%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP157^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n011.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 08:06:59 AM UTC 2026
% Result : Theorem 119.01s 90.21s
% Output : Refutation 119.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 281
% Syntax : Number of formulae : 564 ( 255 unt; 0 typ; 0 def)
% Number of atoms : 2023 ( 548 equ; 10 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 8699 ( 96 ~; 12 |; 132 &;7995 @)
% ( 0 <=>; 464 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 8 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 362 ( 362 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 48 usr; 9 con; 0-7 aty)
% Number of variables : 2578 ( 274 ^;2272 !; 32 ?;2578 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_unit_type,type,
product_unit: $tType ).
thf(a_type,type,
a: $tType ).
thf(ordere890947078_space_decl,type,
ordere890947078_space:
!>[TA: $tType] : $o ).
thf(minus_decl,type,
minus:
!>[TA: $tType] : $o ).
thf(bot_decl,type,
bot:
!>[TA: $tType] : $o ).
thf(ord_decl,type,
ord:
!>[TA: $tType] : $o ).
thf(top_decl,type,
top:
!>[TA: $tType] : $o ).
thf(group_add_decl,type,
group_add:
!>[TA: $tType] : $o ).
thf(ab_group_add_decl,type,
ab_group_add:
!>[TA: $tType] : $o ).
thf(order_top_decl,type,
order_top:
!>[TA: $tType] : $o ).
thf(ordered_ab_group_add_decl,type,
ordered_ab_group_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_decl,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(bNF_Gr_decl,type,
bNF_Gr:
!>[TA: $tType,TB: $tType] : ( ( set @ TB ) > ( TB > TA ) > ( set @ ( product_prod @ TB @ TA ) ) ) ).
thf(bNF_fstOp_decl,type,
bNF_fstOp:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > $o ) > ( TB > TA > $o ) > ( product_prod @ TC @ TA ) > ( product_prod @ TC @ TB ) ) ).
thf(bNF_pick_middlep_decl,type,
bNF_pick_middlep:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > $o ) > ( TB > TA > $o ) > TC > TA > TB ) ).
thf(bNF_sndOp_decl,type,
bNF_sndOp:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > $o ) > ( TB > TA > $o ) > ( product_prod @ TC @ TA ) > ( product_prod @ TB @ TA ) ) ).
thf(bNF_Greatest_image2_decl,type,
bNF_Greatest_image2:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( set @ TC ) > ( TC > TB ) > ( TC > TA ) > ( set @ ( product_prod @ TB @ TA ) ) ) ).
thf(minus_minus_decl,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(the_decl,type,
the:
!>[TA: $tType] : ( ( TA > $o ) > TA ) ).
thf(order_preorder_on_decl,type,
order_preorder_on:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(bot_bot_decl,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(top_top_decl,type,
top_top:
!>[TA: $tType] : TA ).
thf(prefer951318096ood_as_decl,type,
prefer951318096ood_as:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > ( set @ TA ) ) ).
thf(prefer310429814s_good_decl,type,
prefer310429814s_good:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > ( set @ TA ) ) ).
thf(prefer1532642881r_than_decl,type,
prefer1532642881r_than:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > ( set @ TA ) ) ).
thf(prefer199794634erence_decl,type,
prefer199794634erence:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(product_Pair_decl,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(product_Sigma_decl,type,
product_Sigma:
!>[TA: $tType,TB: $tType] : ( ( set @ TB ) > ( TB > ( set @ TA ) ) > ( set @ ( product_prod @ TB @ TA ) ) ) ).
thf(product_curry_decl,type,
product_curry:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( ( product_prod @ TC @ TB ) > TA ) > TC > TB > TA ) ).
thf(produc2004651681e_prod_decl,type,
produc2004651681e_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(product_map_prod_decl,type,
product_map_prod:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( TD > TC ) > ( TB > TA ) > ( product_prod @ TD @ TB ) > ( product_prod @ TC @ TA ) ) ).
thf(product_rec_prod_decl,type,
product_rec_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(product_rec_set_prod_decl,type,
product_rec_set_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA > $o ) ).
thf(product_fst_decl,type,
product_fst:
!>[TA: $tType,TB: $tType] : ( ( product_prod @ TB @ TA ) > TB ) ).
thf(product_snd_decl,type,
product_snd:
!>[TA: $tType,TB: $tType] : ( ( product_prod @ TB @ TA ) > TA ) ).
thf(product_swap_decl,type,
product_swap:
!>[TA: $tType,TB: $tType] : ( ( product_prod @ TB @ TA ) > ( product_prod @ TA @ TB ) ) ).
thf(product_product_decl,type,
product_product:
!>[TA: $tType,TB: $tType] : ( ( set @ TB ) > ( set @ TA ) > ( set @ ( product_prod @ TB @ TA ) ) ) ).
thf(product_scomp_decl,type,
product_scomp:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( TD > ( product_prod @ TC @ TB ) ) > ( TC > TB > TA ) > TD > TA ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(image_decl,type,
image:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > ( set @ TA ) ) ).
thf(lex_prod_decl,type,
lex_prod:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TB ) ) > ( set @ ( product_prod @ TA @ TA ) ) > ( set @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) ) ) ).
thf(same_fst_decl,type,
same_fst:
!>[TA: $tType,TB: $tType] : ( ( TB > $o ) > ( TB > ( set @ ( product_prod @ TA @ TA ) ) ) > ( set @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) ) ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(b_decl,type,
b: set @ a ).
thf(pr_decl,type,
pr: set @ ( product_prod @ a @ a ) ).
thf(y_decl,type,
y: a ).
thf(z_decl,type,
z: a ).
thf(105,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_empty__subsetI) ).
thf(629,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(226,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA,B: set @ TD,C: set @ TA,D: TC > TB,E: set @ TC,F: set @ TB] :
( ( ( image @ TD @ TA @ A @ B )
= C )
=> ( ( ( image @ TC @ TB @ D @ E )
= F )
=> ( ( image @ ( product_prod @ TD @ TC ) @ ( product_prod @ TA @ TB ) @ ( product_map_prod @ TD @ TA @ TC @ TB @ A @ D )
@ ( product_Sigma @ TD @ TC @ B
@ ^ [G: TD] : E ) )
= ( product_Sigma @ TA @ TB @ C
@ ^ [G: TA] : F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_map__prod__surj__on) ).
thf(1024,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA,B: set @ TD,C: set @ TA,D: TC > TB,E: set @ TC,F: set @ TB] :
( ( ( image @ TD @ TA @ A @ B )
= C )
=> ( ( ( image @ TC @ TB @ D @ E )
= F )
=> ( ( image @ ( product_prod @ TD @ TC ) @ ( product_prod @ TA @ TB ) @ ( product_map_prod @ TD @ TA @ TC @ TB @ A @ D )
@ ( product_Sigma @ TD @ TC @ B
@ ^ [G: TD] : E ) )
= ( product_Sigma @ TA @ TB @ C
@ ^ [G: TA] : F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(145,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_prod_Ocollapse) ).
thf(760,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(51,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_empty__Diff) ).
thf(479,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(173,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ TA] :
( ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ TA @ C @ B ) )
=> ( ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ TA @ D @ B ) )
=> ( ( order_preorder_on @ TA @ B @ A )
=> ( prefer199794634erence @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_preference_Ointro) ).
thf(846,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ TA] :
( ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ TA @ C @ B ) )
=> ( ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ TA @ D @ B ) )
=> ( ( order_preorder_on @ TA @ B @ A )
=> ( prefer199794634erence @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(228,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( image @ ( product_prod @ TA @ TB ) @ ( product_prod @ TB @ TA ) @ ( product_swap @ TA @ TB ) @ C ) )
= ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_pair__in__swap__image) ).
thf(1031,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( image @ ( product_prod @ TA @ TB ) @ ( product_prod @ TB @ TA ) @ ( product_swap @ TA @ TB ) @ C ) )
= ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(47,axiom,
! [TA: $tType] : ( minus @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Ominus_5) ).
thf(468,plain,
! [TA: $tType] : ( minus @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(203,axiom,
! [TA: $tType,TB: $tType] :
( ( top_top @ ( TA > TB > $o ) )
= ( ^ [A: TA,B: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_top__empty__eq2) ).
thf(941,plain,
! [TA: $tType,TB: $tType] :
( ( top_top @ ( TA > TB > $o ) )
= ( ^ [A: TA,B: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(75,axiom,
! [TA: $tType,A: TA > TA > $o] :
( ord_less_eq @ ( TA > TA > $o ) @ ( (=) @ TA )
@ ^ [B: TA,C: TA] :
( ( A @ B @ C )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_eq__subset) ).
thf(555,plain,
! [TA: $tType,A: TA > TA > $o] :
( ord_less_eq @ ( TA > TA > $o ) @ ( (=) @ TA )
@ ^ [B: TA,C: TA] :
( ( A @ B @ C )
| ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(254,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( product_curry @ TA @ TB @ TC )
= ( ^ [A: ( product_prod @ TA @ TB ) > TC,B: TA,C: TB] : ( A @ ( product_Pair @ TA @ TB @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_curry__def) ).
thf(1110,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( product_curry @ TA @ TB @ TC )
= ( ^ [A: ( product_prod @ TA @ TB ) > TC,B: TA,C: TB] : ( A @ ( product_Pair @ TA @ TB @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(112,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA,C: TB] :
( ( A @ B @ C )
=> ( A @ ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ C @ B ) ) @ ( product_fst @ TB @ TA @ ( product_Pair @ TB @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_exI__realizer) ).
thf(645,plain,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA,C: TB] :
( ( A @ B @ C )
=> ( A @ ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ C @ B ) ) @ ( product_fst @ TB @ TA @ ( product_Pair @ TB @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(187,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > ( product_prod @ TB @ TC )] :
( ( product_scomp @ TA @ TB @ TC @ ( product_prod @ TB @ TC ) @ A @ ( product_Pair @ TB @ TC ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_scomp__Pair) ).
thf(892,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > ( product_prod @ TB @ TC )] :
( ( product_scomp @ TA @ TB @ TC @ ( product_prod @ TB @ TC ) @ A @ ( product_Pair @ TB @ TC ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(270,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TB,C: set @ ( product_prod @ TA @ TB ),D: TB] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) )
@ ( product_Sigma @ TA @ TB @ A
@ ^ [E: TA] : B )
@ C )
=> ( ( member @ TB @ D @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( image @ ( product_prod @ TA @ TB ) @ TA @ ( product_fst @ TA @ TB ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_subset__fst__imageI) ).
thf(1158,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TB,C: set @ ( product_prod @ TA @ TB ),D: TB] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) )
@ ( product_Sigma @ TA @ TB @ A
@ ^ [E: TA] : B )
@ C )
=> ( ( member @ TB @ D @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( image @ ( product_prod @ TA @ TB ) @ TA @ ( product_fst @ TA @ TB ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(217,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA] :
( ( A
= ( B @ C ) )
=> ( member @ TB @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_range__eqI) ).
thf(994,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA] :
( ( A
= ( B @ C ) )
=> ( member @ TB @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(241,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_Collect__restrict) ).
thf(1073,plain,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(263,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(1142,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(93,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_equalityD2) ).
thf(597,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(180,axiom,
! [TA: $tType] :
( ( prefer199794634erence @ TA )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ C @ A ) )
& ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ D @ A ) )
& ( order_preorder_on @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_preference__def) ).
thf(873,plain,
! [TA: $tType] :
( ( prefer199794634erence @ TA )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ C @ A ) )
& ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ D @ A ) )
& ( order_preorder_on @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(39,axiom,
order_top @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder__top_6) ).
thf(449,plain,
order_top @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(115,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_subsetI) ).
thf(655,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB] :
( ( product_curry @ TA @ TC @ TB
@ ^ [B: product_prod @ TA @ TC] : A )
= ( ^ [B: TA,C: TC] : A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_curry__K) ).
thf(511,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB] :
( ( product_curry @ TA @ TC @ TB
@ ^ [B: product_prod @ TA @ TC] : A )
= ( ^ [B: TA,C: TC] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType] :
( ( product_map_prod @ TA @ TA @ TB @ TB
@ ^ [A: TA] : A
@ ^ [A: TB] : A )
= ( ^ [A: product_prod @ TA @ TB] : A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_map__prod__ident) ).
thf(614,plain,
! [TA: $tType,TB: $tType] :
( ( product_map_prod @ TA @ TA @ TB @ TB
@ ^ [A: TA] : A
@ ^ [A: TB] : A )
= ( ^ [A: product_prod @ TA @ TB] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(121,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ TA] :
( ( ( A
= ( bot_bot @ ( set @ TB ) ) )
=> ( ( image @ ( product_prod @ TB @ TA ) @ TA @ ( product_snd @ TB @ TA )
@ ( product_Sigma @ TB @ TA @ A
@ ^ [C: TB] : B ) )
= ( bot_bot @ ( set @ TA ) ) ) )
& ( ( A
!= ( bot_bot @ ( set @ TB ) ) )
=> ( ( image @ ( product_prod @ TB @ TA ) @ TA @ ( product_snd @ TB @ TA )
@ ( product_Sigma @ TB @ TA @ A
@ ^ [C: TB] : B ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_snd__image__times) ).
thf(677,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ TA] :
( ( ( A
= ( bot_bot @ ( set @ TB ) ) )
=> ( ( image @ ( product_prod @ TB @ TA ) @ TA @ ( product_snd @ TB @ TA )
@ ( product_Sigma @ TB @ TA @ A
@ ^ [C: TB] : B ) )
= ( bot_bot @ ( set @ TA ) ) ) )
& ( ( A
!= ( bot_bot @ ( set @ TB ) ) )
=> ( ( image @ ( product_prod @ TB @ TA ) @ TA @ ( product_snd @ TB @ TA )
@ ( product_Sigma @ TB @ TA @ A
@ ^ [C: TB] : B ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(243,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ! [C: TA,D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_subrelI) ).
thf(1078,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ! [C: TA,D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA > TB] :
( ! [C: TA] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_surjI) ).
thf(384,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA > TB] :
( ! [C: TA] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(67,axiom,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_top__set__def) ).
thf(533,plain,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(131,axiom,
! [TA: $tType,TB: $tType] :
( ( ( bot @ TA )
& ( bot @ TB ) )
=> ( ( bot_bot @ ( product_prod @ TB @ TA ) )
= ( product_Pair @ TB @ TA @ ( bot_bot @ TB ) @ ( bot_bot @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_bot__prod__def) ).
thf(715,plain,
! [TA: $tType,TB: $tType] :
( ( ( bot @ TA )
& ( bot @ TB ) )
=> ( ( bot_bot @ ( product_prod @ TB @ TA ) )
= ( product_Pair @ TB @ TA @ ( bot_bot @ TB ) @ ( bot_bot @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(161,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TA > TC > TB] :
( ( product_scomp @ TC @ TA @ TC @ TB @ ( product_Pair @ TA @ TC @ A ) @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_Pair__scomp) ).
thf(814,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TA > TC > TB] :
( ( product_scomp @ TC @ TA @ TC @ TB @ ( product_Pair @ TA @ TC @ A ) @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(193,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( A
= ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_surjective__pairing) ).
thf(913,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( A
= ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(238,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_subset__eq) ).
thf(1063,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( ( image @ TA @ TB @ A @ B )
= ( bot_bot @ ( set @ TB ) ) )
= ( B
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_image__is__empty) ).
thf(538,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( ( image @ TA @ TB @ A @ B )
= ( bot_bot @ ( set @ TB ) ) )
= ( B
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(199,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_less__eq__set__def) ).
thf(930,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(114,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: TA,C: TB] :
( ( A
= ( product_Pair @ TA @ TB @ B @ C ) )
=> ( ( product_fst @ TA @ TB @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_fstI) ).
thf(651,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: TA,C: TB] :
( ( A
= ( product_Pair @ TA @ TB @ B @ C ) )
=> ( ( product_fst @ TA @ TB @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(171,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_emptyE) ).
thf(841,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(26,axiom,
top @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Otop_7) ).
thf(417,plain,
top @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(12,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ? [C: TA] :
( ( A @ C )
& ! [D: TA] :
( ( A @ D )
=> ( D = C ) ) )
=> ( ( A @ B )
=> ( ( the @ TA @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_the1__equality) ).
thf(372,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ? [C: TA] :
( ( A @ C )
& ! [D: TA] :
( ( A @ D )
=> ( D = C ) ) )
=> ( ( A @ B )
=> ( ( the @ TA @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(126,axiom,
! [TA: $tType] :
( ( minus_minus @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ( minus_minus @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_minus__set__def) ).
thf(702,plain,
! [TA: $tType] :
( ( minus_minus @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ( minus_minus @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(281,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: product_prod @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) )] :
~ ! [B: TG,C: TF,D: TE,E: TD,F: TC,G: TB,H: TA] :
( A
!= ( product_Pair @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ E @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ F @ ( product_Pair @ TB @ TA @ G @ H ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_prod__cases7) ).
thf(1191,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: product_prod @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) )] :
~ ! [B: TG,C: TF,D: TE,E: TD,F: TC,G: TB,H: TA] :
( A
!= ( product_Pair @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ E @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ F @ ( product_Pair @ TB @ TA @ G @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ? [C: TA] :
( B
= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_surjD) ).
thf(460,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ? [C: TA] :
( B
= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(235,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA,D: TA > $o] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_prop__restrict) ).
thf(1055,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA,D: TA > $o] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(134,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ TA,D: TA > ( set @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( product_Sigma @ TA @ TB @ C @ D ) )
=> ( member @ TB @ B @ ( D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_SigmaD2) ).
thf(724,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ TA,D: TA > ( set @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( product_Sigma @ TA @ TB @ C @ D ) )
=> ( member @ TB @ B @ ( D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(89,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_diff__mono) ).
thf(587,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(101,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
& ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_prod_Oexpand) ).
thf(619,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
& ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(170,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > ( set @ TB )] :
( ( product_Sigma @ TA @ TB @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ C )
= ( minus_minus @ ( set @ ( product_prod @ TA @ TB ) ) @ ( product_Sigma @ TA @ TB @ A @ C ) @ ( product_Sigma @ TA @ TB @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_Sigma__Diff__distrib1) ).
thf(838,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > ( set @ TB )] :
( ( product_Sigma @ TA @ TB @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ C )
= ( minus_minus @ ( set @ ( product_prod @ TA @ TB ) ) @ ( product_Sigma @ TA @ TB @ A @ C ) @ ( product_Sigma @ TA @ TB @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(162,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA,B: TC > TB] :
( ( ( image @ TD @ TA @ A @ ( top_top @ ( set @ TD ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ( ( image @ TC @ TB @ B @ ( top_top @ ( set @ TC ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ( ( image @ ( product_prod @ TD @ TC ) @ ( product_prod @ TA @ TB ) @ ( product_map_prod @ TD @ TA @ TC @ TB @ A @ B ) @ ( top_top @ ( set @ ( product_prod @ TD @ TC ) ) ) )
= ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_map__prod__surj) ).
thf(817,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA,B: TC > TB] :
( ( ( image @ TD @ TA @ A @ ( top_top @ ( set @ TD ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ( ( image @ TC @ TB @ B @ ( top_top @ ( set @ TC ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ( ( image @ ( product_prod @ TD @ TC ) @ ( product_prod @ TA @ TB ) @ ( product_map_prod @ TD @ TA @ TC @ TB @ A @ B ) @ ( top_top @ ( set @ ( product_prod @ TD @ TC ) ) ) )
= ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(265,axiom,
! [TA: $tType] :
( ( prefer951318096ood_as @ TA )
= ( ^ [A: TA,B: set @ TA,C: set @ ( product_prod @ TA @ TA )] :
( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ D ) @ C )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_as__good__as__def) ).
thf(1147,plain,
! [TA: $tType] :
( ( prefer951318096ood_as @ TA )
= ( ^ [A: TA,B: set @ TA,C: set @ ( product_prod @ TA @ TA )] :
( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ D ) @ C )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(28,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_subset__refl) ).
thf(421,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(223,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > ( set @ TB ),D: TA > ( set @ TB )] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ord_less_eq @ ( set @ TB ) @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ ( product_Sigma @ TA @ TB @ A @ C ) @ ( product_Sigma @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_Sigma__mono) ).
thf(1013,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > ( set @ TB ),D: TA > ( set @ TB )] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ord_less_eq @ ( set @ TB ) @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ ( product_Sigma @ TA @ TB @ A @ C ) @ ( product_Sigma @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(3,axiom,
! [TA: $tType,A: TA > $o] :
( ? [B: TA] :
( ( A @ B )
& ! [C: TA] :
( ( A @ C )
=> ( C = B ) ) )
=> ( A @ ( the @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_theI_H) ).
thf(284,plain,
! [TA: $tType,A: TA > $o] :
( ? [B: TA] :
( ( A @ B )
& ! [C: TA] :
( ( A @ C )
=> ( C = B ) ) )
=> ( A @ ( the @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(149,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB > TA,C: set @ TA] :
( ! [D: TB] :
( ( A @ D )
=> ( member @ TA @ ( B @ D ) @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( image @ TB @ TA @ B @ ( collect @ TB @ A ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_image__Collect__subsetI) ).
thf(770,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB > TA,C: set @ TA] :
( ! [D: TB] :
( ( A @ D )
=> ( member @ TA @ ( B @ D ) @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( image @ TB @ TA @ B @ ( collect @ TB @ A ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(144,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_DiffE) ).
thf(756,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(155,axiom,
! [TA: $tType,TB: $tType] :
( ( product_swap @ TA @ TB )
= ( ^ [A: product_prod @ TA @ TB] : ( product_Pair @ TB @ TA @ ( product_snd @ TA @ TB @ A ) @ ( product_fst @ TA @ TB @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_prod_Oswap__def) ).
thf(789,plain,
! [TA: $tType,TB: $tType] :
( ( product_swap @ TA @ TB )
= ( ^ [A: product_prod @ TA @ TB] : ( product_Pair @ TB @ TA @ ( product_snd @ TA @ TB @ A ) @ ( product_fst @ TA @ TB @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType] :
( ( (=) @ ( product_prod @ TA @ TB ) )
= ( ^ [A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
& ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_prod__eq__iff) ).
thf(591,plain,
! [TA: $tType,TB: $tType] :
( ( (=) @ ( product_prod @ TA @ TB ) )
= ( ^ [A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
& ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(36,axiom,
bot @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Obot_9) ).
thf(443,plain,
bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(230,axiom,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB )] :
( ( product_Sigma @ TA @ TB @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_Sigma__empty1) ).
thf(1040,plain,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB )] :
( ( product_Sigma @ TA @ TB @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(103,axiom,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA
@ ^ [A: TA] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_UNIV__def) ).
thf(623,plain,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA
@ ^ [A: TA] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(53,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_Collect__mono__iff) ).
thf(485,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TB )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_top__apply) ).
thf(514,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TB )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(267,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TA,C: TB] :
( ( ord_less_eq @ ( set @ TA ) @ ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) ) @ B )
=> ( member @ TA @ ( A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_range__subsetD) ).
thf(1151,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TA,C: TB] :
( ( ord_less_eq @ ( set @ TA ) @ ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) ) @ B )
=> ( member @ TA @ ( A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(159,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TB )
& ( ord @ TA ) )
=> ( ord @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Orderings_Oord_13) ).
thf(806,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TB )
& ( ord @ TA ) )
=> ( ord @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(95,axiom,
! [TA: $tType,TB: $tType] :
( ( minus @ TB )
=> ( ( minus_minus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( minus_minus @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_fun__diff__def) ).
thf(602,plain,
! [TA: $tType,TB: $tType] :
( ( minus @ TB )
=> ( ( minus_minus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( minus_minus @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(150,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( ordere890947078_space @ TA ) )
=> ( ordere890947078_space @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Ordered__Euclidean__Space_Oordered__euclidean__space) ).
thf(774,plain,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( ordere890947078_space @ TA ) )
=> ( ordere890947078_space @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(218,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order_top @ TB )
& ( order_top @ TA ) )
=> ( order_top @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Orderings_Oorder__top_11) ).
thf(998,plain,
! [TA: $tType,TB: $tType] :
( ( ( order_top @ TB )
& ( order_top @ TA ) )
=> ( order_top @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(252,axiom,
! [TA: $tType,TB: $tType] :
( ( ( top @ TA )
& ( top @ TB ) )
=> ( ( product_snd @ TB @ TA @ ( top_top @ ( product_prod @ TB @ TA ) ) )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_snd__top) ).
thf(1104,plain,
! [TA: $tType,TB: $tType] :
( ( ( top @ TA )
& ( top @ TB ) )
=> ( ( product_snd @ TB @ TA @ ( top_top @ ( product_prod @ TB @ TA ) ) )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(19,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_diff__eq__diff__eq) ).
thf(397,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(123,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ TA,D: TA > TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( bNF_Gr @ TA @ TB @ C @ D ) )
=> ( member @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_GrD1) ).
thf(687,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ TA,D: TA > TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( bNF_Gr @ TA @ TB @ C @ D ) )
=> ( member @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(72,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_empty__Collect__eq) ).
thf(546,plain,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(197,axiom,
! [TA: $tType,TB: $tType] :
( ( image @ ( product_prod @ TA @ TB ) @ TA @ ( product_fst @ TA @ TB ) @ ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_range__fst) ).
thf(925,plain,
! [TA: $tType,TB: $tType] :
( ( image @ ( product_prod @ TA @ TB ) @ TA @ ( product_fst @ TA @ TB ) @ ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(268,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_snd__conv) ).
thf(1153,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(13,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_Collect__empty__eq) ).
thf(381,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(232,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( product_swap @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= ( product_Pair @ TB @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_swap__simp) ).
thf(1047,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( product_swap @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= ( product_Pair @ TB @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(236,axiom,
! [TA: $tType,TB: $tType] :
( ( product_Sigma @ TA @ TB @ ( top_top @ ( set @ TA ) )
@ ^ [A: TA] : ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_UNIV__Times__UNIV) ).
thf(1057,plain,
! [TA: $tType,TB: $tType] :
( ( product_Sigma @ TA @ TB @ ( top_top @ ( set @ TA ) )
@ ^ [A: TA] : ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(272,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > ( set @ TB ),C: TA > ( set @ TB )] :
( ( product_Sigma @ TA @ TB @ A
@ ^ [D: TA] : ( minus_minus @ ( set @ TB ) @ ( B @ D ) @ ( C @ D ) ) )
= ( minus_minus @ ( set @ ( product_prod @ TA @ TB ) ) @ ( product_Sigma @ TA @ TB @ A @ B ) @ ( product_Sigma @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_Sigma__Diff__distrib2) ).
thf(1163,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > ( set @ TB ),C: TA > ( set @ TB )] :
( ( product_Sigma @ TA @ TB @ A
@ ^ [D: TA] : ( minus_minus @ ( set @ TB ) @ ( B @ D ) @ ( C @ D ) ) )
= ( minus_minus @ ( set @ ( product_prod @ TA @ TB ) ) @ ( product_Sigma @ TA @ TB @ A @ B ) @ ( product_Sigma @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(192,axiom,
! [TA: $tType,TB: $tType] :
( ( ( minus @ TA )
& ( minus @ TB ) )
=> ! [A: TB,B: TA,C: TB,D: TA] :
( ( minus_minus @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( product_Pair @ TB @ TA @ C @ D ) )
= ( product_Pair @ TB @ TA @ ( minus_minus @ TB @ A @ C ) @ ( minus_minus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_diff__Pair) ).
thf(910,plain,
! [TA: $tType,TB: $tType] :
( ( ( minus @ TA )
& ( minus @ TB ) )
=> ! [A: TB,B: TA,C: TB,D: TA] :
( ( minus_minus @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( product_Pair @ TB @ TA @ C @ D ) )
= ( product_Pair @ TB @ TA @ ( minus_minus @ TB @ A @ C ) @ ( minus_minus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(208,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > $o,D: TA] :
( ( A @ B )
=> ( ( C @ D )
=> ( ( A @ ( product_fst @ TB @ TA @ ( product_Pair @ TB @ TA @ B @ D ) ) )
& ( C @ ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_conjI__realizer) ).
thf(957,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > $o,D: TA] :
( ( A @ B )
=> ( ( C @ D )
=> ( ( A @ ( product_fst @ TB @ TA @ ( product_Pair @ TB @ TA @ B @ D ) ) )
& ( C @ ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(225,axiom,
! [TA: $tType] :
( ( prefer1532642881r_than @ TA )
= ( ^ [A: TA,B: set @ TA,C: set @ ( product_prod @ TA @ TA )] :
( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_no__better__than__def) ).
thf(1021,plain,
! [TA: $tType] :
( ( prefer1532642881r_than @ TA )
= ( ^ [A: TA,B: set @ TA,C: set @ ( product_prod @ TA @ TA )] :
( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(163,axiom,
! [TA: $tType,TB: $tType] :
( ( ( group_add @ TB )
& ( group_add @ TA ) )
=> ( group_add @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Groups_Ogroup__add) ).
thf(820,plain,
! [TA: $tType,TB: $tType] :
( ( ( group_add @ TB )
& ( group_add @ TA ) )
=> ( group_add @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(78,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_3) ).
thf(561,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(17,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_diff__left__mono) ).
thf(392,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(31,axiom,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_subset__empty) ).
thf(429,plain,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(136,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA > TC,C: TA,D: TB,E: TA > TB,F: set @ TA] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member @ TA @ C @ F )
=> ( member @ ( product_prod @ TC @ TB ) @ ( product_Pair @ TC @ TB @ A @ D ) @ ( bNF_Greatest_image2 @ TA @ TC @ TB @ F @ B @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_image2__eqI) ).
thf(729,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA > TC,C: TA,D: TB,E: TA > TB,F: set @ TA] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member @ TA @ C @ F )
=> ( member @ ( product_prod @ TC @ TB ) @ ( product_Pair @ TC @ TB @ A @ D ) @ ( bNF_Greatest_image2 @ TA @ TC @ TB @ F @ B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(141,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_prod__cases6) ).
thf(746,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(247,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA,D: set @ ( product_prod @ TA @ TA )] :
( ( member @ TA @ A @ ( prefer310429814s_good @ TA @ B @ C @ D ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_at__lst__asgd__ge) ).
thf(1091,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA,D: set @ ( product_prod @ TA @ TA )] :
( ( member @ TA @ A @ ( prefer310429814s_good @ TA @ B @ C @ D ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(194,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > ( set @ TB )] :
( ( ( product_Sigma @ TA @ TB @ A @ B )
= ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ( B @ C )
= ( bot_bot @ ( set @ TB ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_Sigma__empty__iff) ).
thf(916,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > ( set @ TB )] :
( ( ( product_Sigma @ TA @ TB @ A @ B )
= ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ( B @ C )
= ( bot_bot @ ( set @ TB ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(80,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_map_prod @ TA @ TA @ TB @ TB
@ ^ [B: TA] : B
@ ^ [B: TB] : B
@ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_prod_Omap__ident) ).
thf(566,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_map_prod @ TA @ TA @ TB @ TB
@ ^ [B: TA] : B
@ ^ [B: TB] : B
@ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(129,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_subset__iff) ).
thf(710,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(174,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( member @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_DiffD2) ).
thf(852,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( member @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(33,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(435,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(87,axiom,
bot @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Obot_19) ).
thf(583,plain,
bot @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( product_scomp @ TA @ TB @ TC @ TD )
= ( ^ [A: TA > ( product_prod @ TB @ TC ),B: TB > TC > TD,C: TA] : ( B @ ( product_fst @ TB @ TC @ ( A @ C ) ) @ ( product_snd @ TB @ TC @ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_scomp__unfold) ).
thf(522,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( product_scomp @ TA @ TB @ TC @ TD )
= ( ^ [A: TA > ( product_prod @ TB @ TC ),B: TB > TC > TD,C: TA] : ( B @ ( product_fst @ TB @ TC @ ( A @ C ) ) @ ( product_snd @ TB @ TC @ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(224,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA] :
( ( ( product_fst @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= C )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_fst__eqD) ).
thf(1017,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA] :
( ( ( product_fst @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= C )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(257,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_prod_Oinject) ).
thf(1121,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(249,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: set @ TA,C: set @ TB] :
( ( member @ ( product_prod @ TA @ TB ) @ A @ ( product_product @ TA @ TB @ B @ C ) )
= ( member @ ( product_prod @ TA @ TB ) @ A
@ ( product_Sigma @ TA @ TB @ B
@ ^ [D: TA] : C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_member__product) ).
thf(1096,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: set @ TA,C: set @ TB] :
( ( member @ ( product_prod @ TA @ TB ) @ A @ ( product_product @ TA @ TB @ B @ C ) )
= ( member @ ( product_prod @ TA @ TB ) @ A
@ ( product_Sigma @ TA @ TB @ B
@ ^ [D: TA] : C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(262,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ TC )] :
( ! [C: TA,D: TB,E: TC] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_prod__induct3) ).
thf(1138,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ TC )] :
( ! [C: TA,D: TB,E: TC] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(153,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_subset__Collect__iff) ).
thf(783,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(56,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_Diff__empty) ).
thf(499,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(215,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ C ) @ ( product_Pair @ TB @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_Pair__mono) ).
thf(989,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ C ) @ ( product_Pair @ TB @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(176,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ TB,D: TB > TA] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( bNF_Gr @ TB @ TA @ C @ D ) )
=> ( ( D @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_GrD2) ).
thf(857,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ TB,D: TB > TA] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( bNF_Gr @ TB @ TA @ C @ D ) )
=> ( ( D @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( product_rec_prod @ TA @ TB @ TC )
= ( ^ [A: TA > TB > TC,B: product_prod @ TA @ TB] : ( the @ TC @ ( product_rec_set_prod @ TA @ TB @ TC @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_old_Orec__prod__def) ).
thf(519,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( product_rec_prod @ TA @ TB @ TC )
= ( ^ [A: TA > TB > TC,B: product_prod @ TA @ TB] : ( the @ TC @ ( product_rec_set_prod @ TA @ TB @ TC @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(140,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_prod__cases) ).
thf(742,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(212,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_in__mono) ).
thf(980,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ TA,C: set @ TB,D: set @ TA] :
( ( ( product_Sigma @ TB @ TA @ A
@ ^ [E: TB] : B )
= ( product_Sigma @ TB @ TA @ C
@ ^ [E: TB] : D ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( ( A
= ( bot_bot @ ( set @ TB ) ) )
| ( B
= ( bot_bot @ ( set @ TA ) ) ) )
& ( ( C
= ( bot_bot @ ( set @ TB ) ) )
| ( D
= ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_times__eq__iff) ).
thf(403,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ TA,C: set @ TB,D: set @ TA] :
( ( ( product_Sigma @ TB @ TA @ A
@ ^ [E: TB] : B )
= ( product_Sigma @ TB @ TA @ C
@ ^ [E: TB] : D ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( ( A
= ( bot_bot @ ( set @ TB ) ) )
| ( B
= ( bot_bot @ ( set @ TA ) ) ) )
& ( ( C
= ( bot_bot @ ( set @ TB ) ) )
| ( D
= ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(184,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ TA] :
( ( image @ ( product_prod @ TB @ TA ) @ ( product_prod @ TA @ TB ) @ ( product_swap @ TB @ TA )
@ ( product_Sigma @ TB @ TA @ A
@ ^ [C: TB] : B ) )
= ( product_Sigma @ TA @ TB @ B
@ ^ [C: TA] : A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_product__swap) ).
thf(884,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ TA] :
( ( image @ ( product_prod @ TB @ TA ) @ ( product_prod @ TA @ TB ) @ ( product_swap @ TB @ TA )
@ ( product_Sigma @ TB @ TA @ A
@ ^ [C: TB] : B ) )
= ( product_Sigma @ TA @ TB @ B
@ ^ [C: TA] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(271,axiom,
! [TA: $tType,TB: $tType,A: TB,B: product_prod @ TA @ TB] :
( ( A
= ( product_snd @ TA @ TB @ B ) )
= ( ? [C: TA] :
( B
= ( product_Pair @ TA @ TB @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_eq__snd__iff) ).
thf(1160,plain,
! [TA: $tType,TB: $tType,A: TB,B: product_prod @ TA @ TB] :
( ( A
= ( product_snd @ TA @ TB @ B ) )
= ( ? [C: TA] :
( B
= ( product_Pair @ TA @ TB @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(54,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_equalityE) ).
thf(488,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(9,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ? [C: TA] :
( ( A @ C )
& ! [D: TA] :
( ( A @ D )
=> ( D = C ) ) )
=> ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( B @ ( the @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_the1I2) ).
thf(339,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ? [C: TA] :
( ( A @ C )
& ! [D: TA] :
( ( A @ D )
=> ( D = C ) ) )
=> ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( B @ ( the @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(200,axiom,
! [TA: $tType,TB: $tType] :
( ( ( top @ TA )
& ( top @ TB ) )
=> ( ( top_top @ ( product_prod @ TB @ TA ) )
= ( product_Pair @ TB @ TA @ ( top_top @ TB ) @ ( top_top @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_top__prod__def) ).
thf(933,plain,
! [TA: $tType,TB: $tType] :
( ( ( top @ TA )
& ( top @ TB ) )
=> ( ( top_top @ ( product_prod @ TB @ TA ) )
= ( product_Pair @ TB @ TA @ ( top_top @ TB ) @ ( top_top @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(242,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
= ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_pred__equals__eq2) ).
thf(1075,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
= ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(108,axiom,
! [TA: $tType] : ( bot @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Obot_4) ).
thf(637,plain,
! [TA: $tType] : ( bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(210,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_Collect__subset) ).
thf(970,plain,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(227,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA,E: set @ ( product_prod @ TB @ TB ),F: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( product_Pair @ TB @ TA @ C @ D ) ) @ ( lex_prod @ TB @ TA @ E @ F ) )
= ( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ A @ C ) @ E )
| ( ( A = C )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_in__lex__prod) ).
thf(1028,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA,E: set @ ( product_prod @ TB @ TB ),F: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( product_Pair @ TB @ TA @ C @ D ) ) @ ( lex_prod @ TB @ TA @ E @ F ) )
= ( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ A @ C ) @ E )
| ( ( A = C )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(244,axiom,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_all__not__in__conv) ).
thf(1082,plain,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(102,axiom,
minus @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Groups_Ominus_20) ).
thf(622,plain,
minus @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(113,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: TB > TA,C: set @ TA] :
( ! [D: TB] :
( ( member @ TB @ D @ A )
=> ( member @ TA @ ( B @ D ) @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( image @ TB @ TA @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_image__subsetI) ).
thf(647,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: TB > TA,C: set @ TA] :
( ! [D: TB] :
( ( member @ TB @ D @ A )
=> ( member @ TA @ ( B @ D ) @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( image @ TB @ TA @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(266,axiom,
member @ a @ z @ ( prefer310429814s_good @ a @ y @ b @ pr ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms) ).
thf(1150,plain,
member @ a @ z @ ( prefer310429814s_good @ a @ y @ b @ pr ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(133,axiom,
! [TA: $tType] :
( ( minus_minus @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ~ ( member @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_set__diff__eq) ).
thf(721,plain,
! [TA: $tType] :
( ( minus_minus @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ~ ( member @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(81,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ( minus_minus @ ( set @ TA ) @ B @ ( minus_minus @ ( set @ TA ) @ C @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_double__diff) ).
thf(569,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ( minus_minus @ ( set @ TA ) @ B @ ( minus_minus @ ( set @ TA ) @ C @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(152,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_old_Oprod_Oinducts) ).
thf(779,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(96,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_equalityD1) ).
thf(605,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(250,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ TA,D: TA > ( set @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( product_Sigma @ TA @ TB @ C @ D ) )
= ( ( member @ TA @ A @ C )
& ( member @ TB @ B @ ( D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_mem__Sigma__iff) ).
thf(1099,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ TA,D: TA > ( set @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( product_Sigma @ TA @ TB @ C @ D ) )
= ( ( member @ TA @ A @ C )
& ( member @ TB @ B @ ( D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(214,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA,D: set @ TA] :
( ( A
= ( B @ C ) )
=> ( ( member @ TA @ C @ D )
=> ( member @ TB @ A @ ( image @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_image__eqI) ).
thf(985,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA,D: set @ TA] :
( ( A
= ( B @ C ) )
=> ( ( member @ TA @ C @ D )
=> ( member @ TB @ A @ ( image @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(237,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA,C: TB,D: TA] :
( ( ord_less_eq @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( ord_less_eq @ TB @ A @ C )
& ( ord_less_eq @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_Pair__le) ).
thf(1060,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA,C: TB,D: TA] :
( ( ord_less_eq @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( ord_less_eq @ TB @ A @ C )
& ( ord_less_eq @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(233,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_DiffD1) ).
thf(1050,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(43,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( minus_minus @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_Diff__eq__empty__iff) ).
thf(457,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( minus_minus @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(156,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image @ TA @ TB @ C @ A )
= ( image @ TA @ TB @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_image__cong) ).
thf(792,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image @ TA @ TB @ C @ A )
= ( image @ TA @ TB @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(202,axiom,
! [TA: $tType,TB: $tType] :
( ( ( top @ TA )
& ( top @ TB ) )
=> ( ( product_fst @ TA @ TB @ ( top_top @ ( product_prod @ TA @ TB ) ) )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_fst__top) ).
thf(938,plain,
! [TA: $tType,TB: $tType] :
( ( ( top @ TA )
& ( top @ TB ) )
=> ( ( product_fst @ TA @ TB @ ( top_top @ ( product_prod @ TA @ TB ) ) )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(59,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: set @ TA] :
( ( image @ TB @ TC @ A @ ( image @ TA @ TB @ B @ C ) )
= ( image @ TA @ TC
@ ^ [D: TA] : ( A @ ( B @ D ) )
@ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_image__image) ).
thf(508,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: set @ TA] :
( ( image @ TB @ TC @ A @ ( image @ TA @ TB @ B @ C ) )
= ( image @ TA @ TC
@ ^ [D: TA] : ( A @ ( B @ D ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(70,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ A )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_Diff__cancel) ).
thf(541,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ A )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(147,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_rec_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_old_Oprod_Orec) ).
thf(765,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_rec_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(274,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TB @ TA ) > $o,B: TB,C: TA] :
( ( product_curry @ TB @ TA @ $o @ A @ B @ C )
=> ( A @ ( product_Pair @ TB @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_curryE) ).
thf(1170,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TB @ TA ) > $o,B: TB,C: TA] :
( ( product_curry @ TB @ TA @ $o @ A @ B @ C )
=> ( A @ ( product_Pair @ TB @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(77,axiom,
! [TA: $tType,A: ( set @ TA ) > TA,B: set @ TA] :
( ( A
@ ( image @ TA @ TA
@ ^ [C: TA] : C
@ B ) )
= ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_Inf_OINF__identity__eq) ).
thf(558,plain,
! [TA: $tType,A: ( set @ TA ) > TA,B: set @ TA] :
( ( A
@ ( image @ TA @ TA
@ ^ [C: TA] : C
@ B ) )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(207,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member @ TB @ C @ ( image @ TA @ TB @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_rev__image__eqI) ).
thf(953,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member @ TB @ C @ ( image @ TA @ TB @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(117,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TB,D: TB,E: TA > ( set @ ( product_prod @ TB @ TB ) )] :
( ( A @ B )
=> ( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ C @ D ) @ ( E @ B ) )
=> ( member @ ( product_prod @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ C ) @ ( product_Pair @ TA @ TB @ B @ D ) ) @ ( same_fst @ TA @ TB @ A @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_same__fstI) ).
thf(662,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TB,D: TB,E: TA > ( set @ ( product_prod @ TB @ TB ) )] :
( ( A @ B )
=> ( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ C @ D ) @ ( E @ B ) )
=> ( member @ ( product_prod @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ C ) @ ( product_Pair @ TA @ TB @ B @ D ) ) @ ( same_fst @ TA @ TB @ A @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(132,axiom,
! [TA: $tType,TB: $tType] :
( ( ( minus @ TA )
& ( minus @ TB ) )
=> ! [A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( product_snd @ TA @ TB @ ( minus_minus @ ( product_prod @ TA @ TB ) @ A @ B ) )
= ( minus_minus @ TB @ ( product_snd @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_snd__diff) ).
thf(718,plain,
! [TA: $tType,TB: $tType] :
( ( ( minus @ TA )
& ( minus @ TB ) )
=> ! [A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( product_snd @ TA @ TB @ ( minus_minus @ ( product_prod @ TA @ TB ) @ A @ B ) )
= ( minus_minus @ TB @ ( product_snd @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(24,axiom,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_top1I) ).
thf(412,plain,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(165,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_surj__pair) ).
thf(824,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(124,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_Pair__inject) ).
thf(689,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(37,axiom,
! [TA: $tType,A: $o,B: TA] :
( ( A
& ( top_top @ ( TA > $o ) @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_top__conj_I2_J) ).
thf(444,plain,
! [TA: $tType,A: $o,B: TA] :
( ( A
& ( top_top @ ( TA > $o ) @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(137,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_prod__cases3) ).
thf(733,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(94,axiom,
ord @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_8) ).
thf(601,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: TA > TB,C: set @ TA] :
( ( ord_less_eq @ ( set @ TB ) @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ C )
& ( A
= ( image @ TA @ TB @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_subset__image__iff) ).
thf(584,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: TA > TB,C: set @ TA] :
( ( ord_less_eq @ ( set @ TB ) @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ C )
& ( A
= ( image @ TA @ TB @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType] :
( ( minus @ TB )
=> ( ( minus_minus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( minus_minus @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_minus__apply) ).
thf(423,plain,
! [TA: $tType,TB: $tType] :
( ( minus @ TB )
=> ( ( minus_minus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( minus_minus @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(221,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_old_Oprod_Oexhaust) ).
thf(1007,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(172,axiom,
! [TA: $tType,TB: $tType,A: TB,B: set @ TB,C: set @ TA,D: set @ TA] :
( ( member @ TB @ A @ B )
=> ( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) )
@ ( product_Sigma @ TA @ TB @ C
@ ^ [E: TA] : B )
@ ( product_Sigma @ TA @ TB @ D
@ ^ [E: TA] : B ) )
= ( ord_less_eq @ ( set @ TA ) @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_Times__subset__cancel2) ).
thf(843,plain,
! [TA: $tType,TB: $tType,A: TB,B: set @ TB,C: set @ TA,D: set @ TA] :
( ( member @ TB @ A @ B )
=> ( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) )
@ ( product_Sigma @ TA @ TB @ C
@ ^ [E: TA] : B )
@ ( product_Sigma @ TA @ TB @ D
@ ^ [E: TA] : B ) )
= ( ord_less_eq @ ( set @ TA ) @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(577,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(85,axiom,
order_top @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oorder__top_16) ).
thf(579,plain,
order_top @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(258,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > ( set @ TB )] :
( ( member @ TA @ A @ B )
=> ( ( member @ TB @ C @ ( D @ A ) )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ C ) @ ( product_Sigma @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_SigmaI) ).
thf(1124,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > ( set @ TB )] :
( ( member @ TA @ A @ B )
=> ( ( member @ TB @ C @ ( D @ A ) )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ C ) @ ( product_Sigma @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(110,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Obot) ).
thf(641,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(201,axiom,
! [TA: $tType,TB: $tType] :
( ( ( top @ TB )
& ( top @ TA ) )
=> ( top @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Orderings_Otop_12) ).
thf(936,plain,
! [TA: $tType,TB: $tType] :
( ( ( top @ TB )
& ( top @ TA ) )
=> ( top @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(82,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_Diff__UNIV) ).
thf(572,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(98,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_cancel__ab__semigroup__add__class_Odiff__right__commute) ).
thf(611,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(130,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] :
( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A
@ ( product_Sigma @ TA @ TB @ ( image @ ( product_prod @ TA @ TB ) @ TA @ ( product_fst @ TA @ TB ) @ A )
@ ^ [B: TA] : ( image @ ( product_prod @ TA @ TB ) @ TB @ ( product_snd @ TA @ TB ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_subset__fst__snd) ).
thf(713,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] :
( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A
@ ( product_Sigma @ TA @ TB @ ( image @ ( product_prod @ TA @ TB ) @ TA @ ( product_fst @ TA @ TB ) @ A )
@ ^ [B: TA] : ( image @ ( product_prod @ TA @ TB ) @ TB @ ( product_snd @ TA @ TB ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(253,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( bNF_sndOp @ TA @ TB @ TC )
= ( ^ [A: TA > TB > $o,B: TB > TC > $o,C: product_prod @ TA @ TC] : ( product_Pair @ TB @ TC @ ( bNF_pick_middlep @ TA @ TB @ TC @ A @ B @ ( product_fst @ TA @ TC @ C ) @ ( product_snd @ TA @ TC @ C ) ) @ ( product_snd @ TA @ TC @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_sndOp__def) ).
thf(1107,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( bNF_sndOp @ TA @ TB @ TC )
= ( ^ [A: TA > TB > $o,B: TB > TC > $o,C: product_prod @ TA @ TC] : ( product_Pair @ TB @ TC @ ( bNF_pick_middlep @ TA @ TB @ TC @ A @ B @ ( product_fst @ TA @ TC @ C ) @ ( product_snd @ TA @ TC @ C ) ) @ ( product_snd @ TA @ TC @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(195,axiom,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_ex__in__conv) ).
thf(919,plain,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(119,axiom,
! [TA: $tType,TB: $tType,A: TB,B: product_prod @ TB @ TA] :
( ( A
= ( product_fst @ TB @ TA @ B ) )
= ( ? [C: TA] :
( B
= ( product_Pair @ TB @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_eq__fst__iff) ).
thf(672,plain,
! [TA: $tType,TB: $tType,A: TB,B: product_prod @ TB @ TA] :
( ( A
= ( product_fst @ TB @ TA @ B ) )
= ( ? [C: TA] :
( B
= ( product_Pair @ TB @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(282,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_prod__induct6) ).
thf(1194,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(167,axiom,
! [TA: $tType,TB: $tType] :
( ( ( bot @ TB )
& ( bot @ TA ) )
=> ( bot @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Orderings_Obot_14) ).
thf(831,plain,
! [TA: $tType,TB: $tType] :
( ( ( bot @ TB )
& ( bot @ TA ) )
=> ( bot @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(138,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) )
=> ~ ! [C: TA] :
( A
!= ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_rangeE) ).
thf(736,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) )
=> ~ ! [C: TA] :
( A
!= ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_swap @ TB @ TA @ ( product_swap @ TA @ TB @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_swap__swap) ).
thf(451,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_swap @ TB @ TA @ ( product_swap @ TA @ TB @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(190,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_UNIV__eq__I) ).
thf(900,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( ( bot_bot @ ( set @ TB ) )
= ( image @ TA @ TB @ A @ B ) )
= ( B
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_empty__is__image) ).
thf(406,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( ( bot_bot @ ( set @ TB ) )
= ( image @ TA @ TB @ A @ B ) )
= ( B
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(182,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_empty__iff) ).
thf(880,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(231,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF,I: TG] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) @ F @ ( product_Pair @ TE @ ( product_prod @ TF @ TG ) @ G @ ( product_Pair @ TF @ TG @ H @ I ) ) ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_prod__induct7) ).
thf(1043,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF,I: TG] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) @ F @ ( product_Pair @ TE @ ( product_prod @ TF @ TG ) @ G @ ( product_Pair @ TF @ TG @ H @ I ) ) ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(186,axiom,
! [TA: $tType,TB: $tType] :
( ( ( minus @ TB )
& ( minus @ TA ) )
=> ( minus @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Groups_Ominus_15) ).
thf(890,plain,
! [TA: $tType,TB: $tType] :
( ( ( minus @ TB )
& ( minus @ TA ) )
=> ( minus @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(50,axiom,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ ( top_top @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_top__greatest) ).
thf(477,plain,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(15,axiom,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
=> ( A
= ( top_top @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_top_Oextremum__uniqueI) ).
thf(387,plain,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
=> ( A
= ( top_top @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(106,axiom,
ord @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oord_18) ).
thf(631,plain,
ord @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(74,axiom,
! [TA: $tType,A: set @ TA] :
( ( image @ TA @ TA
@ ^ [B: TA] : B
@ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_image__ident) ).
thf(552,plain,
! [TA: $tType,A: set @ TA] :
( ( image @ TA @ TA
@ ^ [B: TA] : B
@ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(97,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Otop) ).
thf(609,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(6,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( A
= ( (=) @ TA @ B ) )
=> ( ( the @ TA @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_Nitpick_OThe__psimp) ).
thf(323,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( A
= ( (=) @ TA @ B ) )
=> ( ( the @ TA @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB] :
( ( image @ TA @ TC
@ ^ [C: TA] : ( A @ ( B @ C ) )
@ ( top_top @ ( set @ TA ) ) )
= ( image @ TB @ TC @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_range__composition) ).
thf(594,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB] :
( ( image @ TA @ TC
@ ^ [C: TA] : ( A @ ( B @ C ) )
@ ( top_top @ ( set @ TA ) ) )
= ( image @ TB @ TC @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(135,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA,B: set @ TB,C: set @ TA] :
( ( member @ ( product_prod @ TB @ TA ) @ A
@ ( product_Sigma @ TB @ TA @ B
@ ^ [D: TB] : C ) )
= ( ( member @ TB @ ( product_fst @ TB @ TA @ A ) @ B )
& ( member @ TA @ ( product_snd @ TB @ TA @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_mem__Times__iff) ).
thf(726,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA,B: set @ TB,C: set @ TA] :
( ( member @ ( product_prod @ TB @ TA ) @ A
@ ( product_Sigma @ TB @ TA @ B
@ ^ [D: TB] : C ) )
= ( ( member @ TB @ ( product_fst @ TB @ TA @ A ) @ B )
& ( member @ TA @ ( product_snd @ TB @ TA @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(188,axiom,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_UNIV__witness) ).
thf(895,plain,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_fst @ TB @ TA @ ( product_swap @ TA @ TB @ A ) )
= ( product_snd @ TA @ TB @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_fst__swap) ).
thf(626,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_fst @ TB @ TA @ ( product_swap @ TA @ TB @ A ) )
= ( product_snd @ TA @ TB @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(276,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( ( D = B )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_ssubst__Pair__rhs) ).
thf(1177,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( ( D = B )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(125,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ? [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) )
=> ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_bex__imageD) ).
thf(695,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ? [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) )
=> ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
= ( ! [B: TA] :
? [C: TB] :
( B
= ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_surj__def) ).
thf(394,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
= ( ! [B: TA] :
? [C: TB] :
( B
= ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(219,axiom,
! [TA: $tType,TB: $tType,A: TB,B: set @ TB,C: set @ TA,D: set @ TA] :
( ( member @ TB @ A @ B )
=> ( ( ( product_Sigma @ TA @ TB @ C
@ ^ [E: TA] : B )
= ( product_Sigma @ TA @ TB @ D
@ ^ [E: TA] : B ) )
= ( C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_Times__eq__cancel2) ).
thf(1000,plain,
! [TA: $tType,TB: $tType,A: TB,B: set @ TB,C: set @ TA,D: set @ TA] :
( ( member @ TB @ A @ B )
=> ( ( ( product_Sigma @ TA @ TB @ C
@ ^ [E: TA] : B )
= ( product_Sigma @ TA @ TB @ D
@ ^ [E: TA] : B ) )
= ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(251,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TB,C: set @ ( product_prod @ TA @ TB ),D: TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) )
@ ( product_Sigma @ TA @ TB @ A
@ ^ [E: TA] : B )
@ C )
=> ( ( member @ TA @ D @ A )
=> ( ord_less_eq @ ( set @ TB ) @ B @ ( image @ ( product_prod @ TA @ TB ) @ TB @ ( product_snd @ TA @ TB ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_subset__snd__imageI) ).
thf(1102,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TB,C: set @ ( product_prod @ TA @ TB ),D: TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) )
@ ( product_Sigma @ TA @ TB @ A
@ ^ [E: TA] : B )
@ C )
=> ( ( member @ TA @ D @ A )
=> ( ord_less_eq @ ( set @ TB ) @ B @ ( image @ ( product_prod @ TA @ TB ) @ TB @ ( product_snd @ TA @ TB ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(196,axiom,
! [TA: $tType,TB: $tType,A: set @ TA] :
( ( product_Sigma @ TA @ TB @ A
@ ^ [B: TA] : ( bot_bot @ ( set @ TB ) ) )
= ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_Sigma__empty2) ).
thf(922,plain,
! [TA: $tType,TB: $tType,A: set @ TA] :
( ( product_Sigma @ TA @ TB @ A
@ ^ [B: TA] : ( bot_bot @ ( set @ TB ) ) )
= ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(148,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_UNIV__I) ).
thf(768,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(166,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_prod__induct5) ).
thf(827,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(239,axiom,
! [TA: $tType,TB: $tType] :
( ( image @ ( product_prod @ TB @ TA ) @ ( product_prod @ TA @ TB ) @ ( product_swap @ TB @ TA ) @ ( top_top @ ( set @ ( product_prod @ TB @ TA ) ) ) )
= ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_surj__swap) ).
thf(1066,plain,
! [TA: $tType,TB: $tType] :
( ( image @ ( product_prod @ TB @ TA ) @ ( product_prod @ TA @ TB ) @ ( product_swap @ TB @ TA ) @ ( top_top @ ( set @ ( product_prod @ TB @ TA ) ) ) )
= ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(178,axiom,
! [TA: $tType,TB: $tType] :
( ( image @ ( product_prod @ TB @ TA ) @ TA @ ( product_snd @ TB @ TA ) @ ( top_top @ ( set @ ( product_prod @ TB @ TA ) ) ) )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_range__snd) ).
thf(868,plain,
! [TA: $tType,TB: $tType] :
( ( image @ ( product_prod @ TB @ TA ) @ TA @ ( product_snd @ TB @ TA ) @ ( top_top @ ( set @ ( product_prod @ TB @ TA ) ) ) )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(255,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_pred__subset__eq) ).
thf(1113,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(79,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TC,B: TB > TD,C: product_prod @ TA @ TB] :
( ( product_fst @ TC @ TD @ ( product_map_prod @ TA @ TC @ TB @ TD @ A @ B @ C ) )
= ( A @ ( product_fst @ TA @ TB @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_fst__map__prod) ).
thf(563,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TC,B: TB > TD,C: product_prod @ TA @ TB] :
( ( product_fst @ TC @ TD @ ( product_map_prod @ TA @ TC @ TB @ TD @ A @ B @ C ) )
= ( A @ ( product_fst @ TA @ TB @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(58,axiom,
! [TA: $tType,A: ( set @ TA ) > TA,B: set @ TA] :
( ( A
@ ( image @ TA @ TA
@ ^ [C: TA] : C
@ B ) )
= ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_Sup_OSUP__identity__eq) ).
thf(505,plain,
! [TA: $tType,A: ( set @ TA ) > TA,B: set @ TA] :
( ( A
@ ( image @ TA @ TA
@ ^ [C: TA] : C
@ B ) )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( image @ TB @ TA @ A @ ( bot_bot @ ( set @ TB ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_image__empty) ).
thf(438,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( image @ TB @ TA @ A @ ( bot_bot @ ( set @ TB ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(49,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_Collect__mono) ).
thf(473,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(229,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ! [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
=> ( C @ D ) )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_ball__imageD) ).
thf(1034,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ! [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
=> ( C @ D ) )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(120,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_preference_Onot__outside) ).
thf(675,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] : ( ord_less_eq @ ( set @ TB ) @ ( minus_minus @ ( set @ TB ) @ ( image @ TA @ TB @ A @ B ) @ ( image @ TA @ TB @ A @ C ) ) @ ( image @ TA @ TB @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_image__diff__subset) ).
thf(589,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] : ( ord_less_eq @ ( set @ TB ) @ ( minus_minus @ ( set @ TB ) @ ( image @ TA @ TB @ A @ B ) @ ( image @ TA @ TB @ A @ C ) ) @ ( image @ TA @ TB @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(261,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_prod__induct4) ).
thf(1134,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(142,axiom,
! [TA: $tType,TB: $tType] :
( ( ( minus @ TA )
& ( minus @ TB ) )
=> ! [A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( product_fst @ TA @ TB @ ( minus_minus @ ( product_prod @ TA @ TB ) @ A @ B ) )
= ( minus_minus @ TA @ ( product_fst @ TA @ TB @ A ) @ ( product_fst @ TA @ TB @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_fst__diff) ).
thf(749,plain,
! [TA: $tType,TB: $tType] :
( ( ( minus @ TA )
& ( minus @ TB ) )
=> ! [A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( product_fst @ TA @ TB @ ( minus_minus @ ( product_prod @ TA @ TB ) @ A @ B ) )
= ( minus_minus @ TA @ ( product_fst @ TA @ TB @ A ) @ ( product_fst @ TA @ TB @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(100,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_Diff__subset) ).
thf(617,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(264,axiom,
! [TA: $tType,TB: $tType] :
( ( ( cancel146912293up_add @ TB )
& ( cancel146912293up_add @ TA ) )
=> ( cancel146912293up_add @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Groups_Ocancel__ab__semigroup__add) ).
thf(1145,plain,
! [TA: $tType,TB: $tType] :
( ( ( cancel146912293up_add @ TB )
& ( cancel146912293up_add @ TA ) )
=> ( cancel146912293up_add @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(277,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_Diff__iff) ).
thf(1181,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(169,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA] : ( member @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_rangeI) ).
thf(836,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA] : ( member @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: ( set @ TB ) > $o] :
( ( ! [D: set @ TB] :
( ( ord_less_eq @ ( set @ TB ) @ D @ ( image @ TA @ TB @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ B )
=> ( C @ ( image @ TA @ TB @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_all__subset__image) ).
thf(426,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: ( set @ TB ) > $o] :
( ( ! [D: set @ TB] :
( ( ord_less_eq @ ( set @ TB ) @ D @ ( image @ TA @ TB @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ B )
=> ( C @ ( image @ TA @ TB @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(273,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA,C: TB,D: product_prod @ TA @ TB] :
( ( A @ B @ C )
=> ( ( D
= ( product_Pair @ TA @ TB @ B @ C ) )
=> ( A @ ( product_fst @ TA @ TB @ D ) @ ( product_snd @ TA @ TB @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_BNF__Greatest__Fixpoint_Osubst__Pair) ).
thf(1166,plain,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA,C: TB,D: product_prod @ TA @ TB] :
( ( A @ B @ C )
=> ( ( D
= ( product_Pair @ TA @ TB @ B @ C ) )
=> ( A @ ( product_fst @ TA @ TB @ D ) @ ( product_snd @ TA @ TB @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(66,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_subset__UNIV) ).
thf(531,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(204,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TB @ TA ) > $o,B: TB,C: TA] :
( ( product_curry @ TB @ TA @ $o @ A @ B @ C )
=> ( A @ ( product_Pair @ TB @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_curryD) ).
thf(944,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TB @ TA ) > $o,B: TB,C: TA] :
( ( product_curry @ TB @ TA @ $o @ A @ B @ C )
=> ( A @ ( product_Pair @ TB @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(151,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_prod__cases5) ).
thf(776,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(65,axiom,
! [TA: $tType,A: $o] :
( ( A
=> ( ( collect @ TA
@ ^ [B: TA] : A )
= ( top_top @ ( set @ TA ) ) ) )
& ( ~ A
=> ( ( collect @ TA
@ ^ [B: TA] : A )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_Collect__const) ).
thf(525,plain,
! [TA: $tType,A: $o] :
( ( A
=> ( ( collect @ TA
@ ^ [B: TA] : A )
= ( top_top @ ( set @ TA ) ) ) )
& ( ~ A
=> ( ( collect @ TA
@ ^ [B: TA] : A )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(86,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( minus_minus @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_Diff__idemp) ).
thf(580,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( minus_minus @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ! [D: TA] :
( ( A @ D )
=> ( D = B ) )
=> ( ! [D: TA] :
( ( A @ D )
=> ( C @ D ) )
=> ( C @ ( the @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_theI2) ).
thf(295,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ! [D: TA] :
( ( A @ D )
=> ( D = B ) )
=> ( ! [D: TA] :
( ( A @ D )
=> ( C @ D ) )
=> ( C @ ( the @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(185,axiom,
! [TA: $tType] :
( ( prefer310429814s_good @ TA )
= ( ^ [A: TA,B: set @ TA,C: set @ ( product_prod @ TA @ TA )] :
( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_at__least__as__good__def) ).
thf(887,plain,
! [TA: $tType] :
( ( prefer310429814s_good @ TA )
= ( ^ [A: TA,B: set @ TA,C: set @ ( product_prod @ TA @ TA )] :
( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_snd @ TB @ TA @ ( product_swap @ TA @ TB @ A ) )
= ( product_fst @ TA @ TB @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_snd__swap) ).
thf(414,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_snd @ TB @ TA @ ( product_swap @ TA @ TB @ A ) )
= ( product_fst @ TA @ TB @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(7,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( A @ B )
=> ( ! [C: TA] :
( ( A @ C )
=> ( C = B ) )
=> ( ( the @ TA @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_the__equality) ).
thf(327,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( A @ B )
=> ( ! [C: TA] :
( ( A @ C )
=> ( C = B ) )
=> ( ( the @ TA @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(139,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( product_fst @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_fst__conv) ).
thf(739,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( product_fst @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(23,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA] :
( ( image @ TA @ TA
@ ^ [B: TA] : ( minus_minus @ TA @ B @ A )
@ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_surj__diff__right) ).
thf(409,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA] :
( ( image @ TA @ TA
@ ^ [B: TA] : ( minus_minus @ TA @ B @ A )
@ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(76,axiom,
minus @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Groups_Ominus_10) ).
thf(557,plain,
minus @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(220,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TA] :
( ( ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ A @ B ) )
= C )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_snd__eqD) ).
thf(1003,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TA] :
( ( ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ A @ B ) )
= C )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(127,axiom,
! [TA: $tType,A: set @ TA,B: TA,C: set @ ( product_prod @ TA @ TA )] :
( ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ A )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ B ) @ C )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ C ) ) )
= ( minus_minus @ ( set @ TA ) @ ( prefer310429814s_good @ TA @ B @ A @ C ) @ ( prefer951318096ood_as @ TA @ B @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_strict__contour__is__diff) ).
thf(705,plain,
! [TA: $tType,A: set @ TA,B: TA,C: set @ ( product_prod @ TA @ TA )] :
( ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ A )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ B ) @ C )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ C ) ) )
= ( minus_minus @ ( set @ TA ) @ ( prefer310429814s_good @ TA @ B @ A @ C ) @ ( prefer951318096ood_as @ TA @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(269,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_DiffI) ).
thf(1156,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(35,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( order_preorder_on @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_preference_Otrans__refl) ).
thf(441,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( order_preorder_on @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(57,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_subset__antisym) ).
thf(502,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(45,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_subset__trans) ).
thf(463,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(160,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA,B: set @ TB,C: TB > ( set @ TA )] :
( ( member @ ( product_prod @ TB @ TA ) @ A @ ( product_Sigma @ TB @ TA @ B @ C ) )
=> ~ ! [D: TB] :
( ( member @ TB @ D @ B )
=> ! [E: TA] :
( ( member @ TA @ E @ ( C @ D ) )
=> ( A
!= ( product_Pair @ TB @ TA @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_SigmaE) ).
thf(808,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA,B: set @ TB,C: TB > ( set @ TA )] :
( ( member @ ( product_prod @ TB @ TA ) @ A @ ( product_Sigma @ TB @ TA @ B @ C ) )
=> ~ ! [D: TB] :
( ( member @ TB @ D @ B )
=> ! [E: TA] :
( ( member @ TA @ E @ ( C @ D ) )
=> ( A
!= ( product_Pair @ TB @ TA @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(111,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_diff__right__mono) ).
thf(643,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(71,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] : ( top_top @ ( TB > TA > $o ) @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_top2I) ).
thf(544,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] : ( top_top @ ( TB > TA > $o ) @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(280,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_old_Oprod_Oinject) ).
thf(1188,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(279,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: TA > TC,E: TB > TD] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( member @ ( product_prod @ TC @ TD ) @ ( product_Pair @ TC @ TD @ ( D @ A ) @ ( E @ B ) ) @ ( image @ ( product_prod @ TA @ TB ) @ ( product_prod @ TC @ TD ) @ ( product_map_prod @ TA @ TC @ TB @ TD @ D @ E ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_map__prod__imageI) ).
thf(1186,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: TA > TC,E: TB > TD] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( member @ ( product_prod @ TC @ TD ) @ ( product_Pair @ TC @ TD @ ( D @ A ) @ ( E @ B ) ) @ ( image @ ( product_prod @ TA @ TB ) @ ( product_prod @ TC @ TD ) @ ( product_map_prod @ TA @ TC @ TB @ TD @ D @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(245,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( product_curry @ TA @ TB @ TC )
= ( ^ [A: ( product_prod @ TA @ TB ) > TC,B: TA,C: TB] : ( A @ ( product_Pair @ TA @ TB @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_curry__conv) ).
thf(1085,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( product_curry @ TA @ TB @ TC )
= ( ^ [A: ( product_prod @ TA @ TB ) > TC,B: TA,C: TB] : ( A @ ( product_Pair @ TA @ TB @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(48,axiom,
! [TA: $tType,A: TA,B: $o] :
( ( ( top_top @ ( TA > $o ) @ A )
& B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_top__conj_I1_J) ).
thf(470,plain,
! [TA: $tType,A: TA,B: $o] :
( ( ( top_top @ ( TA > $o ) @ A )
& B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(8,axiom,
! [TA: $tType,A: TA] :
( ( the @ TA
@ ^ [B: TA] : ( B = A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_the__eq__trivial) ).
thf(336,plain,
! [TA: $tType,A: TA] :
( ( the @ TA
@ ^ [B: TA] : ( B = A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(234,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( produc2004651681e_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_internal__case__prod__conv) ).
thf(1052,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( produc2004651681e_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(5,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ? [C: TA] :
( ( A @ C )
& ! [D: TA] :
( ( A @ D )
=> ( D = C ) ) )
=> ( ( A @ B )
= ( B
= ( the @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_theI__unique) ).
thf(314,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ? [C: TA] :
( ( A @ C )
& ! [D: TA] :
( ( A @ D )
=> ( D = C ) ) )
=> ( ( A @ B )
= ( B
= ( the @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(181,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA,B: TB,C: TA] :
( ( A
= ( product_Pair @ TB @ TA @ B @ C ) )
=> ( ( product_snd @ TB @ TA @ A )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_sndI) ).
thf(876,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA,B: TB,C: TA] :
( ( A
= ( product_Pair @ TB @ TA @ B @ C ) )
=> ( ( product_snd @ TB @ TA @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(216,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: set @ TB] :
( ( product_Sigma @ TA @ TB @ ( minus_minus @ ( set @ TA ) @ A @ B )
@ ^ [D: TA] : C )
= ( minus_minus @ ( set @ ( product_prod @ TA @ TB ) )
@ ( product_Sigma @ TA @ TB @ A
@ ^ [D: TA] : C )
@ ( product_Sigma @ TA @ TB @ B
@ ^ [D: TA] : C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_Times__Diff__distrib1) ).
thf(991,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: set @ TB] :
( ( product_Sigma @ TA @ TB @ ( minus_minus @ ( set @ TA ) @ A @ B )
@ ^ [D: TA] : C )
= ( minus_minus @ ( set @ ( product_prod @ TA @ TB ) )
@ ( product_Sigma @ TA @ TB @ A
@ ^ [D: TA] : C )
@ ( product_Sigma @ TA @ TB @ B
@ ^ [D: TA] : C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TD,B: TB > TC,C: product_prod @ TA @ TB] :
( ( product_snd @ TD @ TC @ ( product_map_prod @ TA @ TD @ TB @ TC @ A @ B @ C ) )
= ( B @ ( product_snd @ TA @ TB @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_snd__map__prod) ).
thf(465,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TD,B: TB > TC,C: product_prod @ TA @ TB] :
( ( product_snd @ TD @ TC @ ( product_map_prod @ TA @ TD @ TB @ TC @ A @ B @ C ) )
= ( B @ ( product_snd @ TA @ TB @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(40,axiom,
top @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Otop_17) ).
thf(450,plain,
top @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType] :
( ( product_product @ TA @ TB )
= ( ^ [A: set @ TA,B: set @ TB] :
( product_Sigma @ TA @ TB @ A
@ ^ [C: TA] : B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_Product__Type_Oproduct__def) ).
thf(482,plain,
! [TA: $tType,TB: $tType] :
( ( product_product @ TA @ TB )
= ( ^ [A: set @ TA,B: set @ TB] :
( product_Sigma @ TA @ TB @ A
@ ^ [C: TA] : B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(191,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ TA] :
( ( ( A
= ( bot_bot @ ( set @ TB ) ) )
=> ( ( image @ ( product_prod @ TA @ TB ) @ TA @ ( product_fst @ TA @ TB )
@ ( product_Sigma @ TA @ TB @ B
@ ^ [C: TA] : A ) )
= ( bot_bot @ ( set @ TA ) ) ) )
& ( ( A
!= ( bot_bot @ ( set @ TB ) ) )
=> ( ( image @ ( product_prod @ TA @ TB ) @ TA @ ( product_fst @ TA @ TB )
@ ( product_Sigma @ TA @ TB @ B
@ ^ [C: TA] : A ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_fst__image__times) ).
thf(903,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ TA] :
( ( ( A
= ( bot_bot @ ( set @ TB ) ) )
=> ( ( image @ ( product_prod @ TA @ TB ) @ TA @ ( product_fst @ TA @ TB )
@ ( product_Sigma @ TA @ TB @ B
@ ^ [C: TA] : A ) )
= ( bot_bot @ ( set @ TA ) ) ) )
& ( ( A
!= ( bot_bot @ ( set @ TB ) ) )
=> ( ( image @ ( product_prod @ TA @ TB ) @ TA @ ( product_fst @ TA @ TB )
@ ( product_Sigma @ TA @ TB @ B
@ ^ [C: TA] : A ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(259,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( bNF_fstOp @ TA @ TB @ TC )
= ( ^ [A: TA > TB > $o,B: TB > TC > $o,C: product_prod @ TA @ TC] : ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TC @ C ) @ ( bNF_pick_middlep @ TA @ TB @ TC @ A @ B @ ( product_fst @ TA @ TC @ C ) @ ( product_snd @ TA @ TC @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_fstOp__def) ).
thf(1126,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( bNF_fstOp @ TA @ TB @ TC )
= ( ^ [A: TA > TB > $o,B: TB > TC > $o,C: product_prod @ TA @ TC] : ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TC @ C ) @ ( bNF_pick_middlep @ TA @ TB @ TC @ A @ B @ ( product_fst @ TA @ TC @ C ) @ ( product_snd @ TA @ TC @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(222,axiom,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_top__empty__eq) ).
thf(1010,plain,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(62,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ D ) @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_Diff__mono) ).
thf(517,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ D ) @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(205,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ TA,D: TA > ( set @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( product_Sigma @ TA @ TB @ C @ D ) )
=> ~ ( ( member @ TA @ A @ C )
=> ~ ( member @ TB @ B @ ( D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_SigmaE2) ).
thf(946,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ TA,D: TA > ( set @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( product_Sigma @ TA @ TB @ C @ D ) )
=> ~ ( ( member @ TA @ A @ C )
=> ~ ( member @ TB @ B @ ( D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TB ) @ ( image @ TA @ TB @ C @ A ) @ ( image @ TA @ TB @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_image__mono) ).
thf(390,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TB ) @ ( image @ TA @ TB @ C @ A ) @ ( image @ TA @ TB @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(107,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: TA > TB,C: set @ TA] :
( ( ord_less_eq @ ( set @ TB ) @ A @ ( image @ TA @ TB @ B @ C ) )
=> ~ ! [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ C )
=> ( A
!= ( image @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_subset__imageE) ).
thf(632,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: TA > TB,C: set @ TA] :
( ( ord_less_eq @ ( set @ TB ) @ A @ ( image @ TA @ TB @ B @ C ) )
=> ~ ! [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ C )
=> ( A
!= ( image @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(27,axiom,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
= ( A
= ( top_top @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_top_Oextremum__unique) ).
thf(418,plain,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
= ( A
= ( top_top @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(154,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: TB > TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TB @ TA ) ) @ ( bNF_Gr @ TB @ TA @ A @ B )
@ ( product_Sigma @ TB @ TA @ A
@ ^ [D: TB] : C ) )
= ( ord_less_eq @ ( set @ TA ) @ ( image @ TB @ TA @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_Gr__incl) ).
thf(786,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: TB > TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TB @ TA ) ) @ ( bNF_Gr @ TB @ TA @ A @ B )
@ ( product_Sigma @ TB @ TA @ A
@ ^ [D: TB] : C ) )
= ( ord_less_eq @ ( set @ TA ) @ ( image @ TB @ TA @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(146,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( ordere890947078_space @ TA ) )
=> ( ordered_ab_group_add @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Groups_Oordered__ab__group__add) ).
thf(763,plain,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( ordere890947078_space @ TA ) )
=> ( ordered_ab_group_add @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(122,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TB] :
( ( ord_less_eq @ ( set @ TB ) @ ( image @ TA @ TB @ A @ B ) @ C )
= ( ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( member @ TB @ ( A @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_image__subset__iff) ).
thf(684,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TB] :
( ( ord_less_eq @ ( set @ TB ) @ ( image @ TA @ TB @ A @ B ) @ C )
= ( ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( member @ TB @ ( A @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(73,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less_eq @ TA @ A @ B )
= ( ord_less_eq @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_diff__eq__diff__less__eq) ).
thf(549,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less_eq @ TA @ A @ B )
= ( ord_less_eq @ TA @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(68,axiom,
! [TA: $tType] : ( order_top @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder__top_1) ).
thf(536,plain,
! [TA: $tType] : ( order_top @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(157,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(800,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(256,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TC @ TD,B: TA > TC,C: TB > TD,D: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TC @ TD ) @ A @ ( image @ ( product_prod @ TA @ TB ) @ ( product_prod @ TC @ TD ) @ ( product_map_prod @ TA @ TC @ TB @ TD @ B @ C ) @ D ) )
=> ~ ! [E: TA,F: TB] :
( ( A
= ( product_Pair @ TC @ TD @ ( B @ E ) @ ( C @ F ) ) )
=> ~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ E @ F ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_prod__fun__imageE) ).
thf(1116,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TC @ TD,B: TA > TC,C: TB > TD,D: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TC @ TD ) @ A @ ( image @ ( product_prod @ TA @ TB ) @ ( product_prod @ TC @ TD ) @ ( product_map_prod @ TA @ TC @ TB @ TD @ B @ C ) @ D ) )
=> ~ ! [E: TA,F: TB] :
( ( A
= ( product_Pair @ TC @ TD @ ( B @ E ) @ ( C @ F ) ) )
=> ~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ E @ F ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(143,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA,E: TA] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ D ) @ B ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ E ) @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_preference_Oindiff__trans) ).
thf(752,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA,E: TA] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ D ) @ B ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ E ) @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType] :
( ( minus @ TA )
=> ( minus @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Groups_Ominus) ).
thf(447,plain,
! [TA: $tType,TB: $tType] :
( ( minus @ TA )
=> ( minus @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
=> ( ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_prod__eqI) ).
thf(432,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
=> ( ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(206,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( A
= ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_prod_Oexhaust__sel) ).
thf(950,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( A
= ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(175,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( TA > TB > $o )
@ ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
@ ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
= ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_pred__subset__eq2) ).
thf(854,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( TA > TB > $o )
@ ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
@ ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
= ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(168,axiom,
! [TA: $tType,TB: $tType] :
( ( ( minus @ TA )
& ( minus @ TB ) )
=> ( ( minus_minus @ ( product_prod @ TA @ TB ) )
= ( ^ [A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] : ( product_Pair @ TA @ TB @ ( minus_minus @ TA @ ( product_fst @ TA @ TB @ A ) @ ( product_fst @ TA @ TB @ B ) ) @ ( minus_minus @ TB @ ( product_snd @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_minus__prod__def) ).
thf(833,plain,
! [TA: $tType,TB: $tType] :
( ( ( minus @ TA )
& ( minus @ TB ) )
=> ( ( minus_minus @ ( product_prod @ TA @ TB ) )
= ( ^ [A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] : ( product_Pair @ TA @ TB @ ( minus_minus @ TA @ ( product_fst @ TA @ TB @ A ) @ ( product_fst @ TA @ TB @ B ) ) @ ( minus_minus @ TB @ ( product_snd @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(209,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TB,C: TD,D: TA] :
( ( product_map_prod @ TD @ TC @ TA @ TB @ A @ B @ ( product_Pair @ TD @ TA @ C @ D ) )
= ( product_Pair @ TC @ TB @ ( A @ C ) @ ( B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_map__prod__simp) ).
thf(967,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TB,C: TD,D: TA] :
( ( product_map_prod @ TD @ TC @ TA @ TB @ A @ B @ ( product_Pair @ TD @ TA @ C @ D ) )
= ( product_Pair @ TC @ TB @ ( A @ C ) @ ( B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(10,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( A @ B )
=> ( ! [C: TA] :
( ( A @ C )
=> ( C = B ) )
=> ( A @ ( the @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_theI) ).
thf(358,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( A @ B )
=> ( ! [C: TA] :
( ( A @ C )
=> ( C = B ) )
=> ( A @ ( the @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(118,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB,E: ( set @ TB ) > TB] :
( ( A = B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image @ TA @ TB @ C @ A ) )
= ( E @ ( image @ TA @ TB @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_Sup_OSUP__cong) ).
thf(664,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB,E: ( set @ TB ) > TB] :
( ( A = B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image @ TA @ TB @ C @ A ) )
= ( E @ ( image @ TA @ TB @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ~ ! [C: TA] :
( B
!= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_surjE) ).
thf(400,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ~ ! [C: TA] :
( B
!= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1,conjecture,
member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ z @ y ) @ pr,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ z @ y ) @ pr ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(283,plain,
~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ z @ y ) @ pr ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(198,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_subsetD) ).
thf(928,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(275,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o,D: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ A )
& ( C @ E ) ) )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ B )
& ( D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_subset__CollectI) ).
thf(1172,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o,D: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ A )
& ( C @ E ) ) )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ B )
& ( D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(189,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_equals0I) ).
thf(897,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(248,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_image__iff) ).
thf(1093,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(260,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
=> ~ ! [D: TA] :
( ( A
= ( B @ D ) )
=> ~ ( member @ TA @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_imageE) ).
thf(1129,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
=> ~ ! [D: TA] :
( ( A
= ( B @ D ) )
=> ~ ( member @ TA @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(83,axiom,
! [TA: $tType] : ( top @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Otop_2) ).
thf(575,plain,
! [TA: $tType] : ( top @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(177,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB,E: ( set @ TB ) > TB] :
( ( A = B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image @ TA @ TB @ C @ A ) )
= ( E @ ( image @ TA @ TB @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_Inf_OINF__cong) ).
thf(860,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB,E: ( set @ TB ) > TB] :
( ( A = B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image @ TA @ TB @ C @ A ) )
= ( E @ ( image @ TA @ TB @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(164,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_iso__tuple__UNIV__I) ).
thf(822,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(213,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_prod__cases4) ).
thf(982,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(179,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
( ( member @ TA @ A @ B )
=> ( member @ TB @ ( C @ A ) @ ( image @ TA @ TB @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_imageI) ).
thf(871,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
( ( member @ TA @ A @ B )
=> ( member @ TB @ ( C @ A ) @ ( image @ TA @ TB @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(11,axiom,
! [TA: $tType,A: TA] :
( ( the @ TA @ ( (=) @ TA @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_the__sym__eq__trivial) ).
thf(369,plain,
! [TA: $tType,A: TA] :
( ( the @ TA @ ( (=) @ TA @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(158,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TF > ( product_prod @ TA @ TB ),B: TA > TB > ( product_prod @ TE @ TD ),C: TE > TD > TC] :
( ( product_scomp @ TF @ TE @ TD @ TC @ ( product_scomp @ TF @ TA @ TB @ ( product_prod @ TE @ TD ) @ A @ B ) @ C )
= ( product_scomp @ TF @ TA @ TB @ TC @ A
@ ^ [D: TA] : ( product_scomp @ TB @ TE @ TD @ TC @ ( B @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_scomp__scomp) ).
thf(803,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TF > ( product_prod @ TA @ TB ),B: TA > TB > ( product_prod @ TE @ TD ),C: TE > TD > TC] :
( ( product_scomp @ TF @ TE @ TD @ TC @ ( product_scomp @ TF @ TA @ TB @ ( product_prod @ TE @ TD ) @ A @ B ) @ C )
= ( product_scomp @ TF @ TA @ TB @ TC @ A
@ ^ [D: TA] : ( product_scomp @ TB @ TE @ TD @ TC @ ( B @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(278,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ab_group_add @ TB )
& ( ab_group_add @ TA ) )
=> ( ab_group_add @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Groups_Oab__group__add) ).
thf(1184,plain,
! [TA: $tType,TB: $tType] :
( ( ( ab_group_add @ TB )
& ( ab_group_add @ TA ) )
=> ( ab_group_add @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(116,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ( collect @ TB
@ ^ [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) ) )
= ( image @ TA @ TB @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Compr__image__eq) ).
thf(659,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ( collect @ TB
@ ^ [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) ) )
= ( image @ TA @ TB @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(109,axiom,
! [TA: $tType,TB: $tType] :
( ( order_top @ TA )
=> ( order_top @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder__top) ).
thf(639,plain,
! [TA: $tType,TB: $tType] :
( ( order_top @ TA )
=> ( order_top @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(246,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ TA] :
( ( ( product_Sigma @ TB @ TA @ A
@ ^ [C: TB] : B )
= ( bot_bot @ ( set @ ( product_prod @ TB @ TA ) ) ) )
= ( ( A
= ( bot_bot @ ( set @ TB ) ) )
| ( B
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_Times__empty) ).
thf(1088,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ TA] :
( ( ( product_Sigma @ TB @ TA @ A
@ ^ [C: TB] : B )
= ( bot_bot @ ( set @ ( product_prod @ TB @ TA ) ) ) )
= ( ( A
= ( bot_bot @ ( set @ TB ) ) )
| ( B
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(128,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ TA,D: TA > ( set @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( product_Sigma @ TA @ TB @ C @ D ) )
=> ( member @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_SigmaD1) ).
thf(708,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ TA,D: TA > ( set @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( product_Sigma @ TA @ TB @ C @ D ) )
=> ( member @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(183,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TB @ TA ) > $o,B: TB,C: TA] :
( ( A @ ( product_Pair @ TB @ TA @ B @ C ) )
=> ( product_curry @ TB @ TA @ $o @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_curryI) ).
thf(882,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TB @ TA ) > $o,B: TB,C: TA] :
( ( A @ ( product_Pair @ TB @ TA @ B @ C ) )
=> ( product_curry @ TB @ TA @ $o @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(211,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > ( set @ TB ),D: TA > ( set @ TB )] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( product_Sigma @ TA @ TB @ A @ C )
= ( product_Sigma @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_Sigma__cong) ).
thf(972,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > ( set @ TB ),D: TA > ( set @ TB )] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( product_Sigma @ TA @ TB @ A @ C )
= ( product_Sigma @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(55,axiom,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_set__eq__subset) ).
thf(496,plain,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(42,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA] :
( ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TA )
@ ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ B )
@ ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_translation__subtract__diff) ).
thf(454,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA] :
( ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TA )
@ ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ B )
@ ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(240,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_equals0D) ).
thf(1069,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(1198,plain,
$false,
inference(e,[status(thm)],[629,1024,760,479,846,1031,468,941,555,1110,645,892,1158,994,1073,1142,597,873,449,655,511,614,677,1078,384,533,715,814,913,1063,538,930,651,841,417,372,702,1191,460,1055,724,587,619,838,817,1147,421,1013,284,770,756,789,591,443,1040,623,485,514,1151,806,602,774,998,1104,397,687,546,925,1153,381,1047,1057,1163,910,957,1021,820,561,392,429,729,746,1091,916,566,710,852,435,583,522,1017,1121,1096,1138,783,499,989,857,519,742,980,403,884,1160,488,339,933,1075,637,970,1028,1082,622,647,1150,721,569,779,605,1099,985,1060,1050,457,792,938,508,541,765,1170,558,953,662,718,412,824,689,444,733,601,584,423,1007,843,577,579,1124,641,936,572,611,713,1107,919,672,1194,831,736,451,900,406,880,1043,890,477,387,631,552,609,323,594,726,895,626,1177,695,394,1000,1102,922,768,827,1066,868,1113,563,505,438,473,1034,675,589,1134,749,617,1145,1181,836,426,1166,531,944,776,525,580,295,887,414,327,739,409,557,1003,705,1156,441,502,463,808,643,544,1188,1186,1085,470,336,1052,314,876,991,465,450,482,903,1126,1010,517,946,390,632,418,786,763,684,549,536,800,1116,752,447,432,950,854,833,967,358,664,400,283,928,1172,897,1093,1129,575,860,822,982,871,369,803,1184,659,639,1088,708,882,972,496,454,1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP157^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.22 % Computer : n011.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 20:03:55 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.87/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.31/1.20 % [INFO] Parsing done (413ms).
% 2.31/1.22 % [INFO] Running in sequential loop mode.
% 3.32/1.59 % [INFO] eprover registered as external prover.
% 3.56/1.60 % [INFO] Scanning for conjecture ...
% 3.75/1.76 % [INFO] Found a conjecture (or negated_conjecture) and 289 axioms. Running axiom selection ...
% 4.22/1.90 % [INFO] Axiom selection finished. Selected 280 axioms (removed 9 axioms).
% 5.05/2.27 % [INFO] Problem is higher-order (TPTP THF).
% 5.36/2.31 % [INFO] Type checking passed.
% 5.36/2.31 % [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 ...
% 119.01/90.21 % External prover 'e' found a proof!
% 119.01/90.21 % [INFO] Killing All external provers ...
% 119.01/90.21 % Time passed: 89855ms (effective reasoning time: 88988ms)
% 119.01/90.21 % 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)>
% 119.01/90.21 % Axioms used in derivation (280): tcon_fun___Orderings_Obot, fact_107_range__fst, fact_57_Diff__idemp, fact_208_image__Collect__subsetI, tcon_Set_Oset___Orderings_Obot_4, fact_25_preference_Oindiff__trans, fact_122_prod_Omap__ident, tcon_fun___Groups_Ominus, fact_100_Inf_OINF__cong, fact_238_subset__empty, fact_218_Gr__incl, fact_86_surj__diff__right, fact_63_bex__imageD, fact_152_scomp__scomp, fact_56_image__eqI, fact_79_minus__apply, fact_58_Diff__iff, fact_170_product__swap, fact_246_Sigma__empty2, fact_87_UNIV__I, fact_237_image__empty, fact_133_prod__eqI, fact_26_preference_Onot__outside, fact_229_snd__image__times, fact_77_the1I2, fact_10_prod__cases6, fact_33_curryD, fact_31_curry__K, fact_61_ball__imageD, fact_173_subset__fst__snd, fact_249_times__eq__iff, fact_32_curry__def, fact_147_top__conj_I1_J, fact_66_DiffD2, fact_197_in__mono, fact_167_SigmaD1, fact_72_set__diff__eq, fact_156_in__lex__prod, fact_102_iso__tuple__UNIV__I, tcon_Product__Type_Oprod___Groups_Ogroup__add, fact_219_all__subset__image, fact_80_Inf_OINF__identity__eq, fact_73_theI, fact_189_Collect__mono, fact_13_old_Oprod_Oinducts, fact_248_Diff__eq__empty__iff, fact_69_imageE, fact_11_prod__cases7, fact_115_top__set__def, tcon_Product__Type_Oprod___Orderings_Oord_13, fact_180_image__mono, fact_7_prod__cases3, fact_225_cancel__ab__semigroup__add__class_Odiff__right__commute, tcon_fun___Orderings_Oord, fact_188_subset__trans, fact_169_mem__Times__iff, fact_245_Times__empty, fact_23_curry__conv, fact_5_prod__cases, fact_2_prod_Oinject, fact_143_BNF__Greatest__Fixpoint_Osubst__Pair, fact_12_prod__induct3, fact_132_snd__top, fact_254_equals0D, fact_244_Collect__const, fact_205_prop__restrict, fact_223_diff__eq__diff__less__eq, fact_253_equals0I, fact_199_Diff__subset, fact_60_rev__image__eqI, fact_145_exI__realizer, fact_78_the1__equality, fact_247_Diff__UNIV, fact_84_Nitpick_OThe__psimp, fact_159_UNIV__Times__UNIV, fact_30_swap__swap, fact_172_member__product, fact_174_subset__antisym, fact_178_Sigma__mono, fact_236_empty__is__image, tcon_Set_Oset___Orderings_Otop_2, fact_141_prod_Oexhaust__sel, fact_168_SigmaE, fact_251_bot__prod__def, tcon_Product__Type_Oprod___Orderings_Oorder__top_11, fact_182_subset__imageE, fact_154_image2__eqI, fact_40_pair__in__swap__image, fact_41_preference_Otrans__refl, fact_234_empty__iff, tcon_Product__Type_Oprod___Groups_Ocancel__ab__semigroup__add, fact_104_same__fstI, fact_46_Collect__mem__eq, fact_194_subset__eq, fact_252_ex__in__conv, fact_212_subset__snd__imageI, fact_185_subrelI, fact_241_empty__Diff, tcon_HOL_Obool___Groups_Ominus_10, tcon_Product__Type_Oprod___Groups_Oab__group__add, fact_139_snd__conv, fact_164_Sigma__Diff__distrib1, fact_183_image__subset__iff, fact_126_top2I, fact_94_surjI, fact_90_UNIV__def, fact_130_snd__swap, fact_179_Pair__mono, fact_239_empty__subsetI, fact_113_fst__top, fact_149_sndOp__def, fact_120_eq__fst__iff, fact_148_scomp__unfold, fact_65_imageI, tcon_Product__Type_Ounit___Orderings_Oorder__top_16, fact_226_diff__eq__diff__eq, fact_17_prod__induct5, tcon_HOL_Obool___Orderings_Oord_8, fact_177_Times__subset__cancel2, fact_119_top__empty__eq2, fact_116_fst__eqD, fact_233_all__not__in__conv, fact_207_Collect__subset, fact_216_less__eq__set__def, fact_125_top1I, fact_89_UNIV__eq__I, fact_50_the__sym__eq__trivial, tcon_Set_Oset___Orderings_Oorder__top_1, fact_230_fst__image__times, fact_187_set__eq__subset, fact_243_Sigma__empty1, fact_101_Sup_OSUP__cong, fact_163_Times__eq__cancel2, fact_35_no__better__than__def, fact_108_map__prod__ident, tcon_Product__Type_Ounit___Orderings_Oord_18, fact_118_prod__fun__imageE, fact_105_top__prod__def, fact_70_image__image, fact_45_mem__Collect__eq, fact_224_diff__right__mono, fact_142_prod_Oswap__def, fact_54_translation__subtract__diff, fact_103_top__apply, fact_4_surj__pair, fact_204_top__greatest, tcon_Set_Oset___Groups_Ominus_5, fact_184_subset__image__iff, fact_21_internal__case__prod__conv, fact_203_top_Oextremum__unique, fact_18_prod__induct4, fact_96_surjD, fact_99_fun__diff__def, fact_67_DiffD1, fact_155_map__prod__surj__on, fact_15_prod__induct7, fact_136_eq__snd__iff, fact_68_DiffE, fact_74_theI_H, fact_134_prod_Oexpand, fact_117_fst__conv, fact_128_prod_Ocollapse, fact_47_Collect__cong, fact_52_the__equality, fact_165_SigmaE2, fact_153_Pair__scomp, fact_196_subsetD, fact_192_equalityD2, fact_232_Collect__empty__eq, fact_43_old_Orec__prod__def, fact_242_Diff__cancel, fact_22_ssubst__Pair__rhs, fact_64_image__iff, tcon_fun___Orderings_Otop, fact_214_range__subsetD, fact_190_subset__refl, fact_71_Compr__image__eq, fact_228_diff__left__mono, fact_95_surjE, fact_114_top__empty__eq, fact_150_fstOp__def, fact_97_range__composition, fact_217_pred__subset__eq2, fact_51_the__eq__trivial, fact_250_Sigma__empty__iff, fact_162_Sigma__cong, tcon_Product__Type_Oprod___Orderings_Otop_12, fact_220_eq__subset, fact_24_curryI, fact_191_subset__iff, fact_186_Collect__mono__iff, fact_88_UNIV__witness, fact_111_map__prod__imageI, tcon_Set_Oset___Orderings_Oord_3, fact_37_pred__equals__eq2, fact_235_image__is__empty, tcon_HOL_Obool___Orderings_Obot_9, fact_123_minus__prod__def, fact_42_strict__contour__is__diff, fact_202_top_Oextremum__uniqueI, fact_75_theI2, fact_151_scomp__Pair, fact_83_theI__unique, fact_81_Sup_OSUP__identity__eq, fact_193_equalityD1, fact_8_prod__cases4, fact_138_snd__eqD, fact_9_prod__cases5, fact_92_surj__def, fact_227_diff__mono, fact_62_image__cong, tcon_fun___Orderings_Oorder__top, fact_176_Pair__le, fact_129_fst__swap, fact_200_double__diff, fact_121_fstI, fact_215_pred__subset__eq, fact_38_preference__def, fact_175_subsetI, fact_109_map__prod__simp, fact_98_rangeE, fact_16_prod__induct6, tcon_Product__Type_Ounit___Orderings_Obot_19, fact_158_SigmaI, fact_91_range__eqI, fact_211_image__diff__subset, tcon_HOL_Obool___Orderings_Oorder__top_6, fact_36_as__good__as__def, fact_6_Pair__inject, fact_135_prod__eq__iff, fact_160_Times__Diff__distrib1, fact_39_preference_Ointro, fact_181_image__subsetI, fact_127_snd__map__prod, fact_209_subset__Collect__iff, tcon_Product__Type_Oprod___Orderings_Obot_14, fact_20_at__least__as__good__def, fact_213_subset__fst__imageI, fact_124_range__snd, tcon_Product__Type_Ounit___Orderings_Otop_17, fact_106_map__prod__surj, fact_255_emptyE, fact_19_old_Oprod_Orec, fact_3_old_Oprod_Oinject, fact_222_GrD2, fact_146_top__conj_I2_J, fact_112_fst__diff, tcon_Product__Type_Oprod___Groups_Oordered__ab__group__add, fact_198_Diff__mono, fact_34_curryE, fact_240_Diff__empty, tcon_HOL_Obool___Orderings_Otop_7, fact_55_DiffI, fact_53_image__ident, fact_171_Product__Type_Oproduct__def, fact_195_equalityE, fact_85_surj__swap, fact_14_old_Oprod_Oexhaust, fact_137_sndI, tcon_Product__Type_Oprod___Groups_Ominus_15, tcon_Product__Type_Oprod___Ordered__Euclidean__Space_Oordered__euclidean__space, fact_0_assms, fact_93_rangeI, fact_201_subset__UNIV, fact_131_snd__diff, fact_59_minus__set__def, fact_49_diff__Pair, fact_210_subset__CollectI, fact_206_Collect__restrict, fact_110_fst__map__prod, fact_27_swap__simp, fact_231_empty__Collect__eq, fact_140_surjective__pairing, fact_161_Sigma__Diff__distrib2, fact_144_conjI__realizer, fact_221_GrD1, fact_1_at__lst__asgd__ge, fact_157_mem__Sigma__iff, tcon_Product__Type_Ounit___Groups_Ominus_20, fact_166_SigmaD2
% 119.01/90.21 % No. of inferences in proof: 564
% 119.01/90.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 89855 ms resp. 88988 ms w/o parsing
% 119.53/90.38 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 119.53/90.38 % [INFO] Killing All external provers ...
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