%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW473^1 : TPTP v9.3.1. Released v5.3.0.
% 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 : n012.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 08:40:14 AM UTC 2026
% Result : Theorem 9.04s 2.75s
% Output : Refutation 10.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 195
% Syntax : Number of formulae : 392 ( 111 unt; 0 typ; 0 def)
% Number of atoms : 1314 ( 246 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 2783 ( 72 ~; 36 |; 40 &;2235 @)
% ( 0 <=>; 400 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 704 ( 704 >; 0 *; 0 +; 0 <<)
% Number of symbols : 61 ( 59 usr; 3 con; 0-3 aty)
% Number of variables : 906 ( 36 ^; 860 !; 10 ?; 906 :)
% Comments :
%------------------------------------------------------------------------------
thf(x_a_type,type,
x_a: $tType ).
thf(pname_type,type,
pname: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(finite_card_a_o_o_decl,type,
finite_card_a_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > nat ).
thf(finite221134632me_o_o_decl,type,
finite221134632me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > nat ).
thf(finite_card_nat_o_o_decl,type,
finite_card_nat_o_o: ( ( ( nat > $o ) > $o ) > $o ) > nat ).
thf(finite_card_a_o_decl,type,
finite_card_a_o: ( ( x_a > $o ) > $o ) > nat ).
thf(finite_card_pname_o_decl,type,
finite_card_pname_o: ( ( pname > $o ) > $o ) > nat ).
thf(finite_card_nat_o_decl,type,
finite_card_nat_o: ( ( nat > $o ) > $o ) > nat ).
thf(finite_card_a_decl,type,
finite_card_a: ( x_a > $o ) > nat ).
thf(finite_card_pname_decl,type,
finite_card_pname: ( pname > $o ) > nat ).
thf(finite_card_nat_decl,type,
finite_card_nat: ( nat > $o ) > nat ).
thf(finite_finite_a_o_o_decl,type,
finite_finite_a_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > $o ).
thf(finite1066544169me_o_o_decl,type,
finite1066544169me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > $o ).
thf(finite1676163439at_o_o_decl,type,
finite1676163439at_o_o: ( ( ( nat > $o ) > $o ) > $o ) > $o ).
thf(finite_finite_a_o_decl,type,
finite_finite_a_o: ( ( x_a > $o ) > $o ) > $o ).
thf(finite_finite_a_decl,type,
finite_finite_a: ( x_a > $o ) > $o ).
thf(finite_finite_pname_decl,type,
finite_finite_pname: ( pname > $o ) > $o ).
thf(minus_minus_nat_decl,type,
minus_minus_nat: nat > nat > nat ).
thf(suc_decl,type,
suc: nat > nat ).
thf(ord_less_eq_a_o_o_decl,type,
ord_less_eq_a_o_o: ( ( x_a > $o ) > $o ) > ( ( x_a > $o ) > $o ) > $o ).
thf(ord_less_eq_a_o_decl,type,
ord_less_eq_a_o: ( x_a > $o ) > ( x_a > $o ) > $o ).
thf(ord_less_eq_pname_o_decl,type,
ord_less_eq_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
thf(ord_less_eq_nat_o_decl,type,
ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
thf(ord_less_eq_nat_decl,type,
ord_less_eq_nat: nat > nat > $o ).
thf(collect_a_o_o_decl,type,
collect_a_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > ( ( x_a > $o ) > $o ) > $o ).
thf(collect_a_o_decl,type,
collect_a_o: ( ( x_a > $o ) > $o ) > ( x_a > $o ) > $o ).
thf(collect_a_decl,type,
collect_a: ( x_a > $o ) > x_a > $o ).
thf(collect_pname_decl,type,
collect_pname: ( pname > $o ) > pname > $o ).
thf(image_a_o_o_a_decl,type,
image_a_o_o_a: ( ( ( x_a > $o ) > $o ) > x_a ) > ( ( ( x_a > $o ) > $o ) > $o ) > x_a > $o ).
thf(image_a_o_o_pname_decl,type,
image_a_o_o_pname: ( ( ( x_a > $o ) > $o ) > pname ) > ( ( ( x_a > $o ) > $o ) > $o ) > pname > $o ).
thf(image_pname_o_o_a_decl,type,
image_pname_o_o_a: ( ( ( pname > $o ) > $o ) > x_a ) > ( ( ( pname > $o ) > $o ) > $o ) > x_a > $o ).
thf(image_471733107_pname_decl,type,
image_471733107_pname: ( ( ( pname > $o ) > $o ) > pname ) > ( ( ( pname > $o ) > $o ) > $o ) > pname > $o ).
thf(image_nat_o_o_a_decl,type,
image_nat_o_o_a: ( ( ( nat > $o ) > $o ) > x_a ) > ( ( ( nat > $o ) > $o ) > $o ) > x_a > $o ).
thf(image_nat_o_o_pname_decl,type,
image_nat_o_o_pname: ( ( ( nat > $o ) > $o ) > pname ) > ( ( ( nat > $o ) > $o ) > $o ) > pname > $o ).
thf(image_a_o_a_decl,type,
image_a_o_a: ( ( x_a > $o ) > x_a ) > ( ( x_a > $o ) > $o ) > x_a > $o ).
thf(image_a_o_pname_decl,type,
image_a_o_pname: ( ( x_a > $o ) > pname ) > ( ( x_a > $o ) > $o ) > pname > $o ).
thf(image_a_o_nat_decl,type,
image_a_o_nat: ( ( x_a > $o ) > nat ) > ( ( x_a > $o ) > $o ) > nat > $o ).
thf(image_a_a_decl,type,
image_a_a: ( x_a > x_a ) > ( x_a > $o ) > x_a > $o ).
thf(image_a_pname_decl,type,
image_a_pname: ( x_a > pname ) > ( x_a > $o ) > pname > $o ).
thf(image_a_nat_decl,type,
image_a_nat: ( x_a > nat ) > ( x_a > $o ) > nat > $o ).
thf(image_pname_a_o_o_decl,type,
image_pname_a_o_o: ( pname > ( x_a > $o ) > $o ) > ( pname > $o ) > ( ( x_a > $o ) > $o ) > $o ).
thf(image_504089495me_o_o_decl,type,
image_504089495me_o_o: ( pname > ( pname > $o ) > $o ) > ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(image_pname_nat_o_o_decl,type,
image_pname_nat_o_o: ( pname > ( nat > $o ) > $o ) > ( pname > $o ) > ( ( nat > $o ) > $o ) > $o ).
thf(image_pname_a_o_decl,type,
image_pname_a_o: ( pname > x_a > $o ) > ( pname > $o ) > ( x_a > $o ) > $o ).
thf(image_pname_pname_o_decl,type,
image_pname_pname_o: ( pname > pname > $o ) > ( pname > $o ) > ( pname > $o ) > $o ).
thf(image_pname_nat_o_decl,type,
image_pname_nat_o: ( pname > nat > $o ) > ( pname > $o ) > ( nat > $o ) > $o ).
thf(image_pname_a_decl,type,
image_pname_a: ( pname > x_a ) > ( pname > $o ) > x_a > $o ).
thf(image_pname_pname_decl,type,
image_pname_pname: ( pname > pname ) > ( pname > $o ) > pname > $o ).
thf(image_pname_nat_decl,type,
image_pname_nat: ( pname > nat ) > ( pname > $o ) > nat > $o ).
thf(insert_a_o_decl,type,
insert_a_o: ( x_a > $o ) > ( ( x_a > $o ) > $o ) > ( x_a > $o ) > $o ).
thf(insert_a_decl,type,
insert_a: x_a > ( x_a > $o ) > x_a > $o ).
thf(insert_pname_decl,type,
insert_pname: pname > ( pname > $o ) > pname > $o ).
thf(member_a_o_decl,type,
member_a_o: ( x_a > $o ) > ( ( x_a > $o ) > $o ) > $o ).
thf(member_a_decl,type,
member_a: x_a > ( x_a > $o ) > $o ).
thf(member_pname_decl,type,
member_pname: pname > ( pname > $o ) > $o ).
thf(g_decl,type,
g: x_a > $o ).
thf(p_decl,type,
p: ( x_a > $o ) > ( x_a > $o ) > $o ).
thf(u_decl,type,
u: pname > $o ).
thf(mgt_call_decl,type,
mgt_call: pname > x_a ).
thf(na_decl,type,
na: nat ).
thf(pn_decl,type,
pn: pname ).
thf(61,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_nat_Oinject) ).
thf(365,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(55,axiom,
! [A: ( x_a > $o ) > x_a,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ ( image_a_o_a @ A @ B ) ) @ ( finite_card_a_o @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_card__image__le) ).
thf(347,plain,
! [A: ( x_a > $o ) > x_a,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ ( image_a_o_a @ A @ B ) ) @ ( finite_card_a_o @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(19,axiom,
! [A: ( x_a > $o ) > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ( ord_less_eq_a_o_o @ A @ B )
=> ( ord_less_eq_nat @ ( finite_card_a_o @ A ) @ ( finite_card_a_o @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_card__mono) ).
thf(249,plain,
! [A: ( x_a > $o ) > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ( ord_less_eq_a_o_o @ A @ B )
=> ( ord_less_eq_nat @ ( finite_card_a_o @ A ) @ ( finite_card_a_o @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(167,axiom,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ B ) @ ( finite_card_a @ ( insert_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_card__insert__le) ).
thf(666,plain,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ B ) @ ( finite_card_a @ ( insert_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(102,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( minus_minus_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_diff__Suc__Suc) ).
thf(481,plain,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( minus_minus_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(114,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_Suc__leD) ).
thf(523,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(174,axiom,
! [A: x_a,B: x_a > $o] :
( ( insert_a @ A @ ( insert_a @ A @ B ) )
= ( insert_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_insert__absorb2) ).
thf(683,plain,
! [A: x_a,B: x_a > $o] :
( ( insert_a @ A @ ( insert_a @ A @ B ) )
= ( insert_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(29,axiom,
! [A: pname > $o] : ( ord_less_eq_pname_o @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_order__refl) ).
thf(276,plain,
! [A: pname > $o] : ( ord_less_eq_pname_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(193,axiom,
! [A: x_a,B: x_a > $o] :
( ( insert_a @ A @ B )
= ( collect_a
@ ^ [C: x_a] :
( ( C = A )
| ( member_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_insert__compr__raw) ).
thf(741,plain,
! [A: x_a,B: x_a > $o] :
( ( insert_a @ A @ B )
= ( collect_a
@ ^ [C: x_a] :
( ( C = A )
| ( member_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(65,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_le__antisym) ).
thf(379,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(140,axiom,
! [A: x_a > $o,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ( ord_less_eq_a_o @ C @ A )
=> ( ord_less_eq_a_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_subset__trans) ).
thf(597,plain,
! [A: x_a > $o,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ( ord_less_eq_a_o @ C @ A )
=> ( ord_less_eq_a_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(67,axiom,
! [A: pname > $o,B: pname] : ( ord_less_eq_pname_o @ A @ ( insert_pname @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_subset__insertI) ).
thf(385,plain,
! [A: pname > $o,B: pname] : ( ord_less_eq_pname_o @ A @ ( insert_pname @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(180,axiom,
! [A: x_a,B: x_a,C: x_a > $o] :
( ( insert_a @ A @ ( insert_a @ B @ C ) )
= ( insert_a @ B @ ( insert_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_insert__commute) ).
thf(698,plain,
! [A: x_a,B: x_a,C: x_a > $o] :
( ( insert_a @ A @ ( insert_a @ B @ C ) )
= ( insert_a @ B @ ( insert_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(195,axiom,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ( member_a @ A @ B )
=> ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_set__mp) ).
thf(747,plain,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ( member_a @ A @ B )
=> ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(120,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_le__refl) ).
thf(538,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(169,axiom,
! [A: x_a > $o,B: pname > x_a,C: pname > $o] :
( ( ord_less_eq_a_o @ A @ ( image_pname_a @ B @ C ) )
= ( ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ C )
& ( A
= ( image_pname_a @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_subset__image__iff) ).
thf(670,plain,
! [A: x_a > $o,B: pname > x_a,C: pname > $o] :
( ( ord_less_eq_a_o @ A @ ( image_pname_a @ B @ C ) )
= ( ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ C )
& ( A
= ( image_pname_a @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(75,axiom,
! [A: ( x_a > $o ) > x_a,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( finite_finite_a @ ( image_a_o_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_finite__imageI) ).
thf(404,plain,
! [A: ( x_a > $o ) > x_a,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( finite_finite_a @ ( image_a_o_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(161,axiom,
! [A: x_a > $o,B: pname > x_a,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_a_o @ A @ ( image_pname_a @ B @ C ) )
=> ( finite_finite_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_finite__surj) ).
thf(651,plain,
! [A: x_a > $o,B: pname > x_a,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_a_o @ A @ ( image_pname_a @ B @ C ) )
=> ( finite_finite_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(22,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_diff__commute) ).
thf(257,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(69,axiom,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_pname @ ( insert_pname @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_finite_OinsertI) ).
thf(389,plain,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_pname @ ( insert_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(96,axiom,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ ( insert_pname @ A @ B ) )
= ( finite_finite_pname @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_finite__insert) ).
thf(460,plain,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ ( insert_pname @ A @ B ) )
= ( finite_finite_pname @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(128,axiom,
! [A: ( x_a > $o ) > pname,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( finite_finite_pname @ ( image_a_o_pname @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_finite__imageI) ).
thf(559,plain,
! [A: ( x_a > $o ) > pname,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( finite_finite_pname @ ( image_a_o_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(32,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_pname_o @ ( insert_pname @ A @ B ) @ ( insert_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_insert__mono) ).
thf(284,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_pname_o @ ( insert_pname @ A @ B ) @ ( insert_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(48,axiom,
! [A: nat] :
~ ( ord_less_eq_nat @ ( suc @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_Suc__n__not__le__n) ).
thf(325,plain,
! [A: nat] :
~ ( ord_less_eq_nat @ ( suc @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(34,axiom,
! [A: ( ( pname > $o ) > $o ) > x_a,B: ( ( pname > $o ) > $o ) > $o] :
( ( finite1066544169me_o_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ ( image_pname_o_o_a @ A @ B ) ) @ ( finite221134632me_o_o @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_card__image__le) ).
thf(289,plain,
! [A: ( ( pname > $o ) > $o ) > x_a,B: ( ( pname > $o ) > $o ) > $o] :
( ( finite1066544169me_o_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ ( image_pname_o_o_a @ A @ B ) ) @ ( finite221134632me_o_o @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(10,axiom,
! [A: ( x_a > $o ) > nat,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_nat @ ( image_a_o_nat @ A @ B ) ) @ ( finite_card_a_o @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_card__image__le) ).
thf(216,plain,
! [A: ( x_a > $o ) > nat,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_nat @ ( image_a_o_nat @ A @ B ) ) @ ( finite_card_a_o @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(100,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ B @ ( minus_minus_nat @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_diff__diff__cancel) ).
thf(475,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ B @ ( minus_minus_nat @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(46,axiom,
! [A: pname > pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ord_less_eq_nat @ ( finite_card_pname_o @ ( image_pname_pname_o @ A @ B ) ) @ ( finite_card_pname @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_card__image__le) ).
thf(321,plain,
! [A: pname > pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ord_less_eq_nat @ ( finite_card_pname_o @ ( image_pname_pname_o @ A @ B ) ) @ ( finite_card_pname @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(64,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( suc @ B ) @ A )
= ( suc @ ( minus_minus_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_Suc__diff__le) ).
thf(376,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( suc @ B ) @ A )
= ( suc @ ( minus_minus_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(56,axiom,
! [A: x_a,B: x_a > $o] :
( ( member_a @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_mem__def) ).
thf(353,plain,
! [A: x_a,B: x_a > $o] :
( ( member_a @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(8,axiom,
! [A: nat > $o,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ( ord_less_eq_nat_o @ C @ A )
=> ( ord_less_eq_nat_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_subset__trans) ).
thf(211,plain,
! [A: nat > $o,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ( ord_less_eq_nat_o @ C @ A )
=> ( ord_less_eq_nat_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(159,axiom,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( finite_finite_a @ ( insert_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_finite_OinsertI) ).
thf(646,plain,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( finite_finite_a @ ( insert_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(21,axiom,
! [A: nat > $o,B: nat > $o] :
( ( A = B )
=> ( ord_less_eq_nat_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_equalityD1) ).
thf(253,plain,
! [A: nat > $o,B: nat > $o] :
( ( A = B )
=> ( ord_less_eq_nat_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(72,axiom,
! [A: ( x_a > $o ) > $o,B: ( x_a > $o ) > $o] :
( ( ord_less_eq_a_o_o @ A @ B )
=> ( ( finite_finite_a_o @ B )
=> ( finite_finite_a_o @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_finite__subset) ).
thf(397,plain,
! [A: ( x_a > $o ) > $o,B: ( x_a > $o ) > $o] :
( ( ord_less_eq_a_o_o @ A @ B )
=> ( ( finite_finite_a_o @ B )
=> ( finite_finite_a_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(178,axiom,
! [A: x_a > $o] : ( ord_less_eq_a_o @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_order__refl) ).
thf(692,plain,
! [A: x_a > $o] : ( ord_less_eq_a_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(36,axiom,
! [A: pname > $o] : ( ord_less_eq_pname_o @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_subset__refl) ).
thf(293,plain,
! [A: pname > $o] : ( ord_less_eq_pname_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(6,axiom,
! [A: ( x_a > $o ) > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ( ord_less_eq_a_o_o @ A @ B )
=> ( ( ord_less_eq_nat @ ( finite_card_a_o @ B ) @ ( finite_card_a_o @ A ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_card__seteq) ).
thf(206,plain,
! [A: ( x_a > $o ) > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ( ord_less_eq_a_o_o @ A @ B )
=> ( ( ord_less_eq_nat @ ( finite_card_a_o @ B ) @ ( finite_card_a_o @ A ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(42,axiom,
! [A: pname,B: pname,C: pname > $o] :
( ( ~ ( member_pname @ B @ C )
=> ( B = A ) )
=> ( member_pname @ B @ ( insert_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_insertCI) ).
thf(307,plain,
! [A: pname,B: pname,C: pname > $o] :
( ( ~ ( member_pname @ B @ C )
=> ( B = A ) )
=> ( member_pname @ B @ ( insert_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(92,axiom,
! [A: pname > nat,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ord_less_eq_nat @ ( finite_card_nat @ ( image_pname_nat @ A @ B ) ) @ ( finite_card_pname @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_card__image__le) ).
thf(452,plain,
! [A: pname > nat,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ord_less_eq_nat @ ( finite_card_nat @ ( image_pname_nat @ A @ B ) ) @ ( finite_card_pname @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(172,axiom,
! [A: x_a,B: x_a,C: x_a > $o] :
( ( member_a @ A @ ( insert_a @ B @ C ) )
=> ( ( A != B )
=> ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_insertE) ).
thf(678,plain,
! [A: x_a,B: x_a,C: x_a > $o] :
( ( member_a @ A @ ( insert_a @ B @ C ) )
=> ( ( A != B )
=> ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(27,axiom,
! [A: nat] :
( ( suc @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_Suc__n__not__n) ).
thf(270,plain,
! [A: nat] :
( ( suc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(165,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( finite_finite_a @ B )
=> ( finite_finite_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_finite__subset) ).
thf(661,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( finite_finite_a @ B )
=> ( finite_finite_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(4,axiom,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( insert_a_o @ A @ B )
= ( collect_a_o
@ ^ [C: x_a > $o] :
( ( C = A )
| ( member_a_o @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_insert__compr__raw) ).
thf(201,plain,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( insert_a_o @ A @ B )
= ( collect_a_o
@ ^ [C: x_a > $o] :
( ( C = A )
| ( member_a_o @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,axiom,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ ( insert_a_o @ A @ B ) )
= ( finite_finite_a_o @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_finite__insert) ).
thf(220,plain,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ ( insert_a_o @ A @ B ) )
= ( finite_finite_a_o @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(185,axiom,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ~ ( member_a @ B @ C )
=> ( ( ord_less_eq_a_o @ C @ ( insert_a @ B @ A ) )
= ( ord_less_eq_a_o @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_subset__insert) ).
thf(714,plain,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ~ ( member_a @ B @ C )
=> ( ( ord_less_eq_a_o @ C @ ( insert_a @ B @ A ) )
= ( ord_less_eq_a_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(51,axiom,
! [A: x_a > pname,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ord_less_eq_nat @ ( finite_card_pname @ ( image_a_pname @ A @ B ) ) @ ( finite_card_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_card__image__le) ).
thf(334,plain,
! [A: x_a > pname,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ord_less_eq_nat @ ( finite_card_pname @ ( image_a_pname @ A @ B ) ) @ ( finite_card_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(40,axiom,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_mem__def) ).
thf(302,plain,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(23,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( finite_finite_pname @ B )
=> ( finite_finite_pname @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_finite__subset) ).
thf(260,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( finite_finite_pname @ B )
=> ( finite_finite_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(129,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( member_pname @ A @ B )
=> ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_set__mp) ).
thf(561,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( member_pname @ A @ B )
=> ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(38,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_pname_o @ B @ ( insert_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_subset__insertI2) ).
thf(297,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_pname_o @ B @ ( insert_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(153,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( ord_less_eq_a_o @ A @ B )
=> ( finite_finite_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_rev__finite__subset) ).
thf(630,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( ord_less_eq_a_o @ A @ B )
=> ( finite_finite_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(83,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_diff__le__mono2) ).
thf(429,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(189,axiom,
! [A: pname > x_a,B: x_a > $o,C: pname > $o] :
( ! [D: pname] :
( ( member_pname @ D @ C )
=> ( member_a @ ( A @ D ) @ B ) )
=> ( ord_less_eq_a_o @ ( image_pname_a @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_image__subsetI) ).
thf(729,plain,
! [A: pname > x_a,B: x_a > $o,C: pname > $o] :
( ! [D: pname] :
( ( member_pname @ D @ C )
=> ( member_a @ ( A @ D ) @ B ) )
=> ( ord_less_eq_a_o @ ( image_pname_a @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(1,conjecture,
ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_6) ).
thf(2,negated_conjecture,
~ ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(197,plain,
~ ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(151,axiom,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ( member_a @ B @ C )
=> ( ( ord_less_eq_a_o @ C @ A )
=> ( member_a @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_set__rev__mp) ).
thf(625,plain,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ( member_a @ B @ C )
=> ( ( ord_less_eq_a_o @ C @ A )
=> ( member_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(86,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ~ ( member_pname @ B @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( insert_pname @ B @ A ) )
= ( ord_less_eq_pname_o @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_subset__insert) ).
thf(435,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ~ ( member_pname @ B @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( insert_pname @ B @ A ) )
= ( ord_less_eq_pname_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(136,axiom,
finite_finite_pname @ u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(583,plain,
finite_finite_pname @ u,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(106,axiom,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ( ord_less_eq_pname_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_equalityD1) ).
thf(493,plain,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ( ord_less_eq_pname_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(125,axiom,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ord_less_eq_nat @ ( finite_card_pname @ B ) @ ( finite_card_pname @ ( insert_pname @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_card__insert__le) ).
thf(551,plain,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ord_less_eq_nat @ ( finite_card_pname @ B ) @ ( finite_card_pname @ ( insert_pname @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(94,axiom,
! [A: x_a > x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( finite_finite_a @ ( image_a_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_finite__imageI) ).
thf(456,plain,
! [A: x_a > x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( finite_finite_a @ ( image_a_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(14,axiom,
! [A: nat > $o,B: nat > $o] :
( ( A = B )
=> ~ ( ( ord_less_eq_nat_o @ A @ B )
=> ~ ( ord_less_eq_nat_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_equalityE) ).
thf(229,plain,
! [A: nat > $o,B: nat > $o] :
( ( A = B )
=> ~ ( ( ord_less_eq_nat_o @ A @ B )
=> ~ ( ord_less_eq_nat_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(131,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ B ) )
= ( ( ord_less_eq_nat @ A @ B )
| ( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_le__Suc__eq) ).
thf(566,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ B ) )
= ( ( ord_less_eq_nat @ A @ B )
| ( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(103,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( ( finite_finite_a @ ( collect_a @ B ) )
| ( finite_finite_a @ ( collect_a @ A ) ) )
=> ( finite_finite_a
@ ( collect_a
@ ^ [C: x_a] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_finite__Collect__conjI) ).
thf(484,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( ( finite_finite_a @ ( collect_a @ B ) )
| ( finite_finite_a @ ( collect_a @ A ) ) )
=> ( finite_finite_a
@ ( collect_a
@ ^ [C: x_a] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(135,axiom,
! [A: x_a,B: pname > x_a,C: pname > $o] :
( ( member_a @ A @ ( image_pname_a @ B @ C ) )
=> ~ ! [D: pname] :
( ( A
= ( B @ D ) )
=> ~ ( member_pname @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_imageE) ).
thf(578,plain,
! [A: x_a,B: pname > x_a,C: pname > $o] :
( ( member_a @ A @ ( image_pname_a @ B @ C ) )
=> ~ ! [D: pname] :
( ( A
= ( B @ D ) )
=> ~ ( member_pname @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(44,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( member_pname @ A @ B )
=> ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_in__mono) ).
thf(317,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( member_pname @ A @ B )
=> ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(57,axiom,
! [A: pname,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( member_pname @ B @ ( insert_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_insertI2) ).
thf(356,plain,
! [A: pname,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( member_pname @ B @ ( insert_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(145,axiom,
! [A: pname > x_a,B: pname > $o,C: x_a > $o] :
( ( finite_finite_a @ C )
=> ( ( ord_less_eq_a_o @ C @ ( image_pname_a @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_pname_a @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_finite__subset__image) ).
thf(610,plain,
! [A: pname > x_a,B: pname > $o,C: x_a > $o] :
( ( finite_finite_a @ C )
=> ( ( ord_less_eq_a_o @ C @ ( image_pname_a @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_pname_a @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(108,axiom,
! [A: nat,B: nat > $o,C: nat] :
( ( B @ C )
=> ( ! [D: nat] :
( ( B @ ( suc @ D ) )
=> ( B @ D ) )
=> ( B @ ( minus_minus_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_zero__induct__lemma) ).
thf(499,plain,
! [A: nat,B: nat > $o,C: nat] :
( ( B @ C )
=> ( ! [D: nat] :
( ( B @ ( suc @ D ) )
=> ( B @ D ) )
=> ( B @ ( minus_minus_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(49,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ? [C: nat] :
( B
= ( suc @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_Suc__le__D) ).
thf(328,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ? [C: nat] :
( B
= ( suc @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(104,axiom,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ ( insert_pname @ A @ B ) )
= ( insert_pname @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_insert__absorb2) ).
thf(488,plain,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ ( insert_pname @ A @ B ) )
= ( insert_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(175,axiom,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ( member_a @ A @ B )
=> ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_subsetD) ).
thf(686,plain,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ( member_a @ A @ B )
=> ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(156,axiom,
! [A: pname > x_a,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite_finite_a @ ( image_pname_a @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_pigeonhole__infinite) ).
thf(637,plain,
! [A: pname > x_a,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite_finite_a @ ( image_pname_a @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(150,axiom,
! [A: pname > x_a,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( insert_a @ ( A @ B ) @ ( image_pname_a @ A @ C ) )
= ( image_pname_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_insert__image) ).
thf(622,plain,
! [A: pname > x_a,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( insert_a @ ( A @ B ) @ ( image_pname_a @ A @ C ) )
= ( image_pname_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(181,axiom,
! [A: nat,B: nat,C: nat > x_a > $o] :
( ! [D: nat] : ( ord_less_eq_a_o @ ( C @ D ) @ ( C @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_a_o @ ( C @ A ) @ ( C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_lift__Suc__mono__le) ).
thf(701,plain,
! [A: nat,B: nat,C: nat > x_a > $o] :
( ! [D: nat] : ( ord_less_eq_a_o @ ( C @ D ) @ ( C @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_a_o @ ( C @ A ) @ ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(111,axiom,
! [A: pname > ( nat > $o ) > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite1676163439at_o_o @ ( image_pname_nat_o_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_finite__imageI) ).
thf(515,plain,
! [A: pname > ( nat > $o ) > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite1676163439at_o_o @ ( image_pname_nat_o_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(192,axiom,
! [A: x_a,B: x_a,C: x_a > $o] :
( ( member_a @ A @ ( insert_a @ B @ C ) )
= ( ( A = B )
| ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_insert__iff) ).
thf(738,plain,
! [A: x_a,B: x_a,C: x_a > $o] :
( ( member_a @ A @ ( insert_a @ B @ C ) )
= ( ( A = B )
| ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(187,axiom,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( ( member_a @ A @ B )
=> ( ( finite_card_a @ ( insert_a @ A @ B ) )
= ( finite_card_a @ B ) ) )
& ( ~ ( member_a @ A @ B )
=> ( ( finite_card_a @ ( insert_a @ A @ B ) )
= ( suc @ ( finite_card_a @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_card__insert__if) ).
thf(721,plain,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( ( member_a @ A @ B )
=> ( ( finite_card_a @ ( insert_a @ A @ B ) )
= ( finite_card_a @ B ) ) )
& ( ~ ( member_a @ A @ B )
=> ( ( finite_card_a @ ( insert_a @ A @ B ) )
= ( suc @ ( finite_card_a @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(132,axiom,
! [A: pname > ( x_a > $o ) > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_a_o_o @ ( image_pname_a_o_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_finite__imageI) ).
thf(569,plain,
! [A: pname > ( x_a > $o ) > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_a_o_o @ ( image_pname_a_o_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(15,axiom,
! [A: nat > $o] : ( ord_less_eq_nat_o @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_subset__refl) ).
thf(237,plain,
! [A: nat > $o] : ( ord_less_eq_nat_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(26,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_eq__imp__le) ).
thf(266,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(59,axiom,
! [A: nat,B: nat,C: nat > pname > $o] :
( ! [D: nat] : ( ord_less_eq_pname_o @ ( C @ D ) @ ( C @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_pname_o @ ( C @ A ) @ ( C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_lift__Suc__mono__le) ).
thf(360,plain,
! [A: nat,B: nat,C: nat > pname > $o] :
( ! [D: nat] : ( ord_less_eq_pname_o @ ( C @ D ) @ ( C @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_pname_o @ ( C @ A ) @ ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(117,axiom,
! [A: ( ( nat > $o ) > $o ) > x_a,B: ( ( nat > $o ) > $o ) > $o] :
( ( finite1676163439at_o_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ ( image_nat_o_o_a @ A @ B ) ) @ ( finite_card_nat_o_o @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_card__image__le) ).
thf(530,plain,
! [A: ( ( nat > $o ) > $o ) > x_a,B: ( ( nat > $o ) > $o ) > $o] :
( ( finite1676163439at_o_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ ( image_nat_o_o_a @ A @ B ) ) @ ( finite_card_nat_o_o @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(148,axiom,
! [A: pname > x_a,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_a_o @ ( image_pname_a @ A @ B ) @ ( image_pname_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_image__mono) ).
thf(618,plain,
! [A: pname > x_a,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_a_o @ ( image_pname_a @ A @ B ) @ ( image_pname_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(81,axiom,
! [A: ( x_a > $o ) > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ( ord_less_eq_a_o_o @ A @ B )
=> ( finite_finite_a_o @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_rev__finite__subset) ).
thf(425,plain,
! [A: ( x_a > $o ) > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ( ord_less_eq_a_o_o @ A @ B )
=> ( finite_finite_a_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(110,axiom,
! [A: pname > pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ord_less_eq_nat @ ( finite_card_pname @ ( image_pname_pname @ A @ B ) ) @ ( finite_card_pname @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_card__image__le) ).
thf(513,plain,
! [A: pname > pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ord_less_eq_nat @ ( finite_card_pname @ ( image_pname_pname @ A @ B ) ) @ ( finite_card_pname @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(25,axiom,
! [A: pname > pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_pname @ ( image_pname_pname @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_finite__imageI) ).
thf(264,plain,
! [A: pname > pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_pname @ ( image_pname_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(89,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( ( minus_minus_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ A @ B ) )
= ( minus_minus_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_Nat_Odiff__diff__eq) ).
thf(444,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( ( minus_minus_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ A @ B ) )
= ( minus_minus_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(190,axiom,
! [A: pname > x_a,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_a @ ( image_pname_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_finite__imageI) ).
thf(733,plain,
! [A: pname > x_a,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_a @ ( image_pname_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(137,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( A = B )
=> ~ ( ( ord_less_eq_a_o @ A @ B )
=> ~ ( ord_less_eq_a_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_equalityE) ).
thf(584,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( A = B )
=> ~ ( ( ord_less_eq_a_o @ A @ B )
=> ~ ( ord_less_eq_a_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(179,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( A = B )
=> ( ord_less_eq_a_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_equalityD1) ).
thf(694,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( A = B )
=> ( ord_less_eq_a_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(74,axiom,
! [A: x_a > pname,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( finite_finite_pname @ ( image_a_pname @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_finite__imageI) ).
thf(402,plain,
! [A: x_a > pname,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( finite_finite_pname @ ( image_a_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(33,axiom,
! [A: pname,B: pname,C: pname > $o] :
( ( member_pname @ A @ ( insert_pname @ B @ C ) )
=> ( ( A != B )
=> ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_insertE) ).
thf(286,plain,
! [A: pname,B: pname,C: pname > $o] :
( ( member_pname @ A @ ( insert_pname @ B @ C ) )
=> ( ( A != B )
=> ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(35,axiom,
! [A: x_a > x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ ( image_a_a @ A @ B ) ) @ ( finite_card_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_card__image__le) ).
thf(291,plain,
! [A: x_a > x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ ( image_a_a @ A @ B ) ) @ ( finite_card_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(123,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( ( ( minus_minus_nat @ C @ B )
= ( minus_minus_nat @ A @ B ) )
= ( C = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_eq__diff__iff) ).
thf(545,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( ( ( minus_minus_nat @ C @ B )
= ( minus_minus_nat @ A @ B ) )
= ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(77,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_le__SucI) ).
thf(413,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(31,axiom,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ ( collect_pname @ B ) )
= ( collect_pname
@ ^ [C: pname] :
( ( C != A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_insert__Collect) ).
thf(281,plain,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ ( collect_pname @ B ) )
= ( collect_pname
@ ^ [C: pname] :
( ( C != A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(5,axiom,
! [A: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ A )
=> ( finite_finite_a_o_o
@ ( collect_a_o_o
@ ^ [B: ( x_a > $o ) > $o] : ( ord_less_eq_a_o_o @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_finite__Collect__subsets) ).
thf(204,plain,
! [A: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ A )
=> ( finite_finite_a_o_o
@ ( collect_a_o_o
@ ^ [B: ( x_a > $o ) > $o] : ( ord_less_eq_a_o_o @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(157,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( p @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).
thf(641,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( p @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(70,axiom,
! [A: pname > $o,B: pname > $o] :
( ! [C: pname] :
( ( member_pname @ C @ B )
=> ( member_pname @ C @ A ) )
=> ( ord_less_eq_pname_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_subsetI) ).
thf(391,plain,
! [A: pname > $o,B: pname > $o] :
( ! [C: pname] :
( ( member_pname @ C @ B )
=> ( member_pname @ C @ A ) )
=> ( ord_less_eq_pname_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(66,axiom,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( insert_a_o @ A @ ( collect_a_o @ B ) )
= ( collect_a_o
@ ^ [C: x_a > $o] :
( ( C != A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_insert__Collect) ).
thf(382,plain,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( insert_a_o @ A @ ( collect_a_o @ B ) )
= ( collect_a_o
@ ^ [C: x_a > $o] :
( ( C != A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(43,axiom,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ( ord_less_eq_pname_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_equalityD2) ).
thf(313,plain,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ( ord_less_eq_pname_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(121,axiom,
! [A: pname,B: pname > $o,C: pname] :
( ( insert_pname @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_insert__code) ).
thf(540,plain,
! [A: pname,B: pname > $o,C: pname] :
( ( insert_pname @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(173,axiom,
! [A: x_a > $o] :
( ( finite_finite_a @ A )
=> ( finite_finite_a_o
@ ( collect_a_o
@ ^ [B: x_a > $o] : ( ord_less_eq_a_o @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_finite__Collect__subsets) ).
thf(681,plain,
! [A: x_a > $o] :
( ( finite_finite_a @ A )
=> ( finite_finite_a_o
@ ( collect_a_o
@ ^ [B: x_a > $o] : ( ord_less_eq_a_o @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(28,axiom,
! [A: pname > nat > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ord_less_eq_nat @ ( finite_card_nat_o @ ( image_pname_nat_o @ A @ B ) ) @ ( finite_card_pname @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_card__image__le) ).
thf(274,plain,
! [A: pname > nat > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ord_less_eq_nat @ ( finite_card_nat_o @ ( image_pname_nat_o @ A @ B ) ) @ ( finite_card_pname @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(60,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_eq_nat @ A @ B )
=> ( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_le__SucE) ).
thf(362,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_eq_nat @ A @ B )
=> ( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(109,axiom,
! [A: nat] :
( A
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_n__not__Suc__n) ).
thf(509,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(146,axiom,
ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(616,plain,
ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(141,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( A = B )
=> ( ord_less_eq_a_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_equalityD2) ).
thf(599,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( A = B )
=> ( ord_less_eq_a_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(68,axiom,
! [A: ( ( x_a > $o ) > $o ) > pname,B: ( ( x_a > $o ) > $o ) > $o] :
( ( finite_finite_a_o_o @ B )
=> ( finite_finite_pname @ ( image_a_o_o_pname @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_finite__imageI) ).
thf(387,plain,
! [A: ( ( x_a > $o ) > $o ) > pname,B: ( ( x_a > $o ) > $o ) > $o] :
( ( finite_finite_a_o_o @ B )
=> ( finite_finite_pname @ ( image_a_o_o_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(54,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( member_pname @ A @ B )
=> ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_subsetD) ).
thf(345,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( member_pname @ A @ B )
=> ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(119,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( finite_finite_a
@ ( collect_a
@ ^ [C: x_a] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_a @ ( collect_a @ A ) )
& ( finite_finite_a @ ( collect_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_finite__Collect__disjI) ).
thf(535,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( finite_finite_a
@ ( collect_a
@ ^ [C: x_a] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_a @ ( collect_a @ A ) )
& ( finite_finite_a @ ( collect_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(47,axiom,
! [A: pname > x_a > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ord_less_eq_nat @ ( finite_card_a_o @ ( image_pname_a_o @ A @ B ) ) @ ( finite_card_pname @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_card__image__le) ).
thf(323,plain,
! [A: pname > x_a > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ord_less_eq_nat @ ( finite_card_a_o @ ( image_pname_a_o @ A @ B ) ) @ ( finite_card_pname @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(9,axiom,
! [A: nat > $o,B: nat > $o] :
( ( ord_less_eq_nat_o @ A @ B )
=> ( ( ord_less_eq_nat_o @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_equalityI) ).
thf(213,plain,
! [A: nat > $o,B: nat > $o] :
( ( ord_less_eq_nat_o @ A @ B )
=> ( ( ord_less_eq_nat_o @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(20,axiom,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( finite_finite_a_o @ ( insert_a_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_finite_OinsertI) ).
thf(251,plain,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( finite_finite_a_o @ ( insert_a_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(168,axiom,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ( member_a @ A @ B )
=> ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_in__mono) ).
thf(668,plain,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ( member_a @ A @ B )
=> ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(3,axiom,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( insert_a_o @ A @ B )
= ( collect_a_o
@ ^ [C: x_a > $o] :
( ( C = A )
| ( member_a_o @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_insert__compr) ).
thf(198,plain,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( insert_a_o @ A @ B )
= ( collect_a_o
@ ^ [C: x_a > $o] :
( ( C = A )
| ( member_a_o @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(113,axiom,
! [A: ( x_a > $o ) > pname,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_pname @ ( image_a_o_pname @ A @ B ) ) @ ( finite_card_a_o @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_card__image__le) ).
thf(521,plain,
! [A: ( x_a > $o ) > pname,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_pname @ ( image_a_o_pname @ A @ B ) ) @ ( finite_card_a_o @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(73,axiom,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname
@ ( collect_pname
@ ^ [C: pname] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_pname @ ( collect_pname @ A ) )
& ( finite_finite_pname @ ( collect_pname @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_finite__Collect__disjI) ).
thf(399,plain,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname
@ ( collect_pname
@ ^ [C: pname] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_pname @ ( collect_pname @ A ) )
& ( finite_finite_pname @ ( collect_pname @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(30,axiom,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
= ( ( ord_less_eq_pname_o @ A @ B )
& ( ord_less_eq_pname_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_set__eq__subset) ).
thf(278,plain,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
= ( ( ord_less_eq_pname_o @ A @ B )
& ( ord_less_eq_pname_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(130,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_equalityI) ).
thf(563,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(39,axiom,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ B )
= ( collect_pname
@ ^ [C: pname] :
( ( C = A )
| ( member_pname @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_insert__compr__raw) ).
thf(299,plain,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ B )
= ( collect_pname
@ ^ [C: pname] :
( ( C = A )
| ( member_pname @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(87,axiom,
! [A: pname,B: pname,C: pname > $o] :
( ( member_pname @ A @ ( insert_pname @ B @ C ) )
= ( ( A = B )
| ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_insert__iff) ).
thf(438,plain,
! [A: pname,B: pname,C: pname > $o] :
( ( member_pname @ A @ ( insert_pname @ B @ C ) )
= ( ( A = B )
| ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(84,axiom,
! [A: pname,B: pname > $o] : ( member_pname @ A @ ( insert_pname @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_insertI1) ).
thf(431,plain,
! [A: pname,B: pname > $o] : ( member_pname @ A @ ( insert_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(162,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_nat @ ( finite_card_a @ B ) @ ( finite_card_a @ A ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_card__seteq) ).
thf(653,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_nat @ ( finite_card_a @ B ) @ ( finite_card_a @ A ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(164,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( A = B )
= ( ( ord_less_eq_a_o @ A @ B )
& ( ord_less_eq_a_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_set__eq__subset) ).
thf(658,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( A = B )
= ( ( ord_less_eq_a_o @ A @ B )
& ( ord_less_eq_a_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(13,axiom,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ( ( member_a_o @ A @ B )
=> ( ( finite_card_a_o @ ( insert_a_o @ A @ B ) )
= ( finite_card_a_o @ B ) ) )
& ( ~ ( member_a_o @ A @ B )
=> ( ( finite_card_a_o @ ( insert_a_o @ A @ B ) )
= ( suc @ ( finite_card_a_o @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_card__insert__if) ).
thf(223,plain,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ( ( member_a_o @ A @ B )
=> ( ( finite_card_a_o @ ( insert_a_o @ A @ B ) )
= ( finite_card_a_o @ B ) ) )
& ( ~ ( member_a_o @ A @ B )
=> ( ( finite_card_a_o @ ( insert_a_o @ A @ B ) )
= ( suc @ ( finite_card_a_o @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(144,axiom,
~ ( member_a @ ( mgt_call @ pn ) @ g ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_5) ).
thf(608,plain,
~ ( member_a @ ( mgt_call @ pn ) @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(99,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( ord_less_eq_pname_o @ C @ A )
=> ( member_pname @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_set__rev__mp) ).
thf(473,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( ord_less_eq_pname_o @ C @ A )
=> ( member_pname @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(196,axiom,
! [A: pname > x_a,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( member_a @ ( A @ B ) @ ( image_pname_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_imageI) ).
thf(749,plain,
! [A: pname > x_a,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( member_a @ ( A @ B ) @ ( image_pname_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(147,axiom,
ord_less_eq_nat @ ( suc @ na ) @ ( finite_card_a @ ( image_pname_a @ mgt_call @ u ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(617,plain,
ord_less_eq_nat @ ( suc @ na ) @ ( finite_card_a @ ( image_pname_a @ mgt_call @ u ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(53,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ A @ B ) )
= ( ord_less_eq_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_le__diff__iff) ).
thf(342,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ A @ B ) )
= ( ord_less_eq_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(126,axiom,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
=> ( ( insert_pname @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_insert__absorb) ).
thf(553,plain,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
=> ( ( insert_pname @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(95,axiom,
! [A: x_a > nat,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ord_less_eq_nat @ ( finite_card_nat @ ( image_a_nat @ A @ B ) ) @ ( finite_card_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_card__image__le) ).
thf(458,plain,
! [A: x_a > nat,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ord_less_eq_nat @ ( finite_card_nat @ ( image_a_nat @ A @ B ) ) @ ( finite_card_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(166,axiom,
! [A: x_a,B: x_a > $o,C: x_a] :
( ( insert_a @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_insert__code) ).
thf(663,plain,
! [A: x_a,B: x_a > $o,C: x_a] :
( ( insert_a @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(124,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_Suc__le__mono) ).
thf(548,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(160,axiom,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ ( insert_a @ A @ B ) @ C )
= ( ( member_a @ A @ C )
& ( ord_less_eq_a_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_insert__subset) ).
thf(648,plain,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ ( insert_a @ A @ B ) @ C )
= ( ( member_a @ A @ C )
& ( ord_less_eq_a_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(7,axiom,
! [A: nat > $o] : ( ord_less_eq_nat_o @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_order__refl) ).
thf(209,plain,
! [A: nat > $o] : ( ord_less_eq_nat_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(115,axiom,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ( ord_less_eq_nat @ ( finite_card_pname @ B ) @ ( finite_card_pname @ A ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_card__seteq) ).
thf(525,plain,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ( ord_less_eq_nat @ ( finite_card_pname @ B ) @ ( finite_card_pname @ A ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(177,axiom,
! [A: x_a > $o] : ( ord_less_eq_a_o @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_subset__refl) ).
thf(690,plain,
! [A: x_a > $o] : ( ord_less_eq_a_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(37,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_diff__le__mono) ).
thf(295,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(183,axiom,
! [A: x_a,B: x_a > $o] :
( ( insert_a @ A @ ( collect_a @ B ) )
= ( collect_a
@ ^ [C: x_a] :
( ( C != A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_insert__Collect) ).
thf(705,plain,
! [A: x_a,B: x_a > $o] :
( ( insert_a @ A @ ( collect_a @ B ) )
= ( collect_a
@ ^ [C: x_a] :
( ( C != A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(170,axiom,
! [A: x_a > $o,B: x_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_179_equalityI) ).
thf(673,plain,
! [A: x_a > $o,B: x_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)],[170]) ).
thf(50,axiom,
! [A: pname > $o] :
( ( collect_pname @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_Collect__def) ).
thf(331,plain,
! [A: pname > $o] :
( ( collect_pname @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(88,axiom,
! [A: ( x_a > $o ) > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o
@ ( collect_a_o
@ ^ [C: x_a > $o] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_a_o @ ( collect_a_o @ A ) )
& ( finite_finite_a_o @ ( collect_a_o @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_finite__Collect__disjI) ).
thf(441,plain,
! [A: ( x_a > $o ) > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o
@ ( collect_a_o
@ ^ [C: x_a > $o] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_a_o @ ( collect_a_o @ A ) )
& ( finite_finite_a_o @ ( collect_a_o @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(186,axiom,
! [A: x_a,B: pname > x_a,C: pname,D: pname > $o] :
( ( member_pname @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member_a @ A @ ( image_pname_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_rev__image__eqI) ).
thf(717,plain,
! [A: x_a,B: pname > x_a,C: pname,D: pname > $o] :
( ( member_pname @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member_a @ A @ ( image_pname_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(97,axiom,
! [A: ( ( x_a > $o ) > $o ) > x_a,B: ( ( x_a > $o ) > $o ) > $o] :
( ( finite_finite_a_o_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ ( image_a_o_o_a @ A @ B ) ) @ ( finite_card_a_o_o @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_card__image__le) ).
thf(463,plain,
! [A: ( ( x_a > $o ) > $o ) > x_a,B: ( ( x_a > $o ) > $o ) > $o] :
( ( finite_finite_a_o_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ ( image_a_o_o_a @ A @ B ) ) @ ( finite_card_a_o_o @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(158,axiom,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ~ ( member_a @ A @ B )
=> ( ( finite_card_a @ ( insert_a @ A @ B ) )
= ( suc @ ( finite_card_a @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_card__insert__disjoint) ).
thf(643,plain,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ~ ( member_a @ A @ B )
=> ( ( finite_card_a @ ( insert_a @ A @ B ) )
= ( suc @ ( finite_card_a @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(194,axiom,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ ( insert_a @ A @ B ) )
= ( finite_finite_a @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_finite__insert) ).
thf(744,plain,
! [A: x_a,B: x_a > $o] :
( ( finite_finite_a @ ( insert_a @ A @ B ) )
= ( finite_finite_a @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(52,axiom,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( ( member_pname @ A @ B )
=> ( ( finite_card_pname @ ( insert_pname @ A @ B ) )
= ( finite_card_pname @ B ) ) )
& ( ~ ( member_pname @ A @ B )
=> ( ( finite_card_pname @ ( insert_pname @ A @ B ) )
= ( suc @ ( finite_card_pname @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_card__insert__if) ).
thf(336,plain,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( ( member_pname @ A @ B )
=> ( ( finite_card_pname @ ( insert_pname @ A @ B ) )
= ( finite_card_pname @ B ) ) )
& ( ~ ( member_pname @ A @ B )
=> ( ( finite_card_pname @ ( insert_pname @ A @ B ) )
= ( suc @ ( finite_card_pname @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(182,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( ord_less_eq_a_o @ A @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ A ) @ ( finite_card_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_card__mono) ).
thf(703,plain,
! [A: x_a > $o,B: x_a > $o] :
( ( finite_finite_a @ B )
=> ( ( ord_less_eq_a_o @ A @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ A ) @ ( finite_card_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(163,axiom,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ord_less_eq_a_o @ ( insert_a @ A @ B ) @ ( insert_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_insert__mono) ).
thf(656,plain,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ord_less_eq_a_o @ ( insert_a @ A @ B ) @ ( insert_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(188,axiom,
! [A: x_a > $o,B: x_a] : ( ord_less_eq_a_o @ A @ ( insert_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_subset__insertI) ).
thf(727,plain,
! [A: x_a > $o,B: x_a] : ( ord_less_eq_a_o @ A @ ( insert_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(133,axiom,
! [A: pname > $o,B: x_a,C: pname > x_a,D: pname] :
( ( B
= ( C @ D ) )
=> ( ( member_pname @ D @ A )
=> ( member_a @ B @ ( image_pname_a @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_image__eqI) ).
thf(571,plain,
! [A: pname > $o,B: x_a,C: pname > x_a,D: pname] :
( ( B
= ( C @ D ) )
=> ( ( member_pname @ D @ A )
=> ( member_a @ B @ ( image_pname_a @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(139,axiom,
! [A: pname > x_a,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ ( image_pname_a @ A @ B ) ) @ ( finite_card_pname @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_card__image__le) ).
thf(595,plain,
! [A: pname > x_a,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ord_less_eq_nat @ ( finite_card_a @ ( image_pname_a @ A @ B ) ) @ ( finite_card_pname @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(107,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_order__refl) ).
thf(497,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(98,axiom,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ~ ( ( ord_less_eq_pname_o @ A @ B )
=> ~ ( ord_less_eq_pname_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_equalityE) ).
thf(465,plain,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ~ ( ( ord_less_eq_pname_o @ A @ B )
=> ~ ( ord_less_eq_pname_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(152,axiom,
! [A: pname > x_a,B: pname,C: pname > $o] :
( ( image_pname_a @ A @ ( insert_pname @ B @ C ) )
= ( insert_a @ ( A @ B ) @ ( image_pname_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_image__insert) ).
thf(627,plain,
! [A: pname > x_a,B: pname,C: pname > $o] :
( ( image_pname_a @ A @ ( insert_pname @ B @ C ) )
= ( insert_a @ ( A @ B ) @ ( image_pname_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(91,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ C @ A )
=> ( ord_less_eq_pname_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_subset__trans) ).
thf(450,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ C @ A )
=> ( ord_less_eq_pname_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(127,axiom,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ~ ( member_pname @ A @ B )
=> ( ( finite_card_pname @ ( insert_pname @ A @ B ) )
= ( suc @ ( finite_card_pname @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_card__insert__disjoint) ).
thf(556,plain,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ~ ( member_pname @ A @ B )
=> ( ( finite_card_pname @ ( insert_pname @ A @ B ) )
= ( suc @ ( finite_card_pname @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(176,axiom,
! [A: x_a,B: x_a,C: x_a > $o] :
( ( member_a @ B @ C )
=> ( member_a @ B @ ( insert_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_insertI2) ).
thf(688,plain,
! [A: x_a,B: x_a,C: x_a > $o] :
( ( member_a @ B @ C )
=> ( member_a @ B @ ( insert_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(11,axiom,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_a_o @ B ) @ ( finite_card_a_o @ ( insert_a_o @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_card__insert__le) ).
thf(218,plain,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ord_less_eq_nat @ ( finite_card_a_o @ B ) @ ( finite_card_a_o @ ( insert_a_o @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(62,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_Suc__inject) ).
thf(368,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(112,axiom,
! [A: ( x_a > $o ) > $o,B: ( x_a > $o ) > $o] :
( ( ( finite_finite_a_o @ ( collect_a_o @ B ) )
| ( finite_finite_a_o @ ( collect_a_o @ A ) ) )
=> ( finite_finite_a_o
@ ( collect_a_o
@ ^ [C: x_a > $o] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_finite__Collect__conjI) ).
thf(517,plain,
! [A: ( x_a > $o ) > $o,B: ( x_a > $o ) > $o] :
( ( ( finite_finite_a_o @ ( collect_a_o @ B ) )
| ( finite_finite_a_o @ ( collect_a_o @ A ) ) )
=> ( finite_finite_a_o
@ ( collect_a_o
@ ^ [C: x_a > $o] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(45,axiom,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( finite_finite_pname @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_rev__finite__subset) ).
thf(319,plain,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( finite_finite_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(154,axiom,
! [A: x_a,B: x_a > $o] :
( ( member_a @ A @ B )
=> ( ( insert_a @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_insert__absorb) ).
thf(632,plain,
! [A: x_a,B: x_a > $o] :
( ( member_a @ A @ B )
=> ( ( insert_a @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(79,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ( finite_finite_pname @ ( collect_pname @ B ) )
| ( finite_finite_pname @ ( collect_pname @ A ) ) )
=> ( finite_finite_pname
@ ( collect_pname
@ ^ [C: pname] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_finite__Collect__conjI) ).
thf(418,plain,
! [A: pname > $o,B: pname > $o] :
( ( ( finite_finite_pname @ ( collect_pname @ B ) )
| ( finite_finite_pname @ ( collect_pname @ A ) ) )
=> ( finite_finite_pname
@ ( collect_pname
@ ^ [C: pname] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(18,axiom,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ~ ( member_a_o @ A @ B )
=> ( ( finite_card_a_o @ ( insert_a_o @ A @ B ) )
= ( suc @ ( finite_card_a_o @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_card__insert__disjoint) ).
thf(246,plain,
! [A: x_a > $o,B: ( x_a > $o ) > $o] :
( ( finite_finite_a_o @ B )
=> ( ~ ( member_a_o @ A @ B )
=> ( ( finite_card_a_o @ ( insert_a_o @ A @ B ) )
= ( suc @ ( finite_card_a_o @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(85,axiom,
! [A: nat,B: nat,C: nat > nat] :
( ! [D: nat] : ( ord_less_eq_nat @ ( C @ D ) @ ( C @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( C @ A ) @ ( C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_lift__Suc__mono__le) ).
thf(433,plain,
! [A: nat,B: nat,C: nat > nat] :
( ! [D: nat] : ( ord_less_eq_nat @ ( C @ D ) @ ( C @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( C @ A ) @ ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(101,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less_eq_nat @ A @ B ) )
= ( ord_less_eq_nat @ ( suc @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_not__less__eq__eq) ).
thf(478,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less_eq_nat @ A @ B ) )
= ( ord_less_eq_nat @ ( suc @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(149,axiom,
( ( finite_card_a @ g )
= ( minus_minus_nat @ ( finite_card_a @ ( image_pname_a @ mgt_call @ u ) ) @ ( suc @ na ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
thf(620,plain,
( ( finite_card_a @ g )
= ( minus_minus_nat @ ( finite_card_a @ ( image_pname_a @ mgt_call @ u ) ) @ ( suc @ na ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(90,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ ( insert_pname @ A @ B ) @ C )
= ( ( member_pname @ A @ C )
& ( ord_less_eq_pname_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_insert__subset) ).
thf(447,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ ( insert_pname @ A @ B ) @ C )
= ( ( member_pname @ A @ C )
& ( ord_less_eq_pname_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(76,axiom,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ B )
= ( collect_pname
@ ^ [C: pname] :
( ( C = A )
| ( member_pname @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_insert__compr) ).
thf(410,plain,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ B )
= ( collect_pname
@ ^ [C: pname] :
( ( C = A )
| ( member_pname @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(24,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_nat__le__linear) ).
thf(262,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(80,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ A ) @ B ) @ ( suc @ C ) )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_Suc__diff__diff) ).
thf(422,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ A ) @ B ) @ ( suc @ C ) )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(191,axiom,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ~ ( member_a @ B @ C )
=> ( ~ ( member_a @ B @ A )
=> ( ( ( insert_a @ B @ C )
= ( insert_a @ B @ A ) )
= ( C = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_insert__ident) ).
thf(735,plain,
! [A: x_a > $o,B: x_a,C: x_a > $o] :
( ~ ( member_a @ B @ C )
=> ( ~ ( member_a @ B @ A )
=> ( ( ( insert_a @ B @ C )
= ( insert_a @ B @ A ) )
= ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(63,axiom,
! [A: ( x_a > $o ) > $o] :
( ( collect_a_o @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_Collect__def) ).
thf(373,plain,
! [A: ( x_a > $o ) > $o] :
( ( collect_a_o @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(142,axiom,
! [A: x_a > $o,B: x_a > $o] :
( ! [C: x_a] :
( ( member_a @ C @ B )
=> ( member_a @ C @ A ) )
=> ( ord_less_eq_a_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_subsetI) ).
thf(603,plain,
! [A: x_a > $o,B: x_a > $o] :
( ! [C: x_a] :
( ( member_a @ C @ B )
=> ( member_a @ C @ A ) )
=> ( ord_less_eq_a_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(41,axiom,
! [A: ( ( pname > $o ) > $o ) > pname,B: ( ( pname > $o ) > $o ) > $o] :
( ( finite1066544169me_o_o @ B )
=> ( finite_finite_pname @ ( image_471733107_pname @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_finite__imageI) ).
thf(305,plain,
! [A: ( ( pname > $o ) > $o ) > pname,B: ( ( pname > $o ) > $o ) > $o] :
( ( finite1066544169me_o_o @ B )
=> ( finite_finite_pname @ ( image_471733107_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(58,axiom,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_diff__le__self) ).
thf(358,plain,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(155,axiom,
! [A: x_a,B: x_a > $o] : ( member_a @ A @ ( insert_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_insertI1) ).
thf(635,plain,
! [A: x_a,B: x_a > $o] : ( member_a @ A @ ( insert_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(118,axiom,
! [A: pname,B: pname,C: pname > $o] :
( ( insert_pname @ A @ ( insert_pname @ B @ C ) )
= ( insert_pname @ B @ ( insert_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_insert__commute) ).
thf(532,plain,
! [A: pname,B: pname,C: pname > $o] :
( ( insert_pname @ A @ ( insert_pname @ B @ C ) )
= ( insert_pname @ B @ ( insert_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(78,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ~ ( member_pname @ B @ C )
=> ( ~ ( member_pname @ B @ A )
=> ( ( ( insert_pname @ B @ C )
= ( insert_pname @ B @ A ) )
= ( C = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_insert__ident) ).
thf(415,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ~ ( member_pname @ B @ C )
=> ( ~ ( member_pname @ B @ A )
=> ( ( ( insert_pname @ B @ C )
= ( insert_pname @ B @ A ) )
= ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(16,axiom,
! [A: nat > $o,B: nat > $o] :
( ( A = B )
= ( ( ord_less_eq_nat_o @ A @ B )
& ( ord_less_eq_nat_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_set__eq__subset) ).
thf(239,plain,
! [A: nat > $o,B: nat > $o] :
( ( A = B )
= ( ( ord_less_eq_nat_o @ A @ B )
& ( ord_less_eq_nat_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(17,axiom,
! [A: nat > $o,B: nat > $o] :
( ( A = B )
=> ( ord_less_eq_nat_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_equalityD2) ).
thf(242,plain,
! [A: nat > $o,B: nat > $o] :
( ( A = B )
=> ( ord_less_eq_nat_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(71,axiom,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ord_less_eq_nat @ ( finite_card_pname @ A ) @ ( finite_card_pname @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_card__mono) ).
thf(395,plain,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ord_less_eq_nat @ ( finite_card_pname @ A ) @ ( finite_card_pname @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(134,axiom,
! [A: x_a,B: x_a > $o] :
( ( insert_a @ A @ B )
= ( collect_a
@ ^ [C: x_a] :
( ( C = A )
| ( member_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_insert__compr) ).
thf(575,plain,
! [A: x_a,B: x_a > $o] :
( ( insert_a @ A @ B )
= ( collect_a
@ ^ [C: x_a] :
( ( C = A )
| ( member_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(82,axiom,
! [A: nat,B: nat,C: nat > nat > $o] :
( ! [D: nat] : ( ord_less_eq_nat_o @ ( C @ D ) @ ( C @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat_o @ ( C @ A ) @ ( C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_lift__Suc__mono__le) ).
thf(427,plain,
! [A: nat,B: nat,C: nat > nat > $o] :
( ! [D: nat] : ( ord_less_eq_nat_o @ ( C @ D ) @ ( C @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat_o @ ( C @ A ) @ ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(116,axiom,
! [A: pname > x_a > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_a_o @ ( image_pname_a_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_finite__imageI) ).
thf(528,plain,
! [A: pname > x_a > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_a_o @ ( image_pname_a_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(143,axiom,
member_pname @ pn @ u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
thf(607,plain,
member_pname @ pn @ u,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(122,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_le__trans) ).
thf(543,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(171,axiom,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ord_less_eq_a_o @ B @ ( insert_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_subset__insertI2) ).
thf(676,plain,
! [A: x_a,B: x_a > $o,C: x_a > $o] :
( ( ord_less_eq_a_o @ B @ C )
=> ( ord_less_eq_a_o @ B @ ( insert_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(105,axiom,
! [A: pname > ( pname > $o ) > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite1066544169me_o_o @ ( image_504089495me_o_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_finite__imageI) ).
thf(491,plain,
! [A: pname > ( pname > $o ) > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite1066544169me_o_o @ ( image_504089495me_o_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(138,axiom,
! [A: x_a,B: pname > x_a,C: pname > $o] :
( ( member_a @ A @ ( image_pname_a @ B @ C ) )
= ( ? [D: pname] :
( ( member_pname @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_image__iff) ).
thf(592,plain,
! [A: x_a,B: pname > x_a,C: pname > $o] :
( ( member_a @ A @ ( image_pname_a @ B @ C ) )
= ( ? [D: pname] :
( ( member_pname @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(93,axiom,
! [A: ( ( nat > $o ) > $o ) > pname,B: ( ( nat > $o ) > $o ) > $o] :
( ( finite1676163439at_o_o @ B )
=> ( finite_finite_pname @ ( image_nat_o_o_pname @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_finite__imageI) ).
thf(454,plain,
! [A: ( ( nat > $o ) > $o ) > pname,B: ( ( nat > $o ) > $o ) > $o] :
( ( finite1676163439at_o_o @ B )
=> ( finite_finite_pname @ ( image_nat_o_o_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(184,axiom,
! [A: x_a,B: x_a,C: x_a > $o] :
( ( ~ ( member_a @ B @ C )
=> ( B = A ) )
=> ( member_a @ B @ ( insert_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_insertCI) ).
thf(708,plain,
! [A: x_a,B: x_a,C: x_a > $o] :
( ( ~ ( member_a @ B @ C )
=> ( B = A ) )
=> ( member_a @ B @ ( insert_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(756,plain,
$false,
inference(e,[status(thm)],[365,347,249,666,481,523,683,276,741,379,597,385,698,747,538,670,404,651,257,389,460,559,284,325,289,216,475,321,376,353,211,646,253,397,692,293,206,307,452,678,270,661,201,220,714,334,302,260,561,297,630,429,729,197,625,435,583,493,551,456,229,566,484,578,317,356,610,499,328,488,686,637,622,701,515,738,721,569,237,266,360,530,618,425,513,264,444,733,584,694,402,286,291,545,413,281,204,641,391,382,313,540,681,274,362,509,616,599,387,345,535,323,213,251,668,198,521,399,278,563,299,438,431,653,658,223,608,473,749,617,342,553,458,663,548,648,209,525,690,295,705,673,331,441,717,463,643,744,336,703,656,727,571,595,497,465,627,450,556,688,218,368,517,319,632,418,246,433,478,620,447,410,262,422,735,373,603,305,358,635,532,415,239,242,395,575,427,528,607,543,676,491,592,454,708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWW473^1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % 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
% 0.07/0.13 % Computer : n012.cluster.edu
% 0.07/0.13 % Model : x86_64 x86_64
% 0.07/0.13 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.13 % Memory : 8046.5625MB
% 0.07/0.13 % OS : Linux 6.8.0-71-generic
% 0.07/0.13 % CPULimit : 300
% 0.07/0.13 % WCLimit : 300
% 0.07/0.13 % DateTime : Tue Sep 29 16:05:18 UTC 2026
% 0.07/0.13 % CPUTime :
% 0.07/0.13 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
% 0.56/0.45 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.46/0.72 % [INFO] Parsing done (260ms).
% 1.46/0.72 % [INFO] Running in sequential loop mode.
% 2.06/0.93 % [INFO] eprover registered as external prover.
% 2.06/0.94 % [INFO] Scanning for conjecture ...
% 2.34/1.02 % [INFO] Found a conjecture (or negated_conjecture) and 306 axioms. Running axiom selection ...
% 2.34/1.10 % [INFO] Axiom selection finished. Selected 194 axioms (removed 112 axioms).
% 2.91/1.22 % [INFO] Problem is higher-order (TPTP THF).
% 2.91/1.23 % [INFO] Type checking passed.
% 2.91/1.23 % [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 ...
% 9.04/2.75 % External prover 'e' found a proof!
% 9.04/2.75 % [INFO] Killing All external provers ...
% 9.04/2.75 % Time passed: 2539ms (effective reasoning time: 2022ms)
% 9.04/2.75 % 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)>
% 9.04/2.75 % Axioms used in derivation (194): fact_265_insert__compr__raw, fact_24_finite__imageI, fact_248_subset__trans, fact_277_subset__insert, fact_205_insert__absorb2, fact_58_card__image__le, fact_197_insert__compr, fact_97_card__insert__le, fact_35_finite__imageI, fact_38_finite__imageI, fact_246_subset__trans, fact_274_insert__subset, fact_226_subset__refl, fact_250_equalityE, fact_32_finite__imageI, fact_175_pigeonhole__infinite, fact_200_insert__Collect, fact_255_Collect__def, conj_3, fact_206_insert__absorb2, fact_161_diff__Suc__Suc, fact_221_insertI2, fact_264_insert__compr__raw, fact_178_equalityI, fact_155_le__SucI, fact_137_finite__insert, fact_238_in__mono, fact_144_finite__subset, fact_261_imageI, fact_184_insertCI, fact_215_insert__code, fact_100_card__insert__if, fact_225_subset__refl, fact_181_subsetD, fact_191_insertI1, fact_7_finite__Collect__subsets, fact_228_set__eq__subset, fact_234_equalityD2, fact_154_le__SucE, fact_163_Nat_Odiff__diff__eq, fact_158_not__less__eq__eq, fact_241_set__rev__mp, fact_160_Suc__diff__diff, fact_280_subset__insertI2, fact_254_mem__def, fact_279_subset__insertI2, fact_258_Collect__def, fact_10_finite__imageI, fact_251_equalityE, fact_270_subset__insertI, fact_143_finite__subset, fact_194_insert__compr, fact_179_equalityI, fact_146_finite__subset, fact_218_insert__ident, fact_173_lift__Suc__mono__le, fact_260_image__iff, fact_65_card__image__le, fact_119_Suc__inject, fact_114_finite__Collect__conjI, fact_253_mem__def, fact_128_diff__commute, fact_170_finite__subset__image, fact_224_insert__absorb, fact_34_finite__imageI, fact_229_set__eq__subset, fact_217_insert__ident, conj_2, fact_286_subset__image__iff, fact_20_finite__imageI, fact_187_insertE, fact_282_insert__mono, fact_79_card__image__le, fact_199_insert__Collect, fact_166_diff__le__mono, fact_298_order__refl, fact_47_finite_OinsertI, fact_33_finite__imageI, fact_214_insert__code, fact_113_finite__Collect__conjI, fact_84_card__mono, fact_116_Suc__diff__le, fact_112_finite__Collect__conjI, fact_208_insert__commute, fact_90_card__seteq, fact_59_card__image__le, fact_209_insert__commute, fact_268_insert__compr__raw, fact_21_finite__imageI, fact_95_card__insert__le, fact_168_diff__le__self, fact_231_equalityD1, fact_127_le__refl, fact_177_equalityI, fact_55_card__image__le, fact_63_card__image__le, fact_162_le__diff__iff, fact_291_subsetI, fact_247_subset__trans, fact_103_card__insert__if, fact_190_insertI1, fact_102_card__insert__if, fact_220_insertI2, fact_124_le__trans, fact_126_nat__le__linear, fact_212_insert__iff, fact_223_insert__absorb, fact_108_card__insert__disjoint, fact_242_set__rev__mp, fact_227_subset__refl, fact_39_finite__imageI, fact_171_lift__Suc__mono__le, fact_239_in__mono, fact_72_card__image__le, fact_157_le__Suc__eq, fact_153_Suc__leD, fact_164_eq__diff__iff, conj_1, fact_235_equalityD2, fact_156_Suc__le__mono, fact_169_finite__surj, fact_245_set__mp, fact_232_equalityD1, fact_68_card__image__le, fact_165_diff__diff__cancel, fact_132_finite__Collect__disjI, fact_54_card__image__le, fact_230_set__eq__subset, fact_89_card__seteq, fact_106_card__insert__disjoint, fact_233_equalityD1, fact_271_subset__insertI, fact_287_image__mono, fact_276_subset__insert, fact_296_order__refl, fact_62_card__image__le, fact_244_set__mp, fact_71_card__image__le, fact_83_card__mono, fact_294_image__subsetI, fact_149_rev__finite__subset, fact_283_insert__mono, fact_45_finite_OinsertI, fact_123_le__antisym, fact_172_lift__Suc__mono__le, fact_42_finite__imageI, fact_203_insert__Collect, fact_3_finite__Collect__subsets, fact_140_finite__insert, fact_297_order__refl, fact_249_equalityE, fact_150_rev__finite__subset, fact_290_subsetI, fact_109_card__insert__disjoint, fact_167_diff__le__mono2, fact_185_insertCI, fact_284_image__insert, conj_4, fact_236_equalityD2, fact_262_rev__image__eqI, fact_134_finite__Collect__disjI, fact_174_lift__Suc__mono__le, fact_19_finite__imageI, fact_61_card__image__le, fact_292_zero__induct__lemma, fact_0_assms_I1_J, fact_18_finite__imageI, fact_64_card__image__le, fact_188_insertE, conj_5, fact_69_card__image__le, fact_273_insert__subset, conj_0, fact_136_finite__insert, fact_288_imageE, fact_159_Suc__n__not__le__n, fact_82_card__mono, fact_120_nat_Oinject, fact_129_finite__Collect__disjI, fact_211_insert__iff, fact_193_insert__compr, fact_293_Suc__le__D, fact_152_rev__finite__subset, fact_94_card__insert__le, fact_182_subsetD, fact_122_n__not__Suc__n, fact_295_order__refl, fact_121_Suc__n__not__n, fact_125_eq__imp__le, fact_176_image__eqI, fact_70_card__image__le, fact_88_card__seteq, fact_285_insert__image, fact_51_finite_OinsertI
% 9.04/2.75 % No. of inferences in proof: 392
% 9.04/2.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2539 ms resp. 2022 ms w/o parsing
% 10.08/2.91 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.08/2.91 % [INFO] Killing All external provers ...
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