TSTP Solution File: ITP098^1 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP098^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:47:48 EDT 2024
% Result : Theorem 12.84s 4.18s
% Output : Refutation 13.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 181
% Syntax : Number of formulae : 329 ( 88 unt; 35 typ; 0 def)
% Number of atoms : 974 ( 575 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 2414 ( 38 ~; 0 |; 8 &;1908 @)
% ( 0 <=>; 460 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 11 ( 10 usr)
% Number of type conns : 466 ( 466 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 4 con; 0-3 aty)
% Number of variables : 962 ( 56 ^ 874 !; 32 ?; 962 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_c_a_type,type,
set_c_a: $tType ).
thf(set_a_c_type,type,
set_a_c: $tType ).
thf(set_a_b_type,type,
set_a_b: $tType ).
thf(set_a_a_type,type,
set_a_a: $tType ).
thf(set_c_type,type,
set_c: $tType ).
thf(set_b_type,type,
set_b: $tType ).
thf(set_a_type,type,
set_a: $tType ).
thf(c_type,type,
c: $tType ).
thf(b_type,type,
b: $tType ).
thf(a_type,type,
a: $tType ).
thf(comp_a_a_c_type,type,
comp_a_a_c: ( a > a ) > ( c > a ) > c > a ).
thf(comp_a_b_c_type,type,
comp_a_b_c: ( a > b ) > ( c > a ) > c > b ).
thf(comp_a_c_c_type,type,
comp_a_c_c: ( a > c ) > ( c > a ) > c > c ).
thf(comp_c_a_a_type,type,
comp_c_a_a: ( c > a ) > ( a > c ) > a > a ).
thf(comp_c_b_a_type,type,
comp_c_b_a: ( c > b ) > ( a > c ) > a > b ).
thf(inj_on_a_a_type,type,
inj_on_a_a: ( a > a ) > set_a > $o ).
thf(inj_on_a_b_type,type,
inj_on_a_b: ( a > b ) > set_a > $o ).
thf(inj_on_a_c_type,type,
inj_on_a_c: ( a > c ) > set_a > $o ).
thf(inj_on_c_a_type,type,
inj_on_c_a: ( c > a ) > set_c > $o ).
thf(inj_on_c_b_type,type,
inj_on_c_b: ( c > b ) > set_c > $o ).
thf(inj_on_c_c_type,type,
inj_on_c_c: ( c > c ) > set_c > $o ).
thf(sup_sup_set_a_type,type,
sup_sup_set_a: set_a > set_a > set_a ).
thf(top_top_set_a_type,type,
top_top_set_a: set_a ).
thf(top_top_set_b_type,type,
top_top_set_b: set_b ).
thf(top_top_set_c_type,type,
top_top_set_c: set_c ).
thf(image_a_a_type,type,
image_a_a: ( a > a ) > set_a > set_a ).
thf(image_a_b_type,type,
image_a_b: ( a > b ) > set_a > set_b ).
thf(image_c_a_type,type,
image_c_a: ( c > a ) > set_c > set_a ).
thf(image_c_b_type,type,
image_c_b: ( c > b ) > set_c > set_b ).
thf(member_a_type,type,
member_a: a > set_a > $o ).
thf(member_b_type,type,
member_b: b > set_b > $o ).
thf(member_c_type,type,
member_c: c > set_c > $o ).
thf(f_type,type,
f: a > b ).
thf(g_type,type,
g: c > a ).
thf(h_type,type,
h: c > a ).
thf(129,axiom,
! [A: a > b,B: c > a,C: a > b,D: c > a] :
( ( ( comp_a_b_c @ A @ B )
= ( comp_a_b_c @ C @ D ) )
=> ! [E: c] :
( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_comp__eq__elim) ).
thf(645,plain,
! [A: a > b,B: c > a,C: a > b,D: c > a] :
( ( ( comp_a_b_c @ A @ B )
= ( comp_a_b_c @ C @ D ) )
=> ! [E: c] :
( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(95,axiom,
! [A: c > b] :
( ! [B: c,C: c] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on_c_b @ A @ top_top_set_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_injI) ).
thf(518,plain,
! [A: c > b] :
( ! [B: c,C: c] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on_c_b @ A @ top_top_set_c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(136,axiom,
! [A: c > a,B: a] :
( ( ( image_c_a @ A @ top_top_set_c )
= top_top_set_a )
=> ~ ! [C: c] :
( B
!= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_surjE) ).
thf(666,plain,
! [A: c > a,B: a] :
( ( ( image_c_a @ A @ top_top_set_c )
= top_top_set_a )
=> ~ ! [C: c] :
( B
!= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(85,axiom,
! [A: a > b,B: a,C: a] :
( ( inj_on_a_b @ A @ top_top_set_a )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_inj__eq) ).
thf(481,plain,
! [A: a > b,B: a,C: a] :
( ( inj_on_a_b @ A @ top_top_set_a )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(96,axiom,
! [A: a > c,B: c > a,C: set_c] :
( ( inj_on_c_c @ ( comp_a_c_c @ A @ B ) @ C )
=> ( inj_on_a_c @ A @ ( image_c_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_inj__on__imageI) ).
thf(523,plain,
! [A: a > c,B: c > a,C: set_c] :
( ( inj_on_c_c @ ( comp_a_c_c @ A @ B ) @ C )
=> ( inj_on_a_c @ A @ ( image_c_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(123,axiom,
! [A: c > a,B: c > a,C: a > b,D: a > b] :
( ! [E: a,F: a] :
( ( member_a @ E @ ( image_c_a @ A @ top_top_set_c ) )
=> ( ( member_a @ F @ ( image_c_a @ B @ top_top_set_c ) )
=> ( ( ( C @ E )
= ( D @ F ) )
=> ( E = F ) ) ) )
=> ( ( ( comp_a_b_c @ C @ A )
= ( comp_a_b_c @ D @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_fun_Oinj__map__strong) ).
thf(614,plain,
! [A: c > a,B: c > a,C: a > b,D: a > b] :
( ! [E: a,F: a] :
( ( member_a @ E @ ( image_c_a @ A @ top_top_set_c ) )
=> ( ( member_a @ F @ ( image_c_a @ B @ top_top_set_c ) )
=> ( ( ( C @ E )
= ( D @ F ) )
=> ( E = F ) ) ) )
=> ( ( ( comp_a_b_c @ C @ A )
= ( comp_a_b_c @ D @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(117,axiom,
! [A: c > a] :
( ( ( image_c_a @ A @ top_top_set_c )
= top_top_set_a )
= ( ! [B: a] :
? [C: c] :
( B
= ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_surj__def) ).
thf(597,plain,
! [A: c > a] :
( ( ( image_c_a @ A @ top_top_set_c )
= top_top_set_a )
= ( ! [B: a] :
? [C: c] :
( B
= ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(61,axiom,
! [A: a > c,B: set_a,C: a,D: a] :
( ( inj_on_a_c @ A @ B )
=> ( ( C != D )
=> ( ( member_a @ C @ B )
=> ( ( member_a @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_inj__on__contraD) ).
thf(385,plain,
! [A: a > c,B: set_a,C: a,D: a] :
( ( inj_on_a_c @ A @ B )
=> ( ( C != D )
=> ( ( member_a @ C @ B )
=> ( ( member_a @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(50,axiom,
! [A: a > c,B: set_a,C: a,D: a] :
( ( inj_on_a_c @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member_a @ C @ B )
=> ( ( member_a @ D @ B )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_inj__onD) ).
thf(340,plain,
! [A: a > c,B: set_a,C: a,D: a] :
( ( inj_on_a_c @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member_a @ C @ B )
=> ( ( member_a @ D @ B )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(137,axiom,
! [A: c > a,B: set_c,C: a > b] :
( ( inj_on_c_a @ A @ B )
=> ( ( inj_on_a_b @ C @ ( image_c_a @ A @ B ) )
= ( inj_on_c_b @ ( comp_a_b_c @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_comp__inj__on__iff) ).
thf(670,plain,
! [A: c > a,B: set_c,C: a > b] :
( ( inj_on_c_a @ A @ B )
=> ( ( inj_on_a_b @ C @ ( image_c_a @ A @ B ) )
= ( inj_on_c_b @ ( comp_a_b_c @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(10,axiom,
! [A: set_a,B: a > c,C: a > a] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ! [E: a] :
( ( member_a @ E @ A )
=> ( ( ( B @ ( C @ D ) )
= ( B @ ( C @ E ) ) )
= ( ( B @ D )
= ( B @ E ) ) ) ) )
=> ( ( inj_on_a_a @ C @ A )
=> ( ( inj_on_a_c @ B @ ( image_a_a @ C @ A ) )
= ( inj_on_a_c @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_inj__on__image__iff) ).
thf(174,plain,
! [A: set_a,B: a > c,C: a > a] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ! [E: a] :
( ( member_a @ E @ A )
=> ( ( ( B @ ( C @ D ) )
= ( B @ ( C @ E ) ) )
= ( ( B @ D )
= ( B @ E ) ) ) ) )
=> ( ( inj_on_a_a @ C @ A )
=> ( ( inj_on_a_c @ B @ ( image_a_a @ C @ A ) )
= ( inj_on_a_c @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(12,axiom,
! [A: a > a,B: set_a,C: set_a] :
( ( inj_on_a_a @ A @ ( sup_sup_set_a @ B @ C ) )
=> ( ( ( image_a_a @ A @ B )
= ( image_a_a @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_inj__on__Un__image__eq__iff) ).
thf(185,plain,
! [A: a > a,B: set_a,C: set_a] :
( ( inj_on_a_a @ A @ ( sup_sup_set_a @ B @ C ) )
=> ( ( ( image_a_a @ A @ B )
= ( image_a_a @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(41,axiom,
! [A: set_c,B: c > b] :
( ! [C: c,D: c] :
( ( member_c @ C @ A )
=> ( ( member_c @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on_c_b @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_inj__onI) ).
thf(301,plain,
! [A: set_c,B: c > b] :
( ! [C: c,D: c] :
( ( member_c @ C @ A )
=> ( ( member_c @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on_c_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(131,axiom,
! [A: c > a,B: set_c,C: a > b] :
( ( inj_on_c_a @ A @ B )
=> ( ( inj_on_a_b @ C @ ( image_c_a @ A @ B ) )
=> ( inj_on_c_b @ ( comp_a_b_c @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_comp__inj__on) ).
thf(651,plain,
! [A: c > a,B: set_c,C: a > b] :
( ( inj_on_c_a @ A @ B )
=> ( ( inj_on_a_b @ C @ ( image_c_a @ A @ B ) )
=> ( inj_on_c_b @ ( comp_a_b_c @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(62,axiom,
! [A: a > a,B: c > a,C: set_c] :
( ( inj_on_c_a @ ( comp_a_a_c @ A @ B ) @ C )
=> ( inj_on_c_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_inj__on__imageI2) ).
thf(389,plain,
! [A: a > a,B: c > a,C: set_c] :
( ( inj_on_c_a @ ( comp_a_a_c @ A @ B ) @ C )
=> ( inj_on_c_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(57,axiom,
! [A: c > b,B: c,C: c] :
( ( inj_on_c_b @ A @ top_top_set_c )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_inj__eq) ).
thf(372,plain,
! [A: c > b,B: c,C: c] :
( ( inj_on_c_b @ A @ top_top_set_c )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(147,axiom,
( ( comp_a_b_c @ f @ g )
= ( comp_a_b_c @ f @ h ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(702,plain,
( ( comp_a_b_c @ f @ g )
= ( comp_a_b_c @ f @ h ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(51,axiom,
! [A: c > a] :
( ! [B: c,C: c] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on_c_a @ A @ top_top_set_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_injI) ).
thf(344,plain,
! [A: c > a] :
( ! [B: c,C: c] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on_c_a @ A @ top_top_set_c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(53,axiom,
! [A: set_a,B: a > b,C: a > b] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on_a_b @ B @ A )
= ( inj_on_a_b @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_inj__on__cong) ).
thf(357,plain,
! [A: set_a,B: a > b,C: a > b] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on_a_b @ B @ A )
= ( inj_on_a_b @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(16,axiom,
! [A: a > b,B: b > a] :
( ! [C: b] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_a_b @ A @ top_top_set_a )
= top_top_set_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_surjI) ).
thf(196,plain,
! [A: a > b,B: b > a] :
( ! [C: b] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_a_b @ A @ top_top_set_a )
= top_top_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(127,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_inf__sup__aci_I6_J) ).
thf(638,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(120,axiom,
! [A: a > a,B: c > a,C: c > a] :
( ( ( comp_a_a_c @ A @ B )
= ( comp_a_a_c @ A @ C ) )
=> ( ( inj_on_a_a @ A @ ( sup_sup_set_a @ ( image_c_a @ B @ top_top_set_c ) @ ( image_c_a @ C @ top_top_set_c ) ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_o__inj__on) ).
thf(606,plain,
! [A: a > a,B: c > a,C: c > a] :
( ( ( comp_a_a_c @ A @ B )
= ( comp_a_a_c @ A @ C ) )
=> ( ( inj_on_a_a @ A @ ( sup_sup_set_a @ ( image_c_a @ B @ top_top_set_c ) @ ( image_c_a @ C @ top_top_set_c ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(70,axiom,
! [A: a > a,B: set_a,C: a,D: a] :
( ( inj_on_a_a @ A @ B )
=> ( ( C != D )
=> ( ( member_a @ C @ B )
=> ( ( member_a @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_inj__on__contraD) ).
thf(416,plain,
! [A: a > a,B: set_a,C: a,D: a] :
( ( inj_on_a_a @ A @ B )
=> ( ( C != D )
=> ( ( member_a @ C @ B )
=> ( ( member_a @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(46,axiom,
! [A: a > b] :
( ( ( image_a_b @ A @ top_top_set_a )
= top_top_set_b )
= ( ! [B: b] :
? [C: a] :
( B
= ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_surj__def) ).
thf(325,plain,
! [A: a > b] :
( ( ( image_a_b @ A @ top_top_set_a )
= top_top_set_b )
= ( ! [B: b] :
? [C: a] :
( B
= ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(24,axiom,
! [A: a > a,B: c > a,C: set_c] :
( ( image_a_a @ A @ ( image_c_a @ B @ C ) )
= ( image_c_a @ ( comp_a_a_c @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_image__comp) ).
thf(228,plain,
! [A: a > a,B: c > a,C: set_c] :
( ( image_a_a @ A @ ( image_c_a @ B @ C ) )
= ( image_c_a @ ( comp_a_a_c @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(83,axiom,
! [A: a > a,B: c > a,C: set_c] :
( ( inj_on_c_a @ ( comp_a_a_c @ A @ B ) @ C )
=> ( inj_on_a_a @ A @ ( image_c_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_inj__on__imageI) ).
thf(475,plain,
! [A: a > a,B: c > a,C: set_c] :
( ( inj_on_c_a @ ( comp_a_a_c @ A @ B ) @ C )
=> ( inj_on_a_a @ A @ ( image_c_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(45,axiom,
! [A: a > a,B: a] :
( ( inj_on_a_a @ A @ top_top_set_a )
=> ( ( member_a @ B @ ( image_a_a @ A @ top_top_set_a ) )
= ( ? [C: a] :
( ( B
= ( A @ C ) )
& ! [D: a] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_range__ex1__eq) ).
thf(321,plain,
! [A: a > a,B: a] :
( ( inj_on_a_a @ A @ top_top_set_a )
=> ( ( member_a @ B @ ( image_a_a @ A @ top_top_set_a ) )
= ( ? [C: a] :
( ( B
= ( A @ C ) )
& ! [D: a] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(58,axiom,
( inj_on_a_b
= ( ^ [A: a > b,B: set_a] :
! [C: a] :
( ( member_a @ C @ B )
=> ! [D: a] :
( ( member_a @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_inj__on__def) ).
thf(376,plain,
( inj_on_a_b
= ( ^ [A: a > b,B: set_a] :
! [C: a] :
( ( member_a @ C @ B )
=> ! [D: a] :
( ( member_a @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(20,axiom,
! [A: c > b,B: b > c] :
( ! [C: b] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_c_b @ A @ top_top_set_c )
= top_top_set_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_surjI) ).
thf(211,plain,
! [A: c > b,B: b > c] :
( ! [C: b] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_c_b @ A @ top_top_set_c )
= top_top_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(86,axiom,
! [A: c > a,B: c,C: c] :
( ( inj_on_c_a @ A @ top_top_set_c )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_injD) ).
thf(485,plain,
! [A: c > a,B: c,C: c] :
( ( inj_on_c_a @ A @ top_top_set_c )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(119,axiom,
! [A: c > a,B: set_c,C: set_c] :
( ( inj_on_c_a @ A @ top_top_set_c )
=> ( ( ( image_c_a @ A @ B )
= ( image_c_a @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_inj__image__eq__iff) ).
thf(602,plain,
! [A: c > a,B: set_c,C: set_c] :
( ( inj_on_c_a @ A @ top_top_set_c )
=> ( ( ( image_c_a @ A @ B )
= ( image_c_a @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(73,axiom,
! [A: c > a,B: a] :
( ( inj_on_c_a @ A @ top_top_set_c )
=> ( ( member_a @ B @ ( image_c_a @ A @ top_top_set_c ) )
= ( ? [C: c] :
( ( B
= ( A @ C ) )
& ! [D: c] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_range__ex1__eq) ).
thf(428,plain,
! [A: c > a,B: a] :
( ( inj_on_c_a @ A @ top_top_set_c )
=> ( ( member_a @ B @ ( image_c_a @ A @ top_top_set_c ) )
= ( ? [C: c] :
( ( B
= ( A @ C ) )
& ! [D: c] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(91,axiom,
! [A: a > c] :
( ( inj_on_a_c @ A @ top_top_set_a )
= ( ! [B: a,C: a] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_inj__def) ).
thf(507,plain,
! [A: a > c] :
( ( inj_on_a_c @ A @ top_top_set_a )
= ( ! [B: a,C: a] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(98,axiom,
! [A: a > b] :
( ( inj_on_a_b @ A @ top_top_set_a )
= ( ! [B: a,C: a] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_inj__def) ).
thf(529,plain,
! [A: a > b] :
( ( inj_on_a_b @ A @ top_top_set_a )
= ( ! [B: a,C: a] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(134,axiom,
( comp_a_b_c
= ( ^ [A: a > b,B: c > a,C: c] : ( A @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_comp__def) ).
thf(661,plain,
( comp_a_b_c
= ( ^ [A: a > b,B: c > a,C: c] : ( A @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(93,axiom,
! [A: c > a,B: a > a] :
( ( ( image_c_a @ A @ top_top_set_c )
= top_top_set_a )
=> ( ( ( image_a_a @ B @ top_top_set_a )
= top_top_set_a )
=> ( ( image_c_a @ ( comp_a_a_c @ B @ A ) @ top_top_set_c )
= top_top_set_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_comp__surj) ).
thf(512,plain,
! [A: c > a,B: a > a] :
( ( ( image_c_a @ A @ top_top_set_c )
= top_top_set_a )
=> ( ( ( image_a_a @ B @ top_top_set_a )
= top_top_set_a )
=> ( ( image_c_a @ ( comp_a_a_c @ B @ A ) @ top_top_set_c )
= top_top_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(76,axiom,
! [A: set_a] :
( ( sup_sup_set_a @ A @ top_top_set_a )
= top_top_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_sup__top__right) ).
thf(439,plain,
! [A: set_a] :
( ( sup_sup_set_a @ A @ top_top_set_a )
= top_top_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(22,axiom,
! [A: a > a,B: a,C: set_a] :
( ( inj_on_a_a @ A @ top_top_set_a )
=> ( ( member_a @ ( A @ B ) @ ( image_a_a @ A @ C ) )
= ( member_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_inj__image__mem__iff) ).
thf(220,plain,
! [A: a > a,B: a,C: set_a] :
( ( inj_on_a_a @ A @ top_top_set_a )
=> ( ( member_a @ ( A @ B ) @ ( image_a_a @ A @ C ) )
= ( member_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(55,axiom,
! [A: a > b,B: set_a,C: a,D: a] :
( ( inj_on_a_b @ A @ B )
=> ( ( member_a @ C @ B )
=> ( ( member_a @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_inj__on__eq__iff) ).
thf(366,plain,
! [A: a > b,B: set_a,C: a,D: a] :
( ( inj_on_a_b @ A @ B )
=> ( ( member_a @ C @ B )
=> ( ( member_a @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(52,axiom,
! [A: set_a,B: a > b] :
( ! [C: a,D: a] :
( ( member_a @ C @ A )
=> ( ( member_a @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on_a_b @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_inj__onI) ).
thf(349,plain,
! [A: set_a,B: a > b] :
( ! [C: a,D: a] :
( ( member_a @ C @ A )
=> ( ( member_a @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on_a_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(40,axiom,
! [A: c > b,B: set_c,C: c,D: c] :
( ( inj_on_c_b @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member_c @ C @ B )
=> ( ( member_c @ D @ B )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_inj__onD) ).
thf(297,plain,
! [A: c > b,B: set_c,C: c,D: c] :
( ( inj_on_c_b @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member_c @ C @ B )
=> ( ( member_c @ D @ B )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(72,axiom,
! [A: a > a,B: set_a,C: a,D: a] :
( ( inj_on_a_a @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member_a @ C @ B )
=> ( ( member_a @ D @ B )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_inj__onD) ).
thf(424,plain,
! [A: a > a,B: set_a,C: a,D: a] :
( ( inj_on_a_a @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member_a @ C @ B )
=> ( ( member_a @ D @ B )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(36,axiom,
! [A: c > b,B: b] :
( ( ( image_c_b @ A @ top_top_set_c )
= top_top_set_b )
=> ? [C: c] :
( B
= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_surjD) ).
thf(275,plain,
! [A: c > b,B: b] :
( ( ( image_c_b @ A @ top_top_set_c )
= top_top_set_b )
=> ? [C: c] :
( B
= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(14,axiom,
( comp_c_b_a
= ( ^ [A: c > b,B: a > c,C: a] : ( A @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_comp__apply) ).
thf(192,plain,
( comp_c_b_a
= ( ^ [A: c > b,B: a > c,C: a] : ( A @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(143,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B @ C ) )
= ( sup_sup_set_a @ B @ ( sup_sup_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_inf__sup__aci_I7_J) ).
thf(693,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B @ C ) )
= ( sup_sup_set_a @ B @ ( sup_sup_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(82,axiom,
! [A: set_a,B: a > a] :
( ! [C: a,D: a] :
( ( member_a @ C @ A )
=> ( ( member_a @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on_a_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_inj__onI) ).
thf(467,plain,
! [A: set_a,B: a > a] :
( ! [C: a,D: a] :
( ( member_a @ C @ A )
=> ( ( member_a @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on_a_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(30,axiom,
! [A: c > b,B: a > c,C: set_a] :
( ( inj_on_a_b @ ( comp_c_b_a @ A @ B ) @ C )
=> ( inj_on_a_c @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_inj__on__imageI2) ).
thf(252,plain,
! [A: c > b,B: a > c,C: set_a] :
( ( inj_on_a_b @ ( comp_c_b_a @ A @ B ) @ C )
=> ( inj_on_a_c @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(75,axiom,
! [A: a > c,B: a,C: a] :
( ( inj_on_a_c @ A @ top_top_set_a )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_inj__eq) ).
thf(435,plain,
! [A: a > c,B: a,C: a] :
( ( inj_on_a_c @ A @ top_top_set_a )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(113,axiom,
( sup_sup_set_a
= ( ^ [A: set_a,B: set_a] : ( sup_sup_set_a @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_sup_Ocommute) ).
thf(583,plain,
( sup_sup_set_a
= ( ^ [A: set_a,B: set_a] : ( sup_sup_set_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(140,axiom,
! [A: a > b,B: c > a,C: a > b] :
( ( ( comp_a_b_c @ A @ B )
= ( comp_a_b_c @ C @ B ) )
= ( ! [D: a] :
( ( member_a @ D @ ( image_c_a @ B @ top_top_set_c ) )
=> ( ( A @ D )
= ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_o__eq__conv) ).
thf(682,plain,
! [A: a > b,B: c > a,C: a > b] :
( ( ( comp_a_b_c @ A @ B )
= ( comp_a_b_c @ C @ B ) )
= ( ! [D: a] :
( ( member_a @ D @ ( image_c_a @ B @ top_top_set_c ) )
=> ( ( A @ D )
= ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(23,axiom,
! [A: c > a,B: set_c,C: c,D: c] :
( ( inj_on_c_a @ A @ B )
=> ( ( member_c @ C @ B )
=> ( ( member_c @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_inj__on__eq__iff) ).
thf(224,plain,
! [A: c > a,B: set_c,C: c,D: c] :
( ( inj_on_c_a @ A @ B )
=> ( ( member_c @ C @ B )
=> ( ( member_c @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(111,axiom,
! [A: a > b,B: set_a,C: set_a] :
( ( inj_on_a_b @ A @ ( sup_sup_set_a @ B @ C ) )
=> ( ( ( image_a_b @ A @ B )
= ( image_a_b @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_inj__on__Un__image__eq__iff) ).
thf(578,plain,
! [A: a > b,B: set_a,C: set_a] :
( ( inj_on_a_b @ A @ ( sup_sup_set_a @ B @ C ) )
=> ( ( ( image_a_b @ A @ B )
= ( image_a_b @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(44,axiom,
! [A: c > b,B: set_c,C: c,D: c] :
( ( inj_on_c_b @ A @ B )
=> ( ( C != D )
=> ( ( member_c @ C @ B )
=> ( ( member_c @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_inj__on__contraD) ).
thf(317,plain,
! [A: c > b,B: set_c,C: c,D: c] :
( ( inj_on_c_b @ A @ B )
=> ( ( C != D )
=> ( ( member_c @ C @ B )
=> ( ( member_c @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(13,axiom,
! [A: a > a,B: a] :
( ( ( image_a_a @ A @ top_top_set_a )
= top_top_set_a )
=> ~ ! [C: a] :
( B
!= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_surjE) ).
thf(188,plain,
! [A: a > a,B: a] :
( ( ( image_a_a @ A @ top_top_set_a )
= top_top_set_a )
=> ~ ! [C: a] :
( B
!= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(116,axiom,
! [A: c > a,B: a] :
( ( ( image_c_a @ A @ top_top_set_c )
= top_top_set_a )
=> ? [C: c] :
( B
= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_surjD) ).
thf(593,plain,
! [A: c > a,B: a] :
( ( ( image_c_a @ A @ top_top_set_c )
= top_top_set_a )
=> ? [C: c] :
( B
= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(71,axiom,
! [A: c > a,B: c,C: set_c] :
( ( inj_on_c_a @ A @ top_top_set_c )
=> ( ( member_a @ ( A @ B ) @ ( image_c_a @ A @ C ) )
= ( member_c @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_inj__image__mem__iff) ).
thf(420,plain,
! [A: c > a,B: c,C: set_c] :
( ( inj_on_c_a @ A @ top_top_set_c )
=> ( ( member_a @ ( A @ B ) @ ( image_c_a @ A @ C ) )
= ( member_c @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(89,axiom,
! [A: set_a,B: c > a,C: a > c] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on_a_c @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_inj__on__inverseI) ).
thf(499,plain,
! [A: set_a,B: c > a,C: a > c] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on_a_c @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(47,axiom,
! [A: set_c,B: b > c,C: c > b] :
( ! [D: c] :
( ( member_c @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on_c_b @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_inj__on__inverseI) ).
thf(328,plain,
! [A: set_c,B: b > c,C: c > b] :
( ! [D: c] :
( ( member_c @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on_c_b @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(87,axiom,
! [A: a > a] :
( ! [B: a,C: a] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on_a_a @ A @ top_top_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_injI) ).
thf(489,plain,
! [A: a > a] :
( ! [B: a,C: a] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on_a_a @ A @ top_top_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(115,axiom,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ A @ B ) )
= ( sup_sup_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_sup_Oleft__idem) ).
thf(590,plain,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ A @ B ) )
= ( sup_sup_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(139,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B @ C ) )
= ( sup_sup_set_a @ B @ ( sup_sup_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_sup__left__commute) ).
thf(679,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B @ C ) )
= ( sup_sup_set_a @ B @ ( sup_sup_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(103,axiom,
! [A: set_a,B: a > a,C: a > a] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on_a_a @ B @ A )
= ( inj_on_a_a @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_inj__on__cong) ).
thf(547,plain,
! [A: set_a,B: a > a,C: a > a] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on_a_a @ B @ A )
= ( inj_on_a_a @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(146,axiom,
inj_on_a_b @ f @ ( sup_sup_set_a @ ( image_c_a @ g @ top_top_set_c ) @ ( image_c_a @ h @ top_top_set_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(701,plain,
inj_on_a_b @ f @ ( sup_sup_set_a @ ( image_c_a @ g @ top_top_set_c ) @ ( image_c_a @ h @ top_top_set_c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(132,axiom,
! [A: set_a] :
( ( sup_sup_set_a @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_sup_Oidem) ).
thf(654,plain,
! [A: set_a] :
( ( sup_sup_set_a @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(90,axiom,
! [A: c > b,B: set_c,C: set_c] :
( ( inj_on_c_b @ A @ top_top_set_c )
=> ( ( ( image_c_b @ A @ B )
= ( image_c_b @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_inj__image__eq__iff) ).
thf(503,plain,
! [A: c > b,B: set_c,C: set_c] :
( ( inj_on_c_b @ A @ top_top_set_c )
=> ( ( ( image_c_b @ A @ B )
= ( image_c_b @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(27,axiom,
! [A: c > b,B: a > c,C: c > b,D: a > c] :
( ( ( comp_c_b_a @ A @ B )
= ( comp_c_b_a @ C @ D ) )
=> ! [E: a] :
( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_comp__eq__elim) ).
thf(237,plain,
! [A: c > b,B: a > c,C: c > b,D: a > c] :
( ( ( comp_c_b_a @ A @ B )
= ( comp_c_b_a @ C @ D ) )
=> ! [E: a] :
( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(29,axiom,
! [A: set_c,B: c > a] :
( ! [C: c,D: c] :
( ( member_c @ C @ A )
=> ( ( member_c @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on_c_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_inj__onI) ).
thf(244,plain,
! [A: set_c,B: c > a] :
( ! [C: c,D: c] :
( ( member_c @ C @ A )
=> ( ( member_c @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on_c_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(133,axiom,
! [A: a > b,B: c > a,C: a > b,D: c > a,E: c] :
( ( ( comp_a_b_c @ A @ B )
= ( comp_a_b_c @ C @ D ) )
=> ( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_comp__eq__dest) ).
thf(657,plain,
! [A: a > b,B: c > a,C: a > b,D: c > a,E: c] :
( ( ( comp_a_b_c @ A @ B )
= ( comp_a_b_c @ C @ D ) )
=> ( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(65,axiom,
! [A: set_a,B: a > a,C: a > a] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on_a_a @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_inj__on__inverseI) ).
thf(398,plain,
! [A: set_a,B: a > a,C: a > a] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on_a_a @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(138,axiom,
! [A: a > b,B: c > a,C: c > b,D: c] :
( ( ( comp_a_b_c @ A @ B )
= C )
=> ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_comp__eq__dest__lhs) ).
thf(674,plain,
! [A: a > b,B: c > a,C: c > b,D: c] :
( ( ( comp_a_b_c @ A @ B )
= C )
=> ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(69,axiom,
! [A: c > a,B: a > b] :
( ( ( image_c_a @ A @ top_top_set_c )
= top_top_set_a )
=> ( ( ( image_a_b @ B @ top_top_set_a )
= top_top_set_b )
=> ( ( image_c_b @ ( comp_a_b_c @ B @ A ) @ top_top_set_c )
= top_top_set_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_comp__surj) ).
thf(412,plain,
! [A: c > a,B: a > b] :
( ( ( image_c_a @ A @ top_top_set_c )
= top_top_set_a )
=> ( ( ( image_a_b @ B @ top_top_set_a )
= top_top_set_b )
=> ( ( image_c_b @ ( comp_a_b_c @ B @ A ) @ top_top_set_c )
= top_top_set_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(7,axiom,
( inj_on_c_a
= ( ^ [A: c > a,B: set_c] :
! [C: c] :
( ( member_c @ C @ B )
=> ! [D: c] :
( ( member_c @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_inj__on__def) ).
thf(166,plain,
( inj_on_c_a
= ( ^ [A: c > a,B: set_c] :
! [C: c] :
( ( member_c @ C @ B )
=> ! [D: c] :
( ( member_c @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,conjecture,
g = h,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(2,negated_conjecture,
g != h,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(148,plain,
g != h,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(37,axiom,
! [A: set_a,B: a > b,C: a > a] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ! [E: a] :
( ( member_a @ E @ A )
=> ( ( ( B @ ( C @ D ) )
= ( B @ ( C @ E ) ) )
= ( ( B @ D )
= ( B @ E ) ) ) ) )
=> ( ( inj_on_a_a @ C @ A )
=> ( ( inj_on_a_b @ B @ ( image_a_a @ C @ A ) )
= ( inj_on_a_b @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_inj__on__image__iff) ).
thf(279,plain,
! [A: set_a,B: a > b,C: a > a] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ! [E: a] :
( ( member_a @ E @ A )
=> ( ( ( B @ ( C @ D ) )
= ( B @ ( C @ E ) ) )
= ( ( B @ D )
= ( B @ E ) ) ) ) )
=> ( ( inj_on_a_a @ C @ A )
=> ( ( inj_on_a_b @ B @ ( image_a_a @ C @ A ) )
= ( inj_on_a_b @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(66,axiom,
! [A: set_a] :
( ( sup_sup_set_a @ top_top_set_a @ A )
= top_top_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_sup__top__left) ).
thf(402,plain,
! [A: set_a] :
( ( sup_sup_set_a @ top_top_set_a @ A )
= top_top_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(38,axiom,
! [A: a > b,B: b] :
( ( ( image_a_b @ A @ top_top_set_a )
= top_top_set_b )
=> ? [C: a] :
( B
= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_surjD) ).
thf(286,plain,
! [A: a > b,B: b] :
( ( ( image_a_b @ A @ top_top_set_a )
= top_top_set_b )
=> ? [C: a] :
( B
= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(18,axiom,
! [A: a > a] :
( ( ( image_a_a @ A @ top_top_set_a )
= top_top_set_a )
= ( ! [B: a] :
? [C: a] :
( B
= ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_surj__def) ).
thf(204,plain,
! [A: a > a] :
( ( ( image_a_a @ A @ top_top_set_a )
= top_top_set_a )
= ( ! [B: a] :
? [C: a] :
( B
= ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(32,axiom,
! [A: c > b,B: b] :
( ( ( image_c_b @ A @ top_top_set_c )
= top_top_set_b )
=> ~ ! [C: c] :
( B
!= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_surjE) ).
thf(259,plain,
! [A: c > b,B: b] :
( ( ( image_c_b @ A @ top_top_set_c )
= top_top_set_b )
=> ~ ! [C: c] :
( B
!= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(128,axiom,
! [A: c > a,B: set_c,C: c > a,D: set_c,E: a > b] :
( ( ( image_c_a @ A @ B )
= ( image_c_a @ C @ D ) )
=> ( ( image_c_b @ ( comp_a_b_c @ E @ A ) @ B )
= ( image_c_b @ ( comp_a_b_c @ E @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_image__eq__imp__comp) ).
thf(641,plain,
! [A: c > a,B: set_c,C: c > a,D: set_c,E: a > b] :
( ( ( image_c_a @ A @ B )
= ( image_c_a @ C @ D ) )
=> ( ( image_c_b @ ( comp_a_b_c @ E @ A ) @ B )
= ( image_c_b @ ( comp_a_b_c @ E @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(63,axiom,
! [A: c > a] :
( ( inj_on_c_a @ A @ top_top_set_c )
= ( ! [B: c,C: c] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_inj__def) ).
thf(391,plain,
! [A: c > a] :
( ( inj_on_c_a @ A @ top_top_set_c )
= ( ! [B: c,C: c] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(60,axiom,
! [A: c > a,B: a > c] :
( ( inj_on_c_a @ A @ top_top_set_c )
=> ( ( inj_on_a_c @ B @ top_top_set_a )
=> ( inj_on_a_a @ ( comp_c_a_a @ A @ B ) @ top_top_set_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_inj__compose) ).
thf(382,plain,
! [A: c > a,B: a > c] :
( ( inj_on_c_a @ A @ top_top_set_c )
=> ( ( inj_on_a_c @ B @ top_top_set_a )
=> ( inj_on_a_a @ ( comp_c_a_a @ A @ B ) @ top_top_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(109,axiom,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ ( sup_sup_set_a @ A @ B ) @ B )
= ( sup_sup_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_sup_Oright__idem) ).
thf(572,plain,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ ( sup_sup_set_a @ A @ B ) @ B )
= ( sup_sup_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(43,axiom,
! [A: c > b,B: set_c,C: c,D: c] :
( ( inj_on_c_b @ A @ B )
=> ( ( member_c @ C @ B )
=> ( ( member_c @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_inj__on__eq__iff) ).
thf(313,plain,
! [A: c > b,B: set_c,C: c,D: c] :
( ( inj_on_c_b @ A @ B )
=> ( ( member_c @ C @ B )
=> ( ( member_c @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(11,axiom,
! [A: set_c,B: a > c,C: c > a] :
( ! [D: c] :
( ( member_c @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on_c_a @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_inj__on__inverseI) ).
thf(181,plain,
! [A: set_c,B: a > c,C: c > a] :
( ! [D: c] :
( ( member_c @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on_c_a @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
! [A: c > b] :
( ( ( image_c_b @ A @ top_top_set_c )
= top_top_set_b )
= ( ! [B: b] :
? [C: c] :
( B
= ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_surj__def) ).
thf(159,plain,
! [A: c > b] :
( ( ( image_c_b @ A @ top_top_set_c )
= top_top_set_b )
= ( ! [B: b] :
? [C: c] :
( B
= ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(35,axiom,
! [A: c > b,B: c,C: set_c] :
( ( inj_on_c_b @ A @ top_top_set_c )
=> ( ( member_b @ ( A @ B ) @ ( image_c_b @ A @ C ) )
= ( member_c @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_inj__image__mem__iff) ).
thf(271,plain,
! [A: c > b,B: c,C: set_c] :
( ( inj_on_c_b @ A @ top_top_set_c )
=> ( ( member_b @ ( A @ B ) @ ( image_c_b @ A @ C ) )
= ( member_c @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(54,axiom,
! [A: c > a,B: set_c,C: c > a,D: set_c,E: a > a] :
( ( ( image_c_a @ A @ B )
= ( image_c_a @ C @ D ) )
=> ( ( image_c_a @ ( comp_a_a_c @ E @ A ) @ B )
= ( image_c_a @ ( comp_a_a_c @ E @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_image__eq__imp__comp) ).
thf(362,plain,
! [A: c > a,B: set_c,C: c > a,D: set_c,E: a > a] :
( ( ( image_c_a @ A @ B )
= ( image_c_a @ C @ D ) )
=> ( ( image_c_a @ ( comp_a_a_c @ E @ A ) @ B )
= ( image_c_a @ ( comp_a_a_c @ E @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(108,axiom,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( A
= ( sup_sup_set_a @ B @ C ) )
=> ( ( sup_sup_set_a @ D @ A )
= ( sup_sup_set_a @ B @ ( sup_sup_set_a @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_boolean__algebra__cancel_Osup2) ).
thf(567,plain,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( A
= ( sup_sup_set_a @ B @ C ) )
=> ( ( sup_sup_set_a @ D @ A )
= ( sup_sup_set_a @ B @ ( sup_sup_set_a @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(84,axiom,
! [A: a > b,B: set_a,C: a,D: a] :
( ( inj_on_a_b @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member_a @ C @ B )
=> ( ( member_a @ D @ B )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_inj__onD) ).
thf(477,plain,
! [A: a > b,B: set_a,C: a,D: a] :
( ( inj_on_a_b @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member_a @ C @ B )
=> ( ( member_a @ D @ B )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(88,axiom,
! [A: a > c] :
( ! [B: a,C: a] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on_a_c @ A @ top_top_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_injI) ).
thf(494,plain,
! [A: a > c] :
( ! [B: a,C: a] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on_a_c @ A @ top_top_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(104,axiom,
! [A: a > b,B: a,C: a] :
( ( inj_on_a_b @ A @ top_top_set_a )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_injD) ).
thf(552,plain,
! [A: a > b,B: a,C: a] :
( ( inj_on_a_b @ A @ top_top_set_a )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(121,axiom,
! [A: a > b,B: c > a,C: c > a] :
( ( ( comp_a_b_c @ A @ B )
= ( comp_a_b_c @ A @ C ) )
=> ( ( inj_on_a_b @ A @ ( sup_sup_set_a @ ( image_c_a @ B @ top_top_set_c ) @ ( image_c_a @ C @ top_top_set_c ) ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_o__inj__on) ).
thf(609,plain,
! [A: a > b,B: c > a,C: c > a] :
( ( ( comp_a_b_c @ A @ B )
= ( comp_a_b_c @ A @ C ) )
=> ( ( inj_on_a_b @ A @ ( sup_sup_set_a @ ( image_c_a @ B @ top_top_set_c ) @ ( image_c_a @ C @ top_top_set_c ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(28,axiom,
! [A: c > b,B: a > c,C: c > b,D: a > c,E: a] :
( ( ( comp_c_b_a @ A @ B )
= ( comp_c_b_a @ C @ D ) )
=> ( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_comp__eq__dest) ).
thf(240,plain,
! [A: c > b,B: a > c,C: c > b,D: a > c,E: a] :
( ( ( comp_c_b_a @ A @ B )
= ( comp_c_b_a @ C @ D ) )
=> ( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(4,axiom,
! [A: c > a,B: set_c,C: c,D: c] :
( ( inj_on_c_a @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member_c @ C @ B )
=> ( ( member_c @ D @ B )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_inj__onD) ).
thf(155,plain,
! [A: c > a,B: set_c,C: c,D: c] :
( ( inj_on_c_a @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member_c @ C @ B )
=> ( ( member_c @ D @ B )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(141,axiom,
! [A: c > a,B: a > b,C: a > b] :
( ! [D: a] :
( ( member_a @ D @ ( image_c_a @ A @ top_top_set_c ) )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( comp_a_b_c @ B @ A )
= ( comp_a_b_c @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_o__ext) ).
thf(685,plain,
! [A: c > a,B: a > b,C: a > b] :
( ! [D: a] :
( ( member_a @ D @ ( image_c_a @ A @ top_top_set_c ) )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( comp_a_b_c @ B @ A )
= ( comp_a_b_c @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(80,axiom,
! [A: a > a,B: a,C: a] :
( ( inj_on_a_a @ A @ top_top_set_a )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_inj__eq) ).
thf(455,plain,
! [A: a > a,B: a,C: a] :
( ( inj_on_a_a @ A @ top_top_set_a )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(64,axiom,
! [A: a > a,B: set_a,C: a,D: a] :
( ( inj_on_a_a @ A @ B )
=> ( ( member_a @ C @ B )
=> ( ( member_a @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_inj__on__eq__iff) ).
thf(394,plain,
! [A: a > a,B: set_a,C: a,D: a] :
( ( inj_on_a_a @ A @ B )
=> ( ( member_a @ C @ B )
=> ( ( member_a @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(107,axiom,
! [A: c > a,B: a > c] :
( ! [C: a] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_c_a @ A @ top_top_set_c )
= top_top_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_surjI) ).
thf(563,plain,
! [A: c > a,B: a > c] :
( ! [C: a] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_c_a @ A @ top_top_set_c )
= top_top_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(34,axiom,
! [A: a > a,B: a] :
( ( ( image_a_a @ A @ top_top_set_a )
= top_top_set_a )
=> ? [C: a] :
( B
= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_surjD) ).
thf(267,plain,
! [A: a > a,B: a] :
( ( ( image_a_a @ A @ top_top_set_a )
= top_top_set_a )
=> ? [C: a] :
( B
= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(6,axiom,
! [A: a > b,B: b] :
( ( ( image_a_b @ A @ top_top_set_a )
= top_top_set_b )
=> ~ ! [C: a] :
( B
!= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_surjE) ).
thf(162,plain,
! [A: a > b,B: b] :
( ( ( image_a_b @ A @ top_top_set_a )
= top_top_set_b )
=> ~ ! [C: a] :
( B
!= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(135,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_sup__assoc) ).
thf(663,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(130,axiom,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ A @ B ) )
= ( sup_sup_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_inf__sup__aci_I8_J) ).
thf(648,plain,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ A @ B ) )
= ( sup_sup_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(94,axiom,
( inj_on_a_a
= ( ^ [A: a > a,B: set_a] :
! [C: a] :
( ( member_a @ C @ B )
=> ! [D: a] :
( ( member_a @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_inj__on__def) ).
thf(516,plain,
( inj_on_a_a
= ( ^ [A: a > a,B: set_a] :
! [C: a] :
( ( member_a @ C @ B )
=> ! [D: a] :
( ( member_a @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(15,axiom,
( inj_on_c_b
= ( ^ [A: c > b,B: set_c] :
! [C: c] :
( ( member_c @ C @ B )
=> ! [D: c] :
( ( member_c @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_inj__on__def) ).
thf(194,plain,
( inj_on_c_b
= ( ^ [A: c > b,B: set_c] :
! [C: c] :
( ( member_c @ C @ B )
=> ! [D: c] :
( ( member_c @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(97,axiom,
! [A: a > c,B: a,C: a] :
( ( inj_on_a_c @ A @ top_top_set_a )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_injD) ).
thf(525,plain,
! [A: a > c,B: a,C: a] :
( ( inj_on_a_c @ A @ top_top_set_a )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(142,axiom,
! [A: a > c,B: c > a,C: c > a] :
( ( ( comp_a_c_c @ A @ B )
= ( comp_a_c_c @ A @ C ) )
=> ( ( inj_on_a_c @ A @ ( sup_sup_set_a @ ( image_c_a @ B @ top_top_set_c ) @ ( image_c_a @ C @ top_top_set_c ) ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_o__inj__on) ).
thf(690,plain,
! [A: a > c,B: c > a,C: c > a] :
( ( ( comp_a_c_c @ A @ B )
= ( comp_a_c_c @ A @ C ) )
=> ( ( inj_on_a_c @ A @ ( sup_sup_set_a @ ( image_c_a @ B @ top_top_set_c ) @ ( image_c_a @ C @ top_top_set_c ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(3,axiom,
! [A: set_c,B: c > a,C: c > a] :
( ! [D: c] :
( ( member_c @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on_c_a @ B @ A )
= ( inj_on_c_a @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_inj__on__cong) ).
thf(150,plain,
! [A: set_c,B: c > a,C: c > a] :
( ! [D: c] :
( ( member_c @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on_c_a @ B @ A )
= ( inj_on_c_a @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(68,axiom,
! [A: a > a] :
( ( inj_on_a_a @ A @ top_top_set_a )
= ( ! [B: a,C: a] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_inj__def) ).
thf(409,plain,
! [A: a > a] :
( ( inj_on_a_a @ A @ top_top_set_a )
= ( ! [B: a,C: a] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(33,axiom,
! [A: a > a,B: a > a] :
( ! [C: a] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_a_a @ A @ top_top_set_a )
= top_top_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_surjI) ).
thf(263,plain,
! [A: a > a,B: a > a] :
( ! [C: a] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_a_a @ A @ top_top_set_a )
= top_top_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(114,axiom,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( A
= ( sup_sup_set_a @ B @ C ) )
=> ( ( sup_sup_set_a @ A @ D )
= ( sup_sup_set_a @ B @ ( sup_sup_set_a @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_boolean__algebra__cancel_Osup1) ).
thf(585,plain,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( A
= ( sup_sup_set_a @ B @ C ) )
=> ( ( sup_sup_set_a @ A @ D )
= ( sup_sup_set_a @ B @ ( sup_sup_set_a @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(56,axiom,
( inj_on_a_c
= ( ^ [A: a > c,B: set_a] :
! [C: a] :
( ( member_a @ C @ B )
=> ! [D: a] :
( ( member_a @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_inj__on__def) ).
thf(370,plain,
( inj_on_a_c
= ( ^ [A: a > c,B: set_a] :
! [C: a] :
( ( member_a @ C @ B )
=> ! [D: a] :
( ( member_a @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(49,axiom,
! [A: a > b,B: set_a,C: set_a] :
( ( inj_on_a_b @ A @ top_top_set_a )
=> ( ( ( image_a_b @ A @ B )
= ( image_a_b @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_inj__image__eq__iff) ).
thf(336,plain,
! [A: a > b,B: set_a,C: set_a] :
( ( inj_on_a_b @ A @ top_top_set_a )
=> ( ( ( image_a_b @ A @ B )
= ( image_a_b @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(118,axiom,
( comp_a_b_c
= ( ^ [A: a > b,B: c > a,C: c] : ( A @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_comp__apply) ).
thf(600,plain,
( comp_a_b_c
= ( ^ [A: a > b,B: c > a,C: c] : ( A @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(122,axiom,
( sup_sup_set_a
= ( ^ [A: set_a,B: set_a] : ( sup_sup_set_a @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_inf__sup__aci_I5_J) ).
thf(612,plain,
( sup_sup_set_a
= ( ^ [A: set_a,B: set_a] : ( sup_sup_set_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(25,axiom,
! [A: a > b,B: b] :
( ( inj_on_a_b @ A @ top_top_set_a )
=> ( ( member_b @ B @ ( image_a_b @ A @ top_top_set_a ) )
= ( ? [C: a] :
( ( B
= ( A @ C ) )
& ! [D: a] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_range__ex1__eq) ).
thf(231,plain,
! [A: a > b,B: b] :
( ( inj_on_a_b @ A @ top_top_set_a )
=> ( ( member_b @ B @ ( image_a_b @ A @ top_top_set_a ) )
= ( ? [C: a] :
( ( B
= ( A @ C ) )
& ! [D: a] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(125,axiom,
! [A: c > a,B: c > a,C: a > b,D: a > b] :
( ( A = B )
=> ( ! [E: a] :
( ( member_a @ E @ ( image_c_a @ B @ top_top_set_c ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( comp_a_b_c @ C @ A )
= ( comp_a_b_c @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_o__cong) ).
thf(627,plain,
! [A: c > a,B: c > a,C: a > b,D: a > b] :
( ( A = B )
=> ( ! [E: a] :
( ( member_a @ E @ ( image_c_a @ B @ top_top_set_c ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( comp_a_b_c @ C @ A )
= ( comp_a_b_c @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(79,axiom,
! [A: set_a,B: a > c,C: a > c] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on_a_c @ B @ A )
= ( inj_on_a_c @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_inj__on__cong) ).
thf(450,plain,
! [A: set_a,B: a > c,C: a > c] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on_a_c @ B @ A )
= ( inj_on_a_c @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(105,axiom,
! [A: c > a,B: c,C: c] :
( ( inj_on_c_a @ A @ top_top_set_c )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_inj__eq) ).
thf(556,plain,
! [A: c > a,B: c,C: c] :
( ( inj_on_c_a @ A @ top_top_set_c )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(101,axiom,
! [A: a > b,B: a,C: set_a] :
( ( inj_on_a_b @ A @ top_top_set_a )
=> ( ( member_b @ ( A @ B ) @ ( image_a_b @ A @ C ) )
= ( member_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_inj__image__mem__iff) ).
thf(539,plain,
! [A: a > b,B: a,C: set_a] :
( ( inj_on_a_b @ A @ top_top_set_a )
=> ( ( member_b @ ( A @ B ) @ ( image_a_b @ A @ C ) )
= ( member_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(112,axiom,
( sup_sup_set_a
= ( ^ [A: set_a,B: set_a] : ( sup_sup_set_a @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_sup__commute) ).
thf(581,plain,
( sup_sup_set_a
= ( ^ [A: set_a,B: set_a] : ( sup_sup_set_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(145,axiom,
! [A: a > b,B: c > a,C: set_c] :
( ( inj_on_c_b @ ( comp_a_b_c @ A @ B ) @ C )
=> ( inj_on_a_b @ A @ ( image_c_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_inj__on__imageI) ).
thf(699,plain,
! [A: a > b,B: c > a,C: set_c] :
( ( inj_on_c_b @ ( comp_a_b_c @ A @ B ) @ C )
=> ( inj_on_a_b @ A @ ( image_c_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(9,axiom,
! [A: c > b,B: a > b] :
( ( ? [C: c > a] :
( A
= ( comp_a_b_c @ B @ C ) ) )
= ( ! [C: b] :
( ( member_b @ C @ ( image_c_b @ A @ top_top_set_c ) )
=> ? [D: a] :
( C
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_ex__o__conv) ).
thf(171,plain,
! [A: c > b,B: a > b] :
( ( ? [C: c > a] :
( A
= ( comp_a_b_c @ B @ C ) ) )
= ( ! [C: b] :
( ( member_b @ C @ ( image_c_b @ A @ top_top_set_c ) )
=> ? [D: a] :
( C
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(26,axiom,
( comp_c_b_a
= ( ^ [A: c > b,B: a > c,C: a] : ( A @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_comp__def) ).
thf(235,plain,
( comp_c_b_a
= ( ^ [A: c > b,B: a > c,C: a] : ( A @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(92,axiom,
! [A: a > b,B: c > a,C: set_c] :
( ( inj_on_c_b @ ( comp_a_b_c @ A @ B ) @ C )
=> ( inj_on_c_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_inj__on__imageI2) ).
thf(510,plain,
! [A: a > b,B: c > a,C: set_c] :
( ( inj_on_c_b @ ( comp_a_b_c @ A @ B ) @ C )
=> ( inj_on_c_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(19,axiom,
! [A: c > a,B: set_c,C: c,D: c] :
( ( inj_on_c_a @ A @ B )
=> ( ( C != D )
=> ( ( member_c @ C @ B )
=> ( ( member_c @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_inj__on__contraD) ).
thf(207,plain,
! [A: c > a,B: set_c,C: c,D: c] :
( ( inj_on_c_a @ A @ B )
=> ( ( C != D )
=> ( ( member_c @ C @ B )
=> ( ( member_c @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(100,axiom,
! [A: c > b] :
( ( inj_on_c_b @ A @ top_top_set_c )
= ( ! [B: c,C: c] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_inj__def) ).
thf(536,plain,
! [A: c > b] :
( ( inj_on_c_b @ A @ top_top_set_c )
= ( ! [B: c,C: c] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(39,axiom,
! [A: set_a,B: a > a,C: a > a] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ! [E: a] :
( ( member_a @ E @ A )
=> ( ( ( B @ ( C @ D ) )
= ( B @ ( C @ E ) ) )
= ( ( B @ D )
= ( B @ E ) ) ) ) )
=> ( ( inj_on_a_a @ C @ A )
=> ( ( inj_on_a_a @ B @ ( image_a_a @ C @ A ) )
= ( inj_on_a_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_inj__on__image__iff) ).
thf(290,plain,
! [A: set_a,B: a > a,C: a > a] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ! [E: a] :
( ( member_a @ E @ A )
=> ( ( ( B @ ( C @ D ) )
= ( B @ ( C @ E ) ) )
= ( ( B @ D )
= ( B @ E ) ) ) ) )
=> ( ( inj_on_a_a @ C @ A )
=> ( ( inj_on_a_a @ B @ ( image_a_a @ C @ A ) )
= ( inj_on_a_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(59,axiom,
! [A: c > b,B: c,C: c] :
( ( inj_on_c_b @ A @ top_top_set_c )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_injD) ).
thf(378,plain,
! [A: c > b,B: c,C: c] :
( ( inj_on_c_b @ A @ top_top_set_c )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(78,axiom,
! [A: c > b,B: a > c] :
( ( inj_on_c_b @ A @ top_top_set_c )
=> ( ( inj_on_a_c @ B @ top_top_set_a )
=> ( inj_on_a_b @ ( comp_c_b_a @ A @ B ) @ top_top_set_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_inj__compose) ).
thf(447,plain,
! [A: c > b,B: a > c] :
( ( inj_on_c_b @ A @ top_top_set_c )
=> ( ( inj_on_a_c @ B @ top_top_set_a )
=> ( inj_on_a_b @ ( comp_c_b_a @ A @ B ) @ top_top_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(74,axiom,
! [A: a > b,B: c > a] :
( ( inj_on_a_b @ A @ top_top_set_a )
=> ( ( inj_on_c_a @ B @ top_top_set_c )
=> ( inj_on_c_b @ ( comp_a_b_c @ A @ B ) @ top_top_set_c ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_inj__compose) ).
thf(432,plain,
! [A: a > b,B: c > a] :
( ( inj_on_a_b @ A @ top_top_set_a )
=> ( ( inj_on_c_a @ B @ top_top_set_c )
=> ( inj_on_c_b @ ( comp_a_b_c @ A @ B ) @ top_top_set_c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(8,axiom,
! [A: a > b,B: c > b] :
( ( ? [C: a > c] :
( A
= ( comp_c_b_a @ B @ C ) ) )
= ( ! [C: b] :
( ( member_b @ C @ ( image_a_b @ A @ top_top_set_a ) )
=> ? [D: c] :
( C
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_ex__o__conv) ).
thf(168,plain,
! [A: a > b,B: c > b] :
( ( ? [C: a > c] :
( A
= ( comp_c_b_a @ B @ C ) ) )
= ( ! [C: b] :
( ( member_b @ C @ ( image_a_b @ A @ top_top_set_a ) )
=> ? [D: c] :
( C
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(67,axiom,
! [A: a > b,B: set_a,C: a,D: a] :
( ( inj_on_a_b @ A @ B )
=> ( ( C != D )
=> ( ( member_a @ C @ B )
=> ( ( member_a @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_inj__on__contraD) ).
thf(405,plain,
! [A: a > b,B: set_a,C: a,D: a] :
( ( inj_on_a_b @ A @ B )
=> ( ( C != D )
=> ( ( member_a @ C @ B )
=> ( ( member_a @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(126,axiom,
! [A: set_a] :
( ( sup_sup_set_a @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_sup__idem) ).
thf(635,plain,
! [A: set_a] :
( ( sup_sup_set_a @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(99,axiom,
! [A: set_a,B: b > a,C: a > b] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on_a_b @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_inj__on__inverseI) ).
thf(532,plain,
! [A: set_a,B: b > a,C: a > b] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on_a_b @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(144,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B @ C ) )
= ( sup_sup_set_a @ B @ ( sup_sup_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_sup_Oleft__commute) ).
thf(696,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B @ C ) )
= ( sup_sup_set_a @ B @ ( sup_sup_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(124,axiom,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ A @ B ) )
= ( sup_sup_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_sup__left__idem) ).
thf(624,plain,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ A @ B ) )
= ( sup_sup_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(48,axiom,
! [A: a > c,B: set_a,C: a,D: a] :
( ( inj_on_a_c @ A @ B )
=> ( ( member_a @ C @ B )
=> ( ( member_a @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_inj__on__eq__iff) ).
thf(332,plain,
! [A: a > c,B: set_a,C: a,D: a] :
( ( inj_on_a_c @ A @ B )
=> ( ( member_a @ C @ B )
=> ( ( member_a @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(110,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_sup_Oassoc) ).
thf(575,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( sup_sup_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(81,axiom,
! [A: set_a,B: a > c] :
( ! [C: a,D: a] :
( ( member_a @ C @ A )
=> ( ( member_a @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on_a_c @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_inj__onI) ).
thf(459,plain,
! [A: set_a,B: a > c] :
( ! [C: a,D: a] :
( ( member_a @ C @ A )
=> ( ( member_a @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on_a_c @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(17,axiom,
! [A: c > b,B: b] :
( ( inj_on_c_b @ A @ top_top_set_c )
=> ( ( member_b @ B @ ( image_c_b @ A @ top_top_set_c ) )
= ( ? [C: c] :
( ( B
= ( A @ C ) )
& ! [D: c] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_range__ex1__eq) ).
thf(200,plain,
! [A: c > b,B: b] :
( ( inj_on_c_b @ A @ top_top_set_c )
=> ( ( member_b @ B @ ( image_c_b @ A @ top_top_set_c ) )
= ( ? [C: c] :
( ( B
= ( A @ C ) )
& ! [D: c] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(77,axiom,
! [A: a > b] :
( ! [B: a,C: a] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on_a_b @ A @ top_top_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_injI) ).
thf(442,plain,
! [A: a > b] :
( ! [B: a,C: a] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on_a_b @ A @ top_top_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(31,axiom,
! [A: set_c,B: c > b,C: c > b] :
( ! [D: c] :
( ( member_c @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on_c_b @ B @ A )
= ( inj_on_c_b @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_inj__on__cong) ).
thf(254,plain,
! [A: set_c,B: c > b,C: c > b] :
( ! [D: c] :
( ( member_c @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on_c_b @ B @ A )
= ( inj_on_c_b @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(42,axiom,
! [A: a > a,B: set_a,C: set_a] :
( ( inj_on_a_a @ A @ top_top_set_a )
=> ( ( ( image_a_a @ A @ B )
= ( image_a_a @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_inj__image__eq__iff) ).
thf(309,plain,
! [A: a > a,B: set_a,C: set_a] :
( ( inj_on_a_a @ A @ top_top_set_a )
=> ( ( ( image_a_a @ A @ B )
= ( image_a_a @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(102,axiom,
! [A: a > a,B: a,C: a] :
( ( inj_on_a_a @ A @ top_top_set_a )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_injD) ).
thf(543,plain,
! [A: a > a,B: a,C: a] :
( ( inj_on_a_a @ A @ top_top_set_a )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(21,axiom,
! [A: c > b,B: a > c,C: a > b,D: a] :
( ( ( comp_c_b_a @ A @ B )
= C )
=> ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_comp__eq__dest__lhs) ).
thf(215,plain,
! [A: c > b,B: a > c,C: a > b,D: a] :
( ( ( comp_c_b_a @ A @ B )
= C )
=> ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(106,axiom,
! [A: a > b,B: c > a,C: set_c] :
( ( image_a_b @ A @ ( image_c_a @ B @ C ) )
= ( image_c_b @ ( comp_a_b_c @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_image__comp) ).
thf(560,plain,
! [A: a > b,B: c > a,C: set_c] :
( ( image_a_b @ A @ ( image_c_a @ B @ C ) )
= ( image_c_b @ ( comp_a_b_c @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(707,plain,
$false,
inference(e,[status(thm)],[645,518,666,481,523,614,597,385,340,670,174,185,301,651,389,372,702,344,357,196,638,606,416,325,228,475,321,376,211,485,602,428,507,529,661,512,439,220,366,349,297,424,275,192,693,467,252,435,583,682,224,578,317,188,593,420,499,328,489,590,679,547,701,654,503,237,244,657,398,674,412,166,148,279,402,286,204,259,641,391,382,572,313,181,159,271,362,567,477,494,552,609,240,155,685,455,394,563,267,162,663,648,516,194,525,690,150,409,263,585,370,336,600,612,231,627,450,556,539,581,699,171,235,510,207,536,290,378,447,432,168,405,635,532,696,624,332,575,459,200,442,254,309,543,215,560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : ITP098^1 : TPTP v8.1.2. Released v7.5.0.
% 0.06/0.13 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 6 14:45:54 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.93/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.81/1.14 % [INFO] Parsing done (291ms).
% 2.08/1.15 % [INFO] Running in sequential loop mode.
% 2.79/1.40 % [INFO] eprover registered as external prover.
% 2.79/1.40 % [INFO] cvc4 registered as external prover.
% 2.79/1.41 % [INFO] Scanning for conjecture ...
% 3.10/1.50 % [INFO] Found a conjecture and 355 axioms. Running axiom selection ...
% 3.32/1.60 % [INFO] Axiom selection finished. Selected 145 axioms (removed 210 axioms).
% 3.83/1.73 % [INFO] Problem is higher-order (TPTP THF).
% 3.83/1.75 % [INFO] Type checking passed.
% 3.83/1.75 % [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 ...
% 12.84/4.18 % External prover 'e' found a proof!
% 12.84/4.18 % [INFO] Killing All external provers ...
% 12.84/4.18 % Time passed: 3665ms (effective reasoning time: 3027ms)
% 12.84/4.18 % 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)>
% 12.84/4.18 % Axioms used in derivation (145): fact_263_surjI, fact_294_image__eq__imp__comp, fact_132_sup__left__commute, fact_18_ex__o__conv, fact_272_surjE, fact_39_inj__on__Un__image__eq__iff, fact_215_inj__on__contraD, fact_205_inj__on__inverseI, fact_124_sup__idem, fact_235_inj__on__def, fact_341_inj__on__imageI2, fact_25_o__eq__conv, fact_208_inj__on__inverseI, fact_75_inj__on__imageI, fact_211_inj__on__contraD, fact_315_inj__def, fact_150_inf__sup__aci_I6_J, fact_338_inj__on__imageI2, fact_241_inj__onI, fact_113_comp__surj, fact_230_inj__on__def, fact_218_inj__on__eq__iff, fact_126_sup_Oidem, fact_259_surjI, fact_96_inj__image__eq__iff, fact_204_inj__on__inverseI, fact_279_surjD, fact_219_inj__on__eq__iff, fact_3_o__ext, fact_325_injI, fact_320_inj__eq, fact_87_range__ex1__eq, fact_167_comp__eq__dest__lhs, fact_221_inj__on__eq__iff, fact_321_inj__eq, fact_282_surjD, fact_283_surjD, fact_66_inj__on__imageI, fact_214_inj__on__contraD, fact_11_o__inj__on, fact_21_ex__o__conv, fact_101_inj__image__mem__iff, fact_134_sup_Oleft__commute, fact_136_sup__commute, fact_65_comp__inj__on, fact_331_injD, fact_240_inj__onI, fact_247_inj__onD, fact_209_inj__on__inverseI, fact_7_o__cong, fact_98_inj__image__eq__iff, fact_90_range__ex1__eq, fact_280_surjD, fact_210_inj__on__contraD, fact_229_inj__on__cong, fact_227_inj__on__cong, fact_236_inj__onI, fact_270_surjE, fact_334_injD, fact_43_inj__compose, fact_311_inj__on__image__iff, fact_335_injD, fact_138_sup_Ocommute, fact_171_comp__eq__elim, fact_312_inj__on__image__iff, fact_224_inj__on__cong, fact_314_inj__def, fact_94_inj__image__eq__iff, fact_207_inj__on__inverseI, fact_243_inj__onD, fact_298_image__comp, fact_100_inj__image__mem__iff, fact_228_inj__on__cong, fact_326_injI, fact_10_o__inj__on, fact_166_comp__eq__dest__lhs, fact_225_inj__on__cong, fact_223_inj__on__eq__iff, fact_252_surj__def, fact_8_o__inj__on, fact_181_comp__eq__dest, fact_237_inj__onI, fact_222_inj__on__eq__iff, fact_343_inj__on__imageI2, fact_269_surjE, fact_47_inj__compose, fact_232_inj__on__def, fact_316_inj__def, fact_332_injD, fact_120_sup__left__idem, fact_260_surjI, fact_322_inj__eq, fact_36_inj__on__Un__image__eq__iff, fact_245_inj__onD, fact_329_injI, fact_323_inj__eq, fact_146_boolean__algebra__cancel_Osup1, fact_70_inj__on__imageI, fact_253_surj__def, fact_88_range__ex1__eq, fact_201_comp__def, fact_85_comp__inj__on__iff, fact_310_inj__on__image__iff, fact_95_inj__image__eq__iff, fact_200_comp__def, conj_1, fact_273_surjE, fact_142_sup_Oassoc, fact_28_sup__top__left, fact_328_injI, fact_86_range__ex1__eq, fact_104_inj__image__mem__iff, fact_148_inf__sup__aci_I5_J, fact_249_surj__def, fact_112_comp__surj, fact_333_injD, fact_246_inj__onD, fact_317_inj__def, fact_327_injI, fact_306_image__comp, fact_239_inj__onI, fact_144_boolean__algebra__cancel_Osup2, fact_118_sup_Oright__idem, fact_262_surjI, fact_250_surj__def, fact_347_fun_Oinj__map__strong, fact_129_comp__apply, fact_42_inj__compose, fact_140_sup__assoc, fact_128_comp__apply, fact_242_inj__onD, fact_154_inf__sup__aci_I8_J, fact_319_inj__eq, fact_180_comp__eq__dest, fact_122_sup_Oleft__idem, fact_102_inj__image__mem__iff, conj_0, fact_32_sup__top__right, fact_170_comp__eq__elim, fact_213_inj__on__contraD, fact_295_image__eq__imp__comp, fact_231_inj__on__def, fact_152_inf__sup__aci_I7_J, fact_234_inj__on__def, fact_313_inj__def
% 12.84/4.18 % No. of inferences in proof: 294
% 12.84/4.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3665 ms resp. 3027 ms w/o parsing
% 13.60/4.36 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.60/4.36 % [INFO] Killing All external provers ...
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