%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP031^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n005.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 08:06:29 AM UTC 2026
% Result : Theorem 21.00s 6.42s
% Output : Refutation 22.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 324
% Syntax : Number of formulae : 650 ( 371 unt; 0 typ; 0 def)
% Number of atoms : 1829 ( 693 equ; 4 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 4918 ( 219 ~; 34 |; 126 &;3914 @)
% ( 0 <=>; 625 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 318 ( 318 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 38 usr; 9 con; 0-4 aty)
% Number of variables : 1747 ( 188 ^;1529 !; 30 ?;1747 :)
% Comments :
%------------------------------------------------------------------------------
thf(binary1439146945Tree_a_type,type,
binary1439146945Tree_a: $tType ).
thf(set_a_type,type,
set_a: $tType ).
thf(int_type,type,
int: $tType ).
thf(a_type,type,
a: $tType ).
thf(binary717961607le_T_a_decl,type,
binary717961607le_T_a: binary1439146945Tree_a > a > binary1439146945Tree_a > binary1439146945Tree_a ).
thf(binary476621312_Tip_a_decl,type,
binary476621312_Tip_a: binary1439146945Tree_a ).
thf(binary256242811Tree_a_decl,type,
binary256242811Tree_a: binary1439146945Tree_a > set_a ).
thf(binary1226383794sert_a_decl,type,
binary1226383794sert_a: ( a > int ) > a > binary1439146945Tree_a > binary1439146945Tree_a ).
thf(binary504661350_eqs_a_decl,type,
binary504661350_eqs_a: ( a > int ) > a > set_a ).
thf(binary2053421120memb_a_decl,type,
binary2053421120memb_a: ( a > int ) > a > binary1439146945Tree_a > $o ).
thf(binary945792244etOf_a_decl,type,
binary945792244etOf_a: binary1439146945Tree_a > set_a ).
thf(binary1721989714Tree_a_decl,type,
binary1721989714Tree_a: ( a > int ) > binary1439146945Tree_a > $o ).
thf(binary670562003pred_a_decl,type,
binary670562003pred_a: ( a > int ) > a > a > binary1439146945Tree_a > $o ).
thf(minus_minus_a_o_decl,type,
minus_minus_a_o: ( a > $o ) > ( a > $o ) > a > $o ).
thf(minus_minus_o_decl,type,
minus_minus_o: $o > $o > $o ).
thf(minus_minus_set_a_decl,type,
minus_minus_set_a: set_a > set_a > set_a ).
thf(the_a_decl,type,
the_a: ( a > $o ) > a ).
thf(sup_sup_a_o_decl,type,
sup_sup_a_o: ( a > $o ) > ( a > $o ) > a > $o ).
thf(sup_sup_o_decl,type,
sup_sup_o: $o > $o > $o ).
thf(sup_sup_set_a_decl,type,
sup_sup_set_a: set_a > set_a > set_a ).
thf(bot_bot_a_o_decl,type,
bot_bot_a_o: a > $o ).
thf(bot_bot_o_decl,type,
bot_bot_o: $o ).
thf(bot_bot_set_a_decl,type,
bot_bot_set_a: set_a ).
thf(ord_less_a_o_decl,type,
ord_less_a_o: ( a > $o ) > ( a > $o ) > $o ).
thf(ord_less_int_decl,type,
ord_less_int: int > int > $o ).
thf(ord_less_set_a_decl,type,
ord_less_set_a: set_a > set_a > $o ).
thf(ord_less_eq_a_o_decl,type,
ord_less_eq_a_o: ( a > $o ) > ( a > $o ) > $o ).
thf(ord_less_eq_int_decl,type,
ord_less_eq_int: int > int > $o ).
thf(ord_less_eq_set_a_decl,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(collect_a_decl,type,
collect_a: ( a > $o ) > set_a ).
thf(insert_a_decl,type,
insert_a: a > set_a > set_a ).
thf(is_empty_a_decl,type,
is_empty_a: set_a > $o ).
thf(is_singleton_a_decl,type,
is_singleton_a: set_a > $o ).
thf(pairwise_a_decl,type,
pairwise_a: ( a > a > $o ) > set_a > $o ).
thf(remove_a_decl,type,
remove_a: a > set_a > set_a ).
thf(the_elem_a_decl,type,
the_elem_a: set_a > a ).
thf(member_a_decl,type,
member_a: a > set_a > $o ).
thf(e_decl,type,
e: a ).
thf(h_decl,type,
h: a > int ).
thf(t1_decl,type,
t1: binary1439146945Tree_a ).
thf(t2_decl,type,
t2: binary1439146945Tree_a ).
thf(x_decl,type,
x: a ).
thf(148,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_sup_Obounded__iff) ).
thf(892,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(302,axiom,
! [A: set_a,B: set_a,C: a > $o] :
( ( ! [D: a] :
( ( member_a @ D @ ( sup_sup_set_a @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: a] :
( ( member_a @ D @ A )
=> ( C @ D ) )
& ! [D: a] :
( ( member_a @ D @ B )
=> ( C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_ball__Un) ).
thf(1411,plain,
! [A: set_a,B: set_a,C: a > $o] :
( ( ! [D: a] :
( ( member_a @ D @ ( sup_sup_set_a @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: a] :
( ( member_a @ D @ A )
=> ( C @ D ) )
& ! [D: a] :
( ( member_a @ D @ B )
=> ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(224,axiom,
! [A: a,B: set_a] :
( ( insert_a @ A @ B )
!= bot_bot_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_insert__not__empty) ).
thf(1168,plain,
! [A: a,B: set_a] :
( ( insert_a @ A @ B )
!= bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(207,axiom,
! [A: set_a] :
( ( sup_sup_set_a @ A @ bot_bot_set_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_Un__empty__right) ).
thf(1105,plain,
! [A: set_a] :
( ( sup_sup_set_a @ A @ bot_bot_set_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(247,axiom,
( sup_sup_set_a
= ( ^ [A: set_a,B: set_a] : ( sup_sup_set_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_sup__commute) ).
thf(1237,plain,
( sup_sup_set_a
= ( ^ [A: set_a,B: set_a] : ( sup_sup_set_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(154,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_le__less) ).
thf(909,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(272,axiom,
! [A: a,B: binary1439146945Tree_a,C: binary1439146945Tree_a,D: a] :
( ( member_a @ A @ ( binary256242811Tree_a @ B ) )
=> ( member_a @ A @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ C @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_Tree_Oset__intros_I3_J) ).
thf(1315,plain,
! [A: a,B: binary1439146945Tree_a,C: binary1439146945Tree_a,D: a] :
( ( member_a @ A @ ( binary256242811Tree_a @ B ) )
=> ( member_a @ A @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ C @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(265,axiom,
! [A: a,B: a] :
( ( member_a @ A @ ( insert_a @ B @ bot_bot_set_a ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_singleton__iff) ).
thf(1295,plain,
! [A: a,B: a] :
( ( member_a @ A @ ( insert_a @ B @ bot_bot_set_a ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(199,axiom,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
= ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_subset__empty) ).
thf(1083,plain,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
= ( A = bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(27,axiom,
! [A: set_a,B: set_a,C: a] :
( ( ( sup_sup_set_a @ A @ B )
= ( insert_a @ C @ bot_bot_set_a ) )
= ( ( ( A = bot_bot_set_a )
& ( B
= ( insert_a @ C @ bot_bot_set_a ) ) )
| ( ( A
= ( insert_a @ C @ bot_bot_set_a ) )
& ( B = bot_bot_set_a ) )
| ( ( A
= ( insert_a @ C @ bot_bot_set_a ) )
& ( B
= ( insert_a @ C @ bot_bot_set_a ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_Un__singleton__iff) ).
thf(468,plain,
! [A: set_a,B: set_a,C: a] :
( ( ( sup_sup_set_a @ A @ B )
= ( insert_a @ C @ bot_bot_set_a ) )
= ( ( ( A = bot_bot_set_a )
& ( B
= ( insert_a @ C @ bot_bot_set_a ) ) )
| ( ( A
= ( insert_a @ C @ bot_bot_set_a ) )
& ( B = bot_bot_set_a ) )
| ( ( A
= ( insert_a @ C @ bot_bot_set_a ) )
& ( B
= ( insert_a @ C @ bot_bot_set_a ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(235,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ( insert_a @ A @ ( insert_a @ B @ bot_bot_set_a ) )
= ( insert_a @ C @ ( insert_a @ D @ bot_bot_set_a ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_doubleton__eq__iff) ).
thf(1200,plain,
! [A: a,B: a,C: a,D: a] :
( ( ( insert_a @ A @ ( insert_a @ B @ bot_bot_set_a ) )
= ( insert_a @ C @ ( insert_a @ D @ bot_bot_set_a ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(111,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ ( sup_sup_a_o @ A @ B ) @ C )
= ( ( ord_less_eq_a_o @ A @ C )
& ( ord_less_eq_a_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_sup_Obounded__iff) ).
thf(762,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ ( sup_sup_a_o @ A @ B ) @ C )
= ( ( ord_less_eq_a_o @ A @ C )
& ( ord_less_eq_a_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(177,axiom,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ A @ B ) )
= ( sup_sup_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_inf__sup__aci_I8_J) ).
thf(1005,plain,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ A @ B ) )
= ( sup_sup_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(263,axiom,
! [A: a,B: set_a] :
( ~ ( member_a @ A @ B )
=> ( ( minus_minus_set_a @ ( insert_a @ A @ B ) @ ( insert_a @ A @ bot_bot_set_a ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_Diff__insert__absorb) ).
thf(1290,plain,
! [A: a,B: set_a] :
( ~ ( member_a @ A @ B )
=> ( ( minus_minus_set_a @ ( insert_a @ A @ B ) @ ( insert_a @ A @ bot_bot_set_a ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(173,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( sup_sup_a_o @ A @ ( sup_sup_a_o @ B @ C ) )
= ( sup_sup_a_o @ B @ ( sup_sup_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_sup_Oleft__commute) ).
thf(994,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( sup_sup_a_o @ A @ ( sup_sup_a_o @ B @ C ) )
= ( sup_sup_a_o @ B @ ( sup_sup_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(300,axiom,
! [A: a,B: set_a,C: a] :
( ( ~ ( member_a @ A @ B )
=> ( A = C ) )
=> ( member_a @ A @ ( insert_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_insertCI) ).
thf(1401,plain,
! [A: a,B: set_a,C: a] :
( ( ~ ( member_a @ A @ B )
=> ( A = C ) )
=> ( member_a @ A @ ( insert_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(103,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ~ ( ord_less_set_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_less__imp__not__less) ).
thf(741,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ~ ( ord_less_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(237,axiom,
! [A: a > $o,B: a,C: a > $o] :
( ( ~ ( A @ B )
=> ( C @ B ) )
=> ( sup_sup_a_o @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_sup1CI) ).
thf(1205,plain,
! [A: a > $o,B: a,C: a > $o] :
( ( ~ ( A @ B )
=> ( C @ B ) )
=> ( sup_sup_a_o @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(218,axiom,
! [A: a > $o,B: a > $o] :
( ( sup_sup_a_o @ ( sup_sup_a_o @ A @ B ) @ B )
= ( sup_sup_a_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_sup_Oright__idem) ).
thf(1142,plain,
! [A: a > $o,B: a > $o] :
( ( sup_sup_a_o @ ( sup_sup_a_o @ A @ B ) @ B )
= ( sup_sup_a_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(67,axiom,
! [A: a > $o,B: a > $o] :
( ( sup_sup_a_o @ A @ ( sup_sup_a_o @ A @ B ) )
= ( sup_sup_a_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_sup__left__idem) ).
thf(614,plain,
! [A: a > $o,B: a > $o] :
( ( sup_sup_a_o @ A @ ( sup_sup_a_o @ A @ B ) )
= ( sup_sup_a_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(61,axiom,
! [A: a > $o,B: a > $o,C: a] :
( ( sup_sup_a_o @ A @ B @ C )
=> ( ~ ( A @ C )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_sup1E) ).
thf(597,plain,
! [A: a > $o,B: a > $o,C: a] :
( ( sup_sup_a_o @ A @ B @ C )
=> ( ~ ( A @ C )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(313,axiom,
! [A: set_a] :
( ! [B: a] :
~ ( member_a @ B @ A )
=> ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_equals0I) ).
thf(1437,plain,
! [A: set_a] :
( ! [B: a] :
~ ( member_a @ B @ A )
=> ( A = bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(188,axiom,
( bot_bot_a_o
= ( ^ [A: a] : bot_bot_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_bot__apply) ).
thf(1041,plain,
( bot_bot_a_o
= ( ^ [A: a] : bot_bot_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(43,axiom,
! [A: int,B: int] :
( ~ ( ord_less_int @ A @ B )
=> ( ( ~ ( ord_less_int @ B @ A ) )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_antisym__conv3) ).
thf(533,plain,
! [A: int,B: int] :
( ~ ( ord_less_int @ A @ B )
=> ( ( ~ ( ord_less_int @ B @ A ) )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(32,axiom,
( ord_less_a_o
= ( ^ [A: a > $o,B: a > $o] :
( ( B
= ( sup_sup_a_o @ B @ A ) )
& ( B != A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_sup_Ostrict__order__iff) ).
thf(500,plain,
( ord_less_a_o
= ( ^ [A: a > $o,B: a > $o] :
( ( B
= ( sup_sup_a_o @ B @ A ) )
& ( B != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(121,axiom,
! [A: set_a] :
( ( sup_sup_set_a @ bot_bot_set_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_Un__empty__left) ).
thf(797,plain,
! [A: set_a] :
( ( sup_sup_set_a @ bot_bot_set_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(276,axiom,
ord_less_int @ ( h @ e ) @ ( h @ x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_eLess) ).
thf(1327,plain,
ord_less_int @ ( h @ e ) @ ( h @ x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(242,axiom,
! [A: a > $o] :
( ( sup_sup_a_o @ bot_bot_a_o @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_sup__bot_Oleft__neutral) ).
thf(1222,plain,
! [A: a > $o] :
( ( sup_sup_a_o @ bot_bot_a_o @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(280,axiom,
( ( binary945792244etOf_a @ ( binary1226383794sert_a @ h @ e @ t1 ) )
= ( sup_sup_set_a @ ( minus_minus_set_a @ ( binary945792244etOf_a @ t1 ) @ ( binary504661350_eqs_a @ h @ e ) ) @ ( insert_a @ e @ bot_bot_set_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_c1) ).
thf(1342,plain,
( ( binary945792244etOf_a @ ( binary1226383794sert_a @ h @ e @ t1 ) )
= ( sup_sup_set_a @ ( minus_minus_set_a @ ( binary945792244etOf_a @ t1 ) @ ( binary504661350_eqs_a @ h @ e ) ) @ ( insert_a @ e @ bot_bot_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(156,axiom,
! [A: set_a,B: set_a] :
( ( bot_bot_set_a
= ( sup_sup_set_a @ A @ B ) )
= ( ( A = bot_bot_set_a )
& ( B = bot_bot_set_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_sup__bot_Oneutr__eq__iff) ).
thf(913,plain,
! [A: set_a,B: set_a] :
( ( bot_bot_set_a
= ( sup_sup_set_a @ A @ B ) )
= ( ( A = bot_bot_set_a )
& ( B = bot_bot_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(314,axiom,
! [A: a,B: set_a,C: a,D: set_a] :
( ~ ( member_a @ A @ B )
=> ( ~ ( member_a @ C @ D )
=> ( ( ( insert_a @ A @ B )
= ( insert_a @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_a] :
( ( B
= ( insert_a @ C @ E ) )
& ~ ( member_a @ C @ E )
& ( D
= ( insert_a @ A @ E ) )
& ~ ( member_a @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_insert__eq__iff) ).
thf(1441,plain,
! [A: a,B: set_a,C: a,D: set_a] :
( ~ ( member_a @ A @ B )
=> ( ~ ( member_a @ C @ D )
=> ( ( ( insert_a @ A @ B )
= ( insert_a @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_a] :
( ( B
= ( insert_a @ C @ E ) )
& ~ ( member_a @ C @ E )
& ( D
= ( insert_a @ A @ E ) )
& ~ ( member_a @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(190,axiom,
! [A: a,B: a,C: set_a] :
( ( ( insert_a @ A @ bot_bot_set_a )
= ( insert_a @ B @ C ) )
= ( ( B = A )
& ( ord_less_eq_set_a @ C @ ( insert_a @ A @ bot_bot_set_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_singleton__insert__inj__eq) ).
thf(1046,plain,
! [A: a,B: a,C: set_a] :
( ( ( insert_a @ A @ bot_bot_set_a )
= ( insert_a @ B @ C ) )
= ( ( B = A )
& ( ord_less_eq_set_a @ C @ ( insert_a @ A @ bot_bot_set_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(323,axiom,
! [A: a,B: set_a] : ( member_a @ A @ ( insert_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_insertI1) ).
thf(1475,plain,
! [A: a,B: set_a] : ( member_a @ A @ ( insert_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(287,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( minus_minus_set_a @ B @ C ) )
=> ~ ( member_a @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_DiffD2) ).
thf(1366,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( minus_minus_set_a @ B @ C ) )
=> ~ ( member_a @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(257,axiom,
( minus_minus_set_a
= ( ^ [A: set_a,B: set_a] :
( collect_a
@ ^ [C: a] :
( ( member_a @ C @ A )
& ~ ( member_a @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_set__diff__eq) ).
thf(1265,plain,
( minus_minus_set_a
= ( ^ [A: set_a,B: set_a] :
( collect_a
@ ^ [C: a] :
( ( member_a @ C @ A )
& ~ ( member_a @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(244,axiom,
! [A: set_a] :
( ( sup_sup_set_a @ A @ bot_bot_set_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_sup__bot__right) ).
thf(1228,plain,
! [A: set_a] :
( ( sup_sup_set_a @ A @ bot_bot_set_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(131,axiom,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_set_a @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_order__le__less__subst2) ).
thf(829,plain,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_set_a @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(13,axiom,
! [A: a > $o,B: a] :
( ( A @ B )
=> ( ! [C: a] :
( ( A @ C )
=> ( C = B ) )
=> ( ( the_a @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_the__equality) ).
thf(404,plain,
! [A: a > $o,B: a] :
( ( A @ B )
=> ( ! [C: a] :
( ( A @ C )
=> ( C = B ) )
=> ( ( the_a @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(262,axiom,
! [A: set_a] :
( ( ! [B: a] :
~ ( member_a @ B @ A ) )
= ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_all__not__in__conv) ).
thf(1287,plain,
! [A: set_a] :
( ( ! [B: a] :
~ ( member_a @ B @ A ) )
= ( A = bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(266,axiom,
! [A: a,B: binary1439146945Tree_a,C: binary1439146945Tree_a] : ( member_a @ A @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ B @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_Tree_Oset__intros_I2_J) ).
thf(1298,plain,
! [A: a,B: binary1439146945Tree_a,C: binary1439146945Tree_a] : ( member_a @ A @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(93,axiom,
! [A: binary1439146945Tree_a,B: a,C: binary1439146945Tree_a] :
( binary476621312_Tip_a
!= ( binary717961607le_T_a @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_Tree_Odistinct_I1_J) ).
thf(702,plain,
! [A: binary1439146945Tree_a,B: a,C: binary1439146945Tree_a] :
( binary476621312_Tip_a
!= ( binary717961607le_T_a @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(123,axiom,
! [A: set_a,B: a,C: set_a] :
( ( minus_minus_set_a @ A @ ( insert_a @ B @ C ) )
= ( minus_minus_set_a @ ( minus_minus_set_a @ A @ ( insert_a @ B @ bot_bot_set_a ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_Diff__insert2) ).
thf(802,plain,
! [A: set_a,B: a,C: set_a] :
( ( minus_minus_set_a @ A @ ( insert_a @ B @ C ) )
= ( minus_minus_set_a @ ( minus_minus_set_a @ A @ ( insert_a @ B @ bot_bot_set_a ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(271,axiom,
( bot_bot_a_o
= ( ^ [A: a] : ( member_a @ A @ bot_bot_set_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_bot__empty__eq) ).
thf(1313,plain,
( bot_bot_a_o
= ( ^ [A: a] : ( member_a @ A @ bot_bot_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(232,axiom,
( sup_sup_set_a
= ( ^ [A: set_a,B: set_a] : ( sup_sup_set_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_Un__commute) ).
thf(1191,plain,
( sup_sup_set_a
= ( ^ [A: set_a,B: set_a] : ( sup_sup_set_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(152,axiom,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ ( minus_minus_set_a @ A @ B ) @ B )
= ( sup_sup_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_Un__Diff__cancel2) ).
thf(902,plain,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ ( minus_minus_set_a @ A @ B ) @ B )
= ( sup_sup_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(137,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_subset__antisym) ).
thf(853,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(141,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_less__imp__not__eq) ).
thf(870,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(114,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_order__refl) ).
thf(770,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(285,axiom,
binary1721989714Tree_a @ h @ t2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_s2) ).
thf(1362,plain,
binary1721989714Tree_a @ h @ t2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(64,axiom,
! [A: set_a] :
~ ( ord_less_set_a @ A @ bot_bot_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_not__psubset__empty) ).
thf(606,plain,
! [A: set_a] :
~ ( ord_less_set_a @ A @ bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(282,axiom,
( ( binary1721989714Tree_a @ h @ binary476621312_Tip_a )
=> ( ( binary945792244etOf_a @ ( binary1226383794sert_a @ h @ e @ binary476621312_Tip_a ) )
= ( sup_sup_set_a @ ( minus_minus_set_a @ ( binary945792244etOf_a @ binary476621312_Tip_a ) @ ( binary504661350_eqs_a @ h @ e ) ) @ ( insert_a @ e @ bot_bot_set_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12__092_060open_062sortedTree_Ah_ATip_A_092_060longrightarrow_062_AsetOf_A_Ibinsert_Ah_Ae_ATip_J_A_061_AsetOf_ATip_A_N_Aeqs_Ah_Ae_A_092_060union_062_A_123e_125_092_060close_062) ).
thf(1347,plain,
( ( binary1721989714Tree_a @ h @ binary476621312_Tip_a )
=> ( ( binary945792244etOf_a @ ( binary1226383794sert_a @ h @ e @ binary476621312_Tip_a ) )
= ( sup_sup_set_a @ ( minus_minus_set_a @ ( binary945792244etOf_a @ binary476621312_Tip_a ) @ ( binary504661350_eqs_a @ h @ e ) ) @ ( insert_a @ e @ bot_bot_set_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(304,axiom,
! [A: a] :
( ( member_a @ A @ ( binary504661350_eqs_a @ h @ e ) )
=> ( ord_less_int @ ( h @ A ) @ ( h @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_eqsLessX) ).
thf(1415,plain,
! [A: a] :
( ( member_a @ A @ ( binary504661350_eqs_a @ h @ e ) )
=> ( ord_less_int @ ( h @ A ) @ ( h @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(59,axiom,
! [A: binary1439146945Tree_a,B: a,C: binary1439146945Tree_a] :
( ( binary256242811Tree_a @ ( binary717961607le_T_a @ A @ B @ C ) )
= ( sup_sup_set_a @ ( sup_sup_set_a @ ( binary256242811Tree_a @ A ) @ ( insert_a @ B @ bot_bot_set_a ) ) @ ( binary256242811Tree_a @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_Tree_Osimps_I15_J) ).
thf(591,plain,
! [A: binary1439146945Tree_a,B: a,C: binary1439146945Tree_a] :
( ( binary256242811Tree_a @ ( binary717961607le_T_a @ A @ B @ C ) )
= ( sup_sup_set_a @ ( sup_sup_set_a @ ( binary256242811Tree_a @ A ) @ ( insert_a @ B @ bot_bot_set_a ) ) @ ( binary256242811Tree_a @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(77,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_sup__assoc) ).
thf(646,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(132,axiom,
! [A: int,B: set_a > int,C: set_a,D: set_a] :
( ( ord_less_int @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_order__less__le__subst1) ).
thf(834,plain,
! [A: int,B: set_a > int,C: set_a,D: set_a] :
( ( ord_less_int @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(221,axiom,
! [A: set_a,B: int > set_a,C: int,D: int] :
( ( ord_less_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_order__less__le__subst1) ).
thf(1151,plain,
! [A: set_a,B: int > set_a,C: int,D: int] :
( ( ord_less_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(54,axiom,
! [A: a > $o] :
( ( A != bot_bot_a_o )
= ( ord_less_a_o @ bot_bot_a_o @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_bot_Onot__eq__extremum) ).
thf(574,plain,
! [A: a > $o] :
( ( A != bot_bot_a_o )
= ( ord_less_a_o @ bot_bot_a_o @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(167,axiom,
! [A: a > $o,B: a > $o,C: a > $o,D: a > $o] :
( ( A
= ( sup_sup_a_o @ B @ C ) )
=> ( ( sup_sup_a_o @ A @ D )
= ( sup_sup_a_o @ B @ ( sup_sup_a_o @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_boolean__algebra__cancel_Osup1) ).
thf(966,plain,
! [A: a > $o,B: a > $o,C: a > $o,D: a > $o] :
( ( A
= ( sup_sup_a_o @ B @ C ) )
=> ( ( sup_sup_a_o @ A @ D )
= ( sup_sup_a_o @ B @ ( sup_sup_a_o @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(229,axiom,
! [A: int,B: int] :
( ( A != B )
= ( ( ord_less_int @ A @ B )
| ( ord_less_int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_neq__iff) ).
thf(1183,plain,
! [A: int,B: int] :
( ( A != B )
= ( ( ord_less_int @ A @ B )
| ( ord_less_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(192,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B @ C ) )
= ( sup_sup_set_a @ B @ ( sup_sup_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_sup_Oleft__commute) ).
thf(1051,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B @ C ) )
= ( sup_sup_set_a @ B @ ( sup_sup_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(153,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_less__imp__neq) ).
thf(905,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(87,axiom,
( ord_less_set_a
= ( ^ [A: set_a,B: set_a] :
( ( B
= ( sup_sup_set_a @ B @ A ) )
& ( B != A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_sup_Ostrict__order__iff) ).
thf(687,plain,
( ord_less_set_a
= ( ^ [A: set_a,B: set_a] :
( ( B
= ( sup_sup_set_a @ B @ A ) )
& ( B != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(291,axiom,
! [A: a,B: set_a] :
( ( member_a @ A @ B )
=> ( ( insert_a @ A @ ( minus_minus_set_a @ B @ ( insert_a @ A @ bot_bot_set_a ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_insert__Diff) ).
thf(1377,plain,
! [A: a,B: set_a] :
( ( member_a @ A @ B )
=> ( ( insert_a @ A @ ( minus_minus_set_a @ B @ ( insert_a @ A @ bot_bot_set_a ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(143,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_le__sup__iff) ).
thf(877,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(197,axiom,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_ord__eq__less__subst) ).
thf(1072,plain,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(11,axiom,
! [A: int,B: int > int,C: int,D: int] :
( ( ord_less_eq_int @ A @ ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_order__le__less__subst1) ).
thf(396,plain,
! [A: int,B: int > int,C: int,D: int] :
( ( ord_less_eq_int @ A @ ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(249,axiom,
! [A: a > $o,B: a > $o] :
( ( sup_sup_a_o @ A @ ( sup_sup_a_o @ A @ B ) )
= ( sup_sup_a_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_inf__sup__aci_I8_J) ).
thf(1242,plain,
! [A: a > $o,B: a > $o] :
( ( sup_sup_a_o @ A @ ( sup_sup_a_o @ A @ B ) )
= ( sup_sup_a_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(63,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_a_o @ ( sup_sup_a_o @ A @ B ) @ C )
=> ~ ( ( ord_less_a_o @ A @ C )
=> ~ ( ord_less_a_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_sup_Ostrict__boundedE) ).
thf(602,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_a_o @ ( sup_sup_a_o @ A @ B ) @ C )
=> ~ ( ( ord_less_a_o @ A @ C )
=> ~ ( ord_less_a_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(170,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ord_less_set_a @ A @ ( sup_sup_set_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_sup_Ostrict__coboundedI2) ).
thf(981,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ord_less_set_a @ A @ ( sup_sup_set_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(21,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( A != B )
=> ( ord_less_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_le__neq__trans) ).
thf(452,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( A != B )
=> ( ord_less_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(42,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_less__imp__not__eq2) ).
thf(529,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(8,axiom,
! [A: a > $o,B: a] :
( ? [C: a] :
( ( A @ C )
& ! [D: a] :
( ( A @ D )
=> ( D = C ) ) )
=> ( ( A @ B )
=> ( ( the_a @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_the1__equality) ).
thf(381,plain,
! [A: a > $o,B: a] :
( ? [C: a] :
( ( A @ C )
& ! [D: a] :
( ( A @ D )
=> ( D = C ) ) )
=> ( ( A @ B )
=> ( ( the_a @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(270,axiom,
( ( binary945792244etOf_a @ ( binary1226383794sert_a @ h @ e @ t2 ) )
= ( sup_sup_set_a @ ( minus_minus_set_a @ ( binary945792244etOf_a @ t2 ) @ ( binary504661350_eqs_a @ h @ e ) ) @ ( insert_a @ e @ bot_bot_set_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_c2) ).
thf(1311,plain,
( ( binary945792244etOf_a @ ( binary1226383794sert_a @ h @ e @ t2 ) )
= ( sup_sup_set_a @ ( minus_minus_set_a @ ( binary945792244etOf_a @ t2 ) @ ( binary504661350_eqs_a @ h @ e ) ) @ ( insert_a @ e @ bot_bot_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(194,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_order_Ostrict__trans) ).
thf(1057,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(36,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_less__imp__not__eq2) ).
thf(512,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(19,axiom,
! [A: int] : ( ord_less_eq_int @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_order__refl) ).
thf(439,plain,
! [A: int] : ( ord_less_eq_int @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(4,axiom,
! [A: a > $o,B: a > $o] :
( ? [C: a] :
( ( A @ C )
& ! [D: a] :
( ( A @ D )
=> ( D = C ) ) )
=> ( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ( B @ ( the_a @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_the1I2) ).
thf(334,plain,
! [A: a > $o,B: a > $o] :
( ? [C: a] :
( ( A @ C )
& ! [D: a] :
( ( A @ D )
=> ( D = C ) ) )
=> ( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ( B @ ( the_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(294,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( sup_sup_set_a @ B @ C ) )
=> ( ~ ( member_a @ A @ B )
=> ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_UnE) ).
thf(1387,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( sup_sup_set_a @ B @ C ) )
=> ( ~ ( member_a @ A @ B )
=> ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(105,axiom,
! [A: set_a,B: set_a] :
( ( ( sup_sup_set_a @ A @ B )
= bot_bot_set_a )
= ( ( A = bot_bot_set_a )
& ( B = bot_bot_set_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_sup__bot_Oeq__neutr__iff) ).
thf(746,plain,
! [A: set_a,B: set_a] :
( ( ( sup_sup_set_a @ A @ B )
= bot_bot_set_a )
= ( ( A = bot_bot_set_a )
& ( B = bot_bot_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(212,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B @ C ) )
= ( sup_sup_set_a @ B @ ( sup_sup_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_sup__left__commute) ).
thf(1123,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B @ C ) )
= ( sup_sup_set_a @ B @ ( sup_sup_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(181,axiom,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_order__le__less__subst1) ).
thf(1021,plain,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(117,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_order_Ostrict__trans) ).
thf(778,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(308,axiom,
( ( binary1226383794sert_a @ h @ e @ ( binary717961607le_T_a @ t1 @ x @ t2 ) )
= ( binary717961607le_T_a @ ( binary1226383794sert_a @ h @ e @ t1 ) @ x @ t2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_res) ).
thf(1423,plain,
( ( binary1226383794sert_a @ h @ e @ ( binary717961607le_T_a @ t1 @ x @ t2 ) )
= ( binary717961607le_T_a @ ( binary1226383794sert_a @ h @ e @ t1 ) @ x @ t2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(157,axiom,
! [A: set_a] :
( ( sup_sup_set_a @ A @ bot_bot_set_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_sup__bot_Oright__neutral) ).
thf(916,plain,
! [A: set_a] :
( ( sup_sup_set_a @ A @ bot_bot_set_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(135,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ C @ A )
=> ( ord_less_int @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_dual__order_Ostrict__trans) ).
thf(847,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ C @ A )
=> ( ord_less_int @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(7,axiom,
! [A: a > $o,B: a,C: a > $o] :
( ( A @ B )
=> ( ! [D: a] :
( ( A @ D )
=> ( D = B ) )
=> ( ! [D: a] :
( ( A @ D )
=> ( C @ D ) )
=> ( C @ ( the_a @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_theI2) ).
thf(361,plain,
! [A: a > $o,B: a,C: a > $o] :
( ( A @ B )
=> ( ! [D: a] :
( ( A @ D )
=> ( D = B ) )
=> ( ! [D: a] :
( ( A @ D )
=> ( C @ D ) )
=> ( C @ ( the_a @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(227,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ord_less_set_a @ A @ ( sup_sup_set_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_less__supI2) ).
thf(1178,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ord_less_set_a @ A @ ( sup_sup_set_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(81,axiom,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(665,plain,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(318,axiom,
! [A: set_a,B: set_a] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_subsetI) ).
thf(1457,plain,
! [A: set_a,B: set_a] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(147,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_a_o @ A @ B )
=> ( ord_less_a_o @ A @ ( sup_sup_a_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_sup_Ostrict__coboundedI1) ).
thf(889,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_a_o @ A @ B )
=> ( ord_less_a_o @ A @ ( sup_sup_a_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(109,axiom,
( bot_bot_set_a
= ( collect_a
@ ^ [A: a] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_empty__def) ).
thf(757,plain,
( bot_bot_set_a
= ( collect_a
@ ^ [A: a] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(260,axiom,
! [A: a,B: set_a] :
( ( member_a @ A @ B )
=> ( ( insert_a @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_insert__absorb) ).
thf(1281,plain,
! [A: a,B: set_a] :
( ( member_a @ A @ B )
=> ( ( insert_a @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(296,axiom,
! [A: set_a,B: a,C: set_a] :
( ( ord_less_set_a @ A @ ( insert_a @ B @ C ) )
= ( ( ( member_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) )
& ( ~ ( member_a @ B @ C )
=> ( ( ( member_a @ B @ A )
=> ( ord_less_set_a @ ( minus_minus_set_a @ A @ ( insert_a @ B @ bot_bot_set_a ) ) @ C ) )
& ( ~ ( member_a @ B @ A )
=> ( ord_less_eq_set_a @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_psubset__insert__iff) ).
thf(1392,plain,
! [A: set_a,B: a,C: set_a] :
( ( ord_less_set_a @ A @ ( insert_a @ B @ C ) )
= ( ( ( member_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) )
& ( ~ ( member_a @ B @ C )
=> ( ( ( member_a @ B @ A )
=> ( ord_less_set_a @ ( minus_minus_set_a @ A @ ( insert_a @ B @ bot_bot_set_a ) ) @ C ) )
& ( ~ ( member_a @ B @ A )
=> ( ord_less_eq_set_a @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(57,axiom,
! [A: int,B: set_a > int,C: set_a,D: set_a] :
( ( ord_less_int @ A @ ( B @ C ) )
=> ( ( ord_less_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_order__less__subst1) ).
thf(583,plain,
! [A: int,B: set_a > int,C: set_a,D: set_a] :
( ( ord_less_int @ A @ ( B @ C ) )
=> ( ( ord_less_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(39,axiom,
( sup_sup_set_a
= ( ^ [A: set_a,B: set_a] : ( sup_sup_set_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_sup_Ocommute) ).
thf(522,plain,
( sup_sup_set_a
= ( ^ [A: set_a,B: set_a] : ( sup_sup_set_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(223,axiom,
! [A: set_a,B: set_a,C: set_a > int,D: int] :
( ( ord_less_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_ord__less__eq__subst) ).
thf(1159,plain,
! [A: set_a,B: set_a,C: set_a > int,D: int] :
( ( ord_less_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(24,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_leD) ).
thf(461,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(85,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B @ C ) )
= ( sup_sup_set_a @ B @ ( sup_sup_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_inf__sup__aci_I7_J) ).
thf(682,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B @ C ) )
= ( sup_sup_set_a @ B @ ( sup_sup_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(301,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( minus_minus_set_a @ B @ C ) )
=> ~ ( ( member_a @ A @ B )
=> ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_DiffE) ).
thf(1407,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( minus_minus_set_a @ B @ C ) )
=> ~ ( ( member_a @ A @ B )
=> ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(47,axiom,
! [A: set_a] :
~ ( ord_less_set_a @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_dual__order_Oirrefl) ).
thf(551,plain,
! [A: set_a] :
~ ( ord_less_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(214,axiom,
! [A: a,B: a] :
( ( ( insert_a @ A @ bot_bot_set_a )
= ( insert_a @ B @ bot_bot_set_a ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_singleton__inject) ).
thf(1128,plain,
! [A: a,B: a] :
( ( ( insert_a @ A @ bot_bot_set_a )
= ( insert_a @ B @ bot_bot_set_a ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(283,axiom,
( ( binary1721989714Tree_a @ h @ t2 )
=> ( ( binary945792244etOf_a @ ( binary1226383794sert_a @ h @ e @ t2 ) )
= ( sup_sup_set_a @ ( minus_minus_set_a @ ( binary945792244etOf_a @ t2 ) @ ( binary504661350_eqs_a @ h @ e ) ) @ ( insert_a @ e @ bot_bot_set_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_h2) ).
thf(1350,plain,
( ( binary1721989714Tree_a @ h @ t2 )
=> ( ( binary945792244etOf_a @ ( binary1226383794sert_a @ h @ e @ t2 ) )
= ( sup_sup_set_a @ ( minus_minus_set_a @ ( binary945792244etOf_a @ t2 ) @ ( binary504661350_eqs_a @ h @ e ) ) @ ( insert_a @ e @ bot_bot_set_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(38,axiom,
! [A: set_a] :
~ ( ord_less_set_a @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_less__irrefl) ).
thf(519,plain,
! [A: set_a] :
~ ( ord_less_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(142,axiom,
! [A: set_a,B: set_a,C: $o] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_set_a @ B @ A )
=> C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_less__imp__triv) ).
thf(874,plain,
! [A: set_a,B: set_a,C: $o] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_set_a @ B @ A )
=> C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(277,axiom,
! [A: set_a,B: set_a] :
( ( sup_sup_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) )
= ( ^ [C: a] : ( member_a @ C @ ( sup_sup_set_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_sup__Un__eq) ).
thf(1328,plain,
! [A: set_a,B: set_a] :
( ( sup_sup_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) )
= ( ^ [C: a] : ( member_a @ C @ ( sup_sup_set_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(211,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_less__imp__not__less) ).
thf(1121,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(98,axiom,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ ( minus_minus_set_a @ B @ A ) )
= ( sup_sup_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_Un__Diff__cancel) ).
thf(725,plain,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ ( minus_minus_set_a @ B @ A ) )
= ( sup_sup_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(309,axiom,
! [A: a > int,B: binary1439146945Tree_a,C: a,D: binary1439146945Tree_a] :
( ( binary1721989714Tree_a @ A @ ( binary717961607le_T_a @ B @ C @ D ) )
= ( ( binary1721989714Tree_a @ A @ B )
& ! [E: a] :
( ( member_a @ E @ ( binary945792244etOf_a @ B ) )
=> ( ord_less_int @ ( A @ E ) @ ( A @ C ) ) )
& ! [E: a] :
( ( member_a @ E @ ( binary945792244etOf_a @ D ) )
=> ( ord_less_int @ ( A @ C ) @ ( A @ E ) ) )
& ( binary1721989714Tree_a @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_sortedTree_Osimps_I2_J) ).
thf(1425,plain,
! [A: a > int,B: binary1439146945Tree_a,C: a,D: binary1439146945Tree_a] :
( ( binary1721989714Tree_a @ A @ ( binary717961607le_T_a @ B @ C @ D ) )
= ( ( binary1721989714Tree_a @ A @ B )
& ! [E: a] :
( ( member_a @ E @ ( binary945792244etOf_a @ B ) )
=> ( ord_less_int @ ( A @ E ) @ ( A @ C ) ) )
& ! [E: a] :
( ( member_a @ E @ ( binary945792244etOf_a @ D ) )
=> ( ord_less_int @ ( A @ C ) @ ( A @ E ) ) )
& ( binary1721989714Tree_a @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(204,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( sup_sup_a_o @ A @ ( sup_sup_a_o @ B @ C ) )
= ( sup_sup_a_o @ B @ ( sup_sup_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_inf__sup__aci_I7_J) ).
thf(1096,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( sup_sup_a_o @ A @ ( sup_sup_a_o @ B @ C ) )
= ( sup_sup_a_o @ B @ ( sup_sup_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(6,axiom,
! [A: int,B: int,C: int > int,D: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_order__less__le__subst2) ).
thf(356,plain,
! [A: int,B: int,C: int > int,D: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(172,axiom,
! [A: int,B: int,C: int > set_a,D: set_a] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_set_a @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_order__le__less__subst2) ).
thf(989,plain,
! [A: int,B: int,C: int > set_a,D: set_a] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_set_a @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(298,axiom,
( ord_less_set_a
= ( ^ [A: set_a,B: set_a] :
( ord_less_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_less__set__def) ).
thf(1397,plain,
( ord_less_set_a
= ( ^ [A: set_a,B: set_a] :
( ord_less_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(91,axiom,
! [A: a > $o] :
( ( sup_sup_a_o @ A @ bot_bot_a_o )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_sup__bot_Oright__neutral) ).
thf(697,plain,
! [A: a > $o] :
( ( sup_sup_a_o @ A @ bot_bot_a_o )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(201,axiom,
! [A: set_a,B: set_a] :
( ( ( sup_sup_set_a @ A @ B )
= bot_bot_set_a )
= ( ( A = bot_bot_set_a )
& ( B = bot_bot_set_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_Un__empty) ).
thf(1089,plain,
! [A: set_a,B: set_a] :
( ( ( sup_sup_set_a @ A @ B )
= bot_bot_set_a )
= ( ( A = bot_bot_set_a )
& ( B = bot_bot_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(246,axiom,
! [A: a > $o,B: a > $o] :
( ( bot_bot_a_o
= ( sup_sup_a_o @ A @ B ) )
= ( ( A = bot_bot_a_o )
& ( B = bot_bot_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_sup__bot_Oneutr__eq__iff) ).
thf(1234,plain,
! [A: a > $o,B: a > $o] :
( ( bot_bot_a_o
= ( sup_sup_a_o @ A @ B ) )
= ( ( A = bot_bot_a_o )
& ( B = bot_bot_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(259,axiom,
! [A: a,B: binary1439146945Tree_a] :
( ( member_a @ A @ ( binary256242811Tree_a @ B ) )
=> ( ! [C: binary1439146945Tree_a] :
( ? [D: a,E: binary1439146945Tree_a] :
( B
= ( binary717961607le_T_a @ C @ D @ E ) )
=> ~ ( member_a @ A @ ( binary256242811Tree_a @ C ) ) )
=> ( ! [C: binary1439146945Tree_a,D: binary1439146945Tree_a] :
( B
!= ( binary717961607le_T_a @ C @ A @ D ) )
=> ~ ! [C: binary1439146945Tree_a,D: a,E: binary1439146945Tree_a] :
( ( B
= ( binary717961607le_T_a @ C @ D @ E ) )
=> ~ ( member_a @ A @ ( binary256242811Tree_a @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_Tree_Oset__cases) ).
thf(1270,plain,
! [A: a,B: binary1439146945Tree_a] :
( ( member_a @ A @ ( binary256242811Tree_a @ B ) )
=> ( ! [C: binary1439146945Tree_a] :
( ? [D: a,E: binary1439146945Tree_a] :
( B
= ( binary717961607le_T_a @ C @ D @ E ) )
=> ~ ( member_a @ A @ ( binary256242811Tree_a @ C ) ) )
=> ( ! [C: binary1439146945Tree_a,D: binary1439146945Tree_a] :
( B
!= ( binary717961607le_T_a @ C @ A @ D ) )
=> ~ ! [C: binary1439146945Tree_a,D: a,E: binary1439146945Tree_a] :
( ( B
= ( binary717961607le_T_a @ C @ D @ E ) )
=> ~ ( member_a @ A @ ( binary256242811Tree_a @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(255,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( sup_sup_set_a @ B @ C ) )
= ( ( member_a @ A @ B )
| ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_Un__iff) ).
thf(1259,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( sup_sup_set_a @ B @ C ) )
= ( ( member_a @ A @ B )
| ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(119,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_Un__assoc) ).
thf(783,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(210,axiom,
! [A: a] :
( ( collect_a
@ ^ [B: a] : ( B = A ) )
= ( insert_a @ A @ bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_singleton__conv) ).
thf(1118,plain,
! [A: a] :
( ( collect_a
@ ^ [B: a] : ( B = A ) )
= ( insert_a @ A @ bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(28,axiom,
! [A: binary1439146945Tree_a > $o,B: binary1439146945Tree_a] :
( ( A @ binary476621312_Tip_a )
=> ( ! [C: binary1439146945Tree_a,D: a,E: binary1439146945Tree_a] :
( ( A @ C )
=> ( ( A @ E )
=> ( A @ ( binary717961607le_T_a @ C @ D @ E ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_Tree_Oinduct) ).
thf(471,plain,
! [A: binary1439146945Tree_a > $o,B: binary1439146945Tree_a] :
( ( A @ binary476621312_Tip_a )
=> ( ! [C: binary1439146945Tree_a,D: a,E: binary1439146945Tree_a] :
( ( A @ C )
=> ( ( A @ E )
=> ( A @ ( binary717961607le_T_a @ C @ D @ E ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(183,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ~ ( ord_less_set_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_order_Oasym) ).
thf(1028,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ~ ( ord_less_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(30,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_set_a @ C @ A )
=> ( ord_less_set_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_dual__order_Ostrict__trans) ).
thf(488,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_set_a @ C @ A )
=> ( ord_less_set_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(162,axiom,
! [A: a > $o,B: a > $o,C: a > $o,D: a > $o] :
( ( A
= ( sup_sup_a_o @ B @ C ) )
=> ( ( sup_sup_a_o @ D @ A )
= ( sup_sup_a_o @ B @ ( sup_sup_a_o @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_boolean__algebra__cancel_Osup2) ).
thf(933,plain,
! [A: a > $o,B: a > $o,C: a > $o,D: a > $o] :
( ( A
= ( sup_sup_a_o @ B @ C ) )
=> ( ( sup_sup_a_o @ D @ A )
= ( sup_sup_a_o @ B @ ( sup_sup_a_o @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(48,axiom,
! [A: set_a,B: set_a] :
( ( ( sup_sup_set_a @ A @ B )
= bot_bot_set_a )
= ( ( A = bot_bot_set_a )
& ( B = bot_bot_set_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_sup__eq__bot__iff) ).
thf(554,plain,
! [A: set_a,B: set_a] :
( ( ( sup_sup_set_a @ A @ B )
= bot_bot_set_a )
= ( ( A = bot_bot_set_a )
& ( B = bot_bot_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(319,axiom,
! [A: a,B: binary1439146945Tree_a,C: a,D: binary1439146945Tree_a] :
( ( member_a @ A @ ( binary256242811Tree_a @ B ) )
=> ( member_a @ A @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_Tree_Oset__intros_I1_J) ).
thf(1461,plain,
! [A: a,B: binary1439146945Tree_a,C: a,D: binary1439146945Tree_a] :
( ( member_a @ A @ ( binary256242811Tree_a @ B ) )
=> ( member_a @ A @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(74,axiom,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ A @ B ) )
= ( sup_sup_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_sup_Oleft__idem) ).
thf(637,plain,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ A @ B ) )
= ( sup_sup_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(239,axiom,
! [A: int] :
? [B: int] : ( ord_less_int @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_gt__ex) ).
thf(1214,plain,
! [A: int] :
? [B: int] : ( ord_less_int @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(94,axiom,
( sup_sup_a_o
= ( ^ [A: a > $o,B: a > $o] : ( sup_sup_a_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_sup_Ocommute) ).
thf(706,plain,
( sup_sup_a_o
= ( ^ [A: a > $o,B: a > $o] : ( sup_sup_a_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(306,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ? [C: a] : ( member_a @ C @ ( minus_minus_set_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_psubset__imp__ex__mem) ).
thf(1419,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ? [C: a] : ( member_a @ C @ ( minus_minus_set_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(303,axiom,
binary1721989714Tree_a @ h @ t1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_s1) ).
thf(1414,plain,
binary1721989714Tree_a @ h @ t1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(41,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_a_o @ A @ B )
=> ( ord_less_a_o @ A @ ( sup_sup_a_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_less__supI1) ).
thf(526,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_a_o @ A @ B )
=> ( ord_less_a_o @ A @ ( sup_sup_a_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(69,axiom,
( sup_sup_a_o
= ( ^ [A: a > $o,B: a > $o] : ( sup_sup_a_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_sup__commute) ).
thf(622,plain,
( sup_sup_a_o
= ( ^ [A: a > $o,B: a > $o] : ( sup_sup_a_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(174,axiom,
( the_elem_a
= ( ^ [A: set_a] :
( the_a
@ ^ [B: a] :
( A
= ( insert_a @ B @ bot_bot_set_a ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_the__elem__def) ).
thf(997,plain,
( the_elem_a
= ( ^ [A: set_a] :
( the_a
@ ^ [B: a] :
( A
= ( insert_a @ B @ bot_bot_set_a ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(205,axiom,
! [A: set_a,B: set_a] :
( ( bot_bot_set_a
= ( sup_sup_set_a @ A @ B ) )
= ( ( A = bot_bot_set_a )
& ( B = bot_bot_set_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_bot__eq__sup__iff) ).
thf(1099,plain,
! [A: set_a,B: set_a] :
( ( bot_bot_set_a
= ( sup_sup_set_a @ A @ B ) )
= ( ( A = bot_bot_set_a )
& ( B = bot_bot_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(251,axiom,
! [A: binary1439146945Tree_a] :
( ( A != binary476621312_Tip_a )
=> ~ ! [B: binary1439146945Tree_a,C: a,D: binary1439146945Tree_a] :
( A
!= ( binary717961607le_T_a @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_Tree_Oexhaust) ).
thf(1249,plain,
! [A: binary1439146945Tree_a] :
( ( A != binary476621312_Tip_a )
=> ~ ! [B: binary1439146945Tree_a,C: a,D: binary1439146945Tree_a] :
( A
!= ( binary717961607le_T_a @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(102,axiom,
! [A: set_a] :
( ( minus_minus_set_a @ A @ A )
= bot_bot_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_Diff__cancel) ).
thf(738,plain,
! [A: set_a] :
( ( minus_minus_set_a @ A @ A )
= bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(245,axiom,
! [A: a > $o,B: a > $o] :
( ( sup_sup_a_o @ A @ ( sup_sup_a_o @ A @ B ) )
= ( sup_sup_a_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_sup_Oleft__idem) ).
thf(1231,plain,
! [A: a > $o,B: a > $o] :
( ( sup_sup_a_o @ A @ ( sup_sup_a_o @ A @ B ) )
= ( sup_sup_a_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(195,axiom,
! [A: int,B: int,C: int > int,D: int] :
( ( ord_less_int @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_ord__less__eq__subst) ).
thf(1060,plain,
! [A: int,B: int,C: int > int,D: int] :
( ( ord_less_int @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(176,axiom,
! [A: a,B: set_a,C: a] :
( ( ( insert_a @ A @ B )
= ( insert_a @ C @ bot_bot_set_a ) )
= ( ( A = C )
& ( ord_less_eq_set_a @ B @ ( insert_a @ C @ bot_bot_set_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_singleton__insert__inj__eq_H) ).
thf(1002,plain,
! [A: a,B: set_a,C: a] :
( ( ( insert_a @ A @ B )
= ( insert_a @ C @ bot_bot_set_a ) )
= ( ( A = C )
& ( ord_less_eq_set_a @ B @ ( insert_a @ C @ bot_bot_set_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(52,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ord_less_set_a @ A @ ( sup_sup_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_sup_Ostrict__coboundedI1) ).
thf(569,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ord_less_set_a @ A @ ( sup_sup_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(275,axiom,
! [A: set_a] :
( ( ? [B: a] : ( member_a @ B @ A ) )
= ( A != bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_ex__in__conv) ).
thf(1324,plain,
! [A: set_a] :
( ( ? [B: a] : ( member_a @ B @ A ) )
= ( A != bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(10,axiom,
! [A: a] :
( ( the_a @ ( (=) @ a @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_the__sym__eq__trivial) ).
thf(393,plain,
! [A: a] :
( ( the_a @ ( (=) @ a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(215,axiom,
! [A: set_a] :
( ( sup_sup_set_a @ bot_bot_set_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_sup__bot__left) ).
thf(1131,plain,
! [A: set_a] :
( ( sup_sup_set_a @ bot_bot_set_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(79,axiom,
! [A: a > $o,B: a] :
( ( ( A @ B )
=> ( ( collect_a
@ ^ [C: a] :
( ( B = C )
& ( A @ C ) ) )
= ( insert_a @ B @ bot_bot_set_a ) ) )
& ( ~ ( A @ B )
=> ( ( collect_a
@ ^ [C: a] :
( ( B = C )
& ( A @ C ) ) )
= bot_bot_set_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_Collect__conv__if2) ).
thf(654,plain,
! [A: a > $o,B: a] :
( ( ( A @ B )
=> ( ( collect_a
@ ^ [C: a] :
( ( B = C )
& ( A @ C ) ) )
= ( insert_a @ B @ bot_bot_set_a ) ) )
& ( ~ ( A @ B )
=> ( ( collect_a
@ ^ [C: a] :
( ( B = C )
& ( A @ C ) ) )
= bot_bot_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(171,axiom,
! [A: set_a,B: set_a,C: set_a > int,D: int] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_int @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_order__le__less__subst2) ).
thf(984,plain,
! [A: set_a,B: set_a,C: set_a > int,D: int] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_int @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(155,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ~ ( ord_less_set_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_less__asym_H) ).
thf(911,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ~ ( ord_less_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(312,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ B )
=> ( member_a @ A @ ( sup_sup_set_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_UnI2) ).
thf(1434,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ B )
=> ( member_a @ A @ ( sup_sup_set_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(273,axiom,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_emptyE) ).
thf(1318,plain,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(124,axiom,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ A @ B ) )
= ( sup_sup_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_sup__left__idem) ).
thf(805,plain,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ A @ B ) )
= ( sup_sup_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(35,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_order_Ostrict__implies__not__eq) ).
thf(508,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(159,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_dual__order_Oasym) ).
thf(921,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(186,axiom,
! [A: set_a,B: set_a] :
( ( minus_minus_set_a @ ( minus_minus_set_a @ A @ B ) @ B )
= ( minus_minus_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_Diff__idemp) ).
thf(1035,plain,
! [A: set_a,B: set_a] :
( ( minus_minus_set_a @ ( minus_minus_set_a @ A @ B ) @ B )
= ( minus_minus_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(182,axiom,
( bot_bot_set_a
= ( collect_a @ bot_bot_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_bot__set__def) ).
thf(1026,plain,
( bot_bot_set_a
= ( collect_a @ bot_bot_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(80,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ ( sup_sup_a_o @ A @ B ) @ C )
= ( ( ord_less_eq_a_o @ A @ C )
& ( ord_less_eq_a_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_le__sup__iff) ).
thf(662,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ ( sup_sup_a_o @ A @ B ) @ C )
= ( ( ord_less_eq_a_o @ A @ C )
& ( ord_less_eq_a_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(200,axiom,
! [A: set_a] :
( ( minus_minus_set_a @ bot_bot_set_a @ A )
= bot_bot_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_empty__Diff) ).
thf(1086,plain,
! [A: set_a] :
( ( minus_minus_set_a @ bot_bot_set_a @ A )
= bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(163,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ~ ( ord_less_set_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_less__asym) ).
thf(938,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ~ ( ord_less_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(112,axiom,
! [A: set_a] :
( ( sup_sup_set_a @ bot_bot_set_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_sup__bot_Oleft__neutral) ).
thf(765,plain,
! [A: set_a] :
( ( sup_sup_set_a @ bot_bot_set_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(193,axiom,
! [A: a > $o] :
( ( sup_sup_a_o @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_sup_Oidem) ).
thf(1054,plain,
! [A: a > $o] :
( ( sup_sup_a_o @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(138,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_empty__subsetI) ).
thf(856,plain,
! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(88,axiom,
( ( binary945792244etOf_a @ binary476621312_Tip_a )
= bot_bot_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_setOf_Osimps_I1_J) ).
thf(689,plain,
( ( binary945792244etOf_a @ binary476621312_Tip_a )
= bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(290,axiom,
! [A: a,B: a,C: set_a] :
( ( member_a @ A @ ( insert_a @ B @ C ) )
= ( ( A = B )
| ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_insert__iff) ).
thf(1374,plain,
! [A: a,B: a,C: set_a] :
( ( member_a @ A @ ( insert_a @ B @ C ) )
= ( ( A = B )
| ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(241,axiom,
! [A: set_a] :
( ( minus_minus_set_a @ A @ bot_bot_set_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_Diff__empty) ).
thf(1219,plain,
! [A: set_a] :
( ( minus_minus_set_a @ A @ bot_bot_set_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(130,axiom,
! [A: int,B: int,C: int > int,D: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_order__less__subst2) ).
thf(824,plain,
! [A: int,B: int,C: int > int,D: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(129,axiom,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( A
= ( sup_sup_set_a @ B @ C ) )
=> ( ( sup_sup_set_a @ D @ A )
= ( sup_sup_set_a @ B @ ( sup_sup_set_a @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_boolean__algebra__cancel_Osup2) ).
thf(819,plain,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( A
= ( sup_sup_set_a @ B @ C ) )
=> ( ( sup_sup_set_a @ D @ A )
= ( sup_sup_set_a @ B @ ( sup_sup_set_a @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(16,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ~ ( ord_less_int @ A @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_354_antisym__conv2) ).
thf(423,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ~ ( ord_less_int @ A @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(90,axiom,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ A @ B ) )
= ( sup_sup_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_Un__left__absorb) ).
thf(694,plain,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ A @ B ) )
= ( sup_sup_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(100,axiom,
! [A: a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ ( insert_a @ A @ B ) @ C )
= ( insert_a @ A @ ( sup_sup_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_Un__insert__left) ).
thf(732,plain,
! [A: a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ ( insert_a @ A @ B ) @ C )
= ( insert_a @ A @ ( sup_sup_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(295,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ B )
=> ( member_a @ A @ ( sup_sup_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_UnI1) ).
thf(1389,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ B )
=> ( member_a @ A @ ( sup_sup_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(115,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B @ C ) )
= ( sup_sup_set_a @ B @ ( sup_sup_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_Un__left__commute) ).
thf(772,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B @ C ) )
= ( sup_sup_set_a @ B @ ( sup_sup_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(104,axiom,
! [A: a > $o] :
( ( bot_bot_set_a
= ( collect_a @ A ) )
= ( ! [B: a] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_empty__Collect__eq) ).
thf(743,plain,
! [A: a > $o] :
( ( bot_bot_set_a
= ( collect_a @ A ) )
= ( ! [B: a] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(55,axiom,
! [A: set_a] :
( ( sup_sup_set_a @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Un__absorb) ).
thf(577,plain,
! [A: set_a] :
( ( sup_sup_set_a @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(14,axiom,
! [A: int,B: int > int,C: int,D: int] :
( ( ord_less_int @ A @ ( B @ C ) )
=> ( ( ord_less_eq_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ E @ F )
=> ( ord_less_eq_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_order__less__le__subst1) ).
thf(413,plain,
! [A: int,B: int > int,C: int,D: int] :
( ( ord_less_int @ A @ ( B @ C ) )
=> ( ( ord_less_eq_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ E @ F )
=> ( ord_less_eq_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(253,axiom,
( binary504661350_eqs_a
= ( ^ [A: a > int,B: a] :
( collect_a
@ ^ [C: a] :
( ( A @ C )
= ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_eqs__def) ).
thf(1256,plain,
( binary504661350_eqs_a
= ( ^ [A: a > int,B: a] :
( collect_a
@ ^ [C: a] :
( ( A @ C )
= ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(45,axiom,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ ( sup_sup_set_a @ A @ B ) @ B )
= ( sup_sup_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_sup_Oright__idem) ).
thf(545,plain,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ ( sup_sup_set_a @ A @ B ) @ B )
= ( sup_sup_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(310,axiom,
! [A: a,B: set_a,C: set_a] :
( ~ ( member_a @ A @ B )
=> ( ( minus_minus_set_a @ B @ ( insert_a @ A @ C ) )
= ( minus_minus_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_Diff__insert0) ).
thf(1428,plain,
! [A: a,B: set_a,C: set_a] :
( ~ ( member_a @ A @ B )
=> ( ( minus_minus_set_a @ B @ ( insert_a @ A @ C ) )
= ( minus_minus_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(53,axiom,
( insert_a
= ( ^ [A: a] :
( sup_sup_set_a
@ ( collect_a
@ ^ [B: a] : ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_insert__def) ).
thf(572,plain,
( insert_a
= ( ^ [A: a] :
( sup_sup_set_a
@ ( collect_a
@ ^ [B: a] : ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(289,axiom,
! [A: a,B: set_a,C: a] :
( ( member_a @ A @ B )
=> ( member_a @ A @ ( insert_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_insertI2) ).
thf(1371,plain,
! [A: a,B: set_a,C: a] :
( ( member_a @ A @ B )
=> ( member_a @ A @ ( insert_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(66,axiom,
! [A: a,B: set_a] :
( ( insert_a @ A @ ( minus_minus_set_a @ B @ ( insert_a @ A @ bot_bot_set_a ) ) )
= ( insert_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_insert__Diff__single) ).
thf(611,plain,
! [A: a,B: set_a] :
( ( insert_a @ A @ ( minus_minus_set_a @ B @ ( insert_a @ A @ bot_bot_set_a ) ) )
= ( insert_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(248,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_psubset__trans) ).
thf(1239,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(158,axiom,
! [A: a > int] : ( binary1721989714Tree_a @ A @ binary476621312_Tip_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_sortedTree_Osimps_I1_J) ).
thf(919,plain,
! [A: a > int] : ( binary1721989714Tree_a @ A @ binary476621312_Tip_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(254,axiom,
binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_s) ).
thf(1258,plain,
binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(9,axiom,
( ord_less_int
= ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_less__le) ).
thf(391,plain,
( ord_less_int
= ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(217,axiom,
! [A: set_a,B: a,C: set_a] :
( ( sup_sup_set_a @ A @ ( insert_a @ B @ C ) )
= ( insert_a @ B @ ( sup_sup_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_Un__insert__right) ).
thf(1139,plain,
! [A: set_a,B: a,C: set_a] :
( ( sup_sup_set_a @ A @ ( insert_a @ B @ C ) )
= ( insert_a @ B @ ( sup_sup_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(26,axiom,
( sup_sup_a_o
= ( ^ [A: a > $o,B: a > $o] : ( sup_sup_a_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_inf__sup__aci_I5_J) ).
thf(466,plain,
( sup_sup_a_o
= ( ^ [A: a > $o,B: a > $o] : ( sup_sup_a_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(202,axiom,
( ( binary256242811Tree_a @ binary476621312_Tip_a )
= bot_bot_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_Tree_Osimps_I14_J) ).
thf(1092,plain,
( ( binary256242811Tree_a @ binary476621312_Tip_a )
= bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(320,axiom,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_psubsetD) ).
thf(1464,plain,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(166,axiom,
! [A: int > int > $o,B: int,C: int] :
( ! [D: int,E: int] :
( ( ord_less_int @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: int] : ( A @ D @ D )
=> ( ! [D: int,E: int] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_linorder__less__wlog) ).
thf(947,plain,
! [A: int > int > $o,B: int,C: int] :
( ! [D: int,E: int] :
( ( ord_less_int @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: int] : ( A @ D @ D )
=> ( ! [D: int,E: int] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(238,axiom,
! [A: int,B: int,C: int > set_a,D: set_a] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_set_a @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_order__less__subst2) ).
thf(1209,plain,
! [A: int,B: int,C: int > set_a,D: set_a] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_set_a @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(151,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ~ ( ord_less_set_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_less__not__sym) ).
thf(900,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ~ ( ord_less_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(62,axiom,
! [A: a > $o,B: a,C: a > $o] :
( ( A @ B )
=> ( sup_sup_a_o @ A @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_sup1I1) ).
thf(599,plain,
! [A: a > $o,B: a,C: a > $o] :
( ( A @ B )
=> ( sup_sup_a_o @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(226,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_less__trans) ).
thf(1175,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(144,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_a_o @ A @ B )
=> ( ord_less_a_o @ A @ ( sup_sup_a_o @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_sup_Ostrict__coboundedI2) ).
thf(880,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_a_o @ A @ B )
=> ( ord_less_a_o @ A @ ( sup_sup_a_o @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(78,axiom,
! [A: set_a,B: int > set_a,C: int,D: int] :
( ( ord_less_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_order__less__subst1) ).
thf(649,plain,
! [A: set_a,B: int > set_a,C: int,D: int] :
( ( ord_less_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(189,axiom,
! [A: a > $o,B: a > $o] :
( ( collect_a
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) )
= ( sup_sup_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_Collect__disj__eq) ).
thf(1043,plain,
! [A: a > $o,B: a > $o] :
( ( collect_a
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) )
= ( sup_sup_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(126,axiom,
( insert_a
= ( ^ [A: a] : ( sup_sup_set_a @ ( insert_a @ A @ bot_bot_set_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_insert__is__Un) ).
thf(811,plain,
( insert_a
= ( ^ [A: a] : ( sup_sup_set_a @ ( insert_a @ A @ bot_bot_set_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(72,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_less__imp__not__eq) ).
thf(631,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(279,axiom,
! [A: a,B: a,C: set_a] :
( ( member_a @ A @ ( remove_a @ B @ C ) )
= ( ( member_a @ A @ C )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_member__remove) ).
thf(1339,plain,
! [A: a,B: a,C: set_a] :
( ( member_a @ A @ ( remove_a @ B @ C ) )
= ( ( member_a @ A @ C )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(139,axiom,
! [A: int,B: int,C: int > set_a,D: set_a] :
( ( ord_less_int @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_ord__less__eq__subst) ).
thf(858,plain,
! [A: int,B: int,C: int > set_a,D: set_a] :
( ( ord_less_int @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(128,axiom,
! [A: a > $o] :
( ( sup_sup_a_o @ A @ bot_bot_a_o )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_sup__bot__right) ).
thf(816,plain,
! [A: a > $o] :
( ( sup_sup_a_o @ A @ bot_bot_a_o )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(65,axiom,
( sup_sup_a_o
= ( ^ [A: a > $o,B: a > $o,C: a] : ( sup_sup_o @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_sup__fun__def) ).
thf(609,plain,
( sup_sup_a_o
= ( ^ [A: a > $o,B: a > $o,C: a] : ( sup_sup_o @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(60,axiom,
! [A: int,B: int] :
( ( A != B )
=> ( ~ ( ord_less_int @ A @ B )
=> ( ord_less_int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_neqE) ).
thf(594,plain,
! [A: int,B: int] :
( ( A != B )
=> ( ~ ( ord_less_int @ A @ B )
=> ( ord_less_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(92,axiom,
( ord_less_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_less__le) ).
thf(700,plain,
( ord_less_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(149,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ~ ( ord_less_set_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_dual__order_Oasym) ).
thf(895,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ~ ( ord_less_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(281,axiom,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(1344,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(165,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_dual__order_Ostrict__implies__not__eq) ).
thf(943,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(264,axiom,
( sup_sup_set_a
= ( ^ [A: set_a,B: set_a] :
( collect_a
@ ^ [C: a] :
( ( member_a @ C @ A )
| ( member_a @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_Un__def) ).
thf(1293,plain,
( sup_sup_set_a
= ( ^ [A: set_a,B: set_a] :
( collect_a
@ ^ [C: a] :
( ( member_a @ C @ A )
| ( member_a @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(82,axiom,
! [A: int] :
~ ( ord_less_int @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_dual__order_Oirrefl) ).
thf(668,plain,
! [A: int] :
~ ( ord_less_int @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(86,axiom,
( remove_a
= ( ^ [A: a,B: set_a] : ( minus_minus_set_a @ B @ ( insert_a @ A @ bot_bot_set_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_remove__def) ).
thf(685,plain,
( remove_a
= ( ^ [A: a,B: set_a] : ( minus_minus_set_a @ B @ ( insert_a @ A @ bot_bot_set_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(113,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_less__asym) ).
thf(768,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(250,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_dual__order_Ostrict__implies__not__eq) ).
thf(1245,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(315,axiom,
! [A: set_a,B: set_a,C: a > $o] :
( ( ? [D: a] :
( ( member_a @ D @ ( sup_sup_set_a @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: a] :
( ( member_a @ D @ A )
& ( C @ D ) )
| ? [D: a] :
( ( member_a @ D @ B )
& ( C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_bex__Un) ).
thf(1445,plain,
! [A: set_a,B: set_a,C: a > $o] :
( ( ? [D: a] :
( ( member_a @ D @ ( sup_sup_set_a @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: a] :
( ( member_a @ D @ A )
& ( C @ D ) )
| ? [D: a] :
( ( member_a @ D @ B )
& ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(209,axiom,
! [A: set_a,B: set_a,C: set_a > int,D: int] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_int @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_order__less__subst2) ).
thf(1113,plain,
! [A: set_a,B: set_a,C: set_a > int,D: int] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_int @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(324,axiom,
! [A: a,B: a] :
( ( member_a @ A @ ( insert_a @ B @ bot_bot_set_a ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_singletonD) ).
thf(1477,plain,
! [A: a,B: a] :
( ( member_a @ A @ ( insert_a @ B @ bot_bot_set_a ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(206,axiom,
! [A: a > $o,B: a > $o] :
( ( ( sup_sup_a_o @ A @ B )
= bot_bot_a_o )
= ( ( A = bot_bot_a_o )
& ( B = bot_bot_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_sup__eq__bot__iff) ).
thf(1102,plain,
! [A: a > $o,B: a > $o] :
( ( ( sup_sup_a_o @ A @ B )
= bot_bot_a_o )
= ( ( A = bot_bot_a_o )
& ( B = bot_bot_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(34,axiom,
! [A: a > $o,B: a,C: a > $o] :
( ( A @ B )
=> ( sup_sup_a_o @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_sup1I2) ).
thf(505,plain,
! [A: a > $o,B: a,C: a > $o] :
( ( A @ B )
=> ( sup_sup_a_o @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(22,axiom,
! [A: int,B: int] :
( ( ~ ( ord_less_eq_int @ A @ B ) )
= ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_not__le) ).
thf(455,plain,
! [A: int,B: int] :
( ( ~ ( ord_less_eq_int @ A @ B ) )
= ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(145,axiom,
! [A: a,B: set_a] :
( ( insert_a @ A @ ( insert_a @ A @ B ) )
= ( insert_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_insert__absorb2) ).
thf(883,plain,
! [A: a,B: set_a] :
( ( insert_a @ A @ ( insert_a @ A @ B ) )
= ( insert_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(97,axiom,
! [A: a > $o,B: a > $o] :
( ( bot_bot_a_o
= ( sup_sup_a_o @ A @ B ) )
= ( ( A = bot_bot_a_o )
& ( B = bot_bot_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_bot__eq__sup__iff) ).
thf(722,plain,
! [A: a > $o,B: a > $o] :
( ( bot_bot_a_o
= ( sup_sup_a_o @ A @ B ) )
= ( ( A = bot_bot_a_o )
& ( B = bot_bot_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(268,axiom,
! [A: a,B: set_a,C: set_a] :
( ( ~ ( member_a @ A @ B )
=> ( member_a @ A @ C ) )
=> ( member_a @ A @ ( sup_sup_set_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_UnCI) ).
thf(1304,plain,
! [A: a,B: set_a,C: set_a] :
( ( ~ ( member_a @ A @ B )
=> ( member_a @ A @ C ) )
=> ( member_a @ A @ ( sup_sup_set_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(17,axiom,
! [A: a > $o,B: a] :
( ( A @ B )
=> ( ! [C: a] :
( ( A @ C )
=> ( C = B ) )
=> ( A @ ( the_a @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_theI) ).
thf(426,plain,
! [A: a > $o,B: a] :
( ( A @ B )
=> ( ! [C: a] :
( ( A @ C )
=> ( C = B ) )
=> ( A @ ( the_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(236,axiom,
( is_singleton_a
= ( ^ [A: set_a] :
( A
= ( insert_a @ ( the_elem_a @ A ) @ bot_bot_set_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_is__singleton__the__elem) ).
thf(1203,plain,
( is_singleton_a
= ( ^ [A: set_a] :
( A
= ( insert_a @ ( the_elem_a @ A ) @ bot_bot_set_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(321,axiom,
! [A: set_a,B: a] :
( ( A = bot_bot_set_a )
=> ~ ( member_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_equals0D) ).
thf(1467,plain,
! [A: set_a,B: a] :
( ( A = bot_bot_set_a )
=> ~ ( member_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(46,axiom,
! [A: a > int,B: a] :
( ( binary1226383794sert_a @ A @ B @ binary476621312_Tip_a )
= ( binary717961607le_T_a @ binary476621312_Tip_a @ B @ binary476621312_Tip_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_binsert_Osimps_I1_J) ).
thf(548,plain,
! [A: a > int,B: a] :
( ( binary1226383794sert_a @ A @ B @ binary476621312_Tip_a )
= ( binary717961607le_T_a @ binary476621312_Tip_a @ B @ binary476621312_Tip_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(216,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( B = C )
=> ( ord_less_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_ord__less__eq__trans) ).
thf(1134,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( B = C )
=> ( ord_less_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(322,axiom,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(1472,plain,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(108,axiom,
! [A: set_a] :
( ( sup_sup_set_a @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_sup__idem) ).
thf(754,plain,
! [A: set_a] :
( ( sup_sup_set_a @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(191,axiom,
( is_singleton_a
= ( ^ [A: set_a] :
? [B: a] :
( A
= ( insert_a @ B @ bot_bot_set_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_is__singleton__def) ).
thf(1049,plain,
( is_singleton_a
= ( ^ [A: set_a] :
? [B: a] :
( A
= ( insert_a @ B @ bot_bot_set_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(198,axiom,
( minus_minus_a_o
= ( ^ [A: a > $o,B: a > $o,C: a] : ( minus_minus_o @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_minus__apply) ).
thf(1081,plain,
( minus_minus_a_o
= ( ^ [A: a > $o,B: a > $o,C: a] : ( minus_minus_o @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(106,axiom,
! [A: set_a] :
~ ( ord_less_set_a @ A @ bot_bot_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_bot_Oextremum__strict) ).
thf(749,plain,
! [A: set_a] :
~ ( ord_less_set_a @ A @ bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(68,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( A = B )
=> ( ( ord_less_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_ord__eq__less__trans) ).
thf(617,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( A = B )
=> ( ( ord_less_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(37,axiom,
! [A: set_a] :
( ( A != bot_bot_set_a )
= ( ord_less_set_a @ bot_bot_set_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_bot_Onot__eq__extremum) ).
thf(516,plain,
! [A: set_a] :
( ( A != bot_bot_set_a )
= ( ord_less_set_a @ bot_bot_set_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(219,axiom,
! [A: binary1439146945Tree_a,B: a,C: binary1439146945Tree_a] :
( ( binary945792244etOf_a @ ( binary717961607le_T_a @ A @ B @ C ) )
= ( sup_sup_set_a @ ( sup_sup_set_a @ ( binary945792244etOf_a @ A ) @ ( binary945792244etOf_a @ C ) ) @ ( insert_a @ B @ bot_bot_set_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_setOf_Osimps_I2_J) ).
thf(1145,plain,
! [A: binary1439146945Tree_a,B: a,C: binary1439146945Tree_a] :
( ( binary945792244etOf_a @ ( binary717961607le_T_a @ A @ B @ C ) )
= ( sup_sup_set_a @ ( sup_sup_set_a @ ( binary945792244etOf_a @ A ) @ ( binary945792244etOf_a @ C ) ) @ ( insert_a @ B @ bot_bot_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(180,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( sup_sup_a_o @ ( sup_sup_a_o @ A @ B ) @ C )
= ( sup_sup_a_o @ A @ ( sup_sup_a_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_sup__assoc) ).
thf(1018,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( sup_sup_a_o @ ( sup_sup_a_o @ A @ B ) @ C )
= ( sup_sup_a_o @ A @ ( sup_sup_a_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(23,axiom,
! [A: a] :
( ( the_a
@ ^ [B: a] : ( B = A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_the__eq__trivial) ).
thf(458,plain,
! [A: a] :
( ( the_a
@ ^ [B: a] : ( B = A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(228,axiom,
( minus_minus_a_o
= ( ^ [A: a > $o,B: a > $o,C: a] : ( minus_minus_o @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_fun__diff__def) ).
thf(1181,plain,
( minus_minus_a_o
= ( ^ [A: a > $o,B: a > $o,C: a] : ( minus_minus_o @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(49,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ord_less_set_a @ A @ ( sup_sup_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_less__supI1) ).
thf(557,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ord_less_set_a @ A @ ( sup_sup_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(56,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_less__trans) ).
thf(580,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(75,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( sup_sup_a_o @ A @ ( sup_sup_a_o @ B @ C ) )
= ( sup_sup_a_o @ B @ ( sup_sup_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_sup__left__commute) ).
thf(640,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( sup_sup_a_o @ A @ ( sup_sup_a_o @ B @ C ) )
= ( sup_sup_a_o @ B @ ( sup_sup_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(222,axiom,
! [A: set_a,B: a,C: set_a] :
( ( minus_minus_set_a @ A @ ( insert_a @ B @ C ) )
= ( minus_minus_set_a @ ( minus_minus_set_a @ A @ C ) @ ( insert_a @ B @ bot_bot_set_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_Diff__insert) ).
thf(1156,plain,
! [A: set_a,B: a,C: set_a] :
( ( minus_minus_set_a @ A @ ( insert_a @ B @ C ) )
= ( minus_minus_set_a @ ( minus_minus_set_a @ A @ C ) @ ( insert_a @ B @ bot_bot_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(243,axiom,
! [A: a,B: a,C: set_a] :
( ( insert_a @ A @ ( insert_a @ B @ C ) )
= ( insert_a @ B @ ( insert_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_insert__commute) ).
thf(1225,plain,
! [A: a,B: a,C: set_a] :
( ( insert_a @ A @ ( insert_a @ B @ C ) )
= ( insert_a @ B @ ( insert_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(168,axiom,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( A
= ( sup_sup_set_a @ B @ C ) )
=> ( ( sup_sup_set_a @ A @ D )
= ( sup_sup_set_a @ B @ ( sup_sup_set_a @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_boolean__algebra__cancel_Osup1) ).
thf(971,plain,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( A
= ( sup_sup_set_a @ B @ C ) )
=> ( ( sup_sup_set_a @ A @ D )
= ( sup_sup_set_a @ B @ ( sup_sup_set_a @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(288,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( minus_minus_set_a @ B @ C ) )
= ( ( member_a @ A @ B )
& ~ ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_Diff__iff) ).
thf(1368,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( minus_minus_set_a @ B @ C ) )
= ( ( member_a @ A @ B )
& ~ ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(258,axiom,
! [A: a,B: a,C: set_a] :
( ( member_a @ A @ ( insert_a @ B @ C ) )
=> ( ( A != B )
=> ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_insertE) ).
thf(1267,plain,
! [A: a,B: a,C: set_a] :
( ( member_a @ A @ ( insert_a @ B @ C ) )
=> ( ( A != B )
=> ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(84,axiom,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_ord__less__eq__subst) ).
thf(673,plain,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(311,axiom,
( pairwise_a
= ( ^ [A: a > a > $o,B: set_a] :
! [C: a] :
( ( member_a @ C @ B )
=> ! [D: a] :
( ( member_a @ D @ ( minus_minus_set_a @ B @ ( insert_a @ C @ bot_bot_set_a ) ) )
=> ( A @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_pairwise__alt) ).
thf(1432,plain,
( pairwise_a
= ( ^ [A: a > a > $o,B: set_a] :
! [C: a] :
( ( member_a @ C @ B )
=> ! [D: a] :
( ( member_a @ D @ ( minus_minus_set_a @ B @ ( insert_a @ C @ bot_bot_set_a ) ) )
=> ( A @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(267,axiom,
! [A: a > int,B: binary1439146945Tree_a,C: a] :
( ( binary1721989714Tree_a @ A @ B )
=> ( ( binary2053421120memb_a @ A @ C @ B )
= ( member_a @ C @ ( binary945792244etOf_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_memb__spec) ).
thf(1300,plain,
! [A: a > int,B: binary1439146945Tree_a,C: a] :
( ( binary1721989714Tree_a @ A @ B )
=> ( ( binary2053421120memb_a @ A @ C @ B )
= ( member_a @ C @ ( binary945792244etOf_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(20,axiom,
! [A: a > $o] :
( ? [B: a] :
( ( A @ B )
& ! [C: a] :
( ( A @ C )
=> ( C = B ) ) )
=> ( A @ ( the_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_theI_H) ).
thf(441,plain,
! [A: a > $o] :
( ? [B: a] :
( ( A @ B )
& ! [C: a] :
( ( A @ C )
=> ( C = B ) ) )
=> ( A @ ( the_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(187,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( sup_sup_a_o @ ( sup_sup_a_o @ A @ B ) @ C )
= ( sup_sup_a_o @ A @ ( sup_sup_a_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_inf__sup__aci_I6_J) ).
thf(1038,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( sup_sup_a_o @ ( sup_sup_a_o @ A @ B ) @ C )
= ( sup_sup_a_o @ A @ ( sup_sup_a_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(96,axiom,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_set_a @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_order__less__subst2) ).
thf(717,plain,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_set_a @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(33,axiom,
! [A: a > $o] :
( ( ( collect_a @ A )
= bot_bot_set_a )
= ( ! [B: a] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_Collect__empty__eq) ).
thf(502,plain,
! [A: a > $o] :
( ( ( collect_a @ A )
= bot_bot_set_a )
= ( ! [B: a] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(256,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( minus_minus_set_a @ B @ C ) )
=> ( member_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_DiffD1) ).
thf(1262,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( minus_minus_set_a @ B @ C ) )
=> ( member_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(25,axiom,
! [A: set_a] :
( ( sup_sup_set_a @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_sup_Oidem) ).
thf(463,plain,
! [A: set_a] :
( ( sup_sup_set_a @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(125,axiom,
! [A: a] :
( ( collect_a @ ( (=) @ a @ A ) )
= ( insert_a @ A @ bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_singleton__conv2) ).
thf(808,plain,
! [A: a] :
( ( collect_a @ ( (=) @ a @ A ) )
= ( insert_a @ A @ bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(76,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_a_o @ A @ B )
=> ( ord_less_a_o @ A @ ( sup_sup_a_o @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_less__supI2) ).
thf(643,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_a_o @ A @ B )
=> ( ord_less_a_o @ A @ ( sup_sup_a_o @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(3,axiom,
! [A: int,B: int] :
( ~ ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ A @ B )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_antisym__conv1) ).
thf(331,plain,
! [A: int,B: int] :
( ~ ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ A @ B )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(230,axiom,
! [A: int,B: int] :
( ~ ( ord_less_int @ A @ B )
=> ( ( A != B )
=> ( ord_less_int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_linorder__cases) ).
thf(1186,plain,
! [A: int,B: int] :
( ~ ( ord_less_int @ A @ B )
=> ( ( A != B )
=> ( ord_less_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(261,axiom,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_empty__iff) ).
thf(1284,plain,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(284,axiom,
! [A: set_a] :
( ( A != bot_bot_set_a )
=> ( ! [B: a,C: a] :
( ( member_a @ B @ A )
=> ( ( member_a @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_is__singletonI_H) ).
thf(1353,plain,
! [A: set_a] :
( ( A != bot_bot_set_a )
=> ( ! [B: a,C: a] :
( ( member_a @ B @ A )
=> ( ( member_a @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(203,axiom,
( bot_bot_a_o
= ( ^ [A: a] : bot_bot_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_bot__fun__def) ).
thf(1094,plain,
( bot_bot_a_o
= ( ^ [A: a] : bot_bot_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(178,axiom,
! [A: a > int,B: a,C: a,D: binary1439146945Tree_a] : ( binary670562003pred_a @ A @ B @ C @ D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_sorted__distinct) ).
thf(1008,plain,
! [A: a > int,B: a,C: a,D: binary1439146945Tree_a] : ( binary670562003pred_a @ A @ B @ C @ D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(307,axiom,
( insert_a
= ( ^ [A: a,B: set_a] :
( collect_a
@ ^ [C: a] :
( ( C = A )
| ( member_a @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_insert__compr) ).
thf(1421,plain,
( insert_a
= ( ^ [A: a,B: set_a] :
( collect_a
@ ^ [C: a] :
( ( C = A )
| ( member_a @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(71,axiom,
! [A: set_a] :
( ( is_singleton_a @ A )
=> ~ ! [B: a] :
( A
!= ( insert_a @ B @ bot_bot_set_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_is__singletonE) ).
thf(627,plain,
! [A: set_a] :
( ( is_singleton_a @ A )
=> ~ ! [B: a] :
( A
!= ( insert_a @ B @ bot_bot_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(83,axiom,
! [A: int] :
? [B: int] : ( ord_less_int @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_lt__ex) ).
thf(671,plain,
! [A: int] :
? [B: int] : ( ord_less_int @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(274,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ B )
=> ( ~ ( member_a @ A @ C )
=> ( member_a @ A @ ( minus_minus_set_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_DiffI) ).
thf(1321,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ B )
=> ( ~ ( member_a @ A @ C )
=> ( member_a @ A @ ( minus_minus_set_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(169,axiom,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( ord_less_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_order__less__subst1) ).
thf(976,plain,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( ord_less_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(40,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_less__asym_H) ).
thf(524,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(110,axiom,
! [A: int,B: int] :
( ( ~ ( ord_less_int @ A @ B ) )
= ( ( ord_less_int @ B @ A )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_not__less__iff__gr__or__eq) ).
thf(759,plain,
! [A: int,B: int] :
( ( ~ ( ord_less_int @ A @ B ) )
= ( ( ord_less_int @ B @ A )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(240,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( minus_minus_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( sup_sup_set_a @ ( minus_minus_set_a @ A @ C ) @ ( minus_minus_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_Un__Diff) ).
thf(1216,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( minus_minus_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( sup_sup_set_a @ ( minus_minus_set_a @ A @ C ) @ ( minus_minus_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(213,axiom,
( sup_sup_set_a
= ( ^ [A: set_a,B: set_a] : ( sup_sup_set_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_inf__sup__aci_I5_J) ).
thf(1126,plain,
( sup_sup_set_a
= ( ^ [A: set_a,B: set_a] : ( sup_sup_set_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(179,axiom,
! [A: a > $o,B: a] :
( ( ( A @ B )
=> ( ( collect_a
@ ^ [C: a] :
( ( C = B )
& ( A @ C ) ) )
= ( insert_a @ B @ bot_bot_set_a ) ) )
& ( ~ ( A @ B )
=> ( ( collect_a
@ ^ [C: a] :
( ( C = B )
& ( A @ C ) ) )
= bot_bot_set_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_Collect__conv__if) ).
thf(1010,plain,
! [A: a > $o,B: a] :
( ( ( A @ B )
=> ( ( collect_a
@ ^ [C: a] :
( ( C = B )
& ( A @ C ) ) )
= ( insert_a @ B @ bot_bot_set_a ) ) )
& ( ~ ( A @ B )
=> ( ( collect_a
@ ^ [C: a] :
( ( C = B )
& ( A @ C ) ) )
= bot_bot_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(208,axiom,
! [A: int,B: int,C: int] :
( ( A = B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_ord__eq__less__trans) ).
thf(1108,plain,
! [A: int,B: int,C: int] :
( ( A = B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(316,axiom,
! [A: a,B: set_a] :
( ( member_a @ A @ B )
=> ? [C: set_a] :
( ( B
= ( insert_a @ A @ C ) )
& ~ ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_mk__disjoint__insert) ).
thf(1448,plain,
! [A: a,B: set_a] :
( ( member_a @ A @ B )
=> ? [C: set_a] :
( ( B
= ( insert_a @ A @ C ) )
& ~ ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(231,axiom,
( is_empty_a
= ( ^ [A: set_a] : ( A = bot_bot_set_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_Set_Ois__empty__def) ).
thf(1189,plain,
( is_empty_a
= ( ^ [A: set_a] : ( A = bot_bot_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(134,axiom,
! [A: set_a,B: set_a] :
( ( ( minus_minus_set_a @ A @ B )
= bot_bot_set_a )
= ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_Diff__eq__empty__iff) ).
thf(844,plain,
! [A: set_a,B: set_a] :
( ( ( minus_minus_set_a @ A @ B )
= bot_bot_set_a )
= ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(317,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ B )
=> ( ( minus_minus_set_a @ ( insert_a @ A @ C ) @ B )
= ( minus_minus_set_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_insert__Diff1) ).
thf(1453,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ B )
=> ( ( minus_minus_set_a @ ( insert_a @ A @ C ) @ B )
= ( minus_minus_set_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(12,axiom,
! [A: int,B: int] :
( ( ~ ( ord_less_int @ A @ B ) )
= ( ord_less_eq_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_not__less) ).
thf(401,plain,
! [A: int,B: int] :
( ( ~ ( ord_less_int @ A @ B ) )
= ( ord_less_eq_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(118,axiom,
! [A: a] : ( is_singleton_a @ ( insert_a @ A @ bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_is__singletonI) ).
thf(781,plain,
! [A: a] : ( is_singleton_a @ ( insert_a @ A @ bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(58,axiom,
! [A: a > $o] :
( ( sup_sup_a_o @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_sup__idem) ).
thf(588,plain,
! [A: a > $o] :
( ( sup_sup_a_o @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(252,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( A != B )
=> ( ord_less_set_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_psubsetI) ).
thf(1253,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( A != B )
=> ( ord_less_set_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(127,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( sup_sup_a_o @ ( sup_sup_a_o @ A @ B ) @ C )
= ( sup_sup_a_o @ A @ ( sup_sup_a_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_sup_Oassoc) ).
thf(813,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( sup_sup_a_o @ ( sup_sup_a_o @ A @ B ) @ C )
= ( sup_sup_a_o @ A @ ( sup_sup_a_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(293,axiom,
( minus_minus_set_a
= ( ^ [A: set_a,B: set_a] :
( collect_a
@ ( minus_minus_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_minus__set__def) ).
thf(1385,plain,
( minus_minus_set_a
= ( ^ [A: set_a,B: set_a] :
( collect_a
@ ( minus_minus_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(15,axiom,
! [A: int,B: int,C: int > int,D: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_int @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ E @ F )
=> ( ord_less_eq_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_order__le__less__subst2) ).
thf(418,plain,
! [A: int,B: int,C: int > int,D: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_int @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ E @ F )
=> ( ord_less_eq_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(120,axiom,
! [A: a > int,B: a,C: a,D: binary1439146945Tree_a,E: binary1439146945Tree_a] :
( ( ( ord_less_int @ ( A @ B ) @ ( A @ C ) )
=> ( ( binary1226383794sert_a @ A @ B @ ( binary717961607le_T_a @ D @ C @ E ) )
= ( binary717961607le_T_a @ ( binary1226383794sert_a @ A @ B @ D ) @ C @ E ) ) )
& ( ~ ( ord_less_int @ ( A @ B ) @ ( A @ C ) )
=> ( ( ( ord_less_int @ ( A @ C ) @ ( A @ B ) )
=> ( ( binary1226383794sert_a @ A @ B @ ( binary717961607le_T_a @ D @ C @ E ) )
= ( binary717961607le_T_a @ D @ C @ ( binary1226383794sert_a @ A @ B @ E ) ) ) )
& ( ~ ( ord_less_int @ ( A @ C ) @ ( A @ B ) )
=> ( ( binary1226383794sert_a @ A @ B @ ( binary717961607le_T_a @ D @ C @ E ) )
= ( binary717961607le_T_a @ D @ B @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_binsert_Osimps_I2_J) ).
thf(786,plain,
! [A: a > int,B: a,C: a,D: binary1439146945Tree_a,E: binary1439146945Tree_a] :
( ( ( ord_less_int @ ( A @ B ) @ ( A @ C ) )
=> ( ( binary1226383794sert_a @ A @ B @ ( binary717961607le_T_a @ D @ C @ E ) )
= ( binary717961607le_T_a @ ( binary1226383794sert_a @ A @ B @ D ) @ C @ E ) ) )
& ( ~ ( ord_less_int @ ( A @ B ) @ ( A @ C ) )
=> ( ( ( ord_less_int @ ( A @ C ) @ ( A @ B ) )
=> ( ( binary1226383794sert_a @ A @ B @ ( binary717961607le_T_a @ D @ C @ E ) )
= ( binary717961607le_T_a @ D @ C @ ( binary1226383794sert_a @ A @ B @ E ) ) ) )
& ( ~ ( ord_less_int @ ( A @ C ) @ ( A @ B ) )
=> ( ( binary1226383794sert_a @ A @ B @ ( binary717961607le_T_a @ D @ C @ E ) )
= ( binary717961607le_T_a @ D @ B @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(184,axiom,
! [A: a > $o] :
~ ( ord_less_a_o @ A @ bot_bot_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_bot_Oextremum__strict) ).
thf(1030,plain,
! [A: a > $o] :
~ ( ord_less_a_o @ A @ bot_bot_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(269,axiom,
! [A: a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ ( insert_a @ A @ B ) @ C )
= ( ( member_a @ A @ C )
& ( ord_less_eq_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_insert__subset) ).
thf(1308,plain,
! [A: a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ ( insert_a @ A @ B ) @ C )
= ( ( member_a @ A @ C )
& ( ord_less_eq_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(233,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_less__imp__neq) ).
thf(1193,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(44,axiom,
! [A: int,B: set_a > int,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_ord__eq__less__subst) ).
thf(536,plain,
! [A: int,B: set_a > int,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(122,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_less__not__sym) ).
thf(800,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(175,axiom,
! [A: int] :
~ ( ord_less_int @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_less__irrefl) ).
thf(999,plain,
! [A: int] :
~ ( ord_less_int @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(107,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_order_Oasym) ).
thf(752,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(297,axiom,
( sup_sup_set_a
= ( ^ [A: set_a,B: set_a] :
( collect_a
@ ( sup_sup_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_sup__set__def) ).
thf(1395,plain,
( sup_sup_set_a
= ( ^ [A: set_a,B: set_a] :
( collect_a
@ ( sup_sup_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(292,axiom,
! [A: a,B: set_a] :
( ( member_a @ A @ B )
=> ~ ! [C: set_a] :
( ( B
= ( insert_a @ A @ C ) )
=> ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_Set_Oset__insert) ).
thf(1380,plain,
! [A: a,B: set_a] :
( ( member_a @ A @ B )
=> ~ ! [C: set_a] :
( ( B
= ( insert_a @ A @ C ) )
=> ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(220,axiom,
! [A: a > $o] :
( ( sup_sup_a_o @ bot_bot_a_o @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_sup__bot__left) ).
thf(1148,plain,
! [A: a > $o] :
( ( sup_sup_a_o @ bot_bot_a_o @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(140,axiom,
! [A: a] :
( ( the_elem_a @ ( insert_a @ A @ bot_bot_set_a ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_the__elem__eq) ).
thf(867,plain,
! [A: a] :
( ( the_elem_a @ ( insert_a @ A @ bot_bot_set_a ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(325,axiom,
! [A: a,B: set_a,C: set_a] :
( ~ ( member_a @ A @ B )
=> ( ~ ( member_a @ A @ C )
=> ( ( ( insert_a @ A @ B )
= ( insert_a @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_insert__ident) ).
thf(1480,plain,
! [A: a,B: set_a,C: set_a] :
( ~ ( member_a @ A @ B )
=> ( ~ ( member_a @ A @ C )
=> ( ( ( insert_a @ A @ B )
= ( insert_a @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(101,axiom,
! [A: a > $o,B: a > $o] :
( ( ( sup_sup_a_o @ A @ B )
= bot_bot_a_o )
= ( ( A = bot_bot_a_o )
& ( B = bot_bot_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_sup__bot_Oeq__neutr__iff) ).
thf(735,plain,
! [A: a > $o,B: a > $o] :
( ( ( sup_sup_a_o @ A @ B )
= bot_bot_a_o )
= ( ( A = bot_bot_a_o )
& ( B = bot_bot_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(51,axiom,
! [A: int,B: set_a > int,C: set_a,D: set_a] :
( ( ord_less_eq_int @ A @ ( B @ C ) )
=> ( ( ord_less_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_order__le__less__subst1) ).
thf(564,plain,
! [A: int,B: set_a > int,C: set_a,D: set_a] :
( ( ord_less_eq_int @ A @ ( B @ C ) )
=> ( ( ord_less_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(1,conjecture,
! [A: a] :
( ( member_a @ A @ ( binary504661350_eqs_a @ h @ e ) )
=> ( ( h @ A )
!= ( h @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ! [A: a] :
( ( member_a @ A @ ( binary504661350_eqs_a @ h @ e ) )
=> ( ( h @ A )
!= ( h @ x ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(326,plain,
~ ! [A: a] :
( ( member_a @ A @ ( binary504661350_eqs_a @ h @ e ) )
=> ( ( h @ A )
!= ( h @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(286,axiom,
( ( binary1721989714Tree_a @ h @ t1 )
=> ( ( binary945792244etOf_a @ ( binary1226383794sert_a @ h @ e @ t1 ) )
= ( sup_sup_set_a @ ( minus_minus_set_a @ ( binary945792244etOf_a @ t1 ) @ ( binary504661350_eqs_a @ h @ e ) ) @ ( insert_a @ e @ bot_bot_set_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_h1) ).
thf(1363,plain,
( ( binary1721989714Tree_a @ h @ t1 )
=> ( ( binary945792244etOf_a @ ( binary1226383794sert_a @ h @ e @ t1 ) )
= ( sup_sup_set_a @ ( minus_minus_set_a @ ( binary945792244etOf_a @ t1 ) @ ( binary504661350_eqs_a @ h @ e ) ) @ ( insert_a @ e @ bot_bot_set_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(18,axiom,
! [A: int,B: int] :
( ~ ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_leI) ).
thf(437,plain,
! [A: int,B: int] :
( ~ ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(73,axiom,
( sup_sup_a_o
= ( ^ [A: a > $o,B: a > $o,C: a] : ( sup_sup_o @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_sup__apply) ).
thf(635,plain,
( sup_sup_a_o
= ( ^ [A: a > $o,B: a > $o,C: a] : ( sup_sup_o @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(225,axiom,
! [A: a,B: set_a,C: set_a] :
( ( ( insert_a @ A @ bot_bot_set_a )
= ( sup_sup_set_a @ B @ C ) )
= ( ( ( B = bot_bot_set_a )
& ( C
= ( insert_a @ A @ bot_bot_set_a ) ) )
| ( ( B
= ( insert_a @ A @ bot_bot_set_a ) )
& ( C = bot_bot_set_a ) )
| ( ( B
= ( insert_a @ A @ bot_bot_set_a ) )
& ( C
= ( insert_a @ A @ bot_bot_set_a ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_singleton__Un__iff) ).
thf(1172,plain,
! [A: a,B: set_a,C: set_a] :
( ( ( insert_a @ A @ bot_bot_set_a )
= ( sup_sup_set_a @ B @ C ) )
= ( ( ( B = bot_bot_set_a )
& ( C
= ( insert_a @ A @ bot_bot_set_a ) ) )
| ( ( B
= ( insert_a @ A @ bot_bot_set_a ) )
& ( C = bot_bot_set_a ) )
| ( ( B
= ( insert_a @ A @ bot_bot_set_a ) )
& ( C
= ( insert_a @ A @ bot_bot_set_a ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(150,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_Un__subset__iff) ).
thf(897,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(185,axiom,
! [A: a > int,B: binary1439146945Tree_a,C: a,D: binary1439146945Tree_a] :
( ( binary1721989714Tree_a @ A @ ( binary717961607le_T_a @ B @ C @ D ) )
=> ( binary1721989714Tree_a @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_sortLemmaR) ).
thf(1033,plain,
! [A: a > int,B: binary1439146945Tree_a,C: a,D: binary1439146945Tree_a] :
( ( binary1721989714Tree_a @ A @ ( binary717961607le_T_a @ B @ C @ D ) )
=> ( binary1721989714Tree_a @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(234,axiom,
! [A: a > int,B: binary1439146945Tree_a,C: a,D: binary1439146945Tree_a] :
( ( binary1721989714Tree_a @ A @ ( binary717961607le_T_a @ B @ C @ D ) )
=> ( binary1721989714Tree_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_sortLemmaL) ).
thf(1197,plain,
! [A: a > int,B: binary1439146945Tree_a,C: a,D: binary1439146945Tree_a] :
( ( binary1721989714Tree_a @ A @ ( binary717961607le_T_a @ B @ C @ D ) )
=> ( binary1721989714Tree_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(146,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( A = B )
| ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_less__linear) ).
thf(886,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( A = B )
| ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(161,axiom,
! [A: set_a,B: int > set_a,C: int,D: int] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_order__le__less__subst1) ).
thf(928,plain,
! [A: set_a,B: int > set_a,C: int,D: int] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(99,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_order_Ostrict__implies__not__eq) ).
thf(728,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(136,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_inf__sup__aci_I6_J) ).
thf(850,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(89,axiom,
! [A: int,B: int,C: $o] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ B @ A )
=> C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_less__imp__triv) ).
thf(691,plain,
! [A: int,B: int,C: $o] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ B @ A )
=> C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(299,axiom,
! [A: a] : ( member_a @ A @ ( insert_a @ A @ bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_singletonI) ).
thf(1399,plain,
! [A: a] : ( member_a @ A @ ( insert_a @ A @ bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(70,axiom,
! [A: a,B: a > $o] :
( ( insert_a @ A @ ( collect_a @ B ) )
= ( collect_a
@ ^ [C: a] :
( ( C != A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_insert__Collect) ).
thf(624,plain,
! [A: a,B: a > $o] :
( ( insert_a @ A @ ( collect_a @ B ) )
= ( collect_a
@ ^ [C: a] :
( ( C != A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(133,axiom,
! [A: int,B: int > int,C: int,D: int] :
( ( ord_less_int @ A @ ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_order__less__subst1) ).
thf(839,plain,
! [A: int,B: int > int,C: int,D: int] :
( ( ord_less_int @ A @ ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(278,axiom,
! [A: a,B: set_a,C: set_a] :
( ( ( member_a @ A @ B )
=> ( ( minus_minus_set_a @ ( insert_a @ A @ C ) @ B )
= ( minus_minus_set_a @ C @ B ) ) )
& ( ~ ( member_a @ A @ B )
=> ( ( minus_minus_set_a @ ( insert_a @ A @ C ) @ B )
= ( insert_a @ A @ ( minus_minus_set_a @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_insert__Diff__if) ).
thf(1331,plain,
! [A: a,B: set_a,C: set_a] :
( ( ( member_a @ A @ B )
=> ( ( minus_minus_set_a @ ( insert_a @ A @ C ) @ B )
= ( minus_minus_set_a @ C @ B ) ) )
& ( ~ ( member_a @ A @ B )
=> ( ( minus_minus_set_a @ ( insert_a @ A @ C ) @ B )
= ( insert_a @ A @ ( minus_minus_set_a @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(29,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ~ ( ord_less_set_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_leD) ).
thf(486,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ~ ( ord_less_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(164,axiom,
! [A: a > $o] :
( ( ( collect_a @ A )
= bot_bot_set_a )
= ( A = bot_bot_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_Collect__empty__eq__bot) ).
thf(940,plain,
! [A: a > $o] :
( ( ( collect_a @ A )
= bot_bot_set_a )
= ( A = bot_bot_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(5,axiom,
( ord_less_eq_int
= ( ^ [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_le__less) ).
thf(354,plain,
( ord_less_eq_int
= ( ^ [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(160,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( B = C )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_ord__less__eq__trans) ).
thf(923,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( B = C )
=> ( ord_less_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(31,axiom,
! [A: set_a,B: int > set_a,C: int,D: int] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_ord__eq__less__subst) ).
thf(491,plain,
! [A: set_a,B: int > set_a,C: int,D: int] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(196,axiom,
! [A: binary1439146945Tree_a,B: a,C: binary1439146945Tree_a,D: binary1439146945Tree_a,E: a,F: binary1439146945Tree_a] :
( ( ( binary717961607le_T_a @ A @ B @ C )
= ( binary717961607le_T_a @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_Tree_Oinject) ).
thf(1069,plain,
! [A: binary1439146945Tree_a,B: a,C: binary1439146945Tree_a,D: binary1439146945Tree_a,E: a,F: binary1439146945Tree_a] :
( ( ( binary717961607le_T_a @ A @ B @ C )
= ( binary717961607le_T_a @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(95,axiom,
! [A: int,B: int > int,C: int,D: int] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_ord__eq__less__subst) ).
thf(708,plain,
! [A: int,B: int > int,C: int,D: int] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(305,axiom,
( binary670562003pred_a
= ( ^ [A: a > int,B: a,C: a,D: binary1439146945Tree_a] :
( ( ( binary1721989714Tree_a @ A @ D )
& ( member_a @ B @ ( binary945792244etOf_a @ D ) )
& ( member_a @ C @ ( binary945792244etOf_a @ D ) )
& ( ( A @ B )
= ( A @ C ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_sorted__distinct__pred__def) ).
thf(1417,plain,
( binary670562003pred_a
= ( ^ [A: a > int,B: a,C: a,D: binary1439146945Tree_a] :
( ( ( binary1721989714Tree_a @ A @ D )
& ( member_a @ B @ ( binary945792244etOf_a @ D ) )
& ( member_a @ C @ ( binary945792244etOf_a @ D ) )
& ( ( A @ B )
= ( A @ C ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(116,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_sup_Oassoc) ).
thf(775,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(50,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
=> ~ ( ( ord_less_set_a @ A @ C )
=> ~ ( ord_less_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_sup_Ostrict__boundedE) ).
thf(560,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
=> ~ ( ( ord_less_set_a @ A @ C )
=> ~ ( ord_less_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(1503,plain,
$false,
inference(e,[status(thm)],[892,1411,1168,1105,1237,909,1315,1295,1083,468,1200,762,1005,1290,994,1401,741,1205,1142,614,597,1437,1041,533,500,797,1327,1222,1342,913,1441,1046,1475,1366,1265,1228,829,404,1287,1298,702,802,1313,1191,902,853,870,770,1362,606,1347,1415,591,646,834,1151,574,966,1183,1051,905,687,1377,877,1072,396,1242,602,981,452,529,381,1311,1057,512,439,334,1387,746,1123,1021,778,1423,916,847,361,1178,665,1457,889,757,1281,1392,583,522,1159,461,682,1407,551,1128,1350,519,874,1328,1121,725,1425,1096,356,989,1397,697,1089,1234,1270,1259,783,1118,471,1028,488,933,554,1461,637,1214,706,1419,1414,526,622,997,1099,1249,738,1231,1060,1002,569,1324,393,1131,654,984,911,1434,1318,805,508,921,1035,1026,662,1086,938,765,1054,856,689,1374,1219,824,819,423,694,732,1389,772,743,577,413,1256,545,1428,572,1371,611,1239,919,1258,391,1139,466,1092,1464,947,1209,900,599,1175,880,649,1043,811,631,1339,858,816,609,594,700,895,1344,943,1293,668,685,768,1245,1445,1113,1477,1102,505,455,883,722,1304,426,1203,1467,548,1134,1472,754,1049,1081,749,617,516,1145,1018,458,1181,557,580,640,1156,1225,971,1368,1267,673,1432,1300,441,1038,717,502,1262,463,808,643,331,1186,1284,1353,1094,1008,1421,627,671,1321,976,524,759,1216,1126,1010,1108,1448,1189,844,1453,401,781,588,1253,813,1385,418,786,1030,1308,1193,536,800,999,752,1395,1380,1148,867,1480,735,564,326,1363,437,635,1172,897,1033,1197,886,928,728,850,691,1399,624,839,1331,486,940,354,923,491,1069,708,1417,775,560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP031^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.11/0.21 % Computer : n005.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 19:38:31 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.88/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.33/1.23 % [INFO] Parsing done (444ms).
% 2.33/1.26 % [INFO] Running in sequential loop mode.
% 3.72/1.67 % [INFO] eprover registered as external prover.
% 3.72/1.68 % [INFO] Scanning for conjecture ...
% 4.19/1.82 % [INFO] Found a conjecture (or negated_conjecture) and 358 axioms. Running axiom selection ...
% 4.39/1.98 % [INFO] Axiom selection finished. Selected 323 axioms (removed 35 axioms).
% 5.38/2.25 % [INFO] Problem is higher-order (TPTP THF).
% 5.38/2.28 % [INFO] Type checking passed.
% 5.38/2.29 % [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 ...
% 21.00/6.41 % External prover 'e' found a proof!
% 21.00/6.41 % [INFO] Killing All external provers ...
% 21.00/6.41 % Time passed: 6061ms (effective reasoning time: 5144ms)
% 21.00/6.41 % 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)>
% 21.00/6.41 % Axioms used in derivation (323): fact_107_sup__bot_Oright__neutral, fact_79_DiffD1, fact_287_bot__empty__eq, fact_292_remove__def, fact_193_sup_Ostrict__coboundedI1, fact_117_bot__eq__sup__iff, fact_51_DiffI, fact_136_sup__left__idem, fact_323_empty__subsetI, fact_352_le__neq__trans, fact_42_insert__iff, fact_118_sup__bot__right, fact_199_bot__apply, fact_95_Un__Diff, fact_89_doubleton__eq__iff, fact_30_Un__Diff__cancel2, fact_56_equals0I, fact_84_Collect__disj__eq, fact_340_order__le__less__subst1, fact_5_s, fact_115_sup__eq__bot__iff, fact_209_is__singleton__the__elem, fact_4_s2, fact_9_eqs__def, fact_31_Diff__insert0, fact_324_subset__empty, fact_174_sup_Oleft__commute, fact_305_theI, fact_111_sup__bot_Oleft__neutral, fact_350_not__le, fact_208_minus__set__def, fact_128_sup__idem, fact_281_bot_Oextremum__strict, fact_121_sup__bot__left, fact_134_sup__left__idem, fact_336_less__le, fact_80_DiffE, fact_137_sup_Oright__idem, fact_73_ball__Un, fact_3_s1, fact_88_insert__not__empty, fact_345_order__le__less__subst2, fact_267_ord__less__eq__subst, fact_70_Un__commute, fact_52_singletonI, fact_12__092_060open_062sortedTree_Ah_ATip_A_092_060longrightarrow_062_AsetOf_A_Ibinsert_Ah_Ae_ATip_J_A_061_AsetOf_ATip_A_N_Aeqs_Ah_Ae_A_092_060union_062_A_123e_125_092_060close_062, fact_41_insert__absorb2, fact_125_sup_Oidem, fact_15_setOf_Osimps_I1_J, fact_165_sup__assoc, fact_346_order__less__le__subst1, fact_239_ord__eq__less__trans, fact_304_the__equality, fact_14_setOf_Osimps_I2_J, fact_237_ord__less__eq__trans, fact_196_sup_Ostrict__coboundedI2, fact_257_lt__ex, fact_54_Diff__cancel, fact_227_less__imp__triv, fact_243_less__linear, fact_151_inf__sup__aci_I6_J, fact_317_sup_Obounded__iff, fact_241_less__irrefl, fact_234_less__imp__not__eq, fact_35_Diff__empty, fact_60_insert__commute, fact_145_inf__sup__aci_I8_J, fact_154_inf__sup__aci_I5_J, fact_176_sup_Oleft__commute, fact_100_Un__singleton__iff, fact_331_leD, fact_146_inf__sup__aci_I7_J, fact_81_empty__def, fact_159_boolean__algebra__cancel_Osup2, fact_310_the1__equality, fact_298_Tree_Oset__cases, fact_223_dual__order_Oirrefl, fact_229_less__imp__not__eq2, fact_112_sup__bot_Oeq__neutr__iff, fact_343_order__le__less__subst2, fact_311_psubset__insert__iff, fact_2_res, fact_231_less__not__sym, fact_87_singleton__inject, fact_235_dual__order_Oasym, fact_248_less__asym, fact_127_sup_Oidem, fact_342_order__le__less__subst2, fact_316_subsetI, fact_85_Un__def, fact_143_inf__sup__aci_I8_J, fact_24_Tree_Oexhaust, fact_216_dual__order_Ostrict__trans, fact_21_sortLemmaL, fact_119_sup__bot__right, fact_354_antisym__conv2, fact_313_order__refl, fact_149_inf__sup__aci_I6_J, fact_280_bot_Onot__eq__extremum, fact_161_boolean__algebra__cancel_Osup2, fact_344_order__le__less__subst2, fact_306_theI_H, fact_282_bot_Oextremum__strict, fact_253_order_Oasym, fact_108_sup__bot_Oneutr__eq__iff, fact_179_sup__left__commute, fact_286_sup__Un__eq, fact_198_the__elem__eq, fact_325_insert__subset, fact_214_order_Ostrict__implies__not__eq, fact_187_sup_Ostrict__boundedE, fact_57_equals0D, fact_236_dual__order_Oasym, fact_46_Collect__mem__eq, fact_273_ord__eq__less__subst, fact_68_Un__left__commute, fact_335_le__less, fact_233_less__imp__not__eq, fact_171_sup__commute, fact_228_less__imp__not__eq2, fact_10_h1, fact_251_less__imp__neq, fact_217_dual__order_Ostrict__trans, fact_19_sortedTree_Osimps_I2_J, fact_20_sortedTree_Osimps_I1_J, fact_190_sup_Ostrict__order__iff, fact_130_sup__idem, fact_319_sup_Obounded__iff, fact_96_Collect__conv__if2, fact_288_Collect__empty__eq__bot, fact_212_dual__order_Ostrict__implies__not__eq, fact_300_Set_Ois__empty__def, fact_259_order__less__subst2, fact_18_binsert_Osimps_I1_J, fact_294_member__remove, fact_295_Tree_Oset__intros_I3_J, fact_353_antisym__conv1, fact_32_insert__Diff1, fact_299_Tree_Osimps_I14_J, fact_106_sup__bot_Oright__neutral, fact_38_Collect__empty__eq, fact_189_sup_Ostrict__order__iff, fact_101_insert__is__Un, fact_297_Tree_Oset__intros_I1_J, fact_262_order__less__subst1, fact_44_Un__iff, fact_245_less__trans, fact_326_Un__subset__iff, fact_11_h2, fact_105_Diff__insert, fact_78_DiffD2, fact_266_ord__less__eq__subst, fact_7_c1, fact_272_ord__eq__less__subst, fact_332_leD, fact_82_insert__Collect, fact_97_Collect__conv__if, fact_36_empty__Diff, fact_293_Tree_Osimps_I15_J, fact_65_insertI2, fact_341_order__le__less__subst1, fact_333_leI, fact_28_singleton__conv2, fact_264_order__less__subst1, fact_220_less__imp__not__less, fact_296_Tree_Oset__intros_I2_J, fact_45_mem__Collect__eq, fact_173_sup__commute, fact_92_Un__empty__right, fact_63_insert__ident, fact_122_memb__spec, fact_277_is__singleton__def, fact_202_sup1CI, fact_71_Un__absorb, fact_315_subset__antisym, fact_140_bot__set__def, fact_93_Un__empty__left, fact_320_le__sup__iff, fact_206_not__psubset__empty, fact_181_less__supI1, fact_27_singleton__conv, fact_303_the__eq__trivial, fact_274_bot__fun__def, fact_142_fun__diff__def, fact_180_less__supI1, fact_162_sup_Oassoc, fact_314_order__refl, fact_250_less__imp__neq, fact_69_Un__left__absorb, fact_102_Diff__insert__absorb, fact_289_psubset__trans, fact_23_Tree_Oinduct, fact_347_order__less__le__subst1, fact_339_order__le__less__subst1, fact_16_Tree_Odistinct_I1_J, fact_247_less__asym_H, fact_47_Collect__cong, fact_148_inf__sup__aci_I7_J, fact_186_sup_Ostrict__boundedE, fact_213_order_Ostrict__implies__not__eq, fact_39_all__not__in__conv, fact_75_UnI2, fact_330_Diff__eq__empty__iff, fact_58_emptyE, fact_338_order__le__less__subst1, fact_328_singleton__insert__inj__eq_H, fact_49_Diff__idemp, fact_252_order_Oasym, fact_200_is__singletonI, fact_261_order__less__subst2, fact_76_UnI1, fact_184_less__supI2, fact_270_ord__eq__less__subst, fact_1_eLess, fact_33_Un__insert__left, fact_263_order__less__subst1, fact_271_ord__eq__less__subst, fact_124_sup__apply, fact_224_dual__order_Oirrefl, fact_94_insert__Diff__if, fact_17_binsert_Osimps_I2_J, fact_131_sup_Oleft__idem, fact_6_sorted__distinct, fact_290_less__set__def, fact_329_singleton__insert__inj__eq, fact_116_bot__eq__sup__iff, fact_99_singleton__Un__iff, fact_256_gt__ex, fact_195_sup_Ostrict__coboundedI2, fact_218_linorder__less__wlog, fact_254_neq__iff, fact_29_Un__Diff__cancel, fact_67_insertE, fact_13_Tree_Oinject, fact_242_less__irrefl, fact_225_linorder__cases, fact_48_UnCI, fact_25_sorted__distinct__pred__def, fact_139_sup_Oright__idem, fact_61_insert__eq__iff, fact_133_sup_Oleft__idem, fact_90_singleton__iff, fact_22_sortLemmaR, fact_203_sup1E, fact_337_less__le, fact_72_Un__assoc, fact_167_sup__assoc, fact_109_sup__bot_Oneutr__eq__iff, fact_0_eqsLessX, fact_205_sup1I2, fact_307_theI2, fact_278_is__singletonE, fact_348_order__less__le__subst1, fact_192_sup_Ostrict__coboundedI1, fact_232_less__not__sym, fact_268_ord__less__eq__subst, fact_164_sup_Oassoc, fact_53_Un__empty, fact_207_psubset__imp__ex__mem, fact_238_ord__less__eq__trans, fact_26_insert__Diff__single, fact_158_boolean__algebra__cancel_Osup1, fact_349_order__less__le__subst2, fact_50_Diff__iff, fact_74_bex__Un, fact_210_is__singletonI_H, fact_91_singletonD, fact_230_antisym__conv3, fact_104_insert__Diff, fact_177_sup__left__commute, fact_291_psubsetD, fact_123_minus__apply, fact_83_insert__compr, fact_219_less__imp__not__less, fact_351_not__less, fact_312_pairwise__alt, fact_244_less__trans, fact_86_set__diff__eq, fact_226_less__imp__triv, fact_215_not__less__iff__gr__or__eq, fact_77_UnE, fact_8_c2, fact_62_insert__absorb, fact_168_sup_Ocommute, fact_66_insertI1, fact_98_insert__def, fact_265_order__less__subst1, fact_113_sup__bot_Oeq__neutr__iff, fact_34_Un__insert__right, fact_249_less__asym, fact_155_sup__fun__def, fact_279_bot_Onot__eq__extremum, fact_110_sup__bot_Oleft__neutral, fact_301_the__elem__def, fact_309_the1I2, fact_156_boolean__algebra__cancel_Osup1, fact_141_sup__set__def, fact_170_sup_Ocommute, fact_269_ord__less__eq__subst, fact_260_order__less__subst2, fact_114_sup__eq__bot__iff, fact_103_Diff__insert2, fact_240_ord__eq__less__trans, fact_222_order_Ostrict__trans, fact_221_order_Ostrict__trans, fact_258_order__less__subst2, fact_152_inf__sup__aci_I5_J, fact_327_psubsetI, fact_302_the__sym__eq__trivial, fact_43_insertCI, fact_40_empty__iff, fact_37_empty__Collect__eq, fact_55_ex__in__conv, fact_211_dual__order_Ostrict__implies__not__eq, fact_120_sup__bot__left, fact_322_le__sup__iff, fact_246_less__asym_H, fact_183_less__supI2, fact_255_neqE, fact_59_mk__disjoint__insert, fact_204_sup1I1, fact_334_le__less, fact_64_Set_Oset__insert
% 21.00/6.41 % No. of inferences in proof: 650
% 21.00/6.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6061 ms resp. 5144 ms w/o parsing
% 22.42/6.72 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 22.42/6.73 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------