%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWC111+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 : n006.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 08:52:17 AM UTC 2026
% Result : Theorem 143.55s 69.15s
% Output : Refutation 143.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 126
% Syntax : Number of formulae : 1420 ( 166 unt; 0 typ; 30 def)
% Number of atoms : 6009 (1330 equ; 0 cnn)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 13543 (2161 ~;2479 |; 237 &;7991 @)
% ( 26 <=>; 649 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 54 usr; 9 con; 0-2 aty)
% Number of variables : 1422 ( 25 ^;1325 !; 42 ?;1422 :)
% ( 0 !>; 0 ?*; 0 @-; 30 @+)
% Comments :
%------------------------------------------------------------------------------
thf(ssList_decl,type,
ssList: $i > $o ).
thf(segmentP_decl,type,
segmentP: $i > $i > $o ).
thf(totalorderedP_decl,type,
totalorderedP: $i > $o ).
thf(neq_decl,type,
neq: $i > $i > $o ).
thf(nil_decl,type,
nil: $i ).
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(strictorderedP_decl,type,
strictorderedP: $i > $o ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(frontsegP_decl,type,
frontsegP: $i > $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(sk29_decl,type,
sk29: $i > $i ).
thf(sk30_decl,type,
sk30: $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 ) ) )
| ~ ( nil @ ( B @ neq ) ) )
& ( ( nil = A )
| ( nil != B ) ) )
| ? [E: $i] :
( ( E @ totalorderedP )
& ( C @ ( E @ segmentP ) )
& ( E @ ( D @ segmentP ) )
& ( E @ ( C @ neq ) )
& ( E @ ssList ) )
| ~ ( C @ totalorderedP )
| ~ ( C @ ( D @ segmentP ) )
| ( 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 ) ) )
| ~ ( nil @ ( A @ neq ) ) )
& ( ( nil = sk1 )
| ( nil != A ) ) )
| ? [D: $i] :
( ( D @ totalorderedP )
& ( B @ ( D @ segmentP ) )
& ( D @ ( C @ segmentP ) )
& ( D @ ( B @ neq ) )
& ( D @ ssList ) )
| ~ ( B @ totalorderedP )
| ~ ( B @ ( C @ segmentP ) )
| ( sk1 != B )
| ( A != C ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( ( ( sk1 @ ( sk2 @ segmentP ) )
& ( nil @ ( sk1 @ neq ) ) )
| ~ ( nil @ ( sk2 @ neq ) ) )
& ( ( nil = sk1 )
| ( nil != sk2 ) ) )
| ? [C: $i] :
( ( C @ totalorderedP )
& ( A @ ( C @ segmentP ) )
& ( C @ ( B @ segmentP ) )
& ( C @ ( A @ neq ) )
& ( C @ ssList ) )
| ~ ( A @ totalorderedP )
| ~ ( A @ ( B @ segmentP ) )
| ( sk1 != A )
| ( sk2 != B ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ( ( ( ( ( sk1 @ ( sk2 @ segmentP ) )
& ( nil @ ( sk1 @ neq ) ) )
| ~ ( nil @ ( sk2 @ neq ) ) )
& ( ( nil = sk1 )
| ( nil != sk2 ) ) )
| ? [B: $i] :
( ( B @ totalorderedP )
& ( sk3 @ ( B @ segmentP ) )
& ( B @ ( A @ segmentP ) )
& ( B @ ( sk3 @ neq ) )
& ( B @ ssList ) )
| ~ ( sk3 @ totalorderedP )
| ~ ( sk3 @ ( A @ segmentP ) )
| ( 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(sk29_def,definition,
( sk29
= ( ^ [A: $i] :
@+[B: $i] :
( ? [C: $i] :
( ( ( B @ ( C @ cons ) )
= A )
& ( C @ ssItem ) )
& ( B @ ssList ) ) ) ) ).
thf(sk30_def,definition,
( sk30
= ( ^ [A: $i] :
@+[B: $i] :
( ( ( A @ sk29 @ ( B @ cons ) )
= A )
& ( B @ ssItem ) ) ) ) ).
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 ) ) )
| ~ ( nil @ ( B @ neq ) ) )
& ( ( nil = A )
| ( nil != B ) ) )
| ? [E: $i] :
( ( E @ totalorderedP )
& ( C @ ( E @ segmentP ) )
& ( E @ ( D @ segmentP ) )
& ( E @ ( C @ neq ) )
& ( E @ ssList ) )
| ~ ( C @ totalorderedP )
| ~ ( C @ ( D @ segmentP ) )
| ( 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 ) ) )
| ~ ( nil @ ( B @ neq ) ) )
& ( ( nil = A )
| ( nil != B ) ) )
| ? [E: $i] :
( ( E @ totalorderedP )
& ( C @ ( E @ segmentP ) )
& ( E @ ( D @ segmentP ) )
& ( E @ ( C @ neq ) )
& ( E @ ssList ) )
| ~ ( C @ totalorderedP )
| ~ ( C @ ( D @ segmentP ) )
| ( 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 ) ) )
| ~ ( nil @ ( B @ neq ) ) )
& ( ( nil = A )
| ( nil != B ) ) )
| ? [E: $i] :
( ( E @ totalorderedP )
& ( C @ ( E @ segmentP ) )
& ( E @ ( D @ segmentP ) )
& ( E @ ( C @ neq ) )
& ( E @ ssList ) )
| ~ ( C @ totalorderedP )
| ~ ( C @ ( D @ segmentP ) )
| ( A != C )
| ( B != D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(99,plain,
! [A: $i] :
( ( ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) )
| ( nil != sk1 ) )
& ( ( nil @ ( sk2 @ neq ) )
| ( nil != sk1 ) )
& ( ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) )
| ( nil = sk2 ) )
& ( ( nil @ ( sk2 @ neq ) )
| ( nil = sk2 ) )
& ( ~ ( A @ totalorderedP )
| ~ ( sk3 @ ( A @ segmentP ) )
| ~ ( A @ ( sk4 @ segmentP ) )
| ~ ( A @ ( sk3 @ neq ) )
| ~ ( A @ ssList ) )
& ( sk3 @ totalorderedP )
& ( sk3 @ ( sk4 @ segmentP ) )
& ( 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(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(204,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(205,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)],[204]) ).
thf(210,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[205]) ).
thf(13160,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,210]) ).
thf(13161,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList ) ),
inference(simp,[status(thm)],[13160]) ).
thf(13162,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk9 @ ssList ) ),
inference(pattern_uni,[status(thm)],[13161:[bind(A,$thf( sk2 ))]]) ).
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(138,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(5,axiom,
? [A: $i] :
( ? [B: $i] :
( ( A != B )
& ( B @ ssItem ) )
& ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
thf(125,plain,
? [A: $i] :
( ? [B: $i] :
( ( A != B )
& ( B @ ssItem ) )
& ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(126,plain,
( ( sk5 != sk6 )
& ( sk6 @ ssItem )
& ( sk5 @ ssItem ) ),
inference(cnf,[status(esa)],[125]) ).
thf(127,plain,
sk5 @ ssItem,
inference(cnfConj,[status(thm)],[126]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( nil @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
thf(272,plain,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( nil @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(273,plain,
! [A: $i] :
( ~ ( A @ ( nil @ memberP ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[272]) ).
thf(758,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[127,273]) ).
thf(759,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[758]) ).
thf(760,plain,
~ ( sk5 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[759:[bind(A,$thf( sk5 ))]]) ).
thf(106,plain,
sk1 @ ssList,
inference(cnfConj,[status(thm)],[99]) ).
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(292,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(293,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)],[292]) ).
thf(297,plain,
! [A: $i] :
( ( A @ totalorderP )
| ( A @ sk25 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[293]) ).
thf(61120,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk25 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,297]) ).
thf(61121,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk25 @ ssItem ) ),
inference(simp,[status(thm)],[61120]) ).
thf(61122,plain,
( ( sk1 @ totalorderP )
| ( sk1 @ sk25 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[61121:[bind(A,$thf( sk1 ))]]) ).
thf(61749,plain,
! [A: $i] :
( ( ( sk1 @ sk25 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[61122,273]) ).
thf(61750,plain,
! [A: $i] :
( ( ( sk1 @ sk25 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ totalorderP ) ),
inference(simp,[status(thm)],[61749]) ).
thf(61751,plain,
( ~ ( sk1 @ sk25 @ ( nil @ memberP ) )
| ( sk1 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[61750:[bind(A,$thf( sk1 @ sk25 ))]]) ).
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(249,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(91,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49) ).
thf(518,plain,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(34,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil @ ( A @ app ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax84) ).
thf(234,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil @ ( A @ app ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(250,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)],[249]) ).
thf(251,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ ( A @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[250]) ).
thf(253,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A != B ) ),
inference(lifteq,[status(thm)],[251]) ).
thf(254,plain,
! [A: $i] :
( ~ ( A @ ( A @ neq ) )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[253]) ).
thf(4875,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[127,254]) ).
thf(4876,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[4875]) ).
thf(4877,plain,
~ ( sk5 @ ( sk5 @ neq ) ),
inference(pattern_uni,[status(thm)],[4876:[bind(A,$thf( sk5 ))]]) ).
thf(209,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk8 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[205]) ).
thf(12421,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,209]) ).
thf(12422,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ssItem ) ),
inference(simp,[status(thm)],[12421]) ).
thf(12423,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk8 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[12422:[bind(A,$thf( sk1 ))]]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax68) ).
thf(170,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(171,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[170]) ).
thf(12810,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[12423,171]) ).
thf(12811,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[12810]) ).
thf(12812,plain,
( ( nil @ ( sk1 @ sk8 @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12811:[bind(A,$thf( sk1 @ sk8 ))]]) ).
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(347,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ( A @ hd )
= B )
& ( B @ ssItem ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
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(220,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(221,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)],[220]) ).
thf(226,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk14 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[221]) ).
thf(18965,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk14 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,226]) ).
thf(18966,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk14 @ ssList ) ),
inference(simp,[status(thm)],[18965]) ).
thf(18967,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk14 @ ssList ) ),
inference(pattern_uni,[status(thm)],[18966:[bind(A,$thf( sk2 ))]]) ).
thf(55,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax51) ).
thf(337,plain,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(338,plain,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[337]) ).
thf(19462,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[18967,338]) ).
thf(19463,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[19462]) ).
thf(19464,plain,
( ( nil @ ( sk2 @ sk14 @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[19463:[bind(A,$thf( sk2 @ sk14 ))]]) ).
thf(109,plain,
sk2 = sk4,
inference(cnfConj,[status(thm)],[99]) ).
thf(115,plain,
sk4 = sk2,
inference(lifteq,[status(thm)],[109]) ).
thf(295,plain,
! [A: $i] :
( ( A @ totalorderP )
| ( A @ sk27 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[293]) ).
thf(58654,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk27 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,295]) ).
thf(58655,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk27 @ ssList ) ),
inference(simp,[status(thm)],[58654]) ).
thf(58656,plain,
( ( sk1 @ totalorderP )
| ( sk1 @ sk27 @ ssList ) ),
inference(pattern_uni,[status(thm)],[58655:[bind(A,$thf( sk1 ))]]) ).
thf(47,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax57) ).
thf(284,plain,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(285,plain,
! [A: $i] :
( ( nil @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[284]) ).
thf(59177,plain,
! [A: $i] :
( ( ( sk1 @ sk27 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[58656,285]) ).
thf(59178,plain,
! [A: $i] :
( ( ( sk1 @ sk27 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ totalorderP ) ),
inference(simp,[status(thm)],[59177]) ).
thf(59179,plain,
( ( nil @ ( sk1 @ sk27 @ segmentP ) )
| ( sk1 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[59178:[bind(A,$thf( sk1 @ sk27 ))]]) ).
thf(42,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ app ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
thf(256,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ app ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(257,plain,
! [A: $i] :
( ( ( A @ ( nil @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[256]) ).
thf(258,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[257]) ).
thf(33350,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[105,258]) ).
thf(33351,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[33350]) ).
thf(33352,plain,
( ( sk2 @ ( nil @ app ) )
= sk2 ),
inference(pattern_uni,[status(thm)],[33351:[bind(A,$thf( sk2 ))]]) ).
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(259,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(260,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)],[259]) ).
thf(263,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk20 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[260]) ).
thf(37213,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk20 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,263]) ).
thf(37214,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk20 @ ssList ) ),
inference(simp,[status(thm)],[37213]) ).
thf(37215,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk20 @ ssList ) ),
inference(pattern_uni,[status(thm)],[37214:[bind(A,$thf( sk2 ))]]) ).
thf(37823,plain,
! [A: $i] :
( ( ( sk2 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[37215,285]) ).
thf(37824,plain,
! [A: $i] :
( ( ( sk2 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[37823]) ).
thf(37825,plain,
( ( nil @ ( sk2 @ sk20 @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[37824:[bind(A,$thf( sk2 @ sk20 ))]]) ).
thf(39,axiom,
~ ( nil @ singletonP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).
thf(246,plain,
~ ( nil @ singletonP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(247,plain,
~ ( nil @ singletonP ),
inference(polarity_switch,[status(thm)],[246]) ).
thf(73,axiom,
nil @ strictorderP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax64) ).
thf(440,plain,
nil @ strictorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(265,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)],[260]) ).
thf(269,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)],[265]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ frontsegP ) )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax46) ).
thf(172,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(173,plain,
! [A: $i] :
( ( ( A @ ( nil @ frontsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) )
& ( ( nil = A )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[172]) ).
thf(175,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[173]) ).
thf(177,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[175]) ).
thf(178,plain,
( ( nil @ ( nil @ frontsegP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[177]) ).
thf(62,axiom,
nil @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
thf(382,plain,
nil @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(648,plain,
( ( nil @ ( nil @ frontsegP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[178,382]) ).
thf(649,plain,
nil @ ( nil @ frontsegP ),
inference(simp,[status(thm)],[648]) ).
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(276,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(277,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)],[276]) ).
thf(278,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk22 ) @ ssList )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[277]) ).
thf(47111,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)],[649,278]) ).
thf(47112,plain,
! [B: $i,A: $i] :
( ( ( nil @ ( nil @ frontsegP ) )
!= ( B @ ( A @ frontsegP ) ) )
| ( A @ ( B @ sk22 ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[47111]) ).
thf(47113,plain,
( ( nil @ ( nil @ sk22 ) @ ssList )
| ~ ( nil @ ssList )
| ~ ( nil @ ssList ) ),
inference(pattern_uni,[status(thm)],[47112:[bind(A,$thf( nil )),bind(B,$thf( nil ))]]) ).
thf(47364,plain,
( ( nil @ ( nil @ sk22 ) @ ssList )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[47113]) ).
thf(47486,plain,
( ( nil @ ( nil @ sk22 ) @ ssList )
| ~ $true ),
inference(rewrite,[status(thm)],[47364,382]) ).
thf(47487,plain,
nil @ ( nil @ sk22 ) @ ssList,
inference(simp,[status(thm)],[47486]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax55) ).
thf(242,plain,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(243,plain,
! [A: $i] :
( ( A @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[242]) ).
thf(47541,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47487,243]) ).
thf(47542,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[47541]) ).
thf(47543,plain,
nil @ ( nil @ sk22 ) @ ( nil @ ( nil @ sk22 ) @ segmentP ),
inference(pattern_uni,[status(thm)],[47542:[bind(A,$thf( nil @ ( nil @ sk22 ) ))]]) ).
thf(207,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)],[205]) ).
thf(216,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)],[207]) ).
thf(217,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)],[216]) ).
thf(262,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk17 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[260]) ).
thf(35931,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk17 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,262]) ).
thf(35932,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk17 @ ssItem ) ),
inference(simp,[status(thm)],[35931]) ).
thf(35933,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk17 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[35932:[bind(A,$thf( sk2 ))]]) ).
thf(101,plain,
( ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) )
| ( nil = sk2 ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(113,plain,
( ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) )
| ( sk2 = nil ) ),
inference(lifteq,[status(thm)],[101]) ).
thf(112,plain,
sk3 @ ( sk4 @ segmentP ),
inference(cnfConj,[status(thm)],[99]) ).
thf(107,plain,
sk1 = sk3,
inference(cnfConj,[status(thm)],[99]) ).
thf(116,plain,
sk3 = sk1,
inference(lifteq,[status(thm)],[107]) ).
thf(561,plain,
sk1 @ ( sk2 @ segmentP ),
inference(rewrite,[status(thm)],[112,115,116]) ).
thf(570,plain,
( ~ $true
| ~ ( nil @ ( sk1 @ neq ) )
| ( sk2 = nil ) ),
inference(rewrite,[status(thm)],[113,561]) ).
thf(571,plain,
( ~ ( nil @ ( sk1 @ neq ) )
| ( sk2 = nil ) ),
inference(simp,[status(thm)],[570]) ).
thf(22,axiom,
nil @ totalorderedP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax66) ).
thf(179,plain,
nil @ totalorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(789,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,285]) ).
thf(790,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[789]) ).
thf(791,plain,
nil @ ( sk2 @ segmentP ),
inference(pattern_uni,[status(thm)],[790:[bind(A,$thf( sk2 ))]]) ).
thf(104,plain,
! [A: $i] :
( ~ ( A @ totalorderedP )
| ~ ( sk3 @ ( A @ segmentP ) )
| ~ ( A @ ( sk4 @ segmentP ) )
| ~ ( A @ ( sk3 @ neq ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(543,plain,
! [A: $i] :
( ~ ( A @ totalorderedP )
| ~ ( sk1 @ ( A @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( A @ ( sk1 @ neq ) )
| ~ ( A @ ssList ) ),
inference(rewrite,[status(thm)],[104,115,116]) ).
thf(567,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ segmentP ) )
!= ( sk1 @ ( A @ segmentP ) ) )
| ~ ( A @ totalorderedP )
| ~ $true
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( A @ ( sk1 @ neq ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[561,543]) ).
thf(568,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ segmentP ) )
!= ( sk1 @ ( A @ segmentP ) ) )
| ~ ( A @ totalorderedP )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( A @ ( sk1 @ neq ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[567]) ).
thf(569,plain,
( ~ ( sk2 @ totalorderedP )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) )
| ~ ( sk2 @ ssList ) ),
inference(pattern_uni,[status(thm)],[568:[bind(A,$thf( sk2 ))]]) ).
thf(1449,plain,
( ~ ( sk2 @ totalorderedP )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) )
| ~ $true ),
inference(rewrite,[status(thm)],[569,105]) ).
thf(1450,plain,
( ~ ( sk2 @ totalorderedP )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[1449]) ).
thf(1510,plain,
( ( ( sk2 @ ( sk2 @ segmentP ) )
!= ( nil @ ( sk2 @ segmentP ) ) )
| ~ ( sk2 @ totalorderedP )
| ~ $true
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[791,1450]) ).
thf(1511,plain,
( ( ( sk2 @ ( sk2 @ segmentP ) )
!= ( nil @ ( sk2 @ segmentP ) ) )
| ~ ( sk2 @ totalorderedP )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[1510]) ).
thf(1512,plain,
( ( sk2 != nil )
| ( sk2 != sk2 )
| ~ ( sk2 @ totalorderedP )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[1511]) ).
thf(1529,plain,
( ( sk2 != nil )
| ~ ( sk2 @ totalorderedP )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[1512]) ).
thf(1546,plain,
( ( ( sk2 @ totalorderedP )
!= ( nil @ totalorderedP ) )
| ( sk2 != nil )
| ~ $true
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[179,1529]) ).
thf(1547,plain,
( ( ( sk2 @ totalorderedP )
!= ( nil @ totalorderedP ) )
| ( sk2 != nil )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[1546]) ).
thf(1581,plain,
( ( sk2 != nil )
| ( sk2 != nil )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[1547]) ).
thf(1586,plain,
( ( sk2 != nil )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[1581]) ).
thf(1616,plain,
( ( sk2 != sk2 )
| ( sk2 != nil )
| ~ ( nil @ ( sk1 @ neq ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[571,1586]) ).
thf(1617,plain,
( ( sk2 != sk2 )
| ( sk2 != nil )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[1616]) ).
thf(1618,plain,
( ( sk2 != nil )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[1617:[]]) ).
thf(1653,plain,
( ( sk2 != sk2 )
| ( nil != nil )
| ~ ( nil @ ( sk1 @ neq ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[571,1618]) ).
thf(1654,plain,
( ( sk2 != sk2 )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[1653]) ).
thf(1655,plain,
~ ( nil @ ( sk1 @ neq ) ),
inference(pattern_uni,[status(thm)],[1654:[]]) ).
thf(206,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk7 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[205]) ).
thf(11308,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,206]) ).
thf(11309,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssItem ) ),
inference(simp,[status(thm)],[11308]) ).
thf(11310,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk7 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[11309:[bind(A,$thf( sk2 ))]]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax65) ).
thf(244,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(245,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[244]) ).
thf(11846,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11310,245]) ).
thf(11847,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[11846]) ).
thf(11848,plain,
( ( nil @ ( sk2 @ sk7 @ cons ) @ totalorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[11847:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(174,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[173]) ).
thf(176,plain,
! [A: $i] :
( ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[174]) ).
thf(129,plain,
sk5 != sk6,
inference(cnfConj,[status(thm)],[126]) ).
thf(130,plain,
sk6 != sk5,
inference(lifteq,[status(thm)],[129]) ).
thf(6245,plain,
! [A: $i] :
( ( A != sk6 )
| ( sk5 != nil )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[176,130]) ).
thf(6246,plain,
( ( sk5 != nil )
| ~ ( sk6 @ ( nil @ frontsegP ) )
| ~ ( sk6 @ ssList ) ),
inference(pattern_uni,[status(thm)],[6245:[bind(A,$thf( sk6 ))]]) ).
thf(294,plain,
! [A: $i] :
( ( A @ totalorderP )
| ( A @ sk28 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[293]) ).
thf(56872,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk28 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,294]) ).
thf(56873,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk28 @ ssList ) ),
inference(simp,[status(thm)],[56872]) ).
thf(56874,plain,
( ( sk2 @ totalorderP )
| ( sk2 @ sk28 @ ssList ) ),
inference(pattern_uni,[status(thm)],[56873:[bind(A,$thf( sk2 ))]]) ).
thf(128,plain,
sk6 @ ssItem,
inference(cnfConj,[status(thm)],[126]) ).
thf(78,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax63) ).
thf(456,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(457,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[456]) ).
thf(3779,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[128,457]) ).
thf(3780,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP ) ),
inference(simp,[status(thm)],[3779]) ).
thf(3781,plain,
nil @ ( sk6 @ cons ) @ strictorderP,
inference(pattern_uni,[status(thm)],[3780:[bind(A,$thf( sk6 ))]]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ equalelemsP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax73) ).
thf(339,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ equalelemsP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(340,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ equalelemsP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[339]) ).
thf(1917,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[127,340]) ).
thf(1918,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP ) ),
inference(simp,[status(thm)],[1917]) ).
thf(1919,plain,
nil @ ( sk5 @ cons ) @ equalelemsP,
inference(pattern_uni,[status(thm)],[1918:[bind(A,$thf( sk5 ))]]) ).
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(142,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(4868,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[128,254]) ).
thf(4869,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[4868]) ).
thf(4870,plain,
~ ( sk6 @ ( sk6 @ neq ) ),
inference(pattern_uni,[status(thm)],[4869:[bind(A,$thf( sk6 ))]]) ).
thf(252,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ neq ) )
| ( A = B )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[250]) ).
thf(255,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A = B ) ),
inference(lifteq,[status(thm)],[252]) ).
thf(29342,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ~ $true
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[255,1655]) ).
thf(29343,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A = B ) ),
inference(simp,[status(thm)],[29342]) ).
thf(29344,plain,
( ~ ( nil @ ssItem )
| ~ ( sk1 @ ssItem )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[29343:[bind(A,$thf( sk1 )),bind(B,$thf( nil ))]]) ).
thf(33201,plain,
( ( ( sk5 @ ssItem )
!= ( nil @ ssItem ) )
| ~ $true
| ~ ( sk1 @ ssItem )
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[127,29344]) ).
thf(33202,plain,
( ( ( sk5 @ ssItem )
!= ( nil @ ssItem ) )
| ~ ( sk1 @ ssItem )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[33201]) ).
thf(33264,plain,
( ( sk5 != nil )
| ~ ( sk1 @ ssItem )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[33202]) ).
thf(34405,plain,
( ( ( sk5 @ ssItem )
!= ( sk1 @ ssItem ) )
| ( sk5 != nil )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[127,33264]) ).
thf(34406,plain,
( ( ( sk5 @ ssItem )
!= ( sk1 @ ssItem ) )
| ( sk5 != nil )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[34405]) ).
thf(34421,plain,
( ( sk5 != sk1 )
| ( sk5 != nil )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[34406]) ).
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(286,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ( A @ tl )
= B )
& ( B @ ssList ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(287,plain,
! [A: $i] :
( ( ( ( A @ tl )
= ( A @ sk23 ) )
| ( nil = A )
| ~ ( A @ ssList ) )
& ( ( A @ sk23 @ ssList )
| ( nil = A )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[286]) ).
thf(288,plain,
! [A: $i] :
( ( A @ sk23 @ ssList )
| ( nil = A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[287]) ).
thf(290,plain,
! [A: $i] :
( ( A @ sk23 @ ssList )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[288]) ).
thf(52689,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk23 @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[105,290]) ).
thf(52690,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk23 @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[52689]) ).
thf(52691,plain,
( ( sk2 @ sk23 @ ssList )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[52690:[bind(A,$thf( sk2 ))]]) ).
thf(108,plain,
( ( nil @ ( sk2 @ neq ) )
| ( nil = sk2 ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(117,plain,
( ( nil @ ( sk2 @ neq ) )
| ( sk2 = nil ) ),
inference(lifteq,[status(thm)],[108]) ).
thf(605,plain,
( ( sk2 != sk2 )
| ( sk1 @ ( nil @ segmentP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[117,561]) ).
thf(606,plain,
( ( sk1 @ ( nil @ segmentP ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[605:[]]) ).
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(361,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(362,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ neq ) )
| ( A = B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) )
& ( ( A != B )
| ~ ( B @ ( A @ neq ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[361]) ).
thf(363,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ ( A @ neq ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[362]) ).
thf(365,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ neq ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( A != B ) ),
inference(lifteq,[status(thm)],[363]) ).
thf(366,plain,
! [A: $i] :
( ~ ( A @ ( A @ neq ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[365]) ).
thf(4987,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,366]) ).
thf(4988,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[4987]) ).
thf(4989,plain,
~ ( sk2 @ ( sk2 @ neq ) ),
inference(pattern_uni,[status(thm)],[4988:[bind(A,$thf( sk2 ))]]) ).
thf(5007,plain,
( ( ( sk2 @ ( sk2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[606,4989]) ).
thf(5008,plain,
( ( ( sk2 @ ( sk2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[5007]) ).
thf(5048,plain,
( ( sk2 != nil )
| ( sk2 != sk2 )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[5008]) ).
thf(5057,plain,
( ( sk2 != nil )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[5048]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ segmentP ) )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax58) ).
thf(185,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(186,plain,
! [A: $i] :
( ( ( A @ ( nil @ segmentP ) )
| ( nil != A )
| ~ ( A @ ssList ) )
& ( ( nil = A )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[185]) ).
thf(187,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[186]) ).
thf(189,plain,
! [A: $i] :
( ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[187]) ).
thf(7955,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[106,189]) ).
thf(7956,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[7955]) ).
thf(7957,plain,
( ~ ( sk1 @ ( nil @ segmentP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[7956:[bind(A,$thf( sk1 ))]]) ).
thf(8732,plain,
( ( ( sk1 @ ( nil @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ~ $true
| ( sk1 = nil )
| ( sk2 != nil ) ),
inference(paramod_ordered,[status(thm)],[5057,7957]) ).
thf(8733,plain,
( ( ( sk1 @ ( nil @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ( sk1 = nil )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[8732]) ).
thf(8734,plain,
( ( sk1 = nil )
| ( sk2 != nil ) ),
inference(pattern_uni,[status(thm)],[8733:[]]) ).
thf(8839,plain,
( ( sk2 != sk2 )
| ( sk1 = nil )
| ( nil != nil )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[117,8734]) ).
thf(8840,plain,
( ( sk2 != sk2 )
| ( sk1 = nil )
| ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[8839]) ).
thf(8841,plain,
( ( sk1 = nil )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[8840:[]]) ).
thf(100,plain,
( ( nil @ ( sk2 @ neq ) )
| ( nil != sk1 ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(118,plain,
( ( nil @ ( sk2 @ neq ) )
| ( sk1 != nil ) ),
inference(lifteq,[status(thm)],[100]) ).
thf(9112,plain,
( ( sk1 != sk1 )
| ( nil @ ( sk2 @ neq ) )
| ( nil != nil )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[8841,118]) ).
thf(9113,plain,
( ( sk1 != sk1 )
| ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[9112]) ).
thf(9114,plain,
nil @ ( sk2 @ neq ),
inference(pattern_uni,[status(thm)],[9113:[]]) ).
thf(5011,plain,
( ( sk2 != sk2 )
| ~ ( sk2 @ ( nil @ neq ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[117,4989]) ).
thf(5012,plain,
( ~ ( sk2 @ ( nil @ neq ) )
| ( nil @ ( sk2 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[5011:[]]) ).
thf(5494,plain,
( ( ( sk2 @ ( sk2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true
| ~ ( sk2 @ ( nil @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[5012,4989]) ).
thf(5495,plain,
( ( ( sk2 @ ( sk2 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ ( sk2 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[5494]) ).
thf(5579,plain,
( ( sk2 != nil )
| ( sk2 != sk2 )
| ~ ( sk2 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[5495]) ).
thf(5594,plain,
( ( sk2 != nil )
| ~ ( sk2 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[5579]) ).
thf(9268,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( nil @ neq ) ) )
| ( sk2 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9114,5594]) ).
thf(9269,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( sk2 @ ( nil @ neq ) ) )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[9268]) ).
thf(9314,plain,
( ( sk2 != nil )
| ( sk2 != nil )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[9269]) ).
thf(9335,plain,
sk2 != nil,
inference(simp,[status(thm)],[9314]) ).
thf(55041,plain,
sk2 @ sk23 @ ssList,
inference(simplifyReflect,[status(thm)],[52691,9335]) ).
thf(68,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax45) ).
thf(411,plain,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(412,plain,
! [A: $i] :
( ( nil @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[411]) ).
thf(55130,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[55041,412]) ).
thf(55131,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) ) ),
inference(simp,[status(thm)],[55130]) ).
thf(55132,plain,
nil @ ( sk2 @ sk23 @ frontsegP ),
inference(pattern_uni,[status(thm)],[55131:[bind(A,$thf( sk2 @ sk23 ))]]) ).
thf(289,plain,
! [A: $i] :
( ( ( A @ tl )
= ( A @ sk23 ) )
| ( nil = A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[287]) ).
thf(291,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ( ( A @ sk23 )
= ( A @ tl ) )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[289]) ).
thf(55914,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ sk23 )
= ( A @ tl ) )
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[105,291]) ).
thf(55915,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ sk23 )
= ( A @ tl ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[55914]) ).
thf(55916,plain,
( ( ( sk2 @ sk23 )
= ( sk2 @ tl ) )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[55915:[bind(A,$thf( sk2 ))]]) ).
thf(64220,plain,
( ( sk2 @ sk23 )
= ( sk2 @ tl ) ),
inference(simplifyReflect,[status(thm)],[55916,9335]) ).
thf(64228,plain,
nil @ ( sk2 @ tl @ frontsegP ),
inference(rewrite,[status(thm)],[55132,64220]) ).
thf(47544,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47487,366]) ).
thf(47545,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[47544]) ).
thf(47546,plain,
~ ( nil @ ( nil @ sk22 ) @ ( nil @ ( nil @ sk22 ) @ neq ) ),
inference(pattern_uni,[status(thm)],[47545:[bind(A,$thf( nil @ ( nil @ sk22 ) ))]]) ).
thf(5930,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[106,176]) ).
thf(5931,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[5930]) ).
thf(5932,plain,
( ~ ( sk1 @ ( nil @ frontsegP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[5931:[bind(A,$thf( sk1 ))]]) ).
thf(544,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ totalorderedP )
| ~ ( sk1 @ ( A @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( A @ ( sk1 @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,543]) ).
thf(545,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ totalorderedP )
| ~ ( sk1 @ ( A @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( A @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[544]) ).
thf(546,plain,
( ~ ( sk1 @ totalorderedP )
| ~ ( sk1 @ ( sk1 @ segmentP ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ ( sk1 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[545:[bind(A,$thf( sk1 ))]]) ).
thf(111,plain,
sk3 @ totalorderedP,
inference(cnfConj,[status(thm)],[99]) ).
thf(542,plain,
sk1 @ totalorderedP,
inference(rewrite,[status(thm)],[111,116]) ).
thf(556,plain,
( ~ $true
| ~ ( sk1 @ ( sk1 @ segmentP ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ ( sk1 @ neq ) ) ),
inference(rewrite,[status(thm)],[546,542]) ).
thf(557,plain,
( ~ ( sk1 @ ( sk1 @ segmentP ) )
| ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( sk1 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[556]) ).
thf(581,plain,
( ~ ( sk1 @ ( sk1 @ segmentP ) )
| ~ $true
| ~ ( sk1 @ ( sk1 @ neq ) ) ),
inference(rewrite,[status(thm)],[557,561]) ).
thf(582,plain,
( ~ ( sk1 @ ( sk1 @ segmentP ) )
| ~ ( sk1 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[581]) ).
thf(4216,plain,
! [A: $i] :
( ( ( A @ ( A @ segmentP ) )
!= ( sk1 @ ( sk1 @ segmentP ) ) )
| ~ $true
| ~ ( sk1 @ ( sk1 @ neq ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[243,582]) ).
thf(4217,plain,
! [A: $i] :
( ( ( A @ ( A @ segmentP ) )
!= ( sk1 @ ( sk1 @ segmentP ) ) )
| ~ ( sk1 @ ( sk1 @ neq ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[4216]) ).
thf(4218,plain,
( ~ ( sk1 @ ( sk1 @ neq ) )
| ~ ( sk1 @ ssList ) ),
inference(pattern_uni,[status(thm)],[4217:[bind(A,$thf( sk1 ))]]) ).
thf(4239,plain,
( ~ ( sk1 @ ( sk1 @ neq ) )
| ~ $true ),
inference(rewrite,[status(thm)],[4218,106]) ).
thf(4240,plain,
~ ( sk1 @ ( sk1 @ neq ) ),
inference(simp,[status(thm)],[4239]) ).
thf(6550,plain,
( ( sk1 != sk1 )
| ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[5932,4240]) ).
thf(6551,plain,
( ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[6550:[]]) ).
thf(33017,plain,
( ( ( sk6 @ ssItem )
!= ( nil @ ssItem ) )
| ~ $true
| ~ ( sk1 @ ssItem )
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[128,29344]) ).
thf(33018,plain,
( ( ( sk6 @ ssItem )
!= ( nil @ ssItem ) )
| ~ ( sk1 @ ssItem )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[33017]) ).
thf(33266,plain,
( ( sk6 != nil )
| ~ ( sk1 @ ssItem )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[33018]) ).
thf(11260,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,206]) ).
thf(11261,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssItem ) ),
inference(simp,[status(thm)],[11260]) ).
thf(11262,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk7 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[11261:[bind(A,$thf( sk1 ))]]) ).
thf(11547,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11262,457]) ).
thf(11548,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[11547]) ).
thf(11549,plain,
( ( nil @ ( sk1 @ sk7 @ cons ) @ strictorderP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[11548:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(13145,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,210]) ).
thf(13146,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList ) ),
inference(simp,[status(thm)],[13145]) ).
thf(13147,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk9 @ ssList ) ),
inference(pattern_uni,[status(thm)],[13146:[bind(A,$thf( sk1 ))]]) ).
thf(66,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax61) ).
thf(404,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(11643,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11262,171]) ).
thf(11644,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[11643]) ).
thf(11645,plain,
( ( nil @ ( sk1 @ sk7 @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[11644:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax90) ).
thf(145,plain,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(146,plain,
! [A: $i] :
( ~ ( A @ ( A @ lt ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[145]) ).
thf(12831,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[12423,146]) ).
thf(12832,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[12831]) ).
thf(12833,plain,
( ~ ( sk1 @ sk8 @ ( sk1 @ sk8 @ lt ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12832:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(71,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ duplicatefreeP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax71) ).
thf(435,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ duplicatefreeP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(436,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[435]) ).
thf(264,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk18 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[260]) ).
thf(38592,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk18 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,264]) ).
thf(38593,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk18 @ ssItem ) ),
inference(simp,[status(thm)],[38592]) ).
thf(38594,plain,
( ( sk1 @ strictorderedP )
| ( sk1 @ sk18 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[38593:[bind(A,$thf( sk1 ))]]) ).
thf(39149,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[38594,273]) ).
thf(39150,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[39149]) ).
thf(39151,plain,
( ~ ( sk1 @ sk18 @ ( nil @ memberP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[39150:[bind(A,$thf( sk1 @ sk18 ))]]) ).
thf(188,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ( nil != A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[186]) ).
thf(190,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[188]) ).
thf(191,plain,
( ( nil @ ( nil @ segmentP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[190]) ).
thf(650,plain,
( ( nil @ ( nil @ segmentP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[191,382]) ).
thf(651,plain,
nil @ ( nil @ segmentP ),
inference(simp,[status(thm)],[650]) ).
thf(9242,plain,
( ( ( sk5 @ ( sk5 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9114,4877]) ).
thf(9243,plain,
( ( sk5 @ ( sk5 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[9242]) ).
thf(9316,plain,
( ( sk5 != nil )
| ( sk5 != sk2 ) ),
inference(simp,[status(thm)],[9243]) ).
thf(10795,plain,
! [A: $i] :
( ( A != sk5 )
| ( nil != nil )
| ( sk5 != sk2 )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[176,9316]) ).
thf(10796,plain,
! [A: $i] :
( ( A != sk5 )
| ( sk5 != sk2 )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[10795]) ).
thf(10797,plain,
( ( sk5 != sk2 )
| ~ ( sk5 @ ( nil @ frontsegP ) )
| ~ ( sk5 @ ssList ) ),
inference(pattern_uni,[status(thm)],[10796:[bind(A,$thf( sk5 ))]]) ).
thf(51027,plain,
( ( ( sk5 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk5 != sk2 )
| ~ ( sk5 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,10797]) ).
thf(51028,plain,
( ( ( sk5 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk5 != sk2 )
| ~ ( sk5 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[51027]) ).
thf(51269,plain,
( ( sk5 != sk2 )
| ( sk5 != sk2 )
| ~ ( sk5 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[51028]) ).
thf(51276,plain,
( ( sk5 != sk2 )
| ~ ( sk5 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[51269]) ).
thf(302,plain,
! [A: $i] :
( ( A @ totalorderP )
| ( A @ sk24 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[293]) ).
thf(67095,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk24 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,302]) ).
thf(67096,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk24 @ ssItem ) ),
inference(simp,[status(thm)],[67095]) ).
thf(67097,plain,
( ( sk1 @ totalorderP )
| ( sk1 @ sk24 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[67096:[bind(A,$thf( sk1 ))]]) ).
thf(10782,plain,
! [A: $i] :
( ( A != sk5 )
| ( nil != nil )
| ( sk5 != sk2 )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[189,9316]) ).
thf(10783,plain,
! [A: $i] :
( ( A != sk5 )
| ( sk5 != sk2 )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[10782]) ).
thf(10784,plain,
( ( sk5 != sk2 )
| ~ ( sk5 @ ( nil @ segmentP ) )
| ~ ( sk5 @ ssList ) ),
inference(pattern_uni,[status(thm)],[10783:[bind(A,$thf( sk5 ))]]) ).
thf(46271,plain,
( ( ( sk5 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk5 != sk2 )
| ~ ( sk5 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,10784]) ).
thf(46272,plain,
( ( ( sk5 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk5 != sk2 )
| ~ ( sk5 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[46271]) ).
thf(46498,plain,
( ( sk5 != sk2 )
| ( sk5 != sk2 )
| ~ ( sk5 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[46272]) ).
thf(46530,plain,
( ( sk5 != sk2 )
| ~ ( sk5 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[46498]) ).
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(306,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(307,plain,
! [A: $i] :
( ( ( ( A @ sk29 @ ( A @ sk30 @ cons ) )
= A )
| ( nil = A )
| ~ ( A @ ssList ) )
& ( ( A @ sk30 @ ssItem )
| ( nil = A )
| ~ ( A @ ssList ) )
& ( ( A @ sk29 @ ssList )
| ( nil = A )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[306]) ).
thf(308,plain,
! [A: $i] :
( ( A @ sk29 @ ssList )
| ( nil = A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[307]) ).
thf(311,plain,
! [A: $i] :
( ( A @ sk29 @ ssList )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[308]) ).
thf(73408,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk29 @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[105,311]) ).
thf(73409,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk29 @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[73408]) ).
thf(73410,plain,
( ( sk2 @ sk29 @ ssList )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[73409:[bind(A,$thf( sk2 ))]]) ).
thf(76299,plain,
sk2 @ sk29 @ ssList,
inference(simplifyReflect,[status(thm)],[73410,9335]) ).
thf(76401,plain,
! [A: $i] :
( ( ( sk2 @ sk29 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76299,412]) ).
thf(76402,plain,
! [A: $i] :
( ( ( sk2 @ sk29 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) ) ),
inference(simp,[status(thm)],[76401]) ).
thf(76403,plain,
nil @ ( sk2 @ sk29 @ frontsegP ),
inference(pattern_uni,[status(thm)],[76402:[bind(A,$thf( sk2 @ sk29 ))]]) ).
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(182,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) @ hd )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(183,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ cons ) @ hd )
= B )
| ~ ( B @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[182]) ).
thf(184,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( ( A @ ( B @ cons ) @ hd )
= B ) ),
inference(lifteq,[status(thm)],[183]) ).
thf(225,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk12 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[221]) ).
thf(17835,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk12 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,225]) ).
thf(17836,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk12 @ ssItem ) ),
inference(simp,[status(thm)],[17835]) ).
thf(17837,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk12 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[17836:[bind(A,$thf( sk2 ))]]) ).
thf(18484,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[17837,273]) ).
thf(18485,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[18484]) ).
thf(18486,plain,
( ~ ( sk2 @ sk12 @ ( nil @ memberP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[18485:[bind(A,$thf( sk2 @ sk12 ))]]) ).
thf(261,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk19 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[260]) ).
thf(34485,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk19 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,261]) ).
thf(34486,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk19 @ ssList ) ),
inference(simp,[status(thm)],[34485]) ).
thf(34487,plain,
( ( sk1 @ strictorderedP )
| ( sk1 @ sk19 @ ssList ) ),
inference(pattern_uni,[status(thm)],[34486:[bind(A,$thf( sk1 ))]]) ).
thf(34963,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[34487,338]) ).
thf(34964,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[34963]) ).
thf(34965,plain,
( ( nil @ ( sk1 @ sk19 @ rearsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[34964:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(12469,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,209]) ).
thf(12470,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ssItem ) ),
inference(simp,[status(thm)],[12469]) ).
thf(12471,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk8 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[12470:[bind(A,$thf( sk2 ))]]) ).
thf(12899,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[12471,436]) ).
thf(12900,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[12899]) ).
thf(12901,plain,
( ( nil @ ( sk2 @ sk8 @ cons ) @ duplicatefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12900:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(405,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[404]) ).
thf(1990,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[127,405]) ).
thf(1991,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP ) ),
inference(simp,[status(thm)],[1990]) ).
thf(1992,plain,
nil @ ( sk5 @ cons ) @ totalorderP,
inference(pattern_uni,[status(thm)],[1991:[bind(A,$thf( sk5 ))]]) ).
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(196,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(235,plain,
! [A: $i] :
( ( ( nil @ ( A @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[234]) ).
thf(236,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[235]) ).
thf(26550,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[105,236]) ).
thf(26551,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[26550]) ).
thf(26552,plain,
( ( nil @ ( sk2 @ app ) )
= sk2 ),
inference(pattern_uni,[status(thm)],[26551:[bind(A,$thf( sk2 ))]]) ).
thf(26536,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[106,236]) ).
thf(26537,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[26536]) ).
thf(26538,plain,
( ( nil @ ( sk1 @ app ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[26537:[bind(A,$thf( sk1 ))]]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax31) ).
thf(156,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(157,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[156]) ).
thf(11909,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11310,273]) ).
thf(11910,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[11909]) ).
thf(11911,plain,
( ~ ( sk2 @ sk7 @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[11910:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(11607,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11262,245]) ).
thf(11608,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[11607]) ).
thf(11609,plain,
( ( nil @ ( sk1 @ sk7 @ cons ) @ totalorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[11608:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(268,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk21 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[260]) ).
thf(40805,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk21 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,268]) ).
thf(40806,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk21 @ ssList ) ),
inference(simp,[status(thm)],[40805]) ).
thf(40807,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk21 @ ssList ) ),
inference(pattern_uni,[status(thm)],[40806:[bind(A,$thf( sk2 ))]]) ).
thf(76442,plain,
! [A: $i] :
( ( ( sk2 @ sk29 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[76299,236]) ).
thf(76443,plain,
! [A: $i] :
( ( ( sk2 @ sk29 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[76442]) ).
thf(76444,plain,
( ( nil @ ( sk2 @ sk29 @ app ) )
= ( sk2 @ sk29 ) ),
inference(pattern_uni,[status(thm)],[76443:[bind(A,$thf( sk2 @ sk29 ))]]) ).
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(152,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(228,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk16 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[221]) ).
thf(51,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) )
!= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
thf(314,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) )
!= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(315,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ cons ) )
!= A )
| ~ ( B @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[314]) ).
thf(316,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( ( A @ ( B @ cons ) )
!= A ) ),
inference(lifteq,[status(thm)],[315]) ).
thf(12655,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[12423,436]) ).
thf(12656,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[12655]) ).
thf(12657,plain,
( ( nil @ ( sk1 @ sk8 @ cons ) @ duplicatefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12656:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(309,plain,
! [A: $i] :
( ( A @ sk30 @ ssItem )
| ( nil = A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[307]) ).
thf(312,plain,
! [A: $i] :
( ( A @ sk30 @ ssItem )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[309]) ).
thf(78373,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk30 @ ssItem )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[105,312]) ).
thf(78374,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk30 @ ssItem )
| ( nil = A ) ),
inference(simp,[status(thm)],[78373]) ).
thf(78375,plain,
( ( sk2 @ sk30 @ ssItem )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[78374:[bind(A,$thf( sk2 ))]]) ).
thf(81958,plain,
sk2 @ sk30 @ ssItem,
inference(simplifyReflect,[status(thm)],[78375,9335]) ).
thf(82170,plain,
! [A: $i] :
( ( ( sk2 @ sk30 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81958,405]) ).
thf(82171,plain,
! [A: $i] :
( ( ( sk2 @ sk30 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP ) ),
inference(simp,[status(thm)],[82170]) ).
thf(82172,plain,
nil @ ( sk2 @ sk30 @ cons ) @ totalorderP,
inference(pattern_uni,[status(thm)],[82171:[bind(A,$thf( sk2 @ sk30 ))]]) ).
thf(82185,plain,
! [A: $i] :
( ( ( sk2 @ sk30 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81958,146]) ).
thf(82186,plain,
! [A: $i] :
( ( ( sk2 @ sk30 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[82185]) ).
thf(82187,plain,
~ ( sk2 @ sk30 @ ( sk2 @ sk30 @ lt ) ),
inference(pattern_uni,[status(thm)],[82186:[bind(A,$thf( sk2 @ sk30 ))]]) ).
thf(76347,plain,
! [A: $i] :
( ( ( sk2 @ sk29 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76299,243]) ).
thf(76348,plain,
! [A: $i] :
( ( ( sk2 @ sk29 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[76347]) ).
thf(76349,plain,
sk2 @ sk29 @ ( sk2 @ sk29 @ segmentP ),
inference(pattern_uni,[status(thm)],[76348:[bind(A,$thf( sk2 @ sk29 ))]]) ).
thf(17781,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk12 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,225]) ).
thf(17782,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk12 @ ssItem ) ),
inference(simp,[status(thm)],[17781]) ).
thf(17783,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk12 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[17782:[bind(A,$thf( sk1 ))]]) ).
thf(55895,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ sk23 )
= ( A @ tl ) )
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[106,291]) ).
thf(55896,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ sk23 )
= ( A @ tl ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[55895]) ).
thf(55897,plain,
( ( ( sk1 @ sk23 )
= ( sk1 @ tl ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[55896:[bind(A,$thf( sk1 ))]]) ).
thf(52124,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk23 @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[106,290]) ).
thf(52125,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk23 @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[52124]) ).
thf(52126,plain,
( ( sk1 @ sk23 @ ssList )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[52125:[bind(A,$thf( sk1 ))]]) ).
thf(63054,plain,
( ( ( sk1 @ sk23 )
!= ( sk1 @ sk23 ) )
| ( sk1 @ tl @ ssList )
| ( sk1 = nil )
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[55897,52126]) ).
thf(63055,plain,
( ( ( sk1 @ sk23 )
!= ( sk1 @ sk23 ) )
| ( sk1 @ tl @ ssList )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[63054]) ).
thf(63056,plain,
( ( sk1 @ tl @ ssList )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[63055:[]]) ).
thf(7157,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk1 @ ( nil @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[649,6551]) ).
thf(7158,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( sk1 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[7157]) ).
thf(7178,plain,
( ( sk1 != nil )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[7158]) ).
thf(7190,plain,
( ( sk1 != nil )
| ~ ( sk1 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[7178]) ).
thf(63704,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ neq ) )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[63056,7190]) ).
thf(63705,plain,
( ( sk1 != sk1 )
| ~ ( sk1 @ ( nil @ neq ) )
| ( sk1 @ tl @ ssList ) ),
inference(simp,[status(thm)],[63704]) ).
thf(63706,plain,
( ~ ( sk1 @ ( nil @ neq ) )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[63705:[]]) ).
thf(11924,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11310,254]) ).
thf(11925,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[11924]) ).
thf(11926,plain,
( ~ ( sk2 @ sk7 @ ( sk2 @ sk7 @ neq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[11925:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(211,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk8 @ ( A @ sk7 @ leq ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[205]) ).
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(237,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(238,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)],[237]) ).
thf(36706,plain,
! [A: $i] :
( ( ( sk2 @ sk17 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[35933,273]) ).
thf(36707,plain,
! [A: $i] :
( ( ( sk2 @ sk17 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[36706]) ).
thf(36708,plain,
( ~ ( sk2 @ sk17 @ ( nil @ memberP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[36707:[bind(A,$thf( sk2 @ sk17 ))]]) ).
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(119,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(120,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)],[119]) ).
thf(121,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[120]) ).
thf(4219,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,243]) ).
thf(4220,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[4219]) ).
thf(4221,plain,
sk1 @ ( sk1 @ segmentP ),
inference(pattern_uni,[status(thm)],[4220:[bind(A,$thf( sk1 ))]]) ).
thf(6561,plain,
( ( sk1 != sk1 )
| ( sk1 @ ( nil @ segmentP ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[5932,4221]) ).
thf(6562,plain,
( ( sk1 @ ( nil @ segmentP ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[6561:[]]) ).
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(475,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(922,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,412]) ).
thf(923,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) ) ),
inference(simp,[status(thm)],[922]) ).
thf(924,plain,
nil @ ( sk2 @ frontsegP ),
inference(pattern_uni,[status(thm)],[923:[bind(A,$thf( sk2 ))]]) ).
thf(54547,plain,
! [A: $i] :
( ( ( sk1 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[52126,285]) ).
thf(54548,plain,
! [A: $i] :
( ( ( sk1 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[54547]) ).
thf(54549,plain,
( ( nil @ ( sk1 @ sk23 @ segmentP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[54548:[bind(A,$thf( sk1 @ sk23 ))]]) ).
thf(63021,plain,
( ( ( sk1 @ sk23 )
!= ( sk1 @ sk23 ) )
| ( nil @ ( sk1 @ tl @ segmentP ) )
| ( sk1 = nil )
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[55897,54549]) ).
thf(63022,plain,
( ( ( sk1 @ sk23 )
!= ( sk1 @ sk23 ) )
| ( nil @ ( sk1 @ tl @ segmentP ) )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[63021]) ).
thf(63023,plain,
( ( nil @ ( sk1 @ tl @ segmentP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[63022:[]]) ).
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(353,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(75,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ cyclefreeP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax59) ).
thf(444,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ cyclefreeP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(445,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[444]) ).
thf(2775,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[128,445]) ).
thf(2776,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP ) ),
inference(simp,[status(thm)],[2775]) ).
thf(2777,plain,
nil @ ( sk6 @ cons ) @ cyclefreeP,
inference(pattern_uni,[status(thm)],[2776:[bind(A,$thf( sk6 ))]]) ).
thf(47573,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47487,285]) ).
thf(47574,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[47573]) ).
thf(47575,plain,
nil @ ( nil @ ( nil @ sk22 ) @ segmentP ),
inference(pattern_uni,[status(thm)],[47574:[bind(A,$thf( nil @ ( nil @ sk22 ) ))]]) ).
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(147,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(59338,plain,
! [A: $i] :
( ( ( sk1 @ sk27 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[58656,338]) ).
thf(59339,plain,
! [A: $i] :
( ( ( sk1 @ sk27 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ totalorderP ) ),
inference(simp,[status(thm)],[59338]) ).
thf(59340,plain,
( ( nil @ ( sk1 @ sk27 @ rearsegP ) )
| ( sk1 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[59339:[bind(A,$thf( sk1 @ sk27 ))]]) ).
thf(3806,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[127,457]) ).
thf(3807,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP ) ),
inference(simp,[status(thm)],[3806]) ).
thf(3808,plain,
nil @ ( sk5 @ cons ) @ strictorderP,
inference(pattern_uni,[status(thm)],[3807:[bind(A,$thf( sk5 ))]]) ).
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(133,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(11488,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11262,436]) ).
thf(11489,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[11488]) ).
thf(11490,plain,
( ( nil @ ( sk1 @ sk7 @ cons ) @ duplicatefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[11489:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(12905,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[12471,157]) ).
thf(12906,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[12905]) ).
thf(12907,plain,
( ( sk2 @ sk8 @ ( sk2 @ sk8 @ leq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12906:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(4222,plain,
! [A: $i] :
( ( ( A @ ( A @ segmentP ) )
!= ( sk2 @ ( sk2 @ segmentP ) ) )
| ~ ( sk2 @ totalorderedP )
| ~ $true
| ~ ( sk2 @ ( sk1 @ neq ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[243,1450]) ).
thf(4223,plain,
! [A: $i] :
( ( ( A @ ( A @ segmentP ) )
!= ( sk2 @ ( sk2 @ segmentP ) ) )
| ~ ( sk2 @ totalorderedP )
| ~ ( sk2 @ ( sk1 @ neq ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[4222]) ).
thf(4224,plain,
( ~ ( sk2 @ totalorderedP )
| ~ ( sk2 @ ( sk1 @ neq ) )
| ~ ( sk2 @ ssList ) ),
inference(pattern_uni,[status(thm)],[4223:[bind(A,$thf( sk2 ))]]) ).
thf(4284,plain,
( ~ ( sk2 @ totalorderedP )
| ~ ( sk2 @ ( sk1 @ neq ) )
| ~ $true ),
inference(rewrite,[status(thm)],[4224,105]) ).
thf(4285,plain,
( ~ ( sk2 @ totalorderedP )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[4284]) ).
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(131,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(132,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)],[131]) ).
thf(20742,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,228]) ).
thf(20743,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssList ) ),
inference(simp,[status(thm)],[20742]) ).
thf(20744,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk16 @ ssList ) ),
inference(pattern_uni,[status(thm)],[20743:[bind(A,$thf( sk2 ))]]) ).
thf(21179,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[20744,285]) ).
thf(21180,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[21179]) ).
thf(21181,plain,
( ( nil @ ( sk2 @ sk16 @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[21180:[bind(A,$thf( sk2 @ sk16 ))]]) ).
thf(82100,plain,
! [A: $i] :
( ( ( sk2 @ sk30 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81958,245]) ).
thf(82101,plain,
! [A: $i] :
( ( ( sk2 @ sk30 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[82100]) ).
thf(82102,plain,
nil @ ( sk2 @ sk30 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[82101:[bind(A,$thf( sk2 @ sk30 ))]]) ).
thf(47625,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[47487,236]) ).
thf(47626,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[47625]) ).
thf(47627,plain,
( ( nil @ ( nil @ ( nil @ sk22 ) @ app ) )
= ( nil @ ( nil @ sk22 ) ) ),
inference(pattern_uni,[status(thm)],[47626:[bind(A,$thf( nil @ ( nil @ sk22 ) ))]]) ).
thf(300,plain,
! [A: $i] :
( ( A @ totalorderP )
| ( A @ sk26 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[293]) ).
thf(65283,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk26 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,300]) ).
thf(65284,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk26 @ ssList ) ),
inference(simp,[status(thm)],[65283]) ).
thf(65285,plain,
( ( sk2 @ totalorderP )
| ( sk2 @ sk26 @ ssList ) ),
inference(pattern_uni,[status(thm)],[65284:[bind(A,$thf( sk2 ))]]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ geq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax89) ).
thf(160,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(161,plain,
! [A: $i] :
( ( A @ ( A @ geq ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[160]) ).
thf(11789,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11310,161]) ).
thf(11790,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[11789]) ).
thf(11791,plain,
( ( sk2 @ sk7 @ ( sk2 @ sk7 @ geq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[11790:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(82208,plain,
! [A: $i] :
( ( ( sk2 @ sk30 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81958,254]) ).
thf(82209,plain,
! [A: $i] :
( ( ( sk2 @ sk30 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[82208]) ).
thf(82210,plain,
~ ( sk2 @ sk30 @ ( sk2 @ sk30 @ neq ) ),
inference(pattern_uni,[status(thm)],[82209:[bind(A,$thf( sk2 @ sk30 ))]]) ).
thf(83683,plain,
( ( ( sk2 @ sk30 @ ( sk2 @ sk30 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9114,82210]) ).
thf(83684,plain,
( ( sk2 @ sk30 @ ( sk2 @ sk30 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[83683]) ).
thf(83768,plain,
( ( ( sk2 @ sk30 )
!= nil )
| ( ( sk2 @ sk30 )
!= sk2 ) ),
inference(simp,[status(thm)],[83684]) ).
thf(11670,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11262,273]) ).
thf(11671,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[11670]) ).
thf(11672,plain,
( ~ ( sk1 @ sk7 @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[11671:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(11685,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11262,254]) ).
thf(11686,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[11685]) ).
thf(11687,plain,
( ~ ( sk1 @ sk7 @ ( sk1 @ sk7 @ neq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[11686:[bind(A,$thf( sk1 @ sk7 ))]]) ).
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(534,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(81965,plain,
! [A: $i] :
( ( ( sk2 @ sk30 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81958,340]) ).
thf(81966,plain,
! [A: $i] :
( ( ( sk2 @ sk30 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP ) ),
inference(simp,[status(thm)],[81965]) ).
thf(81967,plain,
nil @ ( sk2 @ sk30 @ cons ) @ equalelemsP,
inference(pattern_uni,[status(thm)],[81966:[bind(A,$thf( sk2 @ sk30 ))]]) ).
thf(222,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)],[221]) ).
thf(232,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)],[222]) ).
thf(233,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)],[232]) ).
thf(12896,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[12471,340]) ).
thf(12897,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[12896]) ).
thf(12898,plain,
( ( nil @ ( sk2 @ sk8 @ cons ) @ equalelemsP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12897:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(40,axiom,
nil @ duplicatefreeP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax72) ).
thf(248,plain,
nil @ duplicatefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(55092,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[55041,366]) ).
thf(55093,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[55092]) ).
thf(55094,plain,
~ ( sk2 @ sk23 @ ( sk2 @ sk23 @ neq ) ),
inference(pattern_uni,[status(thm)],[55093:[bind(A,$thf( sk2 @ sk23 ))]]) ).
thf(64227,plain,
~ ( sk2 @ tl @ ( sk2 @ tl @ neq ) ),
inference(rewrite,[status(thm)],[55094,64220]) ).
thf(19384,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[18967,412]) ).
thf(19385,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[19384]) ).
thf(19386,plain,
( ( nil @ ( sk2 @ sk14 @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[19385:[bind(A,$thf( sk2 @ sk14 ))]]) ).
thf(18237,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[17783,273]) ).
thf(18238,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[18237]) ).
thf(18239,plain,
( ~ ( sk1 @ sk12 @ ( nil @ memberP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[18238:[bind(A,$thf( sk1 @ sk12 ))]]) ).
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(201,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(214,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk10 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[205]) ).
thf(14261,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,214]) ).
thf(14262,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ssList ) ),
inference(simp,[status(thm)],[14261]) ).
thf(14263,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk10 @ ssList ) ),
inference(pattern_uni,[status(thm)],[14262:[bind(A,$thf( sk2 ))]]) ).
thf(47729,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[47487,258]) ).
thf(47730,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[47729]) ).
thf(47731,plain,
( ( nil @ ( nil @ sk22 ) @ ( nil @ app ) )
= ( nil @ ( nil @ sk22 ) ) ),
inference(pattern_uni,[status(thm)],[47730:[bind(A,$thf( nil @ ( nil @ sk22 ) ))]]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ tl @ ssList ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
thf(334,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ tl @ ssList ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(33015,plain,
( ( ( sk6 @ ssItem )
!= ( sk1 @ ssItem ) )
| ~ ( nil @ ssItem )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[128,29344]) ).
thf(33016,plain,
( ( ( sk6 @ ssItem )
!= ( sk1 @ ssItem ) )
| ~ ( nil @ ssItem )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[33015]) ).
thf(33282,plain,
( ( sk6 != sk1 )
| ~ ( nil @ ssItem )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[33016]) ).
thf(38661,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk18 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,264]) ).
thf(38662,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk18 @ ssItem ) ),
inference(simp,[status(thm)],[38661]) ).
thf(38663,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk18 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[38662:[bind(A,$thf( sk2 ))]]) ).
thf(57838,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[56874,338]) ).
thf(57839,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ totalorderP ) ),
inference(simp,[status(thm)],[57838]) ).
thf(57840,plain,
( ( nil @ ( sk2 @ sk28 @ rearsegP ) )
| ( sk2 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[57839:[bind(A,$thf( sk2 @ sk28 ))]]) ).
thf(1438,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[127,245]) ).
thf(1439,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[1438]) ).
thf(1440,plain,
nil @ ( sk5 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[1439:[bind(A,$thf( sk5 ))]]) ).
thf(4342,plain,
( ( ( nil @ ( sk5 @ cons ) @ totalorderedP )
!= ( sk2 @ totalorderedP ) )
| ~ $true
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[1440,4285]) ).
thf(4343,plain,
( ( ( nil @ ( sk5 @ cons ) @ totalorderedP )
!= ( sk2 @ totalorderedP ) )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[4342]) ).
thf(4344,plain,
( ( ( nil @ ( sk5 @ cons ) )
!= sk2 )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[4343]) ).
thf(26,axiom,
nil @ cyclefreeP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax60) ).
thf(192,plain,
nil @ cyclefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
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(162,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(163,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)],[162]) ).
thf(165,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( B @ ( A @ lt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[163]) ).
thf(11906,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11310,405]) ).
thf(11907,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[11906]) ).
thf(11908,plain,
( ( nil @ ( sk2 @ sk7 @ cons ) @ totalorderP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[11907:[bind(A,$thf( sk2 @ sk7 ))]]) ).
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(274,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(275,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)],[274]) ).
thf(786,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,285]) ).
thf(787,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[786]) ).
thf(788,plain,
nil @ ( sk1 @ segmentP ),
inference(pattern_uni,[status(thm)],[787:[bind(A,$thf( sk1 ))]]) ).
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(136,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(137,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[136]) ).
thf(58719,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk27 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,295]) ).
thf(58720,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk27 @ ssList ) ),
inference(simp,[status(thm)],[58719]) ).
thf(58721,plain,
( ( sk2 @ totalorderP )
| ( sk2 @ sk27 @ ssList ) ),
inference(pattern_uni,[status(thm)],[58720:[bind(A,$thf( sk2 ))]]) ).
thf(59706,plain,
! [A: $i] :
( ( ( sk2 @ sk27 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[58721,338]) ).
thf(59707,plain,
! [A: $i] :
( ( ( sk2 @ sk27 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ totalorderP ) ),
inference(simp,[status(thm)],[59706]) ).
thf(59708,plain,
( ( nil @ ( sk2 @ sk27 @ rearsegP ) )
| ( sk2 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[59707:[bind(A,$thf( sk2 @ sk27 ))]]) ).
thf(229,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ sk13 @ ( A @ sk12 @ lt ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[221]) ).
thf(208,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk11 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[205]) ).
thf(11987,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,208]) ).
thf(11988,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssList ) ),
inference(simp,[status(thm)],[11987]) ).
thf(11989,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk11 @ ssList ) ),
inference(pattern_uni,[status(thm)],[11988:[bind(A,$thf( sk2 ))]]) ).
thf(12338,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11989,338]) ).
thf(12339,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[12338]) ).
thf(12340,plain,
( ( nil @ ( sk2 @ sk11 @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12339:[bind(A,$thf( sk2 @ sk11 ))]]) ).
thf(14246,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,214]) ).
thf(14247,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ssList ) ),
inference(simp,[status(thm)],[14246]) ).
thf(14248,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk10 @ ssList ) ),
inference(pattern_uni,[status(thm)],[14247:[bind(A,$thf( sk1 ))]]) ).
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(317,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(318,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( B @ hd @ ( A @ lt ) )
| ~ ( B @ strictorderedP )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) )
& ( ( B @ ( A @ cons ) @ strictorderedP )
| ( nil != B )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) )
& ( ( B @ hd @ ( A @ lt ) )
| ( nil = B )
| ~ ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) )
& ( ( B @ strictorderedP )
| ( nil = B )
| ~ ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) )
& ( ( nil != B )
| ( nil = B )
| ~ ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ) ),
inference(cnf,[status(esa)],[317]) ).
thf(319,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( B @ hd @ ( A @ lt ) )
| ~ ( B @ strictorderedP )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[318]) ).
thf(329,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( B @ hd @ ( A @ lt ) )
| ~ ( B @ strictorderedP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( nil = B ) ),
inference(lifteq,[status(thm)],[319]) ).
thf(80,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ rearsegP ) )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax52) ).
thf(466,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(467,plain,
! [A: $i] :
( ( ( A @ ( nil @ rearsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) )
& ( ( nil = A )
| ~ ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[466]) ).
thf(469,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[467]) ).
thf(471,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[469]) ).
thf(472,plain,
( ( nil @ ( nil @ rearsegP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[471]) ).
thf(664,plain,
( ( nil @ ( nil @ rearsegP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[472,382]) ).
thf(665,plain,
nil @ ( nil @ rearsegP ),
inference(simp,[status(thm)],[664]) ).
thf(21185,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[20744,412]) ).
thf(21186,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[21185]) ).
thf(21187,plain,
( ( nil @ ( sk2 @ sk16 @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[21186:[bind(A,$thf( sk2 @ sk16 ))]]) ).
thf(1390,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[127,171]) ).
thf(1391,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[1390]) ).
thf(1392,plain,
nil @ ( sk5 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[1391:[bind(A,$thf( sk5 ))]]) ).
thf(4078,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[127,161]) ).
thf(4079,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) ) ),
inference(simp,[status(thm)],[4078]) ).
thf(4080,plain,
sk5 @ ( sk5 @ geq ),
inference(pattern_uni,[status(thm)],[4079:[bind(A,$thf( sk5 ))]]) ).
thf(82041,plain,
! [A: $i] :
( ( ( sk2 @ sk30 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81958,457]) ).
thf(82042,plain,
! [A: $i] :
( ( ( sk2 @ sk30 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP ) ),
inference(simp,[status(thm)],[82041]) ).
thf(82043,plain,
nil @ ( sk2 @ sk30 @ cons ) @ strictorderP,
inference(pattern_uni,[status(thm)],[82042:[bind(A,$thf( sk2 @ sk30 ))]]) ).
thf(4992,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[382,366]) ).
thf(4993,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[4992]) ).
thf(4994,plain,
~ ( nil @ ( nil @ neq ) ),
inference(pattern_uni,[status(thm)],[4993:[bind(A,$thf( nil ))]]) ).
thf(34532,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk19 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,261]) ).
thf(34533,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk19 @ ssList ) ),
inference(simp,[status(thm)],[34532]) ).
thf(34534,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk19 @ ssList ) ),
inference(pattern_uni,[status(thm)],[34533:[bind(A,$thf( sk2 ))]]) ).
thf(56807,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk28 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,294]) ).
thf(56808,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk28 @ ssList ) ),
inference(simp,[status(thm)],[56807]) ).
thf(56809,plain,
( ( sk1 @ totalorderP )
| ( sk1 @ sk28 @ ssList ) ),
inference(pattern_uni,[status(thm)],[56808:[bind(A,$thf( sk1 ))]]) ).
thf(57336,plain,
! [A: $i] :
( ( ( sk1 @ sk28 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[56809,412]) ).
thf(57337,plain,
! [A: $i] :
( ( ( sk1 @ sk28 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ totalorderP ) ),
inference(simp,[status(thm)],[57336]) ).
thf(57338,plain,
( ( nil @ ( sk1 @ sk28 @ frontsegP ) )
| ( sk1 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[57337:[bind(A,$thf( sk1 @ sk28 ))]]) ).
thf(574,plain,
( ( sk2 != sk2 )
| ( sk1 @ ( nil @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[571,561]) ).
thf(575,plain,
( ( sk1 @ ( nil @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(pattern_uni,[status(thm)],[574:[]]) ).
thf(718,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ( sk1 @ ( nil @ segmentP ) )
| ~ $true
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[606,575]) ).
thf(719,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[718]) ).
thf(731,plain,
( ( nil != nil )
| ( sk2 != sk1 )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[719]) ).
thf(738,plain,
( ( sk2 != sk1 )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[731]) ).
thf(110,plain,
( ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) )
| ( nil != sk1 ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(114,plain,
( ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) )
| ( sk1 != nil ) ),
inference(lifteq,[status(thm)],[110]) ).
thf(562,plain,
( ~ $true
| ~ ( nil @ ( sk1 @ neq ) )
| ( sk1 != nil ) ),
inference(rewrite,[status(thm)],[114,561]) ).
thf(563,plain,
( ~ ( nil @ ( sk1 @ neq ) )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[562]) ).
thf(632,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ~ $true
| ( sk1 != nil )
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[118,563]) ).
thf(633,plain,
( ( ( nil @ ( sk2 @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[632]) ).
thf(636,plain,
( ( nil != nil )
| ( sk2 != sk1 )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[633]) ).
thf(640,plain,
( ( sk2 != sk1 )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[636]) ).
thf(8744,plain,
( ( sk1 != sk1 )
| ( sk2 != sk1 )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[7957,640]) ).
thf(8745,plain,
( ( sk1 != sk1 )
| ( sk2 != sk1 )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[8744]) ).
thf(8746,plain,
( ( sk2 != sk1 )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[8745:[]]) ).
thf(8893,plain,
( ( ( sk1 @ ( nil @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ( sk2 != sk1 )
| ~ $true
| ( sk2 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[738,8746]) ).
thf(8894,plain,
( ( ( sk1 @ ( nil @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[8893]) ).
thf(8895,plain,
sk2 != sk1,
inference(pattern_uni,[status(thm)],[8894:[]]) ).
thf(11732,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11310,340]) ).
thf(11733,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[11732]) ).
thf(11734,plain,
( ( nil @ ( sk2 @ sk7 @ cons ) @ equalelemsP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[11733:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(872,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,338]) ).
thf(873,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[872]) ).
thf(874,plain,
nil @ ( sk2 @ rearsegP ),
inference(pattern_uni,[status(thm)],[873:[bind(A,$thf( sk2 ))]]) ).
thf(11882,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11310,171]) ).
thf(11883,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[11882]) ).
thf(11884,plain,
( ( nil @ ( sk2 @ sk7 @ cons ) @ strictorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[11883:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(23542,plain,
( ( ( sk6 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk5 != nil )
| ~ $true
| ~ ( sk6 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[649,6246]) ).
thf(23543,plain,
( ( ( sk6 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk5 != nil )
| ~ ( sk6 @ ssList ) ),
inference(simp,[status(thm)],[23542]) ).
thf(23621,plain,
( ( sk6 != nil )
| ( nil != nil )
| ( sk5 != nil )
| ~ ( sk6 @ ssList ) ),
inference(simp,[status(thm)],[23543]) ).
thf(23670,plain,
( ( sk6 != nil )
| ( sk5 != nil )
| ~ ( sk6 @ ssList ) ),
inference(simp,[status(thm)],[23621]) ).
thf(23727,plain,
( ( ( sk6 @ ssList )
!= ( nil @ ssList ) )
| ( sk6 != nil )
| ( sk5 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[382,23670]) ).
thf(23728,plain,
( ( ( sk6 @ ssList )
!= ( nil @ ssList ) )
| ( sk6 != nil )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[23727]) ).
thf(23805,plain,
( ( sk6 != nil )
| ( sk6 != nil )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[23728]) ).
thf(23837,plain,
( ( sk6 != nil )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[23805]) ).
thf(4225,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,243]) ).
thf(4226,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[4225]) ).
thf(4227,plain,
sk2 @ ( sk2 @ segmentP ),
inference(pattern_uni,[status(thm)],[4226:[bind(A,$thf( sk2 ))]]) ).
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(140,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(141,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[140]) ).
thf(8741,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[7957,7190]) ).
thf(8742,plain,
( ( sk1 != sk1 )
| ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[8741]) ).
thf(8743,plain,
( ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[8742:[]]) ).
thf(12744,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[12423,445]) ).
thf(12745,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[12744]) ).
thf(12746,plain,
( ( nil @ ( sk1 @ sk8 @ cons ) @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12745:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(11664,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11262,146]) ).
thf(11665,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[11664]) ).
thf(11666,plain,
( ~ ( sk1 @ sk7 @ ( sk1 @ sk7 @ lt ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[11665:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(13537,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[13162,338]) ).
thf(13538,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[13537]) ).
thf(13539,plain,
( ( nil @ ( sk2 @ sk9 @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[13538:[bind(A,$thf( sk2 @ sk9 ))]]) ).
thf(40755,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk21 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,268]) ).
thf(40756,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk21 @ ssList ) ),
inference(simp,[status(thm)],[40755]) ).
thf(40757,plain,
( ( sk1 @ strictorderedP )
| ( sk1 @ sk21 @ ssList ) ),
inference(pattern_uni,[status(thm)],[40756:[bind(A,$thf( sk1 ))]]) ).
thf(41282,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[40757,338]) ).
thf(41283,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[41282]) ).
thf(41284,plain,
( ( nil @ ( sk1 @ sk21 @ rearsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[41283:[bind(A,$thf( sk1 @ sk21 ))]]) ).
thf(41171,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[40757,412]) ).
thf(41172,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[41171]) ).
thf(41173,plain,
( ( nil @ ( sk1 @ sk21 @ frontsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[41172:[bind(A,$thf( sk1 @ sk21 ))]]) ).
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(123,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(124,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)],[123]) ).
thf(11494,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11262,157]) ).
thf(11495,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[11494]) ).
thf(11496,plain,
( ( sk1 @ sk7 @ ( sk1 @ sk7 @ leq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[11495:[bind(A,$thf( sk1 @ sk7 ))]]) ).
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(193,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(97,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( nil
!= ( A @ ( B @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
thf(537,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( nil
!= ( A @ ( B @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(14426,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[14248,285]) ).
thf(14427,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[14426]) ).
thf(14428,plain,
( ( nil @ ( sk1 @ sk10 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[14427:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(55165,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[55041,236]) ).
thf(55166,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[55165]) ).
thf(55167,plain,
( ( nil @ ( sk2 @ sk23 @ app ) )
= ( sk2 @ sk23 ) ),
inference(pattern_uni,[status(thm)],[55166:[bind(A,$thf( sk2 @ sk23 ))]]) ).
thf(64222,plain,
( ( nil @ ( sk2 @ tl @ app ) )
= ( sk2 @ tl ) ),
inference(rewrite,[status(thm)],[55167,64220]) ).
thf(12953,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[12471,161]) ).
thf(12954,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[12953]) ).
thf(12955,plain,
( ( sk2 @ sk8 @ ( sk2 @ sk8 @ geq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12954:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(81976,plain,
! [A: $i] :
( ( ( sk2 @ sk30 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81958,157]) ).
thf(81977,plain,
! [A: $i] :
( ( ( sk2 @ sk30 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[81976]) ).
thf(81978,plain,
sk2 @ sk30 @ ( sk2 @ sk30 @ leq ),
inference(pattern_uni,[status(thm)],[81977:[bind(A,$thf( sk2 @ sk30 ))]]) ).
thf(35864,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk17 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,262]) ).
thf(35865,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk17 @ ssItem ) ),
inference(simp,[status(thm)],[35864]) ).
thf(35866,plain,
( ( sk1 @ strictorderedP )
| ( sk1 @ sk17 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[35865:[bind(A,$thf( sk1 ))]]) ).
thf(36415,plain,
! [A: $i] :
( ( ( sk1 @ sk17 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[35866,273]) ).
thf(36416,plain,
! [A: $i] :
( ( ( sk1 @ sk17 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[36415]) ).
thf(36417,plain,
( ~ ( sk1 @ sk17 @ ( nil @ memberP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[36416:[bind(A,$thf( sk1 @ sk17 ))]]) ).
thf(82163,plain,
! [A: $i] :
( ( ( sk2 @ sk30 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81958,171]) ).
thf(82164,plain,
! [A: $i] :
( ( ( sk2 @ sk30 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[82163]) ).
thf(82165,plain,
nil @ ( sk2 @ sk30 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[82164:[bind(A,$thf( sk2 @ sk30 ))]]) ).
thf(82048,plain,
! [A: $i] :
( ( ( sk2 @ sk30 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81958,161]) ).
thf(82049,plain,
! [A: $i] :
( ( ( sk2 @ sk30 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) ) ),
inference(simp,[status(thm)],[82048]) ).
thf(82050,plain,
sk2 @ sk30 @ ( sk2 @ sk30 @ geq ),
inference(pattern_uni,[status(thm)],[82049:[bind(A,$thf( sk2 @ sk30 ))]]) ).
thf(1427,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[128,245]) ).
thf(1428,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[1427]) ).
thf(1429,plain,
nil @ ( sk6 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[1428:[bind(A,$thf( sk6 ))]]) ).
thf(11972,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,208]) ).
thf(11973,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssList ) ),
inference(simp,[status(thm)],[11972]) ).
thf(11974,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk11 @ ssList ) ),
inference(pattern_uni,[status(thm)],[11973:[bind(A,$thf( sk1 ))]]) ).
thf(12189,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11974,338]) ).
thf(12190,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[12189]) ).
thf(12191,plain,
( ( nil @ ( sk1 @ sk11 @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12190:[bind(A,$thf( sk1 @ sk11 ))]]) ).
thf(35124,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[34534,285]) ).
thf(35125,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[35124]) ).
thf(35126,plain,
( ( nil @ ( sk2 @ sk19 @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[35125:[bind(A,$thf( sk2 @ sk19 ))]]) ).
thf(41154,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[40757,285]) ).
thf(41155,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[41154]) ).
thf(41156,plain,
( ( nil @ ( sk1 @ sk21 @ segmentP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[41155:[bind(A,$thf( sk1 @ sk21 ))]]) ).
thf(266,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ sk18 @ ( A @ sk17 @ lt ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[260]) ).
thf(223,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk15 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[221]) ).
thf(16898,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk15 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,223]) ).
thf(16899,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk15 @ ssList ) ),
inference(simp,[status(thm)],[16898]) ).
thf(16900,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk15 @ ssList ) ),
inference(pattern_uni,[status(thm)],[16899:[bind(A,$thf( sk1 ))]]) ).
thf(17201,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[16900,338]) ).
thf(17202,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[17201]) ).
thf(17203,plain,
( ( nil @ ( sk1 @ sk15 @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[17202:[bind(A,$thf( sk1 @ sk15 ))]]) ).
thf(919,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,412]) ).
thf(920,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) ) ),
inference(simp,[status(thm)],[919]) ).
thf(921,plain,
nil @ ( sk1 @ frontsegP ),
inference(pattern_uni,[status(thm)],[920:[bind(A,$thf( sk1 ))]]) ).
thf(230,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk13 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[221]) ).
thf(22592,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk13 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,230]) ).
thf(22593,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk13 @ ssItem ) ),
inference(simp,[status(thm)],[22592]) ).
thf(22594,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk13 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[22593:[bind(A,$thf( sk1 ))]]) ).
thf(6100,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[105,176]) ).
thf(6101,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[6100]) ).
thf(6102,plain,
( ~ ( sk2 @ ( nil @ frontsegP ) )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[6101:[bind(A,$thf( sk2 ))]]) ).
thf(10556,plain,
~ ( sk2 @ ( nil @ frontsegP ) ),
inference(simplifyReflect,[status(thm)],[6102,9335]) ).
thf(12980,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[12471,445]) ).
thf(12981,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[12980]) ).
thf(12982,plain,
( ( nil @ ( sk2 @ sk8 @ cons ) @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12981:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(11735,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11310,436]) ).
thf(11736,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[11735]) ).
thf(11737,plain,
( ( nil @ ( sk2 @ sk7 @ cons ) @ duplicatefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[11736:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(18941,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk14 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,226]) ).
thf(18942,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk14 @ ssList ) ),
inference(simp,[status(thm)],[18941]) ).
thf(18943,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk14 @ ssList ) ),
inference(pattern_uni,[status(thm)],[18942:[bind(A,$thf( sk1 ))]]) ).
thf(19268,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[18943,338]) ).
thf(19269,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[19268]) ).
thf(19270,plain,
( ( nil @ ( sk1 @ sk14 @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[19269:[bind(A,$thf( sk1 @ sk14 ))]]) ).
thf(12652,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[12423,340]) ).
thf(12653,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[12652]) ).
thf(12654,plain,
( ( nil @ ( sk1 @ sk8 @ cons ) @ equalelemsP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12653:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(148,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[147]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A = B ) ),
inference(lifteq,[status(thm)],[148]) ).
thf(19378,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[18967,285]) ).
thf(19379,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[19378]) ).
thf(19380,plain,
( ( nil @ ( sk2 @ sk14 @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[19379:[bind(A,$thf( sk2 @ sk14 ))]]) ).
thf(298,plain,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ sk24 @ ( A @ sk25 @ leq ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[293]) ).
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(513,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(8158,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[105,189]) ).
thf(8159,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[8158]) ).
thf(8160,plain,
( ~ ( sk2 @ ( nil @ segmentP ) )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[8159:[bind(A,$thf( sk2 ))]]) ).
thf(11033,plain,
~ ( sk2 @ ( nil @ segmentP ) ),
inference(simplifyReflect,[status(thm)],[8160,9335]) ).
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(180,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(47714,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47487,338]) ).
thf(47715,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[47714]) ).
thf(47716,plain,
nil @ ( nil @ ( nil @ sk22 ) @ rearsegP ),
inference(pattern_uni,[status(thm)],[47715:[bind(A,$thf( nil @ ( nil @ sk22 ) ))]]) ).
thf(12717,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[12423,161]) ).
thf(12718,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[12717]) ).
thf(12719,plain,
( ( sk1 @ sk8 @ ( sk1 @ sk8 @ geq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12718:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(20718,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,228]) ).
thf(20719,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssList ) ),
inference(simp,[status(thm)],[20718]) ).
thf(20720,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk16 @ ssList ) ),
inference(pattern_uni,[status(thm)],[20719:[bind(A,$thf( sk1 ))]]) ).
thf(3923,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[127,157]) ).
thf(3924,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[3923]) ).
thf(3925,plain,
sk5 @ ( sk5 @ leq ),
inference(pattern_uni,[status(thm)],[3924:[bind(A,$thf( sk5 ))]]) ).
thf(11903,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11310,146]) ).
thf(11904,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[11903]) ).
thf(11905,plain,
( ~ ( sk2 @ sk7 @ ( sk2 @ sk7 @ lt ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[11904:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(54611,plain,
! [A: $i] :
( ( ( sk1 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[52126,412]) ).
thf(54612,plain,
! [A: $i] :
( ( ( sk1 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[54611]) ).
thf(54613,plain,
( ( nil @ ( sk1 @ sk23 @ frontsegP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[54612:[bind(A,$thf( sk1 @ sk23 ))]]) ).
thf(37163,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk20 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,263]) ).
thf(37164,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk20 @ ssList ) ),
inference(simp,[status(thm)],[37163]) ).
thf(37165,plain,
( ( sk1 @ strictorderedP )
| ( sk1 @ sk20 @ ssList ) ),
inference(pattern_uni,[status(thm)],[37164:[bind(A,$thf( sk1 ))]]) ).
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(413,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(22646,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk13 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,230]) ).
thf(22647,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk13 @ ssItem ) ),
inference(simp,[status(thm)],[22646]) ).
thf(22648,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk13 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[22647:[bind(A,$thf( sk2 ))]]) ).
thf(23065,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[22594,273]) ).
thf(23066,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[23065]) ).
thf(23067,plain,
( ~ ( sk1 @ sk13 @ ( nil @ memberP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[23066:[bind(A,$thf( sk1 @ sk13 ))]]) ).
thf(54854,plain,
! [A: $i] :
( ( ( sk1 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[52126,338]) ).
thf(54855,plain,
! [A: $i] :
( ( ( sk1 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[54854]) ).
thf(54856,plain,
( ( nil @ ( sk1 @ sk23 @ rearsegP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[54855:[bind(A,$thf( sk1 @ sk23 ))]]) ).
thf(63043,plain,
( ( ( sk1 @ sk23 )
!= ( sk1 @ sk23 ) )
| ( nil @ ( sk1 @ tl @ rearsegP ) )
| ( sk1 = nil )
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[55897,54856]) ).
thf(63044,plain,
( ( ( sk1 @ sk23 )
!= ( sk1 @ sk23 ) )
| ( nil @ ( sk1 @ tl @ rearsegP ) )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[63043]) ).
thf(63045,plain,
( ( nil @ ( sk1 @ tl @ rearsegP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[63044:[]]) ).
thf(13073,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[12471,273]) ).
thf(13074,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[13073]) ).
thf(13075,plain,
( ~ ( sk2 @ sk8 @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[13074:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(65218,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk26 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,300]) ).
thf(65219,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk26 @ ssList ) ),
inference(simp,[status(thm)],[65218]) ).
thf(65220,plain,
( ( sk1 @ totalorderP )
| ( sk1 @ sk26 @ ssList ) ),
inference(pattern_uni,[status(thm)],[65219:[bind(A,$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(395,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(396,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)],[395]) ).
thf(399,plain,
! [B: $i,A: $i] :
( ( nil
= ( B @ ( A @ app ) ) )
| ( nil != A )
| ( nil != B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[396]) ).
thf(402,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
= nil )
| ( nil != A )
| ( nil != B ) ),
inference(lifteq,[status(thm)],[399]) ).
thf(403,plain,
( ~ ( nil @ ssList )
| ( ( nil @ ( nil @ app ) )
= nil ) ),
inference(simp,[status(thm)],[402]) ).
thf(710,plain,
( ~ $true
| ( ( nil @ ( nil @ app ) )
= nil ) ),
inference(rewrite,[status(thm)],[403,382]) ).
thf(711,plain,
( ( nil @ ( nil @ app ) )
= nil ),
inference(simp,[status(thm)],[710]) ).
thf(12774,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[12423,245]) ).
thf(12775,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[12774]) ).
thf(12776,plain,
( ( nil @ ( sk1 @ sk8 @ cons ) @ totalorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12775:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(279,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk22 ) @ ( B @ app ) )
= A )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[277]) ).
thf(281,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( A @ ( B @ sk22 ) @ ( B @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[279]) ).
thf(12661,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[12423,157]) ).
thf(12662,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[12661]) ).
thf(12663,plain,
( ( sk1 @ sk8 @ ( sk1 @ sk8 @ leq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12662:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(310,plain,
! [A: $i] :
( ( ( A @ sk29 @ ( A @ sk30 @ cons ) )
= A )
| ( nil = A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[307]) ).
thf(313,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ( ( A @ sk29 @ ( A @ sk30 @ cons ) )
= A )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[310]) ).
thf(12714,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[12423,457]) ).
thf(12715,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[12714]) ).
thf(12716,plain,
( ( nil @ ( sk1 @ sk8 @ cons ) @ strictorderP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12715:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(143,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ lt ) )
| ( A = B )
| ~ ( B @ ( A @ leq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[142]) ).
thf(144,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ lt ) )
| ~ ( B @ ( A @ leq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A = B ) ),
inference(lifteq,[status(thm)],[143]) ).
thf(12126,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11974,412]) ).
thf(12127,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[12126]) ).
thf(12128,plain,
( ( nil @ ( sk1 @ sk11 @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12127:[bind(A,$thf( sk1 @ sk11 ))]]) ).
thf(2869,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[128,146]) ).
thf(2870,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[2869]) ).
thf(2871,plain,
~ ( sk6 @ ( sk6 @ lt ) ),
inference(pattern_uni,[status(thm)],[2870:[bind(A,$thf( sk6 ))]]) ).
thf(2880,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ lt ) )
!= ( sk6 @ ( sk6 @ lt ) ) )
| ~ $true
| ~ ( B @ ( A @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[121,2871]) ).
thf(2881,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ lt ) )
!= ( sk6 @ ( sk6 @ lt ) ) )
| ~ ( B @ ( A @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[2880]) ).
thf(2882,plain,
( ~ ( sk6 @ ( sk6 @ gt ) )
| ~ ( sk6 @ ssItem )
| ~ ( sk6 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[2881:[bind(A,$thf( sk6 )),bind(B,$thf( sk6 ))]]) ).
thf(2902,plain,
( ~ ( sk6 @ ( sk6 @ gt ) )
| ~ ( sk6 @ ssItem ) ),
inference(simp,[status(thm)],[2882]) ).
thf(2934,plain,
( ~ ( sk6 @ ( sk6 @ gt ) )
| ~ $true ),
inference(rewrite,[status(thm)],[2902,128]) ).
thf(2935,plain,
~ ( sk6 @ ( sk6 @ gt ) ),
inference(simp,[status(thm)],[2934]) ).
thf(181,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)],[180]) ).
thf(35235,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[34534,338]) ).
thf(35236,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[35235]) ).
thf(35237,plain,
( ( nil @ ( sk2 @ sk19 @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[35236:[bind(A,$thf( sk2 @ sk19 ))]]) ).
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(158,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(159,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)],[158]) ).
thf(2027,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[128,436]) ).
thf(2028,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP ) ),
inference(simp,[status(thm)],[2027]) ).
thf(2029,plain,
nil @ ( sk6 @ cons ) @ duplicatefreeP,
inference(pattern_uni,[status(thm)],[2028:[bind(A,$thf( sk6 ))]]) ).
thf(34844,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[34487,285]) ).
thf(34845,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[34844]) ).
thf(34846,plain,
( ( nil @ ( sk1 @ sk19 @ segmentP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[34845:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(9246,plain,
( ( ( sk6 @ ( sk6 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9114,4870]) ).
thf(9247,plain,
( ( sk6 @ ( sk6 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[9246]) ).
thf(9325,plain,
( ( sk6 != nil )
| ( sk6 != sk2 ) ),
inference(simp,[status(thm)],[9247]) ).
thf(10853,plain,
! [A: $i] :
( ( A != sk6 )
| ( nil != nil )
| ( sk6 != sk2 )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[176,9325]) ).
thf(10854,plain,
! [A: $i] :
( ( A != sk6 )
| ( sk6 != sk2 )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[10853]) ).
thf(10855,plain,
( ( sk6 != sk2 )
| ~ ( sk6 @ ( nil @ frontsegP ) )
| ~ ( sk6 @ ssList ) ),
inference(pattern_uni,[status(thm)],[10854:[bind(A,$thf( sk6 ))]]) ).
thf(90858,plain,
( ( ( sk6 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk6 != sk2 )
| ~ ( sk6 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,10855]) ).
thf(90859,plain,
( ( ( sk6 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk6 != sk2 )
| ~ ( sk6 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[90858]) ).
thf(91178,plain,
( ( sk6 != sk2 )
| ( sk6 != sk2 )
| ~ ( sk6 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[90859]) ).
thf(91205,plain,
( ( sk6 != sk2 )
| ~ ( sk6 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[91178]) ).
thf(17126,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[16900,412]) ).
thf(17127,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[17126]) ).
thf(17128,plain,
( ( nil @ ( sk1 @ sk15 @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[17127:[bind(A,$thf( sk1 @ sk15 ))]]) ).
thf(33199,plain,
( ( ( sk5 @ ssItem )
!= ( sk1 @ ssItem ) )
| ~ ( nil @ ssItem )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[127,29344]) ).
thf(33200,plain,
( ( ( sk5 @ ssItem )
!= ( sk1 @ ssItem ) )
| ~ ( nil @ ssItem )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[33199]) ).
thf(33268,plain,
( ( sk5 != sk1 )
| ~ ( nil @ ssItem )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[33200]) ).
thf(23312,plain,
! [A: $i] :
( ( ( sk2 @ sk13 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[22648,273]) ).
thf(23313,plain,
! [A: $i] :
( ( ( sk2 @ sk13 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[23312]) ).
thf(23314,plain,
( ~ ( sk2 @ sk13 @ ( nil @ memberP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[23313:[bind(A,$thf( sk2 @ sk13 ))]]) ).
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(406,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(32,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( A @ ( B @ cons ) @ ssList ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
thf(218,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( A @ ( B @ cons ) @ ssList ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(219,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[218]) ).
thf(41452,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[40807,285]) ).
thf(41453,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[41452]) ).
thf(41454,plain,
( ( nil @ ( sk2 @ sk21 @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[41453:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(37537,plain,
! [A: $i] :
( ( ( sk1 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[37165,285]) ).
thf(37538,plain,
! [A: $i] :
( ( ( sk1 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[37537]) ).
thf(37539,plain,
( ( nil @ ( sk1 @ sk20 @ segmentP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[37538:[bind(A,$thf( sk1 @ sk20 ))]]) ).
thf(41461,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[40807,412]) ).
thf(41462,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[41461]) ).
thf(41463,plain,
( ( nil @ ( sk2 @ sk21 @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[41462:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(87,axiom,
nil @ equalelemsP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax74) ).
thf(509,plain,
nil @ equalelemsP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(11485,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11262,340]) ).
thf(11486,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[11485]) ).
thf(11487,plain,
( ( nil @ ( sk1 @ sk7 @ cons ) @ equalelemsP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[11486:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(301,plain,
! [A: $i] :
( ( A @ totalorderP )
| ( ( A @ sk28 @ ( A @ sk25 @ cons ) @ ( A @ sk27 @ ( A @ sk24 @ cons ) @ ( A @ sk26 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[293]) ).
thf(303,plain,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ( ( A @ sk28 @ ( A @ sk25 @ cons ) @ ( A @ sk27 @ ( A @ sk24 @ cons ) @ ( A @ sk26 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[301]) ).
thf(267,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)],[260]) ).
thf(270,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)],[267]) ).
thf(271,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)],[270]) ).
thf(55261,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[55041,258]) ).
thf(55262,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[55261]) ).
thf(55263,plain,
( ( sk2 @ sk23 @ ( nil @ app ) )
= ( sk2 @ sk23 ) ),
inference(pattern_uni,[status(thm)],[55262:[bind(A,$thf( sk2 @ sk23 ))]]) ).
thf(64221,plain,
( ( sk2 @ tl @ ( nil @ app ) )
= ( sk2 @ tl ) ),
inference(rewrite,[status(thm)],[55263,64220]) ).
thf(12112,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11974,366]) ).
thf(12113,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[12112]) ).
thf(12114,plain,
( ~ ( sk1 @ sk11 @ ( sk1 @ sk11 @ neq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12113:[bind(A,$thf( sk1 @ sk11 ))]]) ).
thf(213,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk7 @ ( A @ sk8 @ leq ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[205]) ).
thf(12109,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11974,243]) ).
thf(12110,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[12109]) ).
thf(12111,plain,
( ( sk1 @ sk11 @ ( sk1 @ sk11 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12110:[bind(A,$thf( sk1 @ sk11 ))]]) ).
thf(76385,plain,
! [A: $i] :
( ( ( sk2 @ sk29 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76299,285]) ).
thf(76386,plain,
! [A: $i] :
( ( ( sk2 @ sk29 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[76385]) ).
thf(76387,plain,
nil @ ( sk2 @ sk29 @ segmentP ),
inference(pattern_uni,[status(thm)],[76386:[bind(A,$thf( sk2 @ sk29 ))]]) ).
thf(92,axiom,
nil @ strictorderedP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax69) ).
thf(520,plain,
nil @ strictorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(2872,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[127,146]) ).
thf(2873,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[2872]) ).
thf(2874,plain,
~ ( sk5 @ ( sk5 @ lt ) ),
inference(pattern_uni,[status(thm)],[2873:[bind(A,$thf( sk5 ))]]) ).
thf(55089,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[55041,243]) ).
thf(55090,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[55089]) ).
thf(55091,plain,
sk2 @ sk23 @ ( sk2 @ sk23 @ segmentP ),
inference(pattern_uni,[status(thm)],[55090:[bind(A,$thf( sk2 @ sk23 ))]]) ).
thf(64226,plain,
sk2 @ tl @ ( sk2 @ tl @ segmentP ),
inference(rewrite,[status(thm)],[55091,64220]) ).
thf(153,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)],[152]) ).
thf(155,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ geq ) )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[153]) ).
thf(322,plain,
! [B: $i,A: $i] :
( ( B @ strictorderedP )
| ( nil = B )
| ~ ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[318]) ).
thf(330,plain,
! [B: $i,A: $i] :
( ( B @ strictorderedP )
| ~ ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( nil = B ) ),
inference(lifteq,[status(thm)],[322]) ).
thf(12272,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11989,285]) ).
thf(12273,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[12272]) ).
thf(12274,plain,
( ( nil @ ( sk2 @ sk11 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12273:[bind(A,$thf( sk2 @ sk11 ))]]) ).
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(494,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(11667,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11262,405]) ).
thf(11668,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[11667]) ).
thf(11669,plain,
( ( nil @ ( sk1 @ sk7 @ cons ) @ totalorderP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[11668:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(35609,plain,
( ( ( sk6 @ ssItem )
!= ( sk1 @ ssItem ) )
| ( sk6 != nil )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[128,33266]) ).
thf(35610,plain,
( ( ( sk6 @ ssItem )
!= ( sk1 @ ssItem ) )
| ( sk6 != nil )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[35609]) ).
thf(35694,plain,
( ( sk6 != sk1 )
| ( sk6 != nil )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[35610]) ).
thf(197,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ cons ) )
= ( A @ ( nil @ ( B @ cons ) @ app ) ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[196]) ).
thf(198,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( ( A @ ( nil @ ( B @ cons ) @ app ) )
= ( A @ ( B @ cons ) ) ) ),
inference(lifteq,[status(thm)],[197]) ).
thf(1379,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[128,171]) ).
thf(1380,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[1379]) ).
thf(1381,plain,
nil @ ( sk6 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[1380:[bind(A,$thf( sk6 ))]]) ).
thf(21063,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[20720,338]) ).
thf(21064,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[21063]) ).
thf(21065,plain,
( ( nil @ ( sk1 @ sk16 @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[21064:[bind(A,$thf( sk1 @ sk16 ))]]) ).
thf(81970,plain,
! [A: $i] :
( ( ( sk2 @ sk30 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81958,436]) ).
thf(81971,plain,
! [A: $i] :
( ( ( sk2 @ sk30 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP ) ),
inference(simp,[status(thm)],[81970]) ).
thf(81972,plain,
nil @ ( sk2 @ sk30 @ cons ) @ duplicatefreeP,
inference(pattern_uni,[status(thm)],[81971:[bind(A,$thf( sk2 @ sk30 ))]]) ).
thf(299,plain,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ sk25 @ ( A @ sk24 @ leq ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[293]) ).
thf(10840,plain,
! [A: $i] :
( ( A != sk6 )
| ( nil != nil )
| ( sk6 != sk2 )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[189,9325]) ).
thf(10841,plain,
! [A: $i] :
( ( A != sk6 )
| ( sk6 != sk2 )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[10840]) ).
thf(10842,plain,
( ( sk6 != sk2 )
| ~ ( sk6 @ ( nil @ segmentP ) )
| ~ ( sk6 @ ssList ) ),
inference(pattern_uni,[status(thm)],[10841:[bind(A,$thf( sk6 ))]]) ).
thf(60411,plain,
( ( ( sk6 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk6 != sk2 )
| ~ ( sk6 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,10842]) ).
thf(60412,plain,
( ( ( sk6 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk6 != sk2 )
| ~ ( sk6 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[60411]) ).
thf(60617,plain,
( ( sk6 != sk2 )
| ( sk6 != sk2 )
| ~ ( sk6 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[60412]) ).
thf(60726,plain,
( ( sk6 != sk2 )
| ~ ( sk6 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[60617]) ).
thf(60886,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk6 @ ( nil @ segmentP ) ) )
| ( sk6 != sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4221,60726]) ).
thf(60887,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk6 @ ( nil @ segmentP ) ) )
| ( sk6 != sk2 ) ),
inference(simp,[status(thm)],[60886]) ).
thf(60901,plain,
( ( sk6 != sk1 )
| ( sk1 != nil )
| ( sk6 != sk2 ) ),
inference(simp,[status(thm)],[60887]) ).
thf(7415,plain,
( ( ( nil @ ( sk1 @ frontsegP ) )
!= ( sk1 @ ( nil @ frontsegP ) ) )
| ( sk1 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[921,6562]) ).
thf(7416,plain,
( ( ( nil @ ( sk1 @ frontsegP ) )
!= ( sk1 @ ( nil @ frontsegP ) ) )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[7415]) ).
thf(7457,plain,
( ( sk1 != nil )
| ( sk1 != nil )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[7416]) ).
thf(7458,plain,
( ( sk1 != nil )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[7457]) ).
thf(14597,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[14263,412]) ).
thf(14598,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[14597]) ).
thf(14599,plain,
( ( nil @ ( sk2 @ sk10 @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[14598:[bind(A,$thf( sk2 @ sk10 ))]]) ).
thf(76350,plain,
! [A: $i] :
( ( ( sk2 @ sk29 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76299,366]) ).
thf(76351,plain,
! [A: $i] :
( ( ( sk2 @ sk29 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[76350]) ).
thf(76352,plain,
~ ( sk2 @ sk29 @ ( sk2 @ sk29 @ neq ) ),
inference(pattern_uni,[status(thm)],[76351:[bind(A,$thf( sk2 @ sk29 ))]]) ).
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(521,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( A @ ( B @ rearsegP ) )
& ( B @ ( A @ rearsegP ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(16919,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk15 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,223]) ).
thf(16920,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk15 @ ssList ) ),
inference(simp,[status(thm)],[16919]) ).
thf(16921,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk15 @ ssList ) ),
inference(pattern_uni,[status(thm)],[16920:[bind(A,$thf( sk2 ))]]) ).
thf(17311,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[16921,285]) ).
thf(17312,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[17311]) ).
thf(17313,plain,
( ( nil @ ( sk2 @ sk15 @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[17312:[bind(A,$thf( sk2 @ sk15 ))]]) ).
thf(134,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[133]) ).
thf(135,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A = B ) ),
inference(lifteq,[status(thm)],[134]) ).
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(239,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(240,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)],[239]) ).
thf(241,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)],[240]) ).
thf(61192,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk25 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,297]) ).
thf(61193,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk25 @ ssItem ) ),
inference(simp,[status(thm)],[61192]) ).
thf(61194,plain,
( ( sk2 @ totalorderP )
| ( sk2 @ sk25 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[61193:[bind(A,$thf( sk2 ))]]) ).
thf(81,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax42) ).
thf(473,plain,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(77004,plain,
( ( ( sk2 @ sk29 @ ( sk2 @ sk29 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9114,76352]) ).
thf(77005,plain,
( ( sk2 @ sk29 @ ( sk2 @ sk29 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[77004]) ).
thf(77089,plain,
( ( ( sk2 @ sk29 )
!= nil )
| ( ( sk2 @ sk29 )
!= sk2 ) ),
inference(simp,[status(thm)],[77005]) ).
thf(90,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( B @ ( A @ rearsegP ) )
=> ( B @ ( A @ ( C @ app ) @ rearsegP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax50) ).
thf(516,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( B @ ( A @ rearsegP ) )
=> ( B @ ( A @ ( C @ app ) @ rearsegP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(11577,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11262,445]) ).
thf(11578,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[11577]) ).
thf(11579,plain,
( ( nil @ ( sk1 @ sk7 @ cons ) @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[11578:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(12852,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[12423,254]) ).
thf(12853,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[12852]) ).
thf(12854,plain,
( ~ ( sk1 @ sk8 @ ( sk1 @ sk8 @ neq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12853:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(19180,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[18943,285]) ).
thf(19181,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[19180]) ).
thf(19182,plain,
( ( nil @ ( sk1 @ sk14 @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[19181:[bind(A,$thf( sk1 @ sk14 ))]]) ).
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(458,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(62061,plain,
! [A: $i] :
( ( ( sk2 @ sk25 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[61194,273]) ).
thf(62062,plain,
! [A: $i] :
( ( ( sk2 @ sk25 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ totalorderP ) ),
inference(simp,[status(thm)],[62061]) ).
thf(62063,plain,
( ~ ( sk2 @ sk25 @ ( nil @ memberP ) )
| ( sk2 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[62062:[bind(A,$thf( sk2 @ sk25 ))]]) ).
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(525,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( ? [C: $i] :
( ? [D: $i] :
( ( ( D @ ( B @ cons ) @ ( C @ app ) )
= A )
& ( D @ ssList ) )
& ( C @ ssList ) )
=> ( B @ ( A @ memberP ) ) )
& ( ( B @ ( A @ memberP ) )
=> ? [C: $i] :
( ? [D: $i] :
( ( ( D @ ( B @ cons ) @ ( C @ app ) )
= A )
& ( D @ ssList ) )
& ( C @ ssList ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(12837,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[12423,273]) ).
thf(12838,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[12837]) ).
thf(12839,plain,
( ~ ( sk1 @ sk8 @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12838:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(3911,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[128,157]) ).
thf(3912,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[3911]) ).
thf(3913,plain,
sk6 @ ( sk6 @ leq ),
inference(pattern_uni,[status(thm)],[3912:[bind(A,$thf( sk6 ))]]) ).
thf(33334,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[106,258]) ).
thf(33335,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[33334]) ).
thf(33336,plain,
( ( sk1 @ ( nil @ app ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[33335:[bind(A,$thf( sk1 ))]]) ).
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(150,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(12269,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11989,366]) ).
thf(12270,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[12269]) ).
thf(12271,plain,
( ~ ( sk2 @ sk11 @ ( sk2 @ sk11 @ neq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12270:[bind(A,$thf( sk2 @ sk11 ))]]) ).
thf(11741,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11310,157]) ).
thf(11742,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[11741]) ).
thf(11743,plain,
( ( sk2 @ sk7 @ ( sk2 @ sk7 @ leq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[11742:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(72770,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk29 @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[106,311]) ).
thf(72771,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk29 @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[72770]) ).
thf(72772,plain,
( ( sk1 @ sk29 @ ssList )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[72771:[bind(A,$thf( sk1 ))]]) ).
thf(74,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( ( A @ tl @ ( A @ hd @ cons ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax78) ).
thf(441,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( ( A @ tl @ ( A @ hd @ cons ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(35130,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[34534,412]) ).
thf(35131,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[35130]) ).
thf(35132,plain,
( ( nil @ ( sk2 @ sk19 @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[35131:[bind(A,$thf( sk2 @ sk19 ))]]) ).
thf(57701,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[56874,412]) ).
thf(57702,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ totalorderP ) ),
inference(simp,[status(thm)],[57701]) ).
thf(57703,plain,
( ( nil @ ( sk2 @ sk28 @ frontsegP ) )
| ( sk2 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[57702:[bind(A,$thf( sk2 @ sk28 ))]]) ).
thf(41572,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[40807,338]) ).
thf(41573,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[41572]) ).
thf(41574,plain,
( ( nil @ ( sk2 @ sk21 @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[41573:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(11786,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11310,457]) ).
thf(11787,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[11786]) ).
thf(11788,plain,
( ( nil @ ( sk2 @ sk7 @ cons ) @ strictorderP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[11787:[bind(A,$thf( sk2 @ sk7 ))]]) ).
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(199,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(37659,plain,
! [A: $i] :
( ( ( sk1 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[37165,338]) ).
thf(37660,plain,
! [A: $i] :
( ( ( sk1 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[37659]) ).
thf(37661,plain,
( ( nil @ ( sk1 @ sk20 @ rearsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[37660:[bind(A,$thf( sk1 @ sk20 ))]]) ).
thf(53,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ hd @ ssItem ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
thf(331,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ hd @ ssItem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(64223,plain,
sk2 @ tl @ ssList,
inference(rewrite,[status(thm)],[55041,64220]) ).
thf(59194,plain,
! [A: $i] :
( ( ( sk1 @ sk27 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[58656,412]) ).
thf(59195,plain,
! [A: $i] :
( ( ( sk1 @ sk27 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ totalorderP ) ),
inference(simp,[status(thm)],[59194]) ).
thf(59196,plain,
( ( nil @ ( sk1 @ sk27 @ frontsegP ) )
| ( sk1 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[59195:[bind(A,$thf( sk1 @ sk27 ))]]) ).
thf(13382,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[13147,338]) ).
thf(13383,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[13382]) ).
thf(13384,plain,
( ( nil @ ( sk1 @ sk9 @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[13383:[bind(A,$thf( sk1 @ sk9 ))]]) ).
thf(4298,plain,
( ( ( nil @ ( sk6 @ cons ) @ totalorderedP )
!= ( sk2 @ totalorderedP ) )
| ~ $true
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[1429,4285]) ).
thf(4299,plain,
( ( ( nil @ ( sk6 @ cons ) @ totalorderedP )
!= ( sk2 @ totalorderedP ) )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[4298]) ).
thf(4351,plain,
( ( ( nil @ ( sk6 @ cons ) )
!= sk2 )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[4299]) ).
thf(37937,plain,
! [A: $i] :
( ( ( sk2 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[37215,338]) ).
thf(37938,plain,
! [A: $i] :
( ( ( sk2 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[37937]) ).
thf(37939,plain,
( ( nil @ ( sk2 @ sk20 @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[37938:[bind(A,$thf( sk2 @ sk20 ))]]) ).
thf(1979,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[128,405]) ).
thf(1980,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP ) ),
inference(simp,[status(thm)],[1979]) ).
thf(1981,plain,
nil @ ( sk6 @ cons ) @ totalorderP,
inference(pattern_uni,[status(thm)],[1980:[bind(A,$thf( sk6 ))]]) ).
thf(154,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[153]) ).
thf(20985,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[20720,412]) ).
thf(20986,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[20985]) ).
thf(20987,plain,
( ( nil @ ( sk1 @ sk16 @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[20986:[bind(A,$thf( sk1 @ sk16 ))]]) ).
thf(62997,plain,
( ( ( sk1 @ sk23 )
!= ( sk1 @ sk23 ) )
| ( nil @ ( sk1 @ tl @ frontsegP ) )
| ( sk1 = nil )
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[55897,54613]) ).
thf(62998,plain,
( ( ( sk1 @ sk23 )
!= ( sk1 @ sk23 ) )
| ( nil @ ( sk1 @ tl @ frontsegP ) )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[62997]) ).
thf(62999,plain,
( ( nil @ ( sk1 @ tl @ frontsegP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[62998:[]]) ).
thf(37829,plain,
! [A: $i] :
( ( ( sk2 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[37215,412]) ).
thf(37830,plain,
! [A: $i] :
( ( ( sk2 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[37829]) ).
thf(37831,plain,
( ( nil @ ( sk2 @ sk20 @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[37830:[bind(A,$thf( sk2 @ sk20 ))]]) ).
thf(12950,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[12471,457]) ).
thf(12951,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[12950]) ).
thf(12952,plain,
( ( nil @ ( sk2 @ sk8 @ cons ) @ strictorderP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12951:[bind(A,$thf( sk2 @ sk8 ))]]) ).
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(446,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(59557,plain,
! [A: $i] :
( ( ( sk2 @ sk27 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[58721,285]) ).
thf(59558,plain,
! [A: $i] :
( ( ( sk2 @ sk27 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ totalorderP ) ),
inference(simp,[status(thm)],[59557]) ).
thf(59559,plain,
( ( nil @ ( sk2 @ sk27 @ segmentP ) )
| ( sk2 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[59558:[bind(A,$thf( sk2 @ sk27 ))]]) ).
thf(54822,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ neq ) )
| ( sk1 @ sk23 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[52126,7190]) ).
thf(54823,plain,
( ( sk1 != sk1 )
| ~ ( sk1 @ ( nil @ neq ) )
| ( sk1 @ sk23 @ ssList ) ),
inference(simp,[status(thm)],[54822]) ).
thf(54824,plain,
( ~ ( sk1 @ ( nil @ neq ) )
| ( sk1 @ sk23 @ ssList ) ),
inference(pattern_uni,[status(thm)],[54823:[]]) ).
thf(57692,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[56874,285]) ).
thf(57693,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ totalorderP ) ),
inference(simp,[status(thm)],[57692]) ).
thf(57694,plain,
( ( nil @ ( sk2 @ sk28 @ segmentP ) )
| ( sk2 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[57693:[bind(A,$thf( sk2 @ sk28 ))]]) ).
thf(14666,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[14263,338]) ).
thf(14667,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[14666]) ).
thf(14668,plain,
( ( nil @ ( sk2 @ sk10 @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[14667:[bind(A,$thf( sk2 @ sk10 ))]]) ).
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(386,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(19190,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[18943,412]) ).
thf(19191,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[19190]) ).
thf(19192,plain,
( ( nil @ ( sk1 @ sk14 @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[19191:[bind(A,$thf( sk1 @ sk14 ))]]) ).
thf(224,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)],[221]) ).
thf(231,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)],[224]) ).
thf(13010,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[12471,245]) ).
thf(13011,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[13010]) ).
thf(13012,plain,
( ( nil @ ( sk2 @ sk8 @ cons ) @ totalorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[13011:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(12275,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11989,412]) ).
thf(12276,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[12275]) ).
thf(12277,plain,
( ( nil @ ( sk2 @ sk11 @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12276:[bind(A,$thf( sk2 @ sk11 ))]]) ).
thf(17389,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[16921,338]) ).
thf(17390,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[17389]) ).
thf(17391,plain,
( ( nil @ ( sk2 @ sk15 @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[17390:[bind(A,$thf( sk2 @ sk15 ))]]) ).
thf(202,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)],[201]) ).
thf(203,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)],[202]) ).
thf(54790,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ( sk1 @ ( nil @ segmentP ) )
| ( sk1 @ sk23 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[52126,7458]) ).
thf(54791,plain,
( ( sk1 != sk1 )
| ( sk1 @ ( nil @ segmentP ) )
| ( sk1 @ sk23 @ ssList ) ),
inference(simp,[status(thm)],[54790]) ).
thf(54792,plain,
( ( sk1 @ ( nil @ segmentP ) )
| ( sk1 @ sk23 @ ssList ) ),
inference(pattern_uni,[status(thm)],[54791:[]]) ).
thf(34858,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[34487,412]) ).
thf(34859,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[34858]) ).
thf(34860,plain,
( ( nil @ ( sk1 @ sk19 @ frontsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[34859:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(34342,plain,
( ( ( sk6 @ ssItem )
!= ( sk1 @ ssItem ) )
| ( sk5 != nil )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[128,33264]) ).
thf(34343,plain,
( ( ( sk6 @ ssItem )
!= ( sk1 @ ssItem ) )
| ( sk5 != nil )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[34342]) ).
thf(34419,plain,
( ( sk6 != sk1 )
| ( sk5 != nil )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[34343]) ).
thf(17119,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[16900,285]) ).
thf(17120,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[17119]) ).
thf(17121,plain,
( ( nil @ ( sk1 @ sk15 @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[17120:[bind(A,$thf( sk1 @ sk15 ))]]) ).
thf(94,axiom,
nil @ totalorderP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax62) ).
thf(524,plain,
nil @ totalorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(35672,plain,
( ( ( sk5 @ ssItem )
!= ( sk1 @ ssItem ) )
| ( sk6 != nil )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[127,33266]) ).
thf(35673,plain,
( ( ( sk5 @ ssItem )
!= ( sk1 @ ssItem ) )
| ( sk6 != nil )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[35672]) ).
thf(35690,plain,
( ( sk5 != sk1 )
| ( sk6 != nil )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[35673]) ).
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(368,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(76532,plain,
! [A: $i] :
( ( ( sk2 @ sk29 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76299,338]) ).
thf(76533,plain,
! [A: $i] :
( ( ( sk2 @ sk29 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[76532]) ).
thf(76534,plain,
nil @ ( sk2 @ sk29 @ rearsegP ),
inference(pattern_uni,[status(thm)],[76533:[bind(A,$thf( sk2 @ sk29 ))]]) ).
thf(82173,plain,
! [A: $i] :
( ( ( sk2 @ sk30 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81958,273]) ).
thf(82174,plain,
! [A: $i] :
( ( ( sk2 @ sk30 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[82173]) ).
thf(82175,plain,
~ ( sk2 @ sk30 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[82174:[bind(A,$thf( sk2 @ sk30 ))]]) ).
thf(139,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)],[138]) ).
thf(12834,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[12423,405]) ).
thf(12835,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[12834]) ).
thf(12836,plain,
( ( nil @ ( sk1 @ sk8 @ cons ) @ totalorderP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12835:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(39443,plain,
! [A: $i] :
( ( ( sk2 @ sk18 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[38663,273]) ).
thf(39444,plain,
! [A: $i] :
( ( ( sk2 @ sk18 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[39443]) ).
thf(39445,plain,
( ~ ( sk2 @ sk18 @ ( nil @ memberP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[39444:[bind(A,$thf( sk2 @ sk18 ))]]) ).
thf(12266,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11989,243]) ).
thf(12267,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[12266]) ).
thf(12268,plain,
( ( sk2 @ sk11 @ ( sk2 @ sk11 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12267:[bind(A,$thf( sk2 @ sk11 ))]]) ).
thf(17314,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[16921,412]) ).
thf(17315,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[17314]) ).
thf(17316,plain,
( ( nil @ ( sk2 @ sk15 @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[17315:[bind(A,$thf( sk2 @ sk15 ))]]) ).
thf(67167,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk24 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,302]) ).
thf(67168,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk24 @ ssItem ) ),
inference(simp,[status(thm)],[67167]) ).
thf(67169,plain,
( ( sk2 @ totalorderP )
| ( sk2 @ sk24 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[67168:[bind(A,$thf( sk2 ))]]) ).
thf(13468,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[13162,285]) ).
thf(13469,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[13468]) ).
thf(13470,plain,
( ( nil @ ( sk2 @ sk9 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[13469:[bind(A,$thf( sk2 @ sk9 ))]]) ).
thf(13316,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[13147,412]) ).
thf(13317,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[13316]) ).
thf(13318,plain,
( ( nil @ ( sk1 @ sk9 @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[13317:[bind(A,$thf( sk1 @ sk9 ))]]) ).
thf(14594,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[14263,285]) ).
thf(14595,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[14594]) ).
thf(14596,plain,
( ( nil @ ( sk2 @ sk10 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[14595:[bind(A,$thf( sk2 @ sk10 ))]]) ).
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(510,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(11550,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11262,161]) ).
thf(11551,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[11550]) ).
thf(11552,plain,
( ( sk1 @ sk7 @ ( sk1 @ sk7 @ geq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[11551:[bind(A,$thf( sk1 @ sk7 ))]]) ).
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(478,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(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(383,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(14433,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[14248,412]) ).
thf(14434,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[14433]) ).
thf(14435,plain,
( ( nil @ ( sk1 @ sk10 @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[14434:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(77732,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk30 @ ssItem )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[106,312]) ).
thf(77733,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk30 @ ssItem )
| ( nil = A ) ),
inference(simp,[status(thm)],[77732]) ).
thf(77734,plain,
( ( sk1 @ sk30 @ ssItem )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[77733:[bind(A,$thf( sk1 ))]]) ).
thf(63663,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ( sk1 @ ( nil @ segmentP ) )
| ( sk1 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[63056,7458]) ).
thf(63664,plain,
( ( sk1 != sk1 )
| ( sk1 @ ( nil @ segmentP ) )
| ( sk1 @ tl @ ssList ) ),
inference(simp,[status(thm)],[63663]) ).
thf(63665,plain,
( ( sk1 @ ( nil @ segmentP ) )
| ( sk1 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[63664:[]]) ).
thf(2794,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[127,445]) ).
thf(2795,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP ) ),
inference(simp,[status(thm)],[2794]) ).
thf(2796,plain,
nil @ ( sk5 @ cons ) @ cyclefreeP,
inference(pattern_uni,[status(thm)],[2795:[bind(A,$thf( sk5 ))]]) ).
thf(761,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[128,273]) ).
thf(762,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[761]) ).
thf(763,plain,
~ ( sk6 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[762:[bind(A,$thf( sk6 ))]]) ).
thf(1906,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[128,340]) ).
thf(1907,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP ) ),
inference(simp,[status(thm)],[1906]) ).
thf(1908,plain,
nil @ ( sk6 @ cons ) @ equalelemsP,
inference(pattern_uni,[status(thm)],[1907:[bind(A,$thf( sk6 ))]]) ).
thf(47582,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47487,412]) ).
thf(47583,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) ) ),
inference(simp,[status(thm)],[47582]) ).
thf(47584,plain,
nil @ ( nil @ ( nil @ sk22 ) @ frontsegP ),
inference(pattern_uni,[status(thm)],[47583:[bind(A,$thf( nil @ ( nil @ sk22 ) ))]]) ).
thf(21263,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[20744,338]) ).
thf(21264,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[21263]) ).
thf(21265,plain,
( ( nil @ ( sk2 @ sk16 @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[21264:[bind(A,$thf( sk2 @ sk16 ))]]) ).
thf(57319,plain,
! [A: $i] :
( ( ( sk1 @ sk28 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[56809,285]) ).
thf(57320,plain,
! [A: $i] :
( ( ( sk1 @ sk28 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ totalorderP ) ),
inference(simp,[status(thm)],[57319]) ).
thf(57321,plain,
( ( nil @ ( sk1 @ sk28 @ segmentP ) )
| ( sk1 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[57320:[bind(A,$thf( sk1 @ sk28 ))]]) ).
thf(76547,plain,
! [A: $i] :
( ( ( sk2 @ sk29 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[76299,258]) ).
thf(76548,plain,
! [A: $i] :
( ( ( sk2 @ sk29 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[76547]) ).
thf(76549,plain,
( ( sk2 @ sk29 @ ( nil @ app ) )
= ( sk2 @ sk29 ) ),
inference(pattern_uni,[status(thm)],[76548:[bind(A,$thf( sk2 @ sk29 ))]]) ).
thf(14502,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[14248,338]) ).
thf(14503,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[14502]) ).
thf(14504,plain,
( ( nil @ ( sk1 @ sk10 @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[14503:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(8340,plain,
! [A: $i] :
( ( A != sk6 )
| ( sk5 != nil )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[189,130]) ).
thf(8341,plain,
( ( sk5 != nil )
| ~ ( sk6 @ ( nil @ segmentP ) )
| ~ ( sk6 @ ssList ) ),
inference(pattern_uni,[status(thm)],[8340:[bind(A,$thf( sk6 ))]]) ).
thf(151,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)],[150]) ).
thf(13471,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[13162,412]) ).
thf(13472,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[13471]) ).
thf(13473,plain,
( ( nil @ ( sk2 @ sk9 @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[13472:[bind(A,$thf( sk2 @ sk9 ))]]) ).
thf(55246,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[55041,338]) ).
thf(55247,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[55246]) ).
thf(55248,plain,
nil @ ( sk2 @ sk23 @ rearsegP ),
inference(pattern_uni,[status(thm)],[55247:[bind(A,$thf( sk2 @ sk23 ))]]) ).
thf(64229,plain,
nil @ ( sk2 @ tl @ rearsegP ),
inference(rewrite,[status(thm)],[55248,64220]) ).
thf(321,plain,
! [B: $i,A: $i] :
( ( B @ hd @ ( A @ lt ) )
| ( nil = B )
| ~ ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[318]) ).
thf(326,plain,
! [B: $i,A: $i] :
( ( B @ hd @ ( A @ lt ) )
| ~ ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( nil = B ) ),
inference(lifteq,[status(thm)],[321]) ).
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(341,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(82069,plain,
! [A: $i] :
( ( ( sk2 @ sk30 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81958,445]) ).
thf(82070,plain,
! [A: $i] :
( ( ( sk2 @ sk30 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP ) ),
inference(simp,[status(thm)],[82069]) ).
thf(82071,plain,
nil @ ( sk2 @ sk30 @ cons ) @ cyclefreeP,
inference(pattern_uni,[status(thm)],[82070:[bind(A,$thf( sk2 @ sk30 ))]]) ).
thf(59566,plain,
! [A: $i] :
( ( ( sk2 @ sk27 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[58721,412]) ).
thf(59567,plain,
! [A: $i] :
( ( ( sk2 @ sk27 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ totalorderP ) ),
inference(simp,[status(thm)],[59566]) ).
thf(59568,plain,
( ( nil @ ( sk2 @ sk27 @ frontsegP ) )
| ( sk2 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[59567:[bind(A,$thf( sk2 @ sk27 ))]]) ).
thf(2907,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ lt ) )
!= ( sk5 @ ( sk5 @ lt ) ) )
| ~ $true
| ~ ( B @ ( A @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[121,2874]) ).
thf(2908,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ lt ) )
!= ( sk5 @ ( sk5 @ lt ) ) )
| ~ ( B @ ( A @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[2907]) ).
thf(2909,plain,
( ~ ( sk5 @ ( sk5 @ gt ) )
| ~ ( sk5 @ ssItem )
| ~ ( sk5 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[2908:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 ))]]) ).
thf(2932,plain,
( ~ ( sk5 @ ( sk5 @ gt ) )
| ~ ( sk5 @ ssItem ) ),
inference(simp,[status(thm)],[2909]) ).
thf(2960,plain,
( ~ ( sk5 @ ( sk5 @ gt ) )
| ~ $true ),
inference(rewrite,[status(thm)],[2932,127]) ).
thf(2961,plain,
~ ( sk5 @ ( sk5 @ gt ) ),
inference(simp,[status(thm)],[2960]) ).
thf(12119,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11974,285]) ).
thf(12120,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[12119]) ).
thf(12121,plain,
( ( nil @ ( sk1 @ sk11 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[12120:[bind(A,$thf( sk1 @ sk11 ))]]) ).
thf(2038,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[127,436]) ).
thf(2039,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP ) ),
inference(simp,[status(thm)],[2038]) ).
thf(2040,plain,
nil @ ( sk5 @ cons ) @ duplicatefreeP,
inference(pattern_uni,[status(thm)],[2039:[bind(A,$thf( sk5 ))]]) ).
thf(11816,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[11310,445]) ).
thf(11817,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[11816]) ).
thf(11818,plain,
( ( nil @ ( sk2 @ sk7 @ cons ) @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[11817:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(296,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ leq ) )
| ( C @ ( B @ leq ) )
| ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
!= A )
| ~ ( F @ ssList )
| ~ ( E @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssItem )
| ~ ( B @ ssItem )
| ~ ( A @ totalorderP )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[293]) ).
thf(304,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ leq ) )
| ( C @ ( B @ leq ) )
| ~ ( F @ ssList )
| ~ ( E @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssItem )
| ~ ( B @ ssItem )
| ~ ( A @ totalorderP )
| ~ ( A @ ssList )
| ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
!= A ) ),
inference(lifteq,[status(thm)],[296]) ).
thf(305,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) )
| ~ ( E @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) @ totalorderP )
| ~ ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) @ ssList ) ),
inference(simp,[status(thm)],[304]) ).
thf(46798,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk5 @ ( nil @ segmentP ) ) )
| ( sk5 != sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4221,46530]) ).
thf(46799,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk5 @ ( nil @ segmentP ) ) )
| ( sk5 != sk2 ) ),
inference(simp,[status(thm)],[46798]) ).
thf(46807,plain,
( ( sk5 != sk1 )
| ( sk1 != nil )
| ( sk5 != sk2 ) ),
inference(simp,[status(thm)],[46799]) ).
thf(194,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[193]) ).
thf(195,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( A = B ) ),
inference(lifteq,[status(thm)],[194]) ).
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(437,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(280,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ frontsegP ) )
| ( ( C @ ( B @ app ) )
!= A )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[277]) ).
thf(282,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ frontsegP ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( C @ ( B @ app ) )
!= A ) ),
inference(lifteq,[status(thm)],[280]) ).
thf(283,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ app ) @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ( A @ app ) @ ssList ) ),
inference(simp,[status(thm)],[282]) ).
thf(200,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)],[199]) ).
thf(4069,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[128,161]) ).
thf(4070,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) ) ),
inference(simp,[status(thm)],[4069]) ).
thf(4071,plain,
sk6 @ ( sk6 @ geq ),
inference(pattern_uni,[status(thm)],[4070:[bind(A,$thf( sk6 ))]]) ).
thf(869,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,338]) ).
thf(870,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[869]) ).
thf(871,plain,
nil @ ( sk1 @ rearsegP ),
inference(pattern_uni,[status(thm)],[870:[bind(A,$thf( sk1 ))]]) ).
thf(37551,plain,
! [A: $i] :
( ( ( sk1 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[37165,412]) ).
thf(37552,plain,
! [A: $i] :
( ( ( sk1 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[37551]) ).
thf(37553,plain,
( ( nil @ ( sk1 @ sk20 @ frontsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[37552:[bind(A,$thf( sk1 @ sk20 ))]]) ).
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(427,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(84,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) @ tl )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax25) ).
thf(491,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) @ tl )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(55121,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[55041,285]) ).
thf(55122,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[55121]) ).
thf(55123,plain,
nil @ ( sk2 @ sk23 @ segmentP ),
inference(pattern_uni,[status(thm)],[55122:[bind(A,$thf( sk2 @ sk23 ))]]) ).
thf(64224,plain,
nil @ ( sk2 @ tl @ segmentP ),
inference(rewrite,[status(thm)],[55123,64220]) ).
thf(13309,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[13147,285]) ).
thf(13310,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[13309]) ).
thf(13311,plain,
( ( nil @ ( sk1 @ sk9 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[13310:[bind(A,$thf( sk1 @ sk9 ))]]) ).
thf(227,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ sk12 @ ( A @ sk13 @ lt ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[221]) ).
thf(55671,plain,
( ( ( sk2 @ sk23 @ ( sk2 @ sk23 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9114,55094]) ).
thf(55672,plain,
( ( sk2 @ sk23 @ ( sk2 @ sk23 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[55671]) ).
thf(55756,plain,
( ( ( sk2 @ sk23 )
!= nil )
| ( ( sk2 @ sk23 )
!= sk2 ) ),
inference(simp,[status(thm)],[55672]) ).
thf(64225,plain,
( ( ( sk2 @ tl )
!= nil )
| ( ( sk2 @ tl )
!= sk2 ) ),
inference(rewrite,[status(thm)],[55756,64220]) ).
thf(20975,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[20720,285]) ).
thf(20976,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[20975]) ).
thf(20977,plain,
( ( nil @ ( sk1 @ sk16 @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[20976:[bind(A,$thf( sk1 @ sk16 ))]]) ).
thf(122,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ gt ) )
| ~ ( A @ ( B @ lt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[120]) ).
thf(57473,plain,
! [A: $i] :
( ( ( sk1 @ sk28 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[56809,338]) ).
thf(57474,plain,
! [A: $i] :
( ( ( sk1 @ sk28 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ totalorderP ) ),
inference(simp,[status(thm)],[57473]) ).
thf(57475,plain,
( ( nil @ ( sk1 @ sk28 @ rearsegP ) )
| ( sk1 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[57474:[bind(A,$thf( sk1 @ sk28 ))]]) ).
thf(212,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)],[205]) ).
thf(215,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)],[212]) ).
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(496,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(77,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( B @ ( A @ app ) @ ssList ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
thf(454,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( B @ ( A @ app ) @ ssList ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(108743,plain,
$false,
inference(e,[status(thm)],[13162,138,760,61751,249,518,234,4877,12812,347,19464,170,115,61122,59179,33352,37825,247,440,269,47543,217,276,35933,1655,11848,6246,56874,3781,1919,142,4870,34421,64228,47546,6551,340,33266,11549,13147,404,185,11645,12833,436,39151,651,51276,67097,46530,76403,184,18486,34965,125,12901,1992,196,26552,26538,542,157,11911,11609,40807,76444,284,152,228,316,12657,82172,82187,189,76349,261,17783,63706,179,11926,211,106,238,36708,121,6562,475,924,63023,353,2777,47575,147,59340,3808,133,11490,12907,4285,312,206,132,21181,411,82102,116,243,292,47627,65285,11791,83768,11672,11687,534,81967,233,12898,248,64227,19386,18239,201,14263,47731,220,366,334,33282,38663,57840,302,4989,160,561,297,4344,192,165,11908,7957,275,788,137,59708,229,361,12340,14248,435,329,665,21187,1392,4080,82043,285,4994,34534,456,57338,8895,11734,874,317,156,11884,23837,4227,141,256,339,8743,12746,5932,11666,13539,41284,41173,124,225,11496,193,537,14428,64222,29344,64220,12955,81978,36417,9316,82165,82050,1429,457,12191,35126,41156,266,17203,311,921,22594,128,237,105,244,10556,12982,11737,19270,161,12654,149,19380,298,81958,412,513,11033,264,35866,180,47716,12719,444,20720,3925,11905,9114,40757,54613,291,37165,259,413,176,17837,22648,23067,63045,13075,286,65220,711,12776,281,12663,204,445,382,313,12716,144,12128,2935,12423,181,35237,159,55897,2029,466,34846,91205,236,17128,33268,23314,406,172,219,274,230,245,2871,16900,41454,37539,41463,509,649,11487,98,303,271,208,64221,12114,54549,140,213,12111,76387,520,2874,33264,64226,155,330,12274,494,11669,37215,35694,198,1381,130,21065,81972,11262,278,223,306,299,226,56809,60901,7458,14599,76352,521,11310,17313,135,241,61194,473,77089,162,255,7190,516,11579,123,12854,19182,458,145,62063,209,525,12839,295,3913,33336,150,12271,11743,11989,263,11974,72772,441,35132,57703,127,41574,11788,199,4240,791,37661,182,331,64223,59196,13384,4351,338,37939,1981,154,20987,62999,37831,12952,314,446,59559,54824,57694,14668,386,19192,231,13012,12277,17391,203,54792,34860,34419,218,18943,17121,524,35690,368,18967,76534,82175,258,158,139,12836,39445,12268,60726,17316,54856,67169,13470,171,13318,14596,246,510,1440,11552,478,383,14435,77734,63665,16921,214,2796,290,119,58656,763,272,1908,300,34487,47584,262,21265,405,57321,273,76549,14504,8341,151,146,13473,64229,210,326,341,82071,38594,59568,2961,12121,2040,63056,11818,305,46807,239,242,294,136,47487,268,52126,195,437,76299,58721,283,395,9325,131,200,9335,4071,871,4221,37553,427,82210,543,491,64224,13311,254,227,64225,20977,337,122,57475,12471,20744,215,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC111+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/10.63 % Computer : n006.cluster.edu
% 0.14/10.63 % Model : x86_64 x86_64
% 0.14/10.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/10.63 % Memory : 8046.5625MB
% 0.14/10.63 % OS : Linux 6.8.0-71-generic
% 0.14/10.63 % CPULimit : 300
% 0.14/10.63 % WCLimit : 300
% 0.14/10.63 % DateTime : Sat Sep 26 12:16:23 UTC 2026
% 0.14/10.63 % CPUTime :
% 0.14/10.63 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.00/11.22 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.80/11.51 % [INFO] Parsing done (289ms).
% 1.80/11.52 % [INFO] Running in sequential loop mode.
% 2.52/11.92 % [INFO] eprover registered as external prover.
% 2.52/11.93 % [INFO] Scanning for conjecture ...
% 2.76/12.06 % [INFO] Found a conjecture (or negated_conjecture) and 95 axioms. Running axiom selection ...
% 2.98/12.17 % [INFO] Axiom selection finished. Selected 95 axioms (removed 0 axioms).
% 3.12/12.29 % [INFO] Problem is first-order (TPTP FOF).
% 3.35/12.32 % [INFO] Type checking passed.
% 3.35/12.32 % [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 ...
% 143.55/69.14 % External prover 'e' found a proof!
% 143.55/69.14 % [INFO] Killing All external provers ...
% 143.55/69.14 % Time passed: 58368ms (effective reasoning time: 57613ms)
% 143.55/69.14 % 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)>
% 143.55/69.15 % 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
% 143.55/69.15 % No. of inferences in proof: 1390
% 143.55/69.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 58368 ms resp. 57613 ms w/o parsing
% 143.76/69.56 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 143.76/69.57 % [INFO] Killing All external provers ...
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