TSTP Solution File: ITP076^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP076^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:47:37 EDT 2024
% Result : Theorem 221.51s 38.44s
% Output : Refutation 222.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 169
% Syntax : Number of formulae : 1216 ( 518 unt; 101 typ; 0 def)
% Number of atoms : 2843 (1371 equ; 10 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 8492 (1143 ~; 742 |; 108 &;6321 @)
% ( 0 <=>; 178 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 253 ( 253 >; 0 *; 0 +; 0 <<)
% Number of symbols : 101 ( 98 usr; 61 con; 0-4 aty)
% Number of variables : 1975 ( 101 ^1741 !; 133 ?;1975 :)
% 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_type,type,
zero_z189798548lle_hf: hF_Mirabelle_hf ).
thf(hF_Mir818139703ollect_type,type,
hF_Mir818139703ollect: ( hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(hF_Mirabelle_HUnion_type,type,
hF_Mirabelle_HUnion: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(hF_Mir1248913145eplace_type,type,
hF_Mir1248913145eplace: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).
thf(hF_Mirabelle_RepFun_type,type,
hF_Mirabelle_RepFun: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf ) > hF_Mirabelle_hf ).
thf(hF_Mirabelle_Replace_type,type,
hF_Mirabelle_Replace: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).
thf(hF_Mirabelle_hfst_type,type,
hF_Mirabelle_hfst: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(hF_Mir199975595nction_type,type,
hF_Mir199975595nction: hF_Mirabelle_hf > $o ).
thf(hF_Mirabelle_hmem_type,type,
hF_Mirabelle_hmem: hF_Mirabelle_hf > hF_Mirabelle_hf > $o ).
thf(hF_Mirabelle_hpair_type,type,
hF_Mirabelle_hpair: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(hF_Mir434065167lation_type,type,
hF_Mir434065167lation: hF_Mirabelle_hf > $o ).
thf(hF_Mir1653039215strict_type,type,
hF_Mir1653039215strict: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(hF_Mirabelle_hsnd_type,type,
hF_Mirabelle_hsnd: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(hF_Mir137170979_hpair_type,type,
hF_Mir137170979_hpair: hF_Mirabelle_hf > $o ).
thf(sup_su638957495lle_hf_type,type,
sup_su638957495lle_hf: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(r_type,type,
r: hF_Mirabelle_hf ).
thf(x_type,type,
x: hF_Mirabelle_hf ).
thf(sk1_type,type,
sk1: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk2_type,type,
sk2: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk3_type,type,
sk3: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk4_type,type,
sk4: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk5_type,type,
sk5: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk6_type,type,
sk6: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk7_type,type,
sk7: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk8_type,type,
sk8: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk9_type,type,
sk9: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk10_type,type,
sk10: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk11_type,type,
sk11: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk12_type,type,
sk12: ( hF_Mirabelle_hf > hF_Mirabelle_hf ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk13_type,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(sk15_type,type,
sk15: ( hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk16_type,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_type,type,
sk17: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk18_type,type,
sk18: hF_Mirabelle_hf ).
thf(sk19_type,type,
sk19: hF_Mirabelle_hf ).
thf(sk20_type,type,
sk20: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk21_type,type,
sk21: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk22_type,type,
sk22: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk23_type,type,
sk23: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk24_type,type,
sk24: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk25_type,type,
sk25: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk26_type,type,
sk26: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk27_type,type,
sk27: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk28_type,type,
sk28: hF_Mirabelle_hf ).
thf(sk29_type,type,
sk29: hF_Mirabelle_hf ).
thf(sk30_type,type,
sk30: hF_Mirabelle_hf ).
thf(sk31_type,type,
sk31: hF_Mirabelle_hf ).
thf(sk32_type,type,
sk32: hF_Mirabelle_hf ).
thf(sk33_type,type,
sk33: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(sk35_type,type,
sk35: hF_Mirabelle_hf ).
thf(sk40_type,type,
sk40: hF_Mirabelle_hf ).
thf(sk45_type,type,
sk45: hF_Mirabelle_hf ).
thf(sk50_type,type,
sk50: hF_Mirabelle_hf ).
thf(sk1147_type,type,
sk1147: hF_Mirabelle_hf ).
thf(sk1149_type,type,
sk1149: hF_Mirabelle_hf ).
thf(sk1525_type,type,
sk1525: hF_Mirabelle_hf ).
thf(sk1526_type,type,
sk1526: hF_Mirabelle_hf ).
thf(sk1575_type,type,
sk1575: hF_Mirabelle_hf ).
thf(sk1576_type,type,
sk1576: hF_Mirabelle_hf ).
thf(sk1577_type,type,
sk1577: hF_Mirabelle_hf ).
thf(sk1604_type,type,
sk1604: hF_Mirabelle_hf ).
thf(sk1605_type,type,
sk1605: hF_Mirabelle_hf ).
thf(sk1606_type,type,
sk1606: hF_Mirabelle_hf ).
thf(sk1607_type,type,
sk1607: hF_Mirabelle_hf ).
thf(sk1671_type,type,
sk1671: hF_Mirabelle_hf ).
thf(sk1672_type,type,
sk1672: hF_Mirabelle_hf ).
thf(sk1734_type,type,
sk1734: hF_Mirabelle_hf ).
thf(sk1770_type,type,
sk1770: hF_Mirabelle_hf ).
thf(sk1901_type,type,
sk1901: hF_Mirabelle_hf ).
thf(sk2002_type,type,
sk2002: hF_Mirabelle_hf ).
thf(sk2003_type,type,
sk2003: hF_Mirabelle_hf ).
thf(sk2039_type,type,
sk2039: hF_Mirabelle_hf ).
thf(sk2040_type,type,
sk2040: hF_Mirabelle_hf ).
thf(sk2072_type,type,
sk2072: hF_Mirabelle_hf ).
thf(sk2073_type,type,
sk2073: hF_Mirabelle_hf ).
thf(sk2075_type,type,
sk2075: hF_Mirabelle_hf ).
thf(sk2076_type,type,
sk2076: hF_Mirabelle_hf ).
thf(sk2103_type,type,
sk2103: hF_Mirabelle_hf ).
thf(sk2104_type,type,
sk2104: hF_Mirabelle_hf ).
thf(sk2105_type,type,
sk2105: hF_Mirabelle_hf ).
thf(sk2106_type,type,
sk2106: hF_Mirabelle_hf ).
thf(sk2203_type,type,
sk2203: hF_Mirabelle_hf ).
thf(sk2204_type,type,
sk2204: hF_Mirabelle_hf ).
thf(sk2448_type,type,
sk2448: hF_Mirabelle_hf ).
thf(sk2449_type,type,
sk2449: hF_Mirabelle_hf ).
thf(sk2453_type,type,
sk2453: hF_Mirabelle_hf ).
thf(sk2458_type,type,
sk2458: hF_Mirabelle_hf ).
thf(sk2466_type,type,
sk2466: hF_Mirabelle_hf ).
thf(sk2467_type,type,
sk2467: hF_Mirabelle_hf ).
thf(sk2650_type,type,
sk2650: hF_Mirabelle_hf ).
thf(sk2651_type,type,
sk2651: hF_Mirabelle_hf ).
thf(sk2652_type,type,
sk2652: hF_Mirabelle_hf ).
thf(sk2653_type,type,
sk2653: hF_Mirabelle_hf ).
thf(sk2748_type,type,
sk2748: hF_Mirabelle_hf ).
thf(sk2757_type,type,
sk2757: hF_Mirabelle_hf ).
thf(sk2825_type,type,
sk2825: hF_Mirabelle_hf ).
thf(sk2828_type,type,
sk2828: hF_Mirabelle_hf ).
thf(3,axiom,
! [A: hF_Mirabelle_hf > $o] :
( ( hF_Mir818139703ollect @ A @ zero_z189798548lle_hf )
= zero_z189798548lle_hf ),
file('/export/starexec/sandbox2/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(67,axiom,
hF_Mir199975595nction @ r,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(287,plain,
hF_Mir199975595nction @ r,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
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/sandbox2/benchmark/theBenchmark.p',fact_13_comprehension) ).
thf(246,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(247,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)],[246]) ).
thf(248,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)],[247]) ).
thf(23600,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ C @ ( sk15 @ B @ A ) )
= ( hF_Mirabelle_hmem @ C @ A ) )
| ( ( hF_Mir199975595nction @ r )
!= ( B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[287,248]) ).
thf(23872,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ r @ ( sk15 @ hF_Mir199975595nction @ A ) )
= ( hF_Mirabelle_hmem @ r @ A ) ),
inference(pre_uni,[status(thm)],[23600:[bind(A,$thf( A )),bind(B,$thf( hF_Mir199975595nction )),bind(C,$thf( r ))]]) ).
thf(13,axiom,
! [A: hF_Mirabelle_hf] :
( ( A = zero_z189798548lle_hf )
= ( ! [B: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ B @ A ) ) ),
file('/export/starexec/sandbox2/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(445,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(455,plain,
! [A: hF_Mirabelle_hf] :
( ( A = zero_z189798548lle_hf )
| ~ ! [B: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ B @ A ) ),
inference(lifteq,[status(thm)],[445]) ).
thf(459,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
| ( A = zero_z189798548lle_hf ) ),
inference(cnf,[status(esa)],[455]) ).
thf(58,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_hpair__neq__fst) ).
thf(258,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(259,plain,
~ ? [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
= A ),
inference(miniscope,[status(thm)],[258]) ).
thf(260,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= A ),
inference(cnf,[status(esa)],[259]) ).
thf(261,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= A ),
inference(lifteq,[status(thm)],[260]) ).
thf(733,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)],[459,261]) ).
thf(734,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)],[733:[bind(A,$thf( hF_Mirabelle_hpair @ D @ E )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(889,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)],[734]) ).
thf(37,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_hmem__ne) ).
thf(175,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(176,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ A @ B )
| ( A != B ) ),
inference(cnf,[status(esa)],[175]) ).
thf(177,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A != B )
| ~ ( hF_Mirabelle_hmem @ A @ B ) ),
inference(lifteq,[status(thm)],[176]) ).
thf(178,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ A ),
inference(simp,[status(thm)],[177]) ).
thf(1012,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(paramod_ordered,[status(thm)],[889,178]) ).
thf(1013,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)],[1012]) ).
thf(1024,plain,
! [A: hF_Mirabelle_hf] :
( ( sk20 @ ( hF_Mirabelle_hpair @ zero_z189798548lle_hf @ A ) )
!= ( hF_Mirabelle_hpair @ zero_z189798548lle_hf @ A ) ),
inference(simp,[status(thm)],[1013]) ).
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/sandbox2/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(22,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= zero_z189798548lle_hf ),
file('/export/starexec/sandbox2/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(699,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(paramod_ordered,[status(thm)],[459,129]) ).
thf(700,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)],[699:[bind(A,$thf( hF_Mirabelle_hpair @ D @ E )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(870,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)],[700]) ).
thf(2018,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(paramod_ordered,[status(thm)],[870,178]) ).
thf(2025,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)],[2018]) ).
thf(2031,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sk20 @ ( hF_Mirabelle_hpair @ A @ B ) )
!= ( hF_Mirabelle_hpair @ A @ B ) ),
inference(simp,[status(thm)],[2025]) ).
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/sandbox2/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(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(14,axiom,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ zero_z189798548lle_hf )
= A ),
file('/export/starexec/sandbox2/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(489,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ A @ B )
= C )
| ( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ A @ B ) )
!= ( sup_su638957495lle_hf @ C @ zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[90,105]) ).
thf(505,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ A @ B )
= C )
| ( A != C )
| ( ( sup_su638957495lle_hf @ A @ B )
!= zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[489]) ).
thf(518,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ B @ A )
= B )
| ( ( sup_su638957495lle_hf @ B @ A )
!= zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[505]) ).
thf(53,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_hpair__neq__snd) ).
thf(242,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(243,plain,
~ ? [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
= B ),
inference(miniscope,[status(thm)],[242]) ).
thf(244,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= B ),
inference(cnf,[status(esa)],[243]) ).
thf(245,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= B ),
inference(lifteq,[status(thm)],[244]) ).
thf(811,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)],[459,245]) ).
thf(812,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)],[811:[bind(A,$thf( hF_Mirabelle_hpair @ D @ E )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(863,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)],[812]) ).
thf(40,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ B )
=> ( ( hF_Mirabelle_HUnion @ A )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_hmem__Sup__ne) ).
thf(185,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(186,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ A @ B )
| ( ( hF_Mirabelle_HUnion @ A )
!= B ) ),
inference(cnf,[status(esa)],[185]) ).
thf(187,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_HUnion @ A )
!= B )
| ~ ( hF_Mirabelle_hmem @ A @ B ) ),
inference(lifteq,[status(thm)],[186]) ).
thf(188,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ),
inference(simp,[status(thm)],[187]) ).
thf(921,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(paramod_ordered,[status(thm)],[863,188]) ).
thf(951,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)],[921]) ).
thf(962,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)],[951]) ).
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/sandbox2/benchmark/theBenchmark.p',fact_29_Replace__cong) ).
thf(234,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(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/sandbox2/benchmark/theBenchmark.p',fact_1_hfunction__def) ).
thf(285,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(286,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)],[285]) ).
thf(325,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)],[286]) ).
thf(1,conjecture,
hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ x ),
file('/export/starexec/sandbox2/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(39419,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)],[325,68]) ).
thf(39420,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)],[39419:[bind(A,$thf( hF_Mir1653039215strict @ r @ x ))]]) ).
thf(39642,plain,
hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) @ ( hF_Mir1653039215strict @ r @ x ),
inference(cnf,[status(esa)],[39420]) ).
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/sandbox2/benchmark/theBenchmark.p',fact_22_PrimReplace__iff) ).
thf(192,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(193,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)],[192]) ).
thf(196,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(cnf,[status(esa)],[193]) ).
thf(200,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)],[196]) ).
thf(6053,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 ) ) )
| $false ),
inference(prim_subst,[status(thm)],[200:[bind(A,$thf( A )),bind(B,$thf( ^ [D: hF_Mirabelle_hf] : ^ [E: hF_Mirabelle_hf] : $false ))]]) ).
thf(6463,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)],[6053]) ).
thf(195,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(cnf,[status(esa)],[193]) ).
thf(199,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)],[195]) ).
thf(5137,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 ) ) )
| $false ),
inference(prim_subst,[status(thm)],[199:[bind(A,$thf( A )),bind(B,$thf( ^ [D: hF_Mirabelle_hf] : ^ [E: hF_Mirabelle_hf] : $false ))]]) ).
thf(5327,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)],[5137]) ).
thf(5636,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(paramod_ordered,[status(thm)],[459,5327]) ).
thf(5637,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir1248913145eplace @ A
@ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : $false )
= zero_z189798548lle_hf ),
inference(pattern_uni,[status(thm)],[5636:[bind(A,$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(5653,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir1248913145eplace @ A
@ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : $false )
= zero_z189798548lle_hf ),
inference(simp,[status(thm)],[5637]) ).
thf(6587,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ),
inference(rewrite,[status(thm)],[6463,5653]) ).
thf(39657,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ) ),
inference(paramod_ordered,[status(thm)],[39642,6587]) ).
thf(39833,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1575 @ sk1577 )
!= A )
| ( ( hF_Mir1653039215strict @ r @ x )
!= zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[39657]) ).
thf(39960,plain,
( ( hF_Mir1653039215strict @ r @ x )
!= zero_z189798548lle_hf ),
inference(simp,[status(thm)],[39833]) ).
thf(42596,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
| ( A
!= ( hF_Mir1653039215strict @ r @ x ) ) ),
inference(paramod_ordered,[status(thm)],[459,39960]) ).
thf(42597,plain,
hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) @ ( hF_Mir1653039215strict @ r @ x ),
inference(pattern_uni,[status(thm)],[42596:[bind(A,$thf( hF_Mir1653039215strict @ r @ x ))]]) ).
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/sandbox2/benchmark/theBenchmark.p',fact_2_hrestrict__iff) ).
thf(282,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(283,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)],[282]) ).
thf(284,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)],[283]) ).
thf(68014,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 @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mir1653039215strict @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[42597,284]) ).
thf(68015,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 ) ) ),
inference(pattern_uni,[status(thm)],[68014:[bind(A,$thf( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )),bind(B,$thf( r )),bind(C,$thf( x ))]]) ).
thf(68428,plain,
( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
= ( hF_Mirabelle_hpair @ sk2650 @ sk2651 ) ),
inference(cnf,[status(esa)],[68015]) ).
thf(68430,plain,
( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
= ( hF_Mirabelle_hpair @ sk2650 @ sk2651 ) ),
inference(lifteq,[status(thm)],[68428]) ).
thf(74177,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
!= A )
| ( ( hF_Mirabelle_hpair @ sk2650 @ sk2651 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[68430,261]) ).
thf(74178,plain,
( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
!= sk2650 ),
inference(pattern_uni,[status(thm)],[74177:[bind(A,$thf( sk2650 )),bind(B,$thf( sk2651 ))]]) ).
thf(39671,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ A @ B )
& ? [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] :
( ( A
= ( hF_Mirabelle_hpair @ D @ E ) )
& ( hF_Mirabelle_hmem @ D @ C ) ) )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mir1653039215strict @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[39642,284]) ).
thf(39672,plain,
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) @ r )
& ? [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1575 @ sk1577 )
= ( hF_Mirabelle_hpair @ A @ B ) )
& ( hF_Mirabelle_hmem @ A @ x ) ) ),
inference(pattern_uni,[status(thm)],[39671:[bind(A,$thf( hF_Mirabelle_hpair @ sk1575 @ sk1577 )),bind(B,$thf( r )),bind(C,$thf( x ))]]) ).
thf(40071,plain,
hF_Mirabelle_hmem @ sk1604 @ x,
inference(cnf,[status(esa)],[39672]) ).
thf(40084,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ sk1604 @ x )
!= ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ) ),
inference(paramod_ordered,[status(thm)],[40071,6587]) ).
thf(40241,plain,
! [A: hF_Mirabelle_hf] :
( ( sk1604 != A )
| ( x != zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[40084]) ).
thf(40349,plain,
x != zero_z189798548lle_hf,
inference(simp,[status(thm)],[40241]) ).
thf(40492,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
| ( A != x ) ),
inference(paramod_ordered,[status(thm)],[459,40349]) ).
thf(40493,plain,
hF_Mirabelle_hmem @ ( sk20 @ x ) @ x,
inference(pattern_uni,[status(thm)],[40492:[bind(A,$thf( x ))]]) ).
thf(43,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
? [C: hF_Mirabelle_hf] :
! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ C )
= ( ( hF_Mirabelle_hmem @ D @ A )
| ( hF_Mirabelle_hmem @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_binary__union) ).
thf(202,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
? [C: hF_Mirabelle_hf] :
! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ C )
= ( ( hF_Mirabelle_hmem @ D @ A )
| ( hF_Mirabelle_hmem @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(203,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ ( sk6 @ B @ A ) )
= ( ( hF_Mirabelle_hmem @ C @ A )
| ( hF_Mirabelle_hmem @ C @ B ) ) ),
inference(cnf,[status(esa)],[202]) ).
thf(204,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ ( sk6 @ B @ A ) )
= ( ( hF_Mirabelle_hmem @ C @ A )
| ( hF_Mirabelle_hmem @ C @ B ) ) ),
inference(lifteq,[status(thm)],[203]) ).
thf(7732,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( ( hF_Mirabelle_hmem @ C @ A )
| ( hF_Mirabelle_hmem @ C @ B ) )
| ( ( hF_Mirabelle_hmem @ C @ ( sk6 @ B @ A ) )
!= ( hF_Mirabelle_hmem @ D @ D ) ) ),
inference(paramod_ordered,[status(thm)],[204,178]) ).
thf(7733,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ B )
| ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[7732:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( sk6 @ E @ F )),bind(D,$thf( sk6 @ E @ F ))]]) ).
thf(7829,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ B ),
inference(cnf,[status(esa)],[7733]) ).
thf(7831,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ B ),
inference(simp,[status(thm)],[7829]) ).
thf(41464,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ B )
!= ( hF_Mirabelle_hmem @ ( sk20 @ x ) @ x ) ),
inference(paramod_ordered,[status(thm)],[40493,7831]) ).
thf(41588,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk6 @ A @ B )
!= ( sk20 @ x ) )
| ( B != x ) ),
inference(simp,[status(thm)],[41464]) ).
thf(41726,plain,
! [A: hF_Mirabelle_hf] :
( ( sk6 @ A @ x )
!= ( sk20 @ x ) ),
inference(simp,[status(thm)],[41588]) ).
thf(55,axiom,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_hmem__not__refl) ).
thf(249,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(40073,plain,
hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) @ r,
inference(cnf,[status(esa)],[39672]) ).
thf(42835,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) @ r )
!= ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ) ),
inference(paramod_ordered,[status(thm)],[40073,6587]) ).
thf(43041,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1575 @ sk1577 )
!= A )
| ( r != zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[42835]) ).
thf(43123,plain,
r != zero_z189798548lle_hf,
inference(simp,[status(thm)],[43041]) ).
thf(43247,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
| ( A != r ) ),
inference(paramod_ordered,[status(thm)],[459,43123]) ).
thf(43248,plain,
hF_Mirabelle_hmem @ ( sk20 @ r ) @ r,
inference(pattern_uni,[status(thm)],[43247:[bind(A,$thf( r ))]]) ).
thf(43454,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r )
!= ( hF_Mirabelle_hmem @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[43248,178]) ).
thf(43487,plain,
! [A: hF_Mirabelle_hf] :
( ( ( sk20 @ r )
!= A )
| ( r != A ) ),
inference(simp,[status(thm)],[43454]) ).
thf(43683,plain,
( ( sk20 @ r )
!= r ),
inference(simp,[status(thm)],[43487]) ).
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/sandbox2/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(3000,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)],[159,178]) ).
thf(3001,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)],[3000:[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(3113,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ B ) @ A ),
inference(cnf,[status(esa)],[3001]) ).
thf(3115,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ B ) @ A ),
inference(simp,[status(thm)],[3113]) ).
thf(7687,plain,
! [E: hF_Mirabelle_hf,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 @ ( sup_su638957495lle_hf @ D @ E ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[204,3115]) ).
thf(7688,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ ( sk6 @ B @ C ) @ A ) @ C )
| ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ ( sk6 @ B @ C ) @ A ) @ B ) ),
inference(pattern_uni,[status(thm)],[7687:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( sup_su638957495lle_hf @ ( sk6 @ H @ I ) @ G )),bind(D,$thf( sk6 @ H @ I )),bind(E,$thf( G ))]]) ).
thf(7796,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ ( sk6 @ B @ C ) @ A ) @ C ),
inference(cnf,[status(esa)],[7688]) ).
thf(7798,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ ( sk6 @ B @ C ) @ A ) @ C ),
inference(simp,[status(thm)],[7796]) ).
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/sandbox2/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 ) ),
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 ) )
| ( A = C ) ),
inference(lifteq,[status(thm)],[167]) ).
thf(170,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sk1 @ A @ ( hF_Mirabelle_hpair @ B @ A ) )
= B ),
introduced(tautology,[new_symbols(inverse(hF_Mirabelle_hpair),[sk1])]) ).
thf(18,axiom,
! [A: hF_Mirabelle_hf] :
( ( zero_z189798548lle_hf = A )
= ( A = zero_z189798548lle_hf ) ),
file('/export/starexec/sandbox2/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(41536,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ x ) @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[40493,178]) ).
thf(41568,plain,
! [A: hF_Mirabelle_hf] :
( ( ( sk20 @ x )
!= A )
| ( x != A ) ),
inference(simp,[status(thm)],[41536]) ).
thf(41694,plain,
( ( sk20 @ x )
!= x ),
inference(simp,[status(thm)],[41568]) ).
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/sandbox2/benchmark/theBenchmark.p',fact_20_hrelation__def) ).
thf(221,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(222,plain,
( hF_Mir434065167lation
= ( ^ [A: hF_Mirabelle_hf] :
! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) ) ) ),
inference(lifteq,[status(thm)],[221]) ).
thf(293,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)],[222]) ).
thf(39643,plain,
hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) @ ( hF_Mir1653039215strict @ r @ x ),
inference(cnf,[status(esa)],[39420]) ).
thf(53948,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 @ sk1575 @ sk1576 ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mir1653039215strict @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[39643,284]) ).
thf(53949,plain,
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) @ r )
& ? [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1575 @ sk1576 )
= ( hF_Mirabelle_hpair @ A @ B ) )
& ( hF_Mirabelle_hmem @ A @ x ) ) ),
inference(pattern_uni,[status(thm)],[53948:[bind(A,$thf( hF_Mirabelle_hpair @ sk1575 @ sk1576 )),bind(B,$thf( r )),bind(C,$thf( x ))]]) ).
thf(54334,plain,
hF_Mirabelle_hmem @ sk2103 @ x,
inference(cnf,[status(esa)],[53949]) ).
thf(540,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)],[293]) ).
thf(559,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ B @ A )
| ( hF_Mir137170979_hpair @ B )
| ~ ( hF_Mir434065167lation @ A ) ),
inference(cnf,[status(esa)],[540]) ).
thf(54359,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ B )
| ~ ( hF_Mir434065167lation @ A )
| ( ( hF_Mirabelle_hmem @ sk2103 @ x )
!= ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[54334,559]) ).
thf(54360,plain,
( ( hF_Mir137170979_hpair @ sk2103 )
| ~ ( hF_Mir434065167lation @ x ) ),
inference(pattern_uni,[status(thm)],[54359:[bind(A,$thf( x )),bind(B,$thf( sk2103 ))]]) ).
thf(56382,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk2103 )
| ~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) )
| ( ( hF_Mir434065167lation @ A )
!= ( hF_Mir434065167lation @ x ) ) ),
inference(paramod_ordered,[status(thm)],[293,54360]) ).
thf(56383,plain,
( ( hF_Mir137170979_hpair @ sk2103 )
| ~ ! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ x )
=> ( hF_Mir137170979_hpair @ A ) ) ),
inference(pattern_uni,[status(thm)],[56382:[bind(A,$thf( x ))]]) ).
thf(56455,plain,
( ( hF_Mirabelle_hmem @ sk2203 @ x )
| ( hF_Mir137170979_hpair @ sk2103 ) ),
inference(cnf,[status(esa)],[56383]) ).
thf(57436,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk2103 )
| ( ( hF_Mirabelle_hmem @ sk2203 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[56455,178]) ).
thf(57503,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk2103 )
| ( sk2203 != A )
| ( x != A ) ),
inference(simp,[status(thm)],[57436]) ).
thf(57644,plain,
( ( hF_Mir137170979_hpair @ sk2103 )
| ( sk2203 != x ) ),
inference(simp,[status(thm)],[57503]) ).
thf(54335,plain,
( ( hF_Mirabelle_hpair @ sk1575 @ sk1576 )
= ( hF_Mirabelle_hpair @ sk2103 @ sk2104 ) ),
inference(cnf,[status(esa)],[53949]) ).
thf(54337,plain,
( ( hF_Mirabelle_hpair @ sk2103 @ sk2104 )
= ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) ),
inference(lifteq,[status(thm)],[54335]) ).
thf(63,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_hfst__conv) ).
thf(277,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(278,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ A @ B ) )
= A ),
inference(cnf,[status(esa)],[277]) ).
thf(279,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ A @ B ) )
= A ),
inference(lifteq,[status(thm)],[278]) ).
thf(57810,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) )
= A )
| ( ( hF_Mirabelle_hpair @ sk2103 @ sk2104 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[54337,279]) ).
thf(57811,plain,
( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) )
= sk2103 ),
inference(pattern_uni,[status(thm)],[57810:[bind(A,$thf( sk2103 )),bind(B,$thf( sk2104 ))]]) ).
thf(58025,plain,
sk2103 = sk1575,
inference(rewrite,[status(thm)],[57811,279]) ).
thf(58740,plain,
( ( hF_Mir137170979_hpair @ sk1575 )
| ( sk2203 != x ) ),
inference(rewrite,[status(thm)],[57644,58025]) ).
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/sandbox2/benchmark/theBenchmark.p',fact_21_is__hpair__def) ).
thf(173,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(174,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)],[173]) ).
thf(292,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)],[174]) ).
thf(521,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)],[292]) ).
thf(525,plain,
! [A: hF_Mirabelle_hf] :
( ( A
= ( hF_Mirabelle_hpair @ ( sk21 @ A ) @ ( sk22 @ A ) ) )
| ~ ( hF_Mir137170979_hpair @ A ) ),
inference(cnf,[status(esa)],[521]) ).
thf(526,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ ( sk21 @ A ) @ ( sk22 @ A ) )
= A )
| ~ ( hF_Mir137170979_hpair @ A ) ),
inference(lifteq,[status(thm)],[525]) ).
thf(69962,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir137170979_hpair @ A )
| ( A != zero_z189798548lle_hf )
| ( ( hF_Mirabelle_hpair @ ( sk21 @ A ) @ ( sk22 @ A ) )
!= ( hF_Mirabelle_hpair @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[526,129]) ).
thf(69963,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir137170979_hpair @ A )
| ( A != zero_z189798548lle_hf ) ),
inference(pattern_uni,[status(thm)],[69962:[bind(A,$thf( E )),bind(B,$thf( sk21 @ E )),bind(C,$thf( sk22 @ E ))]]) ).
thf(70122,plain,
~ ( hF_Mir137170979_hpair @ zero_z189798548lle_hf ),
inference(simp,[status(thm)],[69963]) ).
thf(70147,plain,
( ( sk2203 != x )
| ( ( hF_Mir137170979_hpair @ sk1575 )
!= ( hF_Mir137170979_hpair @ zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[58740,70122]) ).
thf(70171,plain,
( ( sk2203 != x )
| ( sk1575 != zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[70147]) ).
thf(834,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)],[459,68]) ).
thf(835,plain,
( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) @ ( hF_Mir1653039215strict @ r @ x ) )
| ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf ) ),
inference(pattern_uni,[status(thm)],[834:[bind(A,$thf( hF_Mir1653039215strict @ r @ x ))]]) ).
thf(32225,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ A @ B )
& ? [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] :
( ( A
= ( hF_Mirabelle_hpair @ D @ E ) )
& ( hF_Mirabelle_hmem @ D @ C ) ) )
| ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( ( hF_Mirabelle_hmem @ A @ ( hF_Mir1653039215strict @ B @ C ) )
!= ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[284,835]) ).
thf(32226,plain,
( ( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) @ r )
& ? [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
= ( hF_Mirabelle_hpair @ A @ B ) )
& ( hF_Mirabelle_hmem @ A @ x ) ) )
| ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf ) ),
inference(pattern_uni,[status(thm)],[32225:[bind(A,$thf( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )),bind(B,$thf( r )),bind(C,$thf( x ))]]) ).
thf(33027,plain,
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( hF_Mirabelle_hmem @ sk1147 @ x ) ),
inference(cnf,[status(esa)],[32226]) ).
thf(38983,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( ( hF_Mirabelle_hmem @ sk1147 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[33027,178]) ).
thf(39012,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( sk1147 != A )
| ( x != A ) ),
inference(simp,[status(thm)],[38983]) ).
thf(39123,plain,
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( sk1147 != x ) ),
inference(simp,[status(thm)],[39012]) ).
thf(41364,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 ) ) )
| ( sk1147 != x )
| ( ( hF_Mir199975595nction @ A )
!= ( hF_Mir199975595nction @ zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[325,39123]) ).
thf(41365,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 ) ) )
| ( sk1147 != x ) ),
inference(pattern_uni,[status(thm)],[41364:[bind(A,$thf( zero_z189798548lle_hf ))]]) ).
thf(41395,plain,
( ( sk1147 != x )
| ( sk1671 != sk1672 ) ),
inference(cnf,[status(esa)],[41365]) ).
thf(41398,plain,
( ( sk1672 != sk1671 )
| ( sk1147 != x ) ),
inference(lifteq,[status(thm)],[41395]) ).
thf(838,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
| ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
| ( A != x ) ),
inference(paramod_ordered,[status(thm)],[459,68]) ).
thf(839,plain,
( ( hF_Mirabelle_hmem @ ( sk20 @ x ) @ x )
| ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) ) ),
inference(pattern_uni,[status(thm)],[838:[bind(A,$thf( x ))]]) ).
thf(1242,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
| ( hF_Mir137170979_hpair @ B )
| ~ ( hF_Mir434065167lation @ A )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ x ) @ x )
!= ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[839,559]) ).
thf(1243,plain,
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
| ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ~ ( hF_Mir434065167lation @ x ) ),
inference(pattern_uni,[status(thm)],[1242:[bind(A,$thf( x )),bind(B,$thf( sk20 @ x ))]]) ).
thf(1869,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ~ ( hF_Mir434065167lation @ x )
| ( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
!= ( hF_Mir199975595nction @ r ) ) ),
inference(paramod_ordered,[status(thm)],[287,1243]) ).
thf(1887,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ~ ( hF_Mir434065167lation @ x )
| ( ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf )
!= r ) ),
inference(simp,[status(thm)],[1869]) ).
thf(2659,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)],[293,1887]) ).
thf(2660,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)],[2659:[bind(A,$thf( x ))]]) ).
thf(2676,plain,
( ( ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf )
!= r )
| ( hF_Mirabelle_hmem @ sk50 @ x )
| ( hF_Mir137170979_hpair @ ( sk20 @ x ) ) ),
inference(cnf,[status(esa)],[2660]) ).
thf(116,plain,
! [A: hF_Mirabelle_hf] :
( ( zero_z189798548lle_hf = A )
= ( A = zero_z189798548lle_hf ) ),
inference(cnf,[status(esa)],[115]) ).
thf(117,plain,
! [A: hF_Mirabelle_hf] :
( ( zero_z189798548lle_hf = A )
= ( A = zero_z189798548lle_hf ) ),
inference(lifteq,[status(thm)],[116]) ).
thf(448,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( ! [C: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ C @ A ) )
= ( zero_z189798548lle_hf = B ) )
| ( ( A = zero_z189798548lle_hf )
!= ( B = zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[102,117]) ).
thf(449,plain,
! [A: hF_Mirabelle_hf] :
( ( ! [B: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ B @ A ) )
= ( zero_z189798548lle_hf = A ) ),
inference(pattern_uni,[status(thm)],[448:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(836,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
| ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ( A != r ) ),
inference(paramod_ordered,[status(thm)],[459,68]) ).
thf(837,plain,
( ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r )
| ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) ) ),
inference(pattern_uni,[status(thm)],[836:[bind(A,$thf( r ))]]) ).
thf(1052,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ( hF_Mir137170979_hpair @ B )
| ~ ( hF_Mir434065167lation @ A )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r )
!= ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[837,559]) ).
thf(1053,plain,
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ~ ( hF_Mir434065167lation @ r ) ),
inference(pattern_uni,[status(thm)],[1052:[bind(A,$thf( r )),bind(B,$thf( sk20 @ r ))]]) ).
thf(1825,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) )
| ( ( hF_Mir434065167lation @ A )
!= ( hF_Mir434065167lation @ r ) ) ),
inference(paramod_ordered,[status(thm)],[293,1053]) ).
thf(1826,plain,
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ~ ! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ r )
=> ( hF_Mir137170979_hpair @ A ) ) ),
inference(pattern_uni,[status(thm)],[1825:[bind(A,$thf( r ))]]) ).
thf(1855,plain,
( ~ ( hF_Mir137170979_hpair @ sk35 )
| ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) ) ),
inference(cnf,[status(esa)],[1826]) ).
thf(40072,plain,
( ( hF_Mirabelle_hpair @ sk1575 @ sk1577 )
= ( hF_Mirabelle_hpair @ sk1604 @ sk1605 ) ),
inference(cnf,[status(esa)],[39672]) ).
thf(40074,plain,
( ( hF_Mirabelle_hpair @ sk1604 @ sk1605 )
= ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) ),
inference(lifteq,[status(thm)],[40072]) ).
thf(44729,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) )
= A )
| ( ( hF_Mirabelle_hpair @ sk1604 @ sk1605 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[40074,279]) ).
thf(44730,plain,
( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) )
= sk1604 ),
inference(pattern_uni,[status(thm)],[44729:[bind(A,$thf( sk1604 )),bind(B,$thf( sk1605 ))]]) ).
thf(45718,plain,
sk1604 = sk1575,
inference(rewrite,[status(thm)],[44730,279]) ).
thf(45722,plain,
hF_Mirabelle_hmem @ sk1575 @ x,
inference(rewrite,[status(thm)],[40071,45718]) ).
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/sandbox2/benchmark/theBenchmark.p',fact_8_replacement) ).
thf(211,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(212,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)],[211]) ).
thf(213,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(cnf,[status(esa)],[212]) ).
thf(217,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)],[213]) ).
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/sandbox2/benchmark/theBenchmark.p',fact_12_union__of__set) ).
thf(274,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(275,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)],[274]) ).
thf(276,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)],[275]) ).
thf(19,axiom,
! [A: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( ( hF_Mirabelle_Replace @ zero_z189798548lle_hf @ A )
= zero_z189798548lle_hf ),
file('/export/starexec/sandbox2/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 > $o] :
( ( hF_Mirabelle_Replace @ zero_z189798548lle_hf @ A )
= zero_z189798548lle_hf ),
inference(lifteq,[status(thm)],[119]) ).
thf(40096,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ B )
| ~ ( hF_Mir434065167lation @ A )
| ( ( hF_Mirabelle_hmem @ sk1604 @ x )
!= ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[40071,559]) ).
thf(40097,plain,
( ( hF_Mir137170979_hpair @ sk1604 )
| ~ ( hF_Mir434065167lation @ x ) ),
inference(pattern_uni,[status(thm)],[40096:[bind(A,$thf( x )),bind(B,$thf( sk1604 ))]]) ).
thf(43253,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk1604 )
| ~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) )
| ( ( hF_Mir434065167lation @ A )
!= ( hF_Mir434065167lation @ x ) ) ),
inference(paramod_ordered,[status(thm)],[293,40097]) ).
thf(43254,plain,
( ( hF_Mir137170979_hpair @ sk1604 )
| ~ ! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ x )
=> ( hF_Mir137170979_hpair @ A ) ) ),
inference(pattern_uni,[status(thm)],[43253:[bind(A,$thf( x ))]]) ).
thf(43316,plain,
( ( hF_Mirabelle_hmem @ sk1734 @ x )
| ( hF_Mir137170979_hpair @ sk1604 ) ),
inference(cnf,[status(esa)],[43254]) ).
thf(44322,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk1604 )
| ( ( hF_Mirabelle_hmem @ sk1734 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[43316,178]) ).
thf(44359,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk1604 )
| ( sk1734 != A )
| ( x != A ) ),
inference(simp,[status(thm)],[44322]) ).
thf(44473,plain,
( ( hF_Mir137170979_hpair @ sk1604 )
| ( sk1734 != x ) ),
inference(simp,[status(thm)],[44359]) ).
thf(46692,plain,
( ( hF_Mir137170979_hpair @ sk1575 )
| ( sk1734 != x ) ),
inference(rewrite,[status(thm)],[44473,45718]) ).
thf(70150,plain,
( ( sk1734 != x )
| ( ( hF_Mir137170979_hpair @ sk1575 )
!= ( hF_Mir137170979_hpair @ zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[46692,70122]) ).
thf(70178,plain,
( ( sk1734 != x )
| ( sk1575 != zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[70150]) ).
thf(3258,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)],[159,3115]) ).
thf(3259,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)],[3258:[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(3297,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(cnf,[status(esa)],[3259]) ).
thf(3299,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)],[3297]) ).
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/sandbox2/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(22470,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)],[3299,76]) ).
thf(32227,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)],[835,284]) ).
thf(32228,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)],[32227:[bind(A,$thf( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )),bind(B,$thf( r )),bind(C,$thf( x ))]]) ).
thf(33031,plain,
( ( hF_Mirabelle_hmem @ sk1149 @ x )
| ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf ) ),
inference(cnf,[status(esa)],[32228]) ).
thf(52242,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( ( hF_Mirabelle_hmem @ sk1149 @ x )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[33031,188]) ).
thf(52401,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( sk1149 != A )
| ( ( hF_Mirabelle_HUnion @ A )
!= x ) ),
inference(simp,[status(thm)],[52242]) ).
thf(52568,plain,
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( ( hF_Mirabelle_HUnion @ sk1149 )
!= x ) ),
inference(simp,[status(thm)],[52401]) ).
thf(63059,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 @ sk1149 )
!= x )
| ( ( hF_Mir199975595nction @ A )
!= ( hF_Mir199975595nction @ zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[325,52568]) ).
thf(63060,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 @ sk1149 )
!= x ) ),
inference(pattern_uni,[status(thm)],[63059:[bind(A,$thf( zero_z189798548lle_hf ))]]) ).
thf(63100,plain,
( ( ( hF_Mirabelle_HUnion @ sk1149 )
!= x )
| ( sk2466 != sk2467 ) ),
inference(cnf,[status(esa)],[63060]) ).
thf(63103,plain,
( ( sk2467 != sk2466 )
| ( ( hF_Mirabelle_HUnion @ sk1149 )
!= x ) ),
inference(lifteq,[status(thm)],[63100]) ).
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/sandbox2/benchmark/theBenchmark.p',fact_28_RepFun__cong) ).
thf(262,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(263,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)],[262]) ).
thf(265,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(cnf,[status(esa)],[263]) ).
thf(268,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)],[265]) ).
thf(269,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)],[268]) ).
thf(52222,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ sk1149 @ 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)],[325,33031]) ).
thf(52223,plain,
( ( hF_Mirabelle_hmem @ sk1149 @ 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)],[52222:[bind(A,$thf( zero_z189798548lle_hf ))]]) ).
thf(52610,plain,
( ( sk2072 != sk2073 )
| ( hF_Mirabelle_hmem @ sk1149 @ x ) ),
inference(cnf,[status(esa)],[52223]) ).
thf(52613,plain,
( ( sk2073 != sk2072 )
| ( hF_Mirabelle_hmem @ sk1149 @ x ) ),
inference(lifteq,[status(thm)],[52610]) ).
thf(75868,plain,
! [A: hF_Mirabelle_hf] :
( ( sk2073 != sk2072 )
| ( ( hF_Mirabelle_hmem @ sk1149 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[52613,178]) ).
thf(75903,plain,
! [A: hF_Mirabelle_hf] :
( ( sk2073 != sk2072 )
| ( sk1149 != A )
| ( x != A ) ),
inference(simp,[status(thm)],[75868]) ).
thf(76022,plain,
( ( sk2073 != sk2072 )
| ( sk1149 != x ) ),
inference(simp,[status(thm)],[75903]) ).
thf(38,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ A @ B )
& ( hF_Mirabelle_hmem @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_hmem__not__sym) ).
thf(179,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(180,plain,
~ ? [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ B )
& ( hF_Mirabelle_hmem @ B @ A ) ),
inference(miniscope,[status(thm)],[179]) ).
thf(181,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ A @ B )
| ~ ( hF_Mirabelle_hmem @ B @ A ) ),
inference(cnf,[status(esa)],[180]) ).
thf(2001,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(paramod_ordered,[status(thm)],[870,181]) ).
thf(2002,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)],[2001:[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(2035,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)],[2002]) ).
thf(68427,plain,
hF_Mirabelle_hmem @ sk2650 @ x,
inference(cnf,[status(esa)],[68015]) ).
thf(43392,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(paramod_ordered,[status(thm)],[43248,181]) ).
thf(43393,plain,
~ ( hF_Mirabelle_hmem @ r @ ( sk20 @ r ) ),
inference(pattern_uni,[status(thm)],[43392:[bind(A,$thf( sk20 @ r )),bind(B,$thf( r ))]]) ).
thf(68521,plain,
( ( hF_Mirabelle_hmem @ sk2650 @ x )
!= ( hF_Mirabelle_hmem @ r @ ( sk20 @ r ) ) ),
inference(paramod_ordered,[status(thm)],[68427,43393]) ).
thf(68582,plain,
( ( sk2650 != r )
| ( ( sk20 @ r )
!= x ) ),
inference(simp,[status(thm)],[68521]) ).
thf(68429,plain,
hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) @ r,
inference(cnf,[status(esa)],[68015]) ).
thf(69500,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) @ r )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ),
inference(paramod_ordered,[status(thm)],[68429,188]) ).
thf(69704,plain,
! [A: hF_Mirabelle_hf] :
( ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
!= A )
| ( ( hF_Mirabelle_HUnion @ A )
!= r ) ),
inference(simp,[status(thm)],[69500]) ).
thf(69811,plain,
( ( hF_Mirabelle_HUnion @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) )
!= r ),
inference(simp,[status(thm)],[69704]) ).
thf(4855,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(paramod_ordered,[status(thm)],[835,181]) ).
thf(4856,plain,
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ~ ( hF_Mirabelle_hmem @ ( hF_Mir1653039215strict @ r @ x ) @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(pattern_uni,[status(thm)],[4855:[bind(A,$thf( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )),bind(B,$thf( hF_Mir1653039215strict @ r @ x ))]]) ).
thf(42954,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) @ r )
!= ( hF_Mirabelle_hmem @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[40073,178]) ).
thf(42981,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1575 @ sk1577 )
!= A )
| ( r != A ) ),
inference(simp,[status(thm)],[42954]) ).
thf(43185,plain,
( ( hF_Mirabelle_hpair @ sk1575 @ sk1577 )
!= r ),
inference(simp,[status(thm)],[42981]) ).
thf(68552,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ sk2650 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[68427,178]) ).
thf(68635,plain,
! [A: hF_Mirabelle_hf] :
( ( sk2650 != A )
| ( x != A ) ),
inference(simp,[status(thm)],[68552]) ).
thf(68700,plain,
sk2650 != x,
inference(simp,[status(thm)],[68635]) ).
thf(7828,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ A ),
inference(cnf,[status(esa)],[7733]) ).
thf(7830,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ A ),
inference(simp,[status(thm)],[7828]) ).
thf(41441,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ A )
!= ( hF_Mirabelle_hmem @ ( sk20 @ x ) @ x ) ),
inference(paramod_ordered,[status(thm)],[40493,7830]) ).
thf(41638,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk6 @ A @ B )
!= ( sk20 @ x ) )
| ( A != x ) ),
inference(simp,[status(thm)],[41441]) ).
thf(41825,plain,
! [A: hF_Mirabelle_hf] :
( ( sk6 @ x @ A )
!= ( sk20 @ x ) ),
inference(simp,[status(thm)],[41638]) ).
thf(8,axiom,
( sup_su638957495lle_hf
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( sup_su638957495lle_hf @ B @ A ) ) ),
file('/export/starexec/sandbox2/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(289,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(3239,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)],[289,3115]) ).
thf(3240,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ B @ A ) @ A ),
inference(pattern_uni,[status(thm)],[3239:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(40129,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ B @ A ) @ A )
!= ( hF_Mirabelle_hmem @ sk1604 @ x ) ),
inference(paramod_ordered,[status(thm)],[40071,3240]) ).
thf(40217,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ B @ A )
!= sk1604 )
| ( A != x ) ),
inference(simp,[status(thm)],[40129]) ).
thf(40325,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ x )
!= sk1604 ),
inference(simp,[status(thm)],[40217]) ).
thf(50642,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ x )
!= sk1575 ),
inference(rewrite,[status(thm)],[40325,45718]) ).
thf(288,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(28,axiom,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ zero_z189798548lle_hf @ A )
= A ),
file('/export/starexec/sandbox2/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(312,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(317,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)],[312]) ).
thf(320,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)],[317]) ).
thf(69510,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) @ r )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[68429,181]) ).
thf(69511,plain,
~ ( hF_Mirabelle_hmem @ r @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) ),
inference(pattern_uni,[status(thm)],[69510:[bind(A,$thf( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )),bind(B,$thf( r ))]]) ).
thf(74265,plain,
( ~ ( hF_Mirabelle_hmem @ r @ ( hF_Mirabelle_hpair @ sk2650 @ sk2651 ) )
| ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[68430,69511]) ).
thf(74266,plain,
~ ( hF_Mirabelle_hmem @ r @ ( hF_Mirabelle_hpair @ sk2650 @ sk2651 ) ),
inference(pattern_uni,[status(thm)],[74265:[]]) ).
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/sandbox2/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(3112,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ B ) @ B ),
inference(cnf,[status(esa)],[3001]) ).
thf(3114,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ B ) @ B ),
inference(simp,[status(thm)],[3112]) ).
thf(3161,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)],[162,3114]) ).
thf(3162,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)],[3161:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( hF_Mirabelle_HUnion @ E )),bind(D,$thf( hF_Mirabelle_HUnion @ F ))]]) ).
thf(3200,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)],[3162]) ).
thf(3506,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)],[162,3200]) ).
thf(3507,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)],[3506:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( hF_Mirabelle_HUnion @ E )),bind(D,$thf( hF_Mirabelle_HUnion @ F ))]]) ).
thf(3548,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)],[3507]) ).
thf(7254,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)],[105,3548]) ).
thf(7255,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)],[7254:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( zero_z189798548lle_hf ))]]) ).
thf(24,axiom,
( ( hF_Mirabelle_HUnion @ zero_z189798548lle_hf )
= zero_z189798548lle_hf ),
file('/export/starexec/sandbox2/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(134,plain,
( ( hF_Mirabelle_HUnion @ zero_z189798548lle_hf )
= zero_z189798548lle_hf ),
inference(lifteq,[status(thm)],[133]) ).
thf(7364,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)],[7255,134]) ).
thf(40121,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ sk1604 @ x )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ),
inference(paramod_ordered,[status(thm)],[40071,188]) ).
thf(40297,plain,
! [A: hF_Mirabelle_hf] :
( ( sk1604 != A )
| ( ( hF_Mirabelle_HUnion @ A )
!= x ) ),
inference(simp,[status(thm)],[40121]) ).
thf(40474,plain,
( ( hF_Mirabelle_HUnion @ sk1604 )
!= x ),
inference(simp,[status(thm)],[40297]) ).
thf(45719,plain,
( ( hF_Mirabelle_HUnion @ sk1575 )
!= x ),
inference(rewrite,[status(thm)],[40474,45718]) ).
thf(39675,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 @ sk1575 @ sk1577 ) @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[284,39642]) ).
thf(39676,plain,
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) @ r )
& ? [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1575 @ sk1577 )
= ( hF_Mirabelle_hpair @ A @ B ) )
& ( hF_Mirabelle_hmem @ A @ x ) ) ),
inference(pattern_uni,[status(thm)],[39675:[bind(A,$thf( hF_Mirabelle_hpair @ sk1575 @ sk1577 )),bind(B,$thf( r )),bind(C,$thf( x ))]]) ).
thf(40077,plain,
( ( hF_Mirabelle_hpair @ sk1575 @ sk1577 )
= ( hF_Mirabelle_hpair @ sk1606 @ sk1607 ) ),
inference(cnf,[status(esa)],[39676]) ).
thf(40079,plain,
( ( hF_Mirabelle_hpair @ sk1606 @ sk1607 )
= ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) ),
inference(lifteq,[status(thm)],[40077]) ).
thf(50,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_hsnd__conv) ).
thf(228,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(229,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ A @ B ) )
= B ),
inference(cnf,[status(esa)],[228]) ).
thf(230,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ A @ B ) )
= B ),
inference(lifteq,[status(thm)],[229]) ).
thf(48166,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) )
= B )
| ( ( hF_Mirabelle_hpair @ sk1606 @ sk1607 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[40079,230]) ).
thf(48167,plain,
( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) )
= sk1607 ),
inference(pattern_uni,[status(thm)],[48166:[bind(A,$thf( sk1606 )),bind(B,$thf( sk1607 ))]]) ).
thf(48723,plain,
sk1607 = sk1577,
inference(rewrite,[status(thm)],[48167,230]) ).
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/sandbox2/benchmark/theBenchmark.p',fact_39_hrelation__hunion) ).
thf(255,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(256,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)],[255]) ).
thf(257,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)],[256]) ).
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/sandbox2/benchmark/theBenchmark.p',fact_23_HUnion__iff) ).
thf(182,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(183,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)],[182]) ).
thf(184,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)],[183]) ).
thf(3298,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(cnf,[status(esa)],[3259]) ).
thf(3300,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)],[3298]) ).
thf(22730,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)],[3300,76]) ).
thf(3138,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)],[289,3114]) ).
thf(3139,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ B @ A ) @ B ),
inference(pattern_uni,[status(thm)],[3138:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(43410,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ B @ A ) @ B )
!= ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r ) ),
inference(paramod_ordered,[status(thm)],[43248,3139]) ).
thf(43498,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ B @ A )
!= ( sk20 @ r ) )
| ( B != r ) ),
inference(simp,[status(thm)],[43410]) ).
thf(43713,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ r @ A )
!= ( sk20 @ r ) ),
inference(simp,[status(thm)],[43498]) ).
thf(65741,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
!= ( sk20 @ r ) )
| ( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) )
!= ( sup_su638957495lle_hf @ r @ D ) ) ),
inference(paramod_ordered,[status(thm)],[320,43713]) ).
thf(65742,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ r @ A )
!= zero_z189798548lle_hf )
| ( B
!= ( sk20 @ r ) ) ),
inference(pattern_uni,[status(thm)],[65741:[bind(A,$thf( r )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( sup_su638957495lle_hf @ E @ F ))]]) ).
thf(65826,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ r @ A )
!= zero_z189798548lle_hf ),
inference(simp,[status(thm)],[65742]) ).
thf(66052,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 @ r @ C ) ) ),
inference(paramod_ordered,[status(thm)],[289,65826]) ).
thf(66053,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ r )
!= zero_z189798548lle_hf ),
inference(pattern_uni,[status(thm)],[66052:[bind(A,$thf( A )),bind(B,$thf( r )),bind(C,$thf( A ))]]) ).
thf(40153,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ B @ A ) @ B )
!= ( hF_Mirabelle_hmem @ sk1604 @ x ) ),
inference(paramod_ordered,[status(thm)],[40071,3139]) ).
thf(40280,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ B @ A )
!= sk1604 )
| ( B != x ) ),
inference(simp,[status(thm)],[40153]) ).
thf(40446,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ x @ A )
!= sk1604 ),
inference(simp,[status(thm)],[40280]) ).
thf(51498,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ x @ A )
!= sk1575 ),
inference(rewrite,[status(thm)],[40446,45718]) ).
thf(41,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ A @ B )
= ( hF_Mirabelle_hpair @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_hpair__iff) ).
thf(189,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ A @ B )
= ( hF_Mirabelle_hpair @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(57782,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk1 @ A @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) )
= B )
| ( ( hF_Mirabelle_hpair @ sk2103 @ sk2104 )
!= ( hF_Mirabelle_hpair @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[54337,170]) ).
thf(57783,plain,
( ( sk1 @ sk2104 @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) )
= sk2103 ),
inference(pattern_uni,[status(thm)],[57782:[bind(A,$thf( sk2104 )),bind(B,$thf( sk2103 ))]]) ).
thf(57819,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) )
= B )
| ( ( hF_Mirabelle_hpair @ sk2103 @ sk2104 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[54337,230]) ).
thf(57820,plain,
( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) )
= sk2104 ),
inference(pattern_uni,[status(thm)],[57819:[bind(A,$thf( sk2103 )),bind(B,$thf( sk2104 ))]]) ).
thf(58529,plain,
sk2104 = sk1576,
inference(rewrite,[status(thm)],[57820,230]) ).
thf(58827,plain,
( ( sk1 @ sk1576 @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) )
= sk1575 ),
inference(rewrite,[status(thm)],[57783,58529,58025]) ).
thf(10,axiom,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_sup__idem) ).
thf(91,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(92,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ A )
= A ),
inference(cnf,[status(esa)],[91]) ).
thf(93,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ A )
= A ),
inference(lifteq,[status(thm)],[92]) ).
thf(68486,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ B )
!= ( hF_Mirabelle_hmem @ sk2650 @ x ) ),
inference(paramod_ordered,[status(thm)],[68427,7831]) ).
thf(68566,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk6 @ A @ B )
!= sk2650 )
| ( B != x ) ),
inference(simp,[status(thm)],[68486]) ).
thf(68772,plain,
! [A: hF_Mirabelle_hf] :
( ( sk6 @ A @ x )
!= sk2650 ),
inference(simp,[status(thm)],[68566]) ).
thf(1861,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
| ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) )
| ( ( hF_Mir434065167lation @ A )
!= ( hF_Mir434065167lation @ x ) ) ),
inference(paramod_ordered,[status(thm)],[293,1243]) ).
thf(1862,plain,
( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
| ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ~ ! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ x )
=> ( hF_Mir137170979_hpair @ A ) ) ),
inference(pattern_uni,[status(thm)],[1861:[bind(A,$thf( x ))]]) ).
thf(1892,plain,
( ( hF_Mirabelle_hmem @ sk40 @ x )
| ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) ) ),
inference(cnf,[status(esa)],[1862]) ).
thf(23101,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
| ( ( hF_Mirabelle_hmem @ sk40 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1892,178]) ).
thf(23161,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)],[23101]) ).
thf(23304,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
| ( sk40 != x ) ),
inference(simp,[status(thm)],[23161]) ).
thf(25280,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ( sk40 != x )
| ( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
!= ( hF_Mir199975595nction @ r ) ) ),
inference(paramod_ordered,[status(thm)],[287,23304]) ).
thf(25336,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ( sk40 != x )
| ( ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf )
!= r ) ),
inference(simp,[status(thm)],[25280]) ).
thf(41468,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(paramod_ordered,[status(thm)],[40493,181]) ).
thf(41469,plain,
~ ( hF_Mirabelle_hmem @ x @ ( sk20 @ x ) ),
inference(pattern_uni,[status(thm)],[41468:[bind(A,$thf( sk20 @ x )),bind(B,$thf( x ))]]) ).
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/sandbox2/benchmark/theBenchmark.p',fact_25_HCollect__iff) ).
thf(252,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(253,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)],[252]) ).
thf(254,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)],[253]) ).
thf(25690,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ A @ ( hF_Mir818139703ollect @ B @ C ) )
= ( hF_Mirabelle_hmem @ A @ C ) )
| ( ( hF_Mir199975595nction @ r )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[287,254]) ).
thf(25962,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ r @ ( hF_Mir818139703ollect @ hF_Mir199975595nction @ A ) )
= ( hF_Mirabelle_hmem @ r @ A ) ),
inference(pre_uni,[status(thm)],[25690:[bind(A,$thf( r )),bind(B,$thf( hF_Mir199975595nction )),bind(C,$thf( C ))]]) ).
thf(26458,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ r @ ( hF_Mir818139703ollect @ hF_Mir199975595nction @ A ) )
= ( hF_Mirabelle_hmem @ r @ A ) ),
inference(simp,[status(thm)],[25962]) ).
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/sandbox2/benchmark/theBenchmark.p',fact_5_hf__equalityI) ).
thf(208,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(209,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)],[208]) ).
thf(210,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)],[209]) ).
thf(290,plain,
( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mir199975595nction @ r ) ),
inference(paramod_ordered,[status(thm)],[287,68]) ).
thf(291,plain,
( ( hF_Mir1653039215strict @ r @ x )
!= r ),
inference(simp,[status(thm)],[290]) ).
thf(10100,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)],[210,291]) ).
thf(10101,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)],[10100:[bind(A,$thf( A )),bind(B,$thf( hF_Mir1653039215strict @ r @ x ))]]) ).
thf(11658,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)],[10101]) ).
thf(27261,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)],[26458,11658]) ).
thf(27421,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)],[27261]) ).
thf(27472,plain,
( ( ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ r )
!= r )
| ( ( hF_Mir1653039215strict @ r @ x )
!= ( hF_Mir818139703ollect @ hF_Mir199975595nction @ r ) ) ),
inference(simp,[status(thm)],[27421]) ).
thf(44740,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1575 @ sk1577 )
!= B )
| ( ( hF_Mirabelle_hpair @ sk1604 @ sk1605 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[40074,245]) ).
thf(44741,plain,
( ( hF_Mirabelle_hpair @ sk1575 @ sk1577 )
!= sk1605 ),
inference(pattern_uni,[status(thm)],[44740:[bind(A,$thf( sk1604 )),bind(B,$thf( sk1605 ))]]) ).
thf(44738,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) )
= B )
| ( ( hF_Mirabelle_hpair @ sk1604 @ sk1605 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[40074,230]) ).
thf(44739,plain,
( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) )
= sk1605 ),
inference(pattern_uni,[status(thm)],[44738:[bind(A,$thf( sk1604 )),bind(B,$thf( sk1605 ))]]) ).
thf(47636,plain,
sk1605 = sk1577,
inference(rewrite,[status(thm)],[44739,230]) ).
thf(47637,plain,
( ( hF_Mirabelle_hpair @ sk1575 @ sk1577 )
!= sk1577 ),
inference(rewrite,[status(thm)],[44741,47636]) ).
thf(52321,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( ( hF_Mirabelle_hmem @ sk1149 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[33031,178]) ).
thf(52353,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( sk1149 != A )
| ( x != A ) ),
inference(simp,[status(thm)],[52321]) ).
thf(52488,plain,
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( sk1149 != x ) ),
inference(simp,[status(thm)],[52353]) ).
thf(53130,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 ) ) )
| ( sk1149 != x )
| ( ( hF_Mir199975595nction @ A )
!= ( hF_Mir199975595nction @ zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[325,52488]) ).
thf(53131,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 ) ) )
| ( sk1149 != x ) ),
inference(pattern_uni,[status(thm)],[53130:[bind(A,$thf( zero_z189798548lle_hf ))]]) ).
thf(53159,plain,
( ( sk1149 != x )
| ( sk2075 != sk2076 ) ),
inference(cnf,[status(esa)],[53131]) ).
thf(53162,plain,
( ( sk2076 != sk2075 )
| ( sk1149 != x ) ),
inference(lifteq,[status(thm)],[53159]) ).
thf(3159,plain,
! [E: hF_Mirabelle_hf,D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) @ E )
| ( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A @ B ) @ C )
!= ( sup_su638957495lle_hf @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[76,3114]) ).
thf(3160,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ A ) ) @ A ),
inference(pattern_uni,[status(thm)],[3159:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( sup_su638957495lle_hf @ F @ G )),bind(E,$thf( C ))]]) ).
thf(3199,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)],[3160]) ).
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/sandbox2/benchmark/theBenchmark.p',fact_6_hf__ext) ).
thf(223,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(224,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)],[223]) ).
thf(326,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)],[286,222]) ).
thf(328,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)],[326]) ).
thf(442,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)],[224,328]) ).
thf(443,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)],[442]) ).
thf(74166,plain,
( ( ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_hpair @ sk2650 @ sk2651 ) )
!= r )
| ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[68430,69811]) ).
thf(74167,plain,
( ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_hpair @ sk2650 @ sk2651 ) )
!= r ),
inference(pattern_uni,[status(thm)],[74166:[]]) ).
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/sandbox2/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(57378,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk2103 )
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ sk2203 @ x )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[56455,181]) ).
thf(57379,plain,
( ( hF_Mir137170979_hpair @ sk2103 )
| ~ ( hF_Mirabelle_hmem @ x @ sk2203 ) ),
inference(pattern_uni,[status(thm)],[57378:[bind(A,$thf( sk2203 )),bind(B,$thf( x ))]]) ).
thf(77343,plain,
( ( hF_Mir137170979_hpair @ sk1575 )
| ~ ( hF_Mirabelle_hmem @ x @ sk2203 ) ),
inference(rewrite,[status(thm)],[57379,58025]) ).
thf(20,axiom,
( sup_su638957495lle_hf
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( sup_su638957495lle_hf @ B @ A ) ) ),
file('/export/starexec/sandbox2/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(45726,plain,
( ( hF_Mirabelle_hmem @ sk1734 @ x )
| ( hF_Mir137170979_hpair @ sk1575 ) ),
inference(rewrite,[status(thm)],[43316,45718]) ).
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/sandbox2/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(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(1283,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(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/sandbox2/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(351,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 @ zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[85,105]) ).
thf(375,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 )
| ( B != D )
| ( ( sup_su638957495lle_hf @ A @ C )
!= zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[351]) ).
thf(397,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)],[375]) ).
thf(45720,plain,
( ( hF_Mir137170979_hpair @ sk1575 )
| ~ ( hF_Mir434065167lation @ x ) ),
inference(rewrite,[status(thm)],[40097,45718]) ).
thf(48055,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk1575 )
| ~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) )
| ( ( hF_Mir434065167lation @ A )
!= ( hF_Mir434065167lation @ x ) ) ),
inference(paramod_ordered,[status(thm)],[293,45720]) ).
thf(48056,plain,
( ( hF_Mir137170979_hpair @ sk1575 )
| ~ ! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ x )
=> ( hF_Mir137170979_hpair @ A ) ) ),
inference(pattern_uni,[status(thm)],[48055:[bind(A,$thf( x ))]]) ).
thf(48120,plain,
( ( hF_Mirabelle_hmem @ sk1901 @ x )
| ( hF_Mir137170979_hpair @ sk1575 ) ),
inference(cnf,[status(esa)],[48056]) ).
thf(64,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( hF_Mir434065167lation @ ( hF_Mir1653039215strict @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_hrelation__restr) ).
thf(280,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( hF_Mir434065167lation @ ( hF_Mir1653039215strict @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(824,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
| ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( A != r ) ),
inference(paramod_ordered,[status(thm)],[459,287]) ).
thf(825,plain,
( ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r )
| ( hF_Mir199975595nction @ zero_z189798548lle_hf ) ),
inference(pattern_uni,[status(thm)],[824:[bind(A,$thf( r ))]]) ).
thf(1214,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)],[459,825]) ).
thf(1215,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)],[1214:[bind(A,$thf( sk20 @ r ))]]) ).
thf(42882,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) @ r )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[40073,181]) ).
thf(42883,plain,
~ ( hF_Mirabelle_hmem @ r @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) ),
inference(pattern_uni,[status(thm)],[42882:[bind(A,$thf( hF_Mirabelle_hpair @ sk1575 @ sk1577 )),bind(B,$thf( r ))]]) ).
thf(355,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A
= ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ D ) ) )
| ( ( sup_su638957495lle_hf @ A @ zero_z189798548lle_hf )
!= ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ B @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[105,85]) ).
thf(374,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A
= ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ D ) ) )
| ( A != C )
| ( ( sup_su638957495lle_hf @ B @ D )
!= zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[355]) ).
thf(396,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) )
= B )
| ( ( sup_su638957495lle_hf @ A @ C )
!= zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[374]) ).
thf(40076,plain,
hF_Mirabelle_hmem @ sk1606 @ x,
inference(cnf,[status(esa)],[39676]) ).
thf(40719,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ B )
| ~ ( hF_Mir434065167lation @ A )
| ( ( hF_Mirabelle_hmem @ sk1606 @ x )
!= ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[40076,559]) ).
thf(40720,plain,
( ( hF_Mir137170979_hpair @ sk1606 )
| ~ ( hF_Mir434065167lation @ x ) ),
inference(pattern_uni,[status(thm)],[40719:[bind(A,$thf( x )),bind(B,$thf( sk1606 ))]]) ).
thf(43927,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk1606 )
| ~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) )
| ( ( hF_Mir434065167lation @ A )
!= ( hF_Mir434065167lation @ x ) ) ),
inference(paramod_ordered,[status(thm)],[293,40720]) ).
thf(43928,plain,
( ( hF_Mir137170979_hpair @ sk1606 )
| ~ ! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ x )
=> ( hF_Mir137170979_hpair @ A ) ) ),
inference(pattern_uni,[status(thm)],[43927:[bind(A,$thf( x ))]]) ).
thf(43985,plain,
( ( hF_Mirabelle_hmem @ sk1770 @ x )
| ( hF_Mir137170979_hpair @ sk1606 ) ),
inference(cnf,[status(esa)],[43928]) ).
thf(48157,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) )
= A )
| ( ( hF_Mirabelle_hpair @ sk1606 @ sk1607 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[40079,279]) ).
thf(48158,plain,
( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) )
= sk1606 ),
inference(pattern_uni,[status(thm)],[48157:[bind(A,$thf( sk1606 )),bind(B,$thf( sk1607 ))]]) ).
thf(48706,plain,
sk1606 = sk1575,
inference(rewrite,[status(thm)],[48158,279]) ).
thf(48715,plain,
( ( hF_Mirabelle_hmem @ sk1770 @ x )
| ( hF_Mir137170979_hpair @ sk1575 ) ),
inference(rewrite,[status(thm)],[43985,48706]) ).
thf(43389,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ B @ A ) @ A )
!= ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r ) ),
inference(paramod_ordered,[status(thm)],[43248,3240]) ).
thf(43483,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ B @ A )
!= ( sk20 @ r ) )
| ( A != r ) ),
inference(simp,[status(thm)],[43389]) ).
thf(43674,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ r )
!= ( sk20 @ r ) ),
inference(simp,[status(thm)],[43483]) ).
thf(40132,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ sk1604 @ x )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[40071,181]) ).
thf(40133,plain,
~ ( hF_Mirabelle_hmem @ x @ sk1604 ),
inference(pattern_uni,[status(thm)],[40132:[bind(A,$thf( sk1604 )),bind(B,$thf( x ))]]) ).
thf(43413,plain,
( ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r )
!= ( hF_Mirabelle_hmem @ x @ sk1604 ) ),
inference(paramod_ordered,[status(thm)],[43248,40133]) ).
thf(43477,plain,
( ( ( sk20 @ r )
!= x )
| ( sk1604 != r ) ),
inference(simp,[status(thm)],[43413]) ).
thf(58066,plain,
( ( ( sk20 @ r )
!= x )
| ( sk1575 != r ) ),
inference(rewrite,[status(thm)],[43477,45718]) ).
thf(479,plain,
! [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 @ B ) )
= ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ D @ E ) ) )
| ( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ A @ B ) )
!= ( sup_su638957495lle_hf @ C @ E ) ) ),
inference(paramod_ordered,[status(thm)],[90,85]) ).
thf(480,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)],[479:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( D )),bind(E,$thf( sup_su638957495lle_hf @ F @ G ))]]) ).
thf(507,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) )
= ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) ),
inference(simp,[status(thm)],[480]) ).
thf(47642,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
| ( sk1577 = zero_z189798548lle_hf )
| ( A != sk1605 ) ),
inference(paramod_ordered,[status(thm)],[459,47636]) ).
thf(47643,plain,
( ( hF_Mirabelle_hmem @ ( sk20 @ sk1605 ) @ sk1605 )
| ( sk1577 = zero_z189798548lle_hf ) ),
inference(pattern_uni,[status(thm)],[47642:[bind(A,$thf( sk1605 ))]]) ).
thf(50951,plain,
( ( hF_Mirabelle_hmem @ ( sk20 @ sk1577 ) @ sk1577 )
| ( sk1577 = zero_z189798548lle_hf ) ),
inference(rewrite,[status(thm)],[47643,47636]) ).
thf(51093,plain,
! [A: hF_Mirabelle_hf] :
( ( sk1577 = zero_z189798548lle_hf )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ sk1577 ) @ sk1577 )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[50951,178]) ).
thf(51183,plain,
! [A: hF_Mirabelle_hf] :
( ( sk1577 = zero_z189798548lle_hf )
| ( ( sk20 @ sk1577 )
!= A )
| ( sk1577 != A ) ),
inference(simp,[status(thm)],[51093]) ).
thf(51348,plain,
( ( sk1577 = zero_z189798548lle_hf )
| ( ( sk20 @ sk1577 )
!= sk1577 ) ),
inference(simp,[status(thm)],[51183]) ).
thf(45732,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
| ( sk1575 = zero_z189798548lle_hf )
| ( A != sk1604 ) ),
inference(paramod_ordered,[status(thm)],[459,45718]) ).
thf(45733,plain,
( ( hF_Mirabelle_hmem @ ( sk20 @ sk1604 ) @ sk1604 )
| ( sk1575 = zero_z189798548lle_hf ) ),
inference(pattern_uni,[status(thm)],[45732:[bind(A,$thf( sk1604 ))]]) ).
thf(50198,plain,
( ( hF_Mirabelle_hmem @ ( sk20 @ sk1575 ) @ sk1575 )
| ( sk1575 = zero_z189798548lle_hf ) ),
inference(rewrite,[status(thm)],[45733,45718]) ).
thf(51499,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ A @ B )
!= zero_z189798548lle_hf )
| ( C != sk1575 )
| ( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) )
!= ( sup_su638957495lle_hf @ x @ D ) ) ),
inference(paramod_ordered,[status(thm)],[320,51498]) ).
thf(51500,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ x @ A )
!= zero_z189798548lle_hf )
| ( B != sk1575 ) ),
inference(pattern_uni,[status(thm)],[51499:[bind(A,$thf( x )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( sup_su638957495lle_hf @ E @ F ))]]) ).
thf(51584,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ x @ A )
!= zero_z189798548lle_hf ),
inference(simp,[status(thm)],[51500]) ).
thf(74229,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
!= B )
| ( ( hF_Mirabelle_hpair @ sk2650 @ sk2651 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[68430,245]) ).
thf(74230,plain,
( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
!= sk2651 ),
inference(pattern_uni,[status(thm)],[74229:[bind(A,$thf( sk2650 )),bind(B,$thf( sk2651 ))]]) ).
thf(75266,plain,
( ( ( hF_Mirabelle_hpair @ sk2650 @ sk2651 )
!= sk2651 )
| ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[68430,74230]) ).
thf(75267,plain,
( ( hF_Mirabelle_hpair @ sk2650 @ sk2651 )
!= sk2651 ),
inference(pattern_uni,[status(thm)],[75266:[]]) ).
thf(44266,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk1604 )
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ sk1734 @ x )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[43316,181]) ).
thf(44267,plain,
( ( hF_Mir137170979_hpair @ sk1604 )
| ~ ( hF_Mirabelle_hmem @ x @ sk1734 ) ),
inference(pattern_uni,[status(thm)],[44266:[bind(A,$thf( sk1734 )),bind(B,$thf( x ))]]) ).
thf(63505,plain,
( ( hF_Mir137170979_hpair @ sk1575 )
| ~ ( hF_Mirabelle_hmem @ x @ sk1734 ) ),
inference(rewrite,[status(thm)],[44267,45718]) ).
thf(297,plain,
! [F: hF_Mirabelle_hf,E: hF_Mirabelle_hf,D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) @ F )
= ( sup_su638957495lle_hf @ D @ ( sup_su638957495lle_hf @ E @ F ) ) )
| ( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A @ B ) @ C )
!= ( sup_su638957495lle_hf @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[76,76]) ).
thf(298,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ D @ A ) ) @ B )
= ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ C @ D ) @ ( sup_su638957495lle_hf @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[297:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( sup_su638957495lle_hf @ G @ H )),bind(E,$thf( C ))]]) ).
thf(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(simp,[status(thm)],[298]) ).
thf(35051,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)],[306,76]) ).
thf(53952,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 @ sk1575 @ sk1576 ) @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[284,39643]) ).
thf(53953,plain,
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) @ r )
& ? [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1575 @ sk1576 )
= ( hF_Mirabelle_hpair @ A @ B ) )
& ( hF_Mirabelle_hmem @ A @ x ) ) ),
inference(pattern_uni,[status(thm)],[53952:[bind(A,$thf( hF_Mirabelle_hpair @ sk1575 @ sk1576 )),bind(B,$thf( r )),bind(C,$thf( x ))]]) ).
thf(54339,plain,
hF_Mirabelle_hmem @ sk2105 @ x,
inference(cnf,[status(esa)],[53953]) ).
thf(54926,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ B )
| ~ ( hF_Mir434065167lation @ A )
| ( ( hF_Mirabelle_hmem @ sk2105 @ x )
!= ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[54339,559]) ).
thf(54927,plain,
( ( hF_Mir137170979_hpair @ sk2105 )
| ~ ( hF_Mir434065167lation @ x ) ),
inference(pattern_uni,[status(thm)],[54926:[bind(A,$thf( x )),bind(B,$thf( sk2105 ))]]) ).
thf(56458,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk2105 )
| ~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) )
| ( ( hF_Mir434065167lation @ A )
!= ( hF_Mir434065167lation @ x ) ) ),
inference(paramod_ordered,[status(thm)],[293,54927]) ).
thf(56459,plain,
( ( hF_Mir137170979_hpair @ sk2105 )
| ~ ! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ x )
=> ( hF_Mir137170979_hpair @ A ) ) ),
inference(pattern_uni,[status(thm)],[56458:[bind(A,$thf( x ))]]) ).
thf(56519,plain,
( ( hF_Mirabelle_hmem @ sk2204 @ x )
| ( hF_Mir137170979_hpair @ sk2105 ) ),
inference(cnf,[status(esa)],[56459]) ).
thf(58200,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk2105 )
| ( ( hF_Mirabelle_hmem @ sk2204 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[56519,178]) ).
thf(58238,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk2105 )
| ( sk2204 != A )
| ( x != A ) ),
inference(simp,[status(thm)],[58200]) ).
thf(58357,plain,
( ( hF_Mir137170979_hpair @ sk2105 )
| ( sk2204 != x ) ),
inference(simp,[status(thm)],[58238]) ).
thf(54340,plain,
( ( hF_Mirabelle_hpair @ sk1575 @ sk1576 )
= ( hF_Mirabelle_hpair @ sk2105 @ sk2106 ) ),
inference(cnf,[status(esa)],[53953]) ).
thf(54342,plain,
( ( hF_Mirabelle_hpair @ sk2105 @ sk2106 )
= ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) ),
inference(lifteq,[status(thm)],[54340]) ).
thf(58595,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) )
= A )
| ( ( hF_Mirabelle_hpair @ sk2105 @ sk2106 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[54342,279]) ).
thf(58596,plain,
( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) )
= sk2105 ),
inference(pattern_uni,[status(thm)],[58595:[bind(A,$thf( sk2105 )),bind(B,$thf( sk2106 ))]]) ).
thf(58800,plain,
sk2105 = sk1575,
inference(rewrite,[status(thm)],[58596,279]) ).
thf(59306,plain,
( ( hF_Mir137170979_hpair @ sk1575 )
| ( sk2204 != x ) ),
inference(rewrite,[status(thm)],[58357,58800]) ).
thf(70148,plain,
( ( sk2204 != x )
| ( ( hF_Mir137170979_hpair @ sk1575 )
!= ( hF_Mir137170979_hpair @ zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[59306,70122]) ).
thf(70182,plain,
( ( sk2204 != x )
| ( sk1575 != zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[70148]) ).
thf(68452,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ B )
| ~ ( hF_Mir434065167lation @ A )
| ( ( hF_Mirabelle_hmem @ sk2650 @ x )
!= ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[68427,559]) ).
thf(68453,plain,
( ( hF_Mir137170979_hpair @ sk2650 )
| ~ ( hF_Mir434065167lation @ x ) ),
inference(pattern_uni,[status(thm)],[68452:[bind(A,$thf( x )),bind(B,$thf( sk2650 ))]]) ).
thf(70413,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk2650 )
| ~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) )
| ( ( hF_Mir434065167lation @ A )
!= ( hF_Mir434065167lation @ x ) ) ),
inference(paramod_ordered,[status(thm)],[293,68453]) ).
thf(70414,plain,
( ( hF_Mir137170979_hpair @ sk2650 )
| ~ ! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ x )
=> ( hF_Mir137170979_hpair @ A ) ) ),
inference(pattern_uni,[status(thm)],[70413:[bind(A,$thf( x ))]]) ).
thf(70496,plain,
( ( hF_Mirabelle_hmem @ sk2748 @ x )
| ( hF_Mir137170979_hpair @ sk2650 ) ),
inference(cnf,[status(esa)],[70414]) ).
thf(71175,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk2650 )
| ( ( hF_Mirabelle_hmem @ sk2748 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[70496,178]) ).
thf(71230,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk2650 )
| ( sk2748 != A )
| ( x != A ) ),
inference(simp,[status(thm)],[71175]) ).
thf(71368,plain,
( ( hF_Mir137170979_hpair @ sk2650 )
| ( sk2748 != x ) ),
inference(simp,[status(thm)],[71230]) ).
thf(73591,plain,
( ( sk2748 != x )
| ( ( hF_Mir137170979_hpair @ sk2650 )
!= ( hF_Mir137170979_hpair @ zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[71368,70122]) ).
thf(73626,plain,
( ( sk2748 != x )
| ( sk2650 != zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[73591]) ).
thf(281,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] : ( hF_Mir434065167lation @ ( hF_Mir1653039215strict @ A @ B ) ),
inference(cnf,[status(esa)],[280]) ).
thf(548,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
=> ( hF_Mir137170979_hpair @ D ) )
| ( ( hF_Mir434065167lation @ A )
!= ( hF_Mir434065167lation @ ( hF_Mir1653039215strict @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[293,281]) ).
thf(549,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ ( hF_Mir1653039215strict @ A @ B ) )
=> ( hF_Mir137170979_hpair @ C ) ),
inference(pattern_uni,[status(thm)],[548:[bind(A,$thf( hF_Mir1653039215strict @ D @ E )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(555,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ C @ ( hF_Mir1653039215strict @ A @ B ) )
| ( hF_Mir137170979_hpair @ C ) ),
inference(cnf,[status(esa)],[549]) ).
thf(556,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ C @ ( hF_Mir1653039215strict @ A @ B ) )
| ( hF_Mir137170979_hpair @ C ) ),
inference(simp,[status(thm)],[555]) ).
thf(73091,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ C )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ C @ ( hF_Mir1653039215strict @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[42597,556]) ).
thf(73092,plain,
hF_Mir137170979_hpair @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ),
inference(pattern_uni,[status(thm)],[73091:[bind(A,$thf( r )),bind(B,$thf( x )),bind(C,$thf( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ))]]) ).
thf(73255,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) )
!= ( hF_Mir137170979_hpair @ zero_z189798548lle_hf ) ),
inference(paramod_ordered,[status(thm)],[73092,70122]) ).
thf(73298,plain,
( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
!= zero_z189798548lle_hf ),
inference(simp,[status(thm)],[73255]) ).
thf(74244,plain,
( ( ( hF_Mirabelle_hpair @ sk2650 @ sk2651 )
!= zero_z189798548lle_hf )
| ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[68430,73298]) ).
thf(74245,plain,
( ( hF_Mirabelle_hpair @ sk2650 @ sk2651 )
!= zero_z189798548lle_hf ),
inference(pattern_uni,[status(thm)],[74244:[]]) ).
thf(68018,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ A @ B )
& ? [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] :
( ( A
= ( hF_Mirabelle_hpair @ D @ E ) )
& ( hF_Mirabelle_hmem @ D @ C ) ) )
| ( ( hF_Mirabelle_hmem @ A @ ( hF_Mir1653039215strict @ B @ C ) )
!= ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[284,42597]) ).
thf(68019,plain,
( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) @ r )
& ? [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
= ( hF_Mirabelle_hpair @ A @ B ) )
& ( hF_Mirabelle_hmem @ A @ x ) ) ),
inference(pattern_uni,[status(thm)],[68018:[bind(A,$thf( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )),bind(B,$thf( r )),bind(C,$thf( x ))]]) ).
thf(68432,plain,
hF_Mirabelle_hmem @ sk2652 @ x,
inference(cnf,[status(esa)],[68019]) ).
thf(68866,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ B )
| ~ ( hF_Mir434065167lation @ A )
| ( ( hF_Mirabelle_hmem @ sk2652 @ x )
!= ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[68432,559]) ).
thf(68867,plain,
( ( hF_Mir137170979_hpair @ sk2652 )
| ~ ( hF_Mir434065167lation @ x ) ),
inference(pattern_uni,[status(thm)],[68866:[bind(A,$thf( x )),bind(B,$thf( sk2652 ))]]) ).
thf(70510,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk2652 )
| ~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) )
| ( ( hF_Mir434065167lation @ A )
!= ( hF_Mir434065167lation @ x ) ) ),
inference(paramod_ordered,[status(thm)],[293,68867]) ).
thf(70511,plain,
( ( hF_Mir137170979_hpair @ sk2652 )
| ~ ! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ x )
=> ( hF_Mir137170979_hpair @ A ) ) ),
inference(pattern_uni,[status(thm)],[70510:[bind(A,$thf( x ))]]) ).
thf(70595,plain,
( ( hF_Mirabelle_hmem @ sk2757 @ x )
| ( hF_Mir137170979_hpair @ sk2652 ) ),
inference(cnf,[status(esa)],[70511]) ).
thf(72060,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk2652 )
| ( ( hF_Mirabelle_hmem @ sk2757 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[70595,178]) ).
thf(72162,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk2652 )
| ( sk2757 != A )
| ( x != A ) ),
inference(simp,[status(thm)],[72060]) ).
thf(72335,plain,
( ( hF_Mir137170979_hpair @ sk2652 )
| ( sk2757 != x ) ),
inference(simp,[status(thm)],[72162]) ).
thf(68433,plain,
( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
= ( hF_Mirabelle_hpair @ sk2652 @ sk2653 ) ),
inference(cnf,[status(esa)],[68019]) ).
thf(68435,plain,
( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
= ( hF_Mirabelle_hpair @ sk2652 @ sk2653 ) ),
inference(lifteq,[status(thm)],[68433]) ).
thf(74215,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hfst @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) )
= A )
| ( ( hF_Mirabelle_hpair @ sk2650 @ sk2651 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[68430,279]) ).
thf(74216,plain,
( ( hF_Mirabelle_hfst @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) )
= sk2650 ),
inference(pattern_uni,[status(thm)],[74215:[bind(A,$thf( sk2650 )),bind(B,$thf( sk2651 ))]]) ).
thf(76558,plain,
( ( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ sk2652 @ sk2653 ) )
= sk2650 )
| ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[68435,74216]) ).
thf(76559,plain,
( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ sk2652 @ sk2653 ) )
= sk2650 ),
inference(pattern_uni,[status(thm)],[76558:[]]) ).
thf(78746,plain,
sk2652 = sk2650,
inference(rewrite,[status(thm)],[76559,279]) ).
thf(78748,plain,
( ( hF_Mir137170979_hpair @ sk2650 )
| ( sk2757 != x ) ),
inference(rewrite,[status(thm)],[72335,78746]) ).
thf(38909,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ sk1147 @ x )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[33027,181]) ).
thf(38910,plain,
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ~ ( hF_Mirabelle_hmem @ x @ sk1147 ) ),
inference(pattern_uni,[status(thm)],[38909:[bind(A,$thf( sk1147 )),bind(B,$thf( x ))]]) ).
thf(50768,plain,
! [A: hF_Mirabelle_hf] :
( ~ ! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ C ) @ A )
=> ! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ D ) @ A )
=> ( C = D ) ) )
| ~ ( hF_Mirabelle_hmem @ x @ sk1147 )
| ( ( hF_Mir199975595nction @ A )
!= ( hF_Mir199975595nction @ zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[325,38910]) ).
thf(50769,plain,
( ~ ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ B ) @ zero_z189798548lle_hf )
=> ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ C ) @ zero_z189798548lle_hf )
=> ( B = C ) ) )
| ~ ( hF_Mirabelle_hmem @ x @ sk1147 ) ),
inference(pattern_uni,[status(thm)],[50768:[bind(A,$thf( zero_z189798548lle_hf ))]]) ).
thf(50944,plain,
( ~ ( hF_Mirabelle_hmem @ x @ sk1147 )
| ( sk2002 != sk2003 ) ),
inference(cnf,[status(esa)],[50769]) ).
thf(50947,plain,
( ( sk2003 != sk2002 )
| ~ ( hF_Mirabelle_hmem @ x @ sk1147 ) ),
inference(lifteq,[status(thm)],[50944]) ).
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/sandbox2/benchmark/theBenchmark.p',fact_24_Replace__iff) ).
thf(231,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(232,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)],[231]) ).
thf(233,plain,
! [C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_Replace @ B @ C ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ B )
& ( C @ D @ A )
& ! [E: hF_Mirabelle_hf] :
( ( C @ D @ E )
=> ( E = A ) ) ) ) ),
inference(lifteq,[status(thm)],[232]) ).
thf(1833,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ~ ( hF_Mir434065167lation @ r )
| ( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
!= ( hF_Mir199975595nction @ r ) ) ),
inference(paramod_ordered,[status(thm)],[287,1053]) ).
thf(1851,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ~ ( hF_Mir434065167lation @ r )
| ( ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x )
!= r ) ),
inference(simp,[status(thm)],[1833]) ).
thf(2187,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) )
| ( ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x )
!= r )
| ( ( hF_Mir434065167lation @ A )
!= ( hF_Mir434065167lation @ r ) ) ),
inference(paramod_ordered,[status(thm)],[293,1851]) ).
thf(2188,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ~ ! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ r )
=> ( hF_Mir137170979_hpair @ A ) )
| ( ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x )
!= r ) ),
inference(pattern_uni,[status(thm)],[2187:[bind(A,$thf( r ))]]) ).
thf(2204,plain,
( ( ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x )
!= r )
| ( hF_Mirabelle_hmem @ sk45 @ r )
| ( hF_Mir137170979_hpair @ ( sk20 @ r ) ) ),
inference(cnf,[status(esa)],[2188]) ).
thf(2630,plain,
( ~ ( 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)],[287,1855]) ).
thf(2646,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ~ ( hF_Mir137170979_hpair @ sk35 )
| ( ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x )
!= r ) ),
inference(simp,[status(thm)],[2630]) ).
thf(58803,plain,
( ( hF_Mirabelle_hmem @ sk2204 @ x )
| ( hF_Mir137170979_hpair @ sk1575 ) ),
inference(rewrite,[status(thm)],[56519,58800]) ).
thf(48119,plain,
( ~ ( hF_Mir137170979_hpair @ sk1901 )
| ( hF_Mir137170979_hpair @ sk1575 ) ),
inference(cnf,[status(esa)],[48056]) ).
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/sandbox2/benchmark/theBenchmark.p',fact_32_zero__notin__hpair) ).
thf(270,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(271,plain,
~ ? [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ ( hF_Mirabelle_hpair @ A @ B ) ),
inference(miniscope,[status(thm)],[270]) ).
thf(272,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ ( hF_Mirabelle_hpair @ A @ B ) ),
inference(cnf,[status(esa)],[271]) ).
thf(74260,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) )
| ( ( hF_Mirabelle_hpair @ sk2650 @ sk2651 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[68430,272]) ).
thf(74261,plain,
~ ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) ),
inference(pattern_uni,[status(thm)],[74260:[bind(A,$thf( sk2650 )),bind(B,$thf( sk2651 ))]]) ).
thf(216,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(cnf,[status(esa)],[212]) ).
thf(220,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( sk10 @ B @ A )
!= ( sk9 @ B @ A ) )
| ( ( hF_Mirabelle_hmem @ C @ ( sk11 @ B @ A ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) ) ),
inference(lifteq,[status(thm)],[216]) ).
thf(522,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ A )
| ~ ? [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( A
= ( hF_Mirabelle_hpair @ B @ C ) ) ),
inference(bool_ext,[status(thm)],[292]) ).
thf(527,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A
!= ( hF_Mirabelle_hpair @ B @ C ) )
| ( hF_Mir137170979_hpair @ A ) ),
inference(cnf,[status(esa)],[522]) ).
thf(528,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( A
!= ( hF_Mirabelle_hpair @ B @ C ) )
| ( hF_Mir137170979_hpair @ A ) ),
inference(lifteq,[status(thm)],[527]) ).
thf(529,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] : ( hF_Mir137170979_hpair @ ( hF_Mirabelle_hpair @ A @ B ) ),
inference(simp,[status(thm)],[528]) ).
thf(76568,plain,
( ( ( hF_Mirabelle_hpair @ sk2652 @ sk2653 )
!= zero_z189798548lle_hf )
| ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[68435,73298]) ).
thf(76569,plain,
( ( hF_Mirabelle_hpair @ sk2652 @ sk2653 )
!= zero_z189798548lle_hf ),
inference(pattern_uni,[status(thm)],[76568:[]]) ).
thf(78749,plain,
( ( hF_Mirabelle_hpair @ sk2650 @ sk2653 )
!= zero_z189798548lle_hf ),
inference(rewrite,[status(thm)],[76569,78746]) ).
thf(41433,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ B )
| ~ ( hF_Mir434065167lation @ A )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ x ) @ x )
!= ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[40493,559]) ).
thf(41434,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ~ ( hF_Mir434065167lation @ x ) ),
inference(pattern_uni,[status(thm)],[41433:[bind(A,$thf( x )),bind(B,$thf( sk20 @ x ))]]) ).
thf(197,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(cnf,[status(esa)],[193]) ).
thf(201,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( sk5 @ B @ A )
!= ( sk4 @ B @ A ) )
| ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir1248913145eplace @ A @ B ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) ) ),
inference(lifteq,[status(thm)],[197]) ).
thf(40567,plain,
! [A: hF_Mirabelle_hf] :
( ( A = zero_z189798548lle_hf )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
!= ( hF_Mirabelle_hmem @ x @ sk1604 ) ) ),
inference(paramod_ordered,[status(thm)],[459,40133]) ).
thf(40631,plain,
! [A: hF_Mirabelle_hf] :
( ( A = zero_z189798548lle_hf )
| ( ( sk20 @ A )
!= x )
| ( A != sk1604 ) ),
inference(simp,[status(thm)],[40567]) ).
thf(40693,plain,
( ( sk1604 = zero_z189798548lle_hf )
| ( ( sk20 @ sk1604 )
!= x ) ),
inference(simp,[status(thm)],[40631]) ).
thf(62179,plain,
( ( sk1575 = zero_z189798548lle_hf )
| ( ( sk20 @ sk1575 )
!= x ) ),
inference(rewrite,[status(thm)],[40693,45718]) ).
thf(541,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir434065167lation @ A )
| ~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) ) ),
inference(bool_ext,[status(thm)],[293]) ).
thf(561,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk27 @ A ) @ A )
| ( hF_Mir434065167lation @ A ) ),
inference(cnf,[status(esa)],[541]) ).
thf(2086,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ B ) )
= C )
| ( ( sup_su638957495lle_hf @ ( hF_Mirabelle_HUnion @ A ) @ ( hF_Mirabelle_HUnion @ B ) )
!= ( sup_su638957495lle_hf @ C @ C ) ) ),
inference(paramod_ordered,[status(thm)],[162,93]) ).
thf(2087,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ A ) )
= ( hF_Mirabelle_HUnion @ A ) ),
inference(pattern_uni,[status(thm)],[2086:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( hF_Mirabelle_HUnion @ B ))]]) ).
thf(2171,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ A ) )
= ( hF_Mirabelle_HUnion @ A ) ),
inference(simp,[status(thm)],[2087]) ).
thf(2494,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)],[2171,188]) ).
thf(2495,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ A ) @ ( hF_Mirabelle_HUnion @ A ) ),
inference(pattern_uni,[status(thm)],[2494:[bind(A,$thf( D )),bind(B,$thf( sup_su638957495lle_hf @ D @ D ))]]) ).
thf(2549,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ A ) @ ( hF_Mirabelle_HUnion @ A ) ),
inference(simp,[status(thm)],[2495]) ).
thf(2578,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)],[162,2549]) ).
thf(2579,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)],[2578:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( hF_Mirabelle_HUnion @ B ))]]) ).
thf(2606,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)],[2579]) ).
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/sandbox2/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/sandbox2/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(39792,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[39642,178]) ).
thf(39835,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1575 @ sk1577 )
!= A )
| ( ( hF_Mir1653039215strict @ r @ x )
!= A ) ),
inference(simp,[status(thm)],[39792]) ).
thf(39962,plain,
( ( hF_Mir1653039215strict @ r @ x )
!= ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) ),
inference(simp,[status(thm)],[39835]) ).
thf(46412,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk1606 )
| ( ( hF_Mirabelle_hmem @ sk1770 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[43985,178]) ).
thf(46477,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk1606 )
| ( sk1770 != A )
| ( x != A ) ),
inference(simp,[status(thm)],[46412]) ).
thf(46631,plain,
( ( hF_Mir137170979_hpair @ sk1606 )
| ( sk1770 != x ) ),
inference(simp,[status(thm)],[46477]) ).
thf(49156,plain,
( ( hF_Mir137170979_hpair @ sk1575 )
| ( sk1770 != x ) ),
inference(rewrite,[status(thm)],[46631,48706]) ).
thf(41461,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(paramod_ordered,[status(thm)],[40493,3115]) ).
thf(41556,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ A @ B )
!= ( sk20 @ x ) )
| ( A != x ) ),
inference(simp,[status(thm)],[41461]) ).
thf(41669,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ x @ A )
!= ( sk20 @ x ) ),
inference(simp,[status(thm)],[41556]) ).
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/sandbox2/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(3266,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)],[150,3115]) ).
thf(3267,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)],[3266:[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(3282,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)],[3267]) ).
thf(3157,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)],[159,3114]) ).
thf(3158,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)],[3157:[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,$thf( sup_su638957495lle_hf @ H @ I ))]]) ).
thf(3196,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) @ B ),
inference(cnf,[status(esa)],[3158]) ).
thf(3198,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) @ B ),
inference(simp,[status(thm)],[3196]) ).
thf(12,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A @ B ) @ C )
= ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_sup__assoc) ).
thf(97,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ A @ B ) @ C )
= ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(52251,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ sk1149 @ x )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[33031,181]) ).
thf(52252,plain,
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ~ ( hF_Mirabelle_hmem @ x @ sk1149 ) ),
inference(pattern_uni,[status(thm)],[52251:[bind(A,$thf( sk1149 )),bind(B,$thf( x ))]]) ).
thf(62489,plain,
! [A: hF_Mirabelle_hf] :
( ~ ! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ C ) @ A )
=> ! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ B @ D ) @ A )
=> ( C = D ) ) )
| ~ ( hF_Mirabelle_hmem @ x @ sk1149 )
| ( ( hF_Mir199975595nction @ A )
!= ( hF_Mir199975595nction @ zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[325,52252]) ).
thf(62490,plain,
( ~ ! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ B ) @ zero_z189798548lle_hf )
=> ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ A @ C ) @ zero_z189798548lle_hf )
=> ( B = C ) ) )
| ~ ( hF_Mirabelle_hmem @ x @ sk1149 ) ),
inference(pattern_uni,[status(thm)],[62489:[bind(A,$thf( zero_z189798548lle_hf ))]]) ).
thf(62648,plain,
( ~ ( hF_Mirabelle_hmem @ x @ sk1149 )
| ( sk2448 != sk2449 ) ),
inference(cnf,[status(esa)],[62490]) ).
thf(62651,plain,
( ( sk2449 != sk2448 )
| ~ ( hF_Mirabelle_hmem @ x @ sk1149 ) ),
inference(lifteq,[status(thm)],[62648]) ).
thf(53983,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[39643,181]) ).
thf(53984,plain,
~ ( hF_Mirabelle_hmem @ ( hF_Mir1653039215strict @ r @ x ) @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) ),
inference(pattern_uni,[status(thm)],[53983:[bind(A,$thf( hF_Mirabelle_hpair @ sk1575 @ sk1576 )),bind(B,$thf( hF_Mir1653039215strict @ r @ x ))]]) ).
thf(58027,plain,
( ( hF_Mirabelle_hmem @ sk2203 @ x )
| ( hF_Mir137170979_hpair @ sk1575 ) ),
inference(rewrite,[status(thm)],[56455,58025]) ).
thf(44700,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk20 @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) )
!= ( hF_Mirabelle_hpair @ A @ B ) )
| ( ( hF_Mirabelle_hpair @ sk1604 @ sk1605 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[40074,2031]) ).
thf(44701,plain,
( ( hF_Mirabelle_hpair @ sk1604 @ sk1605 )
!= ( sk20 @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) ) ),
inference(pattern_uni,[status(thm)],[44700:[bind(A,$thf( sk1604 )),bind(B,$thf( sk1605 ))]]) ).
thf(62199,plain,
( ( sk20 @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) )
!= ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) ),
inference(rewrite,[status(thm)],[44701,47636,45718]) ).
thf(576,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_Mir434065167lation @ ( hF_Mir1653039215strict @ A @ B ) )
!= ( hF_Mir434065167lation @ C ) ) ),
inference(paramod_ordered,[status(thm)],[281,559]) ).
thf(577,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ A @ ( hF_Mir1653039215strict @ B @ C ) )
| ( hF_Mir137170979_hpair @ A ) ),
inference(pattern_uni,[status(thm)],[576:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( hF_Mir1653039215strict @ E @ F ))]]) ).
thf(578,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ A @ ( hF_Mir1653039215strict @ B @ C ) )
| ( hF_Mir137170979_hpair @ A ) ),
inference(simp,[status(thm)],[577]) ).
thf(74193,plain,
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk2650 @ sk2651 ) @ r )
| ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[68430,68429]) ).
thf(74194,plain,
hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk2650 @ sk2651 ) @ r,
inference(pattern_uni,[status(thm)],[74193:[]]) ).
thf(76454,plain,
( ( ( hF_Mirabelle_hpair @ sk2652 @ sk2653 )
!= sk2650 )
| ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[68435,74178]) ).
thf(76455,plain,
( ( hF_Mirabelle_hpair @ sk2652 @ sk2653 )
!= sk2650 ),
inference(pattern_uni,[status(thm)],[76454:[]]) ).
thf(78754,plain,
( ( hF_Mirabelle_hpair @ sk2650 @ sk2653 )
!= sk2650 ),
inference(rewrite,[status(thm)],[76455,78746]) ).
thf(48318,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk1575 )
| ( ( hF_Mirabelle_hmem @ sk1901 @ x )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[48120,188]) ).
thf(48458,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk1575 )
| ( sk1901 != A )
| ( ( hF_Mirabelle_HUnion @ A )
!= x ) ),
inference(simp,[status(thm)],[48318]) ).
thf(48609,plain,
( ( hF_Mir137170979_hpair @ sk1575 )
| ( ( hF_Mirabelle_HUnion @ sk1901 )
!= x ) ),
inference(simp,[status(thm)],[48458]) ).
thf(1856,plain,
( ( hF_Mirabelle_hmem @ sk35 @ r )
| ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) ) ),
inference(cnf,[status(esa)],[1826]) ).
thf(48383,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk1575 )
| ( ( hF_Mirabelle_hmem @ sk1901 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[48120,178]) ).
thf(48400,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk1575 )
| ( sk1901 != A )
| ( x != A ) ),
inference(simp,[status(thm)],[48383]) ).
thf(48504,plain,
( ( hF_Mir137170979_hpair @ sk1575 )
| ( sk1901 != x ) ),
inference(simp,[status(thm)],[48400]) ).
thf(39361,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 @ sk1147 @ x )
| ( ( hF_Mir199975595nction @ A )
!= ( hF_Mir199975595nction @ zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[325,33027]) ).
thf(39362,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 @ sk1147 @ x ) ),
inference(pattern_uni,[status(thm)],[39361:[bind(A,$thf( zero_z189798548lle_hf ))]]) ).
thf(39563,plain,
( ( hF_Mirabelle_hmem @ sk1147 @ x )
| ( sk1525 != sk1526 ) ),
inference(cnf,[status(esa)],[39362]) ).
thf(39566,plain,
( ( sk1526 != sk1525 )
| ( hF_Mirabelle_hmem @ sk1147 @ x ) ),
inference(lifteq,[status(thm)],[39563]) ).
thf(61058,plain,
! [A: hF_Mirabelle_hf] :
( ( sk1526 != sk1525 )
| ( ( hF_Mirabelle_hmem @ sk1147 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[39566,178]) ).
thf(61078,plain,
! [A: hF_Mirabelle_hf] :
( ( sk1526 != sk1525 )
| ( sk1147 != A )
| ( x != A ) ),
inference(simp,[status(thm)],[61058]) ).
thf(61184,plain,
( ( sk1526 != sk1525 )
| ( sk1147 != x ) ),
inference(simp,[status(thm)],[61078]) ).
thf(44257,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk1604 )
| ( ( hF_Mirabelle_hmem @ sk1734 @ x )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[43316,188]) ).
thf(44364,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk1604 )
| ( sk1734 != A )
| ( ( hF_Mirabelle_HUnion @ A )
!= x ) ),
inference(simp,[status(thm)],[44257]) ).
thf(44487,plain,
( ( hF_Mir137170979_hpair @ sk1604 )
| ( ( hF_Mirabelle_HUnion @ sk1734 )
!= x ) ),
inference(simp,[status(thm)],[44364]) ).
thf(64793,plain,
( ( hF_Mir137170979_hpair @ sk1575 )
| ( ( hF_Mirabelle_HUnion @ sk1734 )
!= x ) ),
inference(rewrite,[status(thm)],[44487,45718]) ).
thf(56454,plain,
( ~ ( hF_Mir137170979_hpair @ sk2203 )
| ( hF_Mir137170979_hpair @ sk2103 ) ),
inference(cnf,[status(esa)],[56383]) ).
thf(58030,plain,
( ~ ( hF_Mir137170979_hpair @ sk2203 )
| ( hF_Mir137170979_hpair @ sk1575 ) ),
inference(rewrite,[status(thm)],[56454,58025]) ).
thf(68462,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ A )
!= ( hF_Mirabelle_hmem @ sk2650 @ x ) ),
inference(paramod_ordered,[status(thm)],[68427,7830]) ).
thf(68601,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk6 @ A @ B )
!= sk2650 )
| ( A != x ) ),
inference(simp,[status(thm)],[68462]) ).
thf(68840,plain,
! [A: hF_Mirabelle_hf] :
( ( sk6 @ x @ A )
!= sk2650 ),
inference(simp,[status(thm)],[68601]) ).
thf(27,axiom,
( sup_su638957495lle_hf
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( sup_su638957495lle_hf @ B @ A ) ) ),
file('/export/starexec/sandbox2/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(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/sandbox2/benchmark/theBenchmark.p',fact_17_replacement__fun) ).
thf(225,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(5,axiom,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ),
file('/export/starexec/sandbox2/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(46356,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk1606 )
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ sk1770 @ x )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[43985,181]) ).
thf(46357,plain,
( ( hF_Mir137170979_hpair @ sk1606 )
| ~ ( hF_Mirabelle_hmem @ x @ sk1770 ) ),
inference(pattern_uni,[status(thm)],[46356:[bind(A,$thf( sk1770 )),bind(B,$thf( x ))]]) ).
thf(65857,plain,
( ( hF_Mir137170979_hpair @ sk1575 )
| ~ ( hF_Mirabelle_hmem @ x @ sk1770 ) ),
inference(rewrite,[status(thm)],[46357,48706]) ).
thf(572,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ C @ B )
| ( hF_Mir137170979_hpair @ C )
| ~ ! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
=> ( hF_Mir137170979_hpair @ D ) )
| ( ( hF_Mir434065167lation @ A )
!= ( hF_Mir434065167lation @ B ) ) ),
inference(paramod_ordered,[status(thm)],[293,559]) ).
thf(573,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ B @ A )
| ( hF_Mir137170979_hpair @ B )
| ~ ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
=> ( hF_Mir137170979_hpair @ C ) ) ),
inference(pattern_uni,[status(thm)],[572:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(579,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir137170979_hpair @ ( sk33 @ B @ A ) )
| ( hF_Mir137170979_hpair @ B )
| ~ ( hF_Mirabelle_hmem @ B @ A ) ),
inference(cnf,[status(esa)],[573]) ).
thf(581,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mir137170979_hpair @ ( sk33 @ B @ A ) )
| ( hF_Mir137170979_hpair @ B )
| ~ ( hF_Mirabelle_hmem @ B @ A ) ),
inference(simp,[status(thm)],[579]) ).
thf(685,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_Mir137170979_hpair @ ( hF_Mirabelle_hpair @ A @ B ) )
!= ( hF_Mir137170979_hpair @ ( sk33 @ D @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[529,581]) ).
thf(686,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)],[685]) ).
thf(4850,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(paramod_ordered,[status(thm)],[835,188]) ).
thf(4911,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)],[4850]) ).
thf(4938,plain,
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( ( hF_Mirabelle_HUnion @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) )
!= ( hF_Mir1653039215strict @ r @ x ) ) ),
inference(simp,[status(thm)],[4911]) ).
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/sandbox2/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(366,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(367,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)],[366:[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(392,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)],[367]) ).
thf(49207,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)],[392,76]) ).
thf(43315,plain,
( ~ ( hF_Mir137170979_hpair @ sk1734 )
| ( hF_Mir137170979_hpair @ sk1604 ) ),
inference(cnf,[status(esa)],[43254]) ).
thf(45725,plain,
( ~ ( hF_Mir137170979_hpair @ sk1734 )
| ( hF_Mir137170979_hpair @ sk1575 ) ),
inference(rewrite,[status(thm)],[43315,45718]) ).
thf(294,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)],[224]) ).
thf(565,plain,
! [A: hF_Mirabelle_hf] :
( ( ( (=) @ hF_Mirabelle_hf @ A )
= hF_Mir434065167lation )
| ( ( ^ [B: hF_Mirabelle_hf] :
! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
= ( hF_Mirabelle_hmem @ C @ B ) ) )
!= ( ^ [B: hF_Mirabelle_hf] :
! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ B )
=> ( hF_Mir137170979_hpair @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[294,222]) ).
thf(569,plain,
! [A: hF_Mirabelle_hf] :
( ( ( (=) @ hF_Mirabelle_hf @ A )
= hF_Mir434065167lation )
| ( ( ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
= ( hF_Mirabelle_hmem @ C @ B ) ) )
!= ( ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ B )
=> ( hF_Mir137170979_hpair @ C ) ) ) ) ),
inference(simp,[status(thm)],[565]) ).
thf(24999,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)],[23872,11658]) ).
thf(25088,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)],[24999]) ).
thf(25175,plain,
( ( ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ r )
!= r )
| ( ( sk15 @ hF_Mir199975595nction @ r )
!= ( hF_Mir1653039215strict @ r @ x ) ) ),
inference(simp,[status(thm)],[25088]) ).
thf(43359,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ B )
| ~ ( hF_Mir434065167lation @ A )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r )
!= ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[43248,559]) ).
thf(43360,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ~ ( hF_Mir434065167lation @ r ) ),
inference(pattern_uni,[status(thm)],[43359:[bind(A,$thf( r )),bind(B,$thf( sk20 @ r ))]]) ).
thf(62788,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) )
| ( ( hF_Mir434065167lation @ A )
!= ( hF_Mir434065167lation @ r ) ) ),
inference(paramod_ordered,[status(thm)],[293,43360]) ).
thf(62789,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ~ ! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ r )
=> ( hF_Mir137170979_hpair @ A ) ) ),
inference(pattern_uni,[status(thm)],[62788:[bind(A,$thf( r ))]]) ).
thf(62865,plain,
( ( hF_Mirabelle_hmem @ sk2458 @ r )
| ( hF_Mir137170979_hpair @ ( sk20 @ r ) ) ),
inference(cnf,[status(esa)],[62789]) ).
thf(2203,plain,
( ( ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x )
!= r )
| ~ ( hF_Mir137170979_hpair @ sk45 )
| ( hF_Mir137170979_hpair @ ( sk20 @ r ) ) ),
inference(cnf,[status(esa)],[2188]) ).
thf(60984,plain,
! [A: hF_Mirabelle_hf] :
( ( sk1526 != sk1525 )
| ( ( hF_Mirabelle_hmem @ sk1147 @ x )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[39566,188]) ).
thf(61140,plain,
! [A: hF_Mirabelle_hf] :
( ( sk1526 != sk1525 )
| ( sk1147 != A )
| ( ( hF_Mirabelle_HUnion @ A )
!= x ) ),
inference(simp,[status(thm)],[60984]) ).
thf(61313,plain,
( ( sk1526 != sk1525 )
| ( ( hF_Mirabelle_HUnion @ sk1147 )
!= x ) ),
inference(simp,[status(thm)],[61140]) ).
thf(62691,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) )
| ( ( hF_Mir434065167lation @ A )
!= ( hF_Mir434065167lation @ x ) ) ),
inference(paramod_ordered,[status(thm)],[293,41434]) ).
thf(62692,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ~ ! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ x )
=> ( hF_Mir137170979_hpair @ A ) ) ),
inference(pattern_uni,[status(thm)],[62691:[bind(A,$thf( x ))]]) ).
thf(62777,plain,
( ( hF_Mirabelle_hmem @ sk2453 @ x )
| ( hF_Mir137170979_hpair @ ( sk20 @ x ) ) ),
inference(cnf,[status(esa)],[62692]) ).
thf(61,axiom,
hF_Mir434065167lation @ zero_z189798548lle_hf,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_hrelation__0) ).
thf(273,plain,
hF_Mir434065167lation @ zero_z189798548lle_hf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(23612,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ C @ ( sk15 @ B @ A ) )
= ( hF_Mirabelle_hmem @ C @ A ) )
| ( ( hF_Mir434065167lation @ zero_z189798548lle_hf )
!= ( B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[273,248]) ).
thf(23826,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ ( sk15 @ hF_Mir434065167lation @ A ) )
= ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ A ) ),
inference(pre_uni,[status(thm)],[23612:[bind(A,$thf( A )),bind(B,$thf( hF_Mir434065167lation )),bind(C,$thf( zero_z189798548lle_hf ))]]) ).
thf(10094,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)],[210,291]) ).
thf(10095,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)],[10094:[bind(A,$thf( hF_Mir1653039215strict @ r @ x )),bind(B,$thf( B ))]]) ).
thf(11655,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)],[10095]) ).
thf(24562,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)],[23826,11655]) ).
thf(24707,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)],[24562]) ).
thf(24822,plain,
( ( ( sk7 @ r @ ( hF_Mir1653039215strict @ r @ x ) )
!= zero_z189798548lle_hf )
| ( ( sk15 @ hF_Mir434065167lation @ r )
!= ( hF_Mir1653039215strict @ r @ x ) ) ),
inference(simp,[status(thm)],[24707]) ).
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/sandbox2/benchmark/theBenchmark.p',fact_26_RepFun__iff) ).
thf(205,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(985,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(paramod_ordered,[status(thm)],[889,188]) ).
thf(1015,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)],[985]) ).
thf(1026,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)],[1015]) ).
thf(40128,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ B )
!= ( hF_Mirabelle_hmem @ sk1604 @ x ) ),
inference(paramod_ordered,[status(thm)],[40071,7831]) ).
thf(40232,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk6 @ A @ B )
!= sk1604 )
| ( B != x ) ),
inference(simp,[status(thm)],[40128]) ).
thf(40337,plain,
! [A: hF_Mirabelle_hf] :
( ( sk6 @ A @ x )
!= sk1604 ),
inference(simp,[status(thm)],[40232]) ).
thf(50737,plain,
! [A: hF_Mirabelle_hf] :
( ( sk6 @ A @ x )
!= sk1575 ),
inference(rewrite,[status(thm)],[40337,45718]) ).
thf(50355,plain,
! [A: hF_Mirabelle_hf] :
( ( sk1575 = zero_z189798548lle_hf )
| ( ( hF_Mirabelle_hmem @ ( sk20 @ sk1575 ) @ sk1575 )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[50198,178]) ).
thf(50439,plain,
! [A: hF_Mirabelle_hf] :
( ( sk1575 = zero_z189798548lle_hf )
| ( ( sk20 @ sk1575 )
!= A )
| ( sk1575 != A ) ),
inference(simp,[status(thm)],[50355]) ).
thf(50473,plain,
( ( sk1575 = zero_z189798548lle_hf )
| ( ( sk20 @ sk1575 )
!= sk1575 ) ),
inference(simp,[status(thm)],[50439]) ).
thf(40105,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ A )
!= ( hF_Mirabelle_hmem @ sk1604 @ x ) ),
inference(paramod_ordered,[status(thm)],[40071,7830]) ).
thf(40269,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk6 @ A @ B )
!= sk1604 )
| ( A != x ) ),
inference(simp,[status(thm)],[40105]) ).
thf(40422,plain,
! [A: hF_Mirabelle_hf] :
( ( sk6 @ x @ A )
!= sk1604 ),
inference(simp,[status(thm)],[40269]) ).
thf(51479,plain,
! [A: hF_Mirabelle_hf] :
( ( sk6 @ x @ A )
!= sk1575 ),
inference(rewrite,[status(thm)],[40422,45718]) ).
thf(57806,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1575 @ sk1576 )
!= zero_z189798548lle_hf )
| ( ( hF_Mirabelle_hpair @ sk2103 @ sk2104 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[54337,129]) ).
thf(57807,plain,
( ( hF_Mirabelle_hpair @ sk1575 @ sk1576 )
!= zero_z189798548lle_hf ),
inference(pattern_uni,[status(thm)],[57806:[bind(A,$thf( sk2103 )),bind(B,$thf( sk2104 ))]]) ).
thf(190,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)],[189]) ).
thf(191,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)],[190]) ).
thf(68144,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[42597,178]) ).
thf(68158,plain,
! [A: hF_Mirabelle_hf] :
( ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
!= A )
| ( ( hF_Mir1653039215strict @ r @ x )
!= A ) ),
inference(simp,[status(thm)],[68144]) ).
thf(68267,plain,
( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mir1653039215strict @ r @ x ) ),
inference(simp,[status(thm)],[68158]) ).
thf(74242,plain,
( ( ( hF_Mir1653039215strict @ r @ x )
!= ( hF_Mirabelle_hpair @ sk2650 @ sk2651 ) )
| ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[68430,68267]) ).
thf(74243,plain,
( ( hF_Mir1653039215strict @ r @ x )
!= ( hF_Mirabelle_hpair @ sk2650 @ sk2651 ) ),
inference(pattern_uni,[status(thm)],[74242:[]]) ).
thf(360,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(361,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)],[360:[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(389,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)],[361]) ).
thf(46743,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)],[389,35051]) ).
thf(43367,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ A )
!= ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r ) ),
inference(paramod_ordered,[status(thm)],[43248,7830]) ).
thf(43508,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk6 @ A @ B )
!= ( sk20 @ r ) )
| ( A != r ) ),
inference(simp,[status(thm)],[43367]) ).
thf(43733,plain,
! [A: hF_Mirabelle_hf] :
( ( sk6 @ r @ A )
!= ( sk20 @ r ) ),
inference(simp,[status(thm)],[43508]) ).
thf(39696,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ),
inference(paramod_ordered,[status(thm)],[39642,188]) ).
thf(39828,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1575 @ sk1577 )
!= A )
| ( ( hF_Mir1653039215strict @ r @ x )
!= ( hF_Mirabelle_HUnion @ A ) ) ),
inference(simp,[status(thm)],[39696]) ).
thf(39952,plain,
( ( hF_Mir1653039215strict @ r @ x )
!= ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) ) ),
inference(simp,[status(thm)],[39828]) ).
thf(46347,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk1606 )
| ( ( hF_Mirabelle_hmem @ sk1770 @ x )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[43985,188]) ).
thf(46505,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk1606 )
| ( sk1770 != A )
| ( ( hF_Mirabelle_HUnion @ A )
!= x ) ),
inference(simp,[status(thm)],[46347]) ).
thf(46676,plain,
( ( hF_Mir137170979_hpair @ sk1606 )
| ( ( hF_Mirabelle_HUnion @ sk1770 )
!= x ) ),
inference(simp,[status(thm)],[46505]) ).
thf(66162,plain,
( ( hF_Mir137170979_hpair @ sk1575 )
| ( ( hF_Mirabelle_HUnion @ sk1770 )
!= x ) ),
inference(rewrite,[status(thm)],[46676,48706]) ).
thf(68480,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ sk2650 @ x )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ),
inference(paramod_ordered,[status(thm)],[68427,188]) ).
thf(68628,plain,
! [A: hF_Mirabelle_hf] :
( ( sk2650 != A )
| ( ( hF_Mirabelle_HUnion @ A )
!= x ) ),
inference(simp,[status(thm)],[68480]) ).
thf(68694,plain,
( ( hF_Mirabelle_HUnion @ sk2650 )
!= x ),
inference(simp,[status(thm)],[68628]) ).
thf(3262,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)],[162,3115]) ).
thf(3263,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)],[3262:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( hF_Mirabelle_HUnion @ E )),bind(D,$thf( hF_Mirabelle_HUnion @ F ))]]) ).
thf(3302,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)],[3263]) ).
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(42873,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) @ r )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ),
inference(paramod_ordered,[status(thm)],[40073,188]) ).
thf(43010,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1575 @ sk1577 )
!= A )
| ( ( hF_Mirabelle_HUnion @ A )
!= r ) ),
inference(simp,[status(thm)],[42873]) ).
thf(43061,plain,
( ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) )
!= r ),
inference(simp,[status(thm)],[43010]) ).
thf(70427,plain,
( ~ ( hF_Mir434065167lation @ x )
| ( ( hF_Mir137170979_hpair @ sk2650 )
!= ( hF_Mir137170979_hpair @ zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[68453,70122]) ).
thf(70476,plain,
( ~ ( hF_Mir434065167lation @ x )
| ( sk2650 != zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[70427]) ).
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 ) )
| ( B = D ) ),
inference(cnf,[status(esa)],[166]) ).
thf(171,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)],[168]) ).
thf(172,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sk2 @ A @ ( hF_Mirabelle_hpair @ A @ B ) )
= B ),
introduced(tautology,[new_symbols(inverse(hF_Mirabelle_hpair),[sk2])]) ).
thf(2509,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)],[162,2171]) ).
thf(2510,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)],[2509:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( hF_Mirabelle_HUnion @ B ))]]) ).
thf(2538,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)],[2510]) ).
thf(215,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(cnf,[status(esa)],[212]) ).
thf(219,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ C @ ( sk11 @ B @ A ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) )
| ( B @ ( sk8 @ B @ A ) @ ( sk10 @ B @ A ) ) ),
inference(lifteq,[status(thm)],[215]) ).
thf(40187,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
| ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ x )
| ( A != sk1604 ) ),
inference(paramod_ordered,[status(thm)],[459,40071]) ).
thf(40188,plain,
( ( hF_Mirabelle_hmem @ ( sk20 @ sk1604 ) @ sk1604 )
| ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ x ) ),
inference(pattern_uni,[status(thm)],[40187:[bind(A,$thf( sk1604 ))]]) ).
thf(66689,plain,
( ( hF_Mirabelle_hmem @ ( sk20 @ sk1575 ) @ sk1575 )
| ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ x ) ),
inference(rewrite,[status(thm)],[40188,45718]) ).
thf(41457,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ x ) @ x )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ),
inference(paramod_ordered,[status(thm)],[40493,188]) ).
thf(41571,plain,
! [A: hF_Mirabelle_hf] :
( ( ( sk20 @ x )
!= A )
| ( ( hF_Mirabelle_HUnion @ A )
!= x ) ),
inference(simp,[status(thm)],[41457]) ).
thf(41696,plain,
( ( hF_Mirabelle_HUnion @ ( sk20 @ x ) )
!= x ),
inference(simp,[status(thm)],[41571]) ).
thf(495,plain,
! [E: hF_Mirabelle_hf,D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ A @ B )
= ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ D @ E ) ) )
| ( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ A @ B ) )
!= ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ C @ D ) @ E ) ) ),
inference(paramod_ordered,[status(thm)],[90,76]) ).
thf(496,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ B @ C ) @ A ) ) )
= ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ B @ C ) @ A ) ),
inference(pattern_uni,[status(thm)],[495:[bind(A,$thf( sup_su638957495lle_hf @ J @ K )),bind(B,$thf( I )),bind(C,$thf( J )),bind(D,$thf( K )),bind(E,$thf( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ J @ K ) @ I ))]]) ).
thf(513,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ B @ C ) @ A ) ) )
= ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ B @ C ) @ A ) ),
inference(simp,[status(thm)],[496]) ).
thf(64873,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ A ) ) ) )
= ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ A ) ) ),
inference(rewrite,[status(thm)],[513,35051,76]) ).
thf(54336,plain,
hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) @ r,
inference(cnf,[status(esa)],[53949]) ).
thf(56025,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) @ r )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[54336,181]) ).
thf(56026,plain,
~ ( hF_Mirabelle_hmem @ r @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) ),
inference(pattern_uni,[status(thm)],[56025:[bind(A,$thf( hF_Mirabelle_hpair @ sk1575 @ sk1576 )),bind(B,$thf( r ))]]) ).
thf(3195,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(cnf,[status(esa)],[3158]) ).
thf(3197,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)],[3195]) ).
thf(563,plain,
! [A: hF_Mirabelle_hf] :
( ( ( (=) @ hF_Mirabelle_hf @ A )
= hF_Mir199975595nction )
| ( ( ^ [B: hF_Mirabelle_hf] :
! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
= ( hF_Mirabelle_hmem @ C @ B ) ) )
!= ( ^ [B: hF_Mirabelle_hf] :
! [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ C @ D ) @ B )
=> ! [E: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ C @ E ) @ B )
=> ( D = E ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[294,286]) ).
thf(567,plain,
! [A: hF_Mirabelle_hf] :
( ( ( (=) @ hF_Mirabelle_hf @ A )
= hF_Mir199975595nction )
| ( ( ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
= ( hF_Mirabelle_hmem @ C @ B ) ) )
!= ( ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ C @ D ) @ B )
=> ! [E: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ C @ E ) @ B )
=> ( D = E ) ) ) ) ) ),
inference(simp,[status(thm)],[563]) ).
thf(546,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mir434065167lation @ A )
= ( B = zero_z189798548lle_hf ) )
| ( ( ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
=> ( hF_Mir137170979_hpair @ C ) ) )
!= ( ! [C: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ C @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[293,102]) ).
thf(552,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mir434065167lation @ A )
= ( B = zero_z189798548lle_hf ) )
| ( ( ^ [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
=> ( hF_Mir137170979_hpair @ C ) ) )
!= ( ^ [C: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ C @ B ) ) ) ),
inference(simp,[status(thm)],[546]) ).
thf(69591,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) @ r )
!= ( hF_Mirabelle_hmem @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[68429,178]) ).
thf(69698,plain,
! [A: hF_Mirabelle_hf] :
( ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
!= A )
| ( r != A ) ),
inference(simp,[status(thm)],[69591]) ).
thf(69809,plain,
( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
!= r ),
inference(simp,[status(thm)],[69698]) ).
thf(194,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(cnf,[status(esa)],[193]) ).
thf(198,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir1248913145eplace @ A @ B ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) )
| ( hF_Mirabelle_hmem @ ( sk3 @ B @ A ) @ A ) ),
inference(lifteq,[status(thm)],[194]) ).
thf(70141,plain,
( ~ ( hF_Mir434065167lation @ x )
| ( ( hF_Mir137170979_hpair @ sk1575 )
!= ( hF_Mir137170979_hpair @ zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[45720,70122]) ).
thf(70180,plain,
( ~ ( hF_Mir434065167lation @ x )
| ( sk1575 != zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[70141]) ).
thf(72373,plain,
! [A: hF_Mirabelle_hf] :
( ~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) )
| ( sk1575 != zero_z189798548lle_hf )
| ( ( hF_Mir434065167lation @ A )
!= ( hF_Mir434065167lation @ x ) ) ),
inference(paramod_ordered,[status(thm)],[293,70180]) ).
thf(72374,plain,
( ~ ! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ x )
=> ( hF_Mir137170979_hpair @ A ) )
| ( sk1575 != zero_z189798548lle_hf ) ),
inference(pattern_uni,[status(thm)],[72373:[bind(A,$thf( x ))]]) ).
thf(72411,plain,
( ( sk1575 != zero_z189798548lle_hf )
| ~ ( hF_Mir137170979_hpair @ sk2825 ) ),
inference(cnf,[status(esa)],[72374]) ).
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/sandbox2/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(354,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(377,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)],[354]) ).
thf(399,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)],[377]) ).
thf(57817,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk2 @ A @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) )
= B )
| ( ( hF_Mirabelle_hpair @ sk2103 @ sk2104 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[54337,172]) ).
thf(57818,plain,
( ( sk2 @ sk2103 @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) )
= sk2104 ),
inference(pattern_uni,[status(thm)],[57817:[bind(A,$thf( sk2103 )),bind(B,$thf( sk2104 ))]]) ).
thf(59366,plain,
( ( sk2 @ sk1575 @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) )
= sk1576 ),
inference(rewrite,[status(thm)],[57818,58529,58025]) ).
thf(264,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(cnf,[status(esa)],[263]) ).
thf(266,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)],[264]) ).
thf(267,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)],[266]) ).
thf(39707,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[39642,181]) ).
thf(39708,plain,
~ ( hF_Mirabelle_hmem @ ( hF_Mir1653039215strict @ r @ x ) @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) ),
inference(pattern_uni,[status(thm)],[39707:[bind(A,$thf( hF_Mirabelle_hpair @ sk1575 @ sk1577 )),bind(B,$thf( hF_Mir1653039215strict @ r @ x ))]]) ).
thf(68490,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ sk2650 @ x )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[68427,181]) ).
thf(68491,plain,
~ ( hF_Mirabelle_hmem @ x @ sk2650 ),
inference(pattern_uni,[status(thm)],[68490:[bind(A,$thf( sk2650 )),bind(B,$thf( x ))]]) ).
thf(44703,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk1 @ A @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) )
= B )
| ( ( hF_Mirabelle_hpair @ sk1604 @ sk1605 )
!= ( hF_Mirabelle_hpair @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[40074,170]) ).
thf(44704,plain,
( ( sk1 @ sk1605 @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) )
= sk1604 ),
inference(pattern_uni,[status(thm)],[44703:[bind(A,$thf( sk1605 )),bind(B,$thf( sk1604 ))]]) ).
thf(48733,plain,
( ( sk1 @ sk1577 @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) )
= sk1575 ),
inference(rewrite,[status(thm)],[44704,47636,45718]) ).
thf(235,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)],[234]) ).
thf(237,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(cnf,[status(esa)],[235]) ).
thf(240,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)],[237]) ).
thf(241,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)],[240]) ).
thf(6,axiom,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ),
file('/export/starexec/sandbox2/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(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/sandbox2/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(490,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(503,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)],[490]) ).
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)],[503]) ).
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/sandbox2/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(547,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( A = zero_z189798548lle_hf )
= ( hF_Mir434065167lation @ B ) )
| ( ( ! [C: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ C @ A ) )
!= ( ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ B )
=> ( hF_Mir137170979_hpair @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[102,293]) ).
thf(553,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( A = zero_z189798548lle_hf )
= ( hF_Mir434065167lation @ B ) )
| ( ( ^ [C: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ C @ A ) )
!= ( ^ [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ B )
=> ( hF_Mir137170979_hpair @ C ) ) ) ) ),
inference(simp,[status(thm)],[547]) ).
thf(493,plain,
! [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 @ B ) @ E )
= ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ D @ E ) ) )
| ( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ A @ B ) )
!= ( sup_su638957495lle_hf @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[90,76]) ).
thf(494,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ B @ C ) @ A ) )
= ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ B @ C ) @ A ) ),
inference(pattern_uni,[status(thm)],[493:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( sup_su638957495lle_hf @ F @ G ))]]) ).
thf(512,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ B @ C ) @ A ) )
= ( sup_su638957495lle_hf @ ( sup_su638957495lle_hf @ B @ C ) @ A ) ),
inference(simp,[status(thm)],[494]) ).
thf(63691,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ A ) ) )
= ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ A ) ) ),
inference(rewrite,[status(thm)],[512,35051,76]) ).
thf(68484,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ A @ B ) @ A )
!= ( hF_Mirabelle_hmem @ sk2650 @ x ) ),
inference(paramod_ordered,[status(thm)],[68427,3115]) ).
thf(68631,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ A @ B )
!= sk2650 )
| ( A != x ) ),
inference(simp,[status(thm)],[68484]) ).
thf(68695,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ x @ A )
!= sk2650 ),
inference(simp,[status(thm)],[68631]) ).
thf(41484,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(paramod_ordered,[status(thm)],[40493,3114]) ).
thf(41545,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ A @ B )
!= ( sk20 @ x ) )
| ( B != x ) ),
inference(simp,[status(thm)],[41484]) ).
thf(41649,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ x )
!= ( sk20 @ x ) ),
inference(simp,[status(thm)],[41545]) ).
thf(58605,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) )
= B )
| ( ( hF_Mirabelle_hpair @ sk2105 @ sk2106 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[54342,230]) ).
thf(58606,plain,
( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) )
= sk2106 ),
inference(pattern_uni,[status(thm)],[58605:[bind(A,$thf( sk2105 )),bind(B,$thf( sk2106 ))]]) ).
thf(58817,plain,
sk2106 = sk1576,
inference(rewrite,[status(thm)],[58606,230]) ).
thf(44725,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1575 @ sk1577 )
!= zero_z189798548lle_hf )
| ( ( hF_Mirabelle_hpair @ sk1604 @ sk1605 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[40074,129]) ).
thf(44726,plain,
( ( hF_Mirabelle_hpair @ sk1575 @ sk1577 )
!= zero_z189798548lle_hf ),
inference(pattern_uni,[status(thm)],[44725:[bind(A,$thf( sk1604 )),bind(B,$thf( sk1605 ))]]) ).
thf(70495,plain,
( ~ ( hF_Mir137170979_hpair @ sk2748 )
| ( hF_Mir137170979_hpair @ sk2650 ) ),
inference(cnf,[status(esa)],[70414]) ).
thf(408,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ B @ A )
= ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ B @ D ) ) )
| ( ( sup_su638957495lle_hf @ A @ A )
!= ( sup_su638957495lle_hf @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[93,85]) ).
thf(409,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ A ) )
= ( sup_su638957495lle_hf @ B @ A ) ),
inference(pattern_uni,[status(thm)],[408:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
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(997,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(paramod_ordered,[status(thm)],[889,79]) ).
thf(1014,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)],[997]) ).
thf(1025,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ zero_z189798548lle_hf @ A )
!= zero_z189798548lle_hf ),
inference(simp,[status(thm)],[1014]) ).
thf(295,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)],[224]) ).
thf(76522,plain,
( ( ( hF_Mirabelle_hpair @ sk2652 @ sk2653 )
!= sk2651 )
| ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[68435,74230]) ).
thf(76523,plain,
( ( hF_Mirabelle_hpair @ sk2652 @ sk2653 )
!= sk2651 ),
inference(pattern_uni,[status(thm)],[76522:[]]) ).
thf(78753,plain,
( ( hF_Mirabelle_hpair @ sk2650 @ sk2653 )
!= sk2651 ),
inference(rewrite,[status(thm)],[76523,78746]) ).
thf(68487,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ B @ A ) @ A )
!= ( hF_Mirabelle_hmem @ sk2650 @ x ) ),
inference(paramod_ordered,[status(thm)],[68427,3240]) ).
thf(68647,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ B @ A )
!= sk2650 )
| ( A != x ) ),
inference(simp,[status(thm)],[68487]) ).
thf(68722,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ x )
!= sk2650 ),
inference(simp,[status(thm)],[68647]) ).
thf(43984,plain,
( ~ ( hF_Mir137170979_hpair @ sk1770 )
| ( hF_Mir137170979_hpair @ sk1606 ) ),
inference(cnf,[status(esa)],[43928]) ).
thf(48713,plain,
( ~ ( hF_Mir137170979_hpair @ sk1770 )
| ( hF_Mir137170979_hpair @ sk1575 ) ),
inference(rewrite,[status(thm)],[43984,48706]) ).
thf(74232,plain,
( ( ( hF_Mirabelle_hpair @ sk2650 @ sk2651 )
!= r )
| ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[68430,69809]) ).
thf(74233,plain,
( ( hF_Mirabelle_hpair @ sk2650 @ sk2651 )
!= r ),
inference(pattern_uni,[status(thm)],[74232:[]]) ).
thf(70143,plain,
( ( sk1901 != x )
| ( ( hF_Mir137170979_hpair @ sk1575 )
!= ( hF_Mir137170979_hpair @ zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[48504,70122]) ).
thf(70173,plain,
( ( sk1901 != x )
| ( sk1575 != zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[70143]) ).
thf(441,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)],[328]) ).
thf(44736,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk2 @ A @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) )
= B )
| ( ( hF_Mirabelle_hpair @ sk1604 @ sk1605 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[40074,172]) ).
thf(44737,plain,
( ( sk2 @ sk1604 @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) )
= sk1605 ),
inference(pattern_uni,[status(thm)],[44736:[bind(A,$thf( sk1604 )),bind(B,$thf( sk1605 ))]]) ).
thf(50154,plain,
( ( sk2 @ sk1575 @ ( hF_Mirabelle_hpair @ sk1575 @ sk1577 ) )
= sk1577 ),
inference(rewrite,[status(thm)],[44737,47636,45718]) ).
thf(24611,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ A )
!= ( hF_Mirabelle_hmem @ ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ r ) @ r ) )
| ( ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ ( sk15 @ hF_Mir434065167lation @ A ) )
!= ( hF_Mirabelle_hmem @ ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ r ) @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[23826,11658]) ).
thf(24737,plain,
! [A: hF_Mirabelle_hf] :
( ( ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ r )
!= zero_z189798548lle_hf )
| ( A != r )
| ( ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ r )
!= zero_z189798548lle_hf )
| ( ( sk15 @ hF_Mir434065167lation @ A )
!= ( hF_Mir1653039215strict @ r @ x ) ) ),
inference(simp,[status(thm)],[24611]) ).
thf(24837,plain,
( ( ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ r )
!= zero_z189798548lle_hf )
| ( ( sk15 @ hF_Mir434065167lation @ r )
!= ( hF_Mir1653039215strict @ r @ x ) ) ),
inference(simp,[status(thm)],[24737]) ).
thf(57821,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1575 @ sk1576 )
!= B )
| ( ( hF_Mirabelle_hpair @ sk2103 @ sk2104 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[54337,245]) ).
thf(57822,plain,
( ( hF_Mirabelle_hpair @ sk1575 @ sk1576 )
!= sk2104 ),
inference(pattern_uni,[status(thm)],[57821:[bind(A,$thf( sk2103 )),bind(B,$thf( sk2104 ))]]) ).
thf(58530,plain,
( ( hF_Mirabelle_hpair @ sk1575 @ sk1576 )
!= sk1576 ),
inference(rewrite,[status(thm)],[57822,58529]) ).
thf(25702,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ A @ ( hF_Mir818139703ollect @ B @ C ) )
= ( hF_Mirabelle_hmem @ A @ C ) )
| ( ( hF_Mir434065167lation @ zero_z189798548lle_hf )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[273,254]) ).
thf(25841,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ ( hF_Mir818139703ollect @ hF_Mir434065167lation @ A ) )
= ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ A ) ),
inference(pre_uni,[status(thm)],[25702:[bind(A,$thf( zero_z189798548lle_hf )),bind(B,$thf( hF_Mir434065167lation )),bind(C,$thf( C ))]]) ).
thf(26288,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)],[25841]) ).
thf(26791,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 @ ( hF_Mir818139703ollect @ hF_Mir434065167lation @ A ) )
!= ( hF_Mirabelle_hmem @ ( sk7 @ r @ ( hF_Mir1653039215strict @ r @ x ) ) @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[26288,11655]) ).
thf(26951,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 )
| ( ( hF_Mir818139703ollect @ hF_Mir434065167lation @ A )
!= ( hF_Mir1653039215strict @ r @ x ) ) ),
inference(simp,[status(thm)],[26791]) ).
thf(27073,plain,
( ( ( sk7 @ r @ ( hF_Mir1653039215strict @ r @ x ) )
!= zero_z189798548lle_hf )
| ( ( hF_Mir1653039215strict @ r @ x )
!= ( hF_Mir818139703ollect @ hF_Mir434065167lation @ r ) ) ),
inference(simp,[status(thm)],[26951]) ).
thf(358,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(359,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)],[358:[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(388,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)],[359]) ).
thf(44910,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)],[388,35051,76]) ).
thf(1997,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(paramod_ordered,[status(thm)],[870,188]) ).
thf(2023,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)],[1997]) ).
thf(2030,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)],[2023]) ).
thf(571,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mir434065167lation @ A )
= ( hF_Mir199975595nction @ A ) )
| ( ( ( hF_Mirabelle_hmem @ sk29 @ sk28 )
=> ( hF_Mir137170979_hpair @ sk29 ) )
!= ( sk28 = sk29 ) )
| ( ( ( hF_Mirabelle_hmem @ sk32 @ sk30 )
= ( hF_Mirabelle_hmem @ sk32 @ sk31 ) )
!= ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk31 @ sk32 ) @ sk30 )
=> ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk31 @ B ) @ sk30 )
=> ( sk32 = B ) ) ) ) ),
inference(func_ext,[status(esa)],[443]) ).
thf(2675,plain,
( ( ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf )
!= r )
| ~ ( hF_Mir137170979_hpair @ sk50 )
| ( hF_Mir137170979_hpair @ ( sk20 @ x ) ) ),
inference(cnf,[status(esa)],[2660]) ).
thf(31,axiom,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ A )
= A ),
file('/export/starexec/sandbox2/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(74227,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hsnd @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) )
= B )
| ( ( hF_Mirabelle_hpair @ sk2650 @ sk2651 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[68430,230]) ).
thf(74228,plain,
( ( hF_Mirabelle_hsnd @ ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) )
= sk2651 ),
inference(pattern_uni,[status(thm)],[74227:[bind(A,$thf( sk2650 )),bind(B,$thf( sk2651 ))]]) ).
thf(7795,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ ( sk6 @ B @ C ) @ A ) @ B ),
inference(cnf,[status(esa)],[7688]) ).
thf(7797,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( sup_su638957495lle_hf @ ( sk6 @ B @ C ) @ A ) @ B ),
inference(simp,[status(thm)],[7795]) ).
thf(72873,plain,
! [A: hF_Mirabelle_hf] :
( ~ ! [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
=> ( hF_Mir137170979_hpair @ B ) )
| ( sk2650 != zero_z189798548lle_hf )
| ( ( hF_Mir434065167lation @ A )
!= ( hF_Mir434065167lation @ x ) ) ),
inference(paramod_ordered,[status(thm)],[293,70476]) ).
thf(72874,plain,
( ~ ! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ x )
=> ( hF_Mir137170979_hpair @ A ) )
| ( sk2650 != zero_z189798548lle_hf ) ),
inference(pattern_uni,[status(thm)],[72873:[bind(A,$thf( x ))]]) ).
thf(72906,plain,
( ( sk2650 != zero_z189798548lle_hf )
| ~ ( hF_Mir137170979_hpair @ sk2828 ) ),
inference(cnf,[status(esa)],[72874]) ).
thf(38898,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( ( hF_Mirabelle_hmem @ sk1147 @ x )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[33027,188]) ).
thf(39064,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( sk1147 != A )
| ( ( hF_Mirabelle_HUnion @ A )
!= x ) ),
inference(simp,[status(thm)],[38898]) ).
thf(39216,plain,
( ~ ( hF_Mir199975595nction @ zero_z189798548lle_hf )
| ( ( hF_Mirabelle_HUnion @ sk1147 )
!= x ) ),
inference(simp,[status(thm)],[39064]) ).
thf(51593,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 @ sk1147 )
!= x )
| ( ( hF_Mir199975595nction @ A )
!= ( hF_Mir199975595nction @ zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[325,39216]) ).
thf(51594,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 @ sk1147 )
!= x ) ),
inference(pattern_uni,[status(thm)],[51593:[bind(A,$thf( zero_z189798548lle_hf ))]]) ).
thf(51632,plain,
( ( ( hF_Mirabelle_HUnion @ sk1147 )
!= x )
| ( sk2039 != sk2040 ) ),
inference(cnf,[status(esa)],[51594]) ).
thf(51635,plain,
( ( sk2040 != sk2039 )
| ( ( hF_Mirabelle_HUnion @ sk1147 )
!= x ) ),
inference(lifteq,[status(thm)],[51632]) ).
thf(26844,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ A )
!= ( hF_Mirabelle_hmem @ ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ r ) @ r ) )
| ( ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ ( hF_Mir818139703ollect @ hF_Mir434065167lation @ A ) )
!= ( hF_Mirabelle_hmem @ ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ r ) @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[26288,11658]) ).
thf(26995,plain,
! [A: hF_Mirabelle_hf] :
( ( ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ r )
!= zero_z189798548lle_hf )
| ( A != r )
| ( ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ r )
!= zero_z189798548lle_hf )
| ( ( hF_Mir818139703ollect @ hF_Mir434065167lation @ A )
!= ( hF_Mir1653039215strict @ r @ x ) ) ),
inference(simp,[status(thm)],[26844]) ).
thf(27099,plain,
( ( ( sk7 @ ( hF_Mir1653039215strict @ r @ x ) @ r )
!= zero_z189798548lle_hf )
| ( ( hF_Mir1653039215strict @ r @ x )
!= ( hF_Mir818139703ollect @ hF_Mir434065167lation @ r ) ) ),
inference(simp,[status(thm)],[26995]) ).
thf(532,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ? [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] :
( A
= ( hF_Mirabelle_hpair @ D @ E ) )
| ( ( hF_Mir137170979_hpair @ A )
!= ( hF_Mir137170979_hpair @ ( hF_Mirabelle_hpair @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[292,529]) ).
thf(533,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
? [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
= ( hF_Mirabelle_hpair @ C @ D ) ),
inference(pattern_uni,[status(thm)],[532:[bind(A,$thf( hF_Mirabelle_hpair @ D @ E )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(537,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
= ( hF_Mirabelle_hpair @ ( sk25 @ B @ A ) @ ( sk26 @ B @ A ) ) ),
inference(cnf,[status(esa)],[533]) ).
thf(538,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ ( sk25 @ B @ A ) @ ( sk26 @ B @ A ) )
= ( hF_Mirabelle_hpair @ A @ B ) ),
inference(lifteq,[status(thm)],[537]) ).
thf(539,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ ( sk25 @ B @ A ) @ ( sk26 @ B @ A ) )
= ( hF_Mirabelle_hpair @ A @ B ) ),
inference(simp,[status(thm)],[538]) ).
thf(214,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(cnf,[status(esa)],[212]) ).
thf(218,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)],[214]) ).
thf(24649,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)],[222,23826]) ).
thf(24650,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)],[24649:[]]) ).
thf(523,plain,
! [A: hF_Mirabelle_hf] :
( ( ( ? [B: hF_Mirabelle_hf] : ( hF_Mir137170979_hpair @ B ) )
= ( hF_Mir137170979_hpair @ A ) )
| ( ( ^ [B: hF_Mirabelle_hf] :
? [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( B
= ( hF_Mirabelle_hpair @ C @ D ) ) )
!= ( ^ [B: hF_Mirabelle_hf] :
? [C: hF_Mirabelle_hf] :
( A
= ( hF_Mirabelle_hpair @ B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[174,292]) ).
thf(524,plain,
! [A: hF_Mirabelle_hf] :
( ( ( ? [B: hF_Mirabelle_hf] : ( hF_Mir137170979_hpair @ B ) )
= ( hF_Mir137170979_hpair @ A ) )
| ( ( ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
? [D: hF_Mirabelle_hf] :
( B
= ( hF_Mirabelle_hpair @ C @ D ) ) )
!= ( ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( A
= ( hF_Mirabelle_hpair @ B @ C ) ) ) ) ),
inference(simp,[status(thm)],[523]) ).
thf(57779,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk20 @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) )
!= ( hF_Mirabelle_hpair @ A @ B ) )
| ( ( hF_Mirabelle_hpair @ sk2103 @ sk2104 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[54337,2031]) ).
thf(57780,plain,
( ( hF_Mirabelle_hpair @ sk2103 @ sk2104 )
!= ( sk20 @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) ) ),
inference(pattern_uni,[status(thm)],[57779:[bind(A,$thf( sk2103 )),bind(B,$thf( sk2104 ))]]) ).
thf(62906,plain,
( ( sk20 @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) )
!= ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) ),
inference(rewrite,[status(thm)],[57780,58529,58025]) ).
thf(1891,plain,
( ~ ( hF_Mir137170979_hpair @ sk40 )
| ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) ) ),
inference(cnf,[status(esa)],[1862]) ).
thf(2901,plain,
( ~ ( hF_Mir137170979_hpair @ sk40 )
| ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf ) )
!= ( hF_Mir199975595nction @ r ) ) ),
inference(paramod_ordered,[status(thm)],[287,1891]) ).
thf(2919,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ x ) )
| ~ ( hF_Mir137170979_hpair @ sk40 )
| ( ( hF_Mir1653039215strict @ r @ zero_z189798548lle_hf )
!= r ) ),
inference(simp,[status(thm)],[2901]) ).
thf(48327,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ sk1575 )
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ sk1901 @ x )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[48120,181]) ).
thf(48328,plain,
( ( hF_Mir137170979_hpair @ sk1575 )
| ~ ( hF_Mirabelle_hmem @ x @ sk1901 ) ),
inference(pattern_uni,[status(thm)],[48327:[bind(A,$thf( sk1901 )),bind(B,$thf( x ))]]) ).
thf(43388,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk6 @ A @ B ) @ B )
!= ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r ) ),
inference(paramod_ordered,[status(thm)],[43248,7831]) ).
thf(43552,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sk6 @ A @ B )
!= ( sk20 @ r ) )
| ( B != r ) ),
inference(simp,[status(thm)],[43388]) ).
thf(43611,plain,
! [A: hF_Mirabelle_hf] :
( ( sk6 @ A @ r )
!= ( sk20 @ r ) ),
inference(simp,[status(thm)],[43552]) ).
thf(933,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(paramod_ordered,[status(thm)],[863,79]) ).
thf(950,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)],[933]) ).
thf(961,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ zero_z189798548lle_hf )
!= zero_z189798548lle_hf ),
inference(simp,[status(thm)],[950]) ).
thf(21389,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ( ( hF_Mirabelle_hmem @ sk35 @ r )
!= ( hF_Mirabelle_hmem @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1856,178]) ).
thf(21424,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)],[21389]) ).
thf(21518,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
| ( sk35 != r ) ),
inference(simp,[status(thm)],[21424]) ).
thf(40193,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ sk1604 @ x )
!= ( hF_Mirabelle_hmem @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[40071,178]) ).
thf(40211,plain,
! [A: hF_Mirabelle_hf] :
( ( sk1604 != A )
| ( x != A ) ),
inference(simp,[status(thm)],[40193]) ).
thf(40316,plain,
sk1604 != x,
inference(simp,[status(thm)],[40211]) ).
thf(45723,plain,
sk1575 != x,
inference(rewrite,[status(thm)],[40316,45718]) ).
thf(24946,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)],[23872,11655]) ).
thf(25047,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)],[24946]) ).
thf(25237,plain,
( ( ( sk7 @ r @ ( hF_Mir1653039215strict @ r @ x ) )
!= r )
| ( ( sk15 @ hF_Mir199975595nction @ r )
!= ( hF_Mir1653039215strict @ r @ x ) ) ),
inference(simp,[status(thm)],[25047]) ).
thf(27204,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)],[26458,11655]) ).
thf(27376,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)],[27204]) ).
thf(27540,plain,
( ( ( sk7 @ r @ ( hF_Mir1653039215strict @ r @ x ) )
!= r )
| ( ( hF_Mir1653039215strict @ r @ x )
!= ( hF_Mir818139703ollect @ hF_Mir199975595nction @ r ) ) ),
inference(simp,[status(thm)],[27376]) ).
thf(74691,plain,
( ( ( hF_Mirabelle_hpair @ sk2650 @ sk2651 )
!= sk2650 )
| ( ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( sk20 @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[68430,74178]) ).
thf(74692,plain,
( ( hF_Mirabelle_hpair @ sk2650 @ sk2651 )
!= sk2650 ),
inference(pattern_uni,[status(thm)],[74691:[]]) ).
thf(54064,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[39643,178]) ).
thf(54115,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1575 @ sk1576 )
!= A )
| ( ( hF_Mir1653039215strict @ r @ x )
!= A ) ),
inference(simp,[status(thm)],[54064]) ).
thf(54248,plain,
( ( hF_Mir1653039215strict @ r @ x )
!= ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) ),
inference(simp,[status(thm)],[54115]) ).
thf(53974,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) @ ( hF_Mir1653039215strict @ r @ x ) )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ),
inference(paramod_ordered,[status(thm)],[39643,188]) ).
thf(54162,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1575 @ sk1576 )
!= A )
| ( ( hF_Mir1653039215strict @ r @ x )
!= ( hF_Mirabelle_HUnion @ A ) ) ),
inference(simp,[status(thm)],[53974]) ).
thf(54333,plain,
( ( hF_Mir1653039215strict @ r @ x )
!= ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) ) ),
inference(simp,[status(thm)],[54162]) ).
thf(14086,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 ) ) )
| $false ),
inference(prim_subst,[status(thm)],[218:[bind(A,$thf( A )),bind(B,$thf( ^ [D: hF_Mirabelle_hf] : ^ [E: hF_Mirabelle_hf] : $false ))]]) ).
thf(14508,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)],[14086]) ).
thf(14922,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(paramod_ordered,[status(thm)],[459,14508]) ).
thf(14923,plain,
! [A: hF_Mirabelle_hf] :
( ( sk11
@ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : $false
@ A )
= zero_z189798548lle_hf ),
inference(pattern_uni,[status(thm)],[14922:[bind(A,$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(14963,plain,
! [A: hF_Mirabelle_hf] :
( ( sk11
@ ^ [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] : $false
@ A )
= zero_z189798548lle_hf ),
inference(simp,[status(thm)],[14923]) ).
thf(330,plain,
! [F: hF_Mirabelle_hf,E: hF_Mirabelle_hf,D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ D @ ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ A @ C ) ) )
= ( sup_su638957495lle_hf @ E @ ( sup_su638957495lle_hf @ D @ F ) ) )
| ( ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ C ) )
!= ( sup_su638957495lle_hf @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[85,85]) ).
thf(331,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ A @ D ) ) )
= ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ D ) ) ) ),
inference(pattern_uni,[status(thm)],[330:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( H )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( sup_su638957495lle_hf @ G @ H ))]]) ).
thf(378,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ ( sup_su638957495lle_hf @ A @ D ) ) )
= ( sup_su638957495lle_hf @ A @ ( sup_su638957495lle_hf @ B @ ( sup_su638957495lle_hf @ C @ D ) ) ) ),
inference(simp,[status(thm)],[331]) ).
thf(206,plain,
! [C: hF_Mirabelle_hf > hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_RepFun @ B @ C ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ B )
& ( A
= ( C @ D ) ) ) ) ),
inference(cnf,[status(esa)],[205]) ).
thf(207,plain,
! [C: hF_Mirabelle_hf > hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_RepFun @ B @ C ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ B )
& ( A
= ( C @ D ) ) ) ) ),
inference(lifteq,[status(thm)],[206]) ).
thf(58535,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ A ) @ A )
| ( sk1576 = zero_z189798548lle_hf )
| ( A != sk2104 ) ),
inference(paramod_ordered,[status(thm)],[459,58529]) ).
thf(58536,plain,
( ( hF_Mirabelle_hmem @ ( sk20 @ sk2104 ) @ sk2104 )
| ( sk1576 = zero_z189798548lle_hf ) ),
inference(pattern_uni,[status(thm)],[58535:[bind(A,$thf( sk2104 ))]]) ).
thf(59869,plain,
( ( hF_Mirabelle_hmem @ ( sk20 @ sk1576 ) @ sk1576 )
| ( sk1576 = zero_z189798548lle_hf ) ),
inference(rewrite,[status(thm)],[58536,58529]) ).
thf(530,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ? [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] :
( C
= ( hF_Mirabelle_hpair @ D @ E ) )
| ( ( hF_Mir137170979_hpair @ ( hF_Mirabelle_hpair @ A @ B ) )
!= ( hF_Mir137170979_hpair @ C ) ) ),
inference(paramod_ordered,[status(thm)],[529,292]) ).
thf(531,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
? [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
= ( hF_Mirabelle_hpair @ C @ D ) ),
inference(pattern_uni,[status(thm)],[530:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( hF_Mirabelle_hpair @ D @ E ))]]) ).
thf(534,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
= ( hF_Mirabelle_hpair @ ( sk23 @ B @ A ) @ ( sk24 @ B @ A ) ) ),
inference(cnf,[status(esa)],[531]) ).
thf(535,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ ( sk23 @ B @ A ) @ ( sk24 @ B @ A ) )
= ( hF_Mirabelle_hpair @ A @ B ) ),
inference(lifteq,[status(thm)],[534]) ).
thf(536,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ ( sk23 @ B @ A ) @ ( sk24 @ B @ A ) )
= ( hF_Mirabelle_hpair @ A @ B ) ),
inference(simp,[status(thm)],[535]) ).
thf(21614,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ( sk35 != r )
| ( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x ) )
!= ( hF_Mir199975595nction @ r ) ) ),
inference(paramod_ordered,[status(thm)],[287,21518]) ).
thf(21658,plain,
( ( hF_Mir137170979_hpair @ ( sk20 @ r ) )
| ( sk35 != r )
| ( ( hF_Mir1653039215strict @ zero_z189798548lle_hf @ x )
!= r ) ),
inference(simp,[status(thm)],[21614]) ).
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/sandbox2/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(43383,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( sk20 @ r ) @ r )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ),
inference(paramod_ordered,[status(thm)],[43248,188]) ).
thf(43533,plain,
! [A: hF_Mirabelle_hf] :
( ( ( sk20 @ r )
!= A )
| ( ( hF_Mirabelle_HUnion @ A )
!= r ) ),
inference(simp,[status(thm)],[43383]) ).
thf(43578,plain,
( ( hF_Mirabelle_HUnion @ ( sk20 @ r ) )
!= r ),
inference(simp,[status(thm)],[43533]) ).
thf(44714,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1575 @ sk1577 )
!= A )
| ( ( hF_Mirabelle_hpair @ sk1604 @ sk1605 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[40074,261]) ).
thf(44715,plain,
( ( hF_Mirabelle_hpair @ sk1575 @ sk1577 )
!= sk1604 ),
inference(pattern_uni,[status(thm)],[44714:[bind(A,$thf( sk1604 )),bind(B,$thf( sk1605 ))]]) ).
thf(45721,plain,
( ( hF_Mirabelle_hpair @ sk1575 @ sk1577 )
!= sk1575 ),
inference(rewrite,[status(thm)],[44715,45718]) ).
thf(45727,plain,
~ ( hF_Mirabelle_hmem @ x @ sk1575 ),
inference(rewrite,[status(thm)],[40133,45718]) ).
thf(53190,plain,
! [C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( sup_su638957495lle_hf @ A @ B )
!= zero_z189798548lle_hf )
| ( ( sup_su638957495lle_hf @ B @ A )
!= ( sup_su638957495lle_hf @ x @ C ) ) ),
inference(paramod_ordered,[status(thm)],[289,51584]) ).
thf(53191,plain,
! [A: hF_Mirabelle_hf] :
( ( sup_su638957495lle_hf @ A @ x )
!= zero_z189798548lle_hf ),
inference(pattern_uni,[status(thm)],[53190:[bind(A,$thf( A )),bind(B,$thf( x )),bind(C,$thf( A ))]]) ).
thf(26880,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)],[222,26288]) ).
thf(26881,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)],[26880:[]]) ).
thf(56016,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) @ r )
!= ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ A ) ) ),
inference(paramod_ordered,[status(thm)],[54336,188]) ).
thf(56162,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1575 @ sk1576 )
!= A )
| ( ( hF_Mirabelle_HUnion @ A )
!= r ) ),
inference(simp,[status(thm)],[56016]) ).
thf(56308,plain,
( ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) )
!= r ),
inference(simp,[status(thm)],[56162]) ).
thf(948,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(paramod_ordered,[status(thm)],[863,178]) ).
thf(949,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)],[948]) ).
thf(960,plain,
! [A: hF_Mirabelle_hf] :
( ( sk20 @ ( hF_Mirabelle_hpair @ A @ zero_z189798548lle_hf ) )
!= ( hF_Mirabelle_hpair @ A @ zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[949]) ).
thf(236,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(cnf,[status(esa)],[235]) ).
thf(238,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)],[236]) ).
thf(239,plain,
! [C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,A: hF_Mirabelle_hf] :
( ( ( B @ ( sk13 @ C @ B @ A @ A ) @ ( sk14 @ C @ B @ A @ A ) )
!= ( C @ ( sk13 @ C @ B @ A @ A ) @ ( sk14 @ C @ B @ A @ A ) ) )
| ( ( hF_Mirabelle_Replace @ A @ B )
= ( hF_Mirabelle_Replace @ A @ C ) ) ),
inference(simp,[status(thm)],[238]) ).
thf(4164,plain,
! [D: hF_Mirabelle_hf,C: hF_Mirabelle_hf,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ B ) ) ) @ ( hF_Mirabelle_HUnion @ C ) )
| ( ( sup_su638957495lle_hf @ ( hF_Mirabelle_HUnion @ A ) @ ( hF_Mirabelle_HUnion @ B ) )
!= ( sup_su638957495lle_hf @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[162,3302]) ).
thf(4165,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_HUnion @ ( sup_su638957495lle_hf @ A @ B ) ) ) @ ( hF_Mirabelle_HUnion @ ( hF_Mirabelle_HUnion @ A ) ) ),
inference(pattern_uni,[status(thm)],[4164:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( hF_Mirabelle_HUnion @ E )),bind(D,$thf( hF_Mirabelle_HUnion @ F ))]]) ).
thf(4193,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)],[4165]) ).
thf(39641,plain,
sk1576 != sk1577,
inference(cnf,[status(esa)],[39420]) ).
thf(39644,plain,
sk1577 != sk1576,
inference(lifteq,[status(thm)],[39641]) ).
thf(70140,plain,
( ( sk1770 != x )
| ( ( hF_Mir137170979_hpair @ sk1575 )
!= ( hF_Mir137170979_hpair @ zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[49156,70122]) ).
thf(70168,plain,
( ( sk1770 != x )
| ( sk1575 != zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[70140]) ).
thf(56094,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ sk1575 @ sk1576 ) @ r )
!= ( hF_Mirabelle_hmem @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[54336,178]) ).
thf(56169,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1575 @ sk1576 )
!= A )
| ( r != A ) ),
inference(simp,[status(thm)],[56094]) ).
thf(56324,plain,
( ( hF_Mirabelle_hpair @ sk1575 @ sk1576 )
!= r ),
inference(simp,[status(thm)],[56169]) ).
thf(560,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mir137170979_hpair @ ( sk27 @ A ) )
| ( hF_Mir434065167lation @ A ) ),
inference(cnf,[status(esa)],[541]) ).
thf(56518,plain,
( ~ ( hF_Mir137170979_hpair @ sk2204 )
| ( hF_Mir137170979_hpair @ sk2105 ) ),
inference(cnf,[status(esa)],[56459]) ).
thf(58805,plain,
( ~ ( hF_Mir137170979_hpair @ sk2204 )
| ( hF_Mir137170979_hpair @ sk1575 ) ),
inference(rewrite,[status(thm)],[56518,58800]) ).
thf(57793,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ sk1575 @ sk1576 )
!= A )
| ( ( hF_Mirabelle_hpair @ sk2103 @ sk2104 )
!= ( hF_Mirabelle_hpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[54337,261]) ).
thf(57794,plain,
( ( hF_Mirabelle_hpair @ sk1575 @ sk1576 )
!= sk2103 ),
inference(pattern_uni,[status(thm)],[57793:[bind(A,$thf( sk2103 )),bind(B,$thf( sk2104 ))]]) ).
thf(58029,plain,
( ( hF_Mirabelle_hpair @ sk1575 @ sk1576 )
!= sk1575 ),
inference(rewrite,[status(thm)],[57794,58025]) ).
thf(60993,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( sk1526 != sk1525 )
| ~ ( hF_Mirabelle_hmem @ B @ A )
| ( ( hF_Mirabelle_hmem @ sk1147 @ x )
!= ( hF_Mirabelle_hmem @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[39566,181]) ).
thf(60994,plain,
( ( sk1526 != sk1525 )
| ~ ( hF_Mirabelle_hmem @ x @ sk1147 ) ),
inference(pattern_uni,[status(thm)],[60993:[bind(A,$thf( sk1147 )),bind(B,$thf( x ))]]) ).
thf(226,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)],[225]) ).
thf(227,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)],[226]) ).
thf(80117,plain,
$false,
inference(e,[status(thm)],[69,23872,1024,138,2031,518,962,234,88,74178,41726,249,43683,7798,170,6587,115,41694,70171,41398,2676,449,40493,1855,45722,217,276,120,70178,22470,63103,269,202,43248,76022,2035,68582,69811,4856,43185,68700,174,185,41825,50642,288,320,74266,7364,45719,48723,257,184,22730,66053,157,51498,559,189,870,58827,93,284,325,289,68772,25336,261,41469,1892,27472,47637,53162,228,3199,179,443,39643,74167,211,106,77343,121,45726,1283,397,48120,280,1215,293,42883,396,48715,43674,58066,507,51348,50198,51584,75267,221,63505,133,35051,70182,73626,74245,7830,78748,23304,50947,292,233,248,117,2204,2646,58803,48119,74261,220,102,73092,68429,270,529,78749,41434,85,201,62179,160,561,192,2606,137,165,39962,49156,41669,33031,3282,252,3198,97,62651,53984,58027,285,224,62199,578,45720,74194,78754,48609,1856,169,48504,61184,64793,58030,188,47636,68840,141,225,77,65857,686,4938,96,109,328,43123,526,49207,74230,45725,129,3115,569,25175,39642,68430,173,62865,52488,134,105,2203,61313,62777,24822,205,1026,11655,7831,279,70496,50737,50473,51479,33027,166,57807,191,74243,3240,48706,46743,286,43733,70122,291,39952,118,281,204,40349,66162,68694,3302,71,43061,181,70476,86,159,43713,172,2538,219,274,66689,41696,230,64873,245,56026,3197,208,76,567,52568,552,103,91,58740,69809,198,72411,39123,40073,130,399,2171,59366,223,135,70180,267,39708,39960,68491,74216,48733,38910,241,78746,80,162,255,112,516,68453,123,553,145,63691,65826,68695,52613,41649,58817,44726,70495,282,150,409,1025,295,78753,68722,48713,74233,70173,59306,199,3114,182,441,50154,24837,58530,27073,39566,68267,45718,73298,44910,72,2030,571,143,2675,23826,154,74228,7797,175,72906,231,51635,3139,27099,5653,556,539,87,46692,218,24650,524,3548,581,62906,2919,48328,43611,961,43393,258,21518,45723,25237,171,27540,74692,54248,54333,14963,26288,378,246,207,11658,52252,272,59869,536,21658,69511,71368,287,151,146,43578,45721,45727,273,53191,43360,262,58800,26881,56308,1891,960,94,2549,210,26458,239,242,294,126,58025,4193,58529,459,39644,54336,68,178,277,70168,163,200,90,56324,50951,83,68427,560,58805,3200,222,58029,100,60994,254,227,39216,42597]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ITP076^1 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n028.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Mon May 6 14:28:09 EDT 2024
% 0.17/0.38 % CPUTime :
% 0.98/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.85/1.11 % [INFO] Parsing done (240ms).
% 1.85/1.12 % [INFO] Running in sequential loop mode.
% 2.45/1.34 % [INFO] eprover registered as external prover.
% 2.45/1.34 % [INFO] cvc4 registered as external prover.
% 2.45/1.34 % [INFO] Scanning for conjecture ...
% 2.61/1.42 % [INFO] Found a conjecture and 355 axioms. Running axiom selection ...
% 2.90/1.48 % [INFO] Axiom selection finished. Selected 65 axioms (removed 290 axioms).
% 3.15/1.56 % [INFO] Problem is higher-order (TPTP THF).
% 3.15/1.57 % [INFO] Type checking passed.
% 3.15/1.58 % [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 ...
% 221.51/38.43 % External prover 'e' found a proof!
% 221.51/38.44 % [INFO] Killing All external provers ...
% 221.51/38.44 % Time passed: 37900ms (effective reasoning time: 37312ms)
% 221.51/38.44 % 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)>
% 221.51/38.44 % 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
% 221.51/38.44 % No. of inferences in proof: 1115
% 221.51/38.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 37900 ms resp. 37312 ms w/o parsing
% 222.35/38.61 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 222.46/38.62 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------