%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWC117+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n019.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 08:52:19 AM UTC 2026
% Result : Theorem 145.48s 37.94s
% Output : Refutation 147.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 119
% Syntax : Number of formulae : 1298 ( 118 unt; 0 typ; 23 def)
% Number of atoms : 5709 (1201 equ; 0 cnn)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 12945 (2007 ~;2416 |; 217 &;7650 @)
% ( 26 <=>; 629 =>; 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 : 50 ( 47 usr; 9 con; 0-2 aty)
% Number of variables : 1303 ( 18 ^;1221 !; 41 ?;1303 :)
% ( 0 !>; 0 ?*; 0 @-; 23 @+)
% Comments :
%------------------------------------------------------------------------------
thf(ssList_decl,type,
ssList: $i > $o ).
thf(segmentP_decl,type,
segmentP: $i > $i > $o ).
thf(equalelemsP_decl,type,
equalelemsP: $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(totalorderedP_decl,type,
totalorderedP: $i > $o ).
thf(hd_decl,type,
hd: $i > $i ).
thf(cyclefreeP_decl,type,
cyclefreeP: $i > $o ).
thf(app_decl,type,
app: $i > $i > $i ).
thf(strictorderP_decl,type,
strictorderP: $i > $o ).
thf(singletonP_decl,type,
singletonP: $i > $o ).
thf(duplicatefreeP_decl,type,
duplicatefreeP: $i > $o ).
thf(memberP_decl,type,
memberP: $i > $i > $o ).
thf(tl_decl,type,
tl: $i > $i ).
thf(totalorderP_decl,type,
totalorderP: $i > $o ).
thf(rearsegP_decl,type,
rearsegP: $i > $i > $o ).
thf(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(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 = A )
& ( nil = B ) )
| ? [E: $i] :
( ( E @ equalelemsP )
& ( C @ ( E @ segmentP ) )
& ( E @ ( D @ segmentP ) )
& ( E @ ( C @ neq ) )
& ( E @ ssList ) )
| ~ ( C @ equalelemsP )
| ~ ( 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 = sk1 )
& ( nil = A ) )
| ? [D: $i] :
( ( D @ equalelemsP )
& ( B @ ( D @ segmentP ) )
& ( D @ ( C @ segmentP ) )
& ( D @ ( B @ neq ) )
& ( D @ ssList ) )
| ~ ( B @ equalelemsP )
| ~ ( 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 = sk1 )
& ( nil = sk2 ) )
| ? [C: $i] :
( ( C @ equalelemsP )
& ( A @ ( C @ segmentP ) )
& ( C @ ( B @ segmentP ) )
& ( C @ ( A @ neq ) )
& ( C @ ssList ) )
| ~ ( A @ equalelemsP )
| ~ ( A @ ( B @ segmentP ) )
| ( sk1 != A )
| ( sk2 != B ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ( ( ( sk1 @ ( sk2 @ segmentP ) )
& ( nil @ ( sk1 @ neq ) ) )
| ( ( nil = sk1 )
& ( nil = sk2 ) )
| ? [B: $i] :
( ( B @ equalelemsP )
& ( sk3 @ ( B @ segmentP ) )
& ( B @ ( A @ segmentP ) )
& ( B @ ( sk3 @ neq ) )
& ( B @ ssList ) )
| ~ ( sk3 @ equalelemsP )
| ~ ( 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(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 = A )
& ( nil = B ) )
| ? [E: $i] :
( ( E @ equalelemsP )
& ( C @ ( E @ segmentP ) )
& ( E @ ( D @ segmentP ) )
& ( E @ ( C @ neq ) )
& ( E @ ssList ) )
| ~ ( C @ equalelemsP )
| ~ ( C @ ( D @ segmentP ) )
| ( A != C )
| ( B != D ) ) ) ) ) ),
file('/export/starexec/sandbox2/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 = A )
& ( nil = B ) )
| ? [E: $i] :
( ( E @ equalelemsP )
& ( C @ ( E @ segmentP ) )
& ( E @ ( D @ segmentP ) )
& ( E @ ( C @ neq ) )
& ( E @ ssList ) )
| ~ ( C @ equalelemsP )
| ~ ( 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 = A )
& ( nil = B ) )
| ? [E: $i] :
( ( E @ equalelemsP )
& ( C @ ( E @ segmentP ) )
& ( E @ ( D @ segmentP ) )
& ( E @ ( C @ neq ) )
& ( E @ ssList ) )
| ~ ( C @ equalelemsP )
| ~ ( 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 ) )
& ( ~ ( A @ equalelemsP )
| ~ ( sk3 @ ( A @ segmentP ) )
| ~ ( A @ ( sk4 @ segmentP ) )
| ~ ( A @ ( sk3 @ neq ) )
| ~ ( A @ ssList ) )
& ( sk3 @ equalelemsP )
& ( sk3 @ ( sk4 @ segmentP ) )
& ( sk1 = sk3 )
& ( sk2 = sk4 )
& ( sk4 @ ssList )
& ( sk3 @ ssList )
& ( sk2 @ ssList )
& ( sk1 @ ssList ) ),
inference(cnf,[status(esa)],[98]) ).
thf(104,plain,
sk1 @ ssList,
inference(cnfConj,[status(thm)],[99]) ).
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/sandbox2/benchmark/theBenchmark.p',ax10) ).
thf(215,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(216,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)],[215]) ).
thf(218,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk14 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[216]) ).
thf(25107,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk14 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,218]) ).
thf(25108,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk14 @ ssList ) ),
inference(simp,[status(thm)],[25107]) ).
thf(25109,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk14 @ ssList ) ),
inference(pattern_uni,[status(thm)],[25108:[bind(A,$thf( sk1 ))]]) ).
thf(103,plain,
sk2 @ ssList,
inference(cnfConj,[status(thm)],[99]) ).
thf(219,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ sk12 @ ( A @ sk13 @ lt ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[216]) ).
thf(26014,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ~ ( A @ sk12 @ ( A @ sk13 @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,219]) ).
thf(26015,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ~ ( A @ sk12 @ ( A @ sk13 @ lt ) ) ),
inference(simp,[status(thm)],[26014]) ).
thf(26016,plain,
( ( sk2 @ strictorderP )
| ~ ( sk2 @ sk12 @ ( sk2 @ sk13 @ lt ) ) ),
inference(pattern_uni,[status(thm)],[26015:[bind(A,$thf( sk2 ))]]) ).
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/sandbox2/benchmark/theBenchmark.p',ax8) ).
thf(199,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(200,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)],[199]) ).
thf(201,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[200]) ).
thf(641,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,201]) ).
thf(642,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList ) ),
inference(simp,[status(thm)],[641]) ).
thf(643,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk9 @ ssList ) ),
inference(pattern_uni,[status(thm)],[642:[bind(A,$thf( sk1 ))]]) ).
thf(661,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[643,201]) ).
thf(662,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[661]) ).
thf(663,plain,
( ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ sk9 @ sk9 @ ssList )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[662:[bind(A,$thf( sk1 @ sk9 ))]]) ).
thf(726,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ~ $true
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[663,201]) ).
thf(727,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[726]) ).
thf(728,plain,
( ( sk1 @ sk9 @ sk9 @ cyclefreeP )
| ( sk1 @ sk9 @ sk9 @ sk9 @ ssList )
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[727:[bind(A,$thf( sk1 @ sk9 @ sk9 ))]]) ).
thf(47,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax57) ).
thf(279,plain,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(280,plain,
! [A: $i] :
( ( nil @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[279]) ).
thf(5948,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ sk9 @ sk9 @ cyclefreeP )
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[728,280]) ).
thf(5949,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ sk9 @ sk9 @ cyclefreeP )
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5948]) ).
thf(5950,plain,
( ( nil @ ( sk1 @ sk9 @ sk9 @ sk9 @ segmentP ) )
| ( sk1 @ sk9 @ sk9 @ cyclefreeP )
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5949:[bind(A,$thf( sk1 @ sk9 @ sk9 @ sk9 ))]]) ).
thf(653,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,201]) ).
thf(654,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList ) ),
inference(simp,[status(thm)],[653]) ).
thf(655,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk9 @ ssList ) ),
inference(pattern_uni,[status(thm)],[654:[bind(A,$thf( sk2 ))]]) ).
thf(667,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[655,201]) ).
thf(668,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[667]) ).
thf(669,plain,
( ( sk2 @ sk9 @ cyclefreeP )
| ( sk2 @ sk9 @ sk9 @ ssList )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[668:[bind(A,$thf( sk2 @ sk9 ))]]) ).
thf(1416,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ~ $true
| ( sk2 @ sk9 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[669,201]) ).
thf(1417,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ( sk2 @ sk9 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1416]) ).
thf(1418,plain,
( ( sk2 @ sk9 @ sk9 @ cyclefreeP )
| ( sk2 @ sk9 @ sk9 @ sk9 @ ssList )
| ( sk2 @ sk9 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1417:[bind(A,$thf( sk2 @ sk9 @ sk9 ))]]) ).
thf(55,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax51) ).
thf(332,plain,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(333,plain,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[332]) ).
thf(6283,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ sk9 @ sk9 @ cyclefreeP )
| ( sk2 @ sk9 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[1418,333]) ).
thf(6284,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ sk9 @ sk9 @ cyclefreeP )
| ( sk2 @ sk9 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[6283]) ).
thf(6285,plain,
( ( nil @ ( sk2 @ sk9 @ sk9 @ sk9 @ rearsegP ) )
| ( sk2 @ sk9 @ sk9 @ cyclefreeP )
| ( sk2 @ sk9 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[6284:[bind(A,$thf( sk2 @ sk9 @ sk9 @ sk9 ))]]) ).
thf(1313,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,333]) ).
thf(1314,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[1313]) ).
thf(1315,plain,
nil @ ( sk1 @ rearsegP ),
inference(pattern_uni,[status(thm)],[1314:[bind(A,$thf( sk1 ))]]) ).
thf(81,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax42) ).
thf(468,plain,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
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/sandbox2/benchmark/theBenchmark.p',ax12) ).
thf(254,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(255,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)],[254]) ).
thf(256,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk19 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[255]) ).
thf(44981,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk19 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,256]) ).
thf(44982,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk19 @ ssList ) ),
inference(simp,[status(thm)],[44981]) ).
thf(44983,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk19 @ ssList ) ),
inference(pattern_uni,[status(thm)],[44982:[bind(A,$thf( sk2 ))]]) ).
thf(68,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax45) ).
thf(406,plain,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(407,plain,
! [A: $i] :
( ( nil @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[406]) ).
thf(45239,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[44983,407]) ).
thf(45240,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[45239]) ).
thf(45241,plain,
( ( nil @ ( sk2 @ sk19 @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[45240:[bind(A,$thf( sk2 @ sk19 ))]]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ neq ) )
<=> ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(244,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(245,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)],[244]) ).
thf(246,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ ( A @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[245]) ).
thf(248,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A != B ) ),
inference(lifteq,[status(thm)],[246]) ).
thf(249,plain,
! [A: $i] :
( ~ ( A @ ( A @ neq ) )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[248]) ).
thf(207,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk7 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[200]) ).
thf(18671,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,207]) ).
thf(18672,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssItem ) ),
inference(simp,[status(thm)],[18671]) ).
thf(18673,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk7 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[18672:[bind(A,$thf( sk1 ))]]) ).
thf(71,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ duplicatefreeP ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax71) ).
thf(430,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ duplicatefreeP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(431,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[430]) ).
thf(19146,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18673,431]) ).
thf(19147,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19146]) ).
thf(19148,plain,
( ( nil @ ( sk1 @ sk7 @ cons ) @ duplicatefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19147:[bind(A,$thf( sk1 @ sk7 ))]]) ).
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/sandbox2/benchmark/theBenchmark.p',ax79) ).
thf(234,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(25,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ segmentP ) )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).
thf(180,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(181,plain,
! [A: $i] :
( ( ( A @ ( nil @ segmentP ) )
| ( nil != A )
| ~ ( A @ ssList ) )
& ( ( nil = A )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[180]) ).
thf(182,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[181]) ).
thf(184,plain,
! [A: $i] :
( ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[182]) ).
thf(11173,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[104,184]) ).
thf(11174,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[11173]) ).
thf(11175,plain,
( ~ ( sk1 @ ( nil @ segmentP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[11174:[bind(A,$thf( sk1 ))]]) ).
thf(258,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk17 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[255]) ).
thf(46645,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk17 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,258]) ).
thf(46646,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk17 @ ssItem ) ),
inference(simp,[status(thm)],[46645]) ).
thf(46647,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk17 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[46646:[bind(A,$thf( sk2 ))]]) ).
thf(247,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ neq ) )
| ( A = B )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[245]) ).
thf(250,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A = B ) ),
inference(lifteq,[status(thm)],[247]) ).
thf(108,plain,
( ~ ( sk1 @ ( sk2 @ segmentP ) )
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(110,plain,
sk3 @ ( sk4 @ segmentP ),
inference(cnfConj,[status(thm)],[99]) ).
thf(105,plain,
sk1 = sk3,
inference(cnfConj,[status(thm)],[99]) ).
thf(112,plain,
sk3 = sk1,
inference(lifteq,[status(thm)],[105]) ).
thf(107,plain,
sk2 = sk4,
inference(cnfConj,[status(thm)],[99]) ).
thf(113,plain,
sk4 = sk2,
inference(lifteq,[status(thm)],[107]) ).
thf(548,plain,
sk1 @ ( sk2 @ segmentP ),
inference(rewrite,[status(thm)],[110,112,113]) ).
thf(549,plain,
( ~ $true
| ~ ( nil @ ( sk1 @ neq ) ) ),
inference(rewrite,[status(thm)],[108,548]) ).
thf(550,plain,
~ ( nil @ ( sk1 @ neq ) ),
inference(simp,[status(thm)],[549]) ).
thf(38164,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ~ $true
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[250,550]) ).
thf(38165,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A = B ) ),
inference(simp,[status(thm)],[38164]) ).
thf(38166,plain,
( ~ ( nil @ ssItem )
| ~ ( sk1 @ ssItem )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[38165:[bind(A,$thf( sk1 )),bind(B,$thf( nil ))]]) ).
thf(25070,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk14 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,218]) ).
thf(25071,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk14 @ ssList ) ),
inference(simp,[status(thm)],[25070]) ).
thf(25072,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk14 @ ssList ) ),
inference(pattern_uni,[status(thm)],[25071:[bind(A,$thf( sk2 ))]]) ).
thf(25302,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[25072,280]) ).
thf(25303,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[25302]) ).
thf(25304,plain,
( ( nil @ ( sk2 @ sk14 @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25303:[bind(A,$thf( sk2 @ sk14 ))]]) ).
thf(77,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( B @ ( A @ app ) @ ssList ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
thf(449,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( B @ ( A @ app ) @ ssList ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(5,axiom,
? [A: $i] :
( ? [B: $i] :
( ( A != B )
& ( B @ ssItem ) )
& ( A @ ssItem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(120,plain,
? [A: $i] :
( ? [B: $i] :
( ( A != B )
& ( B @ ssItem ) )
& ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
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/sandbox2/benchmark/theBenchmark.p',ax56) ).
thf(269,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(225,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk13 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[216]) ).
thf(30514,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk13 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,225]) ).
thf(30515,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk13 @ ssItem ) ),
inference(simp,[status(thm)],[30514]) ).
thf(30516,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk13 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[30515:[bind(A,$thf( sk2 ))]]) ).
thf(202,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk8 @ ( A @ sk7 @ leq ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[200]) ).
thf(209,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk7 @ ( A @ sk8 @ leq ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[200]) ).
thf(20475,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ( A @ sk8 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,209]) ).
thf(20476,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ( A @ sk8 @ leq ) ) ),
inference(simp,[status(thm)],[20475]) ).
thf(20477,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk7 @ ( sk2 @ sk8 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[20476:[bind(A,$thf( sk2 ))]]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderedP ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax65) ).
thf(239,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(240,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[239]) ).
thf(19125,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18673,240]) ).
thf(19126,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19125]) ).
thf(19127,plain,
( ( nil @ ( sk1 @ sk7 @ cons ) @ totalorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19126:[bind(A,$thf( sk1 @ sk7 ))]]) ).
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/sandbox2/benchmark/theBenchmark.p',ax13) ).
thf(408,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(729,plain,
( ~ $true
| ( ( sk1 @ sk9 @ cyclefreeP )
!= ( sk1 @ cyclefreeP ) )
| ( sk1 @ sk9 @ sk9 @ ssList )
| ( sk1 @ cyclefreeP ) ),
inference(eqfactor_ordered,[status(thm)],[663]) ).
thf(730,plain,
( ( ( sk1 @ sk9 @ cyclefreeP )
!= ( sk1 @ cyclefreeP ) )
| ( sk1 @ sk9 @ sk9 @ ssList )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[729]) ).
thf(217,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ sk13 @ ( A @ sk12 @ lt ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[216]) ).
thf(262,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk18 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[255]) ).
thf(51104,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk18 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,262]) ).
thf(51105,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk18 @ ssItem ) ),
inference(simp,[status(thm)],[51104]) ).
thf(51106,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk18 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[51105:[bind(A,$thf( sk2 ))]]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( nil @ memberP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
thf(267,plain,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( nil @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(268,plain,
! [A: $i] :
( ~ ( A @ ( nil @ memberP ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[267]) ).
thf(51605,plain,
! [A: $i] :
( ( ( sk2 @ sk18 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[51106,268]) ).
thf(51606,plain,
! [A: $i] :
( ( ( sk2 @ sk18 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[51605]) ).
thf(51607,plain,
( ~ ( sk2 @ sk18 @ ( nil @ memberP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[51606:[bind(A,$thf( sk2 @ sk18 ))]]) ).
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/sandbox2/benchmark/theBenchmark.p',ax5) ).
thf(271,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(272,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)],[271]) ).
thf(274,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk22 ) @ ( B @ app ) )
= A )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[272]) ).
thf(276,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( A @ ( B @ sk22 ) @ ( B @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[274]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ frontsegP ) )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax46) ).
thf(167,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(168,plain,
! [A: $i] :
( ( ( A @ ( nil @ frontsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) )
& ( ( nil = A )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[167]) ).
thf(170,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[168]) ).
thf(172,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[170]) ).
thf(173,plain,
( ( nil @ ( nil @ frontsegP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[172]) ).
thf(62,axiom,
nil @ ssList,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
thf(377,plain,
nil @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(612,plain,
( ( nil @ ( nil @ frontsegP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[173,377]) ).
thf(613,plain,
nil @ ( nil @ frontsegP ),
inference(simp,[status(thm)],[612]) ).
thf(273,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk22 ) @ ssList )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[272]) ).
thf(59314,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)],[613,273]) ).
thf(59315,plain,
! [B: $i,A: $i] :
( ( ( nil @ ( nil @ frontsegP ) )
!= ( B @ ( A @ frontsegP ) ) )
| ( A @ ( B @ sk22 ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[59314]) ).
thf(59316,plain,
( ( nil @ ( nil @ sk22 ) @ ssList )
| ~ ( nil @ ssList )
| ~ ( nil @ ssList ) ),
inference(pattern_uni,[status(thm)],[59315:[bind(A,$thf( nil )),bind(B,$thf( nil ))]]) ).
thf(59613,plain,
( ( nil @ ( nil @ sk22 ) @ ssList )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[59316]) ).
thf(59631,plain,
( ( nil @ ( nil @ sk22 ) @ ssList )
| ~ $true ),
inference(rewrite,[status(thm)],[59613,377]) ).
thf(59632,plain,
nil @ ( nil @ sk22 ) @ ssList,
inference(simp,[status(thm)],[59631]) ).
thf(59673,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59632,280]) ).
thf(59674,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[59673]) ).
thf(59675,plain,
nil @ ( nil @ ( nil @ sk22 ) @ segmentP ),
inference(pattern_uni,[status(thm)],[59674:[bind(A,$thf( nil @ ( nil @ sk22 ) ))]]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).
thf(237,plain,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(238,plain,
! [A: $i] :
( ( A @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[237]) ).
thf(7006,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[655,238]) ).
thf(7007,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7006]) ).
thf(7008,plain,
( ( sk2 @ sk9 @ ( sk2 @ sk9 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7007:[bind(A,$thf( sk2 @ sk9 ))]]) ).
thf(75,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ cyclefreeP ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax59) ).
thf(439,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ cyclefreeP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(440,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[439]) ).
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/sandbox2/benchmark/theBenchmark.p',ax50) ).
thf(511,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(208,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk8 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[200]) ).
thf(19746,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,208]) ).
thf(19747,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ssItem ) ),
inference(simp,[status(thm)],[19746]) ).
thf(19748,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk8 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[19747:[bind(A,$thf( sk1 ))]]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax31) ).
thf(151,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(152,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[151]) ).
thf(20115,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19748,152]) ).
thf(20116,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[20115]) ).
thf(20117,plain,
( ( sk1 @ sk8 @ ( sk1 @ sk8 @ leq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[20116:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( ( A @ ( B @ geq ) )
& ( B @ ( A @ geq ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax87) ).
thf(142,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(121,plain,
( ( sk5 != sk6 )
& ( sk6 @ ssItem )
& ( sk5 @ ssItem ) ),
inference(cnf,[status(esa)],[120]) ).
thf(122,plain,
sk5 @ ssItem,
inference(cnfConj,[status(thm)],[121]) ).
thf(713,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,268]) ).
thf(714,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[713]) ).
thf(715,plain,
~ ( sk5 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[714:[bind(A,$thf( sk5 ))]]) ).
thf(1325,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,333]) ).
thf(1326,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[1325]) ).
thf(1327,plain,
nil @ ( sk2 @ rearsegP ),
inference(pattern_uni,[status(thm)],[1326:[bind(A,$thf( sk2 ))]]) ).
thf(19234,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18673,268]) ).
thf(19235,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19234]) ).
thf(19236,plain,
( ~ ( sk1 @ sk7 @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19235:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(102,plain,
! [A: $i] :
( ~ ( A @ equalelemsP )
| ~ ( sk3 @ ( A @ segmentP ) )
| ~ ( A @ ( sk4 @ segmentP ) )
| ~ ( A @ ( sk3 @ neq ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(538,plain,
! [A: $i] :
( ~ ( A @ equalelemsP )
| ~ ( sk1 @ ( A @ segmentP ) )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( A @ ( sk1 @ neq ) )
| ~ ( A @ ssList ) ),
inference(rewrite,[status(thm)],[102,112,113]) ).
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/sandbox2/benchmark/theBenchmark.p',ax91) ).
thf(153,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(220,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk16 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[216]) ).
thf(26785,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,220]) ).
thf(26786,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssList ) ),
inference(simp,[status(thm)],[26785]) ).
thf(26787,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk16 @ ssList ) ),
inference(pattern_uni,[status(thm)],[26786:[bind(A,$thf( sk2 ))]]) ).
thf(26962,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[26787,238]) ).
thf(26963,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[26962]) ).
thf(26964,plain,
( ( sk2 @ sk16 @ ( sk2 @ sk16 @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[26963:[bind(A,$thf( sk2 @ sk16 ))]]) ).
thf(65,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( nil
= ( B @ ( A @ app ) ) )
<=> ( ( nil = A )
& ( nil = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax83) ).
thf(390,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(391,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)],[390]) ).
thf(394,plain,
! [B: $i,A: $i] :
( ( nil
= ( B @ ( A @ app ) ) )
| ( nil != A )
| ( nil != B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[391]) ).
thf(397,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
= nil )
| ( nil != A )
| ( nil != B ) ),
inference(lifteq,[status(thm)],[394]) ).
thf(398,plain,
( ~ ( nil @ ssList )
| ( ( nil @ ( nil @ app ) )
= nil ) ),
inference(simp,[status(thm)],[397]) ).
thf(708,plain,
( ~ $true
| ( ( nil @ ( nil @ app ) )
= nil ) ),
inference(rewrite,[status(thm)],[398,377]) ).
thf(709,plain,
( ( nil @ ( nil @ app ) )
= nil ),
inference(simp,[status(thm)],[708]) ).
thf(43323,plain,
( ( ( sk5 @ ssItem )
!= ( nil @ ssItem ) )
| ~ $true
| ~ ( sk1 @ ssItem )
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[122,38166]) ).
thf(43324,plain,
( ( ( sk5 @ ssItem )
!= ( nil @ ssItem ) )
| ~ ( sk1 @ ssItem )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[43323]) ).
thf(43350,plain,
( ( sk5 != nil )
| ~ ( sk1 @ ssItem )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[43324]) ).
thf(261,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk20 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[255]) ).
thf(49907,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk20 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,261]) ).
thf(49908,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk20 @ ssList ) ),
inference(simp,[status(thm)],[49907]) ).
thf(49909,plain,
( ( sk1 @ strictorderedP )
| ( sk1 @ sk20 @ ssList ) ),
inference(pattern_uni,[status(thm)],[49908:[bind(A,$thf( sk1 ))]]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ? [B: $i] :
( ? [C: $i] :
( ( ( B @ ( C @ cons ) )
= A )
& ( C @ ssItem ) )
& ( B @ ssList ) )
| ( nil = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).
thf(301,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(45024,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk19 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,256]) ).
thf(45025,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk19 @ ssList ) ),
inference(simp,[status(thm)],[45024]) ).
thf(45026,plain,
( ( sk1 @ strictorderedP )
| ( sk1 @ sk19 @ ssList ) ),
inference(pattern_uni,[status(thm)],[45025:[bind(A,$thf( sk1 ))]]) ).
thf(45454,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[45026,333]) ).
thf(45455,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[45454]) ).
thf(45456,plain,
( ( nil @ ( sk1 @ sk19 @ rearsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[45455:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(74,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( ( A @ tl @ ( A @ hd @ cons ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax78) ).
thf(436,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( ( A @ tl @ ( A @ hd @ cons ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(206,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk10 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[200]) ).
thf(17790,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,206]) ).
thf(17791,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ssList ) ),
inference(simp,[status(thm)],[17790]) ).
thf(17792,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk10 @ ssList ) ),
inference(pattern_uni,[status(thm)],[17791:[bind(A,$thf( sk2 ))]]) ).
thf(17923,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17792,280]) ).
thf(17924,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17923]) ).
thf(17925,plain,
( ( nil @ ( sk2 @ sk10 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17924:[bind(A,$thf( sk2 @ sk10 ))]]) ).
thf(26977,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[26787,407]) ).
thf(26978,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[26977]) ).
thf(26979,plain,
( ( nil @ ( sk2 @ sk16 @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[26978:[bind(A,$thf( sk2 @ sk16 ))]]) ).
thf(22,axiom,
nil @ totalorderedP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax66) ).
thf(174,plain,
nil @ totalorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(6289,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ sk9 @ sk9 @ cyclefreeP )
| ( sk2 @ sk9 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[1418,280]) ).
thf(6290,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ sk9 @ sk9 @ cyclefreeP )
| ( sk2 @ sk9 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[6289]) ).
thf(6291,plain,
( ( nil @ ( sk2 @ sk9 @ sk9 @ sk9 @ segmentP ) )
| ( sk2 @ sk9 @ sk9 @ cyclefreeP )
| ( sk2 @ sk9 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[6290:[bind(A,$thf( sk2 @ sk9 @ sk9 @ sk9 ))]]) ).
thf(205,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk11 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[200]) ).
thf(17249,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,205]) ).
thf(17250,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssList ) ),
inference(simp,[status(thm)],[17249]) ).
thf(17251,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk11 @ ssList ) ),
inference(pattern_uni,[status(thm)],[17250:[bind(A,$thf( sk1 ))]]) ).
thf(17473,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17251,333]) ).
thf(17474,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17473]) ).
thf(17475,plain,
( ( nil @ ( sk1 @ sk11 @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17474:[bind(A,$thf( sk1 @ sk11 ))]]) ).
thf(45495,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[45026,280]) ).
thf(45496,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[45495]) ).
thf(45497,plain,
( ( nil @ ( sk1 @ sk19 @ segmentP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[45496:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(25497,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[25109,280]) ).
thf(25498,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[25497]) ).
thf(25499,plain,
( ( nil @ ( sk1 @ sk14 @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25498:[bind(A,$thf( sk1 @ sk14 ))]]) ).
thf(26825,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,220]) ).
thf(26826,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk16 @ ssList ) ),
inference(simp,[status(thm)],[26825]) ).
thf(26827,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk16 @ ssList ) ),
inference(pattern_uni,[status(thm)],[26826:[bind(A,$thf( sk1 ))]]) ).
thf(87,axiom,
nil @ equalelemsP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax74) ).
thf(504,plain,
nil @ equalelemsP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(1328,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[663,333]) ).
thf(1329,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1328]) ).
thf(1330,plain,
( ( nil @ ( sk1 @ sk9 @ sk9 @ rearsegP ) )
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1329:[bind(A,$thf( sk1 @ sk9 @ sk9 ))]]) ).
thf(124,plain,
sk5 != sk6,
inference(cnfConj,[status(thm)],[121]) ).
thf(125,plain,
sk6 != sk5,
inference(lifteq,[status(thm)],[124]) ).
thf(731,plain,
( ( ( sk1 @ sk9 )
!= sk1 )
| ( sk1 @ sk9 @ sk9 @ ssList )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[729]) ).
thf(1453,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( ( sk1 @ sk9 )
!= sk1 )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[731,280]) ).
thf(1454,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( ( sk1 @ sk9 )
!= sk1 )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1453]) ).
thf(1455,plain,
( ( nil @ ( sk1 @ sk9 @ sk9 @ segmentP ) )
| ( ( sk1 @ sk9 )
!= sk1 )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1454:[bind(A,$thf( sk1 @ sk9 @ sk9 ))]]) ).
thf(123,plain,
sk6 @ ssItem,
inference(cnfConj,[status(thm)],[121]) ).
thf(43149,plain,
( ( ( sk6 @ ssItem )
!= ( nil @ ssItem ) )
| ~ $true
| ~ ( sk1 @ ssItem )
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[123,38166]) ).
thf(43150,plain,
( ( ( sk6 @ ssItem )
!= ( nil @ ssItem ) )
| ~ ( sk1 @ ssItem )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[43149]) ).
thf(43353,plain,
( ( sk6 != nil )
| ~ ( sk1 @ ssItem )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[43150]) ).
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/sandbox2/benchmark/theBenchmark.p',ax82) ).
thf(196,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(19,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ lt ) )
<=> ( ( B @ ( A @ leq ) )
& ( A != B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax93) ).
thf(157,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(1407,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ sk9 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[669,333]) ).
thf(1408,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ sk9 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1407]) ).
thf(1409,plain,
( ( nil @ ( sk2 @ sk9 @ sk9 @ rearsegP ) )
| ( sk2 @ sk9 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1408:[bind(A,$thf( sk2 @ sk9 @ sk9 ))]]) ).
thf(5951,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ~ $true
| ( sk1 @ sk9 @ sk9 @ cyclefreeP )
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[728,201]) ).
thf(5952,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ( sk1 @ sk9 @ sk9 @ cyclefreeP )
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5951]) ).
thf(5953,plain,
( ( sk1 @ sk9 @ sk9 @ sk9 @ cyclefreeP )
| ( sk1 @ sk9 @ sk9 @ sk9 @ sk9 @ ssList )
| ( sk1 @ sk9 @ sk9 @ cyclefreeP )
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5952:[bind(A,$thf( sk1 @ sk9 @ sk9 @ sk9 ))]]) ).
thf(169,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[168]) ).
thf(171,plain,
! [A: $i] :
( ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[169]) ).
thf(8076,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[104,171]) ).
thf(8077,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[8076]) ).
thf(8078,plain,
( ~ ( sk1 @ ( nil @ frontsegP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[8077:[bind(A,$thf( sk1 ))]]) ).
thf(551,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ segmentP ) )
!= ( A @ ( sk2 @ segmentP ) ) )
| ~ ( A @ equalelemsP )
| ~ ( sk1 @ ( A @ segmentP ) )
| ~ $true
| ~ ( A @ ( sk1 @ neq ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[548,538]) ).
thf(552,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ segmentP ) )
!= ( A @ ( sk2 @ segmentP ) ) )
| ~ ( A @ equalelemsP )
| ~ ( sk1 @ ( A @ segmentP ) )
| ~ ( A @ ( sk1 @ neq ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[551]) ).
thf(553,plain,
( ~ ( sk1 @ equalelemsP )
| ~ ( sk1 @ ( sk1 @ segmentP ) )
| ~ ( sk1 @ ( sk1 @ neq ) )
| ~ ( sk1 @ ssList ) ),
inference(pattern_uni,[status(thm)],[552:[bind(A,$thf( sk1 ))]]) ).
thf(109,plain,
sk3 @ equalelemsP,
inference(cnfConj,[status(thm)],[99]) ).
thf(535,plain,
sk1 @ equalelemsP,
inference(rewrite,[status(thm)],[109,112]) ).
thf(577,plain,
( ~ $true
| ~ ( sk1 @ ( sk1 @ segmentP ) )
| ~ ( sk1 @ ( sk1 @ neq ) )
| ~ $true ),
inference(rewrite,[status(thm)],[553,535,104]) ).
thf(578,plain,
( ~ ( sk1 @ ( sk1 @ segmentP ) )
| ~ ( sk1 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[577]) ).
thf(7051,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,238]) ).
thf(7052,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[7051]) ).
thf(7053,plain,
sk1 @ ( sk1 @ segmentP ),
inference(pattern_uni,[status(thm)],[7052:[bind(A,$thf( sk1 ))]]) ).
thf(7113,plain,
( ~ $true
| ~ ( sk1 @ ( sk1 @ neq ) ) ),
inference(rewrite,[status(thm)],[578,7053]) ).
thf(7114,plain,
~ ( sk1 @ ( sk1 @ neq ) ),
inference(simp,[status(thm)],[7113]) ).
thf(8609,plain,
( ( sk1 != sk1 )
| ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[8078,7114]) ).
thf(8610,plain,
( ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[8609:[]]) ).
thf(43147,plain,
( ( ( sk6 @ ssItem )
!= ( sk1 @ ssItem ) )
| ~ ( nil @ ssItem )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[123,38166]) ).
thf(43148,plain,
( ( ( sk6 @ ssItem )
!= ( sk1 @ ssItem ) )
| ~ ( nil @ ssItem )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[43147]) ).
thf(43340,plain,
( ( sk6 != sk1 )
| ~ ( nil @ ssItem )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[43148]) ).
thf(46467,plain,
( ( ( sk5 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk6 != sk1 )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[122,43340]) ).
thf(46468,plain,
( ( ( sk5 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk6 != sk1 )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[46467]) ).
thf(46477,plain,
( ( sk5 != nil )
| ( sk6 != sk1 )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[46468]) ).
thf(19686,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,208]) ).
thf(19687,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ssItem ) ),
inference(simp,[status(thm)],[19686]) ).
thf(19688,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk8 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[19687:[bind(A,$thf( sk2 ))]]) ).
thf(19957,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19688,240]) ).
thf(19958,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19957]) ).
thf(19959,plain,
( ( nil @ ( sk2 @ sk8 @ cons ) @ totalorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19958:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(1512,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,407]) ).
thf(1513,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) ) ),
inference(simp,[status(thm)],[1512]) ).
thf(1514,plain,
nil @ ( sk2 @ frontsegP ),
inference(pattern_uni,[status(thm)],[1513:[bind(A,$thf( sk2 ))]]) ).
thf(10951,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[103,184]) ).
thf(10952,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[10951]) ).
thf(10953,plain,
( ~ ( sk2 @ ( nil @ segmentP ) )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[10952:[bind(A,$thf( sk2 ))]]) ).
thf(106,plain,
( ( nil != sk1 )
| ( nil != sk2 ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(111,plain,
( ( sk1 != nil )
| ( sk2 != nil ) ),
inference(lifteq,[status(thm)],[106]) ).
thf(11661,plain,
( ( sk2 != sk2 )
| ( sk1 != nil )
| ( nil != nil )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[10953,111]) ).
thf(11662,plain,
( ( sk2 != sk2 )
| ( sk1 != nil )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[11661]) ).
thf(11663,plain,
( ( sk1 != nil )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[11662:[]]) ).
thf(12048,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) )
| ( sk1 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7053,11663]) ).
thf(12049,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[12048]) ).
thf(12109,plain,
( ( sk2 != sk1 )
| ( sk1 != nil )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[12049]) ).
thf(12132,plain,
( ( sk2 != sk1 )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[12109]) ).
thf(12135,plain,
( ( sk1 != sk1 )
| ( sk2 != sk1 )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[11175,12132]) ).
thf(12136,plain,
( ( sk1 != sk1 )
| ( sk2 != sk1 )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[12135]) ).
thf(12137,plain,
( ( sk2 != sk1 )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[12136:[]]) ).
thf(7503,plain,
! [A: $i] :
( ( A != sk6 )
| ( sk5 != nil )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[171,125]) ).
thf(7504,plain,
( ( sk5 != nil )
| ~ ( sk6 @ ( nil @ frontsegP ) )
| ~ ( sk6 @ ssList ) ),
inference(pattern_uni,[status(thm)],[7503:[bind(A,$thf( sk6 ))]]) ).
thf(24365,plain,
( ( ( sk6 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk5 != nil )
| ~ ( sk6 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,7504]) ).
thf(24366,plain,
( ( ( sk6 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk5 != nil )
| ~ ( sk6 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[24365]) ).
thf(24454,plain,
( ( sk6 != sk1 )
| ( sk5 != nil )
| ~ ( sk6 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[24366]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax29) ).
thf(128,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(129,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[128]) ).
thf(130,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A = B ) ),
inference(lifteq,[status(thm)],[129]) ).
thf(961,plain,
! [B: $i,A: $i] :
( ( A != sk6 )
| ( B != sk5 )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[130,125]) ).
thf(962,plain,
! [A: $i] :
( ( A != sk5 )
| ~ ( sk6 @ ( A @ leq ) )
| ~ ( A @ ( sk6 @ leq ) )
| ~ ( A @ ssItem )
| ~ ( sk6 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[961:[bind(A,$thf( sk6 ))]]) ).
thf(1290,plain,
( ~ ( sk6 @ ( sk5 @ leq ) )
| ~ ( sk5 @ ( sk6 @ leq ) )
| ~ ( sk5 @ ssItem )
| ~ ( sk6 @ ssItem ) ),
inference(simp,[status(thm)],[962]) ).
thf(1772,plain,
( ~ ( sk6 @ ( sk5 @ leq ) )
| ~ ( sk5 @ ( sk6 @ leq ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[1290,122,123]) ).
thf(1773,plain,
( ~ ( sk6 @ ( sk5 @ leq ) )
| ~ ( sk5 @ ( sk6 @ leq ) ) ),
inference(simp,[status(thm)],[1772]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ equalelemsP ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax73) ).
thf(334,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ equalelemsP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(335,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ equalelemsP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[334]) ).
thf(19954,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19688,335]) ).
thf(19955,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19954]) ).
thf(19956,plain,
( ( nil @ ( sk2 @ sk8 @ cons ) @ equalelemsP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19955:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(42997,plain,
( ( sk1 != sk1 )
| ( sk2 != sk1 )
| ( nil != nil )
| ~ ( nil @ ssItem )
| ~ ( sk1 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[38166,12132]) ).
thf(42998,plain,
( ( sk1 != sk1 )
| ( sk2 != sk1 )
| ~ ( nil @ ssItem )
| ~ ( sk1 @ ssItem ) ),
inference(simp,[status(thm)],[42997]) ).
thf(42999,plain,
( ( sk2 != sk1 )
| ~ ( nil @ ssItem )
| ~ ( sk1 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[42998:[]]) ).
thf(43536,plain,
( ( ( sk5 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk2 != sk1 )
| ~ $true
| ~ ( sk1 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[122,42999]) ).
thf(43537,plain,
( ( ( sk5 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk2 != sk1 )
| ~ ( sk1 @ ssItem ) ),
inference(simp,[status(thm)],[43536]) ).
thf(43547,plain,
( ( sk5 != nil )
| ( sk2 != sk1 )
| ~ ( sk1 @ ssItem ) ),
inference(simp,[status(thm)],[43537]) ).
thf(7045,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[643,238]) ).
thf(7046,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7045]) ).
thf(7047,plain,
( ( sk1 @ sk9 @ ( sk1 @ sk9 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7046:[bind(A,$thf( sk1 @ sk9 ))]]) ).
thf(59709,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59632,407]) ).
thf(59710,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) ) ),
inference(simp,[status(thm)],[59709]) ).
thf(59711,plain,
nil @ ( nil @ ( nil @ sk22 ) @ frontsegP ),
inference(pattern_uni,[status(thm)],[59710:[bind(A,$thf( nil @ ( nil @ sk22 ) ))]]) ).
thf(222,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)],[216]) ).
thf(228,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)],[222]) ).
thf(221,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk15 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[216]) ).
thf(27877,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk15 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,221]) ).
thf(27878,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk15 @ ssList ) ),
inference(simp,[status(thm)],[27877]) ).
thf(27879,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk15 @ ssList ) ),
inference(pattern_uni,[status(thm)],[27878:[bind(A,$thf( sk1 ))]]) ).
thf(28242,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[27879,407]) ).
thf(28243,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[28242]) ).
thf(28244,plain,
( ( nil @ ( sk1 @ sk15 @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[28243:[bind(A,$thf( sk1 @ sk15 ))]]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderedP ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax68) ).
thf(165,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(166,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[165]) ).
thf(1712,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[123,166]) ).
thf(1713,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[1712]) ).
thf(1714,plain,
nil @ ( sk6 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[1713:[bind(A,$thf( sk6 ))]]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) @ hd )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax23) ).
thf(177,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) @ hd )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(178,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ cons ) @ hd )
= B )
| ~ ( B @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[177]) ).
thf(179,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( ( A @ ( B @ cons ) @ hd )
= B ) ),
inference(lifteq,[status(thm)],[178]) ).
thf(42,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ app ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
thf(251,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ app ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(252,plain,
! [A: $i] :
( ( ( A @ ( nil @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[251]) ).
thf(253,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[252]) ).
thf(51171,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk18 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,262]) ).
thf(51172,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk18 @ ssItem ) ),
inference(simp,[status(thm)],[51171]) ).
thf(51173,plain,
( ( sk1 @ strictorderedP )
| ( sk1 @ sk18 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[51172:[bind(A,$thf( sk1 ))]]) ).
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/sandbox2/benchmark/theBenchmark.p',ax44) ).
thf(348,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(8478,plain,
( ( sk1 != sk1 )
| ~ ( nil @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[8078,550]) ).
thf(8479,plain,
( ~ ( nil @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[8478:[]]) ).
thf(20221,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19748,431]) ).
thf(20222,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[20221]) ).
thf(20223,plain,
( ( nil @ ( sk1 @ sk8 @ cons ) @ duplicatefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[20222:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(259,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk21 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[255]) ).
thf(48476,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk21 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,259]) ).
thf(48477,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk21 @ ssList ) ),
inference(simp,[status(thm)],[48476]) ).
thf(48478,plain,
( ( sk1 @ strictorderedP )
| ( sk1 @ sk21 @ ssList ) ),
inference(pattern_uni,[status(thm)],[48477:[bind(A,$thf( sk1 ))]]) ).
thf(48959,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[48478,280]) ).
thf(48960,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[48959]) ).
thf(48961,plain,
( ( nil @ ( sk1 @ sk21 @ segmentP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[48960:[bind(A,$thf( sk1 @ sk21 ))]]) ).
thf(1413,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ sk9 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[669,280]) ).
thf(1414,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ sk9 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1413]) ).
thf(1415,plain,
( ( nil @ ( sk2 @ sk9 @ sk9 @ segmentP ) )
| ( sk2 @ sk9 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1414:[bind(A,$thf( sk2 @ sk9 @ sk9 ))]]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ geq ) )
<=> ( A @ ( B @ leq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax32) ).
thf(147,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(34,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil @ ( A @ app ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).
thf(229,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil @ ( A @ app ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(230,plain,
! [A: $i] :
( ( ( nil @ ( A @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[229]) ).
thf(231,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[230]) ).
thf(34243,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[103,231]) ).
thf(34244,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[34243]) ).
thf(34245,plain,
( ( nil @ ( sk2 @ app ) )
= sk2 ),
inference(pattern_uni,[status(thm)],[34244:[bind(A,$thf( sk2 ))]]) ).
thf(17222,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,205]) ).
thf(17223,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk11 @ ssList ) ),
inference(simp,[status(thm)],[17222]) ).
thf(17224,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk11 @ ssList ) ),
inference(pattern_uni,[status(thm)],[17223:[bind(A,$thf( sk2 ))]]) ).
thf(17347,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17224,280]) ).
thf(17348,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17347]) ).
thf(17349,plain,
( ( nil @ ( sk2 @ sk11 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17348:[bind(A,$thf( sk2 @ sk11 ))]]) ).
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/sandbox2/benchmark/theBenchmark.p',ax6) ).
thf(453,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(8,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ lt ) )
=> ~ ( A @ ( B @ lt ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax33) ).
thf(131,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(132,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ lt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[131]) ).
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/sandbox2/benchmark/theBenchmark.p',ax34) ).
thf(133,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(2807,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[123,335]) ).
thf(2808,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP ) ),
inference(simp,[status(thm)],[2807]) ).
thf(2809,plain,
nil @ ( sk6 @ cons ) @ equalelemsP,
inference(pattern_uni,[status(thm)],[2808:[bind(A,$thf( sk6 ))]]) ).
thf(1497,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,407]) ).
thf(1498,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) ) ),
inference(simp,[status(thm)],[1497]) ).
thf(1499,plain,
nil @ ( sk1 @ frontsegP ),
inference(pattern_uni,[status(thm)],[1498:[bind(A,$thf( sk1 ))]]) ).
thf(10094,plain,
( ( ( nil @ ( sk1 @ frontsegP ) )
!= ( sk1 @ ( nil @ frontsegP ) ) )
| ~ ( sk1 @ ( nil @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1499,8610]) ).
thf(10095,plain,
( ( ( nil @ ( sk1 @ frontsegP ) )
!= ( sk1 @ ( nil @ frontsegP ) ) )
| ~ ( sk1 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[10094]) ).
thf(10137,plain,
( ( sk1 != nil )
| ( sk1 != nil )
| ~ ( sk1 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[10095]) ).
thf(10152,plain,
( ( sk1 != nil )
| ~ ( sk1 @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[10137]) ).
thf(11781,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[11175,10152]) ).
thf(11782,plain,
( ( sk1 != sk1 )
| ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[11781]) ).
thf(11783,plain,
( ~ ( sk1 @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[11782:[]]) ).
thf(7882,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[103,171]) ).
thf(7883,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[7882]) ).
thf(7884,plain,
( ~ ( sk2 @ ( nil @ frontsegP ) )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[7883:[bind(A,$thf( sk2 ))]]) ).
thf(8389,plain,
( ( sk2 != sk2 )
| ( sk1 @ ( nil @ segmentP ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[7884,548]) ).
thf(8390,plain,
( ( sk1 @ ( nil @ segmentP ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[8389:[]]) ).
thf(9895,plain,
( ( ( nil @ ( sk2 @ frontsegP ) )
!= ( sk2 @ ( nil @ frontsegP ) ) )
| ( sk1 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1514,8390]) ).
thf(9896,plain,
( ( ( nil @ ( sk2 @ frontsegP ) )
!= ( sk2 @ ( nil @ frontsegP ) ) )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[9895]) ).
thf(9960,plain,
( ( sk2 != nil )
| ( sk2 != nil )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[9896]) ).
thf(9967,plain,
( ( sk2 != nil )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[9960]) ).
thf(11915,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ( sk2 != nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[11175,111]) ).
thf(11916,plain,
( ( sk1 != sk1 )
| ( sk2 != nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[11915]) ).
thf(11917,plain,
( ( sk2 != nil )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[11916:[]]) ).
thf(14542,plain,
( ( ( sk1 @ ( nil @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ( sk2 != nil )
| ~ $true
| ( sk2 != nil ) ),
inference(paramod_ordered,[status(thm)],[9967,11917]) ).
thf(14543,plain,
( ( ( sk1 @ ( nil @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[14542]) ).
thf(14544,plain,
sk2 != nil,
inference(pattern_uni,[status(thm)],[14543:[]]) ).
thf(14652,plain,
~ ( sk2 @ ( nil @ frontsegP ) ),
inference(simplifyReflect,[status(thm)],[7884,14544]) ).
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/sandbox2/benchmark/theBenchmark.p',ax70) ).
thf(312,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(48,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ( A @ tl )
= B )
& ( B @ ssList ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax76) ).
thf(281,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ( A @ tl )
= B )
& ( B @ ssList ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(282,plain,
! [A: $i] :
( ( ( ( A @ tl )
= ( A @ sk23 ) )
| ( nil = A )
| ~ ( A @ ssList ) )
& ( ( A @ sk23 @ ssList )
| ( nil = A )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[281]) ).
thf(283,plain,
! [A: $i] :
( ( A @ sk23 @ ssList )
| ( nil = A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[282]) ).
thf(285,plain,
! [A: $i] :
( ( A @ sk23 @ ssList )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[283]) ).
thf(66643,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk23 @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[104,285]) ).
thf(66644,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk23 @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[66643]) ).
thf(66645,plain,
( ( sk1 @ sk23 @ ssList )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[66644:[bind(A,$thf( sk1 ))]]) ).
thf(51929,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[51173,268]) ).
thf(51930,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[51929]) ).
thf(51931,plain,
( ~ ( sk1 @ sk18 @ ( nil @ memberP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[51930:[bind(A,$thf( sk1 @ sk18 ))]]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ gt ) )
<=> ( A @ ( B @ lt ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax35) ).
thf(114,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(115,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)],[114]) ).
thf(116,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[115]) ).
thf(40,axiom,
nil @ duplicatefreeP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax72) ).
thf(243,plain,
nil @ duplicatefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(47132,plain,
! [A: $i] :
( ( ( sk2 @ sk17 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[46647,268]) ).
thf(47133,plain,
! [A: $i] :
( ( ( sk2 @ sk17 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[47132]) ).
thf(47134,plain,
( ~ ( sk2 @ sk17 @ ( nil @ memberP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[47133:[bind(A,$thf( sk2 @ sk17 ))]]) ).
thf(19031,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18673,440]) ).
thf(19032,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19031]) ).
thf(19033,plain,
( ( nil @ ( sk1 @ sk7 @ cons ) @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19032:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(8532,plain,
( ( sk1 != sk1 )
| ( sk1 @ ( nil @ segmentP ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[8078,7053]) ).
thf(8533,plain,
( ( sk1 @ ( nil @ segmentP ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[8532:[]]) ).
thf(16503,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk1 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[613,8533]) ).
thf(16504,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[16503]) ).
thf(16538,plain,
( ( sk1 != nil )
| ( nil != nil )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[16504]) ).
thf(16554,plain,
( ( sk1 != nil )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[16538]) ).
thf(10442,plain,
! [A: $i] :
( ( A != sk6 )
| ( sk5 != nil )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[184,125]) ).
thf(10443,plain,
( ( sk5 != nil )
| ~ ( sk6 @ ( nil @ segmentP ) )
| ~ ( sk6 @ ssList ) ),
inference(pattern_uni,[status(thm)],[10442:[bind(A,$thf( sk6 ))]]) ).
thf(29902,plain,
( ( ( sk6 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk5 != nil )
| ~ ( sk6 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,10443]) ).
thf(29903,plain,
( ( ( sk6 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk5 != nil )
| ~ ( sk6 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[29902]) ).
thf(30009,plain,
( ( sk6 != sk1 )
| ( sk5 != nil )
| ~ ( sk6 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[29903]) ).
thf(63803,plain,
( ( ( sk6 @ ( nil @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ( sk6 != sk1 )
| ( sk5 != nil )
| ~ $true
| ( sk1 != nil ) ),
inference(paramod_ordered,[status(thm)],[16554,30009]) ).
thf(63804,plain,
( ( ( sk6 @ ( nil @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ( sk6 != sk1 )
| ( sk5 != nil )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[63803]) ).
thf(63861,plain,
( ( sk6 != sk1 )
| ( nil != nil )
| ( sk6 != sk1 )
| ( sk5 != nil )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[63804]) ).
thf(63898,plain,
( ( sk6 != sk1 )
| ( sk5 != nil )
| ( sk1 != nil ) ),
inference(simp,[status(thm)],[63861]) ).
thf(117,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ gt ) )
| ~ ( A @ ( B @ lt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[115]) ).
thf(37409,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,249]) ).
thf(37410,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[37409]) ).
thf(37411,plain,
~ ( sk5 @ ( sk5 @ neq ) ),
inference(pattern_uni,[status(thm)],[37410:[bind(A,$thf( sk5 ))]]) ).
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/sandbox2/benchmark/theBenchmark.p',ax7) ).
thf(381,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(5560,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,152]) ).
thf(5561,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[5560]) ).
thf(5562,plain,
sk5 @ ( sk5 @ leq ),
inference(pattern_uni,[status(thm)],[5561:[bind(A,$thf( sk5 ))]]) ).
thf(1419,plain,
( ~ $true
| ( ( sk2 @ sk9 @ cyclefreeP )
!= ( sk2 @ cyclefreeP ) )
| ( sk2 @ sk9 @ sk9 @ ssList )
| ( sk2 @ cyclefreeP ) ),
inference(eqfactor_ordered,[status(thm)],[669]) ).
thf(1421,plain,
( ( ( sk2 @ sk9 )
!= sk2 )
| ( sk2 @ sk9 @ sk9 @ ssList )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1419]) ).
thf(1602,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( ( sk2 @ sk9 )
!= sk2 )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[1421,280]) ).
thf(1603,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( ( sk2 @ sk9 )
!= sk2 )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1602]) ).
thf(1604,plain,
( ( nil @ ( sk2 @ sk9 @ sk9 @ segmentP ) )
| ( ( sk2 @ sk9 )
!= sk2 )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1603:[bind(A,$thf( sk2 @ sk9 @ sk9 ))]]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ geq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax89) ).
thf(155,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(156,plain,
! [A: $i] :
( ( A @ ( A @ geq ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[155]) ).
thf(20155,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19748,156]) ).
thf(20156,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[20155]) ).
thf(20157,plain,
( ( sk1 @ sk8 @ ( sk1 @ sk8 @ geq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[20156:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( B @ segmentP ) )
& ( B @ ( A @ segmentP ) ) )
=> ( C @ ( A @ segmentP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax53) ).
thf(232,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(233,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)],[232]) ).
thf(78,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderP ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax63) ).
thf(451,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(452,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[451]) ).
thf(65773,plain,
! [A: $i] :
( ( A != sk2 )
| ( nil != nil )
| ( A @ sk23 @ ssList )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[285,14544]) ).
thf(65774,plain,
! [A: $i] :
( ( A != sk2 )
| ( A @ sk23 @ ssList )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[65773]) ).
thf(65775,plain,
( ( sk2 @ sk23 @ ssList )
| ~ ( sk2 @ ssList ) ),
inference(pattern_uni,[status(thm)],[65774:[bind(A,$thf( sk2 ))]]) ).
thf(67631,plain,
( ( sk2 @ sk23 @ ssList )
| ~ $true ),
inference(rewrite,[status(thm)],[65775,103]) ).
thf(67632,plain,
sk2 @ sk23 @ ssList,
inference(simp,[status(thm)],[67631]) ).
thf(67709,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[67632,407]) ).
thf(67710,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) ) ),
inference(simp,[status(thm)],[67709]) ).
thf(67711,plain,
nil @ ( sk2 @ sk23 @ frontsegP ),
inference(pattern_uni,[status(thm)],[67710:[bind(A,$thf( sk2 @ sk23 ))]]) ).
thf(270,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)],[269]) ).
thf(96,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( nil != A )
=> ( ( B @ ( A @ app ) @ hd )
= ( A @ hd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax85) ).
thf(529,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(43534,plain,
( ( ( sk5 @ ssItem )
!= ( sk1 @ ssItem ) )
| ( sk2 != sk1 )
| ~ ( nil @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,42999]) ).
thf(43535,plain,
( ( ( sk5 @ ssItem )
!= ( sk1 @ ssItem ) )
| ( sk2 != sk1 )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[43534]) ).
thf(43546,plain,
( ( sk5 != sk1 )
| ( sk2 != sk1 )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[43535]) ).
thf(45883,plain,
( ( ( sk6 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk5 != sk1 )
| ( sk2 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[123,43546]) ).
thf(45884,plain,
( ( ( sk6 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk5 != sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[45883]) ).
thf(45951,plain,
( ( sk6 != nil )
| ( sk5 != sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[45884]) ).
thf(27163,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[26827,238]) ).
thf(27164,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[27163]) ).
thf(27165,plain,
( ( sk1 @ sk16 @ ( sk1 @ sk16 @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[27164:[bind(A,$thf( sk1 @ sk16 ))]]) ).
thf(23793,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ~ ( A @ sk13 @ ( A @ sk12 @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,217]) ).
thf(23794,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ~ ( A @ sk13 @ ( A @ sk12 @ lt ) ) ),
inference(simp,[status(thm)],[23793]) ).
thf(23795,plain,
( ( sk2 @ strictorderP )
| ~ ( sk2 @ sk13 @ ( sk2 @ sk12 @ lt ) ) ),
inference(pattern_uni,[status(thm)],[23794:[bind(A,$thf( sk2 ))]]) ).
thf(158,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)],[157]) ).
thf(160,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( B @ ( A @ lt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[158]) ).
thf(18611,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,207]) ).
thf(18612,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssItem ) ),
inference(simp,[status(thm)],[18611]) ).
thf(18613,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk7 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[18612:[bind(A,$thf( sk2 ))]]) ).
thf(18819,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18613,452]) ).
thf(18820,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18819]) ).
thf(18821,plain,
( ( nil @ ( sk2 @ sk7 @ cons ) @ strictorderP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18820:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(59633,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59632,333]) ).
thf(59634,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[59633]) ).
thf(59635,plain,
nil @ ( nil @ ( nil @ sk22 ) @ rearsegP ),
inference(pattern_uni,[status(thm)],[59634:[bind(A,$thf( nil @ ( nil @ sk22 ) ))]]) ).
thf(20106,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19748,440]) ).
thf(20107,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[20106]) ).
thf(20108,plain,
( ( nil @ ( sk1 @ sk8 @ cons ) @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[20107:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(48987,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[48478,407]) ).
thf(48988,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[48987]) ).
thf(48989,plain,
( ( nil @ ( sk1 @ sk21 @ frontsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[48988:[bind(A,$thf( sk1 @ sk21 ))]]) ).
thf(19912,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19688,156]) ).
thf(19913,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19912]) ).
thf(19914,plain,
( ( sk2 @ sk8 @ ( sk2 @ sk8 @ geq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19913:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(1500,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( ( sk1 @ sk9 )
!= sk1 )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[731,407]) ).
thf(1501,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( ( sk1 @ sk9 )
!= sk1 )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1500]) ).
thf(1502,plain,
( ( nil @ ( sk1 @ sk9 @ sk9 @ frontsegP ) )
| ( ( sk1 @ sk9 )
!= sk1 )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1501:[bind(A,$thf( sk1 @ sk9 @ sk9 ))]]) ).
thf(5954,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ sk9 @ sk9 @ cyclefreeP )
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[728,407]) ).
thf(5955,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ sk9 @ sk9 @ cyclefreeP )
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5954]) ).
thf(5956,plain,
( ( nil @ ( sk1 @ sk9 @ sk9 @ sk9 @ frontsegP ) )
| ( sk1 @ sk9 @ sk9 @ cyclefreeP )
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5955:[bind(A,$thf( sk1 @ sk9 @ sk9 @ sk9 ))]]) ).
thf(786,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,280]) ).
thf(787,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[786]) ).
thf(788,plain,
nil @ ( sk2 @ segmentP ),
inference(pattern_uni,[status(thm)],[787:[bind(A,$thf( sk2 ))]]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ leq ) )
=> ( ( B @ ( A @ lt ) )
| ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax92) ).
thf(137,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(19978,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19688,431]) ).
thf(19979,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19978]) ).
thf(19980,plain,
( ( nil @ ( sk2 @ sk8 @ cons ) @ duplicatefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19979:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ tl @ ssList ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).
thf(329,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ tl @ ssList ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(80,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ rearsegP ) )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52) ).
thf(461,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(48430,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk21 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,259]) ).
thf(48431,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk21 @ ssList ) ),
inference(simp,[status(thm)],[48430]) ).
thf(48432,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk21 @ ssList ) ),
inference(pattern_uni,[status(thm)],[48431:[bind(A,$thf( sk2 ))]]) ).
thf(48673,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[48432,280]) ).
thf(48674,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[48673]) ).
thf(48675,plain,
( ( nil @ ( sk2 @ sk21 @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[48674:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(17344,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17224,238]) ).
thf(17345,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17344]) ).
thf(17346,plain,
( ( sk2 @ sk11 @ ( sk2 @ sk11 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17345:[bind(A,$thf( sk2 @ sk11 ))]]) ).
thf(19080,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18673,156]) ).
thf(19081,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19080]) ).
thf(19082,plain,
( ( sk1 @ sk7 @ ( sk1 @ sk7 @ geq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19081:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(59670,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59632,238]) ).
thf(59671,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[59670]) ).
thf(59672,plain,
nil @ ( nil @ sk22 ) @ ( nil @ ( nil @ sk22 ) @ segmentP ),
inference(pattern_uni,[status(thm)],[59671:[bind(A,$thf( nil @ ( nil @ sk22 ) ))]]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( A @ lt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax90) ).
thf(140,plain,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(141,plain,
! [A: $i] :
( ~ ( A @ ( A @ lt ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[140]) ).
thf(3075,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,141]) ).
thf(3076,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[3075]) ).
thf(3077,plain,
~ ( sk5 @ ( sk5 @ lt ) ),
inference(pattern_uni,[status(thm)],[3076:[bind(A,$thf( sk5 ))]]) ).
thf(3115,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ lt ) )
!= ( sk5 @ ( sk5 @ lt ) ) )
| ~ $true
| ~ ( B @ ( A @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[116,3077]) ).
thf(3116,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ lt ) )
!= ( sk5 @ ( sk5 @ lt ) ) )
| ~ ( B @ ( A @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[3115]) ).
thf(3117,plain,
( ~ ( sk5 @ ( sk5 @ gt ) )
| ~ ( sk5 @ ssItem )
| ~ ( sk5 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[3116:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 ))]]) ).
thf(3133,plain,
( ~ ( sk5 @ ( sk5 @ gt ) )
| ~ ( sk5 @ ssItem ) ),
inference(simp,[status(thm)],[3117]) ).
thf(3190,plain,
( ~ ( sk5 @ ( sk5 @ gt ) )
| ~ $true ),
inference(rewrite,[status(thm)],[3133,122]) ).
thf(3191,plain,
~ ( sk5 @ ( sk5 @ gt ) ),
inference(simp,[status(thm)],[3190]) ).
thf(4583,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,440]) ).
thf(4584,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP ) ),
inference(simp,[status(thm)],[4583]) ).
thf(4585,plain,
nil @ ( sk5 @ cons ) @ cyclefreeP,
inference(pattern_uni,[status(thm)],[4584:[bind(A,$thf( sk5 ))]]) ).
thf(73,axiom,
nil @ strictorderP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax64) ).
thf(435,plain,
nil @ strictorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(2818,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,335]) ).
thf(2819,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP ) ),
inference(simp,[status(thm)],[2818]) ).
thf(2820,plain,
nil @ ( sk5 @ cons ) @ equalelemsP,
inference(pattern_uni,[status(thm)],[2819:[bind(A,$thf( sk5 ))]]) ).
thf(224,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk12 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[216]) ).
thf(94,axiom,
nil @ totalorderP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax62) ).
thf(519,plain,
nil @ totalorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(1760,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[123,240]) ).
thf(1761,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[1760]) ).
thf(1762,plain,
nil @ ( sk6 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[1761:[bind(A,$thf( sk6 ))]]) ).
thf(25510,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[25109,407]) ).
thf(25511,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[25510]) ).
thf(25512,plain,
( ( nil @ ( sk1 @ sk14 @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25511:[bind(A,$thf( sk1 @ sk14 ))]]) ).
thf(43465,plain,
( ( ( sk6 @ ssItem )
!= ( sk1 @ ssItem ) )
| ( sk2 != sk1 )
| ~ ( nil @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[123,42999]) ).
thf(43466,plain,
( ( ( sk6 @ ssItem )
!= ( sk1 @ ssItem ) )
| ( sk2 != sk1 )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[43465]) ).
thf(43539,plain,
( ( sk6 != sk1 )
| ( sk2 != sk1 )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[43466]) ).
thf(44562,plain,
( ( ( sk6 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk6 != sk1 )
| ( sk2 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[123,43539]) ).
thf(44563,plain,
( ( ( sk6 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk6 != sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[44562]) ).
thf(44621,plain,
( ( sk6 != nil )
| ( sk6 != sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[44563]) ).
thf(45182,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[44983,333]) ).
thf(45183,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[45182]) ).
thf(45184,plain,
( ( nil @ ( sk2 @ sk19 @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[45183:[bind(A,$thf( sk2 @ sk19 ))]]) ).
thf(59837,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[59632,231]) ).
thf(59838,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[59837]) ).
thf(59839,plain,
( ( nil @ ( nil @ ( nil @ sk22 ) @ app ) )
= ( nil @ ( nil @ sk22 ) ) ),
inference(pattern_uni,[status(thm)],[59838:[bind(A,$thf( nil @ ( nil @ sk22 ) ))]]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( A @ ( B @ frontsegP ) )
& ( B @ ( A @ frontsegP ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax41) ).
thf(188,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(24361,plain,
( ( ( sk6 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk5 != nil )
| ~ $true
| ~ ( sk6 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[613,7504]) ).
thf(24362,plain,
( ( ( sk6 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk5 != nil )
| ~ ( sk6 @ ssList ) ),
inference(simp,[status(thm)],[24361]) ).
thf(24442,plain,
( ( sk6 != nil )
| ( nil != nil )
| ( sk5 != nil )
| ~ ( sk6 @ ssList ) ),
inference(simp,[status(thm)],[24362]) ).
thf(24503,plain,
( ( sk6 != nil )
| ( sk5 != nil )
| ~ ( sk6 @ ssList ) ),
inference(simp,[status(thm)],[24442]) ).
thf(24541,plain,
( ( ( sk6 @ ssList )
!= ( nil @ ssList ) )
| ( sk6 != nil )
| ( sk5 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[377,24503]) ).
thf(24542,plain,
( ( ( sk6 @ ssList )
!= ( nil @ ssList ) )
| ( sk6 != nil )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[24541]) ).
thf(24639,plain,
( ( sk6 != nil )
| ( sk6 != nil )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[24542]) ).
thf(24652,plain,
( ( sk6 != nil )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[24639]) ).
thf(183,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ( nil != A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[181]) ).
thf(185,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[183]) ).
thf(186,plain,
( ( nil @ ( nil @ segmentP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[185]) ).
thf(614,plain,
( ( nil @ ( nil @ segmentP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[186,377]) ).
thf(615,plain,
nil @ ( nil @ segmentP ),
inference(simp,[status(thm)],[614]) ).
thf(60,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( B @ ( A @ neq ) )
<=> ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
thf(356,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(19894,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19688,452]) ).
thf(19895,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19894]) ).
thf(19896,plain,
( ( nil @ ( sk2 @ sk8 @ cons ) @ strictorderP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19895:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) )
= ( A @ ( nil @ ( B @ cons ) @ app ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax81) ).
thf(191,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(192,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ cons ) )
= ( A @ ( nil @ ( B @ cons ) @ app ) ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[191]) ).
thf(193,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( ( A @ ( nil @ ( B @ cons ) @ app ) )
= ( A @ ( B @ cons ) ) ) ),
inference(lifteq,[status(thm)],[192]) ).
thf(43703,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[104,253]) ).
thf(43704,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[43703]) ).
thf(43705,plain,
( ( sk1 @ ( nil @ app ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[43704:[bind(A,$thf( sk1 ))]]) ).
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/sandbox2/benchmark/theBenchmark.p',ax47) ).
thf(489,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(1790,plain,
( ~ $true
| ( ( sk5 @ ( sk6 @ leq ) )
!= ( sk6 @ ( sk5 @ leq ) ) )
| ~ ( sk6 @ ( sk5 @ leq ) ) ),
inference(eqfactor_ordered,[status(thm)],[1773]) ).
thf(1791,plain,
( ( ( sk5 @ ( sk6 @ leq ) )
!= ( sk6 @ ( sk5 @ leq ) ) )
| ~ ( sk6 @ ( sk5 @ leq ) ) ),
inference(simp,[status(thm)],[1790]) ).
thf(203,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)],[200]) ).
thf(211,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)],[203]) ).
thf(212,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)],[211]) ).
thf(30578,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk13 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,225]) ).
thf(30579,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk13 @ ssItem ) ),
inference(simp,[status(thm)],[30578]) ).
thf(30580,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk13 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[30579:[bind(A,$thf( sk1 ))]]) ).
thf(92,axiom,
nil @ strictorderedP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax69) ).
thf(515,plain,
nil @ strictorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(19909,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19688,141]) ).
thf(19910,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19909]) ).
thf(19911,plain,
( ~ ( sk2 @ sk8 @ ( sk2 @ sk8 @ lt ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19910:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(554,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ segmentP ) )
!= ( sk1 @ ( A @ segmentP ) ) )
| ~ ( A @ equalelemsP )
| ~ $true
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( A @ ( sk1 @ neq ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[548,538]) ).
thf(555,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ segmentP ) )
!= ( sk1 @ ( A @ segmentP ) ) )
| ~ ( A @ equalelemsP )
| ~ ( A @ ( sk2 @ segmentP ) )
| ~ ( A @ ( sk1 @ neq ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[554]) ).
thf(556,plain,
( ~ ( sk2 @ equalelemsP )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) )
| ~ ( sk2 @ ssList ) ),
inference(pattern_uni,[status(thm)],[555:[bind(A,$thf( sk2 ))]]) ).
thf(583,plain,
( ~ ( sk2 @ equalelemsP )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) )
| ~ $true ),
inference(rewrite,[status(thm)],[556,103]) ).
thf(584,plain,
( ~ ( sk2 @ equalelemsP )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[583]) ).
thf(2882,plain,
( ( ( nil @ ( sk5 @ cons ) @ equalelemsP )
!= ( sk2 @ equalelemsP ) )
| ~ $true
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[2820,584]) ).
thf(2883,plain,
( ( ( nil @ ( sk5 @ cons ) @ equalelemsP )
!= ( sk2 @ equalelemsP ) )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[2882]) ).
thf(2896,plain,
( ( ( nil @ ( sk5 @ cons ) )
!= sk2 )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[2883]) ).
thf(7036,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,238]) ).
thf(7037,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[7036]) ).
thf(7038,plain,
sk2 @ ( sk2 @ segmentP ),
inference(pattern_uni,[status(thm)],[7037:[bind(A,$thf( sk2 ))]]) ).
thf(7068,plain,
( ( ( nil @ ( sk5 @ cons ) )
!= sk2 )
| ~ $true
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(rewrite,[status(thm)],[2896,7038]) ).
thf(7069,plain,
( ( ( nil @ ( sk5 @ cons ) )
!= sk2 )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[7068]) ).
thf(49861,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk20 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,261]) ).
thf(49862,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk20 @ ssList ) ),
inference(simp,[status(thm)],[49861]) ).
thf(49863,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk20 @ ssList ) ),
inference(pattern_uni,[status(thm)],[49862:[bind(A,$thf( sk2 ))]]) ).
thf(45939,plain,
( ( ( sk5 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk5 != sk1 )
| ( sk2 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,43546]) ).
thf(45940,plain,
( ( ( sk5 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk5 != sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[45939]) ).
thf(45943,plain,
( ( sk5 != nil )
| ( sk5 != sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[45940]) ).
thf(25311,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[25072,407]) ).
thf(25312,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[25311]) ).
thf(25313,plain,
( ( nil @ ( sk2 @ sk14 @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25312:[bind(A,$thf( sk2 @ sk14 ))]]) ).
thf(3072,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[123,141]) ).
thf(3073,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[3072]) ).
thf(3074,plain,
~ ( sk6 @ ( sk6 @ lt ) ),
inference(pattern_uni,[status(thm)],[3073:[bind(A,$thf( sk6 ))]]) ).
thf(48697,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[48432,407]) ).
thf(48698,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[48697]) ).
thf(48699,plain,
( ( nil @ ( sk2 @ sk21 @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[48698:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(260,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)],[255]) ).
thf(265,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)],[260]) ).
thf(266,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)],[265]) ).
thf(462,plain,
! [A: $i] :
( ( ( A @ ( nil @ rearsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) )
& ( ( nil = A )
| ~ ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[461]) ).
thf(464,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[462]) ).
thf(466,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[464]) ).
thf(467,plain,
( ( nil @ ( nil @ rearsegP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[466]) ).
thf(632,plain,
( ( nil @ ( nil @ rearsegP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[467,377]) ).
thf(633,plain,
nil @ ( nil @ rearsegP ),
inference(simp,[status(thm)],[632]) ).
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/sandbox2/benchmark/theBenchmark.p',ax27) ).
thf(508,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssItem )
=> ( ( A @ ( B @ app ) @ ( C @ cons ) )
= ( A @ ( B @ ( C @ cons ) @ app ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(20170,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19748,166]) ).
thf(20171,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[20170]) ).
thf(20172,plain,
( ( nil @ ( sk1 @ sk8 @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[20171:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(19876,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19688,152]) ).
thf(19877,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19876]) ).
thf(19878,plain,
( ( sk2 @ sk8 @ ( sk2 @ sk8 @ leq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19877:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(23821,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ~ ( A @ sk13 @ ( A @ sk12 @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,217]) ).
thf(23822,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ~ ( A @ sk13 @ ( A @ sk12 @ lt ) ) ),
inference(simp,[status(thm)],[23821]) ).
thf(23823,plain,
( ( sk1 @ strictorderP )
| ~ ( sk1 @ sk13 @ ( sk1 @ sk12 @ lt ) ) ),
inference(pattern_uni,[status(thm)],[23822:[bind(A,$thf( sk1 ))]]) ).
thf(792,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[643,280]) ).
thf(793,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[792]) ).
thf(794,plain,
( ( nil @ ( sk1 @ sk9 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[793:[bind(A,$thf( sk1 @ sk9 ))]]) ).
thf(17512,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17251,407]) ).
thf(17513,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17512]) ).
thf(17514,plain,
( ( nil @ ( sk1 @ sk11 @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17513:[bind(A,$thf( sk1 @ sk11 ))]]) ).
thf(134,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)],[133]) ).
thf(1331,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[643,333]) ).
thf(1332,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1331]) ).
thf(1333,plain,
( ( nil @ ( sk1 @ sk9 @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1332:[bind(A,$thf( sk1 @ sk9 ))]]) ).
thf(18903,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18613,431]) ).
thf(18904,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18903]) ).
thf(18905,plain,
( ( nil @ ( sk2 @ sk7 @ cons ) @ duplicatefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18904:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(1316,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[655,333]) ).
thf(1317,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1316]) ).
thf(1318,plain,
( ( nil @ ( sk2 @ sk9 @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1317:[bind(A,$thf( sk2 @ sk9 ))]]) ).
thf(43467,plain,
( ( ( sk6 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk2 != sk1 )
| ~ $true
| ~ ( sk1 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[123,42999]) ).
thf(43468,plain,
( ( ( sk6 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk2 != sk1 )
| ~ ( sk1 @ ssItem ) ),
inference(simp,[status(thm)],[43467]) ).
thf(43548,plain,
( ( sk6 != nil )
| ( sk2 != sk1 )
| ~ ( sk1 @ ssItem ) ),
inference(simp,[status(thm)],[43468]) ).
thf(17820,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,206]) ).
thf(17821,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk10 @ ssList ) ),
inference(simp,[status(thm)],[17820]) ).
thf(17822,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk10 @ ssList ) ),
inference(pattern_uni,[status(thm)],[17821:[bind(A,$thf( sk1 ))]]) ).
thf(18078,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17822,238]) ).
thf(18079,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18078]) ).
thf(18080,plain,
( ( sk1 @ sk10 @ ( sk1 @ sk10 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18079:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(28936,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk12 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,224]) ).
thf(28937,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk12 @ ssItem ) ),
inference(simp,[status(thm)],[28936]) ).
thf(28938,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk12 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[28937:[bind(A,$thf( sk2 ))]]) ).
thf(29346,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[28938,268]) ).
thf(29347,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[29346]) ).
thf(29348,plain,
( ~ ( sk2 @ sk12 @ ( nil @ memberP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[29347:[bind(A,$thf( sk2 @ sk12 ))]]) ).
thf(257,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)],[255]) ).
thf(264,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)],[257]) ).
thf(143,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[142]) ).
thf(144,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A = B ) ),
inference(lifteq,[status(thm)],[143]) ).
thf(3503,plain,
! [B: $i,A: $i] :
( ( A != sk6 )
| ( B != sk5 )
| ~ ( A @ ( B @ geq ) )
| ~ ( B @ ( A @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[144,125]) ).
thf(3504,plain,
! [A: $i] :
( ( A != sk5 )
| ~ ( sk6 @ ( A @ geq ) )
| ~ ( A @ ( sk6 @ geq ) )
| ~ ( A @ ssItem )
| ~ ( sk6 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[3503:[bind(A,$thf( sk6 ))]]) ).
thf(4263,plain,
( ~ ( sk6 @ ( sk5 @ geq ) )
| ~ ( sk5 @ ( sk6 @ geq ) )
| ~ ( sk5 @ ssItem )
| ~ ( sk6 @ ssItem ) ),
inference(simp,[status(thm)],[3504]) ).
thf(4598,plain,
( ~ ( sk6 @ ( sk5 @ geq ) )
| ~ ( sk5 @ ( sk6 @ geq ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[4263,122,123]) ).
thf(4599,plain,
( ~ ( sk6 @ ( sk5 @ geq ) )
| ~ ( sk5 @ ( sk6 @ geq ) ) ),
inference(simp,[status(thm)],[4598]) ).
thf(91,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax49) ).
thf(513,plain,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(27166,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[26827,280]) ).
thf(27167,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[27166]) ).
thf(27168,plain,
( ( nil @ ( sk1 @ sk16 @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[27167:[bind(A,$thf( sk1 @ sk16 ))]]) ).
thf(44618,plain,
( ( ( sk5 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk6 != sk1 )
| ( sk2 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,43539]) ).
thf(44619,plain,
( ( ( sk5 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk6 != sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[44618]) ).
thf(44631,plain,
( ( sk5 != nil )
| ( sk6 != sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[44619]) ).
thf(148,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)],[147]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[148]) ).
thf(4451,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,431]) ).
thf(4452,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP ) ),
inference(simp,[status(thm)],[4451]) ).
thf(4453,plain,
nil @ ( sk5 @ cons ) @ duplicatefreeP,
inference(pattern_uni,[status(thm)],[4452:[bind(A,$thf( sk5 ))]]) ).
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/sandbox2/benchmark/theBenchmark.p',ax40) ).
thf(175,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(176,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)],[175]) ).
thf(18094,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17822,407]) ).
thf(18095,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18094]) ).
thf(18096,plain,
( ( nil @ ( sk1 @ sk10 @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18095:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(284,plain,
! [A: $i] :
( ( ( A @ tl )
= ( A @ sk23 ) )
| ( nil = A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[282]) ).
thf(286,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ( ( A @ sk23 )
= ( A @ tl ) )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[284]) ).
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/sandbox2/benchmark/theBenchmark.p',ax95) ).
thf(118,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(18837,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18613,156]) ).
thf(18838,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ geq ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18837]) ).
thf(18839,plain,
( ( sk2 @ sk7 @ ( sk2 @ sk7 @ geq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18838:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(1518,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[643,407]) ).
thf(1519,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1518]) ).
thf(1520,plain,
( ( nil @ ( sk1 @ sk9 @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1519:[bind(A,$thf( sk1 @ sk9 ))]]) ).
thf(18882,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18613,240]) ).
thf(18883,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18882]) ).
thf(18884,plain,
( ( nil @ ( sk2 @ sk7 @ cons ) @ totalorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18883:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(18834,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18613,141]) ).
thf(18835,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18834]) ).
thf(18836,plain,
( ~ ( sk2 @ sk7 @ ( sk2 @ sk7 @ lt ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18835:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(770,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[655,280]) ).
thf(771,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[770]) ).
thf(772,plain,
( ( nil @ ( sk2 @ sk9 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[771:[bind(A,$thf( sk2 @ sk9 ))]]) ).
thf(28192,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[27879,333]) ).
thf(28193,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[28192]) ).
thf(28194,plain,
( ( nil @ ( sk1 @ sk15 @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[28193:[bind(A,$thf( sk1 @ sk15 ))]]) ).
thf(19040,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18673,152]) ).
thf(19041,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19040]) ).
thf(19042,plain,
( ( sk1 @ sk7 @ ( sk1 @ sk7 @ leq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19041:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(12144,plain,
( ( sk1 != sk1 )
| ( sk2 != sk1 )
| ( nil != nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[8078,12132]) ).
thf(12145,plain,
( ( sk1 != sk1 )
| ( sk2 != sk1 )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[12144]) ).
thf(12146,plain,
( ( sk2 != sk1 )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[12145:[]]) ).
thf(7060,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ sk9 @ sk9 @ cyclefreeP )
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[728,238]) ).
thf(7061,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk1 @ sk9 @ sk9 @ cyclefreeP )
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7060]) ).
thf(7062,plain,
( ( sk1 @ sk9 @ sk9 @ sk9 @ ( sk1 @ sk9 @ sk9 @ sk9 @ segmentP ) )
| ( sk1 @ sk9 @ sk9 @ cyclefreeP )
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7061:[bind(A,$thf( sk1 @ sk9 @ sk9 @ sk9 ))]]) ).
thf(25275,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[25072,333]) ).
thf(25276,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[25275]) ).
thf(25277,plain,
( ( nil @ ( sk2 @ sk14 @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25276:[bind(A,$thf( sk2 @ sk14 ))]]) ).
thf(5554,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[123,152]) ).
thf(5555,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[5554]) ).
thf(5556,plain,
sk6 @ ( sk6 @ leq ),
inference(pattern_uni,[status(thm)],[5555:[bind(A,$thf( sk6 ))]]) ).
thf(26965,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[26787,280]) ).
thf(26966,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[26965]) ).
thf(26967,plain,
( ( nil @ ( sk2 @ sk16 @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[26966:[bind(A,$thf( sk2 @ sk16 ))]]) ).
thf(1763,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,240]) ).
thf(1764,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[1763]) ).
thf(1765,plain,
nil @ ( sk5 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[1764:[bind(A,$thf( sk5 ))]]) ).
thf(235,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)],[234]) ).
thf(236,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)],[235]) ).
thf(26,axiom,
nil @ cyclefreeP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax60) ).
thf(187,plain,
nil @ cyclefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(50357,plain,
! [A: $i] :
( ( ( sk1 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[49909,333]) ).
thf(50358,plain,
! [A: $i] :
( ( ( sk1 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[50357]) ).
thf(50359,plain,
( ( nil @ ( sk1 @ sk20 @ rearsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[50358:[bind(A,$thf( sk1 @ sk20 ))]]) ).
thf(1490,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ sk9 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[669,407]) ).
thf(1491,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ sk9 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1490]) ).
thf(1492,plain,
( ( nil @ ( sk2 @ sk9 @ sk9 @ frontsegP ) )
| ( sk2 @ sk9 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1491:[bind(A,$thf( sk2 @ sk9 @ sk9 ))]]) ).
thf(50076,plain,
! [A: $i] :
( ( ( sk2 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[49863,333]) ).
thf(50077,plain,
! [A: $i] :
( ( ( sk2 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[50076]) ).
thf(50078,plain,
( ( nil @ ( sk2 @ sk20 @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[50077:[bind(A,$thf( sk2 @ sk20 ))]]) ).
thf(37397,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[123,249]) ).
thf(37398,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[37397]) ).
thf(37399,plain,
~ ( sk6 @ ( sk6 @ neq ) ),
inference(pattern_uni,[status(thm)],[37398:[bind(A,$thf( sk6 ))]]) ).
thf(150,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ geq ) )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[148]) ).
thf(5912,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ leq ) )
!= ( A @ ( B @ leq ) ) )
| ( B @ ( A @ geq ) )
| ~ $true
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[5562,150]) ).
thf(5913,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ leq ) )
!= ( A @ ( B @ leq ) ) )
| ( B @ ( A @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[5912]) ).
thf(5914,plain,
( ( sk5 @ ( sk5 @ geq ) )
| ~ ( sk5 @ ssItem )
| ~ ( sk5 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[5913:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 ))]]) ).
thf(5940,plain,
( ( sk5 @ ( sk5 @ geq ) )
| ~ ( sk5 @ ssItem ) ),
inference(simp,[status(thm)],[5914]) ).
thf(6215,plain,
( ( sk5 @ ( sk5 @ geq ) )
| ~ $true ),
inference(rewrite,[status(thm)],[5940,122]) ).
thf(6216,plain,
sk5 @ ( sk5 @ geq ),
inference(simp,[status(thm)],[6215]) ).
thf(46425,plain,
( ( ( sk6 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk6 != sk1 )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[123,43340]) ).
thf(46426,plain,
( ( ( sk6 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk6 != sk1 )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[46425]) ).
thf(46480,plain,
( ( sk6 != nil )
| ( sk6 != sk1 )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[46426]) ).
thf(25494,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[25109,238]) ).
thf(25495,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[25494]) ).
thf(25496,plain,
( ( sk1 @ sk14 @ ( sk1 @ sk14 @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25495:[bind(A,$thf( sk1 @ sk14 ))]]) ).
thf(20066,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19688,268]) ).
thf(20067,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[20066]) ).
thf(20068,plain,
( ~ ( sk2 @ sk8 @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[20067:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(29000,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk12 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,224]) ).
thf(29001,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk12 @ ssItem ) ),
inference(simp,[status(thm)],[29000]) ).
thf(29002,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk12 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[29001:[bind(A,$thf( sk1 ))]]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( A @ ( B @ cons ) @ ssList ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
thf(213,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( A @ ( B @ cons ) @ ssList ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(66,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderP ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax61) ).
thf(399,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(400,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[399]) ).
thf(19237,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18673,400]) ).
thf(19238,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19237]) ).
thf(19239,plain,
( ( nil @ ( sk1 @ sk7 @ cons ) @ totalorderP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19238:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(3088,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ lt ) )
!= ( sk6 @ ( sk6 @ lt ) ) )
| ~ $true
| ~ ( B @ ( A @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[116,3074]) ).
thf(3089,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ lt ) )
!= ( sk6 @ ( sk6 @ lt ) ) )
| ~ ( B @ ( A @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[3088]) ).
thf(3090,plain,
( ~ ( sk6 @ ( sk6 @ gt ) )
| ~ ( sk6 @ ssItem )
| ~ ( sk6 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[3089:[bind(A,$thf( sk6 )),bind(B,$thf( sk6 ))]]) ).
thf(3102,plain,
( ~ ( sk6 @ ( sk6 @ gt ) )
| ~ ( sk6 @ ssItem ) ),
inference(simp,[status(thm)],[3090]) ).
thf(3164,plain,
( ~ ( sk6 @ ( sk6 @ gt ) )
| ~ $true ),
inference(rewrite,[status(thm)],[3102,123]) ).
thf(3165,plain,
~ ( sk6 @ ( sk6 @ gt ) ),
inference(simp,[status(thm)],[3164]) ).
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/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(520,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(197,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)],[196]) ).
thf(198,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)],[197]) ).
thf(48640,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[48432,333]) ).
thf(48641,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[48640]) ).
thf(48642,plain,
( ( nil @ ( sk2 @ sk21 @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[48641:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(767,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,280]) ).
thf(768,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[767]) ).
thf(769,plain,
nil @ ( sk1 @ segmentP ),
inference(pattern_uni,[status(thm)],[768:[bind(A,$thf( sk1 ))]]) ).
thf(25214,plain,
! [A: $i] :
( ( A != sk5 )
| ( sk6 != nil )
| ( nil != nil )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[184,24652]) ).
thf(25215,plain,
! [A: $i] :
( ( A != sk5 )
| ( sk6 != nil )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[25214]) ).
thf(25216,plain,
( ( sk6 != nil )
| ~ ( sk5 @ ( nil @ segmentP ) )
| ~ ( sk5 @ ssList ) ),
inference(pattern_uni,[status(thm)],[25215:[bind(A,$thf( sk5 ))]]) ).
thf(46712,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk17 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,258]) ).
thf(46713,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk17 @ ssItem ) ),
inference(simp,[status(thm)],[46712]) ).
thf(46714,plain,
( ( sk1 @ strictorderedP )
| ( sk1 @ sk17 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[46713:[bind(A,$thf( sk1 ))]]) ).
thf(47447,plain,
! [A: $i] :
( ( ( sk1 @ sk17 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[46714,268]) ).
thf(47448,plain,
! [A: $i] :
( ( ( sk1 @ sk17 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[47447]) ).
thf(47449,plain,
( ~ ( sk1 @ sk17 @ ( nil @ memberP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[47448:[bind(A,$thf( sk1 @ sk17 ))]]) ).
thf(67673,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[67632,280]) ).
thf(67674,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[67673]) ).
thf(67675,plain,
nil @ ( sk2 @ sk23 @ segmentP ),
inference(pattern_uni,[status(thm)],[67674:[bind(A,$thf( sk2 @ sk23 ))]]) ).
thf(275,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ frontsegP ) )
| ( ( C @ ( B @ app ) )
!= A )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[272]) ).
thf(277,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ frontsegP ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( C @ ( B @ app ) )
!= A ) ),
inference(lifteq,[status(thm)],[275]) ).
thf(278,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ app ) @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ( A @ app ) @ ssList ) ),
inference(simp,[status(thm)],[277]) ).
thf(31176,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[30580,268]) ).
thf(31177,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[31176]) ).
thf(31178,plain,
( ~ ( sk1 @ sk13 @ ( nil @ memberP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[31177:[bind(A,$thf( sk1 @ sk13 ))]]) ).
thf(18991,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18613,268]) ).
thf(18992,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18991]) ).
thf(18993,plain,
( ~ ( sk2 @ sk7 @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18992:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ gt ) )
=> ~ ( A @ ( B @ gt ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax94) ).
thf(135,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ gt ) )
=> ~ ( A @ ( B @ gt ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(20152,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19748,141]) ).
thf(20153,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[20152]) ).
thf(20154,plain,
( ~ ( sk1 @ sk8 @ ( sk1 @ sk8 @ lt ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[20153:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(88,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( A @ ( B @ segmentP ) )
& ( B @ ( A @ segmentP ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax54) ).
thf(505,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( A @ ( B @ segmentP ) )
& ( B @ ( A @ segmentP ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(39,axiom,
~ ( nil @ singletonP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).
thf(241,plain,
~ ( nil @ singletonP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(18801,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18613,152]) ).
thf(18802,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( A @ ( A @ leq ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18801]) ).
thf(18803,plain,
( ( sk2 @ sk7 @ ( sk2 @ sk7 @ leq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18802:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(67667,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[67632,253]) ).
thf(67668,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[67667]) ).
thf(67669,plain,
( ( sk2 @ sk23 @ ( nil @ app ) )
= ( sk2 @ sk23 ) ),
inference(pattern_uni,[status(thm)],[67668:[bind(A,$thf( sk2 @ sk23 ))]]) ).
thf(1420,plain,
( ( ( sk2 @ sk9 @ cyclefreeP )
!= ( sk2 @ cyclefreeP ) )
| ( sk2 @ sk9 @ sk9 @ ssList )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1419]) ).
thf(26938,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[26787,333]) ).
thf(26939,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[26938]) ).
thf(26940,plain,
( ( nil @ ( sk2 @ sk16 @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[26939:[bind(A,$thf( sk2 @ sk16 ))]]) ).
thf(17502,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17251,280]) ).
thf(17503,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17502]) ).
thf(17504,plain,
( ( nil @ ( sk1 @ sk11 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17503:[bind(A,$thf( sk1 @ sk11 ))]]) ).
thf(93,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( A @ ( B @ rearsegP ) )
& ( B @ ( A @ rearsegP ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax48) ).
thf(516,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(43321,plain,
( ( ( sk5 @ ssItem )
!= ( sk1 @ ssItem ) )
| ~ ( nil @ ssItem )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[122,38166]) ).
thf(43322,plain,
( ( ( sk5 @ ssItem )
!= ( sk1 @ ssItem ) )
| ~ ( nil @ ssItem )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[43321]) ).
thf(43330,plain,
( ( sk5 != sk1 )
| ~ ( nil @ ssItem )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[43322]) ).
thf(46308,plain,
( ( ( sk6 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk5 != sk1 )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[123,43330]) ).
thf(46309,plain,
( ( ( sk6 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk5 != sk1 )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[46308]) ).
thf(46358,plain,
( ( sk6 != nil )
| ( sk5 != sk1 )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[46309]) ).
thf(25236,plain,
! [A: $i] :
( ( A != sk5 )
| ( sk6 != nil )
| ( nil != nil )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[171,24652]) ).
thf(25237,plain,
! [A: $i] :
( ( A != sk5 )
| ( sk6 != nil )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[25236]) ).
thf(25238,plain,
( ( sk6 != nil )
| ~ ( sk5 @ ( nil @ frontsegP ) )
| ~ ( sk5 @ ssList ) ),
inference(pattern_uni,[status(thm)],[25237:[bind(A,$thf( sk5 ))]]) ).
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/sandbox2/benchmark/theBenchmark.p',ax14) ).
thf(473,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(45523,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[45026,407]) ).
thf(45524,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[45523]) ).
thf(45525,plain,
( ( nil @ ( sk1 @ sk19 @ frontsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[45524:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(58,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ( A @ hd )
= B )
& ( B @ ssItem ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax75) ).
thf(342,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ( A @ hd )
= B )
& ( B @ ssItem ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
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/sandbox2/benchmark/theBenchmark.p',ax43) ).
thf(194,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(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/sandbox2/benchmark/theBenchmark.p',ax30) ).
thf(145,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(45215,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[44983,280]) ).
thf(45216,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[45215]) ).
thf(45217,plain,
( ( nil @ ( sk2 @ sk19 @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[45216:[bind(A,$thf( sk2 @ sk19 ))]]) ).
thf(7024,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ sk9 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[669,238]) ).
thf(7025,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk2 @ sk9 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7024]) ).
thf(7026,plain,
( ( sk2 @ sk9 @ sk9 @ ( sk2 @ sk9 @ sk9 @ segmentP ) )
| ( sk2 @ sk9 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7025:[bind(A,$thf( sk2 @ sk9 @ sk9 ))]]) ).
thf(710,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[123,268]) ).
thf(711,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[710]) ).
thf(712,plain,
~ ( sk6 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[711:[bind(A,$thf( sk6 ))]]) ).
thf(1596,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( ( sk2 @ sk9 )
!= sk2 )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[1421,333]) ).
thf(1597,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( ( sk2 @ sk9 )
!= sk2 )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1596]) ).
thf(1598,plain,
( ( nil @ ( sk2 @ sk9 @ sk9 @ rearsegP ) )
| ( ( sk2 @ sk9 )
!= sk2 )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1597:[bind(A,$thf( sk2 @ sk9 @ sk9 ))]]) ).
thf(589,plain,
( ( ( sk2 @ ( sk2 @ segmentP ) )
!= ( sk1 @ ( sk2 @ segmentP ) ) )
| ~ ( sk2 @ equalelemsP )
| ~ $true
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[548,584]) ).
thf(590,plain,
( ( ( sk2 @ ( sk2 @ segmentP ) )
!= ( sk1 @ ( sk2 @ segmentP ) ) )
| ~ ( sk2 @ equalelemsP )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[589]) ).
thf(593,plain,
( ( sk2 != sk1 )
| ( sk2 != sk2 )
| ~ ( sk2 @ equalelemsP )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[590]) ).
thf(594,plain,
( ( sk2 != sk1 )
| ~ ( sk2 @ equalelemsP )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[593]) ).
thf(636,plain,
( ( ( sk2 @ equalelemsP )
!= ( sk1 @ equalelemsP ) )
| ( sk2 != sk1 )
| ~ $true
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[535,594]) ).
thf(637,plain,
( ( ( sk2 @ equalelemsP )
!= ( sk1 @ equalelemsP ) )
| ( sk2 != sk1 )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[636]) ).
thf(639,plain,
( ( sk2 != sk1 )
| ( sk2 != sk1 )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[637]) ).
thf(640,plain,
( ( sk2 != sk1 )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[639]) ).
thf(17322,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17224,333]) ).
thf(17323,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17322]) ).
thf(17324,plain,
( ( nil @ ( sk2 @ sk11 @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17323:[bind(A,$thf( sk2 @ sk11 ))]]) ).
thf(27135,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[26827,333]) ).
thf(27136,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[27135]) ).
thf(27137,plain,
( ( nil @ ( sk1 @ sk16 @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[27136:[bind(A,$thf( sk1 @ sk16 ))]]) ).
thf(5942,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ sk9 @ sk9 @ cyclefreeP )
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[728,333]) ).
thf(5943,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ sk9 @ sk9 @ cyclefreeP )
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5942]) ).
thf(5944,plain,
( ( nil @ ( sk1 @ sk9 @ sk9 @ sk9 @ rearsegP ) )
| ( sk1 @ sk9 @ sk9 @ cyclefreeP )
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5943:[bind(A,$thf( sk1 @ sk9 @ sk9 @ sk9 ))]]) ).
thf(18852,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18613,166]) ).
thf(18853,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18852]) ).
thf(18854,plain,
( ( nil @ ( sk2 @ sk7 @ cons ) @ strictorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18853:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(263,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ sk18 @ ( A @ sk17 @ lt ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[255]) ).
thf(5418,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[123,452]) ).
thf(5419,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP ) ),
inference(simp,[status(thm)],[5418]) ).
thf(5420,plain,
nil @ ( sk6 @ cons ) @ strictorderP,
inference(pattern_uni,[status(thm)],[5419:[bind(A,$thf( sk6 ))]]) ).
thf(76,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ singletonP )
<=> ? [B: $i] :
( ( ( nil @ ( B @ cons ) )
= A )
& ( B @ ssItem ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
thf(441,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(67842,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[67632,231]) ).
thf(67843,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[67842]) ).
thf(67844,plain,
( ( nil @ ( sk2 @ sk23 @ app ) )
= ( sk2 @ sk23 ) ),
inference(pattern_uni,[status(thm)],[67843:[bind(A,$thf( sk2 @ sk23 ))]]) ).
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/sandbox2/benchmark/theBenchmark.p',ax88) ).
thf(126,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(127,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)],[126]) ).
thf(82,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( nil != A )
=> ( ( B @ ( A @ app ) @ tl )
= ( B @ ( A @ tl @ app ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax86) ).
thf(470,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(27182,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[26827,407]) ).
thf(27183,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[27182]) ).
thf(27184,plain,
( ( nil @ ( sk1 @ sk16 @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[27183:[bind(A,$thf( sk1 @ sk16 ))]]) ).
thf(50401,plain,
! [A: $i] :
( ( ( sk1 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[49909,280]) ).
thf(50402,plain,
! [A: $i] :
( ( ( sk1 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[50401]) ).
thf(50403,plain,
( ( nil @ ( sk1 @ sk20 @ segmentP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[50402:[bind(A,$thf( sk1 @ sk20 ))]]) ).
thf(27837,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk15 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,221]) ).
thf(27838,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk15 @ ssList ) ),
inference(simp,[status(thm)],[27837]) ).
thf(27839,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk15 @ ssList ) ),
inference(pattern_uni,[status(thm)],[27838:[bind(A,$thf( sk2 ))]]) ).
thf(27992,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[27839,333]) ).
thf(27993,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[27992]) ).
thf(27994,plain,
( ( nil @ ( sk2 @ sk15 @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[27993:[bind(A,$thf( sk2 @ sk15 ))]]) ).
thf(5429,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,452]) ).
thf(5430,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP ) ),
inference(simp,[status(thm)],[5429]) ).
thf(5431,plain,
nil @ ( sk5 @ cons ) @ strictorderP,
inference(pattern_uni,[status(thm)],[5430:[bind(A,$thf( sk5 ))]]) ).
thf(18052,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17822,333]) ).
thf(18053,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18052]) ).
thf(18054,plain,
( ( nil @ ( sk1 @ sk10 @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18053:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(789,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[663,280]) ).
thf(790,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[789]) ).
thf(791,plain,
( ( nil @ ( sk1 @ sk9 @ sk9 @ segmentP ) )
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[790:[bind(A,$thf( sk1 @ sk9 @ sk9 ))]]) ).
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/sandbox2/benchmark/theBenchmark.p',ax19) ).
thf(336,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(17932,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17792,407]) ).
thf(17933,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17932]) ).
thf(17934,plain,
( ( nil @ ( sk2 @ sk10 @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17933:[bind(A,$thf( sk2 @ sk10 ))]]) ).
thf(7066,plain,
( ~ ( sk2 @ equalelemsP )
| ~ $true
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(rewrite,[status(thm)],[584,7038]) ).
thf(7067,plain,
( ~ ( sk2 @ equalelemsP )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[7066]) ).
thf(1715,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,166]) ).
thf(1716,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[1715]) ).
thf(1717,plain,
nil @ ( sk5 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[1716:[bind(A,$thf( sk5 ))]]) ).
thf(154,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)],[153]) ).
thf(19927,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19688,166]) ).
thf(19928,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19927]) ).
thf(19929,plain,
( ( nil @ ( sk2 @ sk8 @ cons ) @ strictorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19928:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(28223,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[27879,280]) ).
thf(28224,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[28223]) ).
thf(28225,plain,
( ( nil @ ( sk1 @ sk15 @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[28224:[bind(A,$thf( sk1 @ sk15 ))]]) ).
thf(29598,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[29002,268]) ).
thf(29599,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[29598]) ).
thf(29600,plain,
( ~ ( sk1 @ sk12 @ ( nil @ memberP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[29599:[bind(A,$thf( sk1 @ sk12 ))]]) ).
thf(17028,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ( A @ sk7 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,202]) ).
thf(17029,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ( A @ sk7 @ leq ) ) ),
inference(simp,[status(thm)],[17028]) ).
thf(17030,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk8 @ ( sk2 @ sk7 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[17029:[bind(A,$thf( sk2 ))]]) ).
thf(19058,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18673,452]) ).
thf(19059,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19058]) ).
thf(19060,plain,
( ( nil @ ( sk1 @ sk7 @ cons ) @ strictorderP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19059:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(17499,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17251,238]) ).
thf(17500,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17499]) ).
thf(17501,plain,
( ( sk1 @ sk11 @ ( sk1 @ sk11 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17500:[bind(A,$thf( sk1 @ sk11 ))]]) ).
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/sandbox2/benchmark/theBenchmark.p',ax67) ).
thf(363,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(1515,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[663,407]) ).
thf(1516,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1515]) ).
thf(1517,plain,
( ( nil @ ( sk1 @ sk9 @ sk9 @ frontsegP ) )
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1516:[bind(A,$thf( sk1 @ sk9 @ sk9 ))]]) ).
thf(18792,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18613,440]) ).
thf(18793,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18792]) ).
thf(18794,plain,
( ( nil @ ( sk2 @ sk7 @ cons ) @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18793:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(2922,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[122,400]) ).
thf(2923,plain,
! [A: $i] :
( ( ( sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP ) ),
inference(simp,[status(thm)],[2922]) ).
thf(2924,plain,
nil @ ( sk5 @ cons ) @ totalorderP,
inference(pattern_uni,[status(thm)],[2923:[bind(A,$thf( sk5 ))]]) ).
thf(20197,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19748,335]) ).
thf(20198,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[20197]) ).
thf(20199,plain,
( ( nil @ ( sk1 @ sk8 @ cons ) @ equalelemsP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[20198:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(50429,plain,
! [A: $i] :
( ( ( sk1 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[49909,407]) ).
thf(50430,plain,
! [A: $i] :
( ( ( sk1 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[50429]) ).
thf(50431,plain,
( ( nil @ ( sk1 @ sk20 @ frontsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[50430:[bind(A,$thf( sk1 @ sk20 ))]]) ).
thf(20133,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19748,452]) ).
thf(20134,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[20133]) ).
thf(20135,plain,
( ( nil @ ( sk1 @ sk8 @ cons ) @ strictorderP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[20134:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(4572,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[123,440]) ).
thf(4573,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP ) ),
inference(simp,[status(thm)],[4572]) ).
thf(4574,plain,
nil @ ( sk6 @ cons ) @ cyclefreeP,
inference(pattern_uni,[status(thm)],[4573:[bind(A,$thf( sk6 ))]]) ).
thf(25466,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[25109,333]) ).
thf(25467,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[25466]) ).
thf(25468,plain,
( ( nil @ ( sk1 @ sk14 @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25467:[bind(A,$thf( sk1 @ sk14 ))]]) ).
thf(19095,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18673,166]) ).
thf(19096,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19095]) ).
thf(19097,plain,
( ( nil @ ( sk1 @ sk7 @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19096:[bind(A,$thf( sk1 @ sk7 ))]]) ).
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/sandbox2/benchmark/theBenchmark.p',ax36) ).
thf(401,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(30924,plain,
! [A: $i] :
( ( ( sk2 @ sk13 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[30516,268]) ).
thf(30925,plain,
! [A: $i] :
( ( ( sk2 @ sk13 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[30924]) ).
thf(30926,plain,
( ~ ( sk2 @ sk13 @ ( nil @ memberP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[30925:[bind(A,$thf( sk2 @ sk13 ))]]) ).
thf(7042,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[663,238]) ).
thf(7043,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7042]) ).
thf(7044,plain,
( ( sk1 @ sk9 @ sk9 @ ( sk1 @ sk9 @ sk9 @ segmentP ) )
| ( sk1 @ sk9 @ cyclefreeP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7043:[bind(A,$thf( sk1 @ sk9 @ sk9 ))]]) ).
thf(46350,plain,
( ( ( sk5 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk5 != sk1 )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[122,43330]) ).
thf(46351,plain,
( ( ( sk5 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk5 != sk1 )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[46350]) ).
thf(46355,plain,
( ( sk5 != nil )
| ( sk5 != sk1 )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[46351]) ).
thf(20312,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19748,400]) ).
thf(20313,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[20312]) ).
thf(20314,plain,
( ( nil @ ( sk1 @ sk8 @ cons ) @ totalorderP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[20313:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(138,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ lt ) )
| ( A = B )
| ~ ( B @ ( A @ leq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[137]) ).
thf(139,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ lt ) )
| ~ ( B @ ( A @ leq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A = B ) ),
inference(lifteq,[status(thm)],[138]) ).
thf(24329,plain,
( ( ( sk6 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk5 != nil )
| ~ ( sk6 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,7504]) ).
thf(24330,plain,
( ( ( sk6 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk5 != nil )
| ~ ( sk6 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[24329]) ).
thf(24436,plain,
( ( sk6 != sk2 )
| ( sk5 != nil )
| ~ ( sk6 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[24330]) ).
thf(20309,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19748,268]) ).
thf(20310,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[20309]) ).
thf(20311,plain,
( ~ ( sk1 @ sk8 @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[20310:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(18994,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18613,400]) ).
thf(18995,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18994]) ).
thf(18996,plain,
( ( nil @ ( sk2 @ sk7 @ cons ) @ totalorderP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18995:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(18081,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17822,280]) ).
thf(18082,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18081]) ).
thf(18083,plain,
( ( nil @ ( sk1 @ sk10 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18082:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(50136,plain,
! [A: $i] :
( ( ( sk2 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[49863,407]) ).
thf(50137,plain,
! [A: $i] :
( ( ( sk2 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[50136]) ).
thf(50138,plain,
( ( nil @ ( sk2 @ sk20 @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[50137:[bind(A,$thf( sk2 @ sk20 ))]]) ).
thf(18879,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18613,335]) ).
thf(18880,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18879]) ).
thf(18881,plain,
( ( nil @ ( sk2 @ sk7 @ cons ) @ equalelemsP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18880:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(68574,plain,
( ( sk1 != sk1 )
| ( sk2 != sk1 )
| ( nil != nil )
| ( sk1 @ sk23 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[66645,12132]) ).
thf(68575,plain,
( ( sk1 != sk1 )
| ( sk2 != sk1 )
| ( sk1 @ sk23 @ ssList ) ),
inference(simp,[status(thm)],[68574]) ).
thf(68576,plain,
( ( sk2 != sk1 )
| ( sk1 @ sk23 @ ssList ) ),
inference(pattern_uni,[status(thm)],[68575:[]]) ).
thf(7015,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ sk9 @ sk9 @ cyclefreeP )
| ( sk2 @ sk9 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[1418,238]) ).
thf(7016,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk2 @ sk9 @ sk9 @ cyclefreeP )
| ( sk2 @ sk9 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7015]) ).
thf(7017,plain,
( ( sk2 @ sk9 @ sk9 @ sk9 @ ( sk2 @ sk9 @ sk9 @ sk9 @ segmentP ) )
| ( sk2 @ sk9 @ sk9 @ cyclefreeP )
| ( sk2 @ sk9 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7016:[bind(A,$thf( sk2 @ sk9 @ sk9 @ sk9 ))]]) ).
thf(119,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)],[118]) ).
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/sandbox2/benchmark/theBenchmark.p',ax77) ).
thf(378,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(9479,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( nil @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[613,8479]) ).
thf(9480,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[9479]) ).
thf(9517,plain,
( ( sk1 != nil )
| ( nil != nil )
| ~ ( nil @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[9480]) ).
thf(9537,plain,
( ( sk1 != nil )
| ~ ( nil @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[9517]) ).
thf(214,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[213]) ).
thf(19867,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19688,440]) ).
thf(19868,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19867]) ).
thf(19869,plain,
( ( nil @ ( sk2 @ sk8 @ cons ) @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19868:[bind(A,$thf( sk2 @ sk8 ))]]) ).
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/sandbox2/benchmark/theBenchmark.p',ax9) ).
thf(287,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(48918,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[48478,333]) ).
thf(48919,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[48918]) ).
thf(48920,plain,
( ( nil @ ( sk1 @ sk21 @ rearsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[48919:[bind(A,$thf( sk1 @ sk21 ))]]) ).
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/sandbox2/benchmark/theBenchmark.p',ax80) ).
thf(432,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(146,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)],[145]) ).
thf(19122,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18673,335]) ).
thf(19123,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19122]) ).
thf(19124,plain,
( ( nil @ ( sk1 @ sk7 @ cons ) @ equalelemsP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19123:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(17353,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17224,407]) ).
thf(17354,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17353]) ).
thf(17355,plain,
( ( nil @ ( sk2 @ sk11 @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17354:[bind(A,$thf( sk2 @ sk11 ))]]) ).
thf(11711,plain,
( ( sk1 != sk1 )
| ~ ( nil @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[11175,550]) ).
thf(11712,plain,
( ~ ( nil @ ( nil @ neq ) )
| ~ ( sk1 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[11711:[]]) ).
thf(189,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[188]) ).
thf(190,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( A = B ) ),
inference(lifteq,[status(thm)],[189]) ).
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/sandbox2/benchmark/theBenchmark.p',ax37) ).
thf(422,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(25299,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[25072,238]) ).
thf(25300,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[25299]) ).
thf(25301,plain,
( ( sk2 @ sk14 @ ( sk2 @ sk14 @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[25300:[bind(A,$thf( sk2 @ sk14 ))]]) ).
thf(28034,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[27839,407]) ).
thf(28035,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[28034]) ).
thf(28036,plain,
( ( nil @ ( sk2 @ sk15 @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[28035:[bind(A,$thf( sk2 @ sk15 ))]]) ).
thf(67670,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[67632,238]) ).
thf(67671,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[67670]) ).
thf(67672,plain,
sk2 @ sk23 @ ( sk2 @ sk23 @ segmentP ),
inference(pattern_uni,[status(thm)],[67671:[bind(A,$thf( sk2 @ sk23 ))]]) ).
thf(5856,plain,
! [B: $i,A: $i] :
( ( ( sk6 @ ( sk6 @ leq ) )
!= ( A @ ( B @ leq ) ) )
| ( B @ ( A @ geq ) )
| ~ $true
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[5556,150]) ).
thf(5857,plain,
! [B: $i,A: $i] :
( ( ( sk6 @ ( sk6 @ leq ) )
!= ( A @ ( B @ leq ) ) )
| ( B @ ( A @ geq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[5856]) ).
thf(5858,plain,
( ( sk6 @ ( sk6 @ geq ) )
| ~ ( sk6 @ ssItem )
| ~ ( sk6 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[5857:[bind(A,$thf( sk6 )),bind(B,$thf( sk6 ))]]) ).
thf(5871,plain,
( ( sk6 @ ( sk6 @ geq ) )
| ~ ( sk6 @ ssItem ) ),
inference(simp,[status(thm)],[5858]) ).
thf(6149,plain,
( ( sk6 @ ( sk6 @ geq ) )
| ~ $true ),
inference(rewrite,[status(thm)],[5871,123]) ).
thf(6150,plain,
sk6 @ ( sk6 @ geq ),
inference(simp,[status(thm)],[6149]) ).
thf(204,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)],[200]) ).
thf(210,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)],[204]) ).
thf(53,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ hd @ ssItem ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
thf(326,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ hd @ ssItem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(43667,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[103,253]) ).
thf(43668,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[43667]) ).
thf(43669,plain,
( ( sk2 @ ( nil @ app ) )
= sk2 ),
inference(pattern_uni,[status(thm)],[43668:[bind(A,$thf( sk2 ))]]) ).
thf(2911,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[123,400]) ).
thf(2912,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP ) ),
inference(simp,[status(thm)],[2911]) ).
thf(2913,plain,
nil @ ( sk6 @ cons ) @ totalorderP,
inference(pattern_uni,[status(thm)],[2912:[bind(A,$thf( sk6 ))]]) ).
thf(97,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( nil
!= ( A @ ( B @ cons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).
thf(532,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( nil
!= ( A @ ( B @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(1608,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( ( sk2 @ sk9 )
!= sk2 )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[1421,407]) ).
thf(1609,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( ( sk2 @ sk9 )
!= sk2 )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1608]) ).
thf(1610,plain,
( ( nil @ ( sk2 @ sk9 @ sk9 @ frontsegP ) )
| ( ( sk2 @ sk9 )
!= sk2 )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1609:[bind(A,$thf( sk2 @ sk9 @ sk9 ))]]) ).
thf(34281,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[104,231]) ).
thf(34282,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[34281]) ).
thf(34283,plain,
( ( nil @ ( sk1 @ app ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[34282:[bind(A,$thf( sk1 ))]]) ).
thf(242,plain,
~ ( nil @ singletonP ),
inference(polarity_switch,[status(thm)],[241]) ).
thf(136,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[135]) ).
thf(28019,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[27839,280]) ).
thf(28020,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[28019]) ).
thf(28021,plain,
( ( nil @ ( sk2 @ sk15 @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[28020:[bind(A,$thf( sk2 @ sk15 ))]]) ).
thf(195,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)],[194]) ).
thf(4440,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[123,431]) ).
thf(4441,plain,
! [A: $i] :
( ( ( sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ duplicatefreeP ) ),
inference(simp,[status(thm)],[4440]) ).
thf(4442,plain,
nil @ ( sk6 @ cons ) @ duplicatefreeP,
inference(pattern_uni,[status(thm)],[4441:[bind(A,$thf( sk6 ))]]) ).
thf(67633,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[67632,333]) ).
thf(67634,plain,
! [A: $i] :
( ( ( sk2 @ sk23 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[67633]) ).
thf(67635,plain,
nil @ ( sk2 @ sk23 @ rearsegP ),
inference(pattern_uni,[status(thm)],[67634:[bind(A,$thf( sk2 @ sk23 ))]]) ).
thf(20513,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ( A @ sk8 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,209]) ).
thf(20514,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ( A @ sk8 @ leq ) ) ),
inference(simp,[status(thm)],[20513]) ).
thf(20515,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk7 @ ( sk1 @ sk8 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[20514:[bind(A,$thf( sk1 ))]]) ).
thf(14651,plain,
~ ( sk2 @ ( nil @ segmentP ) ),
inference(simplifyReflect,[status(thm)],[10953,14544]) ).
thf(2846,plain,
( ( ( nil @ ( sk6 @ cons ) @ equalelemsP )
!= ( sk2 @ equalelemsP ) )
| ~ $true
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[2809,584]) ).
thf(2847,plain,
( ( ( nil @ ( sk6 @ cons ) @ equalelemsP )
!= ( sk2 @ equalelemsP ) )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[2846]) ).
thf(2860,plain,
( ( ( nil @ ( sk6 @ cons ) )
!= sk2 )
| ~ ( sk2 @ ( sk2 @ segmentP ) )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[2847]) ).
thf(7070,plain,
( ( ( nil @ ( sk6 @ cons ) )
!= sk2 )
| ~ $true
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(rewrite,[status(thm)],[2860,7038]) ).
thf(7071,plain,
( ( ( nil @ ( sk6 @ cons ) )
!= sk2 )
| ~ ( sk2 @ ( sk1 @ neq ) ) ),
inference(simp,[status(thm)],[7070]) ).
thf(1503,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[655,407]) ).
thf(1504,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1503]) ).
thf(1505,plain,
( ( nil @ ( sk2 @ sk9 @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1504:[bind(A,$thf( sk2 @ sk9 ))]]) ).
thf(17898,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17792,333]) ).
thf(17899,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17898]) ).
thf(17900,plain,
( ( nil @ ( sk2 @ sk10 @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17899:[bind(A,$thf( sk2 @ sk10 ))]]) ).
thf(17060,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ( A @ sk7 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,202]) ).
thf(17061,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ( A @ sk7 @ leq ) ) ),
inference(simp,[status(thm)],[17060]) ).
thf(17062,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk8 @ ( sk1 @ sk7 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[17061:[bind(A,$thf( sk1 ))]]) ).
thf(59667,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[59632,253]) ).
thf(59668,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk22 ) @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[59667]) ).
thf(59669,plain,
( ( nil @ ( nil @ sk22 ) @ ( nil @ app ) )
= ( nil @ ( nil @ sk22 ) ) ),
inference(pattern_uni,[status(thm)],[59668:[bind(A,$thf( nil @ ( nil @ sk22 ) ))]]) ).
thf(19077,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[18673,141]) ).
thf(19078,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19077]) ).
thf(19079,plain,
( ~ ( sk1 @ sk7 @ ( sk1 @ sk7 @ lt ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19078:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(50112,plain,
! [A: $i] :
( ( ( sk2 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[49863,280]) ).
thf(50113,plain,
! [A: $i] :
( ( ( sk2 @ sk20 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[50112]) ).
thf(50114,plain,
( ( nil @ ( sk2 @ sk20 @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[50113:[bind(A,$thf( sk2 @ sk20 ))]]) ).
thf(51,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) )
!= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
thf(309,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) )
!= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(20069,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19688,400]) ).
thf(20070,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[20069]) ).
thf(20071,plain,
( ( nil @ ( sk2 @ sk8 @ cons ) @ totalorderP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[20070:[bind(A,$thf( sk2 @ sk8 ))]]) ).
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/sandbox2/benchmark/theBenchmark.p',ax11) ).
thf(491,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(17920,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[17792,238]) ).
thf(17921,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[17920]) ).
thf(17922,plain,
( ( sk2 @ sk10 @ ( sk2 @ sk10 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[17921:[bind(A,$thf( sk2 @ sk10 ))]]) ).
thf(223,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)],[216]) ).
thf(226,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ lt ) )
| ( C @ ( B @ lt ) )
| ~ ( F @ ssList )
| ~ ( E @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssItem )
| ~ ( B @ ssItem )
| ~ ( A @ strictorderP )
| ~ ( A @ ssList )
| ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
!= A ) ),
inference(lifteq,[status(thm)],[223]) ).
thf(227,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ( B @ ( A @ lt ) )
| ~ ( E @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) @ strictorderP )
| ~ ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) @ ssList ) ),
inference(simp,[status(thm)],[226]) ).
thf(4654,plain,
( ~ $true
| ( ( sk5 @ ( sk6 @ geq ) )
!= ( sk6 @ ( sk5 @ geq ) ) )
| ~ ( sk6 @ ( sk5 @ geq ) ) ),
inference(eqfactor_ordered,[status(thm)],[4599]) ).
thf(4655,plain,
( ( ( sk5 @ ( sk6 @ geq ) )
!= ( sk6 @ ( sk5 @ geq ) ) )
| ~ ( sk6 @ ( sk5 @ geq ) ) ),
inference(simp,[status(thm)],[4654]) ).
thf(6295,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ sk9 @ sk9 @ cyclefreeP )
| ( sk2 @ sk9 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[1418,407]) ).
thf(6296,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ sk9 @ sk9 @ cyclefreeP )
| ( sk2 @ sk9 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[6295]) ).
thf(6297,plain,
( ( nil @ ( sk2 @ sk9 @ sk9 @ sk9 @ frontsegP ) )
| ( sk2 @ sk9 @ sk9 @ cyclefreeP )
| ( sk2 @ sk9 @ cyclefreeP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[6296:[bind(A,$thf( sk2 @ sk9 @ sk9 @ sk9 ))]]) ).
thf(84,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) @ tl )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax25) ).
thf(486,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) @ tl )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(20200,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[19748,240]) ).
thf(20201,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[20200]) ).
thf(20202,plain,
( ( nil @ ( sk1 @ sk8 @ cons ) @ totalorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[20201:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(1447,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( ( sk1 @ sk9 )
!= sk1 )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[731,333]) ).
thf(1448,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( ( sk1 @ sk9 )
!= sk1 )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1447]) ).
thf(1449,plain,
( ( nil @ ( sk1 @ sk9 @ sk9 @ rearsegP ) )
| ( ( sk1 @ sk9 )
!= sk1 )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1448:[bind(A,$thf( sk1 @ sk9 @ sk9 ))]]) ).
thf(84973,plain,
$false,
inference(e,[status(thm)],[25109,26016,5950,6285,1315,468,45241,333,249,19148,234,11175,46647,38166,25304,449,120,269,30516,202,20477,19127,408,730,217,51607,276,59675,7008,440,655,511,20117,142,715,1327,550,19236,538,153,26964,709,43350,49909,301,45456,436,17925,26979,174,6291,17475,45497,25499,184,26827,504,1330,125,1455,43353,196,157,1409,5953,8610,46477,19959,1514,12137,24454,152,1773,19956,43547,261,7047,59711,228,28244,1714,179,1418,253,51173,238,348,8479,20223,48961,1415,147,34245,17349,453,132,133,2809,11783,14652,312,206,66645,280,221,51931,116,243,47134,19033,63898,117,439,8078,201,37411,381,5562,220,1604,20157,233,452,67711,270,529,12132,45951,27165,23795,160,407,165,18821,42999,59635,43340,20108,334,48989,19914,1502,5956,788,137,19980,19748,329,18673,461,48675,17346,19082,59672,3191,229,67632,4585,435,2820,285,224,519,1762,25512,44621,45184,59839,188,45026,141,24652,18613,156,615,10152,356,256,19896,193,669,43705,489,1791,212,225,30580,515,19911,7069,49863,45943,25313,3074,48699,244,266,633,508,20172,19878,23823,794,17514,134,1333,128,18905,237,1318,205,43548,18080,166,29348,264,180,4599,513,430,279,27168,44631,149,4453,176,191,18096,286,48432,14544,118,18839,1520,281,18884,18836,772,259,7038,28194,19042,3077,144,335,12146,7062,25277,5556,26787,26967,1765,236,187,406,113,219,50359,1492,451,50078,7053,37399,6216,377,46480,98,25496,271,208,7504,20068,29002,535,103,140,213,19239,3165,520,155,198,48642,240,251,769,25216,47449,67675,130,399,278,31178,18993,135,20154,267,505,431,241,167,17251,18803,67669,1420,26940,209,112,17504,516,46358,25238,473,45525,663,548,342,123,194,145,45217,7026,712,1598,640,150,17324,27137,5944,18854,263,199,5420,17822,441,67844,127,470,27184,50403,643,27994,1499,5431,18054,177,791,336,17934,613,7067,19688,1717,46714,154,19929,28225,44983,27839,175,29600,17030,19060,17501,363,1517,218,18794,1421,2924,250,231,20199,8533,104,50431,20135,4574,25468,19097,258,390,114,401,30926,43539,7044,46355,20314,171,139,24436,731,7114,20311,18996,17792,18083,50138,18881,207,68576,7017,119,378,9537,16554,214,19869,287,151,48920,432,262,146,19124,17355,11712,190,422,25301,10443,28036,273,67672,6150,30009,210,326,43546,268,43669,400,2913,532,1610,34283,239,242,126,136,28021,195,4442,67635,728,332,27879,20515,14651,43330,28938,7071,25072,59632,1505,17900,17062,131,59669,48478,19079,122,50114,309,215,51106,20071,491,17224,232,17922,254,227,4655,6297,486,20202,1449]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC117+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.25/0.50 % Computer : n019.cluster.edu
% 0.25/0.50 % Model : x86_64 x86_64
% 0.25/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.50 % Memory : 8046.5625MB
% 0.25/0.50 % OS : Linux 6.8.0-71-generic
% 0.25/0.50 % CPULimit : 300
% 0.25/0.50 % WCLimit : 300
% 0.25/0.50 % DateTime : Sat Sep 26 12:17:48 UTC 2026
% 0.25/0.50 % CPUTime :
% 0.25/0.50 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.32/1.24 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.34/1.66 % [INFO] Parsing done (410ms).
% 2.34/1.68 % [INFO] Running in sequential loop mode.
% 3.66/2.26 % [INFO] eprover registered as external prover.
% 3.66/2.27 % [INFO] Scanning for conjecture ...
% 4.08/2.45 % [INFO] Found a conjecture (or negated_conjecture) and 95 axioms. Running axiom selection ...
% 4.34/2.56 % [INFO] Axiom selection finished. Selected 95 axioms (removed 0 axioms).
% 4.89/2.76 % [INFO] Problem is first-order (TPTP FOF).
% 5.15/2.80 % [INFO] Type checking passed.
% 5.15/2.81 % [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 ...
% 145.48/37.94 % External prover 'e' found a proof!
% 145.48/37.94 % [INFO] Killing All external provers ...
% 145.48/37.94 % Time passed: 37227ms (effective reasoning time: 36252ms)
% 145.48/37.94 % 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)>
% 145.48/37.94 % 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
% 145.48/37.94 % No. of inferences in proof: 1275
% 145.48/37.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 37227 ms resp. 36252 ms w/o parsing
% 147.65/38.31 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 147.65/38.32 % [INFO] Killing All external provers ...
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