%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWC125+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:52:22 AM UTC 2026
% Result : Theorem 140.67s 36.09s
% Output : Refutation 143.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 124
% Syntax : Number of formulae : 1321 ( 129 unt; 0 typ; 28 def)
% Number of atoms : 5817 (1196 equ; 0 cnn)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 13366 (2056 ~;2461 |; 218 &;7956 @)
% ( 26 <=>; 649 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 52 usr; 9 con; 0-2 aty)
% Number of variables : 1339 ( 23 ^;1247 !; 41 ?;1339 :)
% ( 0 !>; 0 ?*; 0 @-; 28 @+)
% Comments :
%------------------------------------------------------------------------------
thf(ssList_decl,type,
ssList: $i > $o ).
thf(neq_decl,type,
neq: $i > $i > $o ).
thf(nil_decl,type,
nil: $i ).
thf(segmentP_decl,type,
segmentP: $i > $i > $o ).
thf(strictorderedP_decl,type,
strictorderedP: $i > $o ).
thf(ssItem_decl,type,
ssItem: $i > $o ).
thf(gt_decl,type,
gt: $i > $i > $o ).
thf(lt_decl,type,
lt: $i > $i > $o ).
thf(geq_decl,type,
geq: $i > $i > $o ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(frontsegP_decl,type,
frontsegP: $i > $i > $o ).
thf(totalorderedP_decl,type,
totalorderedP: $i > $o ).
thf(hd_decl,type,
hd: $i > $i ).
thf(cyclefreeP_decl,type,
cyclefreeP: $i > $o ).
thf(app_decl,type,
app: $i > $i > $i ).
thf(strictorderP_decl,type,
strictorderP: $i > $o ).
thf(singletonP_decl,type,
singletonP: $i > $o ).
thf(duplicatefreeP_decl,type,
duplicatefreeP: $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(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 > $i ).
thf(sk8_decl,type,
sk8: $i > $i ).
thf(sk9_decl,type,
sk9: $i > $i ).
thf(sk10_decl,type,
sk10: $i > $i ).
thf(sk11_decl,type,
sk11: $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i ).
thf(sk13_decl,type,
sk13: $i > $i ).
thf(sk14_decl,type,
sk14: $i > $i ).
thf(sk15_decl,type,
sk15: $i > $i ).
thf(sk16_decl,type,
sk16: $i > $i ).
thf(sk17_decl,type,
sk17: $i > $i ).
thf(sk18_decl,type,
sk18: $i > $i ).
thf(sk19_decl,type,
sk19: $i > $i ).
thf(sk20_decl,type,
sk20: $i > $i ).
thf(sk21_decl,type,
sk21: $i > $i ).
thf(sk22_decl,type,
sk22: $i > $i > $i ).
thf(sk23_decl,type,
sk23: $i > $i ).
thf(sk24_decl,type,
sk24: $i > $i ).
thf(sk25_decl,type,
sk25: $i > $i ).
thf(sk26_decl,type,
sk26: $i > $i ).
thf(sk27_decl,type,
sk27: $i > $i ).
thf(sk28_decl,type,
sk28: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( A @ ( B @ segmentP ) )
& ( nil @ ( A @ neq ) ) )
| ? [E: $i] :
( ( E @ strictorderedP )
& ( C @ ( E @ segmentP ) )
& ( E @ ( D @ segmentP ) )
& ( E @ ( C @ neq ) )
& ( E @ ssList ) )
| ~ ( C @ strictorderedP )
| ~ ( C @ ( D @ segmentP ) )
| ~ ( nil @ ( B @ neq ) )
| ( A != C )
| ( B != D ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( sk1 @ ( A @ segmentP ) )
& ( nil @ ( sk1 @ neq ) ) )
| ? [D: $i] :
( ( D @ strictorderedP )
& ( B @ ( D @ segmentP ) )
& ( D @ ( C @ segmentP ) )
& ( D @ ( B @ neq ) )
& ( D @ ssList ) )
| ~ ( B @ strictorderedP )
| ~ ( B @ ( C @ segmentP ) )
| ~ ( nil @ ( A @ neq ) )
| ( sk1 != B )
| ( A != C ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( sk1 @ ( sk2 @ segmentP ) )
& ( nil @ ( sk1 @ neq ) ) )
| ? [C: $i] :
( ( C @ strictorderedP )
& ( A @ ( C @ segmentP ) )
& ( C @ ( B @ segmentP ) )
& ( C @ ( A @ neq ) )
& ( C @ ssList ) )
| ~ ( A @ strictorderedP )
| ~ ( A @ ( B @ segmentP ) )
| ~ ( nil @ ( sk2 @ neq ) )
| ( sk1 != A )
| ( sk2 != B ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ( ( ( sk1 @ ( sk2 @ segmentP ) )
& ( nil @ ( sk1 @ neq ) ) )
| ? [B: $i] :
( ( B @ strictorderedP )
& ( sk3 @ ( B @ segmentP ) )
& ( B @ ( A @ segmentP ) )
& ( B @ ( sk3 @ neq ) )
& ( B @ ssList ) )
| ~ ( sk3 @ strictorderedP )
| ~ ( sk3 @ ( A @ segmentP ) )
| ~ ( nil @ ( sk2 @ neq ) )
| ( sk1 != sk3 )
| ( sk2 != A ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
( ? [B: $i] :
( ( A != B )
& ( B @ ssItem ) )
& ( A @ ssItem ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
( ( sk5 != A )
& ( A @ ssItem ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [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(sk8_def,definition,
( sk8
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ( ( ( E @ ( B @ cons ) @ ( D @ ( A @ sk7 @ cons ) @ ( C @ app ) @ app ) )
= A )
=> ~ ( ( A @ sk7 @ ( B @ leq ) )
& ( B @ ( A @ sk7 @ leq ) ) ) ) ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( D @ ( A @ sk8 @ cons ) @ ( C @ ( A @ sk7 @ cons ) @ ( B @ app ) @ app ) )
= A )
=> ~ ( ( A @ sk7 @ ( A @ sk8 @ leq ) )
& ( A @ sk8 @ ( A @ sk7 @ leq ) ) ) ) ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( A @ sk8 @ cons ) @ ( B @ ( A @ sk7 @ cons ) @ ( A @ sk9 @ app ) @ app ) )
= A )
=> ~ ( ( A @ sk7 @ ( A @ sk8 @ leq ) )
& ( A @ sk8 @ ( A @ sk7 @ leq ) ) ) ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ( ( ( B @ ( A @ sk8 @ cons ) @ ( A @ sk10 @ ( A @ sk7 @ cons ) @ ( A @ sk9 @ app ) @ app ) )
= A )
=> ~ ( ( A @ sk7 @ ( A @ sk8 @ leq ) )
& ( A @ sk8 @ ( A @ sk7 @ leq ) ) ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [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(sk13_def,definition,
( sk13
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ( ( ( E @ ( B @ cons ) @ ( D @ ( A @ sk12 @ cons ) @ ( C @ app ) @ app ) )
= A )
=> ( ( A @ sk12 @ ( B @ lt ) )
| ( B @ ( A @ sk12 @ lt ) ) ) ) ) ) ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( D @ ( A @ sk13 @ cons ) @ ( C @ ( A @ sk12 @ cons ) @ ( B @ app ) @ app ) )
= A )
=> ( ( A @ sk12 @ ( A @ sk13 @ lt ) )
| ( A @ sk13 @ ( A @ sk12 @ lt ) ) ) ) ) ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( A @ sk13 @ cons ) @ ( B @ ( A @ sk12 @ cons ) @ ( A @ sk14 @ app ) @ app ) )
= A )
=> ( ( A @ sk12 @ ( A @ sk13 @ lt ) )
| ( A @ sk13 @ ( A @ sk12 @ lt ) ) ) ) ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ( ( ( B @ ( A @ sk13 @ cons ) @ ( A @ sk15 @ ( A @ sk12 @ cons ) @ ( A @ sk14 @ app ) @ app ) )
= A )
=> ( ( A @ sk12 @ ( A @ sk13 @ lt ) )
| ( A @ sk13 @ ( A @ sk12 @ lt ) ) ) ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( ^ [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(sk18_def,definition,
( sk18
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ( ( ( E @ ( B @ cons ) @ ( D @ ( A @ sk17 @ cons ) @ ( C @ app ) @ app ) )
= A )
=> ( B @ ( A @ sk17 @ lt ) ) ) ) ) ) ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( D @ ( A @ sk18 @ cons ) @ ( C @ ( A @ sk17 @ cons ) @ ( B @ app ) @ app ) )
= A )
=> ( A @ sk18 @ ( A @ sk17 @ lt ) ) ) ) ) ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( A @ sk18 @ cons ) @ ( B @ ( A @ sk17 @ cons ) @ ( A @ sk19 @ app ) @ app ) )
= A )
=> ( A @ sk18 @ ( A @ sk17 @ lt ) ) ) ) ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ( ( ( B @ ( A @ sk18 @ cons ) @ ( A @ sk20 @ ( A @ sk17 @ cons ) @ ( A @ sk19 @ app ) @ app ) )
= A )
=> ( A @ sk18 @ ( A @ sk17 @ lt ) ) ) ) ) ) ).
thf(sk22_def,definition,
( sk22
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( ( C @ ( A @ app ) )
= B )
& ( C @ ssList ) ) ) ) ).
thf(sk23_def,definition,
( sk23
= ( ^ [A: $i] :
@+[B: $i] :
( ( ( A @ tl )
= B )
& ( B @ ssList ) ) ) ) ).
thf(sk24_def,definition,
( sk24
= ( ^ [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(sk25_def,definition,
( sk25
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ( ( ( E @ ( B @ cons ) @ ( D @ ( A @ sk24 @ cons ) @ ( C @ app ) @ app ) )
= A )
=> ( ( A @ sk24 @ ( B @ leq ) )
| ( B @ ( A @ sk24 @ leq ) ) ) ) ) ) ) ) ) ) ).
thf(sk26_def,definition,
( sk26
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( D @ ( A @ sk25 @ cons ) @ ( C @ ( A @ sk24 @ cons ) @ ( B @ app ) @ app ) )
= A )
=> ( ( A @ sk24 @ ( A @ sk25 @ leq ) )
| ( A @ sk25 @ ( A @ sk24 @ leq ) ) ) ) ) ) ) ) ) ).
thf(sk27_def,definition,
( sk27
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( A @ sk25 @ cons ) @ ( B @ ( A @ sk24 @ cons ) @ ( A @ sk26 @ app ) @ app ) )
= A )
=> ( ( A @ sk24 @ ( A @ sk25 @ leq ) )
| ( A @ sk25 @ ( A @ sk24 @ leq ) ) ) ) ) ) ) ) ).
thf(sk28_def,definition,
( sk28
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ( ( ( B @ ( A @ sk25 @ cons ) @ ( A @ sk27 @ ( A @ sk24 @ cons ) @ ( A @ sk26 @ app ) @ app ) )
= A )
=> ( ( A @ sk24 @ ( A @ sk25 @ leq ) )
| ( A @ sk25 @ ( A @ sk24 @ leq ) ) ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( A @ ( B @ segmentP ) )
& ( nil @ ( A @ neq ) ) )
| ? [E: $i] :
( ( E @ strictorderedP )
& ( C @ ( E @ segmentP ) )
& ( E @ ( D @ segmentP ) )
& ( E @ ( C @ neq ) )
& ( E @ ssList ) )
| ~ ( C @ strictorderedP )
| ~ ( C @ ( D @ segmentP ) )
| ~ ( nil @ ( B @ neq ) )
| ( A != C )
| ( B != D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( A @ ( B @ segmentP ) )
& ( nil @ ( A @ neq ) ) )
| ? [E: $i] :
( ( E @ strictorderedP )
& ( C @ ( E @ segmentP ) )
& ( E @ ( D @ segmentP ) )
& ( E @ ( C @ neq ) )
& ( E @ ssList ) )
| ~ ( C @ strictorderedP )
| ~ ( C @ ( D @ segmentP ) )
| ~ ( nil @ ( B @ neq ) )
| ( A != C )
| ( B != D ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(98,plain,
~ ! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( A @ ( B @ segmentP ) )
& ( nil @ ( A @ neq ) ) )
| ? [E: $i] :
( ( E @ strictorderedP )
& ( C @ ( E @ segmentP ) )
& ( E @ ( D @ segmentP ) )
& ( E @ ( C @ neq ) )
& ( E @ ssList ) )
| ~ ( C @ strictorderedP )
| ~ ( C @ ( D @ segmentP ) )
| ~ ( nil @ ( B @ neq ) )
| ( A != C )
| ( B != D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(99,plain,
! [A: $i] :
( ( ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) ) )
& ( ~ ( A @ strictorderedP )
| ~ ( sk3 @ ( A @ segmentP ) )
| ~ ( A @ ( sk4 @ segmentP ) )
| ~ ( A @ ( sk3 @ neq ) )
| ~ ( A @ ssList ) )
& ( sk3 @ strictorderedP )
& ( sk3 @ ( sk4 @ segmentP ) )
& ( nil @ ( sk2 @ neq ) )
& ( sk1 = sk3 )
& ( sk2 = sk4 )
& ( sk4 @ ssList )
& ( sk3 @ ssList )
& ( sk2 @ ssList )
& ( sk1 @ ssList ) ),
inference(cnf,[status(esa)],[98]) ).
thf(105,plain,
sk2 @ ssList,
inference(cnfConj,[status(thm)],[99]) ).
thf(43,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(253,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)],[43]) ).
thf(254,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ strictorderedP )
| ~ ( A @ sk18 @ ( A @ sk17 @ lt ) )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( ( A @ sk21 @ ( A @ sk18 @ cons ) @ ( A @ sk20 @ ( A @ sk17 @ cons ) @ ( A @ sk19 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( A @ sk21 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( A @ sk20 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( A @ sk19 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( A @ sk18 @ ssItem )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( A @ sk17 @ 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)],[253]) ).
thf(255,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk19 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[254]) ).
thf(43726,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk19 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,255]) ).
thf(43727,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk19 @ ssList ) ),
inference(simp,[status(thm)],[43726]) ).
thf(43728,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk19 @ ssList ) ),
inference(pattern_uni,[status(thm)],[43727:[bind(A,$thf( sk2 ))]]) ).
thf(47,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax57) ).
thf(278,plain,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(279,plain,
! [A: $i] :
( ( nil @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[278]) ).
thf(44077,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[43728,279]) ).
thf(44078,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[44077]) ).
thf(44079,plain,
( ( nil @ ( sk2 @ sk19 @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[44078:[bind(A,$thf( sk2 @ sk19 ))]]) ).
thf(31,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(198,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)],[31]) ).
thf(199,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ cyclefreeP )
| ( A @ sk7 @ ( A @ sk8 @ leq ) )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk8 @ ( A @ sk7 @ leq ) )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( ( A @ sk11 @ ( A @ sk8 @ cons ) @ ( A @ sk10 @ ( A @ sk7 @ cons ) @ ( A @ sk9 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk11 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk10 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk8 @ ssItem )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk7 @ 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)],[198]) ).
thf(200,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk11 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[199]) ).
thf(631,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,200]) ).
thf(632,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssList ) ),
inference(simp,[status(thm)],[631]) ).
thf(633,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk11 @ ssList ) ),
inference(pattern_uni,[status(thm)],[632:[bind(A,$thf( sk2 ))]]) ).
thf(648,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssList )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[633,200]) ).
thf(649,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssList )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[648]) ).
thf(650,plain,
( ( sk2 @ sk11 @ cyclefreeP )
| ( sk2 @ sk11 @ sk11 @ ssList )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[649:[bind(A,$thf( sk2 @ sk11 ))]]) ).
thf(758,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ sk11 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[650,279]) ).
thf(759,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ sk11 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[758]) ).
thf(760,plain,
( ( nil @ ( sk2 @ sk11 @ sk11 @ segmentP ) )
| ( sk2 @ sk11 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[759:[bind(A,$thf( sk2 @ sk11 @ sk11 ))]]) ).
thf(5,axiom,
? [A: $i] :
( ? [B: $i] :
( ( A != B )
& ( B @ ssItem ) )
& ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
thf(119,plain,
? [A: $i] :
( ? [B: $i] :
( ( A != B )
& ( B @ ssItem ) )
& ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(120,plain,
( ( sk5 != sk6 )
& ( sk6 @ ssItem )
& ( sk5 @ ssItem ) ),
inference(cnf,[status(esa)],[119]) ).
thf(121,plain,
sk5 @ ssItem,
inference(cnfConj,[status(thm)],[120]) ).
thf(71,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ duplicatefreeP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax71) ).
thf(429,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ duplicatefreeP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(430,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[429]) ).
thf(2029,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[121,430]) ).
thf(2030,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP ) ),
inference(simp,[status(thm)],[2029]) ).
thf(2031,plain,
nil @ ( sk5 @ cons ) @ duplicatefreeP,
inference(pattern_uni,[status(thm)],[2030:[bind(A,$thf( sk5 ))]]) ).
thf(106,plain,
sk1 @ ssList,
inference(cnfConj,[status(thm)],[99]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ frontsegP ) )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax46) ).
thf(166,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( ( nil = A )
=> ( A @ ( nil @ frontsegP ) ) )
& ( ( A @ ( nil @ frontsegP ) )
=> ( nil = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(167,plain,
! [A: $i] :
( ( ( A @ ( nil @ frontsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) )
& ( ( nil = A )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[166]) ).
thf(168,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[167]) ).
thf(170,plain,
! [A: $i] :
( ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[168]) ).
thf(123,plain,
sk5 != sk6,
inference(cnfConj,[status(thm)],[120]) ).
thf(124,plain,
sk6 != sk5,
inference(lifteq,[status(thm)],[123]) ).
thf(7877,plain,
! [A: $i] :
( ( A != sk6 )
| ( sk5 != nil )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[170,124]) ).
thf(7878,plain,
( ( sk5 != nil )
| ~ ( sk6 @ ( nil @ frontsegP ) )
| ~ ( sk6 @ ssList ) ),
inference(pattern_uni,[status(thm)],[7877:[bind(A,$thf( sk6 ))]]) ).
thf(22208,plain,
( ( ( sk6 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk5 != nil )
| ~ ( sk6 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,7878]) ).
thf(22209,plain,
( ( ( sk6 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk5 != nil )
| ~ ( sk6 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[22208]) ).
thf(22328,plain,
( ( sk6 != sk1 )
| ( sk5 != nil )
| ~ ( sk6 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[22209]) ).
thf(59,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(347,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)],[59]) ).
thf(206,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk8 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[199]) ).
thf(18077,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,206]) ).
thf(18078,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ssItem ) ),
inference(simp,[status(thm)],[18077]) ).
thf(18079,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk8 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[18078:[bind(A,$thf( sk2 ))]]) ).
thf(55,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax51) ).
thf(331,plain,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(332,plain,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[331]) ).
thf(891,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[633,332]) ).
thf(892,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[891]) ).
thf(893,plain,
( ( nil @ ( sk2 @ sk11 @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[892:[bind(A,$thf( sk2 @ sk11 ))]]) ).
thf(94,axiom,
nil @ totalorderP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax62) ).
thf(518,plain,
nil @ totalorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(692,plain,
( ~ $true
| ( ( sk2 @ sk11 @ cyclefreeP )
!= ( sk2 @ cyclefreeP ) )
| ( sk2 @ sk11 @ sk11 @ ssList )
| ( sk2 @ cyclefreeP ) ),
inference(eqfactor_ordered,[status(thm)],[650]) ).
thf(694,plain,
( ( ( sk2 @ sk11 )
!= sk2 )
| ( sk2 @ sk11 @ sk11 @ ssList )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[692]) ).
thf(775,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( ( sk2 @ sk11 )
!= sk2 )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[694,279]) ).
thf(776,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( ( sk2 @ sk11 )
!= sk2 )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[775]) ).
thf(777,plain,
( ( nil @ ( sk2 @ sk11 @ sk11 @ segmentP ) )
| ( ( sk2 @ sk11 )
!= sk2 )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[776:[bind(A,$thf( sk2 @ sk11 @ sk11 ))]]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ segmentP ) )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax58) ).
thf(179,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( ( nil = A )
=> ( A @ ( nil @ segmentP ) ) )
& ( ( A @ ( nil @ segmentP ) )
=> ( nil = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(180,plain,
! [A: $i] :
( ( ( A @ ( nil @ segmentP ) )
| ( nil != A )
| ~ ( A @ ssList ) )
& ( ( nil = A )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[179]) ).
thf(181,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[180]) ).
thf(183,plain,
! [A: $i] :
( ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[181]) ).
thf(104,plain,
nil @ ( sk2 @ neq ),
inference(cnfConj,[status(thm)],[99]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ neq ) )
<=> ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(243,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)],[41]) ).
thf(244,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)],[243]) ).
thf(245,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ ( A @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[244]) ).
thf(247,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A != B ) ),
inference(lifteq,[status(thm)],[245]) ).
thf(248,plain,
! [A: $i] :
( ~ ( A @ ( A @ neq ) )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[247]) ).
thf(36339,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[121,248]) ).
thf(36340,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[36339]) ).
thf(36341,plain,
~ ( sk5 @ ( sk5 @ neq ) ),
inference(pattern_uni,[status(thm)],[36340:[bind(A,$thf( sk5 ))]]) ).
thf(36419,plain,
( ( ( sk5 @ ( sk5 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,36341]) ).
thf(36420,plain,
( ( sk5 @ ( sk5 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[36419]) ).
thf(36425,plain,
( ( sk5 != nil )
| ( sk5 != sk2 ) ),
inference(simp,[status(thm)],[36420]) ).
thf(36524,plain,
! [A: $i] :
( ( A != sk5 )
| ( nil != nil )
| ( sk5 != sk2 )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[183,36425]) ).
thf(36525,plain,
! [A: $i] :
( ( A != sk5 )
| ( sk5 != sk2 )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[36524]) ).
thf(36526,plain,
( ( sk5 != sk2 )
| ~ ( sk5 @ ( nil @ segmentP ) )
| ~ ( sk5 @ ssList ) ),
inference(pattern_uni,[status(thm)],[36525:[bind(A,$thf( sk5 ))]]) ).
thf(59329,plain,
( ( ( sk5 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk5 != sk2 )
| ~ ( sk5 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,36526]) ).
thf(59330,plain,
( ( ( sk5 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk5 != sk2 )
| ~ ( sk5 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[59329]) ).
thf(59522,plain,
( ( sk5 != sk2 )
| ( sk5 != sk2 )
| ~ ( sk5 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[59330]) ).
thf(59573,plain,
( ( sk5 != sk2 )
| ~ ( sk5 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[59522]) ).
thf(33,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(214,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)],[33]) ).
thf(215,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ strictorderP )
| ~ ( A @ sk12 @ ( A @ sk13 @ lt ) )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ~ ( A @ sk13 @ ( A @ sk12 @ lt ) )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( ( A @ sk16 @ ( A @ sk13 @ cons ) @ ( A @ sk15 @ ( A @ sk12 @ cons ) @ ( A @ sk14 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( A @ sk16 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( A @ sk15 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( A @ sk14 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( A @ sk13 @ ssItem )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( A @ sk12 @ 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)],[214]) ).
thf(219,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk12 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[215]) ).
thf(24627,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk12 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,219]) ).
thf(24628,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk12 @ ssItem ) ),
inference(simp,[status(thm)],[24627]) ).
thf(24629,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk12 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[24628:[bind(A,$thf( sk1 ))]]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax68) ).
thf(164,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(165,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[164]) ).
thf(24976,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[24629,165]) ).
thf(24977,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[24976]) ).
thf(24978,plain,
( ( nil @ ( sk1 @ sk12 @ cons ) @ strictorderedP )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[24977:[bind(A,$thf( sk1 @ sk12 ))]]) ).
thf(11,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(136,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)],[11]) ).
thf(137,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ lt ) )
| ( A = B )
| ~ ( B @ ( A @ leq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[136]) ).
thf(138,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ lt ) )
| ~ ( B @ ( A @ leq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A = B ) ),
inference(lifteq,[status(thm)],[137]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ equalelemsP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax73) ).
thf(333,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ equalelemsP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(246,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ neq ) )
| ( A = B )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[244]) ).
thf(249,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A = B ) ),
inference(lifteq,[status(thm)],[246]) ).
thf(49,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(286,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)],[49]) ).
thf(287,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ totalorderP )
| ~ ( A @ sk24 @ ( A @ sk25 @ leq ) )
| ~ ( A @ ssList ) )
& ( ( A @ totalorderP )
| ~ ( A @ sk25 @ ( A @ sk24 @ leq ) )
| ~ ( A @ ssList ) )
& ( ( A @ totalorderP )
| ( ( A @ sk28 @ ( A @ sk25 @ cons ) @ ( A @ sk27 @ ( A @ sk24 @ cons ) @ ( A @ sk26 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) )
& ( ( A @ totalorderP )
| ( A @ sk28 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ totalorderP )
| ( A @ sk27 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ totalorderP )
| ( A @ sk26 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ totalorderP )
| ( A @ sk25 @ ssItem )
| ~ ( A @ ssList ) )
& ( ( A @ totalorderP )
| ( A @ sk24 @ ssItem )
| ~ ( A @ ssList ) )
& ( ( B @ ( C @ leq ) )
| ( C @ ( B @ leq ) )
| ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
!= A )
| ~ ( F @ ssList )
| ~ ( E @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssItem )
| ~ ( B @ ssItem )
| ~ ( A @ totalorderP )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[286]) ).
thf(288,plain,
! [A: $i] :
( ( A @ totalorderP )
| ( A @ sk28 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[287]) ).
thf(67176,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk28 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,288]) ).
thf(67177,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk28 @ ssList ) ),
inference(simp,[status(thm)],[67176]) ).
thf(67178,plain,
( ( sk1 @ totalorderP )
| ( sk1 @ sk28 @ ssList ) ),
inference(pattern_uni,[status(thm)],[67177:[bind(A,$thf( sk1 ))]]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ gt ) )
<=> ( A @ ( B @ lt ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax35) ).
thf(113,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)],[3]) ).
thf(114,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)],[113]) ).
thf(115,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[114]) ).
thf(217,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk15 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[215]) ).
thf(7935,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[105,170]) ).
thf(7936,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[7935]) ).
thf(7937,plain,
( ~ ( sk2 @ ( nil @ frontsegP ) )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[7936:[bind(A,$thf( sk2 ))]]) ).
thf(107,plain,
sk3 @ ( sk4 @ segmentP ),
inference(cnfConj,[status(thm)],[99]) ).
thf(108,plain,
sk2 = sk4,
inference(cnfConj,[status(thm)],[99]) ).
thf(112,plain,
sk4 = sk2,
inference(lifteq,[status(thm)],[108]) ).
thf(109,plain,
sk1 = sk3,
inference(cnfConj,[status(thm)],[99]) ).
thf(111,plain,
sk3 = sk1,
inference(lifteq,[status(thm)],[109]) ).
thf(565,plain,
sk1 @ ( sk2 @ segmentP ),
inference(rewrite,[status(thm)],[107,112,111]) ).
thf(10541,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[106,183]) ).
thf(10542,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[10541]) ).
thf(10543,plain,
( ~ ( sk1 @ ( nil @ segmentP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[10542:[bind(A,$thf( sk1 ))]]) ).
thf(68,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax45) ).
thf(405,plain,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(406,plain,
! [A: $i] :
( ( nil @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[405]) ).
thf(1529,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,406]) ).
thf(1530,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) ) ),
inference(simp,[status(thm)],[1529]) ).
thf(1531,plain,
nil @ ( sk2 @ frontsegP ),
inference(pattern_uni,[status(thm)],[1530:[bind(A,$thf( sk2 ))]]) ).
thf(110,plain,
( ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(566,plain,
( ~ $true
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(rewrite,[status(thm)],[110,565]) ).
thf(567,plain,
~ ( nil @ ( sk1 @ neq ) ),
inference(simp,[status(thm)],[566]) ).
thf(580,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,567]) ).
thf(581,plain,
( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[580]) ).
thf(582,plain,
( ( nil != nil )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[581]) ).
thf(583,plain,
sk2 != sk1,
inference(simp,[status(thm)],[582]) ).
thf(8698,plain,
( ( sk2 != sk2 )
| ( sk1 != nil )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[7937,583]) ).
thf(8699,plain,
( ( sk1 != nil )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[8698:[]]) ).
thf(8883,plain,
( ( ( nil @ ( sk2 @ frontsegP ) )
!= ( sk2 @ ( nil @ frontsegP ) ) )
| ( sk1 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1531,8699]) ).
thf(8884,plain,
( ( ( nil @ ( sk2 @ frontsegP ) )
!= ( sk2 @ ( nil @ frontsegP ) ) )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[8883]) ).
thf(8901,plain,
( ( sk2 != nil )
| ( sk2 != nil )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[8884]) ).
thf(8915,plain,
( ( sk2 != nil )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[8901]) ).
thf(11519,plain,
( ( sk1 != sk1 )
| ( sk2 != nil )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[10543,8915]) ).
thf(11520,plain,
( ( sk1 != sk1 )
| ( sk2 != nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[11519]) ).
thf(11521,plain,
( ( sk2 != nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[11520:[]]) ).
thf(12055,plain,
( ( ( sk1 @ ( sk2 @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ( sk2 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[565,11521]) ).
thf(12056,plain,
( ( ( sk1 @ ( sk2 @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[12055]) ).
thf(12149,plain,
( ( sk1 != sk1 )
| ( sk2 != nil )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[12056]) ).
thf(12169,plain,
sk2 != nil,
inference(simp,[status(thm)],[12149]) ).
thf(12172,plain,
~ ( sk2 @ ( nil @ frontsegP ) ),
inference(simplifyReflect,[status(thm)],[7937,12169]) ).
thf(51,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) )
!= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
thf(308,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) )
!= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(45,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(268,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)],[45]) ).
thf(269,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( A @ ( C @ app ) @ app ) @ segmentP ) )
| ~ ( B @ ( A @ segmentP ) )
| ~ ( D @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[268]) ).
thf(202,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk8 @ ( A @ sk7 @ leq ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[199]) ).
thf(23599,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk15 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,217]) ).
thf(23600,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk15 @ ssList ) ),
inference(simp,[status(thm)],[23599]) ).
thf(23601,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk15 @ ssList ) ),
inference(pattern_uni,[status(thm)],[23600:[bind(A,$thf( sk1 ))]]) ).
thf(76,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ singletonP )
<=> ? [B: $i] :
( ( ( nil @ ( B @ cons ) )
= A )
& ( B @ ssItem ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
thf(440,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)],[76]) ).
thf(122,plain,
sk6 @ ssItem,
inference(cnfConj,[status(thm)],[120]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax65) ).
thf(238,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(239,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[238]) ).
thf(1703,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,239]) ).
thf(1704,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[1703]) ).
thf(1705,plain,
nil @ ( sk6 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[1704:[bind(A,$thf( sk6 ))]]) ).
thf(7695,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[106,170]) ).
thf(7696,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[7695]) ).
thf(7697,plain,
( ~ ( sk1 @ ( nil @ frontsegP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[7696:[bind(A,$thf( sk1 ))]]) ).
thf(207,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk7 @ ( A @ sk8 @ leq ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[199]) ).
thf(18919,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ( A @ sk8 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,207]) ).
thf(18920,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ( A @ sk8 @ leq ) ) ),
inference(simp,[status(thm)],[18919]) ).
thf(18921,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk7 @ ( sk2 @ sk8 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[18920:[bind(A,$thf( sk2 ))]]) ).
thf(83,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(472,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)],[83]) ).
thf(17,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(152,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)],[17]) ).
thf(153,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ lt ) )
| ~ ( C @ ( B @ lt ) )
| ~ ( B @ ( A @ leq ) )
| ~ ( C @ ssItem )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[152]) ).
thf(220,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk14 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[215]) ).
thf(25844,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk14 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,220]) ).
thf(25845,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk14 @ ssList ) ),
inference(simp,[status(thm)],[25844]) ).
thf(25846,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk14 @ ssList ) ),
inference(pattern_uni,[status(thm)],[25845:[bind(A,$thf( sk2 ))]]) ).
thf(26299,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[25846,406]) ).
thf(26300,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[26299]) ).
thf(26301,plain,
( ( nil @ ( sk2 @ sk14 @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[26300:[bind(A,$thf( sk2 @ sk14 ))]]) ).
thf(2040,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,430]) ).
thf(2041,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP ) ),
inference(simp,[status(thm)],[2040]) ).
thf(2042,plain,
nil @ ( sk6 @ cons ) @ duplicatefreeP,
inference(pattern_uni,[status(thm)],[2041:[bind(A,$thf( sk6 ))]]) ).
thf(23,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(174,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)],[23]) ).
thf(18021,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,206]) ).
thf(18022,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ssItem ) ),
inference(simp,[status(thm)],[18021]) ).
thf(18023,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk8 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[18022:[bind(A,$thf( sk1 ))]]) ).
thf(75,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ cyclefreeP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax59) ).
thf(438,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ cyclefreeP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(439,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[438]) ).
thf(18334,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18023,439]) ).
thf(18335,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18334]) ).
thf(18336,plain,
( ( nil @ ( sk1 @ sk8 @ cons ) @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18335:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(262,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk17 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[254]) ).
thf(49829,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk17 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,262]) ).
thf(49830,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk17 @ ssItem ) ),
inference(simp,[status(thm)],[49829]) ).
thf(49831,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk17 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[49830:[bind(A,$thf( sk2 ))]]) ).
thf(1516,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,406]) ).
thf(1517,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) ) ),
inference(simp,[status(thm)],[1516]) ).
thf(1518,plain,
nil @ ( sk1 @ frontsegP ),
inference(pattern_uni,[status(thm)],[1517:[bind(A,$thf( sk1 ))]]) ).
thf(334,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ equalelemsP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[333]) ).
thf(18583,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18079,334]) ).
thf(18584,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18583]) ).
thf(18585,plain,
( ( nil @ ( sk2 @ sk8 @ cons ) @ equalelemsP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18584:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(257,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk21 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[254]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( nil @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
thf(266,plain,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( nil @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(267,plain,
! [A: $i] :
( ~ ( A @ ( nil @ memberP ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[266]) ).
thf(18418,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18023,267]) ).
thf(18419,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18418]) ).
thf(18420,plain,
( ~ ( sk1 @ sk8 @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18419:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(204,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk7 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[199]) ).
thf(17228,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,204]) ).
thf(17229,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssItem ) ),
inference(simp,[status(thm)],[17228]) ).
thf(17230,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk7 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[17229:[bind(A,$thf( sk2 ))]]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax31) ).
thf(150,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(151,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[150]) ).
thf(17841,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17230,151]) ).
thf(17842,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17841]) ).
thf(17843,plain,
( ( sk2 @ sk7 @ ( sk2 @ sk7 @ leq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17842:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(169,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[167]) ).
thf(171,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[169]) ).
thf(172,plain,
( ( nil @ ( nil @ frontsegP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[171]) ).
thf(62,axiom,
nil @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
thf(376,plain,
nil @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(609,plain,
( ( nil @ ( nil @ frontsegP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[172,376]) ).
thf(610,plain,
nil @ ( nil @ frontsegP ),
inference(simp,[status(thm)],[609]) ).
thf(46,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(270,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)],[46]) ).
thf(271,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ frontsegP ) )
| ( ( C @ ( B @ app ) )
!= A )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) )
& ( ( ( A @ ( B @ sk22 ) @ ( B @ app ) )
= A )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ ( B @ sk22 ) @ ssList )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[270]) ).
thf(272,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk22 ) @ ssList )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[271]) ).
thf(56400,plain,
! [B: $i,A: $i] :
( ( ( nil @ ( nil @ frontsegP ) )
!= ( B @ ( A @ frontsegP ) ) )
| ( A @ ( B @ sk22 ) @ ssList )
| ~ $true
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[610,272]) ).
thf(56401,plain,
! [B: $i,A: $i] :
( ( ( nil @ ( nil @ frontsegP ) )
!= ( B @ ( A @ frontsegP ) ) )
| ( A @ ( B @ sk22 ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[56400]) ).
thf(56402,plain,
( ( nil @ ( nil @ sk22 ) @ ssList )
| ~ ( nil @ ssList )
| ~ ( nil @ ssList ) ),
inference(pattern_uni,[status(thm)],[56401:[bind(A,$thf( nil )),bind(B,$thf( nil ))]]) ).
thf(56773,plain,
( ( nil @ ( nil @ sk22 ) @ ssList )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[56402]) ).
thf(56855,plain,
( ( nil @ ( nil @ sk22 ) @ ssList )
| ~ $true ),
inference(rewrite,[status(thm)],[56773,376]) ).
thf(56856,plain,
nil @ ( nil @ sk22 ) @ ssList,
inference(simp,[status(thm)],[56855]) ).
thf(18466,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18023,239]) ).
thf(18467,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18466]) ).
thf(18468,plain,
( ( nil @ ( sk1 @ sk8 @ cons ) @ totalorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18467:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(22226,plain,
( ( ( sk6 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk5 != nil )
| ~ $true
| ~ ( sk6 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[610,7878]) ).
thf(22227,plain,
( ( ( sk6 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk5 != nil )
| ~ ( sk6 @ ssList ) ),
inference(simp,[status(thm)],[22226]) ).
thf(22334,plain,
( ( sk6 != nil )
| ( nil != nil )
| ( sk5 != nil )
| ~ ( sk6 @ ssList ) ),
inference(simp,[status(thm)],[22227]) ).
thf(22370,plain,
( ( sk6 != nil )
| ( sk5 != nil )
| ~ ( sk6 @ ssList ) ),
inference(simp,[status(thm)],[22334]) ).
thf(23291,plain,
( ( ( sk6 @ ssList )
!= ( nil @ ssList ) )
| ( sk6 != nil )
| ( sk5 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[376,22370]) ).
thf(23292,plain,
( ( ( sk6 @ ssList )
!= ( nil @ ssList ) )
| ( sk6 != nil )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[23291]) ).
thf(23371,plain,
( ( sk6 != nil )
| ( sk6 != nil )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[23292]) ).
thf(23389,plain,
( ( sk6 != nil )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[23371]) ).
thf(23409,plain,
! [A: $i] :
( ( A != sk5 )
| ( sk6 != nil )
| ( nil != nil )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[170,23389]) ).
thf(23410,plain,
! [A: $i] :
( ( A != sk5 )
| ( sk6 != nil )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[23409]) ).
thf(23411,plain,
( ( sk6 != nil )
| ~ ( sk5 @ ( nil @ frontsegP ) )
| ~ ( sk5 @ ssList ) ),
inference(pattern_uni,[status(thm)],[23410:[bind(A,$thf( sk5 ))]]) ).
thf(17172,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,204]) ).
thf(17173,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssItem ) ),
inference(simp,[status(thm)],[17172]) ).
thf(17174,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk7 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[17173:[bind(A,$thf( sk1 ))]]) ).
thf(66,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax61) ).
thf(398,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(399,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[398]) ).
thf(17558,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17174,399]) ).
thf(17559,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17558]) ).
thf(17560,plain,
( ( nil @ ( sk1 @ sk7 @ cons ) @ totalorderP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17559:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax55) ).
thf(236,plain,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(237,plain,
! [A: $i] :
( ( A @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[236]) ).
thf(57005,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[56856,237]) ).
thf(57006,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[57005]) ).
thf(57007,plain,
nil @ ( nil @ sk22 ) @ ( nil @ ( nil @ sk22 ) @ segmentP ),
inference(pattern_uni,[status(thm)],[57006:[bind(A,$thf( nil @ ( nil @ sk22 ) ))]]) ).
thf(88,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(504,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)],[88]) ).
thf(25796,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk14 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,220]) ).
thf(25797,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk14 @ ssList ) ),
inference(simp,[status(thm)],[25796]) ).
thf(25798,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk14 @ ssList ) ),
inference(pattern_uni,[status(thm)],[25797:[bind(A,$thf( sk1 ))]]) ).
thf(26170,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[25798,332]) ).
thf(26171,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[26170]) ).
thf(26172,plain,
( ( nil @ ( sk1 @ sk14 @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[26171:[bind(A,$thf( sk1 @ sk14 ))]]) ).
thf(6,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(125,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)],[6]) ).
thf(80,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ rearsegP ) )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax52) ).
thf(460,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( ( nil = A )
=> ( A @ ( nil @ rearsegP ) ) )
& ( ( A @ ( nil @ rearsegP ) )
=> ( nil = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(222,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk16 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[215]) ).
thf(27526,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,222]) ).
thf(27527,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssList ) ),
inference(simp,[status(thm)],[27526]) ).
thf(27528,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk16 @ ssList ) ),
inference(pattern_uni,[status(thm)],[27527:[bind(A,$thf( sk1 ))]]) ).
thf(65,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(389,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)],[65]) ).
thf(27,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(187,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)],[27]) ).
thf(188,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[187]) ).
thf(189,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( A = B ) ),
inference(lifteq,[status(thm)],[188]) ).
thf(18580,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18079,439]) ).
thf(18581,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18580]) ).
thf(18582,plain,
( ( nil @ ( sk2 @ sk8 @ cons ) @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18581:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(70,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(421,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)],[70]) ).
thf(208,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk10 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[199]) ).
thf(19412,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,208]) ).
thf(19413,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ssList ) ),
inference(simp,[status(thm)],[19412]) ).
thf(19414,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk10 @ ssList ) ),
inference(pattern_uni,[status(thm)],[19413:[bind(A,$thf( sk2 ))]]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ( A @ tl )
= B )
& ( B @ ssList ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax76) ).
thf(280,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ( A @ tl )
= B )
& ( B @ ssList ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(281,plain,
! [A: $i] :
( ( ( ( A @ tl )
= ( A @ sk23 ) )
| ( nil = A )
| ~ ( A @ ssList ) )
& ( ( A @ sk23 @ ssList )
| ( nil = A )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[280]) ).
thf(282,plain,
! [A: $i] :
( ( A @ sk23 @ ssList )
| ( nil = A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[281]) ).
thf(284,plain,
! [A: $i] :
( ( A @ sk23 @ ssList )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[282]) ).
thf(879,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,332]) ).
thf(880,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[879]) ).
thf(881,plain,
nil @ ( sk1 @ rearsegP ),
inference(pattern_uni,[status(thm)],[880:[bind(A,$thf( sk1 ))]]) ).
thf(25001,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[24629,430]) ).
thf(25002,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[25001]) ).
thf(25003,plain,
( ( nil @ ( sk1 @ sk12 @ cons ) @ duplicatefreeP )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25002:[bind(A,$thf( sk1 @ sk12 ))]]) ).
thf(77,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( B @ ( A @ app ) @ ssList ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
thf(448,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( B @ ( A @ app ) @ ssList ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(18368,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18023,430]) ).
thf(18369,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18368]) ).
thf(18370,plain,
( ( nil @ ( sk1 @ sk8 @ cons ) @ duplicatefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18369:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(34,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil @ ( A @ app ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax84) ).
thf(228,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil @ ( A @ app ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(229,plain,
! [A: $i] :
( ( ( nil @ ( A @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[228]) ).
thf(230,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[229]) ).
thf(33320,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[106,230]) ).
thf(33321,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[33320]) ).
thf(33322,plain,
( ( nil @ ( sk1 @ app ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[33321:[bind(A,$thf( sk1 ))]]) ).
thf(640,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,200]) ).
thf(641,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssList ) ),
inference(simp,[status(thm)],[640]) ).
thf(642,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk11 @ ssList ) ),
inference(pattern_uni,[status(thm)],[641:[bind(A,$thf( sk1 ))]]) ).
thf(654,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssList )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[642,200]) ).
thf(655,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssList )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[654]) ).
thf(656,plain,
( ( sk1 @ sk11 @ cyclefreeP )
| ( sk1 @ sk11 @ sk11 @ ssList )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[655:[bind(A,$thf( sk1 @ sk11 ))]]) ).
thf(900,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ sk11 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[656,332]) ).
thf(901,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ sk11 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[900]) ).
thf(902,plain,
( ( nil @ ( sk1 @ sk11 @ sk11 @ rearsegP ) )
| ( sk1 @ sk11 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[901:[bind(A,$thf( sk1 @ sk11 @ sk11 ))]]) ).
thf(38525,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ~ $true
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[249,567]) ).
thf(38526,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A = B ) ),
inference(simp,[status(thm)],[38525]) ).
thf(38527,plain,
( ~ ( nil @ ssItem )
| ~ ( sk1 @ ssItem )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[38526:[bind(A,$thf( sk1 )),bind(B,$thf( nil ))]]) ).
thf(41763,plain,
( ( ( sk5 @ ssItem )
!= ( sk1 @ ssItem ) )
| ~ ( nil @ ssItem )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[121,38527]) ).
thf(41764,plain,
( ( ( sk5 @ ssItem )
!= ( sk1 @ ssItem ) )
| ~ ( nil @ ssItem )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[41763]) ).
thf(42100,plain,
( ( sk5 != sk1 )
| ~ ( nil @ ssItem )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[41764]) ).
thf(43525,plain,
( ( ( sk5 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk5 != sk1 )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[121,42100]) ).
thf(43526,plain,
( ( ( sk5 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk5 != sk1 )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[43525]) ).
thf(43576,plain,
( ( sk5 != nil )
| ( sk5 != sk1 )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[43526]) ).
thf(53,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ hd @ ssItem ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
thf(325,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ hd @ ssItem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(57026,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[56856,230]) ).
thf(57027,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[57026]) ).
thf(57028,plain,
( ( nil @ ( nil @ ( nil @ sk22 ) @ app ) )
= ( nil @ ( nil @ sk22 ) ) ),
inference(pattern_uni,[status(thm)],[57027:[bind(A,$thf( nil @ ( nil @ sk22 ) ))]]) ).
thf(27921,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[27528,332]) ).
thf(27922,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[27921]) ).
thf(27923,plain,
( ( nil @ ( sk1 @ sk16 @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[27922:[bind(A,$thf( sk1 @ sk16 ))]]) ).
thf(201,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[199]) ).
thf(15934,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,201]) ).
thf(15935,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList ) ),
inference(simp,[status(thm)],[15934]) ).
thf(15936,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk9 @ ssList ) ),
inference(pattern_uni,[status(thm)],[15935:[bind(A,$thf( sk1 ))]]) ).
thf(16149,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[15936,406]) ).
thf(16150,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[16149]) ).
thf(16151,plain,
( ( nil @ ( sk1 @ sk9 @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[16150:[bind(A,$thf( sk1 @ sk9 ))]]) ).
thf(5271,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,151]) ).
thf(5272,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[5271]) ).
thf(5273,plain,
sk6 @ ( sk6 @ leq ),
inference(pattern_uni,[status(thm)],[5272:[bind(A,$thf( sk6 ))]]) ).
thf(7,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(127,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)],[7]) ).
thf(128,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[127]) ).
thf(129,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A = B ) ),
inference(lifteq,[status(thm)],[128]) ).
thf(1074,plain,
! [B: $i,A: $i] :
( ( A != sk2 )
| ( B != sk1 )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[129,583]) ).
thf(1075,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( sk2 @ ( A @ leq ) )
| ~ ( A @ ( sk2 @ leq ) )
| ~ ( A @ ssItem )
| ~ ( sk2 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[1074:[bind(A,$thf( sk2 ))]]) ).
thf(1405,plain,
( ~ ( sk2 @ ( sk1 @ leq ) )
| ~ ( sk1 @ ( sk2 @ leq ) )
| ~ ( sk1 @ ssItem )
| ~ ( sk2 @ ssItem ) ),
inference(simp,[status(thm)],[1075]) ).
thf(2081,plain,
( ( ( sk6 @ ssItem )
!= ( sk2 @ ssItem ) )
| ~ ( sk2 @ ( sk1 @ leq ) )
| ~ ( sk1 @ ( sk2 @ leq ) )
| ~ ( sk1 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,1405]) ).
thf(2082,plain,
( ( ( sk6 @ ssItem )
!= ( sk2 @ ssItem ) )
| ~ ( sk2 @ ( sk1 @ leq ) )
| ~ ( sk1 @ ( sk2 @ leq ) )
| ~ ( sk1 @ ssItem ) ),
inference(simp,[status(thm)],[2081]) ).
thf(2086,plain,
( ( sk6 != sk2 )
| ~ ( sk2 @ ( sk1 @ leq ) )
| ~ ( sk1 @ ( sk2 @ leq ) )
| ~ ( sk1 @ ssItem ) ),
inference(simp,[status(thm)],[2082]) ).
thf(6400,plain,
( ( ( sk6 @ ( sk6 @ leq ) )
!= ( sk1 @ ( sk2 @ leq ) ) )
| ( sk6 != sk2 )
| ~ ( sk2 @ ( sk1 @ leq ) )
| ~ $true
| ~ ( sk1 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[5273,2086]) ).
thf(6401,plain,
( ( ( sk6 @ ( sk6 @ leq ) )
!= ( sk1 @ ( sk2 @ leq ) ) )
| ( sk6 != sk2 )
| ~ ( sk2 @ ( sk1 @ leq ) )
| ~ ( sk1 @ ssItem ) ),
inference(simp,[status(thm)],[6400]) ).
thf(6479,plain,
( ( sk6 != sk1 )
| ( sk6 != sk2 )
| ( sk6 != sk2 )
| ~ ( sk2 @ ( sk1 @ leq ) )
| ~ ( sk1 @ ssItem ) ),
inference(simp,[status(thm)],[6401]) ).
thf(6508,plain,
( ( sk6 != sk1 )
| ( sk6 != sk2 )
| ~ ( sk2 @ ( sk1 @ leq ) )
| ~ ( sk1 @ ssItem ) ),
inference(simp,[status(thm)],[6479]) ).
thf(6642,plain,
( ( ( sk6 @ ( sk6 @ leq ) )
!= ( sk2 @ ( sk1 @ leq ) ) )
| ( sk6 != sk1 )
| ( sk6 != sk2 )
| ~ $true
| ~ ( sk1 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[5273,6508]) ).
thf(6643,plain,
( ( ( sk6 @ ( sk6 @ leq ) )
!= ( sk2 @ ( sk1 @ leq ) ) )
| ( sk6 != sk1 )
| ( sk6 != sk2 )
| ~ ( sk1 @ ssItem ) ),
inference(simp,[status(thm)],[6642]) ).
thf(6699,plain,
( ( sk6 != sk2 )
| ( sk6 != sk1 )
| ( sk6 != sk1 )
| ( sk6 != sk2 )
| ~ ( sk1 @ ssItem ) ),
inference(simp,[status(thm)],[6643]) ).
thf(6724,plain,
( ( sk6 != sk1 )
| ( sk6 != sk2 )
| ~ ( sk1 @ ssItem ) ),
inference(simp,[status(thm)],[6699]) ).
thf(7408,plain,
( ( ( sk6 @ ssItem )
!= ( sk1 @ ssItem ) )
| ( sk6 != sk1 )
| ( sk6 != sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,6724]) ).
thf(7409,plain,
( ( ( sk6 @ ssItem )
!= ( sk1 @ ssItem ) )
| ( sk6 != sk1 )
| ( sk6 != sk2 ) ),
inference(simp,[status(thm)],[7408]) ).
thf(7411,plain,
( ( sk6 != sk1 )
| ( sk6 != sk1 )
| ( sk6 != sk2 ) ),
inference(simp,[status(thm)],[7409]) ).
thf(7423,plain,
( ( sk6 != sk1 )
| ( sk6 != sk2 ) ),
inference(simp,[status(thm)],[7411]) ).
thf(25084,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[24629,151]) ).
thf(25085,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[25084]) ).
thf(25086,plain,
( ( sk1 @ sk12 @ ( sk1 @ sk12 @ leq ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25085:[bind(A,$thf( sk1 @ sk12 ))]]) ).
thf(203,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( ( A @ sk11 @ ( A @ sk8 @ cons ) @ ( A @ sk10 @ ( A @ sk7 @ cons ) @ ( A @ sk9 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[199]) ).
thf(211,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ~ ( A @ ssList )
| ( ( A @ sk11 @ ( A @ sk8 @ cons ) @ ( A @ sk10 @ ( A @ sk7 @ cons ) @ ( A @ sk9 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[203]) ).
thf(84,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) @ tl )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax25) ).
thf(485,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) @ tl )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(50252,plain,
! [A: $i] :
( ( ( sk2 @ sk17 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[49831,267]) ).
thf(50253,plain,
! [A: $i] :
( ( ( sk2 @ sk17 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[50252]) ).
thf(50254,plain,
( ~ ( sk2 @ sk17 @ ( nil @ memberP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[50253:[bind(A,$thf( sk2 @ sk17 ))]]) ).
thf(701,plain,
( ~ $true
| ( ( sk1 @ sk11 @ cyclefreeP )
!= ( sk1 @ cyclefreeP ) )
| ( sk1 @ sk11 @ sk11 @ ssList )
| ( sk1 @ cyclefreeP ) ),
inference(eqfactor_ordered,[status(thm)],[656]) ).
thf(703,plain,
( ( ( sk1 @ sk11 )
!= sk1 )
| ( sk1 @ sk11 @ sk11 @ ssList )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[701]) ).
thf(832,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( ( sk1 @ sk11 )
!= sk1 )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[703,279]) ).
thf(833,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( ( sk1 @ sk11 )
!= sk1 )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[832]) ).
thf(834,plain,
( ( nil @ ( sk1 @ sk11 @ sk11 @ segmentP ) )
| ( ( sk1 @ sk11 )
!= sk1 )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[833:[bind(A,$thf( sk1 @ sk11 @ sk11 ))]]) ).
thf(16691,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ( A @ sk7 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,202]) ).
thf(16692,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ( A @ sk7 @ leq ) ) ),
inference(simp,[status(thm)],[16691]) ).
thf(16693,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk8 @ ( sk1 @ sk7 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[16692:[bind(A,$thf( sk1 ))]]) ).
thf(92,axiom,
nil @ strictorderedP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax69) ).
thf(514,plain,
nil @ strictorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(686,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssList )
| ~ $true
| ( sk2 @ sk11 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[650,200]) ).
thf(687,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssList )
| ( sk2 @ sk11 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[686]) ).
thf(688,plain,
( ( sk2 @ sk11 @ sk11 @ cyclefreeP )
| ( sk2 @ sk11 @ sk11 @ sk11 @ ssList )
| ( sk2 @ sk11 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[687:[bind(A,$thf( sk2 @ sk11 @ sk11 ))]]) ).
thf(5736,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ sk11 @ sk11 @ cyclefreeP )
| ( sk2 @ sk11 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[688,332]) ).
thf(5737,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ sk11 @ sk11 @ cyclefreeP )
| ( sk2 @ sk11 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5736]) ).
thf(5738,plain,
( ( nil @ ( sk2 @ sk11 @ sk11 @ sk11 @ rearsegP ) )
| ( sk2 @ sk11 @ sk11 @ cyclefreeP )
| ( sk2 @ sk11 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5737:[bind(A,$thf( sk2 @ sk11 @ sk11 @ sk11 ))]]) ).
thf(18708,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18079,239]) ).
thf(18709,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18708]) ).
thf(18710,plain,
( ( nil @ ( sk2 @ sk8 @ cons ) @ totalorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18709:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(9,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(132,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)],[9]) ).
thf(133,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)],[132]) ).
thf(17569,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17174,267]) ).
thf(17570,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17569]) ).
thf(17571,plain,
( ~ ( sk1 @ sk7 @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17570:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(17599,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17174,151]) ).
thf(17600,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17599]) ).
thf(17601,plain,
( ( sk1 @ sk7 @ ( sk1 @ sk7 @ leq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17600:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(1519,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ sk11 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[650,406]) ).
thf(1520,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ sk11 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1519]) ).
thf(1521,plain,
( ( nil @ ( sk2 @ sk11 @ sk11 @ frontsegP ) )
| ( sk2 @ sk11 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1520:[bind(A,$thf( sk2 @ sk11 @ sk11 ))]]) ).
thf(89,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(507,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)],[89]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ geq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax89) ).
thf(154,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(155,plain,
! [A: $i] :
( ( A @ ( A @ geq ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[154]) ).
thf(25040,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[24629,155]) ).
thf(25041,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[25040]) ).
thf(25042,plain,
( ( sk1 @ sk12 @ ( sk1 @ sk12 @ geq ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25041:[bind(A,$thf( sk1 @ sk12 ))]]) ).
thf(23644,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk15 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,217]) ).
thf(23645,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk15 @ ssList ) ),
inference(simp,[status(thm)],[23644]) ).
thf(23646,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk15 @ ssList ) ),
inference(pattern_uni,[status(thm)],[23645:[bind(A,$thf( sk2 ))]]) ).
thf(24081,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[23646,406]) ).
thf(24082,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[24081]) ).
thf(24083,plain,
( ( nil @ ( sk2 @ sk15 @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[24082:[bind(A,$thf( sk2 @ sk15 ))]]) ).
thf(3066,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[121,439]) ).
thf(3067,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP ) ),
inference(simp,[status(thm)],[3066]) ).
thf(3068,plain,
nil @ ( sk5 @ cons ) @ cyclefreeP,
inference(pattern_uni,[status(thm)],[3067:[bind(A,$thf( sk5 ))]]) ).
thf(78,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax63) ).
thf(450,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(451,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[450]) ).
thf(18640,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18079,451]) ).
thf(18641,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18640]) ).
thf(18642,plain,
( ( nil @ ( sk2 @ sk8 @ cons ) @ strictorderP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18641:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(19829,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19414,332]) ).
thf(19830,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19829]) ).
thf(19831,plain,
( ( nil @ ( sk2 @ sk10 @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19830:[bind(A,$thf( sk2 @ sk10 ))]]) ).
thf(44168,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[43728,332]) ).
thf(44169,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[44168]) ).
thf(44170,plain,
( ( nil @ ( sk2 @ sk19 @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[44169:[bind(A,$thf( sk2 @ sk19 ))]]) ).
thf(221,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ sk12 @ ( A @ sk13 @ lt ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[215]) ).
thf(772,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[633,279]) ).
thf(773,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[772]) ).
thf(774,plain,
( ( nil @ ( sk2 @ sk11 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[773:[bind(A,$thf( sk2 @ sk11 ))]]) ).
thf(5244,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[121,151]) ).
thf(5245,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[5244]) ).
thf(5246,plain,
sk5 @ ( sk5 @ leq ),
inference(pattern_uni,[status(thm)],[5245:[bind(A,$thf( sk5 ))]]) ).
thf(24683,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk12 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,219]) ).
thf(24684,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk12 @ ssItem ) ),
inference(simp,[status(thm)],[24683]) ).
thf(24685,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk12 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[24684:[bind(A,$thf( sk2 ))]]) ).
thf(25337,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[24685,151]) ).
thf(25338,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[25337]) ).
thf(25339,plain,
( ( sk2 @ sk12 @ ( sk2 @ sk12 @ leq ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25338:[bind(A,$thf( sk2 @ sk12 ))]]) ).
thf(116,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ gt ) )
| ~ ( A @ ( B @ lt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[114]) ).
thf(18886,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ( A @ sk8 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,207]) ).
thf(18887,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ( A @ sk8 @ leq ) ) ),
inference(simp,[status(thm)],[18886]) ).
thf(18888,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk7 @ ( sk1 @ sk8 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[18887:[bind(A,$thf( sk1 ))]]) ).
thf(42,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ app ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
thf(250,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ app ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(251,plain,
! [A: $i] :
( ( ( A @ ( nil @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[250]) ).
thf(252,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[251]) ).
thf(42244,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[105,252]) ).
thf(42245,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[42244]) ).
thf(42246,plain,
( ( sk2 @ ( nil @ app ) )
= sk2 ),
inference(pattern_uni,[status(thm)],[42245:[bind(A,$thf( sk2 ))]]) ).
thf(258,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ lt ) )
| ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
!= A )
| ~ ( F @ ssList )
| ~ ( E @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssItem )
| ~ ( B @ ssItem )
| ~ ( A @ strictorderedP )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[254]) ).
thf(264,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( E @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssItem )
| ~ ( B @ ssItem )
| ~ ( A @ strictorderedP )
| ~ ( A @ ssList )
| ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
!= A ) ),
inference(lifteq,[status(thm)],[258]) ).
thf(265,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ lt ) )
| ~ ( E @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) @ strictorderedP )
| ~ ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) @ ssList ) ),
inference(simp,[status(thm)],[264]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax90) ).
thf(139,plain,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(140,plain,
! [A: $i] :
( ~ ( A @ ( A @ lt ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[139]) ).
thf(18643,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18079,140]) ).
thf(18644,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18643]) ).
thf(18645,plain,
( ~ ( sk2 @ sk8 @ ( sk2 @ sk8 @ lt ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18644:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(15971,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,201]) ).
thf(15972,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList ) ),
inference(simp,[status(thm)],[15971]) ).
thf(15973,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk9 @ ssList ) ),
inference(pattern_uni,[status(thm)],[15972:[bind(A,$thf( sk2 ))]]) ).
thf(16295,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[15973,406]) ).
thf(16296,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[16295]) ).
thf(16297,plain,
( ( nil @ ( sk2 @ sk9 @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[16296:[bind(A,$thf( sk2 @ sk9 ))]]) ).
thf(25287,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[24685,140]) ).
thf(25288,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[25287]) ).
thf(25289,plain,
( ~ ( sk2 @ sk12 @ ( sk2 @ sk12 @ lt ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25288:[bind(A,$thf( sk2 @ sk12 ))]]) ).
thf(36,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(233,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)],[36]) ).
thf(79,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(452,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)],[79]) ).
thf(64,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(380,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)],[64]) ).
thf(4,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(117,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)],[4]) ).
thf(91,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49) ).
thf(512,plain,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(27583,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,222]) ).
thf(27584,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssList ) ),
inference(simp,[status(thm)],[27583]) ).
thf(27585,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk16 @ ssList ) ),
inference(pattern_uni,[status(thm)],[27584:[bind(A,$thf( sk2 ))]]) ).
thf(62162,plain,
! [A: $i] :
( ( A != sk2 )
| ( nil != nil )
| ( A @ sk23 @ ssList )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[284,12169]) ).
thf(62163,plain,
! [A: $i] :
( ( A != sk2 )
| ( A @ sk23 @ ssList )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[62162]) ).
thf(62164,plain,
( ( sk2 @ sk23 @ ssList )
| ~ ( sk2 @ ssList ) ),
inference(pattern_uni,[status(thm)],[62163:[bind(A,$thf( sk2 ))]]) ).
thf(65459,plain,
( ( sk2 @ sk23 @ ssList )
| ~ $true ),
inference(rewrite,[status(thm)],[62164,105]) ).
thf(65460,plain,
sk2 @ sk23 @ ssList,
inference(simp,[status(thm)],[65459]) ).
thf(65603,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65460,279]) ).
thf(65604,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[65603]) ).
thf(65605,plain,
nil @ ( sk2 @ sk23 @ segmentP ),
inference(pattern_uni,[status(thm)],[65604:[bind(A,$thf( sk2 @ sk23 ))]]) ).
thf(260,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk20 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[254]) ).
thf(33369,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[105,230]) ).
thf(33370,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[33369]) ).
thf(33371,plain,
( ( nil @ ( sk2 @ app ) )
= sk2 ),
inference(pattern_uni,[status(thm)],[33370:[bind(A,$thf( sk2 ))]]) ).
thf(224,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk13 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[215]) ).
thf(29365,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk13 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,224]) ).
thf(29366,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk13 @ ssItem ) ),
inference(simp,[status(thm)],[29365]) ).
thf(29367,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk13 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[29366:[bind(A,$thf( sk1 ))]]) ).
thf(29809,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[29367,267]) ).
thf(29810,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[29809]) ).
thf(29811,plain,
( ~ ( sk1 @ sk13 @ ( nil @ memberP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[29810:[bind(A,$thf( sk1 @ sk13 ))]]) ).
thf(42088,plain,
( ( ( sk6 @ ssItem )
!= ( sk1 @ ssItem ) )
| ~ ( nil @ ssItem )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[122,38527]) ).
thf(42089,plain,
( ( ( sk6 @ ssItem )
!= ( sk1 @ ssItem ) )
| ~ ( nil @ ssItem )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[42088]) ).
thf(42105,plain,
( ( sk6 != sk1 )
| ~ ( nil @ ssItem )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[42089]) ).
thf(44800,plain,
( ( ( sk5 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk6 != sk1 )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[121,42105]) ).
thf(44801,plain,
( ( ( sk5 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk6 != sk1 )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[44800]) ).
thf(44854,plain,
( ( sk5 != nil )
| ( sk6 != sk1 )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[44801]) ).
thf(100,plain,
! [A: $i] :
( ~ ( A @ strictorderedP )
| ~ ( sk3 @ ( A @ segmentP ) )
| ~ ( A @ ( sk4 @ segmentP ) )
| ~ ( A @ ( sk3 @ neq ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(537,plain,
! [A: $i] :
( ~ ( A @ strictorderedP )
| ~ ( sk1 @ ( A @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( A @ ( sk1 @ neq ) )
| ~ ( A @ ssList ) ),
inference(rewrite,[status(thm)],[100,112,111]) ).
thf(571,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ segmentP ) )
!= ( sk1 @ ( A @ segmentP ) ) )
| ~ ( A @ strictorderedP )
| ~ $true
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( A @ ( sk1 @ neq ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[565,537]) ).
thf(572,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ segmentP ) )
!= ( sk1 @ ( A @ segmentP ) ) )
| ~ ( A @ strictorderedP )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( A @ ( sk1 @ neq ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[571]) ).
thf(573,plain,
( ~ ( sk2 @ strictorderedP )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) )
| ~ ( sk2 @ ssList ) ),
inference(pattern_uni,[status(thm)],[572:[bind(A,$thf( sk2 ))]]) ).
thf(909,plain,
( ~ ( sk2 @ strictorderedP )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) )
| ~ $true ),
inference(rewrite,[status(thm)],[573,105]) ).
thf(910,plain,
( ~ ( sk2 @ strictorderedP )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[909]) ).
thf(6844,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,237]) ).
thf(6845,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[6844]) ).
thf(6846,plain,
sk2 @ ( sk2 @ segmentP ),
inference(pattern_uni,[status(thm)],[6845:[bind(A,$thf( sk2 ))]]) ).
thf(6925,plain,
( ~ ( sk2 @ strictorderedP )
| ~ $true
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(rewrite,[status(thm)],[910,6846]) ).
thf(6926,plain,
( ~ ( sk2 @ strictorderedP )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[6925]) ).
thf(44033,plain,
( ( ( sk2 @ strictorderedP )
!= ( sk2 @ strictorderedP ) )
| ~ $true
| ~ ( sk2 @ ( sk1 @ neq ) )
| ( sk2 @ sk19 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[43728,6926]) ).
thf(44034,plain,
( ( ( sk2 @ strictorderedP )
!= ( sk2 @ strictorderedP ) )
| ~ ( sk2 @ ( sk1 @ neq ) )
| ( sk2 @ sk19 @ ssList ) ),
inference(simp,[status(thm)],[44033]) ).
thf(44035,plain,
( ~ ( sk2 @ ( sk1 @ neq ) )
| ( sk2 @ sk19 @ ssList ) ),
inference(pattern_uni,[status(thm)],[44034:[]]) ).
thf(273,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk22 ) @ ( B @ app ) )
= A )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[271]) ).
thf(275,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( A @ ( B @ sk22 ) @ ( B @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[273]) ).
thf(17797,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17230,155]) ).
thf(17798,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17797]) ).
thf(17799,plain,
( ( sk2 @ sk7 @ ( sk2 @ sk7 @ geq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17798:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(41765,plain,
( ( ( sk5 @ ssItem )
!= ( nil @ ssItem ) )
| ~ $true
| ~ ( sk1 @ ssItem )
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[121,38527]) ).
thf(41766,plain,
( ( ( sk5 @ ssItem )
!= ( nil @ ssItem ) )
| ~ ( sk1 @ ssItem )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[41765]) ).
thf(42111,plain,
( ( sk5 != nil )
| ~ ( sk1 @ ssItem )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[41766]) ).
thf(16337,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[15973,332]) ).
thf(16338,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[16337]) ).
thf(16339,plain,
( ( nil @ ( sk2 @ sk9 @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[16338:[bind(A,$thf( sk2 @ sk9 ))]]) ).
thf(290,plain,
! [A: $i] :
( ( A @ totalorderP )
| ( A @ sk27 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[287]) ).
thf(69225,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk27 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,290]) ).
thf(69226,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk27 @ ssList ) ),
inference(simp,[status(thm)],[69225]) ).
thf(69227,plain,
( ( sk2 @ totalorderP )
| ( sk2 @ sk27 @ ssList ) ),
inference(pattern_uni,[status(thm)],[69226:[bind(A,$thf( sk2 ))]]) ).
thf(28,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(190,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)],[28]) ).
thf(191,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ cons ) )
= ( A @ ( nil @ ( B @ cons ) @ app ) ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[190]) ).
thf(192,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( ( A @ ( nil @ ( B @ cons ) @ app ) )
= ( A @ ( B @ cons ) ) ) ),
inference(lifteq,[status(thm)],[191]) ).
thf(69,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(407,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)],[69]) ).
thf(17800,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17230,399]) ).
thf(17801,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17800]) ).
thf(17802,plain,
( ( nil @ ( sk2 @ sk7 @ cons ) @ totalorderP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17801:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(81,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax42) ).
thf(467,plain,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(30,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(195,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)],[30]) ).
thf(196,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)],[195]) ).
thf(197,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)],[196]) ).
thf(48426,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk20 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,260]) ).
thf(48427,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk20 @ ssList ) ),
inference(simp,[status(thm)],[48426]) ).
thf(48428,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk20 @ ssList ) ),
inference(pattern_uni,[status(thm)],[48427:[bind(A,$thf( sk2 ))]]) ).
thf(48763,plain,
( ( ( sk2 @ strictorderedP )
!= ( sk2 @ strictorderedP ) )
| ~ $true
| ~ ( sk2 @ ( sk1 @ neq ) )
| ( sk2 @ sk20 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[48428,6926]) ).
thf(48764,plain,
( ( ( sk2 @ strictorderedP )
!= ( sk2 @ strictorderedP ) )
| ~ ( sk2 @ ( sk1 @ neq ) )
| ( sk2 @ sk20 @ ssList ) ),
inference(simp,[status(thm)],[48763]) ).
thf(48765,plain,
( ~ ( sk2 @ ( sk1 @ neq ) )
| ( sk2 @ sk20 @ ssList ) ),
inference(pattern_uni,[status(thm)],[48764:[]]) ).
thf(74,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( ( A @ tl @ ( A @ hd @ cons ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax78) ).
thf(435,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( ( A @ tl @ ( A @ hd @ cons ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(26105,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[25798,406]) ).
thf(26106,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[26105]) ).
thf(26107,plain,
( ( nil @ ( sk1 @ sk14 @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[26106:[bind(A,$thf( sk1 @ sk14 ))]]) ).
thf(755,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,279]) ).
thf(756,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[755]) ).
thf(757,plain,
nil @ ( sk1 @ segmentP ),
inference(pattern_uni,[status(thm)],[756:[bind(A,$thf( sk1 ))]]) ).
thf(680,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[121,267]) ).
thf(681,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[680]) ).
thf(682,plain,
~ ( sk5 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[681:[bind(A,$thf( sk5 ))]]) ).
thf(43573,plain,
( ( ( sk6 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk5 != sk1 )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[122,42100]) ).
thf(43574,plain,
( ( ( sk6 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk5 != sk1 )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[43573]) ).
thf(43586,plain,
( ( sk6 != nil )
| ( sk5 != sk1 )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[43574]) ).
thf(26364,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[25846,332]) ).
thf(26365,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[26364]) ).
thf(26366,plain,
( ( nil @ ( sk2 @ sk14 @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[26365:[bind(A,$thf( sk2 @ sk14 ))]]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ geq ) )
<=> ( A @ ( B @ leq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax32) ).
thf(146,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)],[15]) ).
thf(147,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ geq ) )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) )
& ( ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ) ),
inference(cnf,[status(esa)],[146]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ geq ) )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[147]) ).
thf(6019,plain,
! [B: $i,A: $i] :
( ( ( sk6 @ ( sk6 @ leq ) )
!= ( A @ ( B @ leq ) ) )
| ( B @ ( A @ geq ) )
| ~ $true
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[5273,149]) ).
thf(6020,plain,
! [B: $i,A: $i] :
( ( ( sk6 @ ( sk6 @ leq ) )
!= ( A @ ( B @ leq ) ) )
| ( B @ ( A @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[6019]) ).
thf(6021,plain,
( ( sk6 @ ( sk6 @ geq ) )
| ~ ( sk6 @ ssItem )
| ~ ( sk6 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[6020:[bind(A,$thf( sk6 )),bind(B,$thf( sk6 ))]]) ).
thf(6039,plain,
( ( sk6 @ ( sk6 @ geq ) )
| ~ ( sk6 @ ssItem ) ),
inference(simp,[status(thm)],[6021]) ).
thf(6089,plain,
( ( sk6 @ ( sk6 @ geq ) )
| ~ $true ),
inference(rewrite,[status(thm)],[6039,122]) ).
thf(6090,plain,
sk6 @ ( sk6 @ geq ),
inference(simp,[status(thm)],[6089]) ).
thf(283,plain,
! [A: $i] :
( ( ( A @ tl )
= ( A @ sk23 ) )
| ( nil = A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[281]) ).
thf(285,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ( ( A @ sk23 )
= ( A @ tl ) )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[283]) ).
thf(95,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(519,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)],[95]) ).
thf(695,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssList )
| ~ $true
| ( sk1 @ sk11 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[656,200]) ).
thf(696,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssList )
| ( sk1 @ sk11 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[695]) ).
thf(697,plain,
( ( sk1 @ sk11 @ sk11 @ cyclefreeP )
| ( sk1 @ sk11 @ sk11 @ sk11 @ ssList )
| ( sk1 @ sk11 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[696:[bind(A,$thf( sk1 @ sk11 @ sk11 ))]]) ).
thf(1981,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[121,399]) ).
thf(1982,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP ) ),
inference(simp,[status(thm)],[1981]) ).
thf(1983,plain,
nil @ ( sk5 @ cons ) @ totalorderP,
inference(pattern_uni,[status(thm)],[1982:[bind(A,$thf( sk5 ))]]) ).
thf(538,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ strictorderedP )
| ~ ( sk1 @ ( A @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( A @ ( sk1 @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,537]) ).
thf(539,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ strictorderedP )
| ~ ( sk1 @ ( A @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( A @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[538]) ).
thf(540,plain,
( ~ ( sk1 @ strictorderedP )
| ~ ( sk1 @ ( sk1 @ segmentP ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ ( sk1 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[539:[bind(A,$thf( sk1 ))]]) ).
thf(103,plain,
sk3 @ strictorderedP,
inference(cnfConj,[status(thm)],[99]) ).
thf(535,plain,
sk1 @ strictorderedP,
inference(rewrite,[status(thm)],[103,111]) ).
thf(552,plain,
( ~ $true
| ~ ( sk1 @ ( sk1 @ segmentP ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ ( sk1 @ neq ) ) ),
inference(rewrite,[status(thm)],[540,535]) ).
thf(553,plain,
( ~ ( sk1 @ ( sk1 @ segmentP ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[552]) ).
thf(586,plain,
( ~ ( sk1 @ ( sk1 @ segmentP ) )
| ~ $true
| ~ ( sk1 @ ( sk1 @ neq ) ) ),
inference(rewrite,[status(thm)],[553,565]) ).
thf(587,plain,
( ~ ( sk1 @ ( sk1 @ segmentP ) )
| ~ ( sk1 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[586]) ).
thf(6823,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,237]) ).
thf(6824,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[6823]) ).
thf(6825,plain,
sk1 @ ( sk1 @ segmentP ),
inference(pattern_uni,[status(thm)],[6824:[bind(A,$thf( sk1 ))]]) ).
thf(6874,plain,
( ~ $true
| ~ ( sk1 @ ( sk1 @ neq ) ) ),
inference(rewrite,[status(thm)],[587,6825]) ).
thf(6875,plain,
~ ( sk1 @ ( sk1 @ neq ) ),
inference(simp,[status(thm)],[6874]) ).
thf(8579,plain,
( ( sk1 != sk1 )
| ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[7697,6875]) ).
thf(8580,plain,
( ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[8579:[]]) ).
thf(9851,plain,
( ( ( nil @ ( sk1 @ frontsegP ) )
!= ( sk1 @ ( nil @ frontsegP ) ) )
| ~ ( sk1 @ ( nil @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1518,8580]) ).
thf(9852,plain,
( ( ( nil @ ( sk1 @ frontsegP ) )
!= ( sk1 @ ( nil @ frontsegP ) ) )
| ~ ( sk1 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[9851]) ).
thf(9911,plain,
( ( sk1 != nil )
| ( sk1 != nil )
| ~ ( sk1 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[9852]) ).
thf(9936,plain,
( ( sk1 != nil )
| ~ ( sk1 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[9911]) ).
thf(4838,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[121,451]) ).
thf(4839,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP ) ),
inference(simp,[status(thm)],[4838]) ).
thf(4840,plain,
nil @ ( sk5 @ cons ) @ strictorderP,
inference(pattern_uni,[status(thm)],[4839:[bind(A,$thf( sk5 ))]]) ).
thf(13,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(141,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)],[13]) ).
thf(8559,plain,
( ( sk1 != sk1 )
| ~ ( nil @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[7697,567]) ).
thf(8560,plain,
( ~ ( nil @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[8559:[]]) ).
thf(9454,plain,
( ( ( nil @ ( sk1 @ frontsegP ) )
!= ( sk1 @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( nil @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1518,8560]) ).
thf(9455,plain,
( ( ( nil @ ( sk1 @ frontsegP ) )
!= ( sk1 @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[9454]) ).
thf(9511,plain,
( ( sk1 != nil )
| ( sk1 != nil )
| ~ ( nil @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[9455]) ).
thf(9531,plain,
( ( sk1 != nil )
| ~ ( nil @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[9511]) ).
thf(11612,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ~ ( nil @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[10543,9531]) ).
thf(11613,plain,
( ( sk1 != sk1 )
| ~ ( nil @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[11612]) ).
thf(11614,plain,
( ~ ( nil @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[11613:[]]) ).
thf(1532,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[633,406]) ).
thf(1533,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1532]) ).
thf(1534,plain,
( ( nil @ ( sk2 @ sk11 @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1533:[bind(A,$thf( sk2 @ sk11 ))]]) ).
thf(18398,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18023,451]) ).
thf(18399,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18398]) ).
thf(18400,plain,
( ( nil @ ( sk1 @ sk8 @ cons ) @ strictorderP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18399:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(19781,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19414,406]) ).
thf(19782,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19781]) ).
thf(19783,plain,
( ( nil @ ( sk2 @ sk10 @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19782:[bind(A,$thf( sk2 @ sk10 ))]]) ).
thf(19,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(156,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)],[19]) ).
thf(24143,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[23646,332]) ).
thf(24144,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[24143]) ).
thf(24145,plain,
( ( nil @ ( sk2 @ sk15 @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[24144:[bind(A,$thf( sk2 @ sk15 ))]]) ).
thf(25108,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[24629,239]) ).
thf(25109,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[25108]) ).
thf(25110,plain,
( ( nil @ ( sk1 @ sk12 @ cons ) @ totalorderedP )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25109:[bind(A,$thf( sk1 @ sk12 ))]]) ).
thf(1538,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( ( sk1 @ sk11 )
!= sk1 )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[703,406]) ).
thf(1539,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( ( sk1 @ sk11 )
!= sk1 )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1538]) ).
thf(1540,plain,
( ( nil @ ( sk1 @ sk11 @ sk11 @ frontsegP ) )
| ( ( sk1 @ sk11 )
!= sk1 )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1539:[bind(A,$thf( sk1 @ sk11 @ sk11 ))]]) ).
thf(26099,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[25798,279]) ).
thf(26100,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[26099]) ).
thf(26101,plain,
( ( nil @ ( sk1 @ sk14 @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[26100:[bind(A,$thf( sk1 @ sk14 ))]]) ).
thf(882,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ sk11 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[650,332]) ).
thf(883,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ sk11 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[882]) ).
thf(884,plain,
( ( nil @ ( sk2 @ sk11 @ sk11 @ rearsegP ) )
| ( sk2 @ sk11 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[883:[bind(A,$thf( sk2 @ sk11 @ sk11 ))]]) ).
thf(57017,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[56856,406]) ).
thf(57018,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) ) ),
inference(simp,[status(thm)],[57017]) ).
thf(57019,plain,
nil @ ( nil @ ( nil @ sk22 ) @ frontsegP ),
inference(pattern_uni,[status(thm)],[57018:[bind(A,$thf( nil @ ( nil @ sk22 ) ))]]) ).
thf(390,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)],[389]) ).
thf(393,plain,
! [B: $i,A: $i] :
( ( nil
= ( B @ ( A @ app ) ) )
| ( nil != A )
| ( nil != B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[390]) ).
thf(396,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
= nil )
| ( nil != A )
| ( nil != B ) ),
inference(lifteq,[status(thm)],[393]) ).
thf(397,plain,
( ~ ( nil @ ssList )
| ( ( nil @ ( nil @ app ) )
= nil ) ),
inference(simp,[status(thm)],[396]) ).
thf(678,plain,
( ~ $true
| ( ( nil @ ( nil @ app ) )
= nil ) ),
inference(rewrite,[status(thm)],[397,376]) ).
thf(679,plain,
( ( nil @ ( nil @ app ) )
= nil ),
inference(simp,[status(thm)],[678]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( A @ ( B @ cons ) @ ssList ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
thf(212,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( A @ ( B @ cons ) @ ssList ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(67274,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk28 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,288]) ).
thf(67275,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk28 @ ssList ) ),
inference(simp,[status(thm)],[67274]) ).
thf(67276,plain,
( ( sk2 @ totalorderP )
| ( sk2 @ sk28 @ ssList ) ),
inference(pattern_uni,[status(thm)],[67275:[bind(A,$thf( sk2 ))]]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ tl @ ssList ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
thf(328,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ tl @ ssList ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(256,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk18 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[254]) ).
thf(23887,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[23601,279]) ).
thf(23888,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[23887]) ).
thf(23889,plain,
( ( nil @ ( sk1 @ sk15 @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[23888:[bind(A,$thf( sk1 @ sk15 ))]]) ).
thf(17740,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17230,165]) ).
thf(17741,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17740]) ).
thf(17742,plain,
( ( nil @ ( sk2 @ sk7 @ cons ) @ strictorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17741:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(85,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(488,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)],[85]) ).
thf(216,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( ( A @ sk16 @ ( A @ sk13 @ cons ) @ ( A @ sk15 @ ( A @ sk12 @ cons ) @ ( A @ sk14 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[215]) ).
thf(225,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ( ( A @ sk16 @ ( A @ sk13 @ cons ) @ ( A @ sk15 @ ( A @ sk12 @ cons ) @ ( A @ sk14 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[216]) ).
thf(17617,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17174,239]) ).
thf(17618,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17617]) ).
thf(17619,plain,
( ( nil @ ( sk1 @ sk7 @ cons ) @ totalorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17618:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(25233,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[24685,165]) ).
thf(25234,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[25233]) ).
thf(25235,plain,
( ( nil @ ( sk2 @ sk12 @ cons ) @ strictorderedP )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25234:[bind(A,$thf( sk2 @ sk12 ))]]) ).
thf(17761,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17230,430]) ).
thf(17762,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17761]) ).
thf(17763,plain,
( ( nil @ ( sk2 @ sk7 @ cons ) @ duplicatefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17762:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(61862,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk23 @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[106,284]) ).
thf(61863,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk23 @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[61862]) ).
thf(61864,plain,
( ( sk1 @ sk23 @ ssList )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[61863:[bind(A,$thf( sk1 ))]]) ).
thf(64994,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ neq ) )
| ( sk1 @ sk23 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[61864,9936]) ).
thf(64995,plain,
( ( sk1 != sk1 )
| ~ ( sk1 @ ( nil @ neq ) )
| ( sk1 @ sk23 @ ssList ) ),
inference(simp,[status(thm)],[64994]) ).
thf(64996,plain,
( ~ ( sk1 @ ( nil @ neq ) )
| ( sk1 @ sk23 @ ssList ) ),
inference(pattern_uni,[status(thm)],[64995:[]]) ).
thf(29,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(193,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)],[29]) ).
thf(8593,plain,
( ( sk1 != sk1 )
| ( sk1 @ ( nil @ segmentP ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[7697,6825]) ).
thf(8594,plain,
( ( sk1 @ ( nil @ segmentP ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[8593:[]]) ).
thf(22,axiom,
nil @ totalorderedP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax66) ).
thf(173,plain,
nil @ totalorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(17791,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17230,451]) ).
thf(17792,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17791]) ).
thf(17793,plain,
( ( nil @ ( sk2 @ sk7 @ cons ) @ strictorderP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17792:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(87,axiom,
nil @ equalelemsP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax74) ).
thf(503,plain,
nil @ equalelemsP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(1625,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[121,165]) ).
thf(1626,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[1625]) ).
thf(1627,plain,
nil @ ( sk5 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[1626:[bind(A,$thf( sk5 ))]]) ).
thf(93,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(515,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)],[93]) ).
thf(23955,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[23601,332]) ).
thf(23956,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[23955]) ).
thf(23957,plain,
( ( nil @ ( sk1 @ sk15 @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[23956:[bind(A,$thf( sk1 @ sk15 ))]]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ gt ) )
=> ~ ( A @ ( B @ gt ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax94) ).
thf(134,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ gt ) )
=> ~ ( A @ ( B @ gt ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1122,plain,
! [B: $i,A: $i] :
( ( A != sk6 )
| ( B != sk5 )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[129,124]) ).
thf(1123,plain,
! [A: $i] :
( ( A != sk5 )
| ~ ( sk6 @ ( A @ leq ) )
| ~ ( A @ ( sk6 @ leq ) )
| ~ ( A @ ssItem )
| ~ ( sk6 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[1122:[bind(A,$thf( sk6 ))]]) ).
thf(1418,plain,
( ~ ( sk6 @ ( sk5 @ leq ) )
| ~ ( sk5 @ ( sk6 @ leq ) )
| ~ ( sk5 @ ssItem )
| ~ ( sk6 @ ssItem ) ),
inference(simp,[status(thm)],[1123]) ).
thf(3148,plain,
( ~ ( sk6 @ ( sk5 @ leq ) )
| ~ ( sk5 @ ( sk6 @ leq ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[1418,121,122]) ).
thf(3149,plain,
( ~ ( sk6 @ ( sk5 @ leq ) )
| ~ ( sk5 @ ( sk6 @ leq ) ) ),
inference(simp,[status(thm)],[3148]) ).
thf(3182,plain,
( ~ $true
| ( ( sk5 @ ( sk6 @ leq ) )
!= ( sk6 @ ( sk5 @ leq ) ) )
| ~ ( sk6 @ ( sk5 @ leq ) ) ),
inference(eqfactor_ordered,[status(thm)],[3149]) ).
thf(3183,plain,
( ( ( sk5 @ ( sk6 @ leq ) )
!= ( sk6 @ ( sk5 @ leq ) ) )
| ~ ( sk6 @ ( sk5 @ leq ) ) ),
inference(simp,[status(thm)],[3182]) ).
thf(52,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(311,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)],[52]) ).
thf(42197,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[106,252]) ).
thf(42198,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[42197]) ).
thf(42199,plain,
( ( sk1 @ ( nil @ app ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[42198:[bind(A,$thf( sk1 ))]]) ).
thf(19775,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19414,279]) ).
thf(19776,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19775]) ).
thf(19777,plain,
( ( nil @ ( sk2 @ sk10 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19776:[bind(A,$thf( sk2 @ sk10 ))]]) ).
thf(10821,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[105,183]) ).
thf(10822,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[10821]) ).
thf(10823,plain,
( ~ ( sk2 @ ( nil @ segmentP ) )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[10822:[bind(A,$thf( sk2 ))]]) ).
thf(12173,plain,
~ ( sk2 @ ( nil @ segmentP ) ),
inference(simplifyReflect,[status(thm)],[10823,12169]) ).
thf(3319,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,140]) ).
thf(3320,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[3319]) ).
thf(3321,plain,
~ ( sk6 @ ( sk6 @ lt ) ),
inference(pattern_uni,[status(thm)],[3320:[bind(A,$thf( sk6 ))]]) ).
thf(17485,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17174,439]) ).
thf(17486,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17485]) ).
thf(17487,plain,
( ( nil @ ( sk1 @ sk7 @ cons ) @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17486:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(22886,plain,
( ~ $true
| ( ( nil @ ( sk1 @ sk7 @ cons ) @ cyclefreeP )
!= ( sk1 @ cyclefreeP ) )
| ( sk1 @ cyclefreeP ) ),
inference(eqfactor_ordered,[status(thm)],[17487]) ).
thf(22888,plain,
( ( ( nil @ ( sk1 @ sk7 @ cons ) )
!= sk1 )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[22886]) ).
thf(48819,plain,
! [A: $i] :
( ( ( sk2 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[48428,406]) ).
thf(48820,plain,
! [A: $i] :
( ( ( sk2 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[48819]) ).
thf(48821,plain,
( ( nil @ ( sk2 @ sk20 @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[48820:[bind(A,$thf( sk2 @ sk20 ))]]) ).
thf(18401,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18023,140]) ).
thf(18402,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18401]) ).
thf(18403,plain,
( ~ ( sk1 @ sk8 @ ( sk1 @ sk8 @ lt ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18402:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(148,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[147]) ).
thf(3077,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,439]) ).
thf(3078,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP ) ),
inference(simp,[status(thm)],[3077]) ).
thf(3079,plain,
nil @ ( sk6 @ cons ) @ cyclefreeP,
inference(pattern_uni,[status(thm)],[3078:[bind(A,$thf( sk6 ))]]) ).
thf(25254,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[24685,430]) ).
thf(25255,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[25254]) ).
thf(25256,plain,
( ( nil @ ( sk2 @ sk12 @ cons ) @ duplicatefreeP )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25255:[bind(A,$thf( sk2 @ sk12 ))]]) ).
thf(16724,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ( A @ sk7 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,202]) ).
thf(16725,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ( A @ sk7 @ leq ) ) ),
inference(simp,[status(thm)],[16724]) ).
thf(16726,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk8 @ ( sk2 @ sk7 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[16725:[bind(A,$thf( sk2 ))]]) ).
thf(6201,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ sk11 @ sk11 @ cyclefreeP )
| ( sk1 @ sk11 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[697,279]) ).
thf(6202,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ sk11 @ sk11 @ cyclefreeP )
| ( sk1 @ sk11 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[6201]) ).
thf(6203,plain,
( ( nil @ ( sk1 @ sk11 @ sk11 @ sk11 @ segmentP ) )
| ( sk1 @ sk11 @ sk11 @ cyclefreeP )
| ( sk1 @ sk11 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[6202:[bind(A,$thf( sk1 @ sk11 @ sk11 @ sk11 ))]]) ).
thf(25227,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[24685,334]) ).
thf(25228,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[25227]) ).
thf(25229,plain,
( ( nil @ ( sk2 @ sk12 @ cons ) @ equalelemsP )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25228:[bind(A,$thf( sk2 @ sk12 ))]]) ).
thf(10232,plain,
( ( ( nil @ ( sk1 @ frontsegP ) )
!= ( sk1 @ ( nil @ frontsegP ) ) )
| ( sk1 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1518,8594]) ).
thf(10233,plain,
( ( ( nil @ ( sk1 @ frontsegP ) )
!= ( sk1 @ ( nil @ frontsegP ) ) )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[10232]) ).
thf(10274,plain,
( ( sk1 != nil )
| ( sk1 != nil )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[10233]) ).
thf(10289,plain,
( ( sk1 != nil )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[10274]) ).
thf(10754,plain,
! [A: $i] :
( ( A != sk6 )
| ( sk5 != nil )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[183,124]) ).
thf(10755,plain,
( ( sk5 != nil )
| ~ ( sk6 @ ( nil @ segmentP ) )
| ~ ( sk6 @ ssList ) ),
inference(pattern_uni,[status(thm)],[10754:[bind(A,$thf( sk6 ))]]) ).
thf(31339,plain,
( ( ( sk6 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk5 != nil )
| ~ ( sk6 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,10755]) ).
thf(31340,plain,
( ( ( sk6 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk5 != nil )
| ~ ( sk6 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[31339]) ).
thf(31506,plain,
( ( sk6 != sk1 )
| ( sk5 != nil )
| ~ ( sk6 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[31340]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) @ hd )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).
thf(176,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) @ hd )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(118,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)],[117]) ).
thf(1793,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[121,334]) ).
thf(1794,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP ) ),
inference(simp,[status(thm)],[1793]) ).
thf(1795,plain,
nil @ ( sk5 @ cons ) @ equalelemsP,
inference(pattern_uni,[status(thm)],[1794:[bind(A,$thf( sk5 ))]]) ).
thf(45003,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk18 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,256]) ).
thf(45004,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk18 @ ssItem ) ),
inference(simp,[status(thm)],[45003]) ).
thf(45005,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk18 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[45004:[bind(A,$thf( sk2 ))]]) ).
thf(259,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ sk18 @ ( A @ sk17 @ lt ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[254]) ).
thf(16289,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[15973,237]) ).
thf(16290,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[16289]) ).
thf(16291,plain,
( ( sk2 @ sk9 @ ( sk2 @ sk9 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[16290:[bind(A,$thf( sk2 @ sk9 ))]]) ).
thf(14,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(144,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)],[14]) ).
thf(57,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(335,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)],[57]) ).
thf(17552,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17174,140]) ).
thf(17553,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17552]) ).
thf(17554,plain,
( ~ ( sk1 @ sk7 @ ( sk1 @ sk7 @ lt ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17553:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(157,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ lt ) )
| ~ ( B @ ( A @ leq ) )
| ( A = B )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) )
& ( ( B @ ( A @ leq ) )
| ~ ( B @ ( A @ lt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) )
& ( ( A != B )
| ~ ( B @ ( A @ lt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ) ),
inference(cnf,[status(esa)],[156]) ).
thf(159,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( B @ ( A @ lt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[157]) ).
thf(18646,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18079,155]) ).
thf(18647,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18646]) ).
thf(18648,plain,
( ( sk2 @ sk8 @ ( sk2 @ sk8 @ geq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18647:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(1804,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,334]) ).
thf(1805,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP ) ),
inference(simp,[status(thm)],[1804]) ).
thf(1806,plain,
nil @ ( sk6 @ cons ) @ equalelemsP,
inference(pattern_uni,[status(thm)],[1805:[bind(A,$thf( sk6 ))]]) ).
thf(1522,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[642,406]) ).
thf(1523,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1522]) ).
thf(1524,plain,
( ( nil @ ( sk1 @ sk11 @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1523:[bind(A,$thf( sk1 @ sk11 ))]]) ).
thf(63,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(377,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)],[63]) ).
thf(69124,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk27 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,290]) ).
thf(69125,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk27 @ ssList ) ),
inference(simp,[status(thm)],[69124]) ).
thf(69126,plain,
( ( sk1 @ totalorderP )
| ( sk1 @ sk27 @ ssList ) ),
inference(pattern_uni,[status(thm)],[69125:[bind(A,$thf( sk1 ))]]) ).
thf(24072,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[23646,237]) ).
thf(24073,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[24072]) ).
thf(24074,plain,
( ( sk2 @ sk15 @ ( sk2 @ sk15 @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[24073:[bind(A,$thf( sk2 @ sk15 ))]]) ).
thf(25224,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[24685,439]) ).
thf(25225,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[25224]) ).
thf(25226,plain,
( ( nil @ ( sk2 @ sk12 @ cons ) @ cyclefreeP )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25225:[bind(A,$thf( sk2 @ sk12 ))]]) ).
thf(65566,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[65460,252]) ).
thf(65567,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[65566]) ).
thf(65568,plain,
( ( sk2 @ sk23 @ ( nil @ app ) )
= ( sk2 @ sk23 ) ),
inference(pattern_uni,[status(thm)],[65567:[bind(A,$thf( sk2 @ sk23 ))]]) ).
thf(17488,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17174,334]) ).
thf(17489,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17488]) ).
thf(17490,plain,
( ( nil @ ( sk1 @ sk7 @ cons ) @ equalelemsP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17489:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(25031,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[24629,451]) ).
thf(25032,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[25031]) ).
thf(25033,plain,
( ( nil @ ( sk1 @ sk12 @ cons ) @ strictorderP )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25032:[bind(A,$thf( sk1 @ sk12 ))]]) ).
thf(65600,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65460,237]) ).
thf(65601,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[65600]) ).
thf(65602,plain,
sk2 @ sk23 @ ( sk2 @ sk23 @ segmentP ),
inference(pattern_uni,[status(thm)],[65601:[bind(A,$thf( sk2 @ sk23 ))]]) ).
thf(66474,plain,
( ( ( sk2 @ sk23 @ ( sk2 @ sk23 @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65602,12173]) ).
thf(66475,plain,
( ( sk2 @ sk23 @ ( sk2 @ sk23 @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[66474]) ).
thf(66522,plain,
( ( ( sk2 @ sk23 )
!= sk2 )
| ( ( sk2 @ sk23 )
!= nil ) ),
inference(simp,[status(thm)],[66475]) ).
thf(61,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(362,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)],[61]) ).
thf(25296,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[24685,399]) ).
thf(25297,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[25296]) ).
thf(25298,plain,
( ( nil @ ( sk2 @ sk12 @ cons ) @ totalorderP )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25297:[bind(A,$thf( sk2 @ sk12 ))]]) ).
thf(45415,plain,
! [A: $i] :
( ( ( sk2 @ sk18 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[45005,267]) ).
thf(45416,plain,
! [A: $i] :
( ( ( sk2 @ sk18 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[45415]) ).
thf(45417,plain,
( ~ ( sk2 @ sk18 @ ( nil @ memberP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[45416:[bind(A,$thf( sk2 @ sk18 ))]]) ).
thf(17811,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17230,267]) ).
thf(17812,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17811]) ).
thf(17813,plain,
( ~ ( sk2 @ sk7 @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17812:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(73,axiom,
nil @ strictorderP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax64) ).
thf(434,plain,
nil @ strictorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(19369,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,208]) ).
thf(19370,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ssList ) ),
inference(simp,[status(thm)],[19369]) ).
thf(19371,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk10 @ ssList ) ),
inference(pattern_uni,[status(thm)],[19370:[bind(A,$thf( sk1 ))]]) ).
thf(19668,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19371,332]) ).
thf(19669,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19668]) ).
thf(19670,plain,
( ( nil @ ( sk1 @ sk10 @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19669:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(57008,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[56856,279]) ).
thf(57009,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[57008]) ).
thf(57010,plain,
nil @ ( nil @ ( nil @ sk22 ) @ segmentP ),
inference(pattern_uni,[status(thm)],[57009:[bind(A,$thf( nil @ ( nil @ sk22 ) ))]]) ).
thf(6847,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[633,237]) ).
thf(6848,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[6847]) ).
thf(6849,plain,
( ( sk2 @ sk11 @ ( sk2 @ sk11 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[6848:[bind(A,$thf( sk2 @ sk11 ))]]) ).
thf(213,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[212]) ).
thf(18610,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18079,430]) ).
thf(18611,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18610]) ).
thf(18612,plain,
( ( nil @ ( sk2 @ sk8 @ cons ) @ duplicatefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18611:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(39,axiom,
~ ( nil @ singletonP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).
thf(240,plain,
~ ( nil @ singletonP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(461,plain,
! [A: $i] :
( ( ( A @ ( nil @ rearsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) )
& ( ( nil = A )
| ~ ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[460]) ).
thf(463,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[461]) ).
thf(465,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[463]) ).
thf(466,plain,
( ( nil @ ( nil @ rearsegP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[465]) ).
thf(625,plain,
( ( nil @ ( nil @ rearsegP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[466,376]) ).
thf(626,plain,
nil @ ( nil @ rearsegP ),
inference(simp,[status(thm)],[625]) ).
thf(6016,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ leq ) )
!= ( A @ ( B @ leq ) ) )
| ( B @ ( A @ geq ) )
| ~ $true
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[5246,149]) ).
thf(6017,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ leq ) )
!= ( A @ ( B @ leq ) ) )
| ( B @ ( A @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[6016]) ).
thf(6018,plain,
( ( sk5 @ ( sk5 @ geq ) )
| ~ ( sk5 @ ssItem )
| ~ ( sk5 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[6017:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 ))]]) ).
thf(6038,plain,
( ( sk5 @ ( sk5 @ geq ) )
| ~ ( sk5 @ ssItem ) ),
inference(simp,[status(thm)],[6018]) ).
thf(6043,plain,
( ( sk5 @ ( sk5 @ geq ) )
| ~ $true ),
inference(rewrite,[status(thm)],[6038,121]) ).
thf(6044,plain,
sk5 @ ( sk5 @ geq ),
inference(simp,[status(thm)],[6043]) ).
thf(888,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,332]) ).
thf(889,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[888]) ).
thf(890,plain,
nil @ ( sk2 @ rearsegP ),
inference(pattern_uni,[status(thm)],[889:[bind(A,$thf( sk2 ))]]) ).
thf(42090,plain,
( ( ( sk6 @ ssItem )
!= ( nil @ ssItem ) )
| ~ $true
| ~ ( sk1 @ ssItem )
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[122,38527]) ).
thf(42091,plain,
( ( ( sk6 @ ssItem )
!= ( nil @ ssItem ) )
| ~ ( sk1 @ ssItem )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[42090]) ).
thf(42101,plain,
( ( sk6 != nil )
| ~ ( sk1 @ ssItem )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[42091]) ).
thf(44731,plain,
( ( ( sk6 @ ssItem )
!= ( sk1 @ ssItem ) )
| ( sk6 != nil )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[122,42101]) ).
thf(44732,plain,
( ( ( sk6 @ ssItem )
!= ( sk1 @ ssItem ) )
| ( sk6 != nil )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[44731]) ).
thf(44734,plain,
( ( sk6 != sk1 )
| ( sk6 != nil )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[44732]) ).
thf(25307,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[24685,267]) ).
thf(25308,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[25307]) ).
thf(25309,plain,
( ~ ( sk2 @ sk12 @ ( nil @ memberP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25308:[bind(A,$thf( sk2 @ sk12 ))]]) ).
thf(19614,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19371,279]) ).
thf(19615,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19614]) ).
thf(19616,plain,
( ( nil @ ( sk1 @ sk10 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19615:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(6832,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ sk11 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[650,237]) ).
thf(6833,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk2 @ sk11 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[6832]) ).
thf(6834,plain,
( ( sk2 @ sk11 @ sk11 @ ( sk2 @ sk11 @ sk11 @ segmentP ) )
| ( sk2 @ sk11 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[6833:[bind(A,$thf( sk2 @ sk11 @ sk11 ))]]) ).
thf(683,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,267]) ).
thf(684,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[683]) ).
thf(685,plain,
~ ( sk6 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[684:[bind(A,$thf( sk6 ))]]) ).
thf(766,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[642,279]) ).
thf(767,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[766]) ).
thf(768,plain,
( ( nil @ ( sk1 @ sk11 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[767:[bind(A,$thf( sk1 @ sk11 ))]]) ).
thf(56967,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[56856,252]) ).
thf(56968,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[56967]) ).
thf(56969,plain,
( ( nil @ ( nil @ sk22 ) @ ( nil @ app ) )
= ( nil @ ( nil @ sk22 ) ) ),
inference(pattern_uni,[status(thm)],[56968:[bind(A,$thf( nil @ ( nil @ sk22 ) ))]]) ).
thf(135,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[134]) ).
thf(65612,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65460,406]) ).
thf(65613,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) ) ),
inference(simp,[status(thm)],[65612]) ).
thf(65614,plain,
nil @ ( sk2 @ sk23 @ frontsegP ),
inference(pattern_uni,[status(thm)],[65613:[bind(A,$thf( sk2 @ sk23 ))]]) ).
thf(72,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(431,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)],[72]) ).
thf(241,plain,
~ ( nil @ singletonP ),
inference(polarity_switch,[status(thm)],[240]) ).
thf(65621,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[65460,230]) ).
thf(65622,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[65621]) ).
thf(65623,plain,
( ( nil @ ( sk2 @ sk23 @ app ) )
= ( sk2 @ sk23 ) ),
inference(pattern_uni,[status(thm)],[65622:[bind(A,$thf( sk2 @ sk23 ))]]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ lt ) )
=> ~ ( A @ ( B @ lt ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax33) ).
thf(130,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ lt ) )
=> ~ ( A @ ( B @ lt ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(46314,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk21 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,257]) ).
thf(46315,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk21 @ ssList ) ),
inference(simp,[status(thm)],[46314]) ).
thf(46316,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk21 @ ssList ) ),
inference(pattern_uni,[status(thm)],[46315:[bind(A,$thf( sk2 ))]]) ).
thf(1650,plain,
( ( ( nil @ ( sk5 @ cons ) @ strictorderedP )
!= ( sk2 @ strictorderedP ) )
| ~ $true
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[1627,910]) ).
thf(1651,plain,
( ( ( nil @ ( sk5 @ cons ) @ strictorderedP )
!= ( sk2 @ strictorderedP ) )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[1650]) ).
thf(1667,plain,
( ( ( nil @ ( sk5 @ cons ) )
!= sk2 )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[1651]) ).
thf(6929,plain,
( ( ( nil @ ( sk5 @ cons ) )
!= sk2 )
| ~ $true
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(rewrite,[status(thm)],[1667,6846]) ).
thf(6930,plain,
( ( ( nil @ ( sk5 @ cons ) )
!= sk2 )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[6929]) ).
thf(778,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ sk11 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[656,279]) ).
thf(779,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ sk11 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[778]) ).
thf(780,plain,
( ( nil @ ( sk1 @ sk11 @ sk11 @ segmentP ) )
| ( sk1 @ sk11 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[779:[bind(A,$thf( sk1 @ sk11 @ sk11 ))]]) ).
thf(1641,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,165]) ).
thf(1642,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[1641]) ).
thf(1643,plain,
nil @ ( sk6 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[1642:[bind(A,$thf( sk6 ))]]) ).
thf(28050,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[27585,279]) ).
thf(28051,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[28050]) ).
thf(28052,plain,
( ( nil @ ( sk2 @ sk16 @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[28051:[bind(A,$thf( sk2 @ sk16 ))]]) ).
thf(223,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ sk13 @ ( A @ sk12 @ lt ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[215]) ).
thf(49171,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk6 @ ( nil @ segmentP ) ) )
| ( sk6 != sk1 )
| ( sk5 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6825,31506]) ).
thf(49172,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk6 @ ( nil @ segmentP ) ) )
| ( sk6 != sk1 )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[49171]) ).
thf(49235,plain,
( ( sk6 != sk1 )
| ( sk1 != nil )
| ( sk6 != sk1 )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[49172]) ).
thf(49295,plain,
( ( sk1 != nil )
| ( sk6 != sk1 )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[49235]) ).
thf(27856,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[27528,406]) ).
thf(27857,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[27856]) ).
thf(27858,plain,
( ( nil @ ( sk1 @ sk16 @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[27857:[bind(A,$thf( sk1 @ sk16 ))]]) ).
thf(1692,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[121,239]) ).
thf(1693,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[1692]) ).
thf(1694,plain,
nil @ ( sk5 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[1693:[bind(A,$thf( sk5 ))]]) ).
thf(44083,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[43728,406]) ).
thf(44084,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[44083]) ).
thf(44085,plain,
( ( nil @ ( sk2 @ sk19 @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[44084:[bind(A,$thf( sk2 @ sk19 ))]]) ).
thf(86,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(490,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)],[86]) ).
thf(97,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( nil
!= ( A @ ( B @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
thf(531,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( nil
!= ( A @ ( B @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(16146,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[15936,279]) ).
thf(16147,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[16146]) ).
thf(16148,plain,
( ( nil @ ( sk1 @ sk9 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[16147:[bind(A,$thf( sk1 @ sk9 ))]]) ).
thf(17734,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17230,334]) ).
thf(17735,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17734]) ).
thf(17736,plain,
( ( nil @ ( sk2 @ sk7 @ cons ) @ equalelemsP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17735:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(60,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( B @ ( A @ neq ) )
<=> ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
thf(355,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)],[60]) ).
thf(6841,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[642,237]) ).
thf(6842,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[6841]) ).
thf(6843,plain,
( ( sk1 @ sk11 @ ( sk1 @ sk11 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[6842:[bind(A,$thf( sk1 @ sk11 ))]]) ).
thf(4857,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,451]) ).
thf(4858,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP ) ),
inference(simp,[status(thm)],[4857]) ).
thf(4859,plain,
nil @ ( sk6 @ cons ) @ strictorderP,
inference(pattern_uni,[status(thm)],[4858:[bind(A,$thf( sk6 ))]]) ).
thf(194,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)],[193]) ).
thf(145,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ leq ) )
| ~ ( C @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ~ ( C @ ssItem )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[144]) ).
thf(36374,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,248]) ).
thf(36375,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[36374]) ).
thf(36376,plain,
~ ( sk6 @ ( sk6 @ neq ) ),
inference(pattern_uni,[status(thm)],[36375:[bind(A,$thf( sk6 ))]]) ).
thf(36470,plain,
( ( ( sk6 @ ( sk6 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,36376]) ).
thf(36471,plain,
( ( sk6 @ ( sk6 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[36470]) ).
thf(36476,plain,
( ( sk6 != nil )
| ( sk6 != sk2 ) ),
inference(simp,[status(thm)],[36471]) ).
thf(17794,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17230,140]) ).
thf(17795,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17794]) ).
thf(17796,plain,
( ~ ( sk2 @ sk7 @ ( sk2 @ sk7 @ lt ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17795:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(885,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[642,332]) ).
thf(886,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[885]) ).
thf(887,plain,
( ( nil @ ( sk1 @ sk11 @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[886:[bind(A,$thf( sk1 @ sk11 ))]]) ).
thf(18337,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18023,334]) ).
thf(18338,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18337]) ).
thf(18339,plain,
( ( nil @ ( sk1 @ sk8 @ cons ) @ equalelemsP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18338:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(25054,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[24629,267]) ).
thf(25055,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[25054]) ).
thf(25056,plain,
( ~ ( sk1 @ sk12 @ ( nil @ memberP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25055:[bind(A,$thf( sk1 @ sk12 ))]]) ).
thf(261,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( ( A @ sk21 @ ( A @ sk18 @ cons ) @ ( A @ sk20 @ ( A @ sk17 @ cons ) @ ( A @ sk19 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[254]) ).
thf(263,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ( ( A @ sk21 @ ( A @ sk18 @ cons ) @ ( A @ sk20 @ ( A @ sk17 @ cons ) @ ( A @ sk19 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[261]) ).
thf(29430,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk13 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,224]) ).
thf(29431,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk13 @ ssItem ) ),
inference(simp,[status(thm)],[29430]) ).
thf(29432,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk13 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[29431:[bind(A,$thf( sk2 ))]]) ).
thf(30062,plain,
! [A: $i] :
( ( ( sk2 @ sk13 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[29432,267]) ).
thf(30063,plain,
! [A: $i] :
( ( ( sk2 @ sk13 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[30062]) ).
thf(30064,plain,
( ~ ( sk2 @ sk13 @ ( nil @ memberP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[30063:[bind(A,$thf( sk2 @ sk13 ))]]) ).
thf(46636,plain,
( ( ( sk2 @ strictorderedP )
!= ( sk2 @ strictorderedP ) )
| ~ $true
| ~ ( sk2 @ ( sk1 @ neq ) )
| ( sk2 @ sk21 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[46316,6926]) ).
thf(46637,plain,
( ( ( sk2 @ strictorderedP )
!= ( sk2 @ strictorderedP ) )
| ~ ( sk2 @ ( sk1 @ neq ) )
| ( sk2 @ sk21 @ ssList ) ),
inference(simp,[status(thm)],[46636]) ).
thf(46638,plain,
( ~ ( sk2 @ ( sk1 @ neq ) )
| ( sk2 @ sk21 @ ssList ) ),
inference(pattern_uni,[status(thm)],[46637:[]]) ).
thf(17549,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17174,451]) ).
thf(17550,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17549]) ).
thf(17551,plain,
( ( nil @ ( sk1 @ sk7 @ cons ) @ strictorderP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17550:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(46689,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[46316,406]) ).
thf(46690,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[46689]) ).
thf(46691,plain,
( ( nil @ ( sk2 @ sk21 @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[46690:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(3313,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[121,140]) ).
thf(3314,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[3313]) ).
thf(3315,plain,
~ ( sk5 @ ( sk5 @ lt ) ),
inference(pattern_uni,[status(thm)],[3314:[bind(A,$thf( sk5 ))]]) ).
thf(19772,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19414,237]) ).
thf(19773,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19772]) ).
thf(19774,plain,
( ( sk2 @ sk10 @ ( sk2 @ sk10 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19773:[bind(A,$thf( sk2 @ sk10 ))]]) ).
thf(23439,plain,
! [A: $i] :
( ( A != sk5 )
| ( sk6 != nil )
| ( nil != nil )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[183,23389]) ).
thf(23440,plain,
! [A: $i] :
( ( A != sk5 )
| ( sk6 != nil )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[23439]) ).
thf(23441,plain,
( ( sk6 != nil )
| ~ ( sk5 @ ( nil @ segmentP ) )
| ~ ( sk5 @ ssList ) ),
inference(pattern_uni,[status(thm)],[23440:[bind(A,$thf( sk5 ))]]) ).
thf(59698,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk5 @ ( nil @ segmentP ) ) )
| ( sk5 != sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6825,59573]) ).
thf(59699,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk5 @ ( nil @ segmentP ) ) )
| ( sk5 != sk2 ) ),
inference(simp,[status(thm)],[59698]) ).
thf(59761,plain,
( ( sk5 != sk1 )
| ( sk1 != nil )
| ( sk5 != sk2 ) ),
inference(simp,[status(thm)],[59699]) ).
thf(6204,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ sk11 @ sk11 @ cyclefreeP )
| ( sk1 @ sk11 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[697,406]) ).
thf(6205,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ sk11 @ sk11 @ cyclefreeP )
| ( sk1 @ sk11 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[6204]) ).
thf(6206,plain,
( ( nil @ ( sk1 @ sk11 @ sk11 @ sk11 @ frontsegP ) )
| ( sk1 @ sk11 @ sk11 @ cyclefreeP )
| ( sk1 @ sk11 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[6205:[bind(A,$thf( sk1 @ sk11 @ sk11 @ sk11 ))]]) ).
thf(19611,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19371,237]) ).
thf(19612,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19611]) ).
thf(19613,plain,
( ( sk1 @ sk10 @ ( sk1 @ sk10 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19612:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(28121,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[27585,332]) ).
thf(28122,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[28121]) ).
thf(28123,plain,
( ( nil @ ( sk2 @ sk16 @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[28122:[bind(A,$thf( sk2 @ sk16 ))]]) ).
thf(24967,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[24629,439]) ).
thf(24968,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[24967]) ).
thf(24969,plain,
( ( nil @ ( sk1 @ sk12 @ cons ) @ cyclefreeP )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[24968:[bind(A,$thf( sk1 @ sk12 ))]]) ).
thf(1541,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ sk11 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[656,406]) ).
thf(1542,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ sk11 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1541]) ).
thf(1543,plain,
( ( nil @ ( sk1 @ sk11 @ sk11 @ frontsegP ) )
| ( sk1 @ sk11 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1542:[bind(A,$thf( sk1 @ sk11 @ sk11 ))]]) ).
thf(36495,plain,
! [A: $i] :
( ( A != sk5 )
| ( nil != nil )
| ( sk5 != sk2 )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[170,36425]) ).
thf(36496,plain,
! [A: $i] :
( ( A != sk5 )
| ( sk5 != sk2 )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[36495]) ).
thf(36497,plain,
( ( sk5 != sk2 )
| ~ ( sk5 @ ( nil @ frontsegP ) )
| ~ ( sk5 @ ssList ) ),
inference(pattern_uni,[status(thm)],[36496:[bind(A,$thf( sk5 ))]]) ).
thf(55704,plain,
( ( ( sk5 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk5 != sk2 )
| ~ ( sk5 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,36497]) ).
thf(55705,plain,
( ( ( sk5 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk5 != sk2 )
| ~ ( sk5 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[55704]) ).
thf(55849,plain,
( ( sk5 != sk2 )
| ( sk5 != sk2 )
| ~ ( sk5 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[55705]) ).
thf(55868,plain,
( ( sk5 != sk2 )
| ~ ( sk5 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[55849]) ).
thf(65705,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65460,332]) ).
thf(65706,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[65705]) ).
thf(65707,plain,
nil @ ( sk2 @ sk23 @ rearsegP ),
inference(pattern_uni,[status(thm)],[65706:[bind(A,$thf( sk2 @ sk23 ))]]) ).
thf(18690,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18079,151]) ).
thf(18691,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18690]) ).
thf(18692,plain,
( ( sk2 @ sk8 @ ( sk2 @ sk8 @ leq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18691:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(182,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ( nil != A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[180]) ).
thf(184,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[182]) ).
thf(185,plain,
( ( nil @ ( nil @ segmentP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[184]) ).
thf(611,plain,
( ( nil @ ( nil @ segmentP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[185,376]) ).
thf(612,plain,
nil @ ( nil @ segmentP ),
inference(simp,[status(thm)],[611]) ).
thf(142,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[141]) ).
thf(143,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A = B ) ),
inference(lifteq,[status(thm)],[142]) ).
thf(18343,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18023,165]) ).
thf(18344,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18343]) ).
thf(18345,plain,
( ( nil @ ( sk1 @ sk8 @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18344:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(28056,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[27585,406]) ).
thf(28057,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[28056]) ).
thf(28058,plain,
( ( nil @ ( sk2 @ sk16 @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[28057:[bind(A,$thf( sk2 @ sk16 ))]]) ).
thf(175,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)],[174]) ).
thf(18589,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18079,165]) ).
thf(18590,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18589]) ).
thf(18591,plain,
( ( nil @ ( sk2 @ sk8 @ cons ) @ strictorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18590:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(1671,plain,
( ( ( nil @ ( sk6 @ cons ) @ strictorderedP )
!= ( sk2 @ strictorderedP ) )
| ~ $true
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[1643,910]) ).
thf(1672,plain,
( ( ( nil @ ( sk6 @ cons ) @ strictorderedP )
!= ( sk2 @ strictorderedP ) )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[1671]) ).
thf(1688,plain,
( ( ( nil @ ( sk6 @ cons ) )
!= sk2 )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[1672]) ).
thf(6927,plain,
( ( ( nil @ ( sk6 @ cons ) )
!= sk2 )
| ~ $true
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(rewrite,[status(thm)],[1688,6846]) ).
thf(6928,plain,
( ( ( nil @ ( sk6 @ cons ) )
!= sk2 )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[6927]) ).
thf(18649,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18079,399]) ).
thf(18650,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18649]) ).
thf(18651,plain,
( ( nil @ ( sk2 @ sk8 @ cons ) @ totalorderP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18650:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(17731,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17230,439]) ).
thf(17732,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17731]) ).
thf(17733,plain,
( ( nil @ ( sk2 @ sk7 @ cons ) @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17732:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(25043,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[24629,399]) ).
thf(25044,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[25043]) ).
thf(25045,plain,
( ( nil @ ( sk1 @ sk12 @ cons ) @ totalorderP )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25044:[bind(A,$thf( sk1 @ sk12 ))]]) ).
thf(18660,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18079,267]) ).
thf(18661,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18660]) ).
thf(18662,plain,
( ~ ( sk2 @ sk8 @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18661:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(35,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(231,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)],[35]) ).
thf(17494,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17174,165]) ).
thf(17495,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17494]) ).
thf(17496,plain,
( ( nil @ ( sk1 @ sk7 @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17495:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(6865,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ sk11 @ sk11 @ cyclefreeP )
| ( sk2 @ sk11 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[688,237]) ).
thf(6866,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk2 @ sk11 @ sk11 @ cyclefreeP )
| ( sk2 @ sk11 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[6865]) ).
thf(6867,plain,
( ( sk2 @ sk11 @ sk11 @ sk11 @ ( sk2 @ sk11 @ sk11 @ sk11 @ segmentP ) )
| ( sk2 @ sk11 @ sk11 @ cyclefreeP )
| ( sk2 @ sk11 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[6866:[bind(A,$thf( sk2 @ sk11 @ sk11 @ sk11 ))]]) ).
thf(769,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,279]) ).
thf(770,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[769]) ).
thf(771,plain,
nil @ ( sk2 @ segmentP ),
inference(pattern_uni,[status(thm)],[770:[bind(A,$thf( sk2 ))]]) ).
thf(46774,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[46316,332]) ).
thf(46775,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[46774]) ).
thf(46776,plain,
( ( nil @ ( sk2 @ sk21 @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[46775:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(25034,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[24629,140]) ).
thf(25035,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[25034]) ).
thf(25036,plain,
( ~ ( sk1 @ sk12 @ ( sk1 @ sk12 @ lt ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25035:[bind(A,$thf( sk1 @ sk12 ))]]) ).
thf(6829,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ sk11 @ sk11 @ cyclefreeP )
| ( sk1 @ sk11 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[697,237]) ).
thf(6830,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk1 @ sk11 @ sk11 @ cyclefreeP )
| ( sk1 @ sk11 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[6829]) ).
thf(6831,plain,
( ( sk1 @ sk11 @ sk11 @ sk11 @ ( sk1 @ sk11 @ sk11 @ sk11 @ segmentP ) )
| ( sk1 @ sk11 @ sk11 @ cyclefreeP )
| ( sk1 @ sk11 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[6830:[bind(A,$thf( sk1 @ sk11 @ sk11 @ sk11 ))]]) ).
thf(48906,plain,
! [A: $i] :
( ( ( sk2 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[48428,332]) ).
thf(48907,plain,
! [A: $i] :
( ( ( sk2 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[48906]) ).
thf(48908,plain,
( ( nil @ ( sk2 @ sk20 @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[48907:[bind(A,$thf( sk2 @ sk20 ))]]) ).
thf(894,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( ( sk2 @ sk11 )
!= sk2 )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[694,332]) ).
thf(895,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( ( sk2 @ sk11 )
!= sk2 )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[894]) ).
thf(896,plain,
( ( nil @ ( sk2 @ sk11 @ sk11 @ rearsegP ) )
| ( ( sk2 @ sk11 )
!= sk2 )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[895:[bind(A,$thf( sk2 @ sk11 @ sk11 ))]]) ).
thf(57120,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[56856,332]) ).
thf(57121,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[57120]) ).
thf(57122,plain,
nil @ ( nil @ ( nil @ sk22 ) @ rearsegP ),
inference(pattern_uni,[status(thm)],[57121:[bind(A,$thf( nil @ ( nil @ sk22 ) ))]]) ).
thf(36553,plain,
! [A: $i] :
( ( A != sk6 )
| ( nil != nil )
| ( sk6 != sk2 )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[170,36476]) ).
thf(36554,plain,
! [A: $i] :
( ( A != sk6 )
| ( sk6 != sk2 )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[36553]) ).
thf(36555,plain,
( ( sk6 != sk2 )
| ~ ( sk6 @ ( nil @ frontsegP ) )
| ~ ( sk6 @ ssList ) ),
inference(pattern_uni,[status(thm)],[36554:[bind(A,$thf( sk6 ))]]) ).
thf(68618,plain,
( ( ( sk6 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk6 != sk2 )
| ~ ( sk6 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,36555]) ).
thf(68619,plain,
( ( ( sk6 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk6 != sk2 )
| ~ ( sk6 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[68618]) ).
thf(68794,plain,
( ( sk6 != sk2 )
| ( sk6 != sk2 )
| ~ ( sk6 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[68619]) ).
thf(68827,plain,
( ( sk6 != sk2 )
| ~ ( sk6 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[68794]) ).
thf(26,axiom,
nil @ cyclefreeP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax60) ).
thf(186,plain,
nil @ cyclefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(46683,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[46316,279]) ).
thf(46684,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[46683]) ).
thf(46685,plain,
( ( nil @ ( sk2 @ sk21 @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[46684:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(23884,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[23601,237]) ).
thf(23885,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[23884]) ).
thf(23886,plain,
( ( sk1 @ sk15 @ ( sk1 @ sk15 @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[23885:[bind(A,$thf( sk1 @ sk15 ))]]) ).
thf(11565,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[10543,9936]) ).
thf(11566,plain,
( ( sk1 != sk1 )
| ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[11565]) ).
thf(11567,plain,
( ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[11566:[]]) ).
thf(27850,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[27528,279]) ).
thf(27851,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[27850]) ).
thf(27852,plain,
( ( nil @ ( sk1 @ sk16 @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[27851:[bind(A,$thf( sk1 @ sk16 ))]]) ).
thf(234,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)],[233]) ).
thf(235,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)],[234]) ).
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(510,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(25293,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[24685,155]) ).
thf(25294,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[25293]) ).
thf(25295,plain,
( ( sk2 @ sk12 @ ( sk2 @ sk12 @ geq ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25294:[bind(A,$thf( sk2 @ sk12 ))]]) ).
thf(17519,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17174,430]) ).
thf(17520,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17519]) ).
thf(17521,plain,
( ( nil @ ( sk1 @ sk7 @ cons ) @ duplicatefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17520:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(16191,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[15936,332]) ).
thf(16192,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[16191]) ).
thf(16193,plain,
( ( nil @ ( sk1 @ sk9 @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[16192:[bind(A,$thf( sk1 @ sk9 ))]]) ).
thf(897,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( ( sk1 @ sk11 )
!= sk1 )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[703,332]) ).
thf(898,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( ( sk1 @ sk11 )
!= sk1 )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[897]) ).
thf(899,plain,
( ( nil @ ( sk1 @ sk11 @ sk11 @ rearsegP ) )
| ( ( sk1 @ sk11 )
!= sk1 )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[898:[bind(A,$thf( sk1 @ sk11 @ sk11 ))]]) ).
thf(18407,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18023,399]) ).
thf(18408,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18407]) ).
thf(18409,plain,
( ( nil @ ( sk1 @ sk8 @ cons ) @ totalorderP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18408:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(1992,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,399]) ).
thf(1993,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP ) ),
inference(simp,[status(thm)],[1992]) ).
thf(1994,plain,
nil @ ( sk6 @ cons ) @ totalorderP,
inference(pattern_uni,[status(thm)],[1993:[bind(A,$thf( sk6 ))]]) ).
thf(5702,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ sk11 @ sk11 @ cyclefreeP )
| ( sk2 @ sk11 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[688,279]) ).
thf(5703,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ sk11 @ sk11 @ cyclefreeP )
| ( sk2 @ sk11 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5702]) ).
thf(5704,plain,
( ( nil @ ( sk2 @ sk11 @ sk11 @ sk11 @ segmentP ) )
| ( sk2 @ sk11 @ sk11 @ cyclefreeP )
| ( sk2 @ sk11 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5703:[bind(A,$thf( sk2 @ sk11 @ sk11 @ sk11 ))]]) ).
thf(3324,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ lt ) )
!= ( sk5 @ ( sk5 @ lt ) ) )
| ~ $true
| ~ ( B @ ( A @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[115,3315]) ).
thf(3325,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ lt ) )
!= ( sk5 @ ( sk5 @ lt ) ) )
| ~ ( B @ ( A @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[3324]) ).
thf(3326,plain,
( ~ ( sk5 @ ( sk5 @ gt ) )
| ~ ( sk5 @ ssItem )
| ~ ( sk5 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[3325:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 ))]]) ).
thf(3350,plain,
( ~ ( sk5 @ ( sk5 @ gt ) )
| ~ ( sk5 @ ssItem ) ),
inference(simp,[status(thm)],[3326]) ).
thf(3378,plain,
( ~ ( sk5 @ ( sk5 @ gt ) )
| ~ $true ),
inference(rewrite,[status(thm)],[3350,121]) ).
thf(3379,plain,
~ ( sk5 @ ( sk5 @ gt ) ),
inference(simp,[status(thm)],[3378]) ).
thf(50,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(300,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)],[50]) ).
thf(16292,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[15973,279]) ).
thf(16293,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[16292]) ).
thf(16294,plain,
( ( nil @ ( sk2 @ sk9 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[16293:[bind(A,$thf( sk2 @ sk9 ))]]) ).
thf(6235,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ sk11 @ sk11 @ cyclefreeP )
| ( sk1 @ sk11 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[697,332]) ).
thf(6236,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ sk11 @ sk11 @ cyclefreeP )
| ( sk1 @ sk11 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[6235]) ).
thf(6237,plain,
( ( nil @ ( sk1 @ sk11 @ sk11 @ sk11 @ rearsegP ) )
| ( sk1 @ sk11 @ sk11 @ cyclefreeP )
| ( sk1 @ sk11 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[6236:[bind(A,$thf( sk1 @ sk11 @ sk11 @ sk11 ))]]) ).
thf(18448,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18023,151]) ).
thf(18449,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18448]) ).
thf(18450,plain,
( ( sk1 @ sk8 @ ( sk1 @ sk8 @ leq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18449:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(205,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)],[199]) ).
thf(209,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)],[205]) ).
thf(210,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)],[209]) ).
thf(58,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ( A @ hd )
= B )
& ( B @ ssItem ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax75) ).
thf(341,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ( A @ hd )
= B )
& ( B @ ssItem ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(19620,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19371,406]) ).
thf(19621,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19620]) ).
thf(19622,plain,
( ( nil @ ( sk1 @ sk10 @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19621:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(31381,plain,
( ( ( sk6 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk5 != nil )
| ~ ( sk6 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,10755]) ).
thf(31382,plain,
( ( ( sk6 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk5 != nil )
| ~ ( sk6 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[31381]) ).
thf(31526,plain,
( ( sk6 != sk2 )
| ( sk5 != nil )
| ~ ( sk6 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[31382]) ).
thf(67,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(400,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)],[67]) ).
thf(24970,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[24629,334]) ).
thf(24971,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[24970]) ).
thf(24972,plain,
( ( nil @ ( sk1 @ sk12 @ cons ) @ equalelemsP )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[24971:[bind(A,$thf( sk1 @ sk12 ))]]) ).
thf(25284,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[24685,451]) ).
thf(25285,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[25284]) ).
thf(25286,plain,
( ( nil @ ( sk2 @ sk12 @ cons ) @ strictorderP )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25285:[bind(A,$thf( sk2 @ sk12 ))]]) ).
thf(23893,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[23601,406]) ).
thf(23894,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[23893]) ).
thf(23895,plain,
( ( nil @ ( sk1 @ sk15 @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[23894:[bind(A,$thf( sk1 @ sk15 ))]]) ).
thf(40,axiom,
nil @ duplicatefreeP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax72) ).
thf(242,plain,
nil @ duplicatefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(16143,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[15936,237]) ).
thf(16144,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[16143]) ).
thf(16145,plain,
( ( sk1 @ sk9 @ ( sk1 @ sk9 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[16144:[bind(A,$thf( sk1 @ sk9 ))]]) ).
thf(126,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ geq ) )
| ~ ( C @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) )
| ~ ( C @ ssItem )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[125]) ).
thf(26293,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[25846,279]) ).
thf(26294,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[26293]) ).
thf(26295,plain,
( ( nil @ ( sk2 @ sk14 @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[26294:[bind(A,$thf( sk2 @ sk14 ))]]) ).
thf(1535,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( ( sk2 @ sk11 )
!= sk2 )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[694,406]) ).
thf(1536,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( ( sk2 @ sk11 )
!= sk2 )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1535]) ).
thf(1537,plain,
( ( nil @ ( sk2 @ sk11 @ sk11 @ frontsegP ) )
| ( ( sk2 @ sk11 )
!= sk2 )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1536:[bind(A,$thf( sk2 @ sk11 @ sk11 ))]]) ).
thf(96,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(528,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)],[96]) ).
thf(131,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[130]) ).
thf(18404,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18023,155]) ).
thf(18405,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18404]) ).
thf(18406,plain,
( ( sk1 @ sk8 @ ( sk1 @ sk8 @ geq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18405:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(274,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ frontsegP ) )
| ( ( C @ ( B @ app ) )
!= A )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[271]) ).
thf(276,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ frontsegP ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( C @ ( B @ app ) )
!= A ) ),
inference(lifteq,[status(thm)],[274]) ).
thf(277,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ app ) @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ( A @ app ) @ ssList ) ),
inference(simp,[status(thm)],[276]) ).
thf(177,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ cons ) @ hd )
= B )
| ~ ( B @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[176]) ).
thf(178,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( ( A @ ( B @ cons ) @ hd )
= B ) ),
inference(lifteq,[status(thm)],[177]) ).
thf(17555,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17174,155]) ).
thf(17556,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17555]) ).
thf(17557,plain,
( ( sk1 @ sk7 @ ( sk1 @ sk7 @ geq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17556:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(82,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(469,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)],[82]) ).
thf(3351,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ lt ) )
!= ( sk6 @ ( sk6 @ lt ) ) )
| ~ $true
| ~ ( B @ ( A @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[115,3321]) ).
thf(3352,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ lt ) )
!= ( sk6 @ ( sk6 @ lt ) ) )
| ~ ( B @ ( A @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[3351]) ).
thf(3353,plain,
( ~ ( sk6 @ ( sk6 @ gt ) )
| ~ ( sk6 @ ssItem )
| ~ ( sk6 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[3352:[bind(A,$thf( sk6 )),bind(B,$thf( sk6 ))]]) ).
thf(3376,plain,
( ~ ( sk6 @ ( sk6 @ gt ) )
| ~ ( sk6 @ ssItem ) ),
inference(simp,[status(thm)],[3353]) ).
thf(3404,plain,
( ~ ( sk6 @ ( sk6 @ gt ) )
| ~ $true ),
inference(rewrite,[status(thm)],[3376,122]) ).
thf(3405,plain,
~ ( sk6 @ ( sk6 @ gt ) ),
inference(simp,[status(thm)],[3404]) ).
thf(24075,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[23646,279]) ).
thf(24076,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[24075]) ).
thf(24077,plain,
( ( nil @ ( sk2 @ sk15 @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[24076:[bind(A,$thf( sk2 @ sk15 ))]]) ).
thf(232,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)],[231]) ).
thf(218,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)],[215]) ).
thf(226,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)],[218]) ).
thf(227,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)],[226]) ).
thf(6862,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ sk11 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[656,237]) ).
thf(6863,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk1 @ sk11 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[6862]) ).
thf(6864,plain,
( ( sk1 @ sk11 @ sk11 @ ( sk1 @ sk11 @ sk11 @ segmentP ) )
| ( sk1 @ sk11 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[6863:[bind(A,$thf( sk1 @ sk11 @ sk11 ))]]) ).
thf(5705,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ sk11 @ sk11 @ cyclefreeP )
| ( sk2 @ sk11 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[688,406]) ).
thf(5706,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ sk11 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ sk11 @ sk11 @ cyclefreeP )
| ( sk2 @ sk11 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5705]) ).
thf(5707,plain,
( ( nil @ ( sk2 @ sk11 @ sk11 @ sk11 @ frontsegP ) )
| ( sk2 @ sk11 @ sk11 @ cyclefreeP )
| ( sk2 @ sk11 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5706:[bind(A,$thf( sk2 @ sk11 @ sk11 @ sk11 ))]]) ).
thf(17859,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17230,239]) ).
thf(17860,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17859]) ).
thf(17861,plain,
( ( nil @ ( sk2 @ sk7 @ cons ) @ totalorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17860:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(48810,plain,
! [A: $i] :
( ( ( sk2 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[48428,279]) ).
thf(48811,plain,
! [A: $i] :
( ( ( sk2 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[48810]) ).
thf(48812,plain,
( ( nil @ ( sk2 @ sk20 @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[48811:[bind(A,$thf( sk2 @ sk20 ))]]) ).
thf(79592,plain,
$false,
inference(e,[status(thm)],[44079,760,2031,22328,347,18079,893,518,777,59573,24978,138,333,249,170,67178,115,217,12172,308,269,202,23601,440,1705,7697,18921,472,153,26301,2042,174,18336,49831,288,18023,565,1518,18585,257,18420,17843,56856,18468,23411,17560,57007,504,26172,125,460,27528,389,189,18582,421,19414,284,881,152,25003,448,18370,33322,902,43576,325,57028,228,27923,164,16151,179,7423,376,106,238,25086,211,253,485,50254,834,16693,121,514,5738,18710,133,17571,17601,1521,507,25042,206,25798,24083,3068,18642,280,19831,44170,221,132,774,5246,25339,116,243,1405,18888,42246,265,248,270,201,18645,220,16297,12169,25289,233,452,380,117,512,439,27585,65605,260,33371,29811,44854,44035,429,275,165,17799,334,42111,16339,69227,192,407,17802,467,6926,252,197,48765,435,26107,583,757,682,10543,43586,26366,6090,285,224,519,697,1983,17174,650,9936,4840,141,610,11614,1534,18400,19783,156,24145,25110,1540,26101,884,57019,679,212,67276,328,256,23889,17742,488,124,225,17619,25235,17763,64996,193,537,8594,642,5273,173,17793,503,1627,515,7878,23957,129,134,237,105,266,633,3183,311,42199,19777,43728,12173,3321,398,22888,48821,18403,430,148,3079,279,25256,16726,6203,166,25229,10289,149,31506,176,694,8580,286,9531,118,1795,204,45005,259,16291,144,36341,15936,335,236,17554,42100,159,406,18648,219,42105,1806,1524,377,69126,98,208,24074,25226,65568,187,113,17490,230,25033,66522,362,451,567,65602,25298,45417,17813,434,19670,535,57010,6849,140,213,18612,240,10755,626,6044,155,198,890,23389,44734,25309,19616,6834,685,399,768,56969,2086,135,65614,267,438,431,241,65623,130,46316,6930,278,780,1643,28052,223,49295,27858,1694,8560,44085,490,531,112,16148,17736,355,6843,38527,6875,255,17487,4859,15973,194,145,36425,36476,17796,887,18339,25056,1531,263,30064,24629,46638,17551,46691,3315,150,48428,29432,331,19774,23441,127,59761,6206,19613,28123,24969,1543,6825,703,42101,154,55868,65707,18692,612,143,18345,656,28058,175,18591,6928,18651,17733,25045,36376,688,18662,250,231,17496,450,6846,104,6867,771,46776,25036,6831,48908,896,57122,17230,68827,186,24685,46685,23886,139,11567,29367,27852,235,510,25295,207,17521,16193,899,214,290,119,18409,3149,19371,272,1994,5704,3379,151,300,16294,262,146,61864,6237,190,183,405,18450,210,341,268,19622,31526,400,24972,25286,23895,239,242,16145,126,136,195,25846,26295,332,1537,528,131,18406,200,277,178,17557,111,122,469,3405,24077,222,232,23646,227,6864,5707,65460,17861,48812]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC125+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.12 % 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
% 0.26/0.51 % Computer : n016.cluster.edu
% 0.26/0.51 % Model : x86_64 x86_64
% 0.26/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.26/0.51 % Memory : 8046.5625MB
% 0.26/0.51 % OS : Linux 6.8.0-71-generic
% 0.26/0.51 % CPULimit : 300
% 0.26/0.51 % WCLimit : 300
% 0.26/0.51 % DateTime : Sat Sep 26 12:23:45 UTC 2026
% 0.26/0.51 % CPUTime :
% 0.26/0.51 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
% 0.97/1.01 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.64/1.26 % [INFO] Parsing done (240ms).
% 1.64/1.27 % [INFO] Running in sequential loop mode.
% 2.72/1.61 % [INFO] eprover registered as external prover.
% 2.72/1.62 % [INFO] Scanning for conjecture ...
% 3.00/1.74 % [INFO] Found a conjecture (or negated_conjecture) and 95 axioms. Running axiom selection ...
% 3.25/1.84 % [INFO] Axiom selection finished. Selected 95 axioms (removed 0 axioms).
% 3.54/1.97 % [INFO] Problem is first-order (TPTP FOF).
% 3.54/1.99 % [INFO] Type checking passed.
% 3.54/2.00 % [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 ...
% 140.67/36.08 % External prover 'e' found a proof!
% 140.67/36.08 % [INFO] Killing All external provers ...
% 140.67/36.09 % Time passed: 35426ms (effective reasoning time: 34813ms)
% 140.67/36.09 % 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)>
% 140.67/36.09 % 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
% 140.67/36.09 % No. of inferences in proof: 1293
% 140.67/36.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 35426 ms resp. 34813 ms w/o parsing
% 143.90/36.72 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 143.90/36.73 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------