%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP033^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:29 AM UTC 2026
% Result : Theorem 52.87s 16.80s
% Output : Refutation 53.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 267
% Syntax : Number of formulae : 618 ( 217 unt; 0 typ; 5 def)
% Number of atoms : 1990 ( 490 equ; 18 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 5278 ( 294 ~; 100 |; 111 &;3915 @)
% ( 0 <=>; 858 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 474 ( 474 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 33 usr; 10 con; 0-5 aty)
% Number of variables : 1834 ( 284 ^;1524 !; 21 ?;1834 :)
% ( 0 !>; 0 ?*; 0 @-; 5 @+)
% Comments :
%------------------------------------------------------------------------------
thf(produc376588196ee_a_a_type,type,
produc376588196ee_a_a: $tType ).
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(binary1774981152rmrm_a_decl,type,
binary1774981152rmrm_a: ( a > int ) > binary1439146945Tree_a > produc376588196ee_a_a ).
thf(bot_bot_o_decl,type,
bot_bot_o: $o ).
thf(bot_bot_set_a_decl,type,
bot_bot_set_a: set_a ).
thf(ord_less_int_decl,type,
ord_less_int: int > int > $o ).
thf(ord_less_set_a_decl,type,
ord_less_set_a: set_a > set_a > $o ).
thf(ord_less_eq_a_o_decl,type,
ord_less_eq_a_o: ( a > $o ) > ( a > $o ) > $o ).
thf(ord_less_eq_int_decl,type,
ord_less_eq_int: int > int > $o ).
thf(ord_less_eq_set_a_decl,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(ordering_top_set_a_decl,type,
ordering_top_set_a: ( set_a > set_a > $o ) > ( set_a > set_a > $o ) > set_a > $o ).
thf(produc374321428ee_a_a_decl,type,
produc374321428ee_a_a: binary1439146945Tree_a > a > produc376588196ee_a_a ).
thf(produc1275654896Tree_a_decl,type,
produc1275654896Tree_a: ( binary1439146945Tree_a > a > binary1439146945Tree_a ) > produc376588196ee_a_a > binary1439146945Tree_a ).
thf(collect_a_decl,type,
collect_a: ( a > $o ) > set_a ).
thf(member_a_decl,type,
member_a: a > set_a > $o ).
thf(h_decl,type,
h: a > int ).
thf(t1_decl,type,
t1: binary1439146945Tree_a ).
thf(t2_decl,type,
t2: binary1439146945Tree_a ).
thf(x_decl,type,
x: a ).
thf(sk1_decl,type,
sk1: ( a > $o ) > ( a > $o ) > ( ( a > $o ) > int ) > int > a > $o ).
thf(sk2_decl,type,
sk2: ( a > $o ) > ( a > $o ) > ( ( a > $o ) > int ) > int > a > $o ).
thf(sk3_decl,type,
sk3: ( a > $o ) > ( a > $o ) > ( ( a > $o ) > set_a ) > set_a > a > $o ).
thf(sk4_decl,type,
sk4: ( a > $o ) > ( a > $o ) > ( ( a > $o ) > set_a ) > set_a > a > $o ).
thf(sk5_decl,type,
sk5: int > int ).
thf(sk124_decl,type,
sk124: a ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: a > $o,B: a > $o,C: ( a > $o ) > int,D: int] :
@+[E: a > $o] :
~ ! [F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_int @ ( C @ E ) @ ( C @ F ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: a > $o,B: a > $o,C: ( a > $o ) > int,D: int] :
@+[E: a > $o] :
~ ( ( ord_less_eq_a_o @ ( sk1 @ A @ B @ C @ D ) @ E )
=> ( ord_less_eq_int @ ( C @ ( sk1 @ A @ B @ C @ D ) ) @ ( C @ E ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: a > $o,B: a > $o,C: ( a > $o ) > set_a,D: set_a] :
@+[E: a > $o] :
~ ! [F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: a > $o,B: a > $o,C: ( a > $o ) > set_a,D: set_a] :
@+[E: a > $o] :
~ ( ( ord_less_eq_a_o @ ( sk3 @ A @ B @ C @ D ) @ E )
=> ( ord_less_eq_set_a @ ( C @ ( sk3 @ A @ B @ C @ D ) ) @ ( C @ E ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: int] :
@+[B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ( ord_less_eq_int @ A @ C ) ) ) ) ).
thf(100,axiom,
! [A: a > $o,B: a > $o,C: ( a > $o ) > a > $o,D: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_a_o @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_a_o @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_ord__le__eq__subst) ).
thf(645,plain,
! [A: a > $o,B: a > $o,C: ( a > $o ) > a > $o,D: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_a_o @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_a_o @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(204,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/sandbox/benchmark/theBenchmark.p',fact_206_set__eq__subset) ).
thf(1024,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)],[204]) ).
thf(240,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/sandbox/benchmark/theBenchmark.p',fact_67_order_Otrans) ).
thf(1190,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)],[240]) ).
thf(130,axiom,
! [A: a > $o,B: set_a > a > $o,C: set_a,D: set_a] :
( ( ord_less_eq_a_o @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_a_o @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_a_o @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_order__subst1) ).
thf(760,plain,
! [A: a > $o,B: set_a > a > $o,C: set_a,D: set_a] :
( ( ord_less_eq_a_o @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_a_o @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_a_o @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(171,axiom,
! [A: int,B: set_a > int,C: set_a,D: set_a] :
( ( ord_less_int @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_order__less__le__subst1) ).
thf(893,plain,
! [A: int,B: set_a > int,C: set_a,D: set_a] :
( ( ord_less_int @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(135,axiom,
! [A: int,B: int] :
( ~ ( ord_less_eq_int @ A @ B )
=> ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_not__le__imp__less) ).
thf(777,plain,
! [A: int,B: int] :
( ~ ( ord_less_eq_int @ A @ B )
=> ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(61,axiom,
! [A: set_a] :
~ ( ord_less_set_a @ A @ bot_bot_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_bot_Oextremum__strict) ).
thf(479,plain,
! [A: set_a] :
~ ( ord_less_set_a @ A @ bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(480,plain,
~ ? [A: set_a] : ( ord_less_set_a @ A @ bot_bot_set_a ),
inference(miniscope,[status(thm)],[479]) ).
thf(481,plain,
! [A: set_a] :
~ ( ord_less_set_a @ A @ bot_bot_set_a ),
inference(cnf,[status(esa)],[480]) ).
thf(223,axiom,
t2 != binary476621312_Tip_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_t2nTip) ).
thf(1103,plain,
t2 != binary476621312_Tip_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(1104,plain,
t2 != binary476621312_Tip_a,
inference(polarity_switch,[status(thm)],[1103]) ).
thf(1105,plain,
t2 != binary476621312_Tip_a,
inference(lifteq,[status(thm)],[1104]) ).
thf(246,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/sandbox/benchmark/theBenchmark.p',fact_198_equalityE) ).
thf(1211,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)],[246]) ).
thf(82,axiom,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_emptyE) ).
thf(582,plain,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(6,axiom,
! [A: set_a,B: ( a > $o ) > set_a,C: a > $o,D: a > $o] :
( ( ord_less_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_a_o @ C @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_order__less__le__subst1) ).
thf(276,plain,
! [A: set_a,B: ( a > $o ) > set_a,C: a > $o,D: a > $o] :
( ( ord_less_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_a_o @ C @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(212,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ C @ A )
=> ( ord_less_int @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_dual__order_Ostrict__trans) ).
thf(1068,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ C @ A )
=> ( ord_less_int @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(125,axiom,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_antisym__conv) ).
thf(741,plain,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(243,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ B @ A )
& ( ord_less_eq_set_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_dual__order_Oeq__iff) ).
thf(1204,plain,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ B @ A )
& ( ord_less_eq_set_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(1205,plain,
( ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ B @ A )
& ( ord_less_eq_set_a @ A @ B ) ) )
= ( (=) @ set_a ) ),
inference(lifteq,[status(thm)],[1204]) ).
thf(233,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_less__not__sym) ).
thf(1142,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(70,axiom,
! [A: int,B: set_a > int,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_ord__eq__less__subst) ).
thf(511,plain,
! [A: int,B: set_a > int,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(245,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/sandbox/benchmark/theBenchmark.p',fact_199_subset__eq) ).
thf(1209,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)],[245]) ).
thf(1210,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
inference(lifteq,[status(thm)],[1209]) ).
thf(17,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_dual__order_Oorder__iff__strict) ).
thf(314,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(315,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( B = A ) ) ) ),
inference(lifteq,[status(thm)],[314]) ).
thf(1529,plain,
( ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( B = A ) ) )
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
inference(rewrite,[status(thm)],[1210,315]) ).
thf(19,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_subset__iff__psubset__eq) ).
thf(321,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(322,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( A = B ) ) ) ),
inference(lifteq,[status(thm)],[321]) ).
thf(1266,plain,
( ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( B = A ) ) )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( A = B ) ) ) ),
inference(rewrite,[status(thm)],[322,315]) ).
thf(1532,plain,
( ( ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( A = B ) ) ) )
| ( ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( B = A ) ) )
!= ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( B = A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1529,1266]) ).
thf(1533,plain,
( ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( A = B ) ) ) ),
inference(pattern_uni,[status(thm)],[1532:[]]) ).
thf(91,axiom,
( ( (=) @ ( a > $o ) )
= ( ^ [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
& ( ord_less_eq_a_o @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_eq__iff) ).
thf(613,plain,
( ( (=) @ ( a > $o ) )
= ( ^ [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
& ( ord_less_eq_a_o @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(614,plain,
( ( ^ [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
& ( ord_less_eq_a_o @ B @ A ) ) )
= ( (=) @ ( a > $o ) ) ),
inference(lifteq,[status(thm)],[613]) ).
thf(87,axiom,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( ord_less_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_order__less__subst1) ).
thf(597,plain,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( ord_less_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(162,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_order_Ostrict__implies__not__eq) ).
thf(858,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(859,plain,
! [B: int,A: int] :
( ~ ( ord_less_int @ A @ B )
| ( A != B ) ),
inference(cnf,[status(esa)],[858]) ).
thf(860,plain,
! [B: int,A: int] :
( ( A != B )
| ~ ( ord_less_int @ A @ B ) ),
inference(lifteq,[status(thm)],[859]) ).
thf(861,plain,
! [A: int] :
~ ( ord_less_int @ A @ A ),
inference(simp,[status(thm)],[860]) ).
thf(216,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_eq__refl) ).
thf(1078,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(75,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_psubset__subset__trans) ).
thf(533,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(67,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_set_a @ C @ A )
=> ( ord_less_set_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_dual__order_Ostrict__trans1) ).
thf(500,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_set_a @ C @ A )
=> ( ord_less_set_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(141,axiom,
! [A: set_a] :
~ ( ord_less_set_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_verit__comp__simplify1_I1_J) ).
thf(797,plain,
! [A: set_a] :
~ ( ord_less_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(116,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_less__imp__le) ).
thf(715,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(147,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_order_Oorder__iff__strict) ).
thf(814,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(262,axiom,
( ( ( binary476621312_Tip_a != binary476621312_Tip_a )
& ( binary1721989714Tree_a @ h @ binary476621312_Tip_a ) )
=> ( binary1721989714Tree_a @ h @ ( binary1217730267_wrm_a @ h @ binary476621312_Tip_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13__092_060open_062Tip_A_092_060noteq_062_ATip_A_092_060and_062_AsortedTree_Ah_ATip_A_092_060longrightarrow_062_AsortedTree_Ah_A_Iwrm_Ah_ATip_J_092_060close_062) ).
thf(1260,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(127,axiom,
! [A: set_a,B: ( a > $o ) > set_a,C: a > $o,D: a > $o] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_a_o @ C @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_order__subst1) ).
thf(747,plain,
! [A: set_a,B: ( a > $o ) > set_a,C: a > $o,D: a > $o] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_a_o @ C @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(186,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/sandbox/benchmark/theBenchmark.p',fact_71_order__class_Oorder_Oeq__iff) ).
thf(945,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)],[186]) ).
thf(172,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/sandbox/benchmark/theBenchmark.p',fact_15_binsert_Osimps_I1_J) ).
thf(898,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)],[172]) ).
thf(200,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ A )
=> ( ord_less_eq_set_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_dual__order_Otrans) ).
thf(1001,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ A )
=> ( ord_less_eq_set_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(255,axiom,
( ( ( t2 != binary476621312_Tip_a )
& ( binary1721989714Tree_a @ h @ t2 ) )
=> ( binary1721989714Tree_a @ h @ ( binary1217730267_wrm_a @ h @ t2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_h2) ).
thf(1243,plain,
( ( ( t2 != binary476621312_Tip_a )
& ( binary1721989714Tree_a @ h @ t2 ) )
=> ( binary1721989714Tree_a @ h @ ( binary1217730267_wrm_a @ h @ t2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(9,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ( ord_less_eq_int @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_pinf_I8_J) ).
thf(287,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)],[9]) ).
thf(288,plain,
! [B: int,A: int] :
( ~ ( ord_less_int @ ( sk5 @ A ) @ B )
| ( ord_less_eq_int @ A @ B ) ),
inference(cnf,[status(esa)],[287]) ).
thf(253,axiom,
! [A: a > int] : ( binary1721989714Tree_a @ A @ binary476621312_Tip_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_sortedTree_Osimps_I1_J) ).
thf(1238,plain,
! [A: a > int] : ( binary1721989714Tree_a @ A @ binary476621312_Tip_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(1239,plain,
! [A: a > int] : ( binary1721989714Tree_a @ A @ binary476621312_Tip_a ),
inference(cnf,[status(esa)],[1238]) ).
thf(1,conjecture,
binary1721989714Tree_a @ h @ t1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( binary1721989714Tree_a @ h @ t1 ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(264,plain,
~ ( binary1721989714Tree_a @ h @ t1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1383,plain,
! [A: a > int] :
( ~ $true
| ( ( binary1721989714Tree_a @ A @ binary476621312_Tip_a )
!= ( binary1721989714Tree_a @ h @ t1 ) ) ),
inference(paramod_ordered,[status(thm)],[1239,264]) ).
thf(1384,plain,
! [A: a > int] :
( ( binary1721989714Tree_a @ A @ binary476621312_Tip_a )
!= ( binary1721989714Tree_a @ h @ t1 ) ),
inference(simp,[status(thm)],[1383]) ).
thf(1385,plain,
! [A: a > int] :
( ( A != h )
| ( t1 != binary476621312_Tip_a ) ),
inference(simp,[status(thm)],[1384]) ).
thf(1386,plain,
t1 != binary476621312_Tip_a,
inference(simp,[status(thm)],[1385]) ).
thf(12,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_empty__subsetI) ).
thf(301,plain,
! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(259,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/sandbox/benchmark/theBenchmark.p',fact_4_sortLemmaR) ).
thf(1254,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)],[259]) ).
thf(156,axiom,
! [A: set_a] :
( ( ! [B: a] :
~ ( member_a @ B @ A ) )
= ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_all__not__in__conv) ).
thf(841,plain,
! [A: set_a] :
( ( ! [B: a] :
~ ( member_a @ B @ A ) )
= ( A = bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(46,axiom,
! [A: a > $o,B: ( a > $o ) > a > $o,C: a > $o,D: a > $o] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_a_o @ C @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_a_o @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_a_o @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_ord__eq__le__subst) ).
thf(417,plain,
! [A: a > $o,B: ( a > $o ) > a > $o,C: a > $o,D: a > $o] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_a_o @ C @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_a_o @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_a_o @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(139,axiom,
! [A: set_a,B: ( a > $o ) > set_a,C: a > $o,D: a > $o] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_a_o @ C @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_ord__eq__le__subst) ).
thf(785,plain,
! [A: set_a,B: ( a > $o ) > set_a,C: a > $o,D: a > $o] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_a_o @ C @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(178,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_equalityD1) ).
thf(917,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(143,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_le__less) ).
thf(802,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(28,axiom,
( ordering_top_set_a
@ ^ [A: set_a,B: set_a] : ( ord_less_eq_set_a @ B @ A )
@ ^ [A: set_a,B: set_a] : ( ord_less_set_a @ B @ A )
@ bot_bot_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_bot_Oordering__top__axioms) ).
thf(357,plain,
( ordering_top_set_a
@ ^ [A: set_a,B: set_a] : ( ord_less_eq_set_a @ B @ A )
@ ^ [A: set_a,B: set_a] : ( ord_less_set_a @ B @ A )
@ bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(57,axiom,
! [A: int,B: int,C: int > set_a,D: set_a] :
( ( ord_less_int @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_ord__less__eq__subst) ).
thf(460,plain,
! [A: int,B: int,C: int > set_a,D: set_a] :
( ( ord_less_int @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(173,axiom,
( ( binary945792244etOf_a @ binary476621312_Tip_a )
= bot_bot_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_setOf_Osimps_I1_J) ).
thf(901,plain,
( ( binary945792244etOf_a @ binary476621312_Tip_a )
= bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(902,plain,
( ( binary945792244etOf_a @ binary476621312_Tip_a )
= bot_bot_set_a ),
inference(lifteq,[status(thm)],[901]) ).
thf(160,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ C )
=> ( ord_less_eq_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_order_Otrans) ).
thf(853,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ C )
=> ( ord_less_eq_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(8,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_subset__psubset__trans) ).
thf(284,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(168,axiom,
! [A: a > int,B: a] :
( ( binary1804682569move_a @ A @ B @ binary476621312_Tip_a )
= binary476621312_Tip_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_remove_Osimps_I1_J) ).
thf(881,plain,
! [A: a > int,B: a] :
( ( binary1804682569move_a @ A @ B @ binary476621312_Tip_a )
= binary476621312_Tip_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(10,axiom,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_ord__less__eq__subst) ).
thf(289,plain,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(18,axiom,
! [A: int,B: int,C: int > set_a,D: set_a] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_set_a @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_order__less__subst2) ).
thf(316,plain,
! [A: int,B: int,C: int > set_a,D: set_a] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_set_a @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(222,axiom,
! [A: int,B: int] :
( ~ ( ord_less_int @ A @ B )
=> ( ( ~ ( ord_less_int @ B @ A ) )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_antisym__conv3) ).
thf(1100,plain,
! [A: int,B: int] :
( ~ ( ord_less_int @ A @ B )
=> ( ( ~ ( ord_less_int @ B @ A ) )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(65,axiom,
! [A: set_a,B: set_a,C: set_a > int,D: int] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_eq_int @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_order__less__le__subst2) ).
thf(492,plain,
! [A: set_a,B: set_a,C: set_a > int,D: int] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_eq_int @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(35,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ~ ( ord_less_set_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_less__not__sym) ).
thf(376,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ~ ( ord_less_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(184,axiom,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_order__subst2) ).
thf(937,plain,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(27,axiom,
! [A: set_a,B: int > set_a,C: int,D: int] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_ord__eq__less__subst) ).
thf(348,plain,
! [A: set_a,B: int > set_a,C: int,D: int] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(145,axiom,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_set_a @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_order__le__less__subst2) ).
thf(806,plain,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_set_a @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(149,axiom,
( ( (=) @ ( a > $o ) )
= ( ^ [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
& ( ord_less_eq_a_o @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_order__class_Oorder_Oeq__iff) ).
thf(821,plain,
( ( (=) @ ( a > $o ) )
= ( ^ [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
& ( ord_less_eq_a_o @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(225,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( A = B )
| ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_less__linear) ).
thf(1109,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( A = B )
| ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(88,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_ord__le__eq__trans) ).
thf(602,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(40,axiom,
( ord_less_eq_int
= ( ^ [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_le__less) ).
thf(397,plain,
( ord_less_eq_int
= ( ^ [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(277,plain,
! [A: set_a,B: ( a > $o ) > set_a,C: a > $o] :
( ( ord_less_set_a @ A @ ( B @ C ) )
=> ! [D: a > $o] :
( ( ord_less_eq_a_o @ C @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
inference(miniscope,[status(thm)],[276]) ).
thf(278,plain,
! [D: a > $o,C: a > $o,B: ( a > $o ) > set_a,A: set_a] :
( ( ~ ( ord_less_set_a @ A @ ( B @ C ) )
| ~ ( ord_less_eq_a_o @ C @ D )
| ( ord_less_eq_a_o @ ( sk3 @ D @ C @ B @ A ) @ ( sk4 @ D @ C @ B @ A ) )
| ( ord_less_set_a @ A @ ( B @ D ) ) )
& ( ~ ( ord_less_set_a @ A @ ( B @ C ) )
| ~ ( ord_less_eq_a_o @ C @ D )
| ~ ( ord_less_eq_set_a @ ( B @ ( sk3 @ D @ C @ B @ A ) ) @ ( B @ ( sk4 @ D @ C @ B @ A ) ) )
| ( ord_less_set_a @ A @ ( B @ D ) ) ) ),
inference(cnf,[status(esa)],[277]) ).
thf(280,plain,
! [D: a > $o,C: a > $o,B: ( a > $o ) > set_a,A: set_a] :
( ~ ( ord_less_set_a @ A @ ( B @ C ) )
| ~ ( ord_less_eq_a_o @ C @ D )
| ~ ( ord_less_eq_set_a @ ( B @ ( sk3 @ D @ C @ B @ A ) ) @ ( B @ ( sk4 @ D @ C @ B @ A ) ) )
| ( ord_less_set_a @ A @ ( B @ D ) ) ),
inference(cnfConj,[status(thm)],[278]) ).
thf(97,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_set_a @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_le__imp__less__or__eq) ).
thf(634,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_set_a @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(122,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_order_Ostrict__trans1) ).
thf(734,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(190,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_less__asym_H) ).
thf(956,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(103,axiom,
! [A: set_a,B: set_a,C: set_a > a > $o,D: a > $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_a_o @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_a_o @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_ord__le__eq__subst) ).
thf(660,plain,
! [A: set_a,B: set_a,C: set_a > a > $o,D: a > $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_a_o @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_a_o @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(3,axiom,
! [A: a > $o] :
( ( ( collect_a @ A )
= bot_bot_set_a )
= ( ! [B: a] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_Collect__empty__eq) ).
thf(265,plain,
! [A: a > $o] :
( ( ( collect_a @ A )
= bot_bot_set_a )
= ( ! [B: a] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(72,axiom,
( bot_bot_set_a
= ( collect_a
@ ^ [A: a] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_empty__def) ).
thf(525,plain,
( bot_bot_set_a
= ( collect_a
@ ^ [A: a] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(526,plain,
( ( collect_a
@ ^ [A: a] : $false )
= bot_bot_set_a ),
inference(lifteq,[status(thm)],[525]) ).
thf(261,axiom,
binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_s) ).
thf(1259,plain,
binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(266,plain,
! [A: a > $o] :
( ( ( collect_a @ A )
= bot_bot_set_a )
= ( ! [B: a] :
~ ( A @ B ) ) ),
inference(cnf,[status(esa)],[265]) ).
thf(267,plain,
! [A: a > $o] :
( ( ( collect_a @ A )
= bot_bot_set_a )
= ( ! [B: a] :
~ ( A @ B ) ) ),
inference(lifteq,[status(thm)],[266]) ).
thf(1269,plain,
! [A: a > $o] :
( ( ( collect_a @ A )
!= bot_bot_set_a )
| ! [B: a] :
~ ( A @ B ) ),
inference(bool_ext,[status(thm)],[267]) ).
thf(1274,plain,
! [A: a > $o] :
( ( ( collect_a @ A )
!= bot_bot_set_a )
| ! [B: a] :
~ ( A @ B ) ),
inference(lifteq,[status(thm)],[1269]) ).
thf(1277,plain,
! [B: a,A: a > $o] :
( ( ( collect_a @ A )
!= bot_bot_set_a )
| ~ ( A @ B ) ),
inference(cnf,[status(esa)],[1274]) ).
thf(1811,plain,
! [B: a,A: a > $o] :
( ( ( collect_a @ A )
!= bot_bot_set_a )
| ~ $true
| ( ( binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) )
!= ( A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1259,1277]) ).
thf(1812,plain,
! [B: a,A: a > $o] :
( ( ( collect_a @ A )
!= bot_bot_set_a )
| ( ( binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) )
!= ( A @ B ) ) ),
inference(simp,[status(thm)],[1811]) ).
thf(1878,plain,
( ( collect_a
@ ^ [A: a] : ( binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ A @ t2 ) ) )
!= bot_bot_set_a ),
inference(pre_uni,[status(thm)],[1812:[bind(A,$thf( ^ [C: a] : ( binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ C @ t2 ) ) )),bind(B,$thf( x ))]]) ).
thf(1941,plain,
( ( bot_bot_set_a != bot_bot_set_a )
| ( ( collect_a
@ ^ [A: a] : ( binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ A @ t2 ) ) )
!= ( collect_a
@ ^ [A: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[526,1878]) ).
thf(1942,plain,
( ( collect_a
@ ^ [A: a] : ( binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ A @ t2 ) ) )
!= ( collect_a
@ ^ [A: a] : $false ) ),
inference(simp,[status(thm)],[1941]) ).
thf(1943,plain,
( ( ^ [A: a] : ( binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ A @ t2 ) ) )
!= ( ^ [A: a] : $false ) ),
inference(simp,[status(thm)],[1942]) ).
thf(48,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_less__imp__not__eq2) ).
thf(428,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(73,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_less__imp__le) ).
thf(527,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(16,axiom,
( ord_less_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_psubset__eq) ).
thf(312,plain,
( ord_less_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(214,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_less__asym) ).
thf(1074,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(244,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/sandbox/benchmark/theBenchmark.p',fact_205_subset__trans) ).
thf(1206,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)],[244]) ).
thf(185,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/sandbox/benchmark/theBenchmark.p',fact_63_antisym) ).
thf(942,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)],[185]) ).
thf(74,axiom,
! [A: a > $o,B: a > $o] :
( ( A = B )
=> ( ord_less_eq_a_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_eq__refl) ).
thf(529,plain,
! [A: a > $o,B: a > $o] :
( ( A = B )
=> ( ord_less_eq_a_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(242,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ord__le__eq__trans) ).
thf(1199,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(37,axiom,
! [A: set_a,B: int > set_a,C: int,D: int] :
( ( ord_less_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_order__less__subst1) ).
thf(381,plain,
! [A: set_a,B: int > set_a,C: int,D: int] :
( ( ord_less_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(32,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ~ ( ord_less_int @ A @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_antisym__conv2) ).
thf(366,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ~ ( ord_less_int @ A @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(220,axiom,
! [A: int,B: int,C: int > int,D: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_order__less__subst2) ).
thf(1091,plain,
! [A: int,B: int,C: int > int,D: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(151,axiom,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_Collect__mem__eq) ).
thf(825,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(302,plain,
! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ),
inference(cnf,[status(esa)],[301]) ).
thf(163,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_order_Ostrict__trans) ).
thf(862,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(5,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ A )
=> ( ord_less_set_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_dual__order_Ostrict__trans2) ).
thf(273,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ A )
=> ( ord_less_set_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(274,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ! [C: set_a] :
( ( ord_less_eq_set_a @ C @ A )
=> ( ord_less_set_a @ C @ B ) ) ),
inference(miniscope,[status(thm)],[273]) ).
thf(275,plain,
! [C: set_a,B: set_a,A: set_a] :
( ~ ( ord_less_set_a @ A @ B )
| ~ ( ord_less_eq_set_a @ C @ A )
| ( ord_less_set_a @ C @ B ) ),
inference(cnf,[status(esa)],[274]) ).
thf(208,axiom,
! [A: int,B: int,C: $o] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ B @ A )
=> C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_less__imp__triv) ).
thf(1042,plain,
! [A: int,B: int,C: $o] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ B @ A )
=> C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(189,axiom,
! [A: binary1439146945Tree_a,B: a,C: binary1439146945Tree_a] :
( binary476621312_Tip_a
!= ( binary717961607le_T_a @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_Tree_Odistinct_I1_J) ).
thf(952,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)],[189]) ).
thf(111,axiom,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_dual__order_Oantisym) ).
thf(693,plain,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(95,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_dual__order_Ostrict__implies__order) ).
thf(630,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(30,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_leD) ).
thf(361,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(167,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/sandbox/benchmark/theBenchmark.p',fact_344_Collect__restrict) ).
thf(879,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)],[167]) ).
thf(50,axiom,
( ord_less_eq_int
= ( ^ [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_order_Oorder__iff__strict) ).
thf(435,plain,
( ord_less_eq_int
= ( ^ [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(170,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_less__imp__not__eq) ).
thf(889,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(235,axiom,
! [A: int,B: int] :
( ( ~ ( ord_less_int @ A @ B ) )
= ( ( ord_less_int @ B @ A )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_not__less__iff__gr__or__eq) ).
thf(1159,plain,
! [A: int,B: int] :
( ( ~ ( ord_less_int @ A @ B ) )
= ( ( ord_less_int @ B @ A )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(129,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_le__less__trans) ).
thf(757,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(108,axiom,
! [A: set_a,B: set_a] :
( ( A != B )
=> ( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_set_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_order_Onot__eq__order__implies__strict) ).
thf(682,plain,
! [A: set_a,B: set_a] :
( ( A != B )
=> ( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_set_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(224,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/sandbox/benchmark/theBenchmark.p',fact_79_order__trans) ).
thf(1106,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)],[224]) ).
thf(219,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_order_Oasym) ).
thf(1089,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(165,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_subset__refl) ).
thf(874,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(92,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( A != B )
=> ( ord_less_set_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_psubsetI) ).
thf(615,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( A != B )
=> ( ord_less_set_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(249,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/sandbox/benchmark/theBenchmark.p',fact_202_subset__iff) ).
thf(1227,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)],[249]) ).
thf(221,axiom,
! [A: set_a,B: set_a,C: a > $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ A
@ ( collect_a
@ ^ [D: a] :
( ( member_a @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: a] :
( ( member_a @ D @ A )
=> ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_subset__Collect__iff) ).
thf(1096,plain,
! [A: set_a,B: set_a,C: a > $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ A
@ ( collect_a
@ ^ [D: a] :
( ( member_a @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: a] :
( ( member_a @ D @ A )
=> ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(202,axiom,
! [A: binary1439146945Tree_a,B: a > int,C: binary1439146945Tree_a,D: a] :
( ( ( A = binary476621312_Tip_a )
=> ( ( binary1217730267_wrm_a @ B @ ( binary717961607le_T_a @ C @ D @ A ) )
= C ) )
& ( ( A != binary476621312_Tip_a )
=> ( ( binary1217730267_wrm_a @ B @ ( binary717961607le_T_a @ C @ D @ A ) )
= ( binary717961607le_T_a @ C @ D @ ( binary1217730267_wrm_a @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_wrm_Osimps) ).
thf(1006,plain,
! [A: binary1439146945Tree_a,B: a > int,C: binary1439146945Tree_a,D: a] :
( ( ( A = binary476621312_Tip_a )
=> ( ( binary1217730267_wrm_a @ B @ ( binary717961607le_T_a @ C @ D @ A ) )
= C ) )
& ( ( A != binary476621312_Tip_a )
=> ( ( binary1217730267_wrm_a @ B @ ( binary717961607le_T_a @ C @ D @ A ) )
= ( binary717961607le_T_a @ C @ D @ ( binary1217730267_wrm_a @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(138,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ C @ B )
=> ~ ( ord_less_eq_int @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_minf_I8_J) ).
thf(783,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ C @ B )
=> ~ ( ord_less_eq_int @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(1856,plain,
( ( ( collect_a
@ ^ [A: a] : bot_bot_o )
!= bot_bot_set_a )
| ~ bot_bot_o ),
inference(prim_subst,[status(thm)],[1277:[bind(A,$thf( ^ [C: a] : bot_bot_o ))]]) ).
thf(119,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ C @ A )
=> ( ord_less_int @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_dual__order_Ostrict__trans2) ).
thf(725,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ C @ A )
=> ( ord_less_int @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(39,axiom,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_ord__eq__less__subst) ).
thf(388,plain,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(22,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/sandbox/benchmark/theBenchmark.p',fact_204_Collect__mono) ).
thf(328,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)],[22]) ).
thf(169,axiom,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_order__subst1) ).
thf(884,plain,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(217,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/sandbox/benchmark/theBenchmark.p',fact_18_Tree_Oexhaust) ).
thf(1082,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)],[217]) ).
thf(104,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( A != B )
=> ( ord_less_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_le__neq__trans) ).
thf(669,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( A != B )
=> ( ord_less_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(98,axiom,
! [A: set_a,B: set_a] :
( ~ ( ord_less_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ A @ B )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_antisym__conv1) ).
thf(637,plain,
! [A: set_a,B: set_a] :
( ~ ( ord_less_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ A @ B )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(64,axiom,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_Collect__cong) ).
thf(489,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)],[64]) ).
thf(84,axiom,
( ord_less_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_order_Ostrict__iff__order) ).
thf(590,plain,
( ord_less_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(107,axiom,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
=> ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_bot_Oextremum__uniqueI) ).
thf(679,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)],[107]) ).
thf(115,axiom,
! [A: a > $o,B: set_a > a > $o,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_a_o @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_a_o @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_ord__eq__le__subst) ).
thf(706,plain,
! [A: a > $o,B: set_a > a > $o,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_a_o @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_a_o @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(59,axiom,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_empty__iff) ).
thf(474,plain,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(475,plain,
~ ? [A: a] : ( member_a @ A @ bot_bot_set_a ),
inference(miniscope,[status(thm)],[474]) ).
thf(476,plain,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
inference(cnf,[status(esa)],[475]) ).
thf(257,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/sandbox/benchmark/theBenchmark.p',fact_10_sorted__distinct__pred__def) ).
thf(1249,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)],[257]) ).
thf(191,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ord_less_eq_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_less__eq__set__def) ).
thf(958,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ord_less_eq_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(959,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ord_less_eq_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) ) ) ),
inference(lifteq,[status(thm)],[958]) ).
thf(1317,plain,
( ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( B = A ) ) )
= ( ^ [A: set_a,B: set_a] :
( ord_less_eq_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) ) ) ),
inference(rewrite,[status(thm)],[959,315]) ).
thf(1538,plain,
( ( ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) )
= ( ^ [A: set_a,B: set_a] :
( ord_less_eq_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) ) ) )
| ( ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( B = A ) ) )
!= ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( B = A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1529,1317]) ).
thf(1539,plain,
( ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) )
= ( ^ [A: set_a,B: set_a] :
( ord_less_eq_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[1538:[]]) ).
thf(101,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ~ ( ord_less_set_a @ A @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_antisym__conv2) ).
thf(654,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ~ ( ord_less_set_a @ A @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(256,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/sandbox/benchmark/theBenchmark.p',fact_3_sortLemmaL) ).
thf(1246,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)],[256]) ).
thf(136,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_order_Ostrict__implies__order) ).
thf(779,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(68,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/sandbox/benchmark/theBenchmark.p',fact_207_Collect__mono__iff) ).
thf(503,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)],[68]) ).
thf(251,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/sandbox/benchmark/theBenchmark.p',fact_9_memb__spec) ).
thf(1231,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)],[251]) ).
thf(197,axiom,
! [A: int,B: int,C: int > int,D: int] :
( ( ord_less_int @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_ord__less__eq__subst) ).
thf(984,plain,
! [A: int,B: int,C: int > int,D: int] :
( ( ord_less_int @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(176,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_less__trans) ).
thf(911,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(26,axiom,
! [A: set_a,B: set_a,C: set_a > a > $o,D: a > $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_a_o @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_a_o @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_a_o @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_order__subst2) ).
thf(343,plain,
! [A: set_a,B: set_a,C: set_a > a > $o,D: a > $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_a_o @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_a_o @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_a_o @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(218,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_dual__order_Oantisym) ).
thf(1086,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(96,axiom,
( ( (=) @ ( a > $o ) )
= ( ^ [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ B @ A )
& ( ord_less_eq_a_o @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_dual__order_Oeq__iff) ).
thf(632,plain,
( ( (=) @ ( a > $o ) )
= ( ^ [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ B @ A )
& ( ord_less_eq_a_o @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(633,plain,
( ( ^ [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ B @ A )
& ( ord_less_eq_a_o @ A @ B ) ) )
= ( (=) @ ( a > $o ) ) ),
inference(lifteq,[status(thm)],[632]) ).
thf(179,axiom,
! [A: int] :
? [B: int] : ( ord_less_int @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_lt__ex) ).
thf(921,plain,
! [A: int] :
? [B: int] : ( ord_less_int @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(78,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/sandbox/benchmark/theBenchmark.p',fact_327_complete__interval) ).
thf(541,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)],[78]) ).
thf(102,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_order_Ostrict__trans1) ).
thf(657,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(398,plain,
( ord_less_eq_int
= ( ^ [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( A = B ) ) ) ),
inference(lifteq,[status(thm)],[397]) ).
thf(213,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/sandbox/benchmark/theBenchmark.p',fact_28_subset__antisym) ).
thf(1071,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)],[213]) ).
thf(205,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_less__imp__not__eq2) ).
thf(1026,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(238,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_dual__order_Oasym) ).
thf(1185,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(140,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_less__le__trans) ).
thf(794,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(181,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( A = B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_ord__eq__le__trans) ).
thf(926,plain,
! [A: set_a,B: set_a,C: 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)],[181]) ).
thf(131,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_order_Ostrict__implies__order) ).
thf(765,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(210,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/sandbox/benchmark/theBenchmark.p',fact_24_binsert_Osimps_I2_J) ).
thf(1054,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)],[210]) ).
thf(239,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/sandbox/benchmark/theBenchmark.p',fact_5_Tree_Oinject) ).
thf(1187,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)],[239]) ).
thf(106,axiom,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_order__less__le__subst2) ).
thf(674,plain,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(175,axiom,
! [A: int,B: int,C: int] :
( ( A = B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_ord__eq__less__trans) ).
thf(906,plain,
! [A: int,B: int,C: int] :
( ( A = B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(11,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_order_Ostrict__trans2) ).
thf(298,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(194,axiom,
! [A: a > int,B: a,C: a,D: binary1439146945Tree_a,E: binary1439146945Tree_a] :
( ( ( ord_less_int @ ( A @ B ) @ ( A @ C ) )
=> ( ( binary1804682569move_a @ A @ B @ ( binary717961607le_T_a @ D @ C @ E ) )
= ( binary717961607le_T_a @ ( binary1804682569move_a @ A @ B @ D ) @ C @ E ) ) )
& ( ~ ( ord_less_int @ ( A @ B ) @ ( A @ C ) )
=> ( ( ( ord_less_int @ ( A @ C ) @ ( A @ B ) )
=> ( ( binary1804682569move_a @ A @ B @ ( binary717961607le_T_a @ D @ C @ E ) )
= ( binary717961607le_T_a @ D @ C @ ( binary1804682569move_a @ A @ B @ E ) ) ) )
& ( ~ ( ord_less_int @ ( A @ C ) @ ( A @ B ) )
=> ( ( ( D = binary476621312_Tip_a )
=> ( ( binary1804682569move_a @ A @ B @ ( binary717961607le_T_a @ D @ C @ E ) )
= E ) )
& ( ( D != binary476621312_Tip_a )
=> ( ( binary1804682569move_a @ A @ B @ ( binary717961607le_T_a @ D @ C @ E ) )
= ( produc1275654896Tree_a
@ ^ [F: binary1439146945Tree_a,G: a] : ( binary717961607le_T_a @ F @ G @ E )
@ ( binary1774981152rmrm_a @ A @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_remove_Osimps_I2_J) ).
thf(965,plain,
! [A: a > int,B: a,C: a,D: binary1439146945Tree_a,E: binary1439146945Tree_a] :
( ( ( ord_less_int @ ( A @ B ) @ ( A @ C ) )
=> ( ( binary1804682569move_a @ A @ B @ ( binary717961607le_T_a @ D @ C @ E ) )
= ( binary717961607le_T_a @ ( binary1804682569move_a @ A @ B @ D ) @ C @ E ) ) )
& ( ~ ( ord_less_int @ ( A @ B ) @ ( A @ C ) )
=> ( ( ( ord_less_int @ ( A @ C ) @ ( A @ B ) )
=> ( ( binary1804682569move_a @ A @ B @ ( binary717961607le_T_a @ D @ C @ E ) )
= ( binary717961607le_T_a @ D @ C @ ( binary1804682569move_a @ A @ B @ E ) ) ) )
& ( ~ ( ord_less_int @ ( A @ C ) @ ( A @ B ) )
=> ( ( ( D = binary476621312_Tip_a )
=> ( ( binary1804682569move_a @ A @ B @ ( binary717961607le_T_a @ D @ C @ E ) )
= E ) )
& ( ( D != binary476621312_Tip_a )
=> ( ( binary1804682569move_a @ A @ B @ ( binary717961607le_T_a @ D @ C @ E ) )
= ( produc1275654896Tree_a
@ ^ [F: binary1439146945Tree_a,G: a] : ( binary717961607le_T_a @ F @ G @ E )
@ ( binary1774981152rmrm_a @ A @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(161,axiom,
! [A: int] :
? [B: int] : ( ord_less_int @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_gt__ex) ).
thf(856,plain,
! [A: int] :
? [B: int] : ( ord_less_int @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(279,plain,
! [D: a > $o,C: a > $o,B: ( a > $o ) > set_a,A: set_a] :
( ~ ( ord_less_set_a @ A @ ( B @ C ) )
| ~ ( ord_less_eq_a_o @ C @ D )
| ( ord_less_eq_a_o @ ( sk3 @ D @ C @ B @ A ) @ ( sk4 @ D @ C @ B @ A ) )
| ( ord_less_set_a @ A @ ( B @ D ) ) ),
inference(cnfConj,[status(thm)],[278]) ).
thf(53,axiom,
! [A: set_a,B: set_a,C: $o] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_set_a @ B @ A )
=> C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_less__imp__triv) ).
thf(444,plain,
! [A: set_a,B: set_a,C: $o] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_set_a @ B @ A )
=> C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(34,axiom,
! [A: a > $o] : ( ord_less_eq_a_o @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_dual__order_Orefl) ).
thf(374,plain,
! [A: a > $o] : ( ord_less_eq_a_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(375,plain,
! [A: a > $o] : ( ord_less_eq_a_o @ A @ A ),
inference(cnf,[status(esa)],[374]) ).
thf(258,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/sandbox/benchmark/theBenchmark.p',fact_19_rm__set) ).
thf(1251,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)],[258]) ).
thf(93,axiom,
! [A: a > $o,B: a > $o,C: ( a > $o ) > set_a,D: set_a] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_ord__le__eq__subst) ).
thf(618,plain,
! [A: a > $o,B: a > $o,C: ( a > $o ) > set_a,D: set_a] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(247,axiom,
! [A: int,B: int > int,C: int,D: int] :
( ( ord_less_int @ A @ ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_order__less__subst1) ).
thf(1219,plain,
! [A: int,B: int > int,C: int,D: int] :
( ( ord_less_int @ A @ ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(150,axiom,
( ord_less_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( B != A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_dual__order_Ostrict__iff__order) ).
thf(823,plain,
( ord_less_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( B != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(824,plain,
( ord_less_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( B != A ) ) ) ),
inference(lifteq,[status(thm)],[823]) ).
thf(134,axiom,
! [A: int,B: int,C: int > int,D: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_order__less__le__subst2) ).
thf(772,plain,
! [A: int,B: int,C: int > int,D: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(285,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ! [C: set_a] :
( ( ord_less_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
inference(miniscope,[status(thm)],[284]) ).
thf(286,plain,
! [C: set_a,B: set_a,A: set_a] :
( ~ ( ord_less_eq_set_a @ A @ B )
| ~ ( ord_less_set_a @ B @ C )
| ( ord_less_set_a @ A @ C ) ),
inference(cnf,[status(esa)],[285]) ).
thf(875,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(cnf,[status(esa)],[874]) ).
thf(81,axiom,
! [A: int,B: int] :
( ~ ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ A @ B )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_antisym__conv1) ).
thf(579,plain,
! [A: int,B: int] :
( ~ ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ A @ B )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(260,axiom,
( ( ( t1 != binary476621312_Tip_a )
& ( binary1721989714Tree_a @ h @ t1 ) )
=> ( binary1721989714Tree_a @ h @ ( binary1217730267_wrm_a @ h @ t1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_h1) ).
thf(1256,plain,
( ( ( t1 != binary476621312_Tip_a )
& ( binary1721989714Tree_a @ h @ t1 ) )
=> ( binary1721989714Tree_a @ h @ ( binary1217730267_wrm_a @ h @ t1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(44,axiom,
( ord_less_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_less__le) ).
thf(413,plain,
( ord_less_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(229,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( B = C )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_ord__less__eq__trans) ).
thf(1124,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( B = C )
=> ( ord_less_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(7,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ C )
=> ( ord_less_eq_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_order__trans) ).
thf(281,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ C )
=> ( ord_less_eq_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(232,axiom,
! [A: int,B: int] :
( ~ ( ord_less_int @ A @ B )
=> ( ( A != B )
=> ( ord_less_int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_linorder__cases) ).
thf(1139,plain,
! [A: int,B: int] :
( ~ ( ord_less_int @ A @ B )
=> ( ( A != B )
=> ( ord_less_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(313,plain,
( ord_less_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( A != B ) ) ) ),
inference(lifteq,[status(thm)],[312]) ).
thf(90,axiom,
! [A: a > $o] : ( ord_less_eq_a_o @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_order__refl) ).
thf(611,plain,
! [A: a > $o] : ( ord_less_eq_a_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(23,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_order_Ostrict__implies__not__eq) ).
thf(332,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(333,plain,
! [B: set_a,A: set_a] :
( ~ ( ord_less_set_a @ A @ B )
| ( A != B ) ),
inference(cnf,[status(esa)],[332]) ).
thf(334,plain,
! [B: set_a,A: set_a] :
( ( A != B )
| ~ ( ord_less_set_a @ A @ B ) ),
inference(lifteq,[status(thm)],[333]) ).
thf(335,plain,
! [A: set_a] :
~ ( ord_less_set_a @ A @ A ),
inference(simp,[status(thm)],[334]) ).
thf(144,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_bot_Oextremum) ).
thf(804,plain,
! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(114,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_psubset__imp__subset) ).
thf(704,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(187,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/sandbox/benchmark/theBenchmark.p',fact_196_in__mono) ).
thf(947,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)],[187]) ).
thf(248,axiom,
! [A: int,B: int] :
( ( A != B )
= ( ( ord_less_int @ A @ B )
| ( ord_less_int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_neq__iff) ).
thf(1224,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)],[248]) ).
thf(105,axiom,
( ord_less_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/sandbox/benchmark/theBenchmark.p',fact_335_subset__not__subset__eq) ).
thf(672,plain,
( ord_less_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)],[105]) ).
thf(195,axiom,
! [A: a,B: set_a,C: set_a,D: a > $o] :
( ( member_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_prop__restrict) ).
thf(979,plain,
! [A: a,B: set_a,C: set_a,D: a > $o] :
( ( member_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(153,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( A = B )
=> ( ( ord_less_eq_a_o @ B @ C )
=> ( ord_less_eq_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ord__eq__le__trans) ).
thf(831,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( A = B )
=> ( ( ord_less_eq_a_o @ B @ C )
=> ( ord_less_eq_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(199,axiom,
! [A: set_a,B: int > set_a,C: int,D: int] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_order__le__less__subst1) ).
thf(996,plain,
! [A: set_a,B: int > set_a,C: int,D: int] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(234,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/sandbox/benchmark/theBenchmark.p',fact_17_Tree_Oinduct) ).
thf(1144,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)],[234]) ).
thf(123,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ~ ( ord_less_set_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_less__imp__not__less) ).
thf(737,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ~ ( ord_less_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(13,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( A != B )
=> ( ord_less_set_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_le__neq__trans) ).
thf(303,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( A != B )
=> ( ord_less_set_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,axiom,
! [A: int,B: ( a > $o ) > int,C: a > $o,D: a > $o] :
( ( ord_less_int @ A @ ( B @ C ) )
=> ( ( ord_less_eq_a_o @ C @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_order__less__le__subst1) ).
thf(268,plain,
! [A: int,B: ( a > $o ) > int,C: a > $o,D: a > $o] :
( ( ord_less_int @ A @ ( B @ C ) )
=> ( ( ord_less_eq_a_o @ C @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(269,plain,
! [A: int,B: ( a > $o ) > int,C: a > $o] :
( ( ord_less_int @ A @ ( B @ C ) )
=> ! [D: a > $o] :
( ( ord_less_eq_a_o @ C @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
inference(miniscope,[status(thm)],[268]) ).
thf(270,plain,
! [D: a > $o,C: a > $o,B: ( a > $o ) > int,A: int] :
( ( ~ ( ord_less_int @ A @ ( B @ C ) )
| ~ ( ord_less_eq_a_o @ C @ D )
| ( ord_less_eq_a_o @ ( sk1 @ D @ C @ B @ A ) @ ( sk2 @ D @ C @ B @ A ) )
| ( ord_less_int @ A @ ( B @ D ) ) )
& ( ~ ( ord_less_int @ A @ ( B @ C ) )
| ~ ( ord_less_eq_a_o @ C @ D )
| ~ ( ord_less_eq_int @ ( B @ ( sk1 @ D @ C @ B @ A ) ) @ ( B @ ( sk2 @ D @ C @ B @ A ) ) )
| ( ord_less_int @ A @ ( B @ D ) ) ) ),
inference(cnf,[status(esa)],[269]) ).
thf(271,plain,
! [D: a > $o,C: a > $o,B: ( a > $o ) > int,A: int] :
( ~ ( ord_less_int @ A @ ( B @ C ) )
| ~ ( ord_less_eq_a_o @ C @ D )
| ( ord_less_eq_a_o @ ( sk1 @ D @ C @ B @ A ) @ ( sk2 @ D @ C @ B @ A ) )
| ( ord_less_int @ A @ ( B @ D ) ) ),
inference(cnfConj,[status(thm)],[270]) ).
thf(38,axiom,
( ord_less_int
= ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
& ~ ( ord_less_eq_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_less__le__not__le) ).
thf(386,plain,
( ord_less_int
= ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
& ~ ( ord_less_eq_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(387,plain,
( ord_less_int
= ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
& ~ ( ord_less_eq_int @ B @ A ) ) ) ),
inference(lifteq,[status(thm)],[386]) ).
thf(21,axiom,
( ord_less_int
= ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
& ( B != A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_dual__order_Ostrict__iff__order) ).
thf(326,plain,
( ord_less_int
= ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
& ( B != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(327,plain,
( ord_less_int
= ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
& ( B != A ) ) ) ),
inference(lifteq,[status(thm)],[326]) ).
thf(1375,plain,
( ( ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
& ~ ( ord_less_eq_int @ B @ A ) ) )
= ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
& ( B != A ) ) ) )
| ( ord_less_int != ord_less_int ) ),
inference(paramod_ordered,[status(thm)],[387,327]) ).
thf(1376,plain,
( ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
& ~ ( ord_less_eq_int @ B @ A ) ) )
= ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
& ( B != A ) ) ) ),
inference(pattern_uni,[status(thm)],[1375:[]]) ).
thf(60,axiom,
( ord_less_int
= ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_less__le) ).
thf(477,plain,
( ord_less_int
= ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(146,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_set_a @ C @ A )
=> ( ord_less_set_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_dual__order_Ostrict__trans) ).
thf(811,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_set_a @ C @ A )
=> ( ord_less_set_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(148,axiom,
! [A: a > $o,B: a > $o,C: ( a > $o ) > int,D: int] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_int @ ( C @ B ) @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_order__le__less__subst2) ).
thf(816,plain,
! [A: a > $o,B: a > $o,C: ( a > $o ) > int,D: int] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_int @ ( C @ B ) @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(20,axiom,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_order__class_Oorder_Oantisym) ).
thf(323,plain,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(86,axiom,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_mem__Collect__eq) ).
thf(594,plain,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(236,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/sandbox/benchmark/theBenchmark.p',fact_29_subsetI) ).
thf(1162,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)],[236]) ).
thf(133,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ C @ A )
=> ( ord_less_eq_a_o @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_dual__order_Otrans) ).
thf(769,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ C @ A )
=> ( ord_less_eq_a_o @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(226,axiom,
! [A: binary1439146945Tree_a,B: a > int] :
( ( A != binary476621312_Tip_a )
=> ( ( binary1774981152rmrm_a @ B @ A )
= ( produc374321428ee_a_a @ ( binary1217730267_wrm_a @ B @ A ) @ ( binary339557810e_rm_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_wrmrm__decomp) ).
thf(1112,plain,
! [A: binary1439146945Tree_a,B: a > int] :
( ( A != binary476621312_Tip_a )
=> ( ( binary1774981152rmrm_a @ B @ A )
= ( produc374321428ee_a_a @ ( binary1217730267_wrm_a @ B @ A ) @ ( binary339557810e_rm_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(158,axiom,
( ord_less_eq_int
= ( ^ [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_dual__order_Oorder__iff__strict) ).
thf(848,plain,
( ord_less_eq_int
= ( ^ [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(113,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_less__imp__not__eq) ).
thf(700,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(71,axiom,
! [A: a > $o,B: a > $o,C: ( a > $o ) > a > $o,D: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ ( C @ B ) @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_a_o @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_a_o @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_order__subst2) ).
thf(520,plain,
! [A: a > $o,B: a > $o,C: ( a > $o ) > a > $o,D: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ ( C @ B ) @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_a_o @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_a_o @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(109,axiom,
! [A: set_a,B: a] :
( ( A = bot_bot_set_a )
=> ~ ( member_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_equals0D) ).
thf(685,plain,
! [A: set_a,B: a] :
( ( A = bot_bot_set_a )
=> ~ ( member_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(41,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ C @ B )
=> ( ord_less_eq_int @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_minf_I6_J) ).
thf(399,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)],[41]) ).
thf(56,axiom,
! [A: a > $o,B: a > $o,C: ( a > $o ) > set_a,D: set_a] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_order__subst2) ).
thf(455,plain,
! [A: a > $o,B: a > $o,C: ( a > $o ) > set_a,D: set_a] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(203,axiom,
! [A: int,B: int > int,C: int,D: int] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_ord__eq__less__subst) ).
thf(1015,plain,
! [A: int,B: int > int,C: int,D: int] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(14,axiom,
! [A: int,B: int] :
( ( A != B )
=> ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_order_Onot__eq__order__implies__strict) ).
thf(306,plain,
! [A: int,B: int] :
( ( A != B )
=> ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(215,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_dual__order_Orefl) ).
thf(1076,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(231,axiom,
! [A: set_a,B: set_a,C: set_a > int,D: int] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_int @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_order__le__less__subst2) ).
thf(1134,plain,
! [A: set_a,B: set_a,C: set_a > int,D: int] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_int @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(154,axiom,
! [A: set_a] :
~ ( ord_less_set_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_less__irrefl) ).
thf(836,plain,
! [A: set_a] :
~ ( ord_less_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(47,axiom,
( ord_less_int
= ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_order_Ostrict__iff__order) ).
thf(426,plain,
( ord_less_int
= ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(237,axiom,
! [A: int > int > $o,B: int,C: int] :
( ! [D: int,E: int] :
( ( ord_less_int @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: int] : ( A @ D @ D )
=> ( ! [D: int,E: int] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_linorder__less__wlog) ).
thf(1166,plain,
! [A: int > int > $o,B: int,C: int] :
( ! [D: int,E: int] :
( ( ord_less_int @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: int] : ( A @ D @ D )
=> ( ! [D: int,E: int] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(110,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_int @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_le__imp__less__or__eq) ).
thf(690,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_int @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(99,axiom,
! [A: int,B: set_a > int,C: set_a,D: set_a] :
( ( ord_less_eq_int @ A @ ( B @ C ) )
=> ( ( ord_less_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_order__le__less__subst1) ).
thf(640,plain,
! [A: int,B: set_a > int,C: set_a,D: set_a] :
( ( ord_less_eq_int @ A @ ( B @ C ) )
=> ( ( ord_less_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(124,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ~ ( ord_less_set_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_order_Oasym) ).
thf(739,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ~ ( ord_less_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(198,axiom,
! [A: int] :
~ ( ord_less_int @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_less__irrefl) ).
thf(993,plain,
! [A: int] :
~ ( ord_less_int @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(673,plain,
( ord_less_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ~ ( ord_less_eq_set_a @ B @ A ) ) ) ),
inference(lifteq,[status(thm)],[672]) ).
thf(83,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( B = C )
=> ( ord_less_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_ord__less__eq__trans) ).
thf(585,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( B = C )
=> ( ord_less_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(117,axiom,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_psubsetD) ).
thf(717,plain,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(252,axiom,
! [A: a > int,B: binary1439146945Tree_a,C: a] :
( ( binary1721989714Tree_a @ A @ B )
=> ( binary1721989714Tree_a @ A @ ( binary1226383794sert_a @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_binsert__sorted) ).
thf(1235,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)],[252]) ).
thf(80,axiom,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_antisym) ).
thf(576,plain,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(126,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_less__le__trans) ).
thf(744,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(24,axiom,
! [A: a > $o,B: a > $o,C: ( a > $o ) > set_a,D: set_a] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_set_a @ ( C @ B ) @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_order__le__less__subst2) ).
thf(336,plain,
! [A: a > $o,B: a > $o,C: ( a > $o ) > set_a,D: set_a] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_set_a @ ( C @ B ) @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(79,axiom,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_set_a @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_order__less__subst2) ).
thf(571,plain,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_set_a @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(1859,plain,
( ( ( collect_a
@ ^ [A: a] : $true )
!= bot_bot_set_a )
| ~ $true ),
inference(prim_subst,[status(thm)],[1277:[bind(A,$thf( ^ [C: a] : $true ))]]) ).
thf(1881,plain,
( ( collect_a
@ ^ [A: a] : $true )
!= bot_bot_set_a ),
inference(simp,[status(thm)],[1859]) ).
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 )
& ! [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/sandbox/benchmark/theBenchmark.p',fact_22_sortedTree_Osimps_I2_J) ).
thf(1240,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)],[254]) ).
thf(66,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_int @ C @ A )
=> ( ord_less_int @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_dual__order_Ostrict__trans1) ).
thf(497,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_int @ C @ A )
=> ( ord_less_int @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(166,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/sandbox/benchmark/theBenchmark.p',fact_197_subsetD) ).
thf(876,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)],[166]) ).
thf(94,axiom,
! [A: set_a] :
~ ( ord_less_set_a @ A @ bot_bot_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_not__psubset__empty) ).
thf(627,plain,
! [A: set_a] :
~ ( ord_less_set_a @ A @ bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(55,axiom,
! [A: set_a,B: set_a,C: set_a > int,D: int] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_int @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_order__less__subst2) ).
thf(450,plain,
! [A: set_a,B: set_a,C: set_a > int,D: int] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_int @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(31,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_order_Ostrict__trans) ).
thf(363,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(62,axiom,
! [A: set_a] :
( ! [B: a] :
~ ( member_a @ B @ A )
=> ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_equals0I) ).
thf(482,plain,
! [A: set_a] :
( ! [B: a] :
~ ( member_a @ B @ A )
=> ( A = bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(1320,plain,
( ( ( ^ [A: set_a,B: set_a] :
( ord_less_eq_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) ) )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( A = B ) ) ) )
| ( ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( B = A ) ) )
!= ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( B = A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1317,1266]) ).
thf(1321,plain,
( ( ^ [A: set_a,B: set_a] :
( ord_less_eq_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) ) )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( A = B ) ) ) ),
inference(pattern_uni,[status(thm)],[1320:[]]) ).
thf(174,axiom,
! [A: int] :
~ ( ord_less_int @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_dual__order_Oirrefl) ).
thf(903,plain,
! [A: int] :
~ ( ord_less_int @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(157,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_dual__order_Ostrict__implies__not__eq) ).
thf(844,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(182,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_dual__order_Ostrict__implies__not__eq) ).
thf(931,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(77,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
| ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_le__less__linear) ).
thf(539,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
| ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(193,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_order__refl) ).
thf(963,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(946,plain,
( ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) )
= ( (=) @ set_a ) ),
inference(lifteq,[status(thm)],[945]) ).
thf(42,axiom,
! [A: set_a,B: set_a,C: set_a > int,D: int] :
( ( ord_less_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_ord__less__eq__subst) ).
thf(401,plain,
! [A: set_a,B: set_a,C: set_a > int,D: int] :
( ( ord_less_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(121,axiom,
! [A: set_a] :
~ ( ord_less_set_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_dual__order_Oirrefl) ).
thf(731,plain,
! [A: set_a] :
~ ( ord_less_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(137,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ~ ( ord_less_set_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_leD) ).
thf(781,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ~ ( ord_less_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(206,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/sandbox/benchmark/theBenchmark.p',fact_77_order__class_Oorder_Oantisym) ).
thf(1030,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)],[206]) ).
thf(241,axiom,
! [A: set_a,B: set_a,C: a > $o,D: a > $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ! [E: a] :
( ( member_a @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq_set_a
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ A )
& ( C @ E ) ) )
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ B )
& ( D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_subset__CollectI) ).
thf(1193,plain,
! [A: set_a,B: set_a,C: a > $o,D: a > $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ! [E: a] :
( ( member_a @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq_set_a
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ A )
& ( C @ E ) ) )
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ B )
& ( D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(272,plain,
! [D: a > $o,C: a > $o,B: ( a > $o ) > int,A: int] :
( ~ ( ord_less_int @ A @ ( B @ C ) )
| ~ ( ord_less_eq_a_o @ C @ D )
| ~ ( ord_less_eq_int @ ( B @ ( sk1 @ D @ C @ B @ A ) ) @ ( B @ ( sk2 @ D @ C @ B @ A ) ) )
| ( ord_less_int @ A @ ( B @ D ) ) ),
inference(cnfConj,[status(thm)],[270]) ).
thf(849,plain,
( ord_less_eq_int
= ( ^ [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( B = A ) ) ) ),
inference(lifteq,[status(thm)],[848]) ).
thf(1309,plain,
( ( ^ [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( A = B ) ) )
= ( ^ [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( B = A ) ) ) ),
inference(rewrite,[status(thm)],[849,398]) ).
thf(76,axiom,
! [A: set_a] :
( ( A != bot_bot_set_a )
= ( ord_less_set_a @ bot_bot_set_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_bot_Onot__eq__extremum) ).
thf(536,plain,
! [A: set_a] :
( ( A != bot_bot_set_a )
= ( ord_less_set_a @ bot_bot_set_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(209,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/sandbox/benchmark/theBenchmark.p',fact_20_rm_Osimps) ).
thf(1045,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)],[209]) ).
thf(177,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) )
= ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_pred__subset__eq) ).
thf(914,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) )
= ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(36,axiom,
! [A: int,B: int] :
( ( ~ ( ord_less_eq_int @ A @ B ) )
= ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_not__le) ).
thf(378,plain,
! [A: int,B: int] :
( ( ~ ( ord_less_eq_int @ A @ B ) )
= ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(142,axiom,
! [A: int,B: int] :
( ~ ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_leI) ).
thf(800,plain,
! [A: int,B: int] :
( ~ ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(227,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_equalityD2) ).
thf(1116,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(128,axiom,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_order__le__less__subst1) ).
thf(752,plain,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(54,axiom,
! [A: a > $o] :
( ( bot_bot_set_a
= ( collect_a @ A ) )
= ( ! [B: a] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_empty__Collect__eq) ).
thf(447,plain,
! [A: a > $o] :
( ( bot_bot_set_a
= ( collect_a @ A ) )
= ( ! [B: a] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(49,axiom,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
= ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_subset__empty) ).
thf(432,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)],[49]) ).
thf(43,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_order_Ostrict__trans2) ).
thf(410,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(188,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/sandbox/benchmark/theBenchmark.p',fact_61_eq__iff) ).
thf(950,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)],[188]) ).
thf(250,axiom,
( ( binary1217730267_wrm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) )
= ( binary717961607le_T_a @ t1 @ x @ ( binary1217730267_wrm_a @ h @ t2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_res) ).
thf(1229,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)],[250]) ).
thf(164,axiom,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_ord__le__eq__subst) ).
thf(865,plain,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(25,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ~ ( ord_less_set_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_less__asym_H) ).
thf(341,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ~ ( ord_less_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(29,axiom,
! [A: set_a] :
( ( ? [B: a] : ( member_a @ B @ A ) )
= ( A != bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_ex__in__conv) ).
thf(358,plain,
! [A: set_a] :
( ( ? [B: a] : ( member_a @ B @ A ) )
= ( A != bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(51,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( A = B )
=> ( ( ord_less_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_ord__eq__less__trans) ).
thf(437,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( A = B )
=> ( ( ord_less_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(207,axiom,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_ord__eq__le__subst) ).
thf(1033,plain,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(152,axiom,
! [A: int,B: int] :
( ( ~ ( ord_less_int @ A @ B ) )
= ( ord_less_eq_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_not__less) ).
thf(828,plain,
! [A: int,B: int] :
( ( ~ ( ord_less_int @ A @ B ) )
= ( ord_less_eq_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(192,axiom,
! [A: int,B: int] :
( ( A != B )
=> ( ~ ( ord_less_int @ A @ B )
=> ( ord_less_int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_neqE) ).
thf(960,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)],[192]) ).
thf(211,axiom,
! [A: set_a] :
( ! [B: a] :
~ ( member_a @ B @ A )
=> ( ord_less_eq_set_a @ A @ bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_subset__emptyI) ).
thf(1065,plain,
! [A: set_a] :
( ! [B: a] :
~ ( member_a @ B @ A )
=> ( ord_less_eq_set_a @ A @ bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(112,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ~ ( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_psubsetE) ).
thf(696,plain,
! [A: set_a,B: set_a] :
( ( ord_less_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)],[112]) ).
thf(118,axiom,
! [A: a > $o,B: ( a > $o ) > a > $o,C: a > $o,D: a > $o] :
( ( ord_less_eq_a_o @ A @ ( B @ C ) )
=> ( ( ord_less_eq_a_o @ C @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_a_o @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_a_o @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_order__subst1) ).
thf(720,plain,
! [A: a > $o,B: ( a > $o ) > a > $o,C: a > $o,D: a > $o] :
( ( ord_less_eq_a_o @ A @ ( B @ C ) )
=> ( ( ord_less_eq_a_o @ C @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_a_o @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_a_o @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(953,plain,
~ ? [A: binary1439146945Tree_a,B: a,C: binary1439146945Tree_a] :
( binary476621312_Tip_a
= ( binary717961607le_T_a @ A @ B @ C ) ),
inference(miniscope,[status(thm)],[952]) ).
thf(954,plain,
! [C: binary1439146945Tree_a,B: a,A: binary1439146945Tree_a] :
( binary476621312_Tip_a
!= ( binary717961607le_T_a @ A @ B @ C ) ),
inference(cnf,[status(esa)],[953]) ).
thf(955,plain,
! [C: binary1439146945Tree_a,B: a,A: binary1439146945Tree_a] :
( ( binary717961607le_T_a @ A @ B @ C )
!= binary476621312_Tip_a ),
inference(lifteq,[status(thm)],[954]) ).
thf(282,plain,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ! [C: a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ord_less_eq_a_o @ A @ C ) ) ),
inference(miniscope,[status(thm)],[281]) ).
thf(283,plain,
! [C: a > $o,B: a > $o,A: a > $o] :
( ~ ( ord_less_eq_a_o @ A @ B )
| ~ ( ord_less_eq_a_o @ B @ C )
| ( ord_less_eq_a_o @ A @ C ) ),
inference(cnf,[status(esa)],[282]) ).
thf(45,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_dual__order_Ostrict__implies__order) ).
thf(415,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(69,axiom,
! [A: int,B: int > int,C: int,D: int] :
( ( ord_less_eq_int @ A @ ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_order__le__less__subst1) ).
thf(506,plain,
! [A: int,B: int > int,C: int,D: int] :
( ( ord_less_eq_int @ A @ ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(132,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ~ ( ord_less_set_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_less__asym) ).
thf(767,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ~ ( ord_less_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(155,axiom,
( ord_less_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/sandbox/benchmark/theBenchmark.p',fact_275_less__le__not__le) ).
thf(839,plain,
( ord_less_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)],[155]) ).
thf(120,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_less__trans) ).
thf(728,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(263,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/sandbox/benchmark/theBenchmark.p',fact_21_wrm__set1) ).
thf(1261,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)],[263]) ).
thf(427,plain,
( ord_less_int
= ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
& ( A != B ) ) ) ),
inference(lifteq,[status(thm)],[426]) ).
thf(1547,plain,
( ~ $true
| ( ( binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) )
!= ( binary1721989714Tree_a @ h @ t1 ) ) ),
inference(paramod_ordered,[status(thm)],[1259,264]) ).
thf(1548,plain,
( ( binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) )
!= ( binary1721989714Tree_a @ h @ t1 ) ),
inference(simp,[status(thm)],[1547]) ).
thf(1549,plain,
( ( h != h )
| ( ( binary717961607le_T_a @ t1 @ x @ t2 )
!= t1 ) ),
inference(simp,[status(thm)],[1548]) ).
thf(1550,plain,
( ( binary717961607le_T_a @ t1 @ x @ t2 )
!= t1 ),
inference(simp,[status(thm)],[1549]) ).
thf(159,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_le__less__trans) ).
thf(850,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(52,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ~ ( ord_less_set_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_dual__order_Oasym) ).
thf(442,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ~ ( ord_less_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(228,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_less__imp__neq) ).
thf(1120,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(230,axiom,
! [A: int,B: int,C: int > set_a,D: set_a] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_order__less__le__subst2) ).
thf(1129,plain,
! [A: int,B: int,C: int > set_a,D: set_a] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(196,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/sandbox/benchmark/theBenchmark.p',fact_209_Collect__subset) ).
thf(982,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)],[196]) ).
thf(201,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_less__imp__not__less) ).
thf(1004,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(33,axiom,
! [A: int,B: set_a > int,C: set_a,D: set_a] :
( ( ord_less_int @ A @ ( B @ C ) )
=> ( ( ord_less_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_order__less__subst1) ).
thf(369,plain,
! [A: int,B: set_a > int,C: set_a,D: set_a] :
( ( ord_less_int @ A @ ( B @ C ) )
=> ( ( ord_less_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_set_a @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(89,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_less__imp__neq) ).
thf(607,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(63,axiom,
! [A: int,B: int] :
( ( ~ ( ord_less_eq_int @ A @ B ) )
= ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_verit__comp__simplify1_I3_J) ).
thf(486,plain,
! [A: int,B: int] :
( ( ~ ( ord_less_eq_int @ A @ B ) )
= ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(183,axiom,
! [A: a > int,B: a,C: a,D: binary1439146945Tree_a] : ( binary670562003pred_a @ A @ B @ C @ D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_sorted__distinct) ).
thf(935,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)],[183]) ).
thf(180,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_antisym__conv) ).
thf(923,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(15,axiom,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
= ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_bot_Oextremum__unique) ).
thf(309,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)],[15]) ).
thf(85,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ~ ( ord_less_eq_int @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_pinf_I6_J) ).
thf(592,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)],[85]) ).
thf(58,axiom,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( ord_less_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_order__less__le__subst1) ).
thf(469,plain,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( ord_less_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(1944,plain,
binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ sk124 @ t2 ),
inference(func_ext,[status(esa)],[1943]) ).
thf(2184,plain,
$false,
inference(e,[status(thm)],[645,1024,1190,760,893,777,481,479,1105,1211,582,276,1068,741,1205,1142,511,1533,614,597,861,1078,533,500,797,715,814,1260,747,945,898,1001,1243,288,1386,301,1529,1254,841,417,785,917,802,357,460,902,853,284,881,289,316,1100,492,376,937,348,806,821,1109,321,602,397,280,634,734,956,660,265,1943,428,527,312,1074,1206,942,529,1199,381,366,1091,825,302,862,275,1238,1042,952,693,630,361,879,435,889,1159,757,682,1106,1089,874,1259,615,1227,1096,1006,783,1856,725,388,1878,328,884,1082,669,526,637,489,590,679,706,901,476,1249,1539,654,1246,779,503,1266,1231,984,911,343,1086,633,921,541,657,398,1071,1026,1185,794,926,765,1054,1187,674,906,298,965,1103,264,856,279,444,375,1251,618,1219,824,772,286,875,579,958,1256,413,1124,281,1139,313,611,1239,335,804,704,947,1224,672,979,1209,831,996,1144,737,303,271,1376,477,811,858,816,323,594,1162,769,1112,848,700,520,685,399,455,1015,306,267,1076,374,1277,1134,823,836,426,1166,525,690,640,327,739,993,673,585,717,1235,1317,576,744,336,613,386,314,571,1881,1240,497,876,627,450,363,482,1321,903,844,931,539,963,946,632,401,731,781,1030,1193,272,1309,536,1045,914,378,800,287,1116,752,447,315,432,410,950,1229,273,865,326,341,358,437,1033,828,960,1065,696,720,955,283,415,506,268,474,767,839,728,1261,427,1550,850,442,1120,332,1129,982,1004,369,607,486,935,923,309,1204,592,469,1944]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP033^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.09/0.21 % Computer : n006.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 19:38:46 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.68/0.53 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.74/0.86 % [INFO] Parsing done (324ms).
% 1.74/0.86 % [INFO] Running in sequential loop mode.
% 2.86/1.19 % [INFO] eprover registered as external prover.
% 3.05/1.20 % [INFO] Scanning for conjecture ...
% 3.25/1.33 % [INFO] Found a conjecture (or negated_conjecture) and 353 axioms. Running axiom selection ...
% 3.46/1.47 % [INFO] Axiom selection finished. Selected 261 axioms (removed 92 axioms).
% 4.42/1.73 % [INFO] Problem is higher-order (TPTP THF).
% 4.42/1.77 % [INFO] Type checking passed.
% 4.42/1.77 % [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 ...
% 52.27/16.79 % External prover 'e' found a proof!
% 52.27/16.79 % [INFO] Killing All external provers ...
% 52.27/16.79 % Time passed: 16488ms (effective reasoning time: 15926ms)
% 52.27/16.79 % 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)>
% 52.87/16.80 % Axioms used in derivation (261): fact_215_le__less, fact_335_subset__not__subset__eq, fact_245_order__less__le__subst2, fact_221_order__le__less__subst1, fact_224_order__le__less__subst1, fact_146_less__irrefl, fact_3_sortLemmaL, fact_213_leI, fact_275_less__le__not__le, fact_9_memb__spec, fact_63_antisym, fact_284_order_Oorder__iff__strict, fact_168_less__imp__triv, fact_170_linorder__cases, fact_321_subset__emptyI, fact_197_subsetD, fact_133_less__imp__neq, fact_12_sorted__distinct, fact_188_dual__order_Ostrict__implies__not__eq, fact_132_less__imp__neq, fact_211_leD, fact_62_eq__iff, fact_348_pred__subset__eq, fact_41_mem__Collect__eq, fact_36_order__refl, fact_90_ord__eq__less__subst, fact_158_less__imp__not__eq, fact_268_less__le__trans, fact_77_order__class_Oorder_Oantisym, fact_206_set__eq__subset, fact_294_dual__order_Ostrict__trans2, fact_250_not__le, fact_262_less__imp__le, fact_255_antisym__conv1, fact_129_order_Oasym, fact_144_less__linear, fact_327_complete__interval, fact_322_minf_I8_J, fact_86_dual__order_Oeq__iff, fact_0_t2nTip, fact_49_order__subst2, fact_217_less__le, fact_305_dual__order_Ostrict__implies__order, fact_27_subset__empty, fact_8_sortedTree_Osimps_I1_J, fact_18_Tree_Oexhaust, fact_238_order__less__le__subst1, fact_15_binsert_Osimps_I1_J, fact_178_less__imp__not__less, fact_161_less__not__sym, fact_75_ord__le__eq__trans, fact_64_antisym, fact_324_pinf_I8_J, fact_241_order__less__le__subst2, fact_192_emptyE, fact_207_Collect__mono__iff, fact_339_psubsetE, fact_17_Tree_Oinduct, fact_1_s, fact_13__092_060open_062Tip_A_092_060noteq_062_ATip_A_092_060and_062_AsortedTree_Ah_ATip_A_092_060longrightarrow_062_AsortedTree_Ah_A_Iwrm_Ah_ATip_J_092_060close_062, fact_29_subsetI, fact_343_prop__restrict, fact_2_res, fact_148_ord__eq__less__trans, fact_235_order__less__le__subst1, fact_317_bot_Oextremum__strict, fact_313_bot_Oextremum__unique, fact_297_order_Ostrict__implies__order, fact_189_dual__order_Ostrict__implies__not__eq, fact_259_antisym__conv2, fact_290_dual__order_Ostrict__trans1, fact_138_less__asym_H, fact_45_order__subst1, fact_244_order__less__le__subst2, fact_242_order__less__le__subst2, fact_111_order__less__subst1, fact_19_rm__set, fact_256_antisym__conv1, fact_110_order__less__subst1, fact_23_remove_Osimps_I1_J, fact_293_dual__order_Ostrict__trans2, fact_201_equalityD2, fact_193_equals0D, fact_220_order__le__less__subst1, fact_141_less__trans, fact_352_wrmrm__decomp, fact_58_ord__le__eq__subst, fact_117_order__less__subst2, fact_152_ord__less__eq__trans, fact_85_dual__order_Oeq__iff, fact_261_less__imp__le, fact_251_not__less, fact_155_dual__order_Oasym, fact_139_less__asym_H, fact_57_ord__le__eq__subst, fact_81_dual__order_Orefl, fact_172_dual__order_Oirrefl, fact_52_order__subst2, fact_209_Collect__subset, fact_98_ord__less__eq__subst, fact_186_order_Ostrict__implies__not__eq, fact_175_order_Ostrict__trans, fact_30_empty__Collect__eq, fact_204_Collect__mono, fact_287_order_Ostrict__iff__order, fact_101_ord__less__eq__subst, fact_184_not__less__iff__gr__or__eq, fact_326_verit__comp__simplify1_I3_J, fact_270_le__less__linear, fact_116_order__less__subst2, fact_264_le__less__trans, fact_185_order_Ostrict__implies__not__eq, fact_11_h2, fact_28_subset__antisym, fact_21_wrm__set1, fact_149_ord__eq__less__trans, fact_349_subset__Collect__iff, fact_78_order__class_Oorder_Oantisym, fact_125_lt__ex, fact_278_order_Ostrict__trans1, fact_128_neq__iff, fact_61_eq__iff, fact_84_dual__order_Otrans, fact_253_le__neq__trans, fact_319_bot_Onot__eq__extremum, fact_218_less__le, fact_214_le__less, fact_32_all__not__in__conv, fact_135_less__asym, fact_47_order__subst1, fact_5_Tree_Oinject, fact_26_empty__subsetI, fact_347_psubsetD, fact_14_Tree_Odistinct_I1_J, fact_181_dual__order_Ostrict__trans, fact_267_less__le__trans, fact_167_less__imp__triv, fact_195_ex__in__conv, fact_60_ord__le__eq__subst, fact_299_dual__order_Oorder__iff__strict, fact_83_dual__order_Otrans, fact_311_bot_Oextremum, fact_89_ord__eq__less__subst, fact_308_order_Onot__eq__order__implies__strict, fact_72_order__class_Oorder_Oeq__iff, fact_350_subset__CollectI, fact_208_empty__def, fact_309_order_Onot__eq__order__implies__strict, fact_7_h1, fact_210_leD, fact_42_Collect__mem__eq, fact_205_subset__trans, fact_274_less__le__not__le, fact_333_subset__iff__psubset__eq, fact_48_order__subst1, fact_281_order_Ostrict__trans2, fact_54_ord__eq__le__subst, fact_344_Collect__restrict, fact_332_not__psubset__empty, fact_82_dual__order_Orefl, fact_70_antisym__conv, fact_160_less__not__sym, fact_99_ord__less__eq__subst, fact_171_dual__order_Oirrefl, fact_336_psubset__subset__trans, fact_252_le__neq__trans, fact_229_order__le__less__subst2, fact_296_order_Ostrict__implies__order, fact_258_antisym__conv2, fact_239_order__less__le__subst1, fact_325_pinf_I6_J, fact_20_rm_Osimps, fact_271_le__imp__less__or__eq, fact_265_le__less__trans, fact_120_order__less__subst2, fact_277_not__le__imp__less, fact_194_equals0I, fact_334_subset__psubset__trans, fact_233_order__le__less__subst2, fact_33_empty__iff, fact_232_order__le__less__subst2, fact_182_dual__order_Ostrict__trans, fact_93_ord__eq__less__subst, fact_164_less__imp__not__eq2, fact_4_sortLemmaR, fact_126_gt__ex, fact_43_Collect__cong, fact_69_antisym__conv, fact_51_order__subst2, fact_291_dual__order_Ostrict__trans1, fact_88_dual__order_Oantisym, fact_337_psubset__imp__subset, fact_315_bot_Oextremum__uniqueI, fact_340_less__eq__set__def, fact_198_equalityE, fact_300_dual__order_Oorder__iff__strict, fact_35_order__refl, fact_6_binsert__sorted, fact_203_subset__refl, fact_202_subset__iff, fact_351_remove_Osimps_I2_J, fact_142_less__trans, fact_236_order__less__le__subst1, fact_55_ord__eq__le__subst, fact_328_bot_Oordering__top__axioms, fact_177_less__imp__not__less, fact_272_le__imp__less__or__eq, fact_87_dual__order_Oantisym, fact_10_sorted__distinct__pred__def, fact_46_order__subst1, fact_174_order_Ostrict__trans, fact_53_ord__eq__le__subst, fact_223_order__le__less__subst1, fact_127_neqE, fact_22_sortedTree_Osimps_I2_J, fact_31_Collect__empty__eq, fact_288_order_Ostrict__iff__order, fact_136_less__asym, fact_282_order_Ostrict__trans2, fact_67_order_Otrans, fact_323_minf_I6_J, fact_130_order_Oasym, fact_92_ord__eq__less__subst, fact_73_ord__eq__le__trans, fact_157_less__imp__not__eq, fact_151_ord__less__eq__trans, fact_102_ord__less__eq__subst, fact_165_less__imp__not__eq2, fact_79_order__trans, fact_303_dual__order_Ostrict__iff__order, fact_76_ord__le__eq__trans, fact_25_setOf_Osimps_I1_J, fact_306_dual__order_Ostrict__implies__order, fact_80_order__trans, fact_50_order__subst2, fact_145_less__irrefl, fact_196_in__mono, fact_71_order__class_Oorder_Oeq__iff, fact_230_order__le__less__subst2, fact_66_eq__refl, fact_108_order__less__subst1, fact_68_order_Otrans, fact_59_ord__le__eq__subst, fact_24_binsert_Osimps_I2_J, fact_180_linorder__less__wlog, fact_74_ord__eq__le__trans, fact_16_wrm_Osimps, fact_119_order__less__subst2, fact_302_dual__order_Ostrict__iff__order, fact_56_ord__eq__le__subst, fact_279_order_Ostrict__trans1, fact_285_order_Oorder__iff__strict, fact_330_psubsetI, fact_107_order__less__subst1, fact_338_psubset__eq, fact_154_dual__order_Oasym, fact_163_antisym__conv3, fact_65_eq__refl, fact_200_equalityD1, fact_341_verit__comp__simplify1_I1_J, fact_199_subset__eq
% 52.87/16.80 % No. of inferences in proof: 613
% 52.87/16.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 16488 ms resp. 15926 ms w/o parsing
% 53.95/17.04 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 53.95/17.04 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------