%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP138^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:54 AM UTC 2026
% Result : Theorem 22.63s 6.24s
% Output : Refutation 23.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 353
% Syntax : Number of formulae : 708 ( 306 unt; 0 typ; 0 def)
% Number of atoms : 1986 ( 721 equ; 16 cnn)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 5927 ( 196 ~; 0 |; 168 &;4682 @)
% ( 0 <=>; 881 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 13 ( 12 usr)
% Number of type conns : 582 ( 582 >; 0 *; 0 +; 0 <<)
% Number of symbols : 71 ( 67 usr; 11 con; 0-2 aty)
% Number of variables : 2291 ( 247 ^;1996 !; 48 ?;2291 :)
% Comments :
%------------------------------------------------------------------------------
thf(produc696645085lle_fm_type,type,
produc696645085lle_fm: $tType ).
thf(set_se800614875lle_tv_type,type,
set_se800614875lle_tv: $tType ).
thf(set_set_list_char_type,type,
set_set_list_char: $tType ).
thf(set_Pa1764573435lle_tv_type,type,
set_Pa1764573435lle_tv: $tType ).
thf(set_list_char_type,type,
set_list_char: $tType ).
thf(paraco1605129243lle_tv_type,type,
paraco1605129243lle_tv: $tType ).
thf(paraco1604210848lle_fm_type,type,
paraco1604210848lle_fm: $tType ).
thf(set_set_o_type,type,
set_set_o: $tType ).
thf(list_char_type,type,
list_char: $tType ).
thf(set_nat_type,type,
set_nat: $tType ).
thf(set_o_type,type,
set_o: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(complete_Sup_Sup_o_decl,type,
complete_Sup_Sup_o: set_o > $o ).
thf(finite_Fpow_o_decl,type,
finite_Fpow_o: set_o > set_set_o ).
thf(finite1803457147t_char_decl,type,
finite1803457147t_char: set_list_char > set_set_list_char ).
thf(finite2011762305lle_tv_decl,type,
finite2011762305lle_tv: set_Pa1764573435lle_tv > set_se800614875lle_tv ).
thf(ord_less_eq_o_o_decl,type,
ord_less_eq_o_o: ( $o > $o ) > ( $o > $o ) > $o ).
thf(ord_le1945897678char_o_decl,type,
ord_le1945897678char_o: ( list_char > $o ) > ( list_char > $o ) > $o ).
thf(ord_le1632188418e_tv_o_decl,type,
ord_le1632188418e_tv_o: ( paraco1605129243lle_tv > $o ) > ( paraco1605129243lle_tv > $o ) > $o ).
thf(ord_less_eq_set_o_decl,type,
ord_less_eq_set_o: set_o > set_o > $o ).
thf(ord_le1836582007t_char_decl,type,
ord_le1836582007t_char: set_list_char > set_list_char > $o ).
thf(ord_less_eq_set_nat_decl,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(ord_le241064091lle_tv_decl,type,
ord_le241064091lle_tv: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > $o ).
thf(ord_le2085948664_set_o_decl,type,
ord_le2085948664_set_o: set_set_o > set_set_o > $o ).
thf(ord_le263913851lle_tv_decl,type,
ord_le263913851lle_tv: set_se800614875lle_tv > set_se800614875lle_tv > $o ).
thf(order_Greatest_set_o_decl,type,
order_Greatest_set_o: ( set_o > $o ) > set_o ).
thf(order_350719188lle_tv_decl,type,
order_350719188lle_tv: ( set_Pa1764573435lle_tv > $o ) > set_Pa1764573435lle_tv ).
thf(top_top_o_o_decl,type,
top_top_o_o: $o > $o ).
thf(top_top_list_char_o_decl,type,
top_top_list_char_o: list_char > $o ).
thf(top_top_nat_o_decl,type,
top_top_nat_o: nat > $o ).
thf(top_to1299250770e_tv_o_decl,type,
top_to1299250770e_tv_o: paraco1605129243lle_tv > $o ).
thf(top_top_set_o_decl,type,
top_top_set_o: set_o ).
thf(top_to748628679t_char_decl,type,
top_to748628679t_char: set_list_char ).
thf(top_top_set_nat_decl,type,
top_top_set_nat: set_nat ).
thf(top_to1057771083lle_tv_decl,type,
top_to1057771083lle_tv: set_Pa1764573435lle_tv ).
thf(top_top_set_set_o_decl,type,
top_top_set_set_o: set_set_o ).
thf(top_to697846397t_char_decl,type,
top_to697846397t_char: set_set_list_char ).
thf(paraco1933902578domain_decl,type,
paraco1933902578domain: set_nat > set_Pa1764573435lle_tv ).
thf(paraco1325918602e_eval_decl,type,
paraco1325918602e_eval: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > paraco1605129243lle_tv ).
thf(paraco69239110le_Con_decl,type,
paraco69239110le_Con: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(paraco1389086619le_Eql_decl,type,
paraco1389086619le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(paraco1745535428le_Eql_decl,type,
paraco1745535428le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(paraco445776468le_Neg_decl,type,
paraco445776468le_Neg: paraco1604210848lle_fm > paraco1604210848lle_fm ).
thf(paraco1480028776le_Pro_decl,type,
paraco1480028776le_Pro: list_char > paraco1604210848lle_fm ).
thf(paraco367965286_Truth_decl,type,
paraco367965286_Truth: paraco1604210848lle_fm ).
thf(paraco1344940915le_Det_decl,type,
paraco1344940915le_Det: $o > paraco1605129243lle_tv ).
thf(paraco327635598_valid_decl,type,
paraco327635598_valid: paraco1604210848lle_fm > $o ).
thf(paraco55203475lid_in_decl,type,
paraco55203475lid_in: set_nat > paraco1604210848lle_fm > $o ).
thf(produc1710735575lle_fm_decl,type,
produc1710735575lle_fm: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > produc696645085lle_fm ).
thf(collect_o_decl,type,
collect_o: ( $o > $o ) > set_o ).
thf(collect_list_char_decl,type,
collect_list_char: ( list_char > $o ) > set_list_char ).
thf(collect_nat_decl,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(collec1111687558lle_tv_decl,type,
collec1111687558lle_tv: ( paraco1605129243lle_tv > $o ) > set_Pa1764573435lle_tv ).
thf(pow_o_decl,type,
pow_o: set_o > set_set_o ).
thf(pow_list_char_decl,type,
pow_list_char: set_list_char > set_set_list_char ).
thf(pow_Pa475453624lle_tv_decl,type,
pow_Pa475453624lle_tv: set_Pa1764573435lle_tv > set_se800614875lle_tv ).
thf(image_o_o_decl,type,
image_o_o: ( $o > $o ) > set_o > set_o ).
thf(image_o_list_char_decl,type,
image_o_list_char: ( $o > list_char ) > set_o > set_list_char ).
thf(image_o_nat_decl,type,
image_o_nat: ( $o > nat ) > set_o > set_nat ).
thf(image_1491822472lle_tv_decl,type,
image_1491822472lle_tv: ( $o > paraco1605129243lle_tv ) > set_o > set_Pa1764573435lle_tv ).
thf(image_list_char_o_decl,type,
image_list_char_o: ( list_char > $o ) > set_list_char > set_o ).
thf(image_890964937t_char_decl,type,
image_890964937t_char: ( list_char > list_char ) > set_list_char > set_list_char ).
thf(image_1187894195lle_tv_decl,type,
image_1187894195lle_tv: ( list_char > paraco1605129243lle_tv ) > set_list_char > set_Pa1764573435lle_tv ).
thf(image_nat_o_decl,type,
image_nat_o: ( nat > $o ) > set_nat > set_o ).
thf(image_nat_list_char_decl,type,
image_nat_list_char: ( nat > list_char ) > set_nat > set_list_char ).
thf(image_nat_nat_decl,type,
image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
thf(image_1151963140lle_tv_decl,type,
image_1151963140lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > set_Pa1764573435lle_tv ).
thf(image_991799618e_tv_o_decl,type,
image_991799618e_tv_o: ( paraco1605129243lle_tv > $o ) > set_Pa1764573435lle_tv > set_o ).
thf(image_1971766583t_char_decl,type,
image_1971766583t_char: ( paraco1605129243lle_tv > list_char ) > set_Pa1764573435lle_tv > set_list_char ).
thf(image_376325286tv_nat_decl,type,
image_376325286tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > set_nat ).
thf(image_335818702lle_tv_decl,type,
image_335818702lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ).
thf(image_set_o_set_o_decl,type,
image_set_o_set_o: ( set_o > set_o ) > set_set_o > set_set_o ).
thf(image_30320477lle_tv_decl,type,
image_30320477lle_tv: ( set_list_char > set_Pa1764573435lle_tv ) > set_set_list_char > set_se800614875lle_tv ).
thf(member_o_decl,type,
member_o: $o > set_o > $o ).
thf(member_list_char_decl,type,
member_list_char: list_char > set_list_char > $o ).
thf(member_nat_decl,type,
member_nat: nat > set_nat > $o ).
thf(member266900804lle_tv_decl,type,
member266900804lle_tv: paraco1605129243lle_tv > set_Pa1764573435lle_tv > $o ).
thf(member1875402276lle_tv_decl,type,
member1875402276lle_tv: set_Pa1764573435lle_tv > set_se800614875lle_tv > $o ).
thf(p_decl,type,
p: paraco1604210848lle_fm ).
thf(65,axiom,
! [A: list_char,B: list_char > $o] :
( ( member_list_char @ A @ ( collect_list_char @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_mem__Collect__eq) ).
thf(892,plain,
! [A: list_char,B: list_char > $o] :
( ( member_list_char @ A @ ( collect_list_char @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(90,axiom,
! [A: $o > list_char,B: $o] : ( member_list_char @ ( A @ B ) @ ( image_o_list_char @ A @ top_top_set_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_rangeI) ).
thf(1036,plain,
! [A: $o > list_char,B: $o] : ( member_list_char @ ( A @ B ) @ ( image_o_list_char @ A @ top_top_set_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(49,axiom,
! [A: $o > $o,B: $o] :
( ( ( image_o_o @ A @ top_top_set_o )
= top_top_set_o )
=> ? [C: $o] :
( B
= ( A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_surjD) ).
thf(629,plain,
! [A: $o > $o,B: $o] :
( ( ( image_o_o @ A @ top_top_set_o )
= top_top_set_o )
=> ? [C: $o] :
( B
= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(217,axiom,
( top_to748628679t_char
= ( collect_list_char @ top_top_list_char_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_top__set__def) ).
thf(1823,plain,
( top_to748628679t_char
= ( collect_list_char @ top_top_list_char_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(112,axiom,
! [A: $o,B: $o > $o,C: set_o] :
( ( member_o @ A @ ( image_o_o @ B @ C ) )
=> ~ ! [D: $o] :
( ( A
= ( B @ D ) )
=> ~ ( member_o @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_imageE) ).
thf(1168,plain,
! [A: $o,B: $o > $o,C: set_o] :
( ( member_o @ A @ ( image_o_o @ B @ C ) )
=> ~ ! [D: $o] :
( ( A
= ( B @ D ) )
=> ~ ( member_o @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(287,axiom,
( ord_le241064091lle_tv
= ( ^ [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
! [C: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ C @ A )
=> ( member266900804lle_tv @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_subset__eq) ).
thf(2109,plain,
( ord_le241064091lle_tv
= ( ^ [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
! [C: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ C @ A )
=> ( member266900804lle_tv @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(135,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( ( paraco1389086619le_Eql @ A @ B )
= ( paraco1389086619le_Eql @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_fm_Oinject_I4_J) ).
thf(1315,plain,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( ( paraco1389086619le_Eql @ A @ B )
= ( paraco1389086619le_Eql @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(39,axiom,
( ( (=) @ set_o )
= ( ^ [A: set_o,B: set_o] :
( ( ord_less_eq_set_o @ A @ B )
& ( ord_less_eq_set_o @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_eq__iff) ).
thf(555,plain,
( ( (=) @ set_o )
= ( ^ [A: set_o,B: set_o] :
( ( ord_less_eq_set_o @ A @ B )
& ( ord_less_eq_set_o @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(52,axiom,
! [A: set_o,B: set_o,C: set_o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( ord_less_eq_set_o @ C @ A )
=> ( ord_less_eq_set_o @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_dual__order_Otrans) ).
thf(666,plain,
! [A: set_o,B: set_o,C: set_o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( ord_less_eq_set_o @ C @ A )
=> ( ord_less_eq_set_o @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(282,axiom,
! [A: list_char > paraco1605129243lle_tv,B: list_char] : ( member266900804lle_tv @ ( A @ B ) @ ( image_1187894195lle_tv @ A @ top_to748628679t_char ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_rangeI) ).
thf(2094,plain,
! [A: list_char > paraco1605129243lle_tv,B: list_char] : ( member266900804lle_tv @ ( A @ B ) @ ( image_1187894195lle_tv @ A @ top_to748628679t_char ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(145,axiom,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > list_char,C: set_list_char] :
( ! [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ A )
=> ( member_list_char @ ( B @ D ) @ C ) )
=> ( ord_le1836582007t_char @ ( image_1971766583t_char @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_image__subsetI) ).
thf(1411,plain,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > list_char,C: set_list_char] :
( ! [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ A )
=> ( member_list_char @ ( B @ D ) @ C ) )
=> ( ord_le1836582007t_char @ ( image_1971766583t_char @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(81,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco445776468le_Neg @ A )
!= ( paraco1389086619le_Eql @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_fm_Odistinct_I21_J) ).
thf(962,plain,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco445776468le_Neg @ A )
!= ( paraco1389086619le_Eql @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(254,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ord_le263913851lle_tv @ ( finite2011762305lle_tv @ A ) @ ( finite2011762305lle_tv @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_Fpow__mono) ).
thf(1982,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ord_le263913851lle_tv @ ( finite2011762305lle_tv @ A ) @ ( finite2011762305lle_tv @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(276,axiom,
! [A: paraco1605129243lle_tv > $o,B: paraco1605129243lle_tv > $o] :
( ! [C: paraco1605129243lle_tv] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le241064091lle_tv @ ( collec1111687558lle_tv @ A ) @ ( collec1111687558lle_tv @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_Collect__mono) ).
thf(2077,plain,
! [A: paraco1605129243lle_tv > $o,B: paraco1605129243lle_tv > $o] :
( ! [C: paraco1605129243lle_tv] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le241064091lle_tv @ ( collec1111687558lle_tv @ A ) @ ( collec1111687558lle_tv @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(241,axiom,
( ( (=) @ set_Pa1764573435lle_tv )
= ( ^ [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
& ( ord_le241064091lle_tv @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_eq__iff) ).
thf(1924,plain,
( ( (=) @ set_Pa1764573435lle_tv )
= ( ^ [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
& ( ord_le241064091lle_tv @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(143,axiom,
! [A: set_o] : ( ord_less_eq_set_o @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_dual__order_Orefl) ).
thf(1406,plain,
! [A: set_o] : ( ord_less_eq_set_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(162,axiom,
( ( (=) @ set_o )
= ( ^ [A: set_o,B: set_o] :
( ( ord_less_eq_set_o @ A @ B )
& ( ord_less_eq_set_o @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_set__eq__subset) ).
thf(1522,plain,
( ( (=) @ set_o )
= ( ^ [A: set_o,B: set_o] :
( ( ord_less_eq_set_o @ A @ B )
& ( ord_less_eq_set_o @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(322,axiom,
! [A: list_char > $o,B: $o] :
( ( ( image_list_char_o @ A @ top_to748628679t_char )
= top_top_set_o )
=> ? [C: list_char] :
( B
= ( A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_surjD) ).
thf(2248,plain,
! [A: list_char > $o,B: $o] :
( ( ( image_list_char_o @ A @ top_to748628679t_char )
= top_top_set_o )
=> ? [C: list_char] :
( B
= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(192,axiom,
! [A: set_nat] :
( ( collect_nat
@ ^ [B: nat] : ( member_nat @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_Collect__mem__eq) ).
thf(1728,plain,
! [A: set_nat] :
( ( collect_nat
@ ^ [B: nat] : ( member_nat @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(289,axiom,
! [A: set_Pa1764573435lle_tv,B: $o > paraco1605129243lle_tv,C: set_o] :
( ( ord_le241064091lle_tv @ A @ ( image_1491822472lle_tv @ B @ C ) )
=> ~ ! [D: set_o] :
( ( ord_less_eq_set_o @ D @ C )
=> ( A
!= ( image_1491822472lle_tv @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_subset__imageE) ).
thf(2114,plain,
! [A: set_Pa1764573435lle_tv,B: $o > paraco1605129243lle_tv,C: set_o] :
( ( ord_le241064091lle_tv @ A @ ( image_1491822472lle_tv @ B @ C ) )
=> ~ ! [D: set_o] :
( ( ord_less_eq_set_o @ D @ C )
=> ( A
!= ( image_1491822472lle_tv @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(62,axiom,
! [A: set_o,B: set_o,C: $o > $o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( ord_less_eq_set_o @ A
@ ( collect_o
@ ^ [D: $o] :
( ( member_o @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: $o] :
( ( member_o @ D @ A )
=> ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_subset__Collect__iff) ).
thf(878,plain,
! [A: set_o,B: set_o,C: $o > $o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( ord_less_eq_set_o @ A
@ ( collect_o
@ ^ [D: $o] :
( ( member_o @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: $o] :
( ( member_o @ D @ A )
=> ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(32,axiom,
! [A: paraco1605129243lle_tv] : ( member266900804lle_tv @ A @ top_to1057771083lle_tv ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_iso__tuple__UNIV__I) ).
thf(523,plain,
! [A: paraco1605129243lle_tv] : ( member266900804lle_tv @ A @ top_to1057771083lle_tv ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(336,axiom,
! [A: nat > $o,B: nat > $o] :
( ! [C: nat] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_nat @ A )
= ( collect_nat @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_Collect__cong) ).
thf(2309,plain,
! [A: nat > $o,B: nat > $o] :
( ! [C: nat] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_nat @ A )
= ( collect_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(113,axiom,
! [A: set_o,B: $o > list_char,C: set_list_char] :
( ! [D: $o] :
( ( member_o @ D @ A )
=> ( member_list_char @ ( B @ D ) @ C ) )
=> ( ord_le1836582007t_char @ ( image_o_list_char @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_image__subsetI) ).
thf(1205,plain,
! [A: set_o,B: $o > list_char,C: set_list_char] :
( ! [D: $o] :
( ( member_o @ D @ A )
=> ( member_list_char @ ( B @ D ) @ C ) )
=> ( ord_le1836582007t_char @ ( image_o_list_char @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(14,axiom,
! [A: list_char > $o,B: set_list_char,C: $o > $o] :
( ( collect_o
@ ^ [D: $o] :
( ( member_o @ D @ ( image_list_char_o @ A @ B ) )
& ( C @ D ) ) )
= ( image_list_char_o @ A
@ ( collect_list_char
@ ^ [D: list_char] :
( ( member_list_char @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_Compr__image__eq) ).
thf(449,plain,
! [A: list_char > $o,B: set_list_char,C: $o > $o] :
( ( collect_o
@ ^ [D: $o] :
( ( member_o @ D @ ( image_list_char_o @ A @ B ) )
& ( C @ D ) ) )
= ( image_list_char_o @ A
@ ( collect_list_char
@ ^ [D: list_char] :
( ( member_list_char @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(284,axiom,
! [A: list_char > paraco1605129243lle_tv] :
( ( ( image_1187894195lle_tv @ A @ top_to748628679t_char )
= top_to1057771083lle_tv )
= ( ! [B: paraco1605129243lle_tv] :
? [C: list_char] :
( B
= ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_surj__def) ).
thf(2099,plain,
! [A: list_char > paraco1605129243lle_tv] :
( ( ( image_1187894195lle_tv @ A @ top_to748628679t_char )
= top_to1057771083lle_tv )
= ( ! [B: paraco1605129243lle_tv] :
? [C: list_char] :
( B
= ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(330,axiom,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv,C: set_Pa1764573435lle_tv] :
( ! [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ A )
=> ( member266900804lle_tv @ ( B @ D ) @ C ) )
=> ( ord_le241064091lle_tv @ ( image_335818702lle_tv @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_image__subsetI) ).
thf(2282,plain,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv,C: set_Pa1764573435lle_tv] :
( ! [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ A )
=> ( member266900804lle_tv @ ( B @ D ) @ C ) )
=> ( ord_le241064091lle_tv @ ( image_335818702lle_tv @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(10,axiom,
! [A: $o,B: $o > $o,C: $o] :
( ( A
= ( B @ C ) )
=> ( member_o @ A @ ( image_o_o @ B @ top_top_set_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_range__eqI) ).
thf(385,plain,
! [A: $o,B: $o > $o,C: $o] :
( ( A
= ( B @ C ) )
=> ( member_o @ A @ ( image_o_o @ B @ top_top_set_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(27,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( paraco1389086619le_Eql @ A @ B )
!= ( paraco1745535428le_Eql @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_fm_Odistinct_I29_J) ).
thf(500,plain,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( paraco1389086619le_Eql @ A @ B )
!= ( paraco1745535428le_Eql @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(36,axiom,
! [A: list_char,B: set_list_char,C: list_char > $o] :
( ( member_list_char @ A @ B )
=> ( member_o @ ( C @ A ) @ ( image_list_char_o @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_imageI) ).
thf(538,plain,
! [A: list_char,B: set_list_char,C: list_char > $o] :
( ( member_list_char @ A @ B )
=> ( member_o @ ( C @ A ) @ ( image_list_char_o @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(199,axiom,
! [A: list_char > $o] :
( ( ( image_list_char_o @ A @ top_to748628679t_char )
= top_top_set_o )
= ( ! [B: $o] :
? [C: list_char] :
( B
= ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_surj__def) ).
thf(1756,plain,
! [A: list_char > $o] :
( ( ( image_list_char_o @ A @ top_to748628679t_char )
= top_top_set_o )
= ( ! [B: $o] :
? [C: list_char] :
( B
= ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(133,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv > $o] :
( ( collec1111687558lle_tv
@ ^ [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ ( image_335818702lle_tv @ A @ B ) )
& ( C @ D ) ) )
= ( image_335818702lle_tv @ A
@ ( collec1111687558lle_tv
@ ^ [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_Compr__image__eq) ).
thf(1310,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv > $o] :
( ( collec1111687558lle_tv
@ ^ [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ ( image_335818702lle_tv @ A @ B ) )
& ( C @ D ) ) )
= ( image_335818702lle_tv @ A
@ ( collec1111687558lle_tv
@ ^ [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(35,axiom,
! [A: list_char,B: set_list_char,C: $o,D: list_char > $o] :
( ( member_list_char @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member_o @ C @ ( image_list_char_o @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_rev__image__eqI) ).
thf(533,plain,
! [A: list_char,B: set_list_char,C: $o,D: list_char > $o] :
( ( member_list_char @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member_o @ C @ ( image_list_char_o @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(314,axiom,
! [A: $o > nat,B: set_o,C: nat > $o] :
( ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ ( image_o_nat @ A @ B ) )
& ( C @ D ) ) )
= ( image_o_nat @ A
@ ( collect_o
@ ^ [D: $o] :
( ( member_o @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_Compr__image__eq) ).
thf(2216,plain,
! [A: $o > nat,B: set_o,C: nat > $o] :
( ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ ( image_o_nat @ A @ B ) )
& ( C @ D ) ) )
= ( image_o_nat @ A
@ ( collect_o
@ ^ [D: $o] :
( ( member_o @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(206,axiom,
! [A: set_list_char,B: set_list_char,C: list_char > paraco1605129243lle_tv] :
( ( ord_le1836582007t_char @ A @ B )
=> ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ C @ A ) @ ( image_1187894195lle_tv @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_image__mono) ).
thf(1782,plain,
! [A: set_list_char,B: set_list_char,C: list_char > paraco1605129243lle_tv] :
( ( ord_le1836582007t_char @ A @ B )
=> ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ C @ A ) @ ( image_1187894195lle_tv @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(263,axiom,
! [A: paraco1605129243lle_tv,B: list_char > paraco1605129243lle_tv,C: list_char,D: set_list_char] :
( ( A
= ( B @ C ) )
=> ( ( member_list_char @ C @ D )
=> ( member266900804lle_tv @ A @ ( image_1187894195lle_tv @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_image__eqI) ).
thf(2020,plain,
! [A: paraco1605129243lle_tv,B: list_char > paraco1605129243lle_tv,C: list_char,D: set_list_char] :
( ( A
= ( B @ C ) )
=> ( ( member_list_char @ C @ D )
=> ( member266900804lle_tv @ A @ ( image_1187894195lle_tv @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(84,axiom,
! [A: $o > $o,B: $o > $o] :
( ( ord_less_eq_set_o @ ( collect_o @ A ) @ ( collect_o @ B ) )
= ( ! [C: $o] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_Collect__mono__iff) ).
thf(973,plain,
! [A: $o > $o,B: $o > $o] :
( ( ord_less_eq_set_o @ ( collect_o @ A ) @ ( collect_o @ B ) )
= ( ! [C: $o] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(190,axiom,
( ( paraco1933902578domain
@ ( collect_nat
@ ^ [A: nat] : $true ) )
= ( collec1111687558lle_tv
@ ^ [A: paraco1605129243lle_tv] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_universal__domain) ).
thf(1724,plain,
( ( paraco1933902578domain
@ ( collect_nat
@ ^ [A: nat] : $true ) )
= ( collec1111687558lle_tv
@ ^ [A: paraco1605129243lle_tv] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(165,axiom,
! [A: paraco1605129243lle_tv > $o,B: set_Pa1764573435lle_tv,C: $o > $o] :
( ( collect_o
@ ^ [D: $o] :
( ( member_o @ D @ ( image_991799618e_tv_o @ A @ B ) )
& ( C @ D ) ) )
= ( image_991799618e_tv_o @ A
@ ( collec1111687558lle_tv
@ ^ [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_Compr__image__eq) ).
thf(1529,plain,
! [A: paraco1605129243lle_tv > $o,B: set_Pa1764573435lle_tv,C: $o > $o] :
( ( collect_o
@ ^ [D: $o] :
( ( member_o @ D @ ( image_991799618e_tv_o @ A @ B ) )
& ( C @ D ) ) )
= ( image_991799618e_tv_o @ A
@ ( collec1111687558lle_tv
@ ^ [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(303,axiom,
! [A: list_char,B: set_list_char,C: paraco1605129243lle_tv,D: list_char > paraco1605129243lle_tv] :
( ( member_list_char @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member266900804lle_tv @ C @ ( image_1187894195lle_tv @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_rev__image__eqI) ).
thf(2173,plain,
! [A: list_char,B: set_list_char,C: paraco1605129243lle_tv,D: list_char > paraco1605129243lle_tv] :
( ( member_list_char @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member266900804lle_tv @ C @ ( image_1187894195lle_tv @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(141,axiom,
! [A: set_list_char,B: set_list_char] :
( ! [C: list_char] :
( ( member_list_char @ C @ A )
=> ( member_list_char @ C @ B ) )
=> ( ord_le1836582007t_char @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_subsetI) ).
thf(1366,plain,
! [A: set_list_char,B: set_list_char] :
( ! [C: list_char] :
( ( member_list_char @ C @ A )
=> ( member_list_char @ C @ B ) )
=> ( ord_le1836582007t_char @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(117,axiom,
! [A: paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv > $o] :
( ( member266900804lle_tv @ A @ B )
=> ( member_o @ ( C @ A ) @ ( image_991799618e_tv_o @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_imageI) ).
thf(1228,plain,
! [A: paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv > $o] :
( ( member266900804lle_tv @ A @ B )
=> ( member_o @ ( C @ A ) @ ( image_991799618e_tv_o @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(124,axiom,
! [A: set_list_char,B: set_list_char] :
( ( ord_le1945897678char_o
@ ^ [C: list_char] : ( member_list_char @ C @ A )
@ ^ [C: list_char] : ( member_list_char @ C @ B ) )
= ( ord_le1836582007t_char @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_pred__subset__eq) ).
thf(1254,plain,
! [A: set_list_char,B: set_list_char] :
( ( ord_le1945897678char_o
@ ^ [C: list_char] : ( member_list_char @ C @ A )
@ ^ [C: list_char] : ( member_list_char @ C @ B ) )
= ( ord_le1836582007t_char @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(209,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ B @ C )
=> ( ord_le241064091lle_tv @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_order_Otrans) ).
thf(1792,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ B @ C )
=> ( ord_le241064091lle_tv @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(343,axiom,
! [A: list_char > list_char] :
( ( ( image_890964937t_char @ A @ top_to748628679t_char )
= top_to748628679t_char )
= ( ! [B: list_char] :
? [C: list_char] :
( B
= ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_surj__def) ).
thf(2339,plain,
! [A: list_char > list_char] :
( ( ( image_890964937t_char @ A @ top_to748628679t_char )
= top_to748628679t_char )
= ( ! [B: list_char] :
? [C: list_char] :
( B
= ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(28,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( ( paraco69239110le_Con @ A @ B )
= ( paraco69239110le_Con @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_fm_Oinject_I3_J) ).
thf(504,plain,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( ( paraco69239110le_Con @ A @ B )
= ( paraco69239110le_Con @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(61,axiom,
! [A: $o > $o,B: $o > $o] :
( ! [C: $o] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_o_o @ A @ top_top_set_o )
= top_top_set_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_surjI) ).
thf(838,plain,
! [A: $o > $o,B: $o > $o] :
( ! [C: $o] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_o_o @ A @ top_top_set_o )
= top_top_set_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(134,axiom,
( ord_le1836582007t_char
= ( ^ [A: set_list_char,B: set_list_char] :
! [C: list_char] :
( ( member_list_char @ C @ A )
=> ( member_list_char @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_subset__iff) ).
thf(1313,plain,
( ord_le1836582007t_char
= ( ^ [A: set_list_char,B: set_list_char] :
! [C: list_char] :
( ( member_list_char @ C @ A )
=> ( member_list_char @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(17,axiom,
! [A: set_o,B: set_o,C: $o > $o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ord_less_eq_set_o @ ( image_o_o @ C @ A ) @ ( image_o_o @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_image__mono) ).
thf(460,plain,
! [A: set_o,B: set_o,C: $o > $o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ord_less_eq_set_o @ ( image_o_o @ C @ A ) @ ( image_o_o @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(226,axiom,
! [A: paraco1605129243lle_tv > $o,B: set_Pa1764573435lle_tv,C: set_o > $o] :
( ( ! [D: set_o] :
( ( ord_less_eq_set_o @ D @ ( image_991799618e_tv_o @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ D @ B )
=> ( C @ ( image_991799618e_tv_o @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_all__subset__image) ).
thf(1860,plain,
! [A: paraco1605129243lle_tv > $o,B: set_Pa1764573435lle_tv,C: set_o > $o] :
( ( ! [D: set_o] :
( ( ord_less_eq_set_o @ D @ ( image_991799618e_tv_o @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ D @ B )
=> ( C @ ( image_991799618e_tv_o @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(127,axiom,
! [A: $o,B: $o > $o] :
( ( member_o @ A @ ( collect_o @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_mem__Collect__eq) ).
thf(1264,plain,
! [A: $o,B: $o > $o] :
( ( member_o @ A @ ( collect_o @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(160,axiom,
! [A: set_o,B: set_o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( ord_less_eq_set_o @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_dual__order_Oantisym) ).
thf(1514,plain,
! [A: set_o,B: set_o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( ord_less_eq_set_o @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(121,axiom,
( top_top_set_o
= ( collect_o @ top_top_o_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_top__set__def) ).
thf(1247,plain,
( top_top_set_o
= ( collect_o @ top_top_o_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(178,axiom,
! [A: set_o,B: set_o] :
( ( A = B )
=> ~ ( ( ord_less_eq_set_o @ A @ B )
=> ~ ( ord_less_eq_set_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_equalityE) ).
thf(1609,plain,
! [A: set_o,B: set_o] :
( ( A = B )
=> ~ ( ( ord_less_eq_set_o @ A @ B )
=> ~ ( ord_less_eq_set_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(86,axiom,
! [A: $o,B: list_char > $o,C: list_char,D: set_list_char] :
( ( A
= ( B @ C ) )
=> ( ( member_list_char @ C @ D )
=> ( member_o @ A @ ( image_list_char_o @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_image__eqI) ).
thf(1013,plain,
! [A: $o,B: list_char > $o,C: list_char,D: set_list_char] :
( ( A
= ( B @ C ) )
=> ( ( member_list_char @ C @ D )
=> ( member_o @ A @ ( image_list_char_o @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(170,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm] :
( paraco367965286_Truth
!= ( paraco69239110le_Con @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_fm_Odistinct_I13_J) ).
thf(1568,plain,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm] :
( paraco367965286_Truth
!= ( paraco69239110le_Con @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(83,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco445776468le_Neg @ A )
!= ( paraco69239110le_Con @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_fm_Odistinct_I19_J) ).
thf(969,plain,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco445776468le_Neg @ A )
!= ( paraco69239110le_Con @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(352,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv > set_o,D: set_o] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ E @ F )
=> ( ord_less_eq_set_o @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_o @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_ord__le__eq__subst) ).
thf(2373,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv > set_o,D: set_o] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ E @ F )
=> ( ord_less_eq_set_o @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_o @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(171,axiom,
! [A: set_o,B: set_o,C: $o > $o,D: $o > $o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ! [E: $o] :
( ( member_o @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq_set_o
@ ( collect_o
@ ^ [E: $o] :
( ( member_o @ E @ A )
& ( C @ E ) ) )
@ ( collect_o
@ ^ [E: $o] :
( ( member_o @ E @ B )
& ( D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_subset__CollectI) ).
thf(1572,plain,
! [A: set_o,B: set_o,C: $o > $o,D: $o > $o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ! [E: $o] :
( ( member_o @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq_set_o
@ ( collect_o
@ ^ [E: $o] :
( ( member_o @ E @ A )
& ( C @ E ) ) )
@ ( collect_o
@ ^ [E: $o] :
( ( member_o @ E @ B )
& ( D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(139,axiom,
( ( (=) @ set_o )
= ( ^ [A: set_o,B: set_o] :
( ( ord_less_eq_set_o @ B @ A )
& ( ord_less_eq_set_o @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_dual__order_Oeq__iff) ).
thf(1362,plain,
( ( (=) @ set_o )
= ( ^ [A: set_o,B: set_o] :
( ( ord_less_eq_set_o @ B @ A )
& ( ord_less_eq_set_o @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(249,axiom,
! [A: $o,B: list_char > $o,C: list_char] :
( ( A
= ( B @ C ) )
=> ( member_o @ A @ ( image_list_char_o @ B @ top_to748628679t_char ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_range__eqI) ).
thf(1963,plain,
! [A: $o,B: list_char > $o,C: list_char] :
( ( A
= ( B @ C ) )
=> ( member_o @ A @ ( image_list_char_o @ B @ top_to748628679t_char ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(304,axiom,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv,C: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ ( image_335818702lle_tv @ B @ C ) )
=> ~ ! [D: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ D @ C )
=> ( A
!= ( image_335818702lle_tv @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_subset__imageE) ).
thf(2178,plain,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv,C: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ ( image_335818702lle_tv @ B @ C ) )
=> ~ ! [D: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ D @ C )
=> ( A
!= ( image_335818702lle_tv @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(146,axiom,
! [A: $o > $o,B: $o > $o,C: set_o] :
( ( image_o_o @ A @ ( image_o_o @ B @ C ) )
= ( image_o_o
@ ^ [D: $o] : ( A @ ( B @ D ) )
@ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_image__image) ).
thf(1415,plain,
! [A: $o > $o,B: $o > $o,C: set_o] :
( ( image_o_o @ A @ ( image_o_o @ B @ C ) )
= ( image_o_o
@ ^ [D: $o] : ( A @ ( B @ D ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(25,axiom,
! [A: paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: list_char,D: paraco1605129243lle_tv > list_char] :
( ( member266900804lle_tv @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member_list_char @ C @ ( image_1971766583t_char @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_rev__image__eqI) ).
thf(492,plain,
! [A: paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: list_char,D: paraco1605129243lle_tv > list_char] :
( ( member266900804lle_tv @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member_list_char @ C @ ( image_1971766583t_char @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(265,axiom,
! [A: set_nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_set_nat @ A
@ ( collect_nat
@ ^ [D: nat] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_less_eq_set_nat @ A @ ( collect_nat @ B ) )
& ( ord_less_eq_set_nat @ A @ ( collect_nat @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_conj__subset__def) ).
thf(2027,plain,
! [A: set_nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_set_nat @ A
@ ( collect_nat
@ ^ [D: nat] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_less_eq_set_nat @ A @ ( collect_nat @ B ) )
& ( ord_less_eq_set_nat @ A @ ( collect_nat @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(181,axiom,
! [A: paraco1604210848lle_fm > $o,B: paraco1604210848lle_fm] :
( ! [C: list_char] : ( A @ ( paraco1480028776le_Pro @ C ) )
=> ( ( A @ paraco367965286_Truth )
=> ( ! [C: paraco1604210848lle_fm] :
( ( A @ C )
=> ( A @ ( paraco445776468le_Neg @ C ) ) )
=> ( ! [C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco69239110le_Con @ C @ D ) ) ) )
=> ( ! [C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco1389086619le_Eql @ C @ D ) ) ) )
=> ( ! [C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco1745535428le_Eql @ C @ D ) ) ) )
=> ( A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_fm_Oinduct) ).
thf(1632,plain,
! [A: paraco1604210848lle_fm > $o,B: paraco1604210848lle_fm] :
( ! [C: list_char] : ( A @ ( paraco1480028776le_Pro @ C ) )
=> ( ( A @ paraco367965286_Truth )
=> ( ! [C: paraco1604210848lle_fm] :
( ( A @ C )
=> ( A @ ( paraco445776468le_Neg @ C ) ) )
=> ( ! [C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco69239110le_Con @ C @ D ) ) ) )
=> ( ! [C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco1389086619le_Eql @ C @ D ) ) ) )
=> ( ! [C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco1745535428le_Eql @ C @ D ) ) ) )
=> ( A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(47,axiom,
! [A: set_list_char,B: set_list_char,C: list_char] :
( ( ord_le1836582007t_char @ A @ B )
=> ( ( member_list_char @ C @ A )
=> ( member_list_char @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_subsetD) ).
thf(623,plain,
! [A: set_list_char,B: set_list_char,C: list_char] :
( ( ord_le1836582007t_char @ A @ B )
=> ( ( member_list_char @ C @ A )
=> ( member_list_char @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(252,axiom,
! [A: set_list_char] : ( ord_le1836582007t_char @ A @ top_to748628679t_char ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_subset__UNIV) ).
thf(1978,plain,
! [A: set_list_char] : ( ord_le1836582007t_char @ A @ top_to748628679t_char ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(31,axiom,
! [A: $o > $o,B: $o] : ( member_o @ ( A @ B ) @ ( image_o_o @ A @ top_top_set_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_rangeI) ).
thf(514,plain,
! [A: $o > $o,B: $o] : ( member_o @ ( A @ B ) @ ( image_o_o @ A @ top_top_set_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(324,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv > set_o,D: set_o] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( ord_less_eq_set_o @ ( C @ B ) @ D )
=> ( ! [E: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ E @ F )
=> ( ord_less_eq_set_o @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_o @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_order__subst2) ).
thf(2254,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv > set_o,D: set_o] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( ord_less_eq_set_o @ ( C @ B ) @ D )
=> ( ! [E: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ E @ F )
=> ( ord_less_eq_set_o @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_o @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(82,axiom,
! [A: set_o > $o,B: set_o] :
( ( A
@ ( image_o_o
@ ^ [C: $o] : C
@ B ) )
= ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_Sup_OSUP__identity__eq) ).
thf(966,plain,
! [A: set_o > $o,B: set_o] :
( ( A
@ ( image_o_o
@ ^ [C: $o] : C
@ B ) )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(7,axiom,
( ord_less_eq_set_o
= ( ^ [A: set_o,B: set_o] :
( ord_less_eq_o_o
@ ^ [C: $o] : ( member_o @ C @ A )
@ ^ [C: $o] : ( member_o @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_less__eq__set__def) ).
thf(376,plain,
( ord_less_eq_set_o
= ( ^ [A: set_o,B: set_o] :
( ord_less_eq_o_o
@ ^ [C: $o] : ( member_o @ C @ A )
@ ^ [C: $o] : ( member_o @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(325,axiom,
! [A: set_o,B: set_o,C: set_o > set_Pa1764573435lle_tv,D: set_Pa1764573435lle_tv] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_o,F: set_o] :
( ( ord_less_eq_set_o @ E @ F )
=> ( ord_le241064091lle_tv @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le241064091lle_tv @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_ord__le__eq__subst) ).
thf(2259,plain,
! [A: set_o,B: set_o,C: set_o > set_Pa1764573435lle_tv,D: set_Pa1764573435lle_tv] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_o,F: set_o] :
( ( ord_less_eq_set_o @ E @ F )
=> ( ord_le241064091lle_tv @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le241064091lle_tv @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(262,axiom,
! [A: nat > $o,B: nat > $o] :
( ( ord_less_eq_set_nat @ ( collect_nat @ A ) @ ( collect_nat @ B ) )
= ( ! [C: nat] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_Collect__mono__iff) ).
thf(2017,plain,
! [A: nat > $o,B: nat > $o] :
( ( ord_less_eq_set_nat @ ( collect_nat @ A ) @ ( collect_nat @ B ) )
= ( ! [C: nat] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(21,axiom,
! [A: set_o,B: set_o] :
( ( A = B )
=> ( ord_less_eq_set_o @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_equalityD2) ).
thf(480,plain,
! [A: set_o,B: set_o] :
( ( A = B )
=> ( ord_less_eq_set_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(269,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( ord_le1632188418e_tv_o
@ ^ [C: paraco1605129243lle_tv] : ( member266900804lle_tv @ C @ A )
@ ^ [C: paraco1605129243lle_tv] : ( member266900804lle_tv @ C @ B ) )
= ( ord_le241064091lle_tv @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_pred__subset__eq) ).
thf(2058,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( ord_le1632188418e_tv_o
@ ^ [C: paraco1605129243lle_tv] : ( member266900804lle_tv @ C @ A )
@ ^ [C: paraco1605129243lle_tv] : ( member266900804lle_tv @ C @ B ) )
= ( ord_le241064091lle_tv @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(100,axiom,
! [A: list_char,B: list_char] :
( ( ( paraco1480028776le_Pro @ A )
= ( paraco1480028776le_Pro @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_fm_Oinject_I1_J) ).
thf(1119,plain,
! [A: list_char,B: list_char] :
( ( ( paraco1480028776le_Pro @ A )
= ( paraco1480028776le_Pro @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(164,axiom,
! [A: set_o] :
( ( collect_o
@ ^ [B: $o] : ( member_o @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_Collect__mem__eq) ).
thf(1526,plain,
! [A: set_o] :
( ( collect_o
@ ^ [B: $o] : ( member_o @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(29,axiom,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv,C: paraco1605129243lle_tv,D: set_Pa1764573435lle_tv] :
( ( A
= ( B @ C ) )
=> ( ( member266900804lle_tv @ C @ D )
=> ( member266900804lle_tv @ A @ ( image_335818702lle_tv @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_image__eqI) ).
thf(507,plain,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv,C: paraco1605129243lle_tv,D: set_Pa1764573435lle_tv] :
( ( A
= ( B @ C ) )
=> ( ( member266900804lle_tv @ C @ D )
=> ( member266900804lle_tv @ A @ ( image_335818702lle_tv @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(251,axiom,
! [A: set_list_char] :
( ! [B: list_char] : ( member_list_char @ B @ A )
=> ( top_to748628679t_char = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_UNIV__eq__I) ).
thf(1975,plain,
! [A: set_list_char] :
( ! [B: list_char] : ( member_list_char @ B @ A )
=> ( top_to748628679t_char = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(234,axiom,
! [A: paraco1605129243lle_tv > $o,B: paraco1605129243lle_tv > paraco1605129243lle_tv,C: set_Pa1764573435lle_tv] :
( ! [D: paraco1605129243lle_tv] :
( ( A @ D )
=> ( member266900804lle_tv @ ( B @ D ) @ C ) )
=> ( ord_le241064091lle_tv @ ( image_335818702lle_tv @ B @ ( collec1111687558lle_tv @ A ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_image__Collect__subsetI) ).
thf(1896,plain,
! [A: paraco1605129243lle_tv > $o,B: paraco1605129243lle_tv > paraco1605129243lle_tv,C: set_Pa1764573435lle_tv] :
( ! [D: paraco1605129243lle_tv] :
( ( A @ D )
=> ( member266900804lle_tv @ ( B @ D ) @ C ) )
=> ( ord_le241064091lle_tv @ ( image_335818702lle_tv @ B @ ( collec1111687558lle_tv @ A ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(54,axiom,
! [A: $o > $o,B: $o] :
( ( ( image_o_o @ A @ top_top_set_o )
= top_top_set_o )
=> ~ ! [C: $o] :
( B
= ( ~ ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_surjE) ).
thf(692,plain,
! [A: $o > $o,B: $o] :
( ( ( image_o_o @ A @ top_top_set_o )
= top_top_set_o )
=> ~ ! [C: $o] :
( B
= ( ~ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(307,axiom,
( top_top_set_nat
= ( collect_nat
@ ^ [A: nat] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_UNIV__def) ).
thf(2190,plain,
( top_top_set_nat
= ( collect_nat
@ ^ [A: nat] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(320,axiom,
! [A: nat,B: nat > $o] :
( ( member_nat @ A @ ( collect_nat @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_mem__Collect__eq) ).
thf(2242,plain,
! [A: nat,B: nat > $o] :
( ( member_nat @ A @ ( collect_nat @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(137,axiom,
! [A: set_o,B: $o > $o,C: set_o] :
( ! [D: $o] :
( ( member_o @ D @ A )
=> ( member_o @ ( B @ D ) @ C ) )
=> ( ord_less_eq_set_o @ ( image_o_o @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_image__subsetI) ).
thf(1345,plain,
! [A: set_o,B: $o > $o,C: set_o] :
( ! [D: $o] :
( ( member_o @ D @ A )
=> ( member_o @ ( B @ D ) @ C ) )
=> ( ord_less_eq_set_o @ ( image_o_o @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(331,axiom,
( paraco55203475lid_in
= ( ^ [A: set_nat,B: paraco1604210848lle_fm] :
! [C: list_char > paraco1605129243lle_tv] :
( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ C @ top_to748628679t_char ) @ ( paraco1933902578domain @ A ) )
=> ( ( paraco1325918602e_eval @ C @ B )
= ( paraco1344940915le_Det @ $true ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_valid__in__def) ).
thf(2286,plain,
( paraco55203475lid_in
= ( ^ [A: set_nat,B: paraco1604210848lle_fm] :
! [C: list_char > paraco1605129243lle_tv] :
( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ C @ top_to748628679t_char ) @ ( paraco1933902578domain @ A ) )
=> ( ( paraco1325918602e_eval @ C @ B )
= ( paraco1344940915le_Det @ $true ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(227,axiom,
! [A: nat,B: set_nat,C: set_nat,D: nat > $o] :
( ( member_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B
@ ( collect_nat
@ ^ [E: nat] :
( ( member_nat @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_prop__restrict) ).
thf(1863,plain,
! [A: nat,B: set_nat,C: set_nat,D: nat > $o] :
( ( member_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B
@ ( collect_nat
@ ^ [E: nat] :
( ( member_nat @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(15,axiom,
! [A: list_char,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco1480028776le_Pro @ A )
!= ( paraco1389086619le_Eql @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_fm_Odistinct_I7_J) ).
thf(452,plain,
! [A: list_char,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco1480028776le_Pro @ A )
!= ( paraco1389086619le_Eql @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(34,axiom,
! [A: list_char,B: $o > list_char] :
( ( member_list_char @ A @ ( image_o_list_char @ B @ top_top_set_o ) )
=> ~ ! [C: $o] :
( A
!= ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_rangeE) ).
thf(529,plain,
! [A: list_char,B: $o > list_char] :
( ( member_list_char @ A @ ( image_o_list_char @ B @ top_top_set_o ) )
=> ~ ! [C: $o] :
( A
!= ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(38,axiom,
! [A: set_o,B: set_o > set_o,C: set_o,D: set_o] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_o @ C @ D )
=> ( ! [E: set_o,F: set_o] :
( ( ord_less_eq_set_o @ E @ F )
=> ( ord_less_eq_set_o @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_o @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_ord__eq__le__subst) ).
thf(546,plain,
! [A: set_o,B: set_o > set_o,C: set_o,D: set_o] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_o @ C @ D )
=> ( ! [E: set_o,F: set_o] :
( ( ord_less_eq_set_o @ E @ F )
=> ( ord_less_eq_set_o @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_o @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(300,axiom,
( ord_le241064091lle_tv
= ( ^ [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
! [C: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ C @ A )
=> ( member266900804lle_tv @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_subset__iff) ).
thf(2164,plain,
( ord_le241064091lle_tv
= ( ^ [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
! [C: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ C @ A )
=> ( member266900804lle_tv @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(9,axiom,
! [A: list_char] :
( ( paraco1480028776le_Pro @ A )
!= paraco367965286_Truth ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_fm_Odistinct_I1_J) ).
thf(381,plain,
! [A: list_char] :
( ( paraco1480028776le_Pro @ A )
!= paraco367965286_Truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(186,axiom,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > $o] :
( ord_le241064091lle_tv
@ ( collec1111687558lle_tv
@ ^ [C: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_Collect__subset) ).
thf(1708,plain,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > $o] :
( ord_le241064091lle_tv
@ ( collec1111687558lle_tv
@ ^ [C: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(195,axiom,
! [A: nat > $o,B: nat > $o,C: set_o] :
( ! [D: nat] :
( ( A @ D )
=> ( member_o @ ( B @ D ) @ C ) )
=> ( ord_less_eq_set_o @ ( image_nat_o @ B @ ( collect_nat @ A ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_image__Collect__subsetI) ).
thf(1736,plain,
! [A: nat > $o,B: nat > $o,C: set_o] :
( ! [D: nat] :
( ( A @ D )
=> ( member_o @ ( B @ D ) @ C ) )
=> ( ord_less_eq_set_o @ ( image_nat_o @ B @ ( collect_nat @ A ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(353,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv,D: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ ( B @ C ) )
=> ( ( ord_le241064091lle_tv @ C @ D )
=> ( ! [E: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ E @ F )
=> ( ord_le241064091lle_tv @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le241064091lle_tv @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_order__subst1) ).
thf(2382,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv,D: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ ( B @ C ) )
=> ( ( ord_le241064091lle_tv @ C @ D )
=> ( ! [E: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ E @ F )
=> ( ord_le241064091lle_tv @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le241064091lle_tv @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(270,axiom,
! [A: list_char] : ( member_list_char @ A @ top_to748628679t_char ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_iso__tuple__UNIV__I) ).
thf(2061,plain,
! [A: list_char] : ( member_list_char @ A @ top_to748628679t_char ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(30,axiom,
( ord_le1836582007t_char
= ( ^ [A: set_list_char,B: set_list_char] :
! [C: list_char] :
( ( member_list_char @ C @ A )
=> ( member_list_char @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_subset__eq) ).
thf(512,plain,
( ord_le1836582007t_char
= ( ^ [A: set_list_char,B: set_list_char] :
! [C: list_char] :
( ( member_list_char @ C @ A )
=> ( member_list_char @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(77,axiom,
! [A: set_o,B: set_o,C: set_o > set_o,D: set_o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_o,F: set_o] :
( ( ord_less_eq_set_o @ E @ F )
=> ( ord_less_eq_set_o @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_o @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_ord__le__eq__subst) ).
thf(942,plain,
! [A: set_o,B: set_o,C: set_o > set_o,D: set_o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_o,F: set_o] :
( ( ord_less_eq_set_o @ E @ F )
=> ( ord_less_eq_set_o @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_o @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(235,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( member266900804lle_tv @ C @ A )
=> ( member266900804lle_tv @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_in__mono) ).
thf(1900,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( member266900804lle_tv @ C @ A )
=> ( member266900804lle_tv @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(295,axiom,
( complete_Sup_Sup_o
= ( member_o @ $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_Sup__bool__def) ).
thf(2147,plain,
( complete_Sup_Sup_o
= ( member_o @ $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(198,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv,D: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ ( C @ B ) @ D )
=> ( ! [E: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ E @ F )
=> ( ord_le241064091lle_tv @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le241064091lle_tv @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_order__subst2) ).
thf(1751,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv,D: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ ( C @ B ) @ D )
=> ( ! [E: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ E @ F )
=> ( ord_le241064091lle_tv @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le241064091lle_tv @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(41,axiom,
! [A: $o,B: set_o,C: set_o,D: $o > $o] :
( ( member_o @ A @ B )
=> ( ( ord_less_eq_set_o @ B
@ ( collect_o
@ ^ [E: $o] :
( ( member_o @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_prop__restrict) ).
thf(561,plain,
! [A: $o,B: set_o,C: set_o,D: $o > $o] :
( ( member_o @ A @ B )
=> ( ( ord_less_eq_set_o @ B
@ ( collect_o
@ ^ [E: $o] :
( ( member_o @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(151,axiom,
! [A: set_o,B: set_o] :
( ( A = B )
=> ( ord_less_eq_set_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_eq__refl) ).
thf(1487,plain,
! [A: set_o,B: set_o] :
( ( A = B )
=> ( ord_less_eq_set_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(180,axiom,
! [A: $o > $o,B: set_o,C: $o > $o] :
( ( collect_o
@ ^ [D: $o] :
( ( member_o @ D @ ( image_o_o @ A @ B ) )
& ( C @ D ) ) )
= ( image_o_o @ A
@ ( collect_o
@ ^ [D: $o] :
( ( member_o @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_Compr__image__eq) ).
thf(1619,plain,
! [A: $o > $o,B: set_o,C: $o > $o] :
( ( collect_o
@ ^ [D: $o] :
( ( member_o @ D @ ( image_o_o @ A @ B ) )
& ( C @ D ) ) )
= ( image_o_o @ A
@ ( collect_o
@ ^ [D: $o] :
( ( member_o @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(142,axiom,
! [A: $o > $o,B: $o > $o] :
( ( image_o_o
@ ^ [C: $o] : ( A @ ( B @ C ) )
@ top_top_set_o )
= ( image_o_o @ A @ ( image_o_o @ B @ top_top_set_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_range__composition) ).
thf(1370,plain,
! [A: $o > $o,B: $o > $o] :
( ( image_o_o
@ ^ [C: $o] : ( A @ ( B @ C ) )
@ top_top_set_o )
= ( image_o_o @ A @ ( image_o_o @ B @ top_top_set_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(22,axiom,
( ord_le1836582007t_char
= ( ^ [A: set_list_char,B: set_list_char] :
( ord_le1945897678char_o
@ ^ [C: list_char] : ( member_list_char @ C @ A )
@ ^ [C: list_char] : ( member_list_char @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_less__eq__set__def) ).
thf(484,plain,
( ord_le1836582007t_char
= ( ^ [A: set_list_char,B: set_list_char] :
( ord_le1945897678char_o
@ ^ [C: list_char] : ( member_list_char @ C @ A )
@ ^ [C: list_char] : ( member_list_char @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(221,axiom,
( ( pow_list_char @ top_to748628679t_char )
= top_to697846397t_char ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_Pow__UNIV) ).
thf(1837,plain,
( ( pow_list_char @ top_to748628679t_char )
= top_to697846397t_char ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(240,axiom,
! [A: paraco1605129243lle_tv,B: list_char > paraco1605129243lle_tv] :
( ( member266900804lle_tv @ A @ ( image_1187894195lle_tv @ B @ top_to748628679t_char ) )
=> ~ ! [C: list_char] :
( A
!= ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_rangeE) ).
thf(1920,plain,
! [A: paraco1605129243lle_tv,B: list_char > paraco1605129243lle_tv] :
( ( member266900804lle_tv @ A @ ( image_1187894195lle_tv @ B @ top_to748628679t_char ) )
=> ~ ! [C: list_char] :
( A
!= ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(169,axiom,
! [A: $o > $o,B: set_o,C: set_o > $o] :
( ( ! [D: set_o] :
( ( ord_less_eq_set_o @ D @ ( image_o_o @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: set_o] :
( ( ord_less_eq_set_o @ D @ B )
=> ( C @ ( image_o_o @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_all__subset__image) ).
thf(1555,plain,
! [A: $o > $o,B: set_o,C: set_o > $o] :
( ( ! [D: set_o] :
( ( ord_less_eq_set_o @ D @ ( image_o_o @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: set_o] :
( ( ord_less_eq_set_o @ D @ B )
=> ( C @ ( image_o_o @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(59,axiom,
! [A: list_char,B: paraco1605129243lle_tv > list_char,C: set_Pa1764573435lle_tv] :
( ( member_list_char @ A @ ( image_1971766583t_char @ B @ C ) )
=> ~ ! [D: paraco1605129243lle_tv] :
( ( A
= ( B @ D ) )
=> ~ ( member266900804lle_tv @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_imageE) ).
thf(830,plain,
! [A: list_char,B: paraco1605129243lle_tv > list_char,C: set_Pa1764573435lle_tv] :
( ( member_list_char @ A @ ( image_1971766583t_char @ B @ C ) )
=> ~ ! [D: paraco1605129243lle_tv] :
( ( A
= ( B @ D ) )
=> ~ ( member266900804lle_tv @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(64,axiom,
! [A: list_char,B: set_list_char,C: list_char > list_char] :
( ( member_list_char @ A @ B )
=> ( member_list_char @ ( C @ A ) @ ( image_890964937t_char @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_imageI) ).
thf(889,plain,
! [A: list_char,B: set_list_char,C: list_char > list_char] :
( ( member_list_char @ A @ B )
=> ( member_list_char @ ( C @ A ) @ ( image_890964937t_char @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(208,axiom,
! [A: paraco1605129243lle_tv,B: list_char > paraco1605129243lle_tv,C: set_list_char] :
( ( member266900804lle_tv @ A @ ( image_1187894195lle_tv @ B @ C ) )
=> ~ ! [D: list_char] :
( ( A
= ( B @ D ) )
=> ~ ( member_list_char @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_imageE) ).
thf(1787,plain,
! [A: paraco1605129243lle_tv,B: list_char > paraco1605129243lle_tv,C: set_list_char] :
( ( member266900804lle_tv @ A @ ( image_1187894195lle_tv @ B @ C ) )
=> ~ ! [D: list_char] :
( ( A
= ( B @ D ) )
=> ~ ( member_list_char @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(345,axiom,
( top_top_set_o
= ( collect_o
@ ^ [A: $o] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_UNIV__def) ).
thf(2345,plain,
( top_top_set_o
= ( collect_o
@ ^ [A: $o] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(128,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm] :
( paraco367965286_Truth
!= ( paraco1389086619le_Eql @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_fm_Odistinct_I15_J) ).
thf(1281,plain,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm] :
( paraco367965286_Truth
!= ( paraco1389086619le_Eql @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(316,axiom,
! [A: list_char > paraco1605129243lle_tv,B: set_list_char,C: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ A @ B ) @ C )
=> ( ord_le263913851lle_tv @ ( image_30320477lle_tv @ ( image_1187894195lle_tv @ A ) @ ( finite1803457147t_char @ B ) ) @ ( finite2011762305lle_tv @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_image__Fpow__mono) ).
thf(2228,plain,
! [A: list_char > paraco1605129243lle_tv,B: set_list_char,C: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ A @ B ) @ C )
=> ( ord_le263913851lle_tv @ ( image_30320477lle_tv @ ( image_1187894195lle_tv @ A ) @ ( finite1803457147t_char @ B ) ) @ ( finite2011762305lle_tv @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(71,axiom,
! [A: set_list_char,B: set_list_char,C: list_char > $o,D: list_char > $o] :
( ( ord_le1836582007t_char @ A @ B )
=> ( ! [E: list_char] :
( ( member_list_char @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_le1836582007t_char
@ ( collect_list_char
@ ^ [E: list_char] :
( ( member_list_char @ E @ A )
& ( C @ E ) ) )
@ ( collect_list_char
@ ^ [E: list_char] :
( ( member_list_char @ E @ B )
& ( D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_subset__CollectI) ).
thf(916,plain,
! [A: set_list_char,B: set_list_char,C: list_char > $o,D: list_char > $o] :
( ( ord_le1836582007t_char @ A @ B )
=> ( ! [E: list_char] :
( ( member_list_char @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_le1836582007t_char
@ ( collect_list_char
@ ^ [E: list_char] :
( ( member_list_char @ E @ A )
& ( C @ E ) ) )
@ ( collect_list_char
@ ^ [E: list_char] :
( ( member_list_char @ E @ B )
& ( D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(19,axiom,
! [A: $o,B: set_o,C: paraco1605129243lle_tv,D: $o > paraco1605129243lle_tv] :
( ( member_o @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member266900804lle_tv @ C @ ( image_1491822472lle_tv @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_rev__image__eqI) ).
thf(467,plain,
! [A: $o,B: set_o,C: paraco1605129243lle_tv,D: $o > paraco1605129243lle_tv] :
( ( member_o @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member266900804lle_tv @ C @ ( image_1491822472lle_tv @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(273,axiom,
! [A: list_char > paraco1605129243lle_tv,B: set_list_char,C: set_Pa1764573435lle_tv > $o] :
( ( ! [D: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ D @ ( image_1187894195lle_tv @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: set_list_char] :
( ( ord_le1836582007t_char @ D @ B )
=> ( C @ ( image_1187894195lle_tv @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_all__subset__image) ).
thf(2068,plain,
! [A: list_char > paraco1605129243lle_tv,B: set_list_char,C: set_Pa1764573435lle_tv > $o] :
( ( ! [D: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ D @ ( image_1187894195lle_tv @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: set_list_char] :
( ( ord_le1836582007t_char @ D @ B )
=> ( C @ ( image_1187894195lle_tv @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(216,axiom,
! [A: $o > list_char,B: list_char] :
( ( ( image_o_list_char @ A @ top_top_set_o )
= top_to748628679t_char )
=> ? [C: $o] :
( B
= ( A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_surjD) ).
thf(1819,plain,
! [A: $o > list_char,B: list_char] :
( ( ( image_o_list_char @ A @ top_top_set_o )
= top_to748628679t_char )
=> ? [C: $o] :
( B
= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(16,axiom,
! [A: paraco1604210848lle_fm] :
( paraco367965286_Truth
!= ( paraco445776468le_Neg @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_fm_Odistinct_I11_J) ).
thf(456,plain,
! [A: paraco1604210848lle_fm] :
( paraco367965286_Truth
!= ( paraco445776468le_Neg @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(196,axiom,
! [A: list_char > paraco1605129243lle_tv,B: set_list_char,C: paraco1605129243lle_tv > $o] :
( ? [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ ( image_1187894195lle_tv @ A @ B ) )
& ( C @ D ) )
=> ? [D: list_char] :
( ( member_list_char @ D @ B )
& ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_bex__imageD) ).
thf(1740,plain,
! [A: list_char > paraco1605129243lle_tv,B: set_list_char,C: paraco1605129243lle_tv > $o] :
( ? [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ ( image_1187894195lle_tv @ A @ B ) )
& ( C @ D ) )
=> ? [D: list_char] :
( ( member_list_char @ D @ B )
& ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(321,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: list_char > paraco1605129243lle_tv] :
( ( image_1187894195lle_tv
@ ^ [C: list_char] : ( A @ ( B @ C ) )
@ top_to748628679t_char )
= ( image_335818702lle_tv @ A @ ( image_1187894195lle_tv @ B @ top_to748628679t_char ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_range__composition) ).
thf(2245,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: list_char > paraco1605129243lle_tv] :
( ( image_1187894195lle_tv
@ ^ [C: list_char] : ( A @ ( B @ C ) )
@ top_to748628679t_char )
= ( image_335818702lle_tv @ A @ ( image_1187894195lle_tv @ B @ top_to748628679t_char ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(335,axiom,
! [A: set_Pa1764573435lle_tv,B: set_o > set_Pa1764573435lle_tv,C: set_o,D: set_o] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_o @ C @ D )
=> ( ! [E: set_o,F: set_o] :
( ( ord_less_eq_set_o @ E @ F )
=> ( ord_le241064091lle_tv @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le241064091lle_tv @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_ord__eq__le__subst) ).
thf(2300,plain,
! [A: set_Pa1764573435lle_tv,B: set_o > set_Pa1764573435lle_tv,C: set_o,D: set_o] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_o @ C @ D )
=> ( ! [E: set_o,F: set_o] :
( ( ord_less_eq_set_o @ E @ F )
=> ( ord_le241064091lle_tv @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le241064091lle_tv @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(350,axiom,
! [A: set_list_char] :
( ( ord_le1836582007t_char @ top_to748628679t_char @ A )
=> ( A = top_to748628679t_char ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_top_Oextremum__uniqueI) ).
thf(2359,plain,
! [A: set_list_char] :
( ( ord_le1836582007t_char @ top_to748628679t_char @ A )
=> ( A = top_to748628679t_char ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(98,axiom,
! [A: set_Pa1764573435lle_tv] :
( ! [B: paraco1605129243lle_tv] : ( member266900804lle_tv @ B @ A )
=> ( top_to1057771083lle_tv = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_UNIV__eq__I) ).
thf(1111,plain,
! [A: set_Pa1764573435lle_tv] :
( ! [B: paraco1605129243lle_tv] : ( member266900804lle_tv @ B @ A )
=> ( top_to1057771083lle_tv = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(173,axiom,
! [A: set_Pa1764573435lle_tv] :
( ( collec1111687558lle_tv
@ ^ [B: paraco1605129243lle_tv] : ( member266900804lle_tv @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_Collect__mem__eq) ).
thf(1587,plain,
! [A: set_Pa1764573435lle_tv] :
( ( collec1111687558lle_tv
@ ^ [B: paraco1605129243lle_tv] : ( member266900804lle_tv @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(104,axiom,
! [A: $o > paraco1605129243lle_tv,B: set_o,C: paraco1605129243lle_tv > $o] :
( ( collec1111687558lle_tv
@ ^ [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ ( image_1491822472lle_tv @ A @ B ) )
& ( C @ D ) ) )
= ( image_1491822472lle_tv @ A
@ ( collect_o
@ ^ [D: $o] :
( ( member_o @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_Compr__image__eq) ).
thf(1138,plain,
! [A: $o > paraco1605129243lle_tv,B: set_o,C: paraco1605129243lle_tv > $o] :
( ( collec1111687558lle_tv
@ ^ [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ ( image_1491822472lle_tv @ A @ B ) )
& ( C @ D ) ) )
= ( image_1491822472lle_tv @ A
@ ( collect_o
@ ^ [D: $o] :
( ( member_o @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(326,axiom,
! [A: nat > $o,B: nat > paraco1605129243lle_tv,C: set_Pa1764573435lle_tv] :
( ! [D: nat] :
( ( A @ D )
=> ( member266900804lle_tv @ ( B @ D ) @ C ) )
=> ( ord_le241064091lle_tv @ ( image_1151963140lle_tv @ B @ ( collect_nat @ A ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_image__Collect__subsetI) ).
thf(2268,plain,
! [A: nat > $o,B: nat > paraco1605129243lle_tv,C: set_Pa1764573435lle_tv] :
( ! [D: nat] :
( ( A @ D )
=> ( member266900804lle_tv @ ( B @ D ) @ C ) )
=> ( ord_le241064091lle_tv @ ( image_1151963140lle_tv @ B @ ( collect_nat @ A ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(153,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm] :
( ( paraco327635598_valid @ ( paraco69239110le_Con @ A @ B ) )
= ( ( paraco327635598_valid @ A )
& ( paraco327635598_valid @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_conjunction) ).
thf(1493,plain,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm] :
( ( paraco327635598_valid @ ( paraco69239110le_Con @ A @ B ) )
= ( ( paraco327635598_valid @ A )
& ( paraco327635598_valid @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(130,axiom,
! [A: set_o,B: $o > $o,C: set_o] :
( ( ord_less_eq_set_o @ A @ ( image_o_o @ B @ C ) )
=> ~ ! [D: set_o] :
( ( ord_less_eq_set_o @ D @ C )
=> ( A
!= ( image_o_o @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_subset__imageE) ).
thf(1292,plain,
! [A: set_o,B: $o > $o,C: set_o] :
( ( ord_less_eq_set_o @ A @ ( image_o_o @ B @ C ) )
=> ~ ! [D: set_o] :
( ( ord_less_eq_set_o @ D @ C )
=> ( A
!= ( image_o_o @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(53,axiom,
! [A: $o,B: $o > $o] :
( ( member_o @ A @ ( image_o_o @ B @ top_top_set_o ) )
=> ~ ! [C: $o] :
( A
= ( ~ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_rangeE) ).
thf(669,plain,
! [A: $o,B: $o > $o] :
( ( member_o @ A @ ( image_o_o @ B @ top_top_set_o ) )
=> ~ ! [C: $o] :
( A
= ( ~ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(337,axiom,
! [A: list_char > paraco1605129243lle_tv,B: set_list_char,C: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ A @ B ) @ C )
=> ( ord_le263913851lle_tv @ ( image_30320477lle_tv @ ( image_1187894195lle_tv @ A ) @ ( pow_list_char @ B ) ) @ ( pow_Pa475453624lle_tv @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_image__Pow__mono) ).
thf(2312,plain,
! [A: list_char > paraco1605129243lle_tv,B: set_list_char,C: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ A @ B ) @ C )
=> ( ord_le263913851lle_tv @ ( image_30320477lle_tv @ ( image_1187894195lle_tv @ A ) @ ( pow_list_char @ B ) ) @ ( pow_Pa475453624lle_tv @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(268,axiom,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1325918602e_eval @ A @ C ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1745535428le_Eql @ B @ C ) )
= ( paraco1344940915le_Det @ $true ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1325918602e_eval @ A @ C ) )
=> ( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1745535428le_Eql @ B @ C ) )
= ( paraco1325918602e_eval @ A @ C ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( ( ( paraco1325918602e_eval @ A @ C )
= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1745535428le_Eql @ B @ C ) )
= ( paraco1325918602e_eval @ A @ B ) ) )
& ( ( ( paraco1325918602e_eval @ A @ C )
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1344940915le_Det @ $false ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1745535428le_Eql @ B @ C ) )
= ( paraco1325918602e_eval @ A @ ( paraco445776468le_Neg @ C ) ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1344940915le_Det @ $false ) )
=> ( ( ( ( paraco1325918602e_eval @ A @ C )
= ( paraco1344940915le_Det @ $false ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1745535428le_Eql @ B @ C ) )
= ( paraco1325918602e_eval @ A @ ( paraco445776468le_Neg @ B ) ) ) )
& ( ( ( paraco1325918602e_eval @ A @ C )
!= ( paraco1344940915le_Det @ $false ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1745535428le_Eql @ B @ C ) )
= ( paraco1344940915le_Det @ $false ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_eval__equality) ).
thf(2038,plain,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1325918602e_eval @ A @ C ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1745535428le_Eql @ B @ C ) )
= ( paraco1344940915le_Det @ $true ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1325918602e_eval @ A @ C ) )
=> ( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1745535428le_Eql @ B @ C ) )
= ( paraco1325918602e_eval @ A @ C ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( ( ( paraco1325918602e_eval @ A @ C )
= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1745535428le_Eql @ B @ C ) )
= ( paraco1325918602e_eval @ A @ B ) ) )
& ( ( ( paraco1325918602e_eval @ A @ C )
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1344940915le_Det @ $false ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1745535428le_Eql @ B @ C ) )
= ( paraco1325918602e_eval @ A @ ( paraco445776468le_Neg @ C ) ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1344940915le_Det @ $false ) )
=> ( ( ( ( paraco1325918602e_eval @ A @ C )
= ( paraco1344940915le_Det @ $false ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1745535428le_Eql @ B @ C ) )
= ( paraco1325918602e_eval @ A @ ( paraco445776468le_Neg @ B ) ) ) )
& ( ( ( paraco1325918602e_eval @ A @ C )
!= ( paraco1344940915le_Det @ $false ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1745535428le_Eql @ B @ C ) )
= ( paraco1344940915le_Det @ $false ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(339,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( A = B )
=> ( ord_le241064091lle_tv @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_equalityD1) ).
thf(2317,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( A = B )
=> ( ord_le241064091lle_tv @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(309,axiom,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > $o] :
( ord_le241064091lle_tv
@ ( collec1111687558lle_tv
@ ^ [C: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_Collect__restrict) ).
thf(2196,plain,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > $o] :
( ord_le241064091lle_tv
@ ( collec1111687558lle_tv
@ ^ [C: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(223,axiom,
( top_top_set_nat
= ( collect_nat @ top_top_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_top__set__def) ).
thf(1842,plain,
( top_top_set_nat
= ( collect_nat @ top_top_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(24,axiom,
! [A: set_o,B: set_o,C: $o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( member_o @ C @ A )
=> ( member_o @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_in__mono) ).
thf(489,plain,
! [A: set_o,B: set_o,C: $o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( member_o @ C @ A )
=> ( member_o @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(245,axiom,
! [A: paraco1605129243lle_tv > nat,B: set_Pa1764573435lle_tv,C: nat > $o] :
( ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ ( image_376325286tv_nat @ A @ B ) )
& ( C @ D ) ) )
= ( image_376325286tv_nat @ A
@ ( collec1111687558lle_tv
@ ^ [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_Compr__image__eq) ).
thf(1937,plain,
! [A: paraco1605129243lle_tv > nat,B: set_Pa1764573435lle_tv,C: nat > $o] :
( ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ ( image_376325286tv_nat @ A @ B ) )
& ( C @ D ) ) )
= ( image_376325286tv_nat @ A
@ ( collec1111687558lle_tv
@ ^ [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(122,axiom,
? [A: $o] : ( member_o @ A @ top_top_set_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_UNIV__witness) ).
thf(1249,plain,
? [A: $o] : ( member_o @ A @ top_top_set_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(131,axiom,
( ord_less_eq_set_o
= ( ^ [A: set_o,B: set_o] :
! [C: $o] :
( ( member_o @ C @ A )
=> ( member_o @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_subset__eq) ).
thf(1297,plain,
( ord_less_eq_set_o
= ( ^ [A: set_o,B: set_o] :
! [C: $o] :
( ( member_o @ C @ A )
=> ( member_o @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(102,axiom,
! [A: set_o > $o,B: set_o] :
( ( A
@ ( image_o_o
@ ^ [C: $o] : C
@ B ) )
= ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_Inf_OINF__identity__eq) ).
thf(1131,plain,
! [A: set_o > $o,B: set_o] :
( ( A
@ ( image_o_o
@ ^ [C: $o] : C
@ B ) )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(168,axiom,
! [A: set_list_char,B: set_list_char,C: list_char] :
( ( ord_le1836582007t_char @ A @ B )
=> ( ( member_list_char @ C @ A )
=> ( member_list_char @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_in__mono) ).
thf(1552,plain,
! [A: set_list_char,B: set_list_char,C: list_char] :
( ( ord_le1836582007t_char @ A @ B )
=> ( ( member_list_char @ C @ A )
=> ( member_list_char @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(349,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( A = B )
=> ( ord_le241064091lle_tv @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_equalityD2) ).
thf(2355,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( A = B )
=> ( ord_le241064091lle_tv @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(255,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_dual__order_Oantisym) ).
thf(1984,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(175,axiom,
! [A: paraco1605129243lle_tv > $o,B: paraco1605129243lle_tv > $o,C: set_o] :
( ! [D: paraco1605129243lle_tv] :
( ( A @ D )
=> ( member_o @ ( B @ D ) @ C ) )
=> ( ord_less_eq_set_o @ ( image_991799618e_tv_o @ B @ ( collec1111687558lle_tv @ A ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_image__Collect__subsetI) ).
thf(1599,plain,
! [A: paraco1605129243lle_tv > $o,B: paraco1605129243lle_tv > $o,C: set_o] :
( ! [D: paraco1605129243lle_tv] :
( ( A @ D )
=> ( member_o @ ( B @ D ) @ C ) )
=> ( ord_less_eq_set_o @ ( image_991799618e_tv_o @ B @ ( collec1111687558lle_tv @ A ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(189,axiom,
! [A: set_list_char,B: set_list_char,C: list_char > paraco1605129243lle_tv,D: list_char > paraco1605129243lle_tv,E: set_Pa1764573435lle_tv > paraco1605129243lle_tv] :
( ( A = B )
=> ( ! [F: list_char] :
( ( member_list_char @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image_1187894195lle_tv @ C @ A ) )
= ( E @ ( image_1187894195lle_tv @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_Sup_OSUP__cong) ).
thf(1715,plain,
! [A: set_list_char,B: set_list_char,C: list_char > paraco1605129243lle_tv,D: list_char > paraco1605129243lle_tv,E: set_Pa1764573435lle_tv > paraco1605129243lle_tv] :
( ( A = B )
=> ( ! [F: list_char] :
( ( member_list_char @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image_1187894195lle_tv @ C @ A ) )
= ( E @ ( image_1187894195lle_tv @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(327,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ B @ C )
=> ( ord_le241064091lle_tv @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_subset__trans) ).
thf(2272,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ B @ C )
=> ( ord_le241064091lle_tv @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(200,axiom,
! [A: list_char,B: list_char > list_char] :
( ( member_list_char @ A @ ( image_890964937t_char @ B @ top_to748628679t_char ) )
=> ~ ! [C: list_char] :
( A
!= ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_rangeE) ).
thf(1759,plain,
! [A: list_char,B: list_char > list_char] :
( ( member_list_char @ A @ ( image_890964937t_char @ B @ top_to748628679t_char ) )
=> ~ ! [C: list_char] :
( A
!= ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(218,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( A = B )
=> ( ord_le241064091lle_tv @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_eq__refl) ).
thf(1825,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( A = B )
=> ( ord_le241064091lle_tv @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(99,axiom,
! [A: paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv,D: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( member266900804lle_tv @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member266900804lle_tv @ C @ ( image_335818702lle_tv @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_rev__image__eqI) ).
thf(1114,plain,
! [A: paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv,D: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( member266900804lle_tv @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member266900804lle_tv @ C @ ( image_335818702lle_tv @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(354,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_antisym) ).
thf(2387,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(118,axiom,
! [A: list_char,B: list_char > list_char,C: set_list_char] :
( ( member_list_char @ A @ ( image_890964937t_char @ B @ C ) )
=> ~ ! [D: list_char] :
( ( A
= ( B @ D ) )
=> ~ ( member_list_char @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_imageE) ).
thf(1231,plain,
! [A: list_char,B: list_char > list_char,C: set_list_char] :
( ( member_list_char @ A @ ( image_890964937t_char @ B @ C ) )
=> ~ ! [D: list_char] :
( ( A
= ( B @ D ) )
=> ~ ( member_list_char @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(259,axiom,
! [A: paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv,D: paraco1605129243lle_tv > $o] :
( ( member266900804lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ B
@ ( collec1111687558lle_tv
@ ^ [E: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_prop__restrict) ).
thf(2006,plain,
! [A: paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv,D: paraco1605129243lle_tv > $o] :
( ( member266900804lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ B
@ ( collec1111687558lle_tv
@ ^ [E: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(55,axiom,
! [A: $o,B: $o > $o,C: set_o] :
( ( member_o @ A @ ( image_o_o @ B @ C ) )
= ( ? [D: $o] :
( ( member_o @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_image__iff) ).
thf(721,plain,
! [A: $o,B: $o > $o,C: set_o] :
( ( member_o @ A @ ( image_o_o @ B @ C ) )
= ( ? [D: $o] :
( ( member_o @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(225,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv > $o] :
( ( ! [D: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ D @ ( image_335818702lle_tv @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ D @ B )
=> ( C @ ( image_335818702lle_tv @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_all__subset__image) ).
thf(1857,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv > $o] :
( ( ! [D: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ D @ ( image_335818702lle_tv @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ D @ B )
=> ( C @ ( image_335818702lle_tv @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(136,axiom,
! [A: $o > $o,B: set_o,C: $o > $o] :
( ! [D: $o] :
( ( member_o @ D @ ( image_o_o @ A @ B ) )
=> ( C @ D ) )
=> ! [D: $o] :
( ( member_o @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_ball__imageD) ).
thf(1318,plain,
! [A: $o > $o,B: set_o,C: $o > $o] :
( ! [D: $o] :
( ( member_o @ D @ ( image_o_o @ A @ B ) )
=> ( C @ D ) )
=> ! [D: $o] :
( ( member_o @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(312,axiom,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1344940915le_Det @ $false ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco445776468le_Neg @ B ) )
= ( paraco1344940915le_Det @ $true ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1344940915le_Det @ $false ) )
=> ( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco445776468le_Neg @ B ) )
= ( paraco1344940915le_Det @ $false ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco445776468le_Neg @ B ) )
= ( paraco1325918602e_eval @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_eval__negation) ).
thf(2203,plain,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1344940915le_Det @ $false ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco445776468le_Neg @ B ) )
= ( paraco1344940915le_Det @ $true ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1344940915le_Det @ $false ) )
=> ( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco445776468le_Neg @ B ) )
= ( paraco1344940915le_Det @ $false ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco445776468le_Neg @ B ) )
= ( paraco1325918602e_eval @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(4,axiom,
! [A: $o > $o,B: set_o,C: set_o] :
( ( ord_less_eq_set_o @ ( image_o_o @ A @ B ) @ C )
=> ( ord_le2085948664_set_o @ ( image_set_o_set_o @ ( image_o_o @ A ) @ ( pow_o @ B ) ) @ ( pow_o @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_image__Pow__mono) ).
thf(360,plain,
! [A: $o > $o,B: set_o,C: set_o] :
( ( ord_less_eq_set_o @ ( image_o_o @ A @ B ) @ C )
=> ( ord_le2085948664_set_o @ ( image_set_o_set_o @ ( image_o_o @ A ) @ ( pow_o @ B ) ) @ ( pow_o @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(37,axiom,
! [A: set_o,B: set_o > set_o,C: set_o,D: set_o] :
( ( ord_less_eq_set_o @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_o @ C @ D )
=> ( ! [E: set_o,F: set_o] :
( ( ord_less_eq_set_o @ E @ F )
=> ( ord_less_eq_set_o @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_o @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_order__subst1) ).
thf(541,plain,
! [A: set_o,B: set_o > set_o,C: set_o,D: set_o] :
( ( ord_less_eq_set_o @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_o @ C @ D )
=> ( ! [E: set_o,F: set_o] :
( ( ord_less_eq_set_o @ E @ F )
=> ( ord_less_eq_set_o @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_o @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(280,axiom,
( top_top_list_char_o
= ( ^ [A: list_char] : ( member_list_char @ A @ top_to748628679t_char ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_top__empty__eq) ).
thf(2089,plain,
( top_top_list_char_o
= ( ^ [A: list_char] : ( member_list_char @ A @ top_to748628679t_char ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(88,axiom,
! [A: set_o] :
( ! [B: $o] : ( member_o @ B @ A )
=> ( top_top_set_o = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_UNIV__eq__I) ).
thf(1026,plain,
! [A: set_o] :
( ! [B: $o] : ( member_o @ B @ A )
=> ( top_top_set_o = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(257,axiom,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1325918602e_eval @ A @ C ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1389086619le_Eql @ B @ C ) )
= ( paraco1344940915le_Det @ $true ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1325918602e_eval @ A @ C ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1389086619le_Eql @ B @ C ) )
= ( paraco1344940915le_Det @ $false ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_eval_Osimps_I5_J) ).
thf(1996,plain,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1325918602e_eval @ A @ C ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1389086619le_Eql @ B @ C ) )
= ( paraco1344940915le_Det @ $true ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1325918602e_eval @ A @ C ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco1389086619le_Eql @ B @ C ) )
= ( paraco1344940915le_Det @ $false ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(51,axiom,
! [A: set_o,B: set_o] :
( ( A = B )
=> ( ord_less_eq_set_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_equalityD1) ).
thf(662,plain,
! [A: set_o,B: set_o] :
( ( A = B )
=> ( ord_less_eq_set_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(158,axiom,
( top_to1299250770e_tv_o
= ( ^ [A: paraco1605129243lle_tv] : ( member266900804lle_tv @ A @ top_to1057771083lle_tv ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_top__empty__eq) ).
thf(1510,plain,
( top_to1299250770e_tv_o
= ( ^ [A: paraco1605129243lle_tv] : ( member266900804lle_tv @ A @ top_to1057771083lle_tv ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(123,axiom,
! [A: set_o] :
( ( image_o_o
@ ^ [B: $o] : B
@ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_image__ident) ).
thf(1251,plain,
! [A: set_o] :
( ( image_o_o
@ ^ [B: $o] : B
@ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(197,axiom,
! [A: set_o,B: $o > paraco1605129243lle_tv,C: set_Pa1764573435lle_tv] :
( ! [D: $o] :
( ( member_o @ D @ A )
=> ( member266900804lle_tv @ ( B @ D ) @ C ) )
=> ( ord_le241064091lle_tv @ ( image_1491822472lle_tv @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_image__subsetI) ).
thf(1747,plain,
! [A: set_o,B: $o > paraco1605129243lle_tv,C: set_Pa1764573435lle_tv] :
( ! [D: $o] :
( ( member_o @ D @ A )
=> ( member266900804lle_tv @ ( B @ D ) @ C ) )
=> ( ord_le241064091lle_tv @ ( image_1491822472lle_tv @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(167,axiom,
! [A: list_char,B: paraco1604210848lle_fm] :
( ( paraco1480028776le_Pro @ A )
!= ( paraco445776468le_Neg @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_fm_Odistinct_I3_J) ).
thf(1548,plain,
! [A: list_char,B: paraco1604210848lle_fm] :
( ( paraco1480028776le_Pro @ A )
!= ( paraco445776468le_Neg @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(43,axiom,
! [A: paraco1605129243lle_tv] : ( member266900804lle_tv @ A @ top_to1057771083lle_tv ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_UNIV__I) ).
thf(573,plain,
! [A: paraco1605129243lle_tv] : ( member266900804lle_tv @ A @ top_to1057771083lle_tv ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(107,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm] :
( ( ( paraco445776468le_Neg @ A )
= ( paraco445776468le_Neg @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_fm_Oinject_I2_J) ).
thf(1146,plain,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm] :
( ( ( paraco445776468le_Neg @ A )
= ( paraco445776468le_Neg @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(333,axiom,
( paraco327635598_valid
= ( ^ [A: paraco1604210848lle_fm] :
! [B: list_char > paraco1605129243lle_tv] :
( ( paraco1325918602e_eval @ B @ A )
= ( paraco1344940915le_Det @ $true ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_valid__def) ).
thf(2292,plain,
( paraco327635598_valid
= ( ^ [A: paraco1604210848lle_fm] :
! [B: list_char > paraco1605129243lle_tv] :
( ( paraco1325918602e_eval @ B @ A )
= ( paraco1344940915le_Det @ $true ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(328,axiom,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv,C: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ ( image_335818702lle_tv @ B @ C ) )
= ( ? [D: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ D @ C )
& ( A
= ( image_335818702lle_tv @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_subset__image__iff) ).
thf(2275,plain,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv,C: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ ( image_335818702lle_tv @ B @ C ) )
= ( ? [D: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ D @ C )
& ( A
= ( image_335818702lle_tv @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(267,axiom,
! [A: set_Pa1764573435lle_tv,B: set_o > set_Pa1764573435lle_tv,C: set_o,D: set_o] :
( ( ord_le241064091lle_tv @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_o @ C @ D )
=> ( ! [E: set_o,F: set_o] :
( ( ord_less_eq_set_o @ E @ F )
=> ( ord_le241064091lle_tv @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le241064091lle_tv @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_order__subst1) ).
thf(2033,plain,
! [A: set_Pa1764573435lle_tv,B: set_o > set_Pa1764573435lle_tv,C: set_o,D: set_o] :
( ( ord_le241064091lle_tv @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_o @ C @ D )
=> ( ! [E: set_o,F: set_o] :
( ( ord_less_eq_set_o @ E @ F )
=> ( ord_le241064091lle_tv @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le241064091lle_tv @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(296,axiom,
( ( (=) @ set_Pa1764573435lle_tv )
= ( ^ [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ B @ A )
& ( ord_le241064091lle_tv @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_dual__order_Oeq__iff) ).
thf(2149,plain,
( ( (=) @ set_Pa1764573435lle_tv )
= ( ^ [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ B @ A )
& ( ord_le241064091lle_tv @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(220,axiom,
! [A: list_char > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( ( image_1187894195lle_tv @ A @ top_to748628679t_char )
= top_to1057771083lle_tv )
=> ? [C: list_char] :
( B
= ( A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_surjD) ).
thf(1833,plain,
! [A: list_char > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( ( image_1187894195lle_tv @ A @ top_to748628679t_char )
= top_to1057771083lle_tv )
=> ? [C: list_char] :
( B
= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(232,axiom,
! [A: set_o,B: set_Pa1764573435lle_tv > set_o,C: set_Pa1764573435lle_tv,D: set_Pa1764573435lle_tv] :
( ( A
= ( B @ C ) )
=> ( ( ord_le241064091lle_tv @ C @ D )
=> ( ! [E: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ E @ F )
=> ( ord_less_eq_set_o @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_o @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_ord__eq__le__subst) ).
thf(1884,plain,
! [A: set_o,B: set_Pa1764573435lle_tv > set_o,C: set_Pa1764573435lle_tv,D: set_Pa1764573435lle_tv] :
( ( A
= ( B @ C ) )
=> ( ( ord_le241064091lle_tv @ C @ D )
=> ( ! [E: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ E @ F )
=> ( ord_less_eq_set_o @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_o @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(306,axiom,
( paraco1325918602e_eval
= ( ^ [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] : ( paraco1325918602e_eval @ A @ ( paraco445776468le_Neg @ ( paraco445776468le_Neg @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_double__negation) ).
thf(2188,plain,
( paraco1325918602e_eval
= ( ^ [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] : ( paraco1325918602e_eval @ A @ ( paraco445776468le_Neg @ ( paraco445776468le_Neg @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(243,axiom,
! [A: $o > list_char,B: list_char > $o] :
( ! [C: list_char] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_o_list_char @ A @ top_top_set_o )
= top_to748628679t_char ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_surjI) ).
thf(1929,plain,
! [A: $o > list_char,B: list_char > $o] :
( ! [C: list_char] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_o_list_char @ A @ top_top_set_o )
= top_to748628679t_char ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(45,axiom,
! [A: $o,B: $o > $o,C: $o,D: set_o] :
( ( A
= ( B @ C ) )
=> ( ( member_o @ C @ D )
=> ( member_o @ A @ ( image_o_o @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_image__eqI) ).
thf(579,plain,
! [A: $o,B: $o > $o,C: $o,D: set_o] :
( ( A
= ( B @ C ) )
=> ( ( member_o @ C @ D )
=> ( member_o @ A @ ( image_o_o @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(210,axiom,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco1325918602e_eval @ A @ ( paraco1389086619le_Eql @ B @ C ) )
= ( paraco1344940915le_Det
@ ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1325918602e_eval @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_eval__equality__simplify) ).
thf(1795,plain,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco1325918602e_eval @ A @ ( paraco1389086619le_Eql @ B @ C ) )
= ( paraco1344940915le_Det
@ ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1325918602e_eval @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(12,axiom,
! [A: set_o,B: set_o,C: set_o > set_o,D: set_o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( ord_less_eq_set_o @ ( C @ B ) @ D )
=> ( ! [E: set_o,F: set_o] :
( ( ord_less_eq_set_o @ E @ F )
=> ( ord_less_eq_set_o @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_o @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_order__subst2) ).
thf(413,plain,
! [A: set_o,B: set_o,C: set_o > set_o,D: set_o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( ord_less_eq_set_o @ ( C @ B ) @ D )
=> ( ! [E: set_o,F: set_o] :
( ( ord_less_eq_set_o @ E @ F )
=> ( ord_less_eq_set_o @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_o @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(299,axiom,
! [A: nat > $o,B: set_nat,C: $o > $o] :
( ( collect_o
@ ^ [D: $o] :
( ( member_o @ D @ ( image_nat_o @ A @ B ) )
& ( C @ D ) ) )
= ( image_nat_o @ A
@ ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_Compr__image__eq) ).
thf(2161,plain,
! [A: nat > $o,B: set_nat,C: $o > $o] :
( ( collect_o
@ ^ [D: $o] :
( ( member_o @ D @ ( image_nat_o @ A @ B ) )
& ( C @ D ) ) )
= ( image_nat_o @ A
@ ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(97,axiom,
! [A: set_list_char,B: set_list_char,C: list_char > $o] :
( ( ord_le1836582007t_char @ A @ B )
=> ( ( ord_le1836582007t_char @ A
@ ( collect_list_char
@ ^ [D: list_char] :
( ( member_list_char @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: list_char] :
( ( member_list_char @ D @ A )
=> ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_subset__Collect__iff) ).
thf(1107,plain,
! [A: set_list_char,B: set_list_char,C: list_char > $o] :
( ( ord_le1836582007t_char @ A @ B )
=> ( ( ord_le1836582007t_char @ A
@ ( collect_list_char
@ ^ [D: list_char] :
( ( member_list_char @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: list_char] :
( ( member_list_char @ D @ A )
=> ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(301,axiom,
! [A: set_o,B: set_o,C: set_o > set_Pa1764573435lle_tv,D: set_Pa1764573435lle_tv] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( ord_le241064091lle_tv @ ( C @ B ) @ D )
=> ( ! [E: set_o,F: set_o] :
( ( ord_less_eq_set_o @ E @ F )
=> ( ord_le241064091lle_tv @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le241064091lle_tv @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_order__subst2) ).
thf(2166,plain,
! [A: set_o,B: set_o,C: set_o > set_Pa1764573435lle_tv,D: set_Pa1764573435lle_tv] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( ord_le241064091lle_tv @ ( C @ B ) @ D )
=> ( ! [E: set_o,F: set_o] :
( ( ord_less_eq_set_o @ E @ F )
=> ( ord_le241064091lle_tv @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le241064091lle_tv @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(144,axiom,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv > $o] :
( ( member266900804lle_tv @ A @ ( collec1111687558lle_tv @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_mem__Collect__eq) ).
thf(1408,plain,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv > $o] :
( ( member266900804lle_tv @ A @ ( collec1111687558lle_tv @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(297,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
( ( A = B )
=> ( ( ord_le241064091lle_tv @ B @ C )
=> ( ord_le241064091lle_tv @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_ord__eq__le__trans) ).
thf(2151,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
( ( A = B )
=> ( ( ord_le241064091lle_tv @ B @ C )
=> ( ord_le241064091lle_tv @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(212,axiom,
! [A: set_list_char] :
( ( ord_le1836582007t_char @ top_to748628679t_char @ A )
= ( A = top_to748628679t_char ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_top_Oextremum__unique) ).
thf(1806,plain,
! [A: set_list_char] :
( ( ord_le1836582007t_char @ top_to748628679t_char @ A )
= ( A = top_to748628679t_char ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(163,axiom,
? [A: paraco1605129243lle_tv] : ( member266900804lle_tv @ A @ top_to1057771083lle_tv ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_UNIV__witness) ).
thf(1524,plain,
? [A: paraco1605129243lle_tv] : ( member266900804lle_tv @ A @ top_to1057771083lle_tv ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(138,axiom,
! [A: $o > $o,B: set_o,C: set_o] :
( ( ord_less_eq_set_o @ ( image_o_o @ A @ B ) @ C )
= ( ! [D: $o] :
( ( member_o @ D @ B )
=> ( member_o @ ( A @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_image__subset__iff) ).
thf(1349,plain,
! [A: $o > $o,B: set_o,C: set_o] :
( ( ord_less_eq_set_o @ ( image_o_o @ A @ B ) @ C )
= ( ! [D: $o] :
( ( member_o @ D @ B )
=> ( member_o @ ( A @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(244,axiom,
! [A: list_char > $o,B: $o] :
( ( ( image_list_char_o @ A @ top_to748628679t_char )
= top_top_set_o )
=> ~ ! [C: list_char] :
( B
= ( ~ ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_surjE) ).
thf(1933,plain,
! [A: list_char > $o,B: $o] :
( ( ( image_list_char_o @ A @ top_to748628679t_char )
= top_top_set_o )
=> ~ ! [C: list_char] :
( B
= ( ~ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(176,axiom,
! [A: paraco1605129243lle_tv > $o,B: paraco1605129243lle_tv > $o] :
( ! [C: paraco1605129243lle_tv] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collec1111687558lle_tv @ A )
= ( collec1111687558lle_tv @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_Collect__cong) ).
thf(1603,plain,
! [A: paraco1605129243lle_tv > $o,B: paraco1605129243lle_tv > $o] :
( ! [C: paraco1605129243lle_tv] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collec1111687558lle_tv @ A )
= ( collec1111687558lle_tv @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(106,axiom,
( top_top_o_o
= ( ^ [A: $o] : ( member_o @ A @ top_top_set_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_top__empty__eq) ).
thf(1144,plain,
( top_top_o_o
= ( ^ [A: $o] : ( member_o @ A @ top_top_set_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(92,axiom,
! [A: $o > paraco1605129243lle_tv,B: $o] : ( member266900804lle_tv @ ( A @ B ) @ ( image_1491822472lle_tv @ A @ top_top_set_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_rangeI) ).
thf(1043,plain,
! [A: $o > paraco1605129243lle_tv,B: $o] : ( member266900804lle_tv @ ( A @ B ) @ ( image_1491822472lle_tv @ A @ top_top_set_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(101,axiom,
! [A: set_o,B: set_o,C: $o > $o,D: $o > $o,E: set_o > $o] :
( ( A = B )
=> ( ! [F: $o] :
( ( member_o @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image_o_o @ C @ A ) )
= ( E @ ( image_o_o @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_Inf_OINF__cong) ).
thf(1122,plain,
! [A: set_o,B: set_o,C: $o > $o,D: $o > $o,E: set_o > $o] :
( ( A = B )
=> ( ! [F: $o] :
( ( member_o @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image_o_o @ C @ A ) )
= ( E @ ( image_o_o @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(272,axiom,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > $o,C: paraco1605129243lle_tv > $o] :
( ( ord_le241064091lle_tv @ A
@ ( collec1111687558lle_tv
@ ^ [D: paraco1605129243lle_tv] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_le241064091lle_tv @ A @ ( collec1111687558lle_tv @ B ) )
& ( ord_le241064091lle_tv @ A @ ( collec1111687558lle_tv @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_conj__subset__def) ).
thf(2065,plain,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > $o,C: paraco1605129243lle_tv > $o] :
( ( ord_le241064091lle_tv @ A
@ ( collec1111687558lle_tv
@ ^ [D: paraco1605129243lle_tv] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_le241064091lle_tv @ A @ ( collec1111687558lle_tv @ B ) )
& ( ord_le241064091lle_tv @ A @ ( collec1111687558lle_tv @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(114,axiom,
! [A: $o > $o] :
( ( ( image_o_o @ A @ top_top_set_o )
= top_top_set_o )
= ( ! [B: $o] :
? [C: $o] :
( B
= ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_surj__def) ).
thf(1209,plain,
! [A: $o > $o] :
( ( ( image_o_o @ A @ top_top_set_o )
= top_top_set_o )
= ( ! [B: $o] :
? [C: $o] :
( B
= ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(290,axiom,
! [A: set_Pa1764573435lle_tv > $o,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv > $o] :
( ( A @ B )
=> ( ! [D: set_Pa1764573435lle_tv] :
( ( A @ D )
=> ( ord_le241064091lle_tv @ D @ B ) )
=> ( ! [D: set_Pa1764573435lle_tv] :
( ( A @ D )
=> ( ! [E: set_Pa1764573435lle_tv] :
( ( A @ E )
=> ( ord_le241064091lle_tv @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_350719188lle_tv @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_GreatestI2__order) ).
thf(2119,plain,
! [A: set_Pa1764573435lle_tv > $o,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv > $o] :
( ( A @ B )
=> ( ! [D: set_Pa1764573435lle_tv] :
( ( A @ D )
=> ( ord_le241064091lle_tv @ D @ B ) )
=> ( ! [D: set_Pa1764573435lle_tv] :
( ( A @ D )
=> ( ! [E: set_Pa1764573435lle_tv] :
( ( A @ E )
=> ( ord_le241064091lle_tv @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_350719188lle_tv @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(278,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_antisym__conv) ).
thf(2084,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(313,axiom,
! [A: list_char > list_char,B: list_char] : ( member_list_char @ ( A @ B ) @ ( image_890964937t_char @ A @ top_to748628679t_char ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_rangeI) ).
thf(2214,plain,
! [A: list_char > list_char,B: list_char] : ( member_list_char @ ( A @ B ) @ ( image_890964937t_char @ A @ top_to748628679t_char ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(264,axiom,
! [A: set_list_char] : ( ord_le1836582007t_char @ A @ top_to748628679t_char ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_top__greatest) ).
thf(2025,plain,
! [A: set_list_char] : ( ord_le1836582007t_char @ A @ top_to748628679t_char ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(57,axiom,
! [A: $o,B: set_o,C: list_char,D: $o > list_char] :
( ( member_o @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member_list_char @ C @ ( image_o_list_char @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_rev__image__eqI) ).
thf(758,plain,
! [A: $o,B: set_o,C: list_char,D: $o > list_char] :
( ( member_o @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member_list_char @ C @ ( image_o_list_char @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(338,axiom,
! [A: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ top_to1057771083lle_tv @ A )
=> ( A = top_to1057771083lle_tv ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_top_Oextremum__uniqueI) ).
thf(2314,plain,
! [A: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ top_to1057771083lle_tv @ A )
=> ( A = top_to1057771083lle_tv ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(288,axiom,
! [A: $o > list_char] :
( ( ( image_o_list_char @ A @ top_top_set_o )
= top_to748628679t_char )
= ( ! [B: list_char] :
? [C: $o] :
( B
= ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_surj__def) ).
thf(2111,plain,
! [A: $o > list_char] :
( ( ( image_o_list_char @ A @ top_top_set_o )
= top_to748628679t_char )
= ( ! [B: list_char] :
? [C: $o] :
( B
= ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(193,axiom,
! [A: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ top_to1057771083lle_tv @ A )
= ( A = top_to1057771083lle_tv ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_top_Oextremum__unique) ).
thf(1731,plain,
! [A: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ top_to1057771083lle_tv @ A )
= ( A = top_to1057771083lle_tv ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(238,axiom,
! [A: set_list_char,B: set_list_char,C: list_char > paraco1605129243lle_tv,D: list_char > paraco1605129243lle_tv] :
( ( A = B )
=> ( ! [E: list_char] :
( ( member_list_char @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image_1187894195lle_tv @ C @ A )
= ( image_1187894195lle_tv @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_image__cong) ).
thf(1909,plain,
! [A: set_list_char,B: set_list_char,C: list_char > paraco1605129243lle_tv,D: list_char > paraco1605129243lle_tv] :
( ( A = B )
=> ( ! [E: list_char] :
( ( member_list_char @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image_1187894195lle_tv @ C @ A )
= ( image_1187894195lle_tv @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(108,axiom,
! [A: set_o,B: $o > $o,C: $o > $o] :
( ( ord_less_eq_set_o @ A
@ ( collect_o
@ ^ [D: $o] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_less_eq_set_o @ A @ ( collect_o @ B ) )
& ( ord_less_eq_set_o @ A @ ( collect_o @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_conj__subset__def) ).
thf(1149,plain,
! [A: set_o,B: $o > $o,C: $o > $o] :
( ( ord_less_eq_set_o @ A
@ ( collect_o
@ ^ [D: $o] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_less_eq_set_o @ A @ ( collect_o @ B ) )
& ( ord_less_eq_set_o @ A @ ( collect_o @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(48,axiom,
! [A: set_o,B: set_o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( ord_less_eq_set_o @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_antisym) ).
thf(626,plain,
! [A: set_o,B: set_o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( ord_less_eq_set_o @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(58,axiom,
! [A: $o > $o,B: $o > $o,C: set_o] :
( ! [D: $o] :
( ( A @ D )
=> ( member_o @ ( B @ D ) @ C ) )
=> ( ord_less_eq_set_o @ ( image_o_o @ B @ ( collect_o @ A ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_image__Collect__subsetI) ).
thf(769,plain,
! [A: $o > $o,B: $o > $o,C: set_o] :
( ! [D: $o] :
( ( A @ D )
=> ( member_o @ ( B @ D ) @ C ) )
=> ( ord_less_eq_set_o @ ( image_o_o @ B @ ( collect_o @ A ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(329,axiom,
! [A: nat > $o,B: nat > $o] :
( ! [C: nat] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_nat @ ( collect_nat @ A ) @ ( collect_nat @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_Collect__mono) ).
thf(2278,plain,
! [A: nat > $o,B: nat > $o] :
( ! [C: nat] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_nat @ ( collect_nat @ A ) @ ( collect_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(183,axiom,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv,C: set_Pa1764573435lle_tv] :
( ( member266900804lle_tv @ A @ ( image_335818702lle_tv @ B @ C ) )
=> ~ ! [D: paraco1605129243lle_tv] :
( ( A
= ( B @ D ) )
=> ~ ( member266900804lle_tv @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_imageE) ).
thf(1688,plain,
! [A: paraco1605129243lle_tv,B: paraco1605129243lle_tv > paraco1605129243lle_tv,C: set_Pa1764573435lle_tv] :
( ( member266900804lle_tv @ A @ ( image_335818702lle_tv @ B @ C ) )
=> ~ ! [D: paraco1605129243lle_tv] :
( ( A
= ( B @ D ) )
=> ~ ( member266900804lle_tv @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(89,axiom,
! [A: $o,B: set_o,C: $o > $o] :
( ( member_o @ A @ B )
=> ( member_o @ ( C @ A ) @ ( image_o_o @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_imageI) ).
thf(1029,plain,
! [A: $o,B: set_o,C: $o > $o] :
( ( member_o @ A @ B )
=> ( member_o @ ( C @ A ) @ ( image_o_o @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(66,axiom,
! [A: set_o,B: $o > $o] :
( ord_less_eq_set_o
@ ( collect_o
@ ^ [C: $o] :
( ( member_o @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_Collect__restrict) ).
thf(895,plain,
! [A: set_o,B: $o > $o] :
( ord_less_eq_set_o
@ ( collect_o
@ ^ [C: $o] :
( ( member_o @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(87,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( paraco69239110le_Con @ A @ B )
!= ( paraco1745535428le_Eql @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_fm_Odistinct_I27_J) ).
thf(1022,plain,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( paraco69239110le_Con @ A @ B )
!= ( paraco1745535428le_Eql @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(323,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( member1875402276lle_tv @ A @ ( pow_Pa475453624lle_tv @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_PowI) ).
thf(2252,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( member1875402276lle_tv @ A @ ( pow_Pa475453624lle_tv @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(74,axiom,
! [A: set_o,B: set_o,C: $o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( member_o @ C @ A )
=> ( member_o @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_subsetD) ).
thf(932,plain,
! [A: set_o,B: set_o,C: $o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( member_o @ C @ A )
=> ( member_o @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(95,axiom,
! [A: paraco1605129243lle_tv,B: $o > paraco1605129243lle_tv,C: set_o] :
( ( member266900804lle_tv @ A @ ( image_1491822472lle_tv @ B @ C ) )
=> ~ ! [D: $o] :
( ( A
= ( B @ D ) )
=> ~ ( member_o @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_imageE) ).
thf(1061,plain,
! [A: paraco1605129243lle_tv,B: $o > paraco1605129243lle_tv,C: set_o] :
( ( member266900804lle_tv @ A @ ( image_1491822472lle_tv @ B @ C ) )
=> ~ ! [D: $o] :
( ( A
= ( B @ D ) )
=> ~ ( member_o @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(69,axiom,
! [A: set_list_char,B: list_char > $o] :
( ord_le1836582007t_char
@ ( collect_list_char
@ ^ [C: list_char] :
( ( member_list_char @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_Collect__restrict) ).
thf(912,plain,
! [A: set_list_char,B: list_char > $o] :
( ord_le1836582007t_char
@ ( collect_list_char
@ ^ [C: list_char] :
( ( member_list_char @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(242,axiom,
! [A: $o > paraco1605129243lle_tv,B: set_o,C: set_Pa1764573435lle_tv > $o] :
( ( ! [D: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ D @ ( image_1491822472lle_tv @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: set_o] :
( ( ord_less_eq_set_o @ D @ B )
=> ( C @ ( image_1491822472lle_tv @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_all__subset__image) ).
thf(1926,plain,
! [A: $o > paraco1605129243lle_tv,B: set_o,C: set_Pa1764573435lle_tv > $o] :
( ( ! [D: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ D @ ( image_1491822472lle_tv @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: set_o] :
( ( ord_less_eq_set_o @ D @ B )
=> ( C @ ( image_1491822472lle_tv @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(347,axiom,
! [A: set_nat,B: nat > $o] :
( ord_less_eq_set_nat
@ ( collect_nat
@ ^ [C: nat] :
( ( member_nat @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_Collect__restrict) ).
thf(2350,plain,
! [A: set_nat,B: nat > $o] :
( ord_less_eq_set_nat
@ ( collect_nat
@ ^ [C: nat] :
( ( member_nat @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(185,axiom,
! [A: set_Pa1764573435lle_tv > $o,B: set_Pa1764573435lle_tv] :
( ( A @ B )
=> ( ! [C: set_Pa1764573435lle_tv] :
( ( A @ C )
=> ( ord_le241064091lle_tv @ C @ B ) )
=> ( ( order_350719188lle_tv @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_Greatest__equality) ).
thf(1699,plain,
! [A: set_Pa1764573435lle_tv > $o,B: set_Pa1764573435lle_tv] :
( ( A @ B )
=> ( ! [C: set_Pa1764573435lle_tv] :
( ( A @ C )
=> ( ord_le241064091lle_tv @ C @ B ) )
=> ( ( order_350719188lle_tv @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(120,axiom,
( ( pow_o @ top_top_set_o )
= top_top_set_set_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_Pow__UNIV) ).
thf(1245,plain,
( ( pow_o @ top_top_set_o )
= top_top_set_set_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(96,axiom,
! [A: $o > $o,B: $o > $o] :
( ! [C: $o] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_o @ ( collect_o @ A ) @ ( collect_o @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_Collect__mono) ).
thf(1066,plain,
! [A: $o > $o,B: $o > $o] :
( ! [C: $o] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_o @ ( collect_o @ A ) @ ( collect_o @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(332,axiom,
! [A: list_char > $o,B: list_char > paraco1605129243lle_tv,C: set_Pa1764573435lle_tv] :
( ! [D: list_char] :
( ( A @ D )
=> ( member266900804lle_tv @ ( B @ D ) @ C ) )
=> ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ B @ ( collect_list_char @ A ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_image__Collect__subsetI) ).
thf(2288,plain,
! [A: list_char > $o,B: list_char > paraco1605129243lle_tv,C: set_Pa1764573435lle_tv] :
( ! [D: list_char] :
( ( A @ D )
=> ( member266900804lle_tv @ ( B @ D ) @ C ) )
=> ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ B @ ( collect_list_char @ A ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(204,axiom,
? [A: list_char] : ( member_list_char @ A @ top_to748628679t_char ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_UNIV__witness) ).
thf(1775,plain,
? [A: list_char] : ( member_list_char @ A @ top_to748628679t_char ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(154,axiom,
! [A: paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv > list_char] :
( ( member266900804lle_tv @ A @ B )
=> ( member_list_char @ ( C @ A ) @ ( image_1971766583t_char @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_imageI) ).
thf(1496,plain,
! [A: paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv > list_char] :
( ( member266900804lle_tv @ A @ B )
=> ( member_list_char @ ( C @ A ) @ ( image_1971766583t_char @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(298,axiom,
! [A: set_Pa1764573435lle_tv,B: list_char > paraco1605129243lle_tv,C: set_list_char] :
( ( ord_le241064091lle_tv @ A @ ( image_1187894195lle_tv @ B @ C ) )
=> ~ ! [D: set_list_char] :
( ( ord_le1836582007t_char @ D @ C )
=> ( A
!= ( image_1187894195lle_tv @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_subset__imageE) ).
thf(2156,plain,
! [A: set_Pa1764573435lle_tv,B: list_char > paraco1605129243lle_tv,C: set_list_char] :
( ( ord_le241064091lle_tv @ A @ ( image_1187894195lle_tv @ B @ C ) )
=> ~ ! [D: set_list_char] :
( ( ord_le1836582007t_char @ D @ C )
=> ( A
!= ( image_1187894195lle_tv @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(72,axiom,
! [A: set_o,B: set_o,C: set_o] :
( ( A = B )
=> ( ( ord_less_eq_set_o @ B @ C )
=> ( ord_less_eq_set_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_ord__eq__le__trans) ).
thf(922,plain,
! [A: set_o,B: set_o,C: set_o] :
( ( A = B )
=> ( ( ord_less_eq_set_o @ B @ C )
=> ( ord_less_eq_set_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(50,axiom,
! [A: paraco1605129243lle_tv > $o,B: paraco1605129243lle_tv > list_char,C: set_list_char] :
( ! [D: paraco1605129243lle_tv] :
( ( A @ D )
=> ( member_list_char @ ( B @ D ) @ C ) )
=> ( ord_le1836582007t_char @ ( image_1971766583t_char @ B @ ( collec1111687558lle_tv @ A ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_image__Collect__subsetI) ).
thf(658,plain,
! [A: paraco1605129243lle_tv > $o,B: paraco1605129243lle_tv > list_char,C: set_list_char] :
( ! [D: paraco1605129243lle_tv] :
( ( A @ D )
=> ( member_list_char @ ( B @ D ) @ C ) )
=> ( ord_le1836582007t_char @ ( image_1971766583t_char @ B @ ( collec1111687558lle_tv @ A ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(80,axiom,
! [A: set_o,B: set_o] :
( ( ord_less_eq_o_o
@ ^ [C: $o] : ( member_o @ C @ A )
@ ^ [C: $o] : ( member_o @ C @ B ) )
= ( ord_less_eq_set_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_pred__subset__eq) ).
thf(959,plain,
! [A: set_o,B: set_o] :
( ( ord_less_eq_o_o
@ ^ [C: $o] : ( member_o @ C @ A )
@ ^ [C: $o] : ( member_o @ C @ B ) )
= ( ord_less_eq_set_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(302,axiom,
( ( (=) @ set_Pa1764573435lle_tv )
= ( ^ [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
& ( ord_le241064091lle_tv @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_set__eq__subset) ).
thf(2171,plain,
( ( (=) @ set_Pa1764573435lle_tv )
= ( ^ [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
& ( ord_le241064091lle_tv @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(191,axiom,
( ord_le241064091lle_tv
= ( ^ [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ord_le1632188418e_tv_o
@ ^ [C: paraco1605129243lle_tv] : ( member266900804lle_tv @ C @ A )
@ ^ [C: paraco1605129243lle_tv] : ( member266900804lle_tv @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_less__eq__set__def) ).
thf(1726,plain,
( ord_le241064091lle_tv
= ( ^ [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ord_le1632188418e_tv_o
@ ^ [C: paraco1605129243lle_tv] : ( member266900804lle_tv @ C @ A )
@ ^ [C: paraco1605129243lle_tv] : ( member266900804lle_tv @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(140,axiom,
( ( (=) @ set_o )
= ( ^ [A: set_o,B: set_o] :
( ( ord_less_eq_set_o @ A @ B )
& ( ord_less_eq_set_o @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_order__class_Oorder_Oeq__iff) ).
thf(1364,plain,
( ( (=) @ set_o )
= ( ^ [A: set_o,B: set_o] :
( ( ord_less_eq_set_o @ A @ B )
& ( ord_less_eq_set_o @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(213,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( member266900804lle_tv @ C @ A )
=> ( member266900804lle_tv @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_subsetD) ).
thf(1809,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( member266900804lle_tv @ C @ A )
=> ( member266900804lle_tv @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(283,axiom,
! [A: list_char > paraco1605129243lle_tv,B: list_char] :
( ( paraco1325918602e_eval @ A @ ( paraco1480028776le_Pro @ B ) )
= ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_eval_Osimps_I1_J) ).
thf(2096,plain,
! [A: list_char > paraco1605129243lle_tv,B: list_char] :
( ( paraco1325918602e_eval @ A @ ( paraco1480028776le_Pro @ B ) )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(230,axiom,
! [A: $o,B: list_char > $o] :
( ( member_o @ A @ ( image_list_char_o @ B @ top_to748628679t_char ) )
=> ~ ! [C: list_char] :
( A
= ( ~ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_rangeE) ).
thf(1873,plain,
! [A: $o,B: list_char > $o] :
( ( member_o @ A @ ( image_list_char_o @ B @ top_to748628679t_char ) )
=> ~ ! [C: list_char] :
( A
= ( ~ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(111,axiom,
! [A: set_o] : ( ord_less_eq_set_o @ A @ top_top_set_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_subset__UNIV) ).
thf(1166,plain,
! [A: set_o] : ( ord_less_eq_set_o @ A @ top_top_set_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(147,axiom,
! [A: set_o > $o,B: set_o] :
( ( A @ B )
=> ( ! [C: set_o] :
( ( A @ C )
=> ( ord_less_eq_set_o @ C @ B ) )
=> ( ( order_Greatest_set_o @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_Greatest__equality) ).
thf(1467,plain,
! [A: set_o > $o,B: set_o] :
( ( A @ B )
=> ( ! [C: set_o] :
( ( A @ C )
=> ( ord_less_eq_set_o @ C @ B ) )
=> ( ( order_Greatest_set_o @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(237,axiom,
! [A: set_nat,B: set_nat,C: nat > $o] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ A
@ ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: nat] :
( ( member_nat @ D @ A )
=> ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_subset__Collect__iff) ).
thf(1905,plain,
! [A: set_nat,B: set_nat,C: nat > $o] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ A
@ ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: nat] :
( ( member_nat @ D @ A )
=> ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(73,axiom,
! [A: list_char,B: list_char > list_char,C: list_char,D: set_list_char] :
( ( A
= ( B @ C ) )
=> ( ( member_list_char @ C @ D )
=> ( member_list_char @ A @ ( image_890964937t_char @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_image__eqI) ).
thf(927,plain,
! [A: list_char,B: list_char > list_char,C: list_char,D: set_list_char] :
( ( A
= ( B @ C ) )
=> ( ( member_list_char @ C @ D )
=> ( member_list_char @ A @ ( image_890964937t_char @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(103,axiom,
! [A: set_o,B: set_o] :
( ! [C: $o] :
( ( member_o @ C @ A )
=> ( member_o @ C @ B ) )
=> ( ord_less_eq_set_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_subsetI) ).
thf(1134,plain,
! [A: set_o,B: set_o] :
( ! [C: $o] :
( ( member_o @ C @ A )
=> ( member_o @ C @ B ) )
=> ( ord_less_eq_set_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(76,axiom,
! [A: set_list_char] :
( ( collect_list_char
@ ^ [B: list_char] : ( member_list_char @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_Collect__mem__eq) ).
thf(939,plain,
! [A: set_list_char] :
( ( collect_list_char
@ ^ [B: list_char] : ( member_list_char @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(1,conjecture,
( ( ! [A: list_char > paraco1605129243lle_tv] :
( ( paraco1325918602e_eval @ A @ p )
= ( paraco1344940915le_Det @ $true ) ) )
!= ( ~ ! [A: list_char > paraco1605129243lle_tv] :
( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ A @ top_to748628679t_char )
@ ( paraco1933902578domain
@ ( collect_nat
@ ^ [B: nat] : $true ) ) )
=> ( ( paraco1325918602e_eval @ A @ p )
= ( paraco1344940915le_Det @ $true ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( ( ! [A: list_char > paraco1605129243lle_tv] :
( ( paraco1325918602e_eval @ A @ p )
= ( paraco1344940915le_Det @ $true ) ) )
!= ( ~ ! [A: list_char > paraco1605129243lle_tv] :
( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ A @ top_to748628679t_char )
@ ( paraco1933902578domain
@ ( collect_nat
@ ^ [B: nat] : $true ) ) )
=> ( ( paraco1325918602e_eval @ A @ p )
= ( paraco1344940915le_Det @ $true ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(355,plain,
~ ( ( ( ! [A: list_char > paraco1605129243lle_tv] :
( ( paraco1325918602e_eval @ A @ p )
= ( paraco1344940915le_Det @ $true ) ) )
!= ( ~ ! [A: list_char > paraco1605129243lle_tv] :
( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ A @ top_to748628679t_char )
@ ( paraco1933902578domain
@ ( collect_nat
@ ^ [B: nat] : $true ) ) )
=> ( ( paraco1325918602e_eval @ A @ p )
= ( paraco1344940915le_Det @ $true ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(56,axiom,
! [A: list_char,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco1480028776le_Pro @ A )
!= ( paraco1745535428le_Eql @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_fm_Odistinct_I9_J) ).
thf(754,plain,
! [A: list_char,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco1480028776le_Pro @ A )
!= ( paraco1745535428le_Eql @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(40,axiom,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > $o,C: set_o] :
( ! [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ A )
=> ( member_o @ ( B @ D ) @ C ) )
=> ( ord_less_eq_set_o @ ( image_991799618e_tv_o @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_image__subsetI) ).
thf(557,plain,
! [A: set_Pa1764573435lle_tv,B: paraco1605129243lle_tv > $o,C: set_o] :
( ! [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ A )
=> ( member_o @ ( B @ D ) @ C ) )
=> ( ord_less_eq_set_o @ ( image_991799618e_tv_o @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(116,axiom,
! [A: $o] : ( member_o @ A @ top_top_set_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_iso__tuple__UNIV__I) ).
thf(1225,plain,
! [A: $o] : ( member_o @ A @ top_top_set_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(308,axiom,
! [A: nat > $o,B: nat > list_char,C: set_list_char] :
( ! [D: nat] :
( ( A @ D )
=> ( member_list_char @ ( B @ D ) @ C ) )
=> ( ord_le1836582007t_char @ ( image_nat_list_char @ B @ ( collect_nat @ A ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_image__Collect__subsetI) ).
thf(2192,plain,
! [A: nat > $o,B: nat > list_char,C: set_list_char] :
( ! [D: nat] :
( ( A @ D )
=> ( member_list_char @ ( B @ D ) @ C ) )
=> ( ord_le1836582007t_char @ ( image_nat_list_char @ B @ ( collect_nat @ A ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(79,axiom,
! [A: paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: $o,D: paraco1605129243lle_tv > $o] :
( ( member266900804lle_tv @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member_o @ C @ ( image_991799618e_tv_o @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_rev__image__eqI) ).
thf(954,plain,
! [A: paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: $o,D: paraco1605129243lle_tv > $o] :
( ( member266900804lle_tv @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member_o @ C @ ( image_991799618e_tv_o @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(150,axiom,
! [A: list_char,B: set_list_char,C: set_list_char,D: list_char > $o] :
( ( member_list_char @ A @ B )
=> ( ( ord_le1836582007t_char @ B
@ ( collect_list_char
@ ^ [E: list_char] :
( ( member_list_char @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_prop__restrict) ).
thf(1484,plain,
! [A: list_char,B: set_list_char,C: set_list_char,D: list_char > $o] :
( ( member_list_char @ A @ B )
=> ( ( ord_le1836582007t_char @ B
@ ( collect_list_char
@ ^ [E: list_char] :
( ( member_list_char @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(211,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( A = B )
=> ~ ( ( ord_le241064091lle_tv @ A @ B )
=> ~ ( ord_le241064091lle_tv @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_equalityE) ).
thf(1798,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( A = B )
=> ~ ( ( ord_le241064091lle_tv @ A @ B )
=> ~ ( ord_le241064091lle_tv @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(33,axiom,
! [A: paraco1604210848lle_fm] :
( ! [B: list_char] :
( A
!= ( paraco1480028776le_Pro @ B ) )
=> ( ( A != paraco367965286_Truth )
=> ( ! [B: paraco1604210848lle_fm] :
( A
!= ( paraco445776468le_Neg @ B ) )
=> ( ! [B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( A
!= ( paraco69239110le_Con @ B @ C ) )
=> ( ! [B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( A
!= ( paraco1389086619le_Eql @ B @ C ) )
=> ~ ! [B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( A
!= ( paraco1745535428le_Eql @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_fm_Oexhaust) ).
thf(525,plain,
! [A: paraco1604210848lle_fm] :
( ! [B: list_char] :
( A
!= ( paraco1480028776le_Pro @ B ) )
=> ( ( A != paraco367965286_Truth )
=> ( ! [B: paraco1604210848lle_fm] :
( A
!= ( paraco445776468le_Neg @ B ) )
=> ( ! [B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( A
!= ( paraco69239110le_Con @ B @ C ) )
=> ( ! [B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( A
!= ( paraco1389086619le_Eql @ B @ C ) )
=> ~ ! [B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( A
!= ( paraco1745535428le_Eql @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(155,axiom,
! [A: list_char,B: $o > list_char,C: set_o] :
( ( member_list_char @ A @ ( image_o_list_char @ B @ C ) )
=> ~ ! [D: $o] :
( ( A
= ( B @ D ) )
=> ~ ( member_o @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_imageE) ).
thf(1499,plain,
! [A: list_char,B: $o > list_char,C: set_o] :
( ( member_list_char @ A @ ( image_o_list_char @ B @ C ) )
=> ~ ! [D: $o] :
( ( A
= ( B @ D ) )
=> ~ ( member_o @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(256,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv,D: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ E @ F )
=> ( ord_le241064091lle_tv @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le241064091lle_tv @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_ord__le__eq__subst) ).
thf(1987,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv,D: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ E @ F )
=> ( ord_le241064091lle_tv @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le241064091lle_tv @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(91,axiom,
! [A: list_char,B: $o > list_char,C: $o] :
( ( A
= ( B @ C ) )
=> ( member_list_char @ A @ ( image_o_list_char @ B @ top_top_set_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_range__eqI) ).
thf(1038,plain,
! [A: list_char,B: $o > list_char,C: $o] :
( ( A
= ( B @ C ) )
=> ( member_list_char @ A @ ( image_o_list_char @ B @ top_top_set_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(229,axiom,
! [A: list_char > list_char,B: list_char] :
( ( ( image_890964937t_char @ A @ top_to748628679t_char )
= top_to748628679t_char )
=> ? [C: list_char] :
( B
= ( A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_surjD) ).
thf(1869,plain,
! [A: list_char > list_char,B: list_char] :
( ( ( image_890964937t_char @ A @ top_to748628679t_char )
= top_to748628679t_char )
=> ? [C: list_char] :
( B
= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(207,axiom,
! [A: list_char > $o,B: list_char] : ( member_o @ ( A @ B ) @ ( image_list_char_o @ A @ top_to748628679t_char ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_rangeI) ).
thf(1785,plain,
! [A: list_char > $o,B: list_char] : ( member_o @ ( A @ B ) @ ( image_list_char_o @ A @ top_to748628679t_char ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(126,axiom,
! [A: set_o] : ( ord_less_eq_set_o @ A @ top_top_set_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_top__greatest) ).
thf(1262,plain,
! [A: set_o] : ( ord_less_eq_set_o @ A @ top_top_set_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(18,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( paraco69239110le_Con @ A @ B )
!= ( paraco1389086619le_Eql @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_fm_Odistinct_I25_J) ).
thf(463,plain,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( paraco69239110le_Con @ A @ B )
!= ( paraco1389086619le_Eql @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(201,axiom,
! [A: list_char,B: set_list_char,C: list_char > paraco1605129243lle_tv] :
( ( member_list_char @ A @ B )
=> ( member266900804lle_tv @ ( C @ A ) @ ( image_1187894195lle_tv @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_imageI) ).
thf(1763,plain,
! [A: list_char,B: set_list_char,C: list_char > paraco1605129243lle_tv] :
( ( member_list_char @ A @ B )
=> ( member266900804lle_tv @ ( C @ A ) @ ( image_1187894195lle_tv @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(78,axiom,
! [A: set_o,B: set_o,C: set_o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( ord_less_eq_set_o @ B @ C )
=> ( ord_less_eq_set_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_order_Otrans) ).
thf(951,plain,
! [A: set_o,B: set_o,C: set_o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( ord_less_eq_set_o @ B @ C )
=> ( ord_less_eq_set_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(129,axiom,
! [A: $o,B: set_o,C: $o > paraco1605129243lle_tv] :
( ( member_o @ A @ B )
=> ( member266900804lle_tv @ ( C @ A ) @ ( image_1491822472lle_tv @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_imageI) ).
thf(1285,plain,
! [A: $o,B: set_o,C: $o > paraco1605129243lle_tv] :
( ( member_o @ A @ B )
=> ( member266900804lle_tv @ ( C @ A ) @ ( image_1491822472lle_tv @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(115,axiom,
! [A: paraco1605129243lle_tv,B: $o > paraco1605129243lle_tv,C: $o,D: set_o] :
( ( A
= ( B @ C ) )
=> ( ( member_o @ C @ D )
=> ( member266900804lle_tv @ A @ ( image_1491822472lle_tv @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_image__eqI) ).
thf(1220,plain,
! [A: paraco1605129243lle_tv,B: $o > paraco1605129243lle_tv,C: $o,D: set_o] :
( ( A
= ( B @ C ) )
=> ( ( member_o @ C @ D )
=> ( member266900804lle_tv @ A @ ( image_1491822472lle_tv @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(315,axiom,
! [A: set_list_char,B: set_list_char,C: list_char > paraco1605129243lle_tv,D: list_char > paraco1605129243lle_tv,E: set_Pa1764573435lle_tv > paraco1605129243lle_tv] :
( ( A = B )
=> ( ! [F: list_char] :
( ( member_list_char @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image_1187894195lle_tv @ C @ A ) )
= ( E @ ( image_1187894195lle_tv @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_Inf_OINF__cong) ).
thf(2219,plain,
! [A: set_list_char,B: set_list_char,C: list_char > paraco1605129243lle_tv,D: list_char > paraco1605129243lle_tv,E: set_Pa1764573435lle_tv > paraco1605129243lle_tv] :
( ( A = B )
=> ( ! [F: list_char] :
( ( member_list_char @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image_1187894195lle_tv @ C @ A ) )
= ( E @ ( image_1187894195lle_tv @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(253,axiom,
! [A: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_subset__refl) ).
thf(1980,plain,
! [A: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(202,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ B @ C )
=> ( ord_le241064091lle_tv @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_order__trans) ).
thf(1766,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ B @ C )
=> ( ord_le241064091lle_tv @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(125,axiom,
! [A: paraco1605129243lle_tv,B: $o > paraco1605129243lle_tv,C: $o] :
( ( A
= ( B @ C ) )
=> ( member266900804lle_tv @ A @ ( image_1491822472lle_tv @ B @ top_top_set_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_range__eqI) ).
thf(1257,plain,
! [A: paraco1605129243lle_tv,B: $o > paraco1605129243lle_tv,C: $o] :
( ( A
= ( B @ C ) )
=> ( member266900804lle_tv @ A @ ( image_1491822472lle_tv @ B @ top_top_set_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(105,axiom,
! [A: $o] : ( member_o @ A @ top_top_set_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_UNIV__I) ).
thf(1141,plain,
! [A: $o] : ( member_o @ A @ top_top_set_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(294,axiom,
( top_to748628679t_char
= ( collect_list_char
@ ^ [A: list_char] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_UNIV__def) ).
thf(2145,plain,
( top_to748628679t_char
= ( collect_list_char
@ ^ [A: list_char] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(250,axiom,
! [A: list_char > paraco1605129243lle_tv,B: $o > list_char] :
( ( image_1491822472lle_tv
@ ^ [C: $o] : ( A @ ( B @ C ) )
@ top_top_set_o )
= ( image_1187894195lle_tv @ A @ ( image_o_list_char @ B @ top_top_set_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_range__composition) ).
thf(1972,plain,
! [A: list_char > paraco1605129243lle_tv,B: $o > list_char] :
( ( image_1491822472lle_tv
@ ^ [C: $o] : ( A @ ( B @ C ) )
@ top_top_set_o )
= ( image_1187894195lle_tv @ A @ ( image_o_list_char @ B @ top_top_set_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(156,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco445776468le_Neg @ A )
!= ( paraco1745535428le_Eql @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_fm_Odistinct_I23_J) ).
thf(1504,plain,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco445776468le_Neg @ A )
!= ( paraco1745535428le_Eql @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(266,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ C @ A )
=> ( ord_le241064091lle_tv @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_dual__order_Otrans) ).
thf(2030,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ C @ A )
=> ( ord_le241064091lle_tv @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(231,axiom,
! [A: list_char > paraco1605129243lle_tv,B: list_char > list_char,C: set_list_char] :
( ( image_1187894195lle_tv @ A @ ( image_890964937t_char @ B @ C ) )
= ( image_1187894195lle_tv
@ ^ [D: list_char] : ( A @ ( B @ D ) )
@ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_image__image) ).
thf(1881,plain,
! [A: list_char > paraco1605129243lle_tv,B: list_char > list_char,C: set_list_char] :
( ( image_1187894195lle_tv @ A @ ( image_890964937t_char @ B @ C ) )
= ( image_1187894195lle_tv
@ ^ [D: list_char] : ( A @ ( B @ D ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(26,axiom,
! [A: paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( member266900804lle_tv @ A @ B )
=> ( member266900804lle_tv @ ( C @ A ) @ ( image_335818702lle_tv @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_imageI) ).
thf(497,plain,
! [A: paraco1605129243lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( member266900804lle_tv @ A @ B )
=> ( member266900804lle_tv @ ( C @ A ) @ ( image_335818702lle_tv @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(179,axiom,
! [A: set_o,B: $o > $o] :
( ord_less_eq_set_o
@ ( collect_o
@ ^ [C: $o] :
( ( member_o @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_Collect__subset) ).
thf(1617,plain,
! [A: set_o,B: $o > $o] :
( ord_less_eq_set_o
@ ( collect_o
@ ^ [C: $o] :
( ( member_o @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(246,axiom,
! [A: paraco1605129243lle_tv,B: list_char > paraco1605129243lle_tv,C: list_char] :
( ( A
= ( B @ C ) )
=> ( member266900804lle_tv @ A @ ( image_1187894195lle_tv @ B @ top_to748628679t_char ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_range__eqI) ).
thf(1940,plain,
! [A: paraco1605129243lle_tv,B: list_char > paraco1605129243lle_tv,C: list_char] :
( ( A
= ( B @ C ) )
=> ( member266900804lle_tv @ A @ ( image_1187894195lle_tv @ B @ top_to748628679t_char ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(261,axiom,
! [A: list_char > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( ( image_1187894195lle_tv @ A @ top_to748628679t_char )
= top_to1057771083lle_tv )
=> ~ ! [C: list_char] :
( B
!= ( A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_surjE) ).
thf(2013,plain,
! [A: list_char > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
( ( ( image_1187894195lle_tv @ A @ top_to748628679t_char )
= top_to1057771083lle_tv )
=> ~ ! [C: list_char] :
( B
!= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(222,axiom,
! [A: set_Pa1764573435lle_tv,B: $o > paraco1605129243lle_tv,C: set_o] :
( ( ord_le241064091lle_tv @ A @ ( image_1491822472lle_tv @ B @ C ) )
= ( ? [D: set_o] :
( ( ord_less_eq_set_o @ D @ C )
& ( A
= ( image_1491822472lle_tv @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_subset__image__iff) ).
thf(1839,plain,
! [A: set_Pa1764573435lle_tv,B: $o > paraco1605129243lle_tv,C: set_o] :
( ( ord_le241064091lle_tv @ A @ ( image_1491822472lle_tv @ B @ C ) )
= ( ? [D: set_o] :
( ( ord_less_eq_set_o @ D @ C )
& ( A
= ( image_1491822472lle_tv @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(182,axiom,
! [A: set_o,B: set_o,C: set_o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( ord_less_eq_set_o @ B @ C )
=> ( ord_less_eq_set_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_subset__trans) ).
thf(1685,plain,
! [A: set_o,B: set_o,C: set_o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( ord_less_eq_set_o @ B @ C )
=> ( ord_less_eq_set_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(248,axiom,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1325918602e_eval @ A @ C ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco69239110le_Con @ B @ C ) )
= ( paraco1325918602e_eval @ A @ B ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1325918602e_eval @ A @ C ) )
=> ( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco69239110le_Con @ B @ C ) )
= ( paraco1325918602e_eval @ A @ C ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( ( ( paraco1325918602e_eval @ A @ C )
= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco69239110le_Con @ B @ C ) )
= ( paraco1325918602e_eval @ A @ B ) ) )
& ( ( ( paraco1325918602e_eval @ A @ C )
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco69239110le_Con @ B @ C ) )
= ( paraco1344940915le_Det @ $false ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_eval_Osimps_I4_J) ).
thf(1949,plain,
! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1325918602e_eval @ A @ C ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco69239110le_Con @ B @ C ) )
= ( paraco1325918602e_eval @ A @ B ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1325918602e_eval @ A @ C ) )
=> ( ( ( ( paraco1325918602e_eval @ A @ B )
= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco69239110le_Con @ B @ C ) )
= ( paraco1325918602e_eval @ A @ C ) ) )
& ( ( ( paraco1325918602e_eval @ A @ B )
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( ( ( paraco1325918602e_eval @ A @ C )
= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco69239110le_Con @ B @ C ) )
= ( paraco1325918602e_eval @ A @ B ) ) )
& ( ( ( paraco1325918602e_eval @ A @ C )
!= ( paraco1344940915le_Det @ $true ) )
=> ( ( paraco1325918602e_eval @ A @ ( paraco69239110le_Con @ B @ C ) )
= ( paraco1344940915le_Det @ $false ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(110,axiom,
! [A: $o,B: paraco1605129243lle_tv > $o,C: paraco1605129243lle_tv,D: set_Pa1764573435lle_tv] :
( ( A
= ( B @ C ) )
=> ( ( member266900804lle_tv @ C @ D )
=> ( member_o @ A @ ( image_991799618e_tv_o @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_image__eqI) ).
thf(1157,plain,
! [A: $o,B: paraco1605129243lle_tv > $o,C: paraco1605129243lle_tv,D: set_Pa1764573435lle_tv] :
( ( A
= ( B @ C ) )
=> ( ( member266900804lle_tv @ C @ D )
=> ( member_o @ A @ ( image_991799618e_tv_o @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(224,axiom,
! [A: $o > $o,B: list_char > $o] :
( ( image_list_char_o
@ ^ [C: list_char] : ( A @ ( B @ C ) )
@ top_to748628679t_char )
= ( image_o_o @ A @ ( image_list_char_o @ B @ top_to748628679t_char ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_range__composition) ).
thf(1844,plain,
! [A: $o > $o,B: list_char > $o] :
( ( image_list_char_o
@ ^ [C: list_char] : ( A @ ( B @ C ) )
@ top_to748628679t_char )
= ( image_o_o @ A @ ( image_list_char_o @ B @ top_to748628679t_char ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(346,axiom,
! [A: set_Pa1764573435lle_tv,B: list_char > paraco1605129243lle_tv,C: set_list_char] :
( ( ord_le241064091lle_tv @ A @ ( image_1187894195lle_tv @ B @ C ) )
= ( ? [D: set_list_char] :
( ( ord_le1836582007t_char @ D @ C )
& ( A
= ( image_1187894195lle_tv @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_subset__image__iff) ).
thf(2347,plain,
! [A: set_Pa1764573435lle_tv,B: list_char > paraco1605129243lle_tv,C: set_list_char] :
( ( ord_le241064091lle_tv @ A @ ( image_1187894195lle_tv @ B @ C ) )
= ( ? [D: set_list_char] :
( ( ord_le1836582007t_char @ D @ C )
& ( A
= ( image_1187894195lle_tv @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(161,axiom,
! [A: list_char,B: $o > list_char,C: $o,D: set_o] :
( ( A
= ( B @ C ) )
=> ( ( member_o @ C @ D )
=> ( member_list_char @ A @ ( image_o_list_char @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_image__eqI) ).
thf(1517,plain,
! [A: list_char,B: $o > list_char,C: $o,D: set_o] :
( ( A
= ( B @ C ) )
=> ( ( member_o @ C @ D )
=> ( member_list_char @ A @ ( image_o_list_char @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(194,axiom,
( ( (=) @ set_Pa1764573435lle_tv )
= ( ^ [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
& ( ord_le241064091lle_tv @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_order__class_Oorder_Oeq__iff) ).
thf(1734,plain,
( ( (=) @ set_Pa1764573435lle_tv )
= ( ^ [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
& ( ord_le241064091lle_tv @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(239,axiom,
! [A: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_order__refl) ).
thf(1918,plain,
! [A: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(348,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ord_le241064091lle_tv @ ( image_335818702lle_tv @ C @ A ) @ ( image_335818702lle_tv @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_image__mono) ).
thf(2352,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv > paraco1605129243lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ord_le241064091lle_tv @ ( image_335818702lle_tv @ C @ A ) @ ( image_335818702lle_tv @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(85,axiom,
! [A: set_o,B: set_o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( ord_less_eq_set_o @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_order__class_Oorder_Oantisym) ).
thf(1010,plain,
! [A: set_o,B: set_o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( ord_less_eq_set_o @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(344,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( member1875402276lle_tv @ A @ ( pow_Pa475453624lle_tv @ B ) )
= ( ord_le241064091lle_tv @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_Pow__iff) ).
thf(2342,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( member1875402276lle_tv @ A @ ( pow_Pa475453624lle_tv @ B ) )
= ( ord_le241064091lle_tv @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(228,axiom,
! [A: nat > nat,B: set_nat,C: nat > $o] :
( ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ ( image_nat_nat @ A @ B ) )
& ( C @ D ) ) )
= ( image_nat_nat @ A
@ ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_Compr__image__eq) ).
thf(1866,plain,
! [A: nat > nat,B: set_nat,C: nat > $o] :
( ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ ( image_nat_nat @ A @ B ) )
& ( C @ D ) ) )
= ( image_nat_nat @ A
@ ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(274,axiom,
! [A: set_o,B: set_o,C: $o > paraco1605129243lle_tv] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ord_le241064091lle_tv @ ( image_1491822472lle_tv @ C @ A ) @ ( image_1491822472lle_tv @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_image__mono) ).
thf(2071,plain,
! [A: set_o,B: set_o,C: $o > paraco1605129243lle_tv] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ord_le241064091lle_tv @ ( image_1491822472lle_tv @ C @ A ) @ ( image_1491822472lle_tv @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(174,axiom,
! [A: $o > $o,B: set_o,C: set_o] :
( ( ord_less_eq_set_o @ ( image_o_o @ A @ B ) @ C )
=> ( ord_le2085948664_set_o @ ( image_set_o_set_o @ ( image_o_o @ A ) @ ( finite_Fpow_o @ B ) ) @ ( finite_Fpow_o @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_image__Fpow__mono) ).
thf(1590,plain,
! [A: $o > $o,B: set_o,C: set_o] :
( ( ord_less_eq_set_o @ ( image_o_o @ A @ B ) @ C )
=> ( ord_le2085948664_set_o @ ( image_set_o_set_o @ ( image_o_o @ A ) @ ( finite_Fpow_o @ B ) ) @ ( finite_Fpow_o @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(148,axiom,
! [A: list_char,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco1480028776le_Pro @ A )
!= ( paraco69239110le_Con @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_fm_Odistinct_I5_J) ).
thf(1476,plain,
! [A: list_char,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm] :
( ( paraco1480028776le_Pro @ A )
!= ( paraco69239110le_Con @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(157,axiom,
! [A: set_o] : ( ord_less_eq_set_o @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_subset__refl) ).
thf(1508,plain,
! [A: set_o] : ( ord_less_eq_set_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(258,axiom,
! [A: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A @ top_to1057771083lle_tv ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_top__greatest) ).
thf(2004,plain,
! [A: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A @ top_to1057771083lle_tv ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(13,axiom,
! [A: $o > $o,B: set_o,C: $o > $o] :
( ? [D: $o] :
( ( member_o @ D @ ( image_o_o @ A @ B ) )
& ( C @ D ) )
=> ? [D: $o] :
( ( member_o @ D @ B )
& ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_bex__imageD) ).
thf(418,plain,
! [A: $o > $o,B: set_o,C: $o > $o] :
( ? [D: $o] :
( ( member_o @ D @ ( image_o_o @ A @ B ) )
& ( C @ D ) )
=> ? [D: $o] :
( ( member_o @ D @ B )
& ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(236,axiom,
! [A: set_nat,B: nat > $o] :
( ord_less_eq_set_nat
@ ( collect_nat
@ ^ [C: nat] :
( ( member_nat @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_Collect__subset) ).
thf(1903,plain,
! [A: set_nat,B: nat > $o] :
( ord_less_eq_set_nat
@ ( collect_nat
@ ^ [C: nat] :
( ( member_nat @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(291,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_subset__antisym) ).
thf(2135,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(260,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv > $o] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ A
@ ( collec1111687558lle_tv
@ ^ [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ A )
=> ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_subset__Collect__iff) ).
thf(2009,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv > $o] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ A
@ ( collec1111687558lle_tv
@ ^ [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ A )
=> ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(152,axiom,
! [A: set_o] : ( ord_less_eq_set_o @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_order__refl) ).
thf(1491,plain,
! [A: set_o] : ( ord_less_eq_set_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(277,axiom,
! [A: list_char > paraco1605129243lle_tv,B: set_list_char,C: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ A @ B ) @ C )
= ( ! [D: list_char] :
( ( member_list_char @ D @ B )
=> ( member266900804lle_tv @ ( A @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_image__subset__iff) ).
thf(2081,plain,
! [A: list_char > paraco1605129243lle_tv,B: set_list_char,C: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ A @ B ) @ C )
= ( ! [D: list_char] :
( ( member_list_char @ D @ B )
=> ( member266900804lle_tv @ ( A @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(42,axiom,
! [A: list_char,B: set_list_char,C: list_char,D: list_char > list_char] :
( ( member_list_char @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member_list_char @ C @ ( image_890964937t_char @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_rev__image__eqI) ).
thf(568,plain,
! [A: list_char,B: set_list_char,C: list_char,D: list_char > list_char] :
( ( member_list_char @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member_list_char @ C @ ( image_890964937t_char @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(205,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( B = C )
=> ( ord_le241064091lle_tv @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_ord__le__eq__trans) ).
thf(1777,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( B = C )
=> ( ord_le241064091lle_tv @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(341,axiom,
! [A: $o > list_char,B: list_char] :
( ( ( image_o_list_char @ A @ top_top_set_o )
= top_to748628679t_char )
=> ~ ! [C: $o] :
( B
!= ( A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_surjE) ).
thf(2330,plain,
! [A: $o > list_char,B: list_char] :
( ( ( image_o_list_char @ A @ top_top_set_o )
= top_to748628679t_char )
=> ~ ! [C: $o] :
( B
!= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(310,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_order__class_Oorder_Oantisym) ).
thf(2198,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ( ord_le241064091lle_tv @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(305,axiom,
! [A: set_o,B: paraco1605129243lle_tv > $o,C: set_Pa1764573435lle_tv] :
( ( ord_less_eq_set_o @ A @ ( image_991799618e_tv_o @ B @ C ) )
=> ~ ! [D: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ D @ C )
=> ( A
!= ( image_991799618e_tv_o @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_subset__imageE) ).
thf(2183,plain,
! [A: set_o,B: paraco1605129243lle_tv > $o,C: set_Pa1764573435lle_tv] :
( ( ord_less_eq_set_o @ A @ ( image_991799618e_tv_o @ B @ C ) )
=> ~ ! [D: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ D @ C )
=> ( A
!= ( image_991799618e_tv_o @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(93,axiom,
! [A: $o,B: paraco1605129243lle_tv > $o,C: set_Pa1764573435lle_tv] :
( ( member_o @ A @ ( image_991799618e_tv_o @ B @ C ) )
=> ~ ! [D: paraco1605129243lle_tv] :
( ( A
= ( B @ D ) )
=> ~ ( member266900804lle_tv @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_imageE) ).
thf(1045,plain,
! [A: $o,B: paraco1605129243lle_tv > $o,C: set_Pa1764573435lle_tv] :
( ( member_o @ A @ ( image_991799618e_tv_o @ B @ C ) )
=> ~ ! [D: paraco1605129243lle_tv] :
( ( A
= ( B @ D ) )
=> ~ ( member266900804lle_tv @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(70,axiom,
( ord_less_eq_set_o
= ( ^ [A: set_o,B: set_o] :
! [C: $o] :
( ( member_o @ C @ A )
=> ( member_o @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_subset__iff) ).
thf(914,plain,
( ord_less_eq_set_o
= ( ^ [A: set_o,B: set_o] :
! [C: $o] :
( ( member_o @ C @ A )
=> ( member_o @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(8,axiom,
! [A: set_o] :
( ( ord_less_eq_set_o @ top_top_set_o @ A )
= ( A = top_top_set_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_top_Oextremum__unique) ).
thf(378,plain,
! [A: set_o] :
( ( ord_less_eq_set_o @ top_top_set_o @ A )
= ( A = top_top_set_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(20,axiom,
! [A: set_list_char,B: list_char > $o] :
( ord_le1836582007t_char
@ ( collect_list_char
@ ^ [C: list_char] :
( ( member_list_char @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_Collect__subset) ).
thf(478,plain,
! [A: set_list_char,B: list_char > $o] :
( ord_le1836582007t_char
@ ( collect_list_char
@ ^ [C: list_char] :
( ( member_list_char @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(351,axiom,
! [A: $o,B: $o] :
( ( ( paraco1344940915le_Det @ A )
= ( paraco1344940915le_Det @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_tv_Oinject_I1_J) ).
thf(2362,plain,
! [A: $o,B: $o] :
( ( ( paraco1344940915le_Det @ A )
= ( paraco1344940915le_Det @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(317,axiom,
! [A: paraco1605129243lle_tv,B: list_char > paraco1605129243lle_tv,C: set_list_char] :
( ( member266900804lle_tv @ A @ ( image_1187894195lle_tv @ B @ C ) )
= ( ? [D: list_char] :
( ( member_list_char @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_image__iff) ).
thf(2230,plain,
! [A: paraco1605129243lle_tv,B: list_char > paraco1605129243lle_tv,C: set_list_char] :
( ( member266900804lle_tv @ A @ ( image_1187894195lle_tv @ B @ C ) )
= ( ? [D: list_char] :
( ( member_list_char @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(233,axiom,
! [A: paraco1605129243lle_tv > $o,B: paraco1605129243lle_tv > $o] :
( ( ord_le241064091lle_tv @ ( collec1111687558lle_tv @ A ) @ ( collec1111687558lle_tv @ B ) )
= ( ! [C: paraco1605129243lle_tv] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_Collect__mono__iff) ).
thf(1893,plain,
! [A: paraco1605129243lle_tv > $o,B: paraco1605129243lle_tv > $o] :
( ( ord_le241064091lle_tv @ ( collec1111687558lle_tv @ A ) @ ( collec1111687558lle_tv @ B ) )
= ( ! [C: paraco1605129243lle_tv] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(334,axiom,
! [A: list_char > paraco1605129243lle_tv,B: set_list_char,C: paraco1605129243lle_tv > $o] :
( ! [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ ( image_1187894195lle_tv @ A @ B ) )
=> ( C @ D ) )
=> ! [D: list_char] :
( ( member_list_char @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_ball__imageD) ).
thf(2294,plain,
! [A: list_char > paraco1605129243lle_tv,B: set_list_char,C: paraco1605129243lle_tv > $o] :
( ! [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ ( image_1187894195lle_tv @ A @ B ) )
=> ( C @ D ) )
=> ! [D: list_char] :
( ( member_list_char @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(293,axiom,
! [A: list_char > paraco1605129243lle_tv] :
( ( paraco1325918602e_eval @ A @ paraco367965286_Truth )
= ( paraco1344940915le_Det @ $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_eval_Osimps_I2_J) ).
thf(2142,plain,
! [A: list_char > paraco1605129243lle_tv] :
( ( paraco1325918602e_eval @ A @ paraco367965286_Truth )
= ( paraco1344940915le_Det @ $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(46,axiom,
! [A: set_o,B: set_o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( ord_less_eq_set_o @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_antisym__conv) ).
thf(620,plain,
! [A: set_o,B: set_o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( ord_less_eq_set_o @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(285,axiom,
! [A: list_char > $o,B: $o > list_char] :
( ! [C: $o] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_list_char_o @ A @ top_to748628679t_char )
= top_top_set_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_surjI) ).
thf(2102,plain,
! [A: list_char > $o,B: $o > list_char] :
( ! [C: $o] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_list_char_o @ A @ top_to748628679t_char )
= top_top_set_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(159,axiom,
( top_to1057771083lle_tv
= ( collec1111687558lle_tv @ top_to1299250770e_tv_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_top__set__def) ).
thf(1512,plain,
( top_to1057771083lle_tv
= ( collec1111687558lle_tv @ top_to1299250770e_tv_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(172,axiom,
! [A: set_o,B: set_o,C: $o > $o,D: $o > $o,E: set_o > $o] :
( ( A = B )
=> ( ! [F: $o] :
( ( member_o @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image_o_o @ C @ A ) )
= ( E @ ( image_o_o @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_Sup_OSUP__cong) ).
thf(1578,plain,
! [A: set_o,B: set_o,C: $o > $o,D: $o > $o,E: set_o > $o] :
( ( A = B )
=> ( ! [F: $o] :
( ( member_o @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image_o_o @ C @ A ) )
= ( E @ ( image_o_o @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(11,axiom,
! [A: set_o,B: set_o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( ord_less_eq_set_o @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_subset__antisym) ).
thf(410,plain,
! [A: set_o,B: set_o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( ord_less_eq_set_o @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(60,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( ( paraco1745535428le_Eql @ A @ B )
= ( paraco1745535428le_Eql @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_fm_Oinject_I5_J) ).
thf(835,plain,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( ( ( paraco1745535428le_Eql @ A @ B )
= ( paraco1745535428le_Eql @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(318,axiom,
! [A: set_o,B: set_Pa1764573435lle_tv > set_o,C: set_Pa1764573435lle_tv,D: set_Pa1764573435lle_tv] :
( ( ord_less_eq_set_o @ A @ ( B @ C ) )
=> ( ( ord_le241064091lle_tv @ C @ D )
=> ( ! [E: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ E @ F )
=> ( ord_less_eq_set_o @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_o @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_order__subst1) ).
thf(2233,plain,
! [A: set_o,B: set_Pa1764573435lle_tv > set_o,C: set_Pa1764573435lle_tv,D: set_Pa1764573435lle_tv] :
( ( ord_less_eq_set_o @ A @ ( B @ C ) )
=> ( ( ord_le241064091lle_tv @ C @ D )
=> ( ! [E: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ E @ F )
=> ( ord_less_eq_set_o @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_o @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(149,axiom,
! [A: set_list_char,B: list_char > $o,C: set_o] :
( ! [D: list_char] :
( ( member_list_char @ D @ A )
=> ( member_o @ ( B @ D ) @ C ) )
=> ( ord_less_eq_set_o @ ( image_list_char_o @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_image__subsetI) ).
thf(1480,plain,
! [A: set_list_char,B: list_char > $o,C: set_o] :
( ! [D: list_char] :
( ( member_list_char @ D @ A )
=> ( member_o @ ( B @ D ) @ C ) )
=> ( ord_less_eq_set_o @ ( image_list_char_o @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(6,axiom,
! [A: set_o] :
( ( ord_less_eq_set_o @ top_top_set_o @ A )
=> ( A = top_top_set_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_top_Oextremum__uniqueI) ).
thf(373,plain,
! [A: set_o] :
( ( ord_less_eq_set_o @ top_top_set_o @ A )
=> ( A = top_top_set_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(311,axiom,
! [A: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_dual__order_Orefl) ).
thf(2201,plain,
! [A: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(215,axiom,
! [A: list_char > paraco1605129243lle_tv,B: list_char > list_char] :
( ( image_1187894195lle_tv
@ ^ [C: list_char] : ( A @ ( B @ C ) )
@ top_to748628679t_char )
= ( image_1187894195lle_tv @ A @ ( image_890964937t_char @ B @ top_to748628679t_char ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_range__composition) ).
thf(1816,plain,
! [A: list_char > paraco1605129243lle_tv,B: list_char > list_char] :
( ( image_1187894195lle_tv
@ ^ [C: list_char] : ( A @ ( B @ C ) )
@ top_to748628679t_char )
= ( image_1187894195lle_tv @ A @ ( image_890964937t_char @ B @ top_to748628679t_char ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(342,axiom,
! [A: list_char,B: list_char > list_char,C: list_char] :
( ( A
= ( B @ C ) )
=> ( member_list_char @ A @ ( image_890964937t_char @ B @ top_to748628679t_char ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_range__eqI) ).
thf(2334,plain,
! [A: list_char,B: list_char > list_char,C: list_char] :
( ( A
= ( B @ C ) )
=> ( member_list_char @ A @ ( image_890964937t_char @ B @ top_to748628679t_char ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(3,axiom,
! [A: set_o,B: set_o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ord_le2085948664_set_o @ ( finite_Fpow_o @ A ) @ ( finite_Fpow_o @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_Fpow__mono) ).
thf(358,plain,
! [A: set_o,B: set_o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ord_le2085948664_set_o @ ( finite_Fpow_o @ A ) @ ( finite_Fpow_o @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(184,axiom,
! [A: set_nat,B: set_nat,C: nat > $o,D: nat > $o] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ! [E: nat] :
( ( member_nat @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq_set_nat
@ ( collect_nat
@ ^ [E: nat] :
( ( member_nat @ E @ A )
& ( C @ E ) ) )
@ ( collect_nat
@ ^ [E: nat] :
( ( member_nat @ E @ B )
& ( D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_subset__CollectI) ).
thf(1693,plain,
! [A: set_nat,B: set_nat,C: nat > $o,D: nat > $o] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ! [E: nat] :
( ( member_nat @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq_set_nat
@ ( collect_nat
@ ^ [E: nat] :
( ( member_nat @ E @ A )
& ( C @ E ) ) )
@ ( collect_nat
@ ^ [E: nat] :
( ( member_nat @ E @ B )
& ( D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(67,axiom,
! [A: $o,B: list_char > $o,C: set_list_char] :
( ( member_o @ A @ ( image_list_char_o @ B @ C ) )
=> ~ ! [D: list_char] :
( ( A
= ( B @ D ) )
=> ~ ( member_list_char @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_imageE) ).
thf(897,plain,
! [A: $o,B: list_char > $o,C: set_list_char] :
( ( member_o @ A @ ( image_list_char_o @ B @ C ) )
=> ~ ! [D: list_char] :
( ( A
= ( B @ D ) )
=> ~ ( member_list_char @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(94,axiom,
! [A: set_o,B: set_o,C: set_o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_set_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_ord__le__eq__trans) ).
thf(1056,plain,
! [A: set_o,B: set_o,C: set_o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_set_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(187,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv > $o] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ord_less_eq_set_o @ ( image_991799618e_tv_o @ C @ A ) @ ( image_991799618e_tv_o @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_image__mono) ).
thf(1710,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv > $o] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ord_less_eq_set_o @ ( image_991799618e_tv_o @ C @ A ) @ ( image_991799618e_tv_o @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(281,axiom,
! [A: set_o,B: paraco1605129243lle_tv > $o,C: set_Pa1764573435lle_tv] :
( ( ord_less_eq_set_o @ A @ ( image_991799618e_tv_o @ B @ C ) )
= ( ? [D: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ D @ C )
& ( A
= ( image_991799618e_tv_o @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_subset__image__iff) ).
thf(2091,plain,
! [A: set_o,B: paraco1605129243lle_tv > $o,C: set_Pa1764573435lle_tv] :
( ( ord_less_eq_set_o @ A @ ( image_991799618e_tv_o @ B @ C ) )
= ( ? [D: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ D @ C )
& ( A
= ( image_991799618e_tv_o @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(271,axiom,
! [A: list_char] : ( member_list_char @ A @ top_to748628679t_char ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_UNIV__I) ).
thf(2063,plain,
! [A: list_char] : ( member_list_char @ A @ top_to748628679t_char ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(119,axiom,
! [A: set_o,B: set_o,C: $o > $o,D: $o > $o] :
( ( A = B )
=> ( ! [E: $o] :
( ( member_o @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image_o_o @ C @ A )
= ( image_o_o @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_image__cong) ).
thf(1236,plain,
! [A: set_o,B: set_o,C: $o > $o,D: $o > $o] :
( ( A = B )
=> ( ! [E: $o] :
( ( member_o @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image_o_o @ C @ A )
= ( image_o_o @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(219,axiom,
! [A: list_char > list_char,B: list_char > list_char] :
( ! [C: list_char] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_890964937t_char @ A @ top_to748628679t_char )
= top_to748628679t_char ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_surjI) ).
thf(1829,plain,
! [A: list_char > list_char,B: list_char > list_char] :
( ! [C: list_char] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_890964937t_char @ A @ top_to748628679t_char )
= top_to748628679t_char ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(44,axiom,
! [A: produc696645085lle_fm] :
( ! [B: list_char > paraco1605129243lle_tv,C: list_char] :
( A
!= ( produc1710735575lle_fm @ B @ ( paraco1480028776le_Pro @ C ) ) )
=> ( ! [B: list_char > paraco1605129243lle_tv] :
( A
!= ( produc1710735575lle_fm @ B @ paraco367965286_Truth ) )
=> ( ! [B: list_char > paraco1605129243lle_tv,C: paraco1604210848lle_fm] :
( A
!= ( produc1710735575lle_fm @ B @ ( paraco445776468le_Neg @ C ) ) )
=> ( ! [B: list_char > paraco1605129243lle_tv,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( A
!= ( produc1710735575lle_fm @ B @ ( paraco69239110le_Con @ C @ D ) ) )
=> ( ! [B: list_char > paraco1605129243lle_tv,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( A
!= ( produc1710735575lle_fm @ B @ ( paraco1389086619le_Eql @ C @ D ) ) )
=> ~ ! [B: list_char > paraco1605129243lle_tv,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( A
!= ( produc1710735575lle_fm @ B @ ( paraco1745535428le_Eql @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_eval_Ocases) ).
thf(575,plain,
! [A: produc696645085lle_fm] :
( ! [B: list_char > paraco1605129243lle_tv,C: list_char] :
( A
!= ( produc1710735575lle_fm @ B @ ( paraco1480028776le_Pro @ C ) ) )
=> ( ! [B: list_char > paraco1605129243lle_tv] :
( A
!= ( produc1710735575lle_fm @ B @ paraco367965286_Truth ) )
=> ( ! [B: list_char > paraco1605129243lle_tv,C: paraco1604210848lle_fm] :
( A
!= ( produc1710735575lle_fm @ B @ ( paraco445776468le_Neg @ C ) ) )
=> ( ! [B: list_char > paraco1605129243lle_tv,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( A
!= ( produc1710735575lle_fm @ B @ ( paraco69239110le_Con @ C @ D ) ) )
=> ( ! [B: list_char > paraco1605129243lle_tv,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( A
!= ( produc1710735575lle_fm @ B @ ( paraco1389086619le_Eql @ C @ D ) ) )
=> ~ ! [B: list_char > paraco1605129243lle_tv,C: paraco1604210848lle_fm,D: paraco1604210848lle_fm] :
( A
!= ( produc1710735575lle_fm @ B @ ( paraco1745535428le_Eql @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(109,axiom,
! [A: list_char,B: paraco1605129243lle_tv > list_char,C: paraco1605129243lle_tv,D: set_Pa1764573435lle_tv] :
( ( A
= ( B @ C ) )
=> ( ( member266900804lle_tv @ C @ D )
=> ( member_list_char @ A @ ( image_1971766583t_char @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_image__eqI) ).
thf(1152,plain,
! [A: list_char,B: paraco1605129243lle_tv > list_char,C: paraco1605129243lle_tv,D: set_Pa1764573435lle_tv] :
( ( A
= ( B @ C ) )
=> ( ( member266900804lle_tv @ C @ D )
=> ( member_list_char @ A @ ( image_1971766583t_char @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(166,axiom,
! [A: set_o > $o,B: set_o,C: set_o > $o] :
( ( A @ B )
=> ( ! [D: set_o] :
( ( A @ D )
=> ( ord_less_eq_set_o @ D @ B ) )
=> ( ! [D: set_o] :
( ( A @ D )
=> ( ! [E: set_o] :
( ( A @ E )
=> ( ord_less_eq_set_o @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_Greatest_set_o @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_GreatestI2__order) ).
thf(1532,plain,
! [A: set_o > $o,B: set_o,C: set_o > $o] :
( ( A @ B )
=> ( ! [D: set_o] :
( ( A @ D )
=> ( ord_less_eq_set_o @ D @ B ) )
=> ( ! [D: set_o] :
( ( A @ D )
=> ( ! [E: set_o] :
( ( A @ E )
=> ( ord_less_eq_set_o @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_Greatest_set_o @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(68,axiom,
! [A: set_list_char,B: list_char > list_char,C: set_list_char] :
( ! [D: list_char] :
( ( member_list_char @ D @ A )
=> ( member_list_char @ ( B @ D ) @ C ) )
=> ( ord_le1836582007t_char @ ( image_890964937t_char @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_image__subsetI) ).
thf(908,plain,
! [A: set_list_char,B: list_char > list_char,C: set_list_char] :
( ! [D: list_char] :
( ( member_list_char @ D @ A )
=> ( member_list_char @ ( B @ D ) @ C ) )
=> ( ord_le1836582007t_char @ ( image_890964937t_char @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(188,axiom,
( top_to1057771083lle_tv
= ( collec1111687558lle_tv
@ ^ [A: paraco1605129243lle_tv] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_UNIV__def) ).
thf(1713,plain,
( top_to1057771083lle_tv
= ( collec1111687558lle_tv
@ ^ [A: paraco1605129243lle_tv] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(132,axiom,
! [A: $o,B: set_o,C: $o,D: $o > $o] :
( ( member_o @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member_o @ C @ ( image_o_o @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_rev__image__eqI) ).
thf(1299,plain,
! [A: $o,B: set_o,C: $o,D: $o > $o] :
( ( member_o @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member_o @ C @ ( image_o_o @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(5,axiom,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm] :
( paraco367965286_Truth
!= ( paraco1745535428le_Eql @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_fm_Odistinct_I17_J) ).
thf(369,plain,
! [A: paraco1604210848lle_fm,B: paraco1604210848lle_fm] :
( paraco367965286_Truth
!= ( paraco1745535428le_Eql @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(292,axiom,
! [A: set_list_char,B: list_char > paraco1605129243lle_tv,C: set_Pa1764573435lle_tv] :
( ! [D: list_char] :
( ( member_list_char @ D @ A )
=> ( member266900804lle_tv @ ( B @ D ) @ C ) )
=> ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_image__subsetI) ).
thf(2138,plain,
! [A: set_list_char,B: list_char > paraco1605129243lle_tv,C: set_Pa1764573435lle_tv] :
( ! [D: list_char] :
( ( member_list_char @ D @ A )
=> ( member266900804lle_tv @ ( B @ D ) @ C ) )
=> ( ord_le241064091lle_tv @ ( image_1187894195lle_tv @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(177,axiom,
! [A: set_o,B: $o > $o,C: set_o] :
( ( ord_less_eq_set_o @ A @ ( image_o_o @ B @ C ) )
= ( ? [D: set_o] :
( ( ord_less_eq_set_o @ D @ C )
& ( A
= ( image_o_o @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_subset__image__iff) ).
thf(1606,plain,
! [A: set_o,B: $o > $o,C: set_o] :
( ( ord_less_eq_set_o @ A @ ( image_o_o @ B @ C ) )
= ( ? [D: set_o] :
( ( ord_less_eq_set_o @ D @ C )
& ( A
= ( image_o_o @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(23,axiom,
! [A: set_o,B: set_o,C: set_o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( ord_less_eq_set_o @ B @ C )
=> ( ord_less_eq_set_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_order__trans) ).
thf(486,plain,
! [A: set_o,B: set_o,C: set_o] :
( ( ord_less_eq_set_o @ A @ B )
=> ( ( ord_less_eq_set_o @ B @ C )
=> ( ord_less_eq_set_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(340,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv,D: set_Pa1764573435lle_tv] :
( ( A
= ( B @ C ) )
=> ( ( ord_le241064091lle_tv @ C @ D )
=> ( ! [E: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ E @ F )
=> ( ord_le241064091lle_tv @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le241064091lle_tv @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_ord__eq__le__subst) ).
thf(2321,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv,C: set_Pa1764573435lle_tv,D: set_Pa1764573435lle_tv] :
( ( A
= ( B @ C ) )
=> ( ( ord_le241064091lle_tv @ C @ D )
=> ( ! [E: set_Pa1764573435lle_tv,F: set_Pa1764573435lle_tv] :
( ( ord_le241064091lle_tv @ E @ F )
=> ( ord_le241064091lle_tv @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le241064091lle_tv @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(275,axiom,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: list_char > paraco1605129243lle_tv,C: set_list_char] :
( ( image_335818702lle_tv @ A @ ( image_1187894195lle_tv @ B @ C ) )
= ( image_1187894195lle_tv
@ ^ [D: list_char] : ( A @ ( B @ D ) )
@ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_image__image) ).
thf(2074,plain,
! [A: paraco1605129243lle_tv > paraco1605129243lle_tv,B: list_char > paraco1605129243lle_tv,C: set_list_char] :
( ( image_335818702lle_tv @ A @ ( image_1187894195lle_tv @ B @ C ) )
= ( image_1187894195lle_tv
@ ^ [D: list_char] : ( A @ ( B @ D ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(319,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ! [C: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ C @ A )
=> ( member266900804lle_tv @ C @ B ) )
=> ( ord_le241064091lle_tv @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_subsetI) ).
thf(2238,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv] :
( ! [C: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ C @ A )
=> ( member266900804lle_tv @ C @ B ) )
=> ( ord_le241064091lle_tv @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(203,axiom,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv > $o,D: paraco1605129243lle_tv > $o] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ! [E: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_le241064091lle_tv
@ ( collec1111687558lle_tv
@ ^ [E: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ E @ A )
& ( C @ E ) ) )
@ ( collec1111687558lle_tv
@ ^ [E: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ E @ B )
& ( D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_subset__CollectI) ).
thf(1769,plain,
! [A: set_Pa1764573435lle_tv,B: set_Pa1764573435lle_tv,C: paraco1605129243lle_tv > $o,D: paraco1605129243lle_tv > $o] :
( ( ord_le241064091lle_tv @ A @ B )
=> ( ! [E: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_le241064091lle_tv
@ ( collec1111687558lle_tv
@ ^ [E: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ E @ A )
& ( C @ E ) ) )
@ ( collec1111687558lle_tv
@ ^ [E: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ E @ B )
& ( D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(214,axiom,
! [A: list_char > list_char,B: list_char] :
( ( ( image_890964937t_char @ A @ top_to748628679t_char )
= top_to748628679t_char )
=> ~ ! [C: list_char] :
( B
!= ( A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_surjE) ).
thf(1812,plain,
! [A: list_char > list_char,B: list_char] :
( ( ( image_890964937t_char @ A @ top_to748628679t_char )
= top_to748628679t_char )
=> ~ ! [C: list_char] :
( B
!= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(63,axiom,
! [A: $o,B: set_o,C: $o > list_char] :
( ( member_o @ A @ B )
=> ( member_list_char @ ( C @ A ) @ ( image_o_list_char @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_imageI) ).
thf(882,plain,
! [A: $o,B: set_o,C: $o > list_char] :
( ( member_o @ A @ B )
=> ( member_list_char @ ( C @ A ) @ ( image_o_list_char @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(75,axiom,
! [A: paraco1605129243lle_tv,B: $o > paraco1605129243lle_tv] :
( ( member266900804lle_tv @ A @ ( image_1491822472lle_tv @ B @ top_top_set_o ) )
=> ~ ! [C: $o] :
( A
!= ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_rangeE) ).
thf(935,plain,
! [A: paraco1605129243lle_tv,B: $o > paraco1605129243lle_tv] :
( ( member266900804lle_tv @ A @ ( image_1491822472lle_tv @ B @ top_top_set_o ) )
=> ~ ! [C: $o] :
( A
!= ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(247,axiom,
! [A: list_char > paraco1605129243lle_tv,B: paraco1605129243lle_tv > list_char] :
( ! [C: paraco1605129243lle_tv] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_1187894195lle_tv @ A @ top_to748628679t_char )
= top_to1057771083lle_tv ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_surjI) ).
thf(1945,plain,
! [A: list_char > paraco1605129243lle_tv,B: paraco1605129243lle_tv > list_char] :
( ! [C: paraco1605129243lle_tv] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_1187894195lle_tv @ A @ top_to748628679t_char )
= top_to1057771083lle_tv ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(286,axiom,
! [A: nat > paraco1605129243lle_tv,B: set_nat,C: paraco1605129243lle_tv > $o] :
( ( collec1111687558lle_tv
@ ^ [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ ( image_1151963140lle_tv @ A @ B ) )
& ( C @ D ) ) )
= ( image_1151963140lle_tv @ A
@ ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_Compr__image__eq) ).
thf(2106,plain,
! [A: nat > paraco1605129243lle_tv,B: set_nat,C: paraco1605129243lle_tv > $o] :
( ( collec1111687558lle_tv
@ ^ [D: paraco1605129243lle_tv] :
( ( member266900804lle_tv @ D @ ( image_1151963140lle_tv @ A @ B ) )
& ( C @ D ) ) )
= ( image_1151963140lle_tv @ A
@ ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(279,axiom,
! [A: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A @ top_to1057771083lle_tv ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_subset__UNIV) ).
thf(2087,plain,
! [A: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A @ top_to1057771083lle_tv ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(2567,plain,
$false,
inference(e,[status(thm)],[892,1036,629,1823,1168,2109,1315,555,666,2094,1411,962,1982,2077,1924,1406,1522,2248,1728,2114,878,523,2309,1205,449,2099,2282,385,500,538,1756,1310,533,2216,1782,2020,973,1724,1529,2173,1366,1228,1254,1792,2339,504,838,1313,460,1860,1264,1514,1247,1609,1013,1568,969,2373,1572,1362,1963,2178,1415,492,2027,1632,623,1978,514,2254,966,376,2259,2017,480,2058,1119,1526,507,1975,1896,692,2190,2242,1345,2286,1863,452,529,546,2164,381,1708,1736,2382,2061,512,942,1900,2147,1751,561,1487,1619,1370,484,1837,1920,1555,830,889,1787,2345,1281,2228,916,467,2068,1819,456,1740,2245,2300,2359,1111,1587,1138,2268,1493,1292,669,2312,2038,2317,2196,1842,489,1937,1249,1297,1131,1552,2355,1984,1599,1715,2272,1759,1825,1114,2387,1231,2006,721,1857,1318,2203,360,541,2089,1026,1996,662,1510,1251,1747,1548,573,1146,2292,2275,2033,2149,1833,1884,2188,1929,579,1795,413,2161,1107,2166,1408,2151,1806,1524,1349,1933,1603,1144,1043,1122,2065,1209,2119,2084,2214,2025,758,2314,2111,1731,1909,1149,626,769,2278,1688,1029,895,1022,2252,932,1061,912,1926,2350,1699,1245,1066,2288,1775,1496,2156,922,658,959,2171,1726,1364,1809,2096,1873,1166,1467,1905,927,1134,939,355,754,557,1225,2192,954,1484,1798,525,1499,1987,1038,1869,1785,1262,463,1763,951,1285,1220,2219,1980,1766,1257,1141,2145,1972,1504,2030,1881,497,1617,1940,2013,1839,1685,1949,1157,1844,2347,1517,1734,1918,2352,1010,2342,1866,2071,1590,1476,1508,2004,418,1903,2135,2009,1491,2081,568,1777,2330,2198,2183,1045,914,378,478,2362,2230,1893,2294,2142,620,2102,1512,1578,410,835,2233,1480,373,2201,1816,2334,358,1693,897,1056,1710,2091,2063,1236,1829,575,1152,1532,908,1713,1299,369,2138,1606,486,2321,2074,2238,1769,1812,882,935,1945,2106,2087]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP138^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.20 % Computer : n014.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 19:59:00 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.85/0.77 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.05/1.15 % [INFO] Parsing done (383ms).
% 2.05/1.17 % [INFO] Running in sequential loop mode.
% 3.16/1.54 % [INFO] eprover registered as external prover.
% 3.16/1.55 % [INFO] Scanning for conjecture ...
% 3.57/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 354 axioms. Running axiom selection ...
% 3.83/1.84 % [INFO] Axiom selection finished. Selected 352 axioms (removed 2 axioms).
% 4.59/2.10 % [INFO] Problem is higher-order (TPTP THF).
% 4.97/2.13 % [INFO] Type checking passed.
% 4.97/2.13 % [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 ...
% 22.63/6.23 % External prover 'e' found a proof!
% 22.63/6.23 % [INFO] Killing All external provers ...
% 22.63/6.23 % Time passed: 5885ms (effective reasoning time: 5055ms)
% 22.63/6.23 % 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)>
% 22.63/6.23 % Axioms used in derivation (352): fact_341_fm_Oinject_I1_J, fact_280_all__subset__image, fact_211_top_Oextremum__unique, fact_143_subset__refl, fact_38_image__Collect__subsetI, fact_248_rangeI, fact_340_fm_Oinject_I5_J, fact_81_ord__le__eq__subst, fact_147_equalityD2, fact_255_subset__UNIV, fact_284_pred__subset__eq, fact_171_Compr__image__eq, fact_201_Collect__subset, fact_214_top__greatest, fact_33_range__composition, fact_352_eval_Ocases, fact_263_surjI, fact_301_top__empty__eq, fact_329_fm_Odistinct_I13_J, fact_4_UNIV__I, fact_146_subset__iff, fact_41_image__Collect__subsetI, fact_239_image__mono, fact_97_rev__image__eqI, fact_48_top__set__def, fact_295_conj__subset__def, fact_174_Compr__image__eq, fact_142_subset__refl, fact_46_top__set__def, fact_318_Greatest__equality, fact_15_image__eqI, fact_140_Collect__mono, fact_107_image__cong, fact_346_fm_Odistinct_I27_J, fact_312_Fpow__mono, fact_94_order__subst1, fact_18_image__eqI, fact_161_in__mono, fact_95_order__subst1, fact_278_all__subset__image, fact_0_universal__domain, fact_125_imageI, fact_75_eq__refl, fact_285_subset__Collect__iff, fact_176_Compr__image__eq, fact_343_eval_Osimps_I1_J, fact_199_Collect__subset, fact_246_range__eqI, fact_42_image__Collect__subsetI, fact_268_surjE, fact_202_UNIV__def, fact_317_Greatest__equality, fact_154_equalityE, fact_85_ord__eq__le__subst, fact_1_tv_Oinject_I1_J, fact_121_image__iff, fact_102_rev__image__eqI, fact_137_subset__trans, fact_110_mem__Collect__eq, fact_7_iso__tuple__UNIV__I, fact_2_valid__in__def, fact_215_subset__image__iff, fact_348_fm_Odistinct_I5_J, fact_134_Collect__mono__iff, fact_347_fm_Odistinct_I29_J, fact_222_subset__imageE, fact_203_UNIV__def, fact_129_imageI, fact_253_subset__UNIV, fact_91_order__subst2, fact_67_ord__eq__le__trans, fact_148_equalityD2, fact_112_mem__Collect__eq, fact_99_rev__image__eqI, fact_123_imageI, fact_351_fm_Odistinct_I1_J, fact_76_antisym, fact_322_PowI, fact_111_mem__Collect__eq, fact_61_order__trans, fact_69_order__class_Oorder_Oeq__iff, fact_256_surj__def, fact_196_prop__restrict, fact_305_eval_Osimps_I2_J, fact_327_Pow__UNIV, fact_192_Collect__restrict, fact_281_valid__def, fact_236_image__mono, fact_8_iso__tuple__UNIV__I, fact_16_image__eqI, fact_304_Inf_OINF__identity__eq, fact_74_eq__refl, fact_169_Compr__image__eq, fact_335_fm_Odistinct_I19_J, fact_197_prop__restrict, fact_249_rangeI, fact_350_fm_Odistinct_I17_J, fact_310_fm_Odistinct_I15_J, fact_316_eval_Osimps_I4_J, fact_282_pred__subset__eq, fact_59_dual__order_Orefl, fact_157_subsetD, fact_165_UNIV__eq__I, fact_138_subset__trans, fact_276_all__subset__image, fact_333_double__negation, fact_296_Sup_OSUP__identity__eq, fact_293_conj__subset__def, fact_290_subset__CollectI, fact_135_set__eq__subset, fact_109_mem__Collect__eq, fact_257_surj__def, fact_177_Compr__image__eq, fact_49_less__eq__set__def, fact_254_subset__UNIV, fact_103_rev__image__eqI, fact_116_Collect__mem__eq, fact_124_imageI, fact_294_conj__subset__def, fact_259_surj__def, fact_98_rev__image__eqI, fact_300_Sup_OSUP__cong, fact_345_fm_Odistinct_I3_J, fact_183_imageE, fact_6_UNIV__I, fact_34_range__composition, fact_72_order_Otrans, fact_307_image__Fpow__mono, fact_320_GreatestI2__order, fact_207_top_Oextremum__uniqueI, fact_206_top_Oextremum__uniqueI, fact_353_Sup__bool__def, fact_119_bex__imageD, fact_68_order__class_Oorder_Oeq__iff, fact_213_top__greatest, fact_170_Compr__image__eq, fact_115_Collect__mem__eq, fact_187_imageE, fact_145_subset__iff, fact_180_image__image, fact_260_surj__def, fact_289_subset__CollectI, fact_155_equalityE, fact_89_order__subst2, fact_188_imageE, fact_88_order__subst2, fact_191_Collect__restrict, fact_223_subset__imageE, fact_158_subsetD, fact_114_Collect__mem__eq, fact_35_range__composition, fact_228_image__subsetI, fact_12_subsetI, fact_270_surjE, fact_286_subset__Collect__iff, fact_189_imageE, fact_313_eval__equality__simplify, fact_233_image__subsetI, fact_235_image__subsetI, fact_208_top_Oextremum__uniqueI, fact_245_range__eqI, fact_261_surjI, fact_39_image__Collect__subsetI, fact_205_UNIV__def, fact_117_Collect__cong, fact_19_image__eqI, fact_57_dual__order_Otrans, fact_251_rangeI, fact_160_in__mono, fact_11_subsetI, fact_66_ord__eq__le__trans, fact_78_eq__iff, fact_229_image__subsetI, fact_331_eval__negation, fact_54_dual__order_Oeq__iff, fact_53_dual__order_Oantisym, fact_31_rangeE, fact_250_rangeI, fact_194_prop__restrict, fact_178_image__image, fact_265_surjI, fact_150_equalityD1, fact_244_range__eqI, fact_105_ball__imageD, fact_243_range__eqI, fact_127_imageI, fact_120_bex__imageD, fact_153_subset__eq, fact_101_rev__image__eqI, fact_279_all__subset__image, fact_168_Compr__image__eq, fact_132_Collect__mono__iff, fact_332_fm_Oinject_I2_J, fact_159_in__mono, fact_212_top__greatest, fact_240_image__mono, fact_92_order__subst1, fact_200_Collect__subset, fact_258_surj__def, fact_65_ord__le__eq__trans, fact_26_rangeE, fact_152_subset__eq, fact_230_image__subsetI, fact_195_prop__restrict, fact_77_antisym, fact_22_image__eqI, fact_269_surjE, fact_3_image__ident, fact_133_Collect__mono__iff, fact_36_range__composition, fact_70_antisym__conv, fact_247_rangeI, fact_288_subset__Collect__iff, fact_179_image__image, fact_299_Sup_OSUP__cong, fact_58_dual__order_Orefl, fact_93_order__subst1, fact_185_imageE, fact_218_subset__image__iff, fact_32_range__composition, fact_100_rev__image__eqI, fact_193_Collect__restrict, fact_321_fm_Oinject_I3_J, fact_118_Collect__cong, fact_79_eq__iff, fact_298_Inf_OINF__cong, fact_266_surjE, fact_241_range__eqI, fact_108_image__cong, fact_130_imageI, fact_204_UNIV__def, fact_43_image__Collect__subsetI, fact_271_surjD, fact_252_rangeI, fact_198_Collect__subset, fact_272_surjD, fact_237_image__mono, fact_190_Collect__restrict, fact_328_fm_Odistinct_I25_J, fact_131_imageI, fact_264_surjI, fact_339_fm_Oinduct, fact_303_top__empty__eq, fact_182_imageE, fact_342_fm_Odistinct_I9_J, fact_164_UNIV__witness, fact_50_less__eq__set__def, fact_106_ball__imageD, fact_209_top_Oextremum__unique, fact_334_fm_Odistinct_I21_J, fact_274_surjD, fact_17_image__eqI, fact_73_order_Otrans, fact_80_ord__le__eq__subst, fact_283_pred__subset__eq, fact_51_less__eq__set__def, fact_144_subset__iff, fact_90_order__subst2, fact_104_rev__image__eqI, fact_326_Pow__UNIV, fact_14_subset__antisym, fact_71_antisym__conv, fact_220_image__subset__iff, fact_267_surjE, fact_83_ord__le__eq__subst, fact_172_Compr__image__eq, fact_63_order__class_Oorder_Oantisym, fact_337_eval__equality, fact_21_image__eqI, fact_122_image__iff, fact_221_image__subset__iff, fact_277_all__subset__image, fact_225_subset__imageE, fact_5_UNIV__I, fact_344_fm_Odistinct_I23_J, fact_175_Compr__image__eq, fact_330_conjunction, fact_226_subset__imageE, fact_210_top_Oextremum__unique, fact_291_subset__CollectI, fact_273_surjD, fact_151_subset__eq, fact_149_equalityD1, fact_349_fm_Odistinct_I7_J, fact_29_rangeE, fact_37_image__Collect__subsetI, fact_20_image__eqI, fact_84_ord__eq__le__subst, fact_27_rangeE, fact_308_eval_Osimps_I5_J, fact_82_ord__le__eq__subst, fact_162_UNIV__witness, fact_173_Compr__image__eq, fact_47_top__set__def, fact_275_surjD, fact_28_rangeE, fact_338_fm_Oexhaust, fact_87_ord__eq__le__subst, fact_181_imageE, fact_156_subsetD, fact_216_subset__image__iff, fact_311_Fpow__mono, fact_306_image__Fpow__mono, fact_319_GreatestI2__order, fact_136_set__eq__subset, fact_45_top__set__def, fact_232_image__subsetI, fact_55_dual__order_Oeq__iff, fact_297_Inf_OINF__cong, fact_309_fm_Oinject_I4_J, fact_23_image__eqI, fact_13_subset__antisym, fact_9_iso__tuple__UNIV__I, fact_186_imageE, fact_60_order__trans, fact_24_order__refl, fact_315_image__Pow__mono, fact_62_order__class_Oorder_Oantisym, fact_262_surjI, fact_231_image__subsetI, fact_234_image__subsetI, fact_224_subset__imageE, fact_25_order__refl, fact_141_Collect__mono, fact_242_range__eqI, fact_219_subset__image__iff, fact_167_UNIV__eq__I, fact_96_rev__image__eqI, fact_292_subset__CollectI, fact_184_imageE, fact_56_dual__order_Otrans, fact_217_subset__image__iff, fact_40_image__Collect__subsetI, fact_336_fm_Odistinct_I11_J, fact_227_image__subsetI, fact_52_dual__order_Oantisym, fact_139_Collect__mono, fact_128_imageI, fact_238_image__mono, fact_64_ord__le__eq__trans, fact_10_subsetI, fact_30_rangeE, fact_44_image__Collect__subsetI, fact_86_ord__eq__le__subst, fact_113_Collect__mem__eq, fact_163_UNIV__witness, fact_126_imageI, fact_166_UNIV__eq__I, fact_314_image__Pow__mono, fact_287_subset__Collect__iff, fact_302_top__empty__eq, fact_324_Pow__iff
% 22.63/6.23 % No. of inferences in proof: 708
% 22.63/6.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5885 ms resp. 5055 ms w/o parsing
% 23.97/6.53 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 23.97/6.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------