%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP076^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:40 AM UTC 2026
% Result : Theorem 206.09s 52.71s
% Output : Refutation 208.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 126
% Syntax : Number of formulae : 1076 ( 504 unt; 0 typ; 60 def)
% Number of atoms : 3046 (1326 equ; 6 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 9076 (1195 ~; 818 |; 177 &;6689 @)
% ( 0 <=>; 197 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 202 ( 202 >; 0 *; 0 +; 0 <<)
% Number of symbols : 83 ( 79 usr; 48 con; 0-4 aty)
% Number of variables : 2007 ( 122 ^;1697 !; 128 ?;2007 :)
% ( 0 !>; 0 ?*; 0 @-; 60 @+)
% Comments :
%------------------------------------------------------------------------------
thf(set_HF_Mirabelle_hf_type,type,
set_HF_Mirabelle_hf: $tType ).
thf(hF_Mirabelle_hf_type,type,
hF_Mirabelle_hf: $tType ).
thf(set_nat_type,type,
set_nat: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(zero_z189798548lle_hf_decl,type,
zero_z189798548lle_hf: hF_Mirabelle_hf ).
thf(hF_Mir818139703ollect_decl,type,
hF_Mir818139703ollect: ( hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(hF_Mirabelle_HUnion_decl,type,
hF_Mirabelle_HUnion: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(hF_Mir1248913145eplace_decl,type,
hF_Mir1248913145eplace: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).
thf(hF_Mirabelle_RepFun_decl,type,
hF_Mirabelle_RepFun: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf ) > hF_Mirabelle_hf ).
thf(hF_Mirabelle_Replace_decl,type,
hF_Mirabelle_Replace: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).
thf(hF_Mirabelle_hfst_decl,type,
hF_Mirabelle_hfst: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(hF_Mir199975595nction_decl,type,
hF_Mir199975595nction: hF_Mirabelle_hf > $o ).
thf(hF_Mirabelle_hmem_decl,type,
hF_Mirabelle_hmem: hF_Mirabelle_hf > hF_Mirabelle_hf > $o ).
thf(hF_Mirabelle_hpair_decl,type,
hF_Mirabelle_hpair: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(hF_Mir434065167lation_decl,type,
hF_Mir434065167lation: hF_Mirabelle_hf > $o ).
thf(hF_Mir1653039215strict_decl,type,
hF_Mir1653039215strict: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(hF_Mirabelle_hsnd_decl,type,
hF_Mirabelle_hsnd: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(hF_Mir137170979_hpair_decl,type,
hF_Mir137170979_hpair: hF_Mirabelle_hf > $o ).
thf(sup_su638957495lle_hf_decl,type,
sup_su638957495lle_hf: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(r_decl,type,
r: hF_Mirabelle_hf ).
thf(x_decl,type,
x: hF_Mirabelle_hf ).
thf(sk1_decl,type,
sk1: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk2_decl,type,
sk2: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk3_decl,type,
sk3: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk4_decl,type,
sk4: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk5_decl,type,
sk5: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk6_decl,type,
sk6: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk7_decl,type,
sk7: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk8_decl,type,
sk8: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk9_decl,type,
sk9: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk10_decl,type,
sk10: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk11_decl,type,
sk11: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk12_decl,type,
sk12: ( hF_Mirabelle_hf > hF_Mirabelle_hf ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk13_decl,type,
sk13: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk14_decl,type,
sk14: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk15_decl,type,
sk15: ( hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk16_decl,type,
sk16: ( hF_Mirabelle_hf > hF_Mirabelle_hf ) > ( hF_Mirabelle_hf > hF_Mirabelle_hf ) > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk17_decl,type,
sk17: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk18_decl,type,
sk18: hF_Mirabelle_hf ).
thf(sk19_decl,type,
sk19: hF_Mirabelle_hf ).
thf(sk20_decl,type,
sk20: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk27_decl,type,
sk27: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk33_decl,type,
sk33: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk35_decl,type,
sk35: hF_Mirabelle_hf ).
thf(sk40_decl,type,
sk40: hF_Mirabelle_hf ).
thf(sk45_decl,type,
sk45: hF_Mirabelle_hf ).
thf(sk50_decl,type,
sk50: hF_Mirabelle_hf ).
thf(sk1075_decl,type,
sk1075: hF_Mirabelle_hf ).
thf(sk1076_decl,type,
sk1076: hF_Mirabelle_hf ).
thf(sk1077_decl,type,
sk1077: hF_Mirabelle_hf ).
thf(sk1078_decl,type,
sk1078: hF_Mirabelle_hf ).
thf(sk1519_decl,type,
sk1519: hF_Mirabelle_hf ).
thf(sk1520_decl,type,
sk1520: hF_Mirabelle_hf ).
thf(sk1521_decl,type,
sk1521: hF_Mirabelle_hf ).
thf(sk1564_decl,type,
sk1564: hF_Mirabelle_hf ).
thf(sk1565_decl,type,
sk1565: hF_Mirabelle_hf ).
thf(sk1566_decl,type,
sk1566: hF_Mirabelle_hf ).
thf(sk1638_decl,type,
sk1638: hF_Mirabelle_hf ).
thf(sk1639_decl,type,
sk1639: hF_Mirabelle_hf ).
thf(sk1640_decl,type,
sk1640: hF_Mirabelle_hf ).
thf(sk1641_decl,type,
sk1641: hF_Mirabelle_hf ).
thf(sk1704_decl,type,
sk1704: hF_Mirabelle_hf ).
thf(sk1705_decl,type,
sk1705: hF_Mirabelle_hf ).
thf(sk1706_decl,type,
sk1706: hF_Mirabelle_hf ).
thf(sk1768_decl,type,
sk1768: hF_Mirabelle_hf ).
thf(sk1804_decl,type,
sk1804: hF_Mirabelle_hf ).
thf(sk1943_decl,type,
sk1943: hF_Mirabelle_hf ).
thf(sk2008_decl,type,
sk2008: hF_Mirabelle_hf ).
thf(sk2009_decl,type,
sk2009: hF_Mirabelle_hf ).
thf(sk2010_decl,type,
sk2010: hF_Mirabelle_hf ).
thf(sk2042_decl,type,
sk2042: hF_Mirabelle_hf ).
thf(sk2043_decl,type,
sk2043: hF_Mirabelle_hf ).
thf(sk2044_decl,type,
sk2044: hF_Mirabelle_hf ).
thf(sk2112_decl,type,
sk2112: hF_Mirabelle_hf ).
thf(sk2113_decl,type,
sk2113: hF_Mirabelle_hf ).
thf(sk2114_decl,type,
sk2114: hF_Mirabelle_hf ).
thf(sk2140_decl,type,
sk2140: hF_Mirabelle_hf ).
thf(sk2141_decl,type,
sk2141: hF_Mirabelle_hf ).
thf(sk2142_decl,type,
sk2142: hF_Mirabelle_hf ).
thf(sk2143_decl,type,
sk2143: hF_Mirabelle_hf ).
thf(sk2237_decl,type,
sk2237: hF_Mirabelle_hf ).
thf(sk2246_decl,type,
sk2246: hF_Mirabelle_hf ).
thf(sk2498_decl,type,
sk2498: hF_Mirabelle_hf ).
thf(sk1_def,definition,
( sk1
= ( @+[A: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf] :
! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( A @ C @ ( hF_Mirabelle_hpair @ B @ C ) )
= B ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf] :
! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( A @ B @ ( hF_Mirabelle_hpair @ B @ C ) )
= C ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf] :
@+[C: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ C @ B )
=> ! [D: hF_Mirabelle_hf] :
( ( A @ C @ D )
=> ! [E: hF_Mirabelle_hf] :
( ( A @ C @ E )
=> ( E = D ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf] :
@+[C: hF_Mirabelle_hf] :
~ ( ( A @ ( sk3 @ A @ B ) @ C )
=> ! [D: hF_Mirabelle_hf] :
( ( A @ ( sk3 @ A @ B ) @ D )
=> ( D = C ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf] :
@+[C: hF_Mirabelle_hf] :
~ ( ( A @ ( sk3 @ A @ B ) @ C )
=> ( C
= ( sk4 @ A @ B ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
@+[C: hF_Mirabelle_hf] :
! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ C )
= ( ( hF_Mirabelle_hmem @ D @ B )
| ( hF_Mirabelle_hmem @ D @ A ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
@+[C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ B )
!= ( hF_Mirabelle_hmem @ C @ A ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf] :
@+[C: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ C @ B )
=> ! [D: hF_Mirabelle_hf] :
( ( A @ C @ D )
=> ! [E: hF_Mirabelle_hf] :
( ( A @ C @ E )
=> ( E = D ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf] :
@+[C: hF_Mirabelle_hf] :
~ ( ( A @ ( sk8 @ A @ B ) @ C )
=> ! [D: hF_Mirabelle_hf] :
( ( A @ ( sk8 @ A @ B ) @ D )
=> ( D = C ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf] :
@+[C: hF_Mirabelle_hf] :
~ ( ( A @ ( sk8 @ A @ B ) @ C )
=> ( C
= ( sk9 @ A @ B ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf] :
@+[C: hF_Mirabelle_hf] :
! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ C )
= ( ? [E: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ E @ B )
& ( A @ E @ D ) ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: hF_Mirabelle_hf > hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
@+[C: hF_Mirabelle_hf] :
! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ C )
= ( ? [E: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ E @ B )
& ( D
= ( A @ E ) ) ) ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
@+[E: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ E @ C )
=> ! [F: hF_Mirabelle_hf] :
( ( B @ E @ F )
= ( A @ E @ F ) ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
@+[E: hF_Mirabelle_hf] :
( ( B @ ( sk13 @ A @ B @ C @ D ) @ E )
!= ( A @ ( sk13 @ A @ B @ C @ D ) @ E ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf] :
@+[C: hF_Mirabelle_hf] :
! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ C )
= ( ( hF_Mirabelle_hmem @ D @ B )
& ( A @ D ) ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: hF_Mirabelle_hf > hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
@+[E: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ E @ C )
=> ( ( B @ E )
= ( A @ E ) ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( ^ [A: hF_Mirabelle_hf] :
@+[B: hF_Mirabelle_hf] :
! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ B )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( hF_Mirabelle_hmem @ C @ D ) ) ) ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( ^ [A: hF_Mirabelle_hf] :
@+[B: hF_Mirabelle_hf] :
~ ~ ( hF_Mirabelle_hmem @ B @ A ) ) ) ).
thf(sk27_def,definition,
( sk27
= ( ^ [A: hF_Mirabelle_hf] :
@+[B: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) ) ) ) ).
thf(sk33_def,definition,
( sk33
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
@+[C: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ C @ B )
=> ( hF_Mir137170979_hpair @ C ) ) ) ) ).
thf(sk35_def,definition,
( sk35
= ( @+[A: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ A @ r )
=> ( hF_Mir137170979_hpair @ A ) ) ) ) ).
thf(sk40_def,definition,
( sk40
= ( @+[A: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ A @ x )
=> ( hF_Mir137170979_hpair @ A ) ) ) ) ).
thf(sk45_def,definition,
( sk45
= ( @+[A: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ A @ r )
=> ( hF_Mir137170979_hpair @ A ) ) ) ) ).
thf(sk50_def,definition,
( sk50
= ( @+[A: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ A @ x )
=> ( hF_Mir137170979_hpair @ A ) ) ) ) ).
thf(sk1075_def,definition,
( sk1075
= ( @+[A: hF_Mirabelle_hf] :
? [B: hF_Mirabelle_hf] :
( ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
= ( hF_Mirabelle_hpair @ A @ B ) )
& ( hF_Mirabelle_hmem @ A @ x ) ) ) ) ).
thf(sk1076_def,definition,
( sk1076
= ( @+[A: hF_Mirabelle_hf] :
( ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
= ( hF_Mirabelle_hpair @ sk1075 @ A ) )
& ( hF_Mirabelle_hmem @ sk1075 @ x ) ) ) ) ).
thf(sk1077_def,definition,
( sk1077
= ( @+[A: hF_Mirabelle_hf] :
? [B: hF_Mirabelle_hf] :
( ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
= ( hF_Mirabelle_hpair @ A @ B ) )
& ( hF_Mirabelle_hmem @ A @ x ) ) ) ) ).
thf(sk1078_def,definition,
( sk1078
= ( @+[A: hF_Mirabelle_hf] :
( ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
= ( hF_Mirabelle_hpair @ sk1077 @ A ) )
& ( hF_Mirabelle_hmem @ sk1077 @ x ) ) ) ) ).
thf(sk1519_def,definition,
( sk1519
= ( @+[A: hF_Mirabelle_hf] :
~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ B ) @ zero_z189798548lle_hf )
=> ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ C ) @ zero_z189798548lle_hf )
=> ( B = C ) ) ) ) ) ).
thf(sk1520_def,definition,
( sk1520
= ( @+[A: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1519 @ A ) @ zero_z189798548lle_hf )
=> ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1519 @ B ) @ zero_z189798548lle_hf )
=> ( A = B ) ) ) ) ) ).
thf(sk1521_def,definition,
( sk1521
= ( @+[A: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1519 @ A ) @ zero_z189798548lle_hf )
=> ( sk1520 = A ) ) ) ) ).
thf(sk1564_def,definition,
( sk1564
= ( @+[A: hF_Mirabelle_hf] :
~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ B ) @ ( hF_Mir1653039215strict @ r @ x ) )
=> ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ C ) @ ( hF_Mir1653039215strict @ r @ x ) )
=> ( B = C ) ) ) ) ) ).
thf(sk1565_def,definition,
( sk1565
= ( @+[A: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ A ) @ ( hF_Mir1653039215strict @ r @ x ) )
=> ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ B ) @ ( hF_Mir1653039215strict @ r @ x ) )
=> ( A = B ) ) ) ) ) ).
thf(sk1566_def,definition,
( sk1566
= ( @+[A: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ A ) @ ( hF_Mir1653039215strict @ r @ x ) )
=> ( sk1565 = A ) ) ) ) ).
thf(sk1638_def,definition,
( sk1638
= ( @+[A: hF_Mirabelle_hf] :
? [B: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1564 @ sk1565 )
= ( hF_Mirabelle_hpair @ A @ B ) )
& ( hF_Mirabelle_hmem @ A @ x ) ) ) ) ).
thf(sk1639_def,definition,
( sk1639
= ( @+[A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1564 @ sk1565 )
= ( hF_Mirabelle_hpair @ sk1638 @ A ) )
& ( hF_Mirabelle_hmem @ sk1638 @ x ) ) ) ) ).
thf(sk1640_def,definition,
( sk1640
= ( @+[A: hF_Mirabelle_hf] :
? [B: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1564 @ sk1565 )
= ( hF_Mirabelle_hpair @ A @ B ) )
& ( hF_Mirabelle_hmem @ A @ x ) ) ) ) ).
thf(sk1641_def,definition,
( sk1641
= ( @+[A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1564 @ sk1565 )
= ( hF_Mirabelle_hpair @ sk1640 @ A ) )
& ( hF_Mirabelle_hmem @ sk1640 @ x ) ) ) ) ).
thf(sk1704_def,definition,
( sk1704
= ( @+[A: hF_Mirabelle_hf] :
~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ B ) @ zero_z189798548lle_hf )
=> ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ C ) @ zero_z189798548lle_hf )
=> ( B = C ) ) ) ) ) ).
thf(sk1705_def,definition,
( sk1705
= ( @+[A: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1704 @ A ) @ zero_z189798548lle_hf )
=> ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1704 @ B ) @ zero_z189798548lle_hf )
=> ( A = B ) ) ) ) ) ).
thf(sk1706_def,definition,
( sk1706
= ( @+[A: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1704 @ A ) @ zero_z189798548lle_hf )
=> ( sk1705 = A ) ) ) ) ).
thf(sk1768_def,definition,
( sk1768
= ( @+[A: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ A @ x )
=> ( hF_Mir137170979_hpair @ A ) ) ) ) ).
thf(sk1804_def,definition,
( sk1804
= ( @+[A: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ A @ x )
=> ( hF_Mir137170979_hpair @ A ) ) ) ) ).
thf(sk1943_def,definition,
( sk1943
= ( @+[A: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ A @ x )
=> ( hF_Mir137170979_hpair @ A ) ) ) ) ).
thf(sk2008_def,definition,
( sk2008
= ( @+[A: hF_Mirabelle_hf] :
~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ B ) @ zero_z189798548lle_hf )
=> ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ C ) @ zero_z189798548lle_hf )
=> ( B = C ) ) ) ) ) ).
thf(sk2009_def,definition,
( sk2009
= ( @+[A: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk2008 @ A ) @ zero_z189798548lle_hf )
=> ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk2008 @ B ) @ zero_z189798548lle_hf )
=> ( A = B ) ) ) ) ) ).
thf(sk2010_def,definition,
( sk2010
= ( @+[A: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk2008 @ A ) @ zero_z189798548lle_hf )
=> ( sk2009 = A ) ) ) ) ).
thf(sk2042_def,definition,
( sk2042
= ( @+[A: hF_Mirabelle_hf] :
~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ B ) @ zero_z189798548lle_hf )
=> ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ C ) @ zero_z189798548lle_hf )
=> ( B = C ) ) ) ) ) ).
thf(sk2043_def,definition,
( sk2043
= ( @+[A: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk2042 @ A ) @ zero_z189798548lle_hf )
=> ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk2042 @ B ) @ zero_z189798548lle_hf )
=> ( A = B ) ) ) ) ) ).
thf(sk2044_def,definition,
( sk2044
= ( @+[A: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk2042 @ A ) @ zero_z189798548lle_hf )
=> ( sk2043 = A ) ) ) ) ).
thf(sk2112_def,definition,
( sk2112
= ( @+[A: hF_Mirabelle_hf] :
~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ B ) @ zero_z189798548lle_hf )
=> ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ C ) @ zero_z189798548lle_hf )
=> ( B = C ) ) ) ) ) ).
thf(sk2113_def,definition,
( sk2113
= ( @+[A: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk2112 @ A ) @ zero_z189798548lle_hf )
=> ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk2112 @ B ) @ zero_z189798548lle_hf )
=> ( A = B ) ) ) ) ) ).
thf(sk2114_def,definition,
( sk2114
= ( @+[A: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk2112 @ A ) @ zero_z189798548lle_hf )
=> ( sk2113 = A ) ) ) ) ).
thf(sk2140_def,definition,
( sk2140
= ( @+[A: hF_Mirabelle_hf] :
? [B: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1564 @ sk1566 )
= ( hF_Mirabelle_hpair @ A @ B ) )
& ( hF_Mirabelle_hmem @ A @ x ) ) ) ) ).
thf(sk2141_def,definition,
( sk2141
= ( @+[A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1564 @ sk1566 )
= ( hF_Mirabelle_hpair @ sk2140 @ A ) )
& ( hF_Mirabelle_hmem @ sk2140 @ x ) ) ) ) ).
thf(sk2142_def,definition,
( sk2142
= ( @+[A: hF_Mirabelle_hf] :
? [B: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1564 @ sk1566 )
= ( hF_Mirabelle_hpair @ A @ B ) )
& ( hF_Mirabelle_hmem @ A @ x ) ) ) ) ).
thf(sk2143_def,definition,
( sk2143
= ( @+[A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1564 @ sk1566 )
= ( hF_Mirabelle_hpair @ sk2142 @ A ) )
& ( hF_Mirabelle_hmem @ sk2142 @ x ) ) ) ) ).
thf(sk2237_def,definition,
( sk2237
= ( @+[A: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ A @ x )
=> ( hF_Mir137170979_hpair @ A ) ) ) ) ).
thf(sk2246_def,definition,
( sk2246
= ( @+[A: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ A @ x )
=> ( hF_Mir137170979_hpair @ A ) ) ) ) ).
thf(sk2498_def,definition,
( sk2498
= ( @+[A: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ A @ x )
=> ( hF_Mir137170979_hpair @ A ) ) ) ) ).
thf(3,axiom,
! [A: hF_Mirabelle_hf > $o] :
( ( hF_Mir818139703ollect @ A @ zero_z189798548lle_hf )
= zero_z189798548lle_hf ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_HCollect__hempty) ).
thf(69,plain,
! [A: hF_Mirabelle_hf > $o] :
( ( hF_Mir818139703ollect @ A @ zero_z189798548lle_hf )
= zero_z189798548lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(33,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ B ) )
= ( sup_su638957495lle_hf @ ( hF_Mirabelle_HUnion @ A ) @ ( hF_Mirabelle_HUnion @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_HUnion__hunion) ).
thf(160,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ B ) )
= ( sup_su638957495lle_hf @ ( hF_Mirabelle_HUnion @ A ) @ ( hF_Mirabelle_HUnion @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(161,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ B ) )
= ( sup_su638957495lle_hf @ ( hF_Mirabelle_HUnion @ A ) @ ( hF_Mirabelle_HUnion @ B ) ) ),
inference(cnf,[status(esa)],[160]) ).
thf(162,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ ( hF_Mirabelle_HUnion @ A ) @ ( hF_Mirabelle_HUnion @ B ) )
= ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ B ) ) ),
inference(lifteq,[status(thm)],[161]) ).
thf(32,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( sup_su638957495lle_hf @ B @ C ) )
= ( ( hF_Mirabelle_hmem @ A @ B )
| ( hF_Mirabelle_hmem @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_hunion__iff) ).
thf(157,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( sup_su638957495lle_hf @ B @ C ) )
= ( ( hF_Mirabelle_hmem @ A @ B )
| ( hF_Mirabelle_hmem @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(158,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( sup_su638957495lle_hf @ B @ C ) )
= ( ( hF_Mirabelle_hmem @ A @ B )
| ( hF_Mirabelle_hmem @ A @ C ) ) ),
inference(cnf,[status(esa)],[157]) ).
thf(159,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( sup_su638957495lle_hf @ B @ C ) )
= ( ( hF_Mirabelle_hmem @ A @ B )
| ( hF_Mirabelle_hmem @ A @ C ) ) ),
inference(lifteq,[status(thm)],[158]) ).
thf(37,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_hmem__ne) ).
thf(178,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(179,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ A @ B )
| ( A != B ) ),
inference(cnf,[status(esa)],[178]) ).
thf(180,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A != B )
| ~ ( hF_Mirabelle_hmem @ A @ B ) ),
inference(lifteq,[status(thm)],[179]) ).
thf(181,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ A ),
inference(simp,[status(thm)],[180]) ).
thf(2698,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( ( hF_Mirabelle_hmem @ A @ B )
| ( hF_Mirabelle_hmem @ A @ C ) )
| ( ( hF_Mirabelle_hmem @ A @ ( sup_su638957495lle_hf @ B @ C ) )
!= ( hF_Mirabelle_hmem @ D @ D ) ) ),
inference(paramod_ordered,[status(thm)],[159,181]) ).
thf(2699,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ B ) @ A )
| ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ B ) @ B ) ),
inference(pattern_uni,[status(thm)],[2698:[bind(A,$thf( sup_su638957495lle_hf @ E @ F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( sup_su638957495lle_hf @ E @ F ))]]) ).
thf(2749,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ B ) @ A )
& ~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ B ) @ B ) ),
inference(cnf,[status(esa)],[2699]) ).
thf(2751,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ B ) @ B ),
inference(cnfConj,[status(thm)],[2749]) ).
thf(2753,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ B ) @ B ),
inference(simp,[status(thm)],[2751]) ).
thf(3279,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ B ) ) @ D )
| ( ( sup_su638957495lle_hf @ ( hF_Mirabelle_HUnion @ A ) @ ( hF_Mirabelle_HUnion @ B ) )
!= ( sup_su638957495lle_hf @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[162,2753]) ).
thf(3280,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ B ) ) @ ( hF_Mirabelle_HUnion @ B ) ),
inference(pattern_uni,[status(thm)],[3279:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( hF_Mirabelle_HUnion @ E )),bind(D,$thf( hF_Mirabelle_HUnion @ F ))]]) ).
thf(3333,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ B ) ) @ ( hF_Mirabelle_HUnion @ B ) ),
inference(simp,[status(thm)],[3280]) ).
thf(3850,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ B ) ) ) @ ( hF_Mirabelle_HUnion @ D ) )
| ( ( sup_su638957495lle_hf @ ( hF_Mirabelle_HUnion @ A ) @ ( hF_Mirabelle_HUnion @ B ) )
!= ( sup_su638957495lle_hf @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[162,3333]) ).
thf(3851,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ B ) ) ) @ ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_HUnion @ B ) ) ),
inference(pattern_uni,[status(thm)],[3850:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( hF_Mirabelle_HUnion @ E )),bind(D,$thf( hF_Mirabelle_HUnion @ F ))]]) ).
thf(3873,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ B ) ) ) @ ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_HUnion @ B ) ) ),
inference(simp,[status(thm)],[3851]) ).
thf(47,axiom,
( hF_Mir434065167lation
= ( ^ [A: hF_Mirabelle_hf] :
! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_hrelation__def) ).
thf(226,plain,
( hF_Mir434065167lation
= ( ^ [A: hF_Mirabelle_hf] :
! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(227,plain,
( hF_Mir434065167lation
= ( ^ [A: hF_Mirabelle_hf] :
! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) ) ) ),
inference(lifteq,[status(thm)],[226]) ).
thf(301,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir434065167lation @ A )
= ( ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) ) ) ),
inference(func_ext,[status(esa)],[227]) ).
thf(66,axiom,
( hF_Mir199975595nction
= ( ^ [A: hF_Mirabelle_hf] :
! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ C ) @ A )
=> ! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ D ) @ A )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_hfunction__def) ).
thf(292,plain,
( hF_Mir199975595nction
= ( ^ [A: hF_Mirabelle_hf] :
! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ C ) @ A )
=> ! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ D ) @ A )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(293,plain,
( hF_Mir199975595nction
= ( ^ [A: hF_Mirabelle_hf] :
! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ C ) @ A )
=> ! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ D ) @ A )
=> ( C = D ) ) ) ) ),
inference(lifteq,[status(thm)],[292]) ).
thf(333,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir199975595nction @ A )
= ( ! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ C ) @ A )
=> ! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ D ) @ A )
=> ( C = D ) ) ) ) ),
inference(func_ext,[status(esa)],[293]) ).
thf(1,conjecture,
hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ x ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(68,plain,
~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ x ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(43850,plain,
! [A: hF_Mirabelle_hf] :
( ~ ! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ C ) @ A )
=> ! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ D ) @ A )
=> ( C = D ) ) )
| ( ( hF_Mir199975595nction @ A )
!= ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[333,68]) ).
thf(43851,plain,
~ ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ B ) @ ( hF_Mir1653039215strict @ r @ x ) )
=> ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ C ) @ ( hF_Mir1653039215strict @ r @ x ) )
=> ( B = C ) ) ),
inference(pattern_uni,[status(thm)],[43850:[bind(A,$thf( hF_Mir1653039215strict @ r @ x ))]]) ).
thf(44019,plain,
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) @ ( hF_Mir1653039215strict @ r @ x ) )
& ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) @ ( hF_Mir1653039215strict @ r @ x ) )
& ( sk1565 != sk1566 ) ),
inference(cnf,[status(esa)],[43851]) ).
thf(44021,plain,
hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) @ ( hF_Mir1653039215strict @ r @ x ),
inference(cnfConj,[status(thm)],[44019]) ).
thf(65,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mir1653039215strict @ B @ C ) )
= ( ( hF_Mirabelle_hmem @ A @ B )
& ? [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] :
( ( A
= ( hF_Mirabelle_hpair @ D @ E ) )
& ( hF_Mirabelle_hmem @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_hrestrict__iff) ).
thf(289,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mir1653039215strict @ B @ C ) )
= ( ( hF_Mirabelle_hmem @ A @ B )
& ? [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] :
( ( A
= ( hF_Mirabelle_hpair @ D @ E ) )
& ( hF_Mirabelle_hmem @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(290,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mir1653039215strict @ B @ C ) )
= ( ( hF_Mirabelle_hmem @ A @ B )
& ? [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] :
( ( A
= ( hF_Mirabelle_hpair @ D @ E ) )
& ( hF_Mirabelle_hmem @ D @ C ) ) ) ),
inference(cnf,[status(esa)],[289]) ).
thf(291,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mir1653039215strict @ B @ C ) )
= ( ( hF_Mirabelle_hmem @ A @ B )
& ? [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] :
( ( A
= ( hF_Mirabelle_hpair @ D @ E ) )
& ( hF_Mirabelle_hmem @ D @ C ) ) ) ),
inference(lifteq,[status(thm)],[290]) ).
thf(60060,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ A @ B )
& ? [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] :
( ( A
= ( hF_Mirabelle_hpair @ D @ E ) )
& ( hF_Mirabelle_hmem @ D @ C ) ) )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mir1653039215strict @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[44021,291]) ).
thf(60061,plain,
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) @ r )
& ? [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1564 @ sk1566 )
= ( hF_Mirabelle_hpair @ A @ B ) )
& ( hF_Mirabelle_hmem @ A @ x ) ) ),
inference(pattern_uni,[status(thm)],[60060:[bind(A,$thf( hF_Mirabelle_hpair @ sk1564 @ sk1566 )),bind(B,$thf( r )),bind(C,$thf( x ))]]) ).
thf(60430,plain,
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) @ r )
& ( ( hF_Mirabelle_hpair @ sk1564 @ sk1566 )
= ( hF_Mirabelle_hpair @ sk2140 @ sk2141 ) )
& ( hF_Mirabelle_hmem @ sk2140 @ x ) ),
inference(cnf,[status(esa)],[60061]) ).
thf(60433,plain,
hF_Mirabelle_hmem @ sk2140 @ x,
inference(cnfConj,[status(thm)],[60430]) ).
thf(548,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir434065167lation @ A )
| ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) ) ),
inference(bool_ext,[status(thm)],[301]) ).
thf(562,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir434065167lation @ A )
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( hF_Mir137170979_hpair @ B ) ),
inference(cnf,[status(esa)],[548]) ).
thf(60524,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir434065167lation @ A )
| ~ $true
| ( hF_Mir137170979_hpair @ B )
| ( ( hF_Mirabelle_hmem @ sk2140 @ x )
!= ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[60433,562]) ).
thf(60525,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir434065167lation @ A )
| ( hF_Mir137170979_hpair @ B )
| ( ( hF_Mirabelle_hmem @ sk2140 @ x )
!= ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(simp,[status(thm)],[60524]) ).
thf(60526,plain,
( ~ ( hF_Mir434065167lation @ x )
| ( hF_Mir137170979_hpair @ sk2140 ) ),
inference(pattern_uni,[status(thm)],[60525:[bind(A,$thf( x )),bind(B,$thf( sk2140 ))]]) ).
thf(62792,plain,
! [A: hF_Mirabelle_hf] :
( ~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) )
| ( hF_Mir137170979_hpair @ sk2140 )
| ( ( hF_Mir434065167lation @ A )
!= ( hF_Mir434065167lation @ x ) ) ),
inference(paramod_ordered,[status(thm)],[301,60526]) ).
thf(62793,plain,
( ~ ! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ x )
=> ( hF_Mir137170979_hpair @ A ) )
| ( hF_Mir137170979_hpair @ sk2140 ) ),
inference(pattern_uni,[status(thm)],[62792:[bind(A,$thf( x ))]]) ).
thf(62869,plain,
( ( ( hF_Mirabelle_hmem @ sk2237 @ x )
| ( hF_Mir137170979_hpair @ sk2140 ) )
& ( ~ ( hF_Mir137170979_hpair @ sk2237 )
| ( hF_Mir137170979_hpair @ sk2140 ) ) ),
inference(cnf,[status(esa)],[62793]) ).
thf(62870,plain,
( ( hF_Mirabelle_hmem @ sk2237 @ x )
| ( hF_Mir137170979_hpair @ sk2140 ) ),
inference(cnfConj,[status(thm)],[62869]) ).
thf(63364,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk2140 )
| ~ $true
| ( ( hF_Mirabelle_hmem @ sk2237 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[62870,181]) ).
thf(63365,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk2140 )
| ( ( hF_Mirabelle_hmem @ sk2237 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(simp,[status(thm)],[63364]) ).
thf(63474,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk2140 )
| ( sk2237 != A )
| ( x != A ) ),
inference(simp,[status(thm)],[63365]) ).
thf(63709,plain,
( ( hF_Mir137170979_hpair @ sk2140 )
| ( sk2237 != x ) ),
inference(simp,[status(thm)],[63474]) ).
thf(60432,plain,
( ( hF_Mirabelle_hpair @ sk1564 @ sk1566 )
= ( hF_Mirabelle_hpair @ sk2140 @ sk2141 ) ),
inference(cnfConj,[status(thm)],[60430]) ).
thf(60434,plain,
( ( hF_Mirabelle_hpair @ sk2140 @ sk2141 )
= ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) ),
inference(lifteq,[status(thm)],[60432]) ).
thf(63,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_hfst__conv) ).
thf(284,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(285,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ A @ B ) )
= A ),
inference(cnf,[status(esa)],[284]) ).
thf(286,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ A @ B ) )
= A ),
inference(lifteq,[status(thm)],[285]) ).
thf(64348,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) )
= A )
| ( ( hF_Mirabelle_hpair @ sk2140 @ sk2141 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[60434,286]) ).
thf(64349,plain,
( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) )
= sk2140 ),
inference(pattern_uni,[status(thm)],[64348:[bind(A,$thf( sk2140 )),bind(B,$thf( sk2141 ))]]) ).
thf(65033,plain,
sk2140 = sk1564,
inference(rewrite,[status(thm)],[64349,286]) ).
thf(65832,plain,
( ( hF_Mir137170979_hpair @ sk1564 )
| ( sk2237 != x ) ),
inference(rewrite,[status(thm)],[63709,65033]) ).
thf(26,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ A @ B ) )
= ( sup_su638957495lle_hf @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_sup__left__idem) ).
thf(138,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ A @ B ) )
= ( sup_su638957495lle_hf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(44020,plain,
hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) @ ( hF_Mir1653039215strict @ r @ x ),
inference(cnfConj,[status(thm)],[44019]) ).
thf(44230,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ A @ B )
& ? [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] :
( ( A
= ( hF_Mirabelle_hpair @ D @ E ) )
& ( hF_Mirabelle_hmem @ D @ C ) ) )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mir1653039215strict @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[44020,291]) ).
thf(44231,plain,
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) @ r )
& ? [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1564 @ sk1565 )
= ( hF_Mirabelle_hpair @ A @ B ) )
& ( hF_Mirabelle_hmem @ A @ x ) ) ),
inference(pattern_uni,[status(thm)],[44230:[bind(A,$thf( hF_Mirabelle_hpair @ sk1564 @ sk1565 )),bind(B,$thf( r )),bind(C,$thf( x ))]]) ).
thf(44625,plain,
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) @ r )
& ( ( hF_Mirabelle_hpair @ sk1564 @ sk1565 )
= ( hF_Mirabelle_hpair @ sk1638 @ sk1639 ) )
& ( hF_Mirabelle_hmem @ sk1638 @ x ) ),
inference(cnf,[status(esa)],[44231]) ).
thf(44627,plain,
( ( hF_Mirabelle_hpair @ sk1564 @ sk1565 )
= ( hF_Mirabelle_hpair @ sk1638 @ sk1639 ) ),
inference(cnfConj,[status(thm)],[44625]) ).
thf(44629,plain,
( ( hF_Mirabelle_hpair @ sk1638 @ sk1639 )
= ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) ),
inference(lifteq,[status(thm)],[44627]) ).
thf(35,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ A @ B )
= ( hF_Mirabelle_hpair @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_hpair__inject) ).
thf(166,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ A @ B )
= ( hF_Mirabelle_hpair @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(167,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( ( hF_Mirabelle_hpair @ A @ B )
!= ( hF_Mirabelle_hpair @ C @ D ) )
| ( A = C ) )
& ( ( ( hF_Mirabelle_hpair @ A @ B )
!= ( hF_Mirabelle_hpair @ C @ D ) )
| ( B = D ) ) ),
inference(cnf,[status(esa)],[166]) ).
thf(169,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ A @ B )
!= ( hF_Mirabelle_hpair @ C @ D ) )
| ( B = D ) ),
inference(cnfConj,[status(thm)],[167]) ).
thf(173,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ A @ B )
!= ( hF_Mirabelle_hpair @ C @ D ) )
| ( B = D ) ),
inference(lifteq,[status(thm)],[169]) ).
thf(174,plain,
? [A: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf] :
! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( A @ B @ ( hF_Mirabelle_hpair @ B @ C ) )
= C ),
inference(detectInverse,[status(thm)],[173]) ).
thf(175,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sk2 @ A @ ( hF_Mirabelle_hpair @ A @ B ) )
= B ),
inference(cnf,[status(esa)],[174]) ).
thf(1697,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sk2 @ A @ ( hF_Mirabelle_hpair @ A @ B ) )
= B ),
inference(lifteq,[status(thm)],[175]) ).
thf(50762,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk2 @ A @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) )
= B )
| ( ( hF_Mirabelle_hpair @ sk1638 @ sk1639 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[44629,1697]) ).
thf(50763,plain,
( ( sk2 @ sk1638 @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) )
= sk1639 ),
inference(pattern_uni,[status(thm)],[50762:[bind(A,$thf( sk1638 )),bind(B,$thf( sk1639 ))]]) ).
thf(50779,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) )
= A )
| ( ( hF_Mirabelle_hpair @ sk1638 @ sk1639 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[44629,286]) ).
thf(50780,plain,
( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) )
= sk1638 ),
inference(pattern_uni,[status(thm)],[50779:[bind(A,$thf( sk1638 )),bind(B,$thf( sk1639 ))]]) ).
thf(51420,plain,
sk1638 = sk1564,
inference(rewrite,[status(thm)],[50780,286]) ).
thf(50,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_hsnd__conv) ).
thf(233,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(234,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ A @ B ) )
= B ),
inference(cnf,[status(esa)],[233]) ).
thf(235,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ A @ B ) )
= B ),
inference(lifteq,[status(thm)],[234]) ).
thf(50802,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) )
= B )
| ( ( hF_Mirabelle_hpair @ sk1638 @ sk1639 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[44629,235]) ).
thf(50803,plain,
( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) )
= sk1639 ),
inference(pattern_uni,[status(thm)],[50802:[bind(A,$thf( sk1638 )),bind(B,$thf( sk1639 ))]]) ).
thf(52188,plain,
sk1639 = sk1565,
inference(rewrite,[status(thm)],[50803,235]) ).
thf(54881,plain,
( ( sk2 @ sk1564 @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) )
= sk1565 ),
inference(rewrite,[status(thm)],[50763,51420,52188]) ).
thf(45,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
= ( hF_Mirabelle_hmem @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_hf__equalityI) ).
thf(212,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
= ( hF_Mirabelle_hmem @ C @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(213,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ ( sk7 @ B @ A ) @ A )
!= ( hF_Mirabelle_hmem @ ( sk7 @ B @ A ) @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[212]) ).
thf(214,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ ( sk7 @ B @ A ) @ A )
!= ( hF_Mirabelle_hmem @ ( sk7 @ B @ A ) @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[213]) ).
thf(67,axiom,
hF_Mir199975595nction @ r,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(294,plain,
hF_Mir199975595nction @ r,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(297,plain,
( ~ $true
| ( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mir199975595nction @ r ) ) ),
inference(paramod_ordered,[status(thm)],[294,68]) ).
thf(298,plain,
( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mir199975595nction @ r ) ),
inference(simp,[status(thm)],[297]) ).
thf(299,plain,
( ( hF_Mir1653039215strict @ r @ x )
!= r ),
inference(simp,[status(thm)],[298]) ).
thf(12146,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ ( sk7 @ B @ A ) @ A )
!= ( hF_Mirabelle_hmem @ ( sk7 @ B @ A ) @ B ) )
| ( A != r )
| ( B
!= ( hF_Mir1653039215strict @ r @ x ) ) ),
inference(paramod_ordered,[status(thm)],[214,299]) ).
thf(12147,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ A ) @ A )
!= ( hF_Mirabelle_hmem @ ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ A ) @ ( hF_Mir1653039215strict @ r @ x ) ) )
| ( A != r ) ),
inference(pattern_uni,[status(thm)],[12146:[bind(A,$thf( A )),bind(B,$thf( hF_Mir1653039215strict @ r @ x ))]]) ).
thf(13783,plain,
( ( hF_Mirabelle_hmem @ ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ r ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ r ) @ r ) ),
inference(simp,[status(thm)],[12147]) ).
thf(44628,plain,
hF_Mirabelle_hmem @ sk1638 @ x,
inference(cnfConj,[status(thm)],[44625]) ).
thf(44716,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir434065167lation @ A )
| ~ $true
| ( hF_Mir137170979_hpair @ B )
| ( ( hF_Mirabelle_hmem @ sk1638 @ x )
!= ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44628,562]) ).
thf(44717,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir434065167lation @ A )
| ( hF_Mir137170979_hpair @ B )
| ( ( hF_Mirabelle_hmem @ sk1638 @ x )
!= ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(simp,[status(thm)],[44716]) ).
thf(44718,plain,
( ~ ( hF_Mir434065167lation @ x )
| ( hF_Mir137170979_hpair @ sk1638 ) ),
inference(pattern_uni,[status(thm)],[44717:[bind(A,$thf( x )),bind(B,$thf( sk1638 ))]]) ).
thf(51423,plain,
( ~ ( hF_Mir434065167lation @ x )
| ( hF_Mir137170979_hpair @ sk1564 ) ),
inference(rewrite,[status(thm)],[44718,51420]) ).
thf(53788,plain,
! [A: hF_Mirabelle_hf] :
( ~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) )
| ( hF_Mir137170979_hpair @ sk1564 )
| ( ( hF_Mir434065167lation @ A )
!= ( hF_Mir434065167lation @ x ) ) ),
inference(paramod_ordered,[status(thm)],[301,51423]) ).
thf(53789,plain,
( ~ ! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ x )
=> ( hF_Mir137170979_hpair @ A ) )
| ( hF_Mir137170979_hpair @ sk1564 ) ),
inference(pattern_uni,[status(thm)],[53788:[bind(A,$thf( x ))]]) ).
thf(53866,plain,
( ( ( hF_Mirabelle_hmem @ sk1943 @ x )
| ( hF_Mir137170979_hpair @ sk1564 ) )
& ( ~ ( hF_Mir137170979_hpair @ sk1943 )
| ( hF_Mir137170979_hpair @ sk1564 ) ) ),
inference(cnf,[status(esa)],[53789]) ).
thf(53867,plain,
( ( hF_Mirabelle_hmem @ sk1943 @ x )
| ( hF_Mir137170979_hpair @ sk1564 ) ),
inference(cnfConj,[status(thm)],[53866]) ).
thf(9,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ A @ B ) )
= ( sup_su638957495lle_hf @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_sup_Oleft__idem) ).
thf(88,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ A @ B ) )
= ( sup_su638957495lle_hf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(43,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
? [C: hF_Mirabelle_hf] :
! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ C )
= ( ( hF_Mirabelle_hmem @ D @ A )
| ( hF_Mirabelle_hmem @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_binary__union) ).
thf(206,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
? [C: hF_Mirabelle_hf] :
! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ C )
= ( ( hF_Mirabelle_hmem @ D @ A )
| ( hF_Mirabelle_hmem @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(207,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ ( sk6 @ B @ A ) )
= ( ( hF_Mirabelle_hmem @ C @ A )
| ( hF_Mirabelle_hmem @ C @ B ) ) ),
inference(cnf,[status(esa)],[206]) ).
thf(208,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ ( sk6 @ B @ A ) )
= ( ( hF_Mirabelle_hmem @ C @ A )
| ( hF_Mirabelle_hmem @ C @ B ) ) ),
inference(lifteq,[status(thm)],[207]) ).
thf(8735,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( ( hF_Mirabelle_hmem @ C @ A )
| ( hF_Mirabelle_hmem @ C @ B ) )
| ( ( hF_Mirabelle_hmem @ C @ ( sk6 @ B @ A ) )
!= ( hF_Mirabelle_hmem @ D @ D ) ) ),
inference(paramod_ordered,[status(thm)],[208,181]) ).
thf(8736,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ B )
| ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[8735:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( sk6 @ E @ F )),bind(D,$thf( sk6 @ E @ F ))]]) ).
thf(8839,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ B )
& ~ ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ A ) ),
inference(cnf,[status(esa)],[8736]) ).
thf(8841,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ A ),
inference(cnfConj,[status(thm)],[8839]) ).
thf(8843,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ A ),
inference(simp,[status(thm)],[8841]) ).
thf(13,axiom,
! [A: hF_Mirabelle_hf] :
( ( A = zero_z189798548lle_hf )
= ( ! [B: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_hempty__iff) ).
thf(100,plain,
! [A: hF_Mirabelle_hf] :
( ( A = zero_z189798548lle_hf )
= ( ! [B: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(101,plain,
! [A: hF_Mirabelle_hf] :
( ( A = zero_z189798548lle_hf )
= ( ! [B: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(cnf,[status(esa)],[100]) ).
thf(102,plain,
! [A: hF_Mirabelle_hf] :
( ( A = zero_z189798548lle_hf )
= ( ! [B: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(lifteq,[status(thm)],[101]) ).
thf(453,plain,
! [A: hF_Mirabelle_hf] :
( ( A = zero_z189798548lle_hf )
| ~ ! [B: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ B @ A ) ),
inference(bool_ext,[status(thm)],[102]) ).
thf(462,plain,
! [A: hF_Mirabelle_hf] :
( ( A = zero_z189798548lle_hf )
| ~ ! [B: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ B @ A ) ),
inference(lifteq,[status(thm)],[453]) ).
thf(468,plain,
! [A: hF_Mirabelle_hf] :
( ( A = zero_z189798548lle_hf )
| ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A ) ),
inference(cnf,[status(esa)],[462]) ).
thf(42,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf] :
( ! [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf,F: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
=> ( ( B @ D @ E )
=> ( ( B @ D @ F )
=> ( F = E ) ) ) )
=> ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir1248913145eplace @ A @ B ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_PrimReplace__iff) ).
thf(195,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf] :
( ! [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf,F: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
=> ( ( B @ D @ E )
=> ( ( B @ D @ F )
=> ( F = E ) ) ) )
=> ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir1248913145eplace @ A @ B ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(196,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
=> ! [D: hF_Mirabelle_hf] :
( ( B @ C @ D )
=> ! [E: hF_Mirabelle_hf] :
( ( B @ C @ E )
=> ( E = D ) ) ) )
=> ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ ( hF_Mir1248913145eplace @ A @ B ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) ) ),
inference(miniscope,[status(thm)],[195]) ).
thf(197,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ ( sk3 @ B @ A ) @ A )
| ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir1248913145eplace @ A @ B ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) ) )
& ( ( B @ ( sk3 @ B @ A ) @ ( sk4 @ B @ A ) )
| ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir1248913145eplace @ A @ B ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) ) )
& ( ( B @ ( sk3 @ B @ A ) @ ( sk5 @ B @ A ) )
| ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir1248913145eplace @ A @ B ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) ) )
& ( ( ( sk5 @ B @ A )
!= ( sk4 @ B @ A ) )
| ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir1248913145eplace @ A @ B ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) ) ) ),
inference(cnf,[status(esa)],[196]) ).
thf(200,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( B @ ( sk3 @ B @ A ) @ ( sk5 @ B @ A ) )
| ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir1248913145eplace @ A @ B ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) ) ),
inference(cnfConj,[status(thm)],[197]) ).
thf(204,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir1248913145eplace @ A @ B ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) )
| ( B @ ( sk3 @ B @ A ) @ ( sk5 @ B @ A ) ) ),
inference(lifteq,[status(thm)],[200]) ).
thf(6710,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ B
@ ( hF_Mir1248913145eplace @ A
@ ^ [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] : $false ) )
= ( ? [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
& $false ) ) )
| $false ),
inference(prim_subst,[status(thm)],[204:[bind(A,$thf( A )),bind(B,$thf( ^ [D: hF_Mirabelle_hf] : ^ [E: hF_Mirabelle_hf] : $false ))]]) ).
thf(6925,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ B
@ ( hF_Mir1248913145eplace @ A
@ ^ [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] : $false ) ),
inference(simp,[status(thm)],[6710]) ).
thf(199,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( B @ ( sk3 @ B @ A ) @ ( sk4 @ B @ A ) )
| ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir1248913145eplace @ A @ B ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) ) ),
inference(cnfConj,[status(thm)],[197]) ).
thf(203,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir1248913145eplace @ A @ B ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) )
| ( B @ ( sk3 @ B @ A ) @ ( sk4 @ B @ A ) ) ),
inference(lifteq,[status(thm)],[199]) ).
thf(5651,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ B
@ ( hF_Mir1248913145eplace @ A
@ ^ [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] : $false ) )
= ( ? [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
& $false ) ) )
| $false ),
inference(prim_subst,[status(thm)],[203:[bind(A,$thf( A )),bind(B,$thf( ^ [D: hF_Mirabelle_hf] : ^ [E: hF_Mirabelle_hf] : $false ))]]) ).
thf(5845,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ B
@ ( hF_Mir1248913145eplace @ A
@ ^ [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] : $false ) ),
inference(simp,[status(thm)],[5651]) ).
thf(6183,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A = zero_z189798548lle_hf )
| ~ $true
| ( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
!= ( hF_Mirabelle_hmem @ C
@ ( hF_Mir1248913145eplace @ B
@ ^ [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[468,5845]) ).
thf(6184,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A = zero_z189798548lle_hf )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
!= ( hF_Mirabelle_hmem @ C
@ ( hF_Mir1248913145eplace @ B
@ ^ [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] : $false ) ) ) ),
inference(simp,[status(thm)],[6183]) ).
thf(6185,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir1248913145eplace @ A
@ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : $false )
= zero_z189798548lle_hf ),
inference(pattern_uni,[status(thm)],[6184:[bind(A,$thf( hF_Mir1248913145eplace @ E @ ^ [E: hF_Mirabelle_hf] : ^ [F: hF_Mirabelle_hf] : $false )),bind(B,$thf( E )),bind(C,$thf( sk20 @ ( hF_Mir1248913145eplace @ E @ ^ [E: hF_Mirabelle_hf] : ^ [F: hF_Mirabelle_hf] : $false ) ))]]) ).
thf(6233,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir1248913145eplace @ A
@ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : $false )
= zero_z189798548lle_hf ),
inference(simp,[status(thm)],[6185]) ).
thf(7297,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ),
inference(rewrite,[status(thm)],[6925,6233]) ).
thf(44748,plain,
! [A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ sk1638 @ x )
!= ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[44628,7297]) ).
thf(44749,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ sk1638 @ x )
!= ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[44748]) ).
thf(44867,plain,
! [A: hF_Mirabelle_hf] :
( ( sk1638 != A )
| ( x != zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[44749]) ).
thf(45037,plain,
x != zero_z189798548lle_hf,
inference(simp,[status(thm)],[44867]) ).
thf(45118,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
| ( zero_z189798548lle_hf != zero_z189798548lle_hf )
| ( A != x ) ),
inference(paramod_ordered,[status(thm)],[468,45037]) ).
thf(45119,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
| ( A != x ) ),
inference(simp,[status(thm)],[45118]) ).
thf(45120,plain,
hF_Mirabelle_hmem @ ( sk20 @ x ) @ x,
inference(pattern_uni,[status(thm)],[45119:[bind(A,$thf( x ))]]) ).
thf(2750,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ B ) @ A ),
inference(cnfConj,[status(thm)],[2749]) ).
thf(2752,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ B ) @ A ),
inference(simp,[status(thm)],[2750]) ).
thf(46345,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ B ) @ A )
!= ( hF_Mirabelle_hmem @ ( sk20 @ x ) @ x ) ) ),
inference(paramod_ordered,[status(thm)],[45120,2752]) ).
thf(46346,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ B ) @ A )
!= ( hF_Mirabelle_hmem @ ( sk20 @ x ) @ x ) ),
inference(simp,[status(thm)],[46345]) ).
thf(46437,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ A @ B )
!= ( sk20 @ x ) )
| ( A != x ) ),
inference(simp,[status(thm)],[46346]) ).
thf(46573,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ x @ A )
!= ( sk20 @ x ) ),
inference(simp,[status(thm)],[46437]) ).
thf(835,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
| ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( A
!= ( hF_Mir1653039215strict @ r @ x ) ) ),
inference(paramod_ordered,[status(thm)],[468,68]) ).
thf(836,plain,
( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) @ ( hF_Mir1653039215strict @ r @ x ) )
| ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf ) ),
inference(pattern_uni,[status(thm)],[835:[bind(A,$thf( hF_Mir1653039215strict @ r @ x ))]]) ).
thf(36027,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ A @ B )
& ? [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] :
( ( A
= ( hF_Mirabelle_hpair @ D @ E ) )
& ( hF_Mirabelle_hmem @ D @ C ) ) )
| ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( ( hF_Mirabelle_hmem @ A @ ( hF_Mir1653039215strict @ B @ C ) )
!= ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[291,836]) ).
thf(36028,plain,
( ( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) @ r )
& ? [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
= ( hF_Mirabelle_hpair @ A @ B ) )
& ( hF_Mirabelle_hmem @ A @ x ) ) )
| ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf ) ),
inference(pattern_uni,[status(thm)],[36027:[bind(A,$thf( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )),bind(B,$thf( r )),bind(C,$thf( x ))]]) ).
thf(36446,plain,
( ( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) @ r )
| ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf ) )
& ( ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
= ( hF_Mirabelle_hpair @ sk1075 @ sk1076 ) )
| ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf ) )
& ( ( hF_Mirabelle_hmem @ sk1075 @ x )
| ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf ) ) ),
inference(cnf,[status(esa)],[36028]) ).
thf(36449,plain,
( ( hF_Mirabelle_hmem @ sk1075 @ x )
| ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf ) ),
inference(cnfConj,[status(thm)],[36446]) ).
thf(38,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ A @ B )
& ( hF_Mirabelle_hmem @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_hmem__not__sym) ).
thf(182,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ A @ B )
& ( hF_Mirabelle_hmem @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(183,plain,
~ ? [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ B )
& ( hF_Mirabelle_hmem @ B @ A ) ),
inference(miniscope,[status(thm)],[182]) ).
thf(184,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ A @ B )
| ~ ( hF_Mirabelle_hmem @ B @ A ) ),
inference(cnf,[status(esa)],[183]) ).
thf(43226,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ~ $true
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ sk1075 @ x )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[36449,184]) ).
thf(43227,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ sk1075 @ x )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(simp,[status(thm)],[43226]) ).
thf(43228,plain,
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ~ ( hF_Mirabelle_hmem @ x @ sk1075 ) ),
inference(pattern_uni,[status(thm)],[43227:[bind(A,$thf( sk1075 )),bind(B,$thf( x ))]]) ).
thf(56194,plain,
! [A: hF_Mirabelle_hf] :
( ~ ! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ C ) @ A )
=> ! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ D ) @ A )
=> ( C = D ) ) )
| ~ ( hF_Mirabelle_hmem @ x @ sk1075 )
| ( ( hF_Mir199975595nction @ A )
!= ( hF_Mir199975595nction @ zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[333,43228]) ).
thf(56195,plain,
( ~ ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ B ) @ zero_z189798548lle_hf )
=> ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ C ) @ zero_z189798548lle_hf )
=> ( B = C ) ) )
| ~ ( hF_Mirabelle_hmem @ x @ sk1075 ) ),
inference(pattern_uni,[status(thm)],[56194:[bind(A,$thf( zero_z189798548lle_hf ))]]) ).
thf(56353,plain,
( ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk2008 @ sk2009 ) @ zero_z189798548lle_hf )
| ~ ( hF_Mirabelle_hmem @ x @ sk1075 ) )
& ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk2008 @ sk2010 ) @ zero_z189798548lle_hf )
| ~ ( hF_Mirabelle_hmem @ x @ sk1075 ) )
& ( ( sk2009 != sk2010 )
| ~ ( hF_Mirabelle_hmem @ x @ sk1075 ) ) ),
inference(cnf,[status(esa)],[56195]) ).
thf(56356,plain,
( ( sk2009 != sk2010 )
| ~ ( hF_Mirabelle_hmem @ x @ sk1075 ) ),
inference(cnfConj,[status(thm)],[56353]) ).
thf(56357,plain,
( ( sk2010 != sk2009 )
| ~ ( hF_Mirabelle_hmem @ x @ sk1075 ) ),
inference(lifteq,[status(thm)],[56356]) ).
thf(7,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) )
= ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_sup_Oleft__commute) ).
thf(83,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) )
= ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(84,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) )
= ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ A @ C ) ) ),
inference(cnf,[status(esa)],[83]) ).
thf(85,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) )
= ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ A @ C ) ) ),
inference(lifteq,[status(thm)],[84]) ).
thf(4,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( ( A
= ( sup_su638957495lle_hf @ B @ C ) )
=> ( ( sup_su638957495lle_hf @ A @ D )
= ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_boolean__algebra__cancel_Osup1) ).
thf(72,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( ( A
= ( sup_su638957495lle_hf @ B @ C ) )
=> ( ( sup_su638957495lle_hf @ A @ D )
= ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(73,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( A
= ( sup_su638957495lle_hf @ B @ C ) )
=> ! [D: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ D )
= ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ D ) ) ) ),
inference(miniscope,[status(thm)],[72]) ).
thf(74,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A
!= ( sup_su638957495lle_hf @ B @ C ) )
| ( ( sup_su638957495lle_hf @ A @ D )
= ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ D ) ) ) ),
inference(cnf,[status(esa)],[73]) ).
thf(75,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A
!= ( sup_su638957495lle_hf @ B @ C ) )
| ( ( sup_su638957495lle_hf @ A @ D )
= ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ D ) ) ) ),
inference(lifteq,[status(thm)],[74]) ).
thf(76,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A @ B ) @ C )
= ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) ),
inference(simp,[status(thm)],[75]) ).
thf(346,plain,
! [F: hF_Mirabelle_hf,E: hF_Mirabelle_hf,D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ A @ C ) ) @ F )
= ( sup_su638957495lle_hf @ D @ ( sup_su638957495lle_hf @ E @ F ) ) )
| ( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) )
!= ( sup_su638957495lle_hf @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[85,76]) ).
thf(347,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ A @ D ) ) @ B )
= ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ C @ D ) @ B ) ) ),
inference(pattern_uni,[status(thm)],[346:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( H )),bind(D,$thf( A )),bind(E,$thf( sup_su638957495lle_hf @ G @ H ))]]) ).
thf(392,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ A @ D ) ) @ B )
= ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ C @ D ) @ B ) ) ),
inference(simp,[status(thm)],[347]) ).
thf(305,plain,
! [F: hF_Mirabelle_hf,E: hF_Mirabelle_hf,D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) @ F )
= ( sup_su638957495lle_hf @ D @ ( sup_su638957495lle_hf @ E @ F ) ) )
| ( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A @ B ) @ C )
!= ( sup_su638957495lle_hf @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[76,76]) ).
thf(306,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ D @ A ) ) @ B )
= ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ C @ D ) @ ( sup_su638957495lle_hf @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[305:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( sup_su638957495lle_hf @ G @ H )),bind(E,$thf( C ))]]) ).
thf(313,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ D @ A ) ) @ B )
= ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ C @ D ) @ ( sup_su638957495lle_hf @ A @ B ) ) ),
inference(simp,[status(thm)],[306]) ).
thf(39480,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ D @ A ) @ B ) )
= ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ D @ ( sup_su638957495lle_hf @ A @ B ) ) ) ),
inference(rewrite,[status(thm)],[313,76]) ).
thf(52384,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A @ D ) @ B ) )
= ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ D @ B ) ) ) ),
inference(rewrite,[status(thm)],[392,39480,76]) ).
thf(168,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ A @ B )
!= ( hF_Mirabelle_hpair @ C @ D ) )
| ( A = C ) ),
inference(cnfConj,[status(thm)],[167]) ).
thf(170,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ A @ B )
!= ( hF_Mirabelle_hpair @ C @ D ) )
| ( A = C ) ),
inference(lifteq,[status(thm)],[168]) ).
thf(44244,plain,
! [A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44020,181]) ).
thf(44245,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ A ) ),
inference(simp,[status(thm)],[44244]) ).
thf(44403,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1564 @ sk1565 )
!= A )
| ( ( hF_Mir1653039215strict @ r @ x )
!= A ) ),
inference(simp,[status(thm)],[44245]) ).
thf(44577,plain,
( ( hF_Mir1653039215strict @ r @ x )
!= ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) ),
inference(simp,[status(thm)],[44403]) ).
thf(8,axiom,
( sup_su638957495lle_hf
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( sup_su638957495lle_hf @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_sup_Ocommute) ).
thf(86,plain,
( sup_su638957495lle_hf
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( sup_su638957495lle_hf @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(87,plain,
( sup_su638957495lle_hf
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( sup_su638957495lle_hf @ B @ A ) ) ),
inference(lifteq,[status(thm)],[86]) ).
thf(296,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ B )
= ( sup_su638957495lle_hf @ B @ A ) ),
inference(func_ext,[status(esa)],[87]) ).
thf(2868,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ B @ A ) @ C )
| ( ( sup_su638957495lle_hf @ A @ B )
!= ( sup_su638957495lle_hf @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[296,2752]) ).
thf(2869,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ B @ A ) @ A ),
inference(pattern_uni,[status(thm)],[2868:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(44655,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ B @ A ) @ A )
!= ( hF_Mirabelle_hmem @ sk1638 @ x ) ) ),
inference(paramod_ordered,[status(thm)],[44628,2869]) ).
thf(44656,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ B @ A ) @ A )
!= ( hF_Mirabelle_hmem @ sk1638 @ x ) ),
inference(simp,[status(thm)],[44655]) ).
thf(44809,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ B @ A )
!= sk1638 )
| ( A != x ) ),
inference(simp,[status(thm)],[44656]) ).
thf(44908,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ x )
!= sk1638 ),
inference(simp,[status(thm)],[44809]) ).
thf(55469,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ x )
!= sk1564 ),
inference(rewrite,[status(thm)],[44908,51420]) ).
thf(44735,plain,
! [A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ sk1638 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44628,181]) ).
thf(44736,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ sk1638 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ),
inference(simp,[status(thm)],[44735]) ).
thf(44828,plain,
! [A: hF_Mirabelle_hf] :
( ( sk1638 != A )
| ( x != A ) ),
inference(simp,[status(thm)],[44736]) ).
thf(44949,plain,
sk1638 != x,
inference(simp,[status(thm)],[44828]) ).
thf(51425,plain,
sk1564 != x,
inference(rewrite,[status(thm)],[44949,51420]) ).
thf(44626,plain,
hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) @ r,
inference(cnfConj,[status(thm)],[44625]) ).
thf(40,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ B )
=> ( ( hF_Mirabelle_HUnion @ A )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_hmem__Sup__ne) ).
thf(188,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ B )
=> ( ( hF_Mirabelle_HUnion @ A )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(189,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ A @ B )
| ( ( hF_Mirabelle_HUnion @ A )
!= B ) ),
inference(cnf,[status(esa)],[188]) ).
thf(190,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_HUnion @ A )
!= B )
| ~ ( hF_Mirabelle_hmem @ A @ B ) ),
inference(lifteq,[status(thm)],[189]) ).
thf(191,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ),
inference(simp,[status(thm)],[190]) ).
thf(47464,plain,
! [A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) @ r )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[44626,191]) ).
thf(47465,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) @ r )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ),
inference(simp,[status(thm)],[47464]) ).
thf(47616,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1564 @ sk1565 )
!= A )
| ( ( hF_Mirabelle_HUnion @ A )
!= r ) ),
inference(simp,[status(thm)],[47465]) ).
thf(47654,plain,
( ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) )
!= r ),
inference(simp,[status(thm)],[47616]) ).
thf(198,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk3 @ B @ A ) @ A )
| ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir1248913145eplace @ A @ B ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) ) ),
inference(cnfConj,[status(thm)],[197]) ).
thf(202,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir1248913145eplace @ A @ B ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) )
| ( hF_Mirabelle_hmem @ ( sk3 @ B @ A ) @ A ) ),
inference(lifteq,[status(thm)],[198]) ).
thf(2939,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ B @ A ) @ D )
| ( ( sup_su638957495lle_hf @ A @ B )
!= ( sup_su638957495lle_hf @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[296,2753]) ).
thf(2940,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ B @ A ) @ B ),
inference(pattern_uni,[status(thm)],[2939:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(18,axiom,
! [A: hF_Mirabelle_hf] :
( ( zero_z189798548lle_hf = A )
= ( A = zero_z189798548lle_hf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_zero__reorient) ).
thf(115,plain,
! [A: hF_Mirabelle_hf] :
( ( zero_z189798548lle_hf = A )
= ( A = zero_z189798548lle_hf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(60431,plain,
hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) @ r,
inference(cnfConj,[status(thm)],[60430]) ).
thf(61676,plain,
! [A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) @ r )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[60431,181]) ).
thf(61677,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) @ r )
!= ( hF_Mirabelle_hmem @ A @ A ) ),
inference(simp,[status(thm)],[61676]) ).
thf(61771,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1564 @ sk1566 )
!= A )
| ( r != A ) ),
inference(simp,[status(thm)],[61677]) ).
thf(61889,plain,
( ( hF_Mirabelle_hpair @ sk1564 @ sk1566 )
!= r ),
inference(simp,[status(thm)],[61771]) ).
thf(59,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf,D: hF_Mirabelle_hf > hF_Mirabelle_hf] :
( ( A = B )
=> ( ! [E: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( hF_Mirabelle_RepFun @ A @ C )
= ( hF_Mirabelle_RepFun @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_RepFun__cong) ).
thf(268,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf,D: hF_Mirabelle_hf > hF_Mirabelle_hf] :
( ( A = B )
=> ( ! [E: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( hF_Mirabelle_RepFun @ A @ C )
= ( hF_Mirabelle_RepFun @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(269,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( A = B )
=> ! [C: hF_Mirabelle_hf > hF_Mirabelle_hf,D: hF_Mirabelle_hf > hF_Mirabelle_hf] :
( ! [E: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( hF_Mirabelle_RepFun @ A @ C )
= ( hF_Mirabelle_RepFun @ B @ D ) ) ) ),
inference(miniscope,[status(thm)],[268]) ).
thf(270,plain,
! [D: hF_Mirabelle_hf > hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( A != B )
| ( hF_Mirabelle_hmem @ ( sk16 @ D @ C @ B @ A ) @ B )
| ( ( hF_Mirabelle_RepFun @ A @ C )
= ( hF_Mirabelle_RepFun @ B @ D ) ) )
& ( ( A != B )
| ( ( C @ ( sk16 @ D @ C @ B @ A ) )
!= ( D @ ( sk16 @ D @ C @ B @ A ) ) )
| ( ( hF_Mirabelle_RepFun @ A @ C )
= ( hF_Mirabelle_RepFun @ B @ D ) ) ) ),
inference(cnf,[status(esa)],[269]) ).
thf(272,plain,
! [D: hF_Mirabelle_hf > hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A != B )
| ( ( C @ ( sk16 @ D @ C @ B @ A ) )
!= ( D @ ( sk16 @ D @ C @ B @ A ) ) )
| ( ( hF_Mirabelle_RepFun @ A @ C )
= ( hF_Mirabelle_RepFun @ B @ D ) ) ),
inference(cnfConj,[status(thm)],[270]) ).
thf(275,plain,
! [D: hF_Mirabelle_hf > hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A != B )
| ( ( C @ ( sk16 @ D @ C @ B @ A ) )
!= ( D @ ( sk16 @ D @ C @ B @ A ) ) )
| ( ( hF_Mirabelle_RepFun @ A @ C )
= ( hF_Mirabelle_RepFun @ B @ D ) ) ),
inference(lifteq,[status(thm)],[272]) ).
thf(276,plain,
! [C: hF_Mirabelle_hf > hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( B @ ( sk16 @ C @ B @ A @ A ) )
!= ( C @ ( sk16 @ C @ B @ A @ A ) ) )
| ( ( hF_Mirabelle_RepFun @ A @ B )
= ( hF_Mirabelle_RepFun @ A @ C ) ) ),
inference(simp,[status(thm)],[275]) ).
thf(47480,plain,
! [A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) @ r )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44626,181]) ).
thf(47481,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) @ r )
!= ( hF_Mirabelle_hmem @ A @ A ) ),
inference(simp,[status(thm)],[47480]) ).
thf(47561,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1564 @ sk1565 )
!= A )
| ( r != A ) ),
inference(simp,[status(thm)],[47481]) ).
thf(47742,plain,
( ( hF_Mirabelle_hpair @ sk1564 @ sk1565 )
!= r ),
inference(simp,[status(thm)],[47561]) ).
thf(334,plain,
( ( hF_Mir434065167lation = hF_Mir199975595nction )
| ( ( ^ [A: hF_Mirabelle_hf] :
! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ C ) @ A )
=> ! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ D ) @ A )
=> ( C = D ) ) ) )
!= ( ^ [A: hF_Mirabelle_hf] :
! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[293,227]) ).
thf(336,plain,
( ( hF_Mir434065167lation = hF_Mir199975595nction )
| ( ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ C ) @ A )
=> ! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ D ) @ A )
=> ( C = D ) ) ) )
!= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) ) ) ) ),
inference(simp,[status(thm)],[334]) ).
thf(449,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mir434065167lation @ A )
= ( hF_Mir199975595nction @ A ) )
| ( ( ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk19 @ B ) @ sk18 )
=> ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk19 @ C ) @ sk18 )
=> ( B = C ) ) ) )
!= ( ( hF_Mirabelle_hmem @ sk19 @ sk18 )
=> ( hF_Mir137170979_hpair @ sk19 ) ) ) ),
inference(func_ext,[status(esa)],[336]) ).
thf(19,axiom,
! [A: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( ( hF_Mirabelle_Replace @ zero_z189798548lle_hf @ A )
= zero_z189798548lle_hf ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_Replace__0) ).
thf(118,plain,
! [A: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( ( hF_Mirabelle_Replace @ zero_z189798548lle_hf @ A )
= zero_z189798548lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(119,plain,
! [A: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( ( hF_Mirabelle_Replace @ zero_z189798548lle_hf @ A )
= zero_z189798548lle_hf ),
inference(cnf,[status(esa)],[118]) ).
thf(120,plain,
! [A: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( ( hF_Mirabelle_Replace @ zero_z189798548lle_hf @ A )
= zero_z189798548lle_hf ),
inference(lifteq,[status(thm)],[119]) ).
thf(52,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,D: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( ( A = B )
=> ( ! [E: hF_Mirabelle_hf,F: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ E @ B )
=> ( ( C @ E @ F )
= ( D @ E @ F ) ) )
=> ( ( hF_Mirabelle_Replace @ A @ C )
= ( hF_Mirabelle_Replace @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_Replace__cong) ).
thf(239,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,D: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( ( A = B )
=> ( ! [E: hF_Mirabelle_hf,F: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ E @ B )
=> ( ( C @ E @ F )
= ( D @ E @ F ) ) )
=> ( ( hF_Mirabelle_Replace @ A @ C )
= ( hF_Mirabelle_Replace @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(240,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( A = B )
=> ! [C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,D: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( ! [E: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ E @ B )
=> ! [F: hF_Mirabelle_hf] :
( ( C @ E @ F )
= ( D @ E @ F ) ) )
=> ( ( hF_Mirabelle_Replace @ A @ C )
= ( hF_Mirabelle_Replace @ B @ D ) ) ) ),
inference(miniscope,[status(thm)],[239]) ).
thf(241,plain,
! [D: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( A != B )
| ( hF_Mirabelle_hmem @ ( sk13 @ D @ C @ B @ A ) @ B )
| ( ( hF_Mirabelle_Replace @ A @ C )
= ( hF_Mirabelle_Replace @ B @ D ) ) )
& ( ( A != B )
| ( ( C @ ( sk13 @ D @ C @ B @ A ) @ ( sk14 @ D @ C @ B @ A ) )
!= ( D @ ( sk13 @ D @ C @ B @ A ) @ ( sk14 @ D @ C @ B @ A ) ) )
| ( ( hF_Mirabelle_Replace @ A @ C )
= ( hF_Mirabelle_Replace @ B @ D ) ) ) ),
inference(cnf,[status(esa)],[240]) ).
thf(243,plain,
! [D: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A != B )
| ( ( C @ ( sk13 @ D @ C @ B @ A ) @ ( sk14 @ D @ C @ B @ A ) )
!= ( D @ ( sk13 @ D @ C @ B @ A ) @ ( sk14 @ D @ C @ B @ A ) ) )
| ( ( hF_Mirabelle_Replace @ A @ C )
= ( hF_Mirabelle_Replace @ B @ D ) ) ),
inference(cnfConj,[status(thm)],[241]) ).
thf(246,plain,
! [D: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A != B )
| ( ( C @ ( sk13 @ D @ C @ B @ A ) @ ( sk14 @ D @ C @ B @ A ) )
!= ( D @ ( sk13 @ D @ C @ B @ A ) @ ( sk14 @ D @ C @ B @ A ) ) )
| ( ( hF_Mirabelle_Replace @ A @ C )
= ( hF_Mirabelle_Replace @ B @ D ) ) ),
inference(lifteq,[status(thm)],[243]) ).
thf(247,plain,
! [C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( B @ ( sk13 @ C @ B @ A @ A ) @ ( sk14 @ C @ B @ A @ A ) )
!= ( C @ ( sk13 @ C @ B @ A @ A ) @ ( sk14 @ C @ B @ A @ A ) ) )
| ( ( hF_Mirabelle_Replace @ A @ B )
= ( hF_Mirabelle_Replace @ A @ C ) ) ),
inference(simp,[status(thm)],[246]) ).
thf(60065,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ A @ B )
& ? [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] :
( ( A
= ( hF_Mirabelle_hpair @ D @ E ) )
& ( hF_Mirabelle_hmem @ D @ C ) ) )
| ( ( hF_Mirabelle_hmem @ A @ ( hF_Mir1653039215strict @ B @ C ) )
!= ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[291,44021]) ).
thf(60066,plain,
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) @ r )
& ? [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1564 @ sk1566 )
= ( hF_Mirabelle_hpair @ A @ B ) )
& ( hF_Mirabelle_hmem @ A @ x ) ) ),
inference(pattern_uni,[status(thm)],[60065:[bind(A,$thf( hF_Mirabelle_hpair @ sk1564 @ sk1566 )),bind(B,$thf( r )),bind(C,$thf( x ))]]) ).
thf(60436,plain,
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) @ r )
& ( ( hF_Mirabelle_hpair @ sk1564 @ sk1566 )
= ( hF_Mirabelle_hpair @ sk2142 @ sk2143 ) )
& ( hF_Mirabelle_hmem @ sk2142 @ x ) ),
inference(cnf,[status(esa)],[60066]) ).
thf(60438,plain,
( ( hF_Mirabelle_hpair @ sk1564 @ sk1566 )
= ( hF_Mirabelle_hpair @ sk2142 @ sk2143 ) ),
inference(cnfConj,[status(thm)],[60436]) ).
thf(60440,plain,
( ( hF_Mirabelle_hpair @ sk2142 @ sk2143 )
= ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) ),
inference(lifteq,[status(thm)],[60438]) ).
thf(65266,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) )
= B )
| ( ( hF_Mirabelle_hpair @ sk2142 @ sk2143 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[60440,235]) ).
thf(65267,plain,
( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) )
= sk2143 ),
inference(pattern_uni,[status(thm)],[65266:[bind(A,$thf( sk2142 )),bind(B,$thf( sk2143 ))]]) ).
thf(65925,plain,
sk2143 = sk1566,
inference(rewrite,[status(thm)],[65267,235]) ).
thf(61,axiom,
hF_Mir434065167lation @ zero_z189798548lle_hf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_hrelation__0) ).
thf(280,plain,
hF_Mir434065167lation @ zero_z189798548lle_hf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(54,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o] :
? [C: hF_Mirabelle_hf] :
! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ C )
= ( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_comprehension) ).
thf(252,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o] :
? [C: hF_Mirabelle_hf] :
! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ C )
= ( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(253,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ ( sk15 @ B @ A ) )
= ( ( hF_Mirabelle_hmem @ C @ A )
& ( B @ C ) ) ),
inference(cnf,[status(esa)],[252]) ).
thf(254,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ ( sk15 @ B @ A ) )
= ( ( hF_Mirabelle_hmem @ C @ A )
& ( B @ C ) ) ),
inference(lifteq,[status(thm)],[253]) ).
thf(26671,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ C @ ( sk15 @ B @ A ) )
= ( ( hF_Mirabelle_hmem @ C @ A )
& $true ) )
| ( ( hF_Mir434065167lation @ zero_z189798548lle_hf )
!= ( B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[280,254]) ).
thf(26672,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ C @ ( sk15 @ B @ A ) )
= ( hF_Mirabelle_hmem @ C @ A ) )
| ( ( hF_Mir434065167lation @ zero_z189798548lle_hf )
!= ( B @ C ) ) ),
inference(simp,[status(thm)],[26671]) ).
thf(27164,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ ( sk15 @ hF_Mir434065167lation @ A ) )
= ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ A ) ),
inference(pre_uni,[status(thm)],[26672:[bind(A,$thf( A )),bind(B,$thf( hF_Mir434065167lation )),bind(C,$thf( zero_z189798548lle_hf ))]]) ).
thf(28085,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ zero_z189798548lle_hf
@ ( sk15
@ ^ [B: hF_Mirabelle_hf] :
! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ B )
=> ( hF_Mir137170979_hpair @ C ) )
@ A ) )
= ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ A ) )
| ( hF_Mir434065167lation != hF_Mir434065167lation ) ),
inference(paramod_ordered,[status(thm)],[227,27164]) ).
thf(28086,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ zero_z189798548lle_hf
@ ( sk15
@ ^ [B: hF_Mirabelle_hf] :
! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ B )
=> ( hF_Mir137170979_hpair @ C ) )
@ A ) )
= ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ A ) ),
inference(pattern_uni,[status(thm)],[28085:[]]) ).
thf(10,axiom,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_sup__idem) ).
thf(91,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(92,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ A )
= A ),
inference(cnf,[status(esa)],[91]) ).
thf(93,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ A )
= A ),
inference(lifteq,[status(thm)],[92]) ).
thf(432,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) )
= D )
| ( ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ A @ C ) )
!= ( sup_su638957495lle_hf @ D @ D ) ) ),
inference(paramod_ordered,[status(thm)],[85,93]) ).
thf(433,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A @ B ) @ B ) )
= ( sup_su638957495lle_hf @ A @ B ) ),
inference(pattern_uni,[status(thm)],[432:[bind(A,$thf( E )),bind(B,$thf( sup_su638957495lle_hf @ E @ F )),bind(C,$thf( F )),bind(D,$thf( sup_su638957495lle_hf @ E @ F ))]]) ).
thf(439,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A @ B ) @ B ) )
= ( sup_su638957495lle_hf @ A @ B ) ),
inference(simp,[status(thm)],[433]) ).
thf(63732,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ B ) ) )
= ( sup_su638957495lle_hf @ A @ B ) ),
inference(rewrite,[status(thm)],[439,39480]) ).
thf(22,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= zero_z189798548lle_hf ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_hpair__nonzero) ).
thf(126,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= zero_z189798548lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(127,plain,
~ ? [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
= zero_z189798548lle_hf ),
inference(miniscope,[status(thm)],[126]) ).
thf(128,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= zero_z189798548lle_hf ),
inference(cnf,[status(esa)],[127]) ).
thf(129,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= zero_z189798548lle_hf ),
inference(lifteq,[status(thm)],[128]) ).
thf(888,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
| ( zero_z189798548lle_hf != zero_z189798548lle_hf )
| ( A
!= ( hF_Mirabelle_hpair @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[468,129]) ).
thf(889,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
| ( A
!= ( hF_Mirabelle_hpair @ B @ C ) ) ),
inference(simp,[status(thm)],[888]) ).
thf(890,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] : ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mirabelle_hpair @ A @ B ) ) @ ( hF_Mirabelle_hpair @ A @ B ) ),
inference(pattern_uni,[status(thm)],[889:[bind(A,$thf( hF_Mirabelle_hpair @ D @ E )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(1034,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] : ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mirabelle_hpair @ A @ B ) ) @ ( hF_Mirabelle_hpair @ A @ B ) ),
inference(simp,[status(thm)],[890]) ).
thf(2096,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mirabelle_hpair @ A @ B ) ) @ ( hF_Mirabelle_hpair @ A @ B ) )
!= ( hF_Mirabelle_hmem @ C @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1034,181]) ).
thf(2097,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mirabelle_hpair @ A @ B ) ) @ ( hF_Mirabelle_hpair @ A @ B ) )
!= ( hF_Mirabelle_hmem @ C @ C ) ),
inference(simp,[status(thm)],[2096]) ).
thf(2113,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk20 @ ( hF_Mirabelle_hpair @ A @ B ) )
!= C )
| ( ( hF_Mirabelle_hpair @ A @ B )
!= C ) ),
inference(simp,[status(thm)],[2097]) ).
thf(2115,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sk20 @ ( hF_Mirabelle_hpair @ A @ B ) )
!= ( hF_Mirabelle_hpair @ A @ B ) ),
inference(simp,[status(thm)],[2113]) ).
thf(64334,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk20 @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) )
!= ( hF_Mirabelle_hpair @ A @ B ) )
| ( ( hF_Mirabelle_hpair @ sk2140 @ sk2141 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[60434,2115]) ).
thf(64335,plain,
( ( hF_Mirabelle_hpair @ sk2140 @ sk2141 )
!= ( sk20 @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) ) ),
inference(pattern_uni,[status(thm)],[64334:[bind(A,$thf( sk2140 )),bind(B,$thf( sk2141 ))]]) ).
thf(64374,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) )
= B )
| ( ( hF_Mirabelle_hpair @ sk2140 @ sk2141 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[60434,235]) ).
thf(64375,plain,
( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) )
= sk2141 ),
inference(pattern_uni,[status(thm)],[64374:[bind(A,$thf( sk2140 )),bind(B,$thf( sk2141 ))]]) ).
thf(65101,plain,
sk2141 = sk1566,
inference(rewrite,[status(thm)],[64375,235]) ).
thf(70783,plain,
( ( sk20 @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) )
!= ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) ),
inference(rewrite,[status(thm)],[64335,65033,65101]) ).
thf(47493,plain,
! [A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) @ r )
!= ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[44626,7297]) ).
thf(47494,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) @ r )
!= ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[47493]) ).
thf(47628,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1564 @ sk1565 )
!= A )
| ( r != zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[47494]) ).
thf(47684,plain,
r != zero_z189798548lle_hf,
inference(simp,[status(thm)],[47628]) ).
thf(47867,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
| ( zero_z189798548lle_hf != zero_z189798548lle_hf )
| ( A != r ) ),
inference(paramod_ordered,[status(thm)],[468,47684]) ).
thf(47868,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
| ( A != r ) ),
inference(simp,[status(thm)],[47867]) ).
thf(47869,plain,
hF_Mirabelle_hmem @ ( sk20 @ r ) @ r,
inference(pattern_uni,[status(thm)],[47868:[bind(A,$thf( r ))]]) ).
thf(48445,plain,
! [A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[47869,181]) ).
thf(48446,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r )
!= ( hF_Mirabelle_hmem @ A @ A ) ),
inference(simp,[status(thm)],[48445]) ).
thf(48602,plain,
! [A: hF_Mirabelle_hf] :
( ( ( sk20 @ r )
!= A )
| ( r != A ) ),
inference(simp,[status(thm)],[48446]) ).
thf(48810,plain,
( ( sk20 @ r )
!= r ),
inference(simp,[status(thm)],[48602]) ).
thf(60439,plain,
hF_Mirabelle_hmem @ sk2142 @ x,
inference(cnfConj,[status(thm)],[60436]) ).
thf(60982,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir434065167lation @ A )
| ~ $true
| ( hF_Mir137170979_hpair @ B )
| ( ( hF_Mirabelle_hmem @ sk2142 @ x )
!= ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[60439,562]) ).
thf(60983,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir434065167lation @ A )
| ( hF_Mir137170979_hpair @ B )
| ( ( hF_Mirabelle_hmem @ sk2142 @ x )
!= ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(simp,[status(thm)],[60982]) ).
thf(60984,plain,
( ~ ( hF_Mir434065167lation @ x )
| ( hF_Mir137170979_hpair @ sk2142 ) ),
inference(pattern_uni,[status(thm)],[60983:[bind(A,$thf( x )),bind(B,$thf( sk2142 ))]]) ).
thf(62888,plain,
! [A: hF_Mirabelle_hf] :
( ~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) )
| ( hF_Mir137170979_hpair @ sk2142 )
| ( ( hF_Mir434065167lation @ A )
!= ( hF_Mir434065167lation @ x ) ) ),
inference(paramod_ordered,[status(thm)],[301,60984]) ).
thf(62889,plain,
( ~ ! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ x )
=> ( hF_Mir137170979_hpair @ A ) )
| ( hF_Mir137170979_hpair @ sk2142 ) ),
inference(pattern_uni,[status(thm)],[62888:[bind(A,$thf( x ))]]) ).
thf(62973,plain,
( ( ( hF_Mirabelle_hmem @ sk2246 @ x )
| ( hF_Mir137170979_hpair @ sk2142 ) )
& ( ~ ( hF_Mir137170979_hpair @ sk2246 )
| ( hF_Mir137170979_hpair @ sk2142 ) ) ),
inference(cnf,[status(esa)],[62889]) ).
thf(62974,plain,
( ( hF_Mirabelle_hmem @ sk2246 @ x )
| ( hF_Mir137170979_hpair @ sk2142 ) ),
inference(cnfConj,[status(thm)],[62973]) ).
thf(64571,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk2142 )
| ~ $true
| ( ( hF_Mirabelle_hmem @ sk2246 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[62974,181]) ).
thf(64572,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk2142 )
| ( ( hF_Mirabelle_hmem @ sk2246 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(simp,[status(thm)],[64571]) ).
thf(64655,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk2142 )
| ( sk2246 != A )
| ( x != A ) ),
inference(simp,[status(thm)],[64572]) ).
thf(64780,plain,
( ( hF_Mir137170979_hpair @ sk2142 )
| ( sk2246 != x ) ),
inference(simp,[status(thm)],[64655]) ).
thf(65240,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) )
= A )
| ( ( hF_Mirabelle_hpair @ sk2142 @ sk2143 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[60440,286]) ).
thf(65241,plain,
( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) )
= sk2142 ),
inference(pattern_uni,[status(thm)],[65240:[bind(A,$thf( sk2142 )),bind(B,$thf( sk2143 ))]]) ).
thf(65908,plain,
sk2142 = sk1564,
inference(rewrite,[status(thm)],[65241,286]) ).
thf(66438,plain,
( ( hF_Mir137170979_hpair @ sk1564 )
| ( sk2246 != x ) ),
inference(rewrite,[status(thm)],[64780,65908]) ).
thf(39,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ B ) )
= ( ? [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ B )
& ( hF_Mirabelle_hmem @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_HUnion__iff) ).
thf(185,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ B ) )
= ( ? [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ B )
& ( hF_Mirabelle_hmem @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(58,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_hpair__neq__fst) ).
thf(264,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(265,plain,
~ ? [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
= A ),
inference(miniscope,[status(thm)],[264]) ).
thf(266,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= A ),
inference(cnf,[status(esa)],[265]) ).
thf(267,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= A ),
inference(lifteq,[status(thm)],[266]) ).
thf(50788,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1564 @ sk1565 )
!= A )
| ( ( hF_Mirabelle_hpair @ sk1638 @ sk1639 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[44629,267]) ).
thf(50789,plain,
( ( hF_Mirabelle_hpair @ sk1564 @ sk1565 )
!= sk1638 ),
inference(pattern_uni,[status(thm)],[50788:[bind(A,$thf( sk1638 )),bind(B,$thf( sk1639 ))]]) ).
thf(51422,plain,
( ( hF_Mirabelle_hpair @ sk1564 @ sk1565 )
!= sk1564 ),
inference(rewrite,[status(thm)],[50789,51420]) ).
thf(2943,plain,
! [E: hF_Mirabelle_hf,D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( ( hF_Mirabelle_hmem @ A @ B )
| ( hF_Mirabelle_hmem @ A @ C ) )
| ( ( hF_Mirabelle_hmem @ A @ ( sup_su638957495lle_hf @ B @ C ) )
!= ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ D @ E ) @ E ) ) ),
inference(paramod_ordered,[status(thm)],[159,2753]) ).
thf(2944,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) @ B )
| ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) @ C ) ),
inference(pattern_uni,[status(thm)],[2943:[bind(A,$thf( sup_su638957495lle_hf @ F @ ( sup_su638957495lle_hf @ H @ I ) )),bind(B,$thf( H )),bind(C,$thf( I )),bind(D,$thf( F )),bind(E,$thf( sup_su638957495lle_hf @ H @ I ))]]) ).
thf(2969,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) @ B )
& ~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) @ C ) ),
inference(cnf,[status(esa)],[2944]) ).
thf(2970,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) @ B ),
inference(cnfConj,[status(thm)],[2969]) ).
thf(2972,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) @ B ),
inference(simp,[status(thm)],[2970]) ).
thf(53,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_hpair__neq__snd) ).
thf(248,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(249,plain,
~ ? [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
= B ),
inference(miniscope,[status(thm)],[248]) ).
thf(250,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= B ),
inference(cnf,[status(esa)],[249]) ).
thf(251,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= B ),
inference(lifteq,[status(thm)],[250]) ).
thf(50786,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1564 @ sk1565 )
!= B )
| ( ( hF_Mirabelle_hpair @ sk1638 @ sk1639 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[44629,251]) ).
thf(50787,plain,
( ( hF_Mirabelle_hpair @ sk1564 @ sk1565 )
!= sk1639 ),
inference(pattern_uni,[status(thm)],[50786:[bind(A,$thf( sk1638 )),bind(B,$thf( sk1639 ))]]) ).
thf(52189,plain,
( ( hF_Mirabelle_hpair @ sk1564 @ sk1565 )
!= sk1565 ),
inference(rewrite,[status(thm)],[50787,52188]) ).
thf(549,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir434065167lation @ A )
| ~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) ) ),
inference(bool_ext,[status(thm)],[301]) ).
thf(563,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mir434065167lation @ A )
| ( hF_Mirabelle_hmem @ ( sk27 @ A ) @ A ) )
& ( ( hF_Mir434065167lation @ A )
| ~ ( hF_Mir137170979_hpair @ ( sk27 @ A ) ) ) ),
inference(cnf,[status(esa)],[549]) ).
thf(565,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir434065167lation @ A )
| ~ ( hF_Mir137170979_hpair @ ( sk27 @ A ) ) ),
inference(cnfConj,[status(thm)],[563]) ).
thf(64,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( hF_Mir434065167lation @ ( hF_Mir1653039215strict @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_hrelation__restr) ).
thf(287,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( hF_Mir434065167lation @ ( hF_Mir1653039215strict @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(288,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] : ( hF_Mir434065167lation @ ( hF_Mir1653039215strict @ A @ B ) ),
inference(cnf,[status(esa)],[287]) ).
thf(48431,plain,
! [A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[47869,191]) ).
thf(48432,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ),
inference(simp,[status(thm)],[48431]) ).
thf(48549,plain,
! [A: hF_Mirabelle_hf] :
( ( ( sk20 @ r )
!= A )
| ( ( hF_Mirabelle_HUnion @ A )
!= r ) ),
inference(simp,[status(thm)],[48432]) ).
thf(48680,plain,
( ( hF_Mirabelle_HUnion @ ( sk20 @ r ) )
!= r ),
inference(simp,[status(thm)],[48549]) ).
thf(51430,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
| ( sk1564 = zero_z189798548lle_hf )
| ( A != sk1638 ) ),
inference(paramod_ordered,[status(thm)],[468,51420]) ).
thf(51431,plain,
( ( hF_Mirabelle_hmem @ ( sk20 @ sk1638 ) @ sk1638 )
| ( sk1564 = zero_z189798548lle_hf ) ),
inference(pattern_uni,[status(thm)],[51430:[bind(A,$thf( sk1638 ))]]) ).
thf(56420,plain,
( ( hF_Mirabelle_hmem @ ( sk20 @ sk1564 ) @ sk1564 )
| ( sk1564 = zero_z189798548lle_hf ) ),
inference(rewrite,[status(thm)],[51431,51420]) ).
thf(60006,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ $true
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[44021,184]) ).
thf(60007,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(simp,[status(thm)],[60006]) ).
thf(60008,plain,
~ ( hF_Mirabelle_hmem @ ( hF_Mir1653039215strict @ r @ x ) @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) ),
inference(pattern_uni,[status(thm)],[60007:[bind(A,$thf( hF_Mirabelle_hpair @ sk1564 @ sk1566 )),bind(B,$thf( hF_Mir1653039215strict @ r @ x ))]]) ).
thf(839,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
| ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
| ( A != x ) ),
inference(paramod_ordered,[status(thm)],[468,68]) ).
thf(840,plain,
( ( hF_Mirabelle_hmem @ ( sk20 @ x ) @ x )
| ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) ) ),
inference(pattern_uni,[status(thm)],[839:[bind(A,$thf( x ))]]) ).
thf(1289,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
| ~ ( hF_Mir434065167lation @ A )
| ~ $true
| ( hF_Mir137170979_hpair @ B )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ x ) @ x )
!= ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[840,562]) ).
thf(1290,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
| ~ ( hF_Mir434065167lation @ A )
| ( hF_Mir137170979_hpair @ B )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ x ) @ x )
!= ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(simp,[status(thm)],[1289]) ).
thf(1291,plain,
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
| ~ ( hF_Mir434065167lation @ x )
| ( hF_Mir137170979_hpair @ ( sk20 @ x ) ) ),
inference(pattern_uni,[status(thm)],[1290:[bind(A,$thf( x )),bind(B,$thf( sk20 @ x ))]]) ).
thf(2198,plain,
( ~ $true
| ~ ( hF_Mir434065167lation @ x )
| ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
!= ( hF_Mir199975595nction @ r ) ) ),
inference(paramod_ordered,[status(thm)],[294,1291]) ).
thf(2199,plain,
( ~ ( hF_Mir434065167lation @ x )
| ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
!= ( hF_Mir199975595nction @ r ) ) ),
inference(simp,[status(thm)],[2198]) ).
thf(2200,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ~ ( hF_Mir434065167lation @ x )
| ( ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf )
!= r ) ),
inference(simp,[status(thm)],[2199]) ).
thf(2646,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) )
| ( ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf )
!= r )
| ( ( hF_Mir434065167lation @ A )
!= ( hF_Mir434065167lation @ x ) ) ),
inference(paramod_ordered,[status(thm)],[301,2200]) ).
thf(2647,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ~ ! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ x )
=> ( hF_Mir137170979_hpair @ A ) )
| ( ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf )
!= r ) ),
inference(pattern_uni,[status(thm)],[2646:[bind(A,$thf( x ))]]) ).
thf(2652,plain,
( ( ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ( hF_Mirabelle_hmem @ sk50 @ x )
| ( ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf )
!= r ) )
& ( ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ~ ( hF_Mir137170979_hpair @ sk50 )
| ( ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf )
!= r ) ) ),
inference(cnf,[status(esa)],[2647]) ).
thf(2654,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ~ ( hF_Mir137170979_hpair @ sk50 )
| ( ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf )
!= r ) ),
inference(cnfConj,[status(thm)],[2652]) ).
thf(36029,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( ( hF_Mirabelle_hmem @ A @ B )
& ? [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] :
( ( A
= ( hF_Mirabelle_hpair @ D @ E ) )
& ( hF_Mirabelle_hmem @ D @ C ) ) )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mir1653039215strict @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[836,291]) ).
thf(36030,plain,
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) @ r )
& ? [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
= ( hF_Mirabelle_hpair @ A @ B ) )
& ( hF_Mirabelle_hmem @ A @ x ) ) ) ),
inference(pattern_uni,[status(thm)],[36029:[bind(A,$thf( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )),bind(B,$thf( r )),bind(C,$thf( x ))]]) ).
thf(36451,plain,
( ( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) @ r ) )
& ( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
= ( hF_Mirabelle_hpair @ sk1077 @ sk1078 ) ) )
& ( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( hF_Mirabelle_hmem @ sk1077 @ x ) ) ),
inference(cnf,[status(esa)],[36030]) ).
thf(36454,plain,
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( hF_Mirabelle_hmem @ sk1077 @ x ) ),
inference(cnfConj,[status(thm)],[36451]) ).
thf(58703,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ~ $true
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ sk1077 @ x )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[36454,184]) ).
thf(58704,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ sk1077 @ x )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(simp,[status(thm)],[58703]) ).
thf(58705,plain,
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ~ ( hF_Mirabelle_hmem @ x @ sk1077 ) ),
inference(pattern_uni,[status(thm)],[58704:[bind(A,$thf( sk1077 )),bind(B,$thf( x ))]]) ).
thf(44657,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ $true
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ sk1638 @ x )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[44628,184]) ).
thf(44658,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ sk1638 @ x )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(simp,[status(thm)],[44657]) ).
thf(44659,plain,
~ ( hF_Mirabelle_hmem @ x @ sk1638 ),
inference(pattern_uni,[status(thm)],[44658:[bind(A,$thf( sk1638 )),bind(B,$thf( x ))]]) ).
thf(45133,plain,
! [A: hF_Mirabelle_hf] :
( ( A = zero_z189798548lle_hf )
| ~ $true
| ( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
!= ( hF_Mirabelle_hmem @ x @ sk1638 ) ) ),
inference(paramod_ordered,[status(thm)],[468,44659]) ).
thf(45134,plain,
! [A: hF_Mirabelle_hf] :
( ( A = zero_z189798548lle_hf )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
!= ( hF_Mirabelle_hmem @ x @ sk1638 ) ) ),
inference(simp,[status(thm)],[45133]) ).
thf(45286,plain,
! [A: hF_Mirabelle_hf] :
( ( A = zero_z189798548lle_hf )
| ( ( sk20 @ A )
!= x )
| ( A != sk1638 ) ),
inference(simp,[status(thm)],[45134]) ).
thf(45362,plain,
( ( sk1638 = zero_z189798548lle_hf )
| ( ( sk20 @ sk1638 )
!= x ) ),
inference(simp,[status(thm)],[45286]) ).
thf(70177,plain,
( ( sk1564 = zero_z189798548lle_hf )
| ( ( sk20 @ sk1564 )
!= x ) ),
inference(rewrite,[status(thm)],[45362,51420]) ).
thf(44235,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ A @ B )
& ? [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] :
( ( A
= ( hF_Mirabelle_hpair @ D @ E ) )
& ( hF_Mirabelle_hmem @ D @ C ) ) )
| ( ( hF_Mirabelle_hmem @ A @ ( hF_Mir1653039215strict @ B @ C ) )
!= ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[291,44020]) ).
thf(44236,plain,
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) @ r )
& ? [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1564 @ sk1565 )
= ( hF_Mirabelle_hpair @ A @ B ) )
& ( hF_Mirabelle_hmem @ A @ x ) ) ),
inference(pattern_uni,[status(thm)],[44235:[bind(A,$thf( hF_Mirabelle_hpair @ sk1564 @ sk1565 )),bind(B,$thf( r )),bind(C,$thf( x ))]]) ).
thf(44631,plain,
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) @ r )
& ( ( hF_Mirabelle_hpair @ sk1564 @ sk1565 )
= ( hF_Mirabelle_hpair @ sk1640 @ sk1641 ) )
& ( hF_Mirabelle_hmem @ sk1640 @ x ) ),
inference(cnf,[status(esa)],[44236]) ).
thf(44633,plain,
( ( hF_Mirabelle_hpair @ sk1564 @ sk1565 )
= ( hF_Mirabelle_hpair @ sk1640 @ sk1641 ) ),
inference(cnfConj,[status(thm)],[44631]) ).
thf(44635,plain,
( ( hF_Mirabelle_hpair @ sk1640 @ sk1641 )
= ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) ),
inference(lifteq,[status(thm)],[44633]) ).
thf(52280,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) )
= B )
| ( ( hF_Mirabelle_hpair @ sk1640 @ sk1641 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[44635,235]) ).
thf(52281,plain,
( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) )
= sk1641 ),
inference(pattern_uni,[status(thm)],[52280:[bind(A,$thf( sk1640 )),bind(B,$thf( sk1641 ))]]) ).
thf(54872,plain,
sk1641 = sk1565,
inference(rewrite,[status(thm)],[52281,235]) ).
thf(46252,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ $true
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ x ) @ x )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[45120,184]) ).
thf(46253,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ x ) @ x )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(simp,[status(thm)],[46252]) ).
thf(46254,plain,
~ ( hF_Mirabelle_hmem @ x @ ( sk20 @ x ) ),
inference(pattern_uni,[status(thm)],[46253:[bind(A,$thf( sk20 @ x )),bind(B,$thf( x ))]]) ).
thf(46312,plain,
! [A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( sk20 @ x ) @ x )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[45120,191]) ).
thf(46313,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ x ) @ x )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ),
inference(simp,[status(thm)],[46312]) ).
thf(46443,plain,
! [A: hF_Mirabelle_hf] :
( ( ( sk20 @ x )
!= A )
| ( ( hF_Mirabelle_HUnion @ A )
!= x ) ),
inference(simp,[status(thm)],[46313]) ).
thf(46581,plain,
( ( hF_Mirabelle_HUnion @ ( sk20 @ x ) )
!= x ),
inference(simp,[status(thm)],[46443]) ).
thf(52190,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
| ( sk1565 = zero_z189798548lle_hf )
| ( A != sk1639 ) ),
inference(paramod_ordered,[status(thm)],[468,52188]) ).
thf(52191,plain,
( ( hF_Mirabelle_hmem @ ( sk20 @ sk1639 ) @ sk1639 )
| ( sk1565 = zero_z189798548lle_hf ) ),
inference(pattern_uni,[status(thm)],[52190:[bind(A,$thf( sk1639 ))]]) ).
thf(58045,plain,
( ( hF_Mirabelle_hmem @ ( sk20 @ sk1565 ) @ sk1565 )
| ( sk1565 = zero_z189798548lle_hf ) ),
inference(rewrite,[status(thm)],[52191,52188]) ).
thf(56,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mir818139703ollect @ B @ C ) )
= ( ( B @ A )
& ( hF_Mirabelle_hmem @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_HCollect__iff) ).
thf(258,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mir818139703ollect @ B @ C ) )
= ( ( B @ A )
& ( hF_Mirabelle_hmem @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(259,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mir818139703ollect @ B @ C ) )
= ( ( B @ A )
& ( hF_Mirabelle_hmem @ A @ C ) ) ),
inference(cnf,[status(esa)],[258]) ).
thf(260,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mir818139703ollect @ B @ C ) )
= ( ( B @ A )
& ( hF_Mirabelle_hmem @ A @ C ) ) ),
inference(lifteq,[status(thm)],[259]) ).
thf(29586,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ A @ ( hF_Mir818139703ollect @ B @ C ) )
= ( $true
& ( hF_Mirabelle_hmem @ A @ C ) ) )
| ( ( hF_Mir199975595nction @ r )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[294,260]) ).
thf(29587,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ A @ ( hF_Mir818139703ollect @ B @ C ) )
= ( hF_Mirabelle_hmem @ A @ C ) )
| ( ( hF_Mir199975595nction @ r )
!= ( B @ A ) ) ),
inference(simp,[status(thm)],[29586]) ).
thf(29883,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ r @ ( hF_Mir818139703ollect @ hF_Mir199975595nction @ A ) )
= ( hF_Mirabelle_hmem @ r @ A ) ),
inference(pre_uni,[status(thm)],[29587:[bind(A,$thf( r )),bind(B,$thf( hF_Mir199975595nction )),bind(C,$thf( C ))]]) ).
thf(30263,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ r @ ( hF_Mir818139703ollect @ hF_Mir199975595nction @ A ) )
= ( hF_Mirabelle_hmem @ r @ A ) ),
inference(simp,[status(thm)],[29883]) ).
thf(12140,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ ( sk7 @ B @ A ) @ A )
!= ( hF_Mirabelle_hmem @ ( sk7 @ B @ A ) @ B ) )
| ( B != r )
| ( A
!= ( hF_Mir1653039215strict @ r @ x ) ) ),
inference(paramod_ordered,[status(thm)],[214,299]) ).
thf(12141,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ ( sk7 @ A @ ( hF_Mir1653039215strict @ r @ x ) ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ ( sk7 @ A @ ( hF_Mir1653039215strict @ r @ x ) ) @ A ) )
| ( A != r ) ),
inference(pattern_uni,[status(thm)],[12140:[bind(A,$thf( hF_Mir1653039215strict @ r @ x )),bind(B,$thf( B ))]]) ).
thf(13780,plain,
( ( hF_Mirabelle_hmem @ ( sk7 @ r @ ( hF_Mir1653039215strict @ r @ x ) ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ ( sk7 @ r @ ( hF_Mir1653039215strict @ r @ x ) ) @ r ) ),
inference(simp,[status(thm)],[12141]) ).
thf(30854,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ r @ A )
!= ( hF_Mirabelle_hmem @ ( sk7 @ r @ ( hF_Mir1653039215strict @ r @ x ) ) @ r ) )
| ( ( hF_Mirabelle_hmem @ r @ ( hF_Mir818139703ollect @ hF_Mir199975595nction @ A ) )
!= ( hF_Mirabelle_hmem @ ( sk7 @ r @ ( hF_Mir1653039215strict @ r @ x ) ) @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[30263,13780]) ).
thf(31034,plain,
! [A: hF_Mirabelle_hf] :
( ( ( sk7 @ r @ ( hF_Mir1653039215strict @ r @ x ) )
!= r )
| ( A != r )
| ( ( sk7 @ r @ ( hF_Mir1653039215strict @ r @ x ) )
!= r )
| ( ( hF_Mir818139703ollect @ hF_Mir199975595nction @ A )
!= ( hF_Mir1653039215strict @ r @ x ) ) ),
inference(simp,[status(thm)],[30854]) ).
thf(31075,plain,
( ( ( sk7 @ r @ ( hF_Mir1653039215strict @ r @ x ) )
!= r )
| ( ( hF_Mir1653039215strict @ r @ x )
!= ( hF_Mir818139703ollect @ hF_Mir199975595nction @ r ) ) ),
inference(simp,[status(thm)],[31034]) ).
thf(956,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
| ( zero_z189798548lle_hf != C )
| ( A
!= ( hF_Mirabelle_hpair @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[468,251]) ).
thf(957,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mirabelle_hpair @ A @ B ) ) @ ( hF_Mirabelle_hpair @ A @ B ) )
| ( zero_z189798548lle_hf != B ) ),
inference(pattern_uni,[status(thm)],[956:[bind(A,$thf( hF_Mirabelle_hpair @ D @ E )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(1009,plain,
! [A: hF_Mirabelle_hf] : ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mirabelle_hpair @ A @ zero_z189798548lle_hf ) ) @ ( hF_Mirabelle_hpair @ A @ zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[957]) ).
thf(5,axiom,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_hmem__hempty) ).
thf(77,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(78,plain,
~ ? [A: hF_Mirabelle_hf] : ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ),
inference(miniscope,[status(thm)],[77]) ).
thf(79,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ),
inference(cnf,[status(esa)],[78]) ).
thf(1133,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mirabelle_hpair @ A @ zero_z189798548lle_hf ) ) @ ( hF_Mirabelle_hpair @ A @ zero_z189798548lle_hf ) )
!= ( hF_Mirabelle_hmem @ B @ zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[1009,79]) ).
thf(1134,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mirabelle_hpair @ A @ zero_z189798548lle_hf ) ) @ ( hF_Mirabelle_hpair @ A @ zero_z189798548lle_hf ) )
!= ( hF_Mirabelle_hmem @ B @ zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[1133]) ).
thf(1137,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk20 @ ( hF_Mirabelle_hpair @ A @ zero_z189798548lle_hf ) )
!= B )
| ( ( hF_Mirabelle_hpair @ A @ zero_z189798548lle_hf )
!= zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[1134]) ).
thf(1147,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ zero_z189798548lle_hf )
!= zero_z189798548lle_hf ),
inference(simp,[status(thm)],[1137]) ).
thf(48,axiom,
( ( (=) @ hF_Mirabelle_hf )
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
= ( hF_Mirabelle_hmem @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_hf__ext) ).
thf(228,plain,
( ( (=) @ hF_Mirabelle_hf )
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
= ( hF_Mirabelle_hmem @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(65911,plain,
( ( hF_Mirabelle_hmem @ sk2246 @ x )
| ( hF_Mir137170979_hpair @ sk1564 ) ),
inference(rewrite,[status(thm)],[62974,65908]) ).
thf(57,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mir434065167lation @ ( sup_su638957495lle_hf @ A @ B ) )
= ( ( hF_Mir434065167lation @ A )
& ( hF_Mir434065167lation @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_hrelation__hunion) ).
thf(261,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mir434065167lation @ ( sup_su638957495lle_hf @ A @ B ) )
= ( ( hF_Mir434065167lation @ A )
& ( hF_Mir434065167lation @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(48379,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ $true
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[47869,184]) ).
thf(48380,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(simp,[status(thm)],[48379]) ).
thf(48381,plain,
~ ( hF_Mirabelle_hmem @ r @ ( sk20 @ r ) ),
inference(pattern_uni,[status(thm)],[48380:[bind(A,$thf( sk20 @ r )),bind(B,$thf( r ))]]) ).
thf(44,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_RepFun @ B @ C ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ B )
& ( A
= ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_RepFun__iff) ).
thf(209,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_RepFun @ B @ C ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ B )
& ( A
= ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(210,plain,
! [C: hF_Mirabelle_hf > hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_RepFun @ B @ C ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ B )
& ( A
= ( C @ D ) ) ) ) ),
inference(cnf,[status(esa)],[209]) ).
thf(211,plain,
! [C: hF_Mirabelle_hf > hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_RepFun @ B @ C ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ B )
& ( A
= ( C @ D ) ) ) ) ),
inference(lifteq,[status(thm)],[210]) ).
thf(51,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_Replace @ B @ C ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ B )
& ( C @ D @ A )
& ! [E: hF_Mirabelle_hf] :
( ( C @ D @ E )
=> ( E = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_Replace__iff) ).
thf(236,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_Replace @ B @ C ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ B )
& ( C @ D @ A )
& ! [E: hF_Mirabelle_hf] :
( ( C @ D @ E )
=> ( E = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(237,plain,
! [C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_Replace @ B @ C ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ B )
& ( C @ D @ A )
& ! [E: hF_Mirabelle_hf] :
( ( C @ D @ E )
=> ( E = A ) ) ) ) ),
inference(cnf,[status(esa)],[236]) ).
thf(238,plain,
! [C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_Replace @ B @ C ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ B )
& ( C @ D @ A )
& ! [E: hF_Mirabelle_hf] :
( ( C @ D @ E )
=> ( E = A ) ) ) ) ),
inference(lifteq,[status(thm)],[237]) ).
thf(20,axiom,
( sup_su638957495lle_hf
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( sup_su638957495lle_hf @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_inf__sup__aci_I5_J) ).
thf(121,plain,
( sup_su638957495lle_hf
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( sup_su638957495lle_hf @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(2070,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ $true
| ~ ( hF_Mirabelle_hmem @ D @ C )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mirabelle_hpair @ A @ B ) ) @ ( hF_Mirabelle_hpair @ A @ B ) )
!= ( hF_Mirabelle_hmem @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1034,184]) ).
thf(2071,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ D @ C )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mirabelle_hpair @ A @ B ) ) @ ( hF_Mirabelle_hpair @ A @ B ) )
!= ( hF_Mirabelle_hmem @ C @ D ) ) ),
inference(simp,[status(thm)],[2070]) ).
thf(2072,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ B ) @ ( sk20 @ ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[2071:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( sk20 @ ( hF_Mirabelle_hpair @ H @ I ) )),bind(D,$thf( hF_Mirabelle_hpair @ H @ I ))]]) ).
thf(2122,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ B ) @ ( sk20 @ ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(simp,[status(thm)],[2072]) ).
thf(15,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A @ B ) @ C )
= ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_inf__sup__aci_I6_J) ).
thf(106,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A @ B ) @ C )
= ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(60074,plain,
! [A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44021,181]) ).
thf(60075,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ A ) ),
inference(simp,[status(thm)],[60074]) ).
thf(60209,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1564 @ sk1566 )
!= A )
| ( ( hF_Mir1653039215strict @ r @ x )
!= A ) ),
inference(simp,[status(thm)],[60075]) ).
thf(60358,plain,
( ( hF_Mir1653039215strict @ r @ x )
!= ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) ),
inference(simp,[status(thm)],[60209]) ).
thf(3244,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ B ) )
= C )
| ( ( sup_su638957495lle_hf @ ( hF_Mirabelle_HUnion @ A ) @ ( hF_Mirabelle_HUnion @ B ) )
!= ( sup_su638957495lle_hf @ C @ C ) ) ),
inference(paramod_ordered,[status(thm)],[162,93]) ).
thf(3245,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ A ) )
= ( hF_Mirabelle_HUnion @ A ) ),
inference(pattern_uni,[status(thm)],[3244:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( hF_Mirabelle_HUnion @ B ))]]) ).
thf(3349,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ A ) )
= ( hF_Mirabelle_HUnion @ A ) ),
inference(simp,[status(thm)],[3245]) ).
thf(3640,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ B @ ( hF_Mirabelle_HUnion @ A ) )
| ( ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ A ) )
!= ( hF_Mirabelle_HUnion @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3349,191]) ).
thf(3641,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ A ) @ ( hF_Mirabelle_HUnion @ A ) ),
inference(pattern_uni,[status(thm)],[3640:[bind(A,$thf( D )),bind(B,$thf( sup_su638957495lle_hf @ D @ D ))]]) ).
thf(3685,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ A ) @ ( hF_Mirabelle_HUnion @ A ) ),
inference(simp,[status(thm)],[3641]) ).
thf(26966,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ C @ ( sk15 @ B @ A ) )
= ( ( hF_Mirabelle_hmem @ C @ A )
& $true ) )
| ( ( hF_Mir199975595nction @ r )
!= ( B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[294,254]) ).
thf(26967,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ C @ ( sk15 @ B @ A ) )
= ( hF_Mirabelle_hmem @ C @ A ) )
| ( ( hF_Mir199975595nction @ r )
!= ( B @ C ) ) ),
inference(simp,[status(thm)],[26966]) ).
thf(27201,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ r @ ( sk15 @ hF_Mir199975595nction @ A ) )
= ( hF_Mirabelle_hmem @ r @ A ) ),
inference(pre_uni,[status(thm)],[26967:[bind(A,$thf( A )),bind(B,$thf( hF_Mir199975595nction )),bind(C,$thf( r ))]]) ).
thf(48428,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir434065167lation @ A )
| ~ $true
| ( hF_Mir137170979_hpair @ B )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r )
!= ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[47869,562]) ).
thf(48429,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir434065167lation @ A )
| ( hF_Mir137170979_hpair @ B )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r )
!= ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(simp,[status(thm)],[48428]) ).
thf(48430,plain,
( ~ ( hF_Mir434065167lation @ r )
| ( hF_Mir137170979_hpair @ ( sk20 @ r ) ) ),
inference(pattern_uni,[status(thm)],[48429:[bind(A,$thf( r )),bind(B,$thf( sk20 @ r ))]]) ).
thf(24,axiom,
( ( hF_Mirabelle_HUnion @ zero_z189798548lle_hf )
= zero_z189798548lle_hf ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_HUnion__hempty) ).
thf(133,plain,
( ( hF_Mirabelle_HUnion @ zero_z189798548lle_hf )
= zero_z189798548lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(2186,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
| ~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) )
| ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ( ( hF_Mir434065167lation @ A )
!= ( hF_Mir434065167lation @ x ) ) ),
inference(paramod_ordered,[status(thm)],[301,1291]) ).
thf(2187,plain,
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
| ~ ! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ x )
=> ( hF_Mir137170979_hpair @ A ) )
| ( hF_Mir137170979_hpair @ ( sk20 @ x ) ) ),
inference(pattern_uni,[status(thm)],[2186:[bind(A,$thf( x ))]]) ).
thf(2205,plain,
( ( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
| ( hF_Mirabelle_hmem @ sk40 @ x )
| ( hF_Mir137170979_hpair @ ( sk20 @ x ) ) )
& ( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
| ~ ( hF_Mir137170979_hpair @ sk40 )
| ( hF_Mir137170979_hpair @ ( sk20 @ x ) ) ) ),
inference(cnf,[status(esa)],[2187]) ).
thf(2207,plain,
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
| ~ ( hF_Mir137170979_hpair @ sk40 )
| ( hF_Mir137170979_hpair @ ( sk20 @ x ) ) ),
inference(cnfConj,[status(thm)],[2205]) ).
thf(3219,plain,
( ~ $true
| ~ ( hF_Mir137170979_hpair @ sk40 )
| ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
!= ( hF_Mir199975595nction @ r ) ) ),
inference(paramod_ordered,[status(thm)],[294,2207]) ).
thf(3220,plain,
( ~ ( hF_Mir137170979_hpair @ sk40 )
| ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
!= ( hF_Mir199975595nction @ r ) ) ),
inference(simp,[status(thm)],[3219]) ).
thf(3226,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ~ ( hF_Mir137170979_hpair @ sk40 )
| ( ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf )
!= r ) ),
inference(simp,[status(thm)],[3220]) ).
thf(354,plain,
! [F: hF_Mirabelle_hf,E: hF_Mirabelle_hf,D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ D @ ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) )
= ( sup_su638957495lle_hf @ E @ ( sup_su638957495lle_hf @ D @ F ) ) )
| ( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A @ B ) @ C )
!= ( sup_su638957495lle_hf @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[76,85]) ).
thf(355,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ D @ A ) ) )
= ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ C @ D ) @ ( sup_su638957495lle_hf @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[354:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( sup_su638957495lle_hf @ G @ H )),bind(F,$thf( C ))]]) ).
thf(396,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ D @ A ) ) )
= ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ C @ D ) @ ( sup_su638957495lle_hf @ B @ A ) ) ),
inference(simp,[status(thm)],[355]) ).
thf(56930,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ D @ A ) ) )
= ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ D @ ( sup_su638957495lle_hf @ B @ A ) ) ) ),
inference(rewrite,[status(thm)],[396,76]) ).
thf(116,plain,
! [A: hF_Mirabelle_hf] :
( ( zero_z189798548lle_hf = A )
= ( A = zero_z189798548lle_hf ) ),
inference(cnf,[status(esa)],[115]) ).
thf(117,plain,
! [A: hF_Mirabelle_hf] :
( ( zero_z189798548lle_hf = A )
= ( A = zero_z189798548lle_hf ) ),
inference(lifteq,[status(thm)],[116]) ).
thf(53868,plain,
( ~ ( hF_Mir137170979_hpair @ sk1943 )
| ( hF_Mir137170979_hpair @ sk1564 ) ),
inference(cnfConj,[status(thm)],[53866]) ).
thf(837,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
| ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ( A != r ) ),
inference(paramod_ordered,[status(thm)],[468,68]) ).
thf(838,plain,
( ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r )
| ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) ) ),
inference(pattern_uni,[status(thm)],[837:[bind(A,$thf( r ))]]) ).
thf(1057,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ~ ( hF_Mir434065167lation @ A )
| ~ $true
| ( hF_Mir137170979_hpair @ B )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r )
!= ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[838,562]) ).
thf(1058,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ~ ( hF_Mir434065167lation @ A )
| ( hF_Mir137170979_hpair @ B )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r )
!= ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(simp,[status(thm)],[1057]) ).
thf(1059,plain,
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ~ ( hF_Mir434065167lation @ r )
| ( hF_Mir137170979_hpair @ ( sk20 @ r ) ) ),
inference(pattern_uni,[status(thm)],[1058:[bind(A,$thf( r )),bind(B,$thf( sk20 @ r ))]]) ).
thf(2144,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) )
| ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ( ( hF_Mir434065167lation @ A )
!= ( hF_Mir434065167lation @ r ) ) ),
inference(paramod_ordered,[status(thm)],[301,1059]) ).
thf(2145,plain,
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ~ ! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ r )
=> ( hF_Mir137170979_hpair @ A ) )
| ( hF_Mir137170979_hpair @ ( sk20 @ r ) ) ),
inference(pattern_uni,[status(thm)],[2144:[bind(A,$thf( r ))]]) ).
thf(2163,plain,
( ( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ( hF_Mirabelle_hmem @ sk35 @ r )
| ( hF_Mir137170979_hpair @ ( sk20 @ r ) ) )
& ( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ~ ( hF_Mir137170979_hpair @ sk35 )
| ( hF_Mir137170979_hpair @ ( sk20 @ r ) ) ) ),
inference(cnf,[status(esa)],[2145]) ).
thf(2164,plain,
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ( hF_Mirabelle_hmem @ sk35 @ r )
| ( hF_Mir137170979_hpair @ ( sk20 @ r ) ) ),
inference(cnfConj,[status(thm)],[2163]) ).
thf(65103,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
| ( sk1566 = zero_z189798548lle_hf )
| ( A != sk2141 ) ),
inference(paramod_ordered,[status(thm)],[468,65101]) ).
thf(65104,plain,
( ( hF_Mirabelle_hmem @ ( sk20 @ sk2141 ) @ sk2141 )
| ( sk1566 = zero_z189798548lle_hf ) ),
inference(pattern_uni,[status(thm)],[65103:[bind(A,$thf( sk2141 ))]]) ).
thf(66634,plain,
( ( hF_Mirabelle_hmem @ ( sk20 @ sk1566 ) @ sk1566 )
| ( sk1566 = zero_z189798548lle_hf ) ),
inference(rewrite,[status(thm)],[65104,65101]) ).
thf(44257,plain,
! [A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[44020,7297]) ).
thf(44258,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[44257]) ).
thf(44391,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1564 @ sk1565 )
!= A )
| ( ( hF_Mir1653039215strict @ r @ x )
!= zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[44258]) ).
thf(44557,plain,
( ( hF_Mir1653039215strict @ r @ x )
!= zero_z189798548lle_hf ),
inference(simp,[status(thm)],[44391]) ).
thf(46323,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ B ) @ B )
!= ( hF_Mirabelle_hmem @ ( sk20 @ x ) @ x ) ) ),
inference(paramod_ordered,[status(thm)],[45120,2753]) ).
thf(46324,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ B ) @ B )
!= ( hF_Mirabelle_hmem @ ( sk20 @ x ) @ x ) ),
inference(simp,[status(thm)],[46323]) ).
thf(46412,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ A @ B )
!= ( sk20 @ x ) )
| ( B != x ) ),
inference(simp,[status(thm)],[46324]) ).
thf(46511,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ x )
!= ( sk20 @ x ) ),
inference(simp,[status(thm)],[46412]) ).
thf(43290,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ~ $true
| ( ( hF_Mirabelle_hmem @ sk1075 @ x )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[36449,191]) ).
thf(43291,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( ( hF_Mirabelle_hmem @ sk1075 @ x )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ) ),
inference(simp,[status(thm)],[43290]) ).
thf(43477,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( sk1075 != A )
| ( ( hF_Mirabelle_HUnion @ A )
!= x ) ),
inference(simp,[status(thm)],[43291]) ).
thf(43675,plain,
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( ( hF_Mirabelle_HUnion @ sk1075 )
!= x ) ),
inference(simp,[status(thm)],[43477]) ).
thf(57989,plain,
! [A: hF_Mirabelle_hf] :
( ~ ! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ C ) @ A )
=> ! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ D ) @ A )
=> ( C = D ) ) )
| ( ( hF_Mirabelle_HUnion @ sk1075 )
!= x )
| ( ( hF_Mir199975595nction @ A )
!= ( hF_Mir199975595nction @ zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[333,43675]) ).
thf(57990,plain,
( ~ ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ B ) @ zero_z189798548lle_hf )
=> ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ C ) @ zero_z189798548lle_hf )
=> ( B = C ) ) )
| ( ( hF_Mirabelle_HUnion @ sk1075 )
!= x ) ),
inference(pattern_uni,[status(thm)],[57989:[bind(A,$thf( zero_z189798548lle_hf ))]]) ).
thf(58033,plain,
( ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk2042 @ sk2043 ) @ zero_z189798548lle_hf )
| ( ( hF_Mirabelle_HUnion @ sk1075 )
!= x ) )
& ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk2042 @ sk2044 ) @ zero_z189798548lle_hf )
| ( ( hF_Mirabelle_HUnion @ sk1075 )
!= x ) )
& ( ( sk2043 != sk2044 )
| ( ( hF_Mirabelle_HUnion @ sk1075 )
!= x ) ) ),
inference(cnf,[status(esa)],[57990]) ).
thf(58036,plain,
( ( sk2043 != sk2044 )
| ( ( hF_Mirabelle_HUnion @ sk1075 )
!= x ) ),
inference(cnfConj,[status(thm)],[58033]) ).
thf(58037,plain,
( ( sk2044 != sk2043 )
| ( ( hF_Mirabelle_HUnion @ sk1075 )
!= x ) ),
inference(lifteq,[status(thm)],[58036]) ).
thf(8840,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ B ),
inference(cnfConj,[status(thm)],[8839]) ).
thf(8842,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ B ),
inference(simp,[status(thm)],[8840]) ).
thf(2923,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ~ $true
| ( ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ B ) @ B )
!= ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[838,2753]) ).
thf(2924,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ( ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ B ) @ B )
!= ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r ) ) ),
inference(simp,[status(thm)],[2923]) ).
thf(2967,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ( ( sup_su638957495lle_hf @ A @ B )
!= ( sk20 @ r ) )
| ( B != r ) ),
inference(simp,[status(thm)],[2924]) ).
thf(2987,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ( ( sup_su638957495lle_hf @ A @ r )
!= ( sk20 @ r ) ) ),
inference(simp,[status(thm)],[2967]) ).
thf(3542,plain,
! [A: hF_Mirabelle_hf] :
( ~ $true
| ( ( sup_su638957495lle_hf @ A @ r )
!= ( sk20 @ r ) )
| ( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
!= ( hF_Mir199975595nction @ r ) ) ),
inference(paramod_ordered,[status(thm)],[294,2987]) ).
thf(3543,plain,
! [A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ A @ r )
!= ( sk20 @ r ) )
| ( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
!= ( hF_Mir199975595nction @ r ) ) ),
inference(simp,[status(thm)],[3542]) ).
thf(3550,plain,
! [A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ A @ r )
!= ( sk20 @ r ) )
| ( ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x )
!= r ) ),
inference(simp,[status(thm)],[3543]) ).
thf(47880,plain,
! [A: hF_Mirabelle_hf] :
( ~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) )
| ( hF_Mir137170979_hpair @ sk1638 )
| ( ( hF_Mir434065167lation @ A )
!= ( hF_Mir434065167lation @ x ) ) ),
inference(paramod_ordered,[status(thm)],[301,44718]) ).
thf(47881,plain,
( ~ ! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ x )
=> ( hF_Mir137170979_hpair @ A ) )
| ( hF_Mir137170979_hpair @ sk1638 ) ),
inference(pattern_uni,[status(thm)],[47880:[bind(A,$thf( x ))]]) ).
thf(47951,plain,
( ( ( hF_Mirabelle_hmem @ sk1768 @ x )
| ( hF_Mir137170979_hpair @ sk1638 ) )
& ( ~ ( hF_Mir137170979_hpair @ sk1768 )
| ( hF_Mir137170979_hpair @ sk1638 ) ) ),
inference(cnf,[status(esa)],[47881]) ).
thf(47952,plain,
( ( hF_Mirabelle_hmem @ sk1768 @ x )
| ( hF_Mir137170979_hpair @ sk1638 ) ),
inference(cnfConj,[status(thm)],[47951]) ).
thf(50268,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk1638 )
| ~ $true
| ( ( hF_Mirabelle_hmem @ sk1768 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[47952,181]) ).
thf(50269,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk1638 )
| ( ( hF_Mirabelle_hmem @ sk1768 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(simp,[status(thm)],[50268]) ).
thf(50402,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk1638 )
| ( sk1768 != A )
| ( x != A ) ),
inference(simp,[status(thm)],[50269]) ).
thf(50579,plain,
( ( hF_Mir137170979_hpair @ sk1638 )
| ( sk1768 != x ) ),
inference(simp,[status(thm)],[50402]) ).
thf(52104,plain,
( ( hF_Mir137170979_hpair @ sk1564 )
| ( sk1768 != x ) ),
inference(rewrite,[status(thm)],[50579,51420]) ).
thf(964,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
| ( zero_z189798548lle_hf != B )
| ( A
!= ( hF_Mirabelle_hpair @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[468,267]) ).
thf(965,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mirabelle_hpair @ A @ B ) ) @ ( hF_Mirabelle_hpair @ A @ B ) )
| ( zero_z189798548lle_hf != A ) ),
inference(pattern_uni,[status(thm)],[964:[bind(A,$thf( hF_Mirabelle_hpair @ D @ E )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(1012,plain,
! [A: hF_Mirabelle_hf] : ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mirabelle_hpair @ zero_z189798548lle_hf @ A ) ) @ ( hF_Mirabelle_hpair @ zero_z189798548lle_hf @ A ) ),
inference(simp,[status(thm)],[965]) ).
thf(1202,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mirabelle_hpair @ zero_z189798548lle_hf @ A ) ) @ ( hF_Mirabelle_hpair @ zero_z189798548lle_hf @ A ) )
!= ( hF_Mirabelle_hmem @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1012,181]) ).
thf(1203,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mirabelle_hpair @ zero_z189798548lle_hf @ A ) ) @ ( hF_Mirabelle_hpair @ zero_z189798548lle_hf @ A ) )
!= ( hF_Mirabelle_hmem @ B @ B ) ),
inference(simp,[status(thm)],[1202]) ).
thf(1211,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk20 @ ( hF_Mirabelle_hpair @ zero_z189798548lle_hf @ A ) )
!= B )
| ( ( hF_Mirabelle_hpair @ zero_z189798548lle_hf @ A )
!= B ) ),
inference(simp,[status(thm)],[1203]) ).
thf(1223,plain,
! [A: hF_Mirabelle_hf] :
( ( sk20 @ ( hF_Mirabelle_hpair @ zero_z189798548lle_hf @ A ) )
!= ( hF_Mirabelle_hpair @ zero_z189798548lle_hf @ A ) ),
inference(simp,[status(thm)],[1211]) ).
thf(29268,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ A @ ( hF_Mir818139703ollect @ B @ C ) )
= ( $true
& ( hF_Mirabelle_hmem @ A @ C ) ) )
| ( ( hF_Mir434065167lation @ zero_z189798548lle_hf )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[280,260]) ).
thf(29269,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ A @ ( hF_Mir818139703ollect @ B @ C ) )
= ( hF_Mirabelle_hmem @ A @ C ) )
| ( ( hF_Mir434065167lation @ zero_z189798548lle_hf )
!= ( B @ A ) ) ),
inference(simp,[status(thm)],[29268]) ).
thf(29906,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ ( hF_Mir818139703ollect @ hF_Mir434065167lation @ A ) )
= ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ A ) ),
inference(pre_uni,[status(thm)],[29269:[bind(A,$thf( zero_z189798548lle_hf )),bind(B,$thf( hF_Mir434065167lation )),bind(C,$thf( C ))]]) ).
thf(30297,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ ( hF_Mir818139703ollect @ hF_Mir434065167lation @ A ) )
= ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ A ) ),
inference(simp,[status(thm)],[29906]) ).
thf(43806,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ sk1075 @ x )
| ~ ! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ C ) @ A )
=> ! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ D ) @ A )
=> ( C = D ) ) )
| ( ( hF_Mir199975595nction @ A )
!= ( hF_Mir199975595nction @ zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[333,36449]) ).
thf(43807,plain,
( ( hF_Mirabelle_hmem @ sk1075 @ x )
| ~ ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ B ) @ zero_z189798548lle_hf )
=> ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ C ) @ zero_z189798548lle_hf )
=> ( B = C ) ) ) ),
inference(pattern_uni,[status(thm)],[43806:[bind(A,$thf( zero_z189798548lle_hf ))]]) ).
thf(43934,plain,
( ( ( hF_Mirabelle_hmem @ sk1075 @ x )
| ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1519 @ sk1520 ) @ zero_z189798548lle_hf ) )
& ( ( hF_Mirabelle_hmem @ sk1075 @ x )
| ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1519 @ sk1521 ) @ zero_z189798548lle_hf ) )
& ( ( hF_Mirabelle_hmem @ sk1075 @ x )
| ( sk1520 != sk1521 ) ) ),
inference(cnf,[status(esa)],[43807]) ).
thf(43937,plain,
( ( hF_Mirabelle_hmem @ sk1075 @ x )
| ( sk1520 != sk1521 ) ),
inference(cnfConj,[status(thm)],[43934]) ).
thf(43938,plain,
( ( sk1521 != sk1520 )
| ( hF_Mirabelle_hmem @ sk1075 @ x ) ),
inference(lifteq,[status(thm)],[43937]) ).
thf(69502,plain,
! [A: hF_Mirabelle_hf] :
( ( sk1521 != sk1520 )
| ~ $true
| ( ( hF_Mirabelle_hmem @ sk1075 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[43938,181]) ).
thf(69503,plain,
! [A: hF_Mirabelle_hf] :
( ( sk1521 != sk1520 )
| ( ( hF_Mirabelle_hmem @ sk1075 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(simp,[status(thm)],[69502]) ).
thf(69590,plain,
! [A: hF_Mirabelle_hf] :
( ( sk1521 != sk1520 )
| ( sk1075 != A )
| ( x != A ) ),
inference(simp,[status(thm)],[69503]) ).
thf(69792,plain,
( ( sk1521 != sk1520 )
| ( sk1075 != x ) ),
inference(simp,[status(thm)],[69590]) ).
thf(41,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ A @ B )
= ( hF_Mirabelle_hpair @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_hpair__iff) ).
thf(192,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ A @ B )
= ( hF_Mirabelle_hpair @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(25,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( ( hF_Mirabelle_Replace @ ( sup_su638957495lle_hf @ A @ B ) @ C )
= ( sup_su638957495lle_hf @ ( hF_Mirabelle_Replace @ A @ C ) @ ( hF_Mirabelle_Replace @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_Replace__hunion) ).
thf(135,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( ( hF_Mirabelle_Replace @ ( sup_su638957495lle_hf @ A @ B ) @ C )
= ( sup_su638957495lle_hf @ ( hF_Mirabelle_Replace @ A @ C ) @ ( hF_Mirabelle_Replace @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(136,plain,
! [C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_Replace @ ( sup_su638957495lle_hf @ A @ B ) @ C )
= ( sup_su638957495lle_hf @ ( hF_Mirabelle_Replace @ A @ C ) @ ( hF_Mirabelle_Replace @ B @ C ) ) ),
inference(cnf,[status(esa)],[135]) ).
thf(137,plain,
! [C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ ( hF_Mirabelle_Replace @ A @ C ) @ ( hF_Mirabelle_Replace @ B @ C ) )
= ( hF_Mirabelle_Replace @ ( sup_su638957495lle_hf @ A @ B ) @ C ) ),
inference(lifteq,[status(thm)],[136]) ).
thf(34,axiom,
! [A: hF_Mirabelle_hf > hF_Mirabelle_hf] :
( ( hF_Mirabelle_RepFun @ zero_z189798548lle_hf @ A )
= zero_z189798548lle_hf ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_RepFun__0) ).
thf(163,plain,
! [A: hF_Mirabelle_hf > hF_Mirabelle_hf] :
( ( hF_Mirabelle_RepFun @ zero_z189798548lle_hf @ A )
= zero_z189798548lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(164,plain,
! [A: hF_Mirabelle_hf > hF_Mirabelle_hf] :
( ( hF_Mirabelle_RepFun @ zero_z189798548lle_hf @ A )
= zero_z189798548lle_hf ),
inference(cnf,[status(esa)],[163]) ).
thf(165,plain,
! [A: hF_Mirabelle_hf > hF_Mirabelle_hf] :
( ( hF_Mirabelle_RepFun @ zero_z189798548lle_hf @ A )
= zero_z189798548lle_hf ),
inference(lifteq,[status(thm)],[164]) ).
thf(229,plain,
( ( (=) @ hF_Mirabelle_hf )
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
= ( hF_Mirabelle_hmem @ C @ B ) ) ) ),
inference(lifteq,[status(thm)],[228]) ).
thf(302,plain,
! [A: hF_Mirabelle_hf] :
( ( (=) @ hF_Mirabelle_hf @ A )
= ( ^ [B: hF_Mirabelle_hf] :
! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
= ( hF_Mirabelle_hmem @ C @ B ) ) ) ),
inference(func_ext,[status(esa)],[229]) ).
thf(348,plain,
! [F: hF_Mirabelle_hf,E: hF_Mirabelle_hf,D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ A @ C ) )
= ( sup_su638957495lle_hf @ D @ ( sup_su638957495lle_hf @ E @ F ) ) )
| ( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) )
!= ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ D @ E ) @ F ) ) ),
inference(paramod_ordered,[status(thm)],[85,76]) ).
thf(349,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A @ B ) @ D ) )
= ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ D ) ) ) ),
inference(pattern_uni,[status(thm)],[348:[bind(A,$thf( sup_su638957495lle_hf @ G @ H )),bind(B,$thf( I )),bind(C,$thf( J )),bind(D,$thf( G )),bind(E,$thf( H )),bind(F,$thf( sup_su638957495lle_hf @ I @ J ))]]) ).
thf(393,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A @ B ) @ D ) )
= ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ D ) ) ) ),
inference(simp,[status(thm)],[349]) ).
thf(53925,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ D ) ) )
= ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ D ) ) ) ),
inference(rewrite,[status(thm)],[393,39480]) ).
thf(12,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A @ B ) @ C )
= ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_sup__assoc) ).
thf(97,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A @ B ) @ C )
= ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(64359,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1564 @ sk1566 )
!= A )
| ( ( hF_Mirabelle_hpair @ sk2140 @ sk2141 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[60434,267]) ).
thf(64360,plain,
( ( hF_Mirabelle_hpair @ sk1564 @ sk1566 )
!= sk2140 ),
inference(pattern_uni,[status(thm)],[64359:[bind(A,$thf( sk2140 )),bind(B,$thf( sk2141 ))]]) ).
thf(65041,plain,
( ( hF_Mirabelle_hpair @ sk1564 @ sk1566 )
!= sk1564 ),
inference(rewrite,[status(thm)],[64360,65033]) ).
thf(46,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( ! [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
=> ( ( B @ C @ D )
=> ( ( B @ C @ E )
=> ( E = D ) ) ) )
=> ? [C: hF_Mirabelle_hf] :
! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ C )
= ( ? [E: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ E @ A )
& ( B @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_replacement) ).
thf(215,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( ! [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
=> ( ( B @ C @ D )
=> ( ( B @ C @ E )
=> ( E = D ) ) ) )
=> ? [C: hF_Mirabelle_hf] :
! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ C )
= ( ? [E: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ E @ A )
& ( B @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(216,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
=> ! [D: hF_Mirabelle_hf] :
( ( B @ C @ D )
=> ! [E: hF_Mirabelle_hf] :
( ( B @ C @ E )
=> ( E = D ) ) ) )
=> ? [C: hF_Mirabelle_hf] :
! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ C )
= ( ? [E: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ E @ A )
& ( B @ E @ D ) ) ) ) ),
inference(miniscope,[status(thm)],[215]) ).
thf(217,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ ( sk8 @ B @ A ) @ A )
| ( ( hF_Mirabelle_hmem @ C @ ( sk11 @ B @ A ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) ) )
& ( ( B @ ( sk8 @ B @ A ) @ ( sk9 @ B @ A ) )
| ( ( hF_Mirabelle_hmem @ C @ ( sk11 @ B @ A ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) ) )
& ( ( B @ ( sk8 @ B @ A ) @ ( sk10 @ B @ A ) )
| ( ( hF_Mirabelle_hmem @ C @ ( sk11 @ B @ A ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) ) )
& ( ( ( sk10 @ B @ A )
!= ( sk9 @ B @ A ) )
| ( ( hF_Mirabelle_hmem @ C @ ( sk11 @ B @ A ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) ) ) ),
inference(cnf,[status(esa)],[216]) ).
thf(219,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( B @ ( sk8 @ B @ A ) @ ( sk9 @ B @ A ) )
| ( ( hF_Mirabelle_hmem @ C @ ( sk11 @ B @ A ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) ) ),
inference(cnfConj,[status(thm)],[217]) ).
thf(223,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ C @ ( sk11 @ B @ A ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) )
| ( B @ ( sk8 @ B @ A ) @ ( sk9 @ B @ A ) ) ),
inference(lifteq,[status(thm)],[219]) ).
thf(15822,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ B
@ ( sk11
@ ^ [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] : $false
@ A ) )
= ( ? [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
& $false ) ) )
| $false ),
inference(prim_subst,[status(thm)],[223:[bind(A,$thf( A )),bind(B,$thf( ^ [D: hF_Mirabelle_hf] : ^ [E: hF_Mirabelle_hf] : $false ))]]) ).
thf(16649,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ B
@ ( sk11
@ ^ [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] : $false
@ A ) ),
inference(simp,[status(thm)],[15822]) ).
thf(16702,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A = zero_z189798548lle_hf )
| ~ $true
| ( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
!= ( hF_Mirabelle_hmem @ C
@ ( sk11
@ ^ [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] : $false
@ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[468,16649]) ).
thf(16703,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A = zero_z189798548lle_hf )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
!= ( hF_Mirabelle_hmem @ C
@ ( sk11
@ ^ [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] : $false
@ B ) ) ) ),
inference(simp,[status(thm)],[16702]) ).
thf(16704,plain,
! [A: hF_Mirabelle_hf] :
( ( sk11
@ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : $false
@ A )
= zero_z189798548lle_hf ),
inference(pattern_uni,[status(thm)],[16703:[bind(A,$thf( sk11 @ ^ [E: hF_Mirabelle_hf] : ^ [F: hF_Mirabelle_hf] : $false @ F )),bind(B,$thf( F )),bind(C,$thf( sk20 @ ( sk11 @ ^ [E: hF_Mirabelle_hf] : ^ [F: hF_Mirabelle_hf] : $false @ F ) ))]]) ).
thf(16801,plain,
! [A: hF_Mirabelle_hf] :
( ( sk11
@ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : $false
@ A )
= zero_z189798548lle_hf ),
inference(simp,[status(thm)],[16704]) ).
thf(2653,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ( hF_Mirabelle_hmem @ sk50 @ x )
| ( ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf )
!= r ) ),
inference(cnfConj,[status(thm)],[2652]) ).
thf(220,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( B @ ( sk8 @ B @ A ) @ ( sk10 @ B @ A ) )
| ( ( hF_Mirabelle_hmem @ C @ ( sk11 @ B @ A ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) ) ),
inference(cnfConj,[status(thm)],[217]) ).
thf(224,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ C @ ( sk11 @ B @ A ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) )
| ( B @ ( sk8 @ B @ A ) @ ( sk10 @ B @ A ) ) ),
inference(lifteq,[status(thm)],[220]) ).
thf(2971,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) @ C ),
inference(cnfConj,[status(thm)],[2969]) ).
thf(2973,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) @ C ),
inference(simp,[status(thm)],[2971]) ).
thf(338,plain,
! [F: hF_Mirabelle_hf,E: hF_Mirabelle_hf,D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ D @ ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ A @ C ) ) )
= ( sup_su638957495lle_hf @ E @ ( sup_su638957495lle_hf @ D @ F ) ) )
| ( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) )
!= ( sup_su638957495lle_hf @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[85,85]) ).
thf(339,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ A @ D ) ) )
= ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ D ) ) ) ),
inference(pattern_uni,[status(thm)],[338:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( H )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( sup_su638957495lle_hf @ G @ H ))]]) ).
thf(388,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ A @ D ) ) )
= ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ D ) ) ) ),
inference(simp,[status(thm)],[339]) ).
thf(27,axiom,
( sup_su638957495lle_hf
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( sup_su638957495lle_hf @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_sup__commute) ).
thf(141,plain,
( sup_su638957495lle_hf
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( sup_su638957495lle_hf @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(30714,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ r @ A )
!= ( hF_Mirabelle_hmem @ ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ r ) @ r ) )
| ( ( hF_Mirabelle_hmem @ r @ ( hF_Mir818139703ollect @ hF_Mir199975595nction @ A ) )
!= ( hF_Mirabelle_hmem @ ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ r ) @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[30263,13783]) ).
thf(30990,plain,
! [A: hF_Mirabelle_hf] :
( ( ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ r )
!= r )
| ( A != r )
| ( ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ r )
!= r )
| ( ( hF_Mir818139703ollect @ hF_Mir199975595nction @ A )
!= ( hF_Mir1653039215strict @ r @ x ) ) ),
inference(simp,[status(thm)],[30714]) ).
thf(31048,plain,
( ( ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ r )
!= r )
| ( ( hF_Mir1653039215strict @ r @ x )
!= ( hF_Mir818139703ollect @ hF_Mir199975595nction @ r ) ) ),
inference(simp,[status(thm)],[30990]) ).
thf(16,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A @ B ) @ B )
= ( sup_su638957495lle_hf @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_sup_Oright__idem) ).
thf(109,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A @ B ) @ B )
= ( sup_su638957495lle_hf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(64342,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1564 @ sk1566 )
!= zero_z189798548lle_hf )
| ( ( hF_Mirabelle_hpair @ sk2140 @ sk2141 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[60434,129]) ).
thf(64343,plain,
( ( hF_Mirabelle_hpair @ sk1564 @ sk1566 )
!= zero_z189798548lle_hf ),
inference(pattern_uni,[status(thm)],[64342:[bind(A,$thf( sk2140 )),bind(B,$thf( sk2141 ))]]) ).
thf(64357,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1564 @ sk1566 )
!= B )
| ( ( hF_Mirabelle_hpair @ sk2140 @ sk2141 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[60434,251]) ).
thf(64358,plain,
( ( hF_Mirabelle_hpair @ sk1564 @ sk1566 )
!= sk2141 ),
inference(pattern_uni,[status(thm)],[64357:[bind(A,$thf( sk2140 )),bind(B,$thf( sk2141 ))]]) ).
thf(65102,plain,
( ( hF_Mirabelle_hpair @ sk1564 @ sk1566 )
!= sk1566 ),
inference(rewrite,[status(thm)],[64358,65101]) ).
thf(47953,plain,
( ~ ( hF_Mir137170979_hpair @ sk1768 )
| ( hF_Mir137170979_hpair @ sk1638 ) ),
inference(cnfConj,[status(thm)],[47951]) ).
thf(51428,plain,
( ~ ( hF_Mir137170979_hpair @ sk1768 )
| ( hF_Mir137170979_hpair @ sk1564 ) ),
inference(rewrite,[status(thm)],[47953,51420]) ).
thf(46309,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir434065167lation @ A )
| ~ $true
| ( hF_Mir137170979_hpair @ B )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ x ) @ x )
!= ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[45120,562]) ).
thf(46310,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir434065167lation @ A )
| ( hF_Mir137170979_hpair @ B )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ x ) @ x )
!= ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(simp,[status(thm)],[46309]) ).
thf(46311,plain,
( ~ ( hF_Mir434065167lation @ x )
| ( hF_Mir137170979_hpair @ ( sk20 @ x ) ) ),
inference(pattern_uni,[status(thm)],[46310:[bind(A,$thf( x )),bind(B,$thf( sk20 @ x ))]]) ).
thf(70966,plain,
! [A: hF_Mirabelle_hf] :
( ~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) )
| ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ( ( hF_Mir434065167lation @ A )
!= ( hF_Mir434065167lation @ x ) ) ),
inference(paramod_ordered,[status(thm)],[301,46311]) ).
thf(70967,plain,
( ~ ! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ x )
=> ( hF_Mir137170979_hpair @ A ) )
| ( hF_Mir137170979_hpair @ ( sk20 @ x ) ) ),
inference(pattern_uni,[status(thm)],[70966:[bind(A,$thf( x ))]]) ).
thf(71069,plain,
( ( ( hF_Mirabelle_hmem @ sk2498 @ x )
| ( hF_Mir137170979_hpair @ ( sk20 @ x ) ) )
& ( ~ ( hF_Mir137170979_hpair @ sk2498 )
| ( hF_Mir137170979_hpair @ ( sk20 @ x ) ) ) ),
inference(cnf,[status(esa)],[70967]) ).
thf(71070,plain,
( ( hF_Mirabelle_hmem @ sk2498 @ x )
| ( hF_Mir137170979_hpair @ ( sk20 @ x ) ) ),
inference(cnfConj,[status(thm)],[71069]) ).
thf(36,axiom,
( hF_Mir137170979_hpair
= ( ^ [A: hF_Mirabelle_hf] :
? [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( A
= ( hF_Mirabelle_hpair @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_is__hpair__def) ).
thf(176,plain,
( hF_Mir137170979_hpair
= ( ^ [A: hF_Mirabelle_hf] :
? [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( A
= ( hF_Mirabelle_hpair @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(177,plain,
( hF_Mir137170979_hpair
= ( ^ [A: hF_Mirabelle_hf] :
? [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( A
= ( hF_Mirabelle_hpair @ B @ C ) ) ) ),
inference(lifteq,[status(thm)],[176]) ).
thf(300,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ A )
= ( ? [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( A
= ( hF_Mirabelle_hpair @ B @ C ) ) ) ),
inference(func_ext,[status(esa)],[177]) ).
thf(530,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ A )
| ~ ? [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( A
= ( hF_Mirabelle_hpair @ B @ C ) ) ),
inference(bool_ext,[status(thm)],[300]) ).
thf(535,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ A )
| ( A
!= ( hF_Mirabelle_hpair @ B @ C ) ) ),
inference(cnf,[status(esa)],[530]) ).
thf(536,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A
!= ( hF_Mirabelle_hpair @ B @ C ) )
| ( hF_Mir137170979_hpair @ A ) ),
inference(lifteq,[status(thm)],[535]) ).
thf(537,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] : ( hF_Mir137170979_hpair @ ( hF_Mirabelle_hpair @ A @ B ) ),
inference(simp,[status(thm)],[536]) ).
thf(28444,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ r @ A )
!= ( hF_Mirabelle_hmem @ ( sk7 @ r @ ( hF_Mir1653039215strict @ r @ x ) ) @ r ) )
| ( ( hF_Mirabelle_hmem @ r @ ( sk15 @ hF_Mir199975595nction @ A ) )
!= ( hF_Mirabelle_hmem @ ( sk7 @ r @ ( hF_Mir1653039215strict @ r @ x ) ) @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[27201,13780]) ).
thf(28488,plain,
! [A: hF_Mirabelle_hf] :
( ( ( sk7 @ r @ ( hF_Mir1653039215strict @ r @ x ) )
!= r )
| ( A != r )
| ( ( sk7 @ r @ ( hF_Mir1653039215strict @ r @ x ) )
!= r )
| ( ( sk15 @ hF_Mir199975595nction @ A )
!= ( hF_Mir1653039215strict @ r @ x ) ) ),
inference(simp,[status(thm)],[28444]) ).
thf(28628,plain,
( ( ( sk7 @ r @ ( hF_Mir1653039215strict @ r @ x ) )
!= r )
| ( ( sk15 @ hF_Mir199975595nction @ r )
!= ( hF_Mir1653039215strict @ r @ x ) ) ),
inference(simp,[status(thm)],[28488]) ).
thf(28056,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ A )
!= ( hF_Mirabelle_hmem @ ( sk7 @ r @ ( hF_Mir1653039215strict @ r @ x ) ) @ r ) )
| ( ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ ( sk15 @ hF_Mir434065167lation @ A ) )
!= ( hF_Mirabelle_hmem @ ( sk7 @ r @ ( hF_Mir1653039215strict @ r @ x ) ) @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[27164,13780]) ).
thf(28131,plain,
! [A: hF_Mirabelle_hf] :
( ( ( sk7 @ r @ ( hF_Mir1653039215strict @ r @ x ) )
!= zero_z189798548lle_hf )
| ( A != r )
| ( ( sk7 @ r @ ( hF_Mir1653039215strict @ r @ x ) )
!= zero_z189798548lle_hf )
| ( ( sk15 @ hF_Mir434065167lation @ A )
!= ( hF_Mir1653039215strict @ r @ x ) ) ),
inference(simp,[status(thm)],[28056]) ).
thf(28295,plain,
( ( ( sk7 @ r @ ( hF_Mir1653039215strict @ r @ x ) )
!= zero_z189798548lle_hf )
| ( ( sk15 @ hF_Mir434065167lation @ r )
!= ( hF_Mir1653039215strict @ r @ x ) ) ),
inference(simp,[status(thm)],[28131]) ).
thf(44645,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ B @ A ) @ B )
!= ( hF_Mirabelle_hmem @ sk1638 @ x ) ) ),
inference(paramod_ordered,[status(thm)],[44628,2940]) ).
thf(44646,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ B @ A ) @ B )
!= ( hF_Mirabelle_hmem @ sk1638 @ x ) ),
inference(simp,[status(thm)],[44645]) ).
thf(44825,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ B @ A )
!= sk1638 )
| ( B != x ) ),
inference(simp,[status(thm)],[44646]) ).
thf(44937,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ x @ A )
!= sk1638 ),
inference(simp,[status(thm)],[44825]) ).
thf(56080,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ x @ A )
!= sk1564 ),
inference(rewrite,[status(thm)],[44937,51420]) ).
thf(11,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf] :
( ( hF_Mirabelle_RepFun @ ( sup_su638957495lle_hf @ A @ B ) @ C )
= ( sup_su638957495lle_hf @ ( hF_Mirabelle_RepFun @ A @ C ) @ ( hF_Mirabelle_RepFun @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_RepFun__hunion) ).
thf(94,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf] :
( ( hF_Mirabelle_RepFun @ ( sup_su638957495lle_hf @ A @ B ) @ C )
= ( sup_su638957495lle_hf @ ( hF_Mirabelle_RepFun @ A @ C ) @ ( hF_Mirabelle_RepFun @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(95,plain,
! [C: hF_Mirabelle_hf > hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_RepFun @ ( sup_su638957495lle_hf @ A @ B ) @ C )
= ( sup_su638957495lle_hf @ ( hF_Mirabelle_RepFun @ A @ C ) @ ( hF_Mirabelle_RepFun @ B @ C ) ) ),
inference(cnf,[status(esa)],[94]) ).
thf(96,plain,
! [C: hF_Mirabelle_hf > hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ ( hF_Mirabelle_RepFun @ A @ C ) @ ( hF_Mirabelle_RepFun @ B @ C ) )
= ( hF_Mirabelle_RepFun @ ( sup_su638957495lle_hf @ A @ B ) @ C ) ),
inference(lifteq,[status(thm)],[95]) ).
thf(221,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( sk10 @ B @ A )
!= ( sk9 @ B @ A ) )
| ( ( hF_Mirabelle_hmem @ C @ ( sk11 @ B @ A ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) ) ),
inference(cnfConj,[status(thm)],[217]) ).
thf(225,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( sk10 @ B @ A )
!= ( sk9 @ B @ A ) )
| ( ( hF_Mirabelle_hmem @ C @ ( sk11 @ B @ A ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) ) ),
inference(lifteq,[status(thm)],[221]) ).
thf(4274,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ~ $true
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[836,184]) ).
thf(4275,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(simp,[status(thm)],[4274]) ).
thf(4276,plain,
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ~ ( hF_Mirabelle_hmem @ ( hF_Mir1653039215strict @ r @ x ) @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(pattern_uni,[status(thm)],[4275:[bind(A,$thf( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )),bind(B,$thf( hF_Mir1653039215strict @ r @ x ))]]) ).
thf(43308,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ~ $true
| ( ( hF_Mirabelle_hmem @ sk1075 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[36449,181]) ).
thf(43309,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( ( hF_Mirabelle_hmem @ sk1075 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(simp,[status(thm)],[43308]) ).
thf(43411,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( sk1075 != A )
| ( x != A ) ),
inference(simp,[status(thm)],[43309]) ).
thf(43546,plain,
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( sk1075 != x ) ),
inference(simp,[status(thm)],[43411]) ).
thf(46171,plain,
! [A: hF_Mirabelle_hf] :
( ~ ! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ C ) @ A )
=> ! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ D ) @ A )
=> ( C = D ) ) )
| ( sk1075 != x )
| ( ( hF_Mir199975595nction @ A )
!= ( hF_Mir199975595nction @ zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[333,43546]) ).
thf(46172,plain,
( ~ ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ B ) @ zero_z189798548lle_hf )
=> ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ C ) @ zero_z189798548lle_hf )
=> ( B = C ) ) )
| ( sk1075 != x ) ),
inference(pattern_uni,[status(thm)],[46171:[bind(A,$thf( zero_z189798548lle_hf ))]]) ).
thf(46209,plain,
( ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1704 @ sk1705 ) @ zero_z189798548lle_hf )
| ( sk1075 != x ) )
& ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1704 @ sk1706 ) @ zero_z189798548lle_hf )
| ( sk1075 != x ) )
& ( ( sk1705 != sk1706 )
| ( sk1075 != x ) ) ),
inference(cnf,[status(esa)],[46172]) ).
thf(46212,plain,
( ( sk1705 != sk1706 )
| ( sk1075 != x ) ),
inference(cnfConj,[status(thm)],[46209]) ).
thf(46213,plain,
( ( sk1706 != sk1705 )
| ( sk1075 != x ) ),
inference(lifteq,[status(thm)],[46212]) ).
thf(110,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A @ B ) @ B )
= ( sup_su638957495lle_hf @ A @ B ) ),
inference(cnf,[status(esa)],[109]) ).
thf(111,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A @ B ) @ B )
= ( sup_su638957495lle_hf @ A @ B ) ),
inference(lifteq,[status(thm)],[110]) ).
thf(1478,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ B ) )
= ( sup_su638957495lle_hf @ A @ B ) ),
inference(rewrite,[status(thm)],[111,76]) ).
thf(456,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( ! [C: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ C @ A ) )
= ( zero_z189798548lle_hf = B ) )
| ( ( A = zero_z189798548lle_hf )
!= ( B = zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[102,117]) ).
thf(457,plain,
! [A: hF_Mirabelle_hf] :
( ( ! [B: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ B @ A ) )
= ( zero_z189798548lle_hf = A ) ),
inference(pattern_uni,[status(thm)],[456:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(966,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
| ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( A != r ) ),
inference(paramod_ordered,[status(thm)],[468,294]) ).
thf(967,plain,
( ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r )
| ( hF_Mir199975595nction @ zero_z189798548lle_hf ) ),
inference(pattern_uni,[status(thm)],[966:[bind(A,$thf( r ))]]) ).
thf(1412,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
| ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ r )
| ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( A
!= ( sk20 @ r ) ) ),
inference(paramod_ordered,[status(thm)],[468,967]) ).
thf(1413,plain,
( ( hF_Mirabelle_hmem @ ( sk20 @ ( sk20 @ r ) ) @ ( sk20 @ r ) )
| ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ r )
| ( hF_Mir199975595nction @ zero_z189798548lle_hf ) ),
inference(pattern_uni,[status(thm)],[1412:[bind(A,$thf( sk20 @ r ))]]) ).
thf(1851,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
| ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ ( sk20 @ r ) )
| ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ r )
| ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( A
!= ( sk20 @ ( sk20 @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[468,1413]) ).
thf(1852,plain,
( ( hF_Mirabelle_hmem @ ( sk20 @ ( sk20 @ ( sk20 @ r ) ) ) @ ( sk20 @ ( sk20 @ r ) ) )
| ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ ( sk20 @ r ) )
| ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ r )
| ( hF_Mir199975595nction @ zero_z189798548lle_hf ) ),
inference(pattern_uni,[status(thm)],[1851:[bind(A,$thf( sk20 @ ( sk20 @ r ) ))]]) ).
thf(134,plain,
( ( hF_Mirabelle_HUnion @ zero_z189798548lle_hf )
= zero_z189798548lle_hf ),
inference(lifteq,[status(thm)],[133]) ).
thf(14,axiom,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ zero_z189798548lle_hf )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_hunion__hempty__right) ).
thf(103,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ zero_z189798548lle_hf )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(104,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ zero_z189798548lle_hf )
= A ),
inference(cnf,[status(esa)],[103]) ).
thf(105,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ zero_z189798548lle_hf )
= A ),
inference(lifteq,[status(thm)],[104]) ).
thf(201,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( sk5 @ B @ A )
!= ( sk4 @ B @ A ) )
| ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir1248913145eplace @ A @ B ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) ) ),
inference(cnfConj,[status(thm)],[197]) ).
thf(205,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( sk5 @ B @ A )
!= ( sk4 @ B @ A ) )
| ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir1248913145eplace @ A @ B ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) ) ),
inference(lifteq,[status(thm)],[201]) ).
thf(60058,plain,
! [A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[44021,191]) ).
thf(60059,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ),
inference(simp,[status(thm)],[60058]) ).
thf(60226,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1564 @ sk1566 )
!= A )
| ( ( hF_Mir1653039215strict @ r @ x )
!= ( hF_Mirabelle_HUnion @ A ) ) ),
inference(simp,[status(thm)],[60059]) ).
thf(60409,plain,
( ( hF_Mir1653039215strict @ r @ x )
!= ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) ) ),
inference(simp,[status(thm)],[60226]) ).
thf(2206,plain,
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
| ( hF_Mirabelle_hmem @ sk40 @ x )
| ( hF_Mir137170979_hpair @ ( sk20 @ x ) ) ),
inference(cnfConj,[status(thm)],[2205]) ).
thf(25097,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
| ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ~ $true
| ( ( hF_Mirabelle_hmem @ sk40 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2206,181]) ).
thf(25098,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
| ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ( ( hF_Mirabelle_hmem @ sk40 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(simp,[status(thm)],[25097]) ).
thf(25169,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
| ( sk40 != A )
| ( x != A ) ),
inference(simp,[status(thm)],[25098]) ).
thf(25286,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
| ( sk40 != x ) ),
inference(simp,[status(thm)],[25169]) ).
thf(26516,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ~ $true
| ( sk40 != x )
| ( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
!= ( hF_Mir199975595nction @ r ) ) ),
inference(paramod_ordered,[status(thm)],[294,25286]) ).
thf(26517,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ( sk40 != x )
| ( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
!= ( hF_Mir199975595nction @ r ) ) ),
inference(simp,[status(thm)],[26516]) ).
thf(26518,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ( sk40 != x )
| ( ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf )
!= r ) ),
inference(simp,[status(thm)],[26517]) ).
thf(2852,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ~ $true
| ( ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ B ) @ A )
!= ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r ) ) ),
inference(paramod_ordered,[status(thm)],[838,2752]) ).
thf(2853,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ( ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ B ) @ A )
!= ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r ) ) ),
inference(simp,[status(thm)],[2852]) ).
thf(2895,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ( ( sup_su638957495lle_hf @ A @ B )
!= ( sk20 @ r ) )
| ( A != r ) ),
inference(simp,[status(thm)],[2853]) ).
thf(2909,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ( ( sup_su638957495lle_hf @ r @ A )
!= ( sk20 @ r ) ) ),
inference(simp,[status(thm)],[2895]) ).
thf(46276,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ B )
!= ( hF_Mirabelle_hmem @ ( sk20 @ x ) @ x ) ) ),
inference(paramod_ordered,[status(thm)],[45120,8842]) ).
thf(46277,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ B )
!= ( hF_Mirabelle_hmem @ ( sk20 @ x ) @ x ) ),
inference(simp,[status(thm)],[46276]) ).
thf(46449,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk6 @ A @ B )
!= ( sk20 @ x ) )
| ( B != x ) ),
inference(simp,[status(thm)],[46277]) ).
thf(46592,plain,
! [A: hF_Mirabelle_hf] :
( ( sk6 @ A @ x )
!= ( sk20 @ x ) ),
inference(simp,[status(thm)],[46449]) ).
thf(44683,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ B )
!= ( hF_Mirabelle_hmem @ sk1638 @ x ) ) ),
inference(paramod_ordered,[status(thm)],[44628,8842]) ).
thf(44684,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ B )
!= ( hF_Mirabelle_hmem @ sk1638 @ x ) ),
inference(simp,[status(thm)],[44683]) ).
thf(44895,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk6 @ A @ B )
!= sk1638 )
| ( B != x ) ),
inference(simp,[status(thm)],[44684]) ).
thf(45104,plain,
! [A: hF_Mirabelle_hf] :
( ( sk6 @ A @ x )
!= sk1638 ),
inference(simp,[status(thm)],[44895]) ).
thf(57967,plain,
! [A: hF_Mirabelle_hf] :
( ( sk6 @ A @ x )
!= sk1564 ),
inference(rewrite,[status(thm)],[45104,51420]) ).
thf(47408,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ $true
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) @ r )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[44626,184]) ).
thf(47409,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) @ r )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(simp,[status(thm)],[47408]) ).
thf(47410,plain,
~ ( hF_Mirabelle_hmem @ r @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) ),
inference(pattern_uni,[status(thm)],[47409:[bind(A,$thf( hF_Mirabelle_hpair @ sk1564 @ sk1565 )),bind(B,$thf( r ))]]) ).
thf(60,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ ( hF_Mirabelle_hpair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_zero__notin__hpair) ).
thf(277,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ ( hF_Mirabelle_hpair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(278,plain,
~ ? [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ ( hF_Mirabelle_hpair @ A @ B ) ),
inference(miniscope,[status(thm)],[277]) ).
thf(279,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ ( hF_Mirabelle_hpair @ A @ B ) ),
inference(cnf,[status(esa)],[278]) ).
thf(4299,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ~ $true
| ( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[836,191]) ).
thf(4300,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ) ),
inference(simp,[status(thm)],[4299]) ).
thf(4338,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
!= A )
| ( ( hF_Mir1653039215strict @ r @ x )
!= ( hF_Mirabelle_HUnion @ A ) ) ),
inference(simp,[status(thm)],[4300]) ).
thf(4359,plain,
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( ( hF_Mirabelle_HUnion @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) )
!= ( hF_Mir1653039215strict @ r @ x ) ) ),
inference(simp,[status(thm)],[4338]) ).
thf(422,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ B @ A )
= ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ B @ D ) ) )
| ( ( sup_su638957495lle_hf @ A @ A )
!= ( sup_su638957495lle_hf @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[93,85]) ).
thf(423,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ A ) )
= ( sup_su638957495lle_hf @ B @ A ) ),
inference(pattern_uni,[status(thm)],[422:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(62,axiom,
! [A: hF_Mirabelle_hf] :
? [B: hF_Mirabelle_hf] :
! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ B )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( hF_Mirabelle_hmem @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_union__of__set) ).
thf(281,plain,
! [A: hF_Mirabelle_hf] :
? [B: hF_Mirabelle_hf] :
! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ B )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( hF_Mirabelle_hmem @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(70,plain,
! [A: hF_Mirabelle_hf > $o] :
( ( hF_Mir818139703ollect @ A @ zero_z189798548lle_hf )
= zero_z189798548lle_hf ),
inference(cnf,[status(esa)],[69]) ).
thf(71,plain,
! [A: hF_Mirabelle_hf > $o] :
( ( hF_Mir818139703ollect @ A @ zero_z189798548lle_hf )
= zero_z189798548lle_hf ),
inference(lifteq,[status(thm)],[70]) ).
thf(374,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ A @ C ) )
= D )
| ( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) )
!= ( sup_su638957495lle_hf @ D @ zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[85,105]) ).
thf(385,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ A @ C ) )
= D )
| ( A != D )
| ( ( sup_su638957495lle_hf @ B @ C )
!= zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[374]) ).
thf(387,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ C @ B ) )
= C )
| ( ( sup_su638957495lle_hf @ A @ B )
!= zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[385]) ).
thf(56116,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ A @ B )
!= zero_z189798548lle_hf )
| ( C != sk1564 )
| ( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ C @ B ) )
!= ( sup_su638957495lle_hf @ x @ D ) ) ),
inference(paramod_ordered,[status(thm)],[387,56080]) ).
thf(56117,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ x @ B )
!= zero_z189798548lle_hf )
| ( A != sk1564 ) ),
inference(pattern_uni,[status(thm)],[56116:[bind(A,$thf( x )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( sup_su638957495lle_hf @ E @ F ))]]) ).
thf(56168,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ x @ A )
!= zero_z189798548lle_hf ),
inference(simp,[status(thm)],[56117]) ).
thf(59199,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ A @ B )
!= zero_z189798548lle_hf )
| ( ( sup_su638957495lle_hf @ B @ A )
!= ( sup_su638957495lle_hf @ x @ C ) ) ),
inference(paramod_ordered,[status(thm)],[296,56168]) ).
thf(59200,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ x )
!= zero_z189798548lle_hf ),
inference(pattern_uni,[status(thm)],[59199:[bind(A,$thf( A )),bind(B,$thf( x )),bind(C,$thf( A ))]]) ).
thf(50765,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk20 @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) )
!= ( hF_Mirabelle_hpair @ A @ B ) )
| ( ( hF_Mirabelle_hpair @ sk1638 @ sk1639 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[44629,2115]) ).
thf(50766,plain,
( ( hF_Mirabelle_hpair @ sk1638 @ sk1639 )
!= ( sk20 @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) ) ),
inference(pattern_uni,[status(thm)],[50765:[bind(A,$thf( sk1638 )),bind(B,$thf( sk1639 ))]]) ).
thf(69315,plain,
( ( sk20 @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) )
!= ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) ),
inference(rewrite,[status(thm)],[50766,51420,52188]) ).
thf(44634,plain,
hF_Mirabelle_hmem @ sk1640 @ x,
inference(cnfConj,[status(thm)],[44631]) ).
thf(45462,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir434065167lation @ A )
| ~ $true
| ( hF_Mir137170979_hpair @ B )
| ( ( hF_Mirabelle_hmem @ sk1640 @ x )
!= ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44634,562]) ).
thf(45463,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir434065167lation @ A )
| ( hF_Mir137170979_hpair @ B )
| ( ( hF_Mirabelle_hmem @ sk1640 @ x )
!= ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(simp,[status(thm)],[45462]) ).
thf(45464,plain,
( ~ ( hF_Mir434065167lation @ x )
| ( hF_Mir137170979_hpair @ sk1640 ) ),
inference(pattern_uni,[status(thm)],[45463:[bind(A,$thf( x )),bind(B,$thf( sk1640 ))]]) ).
thf(49037,plain,
! [A: hF_Mirabelle_hf] :
( ~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) )
| ( hF_Mir137170979_hpair @ sk1640 )
| ( ( hF_Mir434065167lation @ A )
!= ( hF_Mir434065167lation @ x ) ) ),
inference(paramod_ordered,[status(thm)],[301,45464]) ).
thf(49038,plain,
( ~ ! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ x )
=> ( hF_Mir137170979_hpair @ A ) )
| ( hF_Mir137170979_hpair @ sk1640 ) ),
inference(pattern_uni,[status(thm)],[49037:[bind(A,$thf( x ))]]) ).
thf(49110,plain,
( ( ( hF_Mirabelle_hmem @ sk1804 @ x )
| ( hF_Mir137170979_hpair @ sk1640 ) )
& ( ~ ( hF_Mir137170979_hpair @ sk1804 )
| ( hF_Mir137170979_hpair @ sk1640 ) ) ),
inference(cnf,[status(esa)],[49038]) ).
thf(49111,plain,
( ( hF_Mirabelle_hmem @ sk1804 @ x )
| ( hF_Mir137170979_hpair @ sk1640 ) ),
inference(cnfConj,[status(thm)],[49110]) ).
thf(52256,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) )
= A )
| ( ( hF_Mirabelle_hpair @ sk1640 @ sk1641 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[44635,286]) ).
thf(52257,plain,
( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) )
= sk1640 ),
inference(pattern_uni,[status(thm)],[52256:[bind(A,$thf( sk1640 )),bind(B,$thf( sk1641 ))]]) ).
thf(53317,plain,
sk1640 = sk1564,
inference(rewrite,[status(thm)],[52257,286]) ).
thf(53322,plain,
( ( hF_Mirabelle_hmem @ sk1804 @ x )
| ( hF_Mir137170979_hpair @ sk1564 ) ),
inference(rewrite,[status(thm)],[49111,53317]) ).
thf(584,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
=> ( hF_Mir137170979_hpair @ D ) )
| ~ ( hF_Mirabelle_hmem @ C @ B )
| ( hF_Mir137170979_hpair @ C )
| ( ( hF_Mir434065167lation @ A )
!= ( hF_Mir434065167lation @ B ) ) ),
inference(paramod_ordered,[status(thm)],[301,562]) ).
thf(585,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
=> ( hF_Mir137170979_hpair @ C ) )
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( hF_Mir137170979_hpair @ B ) ),
inference(pattern_uni,[status(thm)],[584:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(590,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ ( sk33 @ B @ A ) @ A )
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( hF_Mir137170979_hpair @ B ) )
& ( ~ ( hF_Mir137170979_hpair @ ( sk33 @ B @ A ) )
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( hF_Mir137170979_hpair @ B ) ) ),
inference(cnf,[status(esa)],[585]) ).
thf(592,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir137170979_hpair @ ( sk33 @ B @ A ) )
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( hF_Mir137170979_hpair @ B ) ),
inference(cnfConj,[status(thm)],[590]) ).
thf(594,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir137170979_hpair @ ( sk33 @ B @ A ) )
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( hF_Mir137170979_hpair @ B ) ),
inference(simp,[status(thm)],[592]) ).
thf(802,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ $true
| ~ ( hF_Mirabelle_hmem @ D @ C )
| ( hF_Mir137170979_hpair @ D )
| ( ( hF_Mir137170979_hpair @ ( hF_Mirabelle_hpair @ A @ B ) )
!= ( hF_Mir137170979_hpair @ ( sk33 @ D @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[537,594]) ).
thf(803,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ D @ C )
| ( hF_Mir137170979_hpair @ D )
| ( ( hF_Mir137170979_hpair @ ( hF_Mirabelle_hpair @ A @ B ) )
!= ( hF_Mir137170979_hpair @ ( sk33 @ D @ C ) ) ) ),
inference(simp,[status(thm)],[802]) ).
thf(804,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ D )
| ~ ( hF_Mirabelle_hmem @ D @ C )
| ( ( hF_Mirabelle_hpair @ A @ B )
!= ( sk33 @ D @ C ) ) ),
inference(simp,[status(thm)],[803]) ).
thf(171,plain,
? [A: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf] :
! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( A @ C @ ( hF_Mirabelle_hpair @ B @ C ) )
= B ),
inference(detectInverse,[status(thm)],[170]) ).
thf(172,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sk1 @ B @ ( hF_Mirabelle_hpair @ A @ B ) )
= A ),
inference(cnf,[status(esa)],[171]) ).
thf(799,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sk1 @ B @ ( hF_Mirabelle_hpair @ A @ B ) )
= A ),
inference(lifteq,[status(thm)],[172]) ).
thf(50784,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk1 @ B @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) )
= A )
| ( ( hF_Mirabelle_hpair @ sk1638 @ sk1639 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[44629,799]) ).
thf(50785,plain,
( ( sk1 @ sk1639 @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) )
= sk1638 ),
inference(pattern_uni,[status(thm)],[50784:[bind(A,$thf( sk1638 )),bind(B,$thf( sk1639 ))]]) ).
thf(54921,plain,
( ( sk1 @ sk1565 @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) )
= sk1564 ),
inference(rewrite,[status(thm)],[50785,51420,52188]) ).
thf(1207,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mirabelle_hpair @ zero_z189798548lle_hf @ A ) ) @ ( hF_Mirabelle_hpair @ zero_z189798548lle_hf @ A ) )
!= ( hF_Mirabelle_hmem @ B @ zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[1012,79]) ).
thf(1208,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mirabelle_hpair @ zero_z189798548lle_hf @ A ) ) @ ( hF_Mirabelle_hpair @ zero_z189798548lle_hf @ A ) )
!= ( hF_Mirabelle_hmem @ B @ zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[1207]) ).
thf(1212,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk20 @ ( hF_Mirabelle_hpair @ zero_z189798548lle_hf @ A ) )
!= B )
| ( ( hF_Mirabelle_hpair @ zero_z189798548lle_hf @ A )
!= zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[1208]) ).
thf(1224,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ zero_z189798548lle_hf @ A )
!= zero_z189798548lle_hf ),
inference(simp,[status(thm)],[1212]) ).
thf(51424,plain,
( ( hF_Mirabelle_hmem @ sk1768 @ x )
| ( hF_Mir137170979_hpair @ sk1564 ) ),
inference(rewrite,[status(thm)],[47952,51420]) ).
thf(379,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A
= ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ D ) ) )
| ( ( sup_su638957495lle_hf @ A @ zero_z189798548lle_hf )
!= ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ B @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[105,85]) ).
thf(382,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A
= ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ D ) ) )
| ( A != C )
| ( ( sup_su638957495lle_hf @ B @ D )
!= zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[379]) ).
thf(406,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) )
= B )
| ( ( sup_su638957495lle_hf @ A @ C )
!= zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[382]) ).
thf(271,plain,
! [D: hF_Mirabelle_hf > hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A != B )
| ( hF_Mirabelle_hmem @ ( sk16 @ D @ C @ B @ A ) @ B )
| ( ( hF_Mirabelle_RepFun @ A @ C )
= ( hF_Mirabelle_RepFun @ B @ D ) ) ),
inference(cnfConj,[status(thm)],[270]) ).
thf(273,plain,
! [D: hF_Mirabelle_hf > hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A != B )
| ( ( hF_Mirabelle_RepFun @ A @ C )
= ( hF_Mirabelle_RepFun @ B @ D ) )
| ( hF_Mirabelle_hmem @ ( sk16 @ D @ C @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[271]) ).
thf(274,plain,
! [C: hF_Mirabelle_hf > hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_RepFun @ A @ B )
= ( hF_Mirabelle_RepFun @ A @ C ) )
| ( hF_Mirabelle_hmem @ ( sk16 @ C @ B @ A @ A ) @ A ) ),
inference(simp,[status(thm)],[273]) ).
thf(44719,plain,
! [A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ sk1638 @ x )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[44628,191]) ).
thf(44720,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ sk1638 @ x )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ),
inference(simp,[status(thm)],[44719]) ).
thf(44898,plain,
! [A: hF_Mirabelle_hf] :
( ( sk1638 != A )
| ( ( hF_Mirabelle_HUnion @ A )
!= x ) ),
inference(simp,[status(thm)],[44720]) ).
thf(45105,plain,
( ( hF_Mirabelle_HUnion @ sk1638 )
!= x ),
inference(simp,[status(thm)],[44898]) ).
thf(51427,plain,
( ( hF_Mirabelle_HUnion @ sk1564 )
!= x ),
inference(rewrite,[status(thm)],[45105,51420]) ).
thf(49,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf] :
? [C: hF_Mirabelle_hf] :
! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ C )
= ( ? [E: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ E @ A )
& ( D
= ( B @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_replacement__fun) ).
thf(230,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf] :
? [C: hF_Mirabelle_hf] :
! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ C )
= ( ? [E: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ E @ A )
& ( D
= ( B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(242,plain,
! [D: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A != B )
| ( hF_Mirabelle_hmem @ ( sk13 @ D @ C @ B @ A ) @ B )
| ( ( hF_Mirabelle_Replace @ A @ C )
= ( hF_Mirabelle_Replace @ B @ D ) ) ),
inference(cnfConj,[status(thm)],[241]) ).
thf(244,plain,
! [D: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A != B )
| ( ( hF_Mirabelle_Replace @ A @ C )
= ( hF_Mirabelle_Replace @ B @ D ) )
| ( hF_Mirabelle_hmem @ ( sk13 @ D @ C @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[242]) ).
thf(245,plain,
! [C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_Replace @ A @ B )
= ( hF_Mirabelle_Replace @ A @ C ) )
| ( hF_Mirabelle_hmem @ ( sk13 @ C @ B @ A @ A ) @ A ) ),
inference(simp,[status(thm)],[244]) ).
thf(45405,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ $true
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ sk1640 @ x )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[44634,184]) ).
thf(45406,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ sk1640 @ x )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(simp,[status(thm)],[45405]) ).
thf(45407,plain,
~ ( hF_Mirabelle_hmem @ x @ sk1640 ),
inference(pattern_uni,[status(thm)],[45406:[bind(A,$thf( sk1640 )),bind(B,$thf( x ))]]) ).
thf(48507,plain,
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r )
!= ( hF_Mirabelle_hmem @ x @ sk1640 ) ) ),
inference(paramod_ordered,[status(thm)],[47869,45407]) ).
thf(48508,plain,
( ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r )
!= ( hF_Mirabelle_hmem @ x @ sk1640 ) ),
inference(simp,[status(thm)],[48507]) ).
thf(48521,plain,
( ( ( sk20 @ r )
!= x )
| ( sk1640 != r ) ),
inference(simp,[status(thm)],[48508]) ).
thf(65074,plain,
( ( ( sk20 @ r )
!= x )
| ( sk1564 != r ) ),
inference(rewrite,[status(thm)],[48521,53317]) ).
thf(303,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A = B )
= ( ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
= ( hF_Mirabelle_hmem @ C @ B ) ) ) ),
inference(func_ext,[status(esa)],[229]) ).
thf(186,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ B ) )
= ( ? [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ B )
& ( hF_Mirabelle_hmem @ A @ C ) ) ) ),
inference(cnf,[status(esa)],[185]) ).
thf(187,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ B ) )
= ( ? [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ B )
& ( hF_Mirabelle_hmem @ A @ C ) ) ) ),
inference(lifteq,[status(thm)],[186]) ).
thf(62871,plain,
( ~ ( hF_Mir137170979_hpair @ sk2237 )
| ( hF_Mir137170979_hpair @ sk2140 ) ),
inference(cnfConj,[status(thm)],[62869]) ).
thf(65042,plain,
( ~ ( hF_Mir137170979_hpair @ sk2237 )
| ( hF_Mir137170979_hpair @ sk1564 ) ),
inference(rewrite,[status(thm)],[62871,65033]) ).
thf(450,plain,
( ( hF_Mir434065167lation = hF_Mir199975595nction )
| ( ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) ) )
!= ( (=) @ hF_Mirabelle_hf ) )
| ( ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
= ( hF_Mirabelle_hmem @ C @ B ) ) )
!= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ C ) @ A )
=> ! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ D ) @ A )
=> ( C = D ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[229,336]) ).
thf(451,plain,
( ( hF_Mir434065167lation = hF_Mir199975595nction )
| ( ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) ) )
!= ( (=) @ hF_Mirabelle_hf ) )
| ( ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
= ( hF_Mirabelle_hmem @ C @ B ) ) )
!= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ C ) @ A )
=> ! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ D ) @ A )
=> ( C = D ) ) ) ) ) ),
inference(simp,[status(thm)],[450]) ).
thf(1049,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ~ $true
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[838,184]) ).
thf(1050,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(simp,[status(thm)],[1049]) ).
thf(1051,plain,
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ~ ( hF_Mirabelle_hmem @ r @ ( sk20 @ r ) ) ),
inference(pattern_uni,[status(thm)],[1050:[bind(A,$thf( sk20 @ r )),bind(B,$thf( r ))]]) ).
thf(1659,plain,
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
| ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ~ $true
| ( ( hF_Mirabelle_hmem @ ( sk20 @ x ) @ x )
!= ( hF_Mirabelle_hmem @ r @ ( sk20 @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[840,1051]) ).
thf(1660,plain,
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
| ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ x ) @ x )
!= ( hF_Mirabelle_hmem @ r @ ( sk20 @ r ) ) ) ),
inference(simp,[status(thm)],[1659]) ).
thf(1667,plain,
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
| ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ( ( sk20 @ x )
!= r )
| ( ( sk20 @ r )
!= x ) ),
inference(simp,[status(thm)],[1660]) ).
thf(2156,plain,
( ~ $true
| ~ ( hF_Mir434065167lation @ r )
| ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
!= ( hF_Mir199975595nction @ r ) ) ),
inference(paramod_ordered,[status(thm)],[294,1059]) ).
thf(2157,plain,
( ~ ( hF_Mir434065167lation @ r )
| ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
!= ( hF_Mir199975595nction @ r ) ) ),
inference(simp,[status(thm)],[2156]) ).
thf(2158,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ~ ( hF_Mir434065167lation @ r )
| ( ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x )
!= r ) ),
inference(simp,[status(thm)],[2157]) ).
thf(2535,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) )
| ( ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x )
!= r )
| ( ( hF_Mir434065167lation @ A )
!= ( hF_Mir434065167lation @ r ) ) ),
inference(paramod_ordered,[status(thm)],[301,2158]) ).
thf(2536,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ~ ! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ r )
=> ( hF_Mir137170979_hpair @ A ) )
| ( ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x )
!= r ) ),
inference(pattern_uni,[status(thm)],[2535:[bind(A,$thf( r ))]]) ).
thf(2541,plain,
( ( ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ( hF_Mirabelle_hmem @ sk45 @ r )
| ( ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x )
!= r ) )
& ( ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ~ ( hF_Mir137170979_hpair @ sk45 )
| ( ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x )
!= r ) ) ),
inference(cnf,[status(esa)],[2536]) ).
thf(2542,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ( hF_Mirabelle_hmem @ sk45 @ r )
| ( ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x )
!= r ) ),
inference(cnfConj,[status(thm)],[2541]) ).
thf(89,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ A @ B ) )
= ( sup_su638957495lle_hf @ A @ B ) ),
inference(cnf,[status(esa)],[88]) ).
thf(90,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ A @ B ) )
= ( sup_su638957495lle_hf @ A @ B ) ),
inference(lifteq,[status(thm)],[89]) ).
thf(489,plain,
! [E: hF_Mirabelle_hf,D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ A @ B ) )
= ( sup_su638957495lle_hf @ D @ ( sup_su638957495lle_hf @ C @ E ) ) )
| ( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ A @ B ) )
!= ( sup_su638957495lle_hf @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[90,85]) ).
thf(490,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) )
= ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) ),
inference(pattern_uni,[status(thm)],[489:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( F )),bind(E,$thf( sup_su638957495lle_hf @ F @ G ))]]) ).
thf(520,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) )
= ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) ),
inference(simp,[status(thm)],[490]) ).
thf(50773,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1564 @ sk1565 )
!= zero_z189798548lle_hf )
| ( ( hF_Mirabelle_hpair @ sk1638 @ sk1639 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[44629,129]) ).
thf(50774,plain,
( ( hF_Mirabelle_hpair @ sk1564 @ sk1565 )
!= zero_z189798548lle_hf ),
inference(pattern_uni,[status(thm)],[50773:[bind(A,$thf( sk1638 )),bind(B,$thf( sk1639 ))]]) ).
thf(2945,plain,
! [E: hF_Mirabelle_hf,D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) @ E )
| ( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A @ B ) @ C )
!= ( sup_su638957495lle_hf @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[76,2753]) ).
thf(2946,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ A ) ) @ A ),
inference(pattern_uni,[status(thm)],[2945:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( sup_su638957495lle_hf @ F @ G )),bind(E,$thf( C ))]]) ).
thf(2974,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ A ) ) @ A ),
inference(simp,[status(thm)],[2946]) ).
thf(23,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) )
= ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_sup__left__commute) ).
thf(130,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) )
= ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(64331,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk2 @ A @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) )
= B )
| ( ( hF_Mirabelle_hpair @ sk2140 @ sk2141 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[60434,1697]) ).
thf(64332,plain,
( ( sk2 @ sk2140 @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) )
= sk2141 ),
inference(pattern_uni,[status(thm)],[64331:[bind(A,$thf( sk2140 )),bind(B,$thf( sk2141 ))]]) ).
thf(65934,plain,
( ( sk2 @ sk1564 @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) )
= sk1566 ),
inference(rewrite,[status(thm)],[64332,65033,65101]) ).
thf(6,axiom,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_hemptyE) ).
thf(80,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(2872,plain,
! [E: hF_Mirabelle_hf,D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( ( hF_Mirabelle_hmem @ A @ B )
| ( hF_Mirabelle_hmem @ A @ C ) )
| ( ( hF_Mirabelle_hmem @ A @ ( sup_su638957495lle_hf @ B @ C ) )
!= ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ D @ E ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[159,2752]) ).
thf(2873,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ B @ C ) @ A ) @ B )
| ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ B @ C ) @ A ) @ C ) ),
inference(pattern_uni,[status(thm)],[2872:[bind(A,$thf( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ H @ I ) @ G )),bind(B,$thf( H )),bind(C,$thf( I )),bind(D,$thf( sup_su638957495lle_hf @ H @ I )),bind(E,$thf( G ))]]) ).
thf(2913,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ B @ C ) @ A ) @ B )
& ~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ B @ C ) @ A ) @ C ) ),
inference(cnf,[status(esa)],[2873]) ).
thf(2915,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ B @ C ) @ A ) @ C ),
inference(cnfConj,[status(thm)],[2913]) ).
thf(2917,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ B @ C ) @ A ) @ C ),
inference(simp,[status(thm)],[2915]) ).
thf(25465,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ A ) ) @ C ),
inference(rewrite,[status(thm)],[2917,76]) ).
thf(44164,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ $true
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[44020,184]) ).
thf(44165,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(simp,[status(thm)],[44164]) ).
thf(44166,plain,
~ ( hF_Mirabelle_hmem @ ( hF_Mir1653039215strict @ r @ x ) @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) ),
inference(pattern_uni,[status(thm)],[44165:[bind(A,$thf( hF_Mirabelle_hpair @ sk1564 @ sk1565 )),bind(B,$thf( hF_Mir1653039215strict @ r @ x ))]]) ).
thf(21764,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ~ $true
| ( ( hF_Mirabelle_hmem @ sk35 @ r )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2164,181]) ).
thf(21765,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ( ( hF_Mirabelle_hmem @ sk35 @ r )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(simp,[status(thm)],[21764]) ).
thf(21848,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ( sk35 != A )
| ( r != A ) ),
inference(simp,[status(thm)],[21765]) ).
thf(21949,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ( sk35 != r ) ),
inference(simp,[status(thm)],[21848]) ).
thf(22099,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ~ $true
| ( sk35 != r )
| ( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
!= ( hF_Mir199975595nction @ r ) ) ),
inference(paramod_ordered,[status(thm)],[294,21949]) ).
thf(22100,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ( sk35 != r )
| ( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
!= ( hF_Mir199975595nction @ r ) ) ),
inference(simp,[status(thm)],[22099]) ).
thf(22110,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ( sk35 != r )
| ( ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x )
!= r ) ),
inference(simp,[status(thm)],[22100]) ).
thf(55,axiom,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_hmem__not__refl) ).
thf(255,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(2091,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mirabelle_hpair @ A @ B ) ) @ ( hF_Mirabelle_hpair @ A @ B ) )
!= ( hF_Mirabelle_hmem @ C @ ( hF_Mirabelle_HUnion @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[1034,191]) ).
thf(2092,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mirabelle_hpair @ A @ B ) ) @ ( hF_Mirabelle_hpair @ A @ B ) )
!= ( hF_Mirabelle_hmem @ C @ ( hF_Mirabelle_HUnion @ C ) ) ),
inference(simp,[status(thm)],[2091]) ).
thf(2107,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk20 @ ( hF_Mirabelle_hpair @ A @ B ) )
!= C )
| ( ( hF_Mirabelle_hpair @ A @ B )
!= ( hF_Mirabelle_HUnion @ C ) ) ),
inference(simp,[status(thm)],[2092]) ).
thf(2124,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_HUnion @ ( sk20 @ ( hF_Mirabelle_hpair @ A @ B ) ) )
!= ( hF_Mirabelle_hpair @ A @ B ) ),
inference(simp,[status(thm)],[2107]) ).
thf(506,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A
= ( sup_su638957495lle_hf @ B @ C ) )
| ( ( sup_su638957495lle_hf @ A @ zero_z189798548lle_hf )
!= ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[105,90]) ).
thf(512,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A
= ( sup_su638957495lle_hf @ B @ C ) )
| ( A != B )
| ( ( sup_su638957495lle_hf @ B @ C )
!= zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[506]) ).
thf(516,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ A @ B )
= A )
| ( ( sup_su638957495lle_hf @ A @ B )
!= zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[512]) ).
thf(21,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ A @ B ) )
= ( sup_su638957495lle_hf @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_inf__sup__aci_I8_J) ).
thf(123,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ A @ B ) )
= ( sup_su638957495lle_hf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(1123,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mirabelle_hpair @ A @ zero_z189798548lle_hf ) ) @ ( hF_Mirabelle_hpair @ A @ zero_z189798548lle_hf ) )
!= ( hF_Mirabelle_hmem @ B @ ( hF_Mirabelle_HUnion @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[1009,191]) ).
thf(1124,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mirabelle_hpair @ A @ zero_z189798548lle_hf ) ) @ ( hF_Mirabelle_hpair @ A @ zero_z189798548lle_hf ) )
!= ( hF_Mirabelle_hmem @ B @ ( hF_Mirabelle_HUnion @ B ) ) ),
inference(simp,[status(thm)],[1123]) ).
thf(1136,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk20 @ ( hF_Mirabelle_hpair @ A @ zero_z189798548lle_hf ) )
!= B )
| ( ( hF_Mirabelle_hpair @ A @ zero_z189798548lle_hf )
!= ( hF_Mirabelle_HUnion @ B ) ) ),
inference(simp,[status(thm)],[1124]) ).
thf(1145,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_HUnion @ ( sk20 @ ( hF_Mirabelle_hpair @ A @ zero_z189798548lle_hf ) ) )
!= ( hF_Mirabelle_hpair @ A @ zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[1136]) ).
thf(4306,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ~ $true
| ( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[836,181]) ).
thf(4307,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(simp,[status(thm)],[4306]) ).
thf(4330,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
!= A )
| ( ( hF_Mir1653039215strict @ r @ x )
!= A ) ),
inference(simp,[status(thm)],[4307]) ).
thf(4355,plain,
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mir1653039215strict @ r @ x ) ) ),
inference(simp,[status(thm)],[4330]) ).
thf(29,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( ( A
= ( sup_su638957495lle_hf @ B @ C ) )
=> ( ( sup_su638957495lle_hf @ D @ A )
= ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_boolean__algebra__cancel_Osup2) ).
thf(146,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( ( A
= ( sup_su638957495lle_hf @ B @ C ) )
=> ( ( sup_su638957495lle_hf @ D @ A )
= ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(147,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( A
= ( sup_su638957495lle_hf @ B @ C ) )
=> ! [D: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ D @ A )
= ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ D @ C ) ) ) ),
inference(miniscope,[status(thm)],[146]) ).
thf(148,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A
!= ( sup_su638957495lle_hf @ B @ C ) )
| ( ( sup_su638957495lle_hf @ D @ A )
= ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ D @ C ) ) ) ),
inference(cnf,[status(esa)],[147]) ).
thf(149,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A
!= ( sup_su638957495lle_hf @ B @ C ) )
| ( ( sup_su638957495lle_hf @ D @ A )
= ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ D @ C ) ) ) ),
inference(lifteq,[status(thm)],[148]) ).
thf(150,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ A @ B ) )
= ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ C @ B ) ) ),
inference(simp,[status(thm)],[149]) ).
thf(2882,plain,
! [E: hF_Mirabelle_hf,D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ C @ B ) ) @ D )
| ( ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ A @ B ) )
!= ( sup_su638957495lle_hf @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[150,2752]) ).
thf(2883,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ A @ C ) ) @ A ),
inference(pattern_uni,[status(thm)],[2882:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( C )),bind(E,$thf( sup_su638957495lle_hf @ F @ G ))]]) ).
thf(2899,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ A @ C ) ) @ A ),
inference(simp,[status(thm)],[2883]) ).
thf(46328,plain,
! [A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( sk20 @ x ) @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[45120,181]) ).
thf(46329,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ x ) @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ),
inference(simp,[status(thm)],[46328]) ).
thf(46428,plain,
! [A: hF_Mirabelle_hf] :
( ( ( sk20 @ x )
!= A )
| ( x != A ) ),
inference(simp,[status(thm)],[46329]) ).
thf(46547,plain,
( ( sk20 @ x )
!= x ),
inference(simp,[status(thm)],[46428]) ).
thf(17,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) )
= ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_inf__sup__aci_I7_J) ).
thf(112,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) )
= ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(2914,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ B @ C ) @ A ) @ B ),
inference(cnfConj,[status(thm)],[2913]) ).
thf(2916,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ B @ C ) @ A ) @ B ),
inference(simp,[status(thm)],[2914]) ).
thf(24428,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ A ) ) @ B ),
inference(rewrite,[status(thm)],[2916,76]) ).
thf(193,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ A @ B )
= ( hF_Mirabelle_hpair @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(cnf,[status(esa)],[192]) ).
thf(194,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ A @ B )
= ( hF_Mirabelle_hpair @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(lifteq,[status(thm)],[193]) ).
thf(28,axiom,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ zero_z189798548lle_hf @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_hunion__hempty__left) ).
thf(143,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ zero_z189798548lle_hf @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(144,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ zero_z189798548lle_hf @ A )
= A ),
inference(cnf,[status(esa)],[143]) ).
thf(145,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ zero_z189798548lle_hf @ A )
= A ),
inference(lifteq,[status(thm)],[144]) ).
thf(64354,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk1 @ B @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) )
= A )
| ( ( hF_Mirabelle_hpair @ sk2140 @ sk2141 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[60434,799]) ).
thf(64355,plain,
( ( sk1 @ sk2141 @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) )
= sk2140 ),
inference(pattern_uni,[status(thm)],[64354:[bind(A,$thf( sk2140 )),bind(B,$thf( sk2141 ))]]) ).
thf(66511,plain,
( ( sk1 @ sk1566 @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) )
= sk1564 ),
inference(rewrite,[status(thm)],[64355,65033,65101]) ).
thf(295,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A )
= ( ^ [B: hF_Mirabelle_hf] : ( sup_su638957495lle_hf @ B @ A ) ) ),
inference(func_ext,[status(esa)],[87]) ).
thf(55653,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk1564 )
| ~ $true
| ( ( hF_Mirabelle_hmem @ sk1943 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[53867,181]) ).
thf(55654,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk1564 )
| ( ( hF_Mirabelle_hmem @ sk1943 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(simp,[status(thm)],[55653]) ).
thf(55719,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk1564 )
| ( sk1943 != A )
| ( x != A ) ),
inference(simp,[status(thm)],[55654]) ).
thf(55818,plain,
( ( hF_Mir137170979_hpair @ sk1564 )
| ( sk1943 != x ) ),
inference(simp,[status(thm)],[55719]) ).
thf(320,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) )
= D )
| ( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A @ B ) @ C )
!= ( sup_su638957495lle_hf @ zero_z189798548lle_hf @ D ) ) ),
inference(paramod_ordered,[status(thm)],[76,145]) ).
thf(325,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) )
= D )
| ( ( sup_su638957495lle_hf @ A @ B )
!= zero_z189798548lle_hf )
| ( C != D ) ),
inference(simp,[status(thm)],[320]) ).
thf(327,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) )
= C )
| ( ( sup_su638957495lle_hf @ A @ B )
!= zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[325]) ).
thf(28315,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ r @ A )
!= ( hF_Mirabelle_hmem @ ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ r ) @ r ) )
| ( ( hF_Mirabelle_hmem @ r @ ( sk15 @ hF_Mir199975595nction @ A ) )
!= ( hF_Mirabelle_hmem @ ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ r ) @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[27201,13783]) ).
thf(28574,plain,
! [A: hF_Mirabelle_hf] :
( ( ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ r )
!= r )
| ( A != r )
| ( ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ r )
!= r )
| ( ( sk15 @ hF_Mir199975595nction @ A )
!= ( hF_Mir1653039215strict @ r @ x ) ) ),
inference(simp,[status(thm)],[28315]) ).
thf(28671,plain,
( ( ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ r )
!= r )
| ( ( sk15 @ hF_Mir199975595nction @ r )
!= ( hF_Mir1653039215strict @ r @ x ) ) ),
inference(simp,[status(thm)],[28574]) ).
thf(31305,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ zero_z189798548lle_hf
@ ( hF_Mir818139703ollect
@ ^ [B: hF_Mirabelle_hf] :
! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ B )
=> ( hF_Mir137170979_hpair @ C ) )
@ A ) )
= ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ A ) )
| ( hF_Mir434065167lation != hF_Mir434065167lation ) ),
inference(paramod_ordered,[status(thm)],[227,30297]) ).
thf(31306,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ zero_z189798548lle_hf
@ ( hF_Mir818139703ollect
@ ^ [B: hF_Mirabelle_hf] :
! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ B )
=> ( hF_Mir137170979_hpair @ C ) )
@ A ) )
= ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ A ) ),
inference(pattern_uni,[status(thm)],[31305:[]]) ).
thf(262,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mir434065167lation @ ( sup_su638957495lle_hf @ A @ B ) )
= ( ( hF_Mir434065167lation @ A )
& ( hF_Mir434065167lation @ B ) ) ),
inference(cnf,[status(esa)],[261]) ).
thf(263,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mir434065167lation @ ( sup_su638957495lle_hf @ A @ B ) )
= ( ( hF_Mir434065167lation @ A )
& ( hF_Mir434065167lation @ B ) ) ),
inference(lifteq,[status(thm)],[262]) ).
thf(2165,plain,
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ~ ( hF_Mir137170979_hpair @ sk35 )
| ( hF_Mir137170979_hpair @ ( sk20 @ r ) ) ),
inference(cnfConj,[status(thm)],[2163]) ).
thf(50976,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk1640 )
| ~ $true
| ( ( hF_Mirabelle_hmem @ sk1804 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[49111,181]) ).
thf(50977,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk1640 )
| ( ( hF_Mirabelle_hmem @ sk1804 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(simp,[status(thm)],[50976]) ).
thf(51108,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk1640 )
| ( sk1804 != A )
| ( x != A ) ),
inference(simp,[status(thm)],[50977]) ).
thf(51284,plain,
( ( hF_Mir137170979_hpair @ sk1640 )
| ( sk1804 != x ) ),
inference(simp,[status(thm)],[51108]) ).
thf(53326,plain,
( ( hF_Mir137170979_hpair @ sk1564 )
| ( sk1804 != x ) ),
inference(rewrite,[status(thm)],[51284,53317]) ).
thf(44226,plain,
! [A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[44020,191]) ).
thf(44227,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ),
inference(simp,[status(thm)],[44226]) ).
thf(44398,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1564 @ sk1565 )
!= A )
| ( ( hF_Mir1653039215strict @ r @ x )
!= ( hF_Mirabelle_HUnion @ A ) ) ),
inference(simp,[status(thm)],[44227]) ).
thf(44566,plain,
( ( hF_Mir1653039215strict @ r @ x )
!= ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_hpair @ sk1564 @ sk1565 ) ) ),
inference(simp,[status(thm)],[44398]) ).
thf(65037,plain,
( ( hF_Mirabelle_hmem @ sk2237 @ x )
| ( hF_Mir137170979_hpair @ sk1564 ) ),
inference(rewrite,[status(thm)],[62870,65033]) ).
thf(2543,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ~ ( hF_Mir137170979_hpair @ sk45 )
| ( ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x )
!= r ) ),
inference(cnfConj,[status(thm)],[2541]) ).
thf(378,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A
= ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ B @ D ) ) )
| ( ( sup_su638957495lle_hf @ A @ zero_z189798548lle_hf )
!= ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[105,85]) ).
thf(384,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A
= ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ B @ D ) ) )
| ( A != B )
| ( ( sup_su638957495lle_hf @ C @ D )
!= zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[378]) ).
thf(386,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ A @ C ) )
= A )
| ( ( sup_su638957495lle_hf @ B @ C )
!= zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[384]) ).
thf(10299,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_HUnion @ A ) ) @ ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_HUnion @ C ) ) )
| ( ( sup_su638957495lle_hf @ A @ zero_z189798548lle_hf )
!= ( sup_su638957495lle_hf @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[105,3873]) ).
thf(10300,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_HUnion @ A ) ) @ ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_HUnion @ zero_z189798548lle_hf ) ) ),
inference(pattern_uni,[status(thm)],[10299:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( zero_z189798548lle_hf ))]]) ).
thf(10432,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_HUnion @ A ) ) @ ( hF_Mirabelle_HUnion @ zero_z189798548lle_hf ) ),
inference(rewrite,[status(thm)],[10300,134]) ).
thf(1197,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mirabelle_hpair @ zero_z189798548lle_hf @ A ) ) @ ( hF_Mirabelle_hpair @ zero_z189798548lle_hf @ A ) )
!= ( hF_Mirabelle_hmem @ B @ ( hF_Mirabelle_HUnion @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[1012,191]) ).
thf(1198,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mirabelle_hpair @ zero_z189798548lle_hf @ A ) ) @ ( hF_Mirabelle_hpair @ zero_z189798548lle_hf @ A ) )
!= ( hF_Mirabelle_hmem @ B @ ( hF_Mirabelle_HUnion @ B ) ) ),
inference(simp,[status(thm)],[1197]) ).
thf(1209,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk20 @ ( hF_Mirabelle_hpair @ zero_z189798548lle_hf @ A ) )
!= B )
| ( ( hF_Mirabelle_hpair @ zero_z189798548lle_hf @ A )
!= ( hF_Mirabelle_HUnion @ B ) ) ),
inference(simp,[status(thm)],[1198]) ).
thf(1221,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_HUnion @ ( sk20 @ ( hF_Mirabelle_hpair @ zero_z189798548lle_hf @ A ) ) )
!= ( hF_Mirabelle_hpair @ zero_z189798548lle_hf @ A ) ),
inference(simp,[status(thm)],[1209]) ).
thf(31,axiom,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_sup_Oidem) ).
thf(154,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(51426,plain,
~ ( hF_Mirabelle_hmem @ x @ sk1564 ),
inference(rewrite,[status(thm)],[44659,51420]) ).
thf(49112,plain,
( ~ ( hF_Mir137170979_hpair @ sk1804 )
| ( hF_Mir137170979_hpair @ sk1640 ) ),
inference(cnfConj,[status(thm)],[49110]) ).
thf(53321,plain,
( ~ ( hF_Mir137170979_hpair @ sk1804 )
| ( hF_Mir137170979_hpair @ sk1564 ) ),
inference(rewrite,[status(thm)],[49112,53317]) ).
thf(2619,plain,
( ~ $true
| ~ ( hF_Mir137170979_hpair @ sk35 )
| ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
!= ( hF_Mir199975595nction @ r ) ) ),
inference(paramod_ordered,[status(thm)],[294,2165]) ).
thf(2620,plain,
( ~ ( hF_Mir137170979_hpair @ sk35 )
| ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
!= ( hF_Mir199975595nction @ r ) ) ),
inference(simp,[status(thm)],[2619]) ).
thf(2626,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ~ ( hF_Mir137170979_hpair @ sk35 )
| ( ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x )
!= r ) ),
inference(simp,[status(thm)],[2620]) ).
thf(58757,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ~ $true
| ( ( hF_Mirabelle_hmem @ sk1077 @ x )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[36454,191]) ).
thf(58758,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( ( hF_Mirabelle_hmem @ sk1077 @ x )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ) ),
inference(simp,[status(thm)],[58757]) ).
thf(58936,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( sk1077 != A )
| ( ( hF_Mirabelle_HUnion @ A )
!= x ) ),
inference(simp,[status(thm)],[58758]) ).
thf(59075,plain,
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( ( hF_Mirabelle_HUnion @ sk1077 )
!= x ) ),
inference(simp,[status(thm)],[58936]) ).
thf(50202,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk1638 )
| ~ $true
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ sk1768 @ x )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[47952,184]) ).
thf(50203,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk1638 )
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ sk1768 @ x )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(simp,[status(thm)],[50202]) ).
thf(50204,plain,
( ( hF_Mir137170979_hpair @ sk1638 )
| ~ ( hF_Mirabelle_hmem @ x @ sk1768 ) ),
inference(pattern_uni,[status(thm)],[50203:[bind(A,$thf( sk1768 )),bind(B,$thf( x ))]]) ).
thf(71799,plain,
( ( hF_Mir137170979_hpair @ sk1564 )
| ~ ( hF_Mirabelle_hmem @ x @ sk1768 ) ),
inference(rewrite,[status(thm)],[50204,51420]) ).
thf(3287,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ B ) ) @ C )
| ( ( sup_su638957495lle_hf @ ( hF_Mirabelle_HUnion @ A ) @ ( hF_Mirabelle_HUnion @ B ) )
!= ( sup_su638957495lle_hf @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[162,2752]) ).
thf(3288,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ B ) ) @ ( hF_Mirabelle_HUnion @ A ) ),
inference(pattern_uni,[status(thm)],[3287:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( hF_Mirabelle_HUnion @ E )),bind(D,$thf( hF_Mirabelle_HUnion @ F ))]]) ).
thf(3336,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ B ) ) @ ( hF_Mirabelle_HUnion @ A ) ),
inference(simp,[status(thm)],[3288]) ).
thf(3095,plain,
! [A: hF_Mirabelle_hf] :
( ~ $true
| ( ( sup_su638957495lle_hf @ r @ A )
!= ( sk20 @ r ) )
| ( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
!= ( hF_Mir199975595nction @ r ) ) ),
inference(paramod_ordered,[status(thm)],[294,2909]) ).
thf(3096,plain,
! [A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ r @ A )
!= ( sk20 @ r ) )
| ( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
!= ( hF_Mir199975595nction @ r ) ) ),
inference(simp,[status(thm)],[3095]) ).
thf(3104,plain,
! [A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ r @ A )
!= ( sk20 @ r ) )
| ( ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x )
!= r ) ),
inference(simp,[status(thm)],[3096]) ).
thf(3725,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ B ) ) @ ( hF_Mirabelle_HUnion @ C ) )
| ( ( sup_su638957495lle_hf @ ( hF_Mirabelle_HUnion @ A ) @ ( hF_Mirabelle_HUnion @ B ) )
!= ( sup_su638957495lle_hf @ C @ C ) ) ),
inference(paramod_ordered,[status(thm)],[162,3685]) ).
thf(3726,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ A ) ) @ ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_HUnion @ A ) ) ),
inference(pattern_uni,[status(thm)],[3725:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( hF_Mirabelle_HUnion @ B ))]]) ).
thf(3748,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ A ) ) @ ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_HUnion @ A ) ) ),
inference(simp,[status(thm)],[3726]) ).
thf(62975,plain,
( ~ ( hF_Mir137170979_hpair @ sk2246 )
| ( hF_Mir137170979_hpair @ sk2142 ) ),
inference(cnfConj,[status(thm)],[62973]) ).
thf(65917,plain,
( ~ ( hF_Mir137170979_hpair @ sk2246 )
| ( hF_Mir137170979_hpair @ sk1564 ) ),
inference(rewrite,[status(thm)],[62975,65908]) ).
thf(58773,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ~ $true
| ( ( hF_Mirabelle_hmem @ sk1077 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[36454,181]) ).
thf(58774,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( ( hF_Mirabelle_hmem @ sk1077 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(simp,[status(thm)],[58773]) ).
thf(58870,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( sk1077 != A )
| ( x != A ) ),
inference(simp,[status(thm)],[58774]) ).
thf(59134,plain,
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( sk1077 != x ) ),
inference(simp,[status(thm)],[58870]) ).
thf(51421,plain,
hF_Mirabelle_hmem @ sk1564 @ x,
inference(rewrite,[status(thm)],[44628,51420]) ).
thf(44639,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ A )
!= ( hF_Mirabelle_hmem @ sk1638 @ x ) ) ),
inference(paramod_ordered,[status(thm)],[44628,8843]) ).
thf(44640,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ A )
!= ( hF_Mirabelle_hmem @ sk1638 @ x ) ),
inference(simp,[status(thm)],[44639]) ).
thf(44831,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk6 @ A @ B )
!= sk1638 )
| ( A != x ) ),
inference(simp,[status(thm)],[44640]) ).
thf(44958,plain,
! [A: hF_Mirabelle_hf] :
( ( sk6 @ x @ A )
!= sk1638 ),
inference(simp,[status(thm)],[44831]) ).
thf(56173,plain,
! [A: hF_Mirabelle_hf] :
( ( sk6 @ x @ A )
!= sk1564 ),
inference(rewrite,[status(thm)],[44958,51420]) ).
thf(27929,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ A )
!= ( hF_Mirabelle_hmem @ ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ r ) @ r ) )
| ( ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ ( sk15 @ hF_Mir434065167lation @ A ) )
!= ( hF_Mirabelle_hmem @ ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ r ) @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[27164,13783]) ).
thf(28167,plain,
! [A: hF_Mirabelle_hf] :
( ( ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ r )
!= zero_z189798548lle_hf )
| ( A != r )
| ( ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ r )
!= zero_z189798548lle_hf )
| ( ( sk15 @ hF_Mir434065167lation @ A )
!= ( hF_Mir1653039215strict @ r @ x ) ) ),
inference(simp,[status(thm)],[27929]) ).
thf(28232,plain,
( ( ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ r )
!= zero_z189798548lle_hf )
| ( ( sk15 @ hF_Mir434065167lation @ r )
!= ( hF_Mir1653039215strict @ r @ x ) ) ),
inference(simp,[status(thm)],[28167]) ).
thf(44022,plain,
sk1565 != sk1566,
inference(cnfConj,[status(thm)],[44019]) ).
thf(44023,plain,
sk1566 != sk1565,
inference(lifteq,[status(thm)],[44022]) ).
thf(61662,plain,
! [A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) @ r )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[60431,191]) ).
thf(61663,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) @ r )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ),
inference(simp,[status(thm)],[61662]) ).
thf(61838,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1564 @ sk1566 )
!= A )
| ( ( hF_Mirabelle_HUnion @ A )
!= r ) ),
inference(simp,[status(thm)],[61663]) ).
thf(62045,plain,
( ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) )
!= r ),
inference(simp,[status(thm)],[61838]) ).
thf(30,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A @ B ) @ C )
= ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_sup_Oassoc) ).
thf(151,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A @ B ) @ C )
= ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(4495,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ B ) ) ) @ ( hF_Mirabelle_HUnion @ C ) )
| ( ( sup_su638957495lle_hf @ ( hF_Mirabelle_HUnion @ A ) @ ( hF_Mirabelle_HUnion @ B ) )
!= ( sup_su638957495lle_hf @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[162,3336]) ).
thf(4496,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ B ) ) ) @ ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_HUnion @ A ) ) ),
inference(pattern_uni,[status(thm)],[4495:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( hF_Mirabelle_HUnion @ E )),bind(D,$thf( hF_Mirabelle_HUnion @ F ))]]) ).
thf(4523,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ B ) ) ) @ ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_HUnion @ A ) ) ),
inference(simp,[status(thm)],[4496]) ).
thf(1128,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mirabelle_hpair @ A @ zero_z189798548lle_hf ) ) @ ( hF_Mirabelle_hpair @ A @ zero_z189798548lle_hf ) )
!= ( hF_Mirabelle_hmem @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1009,181]) ).
thf(1129,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mirabelle_hpair @ A @ zero_z189798548lle_hf ) ) @ ( hF_Mirabelle_hpair @ A @ zero_z189798548lle_hf ) )
!= ( hF_Mirabelle_hmem @ B @ B ) ),
inference(simp,[status(thm)],[1128]) ).
thf(1138,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk20 @ ( hF_Mirabelle_hpair @ A @ zero_z189798548lle_hf ) )
!= B )
| ( ( hF_Mirabelle_hpair @ A @ zero_z189798548lle_hf )
!= B ) ),
inference(simp,[status(thm)],[1129]) ).
thf(1148,plain,
! [A: hF_Mirabelle_hf] :
( ( sk20 @ ( hF_Mirabelle_hpair @ A @ zero_z189798548lle_hf ) )
!= ( hF_Mirabelle_hpair @ A @ zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[1138]) ).
thf(59261,plain,
! [A: hF_Mirabelle_hf] :
( ~ ! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ C ) @ A )
=> ! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ D ) @ A )
=> ( C = D ) ) )
| ( sk1077 != x )
| ( ( hF_Mir199975595nction @ A )
!= ( hF_Mir199975595nction @ zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[333,59134]) ).
thf(59262,plain,
( ~ ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ B ) @ zero_z189798548lle_hf )
=> ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ C ) @ zero_z189798548lle_hf )
=> ( B = C ) ) )
| ( sk1077 != x ) ),
inference(pattern_uni,[status(thm)],[59261:[bind(A,$thf( zero_z189798548lle_hf ))]]) ).
thf(59299,plain,
( ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk2112 @ sk2113 ) @ zero_z189798548lle_hf )
| ( sk1077 != x ) )
& ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk2112 @ sk2114 ) @ zero_z189798548lle_hf )
| ( sk1077 != x ) )
& ( ( sk2113 != sk2114 )
| ( sk1077 != x ) ) ),
inference(cnf,[status(esa)],[59262]) ).
thf(59302,plain,
( ( sk2113 != sk2114 )
| ( sk1077 != x ) ),
inference(cnfConj,[status(thm)],[59299]) ).
thf(59303,plain,
( ( sk2114 != sk2113 )
| ( sk1077 != x ) ),
inference(lifteq,[status(thm)],[59302]) ).
thf(3649,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ B ) ) )
= ( hF_Mirabelle_HUnion @ C ) )
| ( ( sup_su638957495lle_hf @ ( hF_Mirabelle_HUnion @ A ) @ ( hF_Mirabelle_HUnion @ B ) )
!= ( sup_su638957495lle_hf @ C @ C ) ) ),
inference(paramod_ordered,[status(thm)],[162,3349]) ).
thf(3650,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ A ) ) )
= ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_HUnion @ A ) ) ),
inference(pattern_uni,[status(thm)],[3649:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( hF_Mirabelle_HUnion @ B ))]]) ).
thf(3673,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ A ) ) )
= ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_HUnion @ A ) ) ),
inference(simp,[status(thm)],[3650]) ).
thf(282,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ ( sk17 @ A ) )
= ( ? [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
& ( hF_Mirabelle_hmem @ B @ C ) ) ) ),
inference(cnf,[status(esa)],[281]) ).
thf(283,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ ( sk17 @ A ) )
= ( ? [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
& ( hF_Mirabelle_hmem @ B @ C ) ) ) ),
inference(lifteq,[status(thm)],[282]) ).
thf(61610,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ $true
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) @ r )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[60431,184]) ).
thf(61611,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) @ r )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(simp,[status(thm)],[61610]) ).
thf(61612,plain,
~ ( hF_Mirabelle_hmem @ r @ ( hF_Mirabelle_hpair @ sk1564 @ sk1566 ) ),
inference(pattern_uni,[status(thm)],[61611:[bind(A,$thf( hF_Mirabelle_hpair @ sk1564 @ sk1566 )),bind(B,$thf( r ))]]) ).
thf(218,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk8 @ B @ A ) @ A )
| ( ( hF_Mirabelle_hmem @ C @ ( sk11 @ B @ A ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) ) ),
inference(cnfConj,[status(thm)],[217]) ).
thf(222,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ C @ ( sk11 @ B @ A ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) )
| ( hF_Mirabelle_hmem @ ( sk8 @ B @ A ) @ A ) ),
inference(lifteq,[status(thm)],[218]) ).
thf(46234,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ $true
| ( ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ A )
!= ( hF_Mirabelle_hmem @ ( sk20 @ x ) @ x ) ) ),
inference(paramod_ordered,[status(thm)],[45120,8843]) ).
thf(46235,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ A )
!= ( hF_Mirabelle_hmem @ ( sk20 @ x ) @ x ) ),
inference(simp,[status(thm)],[46234]) ).
thf(46424,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk6 @ A @ B )
!= ( sk20 @ x ) )
| ( A != x ) ),
inference(simp,[status(thm)],[46235]) ).
thf(46535,plain,
! [A: hF_Mirabelle_hf] :
( ( sk6 @ x @ A )
!= ( sk20 @ x ) ),
inference(simp,[status(thm)],[46424]) ).
thf(231,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ ( sk12 @ B @ A ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( C
= ( B @ D ) ) ) ) ),
inference(cnf,[status(esa)],[230]) ).
thf(232,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ ( sk12 @ B @ A ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( C
= ( B @ D ) ) ) ) ),
inference(lifteq,[status(thm)],[231]) ).
thf(79356,plain,
$false,
inference(e,[status(thm)],[69,3873,65832,138,54881,13783,333,53867,88,8843,468,46573,56357,52384,170,44577,55469,51425,47654,202,2940,115,61889,276,47742,449,120,247,65925,28086,63732,70783,48810,66438,185,51422,2972,52189,301,565,44020,288,48680,2869,56420,60008,2654,58705,70177,54872,46254,46581,157,184,58045,31075,1147,93,284,228,65911,289,261,48381,211,238,121,2122,106,60358,280,293,3685,27201,48430,133,3226,56930,1697,206,292,233,248,117,51420,53868,85,2164,51423,30263,66634,44557,46511,58037,8842,102,3550,52104,1223,30297,260,160,69792,192,137,165,302,53925,252,3349,97,65041,229,16801,2653,224,52188,2115,2973,188,388,141,31048,109,64343,65102,51428,71070,77,537,28628,28295,43228,56080,212,96,225,4276,46213,1478,457,173,129,1852,3333,65908,134,105,205,44626,60409,26518,2909,46592,57967,47410,166,279,264,39480,4359,296,562,176,423,47684,191,286,291,118,281,204,71,59200,69315,2753,53322,236,804,181,54921,1224,86,159,51424,406,274,2987,51427,36449,230,45120,245,65074,303,208,187,65042,451,76,1667,387,103,594,799,91,251,2542,520,50774,2974,7297,130,65934,223,135,2752,299,226,267,2207,80,25465,1413,162,44166,22110,255,2124,209,516,60431,123,1145,4355,2899,1034,46547,112,27164,65101,836,24428,194,145,66511,295,150,55818,327,28671,31306,263,45037,2165,53326,44566,177,46311,182,65037,336,2543,72,386,10432,143,1221,154,51426,53321,2626,87,203,59075,71799,56168,258,3336,3104,3748,21949,65917,53317,13780,235,59134,43675,51421,56173,28232,44021,44023,214,287,62045,151,300,36454,146,4523,1148,239,43546,268,59303,195,47869,3673,94,283,25286,294,126,6233,68,178,277,65033,61612,163,90,43938,83,2206,215,222,46535,232,100,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP076^1 : TPTP v9.3.1. Released v7.5.0.
% 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
% 0.08/0.21 % Computer : n016.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Tue Sep 29 19:52:50 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 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
% 1.01/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.39/1.20 % [INFO] Parsing done (401ms).
% 2.39/1.22 % [INFO] Running in sequential loop mode.
% 3.52/1.62 % [INFO] eprover registered as external prover.
% 3.52/1.62 % [INFO] Scanning for conjecture ...
% 3.70/1.76 % [INFO] Found a conjecture (or negated_conjecture) and 355 axioms. Running axiom selection ...
% 3.92/1.85 % [INFO] Axiom selection finished. Selected 65 axioms (removed 290 axioms).
% 4.19/1.98 % [INFO] Problem is higher-order (TPTP THF).
% 4.19/1.99 % [INFO] Type checking passed.
% 4.19/2.00 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 206.09/52.70 % External prover 'e' found a proof!
% 206.09/52.70 % [INFO] Killing All external provers ...
% 206.09/52.70 % Time passed: 52348ms (effective reasoning time: 51480ms)
% 206.09/52.71 % 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)>
% 206.09/52.71 % Axioms used in derivation (65): fact_26_RepFun__iff, fact_132_inf__sup__aci_I6_J, fact_25_HCollect__iff, fact_117_sup__assoc, fact_13_comprehension, fact_15_hpair__neq__fst, fact_135_inf__sup__aci_I7_J, fact_123_boolean__algebra__cancel_Osup2, fact_120_sup_Oassoc, fact_53_Replace__hunion, fact_3_hpair__iff, fact_43_hunion__hempty__left, fact_20_hrelation__def, fact_67_hemptyE, fact_89_sup_Oidem, fact_111_sup__commute, fact_34_HCollect__hempty, fact_77_hrelation__0, fact_42_hunion__iff, fact_95_sup_Oleft__idem, fact_108_sup_Oleft__commute, fact_105_sup__left__commute, fact_5_hf__equalityI, fact_23_HUnion__iff, fact_16_hpair__neq__snd, fact_68_hempty__iff, fact_22_PrimReplace__iff, fact_50_hunion__hempty__right, fact_247_zero__reorient, fact_17_replacement__fun, fact_21_is__hpair__def, fact_10_hmem__not__sym, fact_14_hmem__not__refl, fact_39_hrelation__hunion, fact_29_Replace__cong, fact_18_hfst__conv, fact_129_inf__sup__aci_I5_J, fact_19_hsnd__conv, fact_138_inf__sup__aci_I8_J, fact_114_sup_Ocommute, fact_37_RepFun__0, fact_28_RepFun__cong, fact_12_union__of__set, fact_126_boolean__algebra__cancel_Osup1, fact_0_hrelation__restr, fact_69_hmem__hempty, fact_2_hrestrict__iff, fact_52_HUnion__hunion, fact_36_Replace__0, fact_98_sup__left__idem, fact_101_sup_Oright__idem, fact_8_replacement, fact_6_hf__ext, fact_24_Replace__iff, fact_32_zero__notin__hpair, fact_70_hpair__nonzero, fact_11_hpair__inject, fact_1_hfunction__def, fact_51_RepFun__hunion, fact_35_HUnion__hempty, conj_0, fact_9_binary__union, fact_7_hmem__ne, fact_92_sup__idem, fact_30_hmem__Sup__ne
% 206.09/52.71 % No. of inferences in proof: 1016
% 206.09/52.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 52348 ms resp. 51480 ms w/o parsing
% 208.69/53.05 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 208.69/53.05 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------