) )
| ~ ( sk9 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1656:[]]) ).
thf(2704,plain,
( ( ( sk9 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk9 @ ( nil @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[697,1657]) ).
thf(2705,plain,
( ( ( sk9 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk9 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[2704]) ).
thf(2721,plain,
( ( sk9 != nil )
| ( nil != nil )
| ~ ( sk9 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[2705]) ).
thf(2723,plain,
( ( sk9 != nil )
| ~ ( sk9 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[2721]) ).
thf(238,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk22 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[233]) ).
thf(54871,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk22 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,238]) ).
thf(54872,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk22 @ ssItem ) ),
inference(simp,[status(thm)],[54871]) ).
thf(54873,plain,
( ( sk6 @ strictorderedP )
| ( sk6 @ sk22 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[54872:[bind(A,$thf( sk6 ))]]) ).
thf(175,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk11 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[167]) ).
thf(10472,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[100,175]) ).
thf(10473,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssItem ) ),
inference(simp,[status(thm)],[10472]) ).
thf(10474,plain,
( ( sk10 @ cyclefreeP )
| ( sk10 @ sk11 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[10473:[bind(A,$thf( sk10 ))]]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax90) ).
thf(230,plain,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(231,plain,
! [A: $i] :
( ~ ( A @ ( A @ lt ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[230]) ).
thf(707,plain,
! [A: $i] :
( ( ( sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[102,231]) ).
thf(708,plain,
! [A: $i] :
( ( ( sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[707]) ).
thf(709,plain,
~ ( sk7 @ ( sk7 @ lt ) ),
inference(pattern_uni,[status(thm)],[708:[bind(A,$thf( sk7 ))]]) ).
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(417,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(1210,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[106,136]) ).
thf(1211,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[1210]) ).
thf(1212,plain,
( ~ ( sk2 @ ( nil @ frontsegP ) )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[1211:[bind(A,$thf( sk2 ))]]) ).
thf(27587,plain,
( ( sk2 != sk2 )
| ( sk2 @ ( nil @ segmentP ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1212,27184]) ).
thf(27588,plain,
( ( sk2 @ ( nil @ segmentP ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[27587:[]]) ).
thf(37781,plain,
( ( ( sk2 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk2 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[697,27588]) ).
thf(37782,plain,
( ( ( sk2 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk2 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[37781]) ).
thf(37907,plain,
( ( sk2 != nil )
| ( nil != nil )
| ( sk2 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[37782]) ).
thf(37934,plain,
( ( sk2 != nil )
| ( sk2 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[37907]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil @ ( A @ app ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax84) ).
thf(196,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil @ ( A @ app ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(197,plain,
! [A: $i] :
( ( ( nil @ ( A @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[196]) ).
thf(198,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[197]) ).
thf(23673,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[100,198]) ).
thf(23674,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[23673]) ).
thf(23675,plain,
( ( nil @ ( sk10 @ app ) )
= sk10 ),
inference(pattern_uni,[status(thm)],[23674:[bind(A,$thf( sk10 ))]]) ).
thf(9657,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,174]) ).
thf(9658,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssItem ) ),
inference(simp,[status(thm)],[9657]) ).
thf(9659,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk12 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[9658:[bind(A,$thf( sk2 ))]]) ).
thf(9969,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[9659,131]) ).
thf(9970,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[9969]) ).
thf(9971,plain,
( ( nil @ ( sk2 @ sk12 @ cons ) @ strictorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[9970:[bind(A,$thf( sk2 @ sk12 ))]]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax57) ).
thf(257,plain,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
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(320,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ( A @ hd )
= B )
& ( B @ ssItem ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(105,plain,
sk8 @ ssItem,
inference(cnfConj,[status(thm)],[99]) ).
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(220,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(221,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)],[220]) ).
thf(222,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ ( A @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[221]) ).
thf(224,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A != B ) ),
inference(lifteq,[status(thm)],[222]) ).
thf(225,plain,
! [A: $i] :
( ~ ( A @ ( A @ neq ) )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[224]) ).
thf(563,plain,
! [A: $i] :
( ( ( sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,225]) ).
thf(564,plain,
! [A: $i] :
( ( ( sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[563]) ).
thf(565,plain,
~ ( sk8 @ ( sk8 @ neq ) ),
inference(pattern_uni,[status(thm)],[564:[bind(A,$thf( sk8 ))]]) ).
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(389,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(150,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ( nil != A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[148]) ).
thf(152,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[150]) ).
thf(153,plain,
( ( nil @ ( nil @ segmentP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[152]) ).
thf(863,plain,
( ( nil @ ( nil @ segmentP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[153,358]) ).
thf(864,plain,
nil @ ( nil @ segmentP ),
inference(simp,[status(thm)],[863]) ).
thf(3461,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[111,151]) ).
thf(3462,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[3461]) ).
thf(3463,plain,
( ~ ( sk6 @ ( nil @ segmentP ) )
| ( sk6 = nil ) ),
inference(pattern_uni,[status(thm)],[3462:[bind(A,$thf( sk6 ))]]) ).
thf(27355,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,205]) ).
thf(27356,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[27355]) ).
thf(27357,plain,
sk6 @ ( sk6 @ segmentP ),
inference(pattern_uni,[status(thm)],[27356:[bind(A,$thf( sk6 ))]]) ).
thf(28124,plain,
( ( sk6 != sk6 )
| ( nil @ ( sk6 @ segmentP ) )
| ~ ( sk6 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[3463,27357]) ).
thf(28125,plain,
( ( nil @ ( sk6 @ segmentP ) )
| ~ ( sk6 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[28124:[]]) ).
thf(52591,plain,
( ( ( sk6 @ ( nil @ segmentP ) )
!= ( nil @ ( nil @ segmentP ) ) )
| ( nil @ ( sk6 @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[864,28125]) ).
thf(52592,plain,
( ( ( sk6 @ ( nil @ segmentP ) )
!= ( nil @ ( nil @ segmentP ) ) )
| ( nil @ ( sk6 @ segmentP ) ) ),
inference(simp,[status(thm)],[52591]) ).
thf(52676,plain,
( ( sk6 != nil )
| ( nil != nil )
| ( nil @ ( sk6 @ segmentP ) ) ),
inference(simp,[status(thm)],[52592]) ).
thf(52756,plain,
( ( sk6 != nil )
| ( nil @ ( sk6 @ segmentP ) ) ),
inference(simp,[status(thm)],[52676]) ).
thf(176,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk13 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[167]) ).
thf(11201,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk13 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,176]) ).
thf(11202,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk13 @ ssList ) ),
inference(simp,[status(thm)],[11201]) ).
thf(11203,plain,
( ( sk6 @ cyclefreeP )
| ( sk6 @ sk13 @ ssList ) ),
inference(pattern_uni,[status(thm)],[11202:[bind(A,$thf( sk6 ))]]) ).
thf(187,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk17 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[183]) ).
thf(16009,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk17 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[100,187]) ).
thf(16010,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk17 @ ssItem ) ),
inference(simp,[status(thm)],[16009]) ).
thf(16011,plain,
( ( sk10 @ strictorderP )
| ( sk10 @ sk17 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[16010:[bind(A,$thf( sk10 ))]]) ).
thf(16607,plain,
! [A: $i] :
( ( ( sk10 @ sk17 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk10 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[16011,246]) ).
thf(16608,plain,
! [A: $i] :
( ( ( sk10 @ sk17 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk10 @ strictorderP ) ),
inference(simp,[status(thm)],[16607]) ).
thf(16609,plain,
( ~ ( sk10 @ sk17 @ ( nil @ memberP ) )
| ( sk10 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[16608:[bind(A,$thf( sk10 @ sk17 ))]]) ).
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(344,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(2895,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[106,151]) ).
thf(2896,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[2895]) ).
thf(2897,plain,
( ~ ( sk2 @ ( nil @ segmentP ) )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[2896:[bind(A,$thf( sk2 ))]]) ).
thf(11049,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk13 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[110,176]) ).
thf(11050,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk13 @ ssList ) ),
inference(simp,[status(thm)],[11049]) ).
thf(11051,plain,
( ( sk5 @ cyclefreeP )
| ( sk5 @ sk13 @ ssList ) ),
inference(pattern_uni,[status(thm)],[11050:[bind(A,$thf( sk5 ))]]) ).
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(155,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(156,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[155]) ).
thf(157,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( A = B ) ),
inference(lifteq,[status(thm)],[156]) ).
thf(1053,plain,
! [A: $i] :
( ( ( sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,131]) ).
thf(1054,plain,
! [A: $i] :
( ( ( sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[1053]) ).
thf(1055,plain,
nil @ ( sk8 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[1054:[bind(A,$thf( sk8 ))]]) ).
thf(16787,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk18 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[108,188]) ).
thf(16788,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk18 @ ssList ) ),
inference(simp,[status(thm)],[16787]) ).
thf(16789,plain,
( ( sk9 @ strictorderP )
| ( sk9 @ sk18 @ ssList ) ),
inference(pattern_uni,[status(thm)],[16788:[bind(A,$thf( sk9 ))]]) ).
thf(27300,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[114,205]) ).
thf(27301,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[27300]) ).
thf(27302,plain,
sk1 @ ( sk1 @ segmentP ),
inference(pattern_uni,[status(thm)],[27301:[bind(A,$thf( sk1 ))]]) ).
thf(27811,plain,
( ( sk1 != sk1 )
| ( sk1 @ ( nil @ segmentP ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1129,27302]) ).
thf(27812,plain,
( ( sk1 @ ( nil @ segmentP ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[27811:[]]) ).
thf(51808,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk1 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[697,27812]) ).
thf(51809,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[51808]) ).
thf(51965,plain,
( ( sk1 != nil )
| ( nil != nil )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[51809]) ).
thf(52008,plain,
( ( sk1 != nil )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[51965]) ).
thf(27154,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[110,205]) ).
thf(27155,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[27154]) ).
thf(27156,plain,
sk5 @ ( sk5 @ segmentP ),
inference(pattern_uni,[status(thm)],[27155:[bind(A,$thf( sk5 ))]]) ).
thf(3172,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[108,151]) ).
thf(3173,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[3172]) ).
thf(3174,plain,
( ~ ( sk9 @ ( nil @ segmentP ) )
| ( sk9 = nil ) ),
inference(pattern_uni,[status(thm)],[3173:[bind(A,$thf( sk9 ))]]) ).
thf(27470,plain,
( ( ( sk5 @ ( sk5 @ segmentP ) )
!= ( sk9 @ ( nil @ segmentP ) ) )
| ~ $true
| ( sk9 = nil ) ),
inference(paramod_ordered,[status(thm)],[27156,3174]) ).
thf(27471,plain,
( ( ( sk5 @ ( sk5 @ segmentP ) )
!= ( sk9 @ ( nil @ segmentP ) ) )
| ( sk9 = nil ) ),
inference(simp,[status(thm)],[27470]) ).
thf(27511,plain,
( ( sk9 != sk5 )
| ( sk5 != nil )
| ( sk9 = nil ) ),
inference(simp,[status(thm)],[27471]) ).
thf(116,plain,
( ( sk6 @ ( sk3 @ ( sk5 @ app ) @ app ) )
= sk4 ),
inference(cnfConj,[status(thm)],[99]) ).
thf(120,plain,
( ( sk6 @ ( sk3 @ ( sk5 @ app ) @ app ) )
= sk4 ),
inference(lifteq,[status(thm)],[116]) ).
thf(557,plain,
( ( sk6 @ ( sk1 @ ( sk5 @ app ) @ app ) )
= sk2 ),
inference(rewrite,[status(thm)],[120,119,123]) ).
thf(558,plain,
( ( ( sk6 @ ( sk1 @ ( sk5 @ app ) @ app ) )
!= ( sk1 @ ( sk5 @ app ) ) )
| ( ( sk6 @ ( sk2 @ app ) )
= sk2 ) ),
inference(paramod_ordered,[status(thm)],[557,557]) ).
thf(559,plain,
( ( sk6 != sk1 )
| ( ( sk1 @ ( sk5 @ app ) )
!= sk5 )
| ( ( sk6 @ ( sk2 @ app ) )
= sk2 ) ),
inference(simp,[status(thm)],[558]) ).
thf(3470,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[100,151]) ).
thf(3471,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[3470]) ).
thf(3472,plain,
( ~ ( sk10 @ ( nil @ segmentP ) )
| ( sk10 = nil ) ),
inference(pattern_uni,[status(thm)],[3471:[bind(A,$thf( sk10 ))]]) ).
thf(3997,plain,
( ( sk10 != sk10 )
| ~ ( sk10 @ ( nil @ neq ) )
| ~ ( sk10 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[3472,893]) ).
thf(3998,plain,
( ~ ( sk10 @ ( nil @ neq ) )
| ~ ( sk10 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[3997:[]]) ).
thf(14374,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk20 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[114,185]) ).
thf(14375,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk20 @ ssList ) ),
inference(simp,[status(thm)],[14374]) ).
thf(14376,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk20 @ ssList ) ),
inference(pattern_uni,[status(thm)],[14375:[bind(A,$thf( sk1 ))]]) ).
thf(1512,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[111,136]) ).
thf(1513,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[1512]) ).
thf(1514,plain,
( ~ ( sk6 @ ( nil @ frontsegP ) )
| ( sk6 = nil ) ),
inference(pattern_uni,[status(thm)],[1513:[bind(A,$thf( sk6 ))]]) ).
thf(1012,plain,
( ( sk2 != sk2 )
| ( sk2 @ cyclefreeP )
| ( nil @ sk15 @ ssList )
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[566,724]) ).
thf(1013,plain,
( ( sk2 @ cyclefreeP )
| ( nil @ sk15 @ ssList )
| ( sk1 != nil ) ),
inference(pattern_uni,[status(thm)],[1012:[]]) ).
thf(3308,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[114,151]) ).
thf(3309,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[3308]) ).
thf(3310,plain,
( ~ ( sk1 @ ( nil @ segmentP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[3309:[bind(A,$thf( sk1 ))]]) ).
thf(3732,plain,
( ( sk1 != sk1 )
| ~ ( sk2 @ ( nil @ neq ) )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[3310,916]) ).
thf(3733,plain,
( ( sk1 != sk1 )
| ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[3732]) ).
thf(3734,plain,
( ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[3733:[]]) ).
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(421,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(7801,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ( A @ sk12 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[110,169]) ).
thf(7802,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ( A @ sk12 @ leq ) ) ),
inference(simp,[status(thm)],[7801]) ).
thf(7803,plain,
( ( sk5 @ cyclefreeP )
| ( sk5 @ sk11 @ ( sk5 @ sk12 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[7802:[bind(A,$thf( sk5 ))]]) ).
thf(27529,plain,
( ( sk2 != sk2 )
| ( nil @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2897,27184]) ).
thf(27530,plain,
( ( nil @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[27529:[]]) ).
thf(35330,plain,
( ( ( sk2 @ ( nil @ segmentP ) )
!= ( nil @ ( nil @ segmentP ) ) )
| ( nil @ ( sk2 @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[864,27530]) ).
thf(35331,plain,
( ( ( sk2 @ ( nil @ segmentP ) )
!= ( nil @ ( nil @ segmentP ) ) )
| ( nil @ ( sk2 @ segmentP ) ) ),
inference(simp,[status(thm)],[35330]) ).
thf(35428,plain,
( ( sk2 != nil )
| ( nil != nil )
| ( nil @ ( sk2 @ segmentP ) ) ),
inference(simp,[status(thm)],[35331]) ).
thf(35463,plain,
( ( sk2 != nil )
| ( nil @ ( sk2 @ segmentP ) ) ),
inference(simp,[status(thm)],[35428]) ).
thf(917,plain,
( ( sk2 != sk2 )
| ~ ( nil @ ( sk2 @ neq ) )
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[566,881]) ).
thf(918,plain,
( ~ ( nil @ ( sk2 @ neq ) )
| ( sk1 != nil ) ),
inference(pattern_uni,[status(thm)],[917:[]]) ).
thf(1566,plain,
( ( sk1 != sk1 )
| ~ ( nil @ ( sk2 @ neq ) )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1129,918]) ).
thf(1567,plain,
( ( sk1 != sk1 )
| ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1566]) ).
thf(1568,plain,
( ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1567:[]]) ).
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(216,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(9647,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[110,174]) ).
thf(9648,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssItem ) ),
inference(simp,[status(thm)],[9647]) ).
thf(9649,plain,
( ( sk5 @ cyclefreeP )
| ( sk5 @ sk12 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[9648:[bind(A,$thf( sk5 ))]]) ).
thf(9852,plain,
! [A: $i] :
( ( ( sk5 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk5 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[9649,246]) ).
thf(9853,plain,
! [A: $i] :
( ( ( sk5 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk5 @ cyclefreeP ) ),
inference(simp,[status(thm)],[9852]) ).
thf(9854,plain,
( ~ ( sk5 @ sk12 @ ( nil @ memberP ) )
| ( sk5 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[9853:[bind(A,$thf( sk5 @ sk12 ))]]) ).
thf(168,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)],[167]) ).
thf(178,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)],[168]) ).
thf(179,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)],[178]) ).
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(211,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(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(514,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(24,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax65) ).
thf(206,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(207,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[206]) ).
thf(28520,plain,
! [A: $i] :
( ( ( sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,207]) ).
thf(28521,plain,
! [A: $i] :
( ( ( sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[28520]) ).
thf(28522,plain,
nil @ ( sk8 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[28521:[bind(A,$thf( sk8 ))]]) ).
thf(888,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,342]) ).
thf(889,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[888]) ).
thf(890,plain,
~ ( sk6 @ ( sk6 @ neq ) ),
inference(pattern_uni,[status(thm)],[889:[bind(A,$thf( sk6 ))]]) ).
thf(3965,plain,
( ( sk6 != sk6 )
| ~ ( nil @ ( sk6 @ neq ) )
| ~ ( sk6 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[3463,890]) ).
thf(3966,plain,
( ~ ( nil @ ( sk6 @ neq ) )
| ~ ( sk6 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[3965:[]]) ).
thf(8319,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ( A @ sk11 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[100,171]) ).
thf(8320,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ( A @ sk11 @ leq ) ) ),
inference(simp,[status(thm)],[8319]) ).
thf(8321,plain,
( ( sk10 @ cyclefreeP )
| ( sk10 @ sk12 @ ( sk10 @ sk11 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[8320:[bind(A,$thf( sk10 ))]]) ).
thf(3735,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ( sk2 = nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[3310,566]) ).
thf(3736,plain,
( ( sk1 != sk1 )
| ( sk2 = nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[3735]) ).
thf(3737,plain,
( ( sk2 = nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[3736:[]]) ).
thf(27468,plain,
( ( ( sk5 @ ( sk5 @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ( sk2 = nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[27156,3737]) ).
thf(27469,plain,
( ( ( sk5 @ ( sk5 @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ( sk2 = nil ) ),
inference(simp,[status(thm)],[27468]) ).
thf(27515,plain,
( ( sk5 != sk1 )
| ( sk5 != nil )
| ( sk2 = nil ) ),
inference(simp,[status(thm)],[27469]) ).
thf(405,plain,
sk43 @ ssItem,
inference(cnfConj,[status(thm)],[404]) ).
thf(572,plain,
! [A: $i] :
( ( ( sk43 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[405,246]) ).
thf(573,plain,
! [A: $i] :
( ( ( sk43 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[572]) ).
thf(574,plain,
~ ( sk43 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[573:[bind(A,$thf( sk43 ))]]) ).
thf(10301,plain,
! [A: $i] :
( ( ( sk10 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk10 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[9774,246]) ).
thf(10302,plain,
! [A: $i] :
( ( ( sk10 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk10 @ cyclefreeP ) ),
inference(simp,[status(thm)],[10301]) ).
thf(10303,plain,
( ~ ( sk10 @ sk12 @ ( nil @ memberP ) )
| ( sk10 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[10302:[bind(A,$thf( sk10 @ sk12 ))]]) ).
thf(19081,plain,
( ( ( sk44 @ ssList )
!= ( sk10 @ ssList ) )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[100,2800]) ).
thf(19082,plain,
( ( ( sk44 @ ssList )
!= ( sk10 @ ssList ) )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[19081]) ).
thf(19085,plain,
( ( sk44 != sk10 )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[19082]) ).
thf(10420,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[108,175]) ).
thf(10421,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssItem ) ),
inference(simp,[status(thm)],[10420]) ).
thf(10422,plain,
( ( sk9 @ cyclefreeP )
| ( sk9 @ sk11 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[10421:[bind(A,$thf( sk9 ))]]) ).
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(265,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(46,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ equalelemsP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax73) ).
thf(312,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ equalelemsP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(237,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk21 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[233]) ).
thf(53373,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk21 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[108,237]) ).
thf(53374,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk21 @ ssItem ) ),
inference(simp,[status(thm)],[53373]) ).
thf(53375,plain,
( ( sk9 @ strictorderedP )
| ( sk9 @ sk21 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[53374:[bind(A,$thf( sk9 ))]]) ).
thf(9738,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[114,174]) ).
thf(9739,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssItem ) ),
inference(simp,[status(thm)],[9738]) ).
thf(9740,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk12 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[9739:[bind(A,$thf( sk1 ))]]) ).
thf(10143,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[9740,131]) ).
thf(10144,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[10143]) ).
thf(10145,plain,
( ( nil @ ( sk1 @ sk12 @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[10144:[bind(A,$thf( sk1 @ sk12 ))]]) ).
thf(19011,plain,
( ( ( sk44 @ ssList )
!= ( sk9 @ ssList ) )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[108,2800]) ).
thf(19012,plain,
( ( ( sk44 @ ssList )
!= ( sk9 @ ssList ) )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[19011]) ).
thf(19095,plain,
( ( sk44 != sk9 )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[19012]) ).
thf(75,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ rearsegP ) )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax52) ).
thf(454,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(455,plain,
! [A: $i] :
( ( ( A @ ( nil @ rearsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) )
& ( ( nil = A )
| ~ ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[454]) ).
thf(457,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[455]) ).
thf(459,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[457]) ).
thf(460,plain,
( ( nil @ ( nil @ rearsegP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[459]) ).
thf(865,plain,
( ( nil @ ( nil @ rearsegP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[460,358]) ).
thf(866,plain,
nil @ ( nil @ rearsegP ),
inference(simp,[status(thm)],[865]) ).
thf(190,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk19 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[183]) ).
thf(18195,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk19 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,190]) ).
thf(18196,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk19 @ ssList ) ),
inference(simp,[status(thm)],[18195]) ).
thf(18197,plain,
( ( sk6 @ strictorderP )
| ( sk6 @ sk19 @ ssList ) ),
inference(pattern_uni,[status(thm)],[18196:[bind(A,$thf( sk6 ))]]) ).
thf(1621,plain,
( ( sk2 != sk2 )
| ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1212,881]) ).
thf(1622,plain,
( ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1621:[]]) ).
thf(10214,plain,
! [A: $i] :
( ( ( sk6 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk6 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[9768,246]) ).
thf(10215,plain,
! [A: $i] :
( ( ( sk6 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk6 @ cyclefreeP ) ),
inference(simp,[status(thm)],[10214]) ).
thf(10216,plain,
( ~ ( sk6 @ sk12 @ ( nil @ memberP ) )
| ( sk6 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[10215:[bind(A,$thf( sk6 @ sk12 ))]]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ tl @ ssList ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
thf(307,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ tl @ ssList ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(3581,plain,
( ( sk2 != sk2 )
| ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2897,881]) ).
thf(3582,plain,
( ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[3581:[]]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax61) ).
thf(380,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(8653,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk14 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,172]) ).
thf(8654,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk14 @ ssList ) ),
inference(simp,[status(thm)],[8653]) ).
thf(8655,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk14 @ ssList ) ),
inference(pattern_uni,[status(thm)],[8654:[bind(A,$thf( sk2 ))]]) ).
thf(18143,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk19 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[114,190]) ).
thf(18144,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk19 @ ssList ) ),
inference(simp,[status(thm)],[18143]) ).
thf(18145,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk19 @ ssList ) ),
inference(pattern_uni,[status(thm)],[18144:[bind(A,$thf( sk1 ))]]) ).
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(201,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(95,axiom,
nil @ totalorderP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax62) ).
thf(534,plain,
nil @ totalorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(3678,plain,
( ( sk9 != sk9 )
| ~ ( nil @ ( sk9 @ neq ) )
| ~ ( sk9 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[3174,884]) ).
thf(3679,plain,
( ~ ( nil @ ( sk9 @ neq ) )
| ~ ( sk9 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[3678:[]]) ).
thf(9720,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[108,174]) ).
thf(9721,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ssItem ) ),
inference(simp,[status(thm)],[9720]) ).
thf(9722,plain,
( ( sk9 @ cyclefreeP )
| ( sk9 @ sk12 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[9721:[bind(A,$thf( sk9 ))]]) ).
thf(7868,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ( A @ sk12 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,169]) ).
thf(7869,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ( A @ sk12 @ leq ) ) ),
inference(simp,[status(thm)],[7868]) ).
thf(7870,plain,
( ( sk6 @ cyclefreeP )
| ( sk6 @ sk11 @ ( sk6 @ sk12 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[7869:[bind(A,$thf( sk6 ))]]) ).
thf(27444,plain,
( ( sk5 != sk5 )
| ( nil @ ( sk5 @ segmentP ) )
| ~ ( sk5 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1178,27156]) ).
thf(27445,plain,
( ( nil @ ( sk5 @ segmentP ) )
| ~ ( sk5 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[27444:[]]) ).
thf(9947,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[9659,246]) ).
thf(9948,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[9947]) ).
thf(9949,plain,
( ~ ( sk2 @ sk12 @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[9948:[bind(A,$thf( sk2 @ sk12 ))]]) ).
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(158,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(159,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ cons ) )
= ( A @ ( nil @ ( B @ cons ) @ app ) ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[158]) ).
thf(160,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( ( A @ ( B @ cons ) )
= ( A @ ( nil @ ( B @ cons ) @ app ) ) ) ),
inference(lifteq,[status(thm)],[159]) ).
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(163,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(164,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)],[163]) ).
thf(165,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)],[164]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ app ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
thf(227,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ app ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(228,plain,
! [A: $i] :
( ( ( A @ ( nil @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[227]) ).
thf(229,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[228]) ).
thf(45954,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[110,229]) ).
thf(45955,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[45954]) ).
thf(45956,plain,
( ( sk5 @ ( nil @ app ) )
= sk5 ),
inference(pattern_uni,[status(thm)],[45955:[bind(A,$thf( sk5 ))]]) ).
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(334,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(15960,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk17 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[114,187]) ).
thf(15961,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk17 @ ssItem ) ),
inference(simp,[status(thm)],[15960]) ).
thf(15962,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk17 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[15961:[bind(A,$thf( sk1 ))]]) ).
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(424,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(27785,plain,
( ( sk1 != sk1 )
| ( nil @ ( sk1 @ segmentP ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[3310,27302]) ).
thf(27786,plain,
( ( nil @ ( sk1 @ segmentP ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[27785:[]]) ).
thf(45147,plain,
( ( ( sk1 @ ( nil @ segmentP ) )
!= ( nil @ ( nil @ segmentP ) ) )
| ( nil @ ( sk1 @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[864,27786]) ).
thf(45148,plain,
( ( ( sk1 @ ( nil @ segmentP ) )
!= ( nil @ ( nil @ segmentP ) ) )
| ( nil @ ( sk1 @ segmentP ) ) ),
inference(simp,[status(thm)],[45147]) ).
thf(45255,plain,
( ( sk1 != nil )
| ( nil != nil )
| ( nil @ ( sk1 @ segmentP ) ) ),
inference(simp,[status(thm)],[45148]) ).
thf(45312,plain,
( ( sk1 != nil )
| ( nil @ ( sk1 @ segmentP ) ) ),
inference(simp,[status(thm)],[45255]) ).
thf(235,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk25 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[233]) ).
thf(49985,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk25 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,235]) ).
thf(49986,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk25 @ ssList ) ),
inference(simp,[status(thm)],[49985]) ).
thf(49987,plain,
( ( sk6 @ strictorderedP )
| ( sk6 @ sk25 @ ssList ) ),
inference(pattern_uni,[status(thm)],[49986:[bind(A,$thf( sk6 ))]]) ).
thf(28498,plain,
! [A: $i] :
( ( ( sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[102,207]) ).
thf(28499,plain,
! [A: $i] :
( ( ( sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[28498]) ).
thf(28500,plain,
nil @ ( sk7 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[28499:[bind(A,$thf( sk7 ))]]) ).
thf(8698,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk14 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[108,172]) ).
thf(8699,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk14 @ ssList ) ),
inference(simp,[status(thm)],[8698]) ).
thf(8700,plain,
( ( sk9 @ cyclefreeP )
| ( sk9 @ sk14 @ ssList ) ),
inference(pattern_uni,[status(thm)],[8699:[bind(A,$thf( sk9 ))]]) ).
thf(38387,plain,
( ( ( sk9 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk9 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[697,27679]) ).
thf(38388,plain,
( ( ( sk9 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk9 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[38387]) ).
thf(38500,plain,
( ( sk9 != nil )
| ( nil != nil )
| ( sk9 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[38388]) ).
thf(38539,plain,
( ( sk9 != nil )
| ( sk9 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[38500]) ).
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(461,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(47679,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk24 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[110,234]) ).
thf(47680,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk24 @ ssList ) ),
inference(simp,[status(thm)],[47679]) ).
thf(47681,plain,
( ( sk5 @ strictorderedP )
| ( sk5 @ sk24 @ ssList ) ),
inference(pattern_uni,[status(thm)],[47680:[bind(A,$thf( sk5 ))]]) ).
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(484,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) @ tl )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(1144,plain,
! [A: $i] :
( ( A != sk44 )
| ( sk43 != nil )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[136,408]) ).
thf(1145,plain,
( ( sk43 != nil )
| ~ ( sk44 @ ( nil @ frontsegP ) )
| ~ ( sk44 @ ssList ) ),
inference(pattern_uni,[status(thm)],[1144:[bind(A,$thf( sk44 ))]]) ).
thf(13802,plain,
( ( ( sk44 @ ssList )
!= ( sk5 @ ssList ) )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[110,1145]) ).
thf(13803,plain,
( ( ( sk44 @ ssList )
!= ( sk5 @ ssList ) )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[13802]) ).
thf(13924,plain,
( ( sk44 != sk5 )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[13803]) ).
thf(1062,plain,
! [A: $i] :
( ( ( sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[102,131]) ).
thf(1063,plain,
! [A: $i] :
( ( ( sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[1062]) ).
thf(1064,plain,
nil @ ( sk7 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[1063:[bind(A,$thf( sk7 ))]]) ).
thf(7836,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ( A @ sk12 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[108,169]) ).
thf(7837,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ( A @ sk12 @ leq ) ) ),
inference(simp,[status(thm)],[7836]) ).
thf(7838,plain,
( ( sk9 @ cyclefreeP )
| ( sk9 @ sk11 @ ( sk9 @ sk12 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[7837:[bind(A,$thf( sk9 ))]]) ).
thf(23480,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[106,198]) ).
thf(23481,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[23480]) ).
thf(23482,plain,
( ( nil @ ( sk2 @ app ) )
= sk2 ),
inference(pattern_uni,[status(thm)],[23481:[bind(A,$thf( sk2 ))]]) ).
thf(737,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[100,170]) ).
thf(738,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList ) ),
inference(simp,[status(thm)],[737]) ).
thf(739,plain,
( ( sk10 @ cyclefreeP )
| ( sk10 @ sk15 @ ssList ) ),
inference(pattern_uni,[status(thm)],[738:[bind(A,$thf( sk10 ))]]) ).
thf(1087,plain,
! [A: $i] :
( ( ( sk10 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList )
| ~ $true
| ( sk10 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[739,170]) ).
thf(1088,plain,
! [A: $i] :
( ( ( sk10 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList )
| ( sk10 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1087]) ).
thf(1089,plain,
( ( sk10 @ sk15 @ cyclefreeP )
| ( sk10 @ sk15 @ sk15 @ ssList )
| ( sk10 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1088:[bind(A,$thf( sk10 @ sk15 ))]]) ).
thf(20511,plain,
! [A: $i] :
( ( ( sk9 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk9 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[20117,246]) ).
thf(20512,plain,
! [A: $i] :
( ( ( sk9 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk9 @ strictorderP ) ),
inference(simp,[status(thm)],[20511]) ).
thf(20513,plain,
( ~ ( sk9 @ sk16 @ ( nil @ memberP ) )
| ( sk9 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[20512:[bind(A,$thf( sk9 @ sk16 ))]]) ).
thf(19075,plain,
( ( ( sk44 @ ssList )
!= ( sk6 @ ssList ) )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,2800]) ).
thf(19076,plain,
( ( ( sk44 @ ssList )
!= ( sk6 @ ssList ) )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[19075]) ).
thf(19092,plain,
( ( sk44 != sk6 )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[19076]) ).
thf(37192,plain,
( ( ( sk6 @ ( sk6 @ segmentP ) )
!= ( sk44 @ ( nil @ segmentP ) ) )
| ( sk44 != sk6 )
| ( sk43 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[27357,19092]) ).
thf(37193,plain,
( ( ( sk6 @ ( sk6 @ segmentP ) )
!= ( sk44 @ ( nil @ segmentP ) ) )
| ( sk44 != sk6 )
| ( sk43 != nil ) ),
inference(simp,[status(thm)],[37192]) ).
thf(37277,plain,
( ( sk44 != sk6 )
| ( sk6 != nil )
| ( sk44 != sk6 )
| ( sk43 != nil ) ),
inference(simp,[status(thm)],[37193]) ).
thf(37288,plain,
( ( sk6 != nil )
| ( sk44 != sk6 )
| ( sk43 != nil ) ),
inference(simp,[status(thm)],[37277]) ).
thf(54576,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk22 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[110,238]) ).
thf(54577,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk22 @ ssItem ) ),
inference(simp,[status(thm)],[54576]) ).
thf(54578,plain,
( ( sk5 @ strictorderedP )
| ( sk5 @ sk22 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[54577:[bind(A,$thf( sk5 ))]]) ).
thf(870,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[114,342]) ).
thf(871,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[870]) ).
thf(872,plain,
~ ( sk1 @ ( sk1 @ neq ) ),
inference(pattern_uni,[status(thm)],[871:[bind(A,$thf( sk1 ))]]) ).
thf(1560,plain,
( ( sk1 != sk1 )
| ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1129,872]) ).
thf(1561,plain,
( ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1560:[]]) ).
thf(1701,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk1 @ ( nil @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[697,1561]) ).
thf(1702,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk1 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[1701]) ).
thf(1720,plain,
( ( sk1 != nil )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[1702]) ).
thf(1722,plain,
( ( sk1 != nil )
| ~ ( sk1 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[1720]) ).
thf(3744,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[3310,1722]) ).
thf(3745,plain,
( ( sk1 != sk1 )
| ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[3744]) ).
thf(3746,plain,
( ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[3745:[]]) ).
thf(1794,plain,
( ( sk10 != sk10 )
| ~ ( nil @ ( sk10 @ neq ) )
| ~ ( sk10 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1523,893]) ).
thf(1795,plain,
( ~ ( nil @ ( sk10 @ neq ) )
| ~ ( sk10 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1794:[]]) ).
thf(6875,plain,
( ( ( sk10 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( sk10 @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[697,1795]) ).
thf(6876,plain,
( ( ( sk10 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( sk10 @ neq ) ) ),
inference(simp,[status(thm)],[6875]) ).
thf(6916,plain,
( ( sk10 != nil )
| ( nil != nil )
| ~ ( nil @ ( sk10 @ neq ) ) ),
inference(simp,[status(thm)],[6876]) ).
thf(6919,plain,
( ( sk10 != nil )
| ~ ( nil @ ( sk10 @ neq ) ) ),
inference(simp,[status(thm)],[6916]) ).
thf(8,axiom,
nil @ totalorderedP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax66) ).
thf(141,plain,
nil @ totalorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(27420,plain,
( ( ( sk5 @ ( sk5 @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) )
| ~ $true
| ( sk2 = nil ) ),
inference(paramod_ordered,[status(thm)],[27156,2897]) ).
thf(27421,plain,
( ( ( sk5 @ ( sk5 @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) )
| ( sk2 = nil ) ),
inference(simp,[status(thm)],[27420]) ).
thf(27518,plain,
( ( sk5 != sk2 )
| ( sk5 != nil )
| ( sk2 = nil ) ),
inference(simp,[status(thm)],[27421]) ).
thf(10438,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[114,175]) ).
thf(10439,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssItem ) ),
inference(simp,[status(thm)],[10438]) ).
thf(10440,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk11 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[10439:[bind(A,$thf( sk1 ))]]) ).
thf(10821,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[10440,246]) ).
thf(10822,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[10821]) ).
thf(10823,plain,
( ~ ( sk1 @ sk11 @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[10822:[bind(A,$thf( sk1 @ sk11 ))]]) ).
thf(2840,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[110,151]) ).
thf(2841,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[2840]) ).
thf(2842,plain,
( ~ ( sk5 @ ( nil @ segmentP ) )
| ( sk5 = nil ) ),
inference(pattern_uni,[status(thm)],[2841:[bind(A,$thf( sk5 ))]]) ).
thf(27460,plain,
( ( sk5 != sk5 )
| ( nil @ ( sk5 @ segmentP ) )
| ~ ( sk5 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2842,27156]) ).
thf(27461,plain,
( ( nil @ ( sk5 @ segmentP ) )
| ~ ( sk5 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[27460:[]]) ).
thf(109,plain,
~ ( sk8 @ ( sk7 @ neq ) ),
inference(cnfConj,[status(thm)],[99]) ).
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(471,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(9870,plain,
! [A: $i] :
( ( ( sk5 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk5 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[9649,131]) ).
thf(9871,plain,
! [A: $i] :
( ( ( sk5 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk5 @ cyclefreeP ) ),
inference(simp,[status(thm)],[9870]) ).
thf(9872,plain,
( ( nil @ ( sk5 @ sk12 @ cons ) @ strictorderedP )
| ( sk5 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[9871:[bind(A,$thf( sk5 @ sk12 ))]]) ).
thf(27551,plain,
( ( sk2 != sk2 )
| ( sk2 @ ( nil @ segmentP ) )
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[566,27184]) ).
thf(27552,plain,
( ( sk2 @ ( nil @ segmentP ) )
| ( sk1 != nil ) ),
inference(pattern_uni,[status(thm)],[27551:[]]) ).
thf(18967,plain,
( ( ( sk44 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,2800]) ).
thf(18968,plain,
( ( ( sk44 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[18967]) ).
thf(19115,plain,
( ( sk44 != sk2 )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[18968]) ).
thf(48964,plain,
( ( ( sk44 @ ( nil @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) )
| ( sk44 != sk2 )
| ( sk43 != nil )
| ~ $true
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[27552,19115]) ).
thf(48965,plain,
( ( ( sk44 @ ( nil @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) )
| ( sk44 != sk2 )
| ( sk43 != nil )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[48964]) ).
thf(49048,plain,
( ( sk44 != sk2 )
| ( nil != nil )
| ( sk44 != sk2 )
| ( sk43 != nil )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[48965]) ).
thf(49067,plain,
( ( sk44 != sk2 )
| ( sk43 != nil )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[49048]) ).
thf(117,plain,
( ( sk10 @ ( nil @ ( sk8 @ cons ) @ ( nil @ ( sk7 @ cons ) @ ( sk9 @ app ) @ app ) @ app ) )
= sk1 ),
inference(cnfConj,[status(thm)],[99]) ).
thf(124,plain,
( ( sk10 @ ( nil @ ( sk8 @ cons ) @ ( nil @ ( sk7 @ cons ) @ ( sk9 @ app ) @ app ) @ app ) )
= sk1 ),
inference(lifteq,[status(thm)],[117]) ).
thf(1658,plain,
( ( sk9 != sk9 )
| ~ ( nil @ ( sk9 @ neq ) )
| ~ ( sk9 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1364,884]) ).
thf(1659,plain,
( ~ ( nil @ ( sk9 @ neq ) )
| ~ ( sk9 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1658:[]]) ).
thf(1773,plain,
( ( sk6 != sk6 )
| ~ ( sk6 @ ( nil @ neq ) )
| ~ ( sk6 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1514,890]) ).
thf(1774,plain,
( ~ ( sk6 @ ( nil @ neq ) )
| ~ ( sk6 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1773:[]]) ).
thf(5658,plain,
( ( ( sk6 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk6 @ ( nil @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[697,1774]) ).
thf(5659,plain,
( ( ( sk6 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk6 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[5658]) ).
thf(5687,plain,
( ( sk6 != nil )
| ( nil != nil )
| ~ ( sk6 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[5659]) ).
thf(5694,plain,
( ( sk6 != nil )
| ~ ( sk6 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[5687]) ).
thf(406,plain,
sk44 @ ssItem,
inference(cnfConj,[status(thm)],[404]) ).
thf(28538,plain,
! [A: $i] :
( ( ( sk44 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[406,207]) ).
thf(28539,plain,
! [A: $i] :
( ( ( sk44 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[28538]) ).
thf(28540,plain,
nil @ ( sk44 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[28539:[bind(A,$thf( sk44 ))]]) ).
thf(103,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 ) )
!= sk6 )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(125,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 ) )
!= sk6 ) ),
inference(lifteq,[status(thm)],[103]) ).
thf(126,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 ) )
!= sk6 ) ),
inference(simp,[status(thm)],[125]) ).
thf(753,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 ) )
!= sk6 ) ),
inference(rewrite,[status(thm)],[126,123]) ).
thf(1619,plain,
( ( sk2 != sk2 )
| ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1212,881]) ).
thf(1620,plain,
( ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1619:[]]) ).
thf(2532,plain,
( ( ( sk2 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk2 @ ( nil @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[697,1620]) ).
thf(2533,plain,
( ( ( sk2 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk2 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[2532]) ).
thf(2558,plain,
( ( sk2 != nil )
| ( nil != nil )
| ~ ( sk2 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[2533]) ).
thf(2561,plain,
( ( sk2 != nil )
| ~ ( sk2 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[2558]) ).
thf(49994,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk25 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[100,235]) ).
thf(49995,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk25 @ ssList ) ),
inference(simp,[status(thm)],[49994]) ).
thf(49996,plain,
( ( sk10 @ strictorderedP )
| ( sk10 @ sk25 @ ssList ) ),
inference(pattern_uni,[status(thm)],[49995:[bind(A,$thf( sk10 ))]]) ).
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(489,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(895,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[715,170]) ).
thf(896,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[895]) ).
thf(897,plain,
( ( sk1 @ sk15 @ cyclefreeP )
| ( sk1 @ sk15 @ sk15 @ ssList )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[896:[bind(A,$thf( sk1 @ sk15 ))]]) ).
thf(1935,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList )
| ~ $true
| ( sk1 @ sk15 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[897,170]) ).
thf(1936,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList )
| ( sk1 @ sk15 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1935]) ).
thf(1937,plain,
( ( sk1 @ sk15 @ sk15 @ cyclefreeP )
| ( sk1 @ sk15 @ sk15 @ sk15 @ ssList )
| ( sk1 @ sk15 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1936:[bind(A,$thf( sk1 @ sk15 @ sk15 ))]]) ).
thf(212,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)],[211]) ).
thf(704,plain,
! [A: $i] :
( ( ( sk43 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[405,231]) ).
thf(705,plain,
! [A: $i] :
( ( ( sk43 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[704]) ).
thf(706,plain,
~ ( sk43 @ ( sk43 @ lt ) ),
inference(pattern_uni,[status(thm)],[705:[bind(A,$thf( sk43 ))]]) ).
thf(2266,plain,
( ( ( sk5 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk5 @ ( nil @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[697,1591]) ).
thf(2267,plain,
( ( ( sk5 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk5 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[2266]) ).
thf(2283,plain,
( ( sk5 != nil )
| ( nil != nil )
| ~ ( sk5 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[2267]) ).
thf(2285,plain,
( ( sk5 != nil )
| ~ ( sk5 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[2283]) ).
thf(1775,plain,
( ( sk6 != sk6 )
| ~ ( nil @ ( sk6 @ neq ) )
| ~ ( sk6 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1514,890]) ).
thf(1776,plain,
( ~ ( nil @ ( sk6 @ neq ) )
| ~ ( sk6 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1775:[]]) ).
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(371,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(372,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)],[371]) ).
thf(375,plain,
! [B: $i,A: $i] :
( ( nil
= ( B @ ( A @ app ) ) )
| ( nil != A )
| ( nil != B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[372]) ).
thf(378,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
= nil )
| ( nil != A )
| ( nil != B ) ),
inference(lifteq,[status(thm)],[375]) ).
thf(379,plain,
( ~ ( nil @ ssList )
| ( ( nil @ ( nil @ app ) )
= nil ) ),
inference(simp,[status(thm)],[378]) ).
thf(2486,plain,
( ~ $true
| ( ( nil @ ( nil @ app ) )
= nil ) ),
inference(rewrite,[status(thm)],[379,358]) ).
thf(2487,plain,
( ( nil @ ( nil @ app ) )
= nil ),
inference(simp,[status(thm)],[2486]) ).
thf(15833,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk17 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[110,187]) ).
thf(15834,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk17 @ ssItem ) ),
inference(simp,[status(thm)],[15833]) ).
thf(15835,plain,
( ( sk5 @ strictorderP )
| ( sk5 @ sk17 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[15834:[bind(A,$thf( sk5 ))]]) ).
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(128,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(129,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)],[128]) ).
thf(47718,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk24 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,234]) ).
thf(47719,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk24 @ ssList ) ),
inference(simp,[status(thm)],[47718]) ).
thf(47720,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk24 @ ssList ) ),
inference(pattern_uni,[status(thm)],[47719:[bind(A,$thf( sk2 ))]]) ).
thf(85,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ geq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax89) ).
thf(503,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(10347,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[110,175]) ).
thf(10348,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssItem ) ),
inference(simp,[status(thm)],[10347]) ).
thf(10349,plain,
( ( sk5 @ cyclefreeP )
| ( sk5 @ sk11 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[10348:[bind(A,$thf( sk5 ))]]) ).
thf(8737,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk14 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[114,172]) ).
thf(8738,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk14 @ ssList ) ),
inference(simp,[status(thm)],[8737]) ).
thf(8739,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk14 @ ssList ) ),
inference(pattern_uni,[status(thm)],[8738:[bind(A,$thf( sk1 ))]]) ).
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(508,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(10738,plain,
! [A: $i] :
( ( ( sk9 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk9 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[10422,246]) ).
thf(10739,plain,
! [A: $i] :
( ( ( sk9 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk9 @ cyclefreeP ) ),
inference(simp,[status(thm)],[10738]) ).
thf(10740,plain,
( ~ ( sk9 @ sk11 @ ( nil @ memberP ) )
| ( sk9 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[10739:[bind(A,$thf( sk9 @ sk11 ))]]) ).
thf(16664,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk18 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[110,188]) ).
thf(16665,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk18 @ ssList ) ),
inference(simp,[status(thm)],[16664]) ).
thf(16666,plain,
( ( sk5 @ strictorderP )
| ( sk5 @ sk18 @ ssList ) ),
inference(pattern_uni,[status(thm)],[16665:[bind(A,$thf( sk5 ))]]) ).
thf(1562,plain,
( ( sk1 != sk1 )
| ~ ( nil @ ( sk1 @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1129,872]) ).
thf(1563,plain,
( ~ ( nil @ ( sk1 @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1562:[]]) ).
thf(725,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[108,170]) ).
thf(726,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList ) ),
inference(simp,[status(thm)],[725]) ).
thf(727,plain,
( ( sk9 @ cyclefreeP )
| ( sk9 @ sk15 @ ssList ) ),
inference(pattern_uni,[status(thm)],[726:[bind(A,$thf( sk9 ))]]) ).
thf(1033,plain,
! [A: $i] :
( ( ( sk9 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList )
| ~ $true
| ( sk9 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[727,170]) ).
thf(1034,plain,
! [A: $i] :
( ( ( sk9 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList )
| ( sk9 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1033]) ).
thf(1035,plain,
( ( sk9 @ sk15 @ cyclefreeP )
| ( sk9 @ sk15 @ sk15 @ ssList )
| ( sk9 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1034:[bind(A,$thf( sk9 @ sk15 ))]]) ).
thf(8260,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ( A @ sk11 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,171]) ).
thf(8261,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ( A @ sk11 @ leq ) ) ),
inference(simp,[status(thm)],[8260]) ).
thf(8262,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk12 @ ( sk2 @ sk11 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[8261:[bind(A,$thf( sk2 ))]]) ).
thf(10357,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,175]) ).
thf(10358,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssItem ) ),
inference(simp,[status(thm)],[10357]) ).
thf(10359,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk11 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[10358:[bind(A,$thf( sk2 ))]]) ).
thf(27813,plain,
( ( sk1 != sk1 )
| ( nil @ ( sk1 @ segmentP ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1129,27302]) ).
thf(27814,plain,
( ( nil @ ( sk1 @ segmentP ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[27813:[]]) ).
thf(3673,plain,
( ( sk9 != sk9 )
| ( nil != nil )
| ~ ( sk9 @ ( nil @ neq ) )
| ~ ( sk9 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[3174,2723]) ).
thf(3674,plain,
( ( sk9 != sk9 )
| ~ ( sk9 @ ( nil @ neq ) )
| ~ ( sk9 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[3673]) ).
thf(3675,plain,
( ~ ( sk9 @ ( nil @ neq ) )
| ~ ( sk9 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[3674:[]]) ).
thf(7815,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ( A @ sk12 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,169]) ).
thf(7816,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ( A @ sk12 @ leq ) ) ),
inference(simp,[status(thm)],[7815]) ).
thf(7817,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk11 @ ( sk2 @ sk12 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[7816:[bind(A,$thf( sk2 ))]]) ).
thf(13913,plain,
( ( ( sk44 @ ssList )
!= ( sk10 @ ssList ) )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[100,1145]) ).
thf(13914,plain,
( ( ( sk44 @ ssList )
!= ( sk10 @ ssList ) )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[13913]) ).
thf(13932,plain,
( ( sk44 != sk10 )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[13914]) ).
thf(10056,plain,
! [A: $i] :
( ( ( sk9 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk9 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[9722,131]) ).
thf(10057,plain,
! [A: $i] :
( ( ( sk9 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk9 @ cyclefreeP ) ),
inference(simp,[status(thm)],[10056]) ).
thf(10058,plain,
( ( nil @ ( sk9 @ sk12 @ cons ) @ strictorderedP )
| ( sk9 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[10057:[bind(A,$thf( sk9 @ sk12 ))]]) ).
thf(23451,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[110,198]) ).
thf(23452,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[23451]) ).
thf(23453,plain,
( ( nil @ ( sk5 @ app ) )
= sk5 ),
inference(pattern_uni,[status(thm)],[23452:[bind(A,$thf( sk5 ))]]) ).
thf(23796,plain,
( ( ( sk1 @ ( sk5 @ app ) )
!= ( nil @ ( sk5 @ app ) ) )
| ( ( sk6 @ ( sk5 @ app ) )
= sk2 ) ),
inference(paramod_ordered,[status(thm)],[23453,557]) ).
thf(23835,plain,
( ( sk1 != nil )
| ( sk5 != sk5 )
| ( ( sk6 @ ( sk5 @ app ) )
= sk2 ) ),
inference(simp,[status(thm)],[23796]) ).
thf(23859,plain,
( ( sk1 != nil )
| ( ( sk6 @ ( sk5 @ app ) )
= sk2 ) ),
inference(simp,[status(thm)],[23835]) ).
thf(24695,plain,
( ( ( sk6 @ ( sk5 @ app ) )
!= ( nil @ ( sk5 @ app ) ) )
| ( sk1 != nil )
| ( sk5 = sk2 ) ),
inference(paramod_ordered,[status(thm)],[23453,23859]) ).
thf(24756,plain,
( ( sk6 != nil )
| ( sk5 != sk5 )
| ( sk1 != nil )
| ( sk5 = sk2 ) ),
inference(simp,[status(thm)],[24695]) ).
thf(24795,plain,
( ( sk6 != nil )
| ( sk1 != nil )
| ( sk5 = sk2 ) ),
inference(simp,[status(thm)],[24756]) ).
thf(904,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[715,342]) ).
thf(905,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[904]) ).
thf(906,plain,
( ~ ( sk1 @ sk15 @ ( sk1 @ sk15 @ neq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[905:[bind(A,$thf( sk1 @ sk15 ))]]) ).
thf(46215,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[100,229]) ).
thf(46216,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[46215]) ).
thf(46217,plain,
( ( sk10 @ ( nil @ app ) )
= sk10 ),
inference(pattern_uni,[status(thm)],[46216:[bind(A,$thf( sk10 ))]]) ).
thf(27366,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[100,205]) ).
thf(27367,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[27366]) ).
thf(27368,plain,
sk10 @ ( sk10 @ segmentP ),
inference(pattern_uni,[status(thm)],[27367:[bind(A,$thf( sk10 ))]]) ).
thf(69,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ cyclefreeP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax59) ).
thf(430,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ cyclefreeP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(14252,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk20 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,185]) ).
thf(14253,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk20 @ ssList ) ),
inference(simp,[status(thm)],[14252]) ).
thf(14254,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk20 @ ssList ) ),
inference(pattern_uni,[status(thm)],[14253:[bind(A,$thf( sk2 ))]]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( A @ ( B @ cons ) @ ssList ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
thf(180,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( A @ ( B @ cons ) @ ssList ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(73,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax63) ).
thf(444,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(28577,plain,
! [A: $i] :
( ( ( sk43 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[405,207]) ).
thf(28578,plain,
! [A: $i] :
( ( ( sk43 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[28577]) ).
thf(28579,plain,
nil @ ( sk43 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[28578:[bind(A,$thf( sk43 ))]]) ).
thf(27581,plain,
( ( sk2 != sk2 )
| ( nil @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[3737,27184]) ).
thf(27582,plain,
( ( nil @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[27581:[]]) ).
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(161,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(710,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[110,170]) ).
thf(711,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList ) ),
inference(simp,[status(thm)],[710]) ).
thf(712,plain,
( ( sk5 @ cyclefreeP )
| ( sk5 @ sk15 @ ssList ) ),
inference(pattern_uni,[status(thm)],[711:[bind(A,$thf( sk5 ))]]) ).
thf(743,plain,
! [A: $i] :
( ( ( sk5 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList )
| ~ $true
| ( sk5 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[712,170]) ).
thf(744,plain,
! [A: $i] :
( ( ( sk5 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList )
| ( sk5 @ cyclefreeP ) ),
inference(simp,[status(thm)],[743]) ).
thf(745,plain,
( ( sk5 @ sk15 @ cyclefreeP )
| ( sk5 @ sk15 @ sk15 @ ssList )
| ( sk5 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[744:[bind(A,$thf( sk5 @ sk15 ))]]) ).
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(279,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(10319,plain,
! [A: $i] :
( ( ( sk10 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk10 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[9774,131]) ).
thf(10320,plain,
! [A: $i] :
( ( ( sk10 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk10 @ cyclefreeP ) ),
inference(simp,[status(thm)],[10319]) ).
thf(10321,plain,
( ( nil @ ( sk10 @ sk12 @ cons ) @ strictorderedP )
| ( sk10 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[10320:[bind(A,$thf( sk10 @ sk12 ))]]) ).
thf(191,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ sk16 @ ( A @ sk17 @ lt ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[183]) ).
thf(13832,plain,
( ( ( sk44 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk43 != nil )
| ~ $true
| ~ ( sk44 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[697,1145]) ).
thf(13833,plain,
( ( ( sk44 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk43 != nil )
| ~ ( sk44 @ ssList ) ),
inference(simp,[status(thm)],[13832]) ).
thf(13929,plain,
( ( sk44 != nil )
| ( nil != nil )
| ( sk43 != nil )
| ~ ( sk44 @ ssList ) ),
inference(simp,[status(thm)],[13833]) ).
thf(13960,plain,
( ( sk44 != nil )
| ( sk43 != nil )
| ~ ( sk44 @ ssList ) ),
inference(simp,[status(thm)],[13929]) ).
thf(14049,plain,
( ( ( sk44 @ ssList )
!= ( nil @ ssList ) )
| ( sk44 != nil )
| ( sk43 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[358,13960]) ).
thf(14050,plain,
( ( ( sk44 @ ssList )
!= ( nil @ ssList ) )
| ( sk44 != nil )
| ( sk43 != nil ) ),
inference(simp,[status(thm)],[14049]) ).
thf(14082,plain,
( ( sk44 != nil )
| ( sk44 != nil )
| ( sk43 != nil ) ),
inference(simp,[status(thm)],[14050]) ).
thf(14111,plain,
( ( sk44 != nil )
| ( sk43 != nil ) ),
inference(simp,[status(thm)],[14082]) ).
thf(14479,plain,
! [A: $i] :
( ( A != sk43 )
| ( sk44 != nil )
| ( nil != nil )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[136,14111]) ).
thf(14480,plain,
! [A: $i] :
( ( A != sk43 )
| ( sk44 != nil )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[14479]) ).
thf(14481,plain,
( ( sk44 != nil )
| ~ ( sk43 @ ( nil @ frontsegP ) )
| ~ ( sk43 @ ssList ) ),
inference(pattern_uni,[status(thm)],[14480:[bind(A,$thf( sk43 ))]]) ).
thf(48013,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk24 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[100,234]) ).
thf(48014,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk24 @ ssList ) ),
inference(simp,[status(thm)],[48013]) ).
thf(48015,plain,
( ( sk10 @ strictorderedP )
| ( sk10 @ sk24 @ ssList ) ),
inference(pattern_uni,[status(thm)],[48014:[bind(A,$thf( sk10 ))]]) ).
thf(14324,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk20 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[108,185]) ).
thf(14325,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk20 @ ssList ) ),
inference(simp,[status(thm)],[14324]) ).
thf(14326,plain,
( ( sk9 @ strictorderP )
| ( sk9 @ sk20 @ ssList ) ),
inference(pattern_uni,[status(thm)],[14325:[bind(A,$thf( sk9 ))]]) ).
thf(13856,plain,
( ( ( sk44 @ ssList )
!= ( sk9 @ ssList ) )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[108,1145]) ).
thf(13857,plain,
( ( ( sk44 @ ssList )
!= ( sk9 @ ssList ) )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[13856]) ).
thf(13920,plain,
( ( sk44 != sk9 )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[13857]) ).
thf(560,plain,
! [A: $i] :
( ( ( sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[102,225]) ).
thf(561,plain,
! [A: $i] :
( ( ( sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[560]) ).
thf(562,plain,
~ ( sk7 @ ( sk7 @ neq ) ),
inference(pattern_uni,[status(thm)],[561:[bind(A,$thf( sk7 ))]]) ).
thf(3999,plain,
( ( sk10 != sk10 )
| ~ ( nil @ ( sk10 @ neq ) )
| ~ ( sk10 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[3472,893]) ).
thf(4000,plain,
( ~ ( nil @ ( sk10 @ neq ) )
| ~ ( sk10 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[3999:[]]) ).
thf(20016,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,192]) ).
thf(20017,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssItem ) ),
inference(simp,[status(thm)],[20016]) ).
thf(20018,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk16 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[20017:[bind(A,$thf( sk2 ))]]) ).
thf(20409,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[20018,246]) ).
thf(20410,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[20409]) ).
thf(20411,plain,
( ~ ( sk2 @ sk16 @ ( nil @ memberP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[20410:[bind(A,$thf( sk2 @ sk16 ))]]) ).
thf(873,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[358,342]) ).
thf(874,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[873]) ).
thf(875,plain,
~ ( nil @ ( nil @ neq ) ),
inference(pattern_uni,[status(thm)],[874:[bind(A,$thf( nil ))]]) ).
thf(575,plain,
! [A: $i] :
( ( ( sk44 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[406,225]) ).
thf(576,plain,
! [A: $i] :
( ( ( sk44 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[575]) ).
thf(577,plain,
~ ( sk44 @ ( sk44 @ neq ) ),
inference(pattern_uni,[status(thm)],[576:[bind(A,$thf( sk44 ))]]) ).
thf(27589,plain,
( ( sk2 != sk2 )
| ( nil @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1212,27184]) ).
thf(27590,plain,
( ( nil @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[27589:[]]) ).
thf(49681,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk25 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,235]) ).
thf(49682,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk25 @ ssList ) ),
inference(simp,[status(thm)],[49681]) ).
thf(49683,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk25 @ ssList ) ),
inference(pattern_uni,[status(thm)],[49682:[bind(A,$thf( sk2 ))]]) ).
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(259,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ( A @ tl )
= B )
& ( B @ ssList ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(53514,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk21 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[100,237]) ).
thf(53515,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk21 @ ssItem ) ),
inference(simp,[status(thm)],[53514]) ).
thf(53516,plain,
( ( sk10 @ strictorderedP )
| ( sk10 @ sk21 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[53515:[bind(A,$thf( sk10 ))]]) ).
thf(8765,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk14 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,172]) ).
thf(8766,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk14 @ ssList ) ),
inference(simp,[status(thm)],[8765]) ).
thf(8767,plain,
( ( sk6 @ cyclefreeP )
| ( sk6 @ sk14 @ ssList ) ),
inference(pattern_uni,[status(thm)],[8766:[bind(A,$thf( sk6 ))]]) ).
thf(27565,plain,
( ( sk2 != sk2 )
| ( sk2 @ ( nil @ segmentP ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1557,27184]) ).
thf(27566,plain,
( ( sk2 @ ( nil @ segmentP ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[27565:[]]) ).
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(144,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) @ hd )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1056,plain,
! [A: $i] :
( ( ( sk44 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[406,131]) ).
thf(1057,plain,
! [A: $i] :
( ( ( sk44 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[1056]) ).
thf(1058,plain,
nil @ ( sk44 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[1057:[bind(A,$thf( sk44 ))]]) ).
thf(78,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax42) ).
thf(466,plain,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(236,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ sk22 @ ( A @ sk21 @ lt ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[233]) ).
thf(181,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[180]) ).
thf(15855,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk17 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,187]) ).
thf(15856,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk17 @ ssItem ) ),
inference(simp,[status(thm)],[15855]) ).
thf(15857,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk17 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[15856:[bind(A,$thf( sk2 ))]]) ).
thf(15939,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk17 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[108,187]) ).
thf(15940,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk17 @ ssItem ) ),
inference(simp,[status(thm)],[15939]) ).
thf(15941,plain,
( ( sk9 @ strictorderP )
| ( sk9 @ sk17 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[15940:[bind(A,$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(382,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(3963,plain,
( ( sk6 != sk6 )
| ~ ( sk6 @ ( nil @ neq ) )
| ~ ( sk6 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[3463,890]) ).
thf(3964,plain,
( ~ ( sk6 @ ( nil @ neq ) )
| ~ ( sk6 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[3963:[]]) ).
thf(217,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)],[216]) ).
thf(219,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ gt ) )
| ~ ( A @ ( B @ lt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[217]) ).
thf(14414,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk20 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,185]) ).
thf(14415,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk20 @ ssList ) ),
inference(simp,[status(thm)],[14414]) ).
thf(14416,plain,
( ( sk6 @ strictorderP )
| ( sk6 @ sk20 @ ssList ) ),
inference(pattern_uni,[status(thm)],[14415:[bind(A,$thf( sk6 ))]]) ).
thf(6402,plain,
( ( ( sk10 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk10 @ ( nil @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[697,1793]) ).
thf(6403,plain,
( ( ( sk10 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk10 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[6402]) ).
thf(6440,plain,
( ( sk10 != nil )
| ( nil != nil )
| ~ ( sk10 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[6403]) ).
thf(6443,plain,
( ( sk10 != nil )
| ~ ( sk10 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[6440]) ).
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(362,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(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(208,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(49812,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk25 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[108,235]) ).
thf(49813,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk25 @ ssList ) ),
inference(simp,[status(thm)],[49812]) ).
thf(49814,plain,
( ( sk9 @ strictorderedP )
| ( sk9 @ sk25 @ ssList ) ),
inference(pattern_uni,[status(thm)],[49813:[bind(A,$thf( sk9 ))]]) ).
thf(11000,plain,
! [A: $i] :
( ( ( sk10 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk10 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[10474,246]) ).
thf(11001,plain,
! [A: $i] :
( ( ( sk10 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk10 @ cyclefreeP ) ),
inference(simp,[status(thm)],[11000]) ).
thf(11002,plain,
( ~ ( sk10 @ sk11 @ ( nil @ memberP ) )
| ( sk10 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[11001:[bind(A,$thf( sk10 @ sk11 ))]]) ).
thf(1009,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[724,170]) ).
thf(1010,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1009]) ).
thf(1011,plain,
( ( sk2 @ sk15 @ cyclefreeP )
| ( sk2 @ sk15 @ sk15 @ ssList )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1010:[bind(A,$thf( sk2 @ sk15 ))]]) ).
thf(64,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ duplicatefreeP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax71) ).
thf(419,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ duplicatefreeP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(59,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax45) ).
thf(387,plain,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(17955,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk19 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[110,190]) ).
thf(17956,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk19 @ ssList ) ),
inference(simp,[status(thm)],[17955]) ).
thf(17957,plain,
( ( sk5 @ strictorderP )
| ( sk5 @ sk19 @ ssList ) ),
inference(pattern_uni,[status(thm)],[17956:[bind(A,$thf( sk5 ))]]) ).
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(535,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(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(139,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(140,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[139]) ).
thf(27,axiom,
nil @ duplicatefreeP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax72) ).
thf(213,plain,
nil @ duplicatefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(2287,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList )
| ~ $true
| ( sk2 @ sk15 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[1011,170]) ).
thf(2288,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList )
| ( sk2 @ sk15 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[2287]) ).
thf(2289,plain,
( ( sk2 @ sk15 @ sk15 @ cyclefreeP )
| ( sk2 @ sk15 @ sk15 @ sk15 @ ssList )
| ( sk2 @ sk15 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[2288:[bind(A,$thf( sk2 @ sk15 @ sk15 ))]]) ).
thf(698,plain,
! [A: $i] :
( ( ( sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,231]) ).
thf(699,plain,
! [A: $i] :
( ( ( sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[698]) ).
thf(700,plain,
~ ( sk8 @ ( sk8 @ lt ) ),
inference(pattern_uni,[status(thm)],[699:[bind(A,$thf( sk8 ))]]) ).
thf(92,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( nil
!= ( A @ ( B @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
thf(520,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( nil
!= ( A @ ( B @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(48890,plain,
( ( ( sk44 @ ( nil @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) )
| ( sk44 != sk2 )
| ( sk43 != nil )
| ~ $true
| ( sk2 != nil ) ),
inference(paramod_ordered,[status(thm)],[37934,19115]) ).
thf(48891,plain,
( ( ( sk44 @ ( nil @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) )
| ( sk44 != sk2 )
| ( sk43 != nil )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[48890]) ).
thf(49040,plain,
( ( sk44 != sk2 )
| ( nil != nil )
| ( sk44 != sk2 )
| ( sk43 != nil )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[48891]) ).
thf(49061,plain,
( ( sk44 != sk2 )
| ( sk43 != nil )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[49040]) ).
thf(1059,plain,
! [A: $i] :
( ( ( sk43 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[405,131]) ).
thf(1060,plain,
! [A: $i] :
( ( ( sk43 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[1059]) ).
thf(1061,plain,
nil @ ( sk43 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[1060:[bind(A,$thf( sk43 ))]]) ).
thf(20197,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,192]) ).
thf(20198,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssItem ) ),
inference(simp,[status(thm)],[20197]) ).
thf(20199,plain,
( ( sk6 @ strictorderP )
| ( sk6 @ sk16 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[20198:[bind(A,$thf( sk6 ))]]) ).
thf(20765,plain,
! [A: $i] :
( ( ( sk6 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk6 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[20199,246]) ).
thf(20766,plain,
! [A: $i] :
( ( ( sk6 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk6 @ strictorderP ) ),
inference(simp,[status(thm)],[20765]) ).
thf(20767,plain,
( ~ ( sk6 @ sk16 @ ( nil @ memberP ) )
| ( sk6 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[20766:[bind(A,$thf( sk6 @ sk16 ))]]) ).
thf(54060,plain,
( ( ( sk5 @ ( sk5 @ segmentP ) )
!= ( sk44 @ ( nil @ segmentP ) ) )
| ( sk44 != sk5 )
| ( sk43 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[27156,19127]) ).
thf(54061,plain,
( ( ( sk5 @ ( sk5 @ segmentP ) )
!= ( sk44 @ ( nil @ segmentP ) ) )
| ( sk44 != sk5 )
| ( sk43 != nil ) ),
inference(simp,[status(thm)],[54060]) ).
thf(54195,plain,
( ( sk44 != sk5 )
| ( sk5 != nil )
| ( sk44 != sk5 )
| ( sk43 != nil ) ),
inference(simp,[status(thm)],[54061]) ).
thf(54230,plain,
( ( sk5 != nil )
| ( sk44 != sk5 )
| ( sk43 != nil ) ),
inference(simp,[status(thm)],[54195]) ).
thf(1042,plain,
! [A: $i] :
( ( ( sk9 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk9 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[727,342]) ).
thf(1043,plain,
! [A: $i] :
( ( ( sk9 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ( sk9 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1042]) ).
thf(1044,plain,
( ~ ( sk9 @ sk15 @ ( sk9 @ sk15 @ neq ) )
| ( sk9 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1043:[bind(A,$thf( sk9 @ sk15 ))]]) ).
thf(20206,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[100,192]) ).
thf(20207,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssItem ) ),
inference(simp,[status(thm)],[20206]) ).
thf(20208,plain,
( ( sk10 @ strictorderP )
| ( sk10 @ sk16 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[20207:[bind(A,$thf( sk10 ))]]) ).
thf(18087,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk19 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[108,190]) ).
thf(18088,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk19 @ ssList ) ),
inference(simp,[status(thm)],[18087]) ).
thf(18089,plain,
( ( sk9 @ strictorderP )
| ( sk9 @ sk19 @ ssList ) ),
inference(pattern_uni,[status(thm)],[18088:[bind(A,$thf( sk9 ))]]) ).
thf(16003,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk17 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,187]) ).
thf(16004,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk17 @ ssItem ) ),
inference(simp,[status(thm)],[16003]) ).
thf(16005,plain,
( ( sk6 @ strictorderP )
| ( sk6 @ sk17 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[16004:[bind(A,$thf( sk6 ))]]) ).
thf(23570,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[108,198]) ).
thf(23571,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[23570]) ).
thf(23572,plain,
( ( nil @ ( sk9 @ app ) )
= sk9 ),
inference(pattern_uni,[status(thm)],[23571:[bind(A,$thf( sk9 ))]]) ).
thf(11128,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk13 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[108,176]) ).
thf(11129,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk13 @ ssList ) ),
inference(simp,[status(thm)],[11128]) ).
thf(11130,plain,
( ( sk9 @ cyclefreeP )
| ( sk9 @ sk13 @ ssList ) ),
inference(pattern_uni,[status(thm)],[11129:[bind(A,$thf( sk9 ))]]) ).
thf(223,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ neq ) )
| ( A = B )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[221]) ).
thf(226,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A = B ) ),
inference(lifteq,[status(thm)],[223]) ).
thf(20142,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[114,192]) ).
thf(20143,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssItem ) ),
inference(simp,[status(thm)],[20142]) ).
thf(20144,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk16 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[20143:[bind(A,$thf( sk1 ))]]) ).
thf(20605,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[20144,246]) ).
thf(20606,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[20605]) ).
thf(20607,plain,
( ~ ( sk1 @ sk16 @ ( nil @ memberP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[20606:[bind(A,$thf( sk1 @ sk16 ))]]) ).
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(505,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(16406,plain,
! [A: $i] :
( ( ( sk1 @ sk17 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[15962,246]) ).
thf(16407,plain,
! [A: $i] :
( ( ( sk1 @ sk17 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[16406]) ).
thf(16408,plain,
( ~ ( sk1 @ sk17 @ ( nil @ memberP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[16407:[bind(A,$thf( sk1 @ sk17 ))]]) ).
thf(3521,plain,
( ( sk5 != sk5 )
| ~ ( nil @ ( sk5 @ neq ) )
| ~ ( sk5 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2842,869]) ).
thf(3522,plain,
( ~ ( nil @ ( sk5 @ neq ) )
| ~ ( sk5 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[3521:[]]) ).
thf(23607,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[114,198]) ).
thf(23608,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[23607]) ).
thf(23609,plain,
( ( nil @ ( sk1 @ app ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[23608:[bind(A,$thf( sk1 ))]]) ).
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(487,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(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(516,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(551,plain,
! [A: $i] :
( ( ( sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,246]) ).
thf(552,plain,
! [A: $i] :
( ( ( sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[551]) ).
thf(553,plain,
~ ( sk8 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[552:[bind(A,$thf( sk8 ))]]) ).
thf(184,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)],[183]) ).
thf(193,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)],[184]) ).
thf(194,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)],[193]) ).
thf(16697,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk18 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,188]) ).
thf(16698,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk18 @ ssList ) ),
inference(simp,[status(thm)],[16697]) ).
thf(16699,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk18 @ ssList ) ),
inference(pattern_uni,[status(thm)],[16698:[bind(A,$thf( sk2 ))]]) ).
thf(67,axiom,
nil @ strictorderP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax64) ).
thf(426,plain,
nil @ strictorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(54604,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk22 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,238]) ).
thf(54605,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk22 @ ssItem ) ),
inference(simp,[status(thm)],[54604]) ).
thf(54606,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk22 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[54605:[bind(A,$thf( sk2 ))]]) ).
thf(162,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)],[161]) ).
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(531,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(33994,plain,
( ( ( sk5 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( nil @ ( sk5 @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[697,27445]) ).
thf(33995,plain,
( ( ( sk5 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( nil @ ( sk5 @ segmentP ) ) ),
inference(simp,[status(thm)],[33994]) ).
thf(34105,plain,
( ( sk5 != nil )
| ( nil != nil )
| ( nil @ ( sk5 @ segmentP ) ) ),
inference(simp,[status(thm)],[33995]) ).
thf(34126,plain,
( ( sk5 != nil )
| ( nil @ ( sk5 @ segmentP ) ) ),
inference(simp,[status(thm)],[34105]) ).
thf(27432,plain,
( ( ( sk5 @ ( sk5 @ segmentP ) )
!= ( sk6 @ ( nil @ segmentP ) ) )
| ~ $true
| ( sk6 = nil ) ),
inference(paramod_ordered,[status(thm)],[27156,3463]) ).
thf(27433,plain,
( ( ( sk5 @ ( sk5 @ segmentP ) )
!= ( sk6 @ ( nil @ segmentP ) ) )
| ( sk6 = nil ) ),
inference(simp,[status(thm)],[27432]) ).
thf(27513,plain,
( ( sk6 != sk5 )
| ( sk5 != nil )
| ( sk6 = nil ) ),
inference(simp,[status(thm)],[27433]) ).
thf(578,plain,
! [A: $i] :
( ( ( sk44 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[406,246]) ).
thf(579,plain,
! [A: $i] :
( ( ( sk44 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[578]) ).
thf(580,plain,
~ ( sk44 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[579:[bind(A,$thf( sk44 ))]]) ).
thf(885,plain,
! [A: $i] :
( ( ( sk5 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk5 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[712,342]) ).
thf(886,plain,
! [A: $i] :
( ( ( sk5 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ( sk5 @ cyclefreeP ) ),
inference(simp,[status(thm)],[885]) ).
thf(887,plain,
( ~ ( sk5 @ sk15 @ ( sk5 @ sk15 @ neq ) )
| ( sk5 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[886:[bind(A,$thf( sk5 @ sk15 ))]]) ).
thf(3753,plain,
( ( sk1 != sk1 )
| ~ ( nil @ ( sk1 @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[3310,872]) ).
thf(3754,plain,
( ~ ( nil @ ( sk1 @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[3753:[]]) ).
thf(10570,plain,
! [A: $i] :
( ( ( sk5 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk5 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[10349,131]) ).
thf(10571,plain,
! [A: $i] :
( ( ( sk5 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk5 @ cyclefreeP ) ),
inference(simp,[status(thm)],[10570]) ).
thf(10572,plain,
( ( nil @ ( sk5 @ sk11 @ cons ) @ strictorderedP )
| ( sk5 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[10571:[bind(A,$thf( sk5 @ sk11 ))]]) ).
thf(8293,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ( A @ sk11 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[114,171]) ).
thf(8294,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ( A @ sk11 @ leq ) ) ),
inference(simp,[status(thm)],[8293]) ).
thf(8295,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk12 @ ( sk1 @ sk11 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[8294:[bind(A,$thf( sk1 ))]]) ).
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(409,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(1096,plain,
! [A: $i] :
( ( ( sk10 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk10 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[739,342]) ).
thf(1097,plain,
! [A: $i] :
( ( ( sk10 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ( sk10 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1096]) ).
thf(1098,plain,
( ~ ( sk10 @ sk15 @ ( sk10 @ sk15 @ neq ) )
| ( sk10 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1097:[bind(A,$thf( sk10 @ sk15 ))]]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax51) ).
thf(310,plain,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(27452,plain,
( ( ( sk5 @ ( sk5 @ segmentP ) )
!= ( sk10 @ ( nil @ segmentP ) ) )
| ~ $true
| ( sk10 = nil ) ),
inference(paramod_ordered,[status(thm)],[27156,3472]) ).
thf(27453,plain,
( ( ( sk5 @ ( sk5 @ segmentP ) )
!= ( sk10 @ ( nil @ segmentP ) ) )
| ( sk10 = nil ) ),
inference(simp,[status(thm)],[27452]) ).
thf(27502,plain,
( ( sk10 != sk5 )
| ( sk5 != nil )
| ( sk10 = nil ) ),
inference(simp,[status(thm)],[27453]) ).
thf(10466,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,175]) ).
thf(10467,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssItem ) ),
inference(simp,[status(thm)],[10466]) ).
thf(10468,plain,
( ( sk6 @ cyclefreeP )
| ( sk6 @ sk11 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[10467:[bind(A,$thf( sk6 ))]]) ).
thf(10913,plain,
! [A: $i] :
( ( ( sk6 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk6 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[10468,246]) ).
thf(10914,plain,
! [A: $i] :
( ( ( sk6 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk6 @ cyclefreeP ) ),
inference(simp,[status(thm)],[10913]) ).
thf(10915,plain,
( ~ ( sk6 @ sk11 @ ( nil @ memberP ) )
| ( sk6 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[10914:[bind(A,$thf( sk6 @ sk11 ))]]) ).
thf(10121,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[9740,246]) ).
thf(10122,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[10121]) ).
thf(10123,plain,
( ~ ( sk1 @ sk12 @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[10122:[bind(A,$thf( sk1 @ sk12 ))]]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( B @ segmentP ) )
& ( B @ ( A @ segmentP ) ) )
=> ( C @ ( A @ segmentP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax53) ).
thf(199,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(53238,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk21 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,237]) ).
thf(53239,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk21 @ ssItem ) ),
inference(simp,[status(thm)],[53238]) ).
thf(53240,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk21 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[53239:[bind(A,$thf( sk2 ))]]) ).
thf(27553,plain,
( ( sk2 != sk2 )
| ( nil @ ( sk2 @ segmentP ) )
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[566,27184]) ).
thf(27554,plain,
( ( nil @ ( sk2 @ segmentP ) )
| ( sk1 != nil ) ),
inference(pattern_uni,[status(thm)],[27553:[]]) ).
thf(113,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ lt ) )
| ( ( D @ ( nil @ ( C @ cons ) @ app ) )
!= sk3 )
| ~ ( D @ ssList )
| ~ ( C @ ssItem )
| ( ( nil @ ( A @ cons ) @ ( B @ app ) )
!= sk5 )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(122,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ lt ) )
| ~ ( D @ ssList )
| ~ ( C @ ssItem )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( D @ ( nil @ ( C @ cons ) @ app ) )
!= sk3 )
| ( ( nil @ ( A @ cons ) @ ( B @ app ) )
!= sk5 ) ),
inference(lifteq,[status(thm)],[113]) ).
thf(585,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ lt ) )
| ~ ( D @ ssList )
| ~ ( C @ ssItem )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( ( D @ ( nil @ ( C @ cons ) @ app ) )
!= sk1 )
| ( ( nil @ ( A @ cons ) @ ( B @ app ) )
!= sk5 ) ),
inference(rewrite,[status(thm)],[122,123]) ).
thf(84,axiom,
nil @ equalelemsP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax74) ).
thf(502,plain,
nil @ equalelemsP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(3,axiom,
nil @ strictorderedP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax69) ).
thf(127,plain,
nil @ strictorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(35679,plain,
( ( ( sk10 @ ( sk10 @ segmentP ) )
!= ( sk44 @ ( nil @ segmentP ) ) )
| ( sk44 != sk10 )
| ( sk43 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[27368,19085]) ).
thf(35680,plain,
( ( ( sk10 @ ( sk10 @ segmentP ) )
!= ( sk44 @ ( nil @ segmentP ) ) )
| ( sk44 != sk10 )
| ( sk43 != nil ) ),
inference(simp,[status(thm)],[35679]) ).
thf(35751,plain,
( ( sk44 != sk10 )
| ( sk10 != nil )
| ( sk44 != sk10 )
| ( sk43 != nil ) ),
inference(simp,[status(thm)],[35680]) ).
thf(35776,plain,
( ( sk10 != nil )
| ( sk44 != sk10 )
| ( sk43 != nil ) ),
inference(simp,[status(thm)],[35751]) ).
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(544,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(173,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( ( A @ sk15 @ ( A @ sk12 @ cons ) @ ( A @ sk14 @ ( A @ sk11 @ cons ) @ ( A @ sk13 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[167]) ).
thf(177,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ~ ( A @ ssList )
| ( ( A @ sk15 @ ( A @ sk12 @ cons ) @ ( A @ sk14 @ ( A @ sk11 @ cons ) @ ( A @ sk13 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[173]) ).
thf(8246,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ( A @ sk11 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[110,171]) ).
thf(8247,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk12 @ ( A @ sk11 @ leq ) ) ),
inference(simp,[status(thm)],[8246]) ).
thf(8248,plain,
( ( sk5 @ cyclefreeP )
| ( sk5 @ sk12 @ ( sk5 @ sk11 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[8247:[bind(A,$thf( sk5 ))]]) ).
thf(3807,plain,
( ( ( sk9 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( sk9 @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[697,1659]) ).
thf(3808,plain,
( ( ( sk9 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( sk9 @ neq ) ) ),
inference(simp,[status(thm)],[3807]) ).
thf(3845,plain,
( ( sk9 != nil )
| ( nil != nil )
| ~ ( nil @ ( sk9 @ neq ) ) ),
inference(simp,[status(thm)],[3808]) ).
thf(3847,plain,
( ( sk9 != nil )
| ~ ( nil @ ( sk9 @ neq ) ) ),
inference(simp,[status(thm)],[3845]) ).
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(359,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(701,plain,
! [A: $i] :
( ( ( sk44 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[406,231]) ).
thf(702,plain,
! [A: $i] :
( ( ( sk44 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[701]) ).
thf(703,plain,
~ ( sk44 @ ( sk44 @ lt ) ),
inference(pattern_uni,[status(thm)],[702:[bind(A,$thf( sk44 ))]]) ).
thf(12,axiom,
nil @ cyclefreeP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax60) ).
thf(154,plain,
nil @ cyclefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
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(314,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(3519,plain,
( ( sk5 != sk5 )
| ~ ( sk5 @ ( nil @ neq ) )
| ~ ( sk5 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2842,869]) ).
thf(3520,plain,
( ~ ( sk5 @ ( nil @ neq ) )
| ~ ( sk5 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[3519:[]]) ).
thf(143,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)],[142]) ).
thf(27579,plain,
( ( sk2 != sk2 )
| ( sk2 @ ( nil @ segmentP ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[3737,27184]) ).
thf(27580,plain,
( ( sk2 @ ( nil @ segmentP ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[27579:[]]) ).
thf(1913,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( sk1 @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[697,1563]) ).
thf(1914,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[1913]) ).
thf(1932,plain,
( ( sk1 != nil )
| ( nil != nil )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[1914]) ).
thf(1934,plain,
( ( sk1 != nil )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[1932]) ).
thf(48004,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk24 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,234]) ).
thf(48005,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk24 @ ssList ) ),
inference(simp,[status(thm)],[48004]) ).
thf(48006,plain,
( ( sk6 @ strictorderedP )
| ( sk6 @ sk24 @ ssList ) ),
inference(pattern_uni,[status(thm)],[48005:[bind(A,$thf( sk6 ))]]) ).
thf(16104,plain,
! [A: $i] :
( ( ( sk5 @ sk17 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk5 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[15835,246]) ).
thf(16105,plain,
! [A: $i] :
( ( ( sk5 @ sk17 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk5 @ strictorderP ) ),
inference(simp,[status(thm)],[16104]) ).
thf(16106,plain,
( ~ ( sk5 @ sk17 @ ( nil @ memberP ) )
| ( sk5 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[16105:[bind(A,$thf( sk5 @ sk17 ))]]) ).
thf(7874,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ( A @ sk12 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[100,169]) ).
thf(7875,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ( A @ sk12 @ leq ) ) ),
inference(simp,[status(thm)],[7874]) ).
thf(7876,plain,
( ( sk10 @ cyclefreeP )
| ( sk10 @ sk11 @ ( sk10 @ sk12 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[7875:[bind(A,$thf( sk10 ))]]) ).
thf(6177,plain,
( ( ( sk6 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( sk6 @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[697,1776]) ).
thf(6178,plain,
( ( ( sk6 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( sk6 @ neq ) ) ),
inference(simp,[status(thm)],[6177]) ).
thf(6206,plain,
( ( sk6 != nil )
| ( nil != nil )
| ~ ( nil @ ( sk6 @ neq ) ) ),
inference(simp,[status(thm)],[6178]) ).
thf(6213,plain,
( ( sk6 != nil )
| ~ ( nil @ ( sk6 @ neq ) ) ),
inference(simp,[status(thm)],[6206]) ).
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(446,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(569,plain,
! [A: $i] :
( ( ( sk43 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[405,225]) ).
thf(570,plain,
! [A: $i] :
( ( ( sk43 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[569]) ).
thf(571,plain,
~ ( sk43 @ ( sk43 @ neq ) ),
inference(pattern_uni,[status(thm)],[570:[bind(A,$thf( sk43 ))]]) ).
thf(45418,plain,
( ( ( sk9 @ ( sk9 @ segmentP ) )
!= ( sk44 @ ( nil @ segmentP ) ) )
| ( sk44 != sk9 )
| ( sk43 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[27267,19095]) ).
thf(45419,plain,
( ( ( sk9 @ ( sk9 @ segmentP ) )
!= ( sk44 @ ( nil @ segmentP ) ) )
| ( sk44 != sk9 )
| ( sk43 != nil ) ),
inference(simp,[status(thm)],[45418]) ).
thf(45472,plain,
( ( sk44 != sk9 )
| ( sk9 != nil )
| ( sk44 != sk9 )
| ( sk43 != nil ) ),
inference(simp,[status(thm)],[45419]) ).
thf(45505,plain,
( ( sk9 != nil )
| ( sk44 != sk9 )
| ( sk43 != nil ) ),
inference(simp,[status(thm)],[45472]) ).
thf(46137,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[114,229]) ).
thf(46138,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[46137]) ).
thf(46139,plain,
( ( sk1 @ ( nil @ app ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[46138:[bind(A,$thf( sk1 ))]]) ).
thf(202,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)],[201]) ).
thf(203,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)],[202]) ).
thf(27692,plain,
( ( sk9 != sk9 )
| ( nil @ ( sk9 @ segmentP ) )
| ~ ( sk9 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[3174,27267]) ).
thf(27693,plain,
( ( nil @ ( sk9 @ segmentP ) )
| ~ ( sk9 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[27692:[]]) ).
thf(218,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[217]) ).
thf(53210,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk21 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[110,237]) ).
thf(53211,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk21 @ ssItem ) ),
inference(simp,[status(thm)],[53210]) ).
thf(53212,plain,
( ( sk5 @ strictorderedP )
| ( sk5 @ sk21 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[53211:[bind(A,$thf( sk5 ))]]) ).
thf(16210,plain,
! [A: $i] :
( ( ( sk2 @ sk17 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[15857,246]) ).
thf(16211,plain,
! [A: $i] :
( ( ( sk2 @ sk17 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[16210]) ).
thf(16212,plain,
( ~ ( sk2 @ sk17 @ ( nil @ memberP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[16211:[bind(A,$thf( sk2 @ sk17 ))]]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ hd @ ssItem ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
thf(304,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ hd @ ssItem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(186,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ sk17 @ ( A @ sk16 @ lt ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[183]) ).
thf(27442,plain,
( ( sk5 != sk5 )
| ( sk5 @ ( nil @ segmentP ) )
| ~ ( sk5 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1178,27156]) ).
thf(27443,plain,
( ( sk5 @ ( nil @ segmentP ) )
| ~ ( sk5 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[27442:[]]) ).
thf(33650,plain,
( ( ( sk5 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk5 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[697,27443]) ).
thf(33651,plain,
( ( ( sk5 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk5 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[33650]) ).
thf(33756,plain,
( ( sk5 != nil )
| ( nil != nil )
| ( sk5 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[33651]) ).
thf(33789,plain,
( ( sk5 != nil )
| ( sk5 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[33756]) ).
thf(14222,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk20 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[110,185]) ).
thf(14223,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk20 @ ssList ) ),
inference(simp,[status(thm)],[14222]) ).
thf(14224,plain,
( ( sk5 @ strictorderP )
| ( sk5 @ sk20 @ ssList ) ),
inference(pattern_uni,[status(thm)],[14223:[bind(A,$thf( sk5 ))]]) ).
thf(11170,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk13 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[114,176]) ).
thf(11171,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk13 @ ssList ) ),
inference(simp,[status(thm)],[11170]) ).
thf(11172,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk13 @ ssList ) ),
inference(pattern_uni,[status(thm)],[11171:[bind(A,$thf( sk1 ))]]) ).
thf(13826,plain,
( ( ( sk44 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,1145]) ).
thf(13827,plain,
( ( ( sk44 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[13826]) ).
thf(13954,plain,
( ( sk44 != sk2 )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[13827]) ).
thf(23664,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[111,198]) ).
thf(23665,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[23664]) ).
thf(23666,plain,
( ( nil @ ( sk6 @ app ) )
= sk6 ),
inference(pattern_uni,[status(thm)],[23665:[bind(A,$thf( sk6 ))]]) ).
thf(10038,plain,
! [A: $i] :
( ( ( sk9 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk9 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[9722,246]) ).
thf(10039,plain,
! [A: $i] :
( ( ( sk9 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk9 @ cyclefreeP ) ),
inference(simp,[status(thm)],[10038]) ).
thf(10040,plain,
( ~ ( sk9 @ sk12 @ ( nil @ memberP ) )
| ( sk9 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[10039:[bind(A,$thf( sk9 @ sk12 ))]]) ).
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(290,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(28,axiom,
~ ( nil @ singletonP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).
thf(214,plain,
~ ( nil @ singletonP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) )
!= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
thf(287,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) )
!= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(18204,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk19 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[100,190]) ).
thf(18205,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk19 @ ssList ) ),
inference(simp,[status(thm)],[18204]) ).
thf(18206,plain,
( ( sk10 @ strictorderP )
| ( sk10 @ sk19 @ ssList ) ),
inference(pattern_uni,[status(thm)],[18205:[bind(A,$thf( sk10 ))]]) ).
thf(1723,plain,
! [A: $i] :
( ( ( sk5 @ sk15 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList )
| ~ $true
| ( sk5 @ sk15 @ cyclefreeP )
| ( sk5 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[745,170]) ).
thf(1724,plain,
! [A: $i] :
( ( ( sk5 @ sk15 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList )
| ( sk5 @ sk15 @ cyclefreeP )
| ( sk5 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1723]) ).
thf(1725,plain,
( ( sk5 @ sk15 @ sk15 @ cyclefreeP )
| ( sk5 @ sk15 @ sk15 @ sk15 @ ssList )
| ( sk5 @ sk15 @ cyclefreeP )
| ( sk5 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1724:[bind(A,$thf( sk5 @ sk15 @ sk15 ))]]) ).
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(432,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(49642,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk25 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[110,235]) ).
thf(49643,plain,
! [A: $i] :
( ( ( sk5 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk25 @ ssList ) ),
inference(simp,[status(thm)],[49642]) ).
thf(49644,plain,
( ( sk5 @ strictorderedP )
| ( sk5 @ sk25 @ ssList ) ),
inference(pattern_uni,[status(thm)],[49643:[bind(A,$thf( sk5 ))]]) ).
thf(145,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ cons ) @ hd )
= B )
| ~ ( B @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[144]) ).
thf(146,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( ( A @ ( B @ cons ) @ hd )
= B ) ),
inference(lifteq,[status(thm)],[145]) ).
thf(1592,plain,
( ( sk5 != sk5 )
| ~ ( nil @ ( sk5 @ neq ) )
| ~ ( sk5 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[1178,869]) ).
thf(1593,plain,
( ~ ( nil @ ( sk5 @ neq ) )
| ~ ( sk5 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1592:[]]) ).
thf(47840,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk24 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[108,234]) ).
thf(47841,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk24 @ ssList ) ),
inference(simp,[status(thm)],[47840]) ).
thf(47842,plain,
( ( sk9 @ strictorderedP )
| ( sk9 @ sk24 @ ssList ) ),
inference(pattern_uni,[status(thm)],[47841:[bind(A,$thf( sk9 ))]]) ).
thf(2365,plain,
( ( ( sk5 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( sk5 @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[697,1593]) ).
thf(2366,plain,
( ( ( sk5 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( sk5 @ neq ) ) ),
inference(simp,[status(thm)],[2365]) ).
thf(2382,plain,
( ( sk5 != nil )
| ( nil != nil )
| ~ ( nil @ ( sk5 @ neq ) ) ),
inference(simp,[status(thm)],[2366]) ).
thf(2385,plain,
( ( sk5 != nil )
| ~ ( nil @ ( sk5 @ neq ) ) ),
inference(simp,[status(thm)],[2382]) ).
thf(3783,plain,
( ( sk1 != sk1 )
| ~ ( nil @ ( sk2 @ neq ) )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[3310,918]) ).
thf(3784,plain,
( ( sk1 != sk1 )
| ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[3783]) ).
thf(3785,plain,
( ~ ( nil @ ( sk2 @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[3784:[]]) ).
thf(14473,plain,
! [A: $i] :
( ( A != sk43 )
| ( sk44 != nil )
| ( nil != nil )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[151,14111]) ).
thf(14474,plain,
! [A: $i] :
( ( A != sk43 )
| ( sk44 != nil )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[14473]) ).
thf(14475,plain,
( ( sk44 != nil )
| ~ ( sk43 @ ( nil @ segmentP ) )
| ~ ( sk43 @ ssList ) ),
inference(pattern_uni,[status(thm)],[14474:[bind(A,$thf( sk43 ))]]) ).
thf(209,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ lt ) )
| ( A = B )
| ~ ( B @ ( A @ leq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[208]) ).
thf(210,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ lt ) )
| ~ ( B @ ( A @ leq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A = B ) ),
inference(lifteq,[status(thm)],[209]) ).
thf(13909,plain,
( ( ( sk44 @ ssList )
!= ( sk6 @ ssList ) )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,1145]) ).
thf(13910,plain,
( ( ( sk44 @ ssList )
!= ( sk6 @ ssList ) )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[13909]) ).
thf(13926,plain,
( ( sk44 != sk6 )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[13910]) ).
thf(27462,plain,
( ( ( sk5 @ ( sk5 @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[27156,3310]) ).
thf(27463,plain,
( ( ( sk5 @ ( sk5 @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[27462]) ).
thf(27516,plain,
( ( sk5 != sk1 )
| ( sk5 != nil )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[27463]) ).
thf(189,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( ( A @ sk20 @ ( A @ sk17 @ cons ) @ ( A @ sk19 @ ( A @ sk16 @ cons ) @ ( A @ sk18 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[183]) ).
thf(195,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ( ( A @ sk20 @ ( A @ sk17 @ cons ) @ ( A @ sk19 @ ( A @ sk16 @ cons ) @ ( A @ sk18 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[189]) ).
thf(11065,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk13 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,176]) ).
thf(11066,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk13 @ ssList ) ),
inference(simp,[status(thm)],[11065]) ).
thf(11067,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk13 @ ssList ) ),
inference(pattern_uni,[status(thm)],[11066:[bind(A,$thf( sk2 ))]]) ).
thf(16886,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk18 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,188]) ).
thf(16887,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk18 @ ssList ) ),
inference(simp,[status(thm)],[16886]) ).
thf(16888,plain,
( ( sk6 @ strictorderP )
| ( sk6 @ sk18 @ ssList ) ),
inference(pattern_uni,[status(thm)],[16887:[bind(A,$thf( sk6 ))]]) ).
thf(2590,plain,
( ( ( sk2 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( sk2 @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[697,1622]) ).
thf(2591,plain,
( ( ( sk2 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[2590]) ).
thf(2616,plain,
( ( sk2 != nil )
| ( nil != nil )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[2591]) ).
thf(2619,plain,
( ( sk2 != nil )
| ~ ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[2616]) ).
thf(20863,plain,
! [A: $i] :
( ( ( sk10 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk10 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[20208,246]) ).
thf(20864,plain,
! [A: $i] :
( ( ( sk10 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk10 @ strictorderP ) ),
inference(simp,[status(thm)],[20863]) ).
thf(20865,plain,
( ~ ( sk10 @ sk16 @ ( nil @ memberP ) )
| ( sk10 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[20864:[bind(A,$thf( sk10 @ sk16 ))]]) ).
thf(10647,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[10359,246]) ).
thf(10648,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[10647]) ).
thf(10649,plain,
( ~ ( sk2 @ sk11 @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[10648:[bind(A,$thf( sk2 @ sk11 ))]]) ).
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(326,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(14420,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk20 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[100,185]) ).
thf(14421,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk20 @ ssList ) ),
inference(simp,[status(thm)],[14420]) ).
thf(14422,plain,
( ( sk10 @ strictorderP )
| ( sk10 @ sk20 @ ssList ) ),
inference(pattern_uni,[status(thm)],[14421:[bind(A,$thf( sk10 ))]]) ).
thf(46206,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[111,229]) ).
thf(46207,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[46206]) ).
thf(46208,plain,
( ( sk6 @ ( nil @ app ) )
= sk6 ),
inference(pattern_uni,[status(thm)],[46207:[bind(A,$thf( sk6 ))]]) ).
thf(11207,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk13 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[100,176]) ).
thf(11208,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk13 @ ssList ) ),
inference(simp,[status(thm)],[11207]) ).
thf(11209,plain,
( ( sk10 @ cyclefreeP )
| ( sk10 @ sk13 @ ssList ) ),
inference(pattern_uni,[status(thm)],[11208:[bind(A,$thf( sk10 ))]]) ).
thf(46082,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[108,229]) ).
thf(46083,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[46082]) ).
thf(46084,plain,
( ( sk9 @ ( nil @ app ) )
= sk9 ),
inference(pattern_uni,[status(thm)],[46083:[bind(A,$thf( sk9 ))]]) ).
thf(77,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ( ( ( C @ ( B @ lt ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ lt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax91) ).
thf(464,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(10552,plain,
! [A: $i] :
( ( ( sk5 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk5 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[10349,246]) ).
thf(10553,plain,
! [A: $i] :
( ( ( sk5 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk5 @ cyclefreeP ) ),
inference(simp,[status(thm)],[10552]) ).
thf(10554,plain,
( ~ ( sk5 @ sk11 @ ( nil @ memberP ) )
| ( sk5 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[10553:[bind(A,$thf( sk5 @ sk11 ))]]) ).
thf(16509,plain,
! [A: $i] :
( ( ( sk6 @ sk17 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk6 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[16005,246]) ).
thf(16510,plain,
! [A: $i] :
( ( ( sk6 @ sk17 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk6 @ strictorderP ) ),
inference(simp,[status(thm)],[16509]) ).
thf(16511,plain,
( ~ ( sk6 @ sk17 @ ( nil @ memberP ) )
| ( sk6 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[16510:[bind(A,$thf( sk6 @ sk17 ))]]) ).
thf(54739,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk22 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[108,238]) ).
thf(54740,plain,
! [A: $i] :
( ( ( sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk22 @ ssItem ) ),
inference(simp,[status(thm)],[54739]) ).
thf(54741,plain,
( ( sk9 @ strictorderedP )
| ( sk9 @ sk22 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[54740:[bind(A,$thf( sk9 ))]]) ).
thf(8771,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk14 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[100,172]) ).
thf(8772,plain,
! [A: $i] :
( ( ( sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk14 @ ssList ) ),
inference(simp,[status(thm)],[8771]) ).
thf(8773,plain,
( ( sk10 @ cyclefreeP )
| ( sk10 @ sk14 @ ssList ) ),
inference(pattern_uni,[status(thm)],[8772:[bind(A,$thf( sk10 ))]]) ).
thf(72,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax31) ).
thf(442,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(17991,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk19 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,190]) ).
thf(17992,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk19 @ ssList ) ),
inference(simp,[status(thm)],[17991]) ).
thf(17993,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk19 @ ssList ) ),
inference(pattern_uni,[status(thm)],[17992:[bind(A,$thf( sk2 ))]]) ).
thf(13871,plain,
( ( ( sk44 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[114,1145]) ).
thf(13872,plain,
( ( ( sk44 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[13871]) ).
thf(13937,plain,
( ( sk44 != sk1 )
| ( sk43 != nil )
| ~ ( sk44 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[13872]) ).
thf(45988,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[106,229]) ).
thf(45989,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[45988]) ).
thf(45990,plain,
( ( sk2 @ ( nil @ app ) )
= sk2 ),
inference(pattern_uni,[status(thm)],[45989:[bind(A,$thf( sk2 ))]]) ).
thf(68,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( ( A @ tl @ ( A @ hd @ cons ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax78) ).
thf(427,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( ( A @ tl @ ( A @ hd @ cons ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(16312,plain,
! [A: $i] :
( ( ( sk9 @ sk17 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk9 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[15941,246]) ).
thf(16313,plain,
! [A: $i] :
( ( ( sk9 @ sk17 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk9 @ strictorderP ) ),
inference(simp,[status(thm)],[16312]) ).
thf(16314,plain,
( ~ ( sk9 @ sk17 @ ( nil @ memberP ) )
| ( sk9 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[16313:[bind(A,$thf( sk9 @ sk17 ))]]) ).
thf(200,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)],[199]) ).
thf(3579,plain,
( ( sk2 != sk2 )
| ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2897,881]) ).
thf(3580,plain,
( ~ ( sk2 @ ( nil @ neq ) )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[3579:[]]) ).
thf(53505,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk21 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,237]) ).
thf(53506,plain,
! [A: $i] :
( ( ( sk6 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk21 @ ssItem ) ),
inference(simp,[status(thm)],[53505]) ).
thf(53507,plain,
( ( sk6 @ strictorderedP )
| ( sk6 @ sk21 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[53506:[bind(A,$thf( sk6 ))]]) ).
thf(215,plain,
~ ( nil @ singletonP ),
inference(polarity_switch,[status(thm)],[214]) ).
thf(16840,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk18 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[114,188]) ).
thf(16841,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk18 @ ssList ) ),
inference(simp,[status(thm)],[16840]) ).
thf(16842,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk18 @ ssList ) ),
inference(pattern_uni,[status(thm)],[16841:[bind(A,$thf( sk1 ))]]) ).
thf(1067,plain,
! [A: $i] :
( ( ( sk6 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList )
| ~ $true
| ( sk6 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[736,170]) ).
thf(1068,plain,
! [A: $i] :
( ( ( sk6 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk15 @ ssList )
| ( sk6 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1067]) ).
thf(1069,plain,
( ( sk6 @ sk15 @ cyclefreeP )
| ( sk6 @ sk15 @ sk15 @ ssList )
| ( sk6 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1068:[bind(A,$thf( sk6 @ sk15 ))]]) ).
thf(88723,plain,
$false,
inference(e,[status(thm)],[1024,249,8283,893,518,468,234,8639,555,1554,523,27679,10234,8315,7850,1793,20305,44507,19127,408,170,247,1591,440,511,1078,20117,27568,550,142,715,16894,9774,174,185,2723,54873,10474,709,417,37934,23675,9971,257,320,565,389,52756,11203,16609,110,344,2897,11051,157,1055,724,16789,52008,196,27511,559,3998,3463,14376,1514,1013,3734,9768,421,7803,35463,881,27588,1568,216,9854,179,211,106,514,28522,3966,8321,238,27515,574,147,10303,19085,10422,265,312,206,53375,10145,19095,866,18197,132,1622,10216,307,3582,380,8655,18145,201,27156,220,534,102,3679,9722,7870,27445,16011,9949,160,165,45956,334,15962,424,45312,192,49987,916,28500,8700,38539,461,47681,229,566,484,13924,1178,1064,403,7838,188,23482,697,1089,20513,37288,54578,169,3746,6919,141,869,884,27518,10823,27461,109,471,9872,49067,124,225,1659,5694,28540,753,2561,49996,489,1937,212,706,2285,1776,2487,15835,129,47720,27786,371,503,10349,105,8739,205,508,10740,16666,1563,1035,8262,10359,27814,3675,7817,13932,10058,128,237,24795,906,46217,27681,27368,430,14254,166,180,444,28579,27582,161,745,279,10321,176,191,14481,48015,1795,14326,13920,204,562,4000,1620,3472,20411,875,577,27590,49683,259,53516,8767,9659,27566,144,1058,466,236,181,15857,15941,382,3964,27357,187,406,172,219,14416,6443,736,23453,230,362,1722,245,98,208,49814,11002,1011,419,890,387,17957,1557,535,140,213,2289,198,108,700,520,49061,155,2842,1061,20767,54230,1044,20208,18089,16005,130,3310,23572,11130,226,1364,20607,505,9740,16408,3522,23609,487,516,553,194,16699,426,54606,162,531,20144,34126,342,123,1145,27513,14111,580,872,887,3754,10572,739,19993,712,557,3737,8295,409,1098,310,27502,10915,10123,199,53240,9649,27554,585,502,127,19115,35776,544,177,182,8248,3847,3174,27184,359,27812,703,154,727,175,314,3520,143,27580,1934,48006,16106,7876,6213,864,446,571,45505,46139,231,27552,203,27693,20199,218,27302,27267,53212,16212,304,158,186,114,171,139,1523,33789,20018,10468,14224,207,11172,1212,19092,13954,23666,27530,10040,290,119,235,246,214,287,151,18206,1774,1725,432,49644,146,1593,190,47842,2385,3785,14475,405,210,13926,1657,27516,358,195,897,11067,16888,2619,20865,10649,2800,326,918,136,14422,1561,46208,11209,46084,464,1129,10554,27443,16511,23859,131,54741,8773,442,17993,13937,45990,427,16314,200,10440,163,111,227,3580,337,53507,215,16842,28125,232,100,454,1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC176+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.40 % Computer : n003.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sat Sep 26 12:26:55 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.85/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.47/1.28 % [INFO] Parsing done (285ms).
% 1.47/1.29 % [INFO] Running in sequential loop mode.
% 2.32/1.68 % [INFO] eprover registered as external prover.
% 2.32/1.69 % [INFO] Scanning for conjecture ...
% 2.73/1.84 % [INFO] Found a conjecture (or negated_conjecture) and 95 axioms. Running axiom selection ...
% 2.95/1.97 % [INFO] Axiom selection finished. Selected 95 axioms (removed 0 axioms).
% 3.29/2.09 % [INFO] Problem is first-order (TPTP FOF).
% 3.29/2.11 % [INFO] Type checking passed.
% 3.29/2.12 % [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 ...
% 120.62/29.60 % External prover 'e' found a proof!
% 120.62/29.60 % [INFO] Killing All external provers ...
% 120.62/29.61 % Time passed: 29054ms (effective reasoning time: 28309ms)
% 120.62/29.61 % 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)>
% 120.62/29.61 % 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
% 120.62/29.61 % No. of inferences in proof: 1211
% 120.62/29.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 29054 ms resp. 28309 ms w/o parsing
% 123.69/30.05 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 123.69/30.06 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------