%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP034^1 : 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 : n026.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 08:06:30 AM UTC 2026
% Result : Theorem 15.27s 5.15s
% Output : Refutation 15.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 257
% Syntax : Number of formulae : 516 ( 288 unt; 0 typ; 0 def)
% Number of atoms : 1222 ( 556 equ; 4 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 3755 ( 134 ~; 34 |; 130 &;3055 @)
% ( 0 <=>; 402 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 110 ( 110 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 8 con; 0-4 aty)
% Number of variables : 1362 ( 126 ^;1174 !; 62 ?;1362 :)
% 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(binary1226383794sert_a_decl,type,
binary1226383794sert_a: ( a > int ) > a > binary1439146945Tree_a > binary1439146945Tree_a ).
thf(binary2053421120memb_a_decl,type,
binary2053421120memb_a: ( a > int ) > a > binary1439146945Tree_a > $o ).
thf(binary1804682569move_a_decl,type,
binary1804682569move_a: ( a > int ) > a > binary1439146945Tree_a > binary1439146945Tree_a ).
thf(binary339557810e_rm_a_decl,type,
binary339557810e_rm_a: ( a > int ) > binary1439146945Tree_a > a ).
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(binary1217730267_wrm_a_decl,type,
binary1217730267_wrm_a: ( a > int ) > binary1439146945Tree_a > binary1439146945Tree_a ).
thf(sup_sup_int_decl,type,
sup_sup_int: int > int > int ).
thf(sup_sup_set_a_decl,type,
sup_sup_set_a: set_a > set_a > set_a ).
thf(bot_bot_set_a_decl,type,
bot_bot_set_a: set_a ).
thf(ord_less_int_decl,type,
ord_less_int: int > int > $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(the_elem_a_decl,type,
the_elem_a: set_a > a ).
thf(member_a_decl,type,
member_a: a > set_a > $o ).
thf(h_decl,type,
h: a > int ).
thf(l_decl,type,
l: a ).
thf(t1_decl,type,
t1: binary1439146945Tree_a ).
thf(t2_decl,type,
t2: binary1439146945Tree_a ).
thf(x_decl,type,
x: a ).
thf(130,axiom,
! [A: int,B: int] :
( ( sup_sup_int @ A @ ( sup_sup_int @ A @ B ) )
= ( sup_sup_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_sup__left__idem) ).
thf(645,plain,
! [A: int,B: int] :
( ( sup_sup_int @ A @ ( sup_sup_int @ A @ B ) )
= ( sup_sup_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(185,axiom,
( sup_sup_int
= ( ^ [A: int,B: int] : ( sup_sup_int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_inf__sup__aci_I5_J) ).
thf(809,plain,
( sup_sup_int
= ( ^ [A: int,B: int] : ( sup_sup_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(235,axiom,
( ord_less_int
= ( ^ [A: int,B: int] :
( ( B
= ( sup_sup_int @ B @ A ) )
& ( B != A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_sup_Ostrict__order__iff) ).
thf(1024,plain,
( ord_less_int
= ( ^ [A: int,B: int] :
( ( B
= ( sup_sup_int @ B @ A ) )
& ( B != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(41,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_125_insert__Collect) ).
thf(365,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)],[41]) ).
thf(197,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_130_doubleton__eq__iff) ).
thf(846,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)],[197]) ).
thf(238,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_int @ A @ ( sup_sup_int @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_less__supI2) ).
thf(1031,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_int @ A @ ( sup_sup_int @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(210,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_126_Un__def) ).
thf(893,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)],[210]) ).
thf(90,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_171_sup_Oright__idem) ).
thf(518,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)],[90]) ).
thf(57,axiom,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_Collect__mono) ).
thf(408,plain,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(204,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_111_mk__disjoint__insert) ).
thf(873,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)],[204]) ).
thf(205,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_209_sup_Ocommute) ).
thf(878,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)],[205]) ).
thf(7,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( B
= ( sup_sup_set_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_sup_OorderE) ).
thf(269,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( B
= ( sup_sup_set_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(48,axiom,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ C ) @ ( sup_sup_set_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_sup_Omono) ).
thf(385,plain,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ C ) @ ( sup_sup_set_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(83,axiom,
! [A: int,B: int] : ( ord_less_eq_int @ A @ ( sup_sup_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_sup__ge2) ).
thf(500,plain,
! [A: int,B: int] : ( ord_less_eq_int @ A @ ( sup_sup_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(75,axiom,
! [A: set_a] :
( ( sup_sup_set_a @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_sup_Oidem) ).
thf(472,plain,
! [A: set_a] :
( ( sup_sup_set_a @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(187,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_234_inf__sup__aci_I8_J) ).
thf(814,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)],[187]) ).
thf(31,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_subset__eq) ).
thf(340,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(220,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ( C != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_pinf_I3_J) ).
thf(930,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ( C != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(138,axiom,
! [A: int,B: int,C: int,D: int] :
( ( A
= ( sup_sup_int @ B @ C ) )
=> ( ( sup_sup_int @ A @ D )
= ( sup_sup_int @ B @ ( sup_sup_int @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_boolean__algebra__cancel_Osup1) ).
thf(670,plain,
! [A: int,B: int,C: int,D: int] :
( ( A
= ( sup_sup_int @ B @ C ) )
=> ( ( sup_sup_int @ A @ D )
= ( sup_sup_int @ B @ ( sup_sup_int @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(163,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_115_bex__Un) ).
thf(747,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)],[163]) ).
thf(217,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_9_binsert_Osimps_I2_J) ).
thf(913,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)],[217]) ).
thf(252,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ C @ B )
=> ~ ( ord_less_eq_int @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_minf_I8_J) ).
thf(1095,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ C @ B )
=> ~ ( ord_less_eq_int @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(60,axiom,
! [A: set_a,B: set_a] :
( ( A
= ( sup_sup_set_a @ A @ B ) )
=> ( ord_less_eq_set_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_sup_OorderI) ).
thf(417,plain,
! [A: set_a,B: set_a] :
( ( A
= ( sup_sup_set_a @ A @ B ) )
=> ( ord_less_eq_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(132,axiom,
( ord_less_eq_int
= ( ^ [A: int,B: int] :
( ( sup_sup_int @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_le__iff__sup) ).
thf(651,plain,
( ord_less_eq_int
= ( ^ [A: int,B: int] :
( ( sup_sup_int @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(153,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_71_insert__absorb2) ).
thf(719,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)],[153]) ).
thf(122,axiom,
! [A: set_a,B: a] :
( ( ord_less_eq_set_a @ A @ ( insert_a @ B @ bot_bot_set_a ) )
=> ( ( A = bot_bot_set_a )
| ( A
= ( insert_a @ B @ bot_bot_set_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_subset__singletonD) ).
thf(619,plain,
! [A: set_a,B: a] :
( ( ord_less_eq_set_a @ A @ ( insert_a @ B @ bot_bot_set_a ) )
=> ( ( A = bot_bot_set_a )
| ( A
= ( insert_a @ B @ bot_bot_set_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(147,axiom,
! [A: set_a] :
( ( sup_sup_set_a @ A @ bot_bot_set_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_sup__bot__right) ).
thf(702,plain,
! [A: set_a] :
( ( sup_sup_set_a @ A @ bot_bot_set_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(33,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_sup_Oabsorb__iff2) ).
thf(344,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(221,axiom,
! [A: int,B: int,C: int > $o] :
( ( ord_less_int @ A @ B )
=> ( ( C @ A )
=> ( ~ ( C @ B )
=> ? [D: int] :
( ( ord_less_eq_int @ A @ D )
& ( ord_less_eq_int @ D @ B )
& ! [E: int] :
( ( ( ord_less_eq_int @ A @ E )
& ( ord_less_int @ E @ D ) )
=> ( C @ E ) )
& ! [E: int] :
( ! [F: int] :
( ( ( ord_less_eq_int @ A @ F )
& ( ord_less_int @ F @ E ) )
=> ( C @ F ) )
=> ( ord_less_eq_int @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_complete__interval) ).
thf(934,plain,
! [A: int,B: int,C: int > $o] :
( ( ord_less_int @ A @ B )
=> ( ( C @ A )
=> ( ~ ( C @ B )
=> ? [D: int] :
( ( ord_less_eq_int @ A @ D )
& ( ord_less_eq_int @ D @ B )
& ! [E: int] :
( ( ( ord_less_eq_int @ A @ E )
& ( ord_less_int @ E @ D ) )
=> ( C @ E ) )
& ! [E: int] :
( ! [F: int] :
( ( ( ord_less_eq_int @ A @ F )
& ( ord_less_int @ F @ E ) )
=> ( C @ F ) )
=> ( ord_less_eq_int @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(38,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_subset__iff) ).
thf(357,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(188,axiom,
! [A: int,B: int] : ( ord_less_eq_int @ A @ ( sup_sup_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_inf__sup__ord_I4_J) ).
thf(817,plain,
! [A: int,B: int] : ( ord_less_eq_int @ A @ ( sup_sup_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(103,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_38_sorted__distinct__pred__def) ).
thf(559,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)],[103]) ).
thf(250,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ( C != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_pinf_I4_J) ).
thf(1087,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ( C != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(118,axiom,
! [A: int] : ( ord_less_eq_int @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_order__refl) ).
thf(606,plain,
! [A: int] : ( ord_less_eq_int @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(13,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( sup_sup_set_a @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_sup_Oabsorb1) ).
thf(289,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( sup_sup_set_a @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(68,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ~ ( ( ord_less_eq_set_a @ A @ B )
=> ~ ( ord_less_eq_set_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_equalityE) ).
thf(448,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ~ ( ( ord_less_eq_set_a @ A @ B )
=> ~ ( ord_less_eq_set_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(254,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_27_sortLemmaL) ).
thf(1100,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)],[254]) ).
thf(166,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_120_Un__left__absorb) ).
thf(756,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)],[166]) ).
thf(193,axiom,
! [A: set_a] :
( ( sup_sup_set_a @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_sup__idem) ).
thf(834,plain,
! [A: set_a] :
( ( sup_sup_set_a @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(76,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_174_sup__left__idem) ).
thf(475,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)],[76]) ).
thf(218,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ C @ B )
=> ( C != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_minf_I3_J) ).
thf(924,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ C @ B )
=> ( C != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(242,axiom,
( ( binary1217730267_wrm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) )
= ( binary717961607le_T_a @ t1 @ x @ ( binary1217730267_wrm_a @ h @ t2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_wrm__res) ).
thf(1040,plain,
( ( binary1217730267_wrm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) )
= ( binary717961607le_T_a @ t1 @ x @ ( binary1217730267_wrm_a @ h @ t2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(257,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_22_sortedTree_Osimps_I2_J) ).
thf(1109,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)],[257]) ).
thf(109,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_73_Un__iff) ).
thf(574,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)],[109]) ).
thf(234,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( sup_sup_int @ A @ B ) @ C )
=> ~ ( ( ord_less_int @ A @ C )
=> ~ ( ord_less_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_sup_Ostrict__boundedE) ).
thf(1020,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( sup_sup_int @ A @ B ) @ C )
=> ~ ( ( ord_less_int @ A @ C )
=> ~ ( ord_less_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(35,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_190_le__sup__iff) ).
thf(348,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)],[35]) ).
thf(226,axiom,
binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_s) ).
thf(981,plain,
binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(53,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( sup_sup_set_a @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_sup__absorb2) ).
thf(397,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( sup_sup_set_a @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(158,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_117_Un__assoc) ).
thf(734,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)],[158]) ).
thf(202,axiom,
! [A: int,B: int,C: int] :
( ( sup_sup_int @ A @ ( sup_sup_int @ B @ C ) )
= ( sup_sup_int @ B @ ( sup_sup_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_sup_Oleft__commute) ).
thf(866,plain,
! [A: int,B: int,C: int] :
( ( sup_sup_int @ A @ ( sup_sup_int @ B @ C ) )
= ( sup_sup_int @ B @ ( sup_sup_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(247,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_45_linorder__neqE__linordered__idom) ).
thf(1072,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)],[247]) ).
thf(231,axiom,
! [A: binary1439146945Tree_a,B: a > int,C: binary1439146945Tree_a,D: a] :
( ( ( A = binary476621312_Tip_a )
=> ( ( binary1217730267_wrm_a @ B @ ( binary717961607le_T_a @ C @ D @ A ) )
= C ) )
& ( ( A != binary476621312_Tip_a )
=> ( ( binary1217730267_wrm_a @ B @ ( binary717961607le_T_a @ C @ D @ A ) )
= ( binary717961607le_T_a @ C @ D @ ( binary1217730267_wrm_a @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_wrm_Osimps) ).
thf(998,plain,
! [A: binary1439146945Tree_a,B: a > int,C: binary1439146945Tree_a,D: a] :
( ( ( A = binary476621312_Tip_a )
=> ( ( binary1217730267_wrm_a @ B @ ( binary717961607le_T_a @ C @ D @ A ) )
= C ) )
& ( ( A != binary476621312_Tip_a )
=> ( ( binary1217730267_wrm_a @ B @ ( binary717961607le_T_a @ C @ D @ A ) )
= ( binary717961607le_T_a @ C @ D @ ( binary1217730267_wrm_a @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(198,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_128_singletonD) ).
thf(849,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)],[198]) ).
thf(93,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_206_sup__commute) ).
thf(527,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)],[93]) ).
thf(20,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_261_sup_OboundedE) ).
thf(307,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)],[20]) ).
thf(14,axiom,
( bot_bot_set_a
= ( collect_a
@ ^ [A: a] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_empty__def) ).
thf(292,plain,
( bot_bot_set_a
= ( collect_a
@ ^ [A: a] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(46,axiom,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) )
= ( ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_Collect__mono__iff) ).
thf(380,plain,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) )
= ( ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(140,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_168_sup__bot_Oneutr__eq__iff) ).
thf(678,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)],[140]) ).
thf(94,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_148_Collect__conv__if2) ).
thf(529,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)],[94]) ).
thf(168,axiom,
! [A: set_a] :
( ( sup_sup_set_a @ A @ bot_bot_set_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_Un__empty__right) ).
thf(761,plain,
! [A: set_a] :
( ( sup_sup_set_a @ A @ bot_bot_set_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(151,axiom,
( insert_a
= ( ^ [A: a] :
( sup_sup_set_a
@ ( collect_a
@ ^ [B: a] : ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_insert__def) ).
thf(714,plain,
( insert_a
= ( ^ [A: a] :
( sup_sup_set_a
@ ( collect_a
@ ^ [B: a] : ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(181,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_113_UnI1) ).
thf(798,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)],[181]) ).
thf(98,axiom,
! [A: int,B: int] : ( ord_less_eq_int @ A @ ( sup_sup_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_inf__sup__ord_I3_J) ).
thf(546,plain,
! [A: int,B: int] : ( ord_less_eq_int @ A @ ( sup_sup_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(179,axiom,
! [A: a > int,B: a] :
( ( binary1804682569move_a @ A @ B @ binary476621312_Tip_a )
= binary476621312_Tip_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_remove_Osimps_I1_J) ).
thf(793,plain,
! [A: a > int,B: a] :
( ( binary1804682569move_a @ A @ B @ binary476621312_Tip_a )
= binary476621312_Tip_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
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_23_Tree_Oexhaust) ).
thf(1091,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(174,axiom,
! [A: int,B: int,C: int] :
( ( sup_sup_int @ A @ ( sup_sup_int @ B @ C ) )
= ( sup_sup_int @ B @ ( sup_sup_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_sup__left__commute) ).
thf(778,plain,
! [A: int,B: int,C: int] :
( ( sup_sup_int @ A @ ( sup_sup_int @ B @ C ) )
= ( sup_sup_int @ B @ ( sup_sup_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(243,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_int @ A @ ( sup_sup_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_less__supI1) ).
thf(1042,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_int @ A @ ( sup_sup_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(18,axiom,
! [A: set_a,B: a > $o] :
( ord_less_eq_set_a
@ ( collect_a
@ ^ [C: a] :
( ( member_a @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_Collect__subset) ).
thf(302,plain,
! [A: set_a,B: a > $o] :
( ord_less_eq_set_a
@ ( collect_a
@ ^ [C: a] :
( ( member_a @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(3,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_order__refl) ).
thf(260,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(104,axiom,
( insert_a
= ( ^ [A: a] : ( sup_sup_set_a @ ( insert_a @ A @ bot_bot_set_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_insert__is__Un) ).
thf(561,plain,
( insert_a
= ( ^ [A: a] : ( sup_sup_set_a @ ( insert_a @ A @ bot_bot_set_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(51,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_set__eq__subset) ).
thf(392,plain,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(16,axiom,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ A @ ( sup_sup_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_Un__upper1) ).
thf(297,plain,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ A @ ( sup_sup_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(64,axiom,
! [A: set_a > set_a > set_a,B: set_a,C: set_a] :
( ! [D: set_a,E: set_a] : ( ord_less_eq_set_a @ D @ ( A @ D @ E ) )
=> ( ! [D: set_a,E: set_a] : ( ord_less_eq_set_a @ E @ ( A @ D @ E ) )
=> ( ! [D: set_a,E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ D )
=> ( ( ord_less_eq_set_a @ F @ D )
=> ( ord_less_eq_set_a @ ( A @ E @ F ) @ D ) ) )
=> ( ( sup_sup_set_a @ B @ C )
= ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_sup__unique) ).
thf(429,plain,
! [A: set_a > set_a > set_a,B: set_a,C: set_a] :
( ! [D: set_a,E: set_a] : ( ord_less_eq_set_a @ D @ ( A @ D @ E ) )
=> ( ! [D: set_a,E: set_a] : ( ord_less_eq_set_a @ E @ ( A @ D @ E ) )
=> ( ! [D: set_a,E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ D )
=> ( ( ord_less_eq_set_a @ F @ D )
=> ( ord_less_eq_set_a @ ( A @ E @ F ) @ D ) ) )
=> ( ( sup_sup_set_a @ B @ C )
= ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(9,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_equalityD2) ).
thf(275,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(144,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_231_inf__sup__aci_I7_J) ).
thf(693,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)],[144]) ).
thf(125,axiom,
! [A: binary1439146945Tree_a,B: a > int] :
( ( ( A != binary476621312_Tip_a )
& ( binary1721989714Tree_a @ B @ A ) )
=> ( binary1721989714Tree_a @ B @ ( binary1217730267_wrm_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_wrm__sort) ).
thf(630,plain,
! [A: binary1439146945Tree_a,B: a > int] :
( ( ( A != binary476621312_Tip_a )
& ( binary1721989714Tree_a @ B @ A ) )
=> ( binary1721989714Tree_a @ B @ ( binary1217730267_wrm_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(73,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_228_inf__sup__aci_I6_J) ).
thf(467,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)],[73]) ).
thf(199,axiom,
( ( binary945792244etOf_a @ binary476621312_Tip_a )
= bot_bot_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_setOf_Osimps_I1_J) ).
thf(852,plain,
( ( binary945792244etOf_a @ binary476621312_Tip_a )
= bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(137,axiom,
! [A: set_a,B: a] :
( ( A = bot_bot_set_a )
=> ~ ( member_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_equals0D) ).
thf(665,plain,
! [A: set_a,B: a] :
( ( A = bot_bot_set_a )
=> ~ ( member_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(71,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_subset__trans) ).
thf(461,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(100,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ A @ ( sup_sup_int @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_sup_OcoboundedI2) ).
thf(551,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ A @ ( sup_sup_int @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(26,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_equalityD1) ).
thf(324,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(256,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_47_setOf_Osimps_I2_J) ).
thf(1106,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)],[256]) ).
thf(106,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ C @ D )
=> ( ord_less_eq_int @ ( sup_sup_int @ A @ C ) @ ( sup_sup_int @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_sup_Omono) ).
thf(566,plain,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ C @ D )
=> ( ord_less_eq_int @ ( sup_sup_int @ A @ C ) @ ( sup_sup_int @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(78,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( sup_sup_int @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_sup_Oabsorb1) ).
thf(484,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( sup_sup_int @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(69,axiom,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ C ) @ ( sup_sup_set_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_Un__mono) ).
thf(456,plain,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ C ) @ ( sup_sup_set_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(196,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ C )
=> ~ ( ( ord_less_eq_int @ A @ C )
=> ~ ( ord_less_eq_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_sup_OboundedE) ).
thf(842,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ C )
=> ~ ( ( ord_less_eq_int @ A @ C )
=> ~ ( ord_less_eq_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(161,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_112_UnE) ).
thf(742,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)],[161]) ).
thf(23,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_subset__refl) ).
thf(317,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(155,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( B
= ( sup_sup_int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_sup_OorderE) ).
thf(725,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( B
= ( sup_sup_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(49,axiom,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ A @ ( sup_sup_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_sup__ge1) ).
thf(388,plain,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ A @ ( sup_sup_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(203,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ C )
=> ~ ( ( ord_less_eq_int @ A @ C )
=> ~ ( ord_less_eq_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_le__supE) ).
thf(869,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ C )
=> ~ ( ( ord_less_eq_int @ A @ C )
=> ~ ( ord_less_eq_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(61,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_44_Collect__cong) ).
thf(420,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)],[61]) ).
thf(201,axiom,
! [A: int > int > int,B: int,C: int] :
( ! [D: int,E: int] : ( ord_less_eq_int @ D @ ( A @ D @ E ) )
=> ( ! [D: int,E: int] : ( ord_less_eq_int @ E @ ( A @ D @ E ) )
=> ( ! [D: int,E: int,F: int] :
( ( ord_less_eq_int @ E @ D )
=> ( ( ord_less_eq_int @ F @ D )
=> ( ord_less_eq_int @ ( A @ E @ F ) @ D ) ) )
=> ( ( sup_sup_int @ B @ C )
= ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_sup__unique) ).
thf(857,plain,
! [A: int > int > int,B: int,C: int] :
( ! [D: int,E: int] : ( ord_less_eq_int @ D @ ( A @ D @ E ) )
=> ( ! [D: int,E: int] : ( ord_less_eq_int @ E @ ( A @ D @ E ) )
=> ( ! [D: int,E: int,F: int] :
( ( ord_less_eq_int @ E @ D )
=> ( ( ord_less_eq_int @ F @ D )
=> ( ord_less_eq_int @ ( A @ E @ F ) @ D ) ) )
=> ( ( sup_sup_int @ B @ C )
= ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(27,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_312_le__supE) ).
thf(328,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)],[27]) ).
thf(95,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_70_insert__iff) ).
thf(537,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)],[95]) ).
thf(129,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_129_singleton__iff) ).
thf(642,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)],[129]) ).
thf(225,axiom,
! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
( ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_pinf_I1_J) ).
thf(970,plain,
! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
( ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(101,axiom,
! [A: set_a] :
( ( sup_sup_set_a @ bot_bot_set_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_sup__bot_Oleft__neutral) ).
thf(554,plain,
! [A: set_a] :
( ( sup_sup_set_a @ bot_bot_set_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(165,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ C @ B )
=> ( ord_less_eq_int @ ( sup_sup_int @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_sup_OboundedI) ).
thf(753,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ C @ B )
=> ( ord_less_eq_int @ ( sup_sup_int @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(213,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_int @ A @ ( sup_sup_int @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_sup_Ostrict__coboundedI2) ).
thf(901,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_int @ A @ ( sup_sup_int @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(142,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_105_insertI2) ).
thf(686,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)],[142]) ).
thf(248,axiom,
! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
( ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_pinf_I2_J) ).
thf(1075,plain,
! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
( ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(229,axiom,
! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
( ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_minf_I2_J) ).
thf(985,plain,
! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
( ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(89,axiom,
! [A: set_a] :
( ( sup_sup_set_a @ bot_bot_set_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_sup__bot__left) ).
thf(515,plain,
! [A: set_a] :
( ( sup_sup_set_a @ bot_bot_set_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(245,axiom,
! [A: binary1439146945Tree_a,B: a > int,C: binary1439146945Tree_a,D: a] :
( ( ( A = binary476621312_Tip_a )
=> ( ( binary339557810e_rm_a @ B @ ( binary717961607le_T_a @ C @ D @ A ) )
= D ) )
& ( ( A != binary476621312_Tip_a )
=> ( ( binary339557810e_rm_a @ B @ ( binary717961607le_T_a @ C @ D @ A ) )
= ( binary339557810e_rm_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_rm_Osimps) ).
thf(1060,plain,
! [A: binary1439146945Tree_a,B: a > int,C: binary1439146945Tree_a,D: a] :
( ( ( A = binary476621312_Tip_a )
=> ( ( binary339557810e_rm_a @ B @ ( binary717961607le_T_a @ C @ D @ A ) )
= D ) )
& ( ( A != binary476621312_Tip_a )
=> ( ( binary339557810e_rm_a @ B @ ( binary717961607le_T_a @ C @ D @ A ) )
= ( binary339557810e_rm_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(216,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ C @ B )
=> ~ ( ord_less_int @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_minf_I7_J) ).
thf(911,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ C @ B )
=> ~ ( ord_less_int @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(107,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ C @ B )
=> ( ord_less_eq_int @ ( sup_sup_int @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_sup__least) ).
thf(569,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ C @ B )
=> ( ord_less_eq_int @ ( sup_sup_int @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(43,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ A @ ( sup_sup_set_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_le__supI2) ).
thf(371,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ A @ ( sup_sup_set_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(123,axiom,
! [A: a,B: set_a] :
( ( insert_a @ A @ B )
!= bot_bot_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_insert__not__empty) ).
thf(622,plain,
! [A: a,B: set_a] :
( ( insert_a @ A @ B )
!= bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(194,axiom,
! [A: set_a] :
( ( ! [B: a] :
~ ( member_a @ B @ A ) )
= ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_all__not__in__conv) ).
thf(837,plain,
! [A: set_a] :
( ( ! [B: a] :
~ ( member_a @ B @ A ) )
= ( A = bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(249,axiom,
ord_less_int @ ( h @ l ) @ ( h @ ( binary339557810e_rm_a @ h @ t2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_hLess) ).
thf(1086,plain,
ord_less_int @ ( h @ l ) @ ( h @ ( binary339557810e_rm_a @ h @ t2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(6,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ B )
=> ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_sup_OboundedI) ).
thf(266,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ B )
=> ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(126,axiom,
! [A: a] :
( ( collect_a @ ( (=) @ a @ A ) )
= ( insert_a @ A @ bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_singleton__conv2) ).
thf(633,plain,
! [A: a] :
( ( collect_a @ ( (=) @ a @ A ) )
= ( insert_a @ A @ bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(86,axiom,
( ord_less_eq_int
= ( ^ [A: int,B: int] :
( B
= ( sup_sup_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_sup_Oorder__iff) ).
thf(508,plain,
( ord_less_eq_int
= ( ^ [A: int,B: int] :
( B
= ( sup_sup_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(21,axiom,
! [A: a > $o] :
( ( bot_bot_set_a
= ( collect_a @ A ) )
= ( ! [B: a] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_empty__Collect__eq) ).
thf(311,plain,
! [A: a > $o] :
( ( bot_bot_set_a
= ( collect_a @ A ) )
= ( ! [B: a] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(236,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_3_Tree_Oinject) ).
thf(1026,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)],[236]) ).
thf(136,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ C @ D )
=> ( ord_less_eq_int @ ( sup_sup_int @ A @ C ) @ ( sup_sup_int @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_sup__mono) ).
thf(662,plain,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ C @ D )
=> ( ord_less_eq_int @ ( sup_sup_int @ A @ C ) @ ( sup_sup_int @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(209,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_218_boolean__algebra__cancel_Osup2) ).
thf(888,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)],[209]) ).
thf(58,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_127_Collect__disj__eq) ).
thf(412,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)],[58]) ).
thf(164,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ A @ ( sup_sup_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_sup_OcoboundedI1) ).
thf(750,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ A @ ( sup_sup_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(88,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_124_insert__compr) ).
thf(513,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)],[88]) ).
thf(255,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_int @ A @ ( sup_sup_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_sup_Ostrict__coboundedI1) ).
thf(1103,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_int @ A @ ( sup_sup_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(5,axiom,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ A @ ( sup_sup_set_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_sup__ge2) ).
thf(264,plain,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ A @ ( sup_sup_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ( sup_sup_set_a @ B @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_sup_Oabsorb__iff1) ).
thf(279,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ( sup_sup_set_a @ B @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(143,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_37_memb__spec) ).
thf(689,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)],[143]) ).
thf(67,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_66_subsetI) ).
thf(444,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)],[67]) ).
thf(189,axiom,
! [A: set_a] :
( ( ? [B: a] : ( member_a @ B @ A ) )
= ( A != bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_ex__in__conv) ).
thf(819,plain,
! [A: set_a] :
( ( ? [B: a] : ( member_a @ B @ A ) )
= ( A != bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(214,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_25_Tree_Odistinct_I1_J) ).
thf(904,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)],[214]) ).
thf(62,axiom,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ C ) @ ( sup_sup_set_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_sup__mono) ).
thf(423,plain,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ C ) @ ( sup_sup_set_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(232,axiom,
! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
( ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_minf_I1_J) ).
thf(1007,plain,
! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
( ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(55,axiom,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_Collect__mem__eq) ).
thf(402,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(172,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_212_sup__assoc) ).
thf(772,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)],[172]) ).
thf(111,axiom,
! [A: a > int] : ( binary1721989714Tree_a @ A @ binary476621312_Tip_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_sortedTree_Osimps_I1_J) ).
thf(579,plain,
! [A: a > int] : ( binary1721989714Tree_a @ A @ binary476621312_Tip_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(11,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ ( sup_sup_set_a @ B @ C ) )
=> ~ ! [D: set_a] :
( ( ord_less_eq_set_a @ D @ B )
=> ! [E: set_a] :
( ( ord_less_eq_set_a @ E @ C )
=> ( A
!= ( sup_sup_set_a @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_subset__UnE) ).
thf(281,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ ( sup_sup_set_a @ B @ C ) )
=> ~ ! [D: set_a] :
( ( ord_less_eq_set_a @ D @ B )
=> ! [E: set_a] :
( ( ord_less_eq_set_a @ E @ C )
=> ( A
!= ( sup_sup_set_a @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1,conjecture,
ord_less_int @ ( h @ l ) @ ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_less_int @ ( h @ l ) @ ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(259,plain,
~ ( ord_less_int @ ( h @ l ) @ ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(110,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_225_inf__sup__aci_I5_J) ).
thf(577,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)],[110]) ).
thf(150,axiom,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_emptyE) ).
thf(711,plain,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(108,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_119_Un__commute) ).
thf(572,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)],[108]) ).
thf(177,axiom,
! [A: binary1439146945Tree_a,B: a > int] :
( ( ( A != binary476621312_Tip_a )
& ( binary1721989714Tree_a @ B @ A ) )
=> ( ord_less_eq_set_a @ ( binary945792244etOf_a @ ( binary1217730267_wrm_a @ B @ A ) ) @ ( binary945792244etOf_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_wrm__set1) ).
thf(787,plain,
! [A: binary1439146945Tree_a,B: a > int] :
( ( ( A != binary476621312_Tip_a )
& ( binary1721989714Tree_a @ B @ A ) )
=> ( ord_less_eq_set_a @ ( binary945792244etOf_a @ ( binary1217730267_wrm_a @ B @ A ) ) @ ( binary945792244etOf_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(29,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( sup_sup_set_a @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_Un__absorb1) ).
thf(335,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( sup_sup_set_a @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(183,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( sup_sup_int @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_sup_Oabsorb2) ).
thf(804,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( sup_sup_int @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(96,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_58_Un__insert__right) ).
thf(540,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)],[96]) ).
thf(169,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_116_ball__Un) ).
thf(764,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)],[169]) ).
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_203_sup_Oleft__commute) ).
thf(831,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(141,axiom,
! [A: int,B: int,C: int,D: int] :
( ( A
= ( sup_sup_int @ B @ C ) )
=> ( ( sup_sup_int @ D @ A )
= ( sup_sup_int @ B @ ( sup_sup_int @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_boolean__algebra__cancel_Osup2) ).
thf(681,plain,
! [A: int,B: int,C: int,D: int] :
( ( A
= ( sup_sup_int @ B @ C ) )
=> ( ( sup_sup_int @ D @ A )
= ( sup_sup_int @ B @ ( sup_sup_int @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(176,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_153_Un__singleton__iff) ).
thf(784,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)],[176]) ).
thf(40,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ A @ ( sup_sup_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_le__supI1) ).
thf(362,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ A @ ( sup_sup_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(159,axiom,
( ord_less_eq_int
= ( ^ [A: int,B: int] :
( ( sup_sup_int @ B @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_sup_Oabsorb__iff1) ).
thf(737,plain,
( ord_less_eq_int
= ( ^ [A: int,B: int] :
( ( sup_sup_int @ B @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(206,axiom,
! [A: a] :
( ( collect_a
@ ^ [B: a] : ( B = A ) )
= ( insert_a @ A @ bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_singleton__conv) ).
thf(880,plain,
! [A: a] :
( ( collect_a
@ ^ [B: a] : ( B = A ) )
= ( insert_a @ A @ bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(121,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_110_insert__commute) ).
thf(616,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)],[121]) ).
thf(45,axiom,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_subsetD) ).
thf(377,plain,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(230,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_pinf_I7_J) ).
thf(996,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(186,axiom,
! [A: a] :
( ( the_elem_a @ ( insert_a @ A @ bot_bot_set_a ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_the__elem__eq) ).
thf(811,plain,
! [A: a] :
( ( the_elem_a @ ( insert_a @ A @ bot_bot_set_a ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(81,axiom,
! [A: a,B: set_a] :
( ( member_a @ A @ B )
=> ( ( insert_a @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_insert__absorb) ).
thf(494,plain,
! [A: a,B: set_a] :
( ( member_a @ A @ B )
=> ( ( insert_a @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(222,axiom,
! [A: binary1439146945Tree_a,B: a > int] :
( ( ( A != binary476621312_Tip_a )
& ( binary1721989714Tree_a @ B @ A ) )
=> ( member_a @ ( binary339557810e_rm_a @ B @ A ) @ ( binary945792244etOf_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_rm__set) ).
thf(964,plain,
! [A: binary1439146945Tree_a,B: a > int] :
( ( ( A != binary476621312_Tip_a )
& ( binary1721989714Tree_a @ B @ A ) )
=> ( member_a @ ( binary339557810e_rm_a @ B @ A ) @ ( binary945792244etOf_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(124,axiom,
! [A: a,B: set_a,C: set_a] :
( ~ ( member_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ ( insert_a @ A @ C ) )
= ( ord_less_eq_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_subset__insert) ).
thf(626,plain,
! [A: a,B: set_a,C: set_a] :
( ~ ( member_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ ( insert_a @ A @ C ) )
= ( ord_less_eq_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(171,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ C )
= ( ( ord_less_eq_int @ A @ C )
& ( ord_less_eq_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_sup_Obounded__iff) ).
thf(769,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ C )
= ( ( ord_less_eq_int @ A @ C )
& ( ord_less_eq_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(258,axiom,
member_a @ l @ ( sup_sup_set_a @ ( sup_sup_set_a @ ( insert_a @ x @ bot_bot_set_a ) @ ( binary945792244etOf_a @ t1 ) ) @ ( binary945792244etOf_a @ ( binary1217730267_wrm_a @ h @ t2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_l__scope) ).
thf(1112,plain,
member_a @ l @ ( sup_sup_set_a @ ( sup_sup_set_a @ ( insert_a @ x @ bot_bot_set_a ) @ ( binary945792244etOf_a @ t1 ) ) @ ( binary945792244etOf_a @ ( binary1217730267_wrm_a @ h @ t2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(237,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_26_sortLemmaR) ).
thf(1029,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)],[237]) ).
thf(211,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ~ ( ord_less_int @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_pinf_I5_J) ).
thf(895,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ~ ( ord_less_int @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(91,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_54_singleton__insert__inj__eq_H) ).
thf(521,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)],[91]) ).
thf(228,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ~ ( ord_less_eq_int @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_pinf_I6_J) ).
thf(983,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ~ ( ord_less_eq_int @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(191,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_109_insert__eq__iff) ).
thf(827,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)],[191]) ).
thf(127,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_160_bot__eq__sup__iff) ).
thf(636,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)],[127]) ).
thf(207,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( sup_sup_int @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_sup__absorb1) ).
thf(883,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( sup_sup_int @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(119,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_106_Set_Oset__insert) ).
thf(608,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)],[119]) ).
thf(52,axiom,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_in__mono) ).
thf(394,plain,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(105,axiom,
! [A: int] :
( ( sup_sup_int @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_sup__idem) ).
thf(563,plain,
! [A: int] :
( ( sup_sup_int @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(17,axiom,
! [A: a > $o] :
( ( ( collect_a @ A )
= bot_bot_set_a )
= ( ! [B: a] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_Collect__empty__eq) ).
thf(299,plain,
! [A: a > $o] :
( ( ( collect_a @ A )
= bot_bot_set_a )
= ( ! [B: a] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(133,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_200_sup__left__commute) ).
thf(653,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)],[133]) ).
thf(85,axiom,
! [A: int] :
( ( sup_sup_int @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_sup_Oidem) ).
thf(505,plain,
! [A: int] :
( ( sup_sup_int @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(65,axiom,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ A @ ( insert_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_subset__insertI2) ).
thf(438,plain,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ A @ ( insert_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(154,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_154_singleton__Un__iff) ).
thf(722,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)],[154]) ).
thf(239,axiom,
( ( ( t1 != binary476621312_Tip_a )
& ( binary1721989714Tree_a @ h @ t1 ) )
=> ! [A: a] :
( ( member_a @ A @ ( binary945792244etOf_a @ ( binary1217730267_wrm_a @ h @ t1 ) ) )
=> ( ord_less_int @ ( h @ A ) @ ( h @ ( binary339557810e_rm_a @ h @ t1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_h1) ).
thf(1034,plain,
( ( ( t1 != binary476621312_Tip_a )
& ( binary1721989714Tree_a @ h @ t1 ) )
=> ! [A: a] :
( ( member_a @ A @ ( binary945792244etOf_a @ ( binary1217730267_wrm_a @ h @ t1 ) ) )
=> ( ord_less_int @ ( h @ A ) @ ( h @ ( binary339557810e_rm_a @ h @ t1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(63,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ A @ ( sup_sup_set_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_sup_OcoboundedI2) ).
thf(426,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ A @ ( sup_sup_set_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(99,axiom,
! [A: int,B: int,C: int] :
( ( sup_sup_int @ ( sup_sup_int @ A @ B ) @ C )
= ( sup_sup_int @ A @ ( sup_sup_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_inf__sup__aci_I6_J) ).
thf(548,plain,
! [A: int,B: int,C: int] :
( ( sup_sup_int @ ( sup_sup_int @ A @ B ) @ C )
= ( sup_sup_int @ A @ ( sup_sup_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(44,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ B )
=> ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_sup__least) ).
thf(374,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ B )
=> ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(32,axiom,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ A @ ( sup_sup_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_inf__sup__ord_I3_J) ).
thf(342,plain,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ A @ ( sup_sup_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(233,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ C @ B )
=> ( ord_less_eq_int @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_minf_I6_J) ).
thf(1018,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ C @ B )
=> ( ord_less_eq_int @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(224,axiom,
( ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) )
= ( binary339557810e_rm_a @ h @ t2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_rm__res) ).
thf(968,plain,
( ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) )
= ( binary339557810e_rm_a @ h @ t2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(80,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_107_insert__ident) ).
thf(490,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)],[80]) ).
thf(139,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( sup_sup_int @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_sup__absorb2) ).
thf(675,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( sup_sup_int @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(131,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_103_insertE) ).
thf(648,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)],[131]) ).
thf(79,axiom,
! [A: set_a] :
( ( sup_sup_set_a @ bot_bot_set_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_Un__empty__left) ).
thf(487,plain,
! [A: set_a] :
( ( sup_sup_set_a @ bot_bot_set_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(102,axiom,
! [A: a,B: set_a] : ( member_a @ A @ ( insert_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_insertI1) ).
thf(557,plain,
! [A: a,B: set_a] : ( member_a @ A @ ( insert_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(148,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_114_UnI2) ).
thf(705,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)],[148]) ).
thf(160,axiom,
! [A: set_a] :
( ( sup_sup_set_a @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_Un__absorb) ).
thf(739,plain,
! [A: set_a] :
( ( sup_sup_set_a @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(66,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( sup_sup_set_a @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_sup_Oabsorb2) ).
thf(441,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( sup_sup_set_a @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(84,axiom,
! [A: int,B: int] :
( ( sup_sup_int @ A @ ( sup_sup_int @ A @ B ) )
= ( sup_sup_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_sup_Oleft__idem) ).
thf(502,plain,
! [A: int,B: int] :
( ( sup_sup_int @ A @ ( sup_sup_int @ A @ B ) )
= ( sup_sup_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(195,axiom,
! [A: int,B: int] : ( ord_less_eq_int @ A @ ( sup_sup_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_sup_Ocobounded2) ).
thf(840,plain,
! [A: int,B: int] : ( ord_less_eq_int @ A @ ( sup_sup_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(30,axiom,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ A @ ( sup_sup_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_sup_Ocobounded1) ).
thf(338,plain,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ A @ ( sup_sup_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(74,axiom,
! [A: int,B: int] : ( ord_less_eq_int @ A @ ( sup_sup_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_sup__ge1) ).
thf(470,plain,
! [A: int,B: int] : ( ord_less_eq_int @ A @ ( sup_sup_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(39,axiom,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_mem__Collect__eq) ).
thf(359,plain,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(241,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ C @ B )
=> ( ord_less_int @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_minf_I5_J) ).
thf(1038,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ C @ B )
=> ( ord_less_int @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(113,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ C @ B )
=> ( ord_less_eq_int @ ( sup_sup_int @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_le__supI) ).
thf(585,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ C @ B )
=> ( ord_less_eq_int @ ( sup_sup_int @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(162,axiom,
! [A: int,B: int,C: int] :
( ( sup_sup_int @ A @ ( sup_sup_int @ B @ C ) )
= ( sup_sup_int @ B @ ( sup_sup_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_inf__sup__aci_I7_J) ).
thf(744,plain,
! [A: int,B: int,C: int] :
( ( sup_sup_int @ A @ ( sup_sup_int @ B @ C ) )
= ( sup_sup_int @ B @ ( sup_sup_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(134,axiom,
! [A: int,B: int] :
( ( sup_sup_int @ ( sup_sup_int @ A @ B ) @ B )
= ( sup_sup_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_sup_Oright__idem) ).
thf(656,plain,
! [A: int,B: int] :
( ( sup_sup_int @ ( sup_sup_int @ A @ B ) @ B )
= ( sup_sup_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(120,axiom,
! [A: int,B: int,C: int] :
( ( sup_sup_int @ ( sup_sup_int @ A @ B ) @ C )
= ( sup_sup_int @ A @ ( sup_sup_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_sup__assoc) ).
thf(613,plain,
! [A: int,B: int,C: int] :
( ( sup_sup_int @ ( sup_sup_int @ A @ B ) @ C )
= ( sup_sup_int @ A @ ( sup_sup_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(116,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_177_sup_Oleft__idem) ).
thf(600,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)],[116]) ).
thf(22,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_67_subset__antisym) ).
thf(314,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)],[22]) ).
thf(82,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_121_Un__left__commute) ).
thf(497,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)],[82]) ).
thf(167,axiom,
! [A: int,B: int] : ( ord_less_eq_int @ A @ ( sup_sup_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_sup_Ocobounded1) ).
thf(759,plain,
! [A: int,B: int] : ( ord_less_eq_int @ A @ ( sup_sup_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(42,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_60_Un__subset__iff) ).
thf(368,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)],[42]) ).
thf(92,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ C )
= ( ( ord_less_eq_int @ A @ C )
& ( ord_less_eq_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_le__sup__iff) ).
thf(524,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ C )
= ( ( ord_less_eq_int @ A @ C )
& ( ord_less_eq_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(112,axiom,
! [A: set_a] :
( ! [B: a] :
~ ( member_a @ B @ A )
=> ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_equals0I) ).
thf(581,plain,
! [A: set_a] :
( ! [B: a] :
~ ( member_a @ B @ A )
=> ( A = bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(24,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( sup_sup_set_a @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_Un__absorb2) ).
thf(319,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( sup_sup_set_a @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(19,axiom,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ ( insert_a @ C @ A ) @ ( insert_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_insert__mono) ).
thf(304,plain,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ ( insert_a @ C @ A ) @ ( insert_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(36,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ B )
=> ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_le__supI) ).
thf(351,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ B )
=> ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(50,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_le__iff__sup) ).
thf(390,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(157,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_162_sup__eq__bot__iff) ).
thf(731,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)],[157]) ).
thf(175,axiom,
! [A: int,B: int,C: int] :
( ( sup_sup_int @ ( sup_sup_int @ A @ B ) @ C )
= ( sup_sup_int @ A @ ( sup_sup_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_sup_Oassoc) ).
thf(781,plain,
! [A: int,B: int,C: int] :
( ( sup_sup_int @ ( sup_sup_int @ A @ B ) @ C )
= ( sup_sup_int @ A @ ( sup_sup_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(114,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_72_UnCI) ).
thf(588,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)],[114]) ).
thf(146,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_215_sup_Oassoc) ).
thf(699,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)],[146]) ).
thf(87,axiom,
! [A: set_a,B: a] :
( ( ord_less_eq_set_a @ A @ ( insert_a @ B @ bot_bot_set_a ) )
= ( ( A = bot_bot_set_a )
| ( A
= ( insert_a @ B @ bot_bot_set_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_subset__singleton__iff) ).
thf(510,plain,
! [A: set_a,B: a] :
( ( ord_less_eq_set_a @ A @ ( insert_a @ B @ bot_bot_set_a ) )
= ( ( A = bot_bot_set_a )
| ( A
= ( insert_a @ B @ bot_bot_set_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(77,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_69_insertCI) ).
thf(478,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)],[77]) ).
thf(8,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( sup_sup_set_a @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_sup__absorb1) ).
thf(272,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( sup_sup_set_a @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(47,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( B
= ( sup_sup_set_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_sup_Oorder__iff) ).
thf(383,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( B
= ( sup_sup_set_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(34,axiom,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ A @ ( sup_sup_set_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_inf__sup__ord_I4_J) ).
thf(346,plain,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ A @ ( sup_sup_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(244,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_24_Tree_Oinduct) ).
thf(1045,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)],[244]) ).
thf(152,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_59_Un__insert__left) ).
thf(716,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)],[152]) ).
thf(12,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_empty__subsetI) ).
thf(287,plain,
! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(223,axiom,
binary1721989714Tree_a @ h @ t1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_s1) ).
thf(967,plain,
binary1721989714Tree_a @ h @ t1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(56,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ A @ ( sup_sup_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_sup_OcoboundedI1) ).
thf(405,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ A @ ( sup_sup_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(200,axiom,
! [A: int,B: int] :
( ( A
= ( sup_sup_int @ A @ B ) )
=> ( ord_less_eq_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_sup_OorderI) ).
thf(854,plain,
! [A: int,B: int] :
( ( A
= ( sup_sup_int @ A @ B ) )
=> ( ord_less_eq_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(178,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ A @ ( sup_sup_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_le__supI1) ).
thf(790,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ A @ ( sup_sup_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(117,axiom,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_empty__iff) ).
thf(603,plain,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(253,axiom,
( ( ( t2 != binary476621312_Tip_a )
& ( binary1721989714Tree_a @ h @ t2 ) )
=> ! [A: a] :
( ( member_a @ A @ ( binary945792244etOf_a @ ( binary1217730267_wrm_a @ h @ t2 ) ) )
=> ( ord_less_int @ ( h @ A ) @ ( h @ ( binary339557810e_rm_a @ h @ t2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_h2) ).
thf(1097,plain,
( ( ( t2 != binary476621312_Tip_a )
& ( binary1721989714Tree_a @ h @ t2 ) )
=> ! [A: a] :
( ( member_a @ A @ ( binary945792244etOf_a @ ( binary1217730267_wrm_a @ h @ t2 ) ) )
=> ( ord_less_int @ ( h @ A ) @ ( h @ ( binary339557810e_rm_a @ h @ t2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(4,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_subset__Un__eq) ).
thf(262,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(184,axiom,
( sup_sup_int
= ( ^ [A: int,B: int] : ( sup_sup_int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_sup__commute) ).
thf(807,plain,
( sup_sup_int
= ( ^ [A: int,B: int] : ( sup_sup_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(54,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_52_sorted__distinct) ).
thf(400,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)],[54]) ).
thf(145,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_77_insert__subset) ).
thf(696,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)],[145]) ).
thf(180,axiom,
( sup_sup_int
= ( ^ [A: int,B: int] : ( sup_sup_int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_sup_Ocommute) ).
thf(796,plain,
( sup_sup_int
= ( ^ [A: int,B: int] : ( sup_sup_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(15,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_187_sup_Obounded__iff) ).
thf(294,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)],[15]) ).
thf(182,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_55_singleton__insert__inj__eq) ).
thf(801,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)],[182]) ).
thf(212,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ C @ B )
=> ( C != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_minf_I4_J) ).
thf(897,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ C @ B )
=> ( C != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(170,axiom,
( ord_less_eq_int
= ( ^ [A: int,B: int] :
( ( sup_sup_int @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_sup_Oabsorb__iff2) ).
thf(767,plain,
( ord_less_eq_int
= ( ^ [A: int,B: int] :
( ( sup_sup_int @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(208,axiom,
! [A: a] : ( member_a @ A @ ( insert_a @ A @ bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_singletonI) ).
thf(886,plain,
! [A: a] : ( member_a @ A @ ( insert_a @ A @ bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(219,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ( ord_less_eq_int @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_pinf_I8_J) ).
thf(928,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ( ord_less_eq_int @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(59,axiom,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ A @ ( sup_sup_set_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_sup_Ocobounded2) ).
thf(415,plain,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ A @ ( sup_sup_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(156,axiom,
! [A: int,B: int] :
( ( sup_sup_int @ A @ ( sup_sup_int @ A @ B ) )
= ( sup_sup_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_inf__sup__aci_I8_J) ).
thf(728,plain,
! [A: int,B: int] :
( ( sup_sup_int @ A @ ( sup_sup_int @ A @ B ) )
= ( sup_sup_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(72,axiom,
! [A: a > int,B: binary1439146945Tree_a,C: a] :
( ( binary1721989714Tree_a @ A @ B )
=> ( binary1721989714Tree_a @ A @ ( binary1226383794sert_a @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_binsert__sorted) ).
thf(464,plain,
! [A: a > int,B: binary1439146945Tree_a,C: a] :
( ( binary1721989714Tree_a @ A @ B )
=> ( binary1721989714Tree_a @ A @ ( binary1226383794sert_a @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(28,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ B )
=> ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_Un__least) ).
thf(332,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ B )
=> ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(70,axiom,
! [A: set_a,B: a] : ( ord_less_eq_set_a @ A @ ( insert_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_subset__insertI) ).
thf(459,plain,
! [A: set_a,B: a] : ( ord_less_eq_set_a @ A @ ( insert_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(215,axiom,
t2 != binary476621312_Tip_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_t2nTip) ).
thf(908,plain,
t2 != binary476621312_Tip_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(190,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_221_boolean__algebra__cancel_Osup1) ).
thf(822,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)],[190]) ).
thf(227,axiom,
member_a @ l @ ( binary945792244etOf_a @ ( binary1217730267_wrm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_ldef) ).
thf(982,plain,
member_a @ l @ ( binary945792244etOf_a @ ( binary1217730267_wrm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(25,axiom,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ A @ ( sup_sup_set_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_Un__upper2) ).
thf(322,plain,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ A @ ( sup_sup_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(37,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_74_subset__empty) ).
thf(354,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)],[37]) ).
thf(135,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_164_sup__bot_Oeq__neutr__iff) ).
thf(659,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)],[135]) ).
thf(97,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_132_singleton__inject) ).
thf(543,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)],[97]) ).
thf(128,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ A @ ( sup_sup_int @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_le__supI2) ).
thf(639,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ A @ ( sup_sup_int @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(115,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_147_Collect__conv__if) ).
thf(592,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)],[115]) ).
thf(246,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_20_binsert_Osimps_I1_J) ).
thf(1069,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)],[246]) ).
thf(149,axiom,
! [A: set_a] :
( ( sup_sup_set_a @ A @ bot_bot_set_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_sup__bot_Oright__neutral) ).
thf(708,plain,
! [A: set_a] :
( ( sup_sup_set_a @ A @ bot_bot_set_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(240,axiom,
binary1721989714Tree_a @ h @ t2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_s2) ).
thf(1037,plain,
binary1721989714Tree_a @ h @ t2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(173,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_61_Un__empty) ).
thf(775,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)],[173]) ).
thf(1176,plain,
$false,
inference(e,[status(thm)],[645,809,1024,365,846,1031,893,518,408,873,878,269,385,500,472,814,340,930,670,747,913,1095,417,651,719,619,702,344,934,357,817,559,1087,606,289,448,1100,756,834,475,924,1040,1109,574,1020,348,981,397,734,866,1072,998,849,527,307,292,380,678,529,761,714,798,546,793,1091,778,1042,302,260,561,392,297,429,275,693,630,467,852,665,461,551,324,1106,566,484,456,842,742,317,725,388,869,420,857,328,537,642,970,554,753,901,686,1075,985,515,1060,911,569,371,622,837,1086,266,633,508,311,1026,662,888,412,750,513,1103,264,279,689,444,819,904,423,1007,402,772,579,281,259,577,711,572,787,335,804,540,764,831,681,784,362,737,880,616,377,996,811,494,964,626,769,1112,1029,895,521,983,827,636,883,608,394,563,299,653,505,438,722,1034,426,548,374,342,1018,968,490,675,648,487,557,705,739,441,502,840,338,470,359,1038,585,744,656,613,600,314,497,759,368,524,581,319,304,351,390,731,781,588,699,510,478,272,383,346,1045,716,287,967,405,854,790,603,1097,262,807,400,696,796,294,801,897,767,886,928,415,728,464,332,459,908,822,982,322,354,659,543,639,592,1069,708,1037,775]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP034^1 : 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
% 0.10/0.22 % Computer : n026.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 19:41:49 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 1.03/0.82 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.25/1.21 % [INFO] Parsing done (392ms).
% 2.25/1.23 % [INFO] Running in sequential loop mode.
% 3.19/1.60 % [INFO] eprover registered as external prover.
% 3.19/1.61 % [INFO] Scanning for conjecture ...
% 3.38/1.74 % [INFO] Found a conjecture (or negated_conjecture) and 352 axioms. Running axiom selection ...
% 3.55/1.87 % [INFO] Axiom selection finished. Selected 256 axioms (removed 96 axioms).
% 4.18/2.09 % [INFO] Problem is higher-order (TPTP THF).
% 4.18/2.12 % [INFO] Type checking passed.
% 4.18/2.12 % [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 ...
% 14.72/5.14 % External prover 'e' found a proof!
% 14.72/5.14 % [INFO] Killing All external provers ...
% 14.72/5.14 % Time passed: 4780ms (effective reasoning time: 3913ms)
% 14.72/5.14 % 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)>
% 15.27/5.15 % Axioms used in derivation (256): fact_264_sup__absorb2, fact_73_Un__iff, fact_104_insertI1, fact_80_equals0D, fact_271_sup_Oabsorb1, fact_262_sup__absorb2, fact_168_sup__bot_Oneutr__eq__iff, fact_124_insert__compr, fact_56_singleton__conv2, fact_166_sup__bot_Oleft__neutral, fact_177_sup_Oleft__idem, fact_64_Collect__empty__eq, fact_88_equalityD1, fact_279_sup_OorderI, fact_252_sup_Ocobounded1, fact_81_equals0I, fact_258_sup_OboundedI, fact_270_sup_Oabsorb2, fact_82_ex__in__conv, fact_26_sortLemmaR, fact_16_sortedTree_Osimps_I1_J, fact_49_minf_I6_J, fact_259_sup_OboundedE, fact_131_insert__not__empty, fact_148_Collect__conv__if2, fact_333_sup_Ostrict__coboundedI1, fact_46_complete__interval, fact_66_subsetI, fact_285_le__iff__sup, fact_57_singleton__conv, fact_59_Un__insert__left, fact_107_insert__ident, fact_115_bex__Un, fact_274_sup__unique, fact_306_sup__ge1, fact_156_sup__bot__left, fact_77_insert__subset, fact_134_subset__insert, fact_318_inf__sup__ord_I4_J, fact_340_order__refl, fact_117_Un__assoc, fact_152_insert__is__Un, fact_113_UnI1, fact_307_le__supI, fact_341_order__refl, fact_280_sup_OorderE, fact_11_minf_I7_J, fact_261_sup_OboundedE, fact_187_sup_Obounded__iff, fact_183_sup_Oidem, fact_63_all__not__in__conv, fact_70_insert__iff, fact_231_inf__sup__aci_I7_J, fact_179_sup__idem, fact_53_setOf_Osimps_I1_J, fact_151_subset__singleton__iff, fact_76_singletonI, fact_93_subset__trans, fact_227_inf__sup__aci_I6_J, fact_140_Un__least, fact_268_sup_Oabsorb2, fact_34_minf_I1_J, fact_324_less__supI2, fact_244_sup_Oabsorb__iff1, fact_86_equalityE, fact_23_Tree_Oexhaust, fact_91_subset__refl, fact_235_sup_OcoboundedI2, fact_38_sorted__distinct__pred__def, fact_304_sup__ge1, fact_203_sup_Oleft__commute, fact_1_rm__res, fact_36_h2, fact_233_inf__sup__aci_I8_J, fact_12_minf_I5_J, fact_288_sup__least, fact_90_subset__iff, fact_294_sup_Omono, fact_24_Tree_Oinduct, fact_95_Collect__mono__iff, fact_133_insert__mono, fact_112_UnE, fact_0_hLess, fact_138_Un__empty__right, fact_295_le__supI2, fact_173_sup__left__idem, fact_146_subset__Un__eq, fact_32_pinf_I5_J, fact_21_wrm_Osimps, fact_188_le__sup__iff, fact_40_wrm__set1, fact_55_singleton__insert__inj__eq, fact_289_sup__mono, fact_103_insertE, fact_13_minf_I4_J, fact_19_rm__set, fact_180_sup__idem, fact_18_binsert__sorted, fact_205_sup__commute, fact_208_sup_Ocommute, fact_110_insert__commute, fact_192_sup__bot_Oright__neutral, fact_255_sup_Oorder__iff, fact_214_sup_Oassoc, fact_44_Collect__cong, fact_121_Un__left__commute, fact_109_insert__eq__iff, fact_249_sup_Ocobounded2, fact_199_sup__left__commute, fact_111_mk__disjoint__insert, fact_230_inf__sup__aci_I7_J, fact_137_Un__empty__left, fact_291_sup__mono, fact_292_sup_Omono, fact_243_sup_Oabsorb__iff2, fact_75_empty__subsetI, fact_160_bot__eq__sup__iff, fact_277_sup_OorderI, fact_8_s2, fact_228_inf__sup__aci_I6_J, fact_176_sup_Oleft__idem, fact_30_pinf_I3_J, fact_310_le__supE, fact_153_Un__singleton__iff, fact_185_sup_Obounded__iff, fact_215_sup_Oassoc, fact_171_sup_Oright__idem, fact_247_sup_Ocobounded2, fact_312_le__supE, fact_147_Collect__conv__if, fact_6_ldef, fact_48_minf_I8_J, fact_129_singleton__iff, fact_238_sup_OcoboundedI1, fact_114_UnI2, fact_144_Un__absorb2, fact_5_wrm__res, fact_54_singleton__insert__inj__eq_H, fact_127_Collect__disj__eq, fact_142_Un__upper2, fact_125_insert__Collect, fact_265_sup__absorb1, fact_37_memb__spec, fact_256_sup_OboundedI, fact_20_binsert_Osimps_I1_J, fact_43_Collect__mem__eq, fact_246_sup_Oabsorb__iff1, fact_61_Un__empty, fact_67_subset__antisym, fact_60_Un__subset__iff, fact_240_sup_OcoboundedI1, fact_122_empty__def, fact_108_insert__absorb, fact_52_sorted__distinct, fact_209_sup_Ocommute, fact_74_subset__empty, fact_327_sup_Ostrict__boundedE, fact_69_insertCI, fact_309_le__supI, fact_58_Un__insert__right, fact_212_sup__assoc, fact_25_Tree_Odistinct_I1_J, fact_89_equalityD2, fact_65_empty__Collect__eq, fact_174_sup__left__idem, fact_105_insertI2, fact_336_sup_Ostrict__coboundedI2, fact_35_h1, fact_217_boolean__algebra__cancel_Osup2, fact_143_Un__absorb1, fact_220_boolean__algebra__cancel_Osup1, fact_162_sup__eq__bot__iff, fact_182_sup_Oidem, fact_158_sup__bot__right, fact_62_empty__iff, fact_300_le__supI1, fact_132_singleton__inject, fact_2_t2nTip, fact_218_boolean__algebra__cancel_Osup2, fact_234_inf__sup__aci_I8_J, fact_315_inf__sup__ord_I3_J, fact_27_sortLemmaL, fact_149_insert__def, fact_273_sup_Oabsorb1, fact_126_Un__def, fact_139_Un__mono, fact_84_in__mono, fact_225_inf__sup__aci_I5_J, fact_301_sup__ge2, fact_28_pinf_I1_J, fact_31_pinf_I4_J, fact_283_le__iff__sup, fact_3_Tree_Oinject, fact_50_pinf_I8_J, fact_14_minf_I3_J, fact_87_subset__eq, fact_120_Un__left__absorb, fact_330_sup_Ostrict__order__iff, fact_119_Un__commute, fact_282_sup_OorderE, fact_51_pinf_I6_J, fact_211_sup__assoc, fact_241_sup_Oabsorb__iff2, fact_313_inf__sup__ord_I3_J, fact_253_sup_Oorder__iff, fact_94_set__eq__subset, fact_141_Un__upper1, fact_9_binsert_Osimps_I2_J, fact_79_emptyE, fact_321_less__supI1, fact_200_sup__left__commute, fact_15_minf_I2_J, fact_202_sup_Oleft__commute, fact_92_Collect__mono, fact_4_s, fact_45_linorder__neqE__linordered__idom, fact_72_UnCI, fact_297_le__supI2, fact_250_sup_Ocobounded1, fact_224_inf__sup__aci_I5_J, fact_118_Un__absorb, fact_298_le__supI1, fact_29_pinf_I2_J, fact_33_pinf_I7_J, fact_22_sortedTree_Osimps_I2_J, fact_128_singletonD, fact_136_subset__insertI2, fact_123_Collect__subset, fact_154_singleton__Un__iff, fact_190_le__sup__iff, fact_71_insert__absorb2, fact_276_sup__unique, fact_303_sup__ge2, fact_130_doubleton__eq__iff, fact_42_mem__Collect__eq, fact_206_sup__commute, fact_106_Set_Oset__insert, fact_237_sup_OcoboundedI2, fact_145_subset__UnE, fact_339_the__elem__eq, fact_47_setOf_Osimps_I2_J, fact_164_sup__bot_Oeq__neutr__iff, fact_17_wrm__sort, fact_10_rm_Osimps, fact_85_subsetD, fact_267_sup__absorb1, fact_150_subset__singletonD, fact_135_subset__insertI, fact_39_l__scope, fact_286_sup__least, fact_170_sup_Oright__idem, fact_7_s1, fact_41_remove_Osimps_I1_J, fact_116_ball__Un, fact_221_boolean__algebra__cancel_Osup1, fact_316_inf__sup__ord_I4_J
% 15.27/5.15 % No. of inferences in proof: 516
% 15.27/5.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4780 ms resp. 3913 ms w/o parsing
% 15.99/5.35 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.99/5.35 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------