TSTP Solution File: ITP029^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ITP029^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:22:13 EDT 2024
% Result : Theorem 9.04s 3.38s
% Output : Refutation 9.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 116
% Syntax : Number of formulae : 210 ( 78 unt; 24 typ; 0 def)
% Number of atoms : 444 ( 134 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 1292 ( 90 ~; 24 |; 24 &; 936 @)
% ( 0 <=>; 218 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 8 ( 7 usr)
% Number of type conns : 93 ( 93 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 9 con; 0-4 aty)
% Number of variables : 478 ( 8 ^ 420 !; 50 ?; 478 :)
% Comments :
%------------------------------------------------------------------------------
thf(binary594033953_set_a_type,type,
binary594033953_set_a: $tType ).
thf(binary1439146945Tree_a_type,type,
binary1439146945Tree_a: $tType ).
thf(set_set_set_a_type,type,
set_set_set_a: $tType ).
thf(set_set_a_type,type,
set_set_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_type,type,
binary717961607le_T_a: binary1439146945Tree_a > a > binary1439146945Tree_a > binary1439146945Tree_a ).
thf(binary476621312_Tip_a_type,type,
binary476621312_Tip_a: binary1439146945Tree_a ).
thf(binary256242811Tree_a_type,type,
binary256242811Tree_a: binary1439146945Tree_a > set_a ).
thf(binary945792244etOf_a_type,type,
binary945792244etOf_a: binary1439146945Tree_a > set_a ).
thf(binary1721989714Tree_a_type,type,
binary1721989714Tree_a: ( a > int ) > binary1439146945Tree_a > $o ).
thf(binary670562003pred_a_type,type,
binary670562003pred_a: ( a > int ) > a > a > binary1439146945Tree_a > $o ).
thf(bot_bot_set_a_type,type,
bot_bot_set_a: set_a ).
thf(ord_less_int_type,type,
ord_less_int: int > int > $o ).
thf(ord_less_eq_set_a_type,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(pred_chain_a_type,type,
pred_chain_a: set_a > ( a > a > $o ) > set_a > $o ).
thf(member_a_type,type,
member_a: a > set_a > $o ).
thf(a2_type,type,
a2: a ).
thf(b_type,type,
b: a ).
thf(h_type,type,
h: a > int ).
thf(t1_type,type,
t1: binary1439146945Tree_a ).
thf(t2_type,type,
t2: binary1439146945Tree_a ).
thf(x_type,type,
x: a ).
thf(76,axiom,
! [A: int] :
? [B: int] : ( ord_less_int @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_gt__ex) ).
thf(385,plain,
! [A: int] :
? [B: int] : ( ord_less_int @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(27,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ C @ B )
=> ( C != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_minf_I4_J) ).
thf(185,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ C @ B )
=> ( C != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(28,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_order_Ostrict__trans) ).
thf(189,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)],[28]) ).
thf(67,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_less__asym) ).
thf(348,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(87,axiom,
( ( member_a @ a2 @ ( binary945792244etOf_a @ t1 ) )
=> ( a2 = b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__092_060open_062a_A_092_060in_062_AsetOf_At1_A_092_060Longrightarrow_062_Aa_A_061_Ab_092_060close_062) ).
thf(403,plain,
( ( member_a @ a2 @ ( binary945792244etOf_a @ t1 ) )
=> ( a2 = b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(88,axiom,
member_a @ a2 @ ( binary945792244etOf_a @ t2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_adef1) ).
thf(406,plain,
member_a @ a2 @ ( binary945792244etOf_a @ t2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(63,axiom,
! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
( ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_pinf_I2_J) ).
thf(314,plain,
! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
( ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(17,axiom,
( ( binary945792244etOf_a @ binary476621312_Tip_a )
= bot_bot_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_setOf_Osimps_I1_J) ).
thf(138,plain,
( ( binary945792244etOf_a @ binary476621312_Tip_a )
= bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(44,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_order_Oasym) ).
thf(249,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(69,axiom,
! [A: int,B: int] :
( ~ ( ord_less_int @ A @ B )
=> ( ( A != B )
=> ( ord_less_int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_linorder__cases) ).
thf(352,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)],[69]) ).
thf(90,axiom,
binary670562003pred_a @ h @ a2 @ b @ binary476621312_Tip_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10__092_060open_062sorted__distinct__pred_Ah_Aa_Ab_ATip_092_060close_062) ).
thf(408,plain,
binary670562003pred_a @ h @ a2 @ b @ binary476621312_Tip_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(52,axiom,
! [A: int,B: int] :
( ( A != B )
= ( ( ord_less_int @ A @ B )
| ( ord_less_int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_neq__iff) ).
thf(276,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)],[52]) ).
thf(12,axiom,
! [A: set_a] :
( ! [B: a] :
~ ( member_a @ B @ A )
=> ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_equals0I) ).
thf(120,plain,
! [A: set_a] :
( ! [B: a] :
~ ( member_a @ B @ A )
=> ( A = bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(32,axiom,
! [A: a > int] : ( binary1721989714Tree_a @ A @ binary476621312_Tip_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_sortedTree_Osimps_I1_J) ).
thf(202,plain,
! [A: a > int] : ( binary1721989714Tree_a @ A @ binary476621312_Tip_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(78,axiom,
binary1721989714Tree_a @ h @ t1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_s1) ).
thf(389,plain,
binary1721989714Tree_a @ h @ t1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(30,axiom,
! [A: int] :
? [B: int] : ( ord_less_int @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_lt__ex) ).
thf(196,plain,
! [A: int] :
? [B: int] : ( ord_less_int @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(83,axiom,
( ( h @ a2 )
= ( h @ b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_hahb) ).
thf(396,plain,
( ( h @ a2 )
= ( h @ b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(93,axiom,
( ( member_a @ a2 @ ( binary945792244etOf_a @ t1 ) )
| ( a2 = x )
| ( member_a @ a2 @ ( binary945792244etOf_a @ t2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12__092_060open_062a_A_092_060in_062_AsetOf_At1_A_092_060or_062_Aa_A_061_Ax_A_092_060or_062_Aa_A_092_060in_062_AsetOf_At2_092_060close_062) ).
thf(411,plain,
( ( member_a @ a2 @ ( binary945792244etOf_a @ t1 ) )
| ( a2 = x )
| ( member_a @ a2 @ ( binary945792244etOf_a @ t2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(42,axiom,
! [A: a > int,B: binary1439146945Tree_a,C: a,D: binary1439146945Tree_a] :
( ( binary1721989714Tree_a @ A @ ( binary717961607le_T_a @ B @ C @ D ) )
=> ( binary1721989714Tree_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_sortLemmaL) ).
thf(243,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)],[42]) ).
thf(62,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ C @ B )
=> ~ ( ord_less_int @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_minf_I7_J) ).
thf(312,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ C @ B )
=> ~ ( ord_less_int @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(34,axiom,
! [A: int,B: int] :
( ( ~ ( ord_less_int @ A @ B ) )
= ( ( ord_less_int @ B @ A )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_not__less__iff__gr__or__eq) ).
thf(206,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)],[34]) ).
thf(60,axiom,
! [A: a > int,B: binary1439146945Tree_a,C: a,D: binary1439146945Tree_a] :
( ( binary1721989714Tree_a @ A @ ( binary717961607le_T_a @ B @ C @ D ) )
= ( ( binary1721989714Tree_a @ A @ B )
& ! [E: a] :
( ( member_a @ E @ ( binary945792244etOf_a @ B ) )
=> ( ord_less_int @ ( A @ E ) @ ( A @ C ) ) )
& ! [E: a] :
( ( member_a @ E @ ( binary945792244etOf_a @ D ) )
=> ( ord_less_int @ ( A @ C ) @ ( A @ E ) ) )
& ( binary1721989714Tree_a @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_sortedTree_Osimps_I2_J) ).
thf(307,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)],[60]) ).
thf(55,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( A = B )
| ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_less__linear) ).
thf(292,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)],[55]) ).
thf(50,axiom,
! [A: int,B: int] :
( ( A != B )
=> ( ~ ( ord_less_int @ A @ B )
=> ( ord_less_int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_neqE) ).
thf(270,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)],[50]) ).
thf(6,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_subset__antisym) ).
thf(102,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)],[6]) ).
thf(74,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_less__trans) ).
thf(380,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)],[74]) ).
thf(11,axiom,
! [A: set_a] :
( ( ? [B: a] : ( member_a @ B @ A ) )
= ( A != bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_ex__in__conv) ).
thf(117,plain,
! [A: set_a] :
( ( ? [B: a] : ( member_a @ B @ A ) )
= ( A != bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(37,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ C @ B )
=> ( ord_less_int @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_minf_I5_J) ).
thf(220,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ C @ B )
=> ( ord_less_int @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(72,axiom,
! [A: int,B: int,C: int > int,D: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_order__less__subst2) ).
thf(366,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)],[72]) ).
thf(58,axiom,
! [A: set_a,B: set_a] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_subsetI) ).
thf(302,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)],[58]) ).
thf(29,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ C @ B )
=> ( C != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_minf_I3_J) ).
thf(192,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ C @ B )
=> ( C != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(89,axiom,
member_a @ b @ ( binary945792244etOf_a @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_bdef) ).
thf(407,plain,
member_a @ b @ ( binary945792244etOf_a @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(71,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( B = C )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_ord__less__eq__trans) ).
thf(361,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)],[71]) ).
thf(4,axiom,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_empty__iff) ).
thf(97,plain,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(64,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_less__imp__not__eq) ).
thf(324,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(65,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_pinf_I7_J) ).
thf(328,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(13,axiom,
! [A: set_a] :
( ( ! [B: a] :
~ ( member_a @ B @ A ) )
= ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_all__not__in__conv) ).
thf(124,plain,
! [A: set_a] :
( ( ! [B: a] :
~ ( member_a @ B @ A ) )
= ( A = bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(36,axiom,
! [A: int,B: int,C: int > int,D: int] :
( ( ord_less_int @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ord__less__eq__subst) ).
thf(212,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)],[36]) ).
thf(3,axiom,
pred_chain_a = pred_chain_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_pred__on_Ochain_Ocong) ).
thf(96,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(80,axiom,
ord_less_int @ ( h @ x ) @ ( h @ a2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_o2) ).
thf(393,plain,
ord_less_int @ ( h @ x ) @ ( h @ a2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(23,axiom,
! [A: binary1439146945Tree_a,B: a,C: binary1439146945Tree_a,D: binary1439146945Tree_a,E: a,F: binary1439146945Tree_a] :
( ( ( binary717961607le_T_a @ A @ B @ C )
= ( binary717961607le_T_a @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_Tree_Oinject) ).
thf(173,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)],[23]) ).
thf(7,axiom,
( ( binary256242811Tree_a @ binary476621312_Tip_a )
= bot_bot_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_Tree_Osimps_I14_J) ).
thf(105,plain,
( ( binary256242811Tree_a @ binary476621312_Tip_a )
= bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(48,axiom,
binary1721989714Tree_a @ h @ t2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_s2) ).
thf(266,plain,
binary1721989714Tree_a @ h @ t2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(84,axiom,
member_a @ a2 @ ( binary945792244etOf_a @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_adef) ).
thf(398,plain,
member_a @ a2 @ ( binary945792244etOf_a @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(57,axiom,
! [A: int,B: int > int,C: int,D: int] :
( ( ord_less_int @ A @ ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_order__less__subst1) ).
thf(298,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)],[57]) ).
thf(20,axiom,
binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_s) ).
thf(148,plain,
binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(53,axiom,
! [A: int,B: int] :
( ( A != B )
=> ( ~ ( ord_less_int @ A @ B )
=> ( ord_less_int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_linorder__neqE__linordered__idom) ).
thf(279,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)],[53]) ).
thf(25,axiom,
! [A: a > int,B: binary1439146945Tree_a,C: a,D: binary1439146945Tree_a] :
( ( binary1721989714Tree_a @ A @ ( binary717961607le_T_a @ B @ C @ D ) )
=> ( binary1721989714Tree_a @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_sortLemmaR) ).
thf(180,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)],[25]) ).
thf(21,axiom,
! [A: binary1439146945Tree_a > $o,B: binary1439146945Tree_a] :
( ( A @ binary476621312_Tip_a )
=> ( ! [C: binary1439146945Tree_a,D: a,E: binary1439146945Tree_a] :
( ( A @ C )
=> ( ( A @ E )
=> ( A @ ( binary717961607le_T_a @ C @ D @ E ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_Tree_Oinduct) ).
thf(149,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)],[21]) ).
thf(24,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ( C != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_pinf_I3_J) ).
thf(176,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ( C != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(33,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_dual__order_Oasym) ).
thf(204,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(19,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_less__imp__neq) ).
thf(144,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(68,axiom,
! [A: a,B: binary1439146945Tree_a,C: binary1439146945Tree_a] : ( member_a @ A @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ B @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_Tree_Oset__intros_I2_J) ).
thf(350,plain,
! [A: a,B: binary1439146945Tree_a,C: binary1439146945Tree_a] : ( member_a @ A @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(77,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_less__imp__not__less) ).
thf(387,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(18,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_dual__order_Ostrict__implies__not__eq) ).
thf(140,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(45,axiom,
! [A: binary1439146945Tree_a] :
( ( A != binary476621312_Tip_a )
=> ~ ! [B: binary1439146945Tree_a,C: a,D: binary1439146945Tree_a] :
( A
!= ( binary717961607le_T_a @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_Tree_Oexhaust) ).
thf(251,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)],[45]) ).
thf(31,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_order_Ostrict__implies__not__eq) ).
thf(198,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(66,axiom,
! [A: int > int > $o,B: int,C: int] :
( ! [D: int,E: int] :
( ( ord_less_int @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: int] : ( A @ D @ D )
=> ( ! [D: int,E: int] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_linorder__less__wlog) ).
thf(330,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)],[66]) ).
thf(85,axiom,
binary670562003pred_a @ h @ a2 @ b @ t2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_h2) ).
thf(399,plain,
binary670562003pred_a @ h @ a2 @ b @ t2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(81,axiom,
binary670562003pred_a @ h @ a2 @ b @ t1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_h1) ).
thf(394,plain,
binary670562003pred_a @ h @ a2 @ b @ t1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(49,axiom,
! [A: int,B: int] :
( ~ ( ord_less_int @ A @ B )
=> ( ( ~ ( ord_less_int @ B @ A ) )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_antisym__conv3) ).
thf(267,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)],[49]) ).
thf(46,axiom,
! [A: int,B: int,C: $o] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ B @ A )
=> C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_less__imp__triv) ).
thf(255,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)],[46]) ).
thf(35,axiom,
! [A: a,B: binary1439146945Tree_a,C: a,D: binary1439146945Tree_a] :
( ( member_a @ A @ ( binary256242811Tree_a @ B ) )
=> ( member_a @ A @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_Tree_Oset__intros_I1_J) ).
thf(209,plain,
! [A: a,B: binary1439146945Tree_a,C: a,D: binary1439146945Tree_a] :
( ( member_a @ A @ ( binary256242811Tree_a @ B ) )
=> ( member_a @ A @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(9,axiom,
! [A: set_a,B: a > a > $o] : ( pred_chain_a @ A @ B @ bot_bot_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_pred__on_Ochain__empty) ).
thf(112,plain,
! [A: set_a,B: a > a > $o] : ( pred_chain_a @ A @ B @ bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(70,axiom,
! [A: set_a,B: a > a > $o,C: a > a > $o,D: set_a] :
( ! [E: a,F: a] :
( ( member_a @ E @ A )
=> ( ( member_a @ F @ A )
=> ( ( B @ E @ F )
=> ( C @ E @ F ) ) ) )
=> ( ( pred_chain_a @ A @ B @ D )
=> ( pred_chain_a @ A @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_chain__mono) ).
thf(355,plain,
! [A: set_a,B: a > a > $o,C: a > a > $o,D: set_a] :
( ! [E: a,F: a] :
( ( member_a @ E @ A )
=> ( ( member_a @ F @ A )
=> ( ( B @ E @ F )
=> ( C @ E @ F ) ) ) )
=> ( ( pred_chain_a @ A @ B @ D )
=> ( pred_chain_a @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(56,axiom,
! [A: a,B: binary1439146945Tree_a,C: binary1439146945Tree_a,D: a] :
( ( member_a @ A @ ( binary256242811Tree_a @ B ) )
=> ( member_a @ A @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ C @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_Tree_Oset__intros_I3_J) ).
thf(295,plain,
! [A: a,B: binary1439146945Tree_a,C: binary1439146945Tree_a,D: a] :
( ( member_a @ A @ ( binary256242811Tree_a @ B ) )
=> ( member_a @ A @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ C @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(54,axiom,
! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
( ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_minf_I2_J) ).
thf(282,plain,
! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
( ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(91,axiom,
member_a @ b @ ( binary945792244etOf_a @ t1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_bdef1) ).
thf(409,plain,
member_a @ b @ ( binary945792244etOf_a @ t1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(61,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ~ ( ord_less_int @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_pinf_I5_J) ).
thf(310,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ~ ( ord_less_int @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(26,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ C @ A )
=> ( ord_less_int @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_dual__order_Ostrict__trans) ).
thf(182,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)],[26]) ).
thf(73,axiom,
! [A: a,B: binary1439146945Tree_a] :
( ( member_a @ A @ ( binary256242811Tree_a @ B ) )
=> ( ! [C: binary1439146945Tree_a] :
( ? [D: a,E: binary1439146945Tree_a] :
( B
= ( binary717961607le_T_a @ C @ D @ E ) )
=> ~ ( member_a @ A @ ( binary256242811Tree_a @ C ) ) )
=> ( ! [C: binary1439146945Tree_a,D: binary1439146945Tree_a] :
( B
!= ( binary717961607le_T_a @ C @ A @ D ) )
=> ~ ! [C: binary1439146945Tree_a,D: a,E: binary1439146945Tree_a] :
( ( B
= ( binary717961607le_T_a @ C @ D @ E ) )
=> ~ ( member_a @ A @ ( binary256242811Tree_a @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_Tree_Oset__cases) ).
thf(370,plain,
! [A: a,B: binary1439146945Tree_a] :
( ( member_a @ A @ ( binary256242811Tree_a @ B ) )
=> ( ! [C: binary1439146945Tree_a] :
( ? [D: a,E: binary1439146945Tree_a] :
( B
= ( binary717961607le_T_a @ C @ D @ E ) )
=> ~ ( member_a @ A @ ( binary256242811Tree_a @ C ) ) )
=> ( ! [C: binary1439146945Tree_a,D: binary1439146945Tree_a] :
( B
!= ( binary717961607le_T_a @ C @ A @ D ) )
=> ~ ! [C: binary1439146945Tree_a,D: a,E: binary1439146945Tree_a] :
( ( B
= ( binary717961607le_T_a @ C @ D @ E ) )
=> ~ ( member_a @ A @ ( binary256242811Tree_a @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(14,axiom,
! [A: binary1439146945Tree_a,B: a,C: binary1439146945Tree_a] :
( binary476621312_Tip_a
!= ( binary717961607le_T_a @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_Tree_Odistinct_I1_J) ).
thf(127,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)],[14]) ).
thf(47,axiom,
! [A: int,B: int > int,C: int,D: int] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_ord__eq__less__subst) ).
thf(258,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)],[47]) ).
thf(79,axiom,
( ( member_a @ b @ ( binary945792244etOf_a @ t1 ) )
| ( b = x )
| ( member_a @ b @ ( binary945792244etOf_a @ t2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_calculation) ).
thf(390,plain,
( ( member_a @ b @ ( binary945792244etOf_a @ t1 ) )
| ( b = x )
| ( member_a @ b @ ( binary945792244etOf_a @ t2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(10,axiom,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_emptyE) ).
thf(114,plain,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(75,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_less__not__sym) ).
thf(383,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(40,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_less__imp__not__eq2) ).
thf(235,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(43,axiom,
! [A: int] :
~ ( ord_less_int @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_dual__order_Oirrefl) ).
thf(246,plain,
! [A: int] :
~ ( ord_less_int @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(92,axiom,
ord_less_int @ ( h @ b ) @ ( h @ a2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062h_Ab_A_060_Ah_Aa_092_060close_062) ).
thf(410,plain,
ord_less_int @ ( h @ b ) @ ( h @ a2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(51,axiom,
! [A: int] :
~ ( ord_less_int @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_verit__comp__simplify1_I1_J) ).
thf(273,plain,
! [A: int] :
~ ( ord_less_int @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(59,axiom,
( binary670562003pred_a
= ( ^ [A: a > int,B: a,C: a,D: binary1439146945Tree_a] :
( ( ( binary1721989714Tree_a @ A @ D )
& ( member_a @ B @ ( binary945792244etOf_a @ D ) )
& ( member_a @ C @ ( binary945792244etOf_a @ D ) )
& ( ( A @ B )
= ( A @ C ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_sorted__distinct__pred__def) ).
thf(305,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)],[59]) ).
thf(8,axiom,
! [A: set_a,B: a] :
( ( A = bot_bot_set_a )
=> ~ ( member_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_equals0D) ).
thf(107,plain,
! [A: set_a,B: a] :
( ( A = bot_bot_set_a )
=> ~ ( member_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(41,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ( C != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_pinf_I4_J) ).
thf(239,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ( C != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(16,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_less__asym_H) ).
thf(136,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(86,axiom,
( ( a2 = x )
=> ( a2 = b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__092_060open_062a_A_061_Ax_A_092_060Longrightarrow_062_Aa_A_061_Ab_092_060close_062) ).
thf(400,plain,
( ( a2 = x )
=> ( a2 = b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(1,conjecture,
a2 = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
a2 != b,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(94,plain,
a2 != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(82,axiom,
ord_less_int @ ( h @ b ) @ ( h @ x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_o1) ).
thf(395,plain,
ord_less_int @ ( h @ b ) @ ( h @ x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(15,axiom,
! [A: int,B: int,C: int] :
( ( A = B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_ord__eq__less__trans) ).
thf(131,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)],[15]) ).
thf(22,axiom,
! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
( ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_pinf_I1_J) ).
thf(163,plain,
! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
( ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(38,axiom,
! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
( ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_minf_I1_J) ).
thf(222,plain,
! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
( ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(39,axiom,
! [A: int] :
~ ( ord_less_int @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_less__irrefl) ).
thf(232,plain,
! [A: int] :
~ ( ord_less_int @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(5,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_order__refl) ).
thf(100,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(475,plain,
$false,
inference(cvc4,[status(thm)],[385,185,189,348,403,406,314,138,249,352,408,276,120,202,389,196,396,411,243,312,206,307,292,270,102,380,117,220,366,302,192,407,361,97,324,328,124,212,96,393,173,105,266,398,298,148,279,180,149,176,204,144,350,387,140,251,198,330,399,394,267,255,209,112,355,295,282,409,310,182,370,127,258,390,114,383,235,246,410,273,305,107,239,136,400,94,395,131,163,222,232,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP029^1 : TPTP v8.2.0. Released v7.5.0.
% 0.03/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n025.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Sat May 18 15:24:09 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.96/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.90/1.15 % [INFO] Parsing done (269ms).
% 1.90/1.16 % [INFO] Running in sequential loop mode.
% 2.71/1.39 % [INFO] eprover registered as external prover.
% 2.71/1.40 % [INFO] cvc4 registered as external prover.
% 2.71/1.40 % [INFO] Scanning for conjecture ...
% 2.95/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 350 axioms. Running axiom selection ...
% 3.20/1.56 % [INFO] Axiom selection finished. Selected 91 axioms (removed 259 axioms).
% 3.59/1.68 % [INFO] Problem is higher-order (TPTP THF).
% 3.59/1.70 % [INFO] Type checking passed.
% 3.59/1.71 % [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 ...
% 9.04/3.38 % External prover 'cvc4' found a proof!
% 9.04/3.38 % [INFO] Killing All external provers ...
% 9.04/3.38 % Time passed: 2853ms (effective reasoning time: 2221ms)
% 9.04/3.38 % 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)>
% 9.04/3.38 % Axioms used in derivation (91): fact_347_subset__antisym, fact_99_order_Oasym, fact_29_minf_I3_J, fact_26_minf_I7_J, fact_22_sortedTree_Osimps_I2_J, fact_134_less__imp__not__eq2, fact_191_Tree_Oset__intros_I1_J, fact_115_less__irrefl, fact_20_s2, fact_141_dual__order_Oirrefl, fact_193_Tree_Oset__intros_I2_J, fact_138_linorder__cases, fact_0_hahb, fact_173_equals0I, fact_4_bdef1, fact_121_ord__less__eq__trans, fact_19_Tree_Oexhaust, fact_111_less__trans, fact_6_o1, fact_346_order__refl, fact_53_not__less__iff__gr__or__eq, fact_44_dual__order_Ostrict__implies__not__eq, fact_30_minf_I2_J, fact_15_adef, fact_18_Tree_Oinduct, fact_24_sorted__distinct__pred__def, fact_118_ord__eq__less__trans, fact_335_chain__mono, fact_333_pred__on_Ochain__empty, fact_162_all__not__in__conv, fact_21_s1, fact_102_less__imp__neq, fact_108_less__asym_H, fact_40_minf_I1_J, fact_34_pinf_I1_J, fact_151_verit__comp__simplify1_I1_J, fact_3_adef1, fact_38_pinf_I5_J, fact_36_pinf_I3_J, fact_147_less__imp__not__less, fact_2__092_060open_062a_A_061_Ax_A_092_060Longrightarrow_062_Aa_A_061_Ab_092_060close_062, fact_52_order_Ostrict__implies__not__eq, fact_83_order__less__subst1, fact_175_ex__in__conv, fact_95_neqE, fact_27_minf_I5_J, fact_12__092_060open_062a_A_092_060in_062_AsetOf_At1_A_092_060or_062_Aa_A_061_Ax_A_092_060or_062_Aa_A_092_060in_062_AsetOf_At2_092_060close_062, fact_10__092_060open_062sorted__distinct__pred_Ah_Aa_Ab_ATip_092_060close_062, fact_9_h1, fact_56_dual__order_Ostrict__trans, fact_112_less__linear, fact_148_linorder__less__wlog, fact_195_Tree_Oset__intros_I3_J, fact_152_setOf_Osimps_I1_J, fact_11_calculation, fact_37_pinf_I4_J, fact_94_gt__ex, fact_32_sortLemmaL, fact_96_neq__iff, fact_127_less__imp__not__eq, fact_35_pinf_I2_J, fact_8_h2, fact_16_s, fact_171_equals0D, fact_130_less__not__sym, fact_7_o2, fact_336_pred__on_Ochain_Ocong, fact_33_sortedTree_Osimps_I1_J, fact_124_dual__order_Oasym, fact_41_linorder__neqE__linordered__idom, fact_92_order__less__subst2, fact_137_less__imp__triv, fact_14_Tree_Oinject, fact_105_less__asym, fact_348_subsetI, fact_74_ord__less__eq__subst, fact_93_lt__ex, fact_169_emptyE, fact_13_bdef, fact_17_Tree_Odistinct_I1_J, fact_39_pinf_I7_J, fact_189_Tree_Oset__cases, fact_28_minf_I4_J, fact_164_empty__iff, fact_1__092_060open_062h_Ab_A_060_Ah_Aa_092_060close_062, fact_5__092_060open_062a_A_092_060in_062_AsetOf_At1_A_092_060Longrightarrow_062_Aa_A_061_Ab_092_060close_062, fact_65_ord__eq__less__subst, fact_131_antisym__conv3, fact_180_Tree_Osimps_I14_J, fact_31_sortLemmaR, fact_144_order_Ostrict__trans
% 9.04/3.38 % No. of inferences in proof: 186
% 9.04/3.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2853 ms resp. 2221 ms w/o parsing
% 9.04/3.44 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.04/3.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------