%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWC149+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n013.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 08:52:30 AM UTC 2026
% Result : Theorem 257.31s 83.12s
% Output : Refutation 255.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 127
% Syntax : Number of formulae : 1640 ( 102 unt; 0 typ; 31 def)
% Number of atoms : 6978 (1823 equ; 0 cnn)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 15606 (2755 ~;3079 |; 213 &;8884 @)
% ( 26 <=>; 649 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 58 ( 55 usr; 9 con; 0-2 aty)
% Number of variables : 1518 ( 26 ^;1405 !; 56 ?;1518 :)
% ( 0 !>; 0 ?*; 0 @-; 31 @+)
% Comments :
%------------------------------------------------------------------------------
thf(ssList_decl,type,
ssList: $i > $o ).
thf(neq_decl,type,
neq: $i > $i > $o ).
thf(nil_decl,type,
nil: $i ).
thf(ssItem_decl,type,
ssItem: $i > $o ).
thf(app_decl,type,
app: $i > $i > $i ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(singletonP_decl,type,
singletonP: $i > $o ).
thf(strictorderedP_decl,type,
strictorderedP: $i > $o ).
thf(lt_decl,type,
lt: $i > $i > $o ).
thf(frontsegP_decl,type,
frontsegP: $i > $i > $o ).
thf(gt_decl,type,
gt: $i > $i > $o ).
thf(totalorderedP_decl,type,
totalorderedP: $i > $o ).
thf(hd_decl,type,
hd: $i > $i ).
thf(segmentP_decl,type,
segmentP: $i > $i > $o ).
thf(cyclefreeP_decl,type,
cyclefreeP: $i > $o ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(strictorderP_decl,type,
strictorderP: $i > $o ).
thf(duplicatefreeP_decl,type,
duplicatefreeP: $i > $o ).
thf(memberP_decl,type,
memberP: $i > $i > $o ).
thf(tl_decl,type,
tl: $i > $i ).
thf(totalorderP_decl,type,
totalorderP: $i > $o ).
thf(rearsegP_decl,type,
rearsegP: $i > $i > $o ).
thf(equalelemsP_decl,type,
equalelemsP: $i > $o ).
thf(geq_decl,type,
geq: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i > $i ).
thf(sk6_decl,type,
sk6: $i > $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 > $i ).
thf(sk21_decl,type,
sk21: $i > $i ).
thf(sk22_decl,type,
sk22: $i > $i ).
thf(sk23_decl,type,
sk23: $i > $i ).
thf(sk24_decl,type,
sk24: $i > $i ).
thf(sk25_decl,type,
sk25: $i > $i ).
thf(sk26_decl,type,
sk26: $i > $i ).
thf(sk27_decl,type,
sk27: $i > $i ).
thf(sk28_decl,type,
sk28: $i > $i ).
thf(sk29_decl,type,
sk29: $i > $i ).
thf(sk37_decl,type,
sk37: $i ).
thf(sk38_decl,type,
sk38: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( B @ singletonP )
| ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( ( G @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ app ) @ app ) )
= D )
& ( G @ ssList ) )
& ( F @ ssItem ) )
& ( E @ ssItem ) )
| ~ ( nil @ ( B @ neq ) )
| ( A != C )
| ( B != D ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( A @ singletonP )
| ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ( ( F @ ( nil @ ( E @ cons ) @ ( nil @ ( D @ cons ) @ app ) @ app ) )
= C )
& ( F @ ssList ) )
& ( E @ ssItem ) )
& ( D @ ssItem ) )
| ~ ( nil @ ( A @ neq ) )
| ( sk1 != B )
| ( A != C ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( sk2 @ singletonP )
| ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ( ( E @ ( nil @ ( D @ cons ) @ ( nil @ ( C @ cons ) @ app ) @ app ) )
= B )
& ( E @ ssList ) )
& ( D @ ssItem ) )
& ( C @ ssItem ) )
| ~ ( nil @ ( sk2 @ neq ) )
| ( sk1 != A )
| ( sk2 != B ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( A @ ssList )
=> ( ( sk2 @ singletonP )
| ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ( ( D @ ( nil @ ( C @ cons ) @ ( nil @ ( B @ cons ) @ app ) @ app ) )
= A )
& ( D @ ssList ) )
& ( C @ ssItem ) )
& ( B @ ssItem ) )
| ~ ( nil @ ( sk2 @ neq ) )
| ( sk1 != sk3 )
| ( sk2 != A ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [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(sk6_def,definition,
( sk6
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ( ( ( E @ ( B @ cons ) @ ( D @ ( A @ sk5 @ cons ) @ ( C @ app ) @ app ) )
= A )
=> ~ ( ( A @ sk5 @ ( B @ leq ) )
& ( B @ ( A @ sk5 @ leq ) ) ) ) ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( D @ ( A @ sk6 @ cons ) @ ( C @ ( A @ sk5 @ cons ) @ ( B @ app ) @ app ) )
= A )
=> ~ ( ( A @ sk5 @ ( A @ sk6 @ leq ) )
& ( A @ sk6 @ ( A @ sk5 @ leq ) ) ) ) ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( A @ sk6 @ cons ) @ ( B @ ( A @ sk5 @ cons ) @ ( A @ sk7 @ app ) @ app ) )
= A )
=> ~ ( ( A @ sk5 @ ( A @ sk6 @ leq ) )
& ( A @ sk6 @ ( A @ sk5 @ leq ) ) ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ( ( ( B @ ( A @ sk6 @ cons ) @ ( A @ sk8 @ ( A @ sk5 @ cons ) @ ( A @ sk7 @ app ) @ app ) )
= A )
=> ~ ( ( A @ sk5 @ ( A @ sk6 @ leq ) )
& ( A @ sk6 @ ( A @ sk5 @ leq ) ) ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( ( B @ ( C @ lt ) )
| ( C @ ( B @ lt ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ( ( ( E @ ( B @ cons ) @ ( D @ ( A @ sk10 @ cons ) @ ( C @ app ) @ app ) )
= A )
=> ( ( A @ sk10 @ ( B @ lt ) )
| ( B @ ( A @ sk10 @ lt ) ) ) ) ) ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( D @ ( A @ sk11 @ cons ) @ ( C @ ( A @ sk10 @ cons ) @ ( B @ app ) @ app ) )
= A )
=> ( ( A @ sk10 @ ( A @ sk11 @ lt ) )
| ( A @ sk11 @ ( A @ sk10 @ lt ) ) ) ) ) ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( A @ sk11 @ cons ) @ ( B @ ( A @ sk10 @ cons ) @ ( A @ sk12 @ app ) @ app ) )
= A )
=> ( ( A @ sk10 @ ( A @ sk11 @ lt ) )
| ( A @ sk11 @ ( A @ sk10 @ lt ) ) ) ) ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ( ( ( B @ ( A @ sk11 @ cons ) @ ( A @ sk13 @ ( A @ sk10 @ cons ) @ ( A @ sk12 @ app ) @ app ) )
= A )
=> ( ( A @ sk10 @ ( A @ sk11 @ lt ) )
| ( A @ sk11 @ ( A @ sk10 @ lt ) ) ) ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( C @ ( B @ lt ) ) ) ) ) ) ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ( ( ( E @ ( B @ cons ) @ ( D @ ( A @ sk15 @ cons ) @ ( C @ app ) @ app ) )
= A )
=> ( B @ ( A @ sk15 @ lt ) ) ) ) ) ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( D @ ( A @ sk16 @ cons ) @ ( C @ ( A @ sk15 @ cons ) @ ( B @ app ) @ app ) )
= A )
=> ( A @ sk16 @ ( A @ sk15 @ lt ) ) ) ) ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( A @ sk16 @ cons ) @ ( B @ ( A @ sk15 @ cons ) @ ( A @ sk17 @ app ) @ app ) )
= A )
=> ( A @ sk16 @ ( A @ sk15 @ lt ) ) ) ) ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ( ( ( B @ ( A @ sk16 @ cons ) @ ( A @ sk18 @ ( A @ sk15 @ cons ) @ ( A @ sk17 @ app ) @ app ) )
= A )
=> ( A @ sk16 @ ( A @ sk15 @ lt ) ) ) ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( ( C @ ( A @ app ) )
= B )
& ( C @ ssList ) ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( ^ [A: $i] :
@+[B: $i] :
( ( ( A @ tl )
= B )
& ( B @ ssList ) ) ) ) ).
thf(sk22_def,definition,
( sk22
= ( ^ [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(sk23_def,definition,
( sk23
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ( ( ( E @ ( B @ cons ) @ ( D @ ( A @ sk22 @ cons ) @ ( C @ app ) @ app ) )
= A )
=> ( ( A @ sk22 @ ( B @ leq ) )
| ( B @ ( A @ sk22 @ leq ) ) ) ) ) ) ) ) ) ) ).
thf(sk24_def,definition,
( sk24
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( D @ ( A @ sk23 @ cons ) @ ( C @ ( A @ sk22 @ cons ) @ ( B @ app ) @ app ) )
= A )
=> ( ( A @ sk22 @ ( A @ sk23 @ leq ) )
| ( A @ sk23 @ ( A @ sk22 @ leq ) ) ) ) ) ) ) ) ) ).
thf(sk25_def,definition,
( sk25
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( A @ sk23 @ cons ) @ ( B @ ( A @ sk22 @ cons ) @ ( A @ sk24 @ app ) @ app ) )
= A )
=> ( ( A @ sk22 @ ( A @ sk23 @ leq ) )
| ( A @ sk23 @ ( A @ sk22 @ leq ) ) ) ) ) ) ) ) ).
thf(sk26_def,definition,
( sk26
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ssList )
=> ( ( ( B @ ( A @ sk23 @ cons ) @ ( A @ sk25 @ ( A @ sk22 @ cons ) @ ( A @ sk24 @ app ) @ app ) )
= A )
=> ( ( A @ sk22 @ ( A @ sk23 @ leq ) )
| ( A @ sk23 @ ( A @ sk22 @ leq ) ) ) ) ) ) ) ).
thf(sk27_def,definition,
( sk27
= ( ^ [A: $i] :
@+[B: $i] :
( ? [C: $i] :
( ( ( B @ ( C @ cons ) )
= A )
& ( C @ ssItem ) )
& ( B @ ssList ) ) ) ) ).
thf(sk28_def,definition,
( sk28
= ( ^ [A: $i] :
@+[B: $i] :
( ( ( A @ sk27 @ ( B @ cons ) )
= A )
& ( B @ ssItem ) ) ) ) ).
thf(sk29_def,definition,
( sk29
= ( ^ [A: $i] :
@+[B: $i] :
( ( ( A @ hd )
= B )
& ( B @ ssItem ) ) ) ) ).
thf(sk37_def,definition,
( sk37
= ( @+[A: $i] :
( ? [B: $i] :
( ( A != B )
& ( B @ ssItem ) )
& ( A @ ssItem ) ) ) ) ).
thf(sk38_def,definition,
( sk38
= ( @+[A: $i] :
( ( sk37 != A )
& ( A @ ssItem ) ) ) ) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( B @ singletonP )
| ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( ( G @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ app ) @ app ) )
= D )
& ( G @ ssList ) )
& ( F @ ssItem ) )
& ( E @ ssItem ) )
| ~ ( nil @ ( B @ neq ) )
| ( A != C )
| ( B != D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( B @ singletonP )
| ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( ( G @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ app ) @ app ) )
= D )
& ( G @ ssList ) )
& ( F @ ssItem ) )
& ( E @ ssItem ) )
| ~ ( nil @ ( B @ neq ) )
| ( A != C )
| ( B != D ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(98,plain,
~ ! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( B @ singletonP )
| ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( ( G @ ( nil @ ( F @ cons ) @ ( nil @ ( E @ cons ) @ app ) @ app ) )
= D )
& ( G @ ssList ) )
& ( F @ ssItem ) )
& ( E @ ssItem ) )
| ~ ( nil @ ( B @ neq ) )
| ( A != C )
| ( B != D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(99,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( sk2 @ singletonP )
& ( ( ( C @ ( nil @ ( B @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk4 )
| ~ ( C @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) )
& ( nil @ ( sk2 @ neq ) )
& ( 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 @ strictorderedP )
<=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( C @ ( B @ lt ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax12) ).
thf(217,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( C @ ( B @ lt ) ) ) ) ) ) ) )
=> ( A @ strictorderedP ) )
& ( ( A @ strictorderedP )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( C @ ( B @ lt ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(218,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ strictorderedP )
| ~ ( A @ sk16 @ ( A @ sk15 @ lt ) )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( ( A @ sk19 @ ( A @ sk16 @ cons ) @ ( A @ sk18 @ ( A @ sk15 @ cons ) @ ( A @ sk17 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( A @ sk19 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( A @ sk18 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( A @ sk17 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( A @ sk16 @ ssItem )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderedP )
| ( A @ sk15 @ 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)],[217]) ).
thf(226,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk18 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[218]) ).
thf(38875,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk18 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,226]) ).
thf(38876,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk18 @ ssList ) ),
inference(simp,[status(thm)],[38875]) ).
thf(38877,plain,
( ( sk1 @ strictorderedP )
| ( sk1 @ sk18 @ ssList ) ),
inference(pattern_uni,[status(thm)],[38876:[bind(A,$thf( sk1 ))]]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax57) ).
thf(242,plain,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(243,plain,
! [A: $i] :
( ( nil @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[242]) ).
thf(39363,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[38877,243]) ).
thf(39364,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[39363]) ).
thf(39365,plain,
( ( nil @ ( sk1 @ sk18 @ segmentP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[39364:[bind(A,$thf( sk1 @ sk18 ))]]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ frontsegP ) )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax46) ).
thf(117,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( ( nil = A )
=> ( A @ ( nil @ frontsegP ) ) )
& ( ( A @ ( nil @ frontsegP ) )
=> ( nil = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(118,plain,
! [A: $i] :
( ( ( A @ ( nil @ frontsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) )
& ( ( nil = A )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[117]) ).
thf(120,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[118]) ).
thf(122,plain,
! [A: $i] :
( ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[120]) ).
thf(123,plain,
( ( nil @ ( nil @ frontsegP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[122]) ).
thf(53,axiom,
nil @ ssList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
thf(343,plain,
nil @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(640,plain,
( ( nil @ ( nil @ frontsegP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[123,343]) ).
thf(641,plain,
nil @ ( nil @ frontsegP ),
inference(simp,[status(thm)],[640]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( B @ ( A @ frontsegP ) )
<=> ? [C: $i] :
( ( ( C @ ( B @ app ) )
= A )
& ( C @ ssList ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
thf(234,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ? [C: $i] :
( ( ( C @ ( B @ app ) )
= A )
& ( C @ ssList ) )
=> ( B @ ( A @ frontsegP ) ) )
& ( ( B @ ( A @ frontsegP ) )
=> ? [C: $i] :
( ( ( C @ ( B @ app ) )
= A )
& ( C @ ssList ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(235,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ frontsegP ) )
| ( ( C @ ( B @ app ) )
!= A )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) )
& ( ( ( A @ ( B @ sk20 ) @ ( B @ app ) )
= A )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ ( B @ sk20 ) @ ssList )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[234]) ).
thf(236,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk20 ) @ ssList )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[235]) ).
thf(44879,plain,
! [B: $i,A: $i] :
( ( ( nil @ ( nil @ frontsegP ) )
!= ( B @ ( A @ frontsegP ) ) )
| ( A @ ( B @ sk20 ) @ ssList )
| ~ $true
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[641,236]) ).
thf(44880,plain,
! [B: $i,A: $i] :
( ( ( nil @ ( nil @ frontsegP ) )
!= ( B @ ( A @ frontsegP ) ) )
| ( A @ ( B @ sk20 ) @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[44879]) ).
thf(44881,plain,
( ( nil @ ( nil @ sk20 ) @ ssList )
| ~ ( nil @ ssList )
| ~ ( nil @ ssList ) ),
inference(pattern_uni,[status(thm)],[44880:[bind(A,$thf( nil )),bind(B,$thf( nil ))]]) ).
thf(45092,plain,
( ( nil @ ( nil @ sk20 ) @ ssList )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[44881]) ).
thf(45181,plain,
( ( nil @ ( nil @ sk20 ) @ ssList )
| ~ $true ),
inference(rewrite,[status(thm)],[45092,343]) ).
thf(45182,plain,
nil @ ( nil @ sk20 ) @ ssList,
inference(simp,[status(thm)],[45181]) ).
thf(45271,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk20 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[45182,243]) ).
thf(45272,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk20 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[45271]) ).
thf(45273,plain,
nil @ ( nil @ ( nil @ sk20 ) @ segmentP ),
inference(pattern_uni,[status(thm)],[45272:[bind(A,$thf( nil @ ( nil @ sk20 ) ))]]) ).
thf(55,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( B @ ( A @ segmentP ) )
<=> ? [C: $i] :
( ? [D: $i] :
( ( ( D @ ( B @ ( C @ app ) @ app ) )
= A )
& ( D @ ssList ) )
& ( C @ ssList ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7) ).
thf(347,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ? [C: $i] :
( ? [D: $i] :
( ( ( D @ ( B @ ( C @ app ) @ app ) )
= A )
& ( D @ ssList ) )
& ( C @ ssList ) )
=> ( B @ ( A @ segmentP ) ) )
& ( ( B @ ( A @ segmentP ) )
=> ? [C: $i] :
( ? [D: $i] :
( ( ( D @ ( B @ ( C @ app ) @ app ) )
= A )
& ( D @ ssList ) )
& ( C @ ssList ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ( A @ tl )
= B )
& ( B @ ssList ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax76) ).
thf(244,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ( A @ tl )
= B )
& ( B @ ssList ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(245,plain,
! [A: $i] :
( ( ( ( A @ tl )
= ( A @ sk21 ) )
| ( nil = A )
| ~ ( A @ ssList ) )
& ( ( A @ sk21 @ ssList )
| ( nil = A )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[244]) ).
thf(247,plain,
! [A: $i] :
( ( ( A @ tl )
= ( A @ sk21 ) )
| ( nil = A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[245]) ).
thf(249,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ( ( A @ sk21 )
= ( A @ tl ) )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[247]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ segmentP ) )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax58) ).
thf(132,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( ( nil = A )
=> ( A @ ( nil @ segmentP ) ) )
& ( ( A @ ( nil @ segmentP ) )
=> ( nil = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(133,plain,
! [A: $i] :
( ( ( A @ ( nil @ segmentP ) )
| ( nil != A )
| ~ ( A @ ssList ) )
& ( ( nil = A )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[132]) ).
thf(134,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[133]) ).
thf(136,plain,
! [A: $i] :
( ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[134]) ).
thf(61,axiom,
? [A: $i] :
( ? [B: $i] :
( ( A != B )
& ( B @ ssItem ) )
& ( A @ ssItem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
thf(388,plain,
? [A: $i] :
( ? [B: $i] :
( ( A != B )
& ( B @ ssItem ) )
& ( A @ ssItem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(389,plain,
( ( sk37 != sk38 )
& ( sk38 @ ssItem )
& ( sk37 @ ssItem ) ),
inference(cnf,[status(esa)],[388]) ).
thf(390,plain,
sk37 @ ssItem,
inference(cnfConj,[status(thm)],[389]) ).
thf(107,plain,
nil @ ( sk2 @ neq ),
inference(cnfConj,[status(thm)],[99]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ neq ) )
<=> ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(205,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( ( A != B )
=> ( B @ ( A @ neq ) ) )
& ( ( B @ ( A @ neq ) )
=> ( A != B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(206,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)],[205]) ).
thf(207,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ ( A @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[206]) ).
thf(209,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A != B ) ),
inference(lifteq,[status(thm)],[207]) ).
thf(210,plain,
! [A: $i] :
( ~ ( A @ ( A @ neq ) )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[209]) ).
thf(648,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ neq ) )
!= ( A @ ( A @ neq ) ) )
| ~ $true
| ~ ( A @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[107,210]) ).
thf(649,plain,
! [A: $i] :
( ( ( nil @ ( sk2 @ neq ) )
!= ( A @ ( A @ neq ) ) )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[648]) ).
thf(650,plain,
! [A: $i] :
( ( nil != A )
| ( sk2 != A )
| ~ ( A @ ssItem ) ),
inference(simp,[status(thm)],[649]) ).
thf(651,plain,
( ( sk2 != nil )
| ~ ( sk2 @ ssItem ) ),
inference(simp,[status(thm)],[650]) ).
thf(720,plain,
( ( ( sk37 @ ssItem )
!= ( sk2 @ ssItem ) )
| ( sk2 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[390,651]) ).
thf(721,plain,
( ( ( sk37 @ ssItem )
!= ( sk2 @ ssItem ) )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[720]) ).
thf(724,plain,
( ( sk37 != sk2 )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[721]) ).
thf(1838,plain,
! [A: $i] :
( ( A != sk37 )
| ( sk2 != nil )
| ( sk2 != nil )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[136,724]) ).
thf(1839,plain,
! [A: $i] :
( ( A != sk37 )
| ( sk2 != nil )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[1838]) ).
thf(1840,plain,
( ( sk2 != nil )
| ~ ( sk37 @ ( nil @ segmentP ) )
| ~ ( sk37 @ ssList ) ),
inference(pattern_uni,[status(thm)],[1839:[bind(A,$thf( sk37 ))]]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ cyclefreeP )
<=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ~ ( ( B @ ( C @ leq ) )
& ( C @ ( B @ leq ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8) ).
thf(151,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ~ ( ( B @ ( C @ leq ) )
& ( C @ ( B @ leq ) ) ) ) ) ) ) ) )
=> ( A @ cyclefreeP ) )
& ( ( A @ cyclefreeP )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ~ ( ( B @ ( C @ leq ) )
& ( C @ ( B @ leq ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(152,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ cyclefreeP )
| ( A @ sk5 @ ( A @ sk6 @ leq ) )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk6 @ ( A @ sk5 @ leq ) )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( ( A @ sk9 @ ( A @ sk6 @ cons ) @ ( A @ sk8 @ ( A @ sk5 @ cons ) @ ( A @ sk7 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk8 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk7 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk6 @ ssItem )
| ~ ( A @ ssList ) )
& ( ( A @ cyclefreeP )
| ( A @ sk5 @ 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)],[151]) ).
thf(157,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[152]) ).
thf(6066,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,157]) ).
thf(6067,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList ) ),
inference(simp,[status(thm)],[6066]) ).
thf(6068,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk9 @ ssList ) ),
inference(pattern_uni,[status(thm)],[6067:[bind(A,$thf( sk1 ))]]) ).
thf(59,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax45) ).
thf(372,plain,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(373,plain,
! [A: $i] :
( ( nil @ ( A @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[372]) ).
thf(8782,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[6068,373]) ).
thf(8783,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[8782]) ).
thf(8784,plain,
( ( nil @ ( sk1 @ sk9 @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[8783:[bind(A,$thf( sk1 @ sk9 ))]]) ).
thf(103,plain,
sk2 @ ssList,
inference(cnfConj,[status(thm)],[99]) ).
thf(2120,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[103,136]) ).
thf(2121,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[2120]) ).
thf(2122,plain,
( ~ ( sk2 @ ( nil @ segmentP ) )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[2121:[bind(A,$thf( sk2 ))]]) ).
thf(119,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[118]) ).
thf(121,plain,
! [A: $i] :
( ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[119]) ).
thf(917,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[103,121]) ).
thf(918,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[917]) ).
thf(919,plain,
( ~ ( sk2 @ ( nil @ frontsegP ) )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[918:[bind(A,$thf( sk2 ))]]) ).
thf(727,plain,
! [A: $i] :
( ( A != sk2 )
| ( nil != nil )
| ~ ( sk2 @ ssItem )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[121,651]) ).
thf(728,plain,
! [A: $i] :
( ( A != sk2 )
| ~ ( sk2 @ ssItem )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[727]) ).
thf(729,plain,
( ~ ( sk2 @ ssItem )
| ~ ( sk2 @ ( nil @ frontsegP ) )
| ~ ( sk2 @ ssList ) ),
inference(pattern_uni,[status(thm)],[728:[bind(A,$thf( sk2 ))]]) ).
thf(1034,plain,
( ~ ( sk2 @ ssItem )
| ~ ( sk2 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[729,103]) ).
thf(1035,plain,
( ~ ( sk2 @ ssItem )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1034]) ).
thf(1269,plain,
( ( sk2 != sk2 )
| ~ ( nil @ ssItem )
| ~ ( sk2 @ ( nil @ frontsegP ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[919,1035]) ).
thf(1270,plain,
( ( sk2 != sk2 )
| ~ ( nil @ ssItem )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1269]) ).
thf(1271,plain,
( ~ ( nil @ ssItem )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1270:[]]) ).
thf(1346,plain,
( ( ( sk2 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[641,1271]) ).
thf(1347,plain,
( ( ( sk2 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[1346]) ).
thf(1356,plain,
( ( sk2 != nil )
| ( nil != nil )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[1347]) ).
thf(1362,plain,
( ( sk2 != nil )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[1356]) ).
thf(2329,plain,
( ( sk2 != sk2 )
| ( nil != nil )
| ~ ( nil @ ssItem )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2122,1362]) ).
thf(2330,plain,
( ( sk2 != sk2 )
| ~ ( nil @ ssItem )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[2329]) ).
thf(2331,plain,
( ~ ( nil @ ssItem )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[2330:[]]) ).
thf(246,plain,
! [A: $i] :
( ( A @ sk21 @ ssList )
| ( nil = A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[245]) ).
thf(248,plain,
! [A: $i] :
( ( A @ sk21 @ ssList )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[246]) ).
thf(51242,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk21 @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[103,248]) ).
thf(51243,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk21 @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[51242]) ).
thf(51244,plain,
( ( sk2 @ sk21 @ ssList )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[51243:[bind(A,$thf( sk2 ))]]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax61) ).
thf(365,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ strictorderP )
<=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( ( B @ ( C @ lt ) )
| ( C @ ( B @ lt ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10) ).
thf(167,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( ( B @ ( C @ lt ) )
| ( C @ ( B @ lt ) ) ) ) ) ) ) ) )
=> ( A @ strictorderP ) )
& ( ( A @ strictorderP )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( ( B @ ( C @ lt ) )
| ( C @ ( B @ lt ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(168,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ strictorderP )
| ~ ( A @ sk10 @ ( A @ sk11 @ lt ) )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ~ ( A @ sk11 @ ( A @ sk10 @ lt ) )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( ( A @ sk14 @ ( A @ sk11 @ cons ) @ ( A @ sk13 @ ( A @ sk10 @ cons ) @ ( A @ sk12 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( A @ sk14 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( A @ sk13 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( A @ sk12 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( A @ sk11 @ ssItem )
| ~ ( A @ ssList ) )
& ( ( A @ strictorderP )
| ( A @ sk10 @ 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)],[167]) ).
thf(171,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk13 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[168]) ).
thf(10150,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk13 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,171]) ).
thf(10151,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk13 @ ssList ) ),
inference(simp,[status(thm)],[10150]) ).
thf(10152,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk13 @ ssList ) ),
inference(pattern_uni,[status(thm)],[10151:[bind(A,$thf( sk2 ))]]) ).
thf(10371,plain,
! [A: $i] :
( ( ( sk2 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10152,373]) ).
thf(10372,plain,
! [A: $i] :
( ( ( sk2 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[10371]) ).
thf(10373,plain,
( ( nil @ ( sk2 @ sk13 @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10372:[bind(A,$thf( sk2 @ sk13 ))]]) ).
thf(392,plain,
sk37 != sk38,
inference(cnfConj,[status(thm)],[389]) ).
thf(393,plain,
sk38 != sk37,
inference(lifteq,[status(thm)],[392]) ).
thf(832,plain,
! [A: $i] :
( ( A != sk38 )
| ( sk37 != nil )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[121,393]) ).
thf(833,plain,
( ( sk37 != nil )
| ~ ( sk38 @ ( nil @ frontsegP ) )
| ~ ( sk38 @ ssList ) ),
inference(pattern_uni,[status(thm)],[832:[bind(A,$thf( sk38 ))]]) ).
thf(1667,plain,
( ( ( sk38 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk37 != nil )
| ~ $true
| ~ ( sk38 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[641,833]) ).
thf(1668,plain,
( ( ( sk38 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk37 != nil )
| ~ ( sk38 @ ssList ) ),
inference(simp,[status(thm)],[1667]) ).
thf(1675,plain,
( ( sk38 != nil )
| ( nil != nil )
| ( sk37 != nil )
| ~ ( sk38 @ ssList ) ),
inference(simp,[status(thm)],[1668]) ).
thf(1680,plain,
( ( sk38 != nil )
| ( sk37 != nil )
| ~ ( sk38 @ ssList ) ),
inference(simp,[status(thm)],[1675]) ).
thf(1689,plain,
( ( ( sk38 @ ssList )
!= ( nil @ ssList ) )
| ( sk38 != nil )
| ( sk37 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[343,1680]) ).
thf(1690,plain,
( ( ( sk38 @ ssList )
!= ( nil @ ssList ) )
| ( sk38 != nil )
| ( sk37 != nil ) ),
inference(simp,[status(thm)],[1689]) ).
thf(1696,plain,
( ( sk38 != nil )
| ( sk38 != nil )
| ( sk37 != nil ) ),
inference(simp,[status(thm)],[1690]) ).
thf(1698,plain,
( ( sk38 != nil )
| ( sk37 != nil ) ),
inference(simp,[status(thm)],[1696]) ).
thf(2307,plain,
! [A: $i] :
( ( A != sk37 )
| ( sk38 != nil )
| ( nil != nil )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[136,1698]) ).
thf(2308,plain,
! [A: $i] :
( ( A != sk37 )
| ( sk38 != nil )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[2307]) ).
thf(2309,plain,
( ( sk38 != nil )
| ~ ( sk37 @ ( nil @ segmentP ) )
| ~ ( sk37 @ ssList ) ),
inference(pattern_uni,[status(thm)],[2308:[bind(A,$thf( sk37 ))]]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax68) ).
thf(115,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1397,plain,
( ( ( sk37 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk2 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[390,1362]) ).
thf(1398,plain,
( ( ( sk37 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[1397]) ).
thf(1400,plain,
( ( sk37 != nil )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[1398]) ).
thf(53142,plain,
( ( sk2 != sk2 )
| ( sk37 != nil )
| ( nil != nil )
| ( sk2 @ sk21 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[51244,1400]) ).
thf(53143,plain,
( ( sk2 != sk2 )
| ( sk37 != nil )
| ( sk2 @ sk21 @ ssList ) ),
inference(simp,[status(thm)],[53142]) ).
thf(53144,plain,
( ( sk37 != nil )
| ( sk2 @ sk21 @ ssList ) ),
inference(pattern_uni,[status(thm)],[53143:[]]) ).
thf(55698,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk37 != nil ) ),
inference(paramod_ordered,[status(thm)],[53144,243]) ).
thf(55699,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk37 != nil ) ),
inference(simp,[status(thm)],[55698]) ).
thf(55700,plain,
( ( nil @ ( sk2 @ sk21 @ segmentP ) )
| ( sk37 != nil ) ),
inference(pattern_uni,[status(thm)],[55699:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(77,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ( ( ( C @ ( B @ lt ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ lt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax91) ).
thf(449,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ( ( ( C @ ( B @ lt ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ lt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil @ ( A @ app ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax84) ).
thf(181,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil @ ( A @ app ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(182,plain,
! [A: $i] :
( ( ( nil @ ( A @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[181]) ).
thf(183,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[182]) ).
thf(45417,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk20 ) @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[45182,183]) ).
thf(45418,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk20 ) @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[45417]) ).
thf(45419,plain,
( ( nil @ ( nil @ ( nil @ sk20 ) @ app ) )
= ( nil @ ( nil @ sk20 ) ) ),
inference(pattern_uni,[status(thm)],[45418:[bind(A,$thf( nil @ ( nil @ sk20 ) ))]]) ).
thf(391,plain,
sk38 @ ssItem,
inference(cnfConj,[status(thm)],[389]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( A @ lt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax90) ).
thf(215,plain,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( A @ lt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(216,plain,
! [A: $i] :
( ~ ( A @ ( A @ lt ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[215]) ).
thf(32597,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[391,216]) ).
thf(32598,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[32597]) ).
thf(32599,plain,
~ ( sk38 @ ( sk38 @ lt ) ),
inference(pattern_uni,[status(thm)],[32598:[bind(A,$thf( sk38 ))]]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ? [B: $i] :
( ? [C: $i] :
( ( ( B @ ( C @ cons ) )
= A )
& ( C @ ssItem ) )
& ( B @ ssList ) )
| ( nil = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).
thf(264,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ? [B: $i] :
( ? [C: $i] :
( ( ( B @ ( C @ cons ) )
= A )
& ( C @ ssItem ) )
& ( B @ ssList ) )
| ( nil = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(265,plain,
! [A: $i] :
( ( ( ( A @ sk27 @ ( A @ sk28 @ cons ) )
= A )
| ( nil = A )
| ~ ( A @ ssList ) )
& ( ( A @ sk28 @ ssItem )
| ( nil = A )
| ~ ( A @ ssList ) )
& ( ( A @ sk27 @ ssList )
| ( nil = A )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[264]) ).
thf(266,plain,
! [A: $i] :
( ( A @ sk27 @ ssList )
| ( nil = A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[265]) ).
thf(269,plain,
! [A: $i] :
( ( A @ sk27 @ ssList )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[266]) ).
thf(718,plain,
( ( ( sk38 @ ssItem )
!= ( sk2 @ ssItem ) )
| ( sk2 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[391,651]) ).
thf(719,plain,
( ( ( sk38 @ ssItem )
!= ( sk2 @ ssItem ) )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[718]) ).
thf(723,plain,
( ( sk38 != sk2 )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[719]) ).
thf(53273,plain,
( ( sk2 != sk2 )
| ( sk38 != sk2 )
| ( nil != nil )
| ( sk2 @ sk21 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[51244,723]) ).
thf(53274,plain,
( ( sk2 != sk2 )
| ( sk38 != sk2 )
| ( sk2 @ sk21 @ ssList ) ),
inference(simp,[status(thm)],[53273]) ).
thf(53275,plain,
( ( sk38 != sk2 )
| ( sk2 @ sk21 @ ssList ) ),
inference(pattern_uni,[status(thm)],[53274:[]]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax51) ).
thf(295,plain,
! [A: $i] :
( ( A @ ssList )
=> ( nil @ ( A @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(296,plain,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[295]) ).
thf(56500,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk38 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[53275,296]) ).
thf(56501,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk38 != sk2 ) ),
inference(simp,[status(thm)],[56500]) ).
thf(56502,plain,
( ( nil @ ( sk2 @ sk21 @ rearsegP ) )
| ( sk38 != sk2 ) ),
inference(pattern_uni,[status(thm)],[56501:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ totalorderP )
<=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( ( B @ ( C @ leq ) )
| ( C @ ( B @ leq ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax9) ).
thf(250,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( ( B @ ( C @ leq ) )
| ( C @ ( B @ leq ) ) ) ) ) ) ) ) )
=> ( A @ totalorderP ) )
& ( ( A @ totalorderP )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( ( B @ ( C @ leq ) )
| ( C @ ( B @ leq ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(251,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ totalorderP )
| ~ ( A @ sk22 @ ( A @ sk23 @ leq ) )
| ~ ( A @ ssList ) )
& ( ( A @ totalorderP )
| ~ ( A @ sk23 @ ( A @ sk22 @ leq ) )
| ~ ( A @ ssList ) )
& ( ( A @ totalorderP )
| ( ( A @ sk26 @ ( A @ sk23 @ cons ) @ ( A @ sk25 @ ( A @ sk22 @ cons ) @ ( A @ sk24 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) )
& ( ( A @ totalorderP )
| ( A @ sk26 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ totalorderP )
| ( A @ sk25 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ totalorderP )
| ( A @ sk24 @ ssList )
| ~ ( A @ ssList ) )
& ( ( A @ totalorderP )
| ( A @ sk23 @ ssItem )
| ~ ( A @ ssList ) )
& ( ( A @ totalorderP )
| ( A @ sk22 @ ssItem )
| ~ ( A @ ssList ) )
& ( ( B @ ( C @ leq ) )
| ( C @ ( B @ leq ) )
| ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
!= A )
| ~ ( F @ ssList )
| ~ ( E @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssItem )
| ~ ( B @ ssItem )
| ~ ( A @ totalorderP )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[250]) ).
thf(258,plain,
! [A: $i] :
( ( A @ totalorderP )
| ( A @ sk26 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[251]) ).
thf(63892,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk26 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,258]) ).
thf(63893,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk26 @ ssList ) ),
inference(simp,[status(thm)],[63892]) ).
thf(63894,plain,
( ( sk2 @ totalorderP )
| ( sk2 @ sk26 @ ssList ) ),
inference(pattern_uni,[status(thm)],[63893:[bind(A,$thf( sk2 ))]]) ).
thf(254,plain,
! [A: $i] :
( ( A @ totalorderP )
| ( A @ sk25 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[251]) ).
thf(57990,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk25 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,254]) ).
thf(57991,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk25 @ ssList ) ),
inference(simp,[status(thm)],[57990]) ).
thf(57992,plain,
( ( sk2 @ totalorderP )
| ( sk2 @ sk25 @ ssList ) ),
inference(pattern_uni,[status(thm)],[57991:[bind(A,$thf( sk2 ))]]) ).
thf(58331,plain,
! [A: $i] :
( ( ( sk2 @ sk25 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[57992,243]) ).
thf(58332,plain,
! [A: $i] :
( ( ( sk2 @ sk25 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ totalorderP ) ),
inference(simp,[status(thm)],[58331]) ).
thf(58333,plain,
( ( nil @ ( sk2 @ sk25 @ segmentP ) )
| ( sk2 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[58332:[bind(A,$thf( sk2 @ sk25 ))]]) ).
thf(55524,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ sk21 )
= ( A @ tl ) )
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[103,249]) ).
thf(55525,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ sk21 )
= ( A @ tl ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[55524]) ).
thf(55526,plain,
( ( ( sk2 @ sk21 )
= ( sk2 @ tl ) )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[55525:[bind(A,$thf( sk2 ))]]) ).
thf(65460,plain,
( ( ( sk2 @ sk21 )
!= ( sk2 @ sk21 ) )
| ( sk2 @ tl @ ssList )
| ( sk2 = nil )
| ( sk2 = nil ) ),
inference(paramod_ordered,[status(thm)],[55526,51244]) ).
thf(65461,plain,
( ( ( sk2 @ sk21 )
!= ( sk2 @ sk21 ) )
| ( sk2 @ tl @ ssList )
| ( sk2 = nil ) ),
inference(simp,[status(thm)],[65460]) ).
thf(65462,plain,
( ( sk2 @ tl @ ssList )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[65461:[]]) ).
thf(1390,plain,
( ( ( sk38 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk2 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[391,1362]) ).
thf(1391,plain,
( ( ( sk38 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[1390]) ).
thf(1399,plain,
( ( sk38 != nil )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[1391]) ).
thf(66358,plain,
( ( sk2 != sk2 )
| ( sk38 != nil )
| ( nil != nil )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[65462,1399]) ).
thf(66359,plain,
( ( sk2 != sk2 )
| ( sk38 != nil )
| ( sk2 @ tl @ ssList ) ),
inference(simp,[status(thm)],[66358]) ).
thf(66360,plain,
( ( sk38 != nil )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[66359:[]]) ).
thf(255,plain,
! [A: $i] :
( ( A @ totalorderP )
| ( A @ sk24 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[251]) ).
thf(60072,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk24 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,255]) ).
thf(60073,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk24 @ ssList ) ),
inference(simp,[status(thm)],[60072]) ).
thf(60074,plain,
( ( sk1 @ totalorderP )
| ( sk1 @ sk24 @ ssList ) ),
inference(pattern_uni,[status(thm)],[60073:[bind(A,$thf( sk1 ))]]) ).
thf(60719,plain,
! [A: $i] :
( ( ( sk1 @ sk24 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[60074,243]) ).
thf(60720,plain,
! [A: $i] :
( ( ( sk1 @ sk24 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ totalorderP ) ),
inference(simp,[status(thm)],[60719]) ).
thf(60721,plain,
( ( nil @ ( sk1 @ sk24 @ segmentP ) )
| ( sk1 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[60720:[bind(A,$thf( sk1 @ sk24 ))]]) ).
thf(645,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[390,210]) ).
thf(646,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[645]) ).
thf(647,plain,
~ ( sk37 @ ( sk37 @ neq ) ),
inference(pattern_uni,[status(thm)],[646:[bind(A,$thf( sk37 ))]]) ).
thf(1014,plain,
( ( ( sk37 @ ( sk37 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[107,647]) ).
thf(1015,plain,
( ( sk37 @ ( sk37 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[1014]) ).
thf(1016,plain,
( ( sk37 != nil )
| ( sk37 != sk2 ) ),
inference(simp,[status(thm)],[1015]) ).
thf(1031,plain,
! [A: $i] :
( ( A != sk37 )
| ( nil != nil )
| ( sk37 != sk2 )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[121,1016]) ).
thf(1032,plain,
! [A: $i] :
( ( A != sk37 )
| ( sk37 != sk2 )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[1031]) ).
thf(1033,plain,
( ( sk37 != sk2 )
| ~ ( sk37 @ ( nil @ frontsegP ) )
| ~ ( sk37 @ ssList ) ),
inference(pattern_uni,[status(thm)],[1032:[bind(A,$thf( sk37 ))]]) ).
thf(8034,plain,
( ( ( sk37 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk37 != sk2 )
| ~ ( sk37 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,1033]) ).
thf(8035,plain,
( ( ( sk37 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk37 != sk2 )
| ~ ( sk37 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[8034]) ).
thf(8057,plain,
( ( sk37 != sk2 )
| ( sk37 != sk2 )
| ~ ( sk37 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[8035]) ).
thf(8082,plain,
( ( sk37 != sk2 )
| ~ ( sk37 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[8057]) ).
thf(156,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk6 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[152]) ).
thf(5590,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk6 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,156]) ).
thf(5591,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk6 @ ssItem ) ),
inference(simp,[status(thm)],[5590]) ).
thf(5592,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk6 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[5591:[bind(A,$thf( sk2 ))]]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderedP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax65) ).
thf(191,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(192,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ totalorderedP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[191]) ).
thf(19460,plain,
! [A: $i] :
( ( ( sk2 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5592,192]) ).
thf(19461,plain,
! [A: $i] :
( ( ( sk2 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19460]) ).
thf(19462,plain,
( ( nil @ ( sk2 @ sk6 @ cons ) @ totalorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19461:[bind(A,$thf( sk2 @ sk6 ))]]) ).
thf(153,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk5 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[152]) ).
thf(682,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk5 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,153]) ).
thf(683,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk5 @ ssItem ) ),
inference(simp,[status(thm)],[682]) ).
thf(684,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk5 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[683:[bind(A,$thf( sk2 ))]]) ).
thf(1386,plain,
( ( ( sk2 @ sk5 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk2 != nil )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[684,1362]) ).
thf(1387,plain,
( ( ( sk2 @ sk5 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk2 != nil )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1386]) ).
thf(1401,plain,
( ( ( sk2 @ sk5 )
!= nil )
| ( sk2 != nil )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1387]) ).
thf(176,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk14 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[168]) ).
thf(12841,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk14 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,176]) ).
thf(12842,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk14 @ ssList ) ),
inference(simp,[status(thm)],[12841]) ).
thf(12843,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk14 @ ssList ) ),
inference(pattern_uni,[status(thm)],[12842:[bind(A,$thf( sk2 ))]]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ segmentP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax55) ).
thf(189,plain,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ segmentP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(190,plain,
! [A: $i] :
( ( A @ ( A @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[189]) ).
thf(18808,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[12843,190]) ).
thf(18809,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[18808]) ).
thf(18810,plain,
( ( sk2 @ sk14 @ ( sk2 @ sk14 @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[18809:[bind(A,$thf( sk2 @ sk14 ))]]) ).
thf(172,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk12 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[168]) ).
thf(10764,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk12 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,172]) ).
thf(10765,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk12 @ ssList ) ),
inference(simp,[status(thm)],[10764]) ).
thf(10766,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk12 @ ssList ) ),
inference(pattern_uni,[status(thm)],[10765:[bind(A,$thf( sk1 ))]]) ).
thf(11078,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10766,296]) ).
thf(11079,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[11078]) ).
thf(11080,plain,
( ( nil @ ( sk1 @ sk12 @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[11079:[bind(A,$thf( sk1 @ sk12 ))]]) ).
thf(18859,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10766,190]) ).
thf(18860,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[18859]) ).
thf(18861,plain,
( ( sk1 @ sk12 @ ( sk1 @ sk12 @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[18860:[bind(A,$thf( sk1 @ sk12 ))]]) ).
thf(177,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk11 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[168]) ).
thf(13672,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk11 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,177]) ).
thf(13673,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk11 @ ssItem ) ),
inference(simp,[status(thm)],[13672]) ).
thf(13674,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk11 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[13673:[bind(A,$thf( sk2 ))]]) ).
thf(32612,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[13674,216]) ).
thf(32613,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[32612]) ).
thf(32614,plain,
( ~ ( sk2 @ sk11 @ ( sk2 @ sk11 @ lt ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[32613:[bind(A,$thf( sk2 @ sk11 ))]]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( A @ ( B @ frontsegP ) )
& ( B @ ( A @ frontsegP ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax41) ).
thf(140,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( A @ ( B @ frontsegP ) )
& ( B @ ( A @ frontsegP ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(141,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[140]) ).
thf(142,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ frontsegP ) )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( A = B ) ),
inference(lifteq,[status(thm)],[141]) ).
thf(13093,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[12843,373]) ).
thf(13094,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[13093]) ).
thf(13095,plain,
( ( nil @ ( sk2 @ sk14 @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[13094:[bind(A,$thf( sk2 @ sk14 ))]]) ).
thf(688,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk5 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,153]) ).
thf(689,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk5 @ ssItem ) ),
inference(simp,[status(thm)],[688]) ).
thf(690,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk5 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[689:[bind(A,$thf( sk1 ))]]) ).
thf(34,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( nil @ memberP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
thf(230,plain,
! [A: $i] :
( ( A @ ssItem )
=> ~ ( A @ ( nil @ memberP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(231,plain,
! [A: $i] :
( ~ ( A @ ( nil @ memberP ) )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[230]) ).
thf(1162,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[690,231]) ).
thf(1163,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1162]) ).
thf(1164,plain,
( ~ ( sk1 @ sk5 @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1163:[bind(A,$thf( sk1 @ sk5 ))]]) ).
thf(220,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk15 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[218]) ).
thf(33500,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk15 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,220]) ).
thf(33501,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk15 @ ssItem ) ),
inference(simp,[status(thm)],[33500]) ).
thf(33502,plain,
( ( sk1 @ strictorderedP )
| ( sk1 @ sk15 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[33501:[bind(A,$thf( sk1 ))]]) ).
thf(33927,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[33502,231]) ).
thf(33928,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[33927]) ).
thf(33929,plain,
( ~ ( sk1 @ sk15 @ ( nil @ memberP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[33928:[bind(A,$thf( sk1 @ sk15 ))]]) ).
thf(82,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( B @ rearsegP ) )
& ( B @ ( A @ rearsegP ) ) )
=> ( C @ ( A @ rearsegP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax47) ).
thf(472,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( B @ rearsegP ) )
& ( B @ ( A @ rearsegP ) ) )
=> ( C @ ( A @ rearsegP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(19466,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[13674,192]) ).
thf(19467,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[19466]) ).
thf(19468,plain,
( ( nil @ ( sk2 @ sk11 @ cons ) @ totalorderedP )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[19467:[bind(A,$thf( sk2 @ sk11 ))]]) ).
thf(225,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk17 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[218]) ).
thf(37486,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk17 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,225]) ).
thf(37487,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk17 @ ssList ) ),
inference(simp,[status(thm)],[37486]) ).
thf(37488,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk17 @ ssList ) ),
inference(pattern_uni,[status(thm)],[37487:[bind(A,$thf( sk2 ))]]) ).
thf(37801,plain,
! [A: $i] :
( ( ( sk2 @ sk17 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[37488,296]) ).
thf(37802,plain,
! [A: $i] :
( ( ( sk2 @ sk17 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[37801]) ).
thf(37803,plain,
( ( nil @ ( sk2 @ sk17 @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[37802:[bind(A,$thf( sk2 @ sk17 ))]]) ).
thf(18878,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,190]) ).
thf(18879,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[18878]) ).
thf(18880,plain,
sk1 @ ( sk1 @ segmentP ),
inference(pattern_uni,[status(thm)],[18879:[bind(A,$thf( sk1 ))]]) ).
thf(19000,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) )
| ~ ( nil @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18880,2331]) ).
thf(19001,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[19000]) ).
thf(19059,plain,
( ( sk2 != sk1 )
| ( sk1 != nil )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[19001]) ).
thf(155,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk7 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[152]) ).
thf(5190,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,155]) ).
thf(5191,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssList ) ),
inference(simp,[status(thm)],[5190]) ).
thf(5192,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk7 @ ssList ) ),
inference(pattern_uni,[status(thm)],[5191:[bind(A,$thf( sk2 ))]]) ).
thf(158,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk5 @ ( A @ sk6 @ leq ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[152]) ).
thf(6638,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk5 @ ( A @ sk6 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,158]) ).
thf(6639,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk5 @ ( A @ sk6 @ leq ) ) ),
inference(simp,[status(thm)],[6638]) ).
thf(6640,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk5 @ ( sk1 @ sk6 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[6639:[bind(A,$thf( sk1 ))]]) ).
thf(13690,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk11 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,177]) ).
thf(13691,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk11 @ ssItem ) ),
inference(simp,[status(thm)],[13690]) ).
thf(13692,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk11 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[13691:[bind(A,$thf( sk1 ))]]) ).
thf(53268,plain,
( ( sk2 != sk2 )
| ( sk38 != nil )
| ( nil != nil )
| ( sk2 @ sk21 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[51244,1399]) ).
thf(53269,plain,
( ( sk2 != sk2 )
| ( sk38 != nil )
| ( sk2 @ sk21 @ ssList ) ),
inference(simp,[status(thm)],[53268]) ).
thf(53270,plain,
( ( sk38 != nil )
| ( sk2 @ sk21 @ ssList ) ),
inference(pattern_uni,[status(thm)],[53269:[]]) ).
thf(56224,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk38 != nil ) ),
inference(paramod_ordered,[status(thm)],[53270,373]) ).
thf(56225,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk38 != nil ) ),
inference(simp,[status(thm)],[56224]) ).
thf(56226,plain,
( ( nil @ ( sk2 @ sk21 @ frontsegP ) )
| ( sk38 != nil ) ),
inference(pattern_uni,[status(thm)],[56225:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(102,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( nil @ ( B @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk4 )
| ~ ( C @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(110,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( ( C @ ( nil @ ( B @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk4 ) ),
inference(lifteq,[status(thm)],[102]) ).
thf(106,plain,
sk2 = sk4,
inference(cnfConj,[status(thm)],[99]) ).
thf(109,plain,
sk4 = sk2,
inference(lifteq,[status(thm)],[106]) ).
thf(535,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( ( C @ ( nil @ ( B @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk2 ) ),
inference(rewrite,[status(thm)],[110,109]) ).
thf(536,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( ( C @ ( nil @ ( B @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk2 ) ),
inference(paramod_ordered,[status(thm)],[104,535]) ).
thf(537,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ssList )
!= ( C @ ssList ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( ( C @ ( nil @ ( B @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk2 ) ),
inference(simp,[status(thm)],[536]) ).
thf(538,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( ( sk1 @ ( nil @ ( B @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[537:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk1 ))]]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ hd @ ssItem ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
thf(289,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ hd @ ssItem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(290,plain,
! [A: $i] :
( ( A @ hd @ ssItem )
| ( nil = A )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[289]) ).
thf(291,plain,
! [A: $i] :
( ( A @ hd @ ssItem )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[290]) ).
thf(113168,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ hd @ ssItem )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[103,291]) ).
thf(113169,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ hd @ ssItem )
| ( nil = A ) ),
inference(simp,[status(thm)],[113168]) ).
thf(113170,plain,
( ( sk2 @ hd @ ssItem )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[113169:[bind(A,$thf( sk2 ))]]) ).
thf(115115,plain,
( ( sk2 != sk2 )
| ( nil != nil )
| ~ ( sk2 @ ssItem )
| ( sk2 @ hd @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[113170,651]) ).
thf(115116,plain,
( ( sk2 != sk2 )
| ~ ( sk2 @ ssItem )
| ( sk2 @ hd @ ssItem ) ),
inference(simp,[status(thm)],[115115]) ).
thf(115117,plain,
( ~ ( sk2 @ ssItem )
| ( sk2 @ hd @ ssItem ) ),
inference(pattern_uni,[status(thm)],[115116:[]]) ).
thf(117081,plain,
! [A: $i] :
( ( ( sk2 @ hd @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ~ ( sk2 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[115117,231]) ).
thf(117082,plain,
! [A: $i] :
( ( ( sk2 @ hd @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ ( sk2 @ ssItem ) ),
inference(simp,[status(thm)],[117081]) ).
thf(117083,plain,
( ~ ( sk2 @ hd @ ( nil @ memberP ) )
| ~ ( sk2 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[117082:[bind(A,$thf( sk2 @ hd ))]]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( B @ segmentP ) )
& ( B @ ( A @ segmentP ) ) )
=> ( C @ ( A @ segmentP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax53) ).
thf(184,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( B @ segmentP ) )
& ( B @ ( A @ segmentP ) ) )
=> ( C @ ( A @ segmentP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(185,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)],[184]) ).
thf(267,plain,
! [A: $i] :
( ( A @ sk28 @ ssItem )
| ( nil = A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[265]) ).
thf(270,plain,
! [A: $i] :
( ( A @ sk28 @ ssItem )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[267]) ).
thf(85153,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk28 @ ssItem )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[103,270]) ).
thf(85154,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk28 @ ssItem )
| ( nil = A ) ),
inference(simp,[status(thm)],[85153]) ).
thf(85155,plain,
( ( sk2 @ sk28 @ ssItem )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[85154:[bind(A,$thf( sk2 ))]]) ).
thf(89294,plain,
( ( sk2 != sk2 )
| ( sk38 != nil )
| ( nil != nil )
| ( sk2 @ sk28 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[85155,1399]) ).
thf(89295,plain,
( ( sk2 != sk2 )
| ( sk38 != nil )
| ( sk2 @ sk28 @ ssItem ) ),
inference(simp,[status(thm)],[89294]) ).
thf(89296,plain,
( ( sk38 != nil )
| ( sk2 @ sk28 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[89295:[]]) ).
thf(93087,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk38 != nil ) ),
inference(paramod_ordered,[status(thm)],[89296,231]) ).
thf(93088,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk38 != nil ) ),
inference(simp,[status(thm)],[93087]) ).
thf(93089,plain,
( ~ ( sk2 @ sk28 @ ( nil @ memberP ) )
| ( sk38 != nil ) ),
inference(pattern_uni,[status(thm)],[93088:[bind(A,$thf( sk2 @ sk28 ))]]) ).
thf(37863,plain,
! [A: $i] :
( ( ( sk2 @ sk17 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[37488,373]) ).
thf(37864,plain,
! [A: $i] :
( ( ( sk2 @ sk17 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[37863]) ).
thf(37865,plain,
( ( nil @ ( sk2 @ sk17 @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[37864:[bind(A,$thf( sk2 @ sk17 ))]]) ).
thf(13968,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[13692,210]) ).
thf(13969,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[13968]) ).
thf(13970,plain,
( ~ ( sk1 @ sk11 @ ( sk1 @ sk11 @ neq ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[13969:[bind(A,$thf( sk1 @ sk11 ))]]) ).
thf(18862,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,190]) ).
thf(18863,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[18862]) ).
thf(18864,plain,
sk2 @ ( sk2 @ segmentP ),
inference(pattern_uni,[status(thm)],[18863:[bind(A,$thf( sk2 ))]]) ).
thf(18959,plain,
( ( sk2 != sk2 )
| ( sk2 @ ( nil @ segmentP ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[919,18864]) ).
thf(18960,plain,
( ( sk2 @ ( nil @ segmentP ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[18959:[]]) ).
thf(19163,plain,
( ( ( sk2 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk2 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[641,18960]) ).
thf(19164,plain,
( ( ( sk2 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk2 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[19163]) ).
thf(19209,plain,
( ( sk2 != nil )
| ( nil != nil )
| ( sk2 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[19164]) ).
thf(19219,plain,
( ( sk2 != nil )
| ( sk2 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[19209]) ).
thf(70,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ singletonP )
<=> ? [B: $i] :
( ( ( nil @ ( B @ cons ) )
= A )
& ( B @ ssItem ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
thf(417,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( ? [B: $i] :
( ( ( nil @ ( B @ cons ) )
= A )
& ( B @ ssItem ) )
=> ( A @ singletonP ) )
& ( ( A @ singletonP )
=> ? [B: $i] :
( ( ( nil @ ( B @ cons ) )
= A )
& ( B @ ssItem ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(42,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( B @ ( A @ cons ) @ strictorderedP )
<=> ( ( ( B @ hd @ ( A @ lt ) )
& ( B @ strictorderedP )
& ( nil != B ) )
| ( nil = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax70) ).
thf(275,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( ( ( B @ hd @ ( A @ lt ) )
& ( B @ strictorderedP )
& ( nil != B ) )
| ( nil = B ) )
=> ( B @ ( A @ cons ) @ strictorderedP ) )
& ( ( B @ ( A @ cons ) @ strictorderedP )
=> ( ( ( B @ hd @ ( A @ lt ) )
& ( B @ strictorderedP )
& ( nil != B ) )
| ( nil = B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(276,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( B @ hd @ ( A @ lt ) )
| ~ ( B @ strictorderedP )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) )
& ( ( B @ ( A @ cons ) @ strictorderedP )
| ( nil != B )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) )
& ( ( B @ hd @ ( A @ lt ) )
| ( nil = B )
| ~ ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) )
& ( ( B @ strictorderedP )
| ( nil = B )
| ~ ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) )
& ( ( nil != B )
| ( nil = B )
| ~ ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ) ),
inference(cnf,[status(esa)],[275]) ).
thf(277,plain,
! [B: $i,A: $i] :
( ( B @ strictorderedP )
| ( nil = B )
| ~ ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[276]) ).
thf(288,plain,
! [B: $i,A: $i] :
( ( B @ strictorderedP )
| ~ ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( nil = B ) ),
inference(lifteq,[status(thm)],[277]) ).
thf(77698,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk27 @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[103,269]) ).
thf(77699,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk27 @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[77698]) ).
thf(77700,plain,
( ( sk2 @ sk27 @ ssList )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[77699:[bind(A,$thf( sk2 ))]]) ).
thf(5267,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk5 @ ssItem )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5192,153]) ).
thf(5268,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk5 @ ssItem )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5267]) ).
thf(5269,plain,
( ( sk2 @ sk7 @ cyclefreeP )
| ( sk2 @ sk7 @ sk5 @ ssItem )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5268:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(19417,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[13692,192]) ).
thf(19418,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[19417]) ).
thf(19419,plain,
( ( nil @ ( sk1 @ sk11 @ cons ) @ totalorderedP )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[19418:[bind(A,$thf( sk1 @ sk11 ))]]) ).
thf(174,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( A @ sk10 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[168]) ).
thf(64,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ duplicatefreeP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax71) ).
thf(404,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ duplicatefreeP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(2398,plain,
( ( sk2 != sk2 )
| ( sk38 != sk2 )
| ( nil != nil )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2122,723]) ).
thf(2399,plain,
( ( sk2 != sk2 )
| ( sk38 != sk2 )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[2398]) ).
thf(2400,plain,
( ( sk38 != sk2 )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[2399:[]]) ).
thf(88605,plain,
( ( sk2 != sk2 )
| ( nil != nil )
| ~ ( sk2 @ ssItem )
| ( sk2 @ sk28 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[85155,651]) ).
thf(88606,plain,
( ( sk2 != sk2 )
| ~ ( sk2 @ ssItem )
| ( sk2 @ sk28 @ ssItem ) ),
inference(simp,[status(thm)],[88605]) ).
thf(88607,plain,
( ~ ( sk2 @ ssItem )
| ( sk2 @ sk28 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[88606:[]]) ).
thf(91317,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ~ ( sk2 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[88607,231]) ).
thf(91318,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ ( sk2 @ ssItem ) ),
inference(simp,[status(thm)],[91317]) ).
thf(91319,plain,
( ~ ( sk2 @ sk28 @ ( nil @ memberP ) )
| ~ ( sk2 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[91318:[bind(A,$thf( sk2 @ sk28 ))]]) ).
thf(93344,plain,
( ( ( sk38 @ ssItem )
!= ( sk2 @ ssItem ) )
| ~ ( sk2 @ sk28 @ ( nil @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[391,91319]) ).
thf(93345,plain,
( ( ( sk38 @ ssItem )
!= ( sk2 @ ssItem ) )
| ~ ( sk2 @ sk28 @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[93344]) ).
thf(93439,plain,
( ( sk38 != sk2 )
| ~ ( sk2 @ sk28 @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[93345]) ).
thf(45414,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk20 ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[45182,190]) ).
thf(45415,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk20 ) @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[45414]) ).
thf(45416,plain,
nil @ ( nil @ sk20 ) @ ( nil @ ( nil @ sk20 ) @ segmentP ),
inference(pattern_uni,[status(thm)],[45415:[bind(A,$thf( nil @ ( nil @ sk20 ) ))]]) ).
thf(115694,plain,
( ( sk2 != sk2 )
| ( sk37 != nil )
| ( nil != nil )
| ( sk2 @ hd @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[113170,1400]) ).
thf(115695,plain,
( ( sk2 != sk2 )
| ( sk37 != nil )
| ( sk2 @ hd @ ssItem ) ),
inference(simp,[status(thm)],[115694]) ).
thf(115696,plain,
( ( sk37 != nil )
| ( sk2 @ hd @ ssItem ) ),
inference(pattern_uni,[status(thm)],[115695:[]]) ).
thf(51841,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk21 @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[104,248]) ).
thf(51842,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk21 @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[51841]) ).
thf(51843,plain,
( ( sk1 @ sk21 @ ssList )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[51842:[bind(A,$thf( sk1 ))]]) ).
thf(53924,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[51843,373]) ).
thf(53925,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[53924]) ).
thf(53926,plain,
( ( nil @ ( sk1 @ sk21 @ frontsegP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[53925:[bind(A,$thf( sk1 @ sk21 ))]]) ).
thf(4522,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,243]) ).
thf(4523,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[4522]) ).
thf(4524,plain,
nil @ ( sk1 @ segmentP ),
inference(pattern_uni,[status(thm)],[4523:[bind(A,$thf( sk1 ))]]) ).
thf(5304,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5192,296]) ).
thf(5305,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5304]) ).
thf(5306,plain,
( ( nil @ ( sk2 @ sk7 @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5305:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ( A @ hd )
= B )
& ( B @ ssItem ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax75) ).
thf(305,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ? [B: $i] :
( ( ( A @ hd )
= B )
& ( B @ ssItem ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(306,plain,
! [A: $i] :
( ( ( ( A @ hd )
= ( A @ sk29 ) )
| ( nil = A )
| ~ ( A @ ssList ) )
& ( ( A @ sk29 @ ssItem )
| ( nil = A )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[305]) ).
thf(307,plain,
! [A: $i] :
( ( A @ sk29 @ ssItem )
| ( nil = A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[306]) ).
thf(309,plain,
! [A: $i] :
( ( A @ sk29 @ ssItem )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[307]) ).
thf(131981,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk29 @ ssItem )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[103,309]) ).
thf(131982,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk29 @ ssItem )
| ( nil = A ) ),
inference(simp,[status(thm)],[131981]) ).
thf(131983,plain,
( ( sk2 @ sk29 @ ssItem )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[131982:[bind(A,$thf( sk2 ))]]) ).
thf(134087,plain,
( ( sk2 != sk2 )
| ( nil != nil )
| ~ ( sk2 @ ssItem )
| ( sk2 @ sk29 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[131983,651]) ).
thf(134088,plain,
( ( sk2 != sk2 )
| ~ ( sk2 @ ssItem )
| ( sk2 @ sk29 @ ssItem ) ),
inference(simp,[status(thm)],[134087]) ).
thf(134089,plain,
( ~ ( sk2 @ ssItem )
| ( sk2 @ sk29 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[134088:[]]) ).
thf(136222,plain,
! [A: $i] :
( ( ( sk2 @ sk29 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ~ ( sk2 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[134089,231]) ).
thf(136223,plain,
! [A: $i] :
( ( ( sk2 @ sk29 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ ( sk2 @ ssItem ) ),
inference(simp,[status(thm)],[136222]) ).
thf(136224,plain,
( ~ ( sk2 @ sk29 @ ( nil @ memberP ) )
| ~ ( sk2 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[136223:[bind(A,$thf( sk2 @ sk29 ))]]) ).
thf(32621,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[684,216]) ).
thf(32622,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[32621]) ).
thf(32623,plain,
( ~ ( sk2 @ sk5 @ ( sk2 @ sk5 @ lt ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[32622:[bind(A,$thf( sk2 @ sk5 ))]]) ).
thf(8785,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,373]) ).
thf(8786,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) ) ),
inference(simp,[status(thm)],[8785]) ).
thf(8787,plain,
nil @ ( sk1 @ frontsegP ),
inference(pattern_uni,[status(thm)],[8786:[bind(A,$thf( sk1 ))]]) ).
thf(52657,plain,
( ( sk2 != sk2 )
| ( sk37 != sk2 )
| ( nil != nil )
| ( sk2 @ sk21 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[51244,724]) ).
thf(52658,plain,
( ( sk2 != sk2 )
| ( sk37 != sk2 )
| ( sk2 @ sk21 @ ssList ) ),
inference(simp,[status(thm)],[52657]) ).
thf(52659,plain,
( ( sk37 != sk2 )
| ( sk2 @ sk21 @ ssList ) ),
inference(pattern_uni,[status(thm)],[52658:[]]) ).
thf(54552,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk37 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[52659,243]) ).
thf(54553,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk37 != sk2 ) ),
inference(simp,[status(thm)],[54552]) ).
thf(54554,plain,
( ( nil @ ( sk2 @ sk21 @ segmentP ) )
| ( sk37 != sk2 ) ),
inference(pattern_uni,[status(thm)],[54553:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ equalelemsP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax73) ).
thf(297,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ equalelemsP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(298,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ equalelemsP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[297]) ).
thf(124764,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[391,298]) ).
thf(124765,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP ) ),
inference(simp,[status(thm)],[124764]) ).
thf(124766,plain,
nil @ ( sk38 @ cons ) @ equalelemsP,
inference(pattern_uni,[status(thm)],[124765:[bind(A,$thf( sk38 ))]]) ).
thf(1991,plain,
! [A: $i] :
( ( A != sk38 )
| ( sk37 != nil )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[136,393]) ).
thf(1992,plain,
( ( sk37 != nil )
| ~ ( sk38 @ ( nil @ segmentP ) )
| ~ ( sk38 @ ssList ) ),
inference(pattern_uni,[status(thm)],[1991:[bind(A,$thf( sk38 ))]]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ( ( ( C @ ( B @ gt ) )
& ( B @ ( A @ gt ) ) )
=> ( C @ ( A @ gt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax95) ).
thf(196,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ( ( ( C @ ( B @ gt ) )
& ( B @ ( A @ gt ) ) )
=> ( C @ ( A @ gt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ gt ) )
=> ~ ( A @ ( B @ gt ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax94) ).
thf(124,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ gt ) )
=> ~ ( A @ ( B @ gt ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(125,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[124]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( ( B @ tl )
= ( A @ tl ) )
& ( ( B @ hd )
= ( A @ hd ) )
& ( nil != A )
& ( nil != B ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax77) ).
thf(344,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( ( B @ tl )
= ( A @ tl ) )
& ( ( B @ hd )
= ( A @ hd ) )
& ( nil != A )
& ( nil != B ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(55555,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ sk21 )
= ( A @ tl ) )
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[104,249]) ).
thf(55556,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ sk21 )
= ( A @ tl ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[55555]) ).
thf(55557,plain,
( ( ( sk1 @ sk21 )
= ( sk1 @ tl ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[55556:[bind(A,$thf( sk1 ))]]) ).
thf(72538,plain,
( ( ( sk1 @ sk21 )
!= ( sk1 @ sk21 ) )
| ( sk1 @ tl @ ssList )
| ( sk1 = nil )
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[55557,51843]) ).
thf(72539,plain,
( ( ( sk1 @ sk21 )
!= ( sk1 @ sk21 ) )
| ( sk1 @ tl @ ssList )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[72538]) ).
thf(72540,plain,
( ( sk1 @ tl @ ssList )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[72539:[]]) ).
thf(2401,plain,
( ( sk2 != sk2 )
| ( sk38 != nil )
| ( nil != nil )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2122,1399]) ).
thf(2402,plain,
( ( sk2 != sk2 )
| ( sk38 != nil )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[2401]) ).
thf(2403,plain,
( ( sk38 != nil )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[2402:[]]) ).
thf(19018,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) )
| ( sk38 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18880,2403]) ).
thf(19019,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) )
| ( sk38 != nil ) ),
inference(simp,[status(thm)],[19018]) ).
thf(19063,plain,
( ( sk2 != sk1 )
| ( sk1 != nil )
| ( sk38 != nil ) ),
inference(simp,[status(thm)],[19019]) ).
thf(10729,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk12 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,172]) ).
thf(10730,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk12 @ ssList ) ),
inference(simp,[status(thm)],[10729]) ).
thf(10731,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk12 @ ssList ) ),
inference(pattern_uni,[status(thm)],[10730:[bind(A,$thf( sk2 ))]]) ).
thf(15941,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A )
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10731,183]) ).
thf(15942,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[15941]) ).
thf(15943,plain,
( ( ( nil @ ( sk2 @ sk12 @ app ) )
= ( sk2 @ sk12 ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[15942:[bind(A,$thf( sk2 @ sk12 ))]]) ).
thf(940,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[104,121]) ).
thf(941,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ frontsegP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[940]) ).
thf(942,plain,
( ~ ( sk1 @ ( nil @ frontsegP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[941:[bind(A,$thf( sk1 ))]]) ).
thf(19030,plain,
( ( sk1 != sk1 )
| ( sk1 @ ( nil @ segmentP ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[942,18880]) ).
thf(19031,plain,
( ( sk1 @ ( nil @ segmentP ) )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[19030:[]]) ).
thf(2380,plain,
( ( sk2 != sk2 )
| ( sk37 != nil )
| ( nil != nil )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2122,1400]) ).
thf(2381,plain,
( ( sk2 != sk2 )
| ( sk37 != nil )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[2380]) ).
thf(2382,plain,
( ( sk37 != nil )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[2381:[]]) ).
thf(19620,plain,
( ( ( sk2 @ ( nil @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ( sk37 != nil )
| ~ $true
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[19031,2382]) ).
thf(19621,plain,
( ( ( sk2 @ ( nil @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ( sk37 != nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[19620]) ).
thf(19685,plain,
( ( sk2 != sk1 )
| ( nil != nil )
| ( sk37 != nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[19621]) ).
thf(19710,plain,
( ( sk2 != sk1 )
| ( sk37 != nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[19685]) ).
thf(19016,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) )
| ( sk38 != sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18880,2400]) ).
thf(19017,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) )
| ( sk38 != sk2 ) ),
inference(simp,[status(thm)],[19016]) ).
thf(19052,plain,
( ( sk2 != sk1 )
| ( sk1 != nil )
| ( sk38 != sk2 ) ),
inference(simp,[status(thm)],[19017]) ).
thf(13043,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[12843,296]) ).
thf(13044,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[13043]) ).
thf(13045,plain,
( ( nil @ ( sk2 @ sk14 @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[13044:[bind(A,$thf( sk2 @ sk14 ))]]) ).
thf(5602,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk6 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,156]) ).
thf(5603,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk6 @ ssItem ) ),
inference(simp,[status(thm)],[5602]) ).
thf(5604,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk6 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[5603:[bind(A,$thf( sk1 ))]]) ).
thf(279,plain,
! [B: $i,A: $i] :
( ( B @ hd @ ( A @ lt ) )
| ( nil = B )
| ~ ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[276]) ).
thf(284,plain,
! [B: $i,A: $i] :
( ( B @ hd @ ( A @ lt ) )
| ~ ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( nil = B ) ),
inference(lifteq,[status(thm)],[279]) ).
thf(134096,plain,
( ( sk2 != sk2 )
| ( sk37 != sk2 )
| ( nil != nil )
| ( sk2 @ sk29 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[131983,724]) ).
thf(134097,plain,
( ( sk2 != sk2 )
| ( sk37 != sk2 )
| ( sk2 @ sk29 @ ssItem ) ),
inference(simp,[status(thm)],[134096]) ).
thf(134098,plain,
( ( sk37 != sk2 )
| ( sk2 @ sk29 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[134097:[]]) ).
thf(136695,plain,
! [A: $i] :
( ( ( sk2 @ sk29 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk37 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[134098,231]) ).
thf(136696,plain,
! [A: $i] :
( ( ( sk2 @ sk29 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk37 != sk2 ) ),
inference(simp,[status(thm)],[136695]) ).
thf(136697,plain,
( ~ ( sk2 @ sk29 @ ( nil @ memberP ) )
| ( sk37 != sk2 ) ),
inference(pattern_uni,[status(thm)],[136696:[bind(A,$thf( sk2 @ sk29 ))]]) ).
thf(52689,plain,
( ( sk2 != sk2 )
| ( nil != nil )
| ~ ( nil @ ssItem )
| ( sk2 @ sk21 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[51244,1362]) ).
thf(52690,plain,
( ( sk2 != sk2 )
| ~ ( nil @ ssItem )
| ( sk2 @ sk21 @ ssList ) ),
inference(simp,[status(thm)],[52689]) ).
thf(52691,plain,
( ~ ( nil @ ssItem )
| ( sk2 @ sk21 @ ssList ) ),
inference(pattern_uni,[status(thm)],[52690:[]]) ).
thf(55315,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ~ ( nil @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[52691,373]) ).
thf(55316,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[55315]) ).
thf(55317,plain,
( ( nil @ ( sk2 @ sk21 @ frontsegP ) )
| ~ ( nil @ ssItem ) ),
inference(pattern_uni,[status(thm)],[55316:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(65659,plain,
( ( sk2 != sk2 )
| ( nil != nil )
| ~ ( sk2 @ ssItem )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[65462,651]) ).
thf(65660,plain,
( ( sk2 != sk2 )
| ~ ( sk2 @ ssItem )
| ( sk2 @ tl @ ssList ) ),
inference(simp,[status(thm)],[65659]) ).
thf(65661,plain,
( ~ ( sk2 @ ssItem )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[65660:[]]) ).
thf(55115,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ~ ( nil @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[52691,243]) ).
thf(55116,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[55115]) ).
thf(55117,plain,
( ( nil @ ( sk2 @ sk21 @ segmentP ) )
| ~ ( nil @ ssItem ) ),
inference(pattern_uni,[status(thm)],[55116:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(10185,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk13 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,171]) ).
thf(10186,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk13 @ ssList ) ),
inference(simp,[status(thm)],[10185]) ).
thf(10187,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk13 @ ssList ) ),
inference(pattern_uni,[status(thm)],[10186:[bind(A,$thf( sk1 ))]]) ).
thf(10525,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10187,373]) ).
thf(10526,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[10525]) ).
thf(10527,plain,
( ( nil @ ( sk1 @ sk13 @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10526:[bind(A,$thf( sk1 @ sk13 ))]]) ).
thf(116,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ strictorderedP )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[115]) ).
thf(1085,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[684,116]) ).
thf(1086,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1085]) ).
thf(1087,plain,
( ( nil @ ( sk2 @ sk5 @ cons ) @ strictorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1086:[bind(A,$thf( sk2 @ sk5 ))]]) ).
thf(5074,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,296]) ).
thf(5075,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[5074]) ).
thf(5076,plain,
nil @ ( sk2 @ rearsegP ),
inference(pattern_uni,[status(thm)],[5075:[bind(A,$thf( sk2 ))]]) ).
thf(11764,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk10 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,174]) ).
thf(11765,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk10 @ ssItem ) ),
inference(simp,[status(thm)],[11764]) ).
thf(11766,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk10 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[11765:[bind(A,$thf( sk1 ))]]) ).
thf(19444,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[11766,192]) ).
thf(19445,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[19444]) ).
thf(19446,plain,
( ( nil @ ( sk1 @ sk10 @ cons ) @ totalorderedP )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[19445:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(222,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk19 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[218]) ).
thf(35656,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk19 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,222]) ).
thf(35657,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk19 @ ssList ) ),
inference(simp,[status(thm)],[35656]) ).
thf(35658,plain,
( ( sk1 @ strictorderedP )
| ( sk1 @ sk19 @ ssList ) ),
inference(pattern_uni,[status(thm)],[35657:[bind(A,$thf( sk1 ))]]) ).
thf(36127,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[35658,243]) ).
thf(36128,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[36127]) ).
thf(36129,plain,
( ( nil @ ( sk1 @ sk19 @ segmentP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[36128:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(159,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)],[152]) ).
thf(163,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)],[159]) ).
thf(164,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)],[163]) ).
thf(642,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[391,210]) ).
thf(643,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[642]) ).
thf(644,plain,
~ ( sk38 @ ( sk38 @ neq ) ),
inference(pattern_uni,[status(thm)],[643:[bind(A,$thf( sk38 ))]]) ).
thf(652,plain,
( ( ( sk38 @ ( sk38 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[107,644]) ).
thf(653,plain,
( ( sk38 @ ( sk38 @ neq ) )
!= ( nil @ ( sk2 @ neq ) ) ),
inference(simp,[status(thm)],[652]) ).
thf(654,plain,
( ( sk38 != nil )
| ( sk38 != sk2 ) ),
inference(simp,[status(thm)],[653]) ).
thf(836,plain,
! [A: $i] :
( ( A != sk38 )
| ( nil != nil )
| ( sk38 != sk2 )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[121,654]) ).
thf(837,plain,
! [A: $i] :
( ( A != sk38 )
| ( sk38 != sk2 )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[836]) ).
thf(838,plain,
( ( sk38 != sk2 )
| ~ ( sk38 @ ( nil @ frontsegP ) )
| ~ ( sk38 @ ssList ) ),
inference(pattern_uni,[status(thm)],[837:[bind(A,$thf( sk38 ))]]) ).
thf(4151,plain,
( ( ( sk38 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk38 != sk2 )
| ~ ( sk38 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,838]) ).
thf(4152,plain,
( ( ( sk38 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk38 != sk2 )
| ~ ( sk38 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[4151]) ).
thf(4166,plain,
( ( sk38 != sk2 )
| ( sk38 != sk2 )
| ~ ( sk38 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[4152]) ).
thf(4173,plain,
( ( sk38 != sk2 )
| ~ ( sk38 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[4166]) ).
thf(37530,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk17 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,225]) ).
thf(37531,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk17 @ ssList ) ),
inference(simp,[status(thm)],[37530]) ).
thf(37532,plain,
( ( sk1 @ strictorderedP )
| ( sk1 @ sk17 @ ssList ) ),
inference(pattern_uni,[status(thm)],[37531:[bind(A,$thf( sk1 ))]]) ).
thf(221,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( A @ sk16 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[218]) ).
thf(34760,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk16 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,221]) ).
thf(34761,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk16 @ ssItem ) ),
inference(simp,[status(thm)],[34760]) ).
thf(34762,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk16 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[34761:[bind(A,$thf( sk2 ))]]) ).
thf(34946,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[34762,116]) ).
thf(34947,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[34946]) ).
thf(34948,plain,
( ( nil @ ( sk2 @ sk16 @ cons ) @ strictorderedP )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[34947:[bind(A,$thf( sk2 @ sk16 ))]]) ).
thf(18887,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10187,190]) ).
thf(18888,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[18887]) ).
thf(18889,plain,
( ( sk1 @ sk13 @ ( sk1 @ sk13 @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[18888:[bind(A,$thf( sk1 @ sk13 ))]]) ).
thf(1988,plain,
! [A: $i] :
( ( A != sk37 )
| ( nil != nil )
| ( sk37 != sk2 )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[136,1016]) ).
thf(1989,plain,
! [A: $i] :
( ( A != sk37 )
| ( sk37 != sk2 )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[1988]) ).
thf(1990,plain,
( ( sk37 != sk2 )
| ~ ( sk37 @ ( nil @ segmentP ) )
| ~ ( sk37 @ ssList ) ),
inference(pattern_uni,[status(thm)],[1989:[bind(A,$thf( sk37 ))]]) ).
thf(17270,plain,
( ( ( sk37 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk37 != sk2 )
| ~ ( sk37 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,1990]) ).
thf(17271,plain,
( ( ( sk37 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk37 != sk2 )
| ~ ( sk37 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[17270]) ).
thf(17326,plain,
( ( sk37 != sk2 )
| ( sk37 != sk2 )
| ~ ( sk37 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[17271]) ).
thf(17352,plain,
( ( sk37 != sk2 )
| ~ ( sk37 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[17326]) ).
thf(19042,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk37 @ ( nil @ segmentP ) ) )
| ( sk37 != sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18880,17352]) ).
thf(19043,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk37 @ ( nil @ segmentP ) ) )
| ( sk37 != sk2 ) ),
inference(simp,[status(thm)],[19042]) ).
thf(19056,plain,
( ( sk37 != sk1 )
| ( sk1 != nil )
| ( sk37 != sk2 ) ),
inference(simp,[status(thm)],[19043]) ).
thf(1282,plain,
( ( sk2 != sk2 )
| ( nil @ ( nil @ neq ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[919,107]) ).
thf(1283,plain,
( ( nil @ ( nil @ neq ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1282:[]]) ).
thf(160,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk8 @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[152]) ).
thf(6981,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,160]) ).
thf(6982,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ssList ) ),
inference(simp,[status(thm)],[6981]) ).
thf(6983,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk8 @ ssList ) ),
inference(pattern_uni,[status(thm)],[6982:[bind(A,$thf( sk2 ))]]) ).
thf(10307,plain,
! [A: $i] :
( ( ( sk2 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10152,243]) ).
thf(10308,plain,
! [A: $i] :
( ( ( sk2 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[10307]) ).
thf(10309,plain,
( ( nil @ ( sk2 @ sk13 @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10308:[bind(A,$thf( sk2 @ sk13 ))]]) ).
thf(1999,plain,
! [A: $i] :
( ( A != sk38 )
| ( nil != nil )
| ( sk38 != sk2 )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[136,654]) ).
thf(2000,plain,
! [A: $i] :
( ( A != sk38 )
| ( sk38 != sk2 )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[1999]) ).
thf(2001,plain,
( ( sk38 != sk2 )
| ~ ( sk38 @ ( nil @ segmentP ) )
| ~ ( sk38 @ ssList ) ),
inference(pattern_uni,[status(thm)],[2000:[bind(A,$thf( sk38 ))]]) ).
thf(34193,plain,
( ( ( sk38 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk38 != sk2 )
| ~ ( sk38 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,2001]) ).
thf(34194,plain,
( ( ( sk38 @ ssList )
!= ( sk2 @ ssList ) )
| ( sk38 != sk2 )
| ~ ( sk38 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[34193]) ).
thf(34281,plain,
( ( sk38 != sk2 )
| ( sk38 != sk2 )
| ~ ( sk38 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[34194]) ).
thf(34348,plain,
( ( sk38 != sk2 )
| ~ ( sk38 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[34281]) ).
thf(2322,plain,
( ( sk2 != sk2 )
| ( sk37 != sk2 )
| ( nil != nil )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2122,724]) ).
thf(2323,plain,
( ( sk2 != sk2 )
| ( sk37 != sk2 )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[2322]) ).
thf(2324,plain,
( ( sk37 != sk2 )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[2323:[]]) ).
thf(1258,plain,
( ( sk2 != sk2 )
| ( sk2 @ cyclefreeP )
| ( nil @ sk5 @ ssItem )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[919,684]) ).
thf(1259,plain,
( ( sk2 @ cyclefreeP )
| ( nil @ sk5 @ ssItem )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1258:[]]) ).
thf(1709,plain,
( ( ( sk2 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk2 @ cyclefreeP )
| ( nil @ sk5 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[641,1259]) ).
thf(1710,plain,
( ( ( sk2 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk2 @ cyclefreeP )
| ( nil @ sk5 @ ssItem ) ),
inference(simp,[status(thm)],[1709]) ).
thf(1713,plain,
( ( sk2 != nil )
| ( nil != nil )
| ( sk2 @ cyclefreeP )
| ( nil @ sk5 @ ssItem ) ),
inference(simp,[status(thm)],[1710]) ).
thf(1714,plain,
( ( sk2 != nil )
| ( sk2 @ cyclefreeP )
| ( nil @ sk5 @ ssItem ) ),
inference(simp,[status(thm)],[1713]) ).
thf(208,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ neq ) )
| ( A = B )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[206]) ).
thf(211,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ neq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A = B ) ),
inference(lifteq,[status(thm)],[208]) ).
thf(19651,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk1 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[641,19031]) ).
thf(19652,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[19651]) ).
thf(19691,plain,
( ( sk1 != nil )
| ( nil != nil )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[19652]) ).
thf(19714,plain,
( ( sk1 != nil )
| ( sk1 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[19691]) ).
thf(53507,plain,
( ( sk1 != sk1 )
| ( nil != nil )
| ( sk1 @ ( nil @ segmentP ) )
| ( sk1 @ sk21 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[51843,19714]) ).
thf(53508,plain,
( ( sk1 != sk1 )
| ( sk1 @ ( nil @ segmentP ) )
| ( sk1 @ sk21 @ ssList ) ),
inference(simp,[status(thm)],[53507]) ).
thf(53509,plain,
( ( sk1 @ ( nil @ segmentP ) )
| ( sk1 @ sk21 @ ssList ) ),
inference(pattern_uni,[status(thm)],[53508:[]]) ).
thf(11746,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk10 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,174]) ).
thf(11747,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk10 @ ssItem ) ),
inference(simp,[status(thm)],[11746]) ).
thf(11748,plain,
( ( sk2 @ strictorderP )
| ( sk2 @ sk10 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[11747:[bind(A,$thf( sk2 ))]]) ).
thf(38828,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk18 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,226]) ).
thf(38829,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk18 @ ssList ) ),
inference(simp,[status(thm)],[38828]) ).
thf(38830,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk18 @ ssList ) ),
inference(pattern_uni,[status(thm)],[38829:[bind(A,$thf( sk2 ))]]) ).
thf(39213,plain,
! [A: $i] :
( ( ( sk2 @ sk18 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[38830,373]) ).
thf(39214,plain,
! [A: $i] :
( ( ( sk2 @ sk18 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[39213]) ).
thf(39215,plain,
( ( nil @ ( sk2 @ sk18 @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[39214:[bind(A,$thf( sk2 @ sk18 ))]]) ).
thf(7013,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,160]) ).
thf(7014,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk8 @ ssList ) ),
inference(simp,[status(thm)],[7013]) ).
thf(7015,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk8 @ ssList ) ),
inference(pattern_uni,[status(thm)],[7014:[bind(A,$thf( sk1 ))]]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( B @ ( A @ frontsegP ) )
=> ( B @ ( C @ ( A @ app ) @ frontsegP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax43) ).
thf(146,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( B @ ( A @ frontsegP ) )
=> ( B @ ( C @ ( A @ app ) @ frontsegP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(147,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)],[146]) ).
thf(6042,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,157]) ).
thf(6043,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk9 @ ssList ) ),
inference(simp,[status(thm)],[6042]) ).
thf(6044,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk9 @ ssList ) ),
inference(pattern_uni,[status(thm)],[6043:[bind(A,$thf( sk2 ))]]) ).
thf(8772,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[6044,373]) ).
thf(8773,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[8772]) ).
thf(8774,plain,
( ( nil @ ( sk2 @ sk9 @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[8773:[bind(A,$thf( sk2 @ sk9 ))]]) ).
thf(58423,plain,
! [A: $i] :
( ( ( sk2 @ sk25 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[57992,296]) ).
thf(58424,plain,
! [A: $i] :
( ( ( sk2 @ sk25 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ totalorderP ) ),
inference(simp,[status(thm)],[58423]) ).
thf(58425,plain,
( ( nil @ ( sk2 @ sk25 @ rearsegP ) )
| ( sk2 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[58424:[bind(A,$thf( sk2 @ sk25 ))]]) ).
thf(79,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( nil != A )
=> ( ( B @ ( A @ app ) @ tl )
= ( B @ ( A @ tl @ app ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax86) ).
thf(453,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( nil != A )
=> ( ( B @ ( A @ app ) @ tl )
= ( B @ ( A @ tl @ app ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(32585,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[11766,216]) ).
thf(32586,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[32585]) ).
thf(32587,plain,
( ~ ( sk1 @ sk10 @ ( sk1 @ sk10 @ lt ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[32586:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(4517,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,243]) ).
thf(4518,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) ) ),
inference(simp,[status(thm)],[4517]) ).
thf(4519,plain,
nil @ ( sk2 @ segmentP ),
inference(pattern_uni,[status(thm)],[4518:[bind(A,$thf( sk2 ))]]) ).
thf(10457,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10187,243]) ).
thf(10458,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[10457]) ).
thf(10459,plain,
( ( nil @ ( sk1 @ sk13 @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10458:[bind(A,$thf( sk1 @ sk13 ))]]) ).
thf(63967,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk26 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,258]) ).
thf(63968,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk26 @ ssList ) ),
inference(simp,[status(thm)],[63967]) ).
thf(63969,plain,
( ( sk1 @ totalorderP )
| ( sk1 @ sk26 @ ssList ) ),
inference(pattern_uni,[status(thm)],[63968:[bind(A,$thf( sk1 ))]]) ).
thf(1117,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[684,210]) ).
thf(1118,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1117]) ).
thf(1119,plain,
( ~ ( sk2 @ sk5 @ ( sk2 @ sk5 @ neq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1118:[bind(A,$thf( sk2 @ sk5 ))]]) ).
thf(67,axiom,
nil @ strictorderP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax64) ).
thf(411,plain,
nil @ strictorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(33474,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk15 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,220]) ).
thf(33475,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk15 @ ssItem ) ),
inference(simp,[status(thm)],[33474]) ).
thf(33476,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk15 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[33475:[bind(A,$thf( sk2 ))]]) ).
thf(33666,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[33476,192]) ).
thf(33667,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[33666]) ).
thf(33668,plain,
( ( nil @ ( sk2 @ sk15 @ cons ) @ totalorderedP )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[33667:[bind(A,$thf( sk2 @ sk15 ))]]) ).
thf(115185,plain,
( ( sk2 != sk2 )
| ( nil != nil )
| ~ ( nil @ ssItem )
| ( sk2 @ hd @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[113170,1362]) ).
thf(115186,plain,
( ( sk2 != sk2 )
| ~ ( nil @ ssItem )
| ( sk2 @ hd @ ssItem ) ),
inference(simp,[status(thm)],[115185]) ).
thf(115187,plain,
( ~ ( nil @ ssItem )
| ( sk2 @ hd @ ssItem ) ),
inference(pattern_uni,[status(thm)],[115186:[]]) ).
thf(5211,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,155]) ).
thf(5212,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk7 @ ssList ) ),
inference(simp,[status(thm)],[5211]) ).
thf(5213,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk7 @ ssList ) ),
inference(pattern_uni,[status(thm)],[5212:[bind(A,$thf( sk1 ))]]) ).
thf(8749,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5213,373]) ).
thf(8750,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[8749]) ).
thf(8751,plain,
( ( nil @ ( sk1 @ sk7 @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[8750:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( B @ ( A @ segmentP ) )
=> ( B @ ( D @ ( A @ ( C @ app ) @ app ) @ segmentP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax56) ).
thf(232,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( B @ ( A @ segmentP ) )
=> ( B @ ( D @ ( A @ ( C @ app ) @ app ) @ segmentP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(233,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)],[232]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ gt ) )
<=> ( A @ ( B @ lt ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax35) ).
thf(201,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( ( A @ ( B @ lt ) )
=> ( B @ ( A @ gt ) ) )
& ( ( B @ ( A @ gt ) )
=> ( A @ ( B @ lt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(1310,plain,
( ( sk1 != sk1 )
| ( sk1 @ cyclefreeP )
| ( nil @ sk5 @ ssItem )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[942,690]) ).
thf(1311,plain,
( ( sk1 @ cyclefreeP )
| ( nil @ sk5 @ ssItem )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(pattern_uni,[status(thm)],[1310:[]]) ).
thf(8710,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5192,373]) ).
thf(8711,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[8710]) ).
thf(8712,plain,
( ( nil @ ( sk2 @ sk7 @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[8711:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(1725,plain,
( ( ( sk2 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( nil @ ( nil @ neq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[641,1283]) ).
thf(1726,plain,
( ( ( sk2 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( nil @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[1725]) ).
thf(1729,plain,
( ( sk2 != nil )
| ( nil != nil )
| ( nil @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[1726]) ).
thf(1730,plain,
( ( sk2 != nil )
| ( nil @ ( nil @ neq ) ) ),
inference(simp,[status(thm)],[1729]) ).
thf(35004,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[34762,231]) ).
thf(35005,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[35004]) ).
thf(35006,plain,
( ~ ( sk2 @ sk16 @ ( nil @ memberP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[35005:[bind(A,$thf( sk2 @ sk16 ))]]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ app ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
thf(212,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ app ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(213,plain,
! [A: $i] :
( ( ( A @ ( nil @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[212]) ).
thf(214,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[213]) ).
thf(31594,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[104,214]) ).
thf(31595,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[31594]) ).
thf(31596,plain,
( ( sk1 @ ( nil @ app ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[31595:[bind(A,$thf( sk1 ))]]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ tl @ ssList ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
thf(292,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( A @ tl @ ssList ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(115903,plain,
( ( sk2 != sk2 )
| ( sk38 != sk2 )
| ( nil != nil )
| ( sk2 @ hd @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[113170,723]) ).
thf(115904,plain,
( ( sk2 != sk2 )
| ( sk38 != sk2 )
| ( sk2 @ hd @ ssItem ) ),
inference(simp,[status(thm)],[115903]) ).
thf(115905,plain,
( ( sk38 != sk2 )
| ( sk2 @ hd @ ssItem ) ),
inference(pattern_uni,[status(thm)],[115904:[]]) ).
thf(11991,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[11766,116]) ).
thf(11992,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[11991]) ).
thf(11993,plain,
( ( nil @ ( sk1 @ sk10 @ cons ) @ strictorderedP )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[11992:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(75,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ ( nil @ rearsegP ) )
<=> ( nil = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax52) ).
thf(439,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( ( nil = A )
=> ( A @ ( nil @ rearsegP ) ) )
& ( ( A @ ( nil @ rearsegP ) )
=> ( nil = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(13846,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[13674,210]) ).
thf(13847,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[13846]) ).
thf(13848,plain,
( ~ ( sk2 @ sk11 @ ( sk2 @ sk11 @ neq ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[13847:[bind(A,$thf( sk2 @ sk11 ))]]) ).
thf(97,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ geq ) )
<=> ( A @ ( B @ leq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax32) ).
thf(529,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( ( A @ ( B @ leq ) )
=> ( B @ ( A @ geq ) ) )
& ( ( B @ ( A @ geq ) )
=> ( A @ ( B @ leq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(56055,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk38 != nil ) ),
inference(paramod_ordered,[status(thm)],[53270,243]) ).
thf(56056,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk38 != nil ) ),
inference(simp,[status(thm)],[56055]) ).
thf(56057,plain,
( ( nil @ ( sk2 @ sk21 @ segmentP ) )
| ( sk38 != nil ) ),
inference(pattern_uni,[status(thm)],[56056:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(13017,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[12843,243]) ).
thf(13018,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[13017]) ).
thf(13019,plain,
( ( nil @ ( sk2 @ sk14 @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[13018:[bind(A,$thf( sk2 @ sk14 ))]]) ).
thf(15977,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[6044,183]) ).
thf(15978,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[15977]) ).
thf(15979,plain,
( ( ( nil @ ( sk2 @ sk9 @ app ) )
= ( sk2 @ sk9 ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[15978:[bind(A,$thf( sk2 @ sk9 ))]]) ).
thf(79455,plain,
( ( sk2 != sk2 )
| ( nil != nil )
| ~ ( sk2 @ ssItem )
| ( sk2 @ sk27 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[77700,651]) ).
thf(79456,plain,
( ( sk2 != sk2 )
| ~ ( sk2 @ ssItem )
| ( sk2 @ sk27 @ ssList ) ),
inference(simp,[status(thm)],[79455]) ).
thf(79457,plain,
( ~ ( sk2 @ ssItem )
| ( sk2 @ sk27 @ ssList ) ),
inference(pattern_uni,[status(thm)],[79456:[]]) ).
thf(19435,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[11748,192]) ).
thf(19436,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[19435]) ).
thf(19437,plain,
( ( nil @ ( sk2 @ sk10 @ cons ) @ totalorderedP )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[19436:[bind(A,$thf( sk2 @ sk10 ))]]) ).
thf(115124,plain,
( ( sk2 != sk2 )
| ( sk37 != sk2 )
| ( nil != nil )
| ( sk2 @ hd @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[113170,724]) ).
thf(115125,plain,
( ( sk2 != sk2 )
| ( sk37 != sk2 )
| ( sk2 @ hd @ ssItem ) ),
inference(simp,[status(thm)],[115124]) ).
thf(115126,plain,
( ( sk37 != sk2 )
| ( sk2 @ hd @ ssItem ) ),
inference(pattern_uni,[status(thm)],[115125:[]]) ).
thf(117493,plain,
! [A: $i] :
( ( ( sk2 @ hd @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk37 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[115126,231]) ).
thf(117494,plain,
! [A: $i] :
( ( ( sk2 @ hd @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk37 != sk2 ) ),
inference(simp,[status(thm)],[117493]) ).
thf(117495,plain,
( ~ ( sk2 @ hd @ ( nil @ memberP ) )
| ( sk37 != sk2 ) ),
inference(pattern_uni,[status(thm)],[117494:[bind(A,$thf( sk2 @ hd ))]]) ).
thf(18818,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7015,190]) ).
thf(18819,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18818]) ).
thf(18820,plain,
( ( sk1 @ sk8 @ ( sk1 @ sk8 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18819:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(260,plain,
! [A: $i] :
( ( A @ totalorderP )
| ( A @ sk22 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[251]) ).
thf(559,plain,
! [B: $i,A: $i] :
( ( ( sk37 @ ssItem )
!= ( B @ ssItem ) )
| ~ $true
| ~ ( A @ ssItem )
| ( ( sk1 @ ( nil @ ( B @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk2 ) ),
inference(paramod_ordered,[status(thm)],[390,538]) ).
thf(560,plain,
! [B: $i,A: $i] :
( ( ( sk37 @ ssItem )
!= ( B @ ssItem ) )
| ~ ( A @ ssItem )
| ( ( sk1 @ ( nil @ ( B @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk2 ) ),
inference(simp,[status(thm)],[559]) ).
thf(561,plain,
! [A: $i] :
( ~ ( A @ ssItem )
| ( ( sk1 @ ( nil @ ( sk37 @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[560:[bind(A,$thf( A )),bind(B,$thf( sk37 ))]]) ).
thf(12879,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk14 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,176]) ).
thf(12880,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ( A @ sk14 @ ssList ) ),
inference(simp,[status(thm)],[12879]) ).
thf(12881,plain,
( ( sk1 @ strictorderP )
| ( sk1 @ sk14 @ ssList ) ),
inference(pattern_uni,[status(thm)],[12880:[bind(A,$thf( sk1 ))]]) ).
thf(13216,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[12881,296]) ).
thf(13217,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[13216]) ).
thf(13218,plain,
( ( nil @ ( sk1 @ sk14 @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[13217:[bind(A,$thf( sk1 @ sk14 ))]]) ).
thf(73,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax63) ).
thf(429,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ strictorderP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( A @ ( B @ cons ) @ ssList ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
thf(165,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( A @ ( B @ cons ) @ ssList ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(60819,plain,
! [A: $i] :
( ( ( sk1 @ sk24 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[60074,296]) ).
thf(60820,plain,
! [A: $i] :
( ( ( sk1 @ sk24 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ totalorderP ) ),
inference(simp,[status(thm)],[60819]) ).
thf(60821,plain,
( ( nil @ ( sk1 @ sk24 @ rearsegP ) )
| ( sk1 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[60820:[bind(A,$thf( sk1 @ sk24 ))]]) ).
thf(7227,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7015,243]) ).
thf(7228,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7227]) ).
thf(7229,plain,
( ( nil @ ( sk1 @ sk8 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7228:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(628,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ( ( sk1 @ ( nil @ ( sk37 @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk2 ) ),
inference(paramod_ordered,[status(thm)],[391,561]) ).
thf(629,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ( ( sk1 @ ( nil @ ( sk37 @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk2 ) ),
inference(simp,[status(thm)],[628]) ).
thf(630,plain,
( ( sk1 @ ( nil @ ( sk37 @ cons ) @ ( nil @ ( sk38 @ cons ) @ app ) @ app ) )
!= sk2 ),
inference(pattern_uni,[status(thm)],[629:[bind(A,$thf( sk38 ))]]) ).
thf(223,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)],[218]) ).
thf(228,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)],[223]) ).
thf(229,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)],[228]) ).
thf(252,plain,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ sk22 @ ( A @ sk23 @ leq ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[251]) ).
thf(197,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)],[196]) ).
thf(19028,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) )
| ( sk37 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18880,2382]) ).
thf(19029,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) )
| ( sk37 != nil ) ),
inference(simp,[status(thm)],[19028]) ).
thf(19058,plain,
( ( sk2 != sk1 )
| ( sk1 != nil )
| ( sk37 != nil ) ),
inference(simp,[status(thm)],[19029]) ).
thf(1020,plain,
! [A: $i] :
( ( A != sk38 )
| ( sk2 != nil )
| ( sk2 != nil )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[121,723]) ).
thf(1021,plain,
! [A: $i] :
( ( A != sk38 )
| ( sk2 != nil )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[1020]) ).
thf(1022,plain,
( ( sk2 != nil )
| ~ ( sk38 @ ( nil @ frontsegP ) )
| ~ ( sk38 @ ssList ) ),
inference(pattern_uni,[status(thm)],[1021:[bind(A,$thf( sk38 ))]]) ).
thf(6430,plain,
( ( ( sk38 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk2 != nil )
| ~ ( sk38 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,1022]) ).
thf(6431,plain,
( ( ( sk38 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk2 != nil )
| ~ ( sk38 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[6430]) ).
thf(6445,plain,
( ( sk38 != sk1 )
| ( sk2 != nil )
| ~ ( sk38 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[6431]) ).
thf(173,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ sk11 @ ( A @ sk10 @ lt ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[168]) ).
thf(11247,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ~ ( A @ sk11 @ ( A @ sk10 @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,173]) ).
thf(11248,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ~ ( A @ sk11 @ ( A @ sk10 @ lt ) ) ),
inference(simp,[status(thm)],[11247]) ).
thf(11249,plain,
( ( sk1 @ strictorderP )
| ~ ( sk1 @ sk11 @ ( sk1 @ sk10 @ lt ) ) ),
inference(pattern_uni,[status(thm)],[11248:[bind(A,$thf( sk1 ))]]) ).
thf(35615,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk19 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,222]) ).
thf(35616,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk19 @ ssList ) ),
inference(simp,[status(thm)],[35615]) ).
thf(35617,plain,
( ( sk2 @ strictorderedP )
| ( sk2 @ sk19 @ ssList ) ),
inference(pattern_uni,[status(thm)],[35616:[bind(A,$thf( sk2 ))]]) ).
thf(35915,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[35617,296]) ).
thf(35916,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[35915]) ).
thf(35917,plain,
( ( nil @ ( sk2 @ sk19 @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[35916:[bind(A,$thf( sk2 @ sk19 ))]]) ).
thf(69208,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk22 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,260]) ).
thf(69209,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk22 @ ssItem ) ),
inference(simp,[status(thm)],[69208]) ).
thf(69210,plain,
( ( sk2 @ totalorderP )
| ( sk2 @ sk22 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[69209:[bind(A,$thf( sk2 ))]]) ).
thf(15899,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A )
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[12843,183]) ).
thf(15900,plain,
! [A: $i] :
( ( ( sk2 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[15899]) ).
thf(15901,plain,
( ( ( nil @ ( sk2 @ sk14 @ app ) )
= ( sk2 @ sk14 ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[15900:[bind(A,$thf( sk2 @ sk14 ))]]) ).
thf(80,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ equalelemsP )
<=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ( ( ( E @ ( C @ cons ) @ ( B @ cons ) @ ( D @ app ) )
= A )
=> ( B = C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax14) ).
thf(456,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ( ( ( E @ ( C @ cons ) @ ( B @ cons ) @ ( D @ app ) )
= A )
=> ( B = C ) ) ) ) ) )
=> ( A @ equalelemsP ) )
& ( ( A @ equalelemsP )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ( ( ( E @ ( C @ cons ) @ ( B @ cons ) @ ( D @ app ) )
= A )
=> ( B = C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(52650,plain,
( ( sk2 != sk2 )
| ( nil != nil )
| ~ ( sk2 @ ssItem )
| ( sk2 @ sk21 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[51244,651]) ).
thf(52651,plain,
( ( sk2 != sk2 )
| ~ ( sk2 @ ssItem )
| ( sk2 @ sk21 @ ssList ) ),
inference(simp,[status(thm)],[52650]) ).
thf(52652,plain,
( ~ ( sk2 @ ssItem )
| ( sk2 @ sk21 @ ssList ) ),
inference(pattern_uni,[status(thm)],[52651:[]]) ).
thf(224,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ sk16 @ ( A @ sk15 @ lt ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[218]) ).
thf(10488,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10187,296]) ).
thf(10489,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[10488]) ).
thf(10490,plain,
( ( nil @ ( sk1 @ sk13 @ rearsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10489:[bind(A,$thf( sk1 @ sk13 ))]]) ).
thf(55788,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk37 != nil ) ),
inference(paramod_ordered,[status(thm)],[53144,296]) ).
thf(55789,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk37 != nil ) ),
inference(simp,[status(thm)],[55788]) ).
thf(55790,plain,
( ( nil @ ( sk2 @ sk21 @ rearsegP ) )
| ( sk37 != nil ) ),
inference(pattern_uni,[status(thm)],[55789:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(52,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( B @ ( A @ cons ) @ totalorderedP )
<=> ( ( ( B @ hd @ ( A @ leq ) )
& ( B @ totalorderedP )
& ( nil != B ) )
| ( nil = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax67) ).
thf(329,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( ( ( B @ hd @ ( A @ leq ) )
& ( B @ totalorderedP )
& ( nil != B ) )
| ( nil = B ) )
=> ( B @ ( A @ cons ) @ totalorderedP ) )
& ( ( B @ ( A @ cons ) @ totalorderedP )
=> ( ( ( B @ hd @ ( A @ leq ) )
& ( B @ totalorderedP )
& ( nil != B ) )
| ( nil = B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(1128,plain,
( ( ( sk1 @ sk5 @ ssItem )
!= ( sk2 @ ssItem ) )
| ( sk2 != nil )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[690,651]) ).
thf(1129,plain,
( ( ( sk1 @ sk5 @ ssItem )
!= ( sk2 @ ssItem ) )
| ( sk2 != nil )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1128]) ).
thf(1178,plain,
( ( ( sk1 @ sk5 )
!= sk2 )
| ( sk2 != nil )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1129]) ).
thf(18797,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5192,190]) ).
thf(18798,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18797]) ).
thf(18799,plain,
( ( sk2 @ sk7 @ ( sk2 @ sk7 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18798:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(87,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssItem )
=> ( ( A @ ( B @ app ) @ ( C @ cons ) )
= ( A @ ( B @ ( C @ cons ) @ app ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax27) ).
thf(493,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssItem )
=> ( ( A @ ( B @ app ) @ ( C @ cons ) )
= ( A @ ( B @ ( C @ cons ) @ app ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(15913,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[6983,183]) ).
thf(15914,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[15913]) ).
thf(15915,plain,
( ( ( nil @ ( sk2 @ sk8 @ app ) )
= ( sk2 @ sk8 ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[15914:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(134693,plain,
( ( sk2 != sk2 )
| ( sk37 != nil )
| ( nil != nil )
| ( sk2 @ sk29 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[131983,1400]) ).
thf(134694,plain,
( ( sk2 != sk2 )
| ( sk37 != nil )
| ( sk2 @ sk29 @ ssItem ) ),
inference(simp,[status(thm)],[134693]) ).
thf(134695,plain,
( ( sk37 != nil )
| ( sk2 @ sk29 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[134694:[]]) ).
thf(38134,plain,
! [A: $i] :
( ( ( sk1 @ sk17 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[37532,373]) ).
thf(38135,plain,
! [A: $i] :
( ( ( sk1 @ sk17 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[38134]) ).
thf(38136,plain,
( ( nil @ ( sk1 @ sk17 @ frontsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[38135:[bind(A,$thf( sk1 @ sk17 ))]]) ).
thf(15894,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5192,183]) ).
thf(15895,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[15894]) ).
thf(15896,plain,
( ( ( nil @ ( sk2 @ sk7 @ app ) )
= ( sk2 @ sk7 ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[15895:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( B @ ( C @ app ) )
= ( B @ ( A @ app ) ) )
=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax79) ).
thf(186,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( B @ ( C @ app ) )
= ( B @ ( A @ app ) ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(187,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)],[186]) ).
thf(188,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)],[187]) ).
thf(89,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ lt ) )
=> ~ ( A @ ( B @ lt ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax33) ).
thf(499,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ lt ) )
=> ~ ( A @ ( B @ lt ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(95,axiom,
nil @ totalorderP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax62) ).
thf(519,plain,
nil @ totalorderP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( nil
= ( B @ ( A @ app ) ) )
<=> ( ( nil = A )
& ( nil = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax83) ).
thf(356,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( ( nil = A )
& ( nil = B ) )
=> ( nil
= ( B @ ( A @ app ) ) ) )
& ( ( nil
= ( B @ ( A @ app ) ) )
=> ( ( nil = A )
& ( nil = B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(357,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)],[356]) ).
thf(360,plain,
! [B: $i,A: $i] :
( ( nil
= ( B @ ( A @ app ) ) )
| ( nil != A )
| ( nil != B )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[357]) ).
thf(363,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( B @ ( A @ app ) )
= nil )
| ( nil != A )
| ( nil != B ) ),
inference(lifteq,[status(thm)],[360]) ).
thf(364,plain,
( ~ ( nil @ ssList )
| ( ( nil @ ( nil @ app ) )
= nil ) ),
inference(simp,[status(thm)],[363]) ).
thf(1591,plain,
( ~ $true
| ( ( nil @ ( nil @ app ) )
= nil ) ),
inference(rewrite,[status(thm)],[364,343]) ).
thf(1592,plain,
( ( nil @ ( nil @ app ) )
= nil ),
inference(simp,[status(thm)],[1591]) ).
thf(54641,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk37 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[52659,296]) ).
thf(54642,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk37 != sk2 ) ),
inference(simp,[status(thm)],[54641]) ).
thf(54643,plain,
( ( nil @ ( sk2 @ sk21 @ rearsegP ) )
| ( sk37 != sk2 ) ),
inference(pattern_uni,[status(thm)],[54642:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(1071,plain,
( ( ( sk2 @ sk5 @ ssItem )
!= ( sk2 @ ssItem ) )
| ( sk2 != nil )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[684,651]) ).
thf(1072,plain,
( ( ( sk2 @ sk5 @ ssItem )
!= ( sk2 @ ssItem ) )
| ( sk2 != nil )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1071]) ).
thf(1121,plain,
( ( ( sk2 @ sk5 )
!= sk2 )
| ( sk2 != nil )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1072]) ).
thf(89122,plain,
( ( sk2 != sk2 )
| ( sk37 != nil )
| ( nil != nil )
| ( sk2 @ sk28 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[85155,1400]) ).
thf(89123,plain,
( ( sk2 != sk2 )
| ( sk37 != nil )
| ( sk2 @ sk28 @ ssItem ) ),
inference(simp,[status(thm)],[89122]) ).
thf(89124,plain,
( ( sk37 != nil )
| ( sk2 @ sk28 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[89123:[]]) ).
thf(5845,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5604,210]) ).
thf(5846,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5845]) ).
thf(5847,plain,
( ~ ( sk1 @ sk6 @ ( sk1 @ sk6 @ neq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5846:[bind(A,$thf( sk1 @ sk6 ))]]) ).
thf(1026,plain,
! [A: $i] :
( ( A != sk37 )
| ( sk2 != nil )
| ( sk2 != nil )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[121,724]) ).
thf(1027,plain,
! [A: $i] :
( ( A != sk37 )
| ( sk2 != nil )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[1026]) ).
thf(1028,plain,
( ( sk2 != nil )
| ~ ( sk37 @ ( nil @ frontsegP ) )
| ~ ( sk37 @ ssList ) ),
inference(pattern_uni,[status(thm)],[1027:[bind(A,$thf( sk37 ))]]) ).
thf(1354,plain,
( ( ( sk37 @ ssItem )
!= ( nil @ ssItem ) )
| ~ $true
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[390,1271]) ).
thf(1355,plain,
( ( ( sk37 @ ssItem )
!= ( nil @ ssItem ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1354]) ).
thf(1361,plain,
( ( sk37 != nil )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1355]) ).
thf(113978,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ hd @ ssItem )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[104,291]) ).
thf(113979,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ hd @ ssItem )
| ( nil = A ) ),
inference(simp,[status(thm)],[113978]) ).
thf(113980,plain,
( ( sk1 @ hd @ ssItem )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[113979:[bind(A,$thf( sk1 ))]]) ).
thf(2194,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[104,136]) ).
thf(2195,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( nil @ segmentP ) )
| ( nil = A ) ),
inference(simp,[status(thm)],[2194]) ).
thf(2196,plain,
( ~ ( sk1 @ ( nil @ segmentP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[2195:[bind(A,$thf( sk1 ))]]) ).
thf(15910,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7015,183]) ).
thf(15911,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[15910]) ).
thf(15912,plain,
( ( ( nil @ ( sk1 @ sk8 @ app ) )
= ( sk1 @ sk8 ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[15911:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(2315,plain,
( ( sk2 != sk2 )
| ( nil != nil )
| ~ ( sk2 @ ssItem )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2122,651]) ).
thf(2316,plain,
( ( sk2 != sk2 )
| ~ ( sk2 @ ssItem )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[2315]) ).
thf(2317,plain,
( ~ ( sk2 @ ssItem )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[2316:[]]) ).
thf(256,plain,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ sk23 @ ( A @ sk22 @ leq ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[251]) ).
thf(53510,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[51843,243]) ).
thf(53511,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[53510]) ).
thf(53512,plain,
( ( nil @ ( sk1 @ sk21 @ segmentP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[53511:[bind(A,$thf( sk1 @ sk21 ))]]) ).
thf(85,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ geq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax89) ).
thf(488,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(134922,plain,
( ( sk2 != sk2 )
| ( sk38 != nil )
| ( nil != nil )
| ( sk2 @ sk29 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[131983,1399]) ).
thf(134923,plain,
( ( sk2 != sk2 )
| ( sk38 != nil )
| ( sk2 @ sk29 @ ssItem ) ),
inference(simp,[status(thm)],[134922]) ).
thf(134924,plain,
( ( sk38 != nil )
| ( sk2 @ sk29 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[134923:[]]) ).
thf(88614,plain,
( ( sk2 != sk2 )
| ( sk37 != sk2 )
| ( nil != nil )
| ( sk2 @ sk28 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[85155,724]) ).
thf(88615,plain,
( ( sk2 != sk2 )
| ( sk37 != sk2 )
| ( sk2 @ sk28 @ ssItem ) ),
inference(simp,[status(thm)],[88614]) ).
thf(88616,plain,
( ( sk37 != sk2 )
| ( sk2 @ sk28 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[88615:[]]) ).
thf(91651,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk37 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[88616,231]) ).
thf(91652,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk37 != sk2 ) ),
inference(simp,[status(thm)],[91651]) ).
thf(91653,plain,
( ~ ( sk2 @ sk28 @ ( nil @ memberP ) )
| ( sk37 != sk2 ) ),
inference(pattern_uni,[status(thm)],[91652:[bind(A,$thf( sk2 @ sk28 ))]]) ).
thf(33738,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[33476,210]) ).
thf(33739,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[33738]) ).
thf(33740,plain,
( ~ ( sk2 @ sk15 @ ( sk2 @ sk15 @ neq ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[33739:[bind(A,$thf( sk2 @ sk15 ))]]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ leq ) )
=> ( ( B @ ( A @ lt ) )
| ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax92) ).
thf(193,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ leq ) )
=> ( ( B @ ( A @ lt ) )
| ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(31569,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[103,214]) ).
thf(31570,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[31569]) ).
thf(31571,plain,
( ( sk2 @ ( nil @ app ) )
= sk2 ),
inference(pattern_uni,[status(thm)],[31570:[bind(A,$thf( sk2 ))]]) ).
thf(631,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ~ $true
| ( ( sk1 @ ( nil @ ( sk37 @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk2 ) ),
inference(paramod_ordered,[status(thm)],[390,561]) ).
thf(632,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ( ( sk1 @ ( nil @ ( sk37 @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk2 ) ),
inference(simp,[status(thm)],[631]) ).
thf(633,plain,
( ( sk1 @ ( nil @ ( sk37 @ cons ) @ ( nil @ ( sk37 @ cons ) @ app ) @ app ) )
!= sk2 ),
inference(pattern_uni,[status(thm)],[632:[bind(A,$thf( sk37 ))]]) ).
thf(1610,plain,
( ( ( nil @ ( sk37 @ cons ) @ ( nil @ ( sk37 @ cons ) @ app ) )
!= ( nil @ ( nil @ app ) ) )
| ( ( sk1 @ ( nil @ app ) )
!= sk2 ) ),
inference(paramod_ordered,[status(thm)],[1592,633]) ).
thf(1621,plain,
( ( ( nil @ ( sk37 @ cons ) )
!= nil )
| ( ( nil @ ( sk37 @ cons ) )
!= nil )
| ( ( sk1 @ ( nil @ app ) )
!= sk2 ) ),
inference(simp,[status(thm)],[1610]) ).
thf(1629,plain,
( ( ( nil @ ( sk37 @ cons ) )
!= nil )
| ( ( sk1 @ ( nil @ app ) )
!= sk2 ) ),
inference(simp,[status(thm)],[1621]) ).
thf(31870,plain,
( ( ( sk2 @ ( nil @ app ) )
!= ( sk1 @ ( nil @ app ) ) )
| ( ( nil @ ( sk37 @ cons ) )
!= nil )
| ( sk2 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[31571,1629]) ).
thf(31871,plain,
( ( ( sk2 @ ( nil @ app ) )
!= ( sk1 @ ( nil @ app ) ) )
| ( ( nil @ ( sk37 @ cons ) )
!= nil ) ),
inference(simp,[status(thm)],[31870]) ).
thf(31947,plain,
( ( sk2 != sk1 )
| ( nil != nil )
| ( ( nil @ ( sk37 @ cons ) )
!= nil ) ),
inference(simp,[status(thm)],[31871]) ).
thf(31982,plain,
( ( sk2 != sk1 )
| ( ( nil @ ( sk37 @ cons ) )
!= nil ) ),
inference(simp,[status(thm)],[31947]) ).
thf(13182,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[12881,243]) ).
thf(13183,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[13182]) ).
thf(13184,plain,
( ( nil @ ( sk1 @ sk14 @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[13183:[bind(A,$thf( sk1 @ sk14 ))]]) ).
thf(10917,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10731,296]) ).
thf(10918,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[10917]) ).
thf(10919,plain,
( ( nil @ ( sk2 @ sk12 @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10918:[bind(A,$thf( sk2 @ sk12 ))]]) ).
thf(66363,plain,
( ( sk2 != sk2 )
| ( sk38 != sk2 )
| ( nil != nil )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[65462,723]) ).
thf(66364,plain,
( ( sk2 != sk2 )
| ( sk38 != sk2 )
| ( sk2 @ tl @ ssList ) ),
inference(simp,[status(thm)],[66363]) ).
thf(66365,plain,
( ( sk38 != sk2 )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[66364:[]]) ).
thf(34786,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk16 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,221]) ).
thf(34787,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderedP )
| ( A @ sk16 @ ssItem ) ),
inference(simp,[status(thm)],[34786]) ).
thf(34788,plain,
( ( sk1 @ strictorderedP )
| ( sk1 @ sk16 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[34787:[bind(A,$thf( sk1 ))]]) ).
thf(35151,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[34788,116]) ).
thf(35152,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[35151]) ).
thf(35153,plain,
( ( nil @ ( sk1 @ sk16 @ cons ) @ strictorderedP )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[35152:[bind(A,$thf( sk1 @ sk16 ))]]) ).
thf(19469,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[390,192]) ).
thf(19470,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[19469]) ).
thf(19471,plain,
nil @ ( sk37 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[19470:[bind(A,$thf( sk37 ))]]) ).
thf(45409,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk20 ) @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[45182,214]) ).
thf(45410,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk20 ) @ ssList )
!= ( A @ ssList ) )
| ( ( A @ ( nil @ app ) )
= A ) ),
inference(simp,[status(thm)],[45409]) ).
thf(45411,plain,
( ( nil @ ( nil @ sk20 ) @ ( nil @ app ) )
= ( nil @ ( nil @ sk20 ) ) ),
inference(pattern_uni,[status(thm)],[45410:[bind(A,$thf( nil @ ( nil @ sk20 ) ))]]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) @ hd )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).
thf(129,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) @ hd )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(19472,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[684,192]) ).
thf(19473,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19472]) ).
thf(19474,plain,
( ( nil @ ( sk2 @ sk5 @ cons ) @ totalorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19473:[bind(A,$thf( sk2 @ sk5 ))]]) ).
thf(19596,plain,
( ( ( sk2 @ ( nil @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ( sk38 != nil )
| ~ $true
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[19031,2403]) ).
thf(19597,plain,
( ( ( sk2 @ ( nil @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ( sk38 != nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[19596]) ).
thf(19682,plain,
( ( sk2 != sk1 )
| ( nil != nil )
| ( sk38 != nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[19597]) ).
thf(19708,plain,
( ( sk2 != sk1 )
| ( sk38 != nil )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[19682]) ).
thf(91,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ rearsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49) ).
thf(503,plain,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(19457,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[690,192]) ).
thf(19458,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19457]) ).
thf(19459,plain,
( ( nil @ ( sk1 @ sk5 @ cons ) @ totalorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19458:[bind(A,$thf( sk1 @ sk5 ))]]) ).
thf(93,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ lt ) )
<=> ( ( B @ ( A @ leq ) )
& ( A != B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax93) ).
thf(508,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( ( ( B @ ( A @ leq ) )
& ( A != B ) )
=> ( B @ ( A @ lt ) ) )
& ( ( B @ ( A @ lt ) )
=> ( ( B @ ( A @ leq ) )
& ( A != B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( D @ ( B @ cons ) @ ( C @ ( A @ cons ) @ frontsegP ) )
<=> ( ( D @ ( C @ frontsegP ) )
& ( A = B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax44) ).
thf(311,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssList )
=> ! [D: $i] :
( ( D @ ssList )
=> ( ( ( ( D @ ( C @ frontsegP ) )
& ( A = B ) )
=> ( D @ ( B @ cons ) @ ( C @ ( A @ cons ) @ frontsegP ) ) )
& ( ( D @ ( B @ cons ) @ ( C @ ( A @ cons ) @ frontsegP ) )
=> ( ( D @ ( C @ frontsegP ) )
& ( A = B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(69254,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk22 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,260]) ).
thf(69255,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk22 @ ssItem ) ),
inference(simp,[status(thm)],[69254]) ).
thf(69256,plain,
( ( sk1 @ totalorderP )
| ( sk1 @ sk22 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[69255:[bind(A,$thf( sk1 ))]]) ).
thf(539,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ssList )
!= ( C @ ssList ) )
| ~ $true
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( ( C @ ( nil @ ( B @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk2 ) ),
inference(paramod_ordered,[status(thm)],[103,535]) ).
thf(540,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ssList )
!= ( C @ ssList ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( ( C @ ( nil @ ( B @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk2 ) ),
inference(simp,[status(thm)],[539]) ).
thf(541,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( ( sk2 @ ( nil @ ( B @ cons ) @ ( nil @ ( A @ cons ) @ app ) @ app ) )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[540:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk2 ))]]) ).
thf(1048,plain,
( ( ( sk38 @ ssItem )
!= ( sk2 @ ssItem ) )
| ~ $true
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[391,1035]) ).
thf(1049,plain,
( ( ( sk38 @ ssItem )
!= ( sk2 @ ssItem ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1048]) ).
thf(1054,plain,
( ( sk38 != sk2 )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1049]) ).
thf(18865,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[6044,190]) ).
thf(18866,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18865]) ).
thf(18867,plain,
( ( sk2 @ sk9 @ ( sk2 @ sk9 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18866:[bind(A,$thf( sk2 @ sk9 ))]]) ).
thf(5417,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5213,296]) ).
thf(5418,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5417]) ).
thf(5419,plain,
( ( nil @ ( sk1 @ sk7 @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5418:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(175,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ sk10 @ ( A @ sk11 @ lt ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[168]) ).
thf(12359,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ~ ( A @ sk10 @ ( A @ sk11 @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,175]) ).
thf(12360,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ~ ( A @ sk10 @ ( A @ sk11 @ lt ) ) ),
inference(simp,[status(thm)],[12359]) ).
thf(12361,plain,
( ( sk2 @ strictorderP )
| ~ ( sk2 @ sk10 @ ( sk2 @ sk11 @ lt ) ) ),
inference(pattern_uni,[status(thm)],[12360:[bind(A,$thf( sk2 ))]]) ).
thf(11118,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10766,373]) ).
thf(11119,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[11118]) ).
thf(11120,plain,
( ( nil @ ( sk1 @ sk12 @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[11119:[bind(A,$thf( sk1 @ sk12 ))]]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( B @ frontsegP ) )
& ( B @ ( A @ frontsegP ) ) )
=> ( C @ ( A @ frontsegP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax40) ).
thf(127,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( B @ frontsegP ) )
& ( B @ ( A @ frontsegP ) ) )
=> ( C @ ( A @ frontsegP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(128,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)],[127]) ).
thf(2233,plain,
! [A: $i] :
( ( A != sk38 )
| ( sk2 != nil )
| ( sk2 != nil )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[136,723]) ).
thf(2234,plain,
! [A: $i] :
( ( A != sk38 )
| ( sk2 != nil )
| ~ ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[2233]) ).
thf(2235,plain,
( ( sk2 != nil )
| ~ ( sk38 @ ( nil @ segmentP ) )
| ~ ( sk38 @ ssList ) ),
inference(pattern_uni,[status(thm)],[2234:[bind(A,$thf( sk38 ))]]) ).
thf(68,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( ( A @ tl @ ( A @ hd @ cons ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax78) ).
thf(412,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( nil != A )
=> ( ( A @ tl @ ( A @ hd @ cons ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(15974,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[103,183]) ).
thf(15975,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[15974]) ).
thf(15976,plain,
( ( nil @ ( sk2 @ app ) )
= sk2 ),
inference(pattern_uni,[status(thm)],[15975:[bind(A,$thf( sk2 ))]]) ).
thf(7437,plain,
( ( ( sk37 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk2 != nil )
| ~ ( sk37 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,1028]) ).
thf(7438,plain,
( ( ( sk37 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk2 != nil )
| ~ ( sk37 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[7437]) ).
thf(7459,plain,
( ( sk37 != sk1 )
| ( sk2 != nil )
| ~ ( sk37 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[7438]) ).
thf(166,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[165]) ).
thf(38013,plain,
! [A: $i] :
( ( ( sk1 @ sk17 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[37532,243]) ).
thf(38014,plain,
! [A: $i] :
( ( ( sk1 @ sk17 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[38013]) ).
thf(38015,plain,
( ( nil @ ( sk1 @ sk17 @ segmentP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[38014:[bind(A,$thf( sk1 @ sk17 ))]]) ).
thf(8769,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,373]) ).
thf(8770,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) ) ),
inference(simp,[status(thm)],[8769]) ).
thf(8771,plain,
nil @ ( sk2 @ frontsegP ),
inference(pattern_uni,[status(thm)],[8770:[bind(A,$thf( sk2 ))]]) ).
thf(58059,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk25 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,254]) ).
thf(58060,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk25 @ ssList ) ),
inference(simp,[status(thm)],[58059]) ).
thf(58061,plain,
( ( sk1 @ totalorderP )
| ( sk1 @ sk25 @ ssList ) ),
inference(pattern_uni,[status(thm)],[58060:[bind(A,$thf( sk1 ))]]) ).
thf(58865,plain,
! [A: $i] :
( ( ( sk1 @ sk25 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[58061,373]) ).
thf(58866,plain,
! [A: $i] :
( ( ( sk1 @ sk25 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ totalorderP ) ),
inference(simp,[status(thm)],[58865]) ).
thf(58867,plain,
( ( nil @ ( sk1 @ sk25 @ frontsegP ) )
| ( sk1 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[58866:[bind(A,$thf( sk1 @ sk25 ))]]) ).
thf(13262,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[12881,373]) ).
thf(13263,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[13262]) ).
thf(13264,plain,
( ( nil @ ( sk1 @ sk14 @ frontsegP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[13263:[bind(A,$thf( sk1 @ sk14 ))]]) ).
thf(71,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( B @ ( A @ app ) @ ssList ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
thf(425,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( B @ ( A @ app ) @ ssList ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(35213,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[34788,231]) ).
thf(35214,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[35213]) ).
thf(35215,plain,
( ~ ( sk1 @ sk16 @ ( nil @ memberP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[35214:[bind(A,$thf( sk1 @ sk16 ))]]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( C @ ( B @ ( A @ app ) @ app ) )
= ( C @ ( B @ app ) @ ( A @ app ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax82) ).
thf(148,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( C @ ( B @ ( A @ app ) @ app ) )
= ( C @ ( B @ app ) @ ( A @ app ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(169,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)],[168]) ).
thf(179,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)],[169]) ).
thf(180,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)],[179]) ).
thf(8716,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[6983,373]) ).
thf(8717,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[8716]) ).
thf(8718,plain,
( ( nil @ ( sk2 @ sk8 @ frontsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[8717:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(35977,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[35617,373]) ).
thf(35978,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[35977]) ).
thf(35979,plain,
( ( nil @ ( sk2 @ sk19 @ frontsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[35978:[bind(A,$thf( sk2 @ sk19 ))]]) ).
thf(13918,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[13692,116]) ).
thf(13919,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[13918]) ).
thf(13920,plain,
( ( nil @ ( sk1 @ sk11 @ cons ) @ strictorderedP )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[13919:[bind(A,$thf( sk1 @ sk11 ))]]) ).
thf(39093,plain,
! [A: $i] :
( ( ( sk2 @ sk18 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[38830,243]) ).
thf(39094,plain,
! [A: $i] :
( ( ( sk2 @ sk18 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[39093]) ).
thf(39095,plain,
( ( nil @ ( sk2 @ sk18 @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[39094:[bind(A,$thf( sk2 @ sk18 ))]]) ).
thf(53697,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[51843,296]) ).
thf(53698,plain,
! [A: $i] :
( ( ( sk1 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[53697]) ).
thf(53699,plain,
( ( nil @ ( sk1 @ sk21 @ rearsegP ) )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[53698:[bind(A,$thf( sk1 @ sk21 ))]]) ).
thf(15996,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[6068,183]) ).
thf(15997,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[15996]) ).
thf(15998,plain,
( ( ( nil @ ( sk1 @ sk9 @ app ) )
= ( sk1 @ sk9 ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[15997:[bind(A,$thf( sk1 @ sk9 ))]]) ).
thf(63,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ( ( ( C @ ( B @ geq ) )
& ( B @ ( A @ geq ) ) )
=> ( C @ ( A @ geq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax88) ).
thf(402,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ( ( ( C @ ( B @ geq ) )
& ( B @ ( A @ geq ) ) )
=> ( C @ ( A @ geq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(134935,plain,
( ( sk2 != sk2 )
| ( sk38 != sk2 )
| ( nil != nil )
| ( sk2 @ sk29 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[131983,723]) ).
thf(134936,plain,
( ( sk2 != sk2 )
| ( sk38 != sk2 )
| ( sk2 @ sk29 @ ssItem ) ),
inference(simp,[status(thm)],[134935]) ).
thf(134937,plain,
( ( sk38 != sk2 )
| ( sk2 @ sk29 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[134936:[]]) ).
thf(18834,plain,
! [A: $i] :
( ( ( sk2 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10152,190]) ).
thf(18835,plain,
! [A: $i] :
( ( ( sk2 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[18834]) ).
thf(18836,plain,
( ( sk2 @ sk13 @ ( sk2 @ sk13 @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[18835:[bind(A,$thf( sk2 @ sk13 ))]]) ).
thf(10961,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10731,373]) ).
thf(10962,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[10961]) ).
thf(10963,plain,
( ( nil @ ( sk2 @ sk12 @ frontsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10962:[bind(A,$thf( sk2 @ sk12 ))]]) ).
thf(1395,plain,
( ( ( sk1 @ sk5 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk2 != nil )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[690,1362]) ).
thf(1396,plain,
( ( ( sk1 @ sk5 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk2 != nil )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1395]) ).
thf(1403,plain,
( ( ( sk1 @ sk5 )
!= nil )
| ( sk2 != nil )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1396]) ).
thf(35866,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[35617,243]) ).
thf(35867,plain,
! [A: $i] :
( ( ( sk2 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[35866]) ).
thf(35868,plain,
( ( nil @ ( sk2 @ sk19 @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[35867:[bind(A,$thf( sk2 @ sk19 ))]]) ).
thf(115890,plain,
( ( sk2 != sk2 )
| ( sk38 != nil )
| ( nil != nil )
| ( sk2 @ hd @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[113170,1399]) ).
thf(115891,plain,
( ( sk2 != sk2 )
| ( sk38 != nil )
| ( sk2 @ hd @ ssItem ) ),
inference(simp,[status(thm)],[115890]) ).
thf(115892,plain,
( ( sk38 != nil )
| ( sk2 @ hd @ ssItem ) ),
inference(pattern_uni,[status(thm)],[115891:[]]) ).
thf(123778,plain,
! [A: $i] :
( ( ( sk2 @ hd @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk38 != nil ) ),
inference(paramod_ordered,[status(thm)],[115892,231]) ).
thf(123779,plain,
! [A: $i] :
( ( ( sk2 @ hd @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk38 != nil ) ),
inference(simp,[status(thm)],[123778]) ).
thf(123780,plain,
( ~ ( sk2 @ hd @ ( nil @ memberP ) )
| ( sk38 != nil ) ),
inference(pattern_uni,[status(thm)],[123779:[bind(A,$thf( sk2 @ hd ))]]) ).
thf(18837,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10731,190]) ).
thf(18838,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[18837]) ).
thf(18839,plain,
( ( sk2 @ sk12 @ ( sk2 @ sk12 @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[18838:[bind(A,$thf( sk2 @ sk12 ))]]) ).
thf(35161,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[34788,192]) ).
thf(35162,plain,
! [A: $i] :
( ( ( sk1 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[35161]) ).
thf(35163,plain,
( ( nil @ ( sk1 @ sk16 @ cons ) @ totalorderedP )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[35162:[bind(A,$thf( sk1 @ sk16 ))]]) ).
thf(202,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)],[201]) ).
thf(204,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ gt ) )
| ~ ( A @ ( B @ lt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[202]) ).
thf(259,plain,
! [A: $i] :
( ( A @ totalorderP )
| ( A @ sk23 @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[251]) ).
thf(4102,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk1 @ cyclefreeP )
| ( nil @ sk5 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[641,1311]) ).
thf(4103,plain,
( ( ( sk1 @ ( nil @ frontsegP ) )
!= ( nil @ ( nil @ frontsegP ) ) )
| ( sk1 @ cyclefreeP )
| ( nil @ sk5 @ ssItem ) ),
inference(simp,[status(thm)],[4102]) ).
thf(4110,plain,
( ( sk1 != nil )
| ( nil != nil )
| ( sk1 @ cyclefreeP )
| ( nil @ sk5 @ ssItem ) ),
inference(simp,[status(thm)],[4103]) ).
thf(4112,plain,
( ( sk1 != nil )
| ( sk1 @ cyclefreeP )
| ( nil @ sk5 @ ssItem ) ),
inference(simp,[status(thm)],[4110]) ).
thf(88661,plain,
( ( sk2 != sk2 )
| ( nil != nil )
| ~ ( nil @ ssItem )
| ( sk2 @ sk28 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[85155,1362]) ).
thf(88662,plain,
( ( sk2 != sk2 )
| ~ ( nil @ ssItem )
| ( sk2 @ sk28 @ ssItem ) ),
inference(simp,[status(thm)],[88661]) ).
thf(88663,plain,
( ~ ( nil @ ssItem )
| ( sk2 @ sk28 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[88662:[]]) ).
thf(92438,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ~ ( nil @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[88663,231]) ).
thf(92439,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[92438]) ).
thf(92440,plain,
( ~ ( sk2 @ sk28 @ ( nil @ memberP ) )
| ~ ( nil @ ssItem ) ),
inference(pattern_uni,[status(thm)],[92439:[bind(A,$thf( sk2 @ sk28 ))]]) ).
thf(15934,plain,
! [A: $i] :
( ( ( sk2 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A )
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10152,183]) ).
thf(15935,plain,
! [A: $i] :
( ( ( sk2 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[15934]) ).
thf(15936,plain,
( ( ( nil @ ( sk2 @ sk13 @ app ) )
= ( sk2 @ sk13 ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[15935:[bind(A,$thf( sk2 @ sk13 ))]]) ).
thf(11235,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ~ ( A @ sk11 @ ( A @ sk10 @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,173]) ).
thf(11236,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ~ ( A @ sk11 @ ( A @ sk10 @ lt ) ) ),
inference(simp,[status(thm)],[11235]) ).
thf(11237,plain,
( ( sk2 @ strictorderP )
| ~ ( sk2 @ sk11 @ ( sk2 @ sk10 @ lt ) ) ),
inference(pattern_uni,[status(thm)],[11236:[bind(A,$thf( sk2 ))]]) ).
thf(32582,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[11748,216]) ).
thf(32583,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[32582]) ).
thf(32584,plain,
( ~ ( sk2 @ sk10 @ ( sk2 @ sk10 @ lt ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[32583:[bind(A,$thf( sk2 @ sk10 ))]]) ).
thf(19020,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) )
| ~ $true
| ( sk2 = nil ) ),
inference(paramod_ordered,[status(thm)],[18880,2122]) ).
thf(19021,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) )
| ( sk2 = nil ) ),
inference(simp,[status(thm)],[19020]) ).
thf(19057,plain,
( ( sk2 != sk1 )
| ( sk1 != nil )
| ( sk2 = nil ) ),
inference(simp,[status(thm)],[19021]) ).
thf(1105,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[684,231]) ).
thf(1106,plain,
! [A: $i] :
( ( ( sk2 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1105]) ).
thf(1107,plain,
( ~ ( sk2 @ sk5 @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1106:[bind(A,$thf( sk2 @ sk5 ))]]) ).
thf(15944,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A )
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5213,183]) ).
thf(15945,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[15944]) ).
thf(15946,plain,
( ( ( nil @ ( sk1 @ sk7 @ app ) )
= ( sk1 @ sk7 ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[15945:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(7107,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[6983,243]) ).
thf(7108,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7107]) ).
thf(7109,plain,
( ( nil @ ( sk2 @ sk8 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7108:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(37746,plain,
! [A: $i] :
( ( ( sk2 @ sk17 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[37488,243]) ).
thf(37747,plain,
! [A: $i] :
( ( ( sk2 @ sk17 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[37746]) ).
thf(37748,plain,
( ( nil @ ( sk2 @ sk17 @ segmentP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[37747:[bind(A,$thf( sk2 @ sk17 ))]]) ).
thf(13956,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[13692,231]) ).
thf(13957,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[13956]) ).
thf(13958,plain,
( ~ ( sk1 @ sk11 @ ( nil @ memberP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[13957:[bind(A,$thf( sk1 @ sk11 ))]]) ).
thf(65,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( B @ app ) )
= ( A @ ( B @ app ) ) )
=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax80) ).
thf(406,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( C @ ( B @ app ) )
= ( A @ ( B @ app ) ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) )
!= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
thf(272,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) )
!= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(273,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ cons ) )
!= A )
| ~ ( B @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[272]) ).
thf(274,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( ( A @ ( B @ cons ) )
!= A ) ),
inference(lifteq,[status(thm)],[273]) ).
thf(1142,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[690,116]) ).
thf(1143,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1142]) ).
thf(1144,plain,
( ( nil @ ( sk1 @ sk5 @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1143:[bind(A,$thf( sk1 @ sk5 ))]]) ).
thf(79462,plain,
( ( sk2 != sk2 )
| ( sk37 != sk2 )
| ( nil != nil )
| ( sk2 @ sk27 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[77700,724]) ).
thf(79463,plain,
( ( sk2 != sk2 )
| ( sk37 != sk2 )
| ( sk2 @ sk27 @ ssList ) ),
inference(simp,[status(thm)],[79462]) ).
thf(79464,plain,
( ( sk37 != sk2 )
| ( sk2 @ sk27 @ ssList ) ),
inference(pattern_uni,[status(thm)],[79463:[]]) ).
thf(45420,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk20 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[45182,373]) ).
thf(45421,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk20 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) ) ),
inference(simp,[status(thm)],[45420]) ).
thf(45422,plain,
nil @ ( nil @ ( nil @ sk20 ) @ frontsegP ),
inference(pattern_uni,[status(thm)],[45421:[bind(A,$thf( nil @ ( nil @ sk20 ) ))]]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ( ( ( C @ ( B @ lt ) )
& ( B @ ( A @ lt ) ) )
=> ( C @ ( A @ lt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax34) ).
thf(113,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ( ( ( C @ ( B @ lt ) )
& ( B @ ( A @ lt ) ) )
=> ( C @ ( A @ lt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7253,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7015,296]) ).
thf(7254,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7253]) ).
thf(7255,plain,
( ( nil @ ( sk1 @ sk8 @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7254:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(78,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ frontsegP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax42) ).
thf(451,plain,
! [A: $i] :
( ( A @ ssList )
=> ( A @ ( A @ frontsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(154,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( A @ sk6 @ ( A @ sk5 @ leq ) )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[152]) ).
thf(4956,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk6 @ ( A @ sk5 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,154]) ).
thf(4957,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk6 @ ( A @ sk5 @ leq ) ) ),
inference(simp,[status(thm)],[4956]) ).
thf(4958,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk6 @ ( sk2 @ sk5 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[4957:[bind(A,$thf( sk2 ))]]) ).
thf(16556,plain,
( ( ( sk37 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk2 != nil )
| ~ ( sk37 @ ( nil @ segmentP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,1840]) ).
thf(16557,plain,
( ( ( sk37 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk2 != nil )
| ~ ( sk37 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[16556]) ).
thf(16600,plain,
( ( sk37 != sk1 )
| ( sk2 != nil )
| ~ ( sk37 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[16557]) ).
thf(6287,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[6068,296]) ).
thf(6288,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[6287]) ).
thf(6289,plain,
( ( nil @ ( sk1 @ sk9 @ rearsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[6288:[bind(A,$thf( sk1 @ sk9 ))]]) ).
thf(47,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssItem )
=> ( ( ( A @ ( C @ cons ) )
= ( B @ ( D @ cons ) ) )
=> ( ( B = A )
& ( C = D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax19) ).
thf(299,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssItem )
=> ( ( ( A @ ( C @ cons ) )
= ( B @ ( D @ cons ) ) )
=> ( ( B = A )
& ( C = D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(300,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B = A )
| ( ( A @ ( C @ cons ) )
!= ( B @ ( D @ cons ) ) )
| ~ ( D @ ssItem )
| ~ ( C @ ssItem )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) )
& ( ( C = D )
| ( ( A @ ( C @ cons ) )
!= ( B @ ( D @ cons ) ) )
| ~ ( D @ ssItem )
| ~ ( C @ ssItem )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[299]) ).
thf(301,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( C @ cons ) )
!= ( B @ ( D @ cons ) ) )
| ~ ( D @ ssItem )
| ~ ( C @ ssItem )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[300]) ).
thf(303,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ssItem )
| ~ ( C @ ssItem )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( C = D )
| ( ( A @ ( C @ cons ) )
!= ( B @ ( D @ cons ) ) ) ),
inference(lifteq,[status(thm)],[301]) ).
thf(268,plain,
! [A: $i] :
( ( ( A @ sk27 @ ( A @ sk28 @ cons ) )
= A )
| ( nil = A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[265]) ).
thf(271,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ( ( A @ sk27 @ ( A @ sk28 @ cons ) )
= A )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[268]) ).
thf(13834,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[13674,231]) ).
thf(13835,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[13834]) ).
thf(13836,plain,
( ~ ( sk2 @ sk11 @ ( nil @ memberP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[13835:[bind(A,$thf( sk2 @ sk11 ))]]) ).
thf(60000,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk24 @ ssList )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,255]) ).
thf(60001,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk24 @ ssList ) ),
inference(simp,[status(thm)],[60000]) ).
thf(60002,plain,
( ( sk2 @ totalorderP )
| ( sk2 @ sk24 @ ssList ) ),
inference(pattern_uni,[status(thm)],[60001:[bind(A,$thf( sk2 ))]]) ).
thf(58,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( A @ ( C @ ( B @ app ) @ memberP ) )
<=> ( ( A @ ( C @ memberP ) )
| ( A @ ( B @ memberP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax36) ).
thf(367,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( ( A @ ( C @ memberP ) )
| ( A @ ( B @ memberP ) ) )
=> ( A @ ( C @ ( B @ app ) @ memberP ) ) )
& ( ( A @ ( C @ ( B @ app ) @ memberP ) )
=> ( ( A @ ( C @ memberP ) )
| ( A @ ( B @ memberP ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(52784,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 = nil ) ),
inference(paramod_ordered,[status(thm)],[51244,243]) ).
thf(52785,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 = nil ) ),
inference(simp,[status(thm)],[52784]) ).
thf(52786,plain,
( ( nil @ ( sk2 @ sk21 @ segmentP ) )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[52785:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(54245,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ~ ( sk2 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[52652,296]) ).
thf(54246,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ ( sk2 @ ssItem ) ),
inference(simp,[status(thm)],[54245]) ).
thf(54247,plain,
( ( nil @ ( sk2 @ sk21 @ rearsegP ) )
| ~ ( sk2 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[54246:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(96,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( B @ ( A @ memberP ) )
<=> ? [C: $i] :
( ? [D: $i] :
( ( ( D @ ( B @ cons ) @ ( C @ app ) )
= A )
& ( D @ ssList ) )
& ( C @ ssList ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
thf(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)],[96]) ).
thf(27,axiom,
nil @ duplicatefreeP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax72) ).
thf(198,plain,
nil @ duplicatefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(108,plain,
~ ( sk2 @ singletonP ),
inference(cnfConj,[status(thm)],[99]) ).
thf(19022,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) )
| ( sk37 != sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18880,2324]) ).
thf(19023,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) )
| ( sk37 != sk2 ) ),
inference(simp,[status(thm)],[19022]) ).
thf(19054,plain,
( ( sk2 != sk1 )
| ( sk1 != nil )
| ( sk37 != sk2 ) ),
inference(simp,[status(thm)],[19023]) ).
thf(52639,plain,
( ( sk2 != sk2 )
| ( nil != nil )
| ( sk2 @ ( nil @ segmentP ) )
| ( sk2 @ sk21 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[51244,19219]) ).
thf(52640,plain,
( ( sk2 != sk2 )
| ( sk2 @ ( nil @ segmentP ) )
| ( sk2 @ sk21 @ ssList ) ),
inference(simp,[status(thm)],[52639]) ).
thf(52641,plain,
( ( sk2 @ ( nil @ segmentP ) )
| ( sk2 @ sk21 @ ssList ) ),
inference(pattern_uni,[status(thm)],[52640:[]]) ).
thf(123404,plain,
! [A: $i] :
( ( ( sk2 @ hd @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk37 != nil ) ),
inference(paramod_ordered,[status(thm)],[115696,231]) ).
thf(123405,plain,
! [A: $i] :
( ( ( sk2 @ hd @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk37 != nil ) ),
inference(simp,[status(thm)],[123404]) ).
thf(123406,plain,
( ~ ( sk2 @ hd @ ( nil @ memberP ) )
| ( sk37 != nil ) ),
inference(pattern_uni,[status(thm)],[123405:[bind(A,$thf( sk2 @ hd ))]]) ).
thf(2574,plain,
( ( ( nil @ sk5 @ ssItem )
!= ( sk2 @ ssItem ) )
| ( sk2 != nil )
| ~ $true
| ( sk2 != nil )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[1714,651]) ).
thf(2575,plain,
( ( ( nil @ sk5 @ ssItem )
!= ( sk2 @ ssItem ) )
| ( sk2 != nil )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[2574]) ).
thf(2664,plain,
( ( ( nil @ sk5 )
!= sk2 )
| ( sk2 != nil )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[2575]) ).
thf(18842,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5213,190]) ).
thf(18843,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18842]) ).
thf(18844,plain,
( ( sk1 @ sk7 @ ( sk1 @ sk7 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18843:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(58688,plain,
! [A: $i] :
( ( ( sk1 @ sk25 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[58061,243]) ).
thf(58689,plain,
! [A: $i] :
( ( ( sk1 @ sk25 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ totalorderP ) ),
inference(simp,[status(thm)],[58688]) ).
thf(58690,plain,
( ( nil @ ( sk1 @ sk25 @ segmentP ) )
| ( sk1 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[58689:[bind(A,$thf( sk1 @ sk25 ))]]) ).
thf(634,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[391,116]) ).
thf(635,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[634]) ).
thf(636,plain,
nil @ ( sk38 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[635:[bind(A,$thf( sk38 ))]]) ).
thf(6626,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk5 @ ( A @ sk6 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,158]) ).
thf(6627,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk5 @ ( A @ sk6 @ leq ) ) ),
inference(simp,[status(thm)],[6626]) ).
thf(6628,plain,
( ( sk2 @ cyclefreeP )
| ( sk2 @ sk5 @ ( sk2 @ sk6 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[6627:[bind(A,$thf( sk2 ))]]) ).
thf(1174,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[690,210]) ).
thf(1175,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[1174]) ).
thf(1176,plain,
( ~ ( sk1 @ sk5 @ ( sk1 @ sk5 @ neq ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[1175:[bind(A,$thf( sk1 @ sk5 ))]]) ).
thf(62,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( A @ ( C @ ( B @ cons ) @ memberP ) )
<=> ( ( A @ ( C @ memberP ) )
| ( A = B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax37) ).
thf(394,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( ( ( A @ ( C @ memberP ) )
| ( A = B ) )
=> ( A @ ( C @ ( B @ cons ) @ memberP ) ) )
& ( ( A @ ( C @ ( B @ cons ) @ memberP ) )
=> ( ( A @ ( C @ memberP ) )
| ( A = B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(12371,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ~ ( A @ sk10 @ ( A @ sk11 @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,175]) ).
thf(12372,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ strictorderP )
| ~ ( A @ sk10 @ ( A @ sk11 @ lt ) ) ),
inference(simp,[status(thm)],[12371]) ).
thf(12373,plain,
( ( sk1 @ strictorderP )
| ~ ( sk1 @ sk10 @ ( sk1 @ sk11 @ lt ) ) ),
inference(pattern_uni,[status(thm)],[12372:[bind(A,$thf( sk1 ))]]) ).
thf(2301,plain,
! [A: $i] :
( ( A != sk37 )
| ( sk38 != nil )
| ( nil != nil )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(paramod_ordered,[status(thm)],[121,1698]) ).
thf(2302,plain,
! [A: $i] :
( ( A != sk37 )
| ( sk38 != nil )
| ~ ( A @ ( nil @ frontsegP ) )
| ~ ( A @ ssList ) ),
inference(simp,[status(thm)],[2301]) ).
thf(2303,plain,
( ( sk38 != nil )
| ~ ( sk37 @ ( nil @ frontsegP ) )
| ~ ( sk37 @ ssList ) ),
inference(pattern_uni,[status(thm)],[2302:[bind(A,$thf( sk37 ))]]) ).
thf(34952,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[34762,192]) ).
thf(34953,plain,
! [A: $i] :
( ( ( sk2 @ sk16 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[34952]) ).
thf(34954,plain,
( ( nil @ ( sk2 @ sk16 @ cons ) @ totalorderedP )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[34953:[bind(A,$thf( sk2 @ sk16 ))]]) ).
thf(238,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ frontsegP ) )
| ( ( C @ ( B @ app ) )
!= A )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[235]) ).
thf(240,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ frontsegP ) )
| ~ ( C @ ssList )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( C @ ( B @ app ) )
!= A ) ),
inference(lifteq,[status(thm)],[238]) ).
thf(241,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ app ) @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ~ ( B @ ( A @ app ) @ ssList ) ),
inference(simp,[status(thm)],[240]) ).
thf(79502,plain,
( ( sk2 != sk2 )
| ( nil != nil )
| ~ ( nil @ ssItem )
| ( sk2 @ sk27 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[77700,1362]) ).
thf(79503,plain,
( ( sk2 != sk2 )
| ~ ( nil @ ssItem )
| ( sk2 @ sk27 @ ssList ) ),
inference(simp,[status(thm)],[79502]) ).
thf(79504,plain,
( ~ ( nil @ ssItem )
| ( sk2 @ sk27 @ ssList ) ),
inference(pattern_uni,[status(thm)],[79503:[]]) ).
thf(32615,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[390,216]) ).
thf(32616,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[32615]) ).
thf(32617,plain,
~ ( sk37 @ ( sk37 @ lt ) ),
inference(pattern_uni,[status(thm)],[32616:[bind(A,$thf( sk37 ))]]) ).
thf(15931,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A )
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[12881,183]) ).
thf(15932,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[15931]) ).
thf(15933,plain,
( ( ( nil @ ( sk1 @ sk14 @ app ) )
= ( sk1 @ sk14 ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[15932:[bind(A,$thf( sk1 @ sk14 ))]]) ).
thf(92,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( nil
!= ( A @ ( B @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
thf(505,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( nil
!= ( A @ ( B @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(5691,plain,
! [A: $i] :
( ( ( sk2 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5592,116]) ).
thf(5692,plain,
! [A: $i] :
( ( ( sk2 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5691]) ).
thf(5693,plain,
( ( nil @ ( sk2 @ sk6 @ cons ) @ strictorderedP )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5692:[bind(A,$thf( sk2 @ sk6 ))]]) ).
thf(92784,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk37 != nil ) ),
inference(paramod_ordered,[status(thm)],[89124,231]) ).
thf(92785,plain,
! [A: $i] :
( ( ( sk2 @ sk28 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk37 != nil ) ),
inference(simp,[status(thm)],[92784]) ).
thf(92786,plain,
( ~ ( sk2 @ sk28 @ ( nil @ memberP ) )
| ( sk37 != nil ) ),
inference(pattern_uni,[status(thm)],[92785:[bind(A,$thf( sk2 @ sk28 ))]]) ).
thf(60899,plain,
! [A: $i] :
( ( ( sk1 @ sk24 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[60074,373]) ).
thf(60900,plain,
! [A: $i] :
( ( ( sk1 @ sk24 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ totalorderP ) ),
inference(simp,[status(thm)],[60899]) ).
thf(60901,plain,
( ( nil @ ( sk1 @ sk24 @ frontsegP ) )
| ( sk1 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[60900:[bind(A,$thf( sk1 @ sk24 ))]]) ).
thf(74,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( B @ ( A @ rearsegP ) )
<=> ? [C: $i] :
( ( ( B @ ( C @ app ) )
= A )
& ( C @ ssList ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).
thf(431,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ? [C: $i] :
( ( ( B @ ( C @ app ) )
= A )
& ( C @ ssList ) )
=> ( B @ ( A @ rearsegP ) ) )
& ( ( B @ ( A @ rearsegP ) )
=> ? [C: $i] :
( ( ( B @ ( C @ app ) )
= A )
& ( C @ ssList ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(67150,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk23 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,259]) ).
thf(67151,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk23 @ ssItem ) ),
inference(simp,[status(thm)],[67150]) ).
thf(67152,plain,
( ( sk1 @ totalorderP )
| ( sk1 @ sk23 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[67151:[bind(A,$thf( sk1 ))]]) ).
thf(86,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( A @ ( B @ segmentP ) )
& ( B @ ( A @ segmentP ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax54) ).
thf(490,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( A @ ( B @ segmentP ) )
& ( B @ ( A @ segmentP ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(161,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ( ( A @ sk9 @ ( A @ sk6 @ cons ) @ ( A @ sk8 @ ( A @ sk5 @ cons ) @ ( A @ sk7 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[152]) ).
thf(162,plain,
! [A: $i] :
( ( A @ cyclefreeP )
| ~ ( A @ ssList )
| ( ( A @ sk9 @ ( A @ sk6 @ cons ) @ ( A @ sk8 @ ( A @ sk5 @ cons ) @ ( A @ sk7 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[161]) ).
thf(60,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ duplicatefreeP )
<=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( B != C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax13) ).
thf(374,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( B != C ) ) ) ) ) ) )
=> ( A @ duplicatefreeP ) )
& ( ( A @ duplicatefreeP )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( B != C ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(84,axiom,
nil @ equalelemsP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax74) ).
thf(487,plain,
nil @ equalelemsP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(3,axiom,
nil @ strictorderedP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax69) ).
thf(112,plain,
nil @ strictorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(94,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( A @ ( B @ rearsegP ) )
& ( B @ ( A @ rearsegP ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax48) ).
thf(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)],[94]) ).
thf(32564,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[13692,216]) ).
thf(32565,plain,
! [A: $i] :
( ( ( sk1 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[32564]) ).
thf(32566,plain,
( ~ ( sk1 @ sk11 @ ( sk1 @ sk11 @ lt ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[32565:[bind(A,$thf( sk1 @ sk11 ))]]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) )
= ( A @ ( nil @ ( B @ cons ) @ app ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax81) ).
thf(143,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) )
= ( A @ ( nil @ ( B @ cons ) @ app ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(144,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ cons ) )
= ( A @ ( nil @ ( B @ cons ) @ app ) ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[143]) ).
thf(145,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( ( A @ ( B @ cons ) )
= ( A @ ( nil @ ( B @ cons ) @ app ) ) ) ),
inference(lifteq,[status(thm)],[144]) ).
thf(65296,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk37 @ ( nil @ segmentP ) ) )
| ( sk37 != sk1 )
| ( sk2 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18880,16600]) ).
thf(65297,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk37 @ ( nil @ segmentP ) ) )
| ( sk37 != sk1 )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[65296]) ).
thf(65410,plain,
( ( sk37 != sk1 )
| ( sk1 != nil )
| ( sk37 != sk1 )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[65297]) ).
thf(65423,plain,
( ( sk1 != nil )
| ( sk37 != sk1 )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[65410]) ).
thf(6168,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[6044,296]) ).
thf(6169,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[6168]) ).
thf(6170,plain,
( ( nil @ ( sk2 @ sk9 @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[6169:[bind(A,$thf( sk2 @ sk9 ))]]) ).
thf(12041,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[11766,210]) ).
thf(12042,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[12041]) ).
thf(12043,plain,
( ~ ( sk1 @ sk10 @ ( sk1 @ sk10 @ neq ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[12042:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(33875,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[33502,192]) ).
thf(33876,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[33875]) ).
thf(33877,plain,
( ( nil @ ( sk1 @ sk15 @ cons ) @ totalorderedP )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[33876:[bind(A,$thf( sk1 @ sk15 ))]]) ).
thf(19429,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5604,192]) ).
thf(19430,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[19429]) ).
thf(19431,plain,
( ( nil @ ( sk1 @ sk6 @ cons ) @ totalorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[19430:[bind(A,$thf( sk1 @ sk6 ))]]) ).
thf(15999,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[104,183]) ).
thf(16000,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A ) ),
inference(simp,[status(thm)],[15999]) ).
thf(16001,plain,
( ( nil @ ( sk1 @ app ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[16000:[bind(A,$thf( sk1 ))]]) ).
thf(89307,plain,
( ( sk2 != sk2 )
| ( sk38 != sk2 )
| ( nil != nil )
| ( sk2 @ sk28 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[85155,723]) ).
thf(89308,plain,
( ( sk2 != sk2 )
| ( sk38 != sk2 )
| ( sk2 @ sk28 @ ssItem ) ),
inference(simp,[status(thm)],[89307]) ).
thf(89309,plain,
( ( sk38 != sk2 )
| ( sk2 @ sk28 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[89308:[]]) ).
thf(39487,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[38877,373]) ).
thf(39488,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[39487]) ).
thf(39489,plain,
( ( nil @ ( sk1 @ sk18 @ frontsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[39488:[bind(A,$thf( sk1 @ sk18 ))]]) ).
thf(4959,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk6 @ ( A @ sk5 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,154]) ).
thf(4960,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ cyclefreeP )
| ( A @ sk6 @ ( A @ sk5 @ leq ) ) ),
inference(simp,[status(thm)],[4959]) ).
thf(4961,plain,
( ( sk1 @ cyclefreeP )
| ( sk1 @ sk6 @ ( sk1 @ sk5 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[4960:[bind(A,$thf( sk1 ))]]) ).
thf(5077,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,296]) ).
thf(5078,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[5077]) ).
thf(5079,plain,
nil @ ( sk1 @ rearsegP ),
inference(pattern_uni,[status(thm)],[5078:[bind(A,$thf( sk1 ))]]) ).
thf(5292,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5192,243]) ).
thf(5293,plain,
! [A: $i] :
( ( ( sk2 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5292]) ).
thf(5294,plain,
( ( nil @ ( sk2 @ sk7 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5293:[bind(A,$thf( sk2 @ sk7 ))]]) ).
thf(11907,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[11748,231]) ).
thf(11908,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[11907]) ).
thf(11909,plain,
( ~ ( sk2 @ sk10 @ ( nil @ memberP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[11908:[bind(A,$thf( sk2 @ sk10 ))]]) ).
thf(6264,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[6068,243]) ).
thf(6265,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[6264]) ).
thf(6266,plain,
( ( nil @ ( sk1 @ sk9 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[6265:[bind(A,$thf( sk1 @ sk9 ))]]) ).
thf(39148,plain,
! [A: $i] :
( ( ( sk2 @ sk18 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[38830,296]) ).
thf(39149,plain,
! [A: $i] :
( ( ( sk2 @ sk18 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[39148]) ).
thf(39150,plain,
( ( nil @ ( sk2 @ sk18 @ rearsegP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[39149:[bind(A,$thf( sk2 @ sk18 ))]]) ).
thf(135,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ( nil != A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[133]) ).
thf(137,plain,
! [A: $i] :
( ( A @ ( nil @ segmentP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[135]) ).
thf(138,plain,
( ( nil @ ( nil @ segmentP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[137]) ).
thf(1224,plain,
( ( nil @ ( nil @ segmentP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[138,343]) ).
thf(1225,plain,
nil @ ( nil @ segmentP ),
inference(simp,[status(thm)],[1224]) ).
thf(149,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)],[148]) ).
thf(150,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)],[149]) ).
thf(80224,plain,
( ( sk2 != sk2 )
| ( sk38 != sk2 )
| ( nil != nil )
| ( sk2 @ sk27 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[77700,723]) ).
thf(80225,plain,
( ( sk2 != sk2 )
| ( sk38 != sk2 )
| ( sk2 @ sk27 @ ssList ) ),
inference(simp,[status(thm)],[80224]) ).
thf(80226,plain,
( ( sk38 != sk2 )
| ( sk2 @ sk27 @ ssList ) ),
inference(pattern_uni,[status(thm)],[80225:[]]) ).
thf(5397,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5213,243]) ).
thf(5398,plain,
! [A: $i] :
( ( ( sk1 @ sk7 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5397]) ).
thf(5399,plain,
( ( nil @ ( sk1 @ sk7 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5398:[bind(A,$thf( sk1 @ sk7 ))]]) ).
thf(66,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax30) ).
thf(409,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(253,plain,
! [A: $i] :
( ( A @ totalorderP )
| ( ( A @ sk26 @ ( A @ sk23 @ cons ) @ ( A @ sk25 @ ( A @ sk22 @ cons ) @ ( A @ sk24 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[251]) ).
thf(263,plain,
! [A: $i] :
( ( A @ totalorderP )
| ~ ( A @ ssList )
| ( ( A @ sk26 @ ( A @ sk23 @ cons ) @ ( A @ sk25 @ ( A @ sk22 @ cons ) @ ( A @ sk24 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[253]) ).
thf(308,plain,
! [A: $i] :
( ( ( A @ hd )
= ( A @ sk29 ) )
| ( nil = A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[306]) ).
thf(310,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ( ( A @ sk29 )
= ( A @ hd ) )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[308]) ).
thf(32606,plain,
! [A: $i] :
( ( ( sk2 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5592,216]) ).
thf(32607,plain,
! [A: $i] :
( ( ( sk2 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[32606]) ).
thf(32608,plain,
( ~ ( sk2 @ sk6 @ ( sk2 @ sk6 @ lt ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[32607:[bind(A,$thf( sk2 @ sk6 ))]]) ).
thf(440,plain,
! [A: $i] :
( ( ( A @ ( nil @ rearsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) )
& ( ( nil = A )
| ~ ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList ) ) ),
inference(cnf,[status(esa)],[439]) ).
thf(442,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ( nil != A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[440]) ).
thf(444,plain,
! [A: $i] :
( ( A @ ( nil @ rearsegP ) )
| ~ ( A @ ssList )
| ( nil != A ) ),
inference(lifteq,[status(thm)],[442]) ).
thf(445,plain,
( ( nil @ ( nil @ rearsegP ) )
| ~ ( nil @ ssList ) ),
inference(simp,[status(thm)],[444]) ).
thf(1234,plain,
( ( nil @ ( nil @ rearsegP ) )
| ~ $true ),
inference(rewrite,[status(thm)],[445,343]) ).
thf(1235,plain,
nil @ ( nil @ rearsegP ),
inference(simp,[status(thm)],[1234]) ).
thf(118440,plain,
! [A: $i] :
( ( ( sk2 @ hd @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ~ ( nil @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[115187,231]) ).
thf(118441,plain,
! [A: $i] :
( ( ( sk2 @ hd @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[118440]) ).
thf(118442,plain,
( ~ ( sk2 @ hd @ ( nil @ memberP ) )
| ~ ( nil @ ssItem ) ),
inference(pattern_uni,[status(thm)],[118441:[bind(A,$thf( sk2 @ hd ))]]) ).
thf(574,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[390,231]) ).
thf(575,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[574]) ).
thf(576,plain,
~ ( sk37 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[575:[bind(A,$thf( sk37 ))]]) ).
thf(55867,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk37 != nil ) ),
inference(paramod_ordered,[status(thm)],[53144,373]) ).
thf(55868,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk37 != nil ) ),
inference(simp,[status(thm)],[55867]) ).
thf(55869,plain,
( ( nil @ ( sk2 @ sk21 @ frontsegP ) )
| ( sk37 != nil ) ),
inference(pattern_uni,[status(thm)],[55868:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(19590,plain,
( ( ( sk2 @ ( nil @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ( sk38 != sk2 )
| ~ $true
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[19031,2400]) ).
thf(19591,plain,
( ( ( sk2 @ ( nil @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ( sk38 != sk2 )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[19590]) ).
thf(19688,plain,
( ( sk2 != sk1 )
| ( nil != nil )
| ( sk38 != sk2 )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[19591]) ).
thf(19712,plain,
( ( sk2 != sk1 )
| ( sk38 != sk2 )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[19688]) ).
thf(28,axiom,
~ ( nil @ singletonP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).
thf(199,plain,
~ ( nil @ singletonP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(52828,plain,
( ( sk2 != sk2 )
| ( nil != nil )
| ( nil @ ( nil @ neq ) )
| ( sk2 @ sk21 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[51244,1730]) ).
thf(52829,plain,
( ( sk2 != sk2 )
| ( nil @ ( nil @ neq ) )
| ( sk2 @ sk21 @ ssList ) ),
inference(simp,[status(thm)],[52828]) ).
thf(52830,plain,
( ( nil @ ( nil @ neq ) )
| ( sk2 @ sk21 @ ssList ) ),
inference(pattern_uni,[status(thm)],[52829:[]]) ).
thf(11047,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10766,243]) ).
thf(11048,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[11047]) ).
thf(11049,plain,
( ( nil @ ( sk1 @ sk12 @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[11048:[bind(A,$thf( sk1 @ sk12 ))]]) ).
thf(7125,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[6983,296]) ).
thf(7126,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[7125]) ).
thf(7127,plain,
( ( nil @ ( sk2 @ sk8 @ rearsegP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[7126:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(124808,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[390,298]) ).
thf(124809,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ equalelemsP ) ),
inference(simp,[status(thm)],[124808]) ).
thf(124810,plain,
nil @ ( sk37 @ cons ) @ equalelemsP,
inference(pattern_uni,[status(thm)],[124809:[bind(A,$thf( sk37 ))]]) ).
thf(67104,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk23 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,259]) ).
thf(67105,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( A @ totalorderP )
| ( A @ sk23 @ ssItem ) ),
inference(simp,[status(thm)],[67104]) ).
thf(67106,plain,
( ( sk2 @ totalorderP )
| ( sk2 @ sk23 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[67105:[bind(A,$thf( sk2 ))]]) ).
thf(56411,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk38 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[53275,243]) ).
thf(56412,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk38 != sk2 ) ),
inference(simp,[status(thm)],[56411]) ).
thf(56413,plain,
( ( nil @ ( sk2 @ sk21 @ segmentP ) )
| ( sk38 != sk2 ) ),
inference(pattern_uni,[status(thm)],[56412:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(1050,plain,
( ( ( sk37 @ ssItem )
!= ( sk2 @ ssItem ) )
| ~ $true
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[390,1035]) ).
thf(1051,plain,
( ( ( sk37 @ ssItem )
!= ( sk2 @ ssItem ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1050]) ).
thf(1052,plain,
( ( sk37 != sk2 )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1051]) ).
thf(53225,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 = nil ) ),
inference(paramod_ordered,[status(thm)],[51244,373]) ).
thf(53226,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 = nil ) ),
inference(simp,[status(thm)],[53225]) ).
thf(53227,plain,
( ( nil @ ( sk2 @ sk21 @ frontsegP ) )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[53226:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(76,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( nil != A )
=> ( ( B @ ( A @ app ) @ hd )
= ( A @ hd ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax85) ).
thf(446,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( nil != A )
=> ( ( B @ ( A @ app ) @ hd )
= ( A @ hd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(18821,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[6983,190]) ).
thf(18822,plain,
! [A: $i] :
( ( ( sk2 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18821]) ).
thf(18823,plain,
( ( sk2 @ sk8 @ ( sk2 @ sk8 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18822:[bind(A,$thf( sk2 @ sk8 ))]]) ).
thf(5734,plain,
! [A: $i] :
( ( ( sk2 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5592,210]) ).
thf(5735,plain,
! [A: $i] :
( ( ( sk2 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5734]) ).
thf(5736,plain,
( ~ ( sk2 @ sk6 @ ( sk2 @ sk6 @ neq ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5735:[bind(A,$thf( sk2 @ sk6 ))]]) ).
thf(54720,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk37 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[52659,373]) ).
thf(54721,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk37 != sk2 ) ),
inference(simp,[status(thm)],[54720]) ).
thf(54722,plain,
( ( nil @ ( sk2 @ sk21 @ frontsegP ) )
| ( sk37 != sk2 ) ),
inference(pattern_uni,[status(thm)],[54721:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(32603,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[690,216]) ).
thf(32604,plain,
! [A: $i] :
( ( ( sk1 @ sk5 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[32603]) ).
thf(32605,plain,
( ~ ( sk1 @ sk5 @ ( sk1 @ sk5 @ lt ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[32604:[bind(A,$thf( sk1 @ sk5 ))]]) ).
thf(312,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ cons ) @ ( C @ ( A @ cons ) @ frontsegP ) )
| ~ ( D @ ( C @ frontsegP ) )
| ( A != B )
| ~ ( D @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) )
& ( ( D @ ( C @ frontsegP ) )
| ~ ( D @ ( B @ cons ) @ ( C @ ( A @ cons ) @ frontsegP ) )
| ~ ( D @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) )
& ( ( A = B )
| ~ ( D @ ( B @ cons ) @ ( C @ ( A @ cons ) @ frontsegP ) )
| ~ ( D @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ) ),
inference(cnf,[status(esa)],[311]) ).
thf(314,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ frontsegP ) )
| ~ ( D @ ( B @ cons ) @ ( C @ ( A @ cons ) @ frontsegP ) )
| ~ ( D @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[312]) ).
thf(32576,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5604,216]) ).
thf(32577,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[32576]) ).
thf(32578,plain,
( ~ ( sk1 @ sk6 @ ( sk1 @ sk6 @ lt ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[32577:[bind(A,$thf( sk1 @ sk6 ))]]) ).
thf(610,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[391,231]) ).
thf(611,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[610]) ).
thf(612,plain,
~ ( sk38 @ ( nil @ memberP ) ),
inference(pattern_uni,[status(thm)],[611:[bind(A,$thf( sk38 ))]]) ).
thf(33718,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[33476,231]) ).
thf(33719,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[33718]) ).
thf(33720,plain,
( ~ ( sk2 @ sk15 @ ( nil @ memberP ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[33719:[bind(A,$thf( sk2 @ sk15 ))]]) ).
thf(11919,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[11748,210]) ).
thf(11920,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ neq ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[11919]) ).
thf(11921,plain,
( ~ ( sk2 @ sk10 @ ( sk2 @ sk10 @ neq ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[11920:[bind(A,$thf( sk2 @ sk10 ))]]) ).
thf(10330,plain,
! [A: $i] :
( ( ( sk2 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10152,296]) ).
thf(10331,plain,
! [A: $i] :
( ( ( sk2 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[10330]) ).
thf(10332,plain,
( ( nil @ ( sk2 @ sk13 @ rearsegP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10331:[bind(A,$thf( sk2 @ sk13 ))]]) ).
thf(19040,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) )
| ~ ( sk2 @ ssItem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18880,2317]) ).
thf(19041,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk2 @ ( nil @ segmentP ) ) )
| ~ ( sk2 @ ssItem ) ),
inference(simp,[status(thm)],[19040]) ).
thf(19060,plain,
( ( sk2 != sk1 )
| ( sk1 != nil )
| ~ ( sk2 @ ssItem ) ),
inference(simp,[status(thm)],[19041]) ).
thf(38076,plain,
! [A: $i] :
( ( ( sk1 @ sk17 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[37532,296]) ).
thf(38077,plain,
! [A: $i] :
( ( ( sk1 @ sk17 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[38076]) ).
thf(38078,plain,
( ( nil @ ( sk1 @ sk17 @ rearsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[38077:[bind(A,$thf( sk1 @ sk17 ))]]) ).
thf(80213,plain,
( ( sk2 != sk2 )
| ( sk38 != nil )
| ( nil != nil )
| ( sk2 @ sk27 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[77700,1399]) ).
thf(80214,plain,
( ( sk2 != sk2 )
| ( sk38 != nil )
| ( sk2 @ sk27 @ ssList ) ),
inference(simp,[status(thm)],[80213]) ).
thf(80215,plain,
( ( sk38 != nil )
| ( sk2 @ sk27 @ ssList ) ),
inference(pattern_uni,[status(thm)],[80214:[]]) ).
thf(34422,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk38 @ ( nil @ segmentP ) ) )
| ( sk38 != sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18880,34348]) ).
thf(34423,plain,
( ( ( sk1 @ ( sk1 @ segmentP ) )
!= ( sk38 @ ( nil @ segmentP ) ) )
| ( sk38 != sk2 ) ),
inference(simp,[status(thm)],[34422]) ).
thf(34508,plain,
( ( sk38 != sk1 )
| ( sk1 != nil )
| ( sk38 != sk2 ) ),
inference(simp,[status(thm)],[34423]) ).
thf(36242,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[35658,373]) ).
thf(36243,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[36242]) ).
thf(36244,plain,
( ( nil @ ( sk1 @ sk19 @ frontsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[36243:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(2345,plain,
( ( sk2 != sk2 )
| ( nil != nil )
| ( nil @ ( nil @ neq ) )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(paramod_ordered,[status(thm)],[2122,1730]) ).
thf(2346,plain,
( ( sk2 != sk2 )
| ( nil @ ( nil @ neq ) )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(simp,[status(thm)],[2345]) ).
thf(2347,plain,
( ( nil @ ( nil @ neq ) )
| ~ ( sk2 @ ( nil @ segmentP ) ) ),
inference(pattern_uni,[status(thm)],[2346:[]]) ).
thf(203,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ lt ) )
| ~ ( B @ ( A @ gt ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[202]) ).
thf(137042,plain,
( ( ( sk38 @ ssItem )
!= ( sk2 @ ssItem ) )
| ~ ( sk2 @ sk29 @ ( nil @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[391,136224]) ).
thf(137043,plain,
( ( ( sk38 @ ssItem )
!= ( sk2 @ ssItem ) )
| ~ ( sk2 @ sk29 @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[137042]) ).
thf(137201,plain,
( ( sk38 != sk2 )
| ~ ( sk2 @ sk29 @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[137043]) ).
thf(55216,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ~ ( nil @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[52691,296]) ).
thf(55217,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[55216]) ).
thf(55218,plain,
( ( nil @ ( sk2 @ sk21 @ rearsegP ) )
| ~ ( nil @ ssItem ) ),
inference(pattern_uni,[status(thm)],[55217:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(1671,plain,
( ( ( sk38 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk37 != nil )
| ~ ( sk38 @ ( nil @ frontsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,833]) ).
thf(1672,plain,
( ( ( sk38 @ ssList )
!= ( sk1 @ ssList ) )
| ( sk37 != nil )
| ~ ( sk38 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1671]) ).
thf(1674,plain,
( ( sk38 != sk1 )
| ( sk37 != nil )
| ~ ( sk38 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1672]) ).
thf(302,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = A )
| ( ( A @ ( C @ cons ) )
!= ( B @ ( D @ cons ) ) )
| ~ ( D @ ssItem )
| ~ ( C @ ssItem )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[300]) ).
thf(304,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ssItem )
| ~ ( C @ ssItem )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( B = A )
| ( ( A @ ( C @ cons ) )
!= ( B @ ( D @ cons ) ) ) ),
inference(lifteq,[status(thm)],[302]) ).
thf(18873,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[6068,190]) ).
thf(18874,plain,
! [A: $i] :
( ( ( sk1 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[18873]) ).
thf(18875,plain,
( ( sk1 @ sk9 @ ( sk1 @ sk9 @ segmentP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[18874:[bind(A,$thf( sk1 @ sk9 ))]]) ).
thf(60355,plain,
! [A: $i] :
( ( ( sk2 @ sk24 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[60002,243]) ).
thf(60356,plain,
! [A: $i] :
( ( ( sk2 @ sk24 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ totalorderP ) ),
inference(simp,[status(thm)],[60355]) ).
thf(60357,plain,
( ( nil @ ( sk2 @ sk24 @ segmentP ) )
| ( sk2 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[60356:[bind(A,$thf( sk2 @ sk24 ))]]) ).
thf(114,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)],[113]) ).
thf(33660,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[33476,116]) ).
thf(33661,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[33660]) ).
thf(33662,plain,
( ( nil @ ( sk2 @ sk15 @ cons ) @ strictorderedP )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[33661:[bind(A,$thf( sk2 @ sk15 ))]]) ).
thf(12,axiom,
nil @ cyclefreeP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax60) ).
thf(139,plain,
nil @ cyclefreeP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5722,plain,
! [A: $i] :
( ( ( sk2 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5592,231]) ).
thf(5723,plain,
! [A: $i] :
( ( ( sk2 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5722]) ).
thf(5724,plain,
( ~ ( sk2 @ sk6 @ ( nil @ memberP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5723:[bind(A,$thf( sk2 @ sk6 ))]]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( ( A @ ( B @ geq ) )
& ( B @ ( A @ geq ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax87) ).
thf(319,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( ( A @ ( B @ geq ) )
& ( B @ ( A @ geq ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(5798,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5604,116]) ).
thf(5799,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5798]) ).
thf(5800,plain,
( ( nil @ ( sk1 @ sk6 @ cons ) @ strictorderedP )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5799:[bind(A,$thf( sk1 @ sk6 ))]]) ).
thf(33623,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk2 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[33476,216]) ).
thf(33624,plain,
! [A: $i] :
( ( ( sk2 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk2 @ strictorderedP ) ),
inference(simp,[status(thm)],[33623]) ).
thf(33625,plain,
( ~ ( sk2 @ sk15 @ ( sk2 @ sk15 @ lt ) )
| ( sk2 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[33624:[bind(A,$thf( sk2 @ sk15 ))]]) ).
thf(33832,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[33502,216]) ).
thf(33833,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( A @ lt ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[33832]) ).
thf(33834,plain,
( ~ ( sk1 @ sk15 @ ( sk1 @ sk15 @ lt ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[33833:[bind(A,$thf( sk1 @ sk15 ))]]) ).
thf(12029,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[11766,231]) ).
thf(12030,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[12029]) ).
thf(12031,plain,
( ~ ( sk1 @ sk10 @ ( nil @ memberP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[12030:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(18831,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ~ $true
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[12881,190]) ).
thf(18832,plain,
! [A: $i] :
( ( ( sk1 @ sk14 @ ssList )
!= ( A @ ssList ) )
| ( A @ ( A @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[18831]) ).
thf(18833,plain,
( ( sk1 @ sk14 @ ( sk1 @ sk14 @ segmentP ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[18832:[bind(A,$thf( sk1 @ sk14 ))]]) ).
thf(278,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( B @ hd @ ( A @ lt ) )
| ~ ( B @ strictorderedP )
| ( nil = B )
| ~ ( B @ ssList )
| ~ ( A @ ssItem ) ),
inference(cnfConj,[status(thm)],[276]) ).
thf(287,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ strictorderedP )
| ~ ( B @ hd @ ( A @ lt ) )
| ~ ( B @ strictorderedP )
| ~ ( B @ ssList )
| ~ ( A @ ssItem )
| ( nil = B ) ),
inference(lifteq,[status(thm)],[278]) ).
thf(31864,plain,
( ( ( nil @ ( sk1 @ app ) )
!= ( sk2 @ ( nil @ app ) ) )
| ( sk2 = sk1 ) ),
inference(paramod_ordered,[status(thm)],[31571,16001]) ).
thf(31912,plain,
( ( sk2 != nil )
| ( sk1 != nil )
| ( sk2 = sk1 ) ),
inference(simp,[status(thm)],[31864]) ).
thf(257,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ leq ) )
| ( C @ ( B @ leq ) )
| ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
!= A )
| ~ ( F @ ssList )
| ~ ( E @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssItem )
| ~ ( B @ ssItem )
| ~ ( A @ totalorderP )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[251]) ).
thf(261,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ leq ) )
| ( C @ ( B @ leq ) )
| ~ ( F @ ssList )
| ~ ( E @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssItem )
| ~ ( B @ ssItem )
| ~ ( A @ totalorderP )
| ~ ( A @ ssList )
| ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
!= A ) ),
inference(lifteq,[status(thm)],[257]) ).
thf(262,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) )
| ~ ( E @ ssList )
| ~ ( D @ ssList )
| ~ ( C @ ssList )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ~ ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) @ totalorderP )
| ~ ( E @ ( B @ cons ) @ ( D @ ( A @ cons ) @ ( C @ app ) @ app ) @ ssList ) ),
inference(simp,[status(thm)],[261]) ).
thf(52992,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 = nil ) ),
inference(paramod_ordered,[status(thm)],[51244,296]) ).
thf(52993,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 = nil ) ),
inference(simp,[status(thm)],[52992]) ).
thf(52994,plain,
( ( nil @ ( sk2 @ sk21 @ rearsegP ) )
| ( sk2 = nil ) ),
inference(pattern_uni,[status(thm)],[52993:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(54146,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ~ ( sk2 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[52652,243]) ).
thf(54147,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ ( sk2 @ ssItem ) ),
inference(simp,[status(thm)],[54146]) ).
thf(54148,plain,
( ( nil @ ( sk2 @ sk21 @ segmentP ) )
| ~ ( sk2 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[54147:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(117807,plain,
( ( ( sk38 @ ssItem )
!= ( sk2 @ ssItem ) )
| ~ ( sk2 @ hd @ ( nil @ memberP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[391,117083]) ).
thf(117808,plain,
( ( ( sk38 @ ssItem )
!= ( sk2 @ ssItem ) )
| ~ ( sk2 @ hd @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[117807]) ).
thf(117935,plain,
( ( sk38 != sk2 )
| ~ ( sk2 @ hd @ ( nil @ memberP ) ) ),
inference(simp,[status(thm)],[117808]) ).
thf(60447,plain,
! [A: $i] :
( ( ( sk2 @ sk24 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk2 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[60002,296]) ).
thf(60448,plain,
! [A: $i] :
( ( ( sk2 @ sk24 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk2 @ totalorderP ) ),
inference(simp,[status(thm)],[60447]) ).
thf(60449,plain,
( ( nil @ ( sk2 @ sk24 @ rearsegP ) )
| ( sk2 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[60448:[bind(A,$thf( sk2 @ sk24 ))]]) ).
thf(65698,plain,
( ( sk2 != sk2 )
| ( nil != nil )
| ~ ( nil @ ssItem )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[65462,1362]) ).
thf(65699,plain,
( ( sk2 != sk2 )
| ~ ( nil @ ssItem )
| ( sk2 @ tl @ ssList ) ),
inference(simp,[status(thm)],[65698]) ).
thf(65700,plain,
( ~ ( nil @ ssItem )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[65699:[]]) ).
thf(78423,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk27 @ ssList )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[104,269]) ).
thf(78424,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk27 @ ssList )
| ( nil = A ) ),
inference(simp,[status(thm)],[78423]) ).
thf(78425,plain,
( ( sk1 @ sk27 @ ssList )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[78424:[bind(A,$thf( sk1 ))]]) ).
thf(85861,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk28 @ ssItem )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[104,270]) ).
thf(85862,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk28 @ ssItem )
| ( nil = A ) ),
inference(simp,[status(thm)],[85861]) ).
thf(85863,plain,
( ( sk1 @ sk28 @ ssItem )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[85862:[bind(A,$thf( sk1 ))]]) ).
thf(132838,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk29 @ ssItem )
| ~ $true
| ( nil = A ) ),
inference(paramod_ordered,[status(thm)],[104,309]) ).
thf(132839,plain,
! [A: $i] :
( ( ( sk1 @ ssList )
!= ( A @ ssList ) )
| ( A @ sk29 @ ssItem )
| ( nil = A ) ),
inference(simp,[status(thm)],[132838]) ).
thf(132840,plain,
( ( sk1 @ sk29 @ ssItem )
| ( sk1 = nil ) ),
inference(pattern_uni,[status(thm)],[132839:[bind(A,$thf( sk1 ))]]) ).
thf(56579,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk38 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[53275,373]) ).
thf(56580,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk38 != sk2 ) ),
inference(simp,[status(thm)],[56579]) ).
thf(56581,plain,
( ( nil @ ( sk2 @ sk21 @ frontsegP ) )
| ( sk38 != sk2 ) ),
inference(pattern_uni,[status(thm)],[56580:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(194,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ lt ) )
| ( A = B )
| ~ ( B @ ( A @ leq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem ) ),
inference(cnf,[status(esa)],[193]) ).
thf(195,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ lt ) )
| ~ ( B @ ( A @ leq ) )
| ~ ( B @ ssItem )
| ~ ( A @ ssItem )
| ( A = B ) ),
inference(lifteq,[status(thm)],[194]) ).
thf(36184,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[35658,296]) ).
thf(36185,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[36184]) ).
thf(36186,plain,
( ( nil @ ( sk1 @ sk19 @ rearsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[36185:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(5833,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[5604,231]) ).
thf(5834,plain,
! [A: $i] :
( ( ( sk1 @ sk6 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[5833]) ).
thf(5835,plain,
( ~ ( sk1 @ sk6 @ ( nil @ memberP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[5834:[bind(A,$thf( sk1 @ sk6 ))]]) ).
thf(83,axiom,
! [A: $i] :
( ( A @ ssList )
=> ( ( A @ totalorderedP )
<=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( C @ ( B @ leq ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11) ).
thf(474,plain,
! [A: $i] :
( ( A @ ssList )
=> ( ( ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( C @ ( B @ leq ) ) ) ) ) ) ) )
=> ( A @ totalorderedP ) )
& ( ( A @ totalorderedP )
=> ! [B: $i] :
( ( B @ ssItem )
=> ! [C: $i] :
( ( C @ ssItem )
=> ! [D: $i] :
( ( D @ ssList )
=> ! [E: $i] :
( ( E @ ssList )
=> ! [F: $i] :
( ( F @ ssList )
=> ( ( ( F @ ( C @ cons ) @ ( E @ ( B @ cons ) @ ( D @ app ) @ app ) )
= A )
=> ( C @ ( B @ leq ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(19653,plain,
( ( ( sk37 @ ( nil @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ( sk37 != sk2 )
| ~ $true
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[19031,17352]) ).
thf(19654,plain,
( ( ( sk37 @ ( nil @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ( sk37 != sk2 )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[19653]) ).
thf(19699,plain,
( ( sk37 != sk1 )
| ( nil != nil )
| ( sk37 != sk2 )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[19654]) ).
thf(19720,plain,
( ( sk37 != sk1 )
| ( sk37 != sk2 )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[19699]) ).
thf(2588,plain,
( ( ( nil @ sk5 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk2 != nil )
| ~ $true
| ( sk2 != nil )
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[1714,1362]) ).
thf(2589,plain,
( ( ( nil @ sk5 @ ssItem )
!= ( nil @ ssItem ) )
| ( sk2 != nil )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[2588]) ).
thf(2668,plain,
( ( ( nil @ sk5 )
!= nil )
| ( sk2 != nil )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[2589]) ).
thf(58788,plain,
! [A: $i] :
( ( ( sk1 @ sk25 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[58061,296]) ).
thf(58789,plain,
! [A: $i] :
( ( ( sk1 @ sk25 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ totalorderP ) ),
inference(simp,[status(thm)],[58788]) ).
thf(58790,plain,
( ( nil @ ( sk1 @ sk25 @ rearsegP ) )
| ( sk1 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[58789:[bind(A,$thf( sk1 @ sk25 ))]]) ).
thf(69,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ cyclefreeP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax59) ).
thf(415,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( nil @ ( A @ cons ) @ cyclefreeP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(60539,plain,
! [A: $i] :
( ( ( sk2 @ sk24 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[60002,373]) ).
thf(60540,plain,
! [A: $i] :
( ( ( sk2 @ sk24 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ totalorderP ) ),
inference(simp,[status(thm)],[60539]) ).
thf(60541,plain,
( ( nil @ ( sk2 @ sk24 @ frontsegP ) )
| ( sk2 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[60540:[bind(A,$thf( sk2 @ sk24 ))]]) ).
thf(65666,plain,
( ( sk2 != sk2 )
| ( sk37 != sk2 )
| ( nil != nil )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[65462,724]) ).
thf(65667,plain,
( ( sk2 != sk2 )
| ( sk37 != sk2 )
| ( sk2 @ tl @ ssList ) ),
inference(simp,[status(thm)],[65666]) ).
thf(65668,plain,
( ( sk37 != sk2 )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[65667:[]]) ).
thf(237,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk20 ) @ ( B @ app ) )
= A )
| ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[235]) ).
thf(239,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ frontsegP ) )
| ~ ( B @ ssList )
| ~ ( A @ ssList )
| ( ( A @ ( B @ sk20 ) @ ( B @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[237]) ).
thf(293,plain,
! [A: $i] :
( ( A @ tl @ ssList )
| ( nil = A )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[292]) ).
thf(294,plain,
! [A: $i] :
( ( A @ tl @ ssList )
| ~ ( A @ ssList )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[293]) ).
thf(8,axiom,
nil @ totalorderedP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax66) ).
thf(126,plain,
nil @ totalorderedP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(134159,plain,
( ( sk2 != sk2 )
| ( nil != nil )
| ~ ( nil @ ssItem )
| ( sk2 @ sk29 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[131983,1362]) ).
thf(134160,plain,
( ( sk2 != sk2 )
| ~ ( nil @ ssItem )
| ( sk2 @ sk29 @ ssItem ) ),
inference(simp,[status(thm)],[134159]) ).
thf(134161,plain,
( ~ ( nil @ ssItem )
| ( sk2 @ sk29 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[134160:[]]) ).
thf(137761,plain,
! [A: $i] :
( ( ( sk2 @ sk29 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ $true
| ~ ( nil @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[134161,231]) ).
thf(137762,plain,
! [A: $i] :
( ( ( sk2 @ sk29 @ ssItem )
!= ( A @ ssItem ) )
| ~ ( A @ ( nil @ memberP ) )
| ~ ( nil @ ssItem ) ),
inference(simp,[status(thm)],[137761]) ).
thf(137763,plain,
( ~ ( sk2 @ sk29 @ ( nil @ memberP ) )
| ~ ( nil @ ssItem ) ),
inference(pattern_uni,[status(thm)],[137762:[bind(A,$thf( sk2 @ sk29 ))]]) ).
thf(10894,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10731,243]) ).
thf(10895,plain,
! [A: $i] :
( ( ( sk2 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[10894]) ).
thf(10896,plain,
( ( nil @ ( sk2 @ sk12 @ segmentP ) )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[10895:[bind(A,$thf( sk2 @ sk12 ))]]) ).
thf(19564,plain,
( ( ( sk2 @ ( nil @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ~ ( nil @ ssItem )
| ~ $true
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[19031,2331]) ).
thf(19565,plain,
( ( ( sk2 @ ( nil @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ~ ( nil @ ssItem )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[19564]) ).
thf(19676,plain,
( ( sk2 != sk1 )
| ( nil != nil )
| ~ ( nil @ ssItem )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[19565]) ).
thf(19706,plain,
( ( sk2 != sk1 )
| ~ ( nil @ ssItem )
| ~ ( sk1 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[19676]) ).
thf(39426,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[38877,296]) ).
thf(39427,plain,
! [A: $i] :
( ( ( sk1 @ sk18 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[39426]) ).
thf(39428,plain,
( ( nil @ ( sk1 @ sk18 @ rearsegP ) )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[39427:[bind(A,$thf( sk1 @ sk18 ))]]) ).
thf(80033,plain,
( ( sk2 != sk2 )
| ( sk37 != nil )
| ( nil != nil )
| ( sk2 @ sk27 @ ssList ) ),
inference(paramod_ordered,[status(thm)],[77700,1400]) ).
thf(80034,plain,
( ( sk2 != sk2 )
| ( sk37 != nil )
| ( sk2 @ sk27 @ ssList ) ),
inference(simp,[status(thm)],[80033]) ).
thf(80035,plain,
( ( sk37 != nil )
| ( sk2 @ sk27 @ ssList ) ),
inference(pattern_uni,[status(thm)],[80034:[]]) ).
thf(200,plain,
~ ( nil @ singletonP ),
inference(polarity_switch,[status(thm)],[199]) ).
thf(170,plain,
! [A: $i] :
( ( A @ strictorderP )
| ( ( A @ sk14 @ ( A @ sk11 @ cons ) @ ( A @ sk13 @ ( A @ sk10 @ cons ) @ ( A @ sk12 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[168]) ).
thf(178,plain,
! [A: $i] :
( ( A @ strictorderP )
| ~ ( A @ ssList )
| ( ( A @ sk14 @ ( A @ sk11 @ cons ) @ ( A @ sk13 @ ( A @ sk10 @ cons ) @ ( A @ sk12 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[170]) ).
thf(90,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ! [C: $i] :
( ( C @ ssList )
=> ( ( B @ ( A @ rearsegP ) )
=> ( B @ ( A @ ( C @ app ) @ rearsegP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax50) ).
thf(501,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(72,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax31) ).
thf(427,plain,
! [A: $i] :
( ( A @ ssItem )
=> ( A @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(6153,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ~ $true
| ( sk2 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[6044,243]) ).
thf(6154,plain,
! [A: $i] :
( ( ( sk2 @ sk9 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(simp,[status(thm)],[6153]) ).
thf(6155,plain,
( ( nil @ ( sk2 @ sk9 @ segmentP ) )
| ( sk2 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[6154:[bind(A,$thf( sk2 @ sk9 ))]]) ).
thf(15968,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A )
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10766,183]) ).
thf(15969,plain,
! [A: $i] :
( ( ( sk1 @ sk12 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[15968]) ).
thf(15970,plain,
( ( ( nil @ ( sk1 @ sk12 @ app ) )
= ( sk1 @ sk12 ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[15969:[bind(A,$thf( sk1 @ sk12 ))]]) ).
thf(1348,plain,
( ( ( sk38 @ ssItem )
!= ( nil @ ssItem ) )
| ~ $true
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(paramod_ordered,[status(thm)],[391,1271]) ).
thf(1349,plain,
( ( ( sk38 @ ssItem )
!= ( nil @ ssItem ) )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1348]) ).
thf(1357,plain,
( ( sk38 != nil )
| ~ ( sk2 @ ( nil @ frontsegP ) ) ),
inference(simp,[status(thm)],[1349]) ).
thf(54346,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ~ ( sk2 @ ssItem ) ),
inference(paramod_ordered,[status(thm)],[52652,373]) ).
thf(54347,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ ( sk2 @ ssItem ) ),
inference(simp,[status(thm)],[54346]) ).
thf(54348,plain,
( ( nil @ ( sk2 @ sk21 @ frontsegP ) )
| ~ ( sk2 @ ssItem ) ),
inference(pattern_uni,[status(thm)],[54347:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(8728,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk1 @ cyclefreeP ) ),
inference(paramod_ordered,[status(thm)],[7015,373]) ).
thf(8729,plain,
! [A: $i] :
( ( ( sk1 @ sk8 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(simp,[status(thm)],[8728]) ).
thf(8730,plain,
( ( nil @ ( sk1 @ sk8 @ frontsegP ) )
| ( sk1 @ cyclefreeP ) ),
inference(pattern_uni,[status(thm)],[8729:[bind(A,$thf( sk1 @ sk8 ))]]) ).
thf(19450,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[391,192]) ).
thf(19451,plain,
! [A: $i] :
( ( ( sk38 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ totalorderedP ) ),
inference(simp,[status(thm)],[19450]) ).
thf(19452,plain,
nil @ ( sk38 @ cons ) @ totalorderedP,
inference(pattern_uni,[status(thm)],[19451:[bind(A,$thf( sk38 ))]]) ).
thf(130,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ cons ) @ hd )
= B )
| ~ ( B @ ssItem )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[129]) ).
thf(131,plain,
! [B: $i,A: $i] :
( ~ ( B @ ssItem )
| ~ ( A @ ssList )
| ( ( A @ ( B @ cons ) @ hd )
= B ) ),
inference(lifteq,[status(thm)],[130]) ).
thf(13800,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[13674,116]) ).
thf(13801,plain,
! [A: $i] :
( ( ( sk2 @ sk11 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[13800]) ).
thf(13802,plain,
( ( nil @ ( sk2 @ sk11 @ cons ) @ strictorderedP )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[13801:[bind(A,$thf( sk2 @ sk11 ))]]) ).
thf(11873,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk2 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[11748,116]) ).
thf(11874,plain,
! [A: $i] :
( ( ( sk2 @ sk10 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk2 @ strictorderP ) ),
inference(simp,[status(thm)],[11873]) ).
thf(11875,plain,
( ( nil @ ( sk2 @ sk10 @ cons ) @ strictorderedP )
| ( sk2 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[11874:[bind(A,$thf( sk2 @ sk10 ))]]) ).
thf(33865,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true
| ( sk1 @ strictorderedP ) ),
inference(paramod_ordered,[status(thm)],[33502,116]) ).
thf(33866,plain,
! [A: $i] :
( ( ( sk1 @ sk15 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ( sk1 @ strictorderedP ) ),
inference(simp,[status(thm)],[33865]) ).
thf(33867,plain,
( ( nil @ ( sk1 @ sk15 @ cons ) @ strictorderedP )
| ( sk1 @ strictorderedP ) ),
inference(pattern_uni,[status(thm)],[33866:[bind(A,$thf( sk1 @ sk15 ))]]) ).
thf(51,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( B @ ( A @ neq ) )
<=> ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
thf(322,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssList )
=> ( ( ( A != B )
=> ( B @ ( A @ neq ) ) )
& ( ( B @ ( A @ neq ) )
=> ( A != B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(58508,plain,
! [A: $i] :
( ( ( sk2 @ sk25 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ~ $true
| ( sk2 @ totalorderP ) ),
inference(paramod_ordered,[status(thm)],[57992,373]) ).
thf(58509,plain,
! [A: $i] :
( ( ( sk2 @ sk25 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ frontsegP ) )
| ( sk2 @ totalorderP ) ),
inference(simp,[status(thm)],[58508]) ).
thf(58510,plain,
( ( nil @ ( sk2 @ sk25 @ frontsegP ) )
| ( sk2 @ totalorderP ) ),
inference(pattern_uni,[status(thm)],[58509:[bind(A,$thf( sk2 @ sk25 ))]]) ).
thf(81,axiom,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) @ tl )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax25) ).
thf(469,plain,
! [A: $i] :
( ( A @ ssList )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( A @ ( B @ cons ) @ tl )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(66197,plain,
( ( sk2 != sk2 )
| ( sk37 != nil )
| ( nil != nil )
| ( sk2 @ tl @ ssList ) ),
inference(paramod_ordered,[status(thm)],[65462,1400]) ).
thf(66198,plain,
( ( sk2 != sk2 )
| ( sk37 != nil )
| ( sk2 @ tl @ ssList ) ),
inference(simp,[status(thm)],[66197]) ).
thf(66199,plain,
( ( sk37 != nil )
| ( sk2 @ tl @ ssList ) ),
inference(pattern_uni,[status(thm)],[66198:[]]) ).
thf(56145,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true
| ( sk38 != nil ) ),
inference(paramod_ordered,[status(thm)],[53270,296]) ).
thf(56146,plain,
! [A: $i] :
( ( ( sk2 @ sk21 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ( sk38 != nil ) ),
inference(simp,[status(thm)],[56145]) ).
thf(56147,plain,
( ( nil @ ( sk2 @ sk21 @ rearsegP ) )
| ( sk38 != nil ) ),
inference(pattern_uni,[status(thm)],[56146:[bind(A,$thf( sk2 @ sk21 ))]]) ).
thf(105,plain,
sk1 = sk3,
inference(cnfConj,[status(thm)],[99]) ).
thf(111,plain,
sk3 = sk1,
inference(lifteq,[status(thm)],[105]) ).
thf(18955,plain,
( ( ( sk2 @ ( sk2 @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ~ $true
| ( sk1 = nil ) ),
inference(paramod_ordered,[status(thm)],[18864,2196]) ).
thf(18956,plain,
( ( ( sk2 @ ( sk2 @ segmentP ) )
!= ( sk1 @ ( nil @ segmentP ) ) )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[18955]) ).
thf(18983,plain,
( ( sk2 != sk1 )
| ( sk2 != nil )
| ( sk1 = nil ) ),
inference(simp,[status(thm)],[18956]) ).
thf(219,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ( ( A @ sk19 @ ( A @ sk16 @ cons ) @ ( A @ sk18 @ ( A @ sk15 @ cons ) @ ( A @ sk17 @ app ) @ app ) )
= A )
| ~ ( A @ ssList ) ),
inference(cnfConj,[status(thm)],[218]) ).
thf(227,plain,
! [A: $i] :
( ( A @ strictorderedP )
| ~ ( A @ ssList )
| ( ( A @ sk19 @ ( A @ sk16 @ cons ) @ ( A @ sk18 @ ( A @ sk15 @ cons ) @ ( A @ sk17 @ app ) @ app ) )
= A ) ),
inference(lifteq,[status(thm)],[219]) ).
thf(637,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[390,116]) ).
thf(638,plain,
! [A: $i] :
( ( ( sk37 @ ssItem )
!= ( A @ ssItem ) )
| ( nil @ ( A @ cons ) @ strictorderedP ) ),
inference(simp,[status(thm)],[637]) ).
thf(639,plain,
nil @ ( sk37 @ cons ) @ strictorderedP,
inference(pattern_uni,[status(thm)],[638:[bind(A,$thf( sk37 ))]]) ).
thf(88,axiom,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax29) ).
thf(496,plain,
! [A: $i] :
( ( A @ ssItem )
=> ! [B: $i] :
( ( B @ ssItem )
=> ( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(45351,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk20 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[45182,296]) ).
thf(45352,plain,
! [A: $i] :
( ( ( nil @ ( nil @ sk20 ) @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[45351]) ).
thf(45353,plain,
nil @ ( nil @ ( nil @ sk20 ) @ rearsegP ),
inference(pattern_uni,[status(thm)],[45352:[bind(A,$thf( nil @ ( nil @ sk20 ) ))]]) ).
thf(16015,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ( ( nil @ ( A @ app ) )
= A )
| ( sk1 @ strictorderP ) ),
inference(paramod_ordered,[status(thm)],[10187,183]) ).
thf(16016,plain,
! [A: $i] :
( ( ( sk1 @ sk13 @ ssList )
!= ( A @ ssList ) )
| ( ( nil @ ( A @ app ) )
= A )
| ( sk1 @ strictorderP ) ),
inference(simp,[status(thm)],[16015]) ).
thf(16017,plain,
( ( ( nil @ ( sk1 @ sk13 @ app ) )
= ( sk1 @ sk13 ) )
| ( sk1 @ strictorderP ) ),
inference(pattern_uni,[status(thm)],[16016:[bind(A,$thf( sk1 @ sk13 ))]]) ).
thf(163462,plain,
$false,
inference(e,[status(thm)],[39365,45273,347,249,1840,8784,234,2331,51244,365,10373,2309,115,217,55700,449,45419,32599,269,56502,63894,58333,66360,60721,8082,19462,1401,18810,11080,18861,32614,142,13095,1164,33929,472,19468,37803,19059,5192,6640,13692,56226,538,153,117083,185,93089,37865,13970,19219,417,288,77700,5269,19419,174,404,2400,93439,651,45416,12843,724,115696,53926,4524,5306,184,136224,32623,8787,54554,124766,1992,196,157,372,60074,125,344,72540,19063,15943,19710,19052,13045,5604,284,136697,55317,289,65661,55117,10527,2403,1087,189,5076,19446,1362,216,36129,164,4173,37532,34948,2122,18889,19056,1283,6983,10309,34348,2324,1714,211,53509,11748,121,39215,7015,147,8774,221,58425,453,32587,4519,10459,63969,1119,132,19714,37488,411,33668,115187,116,243,8751,34762,233,248,117,201,220,1311,2382,8712,1730,35006,31596,292,115905,942,11993,439,13848,270,529,56057,13019,15979,79457,19437,117495,18820,260,160,55557,561,297,13218,429,275,165,11766,60821,7229,18864,192,630,229,252,197,65462,19058,6445,53270,11249,12881,85155,35917,69210,15901,456,52652,224,38830,10490,55790,329,1178,18799,493,15915,134695,38136,1259,156,15896,38877,188,388,499,519,1592,54643,10731,1121,10152,356,89124,5847,1028,1361,113980,33476,2196,15912,2317,212,109,256,53512,488,134924,124,225,91653,33740,193,5213,31982,1016,13184,10919,393,647,66365,35153,19471,654,45411,173,129,19474,19708,503,19459,244,134089,633,205,508,311,69256,541,1054,18867,1035,5419,12361,11120,128,343,2235,298,412,1698,15976,7459,166,38015,35617,264,8771,58867,13264,425,35215,148,180,296,8718,176,53144,35979,291,13920,39095,53699,15998,402,191,134937,18836,10963,1403,35868,123780,18839,35163,204,34788,259,641,391,18880,1271,4112,92440,15936,236,11237,32584,19057,1107,15946,7109,919,37748,13958,181,406,172,274,230,1144,79464,45422,113,7255,451,4958,16600,6289,10766,98,303,271,13836,115892,33502,60002,367,535,103,52786,140,91319,54247,520,6044,155,198,108,19054,52641,123406,1022,2664,18844,88607,58690,636,6628,1176,394,12373,299,226,2303,34954,241,167,79504,32617,15933,505,5693,92786,60901,431,67152,490,162,374,255,487,112,516,32566,145,31571,65423,6170,12043,33877,19431,16001,690,115126,89309,39489,5592,4961,5079,5294,11909,295,6266,39150,1225,150,80226,1400,5399,409,52691,263,310,32608,1235,127,118442,576,55869,19712,199,52659,177,52830,11049,7127,124810,67106,56413,35658,1052,53227,175,446,143,18823,89296,5736,154,54722,32605,45182,13674,314,19031,32578,612,33720,11921,10332,17352,19060,38078,80215,34508,6068,36244,2347,131983,104,250,231,203,137201,55218,1674,304,258,158,18875,390,186,60357,114,33662,171,139,5724,319,5800,33625,18960,115117,684,33834,12031,272,134098,18833,214,287,31912,151,262,146,52994,57992,54148,117935,60449,190,183,373,65700,78425,833,85863,132840,56581,210,195,36186,5835,474,58061,19720,2668,58790,415,305,60541,55526,107,65668,239,242,294,126,136,137763,10896,19706,39428,80035,644,200,178,1399,501,51843,427,6155,15970,1357,54348,723,8730,19452,131,13802,11875,33867,113170,322,58510,469,10187,66199,56147,309,215,222,88616,111,18983,254,227,639,88663,53275,496,45353,16017,232,134161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC149+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.18/10.45 % Computer : n013.cluster.edu
% 0.18/10.45 % Model : x86_64 x86_64
% 0.18/10.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/10.45 % Memory : 8046.5625MB
% 0.18/10.45 % OS : Linux 6.8.0-71-generic
% 0.18/10.45 % CPULimit : 300
% 0.18/10.45 % WCLimit : 300
% 0.18/10.45 % DateTime : Sat Sep 26 12:20:41 UTC 2026
% 0.18/10.45 % CPUTime :
% 0.18/10.46 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.27/11.26 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.21/11.67 % [INFO] Parsing done (412ms).
% 2.21/11.69 % [INFO] Running in sequential loop mode.
% 3.56/12.19 % [INFO] eprover registered as external prover.
% 3.65/12.20 % [INFO] Scanning for conjecture ...
% 3.86/12.39 % [INFO] Found a conjecture (or negated_conjecture) and 95 axioms. Running axiom selection ...
% 4.30/12.55 % [INFO] Axiom selection finished. Selected 95 axioms (removed 0 axioms).
% 4.83/12.74 % [INFO] Problem is first-order (TPTP FOF).
% 4.83/12.78 % [INFO] Type checking passed.
% 4.83/12.78 % [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 ...
% 257.31/83.11 % External prover 'e' found a proof!
% 257.31/83.11 % [INFO] Killing All external provers ...
% 257.31/83.11 % Time passed: 72460ms (effective reasoning time: 71412ms)
% 257.31/83.11 % 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)>
% 257.31/83.12 % 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
% 257.31/83.12 % No. of inferences in proof: 1609
% 257.31/83.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 72460 ms resp. 71412 ms w/o parsing
% 255.51/83.69 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 255.86/83.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------